otter-3.3f/0040755000076400007640000000000010103530625012177 5ustar mccunemccuneotter-3.3f/Contents0100644000076400007640000000136410103530576013725 0ustar mccunemccuneREADME.first quick start info README general information README.make info on compiling README.Win32 info for Microsoft users README.Ivy info on checking proofs index.html HTML summary of this package documents/ reference manuals Makefile top-level makefile source/ Otter ource code mace2/ Mace2 source code (uses Otter source) examples/ Otter examples examples-mace2/ Mace2 examples bin/ this should be initially empty bin-Darwin/ pre-compiled binaries for Macintosh OS X bin-Linux/ pre-compiled binaries for Linux Changelog list of changes to Otter Legal copyright, licence, disclaimer Contents this file otter-3.3f/source/0040755000076400007640000000000010103776005013503 5ustar mccunemccuneotter-3.3f/source/av.c0100644000076400007640000011271210041254332014251 0ustar mccunemccune/* * av.c -- This file has routines for memory management. * */ #include "header.h" /* Size of chunk allocated by malloc */ #define TP_ALLOC_SIZE 1000000 #define ALLOC_ARG_T unsigned static char *Alloc_block; /* location returned by most recent malloc */ static char *Alloc_pos; /* current position in block */ /* a list of available nodes for each type of structure */ static struct term *term_avail; static struct rel *rel_avail; static struct sym_ent *sym_ent_avail; static struct term_ptr *term_ptr_avail; static struct formula_ptr_2 *formula_ptr_2_avail; static struct fpa_tree *fpa_tree_avail; static struct fpa_head *fpa_head_avail; static struct context *context_avail; static struct trail *trail_avail; static struct imd_tree *imd_tree_avail; static struct imd_pos *imd_pos_avail; static struct is_tree *is_tree_avail; static struct is_pos *is_pos_avail; static struct fsub_pos *fsub_pos_avail; static struct literal *literal_avail; static struct clause *clause_avail; static struct list *list_avail; static struct clash_nd *clash_nd_avail; static struct clause_ptr *clause_ptr_avail; static struct ci_ptr *ci_ptr_avail; static struct ilist *ilist_avail; static struct link_node *link_node_avail; static struct ans_lit_node *ans_lit_node_avail; static struct formula_box *formula_box_avail; static struct formula *formula_avail; static struct formula_ptr *formula_ptr_avail; static struct cl_attribute *cl_attribute_avail; static struct glist *glist_avail; static struct g2list *g2list_avail; static struct fnode *fnode_avail; static int Malloc_calls; /* number of calls to malloc */ /* # of gets, frees, and size of avail list for each type of structure */ static unsigned long term_gets, term_frees, term_avails; static unsigned long rel_gets, rel_frees, rel_avails; static unsigned long sym_ent_gets, sym_ent_frees, sym_ent_avails; static unsigned long term_ptr_gets, term_ptr_frees, term_ptr_avails; static unsigned long formula_ptr_2_gets, formula_ptr_2_frees, formula_ptr_2_avails; static unsigned long fpa_tree_gets, fpa_tree_frees, fpa_tree_avails; static unsigned long fpa_head_gets, fpa_head_frees, fpa_head_avails; static unsigned long context_gets, context_frees, context_avails; static unsigned long trail_gets, trail_frees, trail_avails; static unsigned long imd_tree_gets, imd_tree_frees, imd_tree_avails; static unsigned long imd_pos_gets, imd_pos_frees, imd_pos_avails; static unsigned long is_tree_gets, is_tree_frees, is_tree_avails; static unsigned long is_pos_gets, is_pos_frees, is_pos_avails; static unsigned long fsub_pos_gets, fsub_pos_frees, fsub_pos_avails; static unsigned long literal_gets, literal_frees, literal_avails; static unsigned long clause_gets, clause_frees, clause_avails; static unsigned long list_gets, list_frees, list_avails; static unsigned long clash_nd_gets, clash_nd_frees, clash_nd_avails; static unsigned long clause_ptr_gets, clause_ptr_frees, clause_ptr_avails; static unsigned long ci_ptr_gets, ci_ptr_frees, ci_ptr_avails; static unsigned long ilist_gets, ilist_frees, ilist_avails; static unsigned long link_node_gets, link_node_frees, link_node_avails; static unsigned long ans_lit_node_gets, ans_lit_node_frees, ans_lit_node_avails; static unsigned long formula_box_gets, formula_box_frees, formula_box_avails; static unsigned long formula_gets, formula_frees, formula_avails; static unsigned long formula_ptr_gets, formula_ptr_frees, formula_ptr_avails; static unsigned long cl_attribute_gets, cl_attribute_frees, cl_attribute_avails; static unsigned long glist_gets, glist_frees, glist_avails; static unsigned long g2list_gets, g2list_frees, g2list_avails; static unsigned long fnode_gets, fnode_frees, fnode_avails; /************* * * int **tp_alloc(n) * * Allocate n contiguous bytes, aligned on pointer boundry. * *************/ int **tp_alloc(int n) { char *return_block; int scale; /* if n is not a multiple of sizeof(int *), then round up so that it is */ scale = sizeof(int *); if (n % scale != 0) n = n + (scale - (n % scale)); if (Alloc_block == NULL || Alloc_block + TP_ALLOC_SIZE - Alloc_pos < n) { /* try to malloc a new block */ if (n > TP_ALLOC_SIZE) { char s[100]; sprintf(s, "tp_alloc, request too big: %d", n); abend(s); } else if (Parms[MAX_MEM].val != -1 && ((Malloc_calls+1)*TP_ALLOC_SIZE)/1024 > Parms[MAX_MEM].val) { fprintf(stdout, "\nSearch stopped in tp_alloc by max_mem option.\n"); fprintf(stderr, "\n%cSearch stopped in tp_alloc by max_mem option.\n", Bell); if (Flags[FREE_ALL_MEM].val) { /* freeing memory can require additional memory */ fprintf(stdout, " (free_all_mem cleared).\n"); Flags[FREE_ALL_MEM].val = 0; } if (Flags[PRINT_LISTS_AT_END].val) { /* 2/5/92 WWM */ /* printing can require additional memory */ fprintf(stdout, " (print_lists_at_end cleared).\n"); Flags[PRINT_LISTS_AT_END].val = 0; } cleanup(); exit(MAX_MEM_EXIT); } else { Alloc_pos = Alloc_block = (char *) malloc((ALLOC_ARG_T) TP_ALLOC_SIZE); Malloc_calls++; Stats[K_MALLOCED] = (Malloc_calls * (TP_ALLOC_SIZE / 1024.)); if (Alloc_pos == NULL) { /* Don't call abend() so that we can exit with a value. */ output_stats(stdout, 3); fprintf(stdout, "\nABEND, malloc returns NULL (out of memory).\n"); fprintf(stderr, "%cABEND, malloc returns NULL (out of memory).\n", Bell); exit(MALLOC_NULL_EXIT); } } } return_block = Alloc_pos; Alloc_pos += n; return((int **) return_block); } /* tp_alloc */ /************* * * struct term *get_term() * *************/ struct term *get_term(void) { struct term *p; term_gets++; if (term_avail == NULL) p = (struct term *) tp_alloc((int) sizeof(struct term)); else { term_avails--; p = term_avail; term_avail = (struct term *) term_avail->farg; } p->sym_num = 0; p->farg = NULL; p->occ.rel = NULL; p->varnum = 0; p->bits = 0; p->fpa_id = 0; return(p); } /* get_term */ /************* * * free_term() * *************/ void free_term(struct term *p) { term_frees++; term_avails++; p->farg = (struct rel *) term_avail; term_avail = p; } /* free_term */ /************* * * struct rel *get_rel() * *************/ struct rel *get_rel(void) { struct rel *p; rel_gets++; if (rel_avail == NULL) p = (struct rel *) tp_alloc((int) sizeof(struct rel)); else { rel_avails--; p = rel_avail; rel_avail = rel_avail->narg; } p->argval = NULL; p->argof = NULL; p->narg = NULL; p->nocc = NULL; p->path = 0; p->clashable = 0; return(p); } /* get_rel */ /************* * * free_rel() * *************/ void free_rel(struct rel *p) { rel_frees++; rel_avails++; p->narg = rel_avail; rel_avail = p; } /* free_rel */ /************* * * struct sym_ent *get_sym_ent() * *************/ struct sym_ent *get_sym_ent(void) { struct sym_ent *p; sym_ent_gets++; if (sym_ent_avail == NULL) p = (struct sym_ent *) tp_alloc((int) sizeof(struct sym_ent)); else { sym_ent_avails--; p = sym_ent_avail; sym_ent_avail = sym_ent_avail->next; } p->eval_code = 0; p->lex_val = MAX_INT; p->skolem = 0; p->special_unary = 0; p->lex_rpo_status = LRPO_LR_STATUS; p->special_op = 0; p->op_type = 0; p->op_prec = 0; p->next = NULL; return(p); } /* get_sym_ent */ /************* * * free_sym_ent() * *************/ void free_sym_ent(struct sym_ent *p) { sym_ent_frees++; sym_ent_avails++; p->next = sym_ent_avail; sym_ent_avail = p; } /* free_sym_ent */ /************* * * struct term_ptr *get_term_ptr() * *************/ struct term_ptr *get_term_ptr(void) { struct term_ptr *p; term_ptr_gets++; if (term_ptr_avail == NULL) p = (struct term_ptr *) tp_alloc((int) sizeof(struct term_ptr)); else { term_ptr_avails--; p = term_ptr_avail; term_ptr_avail = term_ptr_avail->next; } p->term = NULL; p->next = NULL; return(p); } /* get_term_ptr */ /************* * * free_term_ptr() * *************/ void free_term_ptr(struct term_ptr *p) { term_ptr_frees++; term_ptr_avails++; p->next = term_ptr_avail; term_ptr_avail = p; } /* free_term_ptr */ /************* * * struct formula_ptr_2 *get_formula_ptr_2() * *************/ struct formula_ptr_2 *get_formula_ptr_2(void) { struct formula_ptr_2 *p; formula_ptr_2_gets++; if (formula_ptr_2_avail == NULL) p = (struct formula_ptr_2 *) tp_alloc((int) sizeof(struct formula_ptr_2)); else { formula_ptr_2_avails--; p = formula_ptr_2_avail; formula_ptr_2_avail = formula_ptr_2_avail->next; } p->f = NULL; p->next = NULL; p->prev = NULL; p->left = NULL; p->right = NULL; p->up = NULL; p->down = NULL; return(p); } /* get_formula_ptr_2 */ /************* * * free_formula_ptr_2() * *************/ void free_formula_ptr_2(struct formula_ptr_2 *p) { formula_ptr_2_frees++; formula_ptr_2_avails++; p->next = formula_ptr_2_avail; formula_ptr_2_avail = p; } /* free_formula_ptr_2 */ /************* * * struct fpa_tree *get_fpa_tree() * *************/ struct fpa_tree *get_fpa_tree(void) { struct fpa_tree *p; fpa_tree_gets++; if (fpa_tree_avail == NULL) p = (struct fpa_tree *) tp_alloc((int) sizeof(struct fpa_tree)); else { fpa_tree_avails--; p = fpa_tree_avail; fpa_tree_avail = fpa_tree_avail->left; } p->position = (struct fposition) {NULL, 0}; p->left = NULL; p->right = NULL; p->left_term = NULL; p->right_term = NULL; p->path = NULL; return(p); } /* get_fpa_tree */ /************* * * free_fpa_tree() * *************/ void free_fpa_tree(struct fpa_tree *p) { fpa_tree_frees++; fpa_tree_avails++; p->left = fpa_tree_avail; fpa_tree_avail = p; } /* free_fpa_tree */ /************* * * struct fpa_head *get_fpa_head() * *************/ struct fpa_head *get_fpa_head(void) { struct fpa_head *p; fpa_head_gets++; if (fpa_head_avail == NULL) p = (struct fpa_head *) tp_alloc((int) sizeof(struct fpa_head)); else { fpa_head_avails--; p = fpa_head_avail; fpa_head_avail = fpa_head_avail->next; } p->terms = NULL; p->next = NULL; p->path = NULL; return(p); } /* get_fpa_head */ /************* * * free_fpa_head() * *************/ void free_fpa_head(struct fpa_head *p) { fpa_head_frees++; fpa_head_avails++; p->next = fpa_head_avail; fpa_head_avail = p; } /* free_head */ /************* * * struct context *get_context() * *************/ struct context *get_context(void) { struct context *p; int i; static int count=0; context_gets++; if (context_avail == NULL) { p = (struct context *) tp_alloc((int) sizeof(struct context)); for (i=0; iterms[i] = NULL; p->status[i] = 0; } p->built_in_multiplier = count++; /* never change */ } else { context_avails--; p = context_avail; context_avail = context_avail->contexts[0]; } p->multiplier = -1; return(p); } /* get_context */ /************* * * free_context() * *************/ void free_context(struct context *p) { #if 1 int i; for (i=0; iterms[i] != NULL) { printf("ERROR, context %x, var %d not null.\n", (unsigned) p->contexts[i], i); print_term_nl(stdout, p->terms[i]); p->terms[i] = NULL; } } #endif context_frees++; context_avails++; p->contexts[0] = context_avail; context_avail = p; } /* free_context */ /************* * * struct trail *get_trail() * *************/ struct trail *get_trail(void) { struct trail *p; trail_gets++; if (trail_avail == NULL) p = (struct trail *) tp_alloc((int) sizeof(struct trail)); else { trail_avails--; p = trail_avail; trail_avail = trail_avail->next; } p->next = NULL; return(p); } /* get_trail */ /************* * * free_trail() * *************/ void free_trail(struct trail *p) { trail_frees++; trail_avails++; p->next = trail_avail; trail_avail = p; } /* free_trail */ /************* * * struct imd_tree *get_imd_tree() * *************/ struct imd_tree *get_imd_tree(void) { struct imd_tree *p; imd_tree_gets++; if (imd_tree_avail == NULL) p = (struct imd_tree *) tp_alloc((int) sizeof(struct imd_tree)); else { imd_tree_avails--; p = imd_tree_avail; imd_tree_avail = imd_tree_avail->next; } p->next = NULL; p->kids = NULL; p->type = 0; p->lab = 0; p->atoms = NULL; return(p); } /* get_imd_tree */ /************* * * free_imd_tree() * *************/ void free_imd_tree(struct imd_tree *p) { imd_tree_frees++; imd_tree_avails++; p->next = imd_tree_avail; imd_tree_avail = p; } /* free_imd_tree */ /************* * * struct imd_pos *get_imd_pos() * *************/ struct imd_pos *get_imd_pos(void) { struct imd_pos *p; imd_pos_gets++; if (imd_pos_avail == NULL) p = (struct imd_pos *) tp_alloc((int) sizeof(struct imd_pos)); else { imd_pos_avails--; p = imd_pos_avail; imd_pos_avail = imd_pos_avail->next; } p->next = NULL; return(p); } /* get_imd_pos */ /************* * * free_imd_pos() * *************/ void free_imd_pos(struct imd_pos *p) { imd_pos_frees++; imd_pos_avails++; p->next = imd_pos_avail; imd_pos_avail = p; } /* free_imd_pos */ /************* * * struct is_tree *get_is_tree() * *************/ struct is_tree *get_is_tree(void) { struct is_tree *p; is_tree_gets++; if (is_tree_avail == NULL) p = (struct is_tree *) tp_alloc((int) sizeof(struct is_tree)); else { is_tree_avails--; p = is_tree_avail; is_tree_avail = is_tree_avail->next; } p->next = NULL; p->type = 0; p->lab = 0; p->u.kids = NULL; return(p); } /* get_is_tree */ /************* * * free_is_tree() * *************/ void free_is_tree(struct is_tree *p) { is_tree_frees++; is_tree_avails++; p->next = is_tree_avail; is_tree_avail = p; } /* free_is_tree */ /************* * * struct is_pos *get_is_pos() * *************/ struct is_pos *get_is_pos(void) { struct is_pos *p; is_pos_gets++; if (is_pos_avail == NULL) p = (struct is_pos *) tp_alloc((int) sizeof(struct is_pos)); else { is_pos_avails--; p = is_pos_avail; is_pos_avail = is_pos_avail->next; } p->next = NULL; return(p); } /* get_is_pos */ /************* * * free_is_pos() * *************/ void free_is_pos(struct is_pos *p) { is_pos_frees++; is_pos_avails++; p->next = is_pos_avail; is_pos_avail = p; } /* free_is_pos */ /************* * * struct fsub_pos *get_fsub_pos() * *************/ struct fsub_pos *get_fsub_pos(void) { struct fsub_pos *p; fsub_pos_gets++; if (fsub_pos_avail == NULL) p = (struct fsub_pos *) tp_alloc((int) sizeof(struct fsub_pos)); else { fsub_pos_avails--; p = fsub_pos_avail; fsub_pos_avail = (struct fsub_pos *) fsub_pos_avail->terms; } return(p); } /* get_fsub_pos */ /************* * * free_fsub_pos() * *************/ void free_fsub_pos(struct fsub_pos *p) { fsub_pos_frees++; fsub_pos_avails++; p->terms = (struct term_ptr *) fsub_pos_avail; fsub_pos_avail = p; } /* free_fsub_pos */ /************* * * struct literal *get_literal() * *************/ struct literal *get_literal(void) { struct literal *p; literal_gets++; if (literal_avail == NULL) p = (struct literal *) tp_alloc((int) sizeof(struct literal)); else { literal_avails--; p = literal_avail; literal_avail = literal_avail->next_lit; } p->container = NULL; p->next_lit = NULL; p->sign = 0; p->atom = NULL; return(p); } /* get_literal */ /************* * * free_literal() * *************/ void free_literal(struct literal *p) { literal_frees++; literal_avails++; p->next_lit = literal_avail; literal_avail = p; } /* free_literal */ /************* * * struct clause *get_clause() * *************/ struct clause *get_clause(void) { struct clause *p; clause_gets++; if (clause_avail == NULL) p = (struct clause *) tp_alloc((int) sizeof(struct clause)); else { clause_avails--; p = clause_avail; clause_avail = clause_avail->next_cl; } p->id = 0; p->parents = NULL; p->multi_parents = NULL; p->container = NULL; p->next_cl = NULL; p->prev_cl = NULL; p->first_lit = NULL; p->pick_weight = 0; p->type = NOT_SPECIFIED; p->bits = 0; p->heat_level = 0; p->attributes = NULL; return(p); } /* get_clause */ /************* * * free_clause() * *************/ void free_clause(struct clause *p) { clause_frees++; clause_avails++; p->next_cl = clause_avail; clause_avail = p; } /* free_clause */ /************* * * struct list *get_list() * *************/ struct list *get_list(void) { struct list *p; list_gets++; if (list_avail == NULL) p = (struct list *) tp_alloc((int) sizeof(struct list)); else { list_avails--; p = list_avail; list_avail = (struct list *) list_avail->first_cl; } p->first_cl = NULL; p->last_cl = NULL; p->name[0] = '\0'; return(p); } /* get_list */ /************* * * free_list() * *************/ void free_list(struct list *p) { list_frees++; list_avails++; p->first_cl = (struct clause *) list_avail; list_avail = p; } /* free_list */ /************* * * struct clash_nd *get_clash_nd() * *************/ struct clash_nd *get_clash_nd(void) { struct clash_nd *p; clash_nd_gets++; if (clash_nd_avail == NULL) p = (struct clash_nd *) tp_alloc((int) sizeof(struct clash_nd)); else { clash_nd_avails--; p = clash_nd_avail; clash_nd_avail = clash_nd_avail->next; } p->next = NULL; p->prev = NULL; p->evaluable = 0; return(p); } /* get_clash_nd */ /************* * * free_clash_nd() * *************/ void free_clash_nd(struct clash_nd *p) { clash_nd_frees++; clash_nd_avails++; p->next = clash_nd_avail; clash_nd_avail = p; } /* free_clash_nd */ /************* * * struct clause_ptr *get_clause_ptr() * *************/ struct clause_ptr *get_clause_ptr(void) { struct clause_ptr *p; clause_ptr_gets++; if (clause_ptr_avail == NULL) p = (struct clause_ptr *) tp_alloc((int) sizeof(struct clause_ptr)); else { clause_ptr_avails--; p = clause_ptr_avail; clause_ptr_avail = clause_ptr_avail->next; } p->next = NULL; p->c = NULL; return(p); } /* get_clause_ptr */ /************* * * free_clause_ptr() * *************/ void free_clause_ptr(struct clause_ptr *p) { clause_ptr_frees++; clause_ptr_avails++; p->next = clause_ptr_avail; clause_ptr_avail = p; } /* free_clause_ptr */ /************* * * struct ci_ptr *get_ci_ptr() * *************/ struct ci_ptr *get_ci_ptr(void) { struct ci_ptr *p; ci_ptr_gets++; if (ci_ptr_avail == NULL) p = (struct ci_ptr *) tp_alloc((int) sizeof(struct ci_ptr)); else { ci_ptr_avails--; p = ci_ptr_avail; ci_ptr_avail = ci_ptr_avail->next; } p->next = NULL; p->c = NULL; p->v = NULL; return(p); } /* get_ci_ptr */ /************* * * free_ci_ptr() * *************/ void free_ci_ptr(struct ci_ptr *p) { ci_ptr_frees++; ci_ptr_avails++; p->next = ci_ptr_avail; ci_ptr_avail = p; } /* free_ci_ptr */ /************* * * struct ilist *get_ilist() * *************/ struct ilist *get_ilist(void) { struct ilist *p; ilist_gets++; if (ilist_avail == NULL) p = (struct ilist *) tp_alloc((int) sizeof(struct ilist)); else { ilist_avails--; p = ilist_avail; ilist_avail = ilist_avail->next; } p->next = NULL; p->i = 0; return(p); } /* get_ilist */ /************* * * free_ilist() * *************/ void free_ilist(struct ilist *p) { ilist_frees++; ilist_avails++; p->next = ilist_avail; ilist_avail = p; } /* free_ilist */ /************* * * struct ans_lit_node *get_ans_lit_node() * *************/ struct ans_lit_node *get_ans_lit_node(void) { struct ans_lit_node *p; ans_lit_node_gets++; if (ans_lit_node_avail == NULL) p = (struct ans_lit_node *) tp_alloc((int) sizeof(struct ans_lit_node)); else { ans_lit_node_avails--; p = ans_lit_node_avail; ans_lit_node_avail = ans_lit_node_avail->next; } p->next = NULL; p->parent = NULL; p->lit = NULL; return(p); } /* get_ans_lit_node */ /************* * * void free_ans_lit_node() * *************/ void free_ans_lit_node(struct ans_lit_node *p) { ans_lit_node_frees++; ans_lit_node_avails++; p->next = ans_lit_node_avail; ans_lit_node_avail = p; } /* free_ans_lit_node */ /************* * * struct formula_box *get_formula_box() * *************/ struct formula_box *get_formula_box(void) { struct formula_box *p; formula_box_gets++; if (formula_box_avail == NULL) p = (struct formula_box *) tp_alloc((int) sizeof(struct formula_box)); else { formula_box_avails--; p = formula_box_avail; formula_box_avail = formula_box_avail->next; } p->first_child = p->next = p->parent = NULL; p->f = NULL; p->str[0] = '\0'; p->type = p->subtype = p->length = p->height = p->x_off = p->y_off = 0; p->abs_x_loc = p->abs_y_loc = 0; return(p); } /* get_formula_box */ /************* * * void free_formula_box() * *************/ void free_formula_box(struct formula_box *p) { formula_box_frees++; formula_box_avails++; p->next = formula_box_avail; formula_box_avail = p; } /* free_formula_box */ /************* * * struct formula *get_formula() * *************/ struct formula *get_formula(void) { struct formula *p; formula_gets++; if (formula_avail == NULL) p = (struct formula *) tp_alloc((int) sizeof(struct formula)); else { formula_avails--; p = formula_avail; formula_avail = formula_avail->next; } p->type = 0; p->quant_type = 0; p->parent = p->first_child = p->next = NULL; p->t = NULL; return(p); } /* get_formula */ /************* * * void free_formula() * *************/ void free_formula(struct formula *p) { formula_frees++; formula_avails++; p->next = formula_avail; formula_avail = p; } /* free_formula */ /************* * * struct formula_ptr *get_formula_ptr() * *************/ struct formula_ptr *get_formula_ptr(void) { struct formula_ptr *p; formula_ptr_gets++; if (formula_ptr_avail == NULL) p = (struct formula_ptr *) tp_alloc((int) sizeof(struct formula_ptr)); else { formula_ptr_avails--; p = formula_ptr_avail; formula_ptr_avail = formula_ptr_avail->next; } p->f = NULL; p->next = NULL; return(p); } /* get_formula_ptr */ /************* * * void free_formula_ptr() * *************/ void free_formula_ptr(struct formula_ptr *p) { formula_ptr_frees++; formula_ptr_avails++; p->next = formula_ptr_avail; formula_ptr_avail = p; } /* free_formula_ptr */ /************* * * struct cl_attribute *get_cl_attribute() * *************/ struct cl_attribute *get_cl_attribute(void) { struct cl_attribute *p; cl_attribute_gets++; if (cl_attribute_avail == NULL) p = (struct cl_attribute *) tp_alloc((int) sizeof(struct cl_attribute)); else { cl_attribute_avails--; p = cl_attribute_avail; cl_attribute_avail = cl_attribute_avail->next; } p->name = -1; p->next = NULL; return(p); } /* get_cl_attribute */ /************* * * void free_cl_attribute() * *************/ void free_cl_attribute(struct cl_attribute *p) { cl_attribute_frees++; cl_attribute_avails++; p->next = cl_attribute_avail; cl_attribute_avail = p; } /* free_cl_attribute */ /************* * * struct link_node *get_link_node() * *************/ struct link_node *get_link_node(void) { struct link_node *p; link_node_gets++; if (link_node_avail == NULL) p = (struct link_node *) tp_alloc((int) sizeof(struct link_node)); else { link_node_avails--; p = link_node_avail; link_node_avail = link_node_avail->next_sibling; } p->parent = NULL; p->first_child = NULL; p->child_first_ans = NULL; p->child_last_ans = NULL; p->next_sibling = NULL; p->prev_sibling = NULL; p->first = TRUE; p->unit_deleted = FALSE; /* Initially literal has not been unit deleted */ p->goal = NULL; p->goal_to_resolve = NULL; p->current_clause = NULL; p->subst = NULL; p->unif_position = NULL; p->tr = NULL; p->near_poss_nuc = UNDEFINED; p->farthest_sat = 0; p->target_dist = 0; p->back_up = UNDEFINED; return(p); } /* get_link_node */ /************* * * void free_link_node() * *************/ void free_link_node(struct link_node *p) { link_node_frees++; link_node_avails++; p->next_sibling = link_node_avail; link_node_avail = p; } /* free_link_node */ /************* * * free_imd_pos_list(imd_pos) -- free a list of imd_pos nodes. * *************/ void free_imd_pos_list(struct imd_pos *p) { struct imd_pos *q; if (p != NULL) { q = p; imd_pos_frees++; imd_pos_avails++; while (q->next != NULL) { imd_pos_frees++; imd_pos_avails++; q = q->next; } q->next = imd_pos_avail; imd_pos_avail = p; } } /* free_imd_pos_list */ /************* * * free_is_pos_list(is_pos) -- free a list of is_pos nodes. * *************/ void free_is_pos_list(struct is_pos *p) { struct is_pos *q; if (p != NULL) { q = p; is_pos_frees++; is_pos_avails++; while (q->next != NULL) { is_pos_frees++; is_pos_avails++; q = q->next; } q->next = is_pos_avail; is_pos_avail = p; } } /* free_is_pos_list */ /************* * * struct glist *get_glist() * *************/ struct glist *get_glist(void) { struct glist *p; glist_gets++; if (glist_avail == NULL) p = (struct glist *) tp_alloc((int) sizeof(struct glist)); else { glist_avails--; p = glist_avail; glist_avail = glist_avail->next; } p->v = NULL; p->next = NULL; return(p); } /* get_glist */ /************* * * free_glist() * *************/ void free_glist(struct glist *p) { glist_frees++; glist_avails++; p->next = glist_avail; glist_avail = p; } /* free_glist */ /************* * * struct g2list *get_g2list() * *************/ struct g2list *get_g2list(void) { struct g2list *p; g2list_gets++; if (g2list_avail == NULL) p = (struct g2list *) tp_alloc((int) sizeof(struct g2list)); else { g2list_avails--; p = g2list_avail; g2list_avail = g2list_avail->next; } p->v1 = NULL; p->v2 = NULL; p->next = NULL; return(p); } /* get_g2list */ /************* * * free_g2list() * *************/ void free_g2list(struct g2list *p) { g2list_frees++; g2list_avails++; p->next = g2list_avail; g2list_avail = p; } /* free_g2list */ /************* * * Fnode get_fnode() * *************/ struct fnode *get_fnode(void) { struct fnode *p; fnode_gets++; if (fnode_avail == NULL) p = (void *) tp_alloc(sizeof(struct fnode)); else { fnode_avails--; p = fnode_avail; fnode_avail = fnode_avail->next; } /* initialization */ if (0) { int i; for (i = 0; i < FMAX; i++) p->d[i] = FDEFAULT; } p->next = NULL; /* end of initialization */ return(p); } /* get_fnode */ /************* * * free_fnode() * *************/ void free_fnode(struct fnode *p) { fnode_frees++; fnode_avails++; p->next = fnode_avail; fnode_avail = p; } /* free_fnode */ /************* * * print_mem() * *************/ void print_mem(FILE *fp) { fprintf(fp, "\n------------- memory usage ------------\n"); fprintf(fp, "%d mallocs of %d bytes each, %.1f K.\n", Malloc_calls, TP_ALLOC_SIZE, (Malloc_calls * (TP_ALLOC_SIZE / 1024.))); fprintf(fp, " type (bytes each) gets frees in use avail bytes\n"); fprintf(fp, "sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct sym_ent), sym_ent_gets, sym_ent_frees, sym_ent_gets - sym_ent_frees, sym_ent_avails, (((sym_ent_gets - sym_ent_frees) + sym_ent_avails) * sizeof(struct sym_ent)) / 1024.); fprintf(fp, "term (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct term), term_gets, term_frees, term_gets - term_frees, term_avails, (((term_gets - term_frees) + term_avails) * sizeof(struct term)) / 1024.); fprintf(fp, "rel (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct rel), rel_gets, rel_frees, rel_gets - rel_frees, rel_avails, (((rel_gets - rel_frees) + rel_avails) * sizeof(struct rel)) / 1024.); fprintf(fp, "term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct term_ptr), term_ptr_gets, term_ptr_frees, term_ptr_gets - term_ptr_frees, term_ptr_avails, (((term_ptr_gets - term_ptr_frees) + term_ptr_avails) * sizeof(struct term_ptr)) / 1024.); fprintf(fp, "formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct formula_ptr_2), formula_ptr_2_gets, formula_ptr_2_frees, formula_ptr_2_gets - formula_ptr_2_frees, formula_ptr_2_avails, (((formula_ptr_2_gets - formula_ptr_2_frees) + formula_ptr_2_avails) * sizeof(struct formula_ptr_2)) / 1024.); fprintf(fp, "fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct fpa_head), fpa_head_gets, fpa_head_frees, fpa_head_gets - fpa_head_frees, fpa_head_avails, (((fpa_head_gets - fpa_head_frees) + fpa_head_avails) * sizeof(struct fpa_head)) / 1024.); fprintf(fp, "fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct fnode), fnode_gets, fnode_frees, fnode_gets - fnode_frees, fnode_avails, (((fnode_gets - fnode_frees) + fnode_avails) * sizeof(struct fnode)) / 1024.); fprintf(fp, "fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct fpa_tree), fpa_tree_gets, fpa_tree_frees, fpa_tree_gets - fpa_tree_frees, fpa_tree_avails, (((fpa_tree_gets - fpa_tree_frees) + fpa_tree_avails) * sizeof(struct fpa_tree)) / 1024.); fprintf(fp, "context (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct context), context_gets, context_frees, context_gets - context_frees, context_avails, (((context_gets - context_frees) + context_avails) * sizeof(struct context)) / 1024.); fprintf(fp, "trail (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct trail), trail_gets, trail_frees, trail_gets - trail_frees, trail_avails, (((trail_gets - trail_frees) + trail_avails) * sizeof(struct trail)) / 1024.); fprintf(fp, "imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct imd_tree), imd_tree_gets, imd_tree_frees, imd_tree_gets - imd_tree_frees, imd_tree_avails, (((imd_tree_gets - imd_tree_frees) + imd_tree_avails) * sizeof(struct imd_tree)) / 1024.); fprintf(fp, "imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct imd_pos), imd_pos_gets, imd_pos_frees, imd_pos_gets - imd_pos_frees, imd_pos_avails, (((imd_pos_gets - imd_pos_frees) + imd_pos_avails) * sizeof(struct imd_pos)) / 1024.); fprintf(fp, "is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct is_tree), is_tree_gets, is_tree_frees, is_tree_gets - is_tree_frees, is_tree_avails, (((is_tree_gets - is_tree_frees) + is_tree_avails) * sizeof(struct is_tree)) / 1024.); fprintf(fp, "is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct is_pos), is_pos_gets, is_pos_frees, is_pos_gets - is_pos_frees, is_pos_avails, (((is_pos_gets - is_pos_frees) + is_pos_avails) * sizeof(struct is_pos)) / 1024.); fprintf(fp, "fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct fsub_pos), fsub_pos_gets, fsub_pos_frees, fsub_pos_gets - fsub_pos_frees, fsub_pos_avails, (((fsub_pos_gets - fsub_pos_frees) + fsub_pos_avails) * sizeof(struct fsub_pos)) / 1024.); fprintf(fp, "literal (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct literal), literal_gets, literal_frees, literal_gets - literal_frees, literal_avails, (((literal_gets - literal_frees) + literal_avails) * sizeof(struct literal)) / 1024.); fprintf(fp, "clause (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct clause), clause_gets, clause_frees, clause_gets - clause_frees, clause_avails, (((clause_gets - clause_frees) + clause_avails) * sizeof(struct clause)) / 1024.); fprintf(fp, "list (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct list), list_gets, list_frees, list_gets - list_frees, list_avails, (((list_gets - list_frees) + list_avails) * sizeof(struct list)) / 1024.); fprintf(fp, "clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct clash_nd), clash_nd_gets, clash_nd_frees, clash_nd_gets - clash_nd_frees, clash_nd_avails, (((clash_nd_gets - clash_nd_frees) + clash_nd_avails) * sizeof(struct clash_nd)) / 1024.); fprintf(fp, "clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct clause_ptr), clause_ptr_gets, clause_ptr_frees, clause_ptr_gets - clause_ptr_frees, clause_ptr_avails, (((clause_ptr_gets - clause_ptr_frees) + clause_ptr_avails) * sizeof(struct clause_ptr)) / 1024.); fprintf(fp, "ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct ilist), ilist_gets, ilist_frees, ilist_gets - ilist_frees, ilist_avails, (((ilist_gets - ilist_frees) + ilist_avails) * sizeof(struct ilist)) / 1024.); fprintf(fp, "ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct ci_ptr), ci_ptr_gets, ci_ptr_frees, ci_ptr_gets - ci_ptr_frees, ci_ptr_avails, (((ci_ptr_gets - ci_ptr_frees) + ci_ptr_avails) * sizeof(struct ci_ptr)) / 1024.); fprintf(fp, "link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct link_node), link_node_gets, link_node_frees, link_node_gets - link_node_frees, link_node_avails, (((link_node_gets - link_node_frees) + link_node_avails) * sizeof(struct link_node)) / 1024.); fprintf(fp, "ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct ans_lit_node), ans_lit_node_gets, ans_lit_node_frees, ans_lit_node_gets - ans_lit_node_frees, ans_lit_node_avails, (((ans_lit_node_gets - ans_lit_node_frees) + ans_lit_node_avails) * sizeof(struct ans_lit_node)) / 1024.); fprintf(fp, "formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct formula_box), formula_box_gets, formula_box_frees, formula_box_gets - formula_box_frees, formula_box_avails, (((formula_box_gets - formula_box_frees) + formula_box_avails) * sizeof(struct formula_box)) / 1024.); fprintf(fp, "formula(%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct formula), formula_gets, formula_frees, formula_gets - formula_frees, formula_avails, (((formula_gets - formula_frees) + formula_avails) * sizeof(struct formula)) / 1024.); fprintf(fp, "formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct formula_ptr), formula_ptr_gets, formula_ptr_frees, formula_ptr_gets - formula_ptr_frees, formula_ptr_avails, (((formula_ptr_gets - formula_ptr_frees) + formula_ptr_avails) * sizeof(struct formula_ptr)) / 1024.); fprintf(fp, "cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct cl_attribute), cl_attribute_gets, cl_attribute_frees, cl_attribute_gets - cl_attribute_frees, cl_attribute_avails, (((cl_attribute_gets - cl_attribute_frees) + cl_attribute_avails) * sizeof(struct cl_attribute)) / 1024.); fprintf(fp, "glist (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct glist), glist_gets, glist_frees, glist_gets - glist_frees, glist_avails, (((glist_gets - glist_frees) + glist_avails) * sizeof(struct glist)) / 1024.); fprintf(fp, "g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct g2list), g2list_gets, g2list_frees, g2list_gets - g2list_frees, g2list_avails, (((g2list_gets - g2list_frees) + g2list_avails) * sizeof(struct g2list)) / 1024.); } /* print_mem */ /************* * * print_mem_brief() * *************/ void print_mem_brief(FILE *fp) { fprintf(fp, "\n------------- memory usage ------------\n"); fprintf(fp, "%d mallocs of %d bytes each, %.1f K.\n", Malloc_calls, TP_ALLOC_SIZE, (Malloc_calls * (TP_ALLOC_SIZE / 1024.))); fprintf(fp, " type (bytes each) gets frees in use avail bytes\n"); fprintf(fp, "term (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct term), term_gets, term_frees, term_gets - term_frees, term_avails, (((term_gets - term_frees) + term_avails) * sizeof(struct term)) / 1024.); fprintf(fp, "rel (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct rel), rel_gets, rel_frees, rel_gets - rel_frees, rel_avails, (((rel_gets - rel_frees) + rel_avails) * sizeof(struct rel)) / 1024.); fprintf(fp, "term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct term_ptr), term_ptr_gets, term_ptr_frees, term_ptr_gets - term_ptr_frees, term_ptr_avails, (((term_ptr_gets - term_ptr_frees) + term_ptr_avails) * sizeof(struct term_ptr)) / 1024.); fprintf(fp, "is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K\n", (int) sizeof(struct is_tree), is_tree_gets, is_tree_frees, is_tree_gets - is_tree_frees, is_tree_avails, (((is_tree_gets - is_tree_frees) + is_tree_avails) * sizeof(struct is_tree)) / 1024.); } /* print_mem_brief */ /************* * * int total_mem() -- How many K have been dynamically allocated? * *************/ int total_mem(void) { return( (int) (Malloc_calls * (TP_ALLOC_SIZE / 1024.))); } /* total_mem */ /************* * * total_mem_calls() * *************/ int total_mem_calls(void) { return((int) (Malloc_calls)); } /* total_mem_calls */ /************* * * void print_linked_ur_mem_stats() * *************/ void print_linked_ur_mem_stats(void) { printf("context gets=%lu frees=%lu inuse=%lu\n",context_gets, context_frees, context_gets-context_frees); printf("trail gets=%lu frees=%lu inuse=%lu\n",trail_gets, trail_frees, trail_gets-trail_frees); printf("fpa_tree gets=%lu frees=%lu inuse=%lu\n",fpa_tree_gets, fpa_tree_frees, fpa_tree_gets-fpa_tree_frees); printf("term gets=%lu frees=%lu inuse=%lu\n",term_gets, term_frees, term_gets-term_frees); printf("link_node gets=%lu frees=%lu inuse=%lu\n",link_node_gets,link_node_frees, link_node_gets-link_node_frees); } /* end print_linked_ur_mem_stats */ otter-3.3f/source/pickdiff.c0100644000076400007640000001772507343607002015441 0ustar mccunemccune#include "header.h" /************* * * copy_rels() - copy a list of rel nodes and the associated pointers. * *************/ static struct rel *copy_rels(struct rel *a) { if (a == NULL) return NULL; else { struct rel *r = get_rel(); r->argval = a->argval; r->narg = copy_rels(a->narg); return r; } } /* copy_rels */ /************* * * zap_rels() - free a list of rel nodes (but not the terms they point to) * *************/ static void zap_rels(struct rel *r) { if (r != NULL) { struct rel *a = r->narg; free_rel(r); zap_rels(a); } } /* zap_rels */ /************* * * remove1() - remove (and free) a rel node from a list * *************/ static struct rel *remove1(struct term *x, struct rel *a) { if (a == NULL) return NULL; else if (x == a->argval) { struct rel *r = a->narg; free_rel(a); return r; } else { a->narg = remove1(x, a->narg); return a; } } /* remove1 */ /************* * * add_vecs() - Add two vectors, creating a new vector. The old vectors * are freed. * *************/ static struct ilist *add_vecs(struct ilist *v1, struct ilist *v2) { if (v1 == NULL) return v2; else if (v2 == NULL) return v1; else { struct ilist *v3 = get_ilist(); v3->i = v1->i + v2->i; v3->next = add_vecs(v1->next, v2->next); free_ilist(v1); free_ilist(v2); return v3; } } /* add_vecs */ /************* * * le_vecs(v1, v2) - is vector v1 <= vector v2? * *************/ static int le_vecs(struct ilist *v1, struct ilist *v2) { if (v1 == NULL) return 1; else if (v2 == NULL) return 0; else if (v1->i < v2->i) return 1; else if (v1->i > v2->i) return 0; else return le_vecs(v1->next, v2->next); } /* le_vecs */ static struct ilist *diff(struct term *s, struct term *r); /************* * * diff_lists() - mutually recursive with diff() * *************/ static struct ilist *diff_lists(struct rel *a1, struct rel *a2) { if (a1 == NULL && a2 == NULL) { struct ilist *v = get_ilist(); v->i = 0; return v; } else if (a1 == NULL || a2 == NULL) { struct ilist *v = get_ilist(); v->i = 1; return v; } else { return add_vecs(diff(a1->argval, a2->argval), diff_lists(a1->narg, a2->narg)); } } /* diff_lists */ /************* * * diff() - return a vector representing the difference between two terms. * * This version does not try to minimize differences by permuting arguments. * *************/ static struct ilist *diff(struct term *s, struct term *r) { if (s->type == VARIABLE && r->type == VARIABLE) { struct ilist *v = get_ilist(); v->i = 0; return v; } else if (s->type == VARIABLE || r->type == VARIABLE || s->sym_num != r->sym_num) { struct ilist *v = get_ilist(); v->i = 1; return v; } else { struct ilist *v = get_ilist(); v->i = 0; v->next = diff_lists(s->farg, r->farg); return v; } } /* diff */ static struct ilist *diff2(struct term *s, struct term *r); /************* * * min_diff(+x, +a, -m) - mutually recursive with diff2 and diff2_lists * * Given term x and list of terms a, find the member of a that is * most similar to x. Set m to that member, and return the * difference vector. * *************/ static struct ilist *min_diff(struct term *x, struct rel *a, struct term **m) { if (a == NULL) { struct ilist *v = get_ilist(); v->i = 1000; *m = NULL; return v; } else { struct ilist *v1 = diff2(x, a->argval); struct term *t; struct ilist *v2 = min_diff(x, a->narg, &t); if (le_vecs(v1, v2)) { *m = a->argval; free_ilist_list(v2); return v1; } else { *m = t; free_ilist_list(v1); return v2; } } } /* min_diff */ /************* * * diff2_lists(a1, a2) - mutually recursive with diff2 and min_diff * * The nodes of a2 are freed. * *************/ static struct ilist *diff2_lists(struct rel *a1, struct rel *a2) { if (a1 == NULL && a2 == NULL) { struct ilist *v = get_ilist(); v->i = 0; zap_rels(a2); return v; } else if (a1 == NULL) { struct ilist *v = get_ilist(); v->i = 1; return v; } else { struct term *mint; struct ilist *minv = min_diff(a1->argval, a2, &mint); struct ilist *v = diff2_lists(a1->narg, remove1(mint, a2)); return add_vecs(minv, v); } } /* diff2_lists */ /************* * * diff2() - return a vector representing the difference between two terms. * * This version tries to minimize differences by permuting arguments. * *************/ static struct ilist *diff2(struct term *s, struct term *r) { if (s->type == VARIABLE && r->type == VARIABLE) { struct ilist *v = get_ilist(); v->i = 0; return v; } else if (s->type == VARIABLE || r->type == VARIABLE || s->sym_num != r->sym_num) { struct ilist *v = get_ilist(); v->i = 1; return v; } else { struct ilist *v = get_ilist(); v->i = 0; v->next = diff2_lists(s->farg, copy_rels(r->farg)); return v; } } /* diff2 */ /************* * * cldiff() - return a vector representing the difference between two clauses. * * This version applies to just the first literals, and ignores the sign. * *************/ struct ilist *cldiff(struct clause *c, struct clause *d) { if (c->first_lit == NULL || d->first_lit == NULL || c->first_lit->sign != d->first_lit->sign) { struct ilist *v = get_ilist(); v->i = 1; return v; } else if (Parms[PICK_DIFF].val == 1) return diff(c->first_lit->atom, d->first_lit->atom); else if (Parms[PICK_DIFF].val == 2) return diff2(c->first_lit->atom, d->first_lit->atom); else { abend("cldiff, bad PICK_DIFF"); return NULL; } } /* cldiff */ /************* * * get_ci_of_wt_range() * *************/ static struct ci_ptr *get_ci_of_wt_range(struct clause *c, int min, int max) { if (c == NULL) return NULL; else if (c->pick_weight >= min && c->pick_weight <= max) { struct ci_ptr *p = get_ci_ptr(); p->c = c; p->next = get_ci_of_wt_range(c->next_cl, min, max); return p; } else return get_ci_of_wt_range(c->next_cl, min, max); } /* get_ci_of_wt_range */ /************* * * zap_ci_ptr_list(p) * * Free the nodes and the vectors, but not the clauses. * *************/ void zap_ci_ptr_list(struct ci_ptr *p) { if (p == NULL) return; else { zap_ci_ptr_list(p->next); free_ilist_list(p->v); free_ci_ptr(p); } } /* zap_ci_ptr_list */ /************* * * find_pickdiff_cl() * *************/ struct clause *find_pickdiff_cl(struct list *sos, struct list *usable) { struct clause *c = find_lightest_cl(sos); if (c == NULL) return NULL; else { int min = c->pick_weight; int max = min + Parms[PICK_DIFF_RANGE].val; struct ci_ptr *s = get_ci_of_wt_range(sos->first_cl, min, max); struct ci_ptr *u = get_ci_of_wt_range(usable->first_cl, min, max); struct ci_ptr *p1, *p2; struct ilist *v; /* Find the member of s that is "most different" from members of u. */ for (p1 = s; p1 != NULL; p1 = p1->next) { #if 0 printf("\nSos clause: "); p_clause(p1->c); #endif p1->v = NULL; for (p2 = u; p2 != NULL; p2 = p2->next) { v = cldiff(p1->c, p2->c); #if 0 printf(" Usable clause: "); print_ilist(stdout, v); print_clause(stdout, p2->c); #endif p1->v = add_vecs(p1->v, v); } #if 0 printf("Total difference: "); p_ilist(p1->v); #endif } /* Now, get the Sos clause with the greatest (least?) total difference. */ /* We know that Sos (therefore s) is not empty. */ v = s->v; c = s->c; for (p1 = s->next; p1 != NULL; p1 = p1->next) { int better; if (Flags[PICK_DIFF_SIM].val) better = !le_vecs(v, p1->v); /* looking for least diff */ else better = !le_vecs(p1->v, v); /* looking for most diff */ if (better) { v = p1->v; c = p1->c; } } zap_ci_ptr_list(s); zap_ci_ptr_list(u); return c; } } /* find_pickdiff_cl */ otter-3.3f/source/TAGS0100644000076400007640000011713507622750106014177 0ustar mccunemccune attrib.c,300 } Attributes[11,104 void init_attributes(19,196 int get_attribute_index(57,1205 int attribute_type(76,1540 struct cl_attribute *get_attribute(102,2223 void set_attribute(116,2479 void delete_attributes(151,3083 struct cl_attribute *term_to_attributes(173,3482 void print_attributes(238,4915 av.c,9004 #define TP_ALLOC_SIZE 13,180 #define ALLOC_ARG_T 14,208 #define TP_ALLOC_SIZE 17,253 #define ALLOC_ARG_T 18,280 static char *Alloc_block;21,315 static char *Alloc_pos;22,390 static struct term *term_avail;26,513 static struct rel *rel_avail;27,545 static struct sym_ent *sym_ent_avail;28,575 static struct term_ptr *term_ptr_avail;29,613 static struct formula_ptr_2 *formula_ptr_2_avail;30,653 static struct fpa_tree *fpa_tree_avail;31,703 static struct fpa_head *fpa_head_avail;32,743 static struct context *context_avail;33,783 static struct trail *trail_avail;34,821 static struct imd_tree *imd_tree_avail;35,855 static struct imd_pos *imd_pos_avail;36,895 static struct is_tree *is_tree_avail;37,933 static struct is_pos *is_pos_avail;38,971 static struct fsub_pos *fsub_pos_avail;39,1007 static struct literal *literal_avail;40,1047 static struct clause *clause_avail;41,1085 static struct list *list_avail;42,1121 static struct clash_nd *clash_nd_avail;43,1153 static struct clause_ptr *clause_ptr_avail;44,1193 static struct ci_ptr *ci_ptr_avail;45,1237 static struct ilist *ilist_avail;46,1273 static struct link_node *link_node_avail;48,1308 static struct ans_lit_node *ans_lit_node_avail;49,1350 static struct formula_box *formula_box_avail;50,1398 static struct formula *formula_avail;51,1444 static struct formula_ptr *formula_ptr_avail;52,1482 static struct cl_attribute *cl_attribute_avail;53,1528 static struct glist *glist_avail;54,1576 static struct g2list *g2list_avail;55,1610 static int Malloc_calls;57,1647 static unsigned long term_gets,61,1781 static unsigned long term_gets, term_frees,61,1781 static unsigned long term_gets, term_frees, term_avails;61,1781 static unsigned long rel_gets,62,1838 static unsigned long rel_gets, rel_frees,62,1838 static unsigned long rel_gets, rel_frees, rel_avails;62,1838 static unsigned long sym_ent_gets,63,1892 static unsigned long sym_ent_gets, sym_ent_frees,63,1892 static unsigned long sym_ent_gets, sym_ent_frees, sym_ent_avails;63,1892 static unsigned long term_ptr_gets,64,1958 static unsigned long term_ptr_gets, term_ptr_frees,64,1958 static unsigned long term_ptr_gets, term_ptr_frees, term_ptr_avails;64,1958 static unsigned long formula_ptr_2_gets,65,2027 static unsigned long formula_ptr_2_gets, formula_ptr_2_frees,65,2027 static unsigned long formula_ptr_2_gets, formula_ptr_2_frees, formula_ptr_2_avails;65,2027 static unsigned long fpa_tree_gets,66,2111 static unsigned long fpa_tree_gets, fpa_tree_frees,66,2111 static unsigned long fpa_tree_gets, fpa_tree_frees, fpa_tree_avails;66,2111 static unsigned long fpa_head_gets,67,2180 static unsigned long fpa_head_gets, fpa_head_frees,67,2180 static unsigned long fpa_head_gets, fpa_head_frees, fpa_head_avails;67,2180 static unsigned long context_gets,68,2249 static unsigned long context_gets, context_frees,68,2249 static unsigned long context_gets, context_frees, context_avails;68,2249 static unsigned long trail_gets,69,2315 static unsigned long trail_gets, trail_frees,69,2315 static unsigned long trail_gets, trail_frees, trail_avails;69,2315 static unsigned long imd_tree_gets,70,2375 static unsigned long imd_tree_gets, imd_tree_frees,70,2375 static unsigned long imd_tree_gets, imd_tree_frees, imd_tree_avails;70,2375 static unsigned long imd_pos_gets,71,2444 static unsigned long imd_pos_gets, imd_pos_frees,71,2444 static unsigned long imd_pos_gets, imd_pos_frees, imd_pos_avails;71,2444 static unsigned long is_tree_gets,72,2510 static unsigned long is_tree_gets, is_tree_frees,72,2510 static unsigned long is_tree_gets, is_tree_frees, is_tree_avails;72,2510 static unsigned long is_pos_gets,73,2576 static unsigned long is_pos_gets, is_pos_frees,73,2576 static unsigned long is_pos_gets, is_pos_frees, is_pos_avails;73,2576 static unsigned long fsub_pos_gets,74,2639 static unsigned long fsub_pos_gets, fsub_pos_frees,74,2639 static unsigned long fsub_pos_gets, fsub_pos_frees, fsub_pos_avails;74,2639 static unsigned long literal_gets,75,2708 static unsigned long literal_gets, literal_frees,75,2708 static unsigned long literal_gets, literal_frees, literal_avails;75,2708 static unsigned long clause_gets,76,2774 static unsigned long clause_gets, clause_frees,76,2774 static unsigned long clause_gets, clause_frees, clause_avails;76,2774 static unsigned long list_gets,77,2837 static unsigned long list_gets, list_frees,77,2837 static unsigned long list_gets, list_frees, list_avails;77,2837 static unsigned long clash_nd_gets,78,2894 static unsigned long clash_nd_gets, clash_nd_frees,78,2894 static unsigned long clash_nd_gets, clash_nd_frees, clash_nd_avails;78,2894 static unsigned long clause_ptr_gets,79,2963 static unsigned long clause_ptr_gets, clause_ptr_frees,79,2963 static unsigned long clause_ptr_gets, clause_ptr_frees, clause_ptr_avails;79,2963 static unsigned long ci_ptr_gets,80,3038 static unsigned long ci_ptr_gets, ci_ptr_frees,80,3038 static unsigned long ci_ptr_gets, ci_ptr_frees, ci_ptr_avails;80,3038 static unsigned long ilist_gets,81,3101 static unsigned long ilist_gets, ilist_frees,81,3101 static unsigned long ilist_gets, ilist_frees, ilist_avails;81,3101 static unsigned long link_node_gets,83,3162 static unsigned long link_node_gets, link_node_frees,83,3162 static unsigned long link_node_gets, link_node_frees, link_node_avails;83,3162 static unsigned long ans_lit_node_gets,84,3234 static unsigned long ans_lit_node_gets, ans_lit_node_frees,84,3234 static unsigned long ans_lit_node_gets, ans_lit_node_frees, ans_lit_node_avails;84,3234 static unsigned long formula_box_gets,85,3315 static unsigned long formula_box_gets, formula_box_frees,85,3315 static unsigned long formula_box_gets, formula_box_frees, formula_box_avails;85,3315 static unsigned long formula_gets,86,3393 static unsigned long formula_gets, formula_frees,86,3393 static unsigned long formula_gets, formula_frees, formula_avails;86,3393 static unsigned long formula_ptr_gets,87,3459 static unsigned long formula_ptr_gets, formula_ptr_frees,87,3459 static unsigned long formula_ptr_gets, formula_ptr_frees, formula_ptr_avails;87,3459 static unsigned long cl_attribute_gets,88,3537 static unsigned long cl_attribute_gets, cl_attribute_frees,88,3537 static unsigned long cl_attribute_gets, cl_attribute_frees, cl_attribute_avails;88,3537 static unsigned long glist_gets,89,3618 static unsigned long glist_gets, glist_frees,89,3618 static unsigned long glist_gets, glist_frees, glist_avails;89,3618 static unsigned long g2list_gets,90,3678 static unsigned long g2list_gets, g2list_frees,90,3678 static unsigned long g2list_gets, g2list_frees, g2list_avails;90,3678 int **tp_alloc(100,3870 struct term *get_term(161,5681 void free_term(188,6129 struct rel *get_rel(202,6338 void free_rel(229,6761 struct sym_ent *get_sym_ent(243,6956 void free_sym_ent(274,7520 struct term_ptr *get_term_ptr(288,7745 void free_term_ptr(311,8159 struct formula_ptr_2 *get_formula_ptr_2(325,8401 void free_formula_ptr_2(353,8966 struct fpa_tree *get_fpa_tree(367,9233 void free_fpa_tree(394,9732 struct fpa_head *get_fpa_head(408,9964 void free_fpa_head(432,10397 struct context *get_context(446,10623 void free_context(476,11201 struct trail *get_trail(501,11675 void free_trail(523,12032 struct imd_tree *get_imd_tree(537,12243 void free_imd_tree(563,12705 struct imd_pos *get_imd_pos(577,12935 void free_imd_pos(599,13318 struct is_tree *get_is_tree(613,13541 void free_is_tree(638,13973 struct is_pos *get_is_pos(652,14194 void free_is_pos(674,14564 struct fsub_pos *get_fsub_pos(688,14782 void free_fsub_pos(709,15181 struct literal *get_literal(723,15432 void free_literal(748,15879 struct clause *get_clause(762,16104 void free_clause(800,16762 struct list *get_list(814,16975 void free_list(838,17385 struct clash_nd *get_clash_nd(852,17611 void free_clash_nd(876,18045 struct clause_ptr *get_clause_ptr(890,18281 void free_clause_ptr(913,18718 struct ci_ptr *get_ci_ptr(927,18960 void free_ci_ptr(951,19360 struct ilist *get_ilist(965,19572 void free_ilist(988,19941 struct ans_lit_node *get_ans_lit_node(1002,20160 void free_ans_lit_node(1028,20652 struct formula_box *get_formula_box(1042,20918 void free_formula_box(1070,21533 struct formula *get_formula(1084,21784 void free_formula(1110,22253 struct formula_ptr *get_formula_ptr(1124,22484 void free_formula_ptr(1148,22940 struct cl_attribute *get_cl_attribute(1162,23201 void free_cl_attribute(1186,23671 struct link_node *get_link_node(1200,23933 void free_link_node(1241,24830 void free_imd_pos_list(1255,25105 void free_is_pos_list(1279,25531 struct glist *get_glist(1303,25916 void free_glist(1326,26288 struct g2list *get_g2list(1340,26495 void free_g2list(1364,26897 void print_mem(1378,27095 void print_mem_brief(1424,35128 int total_mem(1444,36542 int total_mem_calls(1455,36704 void print_linked_ur_mem_stats(1466,36867 case.c,1320 #define MAX_SPLIT_DEPTH 14,192 #define POS_CLAUSE 16,258 #define NEG_CLAUSE 17,279 #define MIX_CLAUSE 18,300 #define FORK_FAIL 20,322 #define PARENT 21,343 #define CHILD 22,364 #define CHILD_FAIL 23,385 struct ilist *Current_case 27,476 struct literal_data literal_data36,805 int To_parent,58,1407 int To_parent, From_parent;58,1407 int To_children,59,1481 int To_children, From_children;59,1481 int splitting(67,1637 int max_split_depth(80,1886 int splitable_literal(93,2124 static struct literal_data compare_literal_data(118,2722 int splitable_clause(150,3440 struct clause *compare_splitable_clauses(176,4006 static void init_literal_data(214,5005 static void p_literal_data(225,5216 static void get_literal_data(244,5844 void print_case(306,7396 void p_case(321,7663 void print_case_n(332,7822 void p_case_n(348,8081 void p_assumption_depths(359,8215 struct ilist *current_case(378,8607 void add_subcase(389,8785 int case_depth(409,9135 struct clause *find_clause_to_split(422,9356 struct term *find_atom_to_split(452,10045 int prover_forks(522,12388 int split_clause(648,15559 int split_atom(778,19123 void possible_split(874,21783 void always_split(920,22766 void possible_given_split(949,23338 void assumps_to_parent(998,24566 void exit_with_possible_model(1040,25662 check.c,2529 #define GEN_TAB_SIZE 16,281 struct gen_node gen_node18,307 struct gen_tab gen_tab24,375 static struct gen_tab *Old_proof_tab;30,456 static struct gen_tab *New_proof_old_id_tab;31,494 static struct gen_tab *New_proof_tab;32,539 struct gen_node *get_gen_node(40,636 struct proof_object *get_proof_object(55,889 struct proof_object_node *get_proof_object_node(71,1196 static struct gen_tab *init_gen_tab(97,1745 static int insert_into_gen_tab(115,2102 static void * retrieve_from_gen_tab(150,2734 static void p_gen_tab(164,3014 static int check_eq_lit(182,3325 int trivial_subst(198,3666 struct proof_object_node *connect_new_node(225,4159 static char *po_rule(254,4778 void print_term_s(277,5333 void p_term_s(303,5818 void print_clause_s(316,6024 void p_clause_s(340,6469 void print_clause_s2(353,6684 void p_clause_s2(391,7436 void print_proof_object_node(402,7598 void p_proof_object_node(472,9141 void print_proof_object(483,9335 void p_proof_object(499,9643 static int new_literal_index(512,9890 static void copy_subst_to_proof_object(528,10186 struct clause *cl_copy_delete_literal(570,11016 int variant(606,11960 static int match_literals(649,12693 struct ilist *match_clauses(713,14310 struct clause *cl_append(769,15389 struct clause *identity_resolve(796,15881 static struct clause *identity_paramod(816,16228 void renumber_vars_subst(861,17288 static int translate_unit_deletion(896,17924 static int translate_factor_simp(974,20052 static struct ilist *first_rewrite(1048,22026 static struct ilist *first_rewrite_clause(1111,23466 static int translate_demod_nonunit(1144,24445 static int translate_demod_unit(1244,27438 int finish_translating(1336,30117 static int translate_resolution(1523,35758 static struct ilist *order_new_lits_for_hyper(1671,40348 static int translate_hyper(1716,41236 int ipx(1830,44676 static int translate_ur(1847,44896 static int translate_factor(2016,49226 static struct term *para_position(2083,50938 static int translate_paramod(2106,51351 static void varmap(2251,55688 static BOOLEAN match2(2265,56008 struct proof_object_node *find_match2(2299,56820 static int translate_step(2322,57415 int contains_answer_literal(2435,60710 int contains_rule(2450,60982 struct ilist *trans_2_pos(2467,61232 void type_2_trans(2512,62200 int glist_subsume(2536,62765 void p_proof_object_as_hints(2552,63034 struct literal *remove_answer_literals(2591,63910 void build_proof_object(2617,64504 void init_proof_object_environment(2721,68334 clause.c,3796 #define CLAUSE_TAB_SIZE 12,159 #define CLAUSE_TAB_SIZE 15,204 static struct clause_ptr *Clause_tab[19,285 static int Clause_id_count;22,365 static struct clause *Hidden_clauses;25,449 #define MAX_LITS 28,543 static char Map_array[29,564 void reset_clause_counter(37,664 int next_cl_num(50,884 void assign_cl_id(63,1097 void hot_cl_integrate(96,2160 void cl_integrate(122,2789 void cl_del_int(186,4276 void cl_del_non(278,6192 void cl_int_chk(308,6783 static struct term *literals_to_term(331,7421 struct term *clause_to_term(365,8127 static struct literal *term_to_literals(385,8468 struct clause *term_to_clause(415,9098 struct clause *read_sequent_clause(464,10172 struct clause *read_clause(665,14378 struct list *read_cl_list(718,15478 int set_vars_cl(764,16409 void print_sequent_clause(790,16862 void print_justification(822,17440 void print_clause_bare(891,19729 void print_clause(906,20018 void print_clause_without_just(1006,22016 void p_clause(1086,23587 void print_cl_list(1097,23736 void cl_merge(1120,24140 int tautology(1150,24695 int prf_weight(1177,25193 int proof_length(1211,26006 int subsume(1235,26541 int map_rest(1257,26933 int anc_subsume(1316,28371 struct clause *for_sub_prop(1337,28777 struct clause *forward_subsume(1361,29212 struct clause_ptr *back_subsume(1502,32926 struct clause_ptr *unit_conflict(1583,34845 int propositional_clause(1647,36338 int xx_resolvable(1668,36718 int pos_clause(1699,37356 int answer_lit(1718,37727 int pos_eq_lit(1729,37931 int neg_eq_lit(1740,38135 int eq_lit(1751,38340 int neg_clause(1764,38560 int num_literals(1783,38951 int num_answers(1804,39293 int num_literals_including_answers(1825,39615 int literal_number(1842,39973 int unit_clause(1863,40317 int horn_clause(1878,40563 int equality_clause(1897,40909 int symmetry_clause(1915,41242 struct literal *ith_literal(1950,42061 void append_cl(1975,42415 void prepend_cl(2007,42919 void insert_before_cl(2037,43425 void insert_after_cl(2073,44025 void rem_from_list(2109,44612 void insert_clause(2148,45331 int max_literal_weight(2176,45817 int weight_cl(2199,46325 void hide_clause(2230,47007 struct clause *proof_last_hidden_empty(2242,47188 void del_hidden_clauses(2267,47710 struct clause *cl_copy(2286,48024 int clause_ident(2321,48686 void remove_var_syms(2344,49203 void cl_insert_tab(2361,49497 void cl_delete_tab(2398,50168 struct clause *cl_find(2433,50808 int lit_compare(2461,51283 int ordered_sub_clause(2502,52408 int sub_clause(2547,53492 int sort_lits(2574,53983 void all_cont_cl(2614,54802 void zap_cl_list(2642,55323 int is_eq(2661,55574 void mark_literal(2685,56063 int get_ancestors(2734,57403 struct ilist *clauses_to_ids(2815,59252 void free_clause_ptr_list(2833,59556 struct ilist *get_ancestors2(2849,59842 struct ilist *just_to_supporters(2870,60255 int renumber_vars_term(2917,61429 int renumber_vars(2938,61845 int renum_vars_term(2965,62290 void clear_var_names(3007,63023 void cl_clear_vars(3025,63299 static void distinct_vars_rec(3039,63555 int distinct_vars(3068,64176 struct clause *find_first_cl(3089,64536 struct clause *find_last_cl(3107,64790 struct clause *find_random_cl(3125,65042 struct clause_ptr *get_clauses_of_wt_range(3152,65494 int clause_ptr_list_size(3173,65981 struct clause *nth_clause(3187,66226 void zap_clause_ptr_list(3205,66543 struct clause *find_random_lightest_cl(3219,66789 struct clause *find_mid_lightest_cl(3242,67290 struct clause *find_lightest_cl(3271,68017 struct clause *find_lightest_geo_child(3301,68717 struct clause *find_interactive_cl(3324,69151 struct clause *find_given_clause(3384,70599 struct clause *extract_given_clause(3441,71936 int unit_del(3470,72626 void back_unit_deletion(3581,75077 clocks.c,177 void clock_init(15,218 long clock_val(65,1124 void clock_reset(86,1564 char *get_time(98,1826 long system_time(115,2119 long run_time(144,2637 long wall_seconds(193,3504 control.c,523 static struct Distn pick_weight;65,1861 static struct Distn max_vars;66,1894 void scott_control_memory(68,1925 void control_distn(95,3134 void cull_clauses_over(142,4690 int weight_percentile(170,5630 int variable_percentile(197,6651 int clause_pick_weight(225,7663 void init_distributions(236,8098 void init_a_distribution(264,9007 void get_distn(285,9656 void set_distn(357,11891 void output_distn(460,15045 void output_weight_distn(571,18263 void output_variable_distn(586,18782 int percentile(602,19300 demod.c,673 static struct term *contract_lin(18,350 static void dollar_out_non_list(94,1959 static void dollar_out(110,2287 static struct term *dollar_contract(159,4086 static struct term *replace_special(556,16479 static struct term *demod(593,17616 static struct term *left_most_one_step(692,20357 static struct term *demod_out_in(749,21553 void un_share_special(787,22560 struct term *convenient_demod(814,23003 void zap_term_special(861,24263 struct term *apply_demod(905,25496 void demod_cl(957,26656 void back_demod(1065,29636 int lit_t_f_reduce(1165,32155 int check_input_demod(1229,33653 int dynamic_demodulator(1300,35398 struct clause *new_demod(1364,36893 foreign.c,446 long foo(14,155 long user_test_long(28,343 double user_test_double(45,616 int user_test_bool(62,885 char *user_test_string(79,1152 struct term *user_test_term(96,1460 void declare_user_functions(116,1849 int get_args_for_user_function(211,4633 struct term *long_to_term(289,6201 struct term *double_to_term(307,6517 struct term *bool_to_term(325,6836 struct term *string_to_term(341,7121 struct term *evaluate_user_function(357,7351 formula.c,3021 static int Sk_func_num,11,201 static int Sk_func_num, Sk_const_num;11,201 void print_formula(19,374 void p_formula(87,1809 static struct term *formula_args_to_term(101,2094 struct term *formula_to_term(142,3123 struct formula *term_to_formula(207,4583 struct formula *read_formula(278,6318 struct formula_ptr *read_formula_list(323,7236 void print_formula_list(378,8349 struct formula *copy_formula(396,8720 void zap_formula(433,9494 struct formula *negate_formula(460,9977 struct formula *nnf(495,10754 static void rename_free_formula(603,13339 static struct formula *skolem(631,13962 struct formula *skolemize(722,16180 struct formula *anti_skolemize(742,16544 static void subst_free_term(755,16839 void subst_free_formula(784,17385 void gen_sk_sym(811,17981 int skolem_symbol(849,18677 int contains_skolem_symbol(868,19009 int new_var_name(897,19623 int new_functor_name(926,20173 static void uq_all(949,20570 void unique_all(996,21594 static void mark_free_var_term(1022,22112 static void mark_free_var_formula(1057,22820 struct formula *zap_quant(1084,23547 static void flatten_top_2(1125,24302 void flatten_top(1160,25069 static struct formula *distribute(1183,25530 struct formula *cnf(1264,27078 struct formula *dnf(1307,27910 static void rename_syms_term(1320,28147 void rename_syms_formula(1359,29156 void subst_sn_term(1378,29524 void subst_sn_formula(1405,30065 int gen_subsume_prop(1430,30665 struct formula *subsume_conj(1470,31932 struct formula *subsume_disj(1536,33411 int formula_ident(1599,34728 void conflict_tautology(1634,35671 void ts_and_fs(1676,36657 static int set_vars_term_2(1730,37624 static int set_vars_cl_2(1775,38545 static struct clause *disj_to_clause(1799,38954 static struct list *cnf_to_list(1864,40647 struct list *clausify(1896,41284 struct list *clausify_formula_list(1920,41707 struct formula *negation_inward(1972,42835 struct formula *expand_imp(2017,43811 struct formula *iff_to_conj(2036,44153 struct formula *iff_to_disj(2076,44852 struct formula *nnf_cnf(2109,45476 struct formula *nnf_dnf(2120,45633 struct formula *nnf_skolemize(2131,45796 struct formula *clausify_formed(2142,45979 void rms_conflict_tautology(2164,46459 struct formula *rms_subsume_conj(2219,47554 struct formula *rms_subsume_disj(2285,49035 int free_occurrence(2348,50339 struct formula *rms_distribute_quants(2389,51153 static void separate_free(2428,51980 struct formula *rms_push_free(2492,53263 struct formula *rms_quantifiers(2538,54279 static struct formula *rms_distribute(2614,55990 struct formula *rms(2691,57481 static void introduce_var_term(2739,58440 static void introduce_var(2772,59078 struct formula *renumber_unique(2808,59835 int gen_subsume_rec(2859,61026 int gen_subsume(2904,62504 int gen_conflict(2941,63251 int gen_tautology(2979,64090 struct formula *rms_cnf(3012,64752 struct formula *rms_dnf(3023,64909 static struct formula *push_free(3039,65305 struct formula *distribute_quantifier(3088,66470 fpa.c,919 #define AND 48,1654 #define OR 49,1668 #define LEAF 50,1681 #define MAX_PATH 54,1801 struct fpa_index *alloc_fpa_index(62,1884 static void path_mark_end(83,2261 static int hash_path(112,2855 static int path_comp(130,3100 static int path_size(153,3440 static int *path_copy(171,3650 static void insert_fpa_tab(196,4090 static void delete_fpa_tab(269,5767 void term_fpa_rec(327,7154 void fpa_insert(377,8244 void fpa_delete(404,8886 static struct fpa_tree *get_leaf_node(422,9253 static int all_args_vars(449,9843 static struct fpa_tree *build_tree_local(504,11443 struct fpa_tree *build_tree(598,13534 struct term *next_term(625,14358 struct fpa_tree *build_for_all(732,16809 void zap_prop_tree(771,17605 void print_fpa_tab(786,17889 void p_fpa_tab(818,18475 void print_prop_tree(832,18774 void p_prop_tree(859,19258 void print_path(870,19448 void p_path(904,20072 int new_sym_num(921,20386 geometry.c,348 #define MAX_DEPTH 31,1181 static int is_geometry_symbol(39,1298 static int geo_rewrite_recurse(56,1619 int geo_rewrite(123,3347 static struct term *geo_replace_unif(146,3820 static void geo_generate_unif(173,4302 static void geo_recurse_unif(215,5354 void geometry_rule_unif(260,6528 int child_of_geometry(282,6975 void gl_demod(303,7289 hints2.c,771 struct hint2_data hint2_data17,402 static struct fpa_index *Fpa_hints2_lits 22,460 #define KEEP_BACK_DEMODULATED_HINTS 26,537 static struct literal *first_nonanswer_lit(34,646 static void zap_ilist(52,956 static struct hint2_data *copy_hint2_data(66,1141 void print_hint2_clause(82,1486 void print_hints2_cl_list(113,2080 void hint2_integrate(140,2614 static void index_hint2(161,3093 static void process_hint2_attributes(184,3765 void compile_hints2(220,4715 static struct clause *find_hint2(239,5097 void adjust_weight_with_hints2(278,6063 int hint2_keep_test(323,7395 static void all_containing_hints2(345,7917 static int xx_tautology(375,8538 static struct clause *hint2_subsumed(403,9149 void back_demod_hints(436,9959 void zap_hints2(538,12248 hints.c,307 struct hint_data hint_data65,2095 static void process_hint_attributes(79,2366 void compile_hints(132,3955 void print_hint_clause(147,4228 void p_hint_clause(182,4928 void print_hints_cl_list(193,5088 void p_hints_cl_list(216,5463 void adjust_weight_with_hints(234,5872 int hint_keep_test(305,7377 hot.c,733 static struct fpa_index *Hot_clash_pos_lits;23,696 static struct fpa_index *Hot_clash_neg_lits;24,741 static struct fpa_index *Hot_alphas;25,786 static struct fpa_index *Hot_clash_terms;26,823 static struct fpa_index *Ordinary_clash_pos_lits;30,905 static struct fpa_index *Ordinary_clash_neg_lits;31,955 static struct fpa_index *Ordinary_alphas;32,1005 static struct fpa_index *Ordinary_clash_terms;33,1047 void init_hot(41,1187 int heat_is_on(66,1873 void switch_to_hot_index(78,2060 void switch_to_ordinary_index(92,2354 void hot_index_clause(108,2721 void hot_dynamic(127,3051 static void hot_mark_clash(154,3530 static void hot_unmark_clash(195,4305 void hot_mark_clash_cl(240,5348 void hot_inference(280,6124 imd.c,240 static struct imd_tree *insert_imd_tree(16,242 void imd_insert(95,2022 static struct imd_tree *end_term_imd(147,3611 void imd_delete(208,5012 struct term *contract_imd(294,7012 void print_imd_tree(460,11267 void p_imd_tree(499,12052 index.c,283 static void index_mark_clash(15,262 static void un_index_mark_clash(58,1126 static void index_paramod(105,2227 static void un_index_paramod(158,3583 void index_lits_all(215,5299 void un_index_lits_all(249,6186 void index_lits_clash(284,7182 void un_index_lits_clash(312,7900 io.c,2310 #define SYM_TAB_SIZE 18,343 #define MAX_COMPLEX 19,369 struct sequence_member sequence_member23,509 static struct sym_ent *Sym_tab[31,642 int str_double(51,1050 void double_str(77,1502 int str_int(102,1917 void int_str(131,2379 int str_long(163,2876 int bits_ulong(197,3447 void long_str(216,3768 void ulong_bits(246,4184 void cat_str(268,4684 int str_ident(287,4988 void reverse(301,5198 struct sym_ent *insert_sym(322,5594 int str_to_sn(349,6243 void print_syms(431,8287 void p_syms(451,8621 char *sn_to_str(462,8793 int sn_to_arity(481,9142 struct sym_ent *sn_to_node(502,9510 int sn_to_ec(520,9856 struct sym_ent *sym_tab_member(542,10263 int in_sym_tab(569,10727 void free_sym_tab(591,11074 int is_symbol(615,11472 void mark_as_skolem(630,11760 int is_skolem(651,12076 int initial_str(673,12453 int set_vars(694,12948 int set_vars_term(711,13207 int var_name(754,14105 struct term_ptr *read_list(774,14588 void print_list(828,15652 void bird_print(844,15910 #define OPEN_PAREN 935,18838 #define OTHER_PUNC 936,18860 #define NAME_SYM 937,18882 #define SYM_SYM 938,18904 static int next_token_type(949,19109 void write_term(1014,20632 void display_term(1212,25225 void print_term(1246,25936 void p_term(1265,26285 void d_term(1278,26497 void print_term_nl(1291,26720 int print_term_length(1304,26906 void pretty_print_term(1339,27552 void print_variable(1384,28413 void built_in_symbols(1416,29117 int declare_op(1501,32834 void init_special_ops(1546,33592 int process_op_command(1591,34596 static void fill_in_op_data(1658,36417 static int is_white(1695,37215 void skip_white(1714,37604 static int is_symbol_char(1735,37963 static int is_alpha_numeric(1768,38427 int name_sym(1783,38670 static void get_name(1801,38964 void print_error(1856,40059 static struct term *seq_to_quant_term(1915,41331 static struct term *seq_to_term(1982,42919 static struct term *str_to_args(2143,46540 static struct term *str_to_list(2199,47684 static int str_to_sequence(2284,49893 struct term *str_to_term(2392,52566 int read_buf(2449,54133 struct term *term_fixup(2540,56117 struct term *term_fixup_2(2586,57054 struct term *read_term(2618,57789 void merge_sort(2664,58544 int compare_for_auto_lex_order(2707,59386 void auto_lex_order(2748,60240 is.c,298 static struct is_tree *insert_is_tree(15,220 void is_insert(95,2078 static struct is_tree *end_term_is(122,2848 void is_delete(181,4174 struct term_ptr *is_retrieve(270,6410 struct term *fs_retrieve(393,9646 void canc_fs_pos(441,10658 void print_is_tree(463,11019 void p_is_tree(475,11227 ivy.c,413 static struct proof_object *Initial_proof_object 10,114 static int bnode_to_natural(14,249 static struct term *bnode_to_otterterm(29,535 int special_is_symbol(82,1828 void trans_logic_symbols(90,2082 static struct clause *bnode_to_clause(113,2727 struct proof_object *parse_initial_proof_object(135,3236 struct list *init_proof_object(175,4553 struct proof_object *retrieve_initial_proof_object(198,5273 linkhyp.c,30 void linked_hyper_res(14,141 linkur.c,1421 static void construct_children_nodes(125,4477 static struct clause *subsumable_unit(285,8717 static struct clause *linked_unit_del(425,14029 static struct link_node *backward(557,18387 void linked_ur_res(702,22141 static struct ilist *build_parental_chain(1096,34186 static struct clause *build_ur_resolvent(1145,35395 static BOOLEAN check_down_tree(1206,36948 static BOOLEAN check_up_tree(1259,38146 static struct term *first_unifiable(1314,39544 static struct link_node *forward(1354,40675 static struct link_node *forward_from_resolved_tree(1484,44090 static void free_linked_node_tree(1558,46022 static struct term *generate_resolvent(1588,46923 static struct link_node *initialize_tree(1630,48036 static BOOLEAN is_in_ancestry(1711,50250 static BOOLEAN keep_clause(1776,51994 static void linked_print_clause(1852,53734 static void linked_print_link_node(1908,54886 static void linked_print_link_node_tree(1983,57078 static BOOLEAN more_targets_here(2008,57717 static struct term *next_unifiable(2040,58489 static BOOLEAN poss_nuc_link(2130,60668 static BOOLEAN pass_parms_check(2162,61446 static BOOLEAN pass_target_depth_check(2245,63613 int process_linked_tags(2263,64022 static BOOLEAN process_this_resolution(2430,68927 static int term_ident_subst(2531,71052 static void write_down_tree(2594,72653 static void write_up_tree(2625,73482 static void write_target_distances(2663,74647 lisp.c,747 #define MAX_WORD 3,19 static char Word[4,40 static int Gets,5,68 static int Gets, Frees;5,68 static BOOLEAN str_ident(15,352 static char *new_str_copy(22,524 static Bnode get_bnode(31,746 static void free_bnode(44,1027 /**/ void zap_btree(54,1215 /**/ BOOLEAN true_listp(65,1428 /**/ void fprint_btree(75,1653 /**/ void p_btree(100,2202 static BOOLEAN white_char(109,2387 static BOOLEAN paren(119,2668 static int fill_word(127,2836 /**/ BOOLEAN nullp(154,3405 static BOOLEAN dotp(159,3500 static void dot_trans 166,3671 /**/ Bnode parse_lisp(194,4261 /**/ int atom(229,5019 /**/ Bnode car(234,5152 /**/ Bnode cdr(239,5283 /**/ Bnode cadr(244,5414 /**/ Bnode caddr(249,5552 /**/ int length(254,5697 /**/ int main(263,5876 lists.c,864 void free_ilist_list(16,222 struct ilist *ilist_tack_on(30,419 struct ilist *iset_add(49,705 struct ilist *iset_remove(76,1140 int ilist_member(102,1519 int iset_subset(118,1753 struct ilist *iset_subtract(132,1987 struct ilist *iset_sort(148,2293 struct ilist *idempot_ip(166,2565 struct ilist *reverse_ip(187,2904 struct ilist *ilist_append(204,3217 struct ilist *copy_ilist(222,3513 int ilist_length(240,3784 struct ilist *copy_ilist_segment(254,4011 void print_ilist(272,4333 void p_ilist(288,4606 int glist_length(302,4833 struct glist *copy_glist(316,5063 struct glist *glist_append(334,5365 struct glist *glist_prepend(350,5641 struct glist *glist_tack_on(364,5852 void free_glist_list(383,6147 int g2list_length(399,6420 int member_is_subset(415,6699 struct glist *copy_glist_of_ilists(431,6975 void free_glist_of_ilists(449,7296 lrpo.c,298 static int sym_precedence(16,257 static int lrpo_status(51,1151 static int lrpo_lex(68,1539 static int num_occurrences(109,2537 static struct term *set_multiset_diff(136,3136 static int lrpo_multiset(184,4416 int lrpo(222,5220 int lrpo_greater(267,6403 void order_equalities_lrpo(294,6923 macutils.c,123 #define strID 8,129 #define stackItem 9,147 #define creatorItem 10,167 void AdjustStack(12,190 void SetCreator(26,520 main.c,133 #define OTTER_VERSION 14,265 #define VERSION_DATE 15,294 #define IN_MAIN 17,333 /**/ int main(24,513 void print_banner(183,5005 misc.c,1467 void init(18,202 void abend(60,1132 void read_a_file(80,1504 void sos_argument(788,21367 void read_all_input(856,22776 void set_lex_vals(1020,26897 void set_lrpo_status(1045,27424 void set_special_unary(1066,27899 void set_skolem(1088,28506 void free_all_mem(1105,28820 void output_stats(1207,30934 void print_stats(1252,31787 void print_stats_brief(1342,35899 void p_stats(1367,36794 void print_times(1378,36916 void print_times_brief(1456,40899 void p_times(1511,43173 void append_lists(1522,43347 struct term *copy_term(1580,44619 int biggest_var(1614,45224 int biggest_var_clause(1642,45680 int ground_clause(1661,46004 void zap_list(1672,46211 int occurs_in(1692,46519 int occurrences(1717,46933 int sn_occur(1742,47368 int is_atom(1772,47957 static int id_nested_skolems(1785,48206 int ident_nested_skolems(1824,48906 int ground(1844,49244 void cleanup(1867,49591 int check_stop(1907,50775 void report(1944,51675 void control_memory(1969,52256 static void proof_message(2036,53803 void print_proof(2068,54524 struct clause *check_for_proof(2154,56654 int proper_list(2222,58241 void move_clauses(2242,58663 void automatic_1_settings(2270,59239 int sos_has_pos_nonground(2391,64153 void automatic_2_settings(2423,64855 void log_for_x_show(2544,68959 int same_structure(2569,69821 void zap_variable_names(2599,70364 int commuted_terms(2616,70682 int symbol_count(2651,71595 int commutativity_consequence(2670,71944 multijust.c,2590 static int Asize;24,704 static int Bsize;25,722 static struct glist **Alists;26,740 static struct glist **Blists;27,770 static int *A_to_B;28,800 static int *B_to_A;29,820 static struct ilist *Demod_map;31,841 static struct glist *remove_those_containing(39,990 struct glist *keep_only(61,1421 struct glist *remove_supersets(81,1724 struct glist *remove_all_supersets(103,2140 static int g2_superset(130,2716 struct g2list *g2_remove_supersets(149,3084 static void append_parents(173,3549 int input_clause(205,4270 int first_just_input_only(222,4518 int all_supporters_less_than(238,4809 int derived_from_itself(254,5126 int proof_not_longer_than(265,5337 void possibly_append_parents(292,6126 static void print_multi_supporters(332,7269 static struct glist *just_lists_to_supporters_lists(352,7708 static void build_support_lists(370,8067 int map_demod(400,8917 static void collapse_new_demod2(421,9366 static void multi_map(460,10216 #define INT_BIT 542,12168 static int Set_size;543,12187 static unsigned Compares;544,12235 void set_jset_size(552,12321 int *get_jset(563,12463 int *copy_jset(574,12599 int jset_member(589,12794 void add_to_jset(602,12976 void remove_from_jset(615,13164 static int j_compare(630,13397 #define JHASH_SIZE 653,13851 static struct glist **Jhash;655,13898 static unsigned int Lookups;656,13927 static unsigned int Crashes;657,13956 static void jhash_init(665,14042 static int jhash(676,14199 static int jhash_member_recurse(691,14421 static int jhash_member(714,14821 static struct glist *jhash_insert_recurse(727,15021 static void jhash_insert(761,15701 void print_set(773,15882 void print_set_b_to_a(793,16188 static void print_jhash(813,16511 struct jnode jnode838,17003 static struct jnode *Jstart;847,17280 static struct jnode *Jend;848,17309 static struct jnode *Jcurrent;849,17336 static int Expanded;851,17368 static int Generated;852,17389 static int Pruned;853,17411 static int Subsumed;854,17430 static int Kept;855,17451 static struct jnode *get_jnode(863,17524 static int b_input(879,17807 static int a_input(890,17934 static void print_jnode(901,18073 static void print_jnode_b_to_a(918,18387 int subset_or_input(935,18755 static void jproof(955,19177 static int j_subsumed_recurse(1070,22341 static int j_subsumed(1110,23174 struct ilist *jset_to_ilist(1143,23775 int *ilist_to_jset(1163,24104 static int iset_jset_disjoint(1177,24325 static int j_expand(1193,24593 static int j_search(1265,26186 void multi_just_process(1316,27554 int multi_justifications(1365,28606 nonport.c,222 void non_portable_init(38,675 void sig_handler(62,1053 char *username(110,2313 char *hostname(139,2803 void interact(168,3240 void foreach_sos(342,8254 FILE *init_log_for_x_show(398,9358 int my_process_id(415,9628 options.c,297 void init_options(18,232 void print_options(667,18803 void p_options(708,19596 void auto_change_flag(719,19726 void dependent_flags(742,20284 void auto_change_parm(853,23770 void dependent_parms(879,24357 int change_flag(897,24717 int change_parm(970,26701 void check_options(1051,28876 overbeek.c,205 #define OVERBEEK_WORLD_SIZE 64,1563 static unsigned hash_term2(74,1746 void overbeek_insert(98,2253 int overbeek_weight(130,3070 void print_overbeek_world(160,3720 void check_overbeek_world(197,4482 paramod.c,304 static struct term *apply_substitute(17,337 static struct clause *build_bin_para(76,1757 static void insert_detailed_para_history(154,3988 static void para_from_up(203,5164 static void para_from_alpha(264,6866 void para_from(307,7991 static void para_into_terms(342,8861 void para_into(416,10940 pickdiff.c,520 static struct rel *copy_rels(9,132 static void zap_rels(27,466 static struct rel *remove1(42,705 static struct ilist *add_vecs(64,1101 static int le_vecs(86,1523 static struct ilist *diff_lists(108,1943 static struct ilist *diff(134,2536 static struct ilist *min_diff(167,3336 static struct ilist *diff2_lists(200,3982 static struct ilist *diff2(229,4661 struct ilist *cldiff(258,5343 static struct ci_ptr *get_ci_of_wt_range(282,5911 void zap_ci_ptr_list(305,6428 struct clause *find_pickdiff_cl(322,6676 process.c,183 static void post_process(24,580 void post_proc_all(150,3856 static int given_clause_ok(192,4807 void infer_and_process(213,5232 int proc_gen(356,9056 void pre_process(643,16860 resolve.c,491 static struct clause *build_hyper(17,332 int maximal_lit(176,3908 static void clash(225,5721 void hyper_res(391,9603 void neg_hyper_res(593,14875 void ur_res(797,20244 int one_unary_answer(1044,26456 struct term *build_term(1065,26969 void combine_answers(1100,27563 struct clause *build_bin_res(1162,29148 struct clause *apply_clause(1249,31235 void bin_res(1279,31882 struct clause *first_or_next_factor(1342,33470 void all_factors(1416,35140 int factor_simplify(1457,36226 share.c,563 #define TERM_TAB_SIZE 8,93 #define TERM_TAB_SIZE 11,153 static struct term_ptr *Term_tab[16,221 static struct term_ptr *Bd_kludge;21,422 static int hash_term(34,726 static int term_compare(66,1550 struct term *integrate_term(107,2579 void disintegrate_term(185,4267 void set_up_pointers(255,5783 void zap_term(276,6179 void print_term_tab(306,6760 void p_term_tab(331,7152 void test_terms(345,7393 struct term_ptr *all_instances(379,8091 struct term_ptr *all_instances_fpa(435,9341 void bd_kludge_insert(496,10792 void bd_kludge_delete(520,11178 unify.c,358 #define BIND(BIND10,142 #define DEREFERENCE(DEREFERENCE15,337 int occur_check(28,681 int unify(92,2810 int unify_no_occur_check(172,4568 int match(248,6632 struct term *apply(301,8040 int term_ident(360,9402 void clear_subst_2(394,10240 void clear_subst_1(414,10610 void print_subst(431,10883 void p_subst(453,11364 void print_trail(464,11517 weight.c,742 struct term_ptr *read_wt_list(17,291 static struct is_tree *weight_retrieve(43,858 int noncomplexifying(65,1328 int overbeek_match(81,1650 int weight(112,2278 static int wt_match_dots(176,3653 int wt_match(203,4264 static void set_wt_term(252,5472 static int set_wt_template(287,6371 static void weight_insert(312,7038 void set_wt_list(352,7850 void weight_index_delete(379,8330 static int lex_compare_sym_nums(411,8935 int lex_order(450,9880 int lex_order_vars(517,11860 static int wt_lex_order(587,13822 int lex_check(613,14325 static void get_var_multiset(631,14667 int var_subset(655,15080 static int sym_occur(685,15668 static int sym_elim(719,16451 void order_equalities(764,17537 int term_ident_x_vars(819,18828 otter-3.3f/source/lrpo.c0100644000076400007640000001652110012172126014616 0ustar mccunemccune/* * lrpo.c -- Lexicograpphic recursive path ordering (RPO with status) * */ #include "header.h" /************* * * int sym_precedence(sym_num_1, sym_num_2) * * Return SAME_AS, GREATER_THAN, LESS_THAN, or NOT_COMPARABLE. * *************/ static int sym_precedence(int sym_num_1, int sym_num_2) { int p1, p2, sn; static int warning_given; if (sym_num_1 == sym_num_2) return(SAME_AS); else { p1 = sn_to_node(sym_num_1)->lex_val; p2 = sn_to_node(sym_num_2)->lex_val; if (p1 == MAX_INT || p2 == MAX_INT) { if (!warning_given) { sn = (p1 == MAX_INT ? sym_num_1 : sym_num_2); fprintf(stderr, "%c\nWARNING: at least one symbol, %s, is not lexically comparable.\nIf you use a lex command, you should include all symbols that\nwill be compared. This warning will not be given again.\n", Bell, sn_to_str(sn)); warning_given = 1; } return(NOT_COMPARABLE); } else if (p1 > p2) return(GREATER_THAN); else if (p1 < p2) return(LESS_THAN); else return(SAME_AS); } } /* sym_precedence */ /************* * * int lrpo_status(sym_num) * *************/ static int lrpo_status(int sym_num) { return(sn_to_node(sym_num)->lex_rpo_status); } /* lrpo_status */ /************* * * int lrpo_lex(t1, t2) -- Is t1 > t2 ? * * t1 and t2 have same functor and the functor has lr status. * (If a functor really has rl status, its args have already been * reversed. This is true of all subterms of t1 and t2.) * *************/ static int lrpo_lex(struct term *t1, struct term *t2) { struct rel *r1, *r2; int rc; /* First skip over any identical arguments. */ /* (Same number of args, because same functor.) */ for (r1 = t1->farg, r2 = t2->farg; r1 && term_ident(r1->argval, r2->argval); r1 = r1->narg, r2 = r2->narg) /* empty body */ ; if (!r1) rc = 0; /* t1 and t2 identical */ else if (lrpo(r1->argval, r2->argval)) { /* return (t1 > each remaining arg of t2) */ for (r2 = r2->narg; r2 && lrpo(t1, r2->argval); r2 = r2->narg) /* empty body */ ; rc = (r2 == NULL); } else { /* return (there is a remaining arg of t1 s.t. arg == t2 or arg > t2) */ rc = 0; for (r1 = r1->narg; r1; r1 = r1->narg) { if (term_ident(r1->argval, t2) || lrpo(r1->argval, t2)) rc = 1; } } return(rc); } /* lrpo_lex */ /************* * * int num_occurrences(t_arg, t) -- How many times does t_arg occur * as an argument of t? * *************/ static int num_occurrences(struct term *t_arg, struct term *t) { struct rel *r; int i; for (i = 0, r = t->farg; r; r = r->narg) if (term_ident(r->argval, t_arg)) i++; return(i); } /* num_occurrences */ /************* * * struct term *set_multiset_diff(t1, t2) * * Construct the multiset difference, then return the set of that. * Result must be deallocated by caller with zap_term. * * In other words, viewing a term as a multiset of its arguments, * find the set of t1's arguments that have more occurrences in * t1 than in t2. * *************/ static struct term *set_multiset_diff(struct term *t1, struct term *t2) { struct term *t_result; struct rel *prev, *curr, *r1, *r; int i; t_result = get_term(); prev = NULL; i = 0; for (r1 = t1->farg; r1; r1 = r1->narg) { /* First check if a preceeding occurrence of this arg has */ /* already been done. */ for (r = t1->farg; r != r1 && term_ident(r->argval, r1->argval) == 0; r = r->narg) /* empty body */ ; if (r == r1 && num_occurrences(r1->argval, t1) > num_occurrences(r1->argval, t2)) { i++; curr = get_rel(); curr->argval = copy_term(r1->argval); if (!prev) t_result->farg = curr; else prev->narg = curr; prev = curr; } } t_result->type = (i == 0 ? NAME : COMPLEX) ; /* note that no sym_num is assigned; this should be ok */ return(t_result); } /* set_multiset_diff */ /************* * * int lrpo_multiset(t1, t2) -- Is t1 > t2 in the lrpo multiset ordering? * * t1 and t2 have functors with the same precedence. * * let n(a,t) be the number of occurrences of a (as an argument) in t. * * t1 >(multiset) t2 iff for each arg a2 of t2 with n(a2,t2) > n(a2,t1), * there is an arg a1 of t1 such that n(a1,t1) > n(a1,t2), and a1>a2. * *************/ static int lrpo_multiset(struct term *t1, struct term *t2) { struct term *s1, *s2; struct rel *r1, *r2; int ok; s1 = set_multiset_diff(t1, t2); /* builds and returns a set */ s2 = set_multiset_diff(t2, t1); /* builds and returns a set */ /* * return (s2 not empty and foreach arg a2 of s2 * there is an arg a1 of s1 such that lrpo(a1, a2)). */ if (s2->farg == NULL) ok = 0; else { for (r2 = s2->farg, ok = 1; r2 && ok; r2 = r2->narg) { for (r1 = s1->farg, ok = 0; r1 && !ok ; r1 = r1->narg) ok = lrpo(r1->argval, r2->argval); } } zap_term(s1); zap_term(s2); return(ok); } /* lrpo_multiset */ /************* * * int lrpo(t1, t2) - Is t1 > t2 in the lexicographic recursive * path ordering? * *************/ int lrpo(struct term *t1, struct term *t2) { int p; struct rel *r; if (t1->type == VARIABLE) /* varaiable never greater than anything */ return(0); else if (t2->type == VARIABLE) /* t1 > variable iff t1 properly contains that variable */ return(occurs_in(t2, t1)); else if (t1->sym_num == t2->sym_num && lrpo_status(t1->sym_num) == LRPO_LR_STATUS) return(lrpo_lex(t1, t2)); else { p = sym_precedence(t1->sym_num, t2->sym_num); if (p == SAME_AS) return(lrpo_multiset(t1,t2)); else if (p == GREATER_THAN) { /* return (t1 > each arg of t2) */ for (r = t2->farg; r && lrpo(t1, r->argval); r = r->narg) /* empty body */ ; return(r == NULL); } else { /* LESS_THEN or NOT_COMPARABLE */ /* return (there is an arg of t1 s.t. arg == t2 or arg > t2) */ for (r = t1->farg; r; r = r->narg) { if (term_ident(r->argval, t2) || lrpo(r->argval, t2)) return(1); } return(0); } } } /* lrpo */ /************* * * int lrpo_greater(t1, t2) - Is t1 > t2 in the lexicographic * recursive path ordering? * * Time this routine. * *************/ int lrpo_greater(struct term *t1, struct term *t2) { int rc; #if 0 CLOCK_START(LRPO_TIME); rc = lrpo(t1,t2); CLOCK_STOP(LRPO_TIME); #else rc = lrpo(t1,t2); #endif return(rc); } /* lrpo_greater */ /************* * * order_equalities_lrpo(c) * * For each equality literal (pos or neg), flip args if the right * side is heavier. After possible flip, if the left side is * heavier, set the ORIENTED_EQ_BIT in the atom. * If the atom is flipped, set SCRATCH_BIT. * *************/ void order_equalities_lrpo(struct clause *c) { struct rel *r1, *r2; struct term *alpha, *beta; struct literal *l; for (l = c->first_lit; l; l = l->next_lit) { if (eq_lit(l)) { r1 = l->atom->farg; r2 = r1->narg; alpha = r1->argval; beta = r2->argval; if (lrpo_greater(alpha, beta)) SET_BIT(l->atom->bits, ORIENTED_EQ_BIT); else if (lrpo_greater(beta, alpha)) { r1->argval = beta; r2->argval = alpha; SET_BIT(l->atom->bits, SCRATCH_BIT); SET_BIT(l->atom->bits, ORIENTED_EQ_BIT); } } } } /* order_equalities_lrpo */ otter-3.3f/source/hints2.c0100644000076400007640000003113710014505704015055 0ustar mccunemccune/* * hints2.c -- The second hints mechanism Nov 5, 2002. * */ /* This is a (restricted) implementation of hints that uses indexing. * The restriction: it only does back subsumption of hints. Otherwise, * it should work like the old hints code. * * This new version has many routines similar to the old, but with "hints2" * or "hint2" in the name of the routine. */ #include "header.h" struct hint2_data { int bsub_wt; int bsub_add_wt; }; static struct fpa_index *Fpa_hints2_lits = NULL; /* compiled-in options */ #define KEEP_BACK_DEMODULATED_HINTS 1 /************* * * first_nonanswer_lit(clause) * *************/ static struct literal *first_nonanswer_lit(struct clause *c) { if (c == NULL) return NULL; else { struct literal *lit = c->first_lit; while (lit && answer_lit(lit)) lit = lit->next_lit; return lit; } } /* first_nonanswer_lit */ /************* * * next_nonanswer_lit(literal) * *************/ static struct literal *next_nonanswer_lit(struct literal *lit) { if (lit == NULL) return NULL; else { lit = lit->next_lit; while (lit && answer_lit(lit)) lit = lit->next_lit; return lit; } } /* next_nonanswer_lit */ /************* * * zap_ilist * *************/ static void zap_ilist(struct ilist *p) { if (p != NULL) { zap_ilist(p->next); free_ilist(p); } } /* zap_ilist */ /************* * * copy_hint2_data * *************/ static struct hint2_data *copy_hint2_data(struct hint2_data *p) { struct hint2_data *p2 = malloc(sizeof(struct hint2_data)); p2->bsub_wt = p->bsub_wt; p2->bsub_add_wt = p->bsub_add_wt; return p2; } /* copy_hint2_data */ /************* * * print_hint2_clause() * * (Not in the same form as they were input.) * *************/ void print_hint2_clause(FILE *fp, struct clause *c) { struct hint2_data *hd; struct term *t; hd = (struct hint2_data *) c->parents; fprintf(fp, "%d [", c->id); if (hd) fprintf(fp, "bsub_wt=%d, bsub_add_wt=%d", hd->bsub_wt, hd->bsub_add_wt); fprintf(fp, "] "); t = clause_to_term(c); t = term_fixup_2(t); /* Change -(=(a,b)) to !=(a,b). */ print_term(fp, t); zap_term(t); if (c->attributes) print_attributes(fp, c->attributes); fprintf(fp, ".\n"); } /* print_hint2_clause */ /************* * * print_hints2_cl_list() * *************/ void print_hints2_cl_list(FILE *fp, struct list *lst) { struct clause *cl; if (!lst) fprintf(fp, "(hints2 list nil)\n"); else { fprintf(fp, "list(hints2).\n"); cl = lst->first_cl; while (cl) { print_hint2_clause(fp, cl); cl = cl->next_cl; } fprintf(fp, "end_of_list.\n"); } } /* print_hints2_cl_list */ /************* * * hint2_integrate(c) * * Integrate a hint clause. This orders equalities before calling * the ordinary clause integration routine. * *************/ void hint2_integrate(struct clause *h) { if (Flags[ORDER_EQ].val) { if (Flags[LRPO].val) order_equalities_lrpo(h); else order_equalities(h); } cl_integrate(h); } /* hint2_integrate */ /************* * * index_hint2(clause) * * This inserts (or deletes) the first literal of the clause into the * FPA hints2 index. If back demodulation is enabled for hints, it is * handled by the ordinary indexing for back demodulation. * *************/ static void index_hint2(struct clause *c, int insert) { struct literal *lit = first_nonanswer_lit(c); while (lit != NULL) { if (insert) fpa_insert(lit->atom, Parms[FPA_LITERALS].val, Fpa_hints2_lits); else fpa_delete(lit->atom, Parms[FPA_LITERALS].val, Fpa_hints2_lits); lit = next_nonanswer_lit(lit); } } /* index_hint2 */ /************* * * process_hint2_attributes() * * This "compiles" a hint: (1) Any hint-related attributes on the * clause are put into a hint2_data structure, which is attached * to the hint by borrowing the hint's parent pointer. (2) The hint * is indexed so that it can be found quickly. * *************/ static void process_hint2_attributes(struct clause *c) { struct cl_attribute *a; struct hint2_data *hd; int can_be_used = 0; hd = malloc(sizeof(struct hint2_data)); c->parents = (struct ilist *) hd; hd->bsub_wt = Parms[BSUB_HINT_WT].val; hd->bsub_add_wt = Parms[BSUB_HINT_ADD_WT].val; for (a = c->attributes; a; a = a->next) { switch (a->name) { case BSUB_HINT_WT_ATTR: hd->bsub_wt = a->u.i; break; case BSUB_HINT_ADD_WT_ATTR: hd->bsub_add_wt = a->u.i; break; } } can_be_used = !(hd->bsub_wt == MAX_INT && hd->bsub_add_wt == 0); if (!can_be_used && !Flags[KEEP_HINT_SUBSUMERS].val) { printf("\n%cWARNING, hint cannot be used, because no weights have been\nset for it: ", Bell); print_hint2_clause(stdout, c); } index_hint2(c, 1); /* second arg says "insert" */ } /* process_hint2_attributes */ /************* * * compile_hints2 - compile a list of hints. * *************/ void compile_hints2(void) { struct clause *h; Fpa_hints2_lits = alloc_fpa_index(); for (h = Hints2->first_cl; h != NULL; h = h->next_cl) process_hint2_attributes(h); } /* compile_hints2 */ /************* * * find_hint2(clause) * * This looks for a hint that "matches" a clause. * For now, "matches" means that the clause subsumes the hint. * *************/ struct clause *find_hint2(struct clause *c) { struct literal *lit = first_nonanswer_lit(c); if (lit != NULL) { struct fpa_tree *ut = build_tree(lit->atom, INSTANCE, Parms[FPA_LITERALS].val, Fpa_hints2_lits); struct term *fatom = next_term(ut, 0); while (fatom != NULL) { struct literal *flit = fatom->occ.lit; if (lit->sign == flit->sign) { struct clause *hint = flit->container; if (subsume(c, hint)) { zap_prop_tree(ut); return hint; } } fatom = next_term(ut, 0); } } return NULL; } /* find_hint2 */ /************* * * adjust_weight_with_hints2() * * This routine uses the list Hints2 to adjust or reset * the pick_weight of a clause. * * Look for a hint that "matches" the clause. If a match * is found, change the pick_weight of the clause. * * Also, if the matching hint has a label, the label is copied * to the clause. * *************/ void adjust_weight_with_hints2(struct clause *c) { struct clause *hint; CLOCK_START(HINTS_TIME); hint = find_hint2(c); if (hint != NULL) { struct hint2_data *hd = (struct hint2_data *) hint->parents; if (hd->bsub_wt != MAX_INT) c->pick_weight = hd->bsub_wt; c->pick_weight += hd->bsub_add_wt; /* If the hint has a label, copy it to the clause. */ { struct cl_attribute *a1; if ((a1 = get_attribute(hint, LABEL_ATTR))) { set_attribute(c, LABEL_ATTR, (void *) a1->u.s); } } if (Flags[DEGRADE_HINTS2].val) { /* This is Bob Veroff's hint degradation strategy. It addresses the problem of a hint matching MANY different clauses, which happens more than you might think. This solution: when a hint gets used, make the hint weaker by cutting in half its bsub_add_wt. This assumes that the bsub_add_wt starts as a large negative number. (Bob has ideas about how to generalize this.) */ hd -> bsub_add_wt /= 2; printf("+++ bsub adjust, cl %d, new wt %d\n", hint->id, hd -> bsub_add_wt); } } CLOCK_STOP(HINTS_TIME); } /* adjust_weight_with_hints2 */ /************* * * hint2_keep_test(clause) * * Return TRUE iff KEEP_HINT_SUBSUMERS is set and there is a hint * that "matches" the clause. * *************/ int hint2_keep_test(struct clause *c) { if (!Flags[KEEP_HINT_SUBSUMERS].val) return 0; else { struct clause *hint; CLOCK_START(HINTS_KEEP_TIME); hint = find_hint2(c); CLOCK_STOP(HINTS_KEEP_TIME); return(hint != NULL); } } /* hint2_keep_test */ /************* * * all_containing_hints2(t, cpp) - insert containing clauses of t into *cpp * * Given a term t, find all containing clauses that are in the Hints2 list. * For each, insert the clause into the cpp list. * *************/ static void all_containing_hints2(struct term *t, struct clause_ptr **cpp) { struct rel *r; struct clause *c; struct list *l; if (t->type != VARIABLE && t->varnum != 0) { /* atom */ c = t->occ.lit->container; l = c->container; if (l == Hints2) insert_clause(c, cpp); } else { /* term */ r = t->occ.rel; while (r) { all_containing_hints2(r->argof, cpp); r = r->nocc; } } } /* all_containing_hints2 */ /************* * * xx_tautology - does a clause have a literal that is an instance of x=x? * * This is a pre-subsumption check. * *************/ static int xx_tautology(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit) { struct term *atom = lit->atom; if (lit->sign && is_eq(atom->sym_num) && term_ident(atom->farg->argval, atom->farg->narg->argval)) { return(1); } lit = lit->next_lit; } return(0); } /* xx_tautology */ /************* * * hint2_subsumed(c) * * Use the FPA hint index to look for a hint that subsumes clause c. * * This is not complete, because we only consider the first literal of c. * For example, given clause p|q|r, we will not find hint q|r. * *************/ static struct clause *hint2_subsumed(struct clause *c) { struct literal *lit = first_nonanswer_lit(c); if (lit != NULL) { struct fpa_tree *ut = build_tree(lit->atom, MORE_GEN, Parms[FPA_LITERALS].val, Fpa_hints2_lits); struct term *fatom = next_term(ut, 0); while (fatom != NULL) { struct literal *flit = fatom->occ.lit; if (lit->sign == flit->sign) { struct clause *hint = flit->container; if (subsume(hint, c)) { zap_prop_tree(ut); return hint; } } fatom = next_term(ut, 0); } } return NULL; } /* hint2_subsumed */ /************* * * back_demod_hints(clause) * * This uses the ordinary back demodulation indexing. This works * because hints are integrated into the ordinary shared structures. * *************/ void back_demod_hints(struct clause *d) { struct term *atom; struct term_ptr *tp, *tp2; struct clause_ptr *cp, *cp2; /* return; */ atom = ith_literal(d,1)->atom; if (Flags[INDEX_FOR_BACK_DEMOD].val) tp = all_instances_fpa(atom, Fpa_back_demod); else tp = all_instances(atom); cp = NULL; while (tp) { all_containing_hints2(tp->term, &cp); tp2 = tp; tp = tp->next; free_term_ptr(tp2); } while (cp) { struct clause *h1, *h2; h1 = cp->c; if (h1->container != Hints2) abend("back_demod_hints: clause not in Hints2."); /* Stats[CL_BACK_DEMOD]++; */ h2 = cl_copy(h1); demod_cl(h2); if (1 || Flags[PRINT_BACK_DEMOD].val) { printf(" >> BACK DEMODULATING HINT %d WITH %d.\n", h1->id, d->id); /* printf("before: "); print_hint2_clause(stdout, h1); */ /* printf("after: "); p_clause(h2); */ } /* copy hint data to new hint */ zap_ilist(h2->parents); h2->parents = (struct ilist *) copy_hint2_data((void *) h1->parents); /* If the hint has a label, copy it to the clause. */ { struct cl_attribute *a1; if ((a1 = get_attribute(h1, LABEL_ATTR))) { /* set_attribute(h2, LABEL_ATTR, (void *) a1->u.s); */ set_attribute(h2, LABEL_ATTR, "bd"); } } if (!KEEP_BACK_DEMODULATED_HINTS) { rem_from_list(h1); index_hint2(h1, 0); /* second arg says "delete" */ free(h1->parents); /* hint data */ h1->parents = NULL; cl_del_int(h1); } if (Flags[ORDER_EQ].val) { if (Flags[LRPO].val) order_equalities_lrpo(h2); else order_equalities(h2); } if (xx_tautology(h2) || hint2_subsumed(h2)) { free(h2->parents); /* hint data */ h2->parents = NULL; cl_del_non(h2); } else { hint2_integrate(h2); append_cl(Hints2, h2); index_hint2(h2, 1); /* second arg says "insert" */ if (1 || Flags[PRINT_KEPT].val) { printf("NEW HINT: "); print_hint2_clause(stdout, h2); } } cp2 = cp; cp = cp->next; free_clause_ptr(cp2); } } /* back_demod_hints */ /************* * * zap_hints2 - Free all memory associated with hints2. * * This is used mostly to check for memory leaks. * *************/ void zap_hints2(void) { struct clause *c; c = find_last_cl(Hints2); while (c) { rem_from_list(c); index_hint2(c, 0); /* second arg says "delete" */ free(c->parents); /* hint data */ c->parents = NULL; cl_del_int(c); c = find_last_cl(Hints2); } free_list(Hints2); Hints2 = NULL; } /* zap_hints2 */ otter-3.3f/source/check.c0100644000076400007640000020677310012171521014727 0ustar mccunemccune/* * check.c -- code related to proof objects and proof checking * */ #include "header.h" #include "check.h" /* #define DEBUG */ #define ATTEMPT_FEB_9 /* Gen_tab is a general hash table method. You can insert (id,pointer) * pairs and retrieve the pointer associated with a particular id. */ #define GEN_TAB_SIZE 100 struct gen_node { int id; void *v; struct gen_node *next; }; struct gen_tab { struct gen_node *a[GEN_TAB_SIZE]; }; /* Global variables */ static struct gen_tab *Old_proof_tab; static struct gen_tab *New_proof_old_id_tab; static struct gen_tab *New_proof_tab; /************* * * get_gen_node() * *************/ struct gen_node *get_gen_node(void) { struct gen_node *p; p = (struct gen_node *) tp_alloc((int) sizeof(struct gen_node)); p->id = 0; p->v = NULL; return(p); } /* get_gen_node */ /************* * * get_proof_object() * *************/ struct proof_object *get_proof_object(void) { struct proof_object *p; p = (struct proof_object *) tp_alloc((int) sizeof(struct proof_object)); p->steps = 0; p->first = NULL; p->last = NULL; return(p); } /* get_proof_object */ /************* * * get_proof_object_node() * *************/ struct proof_object_node *get_proof_object_node(void) { struct proof_object_node *p; int i; p = (struct proof_object_node *) tp_alloc((int) sizeof(struct proof_object_node)); p->id = 0; p->old_id = 0; p->parent1 = 0; p->parent2 = 0; p->position1 = NULL; p->position2 = NULL; p->map = NULL; p->rule = P_RULE_UNDEFINED; p->backward_subst = FALSE; for (i = 0; i < 2*MAX_VARS; i++) p->subst[i] = NULL; p->next = NULL; return(p); } /* get_proof_object_node */ /************* * * init_gen_tab() * *************/ static struct gen_tab *init_gen_tab(void) { int i; struct gen_tab *p; p = (struct gen_tab *) tp_alloc(GEN_TAB_SIZE * (int) sizeof(void *)); for (i = 0; i < GEN_TAB_SIZE; i++) p->a[i] = NULL; return(p); } /* init_gen_tab */ /************* * * insert_into_gen_tab() * * If ok, return 1; if already there, return 0. * *************/ static int insert_into_gen_tab(struct gen_tab *tab, int id, void *v) { struct gen_node *p1, *p2, *p3; p1 = tab->a[id%GEN_TAB_SIZE]; p2 = NULL; while (p1 && p1->id < id) { p2 = p1; p1 = p1->next; } if (p1 && p1->id == id) abend("insert_into_gen_tab, key already there"); else { p3 = get_gen_node(); p3->id = id; p3->v = v; p3->next = p1; if (p2) p2->next = p3; else tab->a[id%GEN_TAB_SIZE] = p3; } return(1); } /* insert_into_gen_tab */ /************* * * retrieve_from_gen_tab() * * Return NULL if it is not there. * *************/ static void * retrieve_from_gen_tab(struct gen_tab *tab, int id) { struct gen_node *p; p = tab->a[id%GEN_TAB_SIZE]; while (p && p->id < id) p = p->next; if (p && p->id == id) return(p->v); else return((void *) NULL); } /* retrieve_from_gen_tab */ static void p_gen_tab(struct gen_tab *tab) { struct gen_node *p; int i; for (i = 0; i < GEN_TAB_SIZE; i++) { for (p = tab->a[i]; p; p = p->next) { printf("%d: ", i); p_proof_object_node(p->v); } } } /* p_gen_tab */ /************* * * int check_eq_lit(lit) * *************/ static int check_eq_lit(struct literal *lit) { return(lit->atom->varnum == POS_EQ || lit->atom->varnum == NEG_EQ || lit->atom->varnum == LEX_DEP_DEMOD); } /* check_eq_lit */ /************* * * trivial_subst() * * A substitution is trivial if every (nonempty) entry is * "vi -> vi (NULL context)" * *************/ int trivial_subst(struct context *c) { int i, ok; if (c->multiplier != 0) ok = 0; else for (i = 0, ok = 1; i < MAX_VARS && ok; i++) { if (c->terms[i]) { if (c->terms[i]->type != VARIABLE) ok = 0; else if (c->terms[i]->varnum != i) ok = 0; else ok = (c->contexts[i] == NULL); } } return(ok); } /* trivial_subst */ /************* * * connect_new_node() * * Add a new node to the end of the proof object; return the node. * *************/ struct proof_object_node *connect_new_node(struct proof_object *new_proof) { struct proof_object_node *pn; int rc; pn = get_proof_object_node(); if (new_proof->steps == 0) { new_proof->first = pn; new_proof->last = pn; } else { new_proof->last->next = pn; new_proof->last = pn; } new_proof->steps++; pn->id = new_proof->steps; rc = insert_into_gen_tab(New_proof_tab, pn->id, pn); return(pn); } /* connect_new_node */ /************* * * po_rule() * * Return a poitner to the char string corresponding to the integer * code for a proof object rule. * *************/ static char *po_rule(int rule) { switch (rule) { case P_RULE_UNDEFINED: return("undefined"); case P_RULE_INPUT: return("input"); case P_RULE_EQ_AXIOM: return("eq-axiom"); case P_RULE_INSTANTIATE: return("instantiate"); case P_RULE_PROPOSITIONAL: return("propositional"); case P_RULE_RESOLVE: return("resolve"); case P_RULE_PARAMOD: return("paramod"); case P_RULE_FLIP: return("flip"); default: return("unknown"); } } /* po_rule */ /************* * * print_term_s() * * Print a term, S-expression style. * *************/ void print_term_s(FILE *fp, struct term *t) { if (t->type == VARIABLE) { if (t->sym_num != 0) fprintf(fp, "%s", sn_to_str(t->sym_num)); else fprintf(fp, "v%d", t->varnum); } else { struct rel *r; fprintf(fp, "(%s", sn_to_str(t->sym_num)); for (r = t->farg; r; r = r->narg) { fprintf(fp, " "); print_term_s(fp, r->argval); } fprintf(fp, ")"); } } /* print_term_s */ /************* * * p_term_s() * *************/ void p_term_s(struct term *t) { print_term_s(stdout, t); } /* print_term_s */ /************* * * print_clause_s() * * Print a clause, S-expression style (without a newline). * *************/ void print_clause_s(FILE *fp, struct clause *c) { struct literal *lit; fprintf(fp, "("); for (lit = c->first_lit; lit; lit = lit->next_lit) { if (!lit->sign) fprintf(fp, "(not "); print_term_s(fp, lit->atom); if (!lit->sign) fprintf(fp, ")"); if (lit->next_lit) fprintf(fp, " "); } fprintf(fp, ")"); fflush(fp); } /* print_clause_s */ /************* * * p_clause_s() * *************/ void p_clause_s(struct clause *c) { print_clause_s(stdout, c); } /* print_clause_s */ /************* * * print_clause_s2() * * Print a clause, S-expression style (without a newline). * *************/ void print_clause_s2(FILE *fp, struct clause *c) { if (c->first_lit == NULL) fprintf(fp, "false"); else { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) { if (lit->next_lit) fprintf(fp, "(or "); if (!lit->sign) fprintf(fp, "(not "); if (is_symbol(lit->atom, "$T", 0)) fprintf(fp, "true"); else if (is_symbol(lit->atom, "$F", 0)) fprintf(fp, "false"); else print_term_s(fp, lit->atom); if (!lit->sign) fprintf(fp, ")"); if (lit->next_lit) fprintf(fp, " "); } for (lit = c->first_lit->next_lit; lit; lit = lit->next_lit) fprintf(fp, ")"); } fflush(fp); } /* print_clause_s2 */ /************* * * p_clause_s2() * *************/ void p_clause_s2(struct clause *c) { print_clause_s2(stdout, c); } /* print_clause_s2 */ /************* * * print_proof_object_node() * *************/ void print_proof_object_node(FILE *fp, struct proof_object_node *pn) { int i; fprintf(fp, "(%d ", pn->id); fprintf(fp, "(%s", po_rule(pn->rule)); switch (pn->rule) { case P_RULE_INPUT: case P_RULE_EQ_AXIOM: fprintf(fp, ") "); break; case P_RULE_INSTANTIATE: fprintf(fp, " %d (", pn->parent1); for (i = 0; i < 2*MAX_VARS; i++) { if (pn->subst[i]) { if (pn->backward_subst) { fprintf(fp, "("); print_term_s(fp, pn->subst[i]); fprintf(fp, " . v%d)", i); } else { fprintf(fp, "(v%d . ", i); print_term_s(fp, pn->subst[i]); fprintf(fp, ")"); } } } fprintf(fp, ")) "); break; case P_RULE_RESOLVE: case P_RULE_PARAMOD: fprintf(fp, " %d ", pn->parent1); print_ilist(fp, pn->position1); fprintf(fp, " %d ", pn->parent2); print_ilist(fp, pn->position2); fprintf(fp, ") "); break; case P_RULE_PROPOSITIONAL: fprintf(fp, " %d) ", pn->parent1); break; case P_RULE_FLIP: fprintf(fp, " %d ", pn->parent1); print_ilist(fp, pn->position1); fprintf(fp, ") "); break; default: abend("print_proof_object_node, bad rule"); break; } if (Flags[BUILD_PROOF_OBJECT_2].val) print_clause_s2(fp, pn->c); else print_clause_s(fp, pn->c); if (pn->old_id != 0) fprintf(fp, " (%d)", pn->old_id); /* Otter ID */ else fprintf(fp, " NIL"); /* Otter ID */ fprintf(fp, ")\n"); fflush(fp); } /* print_proof_object_node */ /************* * * p_proof_object_node() * *************/ void p_proof_object_node(struct proof_object_node *pn) { print_proof_object_node(stdout, pn); } /* print_proof_object_node */ /************* * * print_proof_object() * *************/ void print_proof_object(FILE *fp, struct proof_object *po) { struct proof_object_node *pn; fprintf(fp, "(\n"); for (pn = po->first; pn; pn = pn->next) print_proof_object_node(fp, pn); fprintf(fp, ")\n"); } /* print_proof_object */ /************* * * p_proof_object() * *************/ void p_proof_object(struct proof_object *po) { print_proof_object(stdout, po); } /* print_proof_object */ /************* * * new_literal_index() * * Given a list of integers and a value v, return the position of v. * *************/ static int new_literal_index(struct ilist *ip, int v) { int i; for (i = 1; ip && abs(ip->i) != v; ip = ip->next, i++); if (!ip) abend("new_literal_index, bad map"); return(i); } /* new_literal_index */ /************* * * copy_subst_to_proof_object() * *************/ static void copy_subst_to_proof_object(struct context *subst, struct proof_object_node *p) { struct term *t; int i; t = get_term(); t->type = VARIABLE; /* If multiplier=0, only need to copy nonNULL entries, because the * variables won't change. */ if (subst->multiplier == 0) { for (i = 0; i < MAX_VARS; i++) { if (subst->terms[i]) { t->varnum = i; p->subst[i] = apply(t, subst); } } } else { int max; struct proof_object_node *parent; parent = retrieve_from_gen_tab(New_proof_tab, p->parent1); max = biggest_var_clause(parent->c); for (i = 0; i <= max; i++) { t->varnum = i; p->subst[i] = apply(t, subst); } } free_term(t); } /* copy_subst_to_proof_object */ /************* * * cl_copy_delete_literal() * *************/ struct clause *cl_copy_delete_literal(struct clause *c, int n) { struct clause *d; struct literal *l1, *l2; int i; d = cl_copy(c); for (l1 = d->first_lit, l2 = NULL, i = 1; i < n; l2 = l1, l1 = l1->next_lit, i++); if (l2) l2->next_lit = l1->next_lit; else d->first_lit = l1->next_lit; return(d); } /* cl_copy_delete_literal */ /************* * * int variant(t1, c1, t2, c2, trail_address, flip) -- alphabetic variant * * I take a shortcut and just call `match' twice. If speed is a * concern, this routine should be rewritten. * * if (flip), t1 has arity 2 and should be flipped before test. * * WARNING!! if you use the substitutions for anything, use either one, * but don't use both. This is because, for example, when given * p(x), p(y), x is bound to y and y is bound to x! * * The use of the trail is the same as in `unify'. * *************/ int variant(struct term *t1, struct context *c1, struct term *t2, struct context *c2, struct trail **trp, int flip) { struct trail *tpos; struct term *tt; int rc; if (flip) { t1 = copy_term(t1); tt = t1->farg->argval; t1->farg->argval = t1->farg->narg->argval; t1->farg->narg->argval = tt; } tpos = *trp; if (match(t1, c1, t2, trp)) { if (match(t2, c2, t1, trp)) rc = 1; else { clear_subst_2(*trp, tpos); *trp = tpos; rc = 0; } } else rc = 0; if (flip) zap_term(t1); return(rc); } /* variant */ /************* * * match_literals() * * Note that literals are indexed starting with 1, not 0. * *************/ static int match_literals(struct clause *c1, struct context *s1, int *m1, struct clause *c2, struct context *s2, int *m2, struct trail **trp) { struct literal *l1, *l2; int i1, i2, matched, flip; struct trail *t_pos; /* Find the first unmatched literal of c2. */ for (l2 = c2->first_lit, i2=1; l2 && m2[i2]!=0; l2 = l2->next_lit, i2++); if (!l2) return(1); /* Success. All literals matched. */ else { matched = 0; flip = 0; i1 = 1; l1 = c1->first_lit; while (l1 && !matched) { t_pos = *trp; /* save position in trail in case of failure */ if (m1[i1]==0 && l1->sign == l2->sign && variant(l1->atom, s1, l2->atom, s2, trp, flip)) { m1[i1] = (flip ? -i2: i2); m2[i2] = (flip ? -i1: i1); if (match_literals(c1, s1, m1, c2, s2, m2, trp)) matched = 1; else { m1[i1] = 0; m2[i2] = 0; clear_subst_2(*trp, t_pos); *trp = t_pos; } } /* increment */ if (check_eq_lit(l1) && check_eq_lit(l2) && !flip) { flip = 1; } else { l1 = l1->next_lit; i1++; flip = 0; } } return(matched); } } /* match_literals */ /************* * * match_clauses(c1, c2) * * This routine takes 2 clauses that are supposed to be * alphabetic variants (if not, return NULL). The literals * may be in different orders, and equality literals may * be flipped. We find the correspondence and * return it as a list of integers: the i-th integer is the * index in c1 of the i-th literal in c2. If an equality * literal is flipped, the index is negated. * *************/ struct ilist *match_clauses(struct clause *c1, struct clause *c2) { int m1[MAX_LITS+1], m2[MAX_LITS+1]; struct context *s1, *s2; struct trail *tr; int i, rc, n1, n2; struct ilist *ip1, *ip2; n1 = num_literals(c1); n2 = num_literals(c2); if (n1 != n2) abend("match_clauses, different numbers of literals"); s1 = get_context(); s2 = get_context(); for (i = 1; i <= MAX_LITS; i++) { m1[i] = 0; m2[i] = 0; } tr = NULL; rc = match_literals(c1, s1, m1, c2, s2, m2, &tr); if (!rc) { abend("match_clauses, literals don't match"); } clear_subst_1(tr); free_context(s1); free_context(s2); #ifdef DEBUG printf("\nmatch_clauses rc=%d\n", rc); for (i = 1; i <= MAX_LITS; i++) printf("%3d", m1[i]); p_clause(c1); for (i = 1; i <= MAX_LITS; i++) printf("%3d", m2[i]); p_clause(c2); #endif ip1 = NULL; for (i = n1; i > 0; i--) { ip2 = get_ilist(); ip2->i = m2[i]; ip2->next = ip1; ip1 = ip2; } return(ip1); } /* match_clauses */ /************* * * cl_append() * *************/ struct clause *cl_append(struct clause *c1, struct clause *c2) { struct literal *curr, *prev; for (curr = c1->first_lit, prev = NULL; curr; prev = curr, curr = curr->next_lit); if (prev) prev->next_lit = c2->first_lit; else c1->first_lit = c2->first_lit; for (curr = c2->first_lit; curr; curr = curr->next_lit) curr->container = c1; free_clause(c2); return(c1); } /* cl_append */ /************* * * identity_resolve() * *************/ struct clause *identity_resolve(struct clause *c1, int i1, struct clause *c2, int i2) { struct clause *d1, *d2, *res; d1 = cl_copy_delete_literal(c1, i1); d2 = cl_copy_delete_literal(c2, i2); res = cl_append(d1, d2); return(res); } /* identity_resolve */ /************* * * identity_paramod() * *************/ static struct clause *identity_paramod(struct clause *from_cl, struct ilist *from_pos, struct clause *into_cl, struct ilist *into_pos) { struct clause *into_prime, *from_prime, *para; struct literal *from_lit, *into_lit; struct term *beta, *t; struct ilist *ip; struct rel *r; int i; from_lit = ith_literal(from_cl, from_pos->i); if (from_pos->next->i == 1) beta = from_lit->atom->farg->narg->argval; else beta = from_lit->atom->farg->argval; into_prime = cl_copy(into_cl); into_lit = ith_literal(into_prime, into_pos->i); /* Get the into term. */ for (ip = into_pos->next, t = into_lit->atom; ip; ip = ip->next) { for (i = 1, r = t->farg; i < ip->i; i++, r = r->narg); t = r->argval; } /* Now r points at into term t. */ r->argval = copy_term(beta); from_prime = cl_copy_delete_literal(from_cl, from_pos->i); para = cl_append(from_prime, into_prime); return(para); } /* identity_paramod */ /************* * * void renumber_vars_subst() * *************/ void renumber_vars_subst(struct clause *c, struct term **terms) { struct literal *lit; int varnums[MAX_VARS]; int i, ok; struct term *t; ok = 1; for (i = 0; i < MAX_VARS; i++) varnums[i] = -1; lit = c->first_lit; while (lit) { if (renum_vars_term(lit->atom, varnums) == 0) ok = 0; lit = lit->next_lit; } for (i = 0; i < MAX_VARS; i++) { if (varnums[i] != -1 && varnums[i] != i) { t = get_term(); t->type = VARIABLE; t->varnum = i; terms[varnums[i]] = t; } } } /* renumber_vars_subst */ /************* * * translate_unit_deletion() * *************/ static int translate_unit_deletion(struct proof_object_node *current, struct proof_object_node *unit, struct proof_object *new_proof) { struct literal *l1, *l2; struct proof_object_node *instance, *resolvent; struct context *subst; struct trail *tr; int found, index; struct ilist *ip1, *ip2; /* First, find the literal that is deleted. */ subst = get_context(); subst->multiplier = 0; l2 = unit->c->first_lit; for (l1 = current->c->first_lit, found = 0, index = 0; l1 && !found; l1 = l1->next_lit, index++) { tr = NULL; if (l2->sign != l1->sign && match(l2->atom,subst,l1->atom,&tr)) { found = 1; } } if (!found) abend("translate_unit_deletion, unit deletion not found"); /* Set up a new proof object node for the instantiation. */ if (trivial_subst(subst)) instance = unit; else { instance = connect_new_node(new_proof); instance->rule = P_RULE_INSTANTIATE; instance->parent1 = unit->id; instance->c = apply_clause(unit->c, subst); copy_subst_to_proof_object(subst, instance); } clear_subst_1(tr); free_context(subst); /* Set up a node for the resolution (negative lit. always first parent). */ resolvent = connect_new_node(new_proof); resolvent->rule = P_RULE_RESOLVE; ip1 = get_ilist(); resolvent->position1 = ip1; ip2 = get_ilist(); resolvent->position2 = ip2; if (l2->sign) { /* unit positive */ resolvent->parent1 = current->id; resolvent->parent2 = instance->id; ip1->i = index; ip2->i = 1; } else { resolvent->parent1 = instance->id; resolvent->parent2 = current->id; ip1->i = 1; ip2->i = index; } /* Copy the clause then delete the correct literal. */ resolvent->c = cl_copy_delete_literal(current->c, index); return(1); } /* translate_unit_deletion */ /************* * * translate_factor_simp() * * Apply the first factor_simp operation. Note that a sequence of * factor_simps may be applied in a different order in the new proof, * because the order of literals can be different. This should be OK. * *************/ static int translate_factor_simp(struct proof_object_node *current, struct proof_object *new_proof) { struct literal *lit1, *lit2; struct clause *factor; struct context *subst; struct trail *tr; struct proof_object_node *previous, *instance, *merge; int rc; /* May have to renumber the variables. */ if (biggest_var_clause(current->c) >= MAX_VARS) { previous = current; current = connect_new_node(new_proof); current->rule = P_RULE_INSTANTIATE; current->parent1 = previous->id; current->c = cl_copy(previous->c); renumber_vars_subst(current->c, current->subst); } lit1 = NULL; lit2 = NULL; factor = first_or_next_factor(current->c, &lit1, &lit2); while (factor && ! subsume(factor, current->c)) { cl_del_non(factor); factor = first_or_next_factor(current->c, &lit1, &lit2); } if (!factor) abend("translate_factor_simp, factor not found"); cl_del_non(factor); subst = get_context(); subst->multiplier = 0; tr = NULL; rc = unify(lit1->atom, subst, lit2->atom, subst, &tr); if (!rc) abend("translate_factor_simp, literals don't unify"); if (trivial_subst(subst)) instance = current; else { instance = connect_new_node(new_proof); instance->rule = P_RULE_INSTANTIATE; instance->parent1 = current->id; instance->c = apply_clause(current->c, subst); copy_subst_to_proof_object(subst, instance); } clear_subst_1(tr); free_context(subst); /* Build the merge node. */ merge = connect_new_node(new_proof); merge->rule = P_RULE_PROPOSITIONAL; merge->parent1 = instance->id; merge->position1 = get_ilist(); merge->position1->i = literal_number(lit2); merge->c = cl_copy_delete_literal(instance->c, literal_number(lit2)); if (num_literals(instance->c)-1 != num_literals(merge->c)) abend("translate_factor_simp: merge failed"); return(1); } /* translate_factor_simp */ /************* * * first_rewrite() * *************/ static struct ilist *first_rewrite(struct term *t, struct ilist *pos, struct clause *c, struct clause_ptr *demods, struct context *subst, struct trail **trp, int *demod_id) { struct ilist *prev, *last, *pos_ok; struct rel *r; struct clause_ptr *cp; int ok; struct term *atom; if (t->type == COMPLEX) { for (prev = pos; prev->next; prev = prev->next); last = get_ilist(); last->i = 1; prev->next = last; for (r = t->farg; r; r = r->narg, last->i++) { pos_ok = first_rewrite(r->argval,pos,c,demods,subst,trp,demod_id); if (pos_ok) return(pos_ok); } prev->next = NULL; free_ilist(last); } if (t->type != VARIABLE) { for (cp = demods, ok = 0; cp && !ok; cp = cp->next) { atom = cp->c->first_lit->atom; ok = match(atom->farg->argval, subst, t, trp); if (ok && atom->varnum == LEX_DEP_DEMOD) { int mult_flag = 0; struct term *replacement; replacement = apply_demod(atom->farg->narg->argval, subst, &mult_flag); if (Flags[LRPO].val) ok = lrpo_greater(t, replacement); else ok = lex_check(replacement, t) == LESS_THAN; zap_term_special(replacement); if (!ok) { clear_subst_1(*trp); *trp = NULL; } } if (ok) { *demod_id = cp->c->id; return(pos); } } } return(NULL); } /* first_rewrite */ /************* * * first_rewrite_clause() * *************/ static struct ilist *first_rewrite_clause(struct clause *c, struct clause_ptr *demods, struct context *subst, struct trail **trp, int *demod_id) { struct ilist *ip1, *ip2; struct literal *lit; ip1 = get_ilist(); ip1->i = 1; for (lit = c->first_lit; lit; lit = lit->next_lit, ip1->i++) { ip2 = first_rewrite(lit->atom, ip1, c, demods, subst, trp, demod_id); if (ip2) return(ip2); } free_ilist(ip1); return(NULL); } /* first_rewrite_clause */ /************* * * translate_demod_nonunit() * * The sequence of demodulators that apply to the original clause * might not apply to the new clause in the same order, because * the literals might be rearranged. So we collect all of the * demodulators and keep applying the set. This method is still * not perfect, because at a given term, the set of demodulators * might be tried in a different order; an abend is possible. * *************/ static int translate_demod_nonunit(struct proof_object_node *current, struct ilist *ip, struct proof_object *new_proof) { int count1, count2, demod_id; struct ilist *ip0, *ip1, *ip2, *ip3; struct clause_ptr *demods; struct clause *c; struct context *subst; struct trail *tr; struct proof_object_node *instance, *paramod, *pn; #if 0 printf("\ncurrent="); p_clause(current->c); #endif demods = NULL; for (ip1 = ip, count1 = 0; ip1 && ip1->i > 0; ip1 = ip1->next, count1++) { c = cl_find(ip1->i); /* The new versions of the demodulators have to be used, because the variables might be numbered differently. We have to copy the ID and the lex-dep flag into the new version. Sorry this is so messy. */ pn = retrieve_from_gen_tab(New_proof_old_id_tab, c->id); pn->c->id = pn->id; pn->c->first_lit->atom->varnum = c->first_lit->atom->varnum; #if 0 printf("old demod:"); p_clause(c); printf("new demod:"); p_clause(pn->c); #endif insert_clause(pn->c, &demods); /* If not already there. */ } subst = get_context(); subst->multiplier = 0; tr = NULL; count2 = 0; ip0 = first_rewrite_clause(current->c,demods,subst,&tr,&demod_id); while (ip0 && count2 < count1) { count2++; pn = retrieve_from_gen_tab(New_proof_tab, demod_id); if (trivial_subst(subst)) instance = pn; else { instance = connect_new_node(new_proof); instance->parent1 = pn->id; instance->rule = P_RULE_INSTANTIATE; instance->c = apply_clause(pn->c, subst); copy_subst_to_proof_object(subst, instance); } paramod = connect_new_node(new_proof); paramod->rule = P_RULE_PARAMOD; paramod->parent1 = instance->id; ip2 = get_ilist(); ip2->i = 1; paramod->position1 = ip2; ip3 = get_ilist(); ip3->i = 1; ip2->next = ip3; paramod->parent2 = current->id; paramod->position2 = ip0; paramod->c = identity_paramod(instance->c, paramod->position1, current->c, paramod->position2); /* If into literal is negated, must add element to position. * The position vector will no longer be valid for Otter terms. */ if (ith_literal(current->c, ip0->i)->sign == 0) { ip1 = get_ilist(); ip1->i = 1; ip1->next = ip0->next; ip0->next = ip1; } current = paramod; #if 0 printf("after rewrite with %d: ", demod_id); p_clause(current->c); #endif clear_subst_1(tr); tr = NULL; ip0 = first_rewrite_clause(current->c, demods, subst, &tr, &demod_id); } if (ip0 || count1 != count2) { #if 0 fprintf(stdout, "%d rewrites in proof, %d trans.\n", count1, count2); fprintf(stdout, "clause is "); print_clause(stdout, current->c); #endif abend("translate_demod_nonunit, wrong number of rewrites"); } return(1); } /* translate_demod_nonunit */ /************* * * translate_demod_unit() * * With units, we can apply the demodulators in the same order. * *************/ static int translate_demod_unit(struct proof_object_node *current, struct ilist *ip, struct proof_object *new_proof) { int count1, demod_id; struct ilist *ip0, *ip1, *ip2, *ip3; struct clause_ptr *demods; struct clause *c; struct context *subst; struct trail *tr; struct proof_object_node *instance, *paramod, *pn; #if 0 printf("\ncurrent="); p_clause(current->c); #endif subst = get_context(); subst->multiplier = 0; tr = NULL; for (ip1 = ip, count1 = 0; ip1 && ip1->i > 0; ip1 = ip1->next, count1++) { c = cl_find(ip1->i); /* The new versions of the demodulators have to be used, because the variables might be numbered differently. We have to copy the ID and the lex-dep flag into the new version. Sorry this is so messy. */ pn = retrieve_from_gen_tab(New_proof_old_id_tab, c->id); pn->c->id = pn->id; pn->c->first_lit->atom->varnum = c->first_lit->atom->varnum; #if 0 printf("old demod:"); p_clause(c); printf("new demod:"); p_clause(pn->c); #endif demods = NULL; insert_clause(pn->c, &demods); ip0 = first_rewrite_clause(current->c,demods,subst,&tr,&demod_id); free_clause_ptr(demods); if (!ip0) { printf("\nABOUT TO ABEND!\n"); printf("old demod: "); p_clause(c); printf("new demod: "); p_clause(pn->c); printf("clause: "); p_clause(current->c); abend("translate_demod_unit: cannot rewrite"); } pn = retrieve_from_gen_tab(New_proof_tab, demod_id); if (trivial_subst(subst)) instance = pn; else { instance = connect_new_node(new_proof); instance->parent1 = pn->id; instance->rule = P_RULE_INSTANTIATE; instance->c = apply_clause(pn->c, subst); copy_subst_to_proof_object(subst, instance); } paramod = connect_new_node(new_proof); paramod->rule = P_RULE_PARAMOD; paramod->parent1 = instance->id; ip2 = get_ilist(); ip2->i = 1; paramod->position1 = ip2; ip3 = get_ilist(); ip3->i = 1; ip2->next = ip3; paramod->parent2 = current->id; paramod->position2 = ip0; paramod->c = identity_paramod(instance->c, paramod->position1, current->c, paramod->position2); /* If into literal is negated, must add element to position. * The position vector will no longer be valid for Otter terms. */ if (ith_literal(current->c, ip0->i)->sign == 0) { ip2 = get_ilist(); ip2->i = 1; ip2->next = ip0->next; ip0->next = ip2; } current = paramod; #if 0 printf("after rewrite with %d: ", demod_id); p_clause(current->c); #endif clear_subst_1(tr); tr = NULL; } return(1); } /* translate_demod_unit */ /************* * * finish_translating() * * c: the clause from the original proof; The result of this routine * should be equivalent to c. * *************/ int finish_translating(struct clause *c, struct ilist *rest_of_history, struct proof_object_node *current, struct proof_object *new_proof) { int i, j, rc, ok; struct proof_object_node *previous, *pn; struct literal *l1, *l2, *prev_lit; struct ilist *ip1; struct term *t; /* Process rest of history here. This code depends on the order in * which Otter processes generated clauses. * If there is any demodulation, it is first. */ if (rest_of_history && rest_of_history->i == DEMOD_RULE) { rest_of_history = rest_of_history->next; if (num_literals(c) == 1) rc = translate_demod_unit(current, rest_of_history, new_proof); else rc = translate_demod_nonunit(current, rest_of_history, new_proof); while (rest_of_history && rest_of_history->i > 0) rest_of_history = rest_of_history->next; current = new_proof->last; } /* Equality reordering. */ #ifndef ATTEMPT_FEB_9 /* I think all equality reordering is reflected in the justification, so we don't have to do any of it here. */ if (Flags[ORDER_EQ].val) { struct clause *copy; copy = cl_copy(current->c); if (Flags[LRPO].val) order_equalities_lrpo(copy); else order_equalities(copy); for(l1 = copy->first_lit, i = 1; l1; l1 = l1->next_lit, i++) { if (TP_BIT(l1->atom->bits, SCRATCH_BIT)) { previous = current; current = connect_new_node(new_proof); current->parent1 = previous->id; current->position1 = get_ilist(); current->position1->i = i; current->rule = P_RULE_FLIP; current->c = cl_copy(previous->c); for (l2=current->c->first_lit, j=1; jnext_lit, j++); t = l2->atom->farg->argval; l2->atom->farg->argval = l2->atom->farg->narg->argval; l2->atom->farg->narg->argval = t; } } cl_del_non(copy); } #endif while (rest_of_history) { switch (rest_of_history->i) { case UNIT_DEL_RULE: rest_of_history = rest_of_history->next; while (rest_of_history && rest_of_history->i > 0) { pn = retrieve_from_gen_tab(New_proof_old_id_tab, rest_of_history->i); rc = translate_unit_deletion(current, pn, new_proof); current = new_proof->last; rest_of_history = rest_of_history->next; } break; case FACTOR_SIMP_RULE: rc = translate_factor_simp(current, new_proof); current = new_proof->last; rest_of_history = rest_of_history->next; break; case FLIP_EQ_RULE: /* Handled elsewhere (ORDER_EQ above). */ #ifdef ATTEMPT_FEB_9 /* This is an attempted fix. */ i = rest_of_history->next->next->i; l1 = ith_literal(current->c, i); previous = current; current = connect_new_node(new_proof); current->parent1 = previous->id; current->position1 = get_ilist(); current->position1->i = 1; current->rule = P_RULE_FLIP; current->c = cl_copy(previous->c); l2 = ith_literal(current->c, i); t = l2->atom->farg->argval; l2->atom->farg->argval = l2->atom->farg->narg->argval; l2->atom->farg->narg->argval = t; #endif /* Move past flip,LIST_RULE-1,n. */ rest_of_history = rest_of_history->next->next->next; break; case DEMOD_RULE: /* There are cases like this: * [...,demod,...,flip,1,demod,...] * that arise when equality units are flipped. * Demodulation is handled at the beginning of this routine, * so the following should handle things. */ rc = finish_translating(c, rest_of_history, current, new_proof); return(rc); default: abend("finish_translating, bad rule"); } } /* If not ground, renumber variables. */ if (!ground_clause(current->c)) { struct clause *d; d = cl_copy(current->c); rc = renumber_vars(d); if (!clause_ident(current->c, d)) { previous = current; current = connect_new_node(new_proof); current->rule = P_RULE_INSTANTIATE; current->parent1 = previous->id; current->c = cl_copy(previous->c); renumber_vars_subst(current->c, current->subst); } cl_del_non(d); } /* Merge identical literals (keep leftmost occurrence). */ while (num_literals(c) < num_literals(current->c)) { previous = current; current = connect_new_node(new_proof); current->parent1 = previous->id; current->rule = P_RULE_PROPOSITIONAL; current->c = cl_copy(previous->c); ok = 0; i = 1; for (l1 = current->c->first_lit; l1 && !ok; l1 = l1->next_lit, i++) { prev_lit = l1; j = i+1; for (l2 = l1->next_lit; l2 && !ok; prev_lit = l2, l2 = l2->next_lit, j++) { if (l1->sign == l2->sign && term_ident(l1->atom, l2->atom)) { ok = 1; prev_lit->next_lit = l2->next_lit; current->position1 = get_ilist(); current->position1->i = j; /* position of deleted literal */ } } } if (!ok) abend("finish_translating, merge not found.\n"); } /* Now we have to match up the original clause and the new one. * If it's an eq unit, it may be flipped; nonunits should be ok. */ ip1 = match_clauses(c, current->c); if (num_literals(current->c) == 1 && check_eq_lit(current->c->first_lit) && ip1->i == -1) { ip1->i = 1; previous = current; current = connect_new_node(new_proof); current->parent1 = previous->id; current->position1 = get_ilist(); current->position1->i = 1; current->rule = P_RULE_FLIP; current->c = cl_copy(previous->c); l2 = current->c->first_lit; t = l2->atom->farg->argval; l2->atom->farg->argval = l2->atom->farg->narg->argval; l2->atom->farg->narg->argval = t; } /* OK, finally we have the final clause corresponding to old clause c. */ current->map = ip1; current->old_id = c->id; /* rc = insert_into_gen_tab(New_proof_tab, current->id, current); */ rc = insert_into_gen_tab(New_proof_old_id_tab, c->id, current); #if 1 /* Sanity check: no other literals flipped, and each subsumes the other. */ for (ip1 = current->map; ip1; ip1 = ip1->next) if (ip1->i < 0) abend("finish_translating, literal flipped"); if (!subsume(c, current->c) || !subsume(current->c, c)) abend("finish_translating, subsumption failure"); #endif return(1); } /* finish_translating */ /************* * * translate_resolution() * *************/ static int translate_resolution(struct clause *c, struct proof_object *new_proof) { struct ilist *ip, *ip_save; struct proof_object_node *par1_node, *par2_node; int old_index1, old_index2, new_index1, new_index2; struct literal *new_lit1, *new_lit2; int i, rc; struct context *s1, *s2; struct trail *tr; struct proof_object_node *par1_instance_node, *par2_instance_node; struct proof_object_node *resolvent_node; /* First get info from parent list of clause: */ /* [binary, par1, list-1, lit1, par2, list-1, lit2, ...] */ ip = c->parents->next; par1_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); ip = ip->next; if (ip->i != LIST_RULE-1) abend("translate_resolution, can't find first list"); ip = ip->next; old_index1 = ip->i; ip = ip->next; par2_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); ip = ip->next; if (ip->i != LIST_RULE-1) abend("translate_resolution, can't find second list"); ip = ip->next; old_index2 = ip->i; ip_save = ip->next; /* save place for processing rest of parent list. */ /* Now find the corresp. indexes in the new_parents. */ new_index1 = new_literal_index(par1_node->map, old_index1); new_index2 = new_literal_index(par2_node->map, old_index2); /* Get the resolving literals from the new_parents. */ new_lit1 = ith_literal(par1_node->c, new_index1); new_lit2 = ith_literal(par2_node->c, new_index2); #ifdef DEBUG printf("\nBinary resolution: "); p_clause(c); printf("old_par1=%d, old_index1=%d, par1_node->c=%d, new_index1=%d\n", par1_node->old_id, old_index1, par1_node->id, new_index1); printf("old_par2=%d, old_index2=%d, par2_node->c=%d, new_index2=%d\n", par2_node->old_id, old_index2, par2_node->id, new_index2); #endif /* If negative literal is par2, swap par1, par2. */ if (!new_lit2->sign) { struct literal *temp_lit; struct proof_object_node *temp_node; temp_lit = new_lit1; new_lit1 = new_lit2; new_lit2 = temp_lit; temp_node = par1_node; par1_node = par2_node; par2_node = temp_node; i = new_index1; new_index1 = new_index2; new_index2 = i; /* We shouldn't refer to old again, so don't bother to swap them. */ } if (new_lit1->sign || !new_lit2->sign) abend("translate_resolution: signs wrong.\n"); /* Unify the atoms. */ s1 = get_context(); s1->multiplier = 0; s2 = get_context(); s2->multiplier = 1; tr = NULL; rc = unify(new_lit1->atom, s1, new_lit2->atom, s2, &tr); if (!rc) { p_term(new_lit1->atom); p_term(new_lit2->atom); abend("translate_resolution: unify fails on the preceding.\n"); } /* Buid the instance nodes. */ if (trivial_subst(s1)) par1_instance_node = par1_node; else { par1_instance_node = connect_new_node(new_proof); par1_instance_node->parent1 = par1_node->id; par1_instance_node->rule = P_RULE_INSTANTIATE; par1_instance_node->c = apply_clause(par1_node->c, s1); copy_subst_to_proof_object(s1, par1_instance_node); } if (ground_clause(par2_node->c)) par2_instance_node = par2_node; else { par2_instance_node = connect_new_node(new_proof); par2_instance_node->parent1 = par2_node->id; par2_instance_node->rule = P_RULE_INSTANTIATE; par2_instance_node->c = apply_clause(par2_node->c, s2); copy_subst_to_proof_object(s2, par2_instance_node); } clear_subst_1(tr); /* clears both substitution tables */ free_context(s1); free_context(s2); /* Build the resolvent node. */ resolvent_node = connect_new_node(new_proof); resolvent_node->rule = P_RULE_RESOLVE; resolvent_node->parent1 = par1_instance_node->id; resolvent_node->parent2 = par2_instance_node->id; ip = get_ilist(); ip->i = new_index1; resolvent_node->position1 = ip; ip = get_ilist(); ip->i = new_index2; resolvent_node->position2 = ip; resolvent_node->c = identity_resolve(par1_instance_node->c, new_index1, par2_instance_node->c, new_index2); #ifdef DEBUG p_proof_object_node(par1_instance_node); p_proof_object_node(par2_instance_node); p_proof_object_node(resolvent_node); #endif rc = finish_translating(c, ip_save, resolvent_node, new_proof); return(1); } /* translate_resolution */ /************* * * order_new_lits_for_hyper() * * Return a permutation of 1--n, where n is the number of negative literals. * The permutation gives the relative order of negative literals in the * old clause to those in the new. Example: * * new: -q2 -q1 -q3 p1 p2 p3 p4. * map: 4 2 6 1 3 5 7 * * return: 2 1 3. * *************/ static struct ilist *order_new_lits_for_hyper(struct proof_object_node *pn) { struct ilist *ip1, *ip2, *ip3, *ip4, *ip_min; struct literal *lit; int n, i; ip4 = NULL; for (lit = pn->c->first_lit, ip3 = pn->map, n = 0; lit && ip3; lit = lit->next_lit, ip3 = ip3->next) { if (!lit->sign) { n++; ip2 = get_ilist(); ip2->i = -ip3->i; if (!ip4) ip1 = ip2; else ip4->next = ip2; ip4 = ip2; } } for (i = 0; i < n; i++) { ip_min = NULL; for (ip2 = ip1; ip2; ip2 = ip2->next) if (!ip_min || ip2->i < ip_min->i) ip_min = ip2; ip_min->i = n-i; } #if 0 printf("\nCheck_order: "); p_clause(pn->c); for (ip2 = ip1; ip2; ip2 = ip2->next) printf("%d ", ip2->i); printf("\n\n"); #endif return(ip1); } /* order_new_lits_for_hyper */ /************* * * translate_hyper() * *************/ static int translate_hyper(struct clause *c, struct proof_object *new_proof) { struct ilist *ip, *ip1, *ip2, *ip_save; struct proof_object_node *nuc_node, *sat_node, *result_node; struct proof_object_node *nuc_i_node, *sat_i_node, *result_i_node; /* instances */ int i, sat_index, nuc_index, rc; struct literal *nuc_lit, *sat_lit; struct context *s1, *s2; struct trail *tr; s1 = get_context(); s1->multiplier = 0; s2 = get_context(); s2->multiplier = 1; /* [hyper, nuc, sat1, -1001, sat1_index, sat2, -1001, sat2_index, ... */ ip = c->parents->next; nuc_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); ip_save = ip->next; for (ip1 = order_new_lits_for_hyper(nuc_node); ip1; ip1 = ip1->next) { for (ip2 = ip_save, i = 1; i < ip1->i; ip2 = ip2->next->next->next, i++); sat_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip2->i); sat_index = new_literal_index(sat_node->map, ip2->next->next->i); sat_lit = ith_literal(sat_node->c, sat_index); /* Get index of first negative literal in nuc clause. */ for (nuc_lit = nuc_node->c->first_lit, nuc_index = 1; nuc_lit->sign; nuc_lit = nuc_lit->next_lit, nuc_index++); tr = NULL; rc = unify(nuc_lit->atom, s1, sat_lit->atom, s2, &tr); if (nuc_lit->sign == sat_lit->sign || !rc) { p_term(nuc_lit->atom); p_term(sat_lit->atom); abend("translate_hyper: unify fails on the preceding.\n"); } if (trivial_subst(s1)) nuc_i_node = nuc_node; else { nuc_i_node = connect_new_node(new_proof); nuc_i_node->parent1 = nuc_node->id; nuc_i_node->rule = P_RULE_INSTANTIATE; nuc_i_node->c = apply_clause(nuc_node->c, s1); copy_subst_to_proof_object(s1, nuc_i_node); } if (ground_clause(sat_node->c)) sat_i_node = sat_node; else { sat_i_node = connect_new_node(new_proof); sat_i_node->parent1 = sat_node->id; sat_i_node->rule = P_RULE_INSTANTIATE; sat_i_node->c = apply_clause(sat_node->c, s2); copy_subst_to_proof_object(s2, sat_i_node); } clear_subst_1(tr); /* clears both substitution tables */ /* Build the resolvent node. */ result_node = connect_new_node(new_proof); result_node->rule = P_RULE_RESOLVE; result_node->parent1 = nuc_i_node->id; result_node->parent2 = sat_i_node->id; ip = get_ilist(); ip->i = nuc_index; result_node->position1 = ip; ip = get_ilist(); ip->i = sat_index; result_node->position2 = ip; result_node->c = identity_resolve(nuc_i_node->c, nuc_index, sat_i_node->c, sat_index); if (ground_clause(result_node->c)) result_i_node = result_node; else { struct clause *d; d = cl_copy(result_node->c); rc = renumber_vars(d); if (clause_ident(result_node->c, d)) result_i_node = result_node; else { result_i_node = connect_new_node(new_proof); result_i_node->rule = P_RULE_INSTANTIATE; result_i_node->parent1 = result_node->id; result_i_node->c = cl_copy(result_node->c); renumber_vars_subst(result_i_node->c, result_i_node->subst); } cl_del_non(d); } nuc_node = result_i_node; } free_context(s1); free_context(s2); while (ip_save && ip_save->i > 0) ip_save = ip_save->next->next->next; rc = finish_translating(c, ip_save, nuc_node, new_proof); return(1); } /* translate_hyper */ /************* * * ipx() * *************/ int ipx(struct ilist *ip, int n) { int i; for (i=1; ip && i < n; ip = ip->next, i++); if (ip) return(ip->i); else return(MAX_INT); } /* ipx */ /************* * * translate_ur() * *************/ static int translate_ur(struct clause *c, struct proof_object *new_proof) { struct ilist *ip, *ip1, *ip2, *ip3, *sat_ids, *sat_map; struct proof_object_node *nuc_node, *sat_node, *result_node; struct proof_object_node *nuc_i_node, *sat_i_node, *result_i_node; /* instances */ int box_pos, rc, i, skip_first, nuc_index; struct literal *nuc_lit, *sat_lit; struct context *s1, *s2; struct trail *tr; s1 = get_context(); s1->multiplier = 0; s2 = get_context(); s2->multiplier = 1; /* [ur, nuc, -1001, box_pos, sat1, sat2, sat3, ... */ ip = c->parents->next; nuc_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); ip = ip->next->next; box_pos = ip->i; /* Get satellite ids from history list. */ ip2 = NULL; i = 0; for (ip = ip->next; ip && ip->i > 0; ip = ip->next) { /* for each sat. ID */ i++; if (i == box_pos) { /* insert empty slot */ ip1 = get_ilist(); ip1->i = 0; if (ip2) ip2->next = ip1; else sat_ids = ip1; ip2 = ip1; } ip1 = get_ilist(); ip1->i = ip->i; if (ip2) ip2->next = ip1; else sat_ids = ip1; ip2 = ip1; } i++; if (i == box_pos) { /* insert empty slot */ ip1 = get_ilist(); ip1->i = 0; if (ip2) ip2->next = ip1; else sat_ids = ip1; ip2 = ip1; } /* Use the map to permute sat_ids so that it matches the new nucleus. */ ip2 = NULL; for (ip3 = nuc_node->map; ip3; ip3 = ip3->next) { ip1 = get_ilist(); ip1->i = ipx(sat_ids, ip3->i); if (ip2) ip2->next = ip1; else sat_map = ip1; ip2 = ip1; } #if 1 printf("\ntranslate_ur: sat_map for box=%d, orig= ", box_pos); p_clause(c); for (ip1 = sat_map; ip1; ip1 = ip1->next) printf("%d ", ip1->i); p_clause(nuc_node->c); #endif skip_first = 0; for (ip1 = sat_map; ip1; ip1 = ip1->next) { if (ip1->i == 0) skip_first = 1; else { sat_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip1->i); sat_lit = ith_literal(sat_node->c, 1); /* Get index of clash literal in nuc clause. */ nuc_index = (skip_first ? 2 : 1); nuc_lit = ith_literal(nuc_node->c, nuc_index); tr = NULL; rc = unify(nuc_lit->atom, s1, sat_lit->atom, s2, &tr); if (nuc_lit->sign == sat_lit->sign || !rc) { p_term(nuc_lit->atom); p_term(sat_lit->atom); abend("translate_ur: unify fails on the preceding.\n"); } if (trivial_subst(s1)) nuc_i_node = nuc_node; else { nuc_i_node = connect_new_node(new_proof); nuc_i_node->parent1 = nuc_node->id; nuc_i_node->rule = P_RULE_INSTANTIATE; nuc_i_node->c = apply_clause(nuc_node->c, s1); copy_subst_to_proof_object(s1, nuc_i_node); } if (ground_clause(sat_node->c)) sat_i_node = sat_node; else { sat_i_node = connect_new_node(new_proof); sat_i_node->parent1 = sat_node->id; sat_i_node->rule = P_RULE_INSTANTIATE; sat_i_node->c = apply_clause(sat_node->c, s2); copy_subst_to_proof_object(s2, sat_i_node); } clear_subst_1(tr); /* clears both substitution tables */ /* Build the resolvent node. */ result_node = connect_new_node(new_proof); result_node->rule = P_RULE_RESOLVE; result_node->parent1 = nuc_i_node->id; result_node->parent2 = sat_i_node->id; ip2 =get_ilist(); ip2->i =nuc_index; result_node->position1 =ip2; ip2 =get_ilist(); ip2->i =1; result_node->position2 =ip2; result_node->c = identity_resolve(nuc_i_node->c, nuc_index, sat_i_node->c, 1); if (ground_clause(result_node->c)) result_i_node = result_node; else { struct clause *d; d = cl_copy(result_node->c); rc = renumber_vars(d); if (clause_ident(result_node->c, d)) result_i_node = result_node; else { result_i_node = connect_new_node(new_proof); result_i_node->rule = P_RULE_INSTANTIATE; result_i_node->parent1 = result_node->id; result_i_node->c = cl_copy(result_node->c); renumber_vars_subst(result_i_node->c, result_i_node->subst); } cl_del_non(d); } nuc_node = result_i_node; } } free_context(s1); free_context(s2); rc = finish_translating(c, ip, nuc_node, new_proof); return(1); } /* translate_ur */ /************* * * translate_factor() * *************/ static int translate_factor(struct clause *c, struct proof_object *new_proof) { int i1, i2, j, k1, k2; struct literal *lit1, *lit2; struct context *subst; struct trail *tr; struct proof_object_node *parent, *instance, *factor; /* Retrieve the proof object of the parent. */ parent = retrieve_from_gen_tab(New_proof_old_id_tab, c->parents->next->i); /* Get the literal indexes in the old_parent. */ i1 = c->parents->next->next->next->i; i2 = c->parents->next->next->next->next->i; /* Get corresponding indexes in new parent. */ k1 = new_literal_index(parent->map, i1); k2 = new_literal_index(parent->map, i2); /* Get new literals. */ lit1 = ith_literal(parent->c, k1); lit2 = ith_literal(parent->c, k2); /* Unify the literals. */ subst = get_context(); subst->multiplier = 0; tr = NULL; j = unify(lit1->atom, subst, lit2->atom, subst, &tr); if (!j) abend("translate_factor, literals don't unify"); /* Build the instance node. */ instance = connect_new_node(new_proof); instance->rule = P_RULE_INSTANTIATE; instance->parent1 = parent->id; instance->c = apply_clause(parent->c, subst); copy_subst_to_proof_object(subst, instance); clear_subst_1(tr); free_context(subst); /* Build the merge node. */ factor = connect_new_node(new_proof); factor->rule = P_RULE_PROPOSITIONAL; factor->parent1 = instance->id; factor->position1 = get_ilist(); factor->position1->i = k2; factor->c = cl_copy_delete_literal(instance->c, k2); j = finish_translating(c, c->parents->next->next->next->next->next, factor, new_proof); return(1); } /* translate_factor */ /************* * * para_position() * *************/ static struct term *para_position(struct clause *c, struct ilist *ip) { struct literal *l; struct term *t; struct rel *r; int i; l = ith_literal(c, ip->i); t = l->atom; for (ip = ip->next; ip; ip = ip->next) { for (i = 1, r = t->farg; i < ip->i; i++, r = r->narg); t = r->argval; } return(t); } /* para_position */ /************* * * translate_paramod() * *************/ static int translate_paramod(struct clause *c, struct proof_object *new_proof) { struct ilist *ip, *ip_save, *from_pos, *into_pos; struct proof_object_node *from_node, *into_node; int i, rc, n, para_from; struct context *s1, *s2; struct trail *tr; struct proof_object_node *from_instance_node, *into_instance_node; struct proof_object_node *para_node; struct term *from_term, *into_term; /* First get info from parent list of clause: */ /* [rule, par1, list-1, pos1,..., par2, list-1, pos2,..., rest */ para_from = (c->parents->i == PARA_FROM_RULE); ip = c->parents->next; if (para_from) from_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); else into_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); ip = ip->next; if (ip->i >= LIST_RULE) abend("translate_paramod, can't find first list"); n = LIST_RULE - ip->i; /* length of position vector */ ip = ip->next; if (para_from) from_pos = copy_ilist_segment(ip, n); else into_pos = copy_ilist_segment(ip, n); for (i = 0; i < n; i++, ip = ip->next); if (para_from) into_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); else from_node = retrieve_from_gen_tab(New_proof_old_id_tab, ip->i); ip = ip->next; if (ip->i >= LIST_RULE) abend("translate_paramod, can't find second list"); n = LIST_RULE - ip->i; /* length of position vector */ ip = ip->next; if (para_from) into_pos = copy_ilist_segment(ip, n); else from_pos = copy_ilist_segment(ip, n); for (i = 0; i < n; i++, ip = ip->next); ip_save = ip; /* save place for processing rest of parent list. */ /* Now modify the positions so that they corresp. to the new clauses. * Must translate literal index. (Eq literals should be in same direction.) * Same for both from and into. */ from_pos->i = new_literal_index(from_node->map, from_pos->i); into_pos->i = new_literal_index(into_node->map, into_pos->i); /* Get the unifying terms from the new_parents. */ from_term = para_position(from_node->c, from_pos); into_term = para_position(into_node->c, into_pos); #ifdef DEBUG printf("\nParamodulation: "); p_clause(c); #endif /* Unify the terms. */ s1 = get_context(); s1->multiplier = 0; s2 = get_context(); s2->multiplier = 1; tr = NULL; rc = unify(from_term, s1, into_term, s2, &tr); if (!rc) { p_term(from_term); p_term(into_term); abend("translate_paramod: unify fails on the preceding.\n"); } /* Buid the instance nodes. */ if (trivial_subst(s1)) from_instance_node = from_node; else { from_instance_node = connect_new_node(new_proof); from_instance_node->parent1 = from_node->id; from_instance_node->rule = P_RULE_INSTANTIATE; from_instance_node->c = apply_clause(from_node->c, s1); copy_subst_to_proof_object(s1, from_instance_node); } if (ground_clause(into_node->c)) into_instance_node = into_node; else { into_instance_node = connect_new_node(new_proof); into_instance_node->parent1 = into_node->id; into_instance_node->rule = P_RULE_INSTANTIATE; into_instance_node->c = apply_clause(into_node->c, s2); copy_subst_to_proof_object(s2, into_instance_node); } clear_subst_1(tr); /* clears both substitution tables */ free_context(s1); free_context(s2); /* Build the para node. */ para_node = connect_new_node(new_proof); para_node->rule = P_RULE_PARAMOD; para_node->parent1 = from_instance_node->id; para_node->parent2 = into_instance_node->id; para_node->position1 = from_pos; para_node->position2 = into_pos; para_node->c = identity_paramod(from_instance_node->c, from_pos, into_instance_node->c, into_pos); /* If into literal is negated, must add element to position. * Note that the position vector will no longer be valid for Otter terms. */ if (ith_literal(into_node->c, into_pos->i)->sign == 0) { ip = get_ilist(); ip->i = 1; ip->next = into_pos->next; into_pos->next = ip; } #ifdef DEBUG p_proof_object_node(from_instance_node); p_proof_object_node(into_instance_node); p_proof_object_node(para_node); #endif rc = finish_translating(c, ip_save, para_node, new_proof); return(1); } /* translate_paramod */ /************************************************************/ static void varmap(struct term *t, struct term **vars) { if (t->type == VARIABLE) vars[t->varnum] = t; else if (t->type == COMPLEX) { struct rel *r; for (r = t->farg; r; r = r->narg) varmap(r->argval, vars); } } /* varmap */ /************************************************************/ static BOOLEAN match2(struct clause *c1, struct clause *c2, struct term **vars) { int ok; struct literal *l1, *l2; /* For variables, term_ident does not check sym_num field. So, we first check if the clauses are identical, then, get the "substitution". */ for (l1 = c1->first_lit, l2 = c2->first_lit, ok = 1; l1 && l2 && ok; l1 = l1->next_lit, l2 = l2->next_lit) { if (l1->sign != l2->sign) ok = 0; else ok = term_ident(l1->atom, l2->atom); } if (!ok || l1 || l2) return 0; else { int i; for (i = 0; i < MAX_VARS; i++) vars[i] = NULL; for (l1 = c1->first_lit; l1; l1 = l1->next_lit) varmap(l1->atom, vars); return 1; } } /* match2 */ /************************************************************/ struct proof_object_node *find_match2(struct clause *c, struct proof_object *obj, struct term **vars) { struct proof_object_node *pn = obj->first; while (pn && pn->rule == P_RULE_INPUT && !match2(pn->c, c, vars)) pn = pn->next; return (pn && pn->rule == P_RULE_INPUT ? pn : NULL); } /* find_match2 */ /************************************************************/ /************* * * translate_step() * * Translate one step in an Otter proof into a sequene of detailed steps * and add them to New_proof. * * return (ok ? 1 : 0) * *************/ static int translate_step(struct clause *c, struct proof_object *new_proof) { int rc, rule, id; struct proof_object_node *pn; #ifdef DEBUG printf("translating: "); p_clause(c); #endif if (!c->parents) { pn = connect_new_node(new_proof); pn->c = cl_copy(c); pn->old_id = c->id; pn->map = match_clauses(c, pn->c); /* wasteful, but convenient */ rc = insert_into_gen_tab(New_proof_old_id_tab, c->id, pn); if (!retrieve_initial_proof_object()) { pn->rule = P_RULE_INPUT; rc = 1; } else { struct term *vars[MAX_VARS]; struct proof_object_node *initial_step; initial_step = find_match2(c, new_proof, vars); if (!initial_step) abend("translate_step, clauses don't match"); else { int i; pn->rule = P_RULE_INSTANTIATE; pn->parent1 = initial_step->id; for (i = 0; i < MAX_VARS; i++) pn->subst[i] = vars[i]; pn->backward_subst = TRUE; } } } else if (c->parents->i == COPY_RULE && c->parents->next->next->i == PROPOSITIONAL_RULE) { /* special case */ struct proof_object_node *prop_node; id = c->parents->next->i; pn = retrieve_from_gen_tab(New_proof_old_id_tab, id); prop_node = connect_new_node(new_proof); prop_node->parent1 = pn->id; prop_node->c = cl_copy(c); prop_node->rule = P_RULE_PROPOSITIONAL; prop_node->old_id = c->id; prop_node->map = match_clauses(c, prop_node->c); rc = insert_into_gen_tab(New_proof_old_id_tab,c->id,prop_node); } else { rule = c->parents->i; switch (rule) { case NEW_DEMOD_RULE : /* * This is kludgey. The proof object doesn't have separate * steps for NEW_DEMOD, so we just refer to the regular copy. * This means that the old_id field is not quite correct. * Recall that new_demod has old_id 1 greater than its parent. */ id = c->parents->next->i; /* ID of regular copy */ pn = retrieve_from_gen_tab(New_proof_old_id_tab, id); rc = insert_into_gen_tab(New_proof_old_id_tab, c->id, pn); break; case COPY_RULE : id = c->parents->next->i; pn = retrieve_from_gen_tab(New_proof_old_id_tab, id); rc = finish_translating(c, c->parents->next->next, pn, new_proof); break; case BINARY_RES_RULE : case BACK_UNIT_DEL_RULE : rc = translate_resolution(c, new_proof); break; case HYPER_RES_RULE : rc = translate_hyper(c, new_proof); break; case UR_RES_RULE : rc = translate_ur(c, new_proof); break; case FACTOR_RULE : rc = translate_factor(c, new_proof); break; case PARA_INTO_RULE : case PARA_FROM_RULE : rc = translate_paramod(c, new_proof); break; case BACK_DEMOD_RULE : id = c->parents->next->i; pn = retrieve_from_gen_tab(New_proof_old_id_tab, id); rc = finish_translating(c, c->parents->next->next, pn, new_proof); break; default : fprintf(stderr, "translate_step: rule %d not handled.\n", rule); rc = 0; break; } } return(rc); } /* translate_step */ /************* * * contains_answer_literal() * *************/ int contains_answer_literal(struct clause *c) { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) if (answer_lit(lit)) return(1); return(0); } /* contains_answer_literal */ /************* * * contains_rule() * *************/ int contains_rule(struct clause *c, int rule) { struct ilist *ip; for (ip = c->parents; ip; ip = ip->next) if (ip->i == rule) return(1); return(0); } /* contains_rule */ /************* * * trans_2_pos() * *************/ struct ilist *trans_2_pos(int id, struct ilist *pos) { int n, i; struct clause *c; struct proof_object_node *pn; struct ilist *new, *p1; if (pos == NULL) abend("trans_2_pos: NULL pos"); pn = retrieve_from_gen_tab(New_proof_tab, id); if (pn == NULL) abend("trans_2_pos: proof node not found"); c = pn->c; if (c == NULL) abend("trans_2_pos: clause not found"); if (num_literals(c) == 0) abend("trans_2_pos: empty clause"); n = num_literals(c); new = copy_ilist(pos->next); /* copy all but first */ if (pos->i != n) { p1 = get_ilist(); p1->i = 1; p1->next = new; new = p1; } for (i = 2; i <= pos->i; i++) { p1 = get_ilist(); p1->i = 2; p1->next = new; new = p1; } return new; } /* trans_2_pos */ /************* * * type_2_trans() * * Change the given proof object from type 1 to a type 2 by * changing the position vectors in the justifications. * *************/ void type_2_trans(struct proof_object *po) { struct proof_object_node *pn; struct ilist *ip; for (pn = po->first; pn; pn = pn->next) { if (pn->parent1 != 0 && pn->position1) { ip = trans_2_pos(pn->parent1, pn->position1); free_ilist_list(pn->position1); pn->position1 = ip; } if (pn->parent2 != 0 && pn->position2) { ip = trans_2_pos(pn->parent2, pn->position2); free_ilist_list(pn->position2); pn->position2 = ip; } } } /* type_2_trans */ /************* * * glist_subsume(c, g) * *************/ int glist_subsume(struct clause *c, struct glist *g) { if (g == NULL) return 0; else if (subsume(g->v, c)) return 1; else return (glist_subsume(c, g->next)); } /* glist_subsume */ /************* * * p_proof_object_as_hints() * *************/ void p_proof_object_as_hints(struct proof_object *po) { struct proof_object_node *pn; struct glist *h = NULL; struct glist *p; for (pn = po->first; pn; pn = pn->next) { struct clause *d = cl_copy(pn->c); if (Flags[ORDER_EQ].val) { if (Flags[LRPO].val) order_equalities_lrpo(d); else order_equalities(d); } renumber_vars(d); if (!glist_subsume(d, h)) { h = glist_tack_on(h, d); } else cl_del_non(d); } printf("list(%s). %% Hints from process %d, %s", Internal_flags[HINTS2_PRESENT] ? "hints2" : "hints", my_process_id(), get_time()); for (p = h; p != NULL; p = p->next) { print_clause_bare(stdout, p->v); printf(".\n"); cl_del_non(p->v); } printf("end_of_list.\n"); free_glist_list(h); } /* p_proof_object_as_hints */ /************* * * remove_answer_literals() * *************/ struct literal *remove_answer_literals(struct literal *lit) { if (lit == NULL) return NULL; else if (answer_lit(lit)) { struct literal *lit2 = lit->next_lit; lit->atom->occ.lit = NULL; zap_term(lit->atom); free_literal(lit); return remove_answer_literals(lit2); } else { lit->next_lit = remove_answer_literals(lit->next_lit); return lit; } } /* remove_answer_literals */ /************* * * build_proof_object() * * Given a clause (not necessarily empty), build and print the proof * object corresponding to the clause. * *************/ void build_proof_object(struct clause *c) { struct clause_ptr *cp1, *cp2; struct ilist *ip1; int level, i, rc; struct clause *d; struct proof_object *new_proof; if (!Flags[ORDER_HISTORY].val) abend("build_proof_object: flag order_history must be set"); else if (!Flags[DETAILED_HISTORY].val) abend("build_proof_object: flag detailed_history must be set"); cp1 = NULL; level = get_ancestors(c, &cp1, &ip1); for (cp2 = cp1; cp2; cp2 = cp2->next) { if (contains_answer_literal(cp2->c)) { /* Copy the clause and remove answer literals. * We won't worry about freeing this copy when we're done. * This small memory leak shouldn't make much difference. */ struct clause *c = cl_copy(cp2->c); c->parents = copy_ilist(cp2->c->parents); c->id = cp2->c->id; c->first_lit = remove_answer_literals(c->first_lit); cp2->c = c; } } for (cp2 = cp1; cp2; cp2 = cp2->next) { if (contains_answer_literal(cp2->c)) abend("build_proof_object: proof objects cannot contain answer literals"); else if (contains_rule(cp2->c, NEG_HYPER_RES_RULE)) abend("build_proof_object: neg_hyper_res not allowed"); else if (contains_rule(cp2->c, GEO_RULE)) abend("build_proof_object: gL rule not allowed"); else if (contains_rule(cp2->c, GEO_ID_RULE)) abend("build_proof_object: gL-id not allowed"); else if (contains_rule(cp2->c, LINKED_UR_RES_RULE)) abend("build_proof_object: linked_ur_res not allowed"); else if (contains_rule(cp2->c, EVAL_RULE)) abend("build_proof_object: eval rule not allowed"); else if (contains_rule(cp2->c, CLAUSIFY_RULE)) abend("build_proof_object: clausify rule not allowed"); } /* Old_proof_tab has the original clauses, indexed by their own IDs. New_proof_old_id_tab has proof nodes, indexed by original IDs. New_proof_tab has proof nodes, indexed by their own IDs. */ new_proof = retrieve_initial_proof_object(); /* If an intial proof object already exists, then New_proof_tab already exists also (it was built at the same time). Unfortunately, we have a problem if there is an initial proof object and this is the second call to build_proof object: New_proof_tab has been changed, so we cannot use it as we start building from the initial proof object. Therefore, we allow at most one proof when we are using initial proof objects. See abend below. (I think this can be fixed by keeping a copy of New_proof_tab when the initial proof object is created. */ /* If we don't have an initial proof object, start a new one. */ if (new_proof == NULL) { new_proof = get_proof_object(); New_proof_tab = init_gen_tab(); } else { if (Old_proof_tab != NULL) abend("build_proof_object, at most one proof object can be built when an initial proof object is given"); } Old_proof_tab = init_gen_tab(); New_proof_old_id_tab = init_gen_tab(); for (cp2 = cp1; cp2; cp2 = cp2->next) { i = insert_into_gen_tab(Old_proof_tab, cp2->c->id, cp2->c); } for (cp2 = cp1, rc = 1; cp2 && rc; cp2 = cp2->next) { d = (struct clause *) retrieve_from_gen_tab(Old_proof_tab, cp2->c->id); rc = translate_step(cp2->c, new_proof); } if (Flags[PRINT_PROOF_AS_HINTS].val) p_proof_object_as_hints(new_proof); else { if (Flags[BUILD_PROOF_OBJECT_2].val) type_2_trans(new_proof); /* translate to type 2 proof object */ printf("\n;; BEGINNING OF PROOF OBJECT\n"); p_proof_object(new_proof); printf(";; END OF PROOF OBJECT\n"); } } /* build_proof_object */ /************************************************************/ void init_proof_object_environment(void) { New_proof_tab = init_gen_tab(); } otter-3.3f/source/foreign.h0100644000076400007640000000762107343604666015327 0ustar mccunemccune/* * foreign.h -- header file for user-defined foreign functions * */ /* HOW TO WRITE YOUR OWN C ROUTINE WHICH CAN BE CALLED TO DEMODULATE A TERM DURING OTTER'S DEMODULATION The Otter types don't correspond exactly to the C types. In Otter, the types, except `term', are all constants (in the theorem-proving sense), and in C, the types are what you would expect them to be. TYPES: - long In C and in Otter, a long integer. - double In C, a double; in Otter, a double surrounded by double quotes. - bool In C, an int; in Otter, $T or $F. - string In C, a pointer to a string; in Otter, any constant. - term An Otter term. To include a new function, you have to (1) declare the function, argument types, and result type, (2) insert a call to your function in the Otter code, (3) write your C routine, and (4) remake Otter. The only Otter files you need to change are foreign.h and foreign.c. When Otter is demodulating and comes across a 'call' to your function, it will first check the argument types. If they are incorrect (for example a variable is not instantiated) the term will not be rewritten; if the arguments are OK, your C routine will be called, and the result of your C routine will be made into an appropriate Otter term which is the result of the rewriting step. (Don't forget that many times you can avoid having to do all of this by just writing your function with demodulators and using existing built in functions. For example, if you need the max of two doubles, you can just use the demodulator float_max(x,y) = $IF($FGT(x,y), x, y). For other examples of programming with demodulators, see eval.in in the Otter test suite. See file demod.c, routine dollar_contract, for the current set of evaluable functions.) STEP-BY-STEP INSTRUCTIONS 0. Say you want to write a function foo that takes a long, a double, and a string as arguments and produces a long, i.e., long foo(long n, double x, char *s) The Otter-language name must start with $, say $FOO, and you will be evaluating Otter terms like $FOO(32, "-4.5e-10", flag32) 1. To declare the function and its types, (A) In the file foreign.h, #define a symbol, which will be used as an index into a table (see FOO_FUNC in foreign.h). (B) In file foreign.c, in routine declare_user_functions, declare the function and its types (look for FOO_FUNC in foreign.c). The types are LONG_TYPE, DOUBLE_TYPE, BOOL_TYPE, STRING_TYPE, and TERM_TYPE. 2. In file foreign.c, in routine evaluate_user_function, insert a call to your function and a call to translate the result to an Otter term (look for FOO_FUNC in foreign.c). The routines to translate C types to otter terms are long_to_term, double_to_term, bool_to_term, and string_to_term. See foreign.c for examples. 3. Write your C routine. I have inserted the test routines into foreign.c, but you may wish to organize yours into separate files. (If your routines involve TERM_TYPE, you must #include "header.h".) 4. Remake Otter; foreign.c is the only Otter file that will need to be recompiled. 5. Test your new function by using the input file foreign.in. */ #define MAX_USER_ARGS 20 /* maximum arity for user-defined C functions */ #define LONG_TYPE 1 /* types for user-defined C functions */ #define DOUBLE_TYPE 2 #define BOOL_TYPE 3 #define STRING_TYPE 4 #define TERM_TYPE 5 struct user_function { /* entry in table of user-defined functions */ int arity; int arg_types[MAX_USER_ARGS]; int result_type; }; #define MAX_USER_FUNCTIONS 100 /* size of table */ /* indexes into table of user-defined functions */ #define FOO_FUNC 1 #define TEST_LONG_FUNC 2 #define TEST_DOUBLE_FUNC 3 #define TEST_BOOL_FUNC 4 #define TEST_STRING_FUNC 5 #define TEST_TERM_FUNC 6 otter-3.3f/source/share.c0100644000076400007640000002705707705543530014772 0ustar mccunemccune/* * share.c -- routines to manage the shared data structures * */ #include "header.h" #define TERM_TAB_SIZE 3793 /* Hash table of shared terms */ static struct term_ptr *Term_tab[TERM_TAB_SIZE]; /* alphas and betas of pos eq lits are not shared, so they are put here */ /* so that back dedmodulation can find them */ static struct term_ptr *Bd_kludge; /************* * * int hash_term(term) * * Return the hash value of a term. It is assumed that * the subterms are already integrated. The hash value is * constructed from the function symbol and the addresses of the * subterms. * *************/ static int hash_term(struct term *t) { struct rel *r; int hashval; if (t->type == NAME) /* name */ hashval = t->sym_num; else if (t->type == VARIABLE) /* variable */ hashval = t->sym_num + t->varnum + 25; else { /* complex */ hashval = t->sym_num; r = t->farg; while (r != NULL) { hashval >>= 1; /* shift right one bit */ hashval ^= (int) r->argval; /* exclusive or */ r = r->narg; } } return(abs(hashval) % TERM_TAB_SIZE); } /* hash_term */ /************* * * int term_compare(t1, t2) * * Special purpose term comparison for term integration. * Succeed iff functors are identical and subterm pointers are * identical. (Note that this routine is not recursive.) * (For general purpose routine, see `term_ident'.) * *************/ static int term_compare(struct term *t1, struct term *t2) { struct rel *r1, *r2; if (t1->type != t2->type) return(0); else if (t1->type == NAME) /* name */ return(t1->sym_num == t2->sym_num); else if (t1->type == VARIABLE) /* variable */ return(t1->varnum == t2->varnum && t1->sym_num == t2->sym_num); else if (t1->sym_num != t2->sym_num) return(0); /* both complex with different functors */ else { r1 = t1->farg; r2 = t2->farg; while (r1 != NULL && r2 != NULL) { if (r1->argval != r2->argval) return(0); else { r1 = r1->narg; r2 = r2->narg; } } return(r1 == NULL && r2 == NULL); } } /* term_compare */ /************* * * struct term *integrate_term(term) * * Incorporate a term into the shared data structures. * Either ther term itself is integrated and returned, or * the term is deallocated and a previously integrated copy * is returned. A good way to invoke it is * * t = integrate(t) * *************/ struct term *integrate_term(struct term *t) { int hashval, found; struct term_ptr *p, *prev; struct rel *r, *r2; if (t->type == COMPLEX) { /* complex term */ r = t->farg; while (r != NULL) { r->argval = integrate_term(r->argval); r = r->narg; } } hashval = hash_term(t); p = Term_tab[hashval]; prev = NULL; found = 0; while (found == 0 && p != NULL) if (term_compare(t, p->term)) found = 1; else { prev = p; p = p->next; } if (found) { /* p->term is integrated copy */ if (t == p->term) { print_term_nl(stdout, t); abend("integrate_term, already integrated."); } if (t->type == COMPLEX) { /* if complex, free rels */ r = t->farg; while (r != NULL) { r2 = r; r = r->narg; free_rel(r2); } } free_term(t); return(p->term); } else { /* not in bucket, so insert at end of bucket and return */ if (t->type == COMPLEX) { /* if complex, set up containment lists */ r = t->farg; while (r != NULL) { r->argof = t; r->nocc = r->argval->occ.rel; r->argval->occ.rel = r; r = r->narg; } } p = get_term_ptr(); p->term = t; p->next = NULL; if (prev == NULL) Term_tab[hashval] = p; else prev->next = p; if (Flags[BACK_DEMOD].val && Flags[INDEX_FOR_BACK_DEMOD].val) fpa_insert(t, Parms[FPA_TERMS].val, Fpa_back_demod); return(t); } } /* integrate_term */ /************* * * disintegrate_term(term) * * Remove a previously integrated term from the shared data * structures. A warning is printed if the term has a list of * superterms. * *************/ void disintegrate_term(struct term *t) { int hashval; struct rel *r1, *r2, *r3; struct term_ptr *p1, *p2; if (t->occ.rel != NULL) { fprintf(stderr, "WARNING, disintegrate_term, contained term.\n"); printf("WARNING, disintegrate_term, contained term: "); print_term_nl(stdout, t); } else { hashval = hash_term(t); p1 = Term_tab[hashval]; p2 = NULL; while (p1 != NULL && p1->term != t) { p2 = p1; p1 = p1->next; } if (p1 == NULL) abend("disintegrate_term, cannot find term."); else { if (p2 == NULL) Term_tab[hashval] = p1->next; else p2->next = p1->next; free_term_ptr(p1); if (Flags[BACK_DEMOD].val && Flags[INDEX_FOR_BACK_DEMOD].val) { CLOCK_START(UN_INDEX_TIME); fpa_delete(t, Parms[FPA_TERMS].val, Fpa_back_demod); CLOCK_STOP(UN_INDEX_TIME); } if (t->type == COMPLEX) { r1 = t->farg; while (r1 != NULL) { r2 = r1->argval->occ.rel; r3 = NULL; while (r2 != NULL && r2 != r1) { r3 = r2; r2 = r2->nocc; } if (r2 == NULL) { print_term_nl(stdout, t); abend("disintegrate_term, bad containment."); } else { if (r3 == NULL) r1->argval->occ.rel = r1->nocc; else r3->nocc = r1->nocc; if (r1->argval->occ.rel == NULL) disintegrate_term(r2->argval); } r3 = r1; r1 = r1->narg; free_rel(r3); } } free_term(t); } } } /* disintegrate_term */ /************* * * set_up_pointers(t) * *************/ void set_up_pointers(struct term *t) { struct rel *r; for (r = t->farg; r; r = r->narg) { r->argof = t; r->argval->occ.rel = r; set_up_pointers(r->argval); } } /* set_up_pointers */ /************* * * zap_term(term) * * Deallocate a nonshared term. A warning is printed * the term or any of its subterms contains a list of superterms. * *************/ void zap_term(struct term *t) { struct rel *r1, *r2; if (t->occ.rel != NULL) { fprintf(stderr, "WARNING, zap_term, contained term.\n"); printf("WARNING, zap_term, contained term: "); print_term_nl(stdout, t); printf("\n"); } else { if (t->type == COMPLEX) { /* complex term */ r1 = t->farg; while (r1 != NULL) { zap_term(r1->argval); r2 = r1; r1 = r1->narg; free_rel(r2); } } free_term(t); } } /* zap_term */ /************* * * print_term_tab(file_ptr) -- Print the table of integrated terms. * *************/ void print_term_tab(FILE *fp) { int i; struct term_ptr *p; for(i=0; iterm); fprintf(fp, " "); p = p->next; } fprintf(fp, "\n"); } } /* print_term_tab */ /************* * * p_term_tab() * *************/ void p_term_tab(void) { print_term_tab(stdout); } /* p_term_tab */ /************* * * test_terms(file_ptr) * * Print the list of integrated terms. For each term, list its * subterms and superterms. * *************/ void test_terms(FILE *fp) { int i; struct term_ptr *p; struct rel *r; for(i=0; iterm); fprintf(fp, " containing terms: "); r = p->term->occ.rel; while (r != NULL) { print_term(fp, r->argof); fprintf(fp, " "); r = r->nocc; } fprintf(fp, "\n"); p = p->next; } } } /* test_terms */ /************* * * struct term_ptr *all_instances(atom) * * Get all terms (in table of shared terms) that can be rewritten * with demodulator (atom). Handles lex-dependent demod correctly. * *************/ struct term_ptr *all_instances(struct term *atom) { struct term *alpha, *beta, *t; struct term_ptr *tp, *tp1, *instances; struct context *subst; struct trail *tr; int i, lex_dependent, ok; alpha = atom->farg->argval; beta = atom->farg->narg->argval; lex_dependent = (atom->varnum == LEX_DEP_DEMOD); instances = NULL; subst = get_context(); subst->multiplier = 1; for (i = 0; i <= TERM_TAB_SIZE; i++) { tp = (i == TERM_TAB_SIZE ? Bd_kludge : Term_tab[i]); while (tp != NULL) { tr = NULL; if (match(alpha, subst, tp->term, &tr)) { if (lex_dependent == 0) ok = 1; else { t = apply(beta, subst); if (Flags[LRPO].val) ok = lrpo_greater(tp->term, t); else ok = (lex_check(t, tp->term) == LESS_THAN); zap_term(t); } if (ok) { tp1 = get_term_ptr(); tp1->term = tp->term; tp1->next = instances; instances = tp1; } clear_subst_1(tr); } tp = tp->next; } } free_context(subst); return(instances); } /* all_instances */ /************* * * struct term_ptr *all_instances_fpa(atom) * * Get all terms (in table of shared terms) that can be rewritten * with demodulator (atom). Handles lex-dependent demod correctly. * *************/ struct term_ptr *all_instances_fpa(struct term *atom, struct fpa_index *fpa) { struct term *alpha, *beta, *t, *found; struct term_ptr *tp1, *instances; struct context *subst; struct trail *tr; int lex_dependent, ok; struct fpa_tree *ut; alpha = atom->farg->argval; beta = atom->farg->narg->argval; lex_dependent = (atom->varnum == LEX_DEP_DEMOD); instances = NULL; subst = get_context(); subst->multiplier = 1; ut = build_tree(alpha, INSTANCE, Parms[FPA_TERMS].val, fpa); found = next_term(ut, 0); while (found != NULL) { tr = NULL; if (match(alpha, subst, found, &tr)) { if (lex_dependent == 0) ok = 1; else { t = apply(beta, subst); if (Flags[LRPO].val) ok = lrpo_greater(found, t); else ok = (lex_check(t, found) == LESS_THAN); zap_term(t); } if (ok) { tp1 = get_term_ptr(); tp1->term = found; tp1->next = instances; instances = tp1; } clear_subst_1(tr); } found = next_term(ut, 0); } free_context(subst); return(instances); } /* all_instances_fpa */ /************* * * bd_kludge_insert(t) * * This has to do with finding terms that can be back demodulated. * Terms are made available (either indexed or in table of shared * terms) when integrated. However, alphas and betas are not shared, * so this routine makes them available, either indexed or inserted * into the Bd_kludge list. * *************/ void bd_kludge_insert(struct term *t) { struct term_ptr *tp; if (Flags[INDEX_FOR_BACK_DEMOD].val) fpa_insert(t, Parms[FPA_TERMS].val, Fpa_back_demod); else { tp = get_term_ptr(); tp->term = t; tp->next = Bd_kludge; Bd_kludge = tp; } } /* bd_kludge_insert */ /************* * * bd_kludge_delete(t) * * See Bd_kludge_insert. * *************/ void bd_kludge_delete(struct term *t) { struct term_ptr *tp1, *tp2; if (Flags[INDEX_FOR_BACK_DEMOD].val) { CLOCK_START(UN_INDEX_TIME); fpa_delete(t, Parms[FPA_TERMS].val, Fpa_back_demod); CLOCK_STOP(UN_INDEX_TIME); } else { tp1 = Bd_kludge; tp2 = NULL; while (tp1 != NULL && tp1->term != t) { tp2 = tp1; tp1 = tp1->next; } if (tp1 == NULL) { fprintf(stderr, "WARNING, bd_kludge_delete, term not found.\n"); printf("WARNING, bd_kludge_delete, term not found: "); print_term_nl(stdout, t); } else if (tp2 != NULL) tp2->next = tp1->next; else Bd_kludge = tp1->next; free_term_ptr(tp1); } } /* bd_kludge_delete */ otter-3.3f/source/header.h.diffs0100644000076400007640000000007010041245667016176 0ustar mccunemccune246a247 > #include "fpa2.h" /* new fpa code */ otter-3.3f/source/formed/0040755000076400007640000000000007714312621014763 5ustar mccunemccuneotter-3.3f/source/formed/display.c0100644000076400007640000007011206407523114016571 0ustar mccunemccune/* * display.c -- These routines are part of the FormEd program. * */ #include "../header.h" #include "formed.h" String Fallback_resources[] = { "*Command.height: 20", "*Command.width: 85", "*to_conj.width: 70", "*to_disj.width: 70", "*iff_form.cancel.width: 70", "*smallfont.width: 75", "*medfont.width: 75", "*largefont.height: 30", "*largefont.width: 75", "*font_form.cancel.width: 75", "*help.width: 75", "*font_menu.width: 75", "*save.width: 75", "*load.width: 75", "*quit.width: 75", "*edit.width: 75", "*unedit.width: 85", "*reedit.width: 85", "*new_formula.width: 95", "*delete_formula.width: 95", "*add_quantifiers.height: 30", "*help_menu_form*width: 150", "*help_return.width: 128", NULL }; /************************* * * void setup_display(argc, argv) * *****************************/ void setup_display(argc, argv) int argc; char *argv[]; { Widget toplevel, title, button_form, view; /* general form */ /* also includes Outline, Canvas */ Widget button_menus; /* can contain Place_holder */ Widget displayButtons, edit_menu, logic_menu, comp_redo, comp_undo, next, previous, save, load, help, font_menu, quit; int i; int n; Arg arg[25]; /*** set up initial shell ***/ toplevel = XtAppInitialize(&App_con,"Toplevel",NULL,0,&argc,argv, Fallback_resources, NULL, 0); /* set display information, for initial font & color info */ Dpy = XtDisplay(toplevel); Def_screen = DefaultScreen(Dpy); Frame_depth = DefaultDepth(Dpy, Def_screen); Cmap = DefaultColormap(Dpy, Def_screen); /* set foreground & background variables */ if (Frame_depth > 1) { if (Fore_set) Foreground = convert_color(User_fore); /* note: convert_color uses */ else /* values of Dpy,Cmap,Def_screen*/ Foreground = convert_color("black"); if (Back_set) Background = convert_color(User_back); else Background = convert_color("white"); } else{ Foreground = convert_color("black"); Background = convert_color("white"); } /*** the containing form ***/ n = 0; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNforeground, Foreground); n++; Outline = XtCreateManagedWidget("Outline",formWidgetClass,toplevel,arg,n); /*** title ***/ n = 0; XtSetArg(arg[n], XtNhorizDistance, 450); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, MEDFONT)); n++; XtSetArg(arg[n], XtNlabel, "FormEd"); n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNborderWidth, 0); n++; title = XtCreateManagedWidget("title",labelWidgetClass, Outline, arg, n); /*** button holder ***/ n = 0; XtSetArg(arg[n], XtNfromVert, title); n++; XtSetArg(arg[n], XtNborderWidth, 3); n++; XtSetArg(arg[n], XtNbackground, Foreground); n++; button_form = XtCreateManagedWidget("button_form",formWidgetClass, Outline, arg, n); /** button menus (logic, edit, place_holder will go here) **/ n = 0; XtSetArg(arg[n], XtNborderWidth, 1); n++; button_menus = XtCreateManagedWidget("button_menus", formWidgetClass,button_form, arg, n); /* create the logic & edit widgets, but do not manage them */ /* also, put the widgets in appropriate lists, so they can be */ /* managed & unmanaged with one call to Xt(un)manageChildren */ /* use accum_size to determine how big the initial place holder */ /* needs to be */ Logic_buttons = (WidgetList) XtMalloc(NUM_LOGIC_BUTTONS * sizeof(Widget)); i = 0; Logic_area_width = Logic_area_height = 0; /* clausify button */ n = 0; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNlabel, "Clausify");n++; Logic_buttons[i] = XtCreateWidget("clausify",commandWidgetClass,button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, clausify_callback, NULL); accum_size(Logic_buttons[i], ADD, ADD, LOGIC_MENU); i++; /* operate button */ n = 0; XtSetArg(arg[n], XtNfromVert, Logic_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Operate");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("operate",commandWidgetClass,button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, operate_callback, NULL); accum_size(Logic_buttons[i], IGNORE, ADD, LOGIC_MENU); i++; /* nnf button */ n = 0; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "NNF");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("nnf",commandWidgetClass, button_menus,arg,n); XtAddCallback(Logic_buttons[i], XtNcallback, nnf_callback, NULL); accum_size(Logic_buttons[i], ADD, IGNORE, LOGIC_MENU); i++; /* skolemize button */ n = 0; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Logic_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Skolemize");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("skolemize",commandWidgetClass, button_menus,arg,n); XtAddCallback(Logic_buttons[i], XtNcallback, skolemize_callback, NULL); i++; /* cnf button */ n = 0; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "CNF");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("cnf",commandWidgetClass, button_menus,arg,n); XtAddCallback(Logic_buttons[i], XtNcallback, cnf_callback, NULL); accum_size(Logic_buttons[i], ADD, IGNORE, LOGIC_MENU); i++; /* cnf_simp button */ n = 0; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Logic_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "CNF simp");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("cnf_simp",commandWidgetClass, button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, cnf_simp_callback, NULL); i++; /* dnf button */ n = 0; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "DNF");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("dnf",commandWidgetClass, button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, dnf_callback, NULL); accum_size(Logic_buttons[i], ADD, IGNORE, LOGIC_MENU); i++; /* dnf_simp button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Logic_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "DNF simp");n++; Logic_buttons[i] = XtCreateWidget("dnf_simp",commandWidgetClass, button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, dnf_simp_callback, NULL); i++; /* redo button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Redo");n++; Logic_buttons[i] = XtCreateWidget("redo",commandWidgetClass, button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, redo_callback, NULL); accum_size(Logic_buttons[i], ADD, IGNORE, LOGIC_MENU); i++; /* undo button */ n = 0; XtSetArg(arg[n], XtNfromHoriz, Logic_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Logic_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Undo");n++; XtSetArg(arg[n], XtNbackground, Background);n++; Logic_buttons[i] = XtCreateWidget("undo",commandWidgetClass, button_menus, arg, n); XtAddCallback(Logic_buttons[i], XtNcallback, undo_callback, NULL); i++; /** edit buttons **/ Edit_buttons = (WidgetList) XtMalloc(NUM_EDIT_BUTTONS * sizeof(Widget)); i = 0; Edit_area_width = Edit_area_height = 0; /* edit button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Edit");n++; Edit_buttons[i] = XtCreateWidget("edit",commandWidgetClass,button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, edit_callback, NULL); accum_size(Edit_buttons[i], ADD, ADD, EDIT_MENU); i++; /* abbreviate button */ n = 0; XtSetArg(arg[n], XtNfromVert, Edit_buttons[i-1]); n++; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Abbreviate");n++; Edit_buttons[i] = XtCreateWidget("edit",commandWidgetClass,button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, abbreviate_callback, NULL); accum_size(Edit_buttons[i], IGNORE, ADD, EDIT_MENU); i++; /* conjoin button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Conjoin");n++; Edit_buttons[i] = XtCreateWidget("conjoin",commandWidgetClass, button_menus,arg,n); XtAddCallback(Edit_buttons[i], XtNcallback, conjoin_callback, NULL); accum_size(Edit_buttons[i], ADD, IGNORE, EDIT_MENU); i++; /* disjoin button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Edit_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Disjoin");n++; Edit_buttons[i] = XtCreateWidget("disjoin",commandWidgetClass, button_menus,arg,n); XtAddCallback(Edit_buttons[i], XtNcallback, disjoin_callback, NULL); i++; /* quantify button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Quantify");n++; Edit_buttons[i] = XtCreateWidget("quantify",commandWidgetClass, button_menus,arg,n); XtAddCallback(Edit_buttons[i], XtNcallback, quantify_callback, NULL); accum_size(Edit_buttons[i], ADD, IGNORE, EDIT_MENU); i++; /* negate button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Edit_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Negate");n++; Edit_buttons[i] = XtCreateWidget("negate",commandWidgetClass, button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, negate_callback, NULL); i++; /* new formula button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "New formula");n++; Edit_buttons[i] = XtCreateWidget("new_formula",commandWidgetClass, button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, new_formula_callback, NULL); accum_size(Edit_buttons[i], ADD, IGNORE, EDIT_MENU); i++; /* delete formula button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Edit_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Delete formula");n++; Edit_buttons[i] = XtCreateWidget("delete_formula",commandWidgetClass, button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, delete_formula_callback, NULL); i++; /* reedit button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-2]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Re-edit");n++; Edit_buttons[i] = XtCreateWidget("reedit",commandWidgetClass, button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, reedit_callback, NULL); accum_size(Edit_buttons[i], ADD, IGNORE, EDIT_MENU); i++; /* unedit button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, Edit_buttons[i-3]); n++; XtSetArg(arg[n], XtNfromVert, Edit_buttons[i-1]); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Unedit");n++; Edit_buttons[i] = XtCreateWidget("unedit",commandWidgetClass, button_menus, arg, n); XtAddCallback(Edit_buttons[i], XtNcallback, unedit_callback, NULL); i++; /** Place holder for button menus **/ n = 0; XtSetArg(arg[n], XtNborderWidth, 1); n++; if (Logic_area_width > Edit_area_width) { XtSetArg(arg[n], XtNwidth, Logic_area_width + 25); n++; } else{ XtSetArg(arg[n], XtNwidth, Edit_area_width + 25); n++; } if (Logic_area_height > Edit_area_height) { XtSetArg(arg[n], XtNheight, Logic_area_height + 6); n++; } else{ XtSetArg(arg[n], XtNheight, Edit_area_height + 6); n++; } XtSetArg(arg[n], XtNlabel, "Welcome to FormEd"); n++; XtSetArg(arg[n], XtNbackground, Background);n++; Place_holder = XtCreateManagedWidget("Place_holder",labelWidgetClass, button_menus, arg, n); Crnt_button_menu = PLACE_HOLDER; /** display buttons **/ n = 0; XtSetArg(arg[n], XtNborderWidth, 1); n++; XtSetArg(arg[n], XtNfromHoriz, button_menus); n++; displayButtons = XtCreateManagedWidget("displayButtons", formWidgetClass, button_form, arg, n); /* edit menu button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNshapeStyle,XmuShapeRoundedRectangle); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Edit Menu");n++; edit_menu = XtCreateManagedWidget("edit_menu",commandWidgetClass, displayButtons,arg,n); XtAddCallback(edit_menu, XtNcallback, edit_menu_callback, NULL); /* logic menu button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromVert, edit_menu); n++; XtSetArg(arg[n], XtNshapeStyle, XmuShapeRoundedRectangle); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Logic Menu");n++; logic_menu = XtCreateManagedWidget("logic_menu",commandWidgetClass, displayButtons,arg,n); XtAddCallback(logic_menu, XtNcallback, logic_menu_callback, NULL); /* complete redo action button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, edit_menu); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Redo All");n++; comp_redo = XtCreateManagedWidget("comp_redo",commandWidgetClass, displayButtons,arg,n); XtAddCallback(comp_redo, XtNcallback, comp_redo_callback, NULL); /* comp_undo action button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, edit_menu); n++; XtSetArg(arg[n], XtNfromVert, comp_redo); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Undo All");n++; comp_undo = XtCreateManagedWidget("comp_undo",commandWidgetClass, displayButtons,arg,n); XtAddCallback(comp_undo, XtNcallback, comp_undo_callback, NULL); /* next formula button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, comp_redo); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Next");n++; next = XtCreateManagedWidget("next",commandWidgetClass, displayButtons,arg,n); XtAddCallback(next, XtNcallback, next_callback, NULL); /* previous formula button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, comp_redo); n++; XtSetArg(arg[n], XtNfromVert, next); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Previous");n++; previous = XtCreateManagedWidget("previous",commandWidgetClass, displayButtons,arg,n); XtAddCallback(previous, XtNcallback, previous_callback, NULL); /* save button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, next); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Save");n++; save = XtCreateManagedWidget("save",commandWidgetClass, displayButtons,arg,n); XtAddCallback(save, XtNcallback, save_callback, NULL); /* load button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, next); n++; XtSetArg(arg[n], XtNfromVert, save); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Load");n++; load = XtCreateManagedWidget("load",commandWidgetClass, displayButtons,arg,n); XtAddCallback(load, XtNcallback, load_callback, NULL); /* help button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, save); n++; XtSetArg(arg[n], XtNborderWidth, 1); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Help");n++; help = XtCreateManagedWidget("help",commandWidgetClass, displayButtons,arg,n); XtAddCallback(help, XtNcallback, help_callback, NULL); /* font menu */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, save); n++; XtSetArg(arg[n], XtNfromVert, help); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Font"); n++; font_menu=XtCreateManagedWidget("font_menu", commandWidgetClass, displayButtons, arg, n); XtAddCallback(font_menu, XtNcallback, font_menu_callback, NULL); /* quit button */ n = 0; XtSetArg(arg[n], XtNbackground, Background);n++; XtSetArg(arg[n], XtNfromHoriz, help); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Quit");n++; quit = XtCreateManagedWidget("quit",commandWidgetClass, displayButtons,arg,n); XtAddCallback(quit, XtNcallback, quit_callback, NULL); /*** the viewport ***/ n = 0; XtSetArg(arg[n], XtNfromVert, button_form); n++; XtSetArg(arg[n], XtNallowHoriz, True); n++; XtSetArg(arg[n], XtNallowVert, True); n++; XtSetArg(arg[n], XtNheight, VIEWPORT_HEIGHT); n++; XtSetArg(arg[n], XtNwidth, VIEWPORT_WIDTH); n++; XtSetArg(arg[n], XtNborderWidth, 3); n++; view = XtCreateManagedWidget("view",viewportWidgetClass,Outline,arg,n); /* the canvas - made a composite widget because a form widget without */ /* children at this point will not make scrollbars */ n = 0; XtSetArg(arg[n], XtNforeground, Foreground); n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNborderWidth, 0); n++; XtSetArg(arg[n], XtNheight, CANVAS_HEIGHT); n++; XtSetArg(arg[n], XtNwidth, CANVAS_WIDTH); n++; Canvas = XtCreateManagedWidget("canvas",compositeWidgetClass, view, arg, n); XtRealizeWidget(toplevel); /* get window attributes */ Win = XtWindow(Canvas); /* set the graphics context */ Gc = XCreateGC(Dpy, Win, (unsigned long) 0, NULL); XSetForeground(Dpy, Gc, Foreground); XSetBackground(Dpy, Gc, Background); /* set up font information - default is currently MEDFONT */ /* the pixmaps are set up within this according to font */ setup_font(MEDFONT); /* for highlighting */ /* Pattern = XCreateBitmapFromData(Dpy, Win, pattern_bits, pattern_width, pattern_height); */ /* needed to save window contents for reexposure */ W_attr.backing_store = Always; W_attr.save_under = True; XChangeWindowAttributes(Dpy, Win,(CWBackingStore|CWSaveUnder), &W_attr); /* miscellaneous initializations */ XtAddEventHandler(Canvas, ButtonPressMask, False, select_area, NULL); Display_setup = 1; /* set so know if have an initial display */ } /* end setup_display */ /************* * * setup_operator_pixmaps(font_string) * *************/ setup_operator_pixmaps(font_string) char font_string[]; { if (strcmp(font_string, SMALLFONT) == 0) { Spacing = SMALL_SPACING; Or_bits = or_sm_bits; And_bits = and_sm_bits; Not_bits = not_sm_bits; Imp_bits = imp_sm_bits; Iff_bits = iff_sm_bits; Exists_bits = exists_sm_bits; All_bits = all_sm_bits; Or_width = or_sm_width; And_width = and_sm_width; Not_width = not_sm_width; Imp_width = imp_sm_width; Iff_width = iff_sm_width; Exists_width = exists_sm_width; All_width = all_sm_width; Or_height = or_sm_height; And_height = and_sm_height; Not_height = not_sm_height; Imp_height = imp_sm_height; Iff_height = iff_sm_height; Exists_height = exists_sm_height; All_height = all_sm_height; } else if (strcmp(font_string,MEDFONT) == 0) { Spacing = MED_SPACING; Or_bits = or_md_bits; And_bits = and_md_bits; Not_bits = not_md_bits; Imp_bits = imp_md_bits; Iff_bits = iff_md_bits; Exists_bits = exists_md_bits; All_bits = all_md_bits; Or_width = or_md_width; And_width = and_md_width; Not_width = not_md_width; Imp_width = imp_md_width; Iff_width = iff_md_width; Exists_width = exists_md_width; All_width = all_md_width; Or_height = or_md_height; And_height = and_md_height; Not_height = not_md_height; Imp_height = imp_md_height; Iff_height = iff_md_height; Exists_height = exists_md_height; All_height = all_md_height; } else { /* LARGEFONT */ Spacing = LARGE_SPACING; Or_bits = or_lg_bits; And_bits = and_lg_bits; Not_bits = not_lg_bits; Imp_bits = imp_lg_bits; Iff_bits = iff_lg_bits; Exists_bits = exists_lg_bits; All_bits = all_lg_bits; Or_width = or_lg_width; And_width = and_lg_width; Not_width = not_lg_width; Imp_width = imp_lg_width; Iff_width = iff_lg_width; Exists_width = exists_lg_width; All_width = all_lg_width; Or_height = or_lg_height; And_height = and_lg_height; Not_height = not_lg_height; Imp_height = imp_lg_height; Iff_height = iff_lg_height; Exists_height = exists_lg_height; All_height = all_lg_height; } Or = XCreatePixmapFromBitmapData(Dpy, Win, Or_bits, Or_width, Or_height, Foreground, Background, Frame_depth); And = XCreatePixmapFromBitmapData(Dpy, Win, And_bits, And_width, And_height, Foreground, Background, Frame_depth); Not = XCreatePixmapFromBitmapData(Dpy, Win, Not_bits, Not_width, Not_height, Foreground, Background, Frame_depth); Imp = XCreatePixmapFromBitmapData(Dpy, Win, Imp_bits, Imp_width, Imp_height, Foreground, Background, Frame_depth); Iff = XCreatePixmapFromBitmapData(Dpy, Win, Iff_bits, Iff_width, Iff_height, Foreground, Background, Frame_depth); Exists = XCreatePixmapFromBitmapData(Dpy, Win, Exists_bits, Exists_width, Exists_height, Foreground, Background, Frame_depth); All = XCreatePixmapFromBitmapData(Dpy, Win, All_bits, All_width, All_height, Foreground, Background, Frame_depth); Or_invert = XCreatePixmapFromBitmapData(Dpy, Win, Or_bits, Or_width, Or_height, Background, Foreground, Frame_depth); And_invert = XCreatePixmapFromBitmapData(Dpy, Win, And_bits, And_width, And_height, Background, Foreground, Frame_depth); Not_invert = XCreatePixmapFromBitmapData(Dpy, Win, Not_bits, Not_width, Not_height, Background, Foreground, Frame_depth); Imp_invert = XCreatePixmapFromBitmapData(Dpy, Win, Imp_bits, Imp_width, Imp_height, Background, Foreground, Frame_depth); Iff_invert = XCreatePixmapFromBitmapData(Dpy, Win, Iff_bits, Iff_width, Iff_height, Background, Foreground, Frame_depth); Exists_invert = XCreatePixmapFromBitmapData(Dpy, Win, Exists_bits, Exists_width, Exists_height, Background, Foreground, Frame_depth); All_invert = XCreatePixmapFromBitmapData(Dpy, Win, All_bits, All_width, All_height, Background, Foreground, Frame_depth); } /* setup_operator_pixmaps */ /************* * * convert_color(colorname) * *************/ int convert_color(colorname) char *colorname; { XColor color, ignore; if (XAllocNamedColor(Dpy, Cmap, colorname, &color, &ignore)) return(color.pixel); else{ printf("Warning: couldn't allocate color %s\n", colorname); return(BlackPixel(Dpy, Def_screen)); } } /* convert_color */ /************* * * void user_error(message_string) * *************/ void user_error(message_string) char message_string[]; { int n; Arg arg[10]; Dimension width, height; Position x, y; Widget message_form, message_text, message_label; kill_message(); /* create a popup widget for the message */ /* place it in the bottom center of the viewport */ /* get coordinates */ n = 0; XtSetArg(arg[n], XtNwidth, &width); n++; XtSetArg(arg[n], XtNheight, &height); n++; XtGetValues(Outline, arg, n); XtTranslateCoords(Outline, (Position)(275), (Position)(height-100), &x, &y); /* create the popup */ n = 0; XtSetArg(arg[n], XtNx, x); n++; XtSetArg(arg[n], XtNy, y); n++; Message = XtCreatePopupShell("Message", transientShellWidgetClass, Outline, arg, n); /* form widget to hold the text & label */ n = 0; message_form = XtCreateManagedWidget("message_form", formWidgetClass, Message, arg, n); /* message label */ n = 0; XtSetArg(arg[n], XtNlabel, "Messages");n++; XtSetArg(arg[n], XtNwidth, 400); n++; XtSetArg(arg[n], XtNborderWidth, 0); n++; message_label = XtCreateManagedWidget("message_label", labelWidgetClass, message_form, arg, n); /* text widget */ n = 0; XtSetArg(arg[n], XtNfromVert, message_label); n++; XtSetArg(arg[n], XtNforeground, Foreground); n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNstring, message_string); n++; XtSetArg(arg[n], XtNwidth, 400); n++; XtSetArg(arg[n], XtNheight, 40); n++; message_text = XtCreateManagedWidget("message_text", asciiTextWidgetClass, message_form, arg, n); Have_message = 1; XtPopup(Message, XtGrabNone); } /* user_error */ /************* * * void setup_font(font_string) * *************/ void setup_font(font_string) char font_string[]; { Font fid; /* get font ID */ fid = XLoadFont(Dpy, font_string); /* get font structure */ Font_struct = XQueryFont(Dpy, fid); /* set max height of characters in font */ Font_char_ht = (Font_struct->max_bounds).ascent + (Font_struct->max_bounds).descent; Font_ascent = (Font_struct -> max_bounds).ascent; /* set the font in the graphics context */ XSetFont(Dpy, Gc, fid); /* set up the appropriate operator pixmaps */ setup_operator_pixmaps(font_string); } /* setup_font */ /************* * * void kill_message() * *************/ void kill_message() { if (Have_message) { XtDestroyWidget(Message); Have_message = 0; } } /* kill message */ /************************* * * void accum_size(w, add_width, add_height, flag) * *****************************/ void accum_size(w, add_width, add_height, flag) Widget w; int add_width; int add_height; int flag; { int n; Arg arg[2]; Dimension width, height; n = 0; XtSetArg(arg[n], XtNwidth, &width); n++; XtSetArg(arg[n], XtNheight, &height); n++; XtGetValues(w, arg, n); switch (flag) { case LOGIC_MENU: if (add_width) Logic_area_width += width; if (add_height) Logic_area_height += height; break; case EDIT_MENU: if (add_width) Edit_area_width += width; if (add_height) Edit_area_height += height; break; } } /* accum_size */ otter-3.3f/source/formed/formed.h0100644000076400007640000002654506354300243016415 0ustar mccunemccune/* * formed.h -- FormEd (Formula Editor) X Windows program. * */ /* C Includes */ #include #include /* X Includes */ #include #include #include #include #include #include #include #include #include #include #include /* bitmaps */ #define all_lg_width 16 #define all_lg_height 16 static char all_lg_bits[] = { 0x03, 0xc0, 0x03, 0xc0, 0x06, 0x60, 0x06, 0x60, 0x0c, 0x30, 0x0c, 0x30, 0xf8, 0x1f, 0xf8, 0x1f, 0x30, 0x0c, 0x30, 0x0c, 0x60, 0x06, 0x60, 0x06, 0xc0, 0x03, 0xc0, 0x03, 0x80, 0x01, 0x80, 0x01}; #define all_md_width 12 #define all_md_height 12 static char all_md_bits[] = { 0x03, 0x0c, 0x03, 0x0c, 0x06, 0x06, 0x06, 0x06, 0xfc, 0x03, 0xfc, 0x03, 0x98, 0x01, 0x98, 0x01, 0xf0, 0x00, 0xf0, 0x00, 0x60, 0x00, 0x60, 0x00}; #define all_sm_width 8 #define all_sm_height 8 static char all_sm_bits[] = { 0x81, 0x81, 0x42, 0x7e, 0x24, 0x24, 0x18, 0x18}; #define and_lg_width 16 #define and_lg_height 16 static char and_lg_bits[] = { 0xc0, 0x01, 0x60, 0x03, 0x60, 0x03, 0x60, 0x03, 0x40, 0x01, 0xc0, 0x00, 0xc0, 0x00, 0xe0, 0x01, 0x30, 0x33, 0x18, 0x33, 0x0c, 0x26, 0x0c, 0x1c, 0x0c, 0x0c, 0x0c, 0x1c, 0xf8, 0x37, 0xf0, 0x33}; #define and_md_width 12 #define and_md_height 12 static char and_md_bits[] = { 0x70, 0x00, 0x58, 0x00, 0x58, 0x00, 0x30, 0x00, 0x30, 0x00, 0x68, 0x00, 0xcc, 0x06, 0x86, 0x04, 0x86, 0x03, 0x86, 0x01, 0xc6, 0x02, 0x7c, 0x06}; #define and_sm_width 8 #define and_sm_height 8 static char and_sm_bits[] = { 0x08, 0x14, 0x14, 0x08, 0x14, 0x52, 0x22, 0x5c}; #define exists_lg_width 14 #define exists_lg_height 18 static char exists_lg_bits[] = { 0x00, 0x00, 0xfe, 0x1f, 0xfe, 0x1f, 0x00, 0x18, 0x00, 0x18, 0x00, 0x18, 0x00, 0x18, 0x00, 0x18, 0xf8, 0x1f, 0xf8, 0x1f, 0x00, 0x18, 0x00, 0x18, 0x00, 0x18, 0x00, 0x18, 0x00, 0x18, 0xfe, 0x1f, 0xfe, 0x1f, 0x00, 0x00}; #define exists_md_width 12 #define exists_md_height 14 static char exists_md_bits[] = { 0x00, 0x00, 0xfe, 0x07, 0xfe, 0x07, 0x00, 0x04, 0x00, 0x04, 0x00, 0x04, 0xf8, 0x07, 0xf8, 0x07, 0x00, 0x04, 0x00, 0x04, 0x00, 0x04, 0xfe, 0x07, 0xfe, 0x07, 0x00, 0x00}; #define exists_sm_width 8 #define exists_sm_height 11 static char exists_sm_bits[] = { 0x00, 0x7e, 0x40, 0x40, 0x40, 0x7c, 0x40, 0x40, 0x40, 0x7e, 0x00}; #define iff_lg_width 16 #define iff_lg_height 16 static char iff_lg_bits[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x10, 0x0c, 0x30, 0xfe, 0x7f, 0xff, 0xff, 0xfe, 0x7f, 0x0c, 0x30, 0x08, 0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}; #define iff_md_width 12 #define iff_md_height 12 static char iff_md_bits[] = { 0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x06, 0x06, 0xff, 0x0f, 0xff, 0x0f, 0x06, 0x06, 0x04, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}; #define iff_sm_width 8 #define iff_sm_height 8 static char iff_sm_bits[] = { 0x00, 0x24, 0x42, 0xff, 0x42, 0x24, 0x00, 0x00}; #define imp_lg_width 16 #define imp_lg_height 16 static char imp_lg_bits[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x18, 0x00, 0x38, 0xff, 0x7f, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x38, 0x00, 0x18, 0x00, 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}; #define imp_md_width 12 #define imp_md_height 12 static char imp_md_bits[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x00, 0x06, 0xff, 0x0f, 0xff, 0x0f, 0x00, 0x06, 0x00, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}; #define imp_sm_width 8 #define imp_sm_height 8 static char imp_sm_bits[] = { 0x00, 0x20, 0x40, 0xff, 0x40, 0x20, 0x00, 0x00}; #define not_lg_width 16 #define not_lg_height 16 static char not_lg_bits[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0x00, 0xc0, 0x00, 0xc0, 0x00, 0xc0, 0x00, 0xc0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}; #define not_md_width 12 #define not_md_height 12 static char not_md_bits[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0x0f, 0xff, 0x0f, 0x00, 0x0c, 0x00, 0x0c, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}; #define not_sm_width 8 #define not_sm_height 8 static char not_sm_bits[] = { 0x00, 0x00, 0x00, 0xff, 0x80, 0x80, 0x00, 0x00}; #define or_lg_width 16 #define or_lg_height 16 static char or_lg_bits[] = { 0x03, 0xc0, 0x03, 0xc0, 0x06, 0x60, 0x06, 0x60, 0x0c, 0x30, 0x0c, 0x30, 0x18, 0x18, 0x18, 0x18, 0x30, 0x0c, 0x30, 0x0c, 0x60, 0x06, 0x60, 0x06, 0xc0, 0x03, 0xc0, 0x03, 0x80, 0x01, 0x80, 0x01}; #define or_md_width 12 #define or_md_height 12 static char or_md_bits[] = { 0x03, 0x0c, 0x03, 0x0c, 0x06, 0x06, 0x06, 0x06, 0x0c, 0x03, 0x0c, 0x03, 0x98, 0x01, 0x98, 0x01, 0xf0, 0x00, 0xf0, 0x00, 0x60, 0x00, 0x60, 0x00}; #define or_sm_width 8 #define or_sm_height 8 static char or_sm_bits[] = { 0x81, 0x81, 0x42, 0x42, 0x24, 0x24, 0x18, 0x18}; #define pattern_width 4 #define pattern_height 4 static char pattern_bits[] = { 0x05, 0x0a, 0x05, 0x0a}; #define LABELFONT "-*-helvetica-*-r-*-*-*-120-*-*-*-*-*-*" #define LARGEFONT "-*-helvetica-*-r-*-*-*-240-*-*-*-*-*-*" #define MEDFONT "-*-helvetica-*-r-*-*-*-140-*-*-*-*-*-*" #define SMALLFONT "-*-helvetica-medium-r-*-*-*-100-*-*-*-*-*-*" #define SMALLFONT_DIM 8 #define MEDFONT_DIM 12 #define LARGEFONT_DIM 16 #define SMALL_SPACING 3 #define MED_SPACING 5 #define LARGE_SPACING 7 #define VIEWPORT_HEIGHT 600 #define VIEWPORT_WIDTH 1000 #define CANVAS_HEIGHT 1000 #define CANVAS_WIDTH 1000 #define FORMULA 1 #define OPERATOR 2 #define OR_OP 1 /* subtypes of operator */ #define AND_OP 2 #define NOT_OP 3 #define EXISTS_OP 4 #define ALL_OP 5 #define IFF_OP 6 #define IMP_OP 7 #define TEXT_LENGTH 500 #define PLACE_HOLDER 0 #define LOGIC_MENU 1 #define EDIT_MENU 2 #define NUM_LOGIC_BUTTONS 10 #define NUM_EDIT_BUTTONS 10 #define ADD 1 /* for use in accum_size */ #define IGNORE 0 /* The rest of this file is communal (global) variables. */ /* Names of global variables have first letter capitalized. */ #ifdef IN_MAIN #define CLASS /* empty string if included by main program */ #else #define CLASS extern /* extern if included by anything else */ #endif CLASS XtAppContext App_con; CLASS Display *Dpy; /* variables for window setup */ CLASS Window Win; CLASS XSetWindowAttributes W_attr; CLASS GC Gc; CLASS int Def_screen; CLASS int Frame_depth; CLASS Colormap Cmap; CLASS int Foreground, Background; CLASS int Display_setup; /* flag for if display has been initialized */ CLASS int Fore_set, Back_set, Load_file; /* command line options */ CLASS char User_fore[25], User_back[25]; CLASS char Crnt_file[25]; /* the current filename in use */ CLASS int Have_message; /* for if have a message widget displayed */ CLASS char Error_string[50]; /* for building error messages */ CLASS XFontStruct *Font_struct; /* structure holding font information */ CLASS int Font_char_ht; /* max height for characters in the font */ CLASS int Font_ascent; /* max baseline to top edge of character */ /* pixel maps for operators and inversions */ CLASS Pixmap And, Or, Not, All, Exists, Imp, Iff; CLASS Pixmap And_invert, Or_invert, Not_invert, All_invert, Exists_invert, Imp_invert, Iff_invert; CLASS Pixmap Pattern; /* when font size is selected, following are set */ CLASS int Spacing; CLASS char *Or_bits, *And_bits, *Not_bits, *Imp_bits, *Iff_bits, *Exists_bits, *All_bits; CLASS int Or_width, And_width, Not_width, Imp_width, Iff_width, Exists_width, All_width; CLASS int Or_height, And_height, Not_height, Imp_height, Iff_height, Exists_height, All_height; CLASS struct formula_ptr_2 *Crnt_formula; /* the top level formula */ CLASS struct formula_ptr_2 *Top_formula; /* the head of the formula list */ CLASS struct formula_ptr_2 *Crnt_transform; /*the current formula displayed*/ CLASS struct formula_box *B; /* the top level formula box */ CLASS int Highlighted; /* is a formula currently highlighted? */ CLASS struct formula_box *Sel_area; /* the currently selected formula box */ CLASS Widget Outline; /* widgets referenced in callbacks */ CLASS Widget Canvas; CLASS Widget Popup, Edit_popup, Font_popup, Message; /* popups */ CLASS Widget Place_holder; CLASS Widget Edit_text; CLASS Widget Help_text; CLASS char Edit_str[TEXT_LENGTH*2]; /* for conjoining, disjoining of */ /* formulas */ CLASS int Crnt_button_menu; /* the child(ren) currently displayed in the */ /* button menu */ /* the list of children to manage in button_menu */ CLASS WidgetList Logic_buttons; CLASS WidgetList Edit_buttons; /* space needed for logic & edit buttons */ CLASS int Logic_area_width, Logic_area_height; CLASS int Edit_area_width, Edit_area_height; CLASS String Str; /* string in the edit window */ CLASS String File_str; /* string in the file window */ CLASS char Help_str[500]; /* string in the help window */ CLASS Widget Help_popup; /* help widgets */ /* these need to be global so can reset sensitivities */ CLASS Widget Help_info, Edit_help, Logic_help, Formula_control_help, Select_area_help, Cancel; /**** function prototypes for formed.c, display.c, and callbacks.c. ****/ /* formed.c */ void proc_command_line(); int sprint_formula(); void select_area(); void draw_formula_box_inverted(); void display_formula(); struct formula_box *do_box_geometry(); struct formula_box *arrange_box(); void draw_formula_box(); void draw_inverted_operators(); struct formula_box *find_point(); void install_up_pointers(); void free_formula_box_tree(); void transform(); struct formula_box *find_sub_box(); void free_formulas(); /* display.c */ void setup_display(); int convert_color(); void user_error(); void setup_font(); void kill_message(); void accum_size(); /* callbacks.c */ void edit_menu_callback(); void logic_menu_callback(); void comp_redo_callback(); void comp_undo_callback(); void next_callback(); void previous_callback(); void font_callback(); void quit_callback(); void help_callback(); void help_info_callback(); void return_help_menu(); void set_help_string(); void destroy_popup(); void load_callback(); void set_load_file(); int load_formula_list(); void save_callback(); void set_save_file(); int save_formula_list(); void clausify_callback(); void operate_callback(); void nnf_callback(); void skolemize_callback(); void cnf_callback(); void cnf_simp_callback(); void rms_cnf_callback(); void rms_dnf_callback(); void dnf_callback(); void dnf_simp_callback(); void redo_callback(); void undo_callback(); void expandConj_callback(); void expandDisj_callback(); void edit_callback(); void abbreviate_callback(); void replace_callback(); void edit_transform(); struct formula *str_to_formula(); struct formula *replace_text(); struct formula *make_deleted(); struct formula *join_formulas(); struct formula_ptr_2 *find_end(); void clear_text_callback(); void conjoin_callback(); void conjoin_with_callback(); void disjoin_callback(); void disjoin_with_callback(); void quantify_callback(); void add_quantify_callback(); void negate_callback(); void new_formula_callback(); void insert_formula_callback(); void delete_formula_callback(); void unedit_callback(); void reedit_callback(); void font_menu_callback(); void create_menu_popup(); void create_edit_popup(); otter-3.3f/source/formed/display.o0100644000076400007640000006152407710023424016611 0ustar mccunemccuneELFœ.4( U‰åWVSìjjhÿu U‰ÐPjjhêhèüÿÿÿ‰…ÿÿÿƒÄ$Pèüÿÿÿ£‹„‰‹ˆŒ’Áâ‹L$‰ ‹€Œ‹D0£ƒÄƒù~Jƒ=t ƒì hë vƒì hóèüÿÿÿ£ƒÄƒ=t ƒì hë%ƒì hùë‰öƒì hóèüÿÿÿ£Ç$ùèüÿÿÿ£ƒÄµÿÿÿÇ…ÿÿÿ4¡‰…ÿÿÿÇ… ÿÿÿÖ¡‰…$ÿÿÿƒì jVÿµÿÿÿÿ5hÿèüÿÿÿ£Ç…ÿÿÿÇ…ÿÿÿÂÇ… ÿÿÿǃÄhÿ5èüÿÿÿ‰…$ÿÿÿÇ…(ÿÿÿ­Ç…,ÿÿÿÇ…0ÿÿÿ4¡‰…4ÿÿÿÇ…8ÿÿÿ|Ç…<ÿÿÿÇ$Vÿ5ÿ5hèüÿÿÿÇ…ÿÿÿ"‰…ÿÿÿÇ… ÿÿÿ|Ç…$ÿÿÿÇ…(ÿÿÿ4¡‰…,ÿÿÿƒÄjVÿ5ÿ5h+èüÿÿÿ‰…ÿÿÿÇ…ÿÿÿ|Ç…ÿÿÿƒÄjVPÿ5h7èüÿÿÿ‰… ÿÿÿƒÄj(èüÿÿÿ£ÇÇÇ…ÿÿÿǃÄh@ÿ5èüÿÿÿ‰…ÿÿÿÇ… ÿÿÿ4¡‰…$ÿÿÿÇ…(ÿÿÿ­Ç…,ÿÿÿDÇ$Vÿµ ÿÿÿÿ5hMèüÿÿÿ‹‰ƒÄ jhhˆ¡ÿ0èüÿÿÿjjj¡ÿ0èüÿÿÿÇ…ÿÿÿ"¡‹‰…ÿÿÿÇ… ÿÿÿǃÄh@ÿ5èüÿÿÿ‰…$ÿÿÿÇ…(ÿÿÿ­Ç…,ÿÿÿVÇ…0ÿÿÿ4¡‰…4ÿÿÿÇ$Vÿµ ÿÿÿÿ5h^èüÿÿÿ‹‰BƒÄ jhhˆ¡ÿpèüÿÿÿjjj¡ÿpèüÿÿÿÇ…ÿÿÿf¡‹‰…ÿÿÿÇ… ÿÿÿǃÄh@ÿ5èüÿÿÿ‰…$ÿÿÿÇ…(ÿÿÿ­Ç…,ÿÿÿpÇ…0ÿÿÿ4¡‰…4ÿÿÿÇ$Vÿµ ÿÿÿÿ5htèüÿÿÿ‹‰BƒÄ jhhˆ¡ÿpèüÿÿÿjjj¡ÿpèüÿÿÿÇ…ÿÿÿf‹‹‰…ÿÿÿÇ… 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…ÿtƒû(uƒìÿuSèªüÿƒÄƇ Y ‰Øeô[^_]ÉöU‰åSƒì‹E»€xtƒìhÂ'ÿp èwüÿÿƒÄ„Àt»‰Ø‹]üÉÃU‰åSƒì‹E»€xtƒìhá ÿp è?üÿÿƒÄ„Àt»‰Ø‹]üÉÃU‰åVS‹]¾€{…°ƒì ÿ3è¦ÿÿÿƒÄ„À„‹‹C€xubƒì ÿpèOÿÿÿƒÄ„ÀtP…ötLƒì ‹Cÿ0èoÿÿÿƒÄ„Àu8‹C‹‰Fƒì ‹CÿpèFüÿÿƒÄÿsè;üÿÿƒÄÿ3è1üÿÿ‰$è)üÿÿƒÄë ƒìh!·ÿ5 Ô艩üÿÇ$èý«üÿ‰Þ‹[€{„Qÿÿÿeø[^]ÉöU‰åWVSƒì‹}WèÊýÿÿ‰ÃƒÄh€öh Y è6ûÿÿƒÄ„ÀuèŠûÿÿ‰ÃÆCƒì h Y è;ûÿÿ‰C ‰Øëi¸ƒû)t_ƒû(uUè\ûÿÿ‰Æ‰óë‰öÆC‰èIûÿÿ‰C‰Ãƒì WèÿÿÿƒÄ…Àuàƒì WèS¬üÿÇ$Â'èãúÿÿ‰C ÆC‰4$è„þÿÿ‰ðë¸eô[^_]ÃvU‰å‹E¾@]ÃU‰å‹E‹]ÉöU‰å‹E‹@]ÃU‰å‹E‹@‹]ÃvU‰å‹E‹@‹@‹]ÃU‰åSƒì‹]Sè¬ÿÿÿƒÄ…Àuƒì Sè´ÿÿÿ‰$èØÿÿÿƒÄ@ë‰ö¸‹]üÉÉöU‰åSƒì¡¨Ò»¨Òƒøÿtv¼'ƒëÿЋƒøÿuôX[]ÃU‰åƒì‰ì]öU‰åSRè[Ãîævè÷«üÿ‹]üÉÃL¦d¦|¦̦¸¦¤¦¦ð«ü«¬¬ ¬,¬8¬°¬à¬­œ­È­p­@­¯D¯p¯ô¯ °ȯœ¯-fbl Error: Illegal option.(nil)[] != = FALSEall exists & | <-> *** STRING TOO LONG *** Usage: xform2 [-f color] [-b color] [-l filename] arrange_box_symbol: unknown operator. arrange_box: unknown operator. draw_formula_box: unknown operator. draw_inverted_operators: unknown operator. That transformation wouldn't do anything. *help_return.width: 128*help_menu_form*width: 150*add_quantifiers.height: 30*delete_formula.width: 95*new_formula.width: 95*reedit.width: 85*unedit.width: 85*edit.width: 75*quit.width: 75*load.width: 75*save.width: 75*font_menu.width: 75*help.width: 75*font_form.cancel.width: 75*largefont.width: 75*largefont.height: 30*medfont.width: 75*smallfont.width: 75*iff_form.cancel.width: 70*to_disj.width: 70*to_conj.width: 70*Command.width: 85*Command.height: 20ToplevelblackwhiteOutlinehorizDistancetitlefromVertbutton_formbutton_menusClausifyclausifyOperateoperatefromHorizNNFnnfSkolemizeskolemizeCNFcnfCNF simpcnf_simpDNFdnfDNF simpdnf_simpRedoUndoEditAbbreviateConjoinconjoinDisjoindisjoinQuantifyquantifyNegatenegateNew formulanew_formulaDelete formuladelete_formulaRe-editreeditUnedituneditWelcome to FormEdPlace_holderdisplayButtonsshapeStyleEdit Menuedit_menuLogic Menulogic_menuRedo Allcomp_redoUndo Allcomp_undoNextnextPreviouspreviousSavesaveLoadloadFontfont_menuQuitquitviewcanvasMessagemessage_formMessagesmessage_labelmessage_text-*-helvetica-*-r-*-*-*-140-*-*-*-*-*-*-*-helvetica-*-r-*-*-*-120-*-*-*-*-*-*-*-helvetica-medium-r-*-*-*-100-*-*-*-*-*-*Warning: couldn't allocate color %s Nothing exists to be redone. End of formula list. Beginning of formula list. help_menu_formHow to use Helphelp_infoEdit Menu Buttonsedit_helpLogic Menu Buttonslogic_helpFormula Control Buttonsformula_control_helpSelecting Formula Areasselect_area_helpCancelcancelHelp_popuphelp_formhelp_labelReturn to Help Menuhelp_returndefaultColumnshelp_listwrapdisplayCarethelp_textload_formFilename:load_labelfile_textLoad fileload_fileFile loaded. Error: Cannot open save_formsave_labelSave filesave_fileFile saved. Error: cannot open Iff_opiff_formTo Conjto_conjTo Disjto_disjNothing more to be redone. Nothing more to be undone. called abbreviate_callback. Empty formula list. fontsfont_formSmallsmallfontMediummedfontLargelargefontEdit_popupedit_formhighlightThicknessClearclear_textscrollVerticalautoFilledit_textReplacereplaceConjoin withconjoin_withDisjoin withdisjoin_with Add Quantifiersadd_quantifiersInsertinsert Unedit Use: To undo an edit transformation that has already been done to a formula. Results: The un-edited formula is displayed, and it becomes the current formula. Re-edit Use: To redo an edit transformation that has already been done to a formula. Results: The re-edited formula is displayed, and it becomes the current formula. Delete formula Use: To remove the currently displayed formula from the current list of formulas or to delete a subformula from a conjunction or a disjunction. Results: If the entire formula is selected, it is deleted. If an immediate subformula of a conjunction or a disjunction is selected, that subformula is deleted form the formula. New formula Use: To add a new formula to the current list of formulas. Results: A window in which the text may be edited (Emacs style), containing buttons for insertion of the formula, clearing the text, and cancelling the command appears. The formula is inserted after the current formula and will then be displayed. Negate Use: To negate selected text from the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: After negation the new formula will be displayed. Quantify Use: To quantify selected text from the displayed formula. Input format: [all var_name] or [exists var_name] Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the quantifiers may be edited (Emacs style), containing buttons for adding the quantifiers, clearing of the text, and cancelling of the command appears. After adding the quantifiers, the new formula will be displayed. Disjoin Use: To disjoin text with selected text from the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the text may be edited (Emacs style), containing buttons for disjoining the new text with the selected area, clearing of the text, and cancelling of the command appears. After disjoining of the two, the new formula will be displayed. Conjoin Use: To conjoin text with selected text from the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the text may be edited (Emacs style), containing buttons for conjoining the new text with the selected area, clearing of the text, and cancelling of the command appears. After conjoining the two, the new formula will be displayed. Edit Use: To replace selected text in the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the text may be edited (Emacs style), containing buttons for replacement of the text, clearing of the text, and cancelling of the command appears. After replacement, the new formula will be displayed. Undo Use: To undo a logic transformation that has already been done to a formula. Results: The undone formula is displayed, and it becomes the current formula. Redo Use: To redo a logic transformation that has already been done to a formula. Results: The re-done formula is displayed, and it becomes the current formula. DNF simp Use: To transform the selected area to its disjunctive normal form with any simplifications that can be made done (i.e. (p | -p) simplifies to True). Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in disjunctive normal form (simplified) is displayed. DNF Use: To transform the selected area to its disjunctive normal form. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in disjunctive normal form is displayed. CNF simp Use: To transform the selected area to its conjunctive normal form with any simplifications that can be made done (i.e. (p | -p) simplifies to True). Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in conjunctive normal form (simplified) is displayed. CNF Use: To transform the selected area to its conjunctive normal form. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in conjunctive normal form is displayed. Skolemize Use: To skolemize the displayed formula. Selection requirements: Operates on entire formula, no selections should be made. Results: The skolemized formula is displayed. NNF Use: To transform the selected area to its negation normal form. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in negation normal form is displayed. Operate Use: To expand the implicational and biconditional operators, and move negations inward. Selection requirements: An implicational, biconditional, or negation operator must be selected. Results: The transformed formula (wrt the operator selected) is displayed. Clausify Use: To completely clausify the displayed formula. Selection requirements: Operates on entire formula, no selections should be made. Results: The clausified formula is displayed. Quit Use: To exit the formula editor. Font Use: To change the font being used in the display. Load Use: To load a list of formulas from a specified file. Save Use: To save the current list of formulas in a specified file. The current state of the formula (after all edit & logic transformations) is the version saved. Previous Use: To display the previous formula in the list of formulas. Next Use: To display the next formula in the list of formulas. Undo All Use: To completely undo the edit and logic transformations that have been done to the current formula, i.e. display the original formula. Redo All Use: To completely redo the edit and logic transformations that have been done to the current formula and display that formula. Logic Menu Use: Brings up a set of buttons for logic transformations to the current formula in the left panel. Edit Menu Use: Brings up a set of buttons for edit-type transformations to the current formula in the left panel.Edit panel already displayed. Logic panel already displayed. No formulas are currently loaded. Clausify is done on the entire formula, no selections necessary. WARNING: further logic transformations may be unsound, becuase universal quantifiers are gone. Operate requires selection of an operator (not, imp, iff). Operate requires selection of not, imp, or iff operators.NNF requires a formula (or subformula) as a selection. Skolemize is done on the entire formula, no selections necessary. CNF requires a formula (or subformula) as a selection. RMS CNF requires a formula (or subformula) as a selection. RMS DNF requires a formula (or subformula) as a selection. DNF requires a formula (or subformula) as a selection. Edit requires a formula (or subformula) as a selection. end of formula not at end of string (missing parentheses?) Error in converting string to formula. See standard output for more details.Conjoin requires a formula (or subformula) as a selection. Disjoin requires a formula (or subformula) as a selection. Quantify requires a formula (or subformula) as a selection. Negate requires a formula (or subformula) as a selection. Delete formula removes from the original formula list, not from the edit/logic transformed formulas.Delete formula cannot delete an operator.Deletion of a subformula must be from a conjunction or a disjunction.No formulas are currently loaded.Nothing more to be un-edited. Nothing more to be re-edited. -*-helvetica-*-r-*-*-*-240-*-*-*-*-*-*tp_alloc, request too big: %d (free_all_mem cleared). Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. ------------- memory usage ------------ %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu ï?@P?$Quantified$Hyps$Concs$ANS$Ans$ans$NUCLEUS$BOTH$LINK$SATELLITE$FSUB$BSUB$EQUIV%d %s/%d, lex_val=%d is_skolem, no symbol for %d.end_of_listend_of_list. $nil$cons|%s%s%s( %c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$T$F$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE#<->&!====/=@<@>@<=@>=+/xfxinfixxfyinfix_rightyfxinfix_leftprefixxfpostfixprefix_assocyfpostfix_assoc ***HERE*** adjusted term: ERROR, comma or ) expected: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, term too big: exists ERROR, text after term: %c WARNING, multiple arity: %s/%d, %s/%d. %c WARNING, unrecognized $ symbol: %s. mark_as_skolem, no symbol for %d.op command must have arity 3. ERROR: first argument of op command must be 1..999. ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: list in op command must be all names. ERROR: third argument of op command must be a name or a list. ERROR, name too big, max is %d; ERROR, quoted name has no end; ERROR, functor has no arguments: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, unrecognized error in term: ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.integrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.WARNING, CLOCK_START: clock %d already on. WARNING, CLOCK_STOP: clock %d already off. disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: bucket %d: bucket %d: containing terms: build_tree_local, var and not more general.new_sym_num: too many symbols requested. fpa index %p bucket %d and or Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>ERROR, too many variables, max is %d: ERROR, weight template: ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause. literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p ERROR, clause contains variable literal: ERROR, arrow not found in sequent: ERROR, input clause contains too many variables: ERROR, input clause contains Skolem symbol: ERROR, input literal contains Skolem symbol: forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.WARNING, clause %d not found, proof is incomplete. interaction failure: cannot find tty. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %c Not an integer: "%s", try again. Turning off interactive_given mode. Ok, clause %d will be given. unit_del, too many variables introduced.cl_del_int, bad clause.checking clause, address:%p , .%dbinaryneg_hyperpara_intopara_fromfactor_simplinked_urevalgL-idgLcopyflipback_unit_delsplitsplit_negpropositional(heat=%d) [] | (list nil) equalEqfind_random_cl, sos bad./dev/tty%c Clause %d not found. %c Clause %d not in sos. €¡t¡h¡\¡P¡D¡8¡´  ¡¡ô ä Ô Ä ¤ ,¡¡” „ t d T D ur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).build_term, bad arity.ifERROR, skolem gets: $c$fintroduce_var, bad formula.renumber_unique, bad formula.Tù€ùhùhùhùhù¼ù¶ ÀÀ<¨¶XÔÔp(˜ ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.renumber_unique, too many vars.>>>> Starting back demodulation with %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. keeping clause because it matches a hint. Following clause subsumed by %d during input processing: %cSearch stopped by max_proofs option. Search stopped by max_proofs option. %d back subsumes %d. after demodulation: deleted because weight=%d. Subsumed by %d. ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) Process %d finished %s/dev/null%.12f********** %s includeERROR, cannot open file %s. setclearassignERROR, bad argument to list: axiomsdemodulatorspassivehotmace_constraintsforeachERROR, unknown list: formula_listERROR, unknown formula_list: weight_listpurge_genpick_givenpick_and_purgeERROR, unknown Weight_list: lexlrpo_multiset_statuslrpo_lr_statusoverbeek_termssplit_atomsspecial_unaryfloat_formatmake_evaluableinitial_proof_objectoverbeek_worldoverbeek_world: term errorsERROR, command not found: list(sos). ERROR, bad demodulator: ------------> process sos: %2d:%-4d %2d:%-4d All others: %d. (hot clauses kept)%7ld user CPU time %10.2f system CPU time %10.2f wall-clock time %7ld input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f list(usable). list(demodulators). sos_size=%d %c--- refuted case %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d.%d,clauses in usable. paramodulation is disabled. given %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f %c********** ABNORMAL END ********** ********** ABNORMAL END ********** ERROR, bad argument to include: ------- start included file %s------- ------- end included file %s------- NOTICE: Please change 'axioms' to 'usable'. Name of axioms list is now 'usable'. -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, bad argument to Weight_list: ----> ERROR, already have purge weight list. ----> ERROR, already have pick weight list. ----> ERROR, already have pick weight list or purge weight list. ----> ERROR, already have term weight list. ERROR, argument of lex term is not a list: ERROR, argument of lrpo_status term is not a list: ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. ERROR, argument of skolem term is not a list: ERROR, argument of overbeek_terms is not a list: ERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: ERROR, argument of special_unary term is not a list: ERROR, float_format term must have one argument. ERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: overbeek_world: too many variablesERROR, sos_arg set, but no argument found. ERROR, characters after term: ERROR, clause contains too many variables: list(hints) and list(hints2) are incompatible. ------------> process usable: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld ----------- times (seconds) ----------- (%ld hr, %ld min, %ld sec) (%ld hr, %ld min, %ld sec) ============ end of search ============ That finishes the proof of the theorem. ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. %c-- HEY %s, WE HAVE A PROOF!! -- ---------------- PROOF ---------------- ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> Passive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will be ordered hyperresolution with the propositional optimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists will be printed at the end of the search. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, with positive clauses in sos and nonpositive There is a clause for symmetry of equality, so it is assumed that equality is fully axiomatized; therefore, This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it is Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty); therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set the propositional flag and use ordered hyperresolution. Setting pick_given_ratio to 2, because all clauses are units. Setting hyper_res, because there are nonunits. Setting ur_res, because this is a nonunit set containing either equality literals or non-Horn clauses. Clearing order_hyper, because all clauses are Horn. Setting factor and unit_deletion, because there are non-Horn clauses. Equality is present, so we set the knuth_bendix flag. As an incomplete heuristic, we paramodulate with units only. There is a clause for symmetry of equality, so it is @@%c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. constructing nodes for remaining lits: ERROR: constructing children told target here with already target set ERROR ... non UNIT clause looks UNIT ERROR: constructing children told target here and target not found here FPA indexing not supported for linked res subsumable unitUD entering linked_unit_del, passed term follows FPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c follows UD exiting linked_unit_del, not subsumed attempted to back up from a node with a child ERROR: unable to initialize linked UR inference tree ********tree before BIG loop open lit %d nres %d attempting to find clash for term first time = %c res_count = %d ERROR: moved forward to %p first = FALSE ERROR: found non_target back_up < 0 ERROR: left_sibling chain to NULL ***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d ***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable() ERROR: forward failed, has first_child that's NOT tar ERROR: forward failed with target child (has sibs) ERROR: couldn't get context for dummy node ERROR: couldn't get link node for dummy ERROR: couldn't get context for given node checking is_in_ancestry on lit parent = %p prev_sibling = %p next_sibling = %p first_child = %p first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d subst = %p subst->multiplier = %d tr = %p unif_position = %p ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tar NUC failed depth check TRASHED couldn't get link_node couldn't get context from clause couldn't get context node UD ********entering Linked UR *********** in clause clashed against term: in clause did not attempt to resolve ... appears in ancestry resolvent = [] -- FAIL -- couldn't get given link_node at %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: << -----start node at %p------ current_clause >> (NIL) << goal to resolve ... from literal -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d NUC in on only tar TRASHED ”ĠĬĸÄÄÄlinked hyper not implemented yet. enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s enter user_test_term: %ld %f %d %s evaluate_user_function, bad code.@"Returned string"new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.¸ÓüÓ@Ô¬ÔÌÔTÖ|Ö´ÖðÖ$×X×geo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH. HOT NEW CLAUSE!: SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. %cSearch stopped by SIGINT. Commands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- killed level %d search during interaction. killed level %d search during interaction. --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- %s%c The job finished %s??? Search stopped by SIGINT. Malformed term. fork%c Fork failed. statskill ok. continue ok.optionssymbols command not understood. Command not understood. ok. > %. %s Job %d Fork failedXlog_%dinsert_into_gen_tab, key already thereprint_proof_object_node, bad rulematch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewritestranslate_demod_unit: cannot rewritefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: proof node not foundlist(%s). %% Hints from process %d, %sbuild_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is given ;; BEGINNING OF PROOF OBJECT undefinedeq-axiominstantiateresolveparamodunknownv%d(%s(not false(or true(%d %d ( . v%d)(v%d . )) %d %d) (%d) NILnew_literal_index, bad mapfinish_translating, bad ruletrans_2_pos: NULL postrans_2_pos: clause not foundtrans_2_pos: empty clause;; END OF PROOF OBJECT ÌîÔîÜîäîìîôîüîï,ò,ò@òPóøòøòhó<ÀÀÀÀÀÀÀ pÀÀ€€`ÀP< %cWARNING, hint will not be used, because no weights have been set for it: ”%Œ%œ%¬%¤%´%%d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d(hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). bdNEW HINT: %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bsub_hint_wtfsub_hint_wtequiv_hint_wtbsub_hint_add_wtfsub_hint_add_wtequiv_hint_add_wt # %s(%fattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer:  5 5 5 5 5 5¨50606<6L6T647|7ˆ7˜7¬7H8\8€8”8¨8Atom: %d%s%d]Refuted case The Assumption for case was not used; s:therefore we skip case%s Splitting on clause Case (process %d): Assumption: case failure Splitting on atom sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d I tried to split, but I could not find a suitable clause. Case splitting (fork) failed. Returning to search. %c That finishes the proof of the theorem. I tried to split, but I could not find a suitable atom. always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch Here are the clauses in Usable and SoS. It seems that no more inferences or splitting can be done. If the search strategy is complete, these clauses should lead to a model of the input. INPUTEQ-AXIOMparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)parse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object cldiff, bad PICK_DIFFoverbeek_insert, bad term start of Overbeek_world overbeek_insert, bad weight in termThere is no Overbeek World to print! end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check! check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: CLAUSE %d -1 -2 ========== Jhash ========== [%d] resolved: IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof ===== build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not foundLevel %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ============ ============ end multijust ============ integer divide by 0.float divide by 0. demod term: --> result: demod<%d> WARNING, demod_limit. lex dependent demodulator: LRPO dependent demodulator: ERROR, dollar_contract, bad op_code: %d. ERROR, dollar_contract, bad op_type: %d. WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. >> back demodulating %d with %d. Flipping following input demodulator due to lrpo ordering:     ,,,,,,€€€€ˆˆˆˆˆˆx˜˜ ¨ŽŽŽŽ88DDPXXXXXX°°°°`¸hhhhhpè4œ‚€ƒ@„¼„˜…´…˜†¬†0‡¨ˆHŠ\‹DŒÄŒ8LŽ¬€¼€Ѐà€ô€Äè ‚0‚T‚x‚ð„… …8…X…p…Ø…ô…,†d†€†8‰h‰˜‰ȉø‰Š WARNING, instance of x=x cannot be inserted into demod_imd index: contract_imd, increase MAX_AL_TERM_DEPTH.start of index-match-demodulate treeimd_delete, can't find alpha.imd_delete, can't find atom.v%d %s demod=is_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p binary_resneg_hyper_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subfree_all_memno_faplno_fanlprint_keptdemod_historysort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_allpara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestsos_argfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdegrade_hints2fpa_literalsfpa_termsdemod_limitmax_givenmax_levelsmax_secondsneg_weightmax_keptmax_genmax_memmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_maxset(clear(%s). assign(%s, %d). dependent: %s(%s). ERROR: flag name not found. lex_rpoprint_levelnew_functionsWARNING: flag already set. flag already clear. parameter name not found. reduce_weight_limit already has that value. delete_identical_nested_skolemdiscard_commutativity_consequences --------------- options --------------- dependent: assign(%s, %d). must have one simple argument. ERROR, flag `lex_rpo' has been changed to `lrpo'. ERROR, flag `print_level' no longer exists. ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. must have two simple arguments. ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. integer must be in range [%d,%d]. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatible\ÈsÊsÊsÊsÊsÊsÊsÊxÈsÊsÊsÊsÊsÊsÊsÊsÊsÊsÊsÊÈsÊsÊsÊ$ÊsÊsÊsÊsÊsÊsÊsÊsÊsÊsÊPÈDÈsÊ8ÈœÇÇsÊsÊsÊ<ÊsÊsÊsÊsÊsÊsÊ„ÈsÊsÊüÉäÉäÉsÊsÊsÊsÊsÊsÊsÊsÊsÊsÊsÊœÈsÊsÊsÊsÊsÊsÊ0ÊsÊsÊsÊsÊsÊØɸÈHÉsÊsÊsÊsÊÊÊÊapply_substitute, term not COMPLEX.apply_substitute: term too deep.dot_trans, bad dot notation fill_word, word too big: |%s| ´ÒÀÀ`` 0 0øø0 0 ``ÀÀ€€  üü˜˜ðð``B~$$À```@ÀÀà033 &  ø7ð3pXX00h̆††Æ|R"\þþøøþþþþøøþþ~@@@|@@@~ 0þÿÿþ 0ÿÿ$BÿB$8ÿÿÿÿ8ÿÿ @ÿ@ ÿÿÿÿÀÀÀÀÿÿ ÿ€€ÀÀ`` 0 00 0 ``ÀÀ€€    ˜˜ðð``BB$$  ÀÀ`` 0 0øø0 0 ``ÀÀ€€  üü˜˜ðð``B~$$À```@ÀÀà033 &  ø7ð3pXX00h̆††Æ|R"\þþøøþþþþøøþþ~@@@|@@@~ 0þÿÿþ 0ÿÿ$BÿB$8ÿÿÿÿ8ÿÿ @ÿ@ ÿÿÿÿÀÀÀÀÿÿ ÿ€€ÀÀ`` 0 00 0 ``ÀÀ€€    ˜˜ðð``BB$$  ð ðøïåïÊïµï¢ïŒïwï[ïJï4ï#ïïïðîÞîÌî´îšî~îcîKîÀÀ`` 0 0øø0 0 ``ÀÀ€€  üü˜˜ðð``B~$$À```@ÀÀà033 &  ø7ð3pXX00h̆††Æ|R"\þþøøþþþþøøþþ~@@@|@@@~ 0þÿÿþ 0ÿÿ$BÿB$8ÿÿÿÿ8ÿÿ @ÿ@ ÿÿÿÿÀÀÀÀÿÿ ÿ€€ÀÀ`` 0 00 0 ``ÀÀ€€    ˜˜ðð``BB$$  ññ.ñ>ñPñ^ñvñ”ñ£ñˆðšð´ð¼ðÐðØðêðòðñ ñêñþñò'ò:òDòVò`òjòyò How to use Help To use the help facility, click on a set of information from the menu panel. A window will appear containing information on that topic. The Edit, Logic, and Formula Control help topics also contain subtopics which may be clicked on for more specific information. You must return to the help menu and click on Cancel to exit the help facility. Selecting Formula Areas For some operations, a part of the displayed formula may be selected on which to operate. Simply clicking in the formula display area will cause an area, corresponding to the location of the mouse, to be "highlighted". To unselect an area, simply click again in the same area. If no area is highlighted, the default selected area is the entire formula and subsequent operations will act on the entire formula.Ààÿýü ú@ù€øÀ÷  à   €`à `€à@à€À€@Œþm  ’ Àë(HŠ8„ ¥ ¸ÒXHàhþÿÿo°ÿÿÿoðÿÿoîŽÿÿÿÿÿÿÿÿÈÑÎ’Þ’î’þ’““.“>“N“^“n“~“Ž“ž“®“¾“ΓÞ“î“þ“””.”>”N”^”n”~”Ž”ž”®”¾”ΔÞ”î”þ”••.•>•N•^•n•~•Ž•ž•®•¾•ΕÞ•î•þ•––.–>–N–^–n–~–Ž–ž–®–¾–ΖÞ–î–þ–——.—>—N—^—n—¢ƒd¤—d¤—9<H€r€Œ€»€ó€0€€Ò€ý€,€V€€™€´€Õ€€1€V€€€©‚¢¢ ‚cV$‚ï[L‚b‚y‚¢¢¢‚ØƀǢڀ ñ€!€"€#3€%K€&a€1x€2€3§€4À€5Ø€6ñ€8 €9"€;B€=X€>n€?„€@š€A±€BÉ€C߀Dö€E €F$€G;€HT€Ii€NÏ€Qç€R€S€T9€UU€Vm€X…€[Ÿ€^·€eÍ€hç€l €q €r5 €uP €vm €yˆ €z¥ €}½ €€Ö €ƒñ €„ €‡& €Š@ ‚Ë”t ‚Fœ €¢Ò € €#V €Y €4u €< €Cú €F €S© €Zç €^€Ù€lù€tM€yn€ö€†4€Œ¢¢‚ L€b€8¢w‚Š‚b‚¢œ‚¢É€K¢¢L€€#Ô‚ç‚5ÁLÂwŠ‚Âœ¢Âø€×€€H8€Kg€L˜€UË€Z€^?€aw€b¯€\€€û€r€­¢¢–€5 €7!€89€9S€:¢m d¤—init.c/usr/src/build/87998-i386/BUILD/glibc-2.2.5/csu/gcc2_compiled.int:t(0,1)=r(0,1);-2147483648;2147483647;char:t(0,2)=r(0,2);0;127;long int:t(0,3)=r(0,3);-2147483648;2147483647;unsigned int:t(0,4)=r(0,4);0000000000000;0037777777777;long unsigned int:t(0,5)=r(0,5);0000000000000;0037777777777;long long int:t(0,6)=@s64;r(0,6);01000000000000000000000;0777777777777777777777;long long unsigned int:t(0,7)=@s64;r(0,7);0000000000000;01777777777777777777777;short int:t(0,8)=@s16;r(0,8);-32768;32767;short unsigned int:t(0,9)=@s16;r(0,9);0;65535;signed char:t(0,10)=@s8;r(0,10);-128;127;unsigned char:t(0,11)=@s8;r(0,11);0;255;float:t(0,12)=r(0,1);4;0;double:t(0,13)=r(0,1);8;0;long double:t(0,14)=r(0,1);12;0;complex int:t(0,15)=s8real:(0,1),0,32;imag:(0,1),32,32;;complex float:t(0,16)=r(0,16);8;0;complex double:t(0,17)=r(0,17);16;0;complex long double:t(0,18)=r(0,18);24;0;__builtin_va_list:t(0,19)=*(0,20)=(0,20)../include/libc-symbols.h/usr/src/build/87998-i386/BUILD/glibc-2.2.5/build-i386-linux/config.h../sysdeps/gnu/_G_config.h../sysdeps/unix/sysv/linux/bits/types.h../include/features.h../include/sys/cdefs.h../misc/sys/cdefs.h/usr/lib/gcc-lib/i386-redhat-linux/2.96/include/stddef.hsize_t:t(8,1)=(0,4)__u_char:t(4,1)=(0,11)__u_short:t(4,2)=(0,9)__u_int:t(4,3)=(0,4)__u_long:t(4,4)=(0,5)__u_quad_t:t(4,5)=(0,7)__quad_t:t(4,6)=(0,6)__int8_t:t(4,7)=(0,10)__uint8_t:t(4,8)=(0,11)__int16_t:t(4,9)=(0,8)__uint16_t:t(4,10)=(0,9)__int32_t:t(4,11)=(0,1)__uint32_t:t(4,12)=(0,4)__int64_t:t(4,13)=(0,6)__uint64_t:t(4,14)=(0,7)__qaddr_t:t(4,15)=(4,16)=*(4,6)__dev_t:t(4,17)=(4,5)__uid_t:t(4,18)=(4,3)__gid_t:t(4,19)=(4,3)__ino_t:t(4,20)=(4,4)__mode_t:t(4,21)=(4,3)__nlink_t:t(4,22)=(4,3)__off_t:t(4,23)=(0,3)__loff_t:t(4,24)=(4,6)__pid_t:t(4,25)=(0,1)__ssize_t:t(4,26)=(0,1)__rlim_t:t(4,27)=(4,4)__rlim64_t:t(4,28)=(4,5)__id_t:t(4,29)=(4,3)__fsid_t:t(4,30)=(4,31)=s8__val:(4,32)=ar(4,33)=r(4,33);0000000000000;0037777777777;;0;1;(0,1),0,64;;__daddr_t:t(4,34)=(0,1)__caddr_t:t(4,35)=(4,36)=*(0,2)__time_t:t(4,37)=(0,3)__useconds_t:t(4,38)=(0,4)__suseconds_t:t(4,39)=(0,3)__swblk_t:t(4,40)=(0,3)__clock_t:t(4,41)=(0,3)__clockid_t:t(4,42)=(0,1)__timer_t:t(4,43)=(0,1)__key_t:t(4,44)=(0,1)__ipc_pid_t:t(4,45)=(0,9)__blksize_t:t(4,46)=(0,3)__blkcnt_t:t(4,47)=(0,3)__blkcnt64_t:t(4,48)=(4,6)__fsblkcnt_t:t(4,49)=(4,4)__fsblkcnt64_t:t(4,50)=(4,5)__fsfilcnt_t:t(4,51)=(4,4)__fsfilcnt64_t:t(4,52)=(4,5)__ino64_t:t(4,53)=(4,5)__off64_t:t(4,54)=(4,24)__t_scalar_t:t(4,55)=(0,3)__t_uscalar_t:t(4,56)=(0,5)__intptr_t:t(4,57)=(0,1)__socklen_t:t(4,58)=(0,4)../linuxthreads/sysdeps/pthread/bits/pthreadtypes.h../sysdeps/unix/sysv/linux/bits/sched.h__sched_param:T(10,1)=s4__sched_priority:(0,1),0,32;;_pthread_fastlock:T(9,1)=s8__status:(0,3),0,32;__spinlock:(0,1),32,32;;_pthread_descr:t(9,2)=(9,3)=*(9,4)=xs_pthread_descr_struct:__pthread_attr_s:T(9,5)=s36__detachstate:(0,1),0,32;__schedpolicy:(0,1),32,32;__schedparam:(10,1),64,32;__inheritsched:(0,1),96,32;__scope:(0,1),128,32;__guardsize:(8,1),160,32;__stackaddr_set:(0,1),192,32;__stackaddr:(0,19),224,32;__stacksize:(8,1),256,32;;pthread_attr_t:t(9,6)=(9,5)pthread_cond_t:t(9,7)=(9,8)=s12__c_lock:(9,1),0,64;__c_waiting:(9,2),64,32;;pthread_condattr_t:t(9,9)=(9,10)=s4__dummy:(0,1),0,32;;pthread_key_t:t(9,11)=(0,4)pthread_mutex_t:t(9,12)=(9,13)=s24__m_reserved:(0,1),0,32;__m_count:(0,1),32,32;__m_owner:(9,2),64,32;__m_kind:(0,1),96,32;__m_lock:(9,1),128,64;;pthread_mutexattr_t:t(9,14)=(9,15)=s4__mutexkind:(0,1),0,32;;pthread_once_t:t(9,16)=(0,1)_pthread_rwlock_t:T(9,17)=s32__rw_lock:(9,1),0,64;__rw_readers:(0,1),64,32;__rw_writer:(9,2),96,32;__rw_read_waiting:(9,2),128,32;__rw_write_waiting:(9,2),160,32;__rw_kind:(0,1),192,32;__rw_pshared:(0,1),224,32;;pthread_rwlock_t:t(9,18)=(9,17)pthread_rwlockattr_t:t(9,19)=(9,20)=s8__lockkind:(0,1),0,32;__pshared:(0,1),32,32;;pthread_spinlock_t:t(9,21)=(0,1)pthread_barrier_t:t(9,22)=(9,23)=s20__ba_lock:(9,1),0,64;__ba_required:(0,1),64,32;__ba_present:(0,1),96,32;__ba_waiting:(9,2),128,32;;pthread_barrierattr_t:t(9,24)=(9,25)=s4__pshared:(0,1),0,32;;pthread_t:t(9,26)=(0,5)wchar_t:t(11,1)=(0,3)wint_t:t(11,2)=(0,4)../include/wchar.h../wcsmbs/wchar.h../sysdeps/unix/sysv/linux/i386/bits/wchar.h__mbstate_t:t(13,1)=(13,2)=s8__count:(0,1),0,32;__value:(13,3)=u4__wch:(11,2),0,32;__wchb:(13,4)=ar(4,33);0;3;(0,2),0,32;;,32,32;;_G_fpos_t:t(3,1)=(3,2)=s12__pos:(4,23),0,32;__state:(13,1),32,64;;_G_fpos64_t:t(3,3)=(3,4)=s16__pos:(4,54),0,64;__state:(13,1),64,64;;../include/gconv.h../iconv/gconv.h :T(17,1)=e__GCONV_OK:0,__GCONV_NOCONV:1,__GCONV_NODB:2,__GCONV_NOMEM:3,__GCONV_EMPTY_INPUT:4,__GCONV_FULL_OUTPUT:5,__GCONV_ILLEGAL_INPUT:6,__GCONV_INCOMPLETE_INPUT:7,__GCONV_ILLEGAL_DESCRIPTOR:8,__GCONV_INTERNAL_ERROR:9,; :T(17,2)=e__GCONV_IS_LAST:1,__GCONV_IGNORE_ERRORS:2,;__gconv_fct:t(17,3)=(17,4)=*(17,5)=f(0,1)__gconv_init_fct:t(17,6)=(17,7)=*(17,8)=f(0,1)__gconv_end_fct:t(17,9)=(17,10)=*(17,11)=f(0,20)__gconv_trans_fct:t(17,12)=(17,13)=*(17,14)=f(0,1)__gconv_trans_context_fct:t(17,15)=(17,16)=*(17,17)=f(0,1)__gconv_trans_query_fct:t(17,18)=(17,19)=*(17,20)=f(0,1)__gconv_trans_init_fct:t(17,21)=(17,22)=*(17,23)=f(0,1)__gconv_trans_end_fct:t(17,24)=(17,25)=*(17,26)=f(0,20)__gconv_trans_data:T(17,27)=s20__trans_fct:(17,12),0,32;__trans_context_fct:(17,15),32,32;__trans_end_fct:(17,24),64,32;__data:(0,19),96,32;__next:(17,28)=*(17,27),128,32;;__gconv_step:T(17,29)=s56__shlib_handle:(17,30)=*(17,31)=xs__gconv_loaded_object:,0,32;__modname:(17,32)=*(0,2),32,32;__counter:(0,1),64,32;__from_name:(4,36),96,32;__to_name:(4,36),128,32;__fct:(17,3),160,32;__init_fct:(17,6),192,32;__end_fct:(17,9),224,32;__min_needed_from:(0,1),256,32;__max_needed_from:(0,1),288,32;__min_needed_to:(0,1),320,32;__max_needed_to:(0,1),352,32;__stateful:(0,1),384,32;__data:(0,19),416,32;;__gconv_step_data:T(17,33)=s36__outbuf:(17,34)=*(0,11),0,32;__outbufend:(17,34),32,32;__flags:(0,1),64,32;__invocation_counter:(0,1),96,32;__internal_use:(0,1),128,32;__statep:(17,35)=*(13,1),160,32;__state:(13,1),192,64;__trans:(17,28),256,32;;__gconv_info:T(17,36)=s8__nsteps:(8,1),0,32;__steps:(17,37)=*(17,29),32,32;__data:(17,38)=ar(4,33);0;-1;(17,33),64,0;;__gconv_t:t(17,39)=(17,40)=*(17,36)_G_iconv_t:t(3,5)=(3,6)=u44__cd:(17,36),0,64;__combined:(3,7)=s44__cd:(17,36),0,64;__data:(17,33),64,288;;,0,352;;_G_int16_t:t(3,8)=(0,8)_G_int32_t:t(3,9)=(0,1)_G_uint16_t:t(3,10)=(0,9)_G_uint32_t:t(3,11)=(0,4)_IO_stdin_used:G(0,1)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)01.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.01.symtab.strtab.shstrtab.interp.note.ABI-tag.hash.dynsym.dynstr.gnu.version.gnu.version_r.rel.dyn.rel.plt.init.text.fini.rodata.data.eh_frame.dynamic.ctors.dtors.got.bss.stab.stabstr.comment.noteô€ô# 1((7 8„8?HŠH ¥GÿÿÿoîŽîÂTþÿÿo°°0c ààhl HHX u ’ p¸’¸À{€—€@TÀëÀk‡àëàkË `Ç`7d •ÄÑÄAŸÈÑÈAਨҨB¯°Ò°B¶¸Ò¸B<»ÔD°Å ÀD¤ ƤKƒÏ'et Ø›np rÞtw€b` ôÙOô€(8„HŠîŽ°àH  ’ ¸’ €— Àë àë`ÇÄÑÈѨҰҸÒÔñÿñÿ¤— "¤— 2ñÿЗ =hÇA°ÒOlÇ[З qÄÑ„0˜ ŒÞ˜@˜ ¤p˜ ¯pǽ¨Ò2ñÿ€ë Ë€ë á¬Ò¤°ë 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gate_callbackfind_mid_lightest_clp_term_tabgeometry_rule_unifrewind@@GLIBC_2.0unique_allNull_outputp_formularms_conflict_tautologyWeight_purge_genprint_justificationclause_identcaddrfree_fpa_headfree_sym_tabset_lex_valsprint_clause_s2un_index_lits_clashneg_eq_litp_imd_treesplitable_literalclause_ptr_list_sizeformWidgetClassclear_subst_2formula_identcat_strnnf_callbackFore_setprint_clause_sCrnt_formulacurrent_caseXtMallocadd_subcaseur_resmulti_just_processremove_all_supersetsremove_supersetsproof_length_initset_vars_clIff_widthPopupfind_endXtWindowabendfree_g2listtp_allocUser_backauto_lex_ordercontains_answer_literalmalloc@@GLIBC_2.0zap_ci_ptr_liststr_2_formulaanti_skolemizebuild_treeiset_removeNot_heightprint_mem_briefsplittingMessagetrivial_substfscanf@@GLIBC_2.0free_ilist_listcopy_formulagetppid@@GLIBC_2.0read_clauseneg_hyper_resBfree_formula_box_treeXTextWidthpipe@@GLIBC_2.0cnfAttributesun_index_lits_allsplit_clauseterm_ident_x_varsTo_childrenchange_parmprint_clause_without_justfree_clause_ptrapply_clauseget_proof_object_nodeclausify_formula_list__deregister_frame_info@@GLIBC_2.0Or_bitsOutlineprint_linked_ur_mem_statsfree_relDots_sym_numparse_lispeq_litcl_clear_varsdependent_flagsnegation_inwardback_demodalways_splitImp_bitsTo_parentfree_imd_posglist_appendread_wt_listall_instances_fpareturn_help_menup_proof_object_nodebird_printFrom_childrenclock_initdouble_strinsert_symstdout@@GLIBC_2.0append_clstderr@@GLIBC_2.0order_equalities_lrpoNotzap_hints2subst_sn_formulabin_resfactor_simplifycompare_splitable_clausesExists_inverthint_keep_testclock_resetprint_proof_objectconvert_colorrms_subsume_conjreplace_textis_insertprint_memp_clause_sget_listrms_cnfwall_secondsDemod_imdunit_delis_skolemquantify_callbackcompile_hintsXtAddCallbacksplit_atomis_symbolsymmetry_clauseconvenient_demodcl_del_intwrite_termindex_lits_clashnnf_dnffpa_deletefree_fpa_treeCmapattribute_typesetup_operator_pixmapssos_argumentget_is_treeproc_gensubsume_conjrun_timeFpa_neg_litsfs_retrievecl_int_chkoccur_checkprint_symssubst_free_formulaprf_weightprint_term_nllex_order_varsFont_structclause_to_termSelect_area_help_textnew_formula_callbacklinked_ur_restime@@GLIBC_2.0get_relhorn_clausesystem_timemake_deletedfinish_translatingImp_heightfree_fsub_pos_startcontains_skolem_symbolrms_quantifierssub_clauseis_deleteHave_messagematch_clausescompare_for_auto_lex_orderevaluate_user_functionall_factorsget_is_posread_sequent_clausefree_formula_boxcl_copy_delete_literalprint_trailsubsumeWeight_pick_given_indexforeach_sosmark_as_skolemAllrms_distribute_quantsis_eqp_proof_object_as_hintsbits_ulonginsert_buttonXtDisplaycnf_callbackget_ci_ptrfree_clauseilist_to_jsetterm_to_clauseorder_equalitiessprint_formuladeclare_user_functionslogic_menu_callbackget_termilist_appendinsert_clausereplace_buttonDemodulatorscase_depthinitial_strsn_to_nodesplitable_clausehot_inferencein_sym_tabOverbeek_termsprint_case_nFpa_alphasdouble_to_termglist_prependXSetBackgroundsame_structurelrpo_greateroutput_statsget_formula_ptriset_addp_optionsfree_sym_entnew_functor_nameCanvasget_imd_posgen_subsumebuild_termzap_prop_treepossible_given_splitprint_errorfree_link_nodeinitcdrfind_lightest_geo_childclock_valcl_mergeuser_errorkill_messagepretty_print_termskolemize_callbackprint_term_sfree_is_posfree_is_pos_listIffcl_insert_tabimd_insertindex_lits_allstrncmp@@GLIBC_2.0print_hints2_cl_listlong_to_termneg_clauseget_ilistget_attribute_indexLoad_fileautomatic_2_settingsdo_box_geometryprepend_clgen_tautologynullpp_statsfont_menu_callbackXChangeWindowAttributesprint_overbeek_worldSel_areafind_match2From_parentdraw_inverted_operatorsnth_clausep_symsfind_first_clstr_to_termis_retrieveForegroundcomp_redo_callback__bss_startXtDestroyWidgethot_index_clauseredo_callbackprint_formula_listzap_clause_ptr_listmaincleanupcomp_undo_callbackget_clauseconjoin_callbackassign_cl_idparse_initial_proof_objectrms_dnfjoin_formulasadd_quantifiers_buttonWeight_pick_givensn_to_aritycreate_edit_popupone_unary_answerrms_subsume_disjstr_doubleW_attrfind_clause_to_splitpos_eq_litFrame_depthpossible_splithot_dynamiccl_find__libc_start_main@@GLIBC_2.0print_listfree_term_ptrFont_char_htg2list_lengthSosadd_to_jsetrmslog_for_x_showmax_literal_weightall_supporters_less_thanget_trailmap_restpara_fromfree_imd_treeAnd_bitsImp_invertget_link_nodeIgnore_sym_numprint_set_b_to_aintegrate_termun_share_specialp_case_nrenumber_uniquepost_proc_allterm_fixupread_a_fileXLoadQueryFontdel_hidden_clausesfor_sub_propHighlightedget_proof_objectfirst_or_next_factorstrcat@@GLIBC_2.0anc_subsumetotal_memanswer_litprint_hints_cl_listhelp_info_callbackprint_variablep_proof_objectmove_clausesmax_split_depthAll_heightdata_startasctime@@GLIBC_2.0nnffree_formulasrms_push_freePlace_holderSubsume_countnext_cl_numprintf@@GLIBC_2.0propositional_clauseSplit_atomsXtAddEventHandlerfind_lightest_clfind_random_clEdit_strzap_termlistWidgetClassgetuid@@GLIBC_2.0_finiprint_sequent_clausedraw_formula_boxmemcpy@@GLIBC_2.0connect_new_nodeautomatic_1_settingsp_is_treegl_de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0ustar mccunemccune/* * help_strings.h -- For FormEd X Winwods Program. * */ String Edit_help_items[] = { "Edit", "Conjoin", "Disjoin", "Quantify", "Negate", "New formula", "Delete formula", "Re-edit", "Unedit", NULL }; String Logic_help_items[] = { "Clausify", "Operate", "NNF", "Skolemize", "CNF", "CNF simp", "DNF", "DNF simp", "Redo", "Undo", NULL }; String Formula_control_help_items[] = { "Edit Menu", "Logic Menu", "Redo All", "Undo All", "Next", "Previous", "Save", "Load", "Font", "Quit", NULL }; char Help_info_text[] = "\tHow to use Help\n\nTo use the help facility, click on a set of information from the menu panel. A window will appear containing information on that topic.\n\tThe Edit, Logic, and Formula Control help topics also contain subtopics which may be clicked on for more specific information.\n\tYou must return to the help menu and click on Cancel to exit the help facility."; char Select_area_help_text[] = "\tSelecting Formula Areas\n\nFor some operations, a part of the displayed formula may be selected on which to operate. Simply clicking in the formula display area will cause an area, corresponding to the location of the mouse, to be \"highlighted\". To unselect an area, simply click again in the same area.\n\tIf no area is highlighted, the default selected area is the entire formula and subsequent operations will act on the entire formula."; String Edit_help_text[] = { "\t\tEdit\n\nUse: To replace selected text in the displayed formula.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: A window in which the text may be edited (Emacs style), containing buttons for replacement of the text, clearing of the text, and cancelling of the command appears. After replacement, the new formula will be displayed.", "\t\tConjoin\n\nUse: To conjoin text with selected text from the displayed formula.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: A window in which the text may be edited (Emacs style), containing buttons for conjoining the new text with the selected area, clearing of the text, and cancelling of the command appears. After conjoining the two, the new formula will be displayed.", "\t\tDisjoin\n\nUse: To disjoin text with selected text from the displayed formula.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: A window in which the text may be edited (Emacs style), containing buttons for disjoining the new text with the selected area, clearing of the text, and cancelling of the command appears. After disjoining of the two, the new formula will be displayed.", "\t\tQuantify\n\nUse: To quantify selected text from the displayed formula.\n\nInput format: [all var_name] or [exists var_name]\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: A window in which the quantifiers may be edited (Emacs style), containing buttons for adding the quantifiers, clearing of the text, and cancelling of the command appears. After adding the quantifiers, the new formula will be displayed.", "\t\tNegate\n\nUse: To negate selected text from the displayed formula.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: After negation the new formula will be displayed.", "\t\tNew formula\n\nUse: To add a new formula to the current list of formulas.\n\nResults: A window in which the text may be edited (Emacs style), containing buttons for insertion of the formula, clearing the text, and cancelling the command appears. The formula is inserted after the current formula and will then be displayed.", "\t\tDelete formula\n\nUse: To remove the currently displayed formula from the current list of formulas or to delete a subformula from a conjunction or a disjunction.\n\nResults: If the entire formula is selected, it is deleted. If an immediate subformula of a conjunction or a disjunction is selected, that subformula is deleted form the formula.", "\t\tRe-edit\n\nUse: To redo an edit transformation that has already been done to a formula.\n\nResults: The re-edited formula is displayed, and it becomes the current formula.", "\t\tUnedit\n\nUse: To undo an edit transformation that has already been done to a formula.\n\nResults: The un-edited formula is displayed, and it becomes the current formula.", NULL }; String Logic_help_text[] = { "\t\tClausify\n\nUse: To completely clausify the displayed formula.\n\nSelection requirements: Operates on entire formula, no selections should be made.\n\nResults: The clausified formula is displayed.", "\t\tOperate\n\nUse: To expand the implicational and biconditional operators, and move negations inward.\n\nSelection requirements: An implicational, biconditional, or negation operator must be selected.\n\nResults: The transformed formula (wrt the operator selected) is displayed.", "\t\tNNF\n\nUse: To transform the selected area to its negation normal form.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: The formula with its selected area in negation normal form is displayed.", "\t\tSkolemize\n\nUse: To skolemize the displayed formula.\n\nSelection requirements: Operates on entire formula, no selections should be made.\n\nResults: The skolemized formula is displayed.", "\t\tCNF\n\nUse: To transform the selected area to its conjunctive normal form.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: The formula with its selected area in conjunctive normal form is displayed.", "\t\tCNF simp\n\nUse: To transform the selected area to its conjunctive normal form with any simplifications that can be made done (i.e. (p | -p) simplifies to True).\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: The formula with its selected area in conjunctive normal form (simplified) is displayed.", "\t\tDNF\n\nUse: To transform the selected area to its disjunctive normal form.\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: The formula with its selected area in disjunctive normal form is displayed.", "\t\tDNF simp\n\nUse: To transform the selected area to its disjunctive normal form with any simplifications that can be made done (i.e. (p | -p) simplifies to True).\n\nSelection requirements: Any piece of the formula may be selected, provided it contains more than just an operator.\n\nResults: The formula with its selected area in disjunctive normal form (simplified) is displayed.", "\t\tRedo\n\nUse: To redo a logic transformation that has already been done to a formula.\n\nResults: The re-done formula is displayed, and it becomes the current formula.", "\t\tUndo\n\nUse: To undo a logic transformation that has already been done to a formula.\n\nResults: The undone formula is displayed, and it becomes the current formula.", NULL }; String Formula_control_help_text[] = { "\t\tEdit Menu\n\nUse: Brings up a set of buttons for edit-type transformations to the current formula in the left panel.", "\t\tLogic Menu\n\nUse: Brings up a set of buttons for logic transformations to the current formula in the left panel.", "\t\tRedo All\n\nUse: To completely redo the edit and logic transformations that have been done to the current formula and display that formula.", "\t\tUndo All\n\nUse: To completely undo the edit and logic transformations that have been done to the current formula, i.e. display the original formula.", "\t\tNext\n\nUse: To display the next formula in the list of formulas.", "\t\tPrevious\n\nUse: To display the previous formula in the list of formulas.", "\t\tSave\n\nUse: To save the current list of formulas in a specified file. The current state of the formula (after all edit & logic transformations) is the version saved.", "\t\tLoad\n\nUse: To load a list of formulas from a specified file.", "\t\tFont\n\nUse: To change the font being used in the display.", "\t\tQuit\n\nUse: To exit the formula editor.", NULL }; otter-3.3f/source/formed/Makefile0100644000076400007640000000223607707040124016421 0ustar mccunemccune DFLAGS = -DTP_NAMES -DTP_SIGNAL -DTP_FORK -DTP_RUSAGE CC = gcc ############################################################################# # Specify the compiler flags; include DFLAGS (above) # # optimized CFLAGS = -O $(DFLAGS) # # save symbols for debuggers # CFLAGS = -g $(DFLAGS) # # optimized, debugging (gcc and gdb can handle this) # CFLAGS = -O -g $(DFLAGS) # # gprof profiling # CFLAGS = -pg -O $(DFLAGS) ############################################################################# ############################################################################# # # The following is for FormEd, a program for displaying and # editing formulas. # # # XLIBS = -lXaw -lXmu -lXext -lXt -lX11 -lm # # We used to need the following at MCS; you may need something similar. # XLIBS = -L/usr/local/X11R5/lib -lXaw -lXmu -lXext -lXt -lX11 -lm # CFLAGS = -O $(DFLAGS) -I/usr/include/X11 # # The following works on a RedHat 7.3 computer XLIBS = -L/usr/X11R6/lib -lXaw formed: formed.o display.o callback.o $(CC) $(CFLAGS) formed.o display.o callback.o \ ../libotter.a $(XLIBS) -o formed display.o callback.o formed.o: formed.h clean realclean: /bin/rm -f *.o formed otter-3.3f/source/formed/callback.c0100644000076400007640000015617506407523123016676 0ustar mccunemccune/* * callbacks.c -- Callbacks for the FormEd program. * */ #include "../header.h" #include "formed.h" #include "help_str.h" Widget replace_button(); Widget conjoin_button(); Widget disjoin_button(); Widget add_quantifiers_button(); Widget insert_button(); Widget create_one_line_text_widget(); /************************* * * void edit_menu_callback(w, client_data, call_data) * *****************************/ void edit_menu_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { int same_display; same_display = 0; /* unmanage the current child, or list of children if not the placeholder */ switch(Crnt_button_menu) { case PLACE_HOLDER: XtUnmanageChild(Place_holder); break; case EDIT_MENU: user_error("Edit panel already displayed.\n"); same_display = 1; break; case LOGIC_MENU: XtUnmanageChildren(Logic_buttons, NUM_LOGIC_BUTTONS); break; } if (!same_display) { XtManageChildren(Edit_buttons, NUM_EDIT_BUTTONS); Crnt_button_menu = EDIT_MENU; } } /* edit_menu_callback */ /************************* * * void logic_menu_callback(w, client_data, call_data) * *****************************/ void logic_menu_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { int same_display; same_display = 0; /* unmanage the current child, or list of children if not the placeholder */ switch(Crnt_button_menu) { case PLACE_HOLDER: XtUnmanageChild(Place_holder); break; case LOGIC_MENU: user_error("Logic panel already displayed.\n"); same_display = 1; break; case EDIT_MENU: XtUnmanageChildren(Edit_buttons, NUM_EDIT_BUTTONS); break; } if (!same_display) { XtManageChildren(Logic_buttons, NUM_LOGIC_BUTTONS); Crnt_button_menu = LOGIC_MENU; } } /* logic_menu_callback */ /************************* * * void comp_redo_callback(w, client_data, call_data) * *****************************/ void comp_redo_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Crnt_formula->right == NULL && Crnt_formula->up == NULL) user_error("Nothing exists to be redone.\n"); else { Crnt_transform = find_end(Crnt_formula); display_formula(Crnt_transform); } } else user_error("No formulas are currently loaded.\n"); } /* end comp_redo_callback */ /************************* * * void comp_undo_callback(w, client_data, call_data) * *****************************/ void comp_undo_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { Crnt_transform = Crnt_formula; display_formula(Crnt_transform); } else user_error("No formulas are currently loaded.\n"); } /* end comp_undo_callback */ /************************* * * void next_callback(w, client_data, call_data) * *****************************/ void next_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { /* display next formula, if have one */ if (Crnt_formula->next) { Crnt_formula = Crnt_formula->next; Crnt_transform = find_end(Crnt_formula); display_formula(Crnt_transform); } else user_error("End of formula list.\n"); } else user_error("No formulas are currently loaded.\n"); } /* next_callback */ /************************* * * void previous_callback(w, client_data, call_data) * *****************************/ void previous_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { /* display previous formula, if have one */ if (Crnt_formula->prev) { Crnt_formula = Crnt_formula->prev; Crnt_transform = find_end(Crnt_formula); display_formula(Crnt_transform); } else user_error("Beginning of formula list.\n"); } else user_error("No formulas are currently loaded.\n"); } /* end previous_callback */ /************************* * * void font_callback(w, client_data, call_data) * *****************************/ void font_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { XtDestroyWidget(Popup); /* redisplay formula if have one */ setup_font((char *) client_data); if (Crnt_formula) display_formula(Crnt_transform); } /* end font_callback */ /************************* * * void quit_callback(w, client_data, call_data) * *****************************/ void quit_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { print_mem(stdout); exit(0); } /* end quit_callback */ /************************* * * void help_callback(w, client_data, call_data) * *****************************/ void help_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { Widget help_menu_form; int n; Arg arg[10]; create_menu_popup("Help", w); /* create the popup shell */ n = 0; XtSetArg(arg[n], XtNbackground, Background); n++; help_menu_form = XtCreateManagedWidget("help_menu_form", formWidgetClass, Popup, arg, n); /* command buttons */ /* how to use help */ n = 0; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "How to use Help");n++; Help_info = XtCreateManagedWidget("help_info",commandWidgetClass, help_menu_form,arg,n); XtAddCallback(Help_info, XtNcallback, help_info_callback, Help_info); /* Edit buttons */ n = 0; XtSetArg(arg[n], XtNfromVert, Help_info); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Edit Menu Buttons");n++; Edit_help = XtCreateManagedWidget("edit_help", commandWidgetClass, help_menu_form, arg, n); XtAddCallback(Edit_help, XtNcallback, help_info_callback, Edit_help); /* Logic buttons */ n = 0; XtSetArg(arg[n], XtNfromVert, Edit_help); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Logic Menu Buttons");n++; Logic_help = XtCreateManagedWidget("logic_help", commandWidgetClass, help_menu_form, arg, n); XtAddCallback(Logic_help, XtNcallback, help_info_callback, Logic_help); /* formula control buttons */ n = 0; XtSetArg(arg[n], XtNfromVert, Logic_help); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Formula Control Buttons");n++; Formula_control_help = XtCreateManagedWidget("formula_control_help", commandWidgetClass, help_menu_form, arg, n); XtAddCallback(Formula_control_help, XtNcallback, help_info_callback, Formula_control_help); /* selecting formula area information */ n = 0; XtSetArg(arg[n], XtNfromVert, Formula_control_help); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Selecting Formula Areas");n++; Select_area_help = XtCreateManagedWidget("select_area_help", commandWidgetClass, help_menu_form, arg, n); XtAddCallback(Select_area_help, XtNcallback, help_info_callback, Select_area_help); /* cancel */ n = 0; XtSetArg(arg[n], XtNfromVert, Select_area_help); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Cancel"); n++; Cancel = XtCreateManagedWidget("cancel",commandWidgetClass, help_menu_form, arg, n); XtAddCallback(Cancel, XtNcallback, destroy_popup, Popup); XtPopup(Popup, XtGrabNone); } /* end help_callback */ /************************* * * void help_info_callback(entry, client_data, call_data) * *****************************/ void help_info_callback(entry,client_data, call_data) Widget entry; XtPointer client_data; XtPointer call_data; { Widget selected_help = (Widget) client_data; int n; Arg arg[10]; Dimension width, height; Position x, y; Widget help_label, help_form, help_return, help_list; /* make the buttons in the main menu insensitive */ /* until a return to menu has been issued */ XtSetArg(arg[0], XtNsensitive, False); XtSetValues(Help_info, arg, 1); XtSetArg(arg[0], XtNsensitive, False); XtSetValues(Edit_help, arg, 1); XtSetArg(arg[0], XtNsensitive, False); XtSetValues(Logic_help, arg, 1); XtSetArg(arg[0], XtNsensitive, False); XtSetValues(Formula_control_help, arg, 1); XtSetArg(arg[0], XtNsensitive, False); XtSetValues(Select_area_help, arg, 1); XtSetArg(arg[0], XtNsensitive, False); XtSetValues(Cancel, arg, 1); /* create the shell */ n = 0; XtSetArg(arg[n], XtNwidth, &width); n++; XtSetArg(arg[n], XtNheight, &height); n++; XtGetValues(Outline, arg, n); XtTranslateCoords(Outline, (Position)((width/2)-200), (Position)(height/2-150), &x, &y); n = 0; XtSetArg(arg[n], XtNx, x); n++; XtSetArg(arg[n], XtNy, y); n++; Help_popup = XtCreatePopupShell("Help_popup", transientShellWidgetClass, Outline, arg, n); /* form widget to hold buttons & text */ n = 0; XtSetArg(arg[n], XtNforeground, Foreground); n++; help_form = XtCreateManagedWidget("help_form", formWidgetClass, Help_popup, arg, n); /* help label */ n = 0; XtSetArg(arg[n], XtNlabel, "Help"); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNwidth, 300); n++; XtSetArg(arg[n], XtNborderWidth, 0); n++; help_label = XtCreateManagedWidget("help_label", labelWidgetClass, help_form, arg, n); /* return to help menu selection */ n = 0; XtSetArg(arg[n], XtNfromVert, help_label); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Return to Help Menu"); n++; help_return = XtCreateManagedWidget("help_return", commandWidgetClass, help_form, arg, n); XtAddCallback(help_return, XtNcallback, return_help_menu, NULL); /* list of buttons to choose for information on */ if (selected_help == Help_info) strcpy(Help_str, Help_info_text); else if (selected_help == Select_area_help) strcpy(Help_str, Select_area_help_text); else { n = 0; XtSetArg(arg[n], XtNfromVert, help_return); n++; if (selected_help == Edit_help) { XtSetArg(arg[n], XtNdefaultColumns, 3); n++; XtSetArg(arg[n], XtNlist, Edit_help_items); n++; } else if (selected_help == Logic_help) { XtSetArg(arg[n], XtNdefaultColumns, 4); n++; XtSetArg(arg[n], XtNlist, Logic_help_items); n++; } else if (selected_help == Formula_control_help) { XtSetArg(arg[n], XtNdefaultColumns, 4); n++; XtSetArg(arg[n], XtNlist, Formula_control_help_items); n++; } help_list = XtCreateManagedWidget("help_list", listWidgetClass, help_form, arg, n); XtAddCallback(help_list, XtNcallback, set_help_string, selected_help); strcpy(Help_str, " "); } /* text box */ n = 0; if ((selected_help == Help_info) || (selected_help == Select_area_help)) { XtSetArg(arg[n], XtNfromVert, help_return); n++; } else { XtSetArg(arg[n], XtNfromVert, help_list); n++; } XtSetArg(arg[n], XtNforeground, Foreground); n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNstring, Help_str); n++; XtSetArg(arg[n], XtNwrap, XawtextWrapWord); n++; XtSetArg(arg[n], XtNdisplayCaret, False); n++; XtSetArg(arg[n], XtNwidth, 300); n++; XtSetArg(arg[n], XtNheight, 275); n++; Help_text = XtCreateManagedWidget("help_text",asciiTextWidgetClass, help_form, arg, n); XtPopup(Help_popup, XtGrabNone); } /* help_info_callback */ /************************* * * void return_help_menu(entry, client_data, call_data) * *****************************/ void return_help_menu(entry,client_data, call_data) Widget entry; XtPointer client_data; XtPointer call_data; { Arg arg[1]; /* reset the sensitivity of the help menu buttons */ XtSetArg(arg[0], XtNsensitive, True); XtSetValues(Help_info, arg, 1); XtSetArg(arg[0], XtNsensitive, True); XtSetValues(Edit_help, arg, 1); XtSetArg(arg[0], XtNsensitive, True); XtSetValues(Logic_help, arg, 1); XtSetArg(arg[0], XtNsensitive, True); XtSetValues(Formula_control_help, arg, 1); XtSetArg(arg[0], XtNsensitive, True); XtSetValues(Select_area_help, arg, 1); XtSetArg(arg[0], XtNsensitive, True); XtSetValues(Cancel, arg, 1); /* destroy the help popup */ XtDestroyWidget(Help_popup); /* redisplay formula if have one */ if (Crnt_formula) display_formula(Crnt_transform); } /* return_help_menu */ /************************* * * void set_help_string(entry, client_data, call_data) * *****************************/ void set_help_string(entry,client_data, call_data) Widget entry; XtPointer client_data; XtPointer call_data; { XawListReturnStruct *item = (XawListReturnStruct *)call_data; Widget help_set = (Widget) client_data; /* which set of help selected */ Arg arg[1]; /* get appropriate string */ if (help_set == Edit_help) strcpy(Help_str, Edit_help_text[item->list_index]); else if (help_set == Logic_help) strcpy(Help_str, Logic_help_text[item->list_index]); else strcpy(Help_str, Formula_control_help_text[item->list_index]); /* reset the string in the widget */ XtSetArg(arg[0], XtNstring, Help_str); XtSetValues(Help_text, arg, 1); } /* set_help_string */ /************************* * * void destroy_popup(w, client_data, call_data) * *****************************/ void destroy_popup(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { XtDestroyWidget(client_data); /* redisplay formula if have one */ if (Crnt_formula) display_formula(Crnt_transform); } /* destroy_popup */ /************************* * * void load_callback(entry, client_data, call_data) * *****************************/ void load_callback(entry,client_data, call_data) Widget entry; XtPointer client_data; XtPointer call_data; { Widget load_form, load_label, file_text, load_file, cancel; Arg arg[10]; int n; create_menu_popup("Load", entry); /* create the popup shell */ n = 0; XtSetArg(arg[n], XtNbackground, Background); n++; load_form = XtCreateManagedWidget("load_form", formWidgetClass, Popup, arg, n); n = 0; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNborderWidth, 0); n++; XtSetArg(arg[n], XtNlabel, "Filename:");n++; load_label = XtCreateManagedWidget("load_label", labelWidgetClass, load_form,arg,n); /* file name */ n = 0; XtSetArg(arg[n], XtNfromVert, load_label); n++; XtSetArg(arg[n], XtNforeground, Foreground); n++; XtSetArg(arg[n], XtNeditType, XawtextEdit); n++; XtSetArg(arg[n], XtNwidth, 176); n++; XtSetArg(arg[n], XtNstring, Crnt_file); n++; file_text = XtCreateManagedWidget("file_text", asciiTextWidgetClass, load_form, arg, n); n = 0; XtSetArg(arg[n], XtNfromVert, file_text); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Load file");n++; load_file = XtCreateManagedWidget("load_file",commandWidgetClass, load_form,arg,n); XtAddCallback(load_file, XtNcallback, set_load_file, file_text); n = 0; XtSetArg(arg[n], XtNfromVert, file_text); n++; XtSetArg(arg[n], XtNfromHoriz, load_file); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Cancel");n++; cancel = XtCreateManagedWidget("cancel",commandWidgetClass, load_form,arg,n); XtAddCallback(cancel, XtNcallback, destroy_popup, Popup); XtPopup(Popup, XtGrabNone); } /* end load_callback */ /************************* * * void set_load_file(button, client_data, call_data) * *****************************/ void set_load_file(button, client_data, call_data) Widget button; XtPointer client_data; XtPointer call_data; { Widget file_name = (Widget) client_data; int c; Arg arg[1]; XtSetArg(arg[0], XtNstring, &File_str); XtGetValues(file_name, arg, 1); strcpy(Crnt_file, File_str); /* attempt to save list, if any errors, return to popup */ /* if no errors, set up pointers and display first formula */ c = load_formula_list(Crnt_file); if (c) { XtDestroyWidget(Popup); /* remove load file popup */ /* display first formula */ Top_formula = Crnt_formula; Crnt_transform = Crnt_formula; display_formula(Crnt_transform); if (Display_setup) user_error("File loaded.\n"); } } /* set_load_file */ /************************* * * int load_formula_list(filename) * *****************************/ int load_formula_list(filename) char filename[]; { int errors; struct formula_ptr *p1, *p2; struct formula_ptr_2 *q1, *q2; struct formula *f; FILE *fp; fp = fopen(Crnt_file, "r"); if (fp == NULL && Display_setup) { strcpy(Error_string, "Error: Cannot open "); strcat(Error_string, Crnt_file); strcat(Error_string, ".\n"); user_error(Error_string); return(0); } else { p1 = read_formula_list(fp, &errors); if (errors) exit(1); q2 = NULL; while (p1) { q1 = get_formula_ptr_2(); q1->f = p1->f; install_up_pointers(q1->f); q1->f->parent = NULL; q1->prev = q2; if (q2) q2->next = q1; else Crnt_formula = q1; q2 = q1; p2 = p1; p1 = p1->next; free_formula_ptr(p2); } /* print out formulas loaded in to the screen */ q2 = Crnt_formula; while (q2 != NULL) { print_formula(stdout, q2->f); fprintf(stdout, ".\n"); q2 = q2->next; } fclose(fp); return(1); } } /* load_formula_list */ /************************* * * void save_callback(w, client_data, call_data) * *****************************/ void save_callback(entry,client_data, call_data) Widget entry; XtPointer client_data; XtPointer call_data; { Widget save_form, save_label, file_text, save_file, cancel; Arg arg[10]; int n; if (Crnt_formula) { create_menu_popup("Save", entry); /* create the popup shell */ n = 0; XtSetArg(arg[n], XtNbackground, Background); n++; save_form = XtCreateManagedWidget("save_form", formWidgetClass, Popup, arg, n); n = 0; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNbackground, Background); n++; XtSetArg(arg[n], XtNborderWidth, 0); n++; XtSetArg(arg[n], XtNlabel, "Filename:");n++; save_label = XtCreateManagedWidget("save_label", labelWidgetClass, save_form,arg,n); /* file name */ n = 0; XtSetArg(arg[n], XtNfromVert, save_label); n++; XtSetArg(arg[n], XtNforeground, Foreground); n++; XtSetArg(arg[n], XtNeditType, XawtextEdit); n++; XtSetArg(arg[n], XtNwidth, 176); n++; XtSetArg(arg[n], XtNstring, Crnt_file); n++; file_text = XtCreateManagedWidget("file_text", asciiTextWidgetClass, save_form, arg, n); n = 0; XtSetArg(arg[n], XtNfromVert, file_text); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Save file");n++; save_file = XtCreateManagedWidget("save_file",commandWidgetClass, save_form,arg,n); XtAddCallback(save_file, XtNcallback, set_save_file, file_text); n = 0; XtSetArg(arg[n], XtNfromVert, file_text); n++; XtSetArg(arg[n], XtNfromHoriz, save_file); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Cancel");n++; cancel = XtCreateManagedWidget("cancel",commandWidgetClass, save_form,arg,n); XtAddCallback(cancel, XtNcallback, destroy_popup, Popup); XtPopup(Popup, XtGrabNone); } else user_error("No formulas are currently loaded.\n"); } /* end save_callback */ /************************* * * void set_save_file(button, client_data, call_data) * *****************************/ void set_save_file(button, client_data, call_data) Widget button; XtPointer client_data; XtPointer call_data; { Widget file_name = (Widget) client_data; int c; Arg arg[1]; XtSetArg(arg[0], XtNstring, &File_str); XtGetValues(file_name, arg, 1); strcpy(Crnt_file, File_str); /* attempt to save list, if any errors, return to popup */ c = save_formula_list(Crnt_file); if (c) { XtDestroyWidget(Popup); /* redisplay formula if have one */ if (Crnt_formula) display_formula(Crnt_transform); if (Display_setup) user_error("File saved.\n"); } } /* set_save_file */ /************************* * * int save_formula_list(filename) * *****************************/ int save_formula_list(filename) char filename[]; { FILE *fp; struct formula_ptr_2 *p, *q; if ((fp = fopen(filename,"w")) == NULL && Display_setup) { strcpy(Error_string, "Error: cannot open "); strcat(Error_string, filename); strcat(Error_string, ".\n"); user_error(Error_string); return(0); } else { /* save the formula list pointed to by Top_formula */ p = Top_formula; while(p) { q = find_end(p); /* find end of current transformation list */ print_formula(fp, q->f); fprintf(fp,".\n"); p = p->next; } fclose(fp); return(1); } } /* save_formula_list */ /******************* * LOGIC CALLBACKS ********************/ /************************* * * void clausify_callback(w, client_data, call_data) * *****************************/ void clausify_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area != B) user_error("Clausify is done on the entire formula,\nno selections necessary.\n"); else { f = Sel_area->f; transform(f, clausify_formed); user_error("WARNING: further logic transformations may be unsound,\nbecuase universal quantifiers are gone.\n"); } } else user_error("No formulas are currently loaded.\n"); } /* end clausify_callback */ /************************* * * void operate_callback(w, client_data, call_data) * *****************************/ void operate_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; int n; Arg arg[10]; Widget to_conj, to_disj, cancel, iff_form; if (Crnt_formula) { if (Sel_area->type != OPERATOR) user_error("Operate requires selection of\nan operator (not, imp, iff).\n"); else { /* depending on type of operator, perform transformation */ switch(Sel_area->subtype) { case NOT_OP: f = Sel_area->parent->f; transform(f, negation_inward); break; case IMP_OP: f = Sel_area->parent->f; transform(f, expand_imp); break; case IFF_OP: /* create a popup widget, for to conj or disj */ create_menu_popup("Iff_op", w); n = 0; XtSetArg(arg[n], XtNbackground, Background); n++; iff_form = XtCreateManagedWidget("iff_form", formWidgetClass, Popup, arg, n); /* command buttons */ n = 0; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "To Conj");n++; to_conj = XtCreateManagedWidget("to_conj",commandWidgetClass, iff_form,arg,n); XtAddCallback(to_conj, XtNcallback, expandConj_callback, NULL); n = 0; XtSetArg(arg[n], XtNfromVert, to_conj); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "To Disj");n++; to_disj = XtCreateManagedWidget("to_disj",commandWidgetClass, iff_form,arg,n); XtAddCallback(to_disj, XtNcallback, expandDisj_callback, NULL); n = 0; XtSetArg(arg[n], XtNfromVert, to_disj); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT));n++; XtSetArg(arg[n], XtNlabel, "Cancel");n++; cancel = XtCreateManagedWidget("cancel",commandWidgetClass, iff_form,arg,n); XtAddCallback(cancel, XtNcallback, destroy_popup, Popup); XtPopup(Popup, XtGrabNone); break; default: user_error("Operate requires selection of not, imp, or iff operators."); break; } } } else user_error("No formulas are currently loaded.\n"); } /* operate_callback */ /************************* * * void nnf_callback(w, client_data, call_data) * *****************************/ void nnf_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("NNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; transform(f, nnf); } } else user_error("No formulas are currently loaded.\n"); } /* end nnf_callback */ /************************* * * void skolemize_callback(w, client_data, call_data) * *****************************/ void skolemize_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area != B) user_error("Skolemize is done on the entire formula,\nno selections necessary.\n"); else { f = Sel_area->f; transform(f, nnf_skolemize); } } else user_error("No formulas are currently loaded.\n"); } /* end skolemize_callback */ /************************* * * void cnf_callback(w, client_data, call_data) * *****************************/ void cnf_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("CNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; transform(f, nnf_cnf); } } else user_error("No formulas are currently loaded.\n"); } /* end cnf_callback */ /************************* * * void cnf_simp_callback(w, client_data, call_data) * *****************************/ void cnf_simp_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("CNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; Flags[SIMPLIFY_FOL].val = 1; transform(f, rms_cnf); /* nnf_cnf, or rms_cnf for quants */ Flags[SIMPLIFY_FOL].val = 0; } } else user_error("No formulas are currently loaded.\n"); } /* end cnf_simp_callback */ /************************* * * void rms_cnf_callback(w, client_data, call_data) * *****************************/ void rms_cnf_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("RMS CNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; transform(f, rms_cnf); } } else user_error("No formulas are currently loaded.\n"); } /* end rms_cnf_callback */ /************************* * * void rms_dnf_callback(w, client_data, call_data) * *****************************/ void rms_dnf_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("RMS DNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; transform(f, rms_dnf); } } else user_error("No formulas are currently loaded.\n"); } /* end rms_dnf_callback */ /************************* * * void dnf_callback(w, client_data, call_data) * *****************************/ void dnf_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("DNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; transform(f, nnf_dnf); } } else user_error("No formulas are currently loaded.\n"); } /* end dnf_callback */ /************************* * * void dnf_simp_callback(w, client_data, call_data) * *****************************/ void dnf_simp_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type != FORMULA) user_error("DNF requires a formula (or subformula) as a selection.\n"); else { f = Sel_area->f; Flags[SIMPLIFY_FOL].val = 1; transform(f, rms_dnf); /* nnf_dnf, or rms_dnf for quants */ Flags[SIMPLIFY_FOL].val = 0; } } else user_error("No formulas are currently loaded.\n"); } /* end dnf_simp_callback */ /************************* * * void redo_callback(w, client_data, call_data) * *****************************/ void redo_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Crnt_transform->right == NULL) user_error("Nothing more to be redone.\n"); else { Crnt_transform = Crnt_transform->right; display_formula(Crnt_transform); } } else user_error("No formulas are currently loaded.\n"); } /* end redo_callback */ /************************* * * void undo_callback(w, client_data, call_data) * *****************************/ void undo_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Crnt_transform->left == NULL) user_error("Nothing more to be undone.\n"); else { Crnt_transform = Crnt_transform->left; display_formula(Crnt_transform); } } else user_error("No formulas are currently loaded.\n"); } /* end undo_callback */ /************************* * * void expandConj_callback(w, client_data, call_data) * *****************************/ void expandConj_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; XtDestroyWidget(Popup); /* remove the popup with iff options */ f = Sel_area->parent->f; transform(f, iff_to_conj); } /* end expandConj_callback */ /************************* * * void expandDisj_callback(w, client_data, call_data) * *****************************/ void expandDisj_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; XtDestroyWidget(Popup); /* remove the popup with iff options */ f = Sel_area->parent->f; transform(f, iff_to_disj); } /* end expandDisj_callback */ /************************* * * void edit_callback(w, client_data, call_data) * *****************************/ void edit_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; strcpy(Edit_str, "\0"); if (Crnt_formula) { if (Sel_area->type == FORMULA) { /* get the selected area in a string */ f = Sel_area->f; sprint_formula(Edit_str, f); /* create a popup text widget with a replace button */ create_edit_popup(replace_button); } else user_error("Edit requires a formula (or subformula) as a selection.\n"); } else user_error("No formulas are currently loaded.\n"); } /* end edit_callback */ /************************* * * void abbreviate_callback(w, client_data, call_data) * *****************************/ void abbreviate_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; printf("called abbreviate_callback.\n"); } /* abbreviate_callback */ /************************* * * void replace_callback(w, client_data, call_data) * *****************************/ void replace_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { Arg arg[1]; struct formula *f1 = (struct formula *) client_data; XtSetArg(arg[0], XtNstring, &Str); XtGetValues(Edit_text, arg, 1); edit_transform(f1, replace_text); if (!Have_message) XtDestroyWidget(Edit_popup); } /* end replace_callback */ /************************* * * void edit_transform(f, trans_proc, flag) * *****************************/ void edit_transform(f, trans_proc, flag) struct formula *f; struct formula *(*trans_proc)(); int flag; { struct formula *copy, *parent, *prev, *f1, *save_next; struct formula_ptr_2 *p, *q; struct formula_box *sub_box; parent = f->parent; if (parent) { prev = NULL; for (f1 = parent->first_child; f1 != f; f1 = f1->next) prev = f1; } copy = copy_formula(Crnt_transform->f); install_up_pointers(copy); save_next = f->next; f = trans_proc(f, flag); /* f == NULL means failure, so do not update */ if (f != NULL) { f->next = save_next; install_up_pointers(f); if (parent) { /* if not at the top */ if (prev) prev->next = f; else parent->first_child = f; f->parent = parent; } else { Crnt_transform->f = f; f->parent = NULL; } /* free any undone/unedited formulas */ if (Crnt_transform->right) { free_formulas(Crnt_transform->right); Crnt_transform->right = NULL; } else if (Crnt_transform->up) { free_formulas(Crnt_transform->up); Crnt_transform->up = NULL; } p = get_formula_ptr_2(); p->f = Crnt_transform->f; Crnt_transform->up = p; p->down = Crnt_transform; Crnt_transform->f = copy; Crnt_transform = p; display_formula(Crnt_transform); /* now highlight (and select) the transformed subterm */ sub_box = find_sub_box(B, f); if (sub_box && sub_box != B) { Sel_area = sub_box; Highlighted = 1; draw_formula_box_inverted(Sel_area, Sel_area->abs_x_loc, Sel_area->abs_y_loc); } } } /* edit_transform */ /************* * * struct formula *str_2_formula(buf) * *************/ struct formula *str_2_formula(buf) char *buf; { struct term *t; struct formula *f; int i = 0; t = str_to_term(buf, &i, 0); if (t) { skip_white(buf, &i); if (buf[i] != '\0' && buf[i] != '.') { fprintf(stderr, "end of formula not at end of string (missing parentheses?)\n"); zap_term(t); f = NULL; } else { t = term_fixup(t); f = term_to_formula(t); zap_term(t); } } else f = NULL; return(f); } /* str_2_formula */ /************************* * * struct formula *replace_text(f, flag) * *****************************/ struct formula *replace_text(f, flag) struct formula *f; int flag; { f = str_2_formula(Str); /* convert the string to a formula */ if (f == NULL) user_error("Error in converting string to formula.\nSee standard output for more details."); return(f); } /* replace_text */ /************************* * * struct formula *make_deleted(f, flag) * *****************************/ struct formula *make_deleted(f, flag) struct formula *f; int flag; { struct formula *f1, *prev; int i; /* flag is index of subformula to be deleted */ f1 = f->first_child; i = 1; prev = NULL; while (i != flag) { prev = f1; f1 = f1->next; i++; } if (prev) prev->next = f1->next; else f->first_child = f1->next; zap_formula(f1); if (f->first_child && f->first_child->next == NULL) { /* if just one remaining */ f1 = f; f = f->first_child; f->next = f1->next; free_formula(f1); } return(f); } /* make_deleted */ /************************* * * struct formula *join_formulas(f, flag) * *****************************/ struct formula *join_formulas(f, flag) struct formula *f; int flag; { f = str_2_formula(Edit_str); /* convert new string to formula */ if (f == NULL) user_error("Error in converting string to formula.\nSee standard output for more details."); return(f); } /* join_formulas */ /************************* * * struct formula_ptr_2 *find_end(q) * *****************************/ struct formula_ptr_2 *find_end(q) struct formula_ptr_2 *q; { while( q->right || q->up) { if (q->right) q = find_end(q->right); else q = find_end(q->up); } return(q); } /* find_end */ /************************* * * void clear_text_callback(w, client_data, call_data) * *****************************/ void clear_text_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { Arg arg[1]; Widget text = (Widget) client_data; XtSetArg(arg[0], XtNstring, ""); XtSetValues(text, arg, 1); } /* end clear_text_callback */ /************************* * * void conjoin_callback(w, client_data, call_data) * *****************************/ void conjoin_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Sel_area->type == FORMULA) { strcpy(Edit_str, "\0"); /* create a popup text widget with a conjoin button */ create_edit_popup(conjoin_button); } else user_error("Conjoin requires a formula (or subformula)\nas a selection.\n"); } else user_error("No formulas are currently loaded.\n"); } /* end conjoin_callback */ /************************* * * void conjoin_with_callback(w, client_data, call_data) * *****************************/ void conjoin_with_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { char temp_str[TEXT_LENGTH]; int i; Arg arg[1]; /* build a string consisting of "( Sel_area & New_text )" */ strcpy(Edit_str, "("); i = sprint_formula(temp_str, Sel_area->f); strcat(Edit_str, temp_str); strcat(Edit_str, " & "); XtSetArg(arg[0], XtNstring, &Str); XtGetValues(Edit_text, arg, 1); strcat(Edit_str, Str); strcat(Edit_str, ")"); edit_transform(Sel_area->f, join_formulas, 0); /* if no message, conjoin was successful, destroy popup */ /* o.w. leave it for possible correction */ if (!Have_message) XtDestroyWidget(Edit_popup); } /* end conjoin_with_callback */ /************************* * * void disjoin_callback(w, client_data, call_data) * *****************************/ void disjoin_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Sel_area->type == FORMULA) { strcpy(Edit_str, "\0"); /* create a popup text widget with a disjoin button */ create_edit_popup(disjoin_button); } else user_error("Disjoin requires a formula (or subformula)\nas a selection.\n"); } else user_error("No formulas are currently loaded.\n"); } /* end disjoin_callback */ /************************* * * void disjoin_with_callback(w, client_data, call_data) * *****************************/ void disjoin_with_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { char temp_str[TEXT_LENGTH]; int i; Arg arg[1]; /* build a string consisting of "( Sel_area | New_text )" */ strcpy(Edit_str, "("); i = sprint_formula(temp_str, Sel_area->f); strcat(Edit_str, temp_str); strcat(Edit_str, " | "); XtSetArg(arg[0], XtNstring, &Str); XtGetValues(Edit_text, arg, 1); strcat(Edit_str, Str); strcat(Edit_str, ")"); edit_transform(Sel_area->f, join_formulas, 0); /* if no message, disjoin was successful, destroy popup */ /* o.w. leave it for possible correction */ if (!Have_message) XtDestroyWidget(Edit_popup); } /* end disjoin_with_callback */ /************************* * * void quantify_callback(w, client_data, call_data) * *****************************/ void quantify_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Sel_area->type == FORMULA) { strcpy(Edit_str, "\0"); /* create a popup text widget with an add_quantifiers button */ create_edit_popup(add_quantifiers_button); } else user_error("Quantify requires a formula (or subformula)\nas a selection.\n"); } else user_error("No formulas are currently loaded.\n"); } /* end quantify_callback */ /************************* * * void add_quantify_callback(w, client_data, call_data) * *****************************/ void add_quantify_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { char temp_str[TEXT_LENGTH]; int i; Arg arg[1]; /* build a string consisting of "(New_quantifiers Sel_area)" */ strcpy(Edit_str, "("); XtSetArg(arg[0], XtNstring, &Str); XtGetValues(Edit_text, arg, 1); strcat(Edit_str, Str); strcat(Edit_str, " "); i = sprint_formula(temp_str, Sel_area->f); strcat(Edit_str, temp_str); strcat(Edit_str, ")"); edit_transform(Sel_area->f, join_formulas, 0); /* if no message, quantification was successful, destroy popup */ /* o.w. leave it for possible correction */ if (!Have_message) XtDestroyWidget(Edit_popup); } /* end add_quantify_callback */ /************************* * * void negate_callback(w, client_data, call_data) * *****************************/ void negate_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; if (Crnt_formula) { if (Sel_area->type == FORMULA) { f = Sel_area->f; /* negate the formula (or subformula) and place in list */ edit_transform(f, negate_formula, 0); } else user_error("Negate requires a formula (or subformula)\nas a selection.\n"); } else user_error("No formulas are currently loaded.\n"); } /* end negate_callback */ /************************* * * void new_formula_callback(w, client_data, call_data) * *****************************/ void new_formula_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { strcpy(Edit_str, "\0"); /* create a popup text widget with an insert button */ create_edit_popup(insert_button); } /* end new_formula_callback */ /************************* * * void insert_formula_callback(w, client_data, call_data) * *****************************/ void insert_formula_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula *f; struct formula_ptr_2 *q; int i; Arg arg[1]; XtSetArg(arg[0], XtNstring, &Str); XtGetValues(Edit_text, arg, 1); f = str_2_formula(Str); /* convert string to formula form */ if (f) { /* setup in a formula list node */ install_up_pointers(f); f->parent = NULL; q = get_formula_ptr_2(); q->f = f; /* insert into formula list after current formula */ if (Crnt_formula) { q->next = Crnt_formula->next; Crnt_formula->next = q; } else Top_formula = q; if (q->next) q->next->prev = q; q->prev = Crnt_formula; Crnt_formula = q; Crnt_transform = q; XtDestroyWidget(Edit_popup); display_formula(Crnt_transform); } else user_error("Error in converting string to formula.\nSee standard output for more details."); } /* end insert_formula_callback */ /************************* * * void delete_formula_callback(w, client_data, call_data) * *****************************/ void delete_formula_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { struct formula_ptr_2 *p; struct formula *f, *f1; int i; if (Crnt_formula) { if (Sel_area == B) { if (Crnt_formula == Crnt_transform) { p = Crnt_formula; /* hold for freeing nodes */ /* remove formula from list */ if (Crnt_formula->prev) Crnt_formula->prev->next = Crnt_formula->next; else Top_formula = Crnt_formula->next; if (Crnt_formula->next) { Crnt_formula->next->prev = Crnt_formula->prev; Crnt_formula = Crnt_formula->next; } else Crnt_formula = Crnt_formula->prev; Crnt_transform = Crnt_formula; if (Top_formula == NULL) { XClearWindow(Dpy,Win); user_error("Empty formula list.\n"); } else display_formula(Crnt_transform); free_formulas(p); /* kill all the transformations of the */ /* deleted formula */ } else user_error("Delete formula removes from the original formula list,\nnot from the edit/logic transformed formulas."); } else if (Sel_area->type == OPERATOR) user_error("Delete formula cannot delete an operator."); else if (Sel_area->parent->subtype != AND_FORM && Sel_area->parent->subtype != OR_FORM) user_error("Deletion of a subformula must be from a\nconjunction or a disjunction."); else { f = Sel_area->parent->f; /* t is AND or OR */ /* find index of subformula to be deleted, and send that in */ i = 1; for (f1 = f->first_child; f1 != Sel_area->f; f1 = f1->next) i++; edit_transform(f, make_deleted, i); } } else user_error("No formulas are currently loaded."); } /* end delete_formula_callback */ /************************* * * void unedit_callback(w, client_data, call_data) * *****************************/ void unedit_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Crnt_transform->down == NULL) user_error("Nothing more to be un-edited.\n"); else { Crnt_transform = Crnt_transform->down; display_formula(Crnt_transform); } } else user_error("No formulas are currently loaded.\n"); } /* end unedit_callback */ /************************* * * void reedit_callback(w, client_data, call_data) * *****************************/ void reedit_callback(w,client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { if (Crnt_formula) { if (Crnt_transform->up == NULL) user_error("Nothing more to be re-edited.\n"); else { Crnt_transform = Crnt_transform->up; display_formula(Crnt_transform); } } else user_error("No formulas are currently loaded.\n"); } /* end reedit_callback */ /************************* * * void font_menu_callback(w, client_data, call_data) * *****************************/ void font_menu_callback(w, client_data, call_data) Widget w; XtPointer client_data; XtPointer call_data; { Widget font_form, smallfont, medfont, largefont, cancel; int n; Arg arg[10]; create_menu_popup("fonts", w); /* create the popup shell */ n = 0; XtSetArg(arg[n], XtNbackground, Background); n++; font_form = XtCreateManagedWidget("font_form", formWidgetClass, Popup, arg, n); /* command buttons */ /* small font */ n = 0; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, SMALLFONT));n++; XtSetArg(arg[n], XtNlabel, "Small");n++; smallfont = XtCreateManagedWidget("smallfont",commandWidgetClass, font_form,arg,n); XtAddCallback(smallfont, XtNcallback, font_callback, SMALLFONT); /* medium font */ n = 0; XtSetArg(arg[n], XtNfromVert, smallfont); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, MEDFONT));n++; XtSetArg(arg[n], XtNlabel, "Medium");n++; medfont = XtCreateManagedWidget("medfont", commandWidgetClass, font_form, arg, n); XtAddCallback(medfont, XtNcallback, font_callback, MEDFONT); /* large font */ n = 0; XtSetArg(arg[n], XtNfromVert, medfont); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LARGEFONT));n++; XtSetArg(arg[n], XtNlabel, "Large");n++; largefont = XtCreateManagedWidget("largefont", commandWidgetClass, font_form, arg, n); XtAddCallback(largefont, XtNcallback, font_callback, LARGEFONT); /* cancel */ n = 0; XtSetArg(arg[n], XtNfromVert,largefont); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Cancel"); n++; cancel = XtCreateManagedWidget("cancel",commandWidgetClass, font_form, arg, n); XtAddCallback(cancel, XtNcallback, destroy_popup, Popup); XtPopup(Popup, XtGrabNone); } /* font_menu_callback */ /************************* * * void create_menu_popup(name, parent) * *****************************/ void create_menu_popup(name, parent) char name[]; Widget parent; { Dimension width, height; Position x, y; int n; Arg arg[5]; n = 0; XtSetArg(arg[n], XtNwidth, &width); n++; XtSetArg(arg[n], XtNheight, &height); n++; XtGetValues(parent, arg, n); XtTranslateCoords(parent, (Position) (width/2), (Position) (height/2), &x, &y); n = 0; XtSetArg(arg[n], XtNx, x); n++; XtSetArg(arg[n], XtNy, y); n++; XtSetArg(arg[n], XtNborderWidth, 1);n++; Popup = XtCreatePopupShell(name,transientShellWidgetClass, Outline, arg,n); } /* create_menu_popup */ /************************* * * void create_edit_popup(create_text_op_button) * *****************************/ void create_edit_popup(create_text_op_button) Widget (*create_text_op_button)(); { Dimension width, height; Position x,y; int n; Arg arg[15]; Widget edit_form, text_op_button, clear_text, cancel_edit; /* create the shell */ n = 0; XtSetArg(arg[n], XtNwidth, &width); n++; XtSetArg(arg[n], XtNheight, &height); n++; XtGetValues(Outline, arg, n); XtTranslateCoords(Outline, (Position)((width/2)-200), (Position)(height/2), &x, &y); n = 0; XtSetArg(arg[n], XtNx, x); n++; XtSetArg(arg[n], XtNy, y); n++; Edit_popup = XtCreatePopupShell("Edit_popup", transientShellWidgetClass, Outline, arg, n); /* form widget to hold the buttons & text */ n = 0; XtSetArg(arg[n], XtNbackground, Foreground); n++; XtSetArg(arg[n], XtNforeground, Foreground); n++; edit_form = XtCreateManagedWidget("edit_form",formWidgetClass, Edit_popup, arg, n); /* text_op_button */ text_op_button = create_text_op_button(edit_form); /* clear text button */ n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfromVert, text_op_button); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Clear"); n++; clear_text = XtCreateManagedWidget("clear_text", commandWidgetClass, edit_form, arg, n); /* cancel button */ n = 0; XtSetArg(arg[n], XtNfromVert, clear_text); n++; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Cancel"); n++; cancel_edit = XtCreateManagedWidget("cancel", commandWidgetClass, edit_form, arg, n); XtAddCallback(cancel_edit, XtNcallback, destroy_popup, Edit_popup); /* text widget */ n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfromHoriz, text_op_button); n++; XtSetArg(arg[n], XtNforeground, Foreground); n++; XtSetArg(arg[n], XtNeditType, XawtextEdit); n++; XtSetArg(arg[n], XtNscrollVertical, XawtextScrollWhenNeeded); n++; XtSetArg(arg[n], XtNautoFill, True); n++; XtSetArg(arg[n], XtNheight, 150); n++; XtSetArg(arg[n], XtNwidth, 300); n++; XtSetArg(arg[n], XtNwrap, XawtextWrapWord); n++; XtSetArg(arg[n], XtNstring, Edit_str); n++; Edit_text = XtCreateManagedWidget("edit_text", asciiTextWidgetClass, edit_form, arg, n); XtAddCallback(clear_text, XtNcallback, clear_text_callback, (XtPointer) Edit_text); XtPopup(Edit_popup, XtGrabNone); } /* create_edit_popup */ /************************* * * Widget replace_button(parent) * *****************************/ Widget replace_button(parent) Widget parent; { Widget button; int n; Arg arg[5]; n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Replace"); n++; button = XtCreateManagedWidget("replace", commandWidgetClass, parent, arg, n); XtAddCallback(button, XtNcallback, replace_callback, (XtPointer)(Sel_area->f)); return(button); } /* replace_button */ /************************* * * Widget conjoin_button(parent) * *****************************/ Widget conjoin_button(parent) Widget parent; { Widget button; int n; Arg arg[5]; n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Conjoin with"); n++; button = XtCreateManagedWidget("conjoin_with", commandWidgetClass, parent, arg, n); XtAddCallback(button, XtNcallback, conjoin_with_callback, NULL); return(button); } /* conjoin_button */ /************************* * * Widget disjoin_button(parent) * *****************************/ Widget disjoin_button(parent) Widget parent; { Widget button; int n; Arg arg[5]; n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Disjoin with"); n++; button = XtCreateManagedWidget("disjoin_with", commandWidgetClass, parent, arg, n); XtAddCallback(button, XtNcallback, disjoin_with_callback, NULL); return(button); } /* disjoin_button */ /************************* * * Widget add_quantifiers_button(parent) * *****************************/ Widget add_quantifiers_button(parent) Widget parent; { Widget button; int n; Arg arg[5]; n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, " Add\nQuantifiers"); n++; button = XtCreateManagedWidget("add_quantifiers", commandWidgetClass, parent, arg, n); XtAddCallback(button, XtNcallback, add_quantify_callback, NULL); return(button); } /* add_quantifiers_button */ /************************* * * Widget insert_button(parent) * *****************************/ Widget insert_button(parent) Widget parent; { Widget button; int n; Arg arg[5]; n = 0; XtSetArg(arg[n], XtNhighlightThickness, 0); n++; XtSetArg(arg[n], XtNfont, XLoadQueryFont(Dpy, LABELFONT)); n++; XtSetArg(arg[n], XtNlabel, "Insert"); n++; button = XtCreateManagedWidget("insert", commandWidgetClass, parent, arg, n); XtAddCallback(button, XtNcallback, insert_formula_callback, NULL); return(button); } /* insert_button */ otter-3.3f/source/formed/formed.in0100644000076400007640000001074006407523271016571 0ustar mccunemccune% Andrews challenge -( ( (exists x (all y (p(x) <-> p(y)))) <-> ((exists u q(u)) <-> (all v p(v))) ) <-> ( (exists w (all z (q(z) <-> q(w)))) <-> ((exists x1 p(x1)) <-> (all x2 q(x2))) ) ). % Lifschitz problem -(exists x exists x1 all y exists z exists z1 ( ( -p(y,y) | p(x,x) | -s(z,x) ) & ( s(x,y) | -s(y,z) | q(z1,z1) ) & ( q(x1,y) | -q(y,z1) | s(x1,x1) ) )). % From the Steamroller (all x (Animal(x) -> ( (all y (Plant(y) -> Eats(x,y))) | (all z (( Animal(z) & Smaller(z,x) & (exists u (Plant(u) & Eats(z,u)))) -> Eats(x,z)))))). -(exists x exists y ( -$answer(Eats(x,y)) & Animal(x) & Animal(y) & Eats(x,y) & (all z (Grain(z) -> Eats(y,z))))). % from open house problems. -( ( ( (p1 -> (p2 | p3)) & (-p1 -> (p3 | p4)) ) & ( ( (p3 -> -p6) & (-p3 -> (p4 -> p1)) ) & ( -(p2 & p5) & (p2 -> p5) ) ) ) -> -(p3 -> p6) ). % From O'Keef's induction problem (all X (list(X) <-> ( (X = []) | (exists Y exists Z ((X = [Y|Z]) & list(Z))) ))). ( ( (all Y (list(Y) -> list(append([], Y)))) & (all X ( (list(X) & (all Y (list(Y) -> list(append(X,Y))))) -> (all Z (all Y (list(Y) -> list(append([Z|X],Y))))) ) ) ) -> (all X (list(X) -> (all Y (list(Y) -> list(append(X,Y)))))) ). % Induction formulas for associativity of append. ( (all x ( (all y (LT(y,x) -> (all u all v (app(app(y,u),v) = app(y,app(u,v)))) )) -> (all u all v (app(app(x,u),v) = app(x,app(u,v)))))) -> (all x all y all z (app(app(x,y),z) = app(x,app(y,z))))). ( ( (all y all z (app(app([],y),z) = app([],app(y,z)))) & (all x ( (all y all z (app(app(x,y),z) = app(x,app(y,z)))) -> (all u all y all z (app(app([u|x],y),z) = app([u|x],app(y,z)) ))))) -> (all x all y all z (app(app(x,y),z) = app(x,app(y,z))))). % Upper bound induction formula ( ( (exists z all y (mem(y,[]) -> ge(z,y))) & (all x ( (exists z all y (mem(y,x) -> ge(z,y))) -> (all u (exists z (-$Ans(z) & (all y (mem(y,[u|x]) -> ge(z,y)) )))) ) ) ) -> (all x exists z all y (mem(y,x) -> ge(z,y))) ). % set theory formulas from skolem experiments. (all R (SINGVAL(R) <-> (all u all v all w ((EL(op(u,v),R) & EL(op(u,w),R)) -> (v = w))))). (all F (FUNCTION(F) <-> (RELATION(F) & SINGVAL(F)))). (all z all F all G (EL(z,compose(F,G)) <-> (exists u exists v exists w ((z = op( u,w)) & EL(op(u,v),F) & EL(op(v,w),G))))). (all R (RELATION(R) <-> (all u (EL(u,R) -> (exists x exists y (u = op(x,y))))))) . % From ~swinker/proj/ar/yu/homom.clauses (all G (Group_op(G) <-> ((all x all y ((Member(x,G) & Member(y,G)) -> Member(op(x,y),G))) & (all x all y all z ((Member(x,G) & Member(y,G) & Member(z,G)) -> (op(op(x,y),z) = op(x,op(y,z))))) & (exists e (Member(e,G) & (all x (Member(x,G) -> ((op(e,x) = x) & (op(x,e) = x) & (exists y (Member(y,G) & (op(y,x) = e) & (op(x,y) = e))))))))))). (all X all Y (SUBSET(X,Y) <-> (all Z (MEMBER(Z,X) -> MEMBER(Z,Y))))). (all G all H (SUBGROUP_OP(G,H) <-> (GROUP_OP(G) & GROUP_OP(H) & SUBSET(G,H)))). (all N all G (NORMAL_SUBGROUP_OP(N,G) <-> (SUBGROUP_OP(N,G) & (all X all Y ((MEMBER(X,N) & MEMBER(Y,G)) -> MEMBER(OP(OP(Y,X),inv(Y,e(G),G)),N)))))). (all G all H (HOMO_PHI(G,H) <-> (all X all Y ((MEMBER(X,G) & MEMBER(Y,G)) -> (MEMBER(PHI(X),H) & MEMBER(PHI(Y),H) & EQUAL(PHI(OP(X,Y)),OP1(PHI(X),PHI(Y)))))))). (all X all G all Y (MEMBER(X,phi_inv(G,Y)) <-> (MEMBER(X,G) & EQUAL(phi(X),Y)))). (all G all H ((HOMO_PHI(G,H) & GROUP_OP(G) & GROUP_OP1(H)) -> EQUAL(ker_phi(G,H),phi_inv(G,e1(H))))). (all G all H ((HOMO_PHI(G,H) & GROUP_OP(G) & GROUP_OP1(H)) -> (SUBSET(ker_phi(G,H),phi_inv(G,e1(H))) & SUBSET(phi_inv(G,e1(H)),ker_phi(G,H))))). (all G all H ((GROUP_OP(G) & GROUP_OP1(H) & HOMO_PHI(G,H)) -> NORMAL_SUBGROUP_OP(phi_inv(G,e1(H)),G))). otter-3.3f/source/formed/callback.o0100644000076400007640000011515407710023425016700 0ustar mccunemccuneELF\4( U‰åSƒì»¡ƒøt:ƒø …Àt ëBvƒøtë8ƒì ÿ5èüÿÿÿë$ƒì hÀèüÿÿÿ»ëƒìj ÿ5èüÿÿÿƒÄ…Ûuƒìj ÿ5èüÿÿÿǃċ]üÉÃvU‰åSƒì»¡ƒøt&ƒø …Àt ëBvƒøt'ë8ƒì ÿ5èüÿÿÿë$ƒì hàèüÿÿÿ»ëƒìj ÿ5èüÿÿÿƒÄ…Ûuƒìj ÿ5èüÿÿÿǃċ]üÉÃvU‰åƒìƒ=t=¡ƒxuƒxu ƒì hÛë*‰öƒì ÿ5èüÿÿÿ£‰$èüÿÿÿëvƒì hèüÿÿÿƒÄÉÉöU‰åƒìƒ=t¡£ƒì Pèüÿÿÿë ƒì hèüÿÿÿƒÄÉÉöU‰åƒìƒ=t9¡ƒxt"‹@£ƒì Pèüÿÿÿ£‰$èüÿÿÿë‰öƒì hùë ‰öƒì hèüÿÿÿƒÄÉÉöU‰åƒìƒ=t9¡ƒxt"‹@£ƒì Pèüÿÿÿ£‰$èüÿÿÿë‰öƒì hë ‰öƒì hèüÿÿÿƒÄÉÉöU‰åSƒì‹] ÿ5èüÿÿÿ‰$èüÿÿÿƒÄƒ=tƒì ÿ5èüÿÿÿƒÄ‹]üÉÃU‰åƒìÿ5èüÿÿÿÇ$èüÿÿÿvU‰åVSƒìXÿuh+èüÿÿÿ]¨ÇE¨4¡‰E¬Ç$Sÿ5ÿ5h0èüÿÿÿ‰ÆÇE¨ÇƒÄh@ÿ5èüÿÿÿ‰E¬ÇE°­ÇE´?Ç$SVÿ5hOèüÿÿÿ£ƒÄ PhhˆPèüÿÿÿÇE¨Y¡‰E¬ÇE°ÇƒÄh@ÿ5èüÿÿÿ‰E´ÇE¸­ÇE¼bÇ$SVÿ5htèüÿÿÿ£ƒÄ PhhˆPèüÿÿÿÇE¨Y¡‰E¬ÇE°ÇƒÄh@ÿ5èüÿÿÿ‰E´ÇE¸­ÇE¼~Ç$SVÿ5h‘èüÿÿÿ£ƒÄ PhhˆPèüÿÿÿÇE¨Y¡‰E¬ÇE°ÇƒÄh@ÿ5èüÿÿÿ‰E´ÇE¸­ÇE¼œÇ$SVÿ5h´èüÿÿÿ£ƒÄ PhhˆPèüÿÿÿÇE¨Y¡‰E¬ÇE°ÇƒÄh@ÿ5èüÿÿÿ‰E´ÇE¸­ÇE¼ÉÇ$SVÿ5háèüÿÿÿ£ƒÄ 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jhhˆSèüÿÿÿ‰Øeø[^]ÃvU‰åVSƒì8‹u]ÈÇEÈ4ÇEÌÇEÐÇh@ÿ5èüÿÿÿ‰EÔÇEØ­ÇEܾÇ$SVÿ5hÓèüÿÿÿ‰ÃƒÄ jhhˆSèüÿÿÿ‰Øeø[^]ÃvU‰åVSƒì8‹u]ÈÇEÈ4ÇEÌÇEÐÇh@ÿ5èüÿÿÿ‰EÔÇEØ­ÇEÜãÇ$SVÿ5hêèüÿÿÿ‰ÃƒÄ jhhˆSèüÿÿÿ‰Øeø[^]ÃvÀÀ`` 0 0øø0 0 ``ÀÀ€€  üü˜˜ðð``B~$$À```@ÀÀà033 &  ø7ð3pXX00h̆††Æ|R"\þþøøþþþþøøþþ~@@@|@@@~ 0þÿÿþ 0ÿÿ$BÿB$8ÿÿÿÿ8ÿÿ @ÿ@ ÿÿÿÿÀÀÀÀÿÿ ÿ€€ÀÀ`` 0 00 0 ``ÀÀ€€    ˜˜ðð``BB$$  JB:1*‰}sofbYTOÑƽ´¯¦¡œ—’ How to use Help To use the help facility, click on a set of information from the menu panel. A window will appear containing information on that topic. The Edit, Logic, and Formula Control help topics also contain subtopics which may be clicked on for more specific information. You must return to the help menu and click on Cancel to exit the help facility. Selecting Formula Areas For some operations, a part of the displayed formula may be selected on which to operate. Simply clicking in the formula display area will cause an area, corresponding to the location of the mouse, to be "highlighted". To unselect an area, simply click again in the same area. If no area is highlighted, the default selected area is the entire formula and subsequent operations will act on the entire formula. @@@à€À`@ `@À  `   @À € ÀÀ€@01.01UneditRe-editDelete formulaNew formulaNegateQuantifyDisjoinConjoinEditUndoRedoDNF simpDNFCNF simpCNFSkolemizeNNFOperateClausifyQuitFontLoadSavePreviousNextUndo AllRedo AllLogic MenuEdit MenuNothing exists to be redone. End of formula list. Beginning of formula list. Helphelp_menu_formHow to use Helphelp_infofromVertEdit Menu Buttonsedit_helpLogic Menu Buttonslogic_helpFormula Control Buttonsformula_control_helpSelecting Formula Areasselect_area_helpCancelcancelHelp_popuphelp_formhelp_labelReturn to Help Menuhelp_returndefaultColumnslisthelp_list wrapdisplayCarethelp_textload_formFilename:load_labelfile_textLoad fileload_filefromHorizFile loaded. rError: Cannot open . save_formsave_labelSave filesave_fileFile saved. wError: cannot open Iff_opiff_formTo Conjto_conjTo Disjto_disjNothing more to be redone. Nothing more to be undone. called abbreviate_callback. ( & ) | Empty formula list. fontsfont_formSmallsmallfontMediummedfontLargelargefontEdit_popupedit_formhighlightThicknessClearclear_textscrollVerticalautoFilledit_textReplacereplaceConjoin withconjoin_withDisjoin withdisjoin_with Add Quantifiersadd_quantifiersInsertinsert Unedit Use: To undo an edit transformation that has already been done to a formula. Results: The un-edited formula is displayed, and it becomes the current formula. Re-edit Use: To redo an edit transformation that has already been done to a formula. Results: The re-edited formula is displayed, and it becomes the current formula. Delete formula Use: To remove the currently displayed formula from the current list of formulas or to delete a subformula from a conjunction or a disjunction. Results: If the entire formula is selected, it is deleted. If an immediate subformula of a conjunction or a disjunction is selected, that subformula is deleted form the formula. New formula Use: To add a new formula to the current list of formulas. Results: A window in which the text may be edited (Emacs style), containing buttons for insertion of the formula, clearing the text, and cancelling the command appears. The formula is inserted after the current formula and will then be displayed. Negate Use: To negate selected text from the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: After negation the new formula will be displayed. Quantify Use: To quantify selected text from the displayed formula. Input format: [all var_name] or [exists var_name] Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the quantifiers may be edited (Emacs style), containing buttons for adding the quantifiers, clearing of the text, and cancelling of the command appears. After adding the quantifiers, the new formula will be displayed. Disjoin Use: To disjoin text with selected text from the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the text may be edited (Emacs style), containing buttons for disjoining the new text with the selected area, clearing of the text, and cancelling of the command appears. After disjoining of the two, the new formula will be displayed. Conjoin Use: To conjoin text with selected text from the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the text may be edited (Emacs style), containing buttons for conjoining the new text with the selected area, clearing of the text, and cancelling of the command appears. After conjoining the two, the new formula will be displayed. Edit Use: To replace selected text in the displayed formula. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: A window in which the text may be edited (Emacs style), containing buttons for replacement of the text, clearing of the text, and cancelling of the command appears. After replacement, the new formula will be displayed. Undo Use: To undo a logic transformation that has already been done to a formula. Results: The undone formula is displayed, and it becomes the current formula. Redo Use: To redo a logic transformation that has already been done to a formula. Results: The re-done formula is displayed, and it becomes the current formula. DNF simp Use: To transform the selected area to its disjunctive normal form with any simplifications that can be made done (i.e. (p | -p) simplifies to True). Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in disjunctive normal form (simplified) is displayed. DNF Use: To transform the selected area to its disjunctive normal form. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in disjunctive normal form is displayed. CNF simp Use: To transform the selected area to its conjunctive normal form with any simplifications that can be made done (i.e. (p | -p) simplifies to True). Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in conjunctive normal form (simplified) is displayed. CNF Use: To transform the selected area to its conjunctive normal form. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in conjunctive normal form is displayed. Skolemize Use: To skolemize the displayed formula. Selection requirements: Operates on entire formula, no selections should be made. Results: The skolemized formula is displayed. NNF Use: To transform the selected area to its negation normal form. Selection requirements: Any piece of the formula may be selected, provided it contains more than just an operator. Results: The formula with its selected area in negation normal form is displayed. Operate Use: To expand the implicational and biconditional operators, and move negations inward. Selection requirements: An implicational, biconditional, or negation operator must be selected. Results: The transformed formula (wrt the operator selected) is displayed. Clausify Use: To completely clausify the displayed formula. Selection requirements: Operates on entire formula, no selections should be made. Results: The clausified formula is displayed. Quit Use: To exit the formula editor. Font Use: To change the font being used in the display. Load Use: To load a list of formulas from a specified file. Save Use: To save the current list of formulas in a specified file. The current state of the formula (after all edit & logic transformations) is the version saved. Previous Use: To display the previous formula in the list of formulas. Next Use: To display the next formula in the list of formulas. Undo All Use: To completely undo the edit and logic transformations that have been done to the current formula, i.e. display the original formula. Redo All Use: To completely redo the edit and logic transformations that have been done to the current formula and display that formula. Logic Menu Use: Brings up a set of buttons for logic transformations to the current formula in the left panel. Edit Menu Use: Brings up a set of buttons for edit-type transformations to the current formula in the left panel.Edit panel already displayed. Logic panel already displayed. No formulas are currently loaded. -*-helvetica-*-r-*-*-*-120-*-*-*-*-*-*Clausify is done on the entire formula, no selections necessary. WARNING: further logic transformations may be unsound, becuase universal quantifiers are gone. Operate requires selection of an operator (not, imp, iff). Operate requires selection of not, imp, or iff operators.NNF requires a formula (or subformula) as a selection. Skolemize is done on the entire formula, no selections necessary. CNF requires a formula (or subformula) as a selection. RMS CNF requires a formula (or subformula) as a selection. RMS DNF requires a formula (or subformula) as a selection. DNF requires a formula (or subformula) as a selection. Edit requires a formula (or subformula) as a selection. end of formula not at end of string (missing parentheses?) Error in converting string to formula. See standard output for more details.Conjoin requires a formula (or subformula) as a selection. Disjoin requires a formula (or subformula) as a selection. Quantify requires a formula (or subformula) as a selection. Negate requires a formula (or subformula) as a selection. Delete formula removes from the original formula list, not from the edit/logic transformed formulas.Delete formula cannot delete an operator.Deletion of a subformula must be from a conjunction or a disjunction.No formulas are currently loaded.Nothing more to be un-edited. Nothing more to be re-edited. -*-helvetica-medium-r-*-*-*-100-*-*-*-*-*-*-*-helvetica-*-r-*-*-*-140-*-*-*-*-*-*-*-helvetica-*-r-*-*-*-240-*-*-*-*-*-*GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110).symtab.strtab.shstrtab.rel.text.rel.data.bss.note.rodata.str1.1.rodata.str1.32.rodata.comment4@, „u# )€,  % œ˜Ð / 24 2:2´2ñI2À7 # Y`[ab[7™[j4^° ! äjž ñÿ  ' 38?@ K`Wxc€$r¤À Ë œë¨´  À+ÌCØK äkðƒü‹ «ÃË  *Ð(:ø,K$,f`luඋ˜(šÀ,ªì,ĉ×èõ1>OŒ‰c^vƒ4Œ›«x6¾°ZÌ ZÞh?ìò ¨",1ÈÜ?&¥Q[fvŒŸ²¼¤ªÏÝçò° --5AIUg”Ÿª»P áÌÕÜì4 züà û)3Ü ŒAJhE\hv|‰—©»Ïàîöý°  Ð`½+ Z=FHXb|8sƒŽ.¢0.¶´NÃÇRÚèXNõý¨b N.\N?G¬NT\übn`N|°NŠ–¢`^°¹È¼)ƒ×¼&éÀýÔY#8200h?LWdr‹¥˜ž³¿ÊÑÚåõlt   à1) H%= pNN @*}] ÀÍs N„ À*}“ àÍ© °N» @+}Ò Íè Ð Nø  ! 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‹›Œ…Ût…ÀtÔ…Àu‹Eeô[^_]ÃU‰åVS‹u‹^…Ût‰3ƒì SèüÿÿÿƒÄ‹[…Ûuëeø[^]ÃU‰åVS‹u‹†ˆ…Àt‰ö‹˜Œƒì Pèüÿÿÿ‰ØƒÄ…Àuèƒì Vèüÿÿÿeø[^]ÃU‰åWVSƒì ‹]‹3…öt¿‹F9Øt ‰ö‰Ç‹G9Øu÷ƒì ¡ÿ0èüÿÿÿ‰Eð‰$èüÿÿÿ‰$ÿU ‰Ã‰$èüÿÿÿƒÄ…öt…ÿt‰_ë‰^‰3롉ǃìÿuð¡ÿ0èüÿÿÿƒÄ…Àtƒì h èüÿÿÿƒÄÿuðèüÿÿÿéÆ¡ƒxtƒì ÿpèüÿÿÿ¡Ç@ë"¡ƒxtƒì ÿpèüÿÿÿ¡Ç@ƒÄèüÿÿÿ‹‹‰‹‰B‹‰P ‹‹Mð‰ £ƒì PèüÿÿÿƒÄSÿ5èüÿÿÿƒÄ…Àt/;t'£Çƒìÿ°„ÿ°€PèüÿÿÿƒÄeô[^_]ÃU‰åVS‹U‹u ‰Ð9rt-‹šˆ¸…ÛtvƒìVSèüÿÿÿƒÄ‹›Œ…Ût…Àtåeø[^]ÉöU‰åVS‹]…Ût,‰Þƒ{t‹[ëv‹[ƒì ÿ6èüÿÿÿ‰4$èüÿÿÿƒÄ…ÛuÔeø[^]ÃÀÀ`` 0 0øø0 0 ``ÀÀ€€  üü˜˜ðð``B~$$À```@ÀÀà033 &  ø7ð3pXX00h̆††Æ|R"\þþøøþþþþøøþþ~@@@|@@@~ 0þÿÿþ 0ÿÿ$BÿB$8ÿÿÿÿ8ÿÿ @ÿ@ ÿÿÿÿÀÀÀÀÿÿ ÿ€€ÀÀ`` 0 00 0 ``ÀÀ€€    ˜˜ðð``BB$$  01.01Ì ä ü L8$p|ˆ” ¬¸0`HðÀ˜Äðt H-fbl Error: Illegal option.%d(nil)[]= != = TRUEFALSE(all exists ) & | -> <-> *** STRING TOO LONG *** Usage: xform2 [-f color] [-b color] [-l filename] arrange_box_symbol: unknown operator. arrange_box: unknown operator. draw_formula_box: unknown operator. draw_inverted_operators: unknown operator. That transformation wouldn't do anything. GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110).symtab.strtab.shstrtab.rel.text.data.bss.note.rel.rodata.rodata.str1.1.rodata.str1.32.comment40 ì:x %dÐ+404:P6 dEà B2à~Q2`` aÀ7÷j”"0 . 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Z4 U: V? WT [] Pf So Pw S€ Q… P P¢ \¨ SØ UÞ Xä Vé Yò Tø Uþ V W Z U V ]( [1 Z7 U= VB WK TQ UW V\ ]g ^{ O Q Q’ _¢ `§ Q° X¶ V» aÈ QÍ [Ò Q× PÝ S c. cK co cÜ cè c c co c{ c° c¸ cø dB H e_ D f„ gŒ h© dÇ Í iÕ jå kí lý mnop%q-r9sAtMuUvfkwpeww|xœdäêeÿDf$g,hMd™fžg©hÍ`1bUd–f›g£h½`îbd:`]byd¥`bdI`¥bÁd`EbjÊÏwÔeÛwàxìF+9j?iIUOXUyilokyUX…z™nŸm©U¯Xµ{ÉpÏoÙUßXå|ùrÿq UX}%v+u5U;XA~QtWsaUgXmsVx€Šw”e›w xÖàUæXìVñ‚UX#V(ƒN[“Ÿj¥i¯UµX»„ËlÑkÛUáXç…÷nýmU X†#p)o3U9X?‡OrUq_UeXkˆ{vu‹U‘X—‰§t­s·U½XÊÉV΀Þãwèeïwôx!^›R׋ _ŒU3\Žg‹w‹•3¨3¯¾ÃxÎÙ3ê‘ï3ý3‘3"’(323;3D3N3W<aQf“sQzP€S™\Ò“” $(048<@DHPTX\`dhptx|€„ˆotter-3.3f/source/formed/README0100644000076400007640000000262207707037415015651 0ustar mccunemccuneFormEd 0.9 NOTE (July 21, 2003): This compiles and runs in our Linux environment, RedHat 7.3. I haven't tested it recently in other environments. FormEd is a formula editor for first-order logic formulas. It's not connected to Otter, but it's lots of fun to play with. The primary documentation is on-line with the "Help" button. It is described in ``FormEd: An X Window System Application for Managing First-Order Formulas'', by Tamara Henry and William McCune. That report is not available electronically, but I can send a hard copy if you like. To make FormEd, first make sure that ../libotter.a exists, then (in this directory) % make formed If you get errors because .h files or libraries are not in the right place, see the Makefile or consult your local X Windows expert. To test FormEd, start it like this: % formed -l formed.in FormEd 0.9 has an interesting experimental feature not in Otter 3.x: the ability to simplify quantified formulas by quantifier transformation. Try the buttons "CNF simp" and "DNF simp". W. McCune MCS-221 Argonne National Laboratory Argonne, IL 60439-4844 U.S.A. otter@mcs.anl.gov =========================================== Bugs observed while preparing the Otter 3.1 release. (1) Sometimes Formed pops up a message window. If you close the message window, sometimes Formed will exit. (2) I got a segmentation error when testing "clausify" on a large formula. otter-3.3f/source/formed/formed.c0100644000076400007640000006541506407523056016417 0ustar mccunemccune/* * formed.c -- FormEd (Formula Editor) X Windows program. * */ #define IN_MAIN #include "formed.h" #include "../header.h" /************* * * main(argc, argv) * *************/ main(argc, argv) int argc; char *argv[]; { init(); Flags[CHECK_ARITY].val = 0; Parms[MAX_MEM].val = 4000; Crnt_formula = NULL; Crnt_transform = NULL; Display_setup = 0; Have_message = 0; strcpy(Crnt_file,"\0"); /* process any command line arguments */ proc_command_line(argc, argv); if(Load_file) load_formula_list(Crnt_file); /* note - errors caught inside routine */ /* if had a load error, just display screen, user can load via button */ /* set up initial display & event handlers */ setup_display(argc, argv); /* if have a file loaded */ if(Crnt_formula) { Top_formula = Crnt_formula; Crnt_transform = Crnt_formula; /* display the first formula */ display_formula(Crnt_transform); } /* start events - callbacks will handle from now on*/ XtAppMainLoop(App_con); } /* main */ /************************* * * void proc_command_line(argc,argv) * *****************************/ void proc_command_line(argc, argv) int argc; char *argv[]; { int opt_count,c; int opt_index = 0; char *option; /* get & process any command line arguments */ opt_count = argc; Fore_set = 0; Back_set = 0; Load_file = 0; while(--opt_count > 0 && (strncmp("-",argv[++opt_index],1)==0)) { option = strpbrk(argv[opt_index], "fbl"); if (option) { c = *option; switch(c) { case 'f': Fore_set = 1; strcpy( User_fore,argv[++opt_index]); opt_count--; break; case 'b': Back_set = 1; strcpy( User_back,argv[++opt_index]); opt_count--; break; case 'l': Load_file = 1; strcpy( Crnt_file,argv[++opt_index]); opt_count--; break; default: printf("\nError: Illegal option."); printf("\nUsage: xform2 [-f color] [-b color] [-l filename]\n\n"); exit(0); break; } } else { printf("\nError: Illegal option."); printf("\nUsage: xform2 [-f color] [-b color] [-l filename]\n\n"); exit(0); } } } /* end proc_command_line */ /************* * * str_print_variable(str, ip, variable) * *************/ static void str_print_variable(str, ip, t) char *str; int *ip; struct term *t; { int i; char *s2, s3[100]; if (t->sym_num != 0) { s2 = sn_to_str(t->sym_num); strcpy( str += *ip,s2); *ip += strlen(s2); } else if (Flags[PROLOG_STYLE_VARIABLES].val) { str[(*ip)++] = (t->varnum % 26) + 'A'; i = t->varnum / 26; if (i > 0) { sprintf(s3, "%d", i); strcpy( str+*ip,s3); *ip += strlen(s3); } } else { if (t->varnum <= 2) str[(*ip)++] = t->varnum + 'x'; else if (t->varnum <= 5) str[(*ip)++] = t->varnum + 'r'; else { str[(*ip)++] = 'v'; sprintf(s3, "%d", t->varnum); strcpy( str+*ip,s3); *ip += strlen(s3); } } } /* str_print_variable */ /************* * * str_print_term(string, ip, term) -- Print a term to a file. * * Variables 0-5 are printed as x,y,z,u,v,w, and equalities * and negated equalities are printed in infix. * *************/ static void str_print_term(str, ip, t) char *str; int *ip; struct term *t; { struct rel *r; struct term *t1; char *s2; if (t == NULL) { strcpy( str+*ip,"(nil)"); *ip += 5; } else if (t->type == NAME) { /* name */ if (t->sym_num == Nil_sym_num) { strcpy( str+*ip,"[]"); *ip += 2; } else { s2 = sn_to_str(t->sym_num); strcpy( str+*ip,s2); *ip += strlen(s2); } } else if (t->type == VARIABLE) /* variable */ str_print_variable(str, ip, t); else { /* complex */ if (t->sym_num == Cons_sym_num) { /* list notation */ str[(*ip)++] = '['; str_print_term(str, ip, t->farg->argval); if (proper_list(t) == 0) { str[(*ip)++] = '|'; str_print_term(str, ip, t->farg->narg->argval); str[(*ip)++] = ']'; } else { t1 = t->farg->narg->argval; while (t1->sym_num != Nil_sym_num) { str[(*ip)++] = ','; str_print_term(str, ip, t1->farg->argval); t1 = t1->farg->narg->argval; } str[(*ip)++] = ']'; } } /* list notation */ else if (is_symbol(t, "=", 2) && t->varnum != TERM) { /* (t1 = t2) or (t1 != t2) */ str[(*ip)++] = '('; str_print_term(str, ip, t->farg->argval); if (t->occ.lit != NULL && t->occ.lit->sign == 0) { strcpy( str+*ip," != "); *ip += 4; } else { strcpy( str+*ip," = "); *ip += 3; } str_print_term(str, ip, t->farg->narg->argval); str[(*ip)++] = ')'; } else { s2 = sn_to_str(t->sym_num); strcpy( str+*ip,s2); *ip += strlen(s2); str[(*ip)++] = '('; r = t->farg; while(r != NULL) { str_print_term(str, ip, r->argval); r = r->narg; if(r != NULL) str[(*ip)++] = ','; } str[(*ip)++] = ')'; } } } /* str_print_term */ /************* * * int sprint_term(s, t) -- return length of s. * *************/ static int sprint_term(s, t) char *s; struct term *t; { int i; i = 0; str_print_term(s, &i, t); s[i] = '\0'; return(i); } /* sprint_term */ /************* * * static void str_print_formula(str, ip, f) * * Print a formula to a string and count the length of the string. * *************/ static void str_print_formula(str, ip, f) char *str; int *ip; struct formula *f; { char op[MAX_NAME]; struct formula *f1; if (f == NULL) { strcpy( str+*ip,"(nil)"); *ip += 5; } else if (f->type == ATOM_FORM) { str_print_term(str, ip, f->t); } else if (f->type == NOT_FORM) { strcpy( str+*ip,"-"); *ip += 1; str_print_formula(str, ip, f->first_child); } else if (f->type == AND_FORM && f->first_child == NULL) { strcpy( str+*ip,"TRUE"); *ip += 4; } else if (f->type == OR_FORM && f->first_child == NULL) { strcpy( str+*ip,"FALSE"); *ip += 5; } else if (f->type == QUANT_FORM) { strcpy( str+*ip,"("); *ip += 1; if (f->quant_type == ALL_QUANT) { strcpy( str+*ip,"all "); *ip += 4; } else { strcpy( str+*ip,"exists "); *ip += 7; } str_print_term(str, ip, f->t); strcpy( str+*ip," "); *ip += 1; str_print_formula(str, ip, f->first_child); strcpy( str+*ip,")"); *ip += 1; } else { if (f->type == AND_FORM) strcpy( op," & "); else if (f->type == OR_FORM) strcpy( op," | "); else if (f->type == IMP_FORM) strcpy( op," -> "); else if (f->type == IFF_FORM) strcpy( op," <-> "); else op[0] = '\0'; strcpy( str+*ip,"("); *ip += 1; for (f1 = f->first_child; f1; f1 = f1->next) { str_print_formula(str, ip, f1); if (f1->next) { strcpy( str+*ip,op); *ip += strlen(op); } } strcpy( str+*ip,")"); *ip += 1; } } /* str_print_formula */ /************* * * int sprint_formula(s, f) -- return length of s. * *************/ int sprint_formula(s, f) char *s; struct formula *f; { int i; i = 0; str_print_formula(s, &i, f); s[i] = '\0'; return(i); } /* sprint_formula */ /************************* * * void select_area(w, client_data, event) * *****************************/ void select_area(w, client_data, event) Widget w; caddr_t client_data; XEvent *event; { struct formula_box *prev_area; XButtonEvent *button_prssd; /* button pressed */ button_prssd = (XButtonEvent *) event; kill_message(); /* only find & highlight box if have a formula displayed */ if(Crnt_transform != NULL) { prev_area = Sel_area; Sel_area = find_point(B, button_prssd->x, button_prssd->y, B->x_off, B->y_off); if (Highlighted) { /* clear previous selection by simply redrawing it*/ XSetForeground(Dpy, Gc, Background); XFillRectangle(Dpy, Win, Gc, prev_area->abs_x_loc, prev_area->abs_y_loc, prev_area->length, prev_area->height); XSetForeground(Dpy, Gc, Foreground); draw_formula_box(prev_area, prev_area->abs_x_loc, prev_area->abs_y_loc); } /* highlight area if not same selection, and inside formula box */ if(Sel_area == NULL || (Highlighted && prev_area == Sel_area)) { Highlighted = 0; Sel_area = B; } else { draw_formula_box_inverted(Sel_area, Sel_area->abs_x_loc, Sel_area->abs_y_loc); Highlighted = 1; } } } /* select_area */ /************* * * draw_formula_box_inverted(b, x, y) * *************/ void draw_formula_box_inverted(b, x, y) struct formula_box *b; int x, y; { /* couldn't make this work. XSetFillStyle(Dpy, Win, FillTiled); XSetTile(Dpy, Win, Pattern); */ XFillRectangle(Dpy, Win, Gc, x, y, b->length, b->height); XSetForeground(Dpy, Gc, Background); XSetBackground(Dpy, Gc, Foreground); draw_formula_box(b, x, y); XSetForeground(Dpy, Gc, Foreground); XSetBackground(Dpy, Gc, Background); draw_inverted_operators(b, x, y); /* XSetFillStyle(Dpy, Win, FillSolid); */ } /* draw_formula_box_inverted */ /************************* * * void display_formula(p1) * *****************************/ void display_formula(p1) struct formula_ptr_2 *p1; { /* set up the formula box locations and sizes for the display */ /* the top box is global because it must be accessed thru event handlers */ kill_message(); if (B) free_formula_box_tree(B); B = arrange_box(p1->f); /* draw the formula on the canvas */ XClearWindow(Dpy, Win); draw_formula_box(B,5,5); Sel_area = B; Highlighted = 0; } /* end display_formula */ /************************* * * struct formula_box *do_box_geometry(b, op) * *****************************/ struct formula_box *do_box_geometry(b, op) struct formula_box *b; int op; { struct formula_box *b1; int height, length, n, x_center_line, y_center_line, x_current, y_current; if (op == NOT_FORM) { /*** set up negation type geometry ***/ b1 = b->first_child; /* op_box */ length = Spacing + b1->length + Spacing + (b1->next)->length + Spacing; if (b1->height > (b1-> next)->height) height = b1->height; else height = (b1->next)->height; height = Spacing + height + Spacing; b->length = length; b->height = height; y_center_line = height / 2; b1->x_off = Spacing; b1->y_off = y_center_line - b1->height/2; (b1->next)->x_off = Spacing + b1->length + Spacing; (b1->next)->y_off = y_center_line - (b1->next)->height/2; } else if (op == AND_FORM) { /*** set up conjunction type geometry ***/ length = height = 0; for (b1 = b->first_child, n=0; b1; b1 = b1->next, n++) { height += b1->height; length = (b1->length > length ? b1->length : length); } height = Spacing + height + (n-1)*Spacing + Spacing; length = Spacing + length + Spacing; b->length = length; b->height = height; x_center_line = length / 2; y_current = 0; for (b1 = b->first_child; b1; b1 = b1->next) { b1->y_off = y_current + Spacing; y_current += Spacing + b1->height; if (0) /* center conjuncts */ b1->x_off = x_center_line - b1->length/2; else /* left justify conjuncts */ b1->x_off = Spacing; } } else { /*** set up disjunction type of geometry (includes iff,imp,quant's) ***/ length = height = 0; for (b1 = b->first_child, n=0; b1; b1 = b1->next, n++) { length += b1->length; height = (b1->height > height ? b1->height : height); } length = Spacing + length + (n-1)*Spacing + Spacing; height = Spacing + height + Spacing; b->length = length; b->height = height; y_center_line = height / 2; x_current = 0; for (b1 = b->first_child; b1; b1 = b1->next) { b1->x_off = x_current + Spacing; x_current += Spacing + b1->length; b1->y_off = y_center_line - b1->height/2; } } return(b); } /* end do_box_geometry */ /************* * * static struct formula_box *arrange_box_term(t) * *************/ static struct formula_box *arrange_box_term(t) struct term *t; { struct formula_box *b; char str[1000]; int len; b = get_formula_box(); b->type = FORMULA; /* change to TERM later */ b->subtype = ATOM_FORM; b->f = NULL; /* get the string */ sprint_term(str, t); len = strlen(str); if (len >= 100) strcpy( b->str,"*** STRING TOO LONG ***"); else strcpy( b->str,str); /* HERE find size of string and assign to length and width */ b->length = XTextWidth(Font_struct, b->str, strlen(b->str)); b->height = Font_char_ht; return(b); } /* arrange_box_term */ /************* * * static struct formula_box *arrange_box_symbol(op) * *************/ static struct formula_box *arrange_box_symbol(op) int op; { struct formula_box *b; b = get_formula_box(); b->type = OPERATOR; b->subtype = op; switch (op) { case OR_OP: b->length = Or_width; b->height = Or_height; break; case AND_OP: b->length = And_width; b->height = And_height; break; case NOT_OP: b->length = Not_width; b->height = Not_height; break; case IMP_OP: b->length = Imp_width; b->height = Imp_height; break; case IFF_OP: b->length = Iff_width; b->height = Iff_height; break; case ALL_OP: b->length = All_width; b->height = All_height; break; case EXISTS_OP: b->length = Exists_width; b->height = Exists_height; break; default: strcpy(Error_string, "arrange_box_symbol: unknown operator.\n"); user_error(Error_string); } return(b); } /* arrange_box_symbol */ /************* * * static struct formula_box *arrange_box_atom(f) * *************/ static struct formula_box *arrange_box_atom(f) struct formula *f; { struct formula_box *b; char str[1000]; int len; b = get_formula_box(); b->type = FORMULA; b->subtype = ATOM_FORM; b->f = f; /* get the string */ sprint_term(str, f->t); len = strlen(str); if (len >= 100) strcpy( b->str,"*** STRING TOO LONG ***"); else strcpy( b->str,str); /* HERE find size of string and assign to length and width */ b->length = XTextWidth(Font_struct, b->str, strlen(b->str)); b->height = Font_char_ht; return(b); } /* arrange_box_atom */ /************* * * static struct formula_box *arrange_box_or(f) * *************/ static struct formula_box *arrange_box_or(f) struct formula *f; { struct formula_box *b, *sub_box, *op_box; struct formula *f1; b = get_formula_box(); b->type = FORMULA; b->subtype = OR_FORM; b->f = f; if (f->first_child == NULL) { /* speicial case: empty disjunction is FALSE */ strcpy( b->str,"FALSE"); b->length = XTextWidth(Font_struct, b->str, strlen(b->str)); b->height = Font_char_ht; } else { for (f1 = f->first_child, op_box = NULL; f1; f1 = f1->next) { sub_box = arrange_box(f1); sub_box->parent = b; if (op_box) op_box->next = sub_box; else b->first_child = sub_box; if (f1->next) { op_box = arrange_box_symbol(OR_OP); sub_box->next = op_box; op_box->parent = b; } } b = do_box_geometry(b, OR_FORM); } return(b); } /* arrange_box_or */ /************* * * static struct formula_box *arrange_box_and(f) * *************/ static struct formula_box *arrange_box_and(f) struct formula *f; { struct formula_box *b, *sub_box, *op_box; struct formula *f1; b = get_formula_box(); b->type = FORMULA; b->subtype = AND_FORM; b->f = f; if (f->first_child == NULL) { /* speicial case: empty conjunction is TRUE */ strcpy( b->str,"TRUE"); b->length = XTextWidth(Font_struct, b->str, strlen(b->str)); b->height = Font_char_ht; } else { for (f1 = f->first_child, op_box = NULL; f1; f1 = f1->next) { sub_box = arrange_box(f1); sub_box->parent = b; if (op_box) op_box->next = sub_box; else b->first_child = sub_box; if (0 && f1->next) { /* display '&' */ op_box = arrange_box_symbol(AND_OP); sub_box->next = op_box; op_box->parent = b; } else /* don't display '&' */ op_box = sub_box; } b = do_box_geometry(b, AND_FORM); } return(b); } /* arrange_box_and */ /************* * * static struct formula_box *arrange_box_not(f) * *************/ static struct formula_box *arrange_box_not(f) struct formula *f; { struct formula_box *b, *sub_box, *op_box; b = get_formula_box(); b->type = FORMULA; b->subtype = NOT_FORM; b->f = f; op_box = arrange_box_symbol(NOT_OP); sub_box = arrange_box(f->first_child); op_box->parent = b; sub_box->parent = b; b->first_child = op_box; op_box->next = sub_box; b = do_box_geometry(b, NOT_FORM); return(b); } /* arrange_box_not */ /************* * * static struct formula_box *arrange_box_imp(f) * *************/ static struct formula_box *arrange_box_imp(f) struct formula *f; { struct formula_box *b, *sub_box, *op_box; struct formula *f1; b = get_formula_box(); b->type = FORMULA; b->subtype = IMP_FORM; b->f = f; for (f1 = f->first_child, op_box = NULL; f1; f1 = f1->next) { sub_box = arrange_box(f1); sub_box->parent = b; if (op_box) op_box->next = sub_box; else b->first_child = sub_box; if (f1->next) { op_box = arrange_box_symbol(IMP_OP); sub_box->next = op_box; op_box->parent = b; } } b = do_box_geometry(b, IMP_FORM); return(b); } /* arrange_box_imp */ /************* * * static struct formula_box *arrange_box_iff(f) * *************/ static struct formula_box *arrange_box_iff(f) struct formula *f; { struct formula_box *b, *sub_box, *op_box; struct formula *f1; b = get_formula_box(); b->type = FORMULA; b->subtype = IFF_FORM; b->f = f; for (f1 = f->first_child, op_box = NULL; f1; f1 = f1->next) { sub_box = arrange_box(f1); sub_box->parent = b; if (op_box) op_box->next = sub_box; else b->first_child = sub_box; if (f1->next) { op_box = arrange_box_symbol(IFF_OP); sub_box->next = op_box; op_box->parent = b; } } b = do_box_geometry(b, IFF_FORM); return(b); } /* arrange_box_iff */ /************* * * static struct formula_box *arrange_box_quant(f) * *************/ static struct formula_box *arrange_box_quant(f) struct formula *f; { struct formula_box *b, *sub_box, *op_box, *b1; struct quantifier *q; b = get_formula_box(); b->type = FORMULA; b->subtype = QUANT_FORM; b->f = f; /* pick off quantifier and its variable */ if (f->quant_type == ALL_QUANT) op_box = arrange_box_symbol(ALL_OP); else op_box = arrange_box_symbol(EXISTS_OP); op_box->parent = b; b->first_child = op_box; sub_box = arrange_box_term(f->t); sub_box->parent = b; op_box->next = sub_box; b1 = sub_box; sub_box = arrange_box(f->first_child); sub_box->parent = b; if (b1) b1->next = sub_box; else b->first_child = sub_box; b = do_box_geometry(b, QUANT_FORM); return(b); } /* arrange_box_quant */ /************* * * struct formula_box *arrange_box(f) * *************/ struct formula_box *arrange_box(f) struct formula *f; { switch (f->type) { case ATOM_FORM: return(arrange_box_atom(f)); break; case NOT_FORM: return(arrange_box_not(f)); break; case AND_FORM: return(arrange_box_and(f)); break; case OR_FORM: return(arrange_box_or(f)); break; case IMP_FORM: return(arrange_box_imp(f)); break; case IFF_FORM: return(arrange_box_iff(f)); break; case QUANT_FORM: return(arrange_box_quant(f)); break; default: strcpy(Error_string, "arrange_box: unknown operator.\n"); user_error(Error_string); exit(1); return(NULL); break; } } /* arrange_box */ /************* * * draw_formula_box(b, x, y) * *************/ void draw_formula_box(b, x, y) struct formula_box *b; int x; int y; { struct formula_box *b1; /* save absolute address of the box in the Window */ b->abs_x_loc = x; b->abs_y_loc = y; if (b->type == OPERATOR) { /* operator at position (x,y) */ switch(b->subtype) { case OR_OP: XCopyArea(Dpy, Or, Win, Gc, 0,0, Or_width, Or_height, x, y); break; case AND_OP: XCopyArea(Dpy, And, Win, Gc, 0, 0, And_width, And_height, x, y); break; case NOT_OP: XCopyArea(Dpy, Not, Win, Gc, 0, 0, Not_width, Not_height, x, y); break; case IMP_OP: XCopyArea(Dpy, Imp, Win, Gc, 0, 0, Imp_width, Imp_height, x, y); break; case IFF_OP: XCopyArea(Dpy, Iff, Win, Gc, 0, 0, Iff_width, Iff_height, x, y); break; case EXISTS_OP: XCopyArea(Dpy, Exists, Win, Gc, 0, 0, Exists_width, Exists_height, x, y); break; case ALL_OP: XCopyArea(Dpy, All, Win, Gc, 0, 0, All_width, All_height, x, y); break; default: strcpy(Error_string, "draw_formula_box: unknown operator.\n"); user_error(Error_string); } } else if (b->subtype == ATOM_FORM || b->first_child == NULL) { /* draw string b->str at position (x,y) */ XDrawImageString(Dpy, Win, Gc, x, y + Font_ascent, b->str, strlen(b->str)); } else { /* non-atomic formula */ if (b->subtype != NOT_FORM && b->subtype != QUANT_FORM) XDrawRectangle(Dpy, Win, Gc, x, y, b->length, b->height); for (b1 = b->first_child; b1; b1 = b1->next) draw_formula_box(b1, x + b1->x_off, y + b1->y_off); } } /* draw_formula_box */ /************* * * draw_inverted_operators(b, x, y) * *************/ void draw_inverted_operators(b, x, y) struct formula_box *b; int x; int y; { struct formula_box *b1; if (b->type == OPERATOR) { /* operator at position (x,y) */ switch(b->subtype) { case OR_OP: XCopyArea(Dpy, Or_invert, Win, Gc, 0,0, Or_width, Or_height, x, y); break; case AND_OP: XCopyArea(Dpy, And_invert, Win, Gc, 0, 0, And_width, And_height, x, y); break; case NOT_OP: XCopyArea(Dpy, Not_invert, Win, Gc, 0, 0, Not_width, Not_height, x, y); break; case IMP_OP: XCopyArea(Dpy, Imp_invert, Win, Gc, 0, 0, Imp_width, Imp_height, x, y); break; case IFF_OP: XCopyArea(Dpy, Iff_invert, Win, Gc, 0, 0, Iff_width, Iff_height, x, y); break; case EXISTS_OP: XCopyArea(Dpy, Exists_invert, Win, Gc, 0, 0, Exists_width, Exists_height, x, y); break; case ALL_OP: XCopyArea(Dpy, All_invert, Win, Gc, 0, 0, All_width, All_height, x, y); break; default: strcpy(Error_string, "draw_inverted_operators: unknown operator.\n"); user_error(Error_string); } } else if (b->subtype == ATOM_FORM) { ; /* do nothing */ } else { /* non-atomic formula */ for (b1 = b->first_child; b1; b1 = b1->next) draw_inverted_operators(b1, x + b1->x_off, y + b1->y_off); } } /* draw_inverted_operators */ /************* * * struct formula_box *find_point(b, x, y, xb, yb) * * (x,y) is the point to find. * (xb,yb) is the address of b. * *************/ struct formula_box *find_point(b, x, y, xb, yb) struct formula_box *b; int x; int y; int xb; int yb; { struct formula_box *b1, *b_xy; if (x < xb || x > xb+b->length || y < yb || y > yb+b->height) return(NULL); /* out of bounds */ else { for (b1 = b->first_child, b_xy = NULL; b1 && !b_xy; b1 = b1->next) b_xy = find_point(b1, x, y, xb+b1->x_off, yb+b1->y_off); return(b_xy ? b_xy : b); } } /* find_formula_box */ /************* * * void install_up_pointers(f) * *************/ void install_up_pointers(f) struct formula *f; { struct formula *f1; for (f1 = f->first_child; f1; f1 = f1->next) { f1->parent = f; install_up_pointers(f1); } } /* install_up_pointers */ /************* * * void free_formula_box_tree(b) * *************/ void free_formula_box_tree(b) struct formula_box *b; { struct formula_box *g1, *g2; g1 = b->first_child; while (g1) { g2 = g1->next; free_formula_box_tree(g1); g1 = g2; } free_formula_box(b); } /* free_formula_box_tree */ /************* * * void transform(f, trans_proc) * *************/ void transform(f, trans_proc) struct formula *f; struct formula *(*trans_proc)(); { struct formula *parent, *prev, *f1; struct formula *copy; struct formula_ptr_2 *p; struct formula_box *sub_box; parent = f->parent; if (parent) { prev = NULL; for (f1 = parent->first_child; f1 != f; f1 = f1->next) prev = f1; } copy = copy_formula(Crnt_transform->f); install_up_pointers(copy); f = trans_proc(f); install_up_pointers(f); if (parent) { /* if not at the top */ if (prev) prev->next = f; else parent->first_child = f; f->parent = parent; } else { Crnt_transform->f = f; f->parent = NULL; } if (formula_ident(Crnt_transform->f, copy)) { user_error("That transformation wouldn't do anything.\n"); zap_formula(copy); } else { /* free any undone/unedited formulas */ if(Crnt_transform->right) { free_formulas(Crnt_transform->right); Crnt_transform->right = NULL; } else if(Crnt_transform->up) { free_formulas(Crnt_transform->up); Crnt_transform->up = NULL; } p = get_formula_ptr_2(); p->f = Crnt_transform->f; Crnt_transform->right = p; p->left = Crnt_transform; Crnt_transform->f = copy; Crnt_transform = p; display_formula(Crnt_transform); /* now highlight (and select) the transformed subterm */ sub_box = find_sub_box(B, f); if (sub_box && sub_box != B) { Sel_area = sub_box; Highlighted = 1; draw_formula_box_inverted(Sel_area, Sel_area->abs_x_loc, Sel_area->abs_y_loc); } } } /* transform */ /************* * * struct formula_box *find_sub_box(b, f) * *************/ struct formula_box *find_sub_box(b, f) struct formula_box *b; struct formula *f; { struct formula_box *b1, *b2; if (b->f == f) b2 = b; else { for (b1 = b->first_child, b2 = NULL; b1 && !b2; b1 = b1->next) b2 = find_sub_box(b1, f); } return(b2); } /* find_sub_box */ /************* * * void free_formulas(p) * *************/ void free_formulas(p) struct formula_ptr_2 *p; { struct formula_ptr_2 *q; while(p) { q = p; if(p->right) p = p->right; else p = p->up; zap_formula(q->f); free_formula_ptr_2(q); } } /* free_formulas */ otter-3.3f/source/misc.c0100644000076400007640000021046010103775432014605 0ustar mccunemccune/* * misc.c -- Miscellaneous routines. * */ #include "header.h" /************* * * init() -- initialize global variables * *************/ void init(void) { Stats[INIT_WALL_SECONDS] = wall_seconds(); clock_init(); init_options(); init_attributes(); Null_output = fopen("/dev/null", "w"); Bell = '\007'; built_in_symbols(); init_special_ops(); declare_user_functions(); strcpy(Float_format, "%.12f"); Is_pos_lits = get_is_tree(); /* index for forward subsumption */ Is_neg_lits = get_is_tree(); /* index for forward subsumption */ Demod_imd = get_imd_tree(); /* index for demodulation */ Fpa_pos_lits = alloc_fpa_index(); Fpa_neg_lits = alloc_fpa_index(); Fpa_clash_pos_lits= alloc_fpa_index(); Fpa_clash_neg_lits= alloc_fpa_index(); Fpa_clash_terms = alloc_fpa_index(); Fpa_alphas = alloc_fpa_index(); Fpa_back_demod = alloc_fpa_index(); } /* init */ /************* * * abend * *************/ void abend(char *str) { output_stats(stdout, 3); fprintf(stderr, "\n%c********** ABNORMAL END **********\n\n", Bell); fprintf(stderr, "********** %s\n", str); fprintf(stdout, "\n********** ABNORMAL END **********\n\n"); fprintf(stdout, "********** %s\n", str); exit(ABEND_EXIT); } /* abend */ /************* * * read_a_file() * *************/ void read_a_file(FILE *in_fp, FILE *out_fp) { struct list *l; struct term *t, *t1; struct clause *c; int rc, error, list_errors, i, j; struct formula_ptr *formp; char *s; int quit_early = 0; t = read_term(in_fp, &rc); while ((t || rc == 0) && !quit_early) { error = 0; if (!t) error = 1; else if (t->type != COMPLEX) error = 1; else if (str_ident("include", sn_to_str(t->sym_num))) { t1 = t->farg->argval; if (t1->type == COMPLEX || t->farg->narg) { fprintf(out_fp, "ERROR, bad argument to include: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { char fn[MAX_NAME]; FILE *local_in_fp; s = sn_to_str(t1->sym_num); /* If filename is quoted, get rid of the quotes. */ if (s[0] == '\"' || s[0] == '\'') { strcpy(fn, s+1); fn[strlen(fn)-1] = '\0'; } else strcpy(fn, s); local_in_fp = fopen(fn, "r"); if (local_in_fp == NULL) { fprintf(out_fp, "ERROR, cannot open file %s.\n", fn); Stats[INPUT_ERRORS]++; } else { print_term_nl(out_fp, t); if (Flags[ECHO_INCLUDED_FILES].val) { fprintf(out_fp, "------- start included file %s-------\n", fn); read_a_file(local_in_fp, out_fp); fprintf(out_fp, "------- end included file %s-------\n", fn); } else read_a_file(local_in_fp, Null_output); fclose(local_in_fp); } } } else if (str_ident("set", sn_to_str(t->sym_num))) { i = change_flag(out_fp, t, 1); if (i != -1) { print_term_nl(out_fp, t); dependent_flags(out_fp, i); } } else if (str_ident("clear", sn_to_str(t->sym_num))) { i = change_flag(out_fp, t, 0); if (i != -1) { print_term_nl(out_fp, t); dependent_flags(out_fp, i); } } else if (str_ident("assign", sn_to_str(t->sym_num))) { i = change_parm(out_fp, t); if (i != -1) { print_term_nl(out_fp, t); dependent_parms(out_fp, i); } } else if (str_ident("list", sn_to_str(t->sym_num))) { t1 = t->farg->argval; if (t1->type == COMPLEX || t->farg->narg) { fprintf(out_fp, "ERROR, bad argument to list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else if (str_ident("usable", sn_to_str(t1->sym_num)) || str_ident("axioms", sn_to_str(t1->sym_num))) { if (str_ident("axioms", sn_to_str(t1->sym_num))) fprintf(stderr, "NOTICE: Please change 'axioms' to 'usable'.\n"); fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; else if (Flags[PROCESS_INPUT].val == 0) { c = l->first_cl; while (c) { Stats[INPUT_ERRORS] += process_linked_tags(c); cl_integrate(c); c = c->next_cl; } } print_cl_list(out_fp, l); append_lists(Usable,l); } else if (str_ident("sos", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; else if (Flags[PROCESS_INPUT].val == 0) { c = l->first_cl; while (c) { cl_integrate(c); c = c->next_cl; } } print_cl_list(out_fp, l); append_lists(Sos,l); } else if (str_ident("demodulators", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; c = l->first_cl; while (c) { cl_integrate(c); c = c->next_cl; } print_cl_list(out_fp, l); append_lists(Demodulators,l); } else if (str_ident("passive", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; c = l->first_cl; /* always integrate, because never pre_processed */ while (c) { cl_integrate(c); c = c->next_cl; } print_cl_list(out_fp, l); append_lists(Passive,l); } else if (str_ident("hot", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; c = l->first_cl; /* always integrate, because never pre_processed */ while (c) { hot_cl_integrate(c); c = c->next_cl; } print_cl_list(out_fp, l); append_lists(Hot,l); } else if (str_ident("hints", sn_to_str(t1->sym_num))) { Internal_flags[HINTS_PRESENT] = 1; fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; /* always integrate, because never pre_processed */ for (c = l->first_cl; c; c = c->next_cl) hint2_integrate(c); print_hints_cl_list(out_fp, l); append_lists(Hints,l); } else if (str_ident("hints2", sn_to_str(t1->sym_num))) { Internal_flags[HINTS2_PRESENT] = 1; fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; /* always integrate, because never pre_processed */ for (c = l->first_cl; c; c = c->next_cl) hint2_integrate(c); print_hints_cl_list(out_fp, l); append_lists(Hints2,l); } else if (str_ident("mace_constraints", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; /* don't integrate */ print_cl_list(out_fp, l); append_lists(Mace_constraints,l); } else if (str_ident("foreach", sn_to_str(t1->sym_num))) { Internal_flags[FOREACH_SOS] = 1; quit_early = 1; } else { if (str_ident("axioms", sn_to_str(t1->sym_num))) fprintf(stderr, "Name of axioms list is now 'usable'.\n"); fprintf(out_fp, "ERROR, unknown list: "); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); print_cl_list(out_fp, l); Stats[INPUT_ERRORS]++; } } else if (str_ident("formula_list", sn_to_str(t->sym_num))) { t1 = t->farg->argval; if (t1->type == COMPLEX || t->farg->narg) { fprintf(out_fp, "ERROR, bad argument to list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else if (str_ident("usable", sn_to_str(t1->sym_num)) || str_ident("axioms", sn_to_str(t1->sym_num))) { if (str_ident("axioms", sn_to_str(t1->sym_num))) fprintf(stderr, "NOTICE: Please change 'axioms' to 'usable'.\n"); fprintf(out_fp, "\n"); print_term_nl(out_fp, t); formp = read_formula_list(in_fp, &list_errors); print_formula_list(out_fp,formp); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; else { CLOCK_START(CLAUSIFY_TIME); l = clausify_formula_list(formp); CLOCK_STOP(CLAUSIFY_TIME); if (Flags[PROCESS_INPUT].val == 0) { c = l->first_cl; while (c) { cl_integrate(c); c = c->next_cl; } } fprintf(out_fp, "\n-------> usable clausifies to:\n\nlist(usable).\n"); print_cl_list(out_fp, l); append_lists(Usable,l); } } else if (str_ident("sos", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); formp = read_formula_list(in_fp, &list_errors); print_formula_list(out_fp,formp); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; else { CLOCK_START(CLAUSIFY_TIME); l = clausify_formula_list(formp); CLOCK_STOP(CLAUSIFY_TIME); if (Flags[PROCESS_INPUT].val == 0) { c = l->first_cl; while (c) { cl_integrate(c); c = c->next_cl; } } fprintf(out_fp, "\n-------> sos clausifies to:\n\nlist(sos).\n"); print_cl_list(out_fp, l); append_lists(Sos,l); } } else if (str_ident("passive", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); formp = read_formula_list(in_fp, &list_errors); print_formula_list(out_fp,formp); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; else { CLOCK_START(CLAUSIFY_TIME); l = clausify_formula_list(formp); CLOCK_STOP(CLAUSIFY_TIME); c = l->first_cl; /* always integrate, because never pre_processed */ while (c) { cl_integrate(c); c = c->next_cl; } fprintf(out_fp, "\n-------> passive clausifies to:\n\nlist(passive).\n"); print_cl_list(out_fp, l); append_lists(Passive,l); } } else if (str_ident("hot", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); formp = read_formula_list(in_fp, &list_errors); print_formula_list(out_fp,formp); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; else { CLOCK_START(CLAUSIFY_TIME); l = clausify_formula_list(formp); CLOCK_STOP(CLAUSIFY_TIME); c = l->first_cl; /* always integrate, because never pre_processed */ while (c) { hot_cl_integrate(c); c = c->next_cl; } fprintf(out_fp, "\n-------> hot list clausifies to:\n\nlist(hot).\n"); print_cl_list(out_fp, l); append_lists(Hot,l); } } else { if (str_ident("axioms", sn_to_str(t1->sym_num))) fprintf(stderr, "Name of axioms list is now 'usable'.\n"); fprintf(out_fp, "ERROR, unknown formula_list: "); print_term_nl(out_fp, t); l = read_cl_list(in_fp, &list_errors); print_cl_list(out_fp, l); Stats[INPUT_ERRORS]++; } } else if (str_ident("weight_list", sn_to_str(t->sym_num))) { t1 = t->farg->argval; if (t1->type != NAME || t->farg->narg) { fprintf(out_fp, "ERROR, bad argument to Weight_list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else if (str_ident("purge_gen", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); if (Weight_purge_gen) { fprintf(out_fp, "----> ERROR, already have purge weight list.\n"); Stats[INPUT_ERRORS] ++; } Weight_purge_gen = read_wt_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; Weight_purge_gen_index = get_is_tree(); set_wt_list(Weight_purge_gen, Weight_purge_gen_index, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; print_list(out_fp, Weight_purge_gen); } else if (str_ident("pick_given", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); if (Weight_pick_given) { fprintf(out_fp, "----> ERROR, already have pick weight list.\n"); Stats[INPUT_ERRORS] ++; } Weight_pick_given = read_wt_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; Weight_pick_given_index = get_is_tree(); set_wt_list(Weight_pick_given, Weight_pick_given_index, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; print_list(out_fp, Weight_pick_given); } else if (str_ident("pick_and_purge", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); if (Weight_pick_given || Weight_purge_gen) { fprintf(out_fp, "----> ERROR, already have pick weight list or purge weight list.\n"); Stats[INPUT_ERRORS] ++; } Weight_pick_given = Weight_purge_gen = read_wt_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; Weight_pick_given_index = Weight_purge_gen_index = get_is_tree(); set_wt_list(Weight_pick_given, Weight_pick_given_index, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; print_list(out_fp, Weight_pick_given); } else if (str_ident("terms", sn_to_str(t1->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); if (Weight_terms) { fprintf(out_fp, "----> ERROR, already have term weight list.\n"); Stats[INPUT_ERRORS] ++; } Weight_terms = read_wt_list(in_fp, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; Weight_terms_index = get_is_tree(); set_wt_list(Weight_terms, Weight_terms_index, &list_errors); if (list_errors != 0) Stats[INPUT_ERRORS] += list_errors; print_list(out_fp, Weight_terms); } else { fprintf(out_fp, "ERROR, unknown Weight_list: "); print_term_nl(out_fp, t); Weight_pick_given = read_wt_list(in_fp, &list_errors); print_list(out_fp, Weight_pick_given); Stats[INPUT_ERRORS]++; } } else if (str_ident("lex", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg || proper_list(t->farg->argval) == 0) { fprintf(out_fp, "ERROR, argument of lex term is not a list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); set_lex_vals(t); Internal_flags[LEX_VALS_SET] = 1; } } else if (str_ident("lrpo_multiset_status", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg || proper_list(t->farg->argval) == 0) { fprintf(out_fp, "ERROR, argument of lrpo_status term is not a list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); set_lrpo_status(t, LRPO_MULTISET_STATUS); } } else if (str_ident("lrpo_lr_status", sn_to_str(t->sym_num))) { fprintf(out_fp, "\nERROR, the command lrpo_lr_status no longer exists.\n"); fprintf(stderr, "\nERROR, the command lrpo_lr_status no longer exists.\n"); fprintf(stderr, "Symbols have lr status by default. The command\n"); fprintf(stderr, "lrpo_multiset_status gives symbols multiset status.\n"); Stats[INPUT_ERRORS]++; } else if (str_ident("skolem", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg || proper_list(t->farg->argval) == 0) { fprintf(out_fp, "ERROR, argument of skolem term is not a list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); set_skolem(t); } } else if (str_ident("overbeek_terms", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg || proper_list(t->farg->argval) == 0) { fprintf(out_fp, "ERROR, argument of overbeek_terms is not a list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); Overbeek_terms = copy_term(t->farg->argval); set_vars(Overbeek_terms); } } else if (str_ident("split_atoms", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg || proper_list(t->farg->argval) == 0) { fprintf(out_fp, "ERROR, argument of split_atoms is not a list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { Split_atoms = copy_term(t->farg->argval); set_vars(Split_atoms); if (!ground(Split_atoms)) { fprintf(out_fp, "ERROR, split_atoms must be gound: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); } } } else if (str_ident("special_unary", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg || proper_list(t->farg->argval) == 0) { fprintf(out_fp, "ERROR, argument of special_unary term is not a list: "); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); set_special_unary(t); Internal_flags[SPECIAL_UNARY_PRESENT] = 1; } } else if (str_ident("op", sn_to_str(t->sym_num))) { print_term_nl(out_fp, t); if (!process_op_command(t)) Stats[INPUT_ERRORS]++; } else if (str_ident("float_format", sn_to_str(t->sym_num))) { if (t->farg == NULL || t->farg->narg) { fprintf(out_fp, "ERROR, float_format term must have one argument.\n"); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { print_term_nl(out_fp, t); s = sn_to_str(t->farg->argval->sym_num); /* Assume it's well formed. Remove quotes. */ i = strlen(s); for (j = 1; j < i-1 ; j++) Float_format[j-1] = s[j]; Float_format[i-2] = '\0'; } } else if (str_ident("make_evaluable", sn_to_str(t->sym_num))) { if (sn_to_arity(t->sym_num) != 2) { fprintf(out_fp, "ERROR, make_evaluable term must have two arguments:\n"); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { int i1, i2; struct sym_ent *p1, *p2; i1 = t->farg->argval->sym_num; i2 = t->farg->narg->argval->sym_num; p1 = sn_to_node(i1); p2 = sn_to_node(i2); if (p2->eval_code < 1) { fprintf(out_fp, "ERROR, second arg is not evaluable:\n"); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else if (p1->arity != p2->arity) { fprintf(out_fp, "ERROR, args have different arities:\n"); print_term_nl(out_fp, t); Stats[INPUT_ERRORS]++; } else { print_term_nl(out_fp, t); p1->eval_code = p2->eval_code; } } } else if (str_ident("initial_proof_object", sn_to_str(t->sym_num))) { fprintf(out_fp, "\n"); print_term_nl(out_fp, t); l = init_proof_object(in_fp, out_fp); if (l == NULL) Stats[INPUT_ERRORS]++; else { if (Flags[PROCESS_INPUT].val == 0) { c = l->first_cl; while (c) { Stats[INPUT_ERRORS] += process_linked_tags(c); cl_integrate(c); c = c->next_cl; } } print_cl_list(out_fp, l); append_lists(Usable,l); } } /* initial_proof_object */ else if (str_ident("overbeek_world", sn_to_str(t->sym_num))) { int errors = 0; struct term_ptr *p1, *p2; fprintf(out_fp, "\n"); print_term_nl(out_fp, t); p1 = read_list(in_fp, &errors, 0); /* don't integrate */ if (errors > 0) abend("overbeek_world: term errors"); for (p2 = p1; p2; p2 = p2->next) { int ok = set_vars(p2->term); if (!ok) abend("overbeek_world: too many variables"); renumber_vars_term(p2->term); zap_variable_names(p2->term); overbeek_insert(p2->term); print_term_nl(out_fp, p2->term); } fprintf(out_fp, "end_of_list.\n"); #if 0 check_overbeek_world(); #endif } /* overbeek_world */ else error = 1; if (error) { Stats[INPUT_ERRORS]++; if (t) { fprintf(out_fp, "ERROR, command not found: "); print_term_nl(out_fp, t); } } if (t) zap_term(t); if (!quit_early) t = read_term(in_fp, &rc); } } /* read_a_file */ /************* * * sos_argument() * *************/ void sos_argument(char *buf) { struct term *t; int p = 0; t = str_to_term(buf, &p, 0); if (t == NULL) { Stats[INPUT_ERRORS]++; } else { skip_white(buf, &p); if (buf[p] == '.') p++; skip_white(buf, &p); if (buf[p] != '\0') { fprintf(stdout, "\nERROR, characters after term:\n"); print_error(stdout, buf, p); Stats[INPUT_ERRORS]++; } else { t = term_fixup(t); if (!set_vars(t)) { fprintf(stdout, "\nERROR, clause contains too many variables:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); Stats[INPUT_ERRORS]++; } else if (contains_skolem_symbol(t)) { fprintf(stdout, "\nERROR, input clause contains Skolem symbol:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); Stats[INPUT_ERRORS]++; } else { struct clause *c = term_to_clause(t); zap_term(t); if (c == NULL) Stats[INPUT_ERRORS]++; if (Flags[PROCESS_INPUT].val == 0) { cl_integrate(c); } fprintf(stdout, "\nlist(sos).\n"); print_clause(stdout, c); fprintf(stdout, "end_of_list.\n"); append_cl(Sos, c); Stats[SOS_SIZE]++; } } } } /* sos_argument */ /************* * * read_all_input() * *************/ void read_all_input(int argc, char **argv) { struct list *l; struct clause *c, *c2; FILE *in_fp, *out_fp; Usable = get_list(); Sos = get_list(); Demodulators = get_list(); Passive = get_list(); Hot = get_list(); Hints = get_list(); Hints2 = get_list(); Mace_constraints = get_list(); in_fp = stdin; out_fp = stdout; /* otter < in > out otter -f f1 f2 f3 > out otter -s 'f(x,x)=x.' < in > out otter -s 'f(x,x)=x.' -f f1 f2 f3 > out */ /* Always turn on input clock, in case it is set in the input. This prevents a warning message about trying to stop a clock that is not running. */ { int clock_flag = Flags[CLOCKS].val; /* save */ Flags[CLOCKS].val = 1; /* set */ CLOCK_START(INPUT_TIME); Flags[CLOCKS].val = clock_flag; /* restore */ } if ((argc > 1 && str_ident(argv[1], "-f")) || (argc > 3 && str_ident(argv[3], "-f"))) { /* read from files given in rest of arguments */ int n = (argc > 1 && str_ident(argv[1], "-f")) ? 2 : 4; int i; for (i = n; i < argc; i++) { in_fp = fopen(argv[i], "r"); if (in_fp == NULL) { printf("\nERROR, input file %s not found.\n", argv[i]); Stats[INPUT_ERRORS]++; } else { printf("\n%% Reading file %s.\n", argv[i]); read_a_file(in_fp, out_fp); /* read from file arg */ } } } else read_a_file(in_fp, out_fp); /* read from stdin */ CLOCK_STOP(INPUT_TIME); if (argc > 1 && str_ident(argv[1], "-s")) if (argc < 3) { printf("ERROR, missing sos (-s) argument.\n"); Stats[INPUT_ERRORS]++; } else { printf("\n%% Reading sos clause from the command line.\n"); sos_argument(argv[2]); /* get sos clause from command line */ } if (Internal_flags[FOREACH_SOS]) foreach_sos(); /* fork children to do rest of clauses on stdin */ if (Stats[INPUT_ERRORS] == 0) { if (!Internal_flags[LEX_VALS_SET]) auto_lex_order(); if (Flags[AUTO2].val) automatic_2_settings(); else if (Flags[AUTO1].val) automatic_1_settings(); check_options(); /* process demodulators */ for (c = Demodulators->first_cl; c; c = c->next_cl) { if (check_input_demod(c)) { if (!Flags[DEMOD_LINEAR].val) imd_insert(c, Demod_imd); } else { Stats[INPUT_ERRORS]++; printf("ERROR, bad demodulator: "); print_clause(stdout, c); } } /* Index passive list; don't pre_process, even if flag is set. */ for (c = Passive->first_cl; c; c = c->next_cl) index_lits_all(c); /* Index hot list. */ if (Hot->first_cl) { init_hot(); for (c = Hot->first_cl; c; c = c->next_cl) hot_index_clause(c); } /* Compile and index hints. */ if (Internal_flags[HINTS_PRESENT] && Internal_flags[HINTS2_PRESENT]) abend("list(hints) and list(hints2) are incompatible."); if (Internal_flags[HINTS_PRESENT]) compile_hints(); else if (Internal_flags[HINTS2_PRESENT]) compile_hints2(); /* Process input if flag is set. */ if (Flags[PROCESS_INPUT].val) { CLOCK_START(PROCESS_INPUT_TIME); printf("\n------------> process usable:\n"); l = Usable; Usable = get_list(); Stats[USABLE_SIZE] = 0; c = l->first_cl; while (c) { c2 = c; c = c->next_cl; cl_clear_vars(c2); /* destroy input variable names */ pre_process(c2, 1, Usable); } free_list(l); c2 = NULL; post_proc_all((struct clause *) NULL, 1, Usable); printf("\n------------> process sos:\n"); l = Sos; Sos = get_list(); Stats[SOS_SIZE] = 0; c = l->first_cl; while (c) { c2 = c; c = c->next_cl; cl_clear_vars(c2); /* destroy input variable names */ pre_process(c2, 1, Sos); } free_list(l); c2 = NULL; post_proc_all((struct clause *) NULL, 1, Sos); if (Flags[INPUT_SOS_FIRST].val) for (c = Sos->first_cl; c; c = c->next_cl) c->pick_weight = -MAX_INT; CLOCK_STOP(PROCESS_INPUT_TIME); } else { /* index usable and sos (not passive) */ for (c = Usable->first_cl; c; c = c->next_cl) { index_lits_clash(c); index_lits_all(c); } for (c = Sos->first_cl; c; c = c->next_cl) { index_lits_all(c); if (Flags[INPUT_SOS_FIRST].val) c->pick_weight = -MAX_INT; else { c->pick_weight = weight_cl(c, Weight_pick_given_index); if (Internal_flags[HINTS_PRESENT]) adjust_weight_with_hints(c); else if (Internal_flags[HINTS2_PRESENT]) adjust_weight_with_hints2(c); } } } } printf("\n======= end of input processing =======\n"); fflush(stdout); Max_input_id = next_cl_num() - 1; fflush(stdout); } /* read_all_input */ /************* * * set_lex_vals(t) * * t is a lex term with a list as its one and only argument. * Set lexical values of the members to 1, 2, 3, ... . * *************/ void set_lex_vals(struct term *t) { struct rel *r; int i; struct sym_ent *p; /* Symbols get lex vals 2, 4, 6, 8, ... . */ for ( r = t->farg, i = 0; r->argval->sym_num != Nil_sym_num; r = r->argval->farg->narg, i++) { p = sn_to_node(r->argval->farg->argval->sym_num); p->lex_val = i*2 + 2; } } /* set_lex_vals */ /************* * * set_lrpo_status(t, val) - * t is a lex term with a list as its one and only argument. * Set lrpo_status values of the members to 1. * *************/ void set_lrpo_status(struct term *t, int val) { struct rel *r; struct sym_ent *p; for (r = t->farg; r->argval->sym_num != Nil_sym_num; r = r->argval->farg->narg) { p = sn_to_node(r->argval->farg->argval->sym_num); p->lex_rpo_status = val; } } /* set_lrpo_status */ /************* * * set_special_unary(t) * * t is a lex term with a list as its one and only argument. * Set special_unary values of the members to 1. * *************/ void set_special_unary(struct term *t) { struct rel *r; struct sym_ent *p; for (r = t->farg; r->argval->sym_num != Nil_sym_num; r = r->argval->farg->narg) { p = sn_to_node(r->argval->farg->argval->sym_num); p->special_unary = 1; } } /* set_special_unary */ /************* * * set_skolem(t) * * t is a lex term with a list as its one and only argument. * Set the major function symbol (including constants) of each member of the * list to be a skolem symbol. (This is called only when skolem symbols * are not created by skolemization by OTTER.) * *************/ void set_skolem(struct term *t) { struct rel *r; struct sym_ent *p; for (r = t->farg; r->argval->sym_num != Nil_sym_num; r = r->argval->farg->narg) { p = sn_to_node(r->argval->farg->argval->sym_num); p->skolem = 1; } } /* set_skolem */ /************* * * free_all_mem() * *************/ void free_all_mem(void) { struct clause *c; c = find_last_cl(Usable); while (c) { rem_from_list(c); un_index_lits_clash(c); un_index_lits_all(c); cl_del_int(c); c = find_last_cl(Usable); } free_list(Usable); Usable = NULL; c = find_last_cl(Sos); while (c) { rem_from_list(c); un_index_lits_all(c); cl_del_int(c); c = find_last_cl(Sos); } free_list(Sos); Sos = NULL; c = find_last_cl(Passive); while (c) { rem_from_list(c); un_index_lits_all(c); cl_del_int(c); c = find_last_cl(Passive); } free_list(Passive); Passive = NULL; c = find_last_cl(Demodulators); while (c) { rem_from_list(c); if (Flags[DEMOD_LINEAR].val == 0) /* if imd indexing */ imd_delete(c, Demod_imd); cl_del_int(c); c = find_last_cl(Demodulators); } free_list(Demodulators); Demodulators = NULL; zap_hints2(); free_imd_tree(Demod_imd); /* Weight_purge_gen and Weight_pick_given might point to the same list */ if (Weight_purge_gen) { weight_index_delete(Weight_purge_gen_index); zap_list(Weight_purge_gen); if (Weight_purge_gen == Weight_pick_given) { Weight_pick_given = NULL; Weight_pick_given_index = NULL; } Weight_purge_gen = NULL; Weight_purge_gen_index = NULL; } if (Weight_pick_given) { weight_index_delete(Weight_pick_given_index); zap_list(Weight_pick_given); Weight_pick_given = NULL; Weight_pick_given_index = NULL; } if (Weight_terms) { weight_index_delete(Weight_terms_index); zap_list(Weight_terms); Weight_terms = NULL; Weight_terms_index = NULL; } free_is_tree(Is_pos_lits); free_is_tree(Is_neg_lits); Is_pos_lits = Is_neg_lits = NULL; del_hidden_clauses(); free_sym_tab(); } /* free_all_mem */ /************* * * output_stats(fp, level) -- print memory, clause, and time stats * *************/ void output_stats(FILE *fp, int level) { if (level >= 4) print_options(fp); if (level >= 3) print_mem(fp); if (level >= 2) { print_stats(fp); print_times(fp); } else if (level == 1) { print_stats_brief(fp); print_times_brief(fp); } #if 1 if (level >= 3) { int i, j; fprintf(fp, "\nForward subsumption counts, subsumer:number_subsumed.\n"); for (i = 0; i < 10; i++) { for (j = 1; j < 10; j++) fprintf(fp, "%2d:%-4d ", 10*i+j, Subsume_count[10*i+j]); if (i < 9) /* don't do 100 */ fprintf(fp, "%2d:%-4d\n", 10*i+10, Subsume_count[10*i+10]); else fprintf(fp, "\n"); } fprintf(fp, "All others: %d.\n", Subsume_count[0]); } #endif } /* output_stats */ /************* * * print_stats(fp) * *************/ void print_stats(FILE *fp) { if (splitting()) fprintf(fp, "\n------- statistics (process %d) -------\n", my_process_id()); else fprintf(fp, "\n-------------- statistics -------------\n"); #if 0 fprintf(fp, "clauses input %7ld\n", Stats[CL_INPUT]); #endif fprintf(fp, "clauses given %7ld\n", Stats[CL_GIVEN]); fprintf(fp, "clauses generated %7ld\n", Stats[CL_GENERATED]); if (Hot->first_cl) fprintf(fp, " (hot clauses generated)%7ld\n", Stats[HOT_GENERATED]); if (Flags[BINARY_RES].val) fprintf(fp, " binary_res generated %7ld\n", Stats[BINARY_RES_GEN]); if (Flags[HYPER_RES].val) fprintf(fp, " hyper_res generated %7ld\n", Stats[HYPER_RES_GEN]); if (Flags[NEG_HYPER_RES].val) fprintf(fp, " neg_hyper_res generated%7ld\n", Stats[NEG_HYPER_RES_GEN]); if (Flags[PARA_FROM].val) fprintf(fp, " para_from generated %7ld\n", Stats[PARA_FROM_GEN]); if (Flags[PARA_INTO].val) fprintf(fp, " para_into generated %7ld\n", Stats[PARA_INTO_GEN]); if (Flags[FACTOR].val) fprintf(fp, " factors generated %7ld\n", Stats[FACTOR_GEN]); if (Flags[GEOMETRIC_RULE].val) fprintf(fp, " gL rule generated %7ld\n", Stats[GEO_GEN]); if (Flags[DEMOD_INF].val) fprintf(fp, " demod_inf generated %7ld\n", Stats[DEMOD_INF_GEN]); if (Flags[UR_RES].val) fprintf(fp, " ur_res generated %7ld\n", Stats[UR_RES_GEN]); if (Flags[LINKED_UR_RES].val) fprintf(fp, " linked_ur_res generated%7ld\n", Stats[LINKED_UR_RES_GEN]); if (Flags[BACK_UNIT_DELETION].val) fprintf(fp, " back unit del. gen. %7ld\n", Stats[BACK_UNIT_DEL_GEN]); fprintf(fp, "demod & eval rewrites %7ld\n", Stats[REWRITES]); fprintf(fp, "clauses wt,lit,sk delete %7ld\n", Stats[CL_WT_DELETE]); fprintf(fp, "tautologies deleted %7ld\n", Stats[CL_TAUTOLOGY]); fprintf(fp, "clauses forward subsumed %7ld\n", Stats[CL_FOR_SUB]); if (Flags[ANCESTOR_SUBSUME].val) fprintf(fp, "cl not subsumed due to ancestor_subsume %7ld\n", Stats[CL_NOT_ANC_SUBSUMED]); fprintf(fp, " (subsumed by sos) %7ld\n", Stats[FOR_SUB_SOS]); fprintf(fp, "unit deletions %7ld\n", Stats[UNIT_DELETES]); fprintf(fp, "factor simplifications %7ld\n", Stats[FACTOR_SIMPLIFICATIONS]); fprintf(fp, "clauses kept %7ld\n", Stats[CL_KEPT]); if (Hot->first_cl) fprintf(fp, " (hot clauses kept) %7ld\n", Stats[HOT_KEPT]); fprintf(fp, "new demodulators %7ld\n", Stats[NEW_DEMODS]); fprintf(fp, "empty clauses %7ld\n", Stats[EMPTY_CLAUSES]); fprintf(fp, "clauses back demodulated %7ld\n", Stats[CL_BACK_DEMOD]); fprintf(fp, "clauses back subsumed %7ld\n", Stats[CL_BACK_SUB]); fprintf(fp, "usable size %7ld\n", Stats[USABLE_SIZE]); fprintf(fp, "sos size %7ld\n", Stats[SOS_SIZE]); fprintf(fp, "demodulators size %7ld\n", Stats[DEMODULATORS_SIZE]); fprintf(fp, "passive size %7ld\n", Stats[PASSIVE_SIZE]); fprintf(fp, "hot size %7ld\n", Stats[HOT_SIZE]); fprintf(fp, "Kbytes malloced %7ld\n", Stats[K_MALLOCED]); if (Flags[LINKED_UR_RES].val) { fprintf(fp, "linked UR depth hits %7ld\n", Stats[LINKED_UR_DEPTH_HITS]); fprintf(fp, "linked UR deduct hits %7ld\n", Stats[LINKED_UR_DED_HITS]); } /* The following are output only if not 0. */ /* They aren't errors, but they are anomalies. */ if (Stats[CL_VAR_DELETES] != 0) fprintf(fp, "cl deletes, too many vars %7ld\n", Stats[CL_VAR_DELETES]); if (Stats[FPA_OVERLOADS] != 0) fprintf(fp, "fpa argument overloads %7ld\n", Stats[FPA_OVERLOADS]); if (Stats[FPA_UNDERLOADS] != 0) fprintf(fp, "fpa argument underloads %7ld\n", Stats[FPA_UNDERLOADS]); if (Stats[DEMOD_LIMITS] != 0) fprintf(fp, "demodulations stopped by limit %7ld\n", Stats[DEMOD_LIMITS]); } /* print_stats */ /************* * * print_stats_brief(fp) * *************/ void print_stats_brief(FILE *fp) { if (splitting()) fprintf(fp, "\n------- statistics (process %d) -------\n", my_process_id()); else fprintf(fp, "\n-------------- statistics -------------\n"); fprintf(fp, "clauses given %7ld\n", Stats[CL_GIVEN]); fprintf(fp, "clauses generated %7ld\n", Stats[CL_GENERATED]); if (Hot && Hot->first_cl) fprintf(fp, " (hot clauses generated)%7ld\n", Stats[HOT_GENERATED]); fprintf(fp, "clauses kept %7ld\n", Stats[CL_KEPT]); if (Hot && Hot->first_cl) fprintf(fp, " (hot clauses kept)%7ld\n", Stats[HOT_KEPT]); fprintf(fp, "clauses forward subsumed %7ld\n", Stats[CL_FOR_SUB]); fprintf(fp, "clauses back subsumed %7ld\n", Stats[CL_BACK_SUB]); fprintf(fp, "Kbytes malloced %7ld\n", Stats[K_MALLOCED]); } /* print_stats_brief */ /************* * * p_stats() * *************/ void p_stats(void) { print_stats(stdout); } /* p_stats */ /************* * * print_times(fp) * *************/ void print_times(FILE *fp) { long t, min, hr; fprintf(fp, "\n----------- times (seconds) -----------\n"); t = run_time(); fprintf(fp, "user CPU time %10.2f ", t / 1000.); t = t / 1000; hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); t = system_time(); fprintf(fp, "system CPU time %10.2f ", t / 1000.); t = t / 1000; hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); t = wall_seconds() - Stats[INIT_WALL_SECONDS]; fprintf(fp, "wall-clock time %7ld ", t); hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); if (Flags[CLOCKS].val) { #ifndef TP_ABSOLUTELY_NO_CLOCKS fprintf(fp, "input time %10.2f\n", clock_val(INPUT_TIME) / 1000.); fprintf(fp, " clausify time %10.2f\n", clock_val(CLAUSIFY_TIME) / 1000.); if (Flags[PROCESS_INPUT].val) fprintf(fp, " process input %10.2f\n", clock_val(PROCESS_INPUT_TIME) / 1000.); fprintf(fp, "pick given time %10.2f\n", clock_val(PICK_GIVEN_TIME) / 1000.); if (Flags[BINARY_RES].val) fprintf(fp, "binary_res time %10.2f\n", clock_val(BINARY_TIME) / 1000.); if (Flags[HYPER_RES].val) fprintf(fp, "hyper_res time %10.2f\n", clock_val(HYPER_TIME) / 1000.); if (Flags[NEG_HYPER_RES].val) fprintf(fp, "neg_hyper_res time%9.2f\n", clock_val(NEG_HYPER_TIME) / 1000.); if (Flags[UR_RES].val) fprintf(fp, "ur_res time %10.2f\n", clock_val(UR_TIME) / 1000.); if (Flags[PARA_INTO].val) fprintf(fp, "para_into time %10.2f\n", clock_val(PARA_INTO_TIME) / 1000.); if (Flags[PARA_FROM].val) fprintf(fp, "para_from time %10.2f\n", clock_val(PARA_FROM_TIME) / 1000.); if (Flags[LINKED_UR_RES].val) fprintf(fp, "linked_ur time %10.2f\n", clock_val(LINKED_UR_TIME) / 1000.); if (Flags[BACK_UNIT_DELETION].val) fprintf(fp, "back unit del time%9.2f\n", clock_val(BACK_UNIT_DEL_TIME) / 1000.); fprintf(fp, "pre_process time %10.2f\n", clock_val(PRE_PROC_TIME) / 1000.); fprintf(fp, " renumber time %10.2f\n", clock_val(RENUMBER_TIME) / 1000.); fprintf(fp, " demod time %10.2f\n", clock_val(DEMOD_TIME) / 1000.); fprintf(fp, " order equalities%9.2f\n", clock_val(ORDER_EQ_TIME) / 1000.); fprintf(fp, " unit deleletion%10.2f\n", clock_val(UNIT_DEL_TIME) / 1000.); fprintf(fp, " factor simplify%10.2f\n", clock_val(FACTOR_SIMP_TIME) / 1000.); fprintf(fp, " weigh cl time %10.2f\n", clock_val(WEIGH_CL_TIME) / 1000.); fprintf(fp, " hints keep time%10.2f\n", clock_val(HINTS_KEEP_TIME) / 1000.); fprintf(fp, " sort lits time %10.2f\n", clock_val(SORT_LITS_TIME) / 1000.); fprintf(fp, " forward subsume%10.2f\n", clock_val(FOR_SUB_TIME) / 1000.); fprintf(fp, " delete cl time %10.2f\n", clock_val(DEL_CL_TIME) / 1000.); fprintf(fp, " keep cl time %10.2f\n", clock_val(KEEP_CL_TIME) / 1000.); fprintf(fp, " hints time %10.2f\n", clock_val(HINTS_TIME) / 1000.); fprintf(fp, " print_cl time %10.2f\n", clock_val(PRINT_CL_TIME) / 1000.); fprintf(fp, " conflict time %10.2f\n", clock_val(CONFLICT_TIME) / 1000.); fprintf(fp, " new demod time %10.2f\n", clock_val(NEW_DEMOD_TIME) / 1000.); fprintf(fp, "post_process time%10.2f\n", clock_val(POST_PROC_TIME) / 1000.); fprintf(fp, " back demod time%10.2f\n", clock_val(BACK_DEMOD_TIME) / 1000.); fprintf(fp, " back subsume %10.2f\n", clock_val(BACK_SUB_TIME) / 1000.); fprintf(fp, " factor time %10.2f\n", clock_val(FACTOR_TIME) / 1000.); if (Hot->first_cl) fprintf(fp, " hot list time %10.2f\n", clock_val(HOT_TIME) / 1000.); fprintf(fp, " unindex time %10.2f\n", clock_val(UN_INDEX_TIME) / 1000.); #endif /* ndef TP_ABSOLUTELY_NO_CLOCKS */ } } /* print_times */ /************* * * print_times_brief(fp) * *************/ void print_times_brief(FILE *fp) { long t, min, hr; fprintf(fp, "\n----------- times (seconds) -----------\n"); t = run_time(); fprintf(fp, "user CPU time %10.2f ", t / 1000.); t = t / 1000; hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); t = system_time(); fprintf(fp, "system CPU time %10.2f ", t / 1000.); t = t / 1000; hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); t = wall_seconds() - Stats[INIT_WALL_SECONDS]; fprintf(fp, "wall-clock time %7ld ", t); hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); if (Flags[CLOCKS].val) { if (Flags[BINARY_RES].val) fprintf(fp, "binary_res time %10.2f\n", clock_val(BINARY_TIME) / 1000.); if (Flags[HYPER_RES].val) fprintf(fp, "hyper_res time %10.2f\n", clock_val(HYPER_TIME) / 1000.); if (Flags[NEG_HYPER_RES].val) fprintf(fp, "neg_hyper time %10.2f\n", clock_val(NEG_HYPER_TIME) / 1000.); if (Flags[UR_RES].val) fprintf(fp, "UR_res time %10.2f\n", clock_val(UR_TIME) / 1000.); if (Flags[PARA_INTO].val) fprintf(fp, "para_into time %10.2f\n", clock_val(PARA_INTO_TIME) / 1000.); if (Flags[PARA_FROM].val) fprintf(fp, "para_from time %10.2f\n", clock_val(PARA_FROM_TIME) / 1000.); if (Flags[LINKED_UR_RES].val) fprintf(fp, "linked_ur time %10.2f\n", clock_val(LINKED_UR_TIME) / 1000.); fprintf(fp, "for_sub time %10.2f\n", clock_val(FOR_SUB_TIME) / 1000.); fprintf(fp, "back_sub time %10.2f\n", clock_val(BACK_SUB_TIME) / 1000.); fprintf(fp, "conflict time %10.2f\n", clock_val(CONFLICT_TIME) / 1000.); if ((Demodulators && Demodulators->first_cl) || Internal_flags[DOLLAR_PRESENT]) fprintf(fp, "demod time %10.2f\n", clock_val(DEMOD_TIME) / 1000.); if (Hot && Hot->first_cl) fprintf(fp, " hot list time %10.2f\n", clock_val(HOT_TIME) / 1000.); } } /* print_times_brief */ /************* * * p_times() * *************/ void p_times(void) { print_times(stdout); } /* p_times */ /************* * * append_lists(l1, l2) -- append l2 to l1 and free the header node l2 * *************/ void append_lists(struct list *l1, struct list *l2) { struct clause *c; int i; if (l1->last_cl) /* if l1 not empty */ l1->last_cl->next_cl = l2->first_cl; else l1->first_cl = l2->first_cl; if (l2->first_cl) { /* if l2 not empty */ l2->first_cl->prev_cl = l1->last_cl; l1->last_cl = l2->last_cl; } for (c = l2->first_cl, i = 0; c; c = c->next_cl, i++) c->container = l1; if (l1 == Usable) Stats[USABLE_SIZE] += i; else if (l1 == Sos) Stats[SOS_SIZE] += i; else if (l1 == Demodulators) Stats[DEMODULATORS_SIZE] += i; else if (l1 == Passive) Stats[PASSIVE_SIZE] += i; else if (l1 == Hot) Stats[HOT_SIZE] += i; if (l2 == Usable) Stats[USABLE_SIZE] -= i; else if (l2 == Sos) Stats[SOS_SIZE] -= i; else if (l2 == Demodulators) Stats[DEMODULATORS_SIZE] -= i; else if (l2 == Passive) Stats[PASSIVE_SIZE] -= i; else if (l2 == Hot) Stats[HOT_SIZE] -= i; free_list(l2); } /* append_lists */ /************* * * struct term *copy_term(term) -- Return a copy of the term. * * The bits field is not copied. * *************/ struct term *copy_term(struct term *t) { struct rel *r, *r2, *r3; struct term *t2; t2 = get_term(); t2->type = t->type; t2->sym_num = t->sym_num; t2->varnum = t->varnum; if (t->type != COMPLEX) return(t2); else { r3 = NULL; r = t->farg; while (r) { r2 = get_rel(); if (r3 == NULL) t2->farg = r2; else r3->narg = r2; r2->argval = copy_term(r->argval); r3 = r2; r = r->narg; } return(t2); } } /* copy_term */ /************* * * int biggest_var(term) -- return largest variable number (-1 if none) * *************/ int biggest_var(struct term *t) { struct rel *r; int i, j; if (t->type == VARIABLE) return(t->varnum); else if (t->type == NAME) return(-1); else { r = t->farg; i = -1; while (r) { j = biggest_var(r->argval); if (j > i) i = j; r = r->narg; } return(i); } } /* biggest_var */ /************* * * int biggest_var_clause(c) -- return largest variable number (-1 if none) * *************/ int biggest_var_clause(struct clause *c) { struct literal *lit; int i, max; max = -1; for (lit = c->first_lit; lit; lit = lit->next_lit) { i = biggest_var(lit->atom); max = (i > max ? i : max); } return(max); } /* biggest_var_clause */ /************* * * int ground_clause(c) * *************/ int ground_clause(struct clause *c) { return(biggest_var_clause(c) == -1); } /* ground_var_clause */ /************* * * zap_list(term_ptr) -- Free a list of nonintegrated terms. * *************/ void zap_list(struct term_ptr *p) { struct term_ptr *q; while (p) { zap_term(p->term); q = p; p = p->next; free_term_ptr(q); } } /* zap_list */ /************* * * int occurs_in(t1, t2) -- Does t1 occur in t2? * * term_ident is used to check identity. * *************/ int occurs_in(struct term *t1, struct term *t2) { struct rel *r; if (term_ident(t1, t2)) return(1); else if (t2->type != COMPLEX) return(0); else { r = t2->farg; while (r && occurs_in(t1, r->argval) == 0) r = r->narg; return(r != NULL); } } /* occurs_in */ /************* * * occurrences(s, t) * * How many occurrences of s are there in t. * *************/ int occurrences(struct term *s, struct term *t) { if (term_ident(s, t)) return(1); else if (t->type != COMPLEX) return(0); else { struct rel *r; int count; for (r = t->farg, count = 0; r; r = r->narg) count += occurrences(s, r->argval); return(count); } } /* occurrences */ /************* * * int sn_occur(sn, t) * * Is sn the sym_num of t or any subterms of t? * *************/ int sn_occur(int sn, struct term *t) { struct rel *r; int occurs; if (t->type != COMPLEX) return(t->sym_num == sn); else if (t->sym_num == sn) return(1); else { occurs = 0; r = t->farg; while (r && occurs == 0) { occurs = sn_occur(sn, r->argval); r = r->narg; } return(occurs); } } /* sn_occur */ /************* * * is is_atom(t) -- Is t an atom? * * A term is an atom iff it is not a variable and varnum != 0. * (The varnum field of an atom gives its type---equality, answer, evaluable, etc.) * *************/ int is_atom(struct term *t) { return(t->type != VARIABLE && t->varnum != 0); } /* is_atom */ /************* * * int id_nested_skolems(t) * * Does t or any of its subterms have the identical_nested_skolems property? * *************/ static int id_nested_skolems(struct term *t) { struct rel *r; int occurs; if (t->type != COMPLEX) return(0); else { occurs = 0; if (is_skolem(t->sym_num)) { r = t->farg; while (r && occurs == 0) { occurs = sn_occur(t->sym_num, r->argval); r = r->narg; } } if (occurs) return(1); else { occurs = 0; r = t->farg; while (r && occurs == 0) { occurs = id_nested_skolems(r->argval); r = r->narg; } return(occurs); } } } /* id_nested_skolems */ /************* * * int ident_nested_skolems(c) * * Do any of the terms in clause c have the * identical_nested_skolems property? * *************/ int ident_nested_skolems(struct clause *c) { struct literal *l; int occurs; l = c->first_lit; occurs = 0; while (l && occurs == 0) { occurs = id_nested_skolems(l->atom); l = l->next_lit; } return(occurs); } /* ident_nested_skolems */ /************* * * int ground(t) -- is a term ground? * *************/ int ground(struct term *t) { struct rel *r; int ok; if (t->type == NAME) return(1); else if (t->type == VARIABLE) return(0); else { /* COMPLEX */ ok = 1; for (r = t->farg; r && ok; r = r->narg) ok = ground(r->argval); return(ok); } } /* ground */ /************* * * void cleanup() * *************/ void cleanup(void) { printf("\n============ end of search ============\n"); if (Flags[PRINT_LISTS_AT_END].val) { printf("\nlist(usable).\n"); print_cl_list(stdout, Usable); printf("\nlist(sos).\n"); print_cl_list(stdout, Sos); if (Demodulators) { printf("\nlist(demodulators).\n"); print_cl_list(stdout, Demodulators); } printf("\n"); } if (Flags[FREE_ALL_MEM].val && ! multi_justifications()) free_all_mem(); output_stats(stdout, Parms[STATS_LEVEL].val); if (Stats[EMPTY_CLAUSES] > 0 && (!splitting() || current_case() == NULL)) printf("\nThat finishes the proof of the theorem.\n"); printf("\nProcess %d finished %s", my_process_id(), get_time()); } /* cleanup */ /************* * * int check_stop() -- Should the search be terminated? * * return: * KEEP_SEARCHING if we should not stop; * MAX_GIVEN_EXIT if we should stop because of max_given option; * MAX_SECONDS_EXIT if we should stop because of max_seconds option; * MAX_GEN_EXIT if we should stop because of max_gen option; * MAX_KEPT_EXIT if we should stop because of max_kept option. * MAX_LEVELS_EXIT if we should stop because of max_levels option. * *************/ int check_stop(void) { long given, seconds, gen, kept; int max_given, max_seconds, max_gen, max_kept; given = Stats[CL_GIVEN]; gen = Stats[CL_GENERATED]; kept = Stats[CL_KEPT]; if (splitting()) seconds = wall_seconds() - Stats[INIT_WALL_SECONDS]; else seconds = run_time() / 1000; max_given = Parms[MAX_GIVEN].val; max_seconds = Parms[MAX_SECONDS].val; max_gen = Parms[MAX_GEN].val; max_kept = Parms[MAX_KEPT].val; if (max_given != -1 && given >= max_given) return(MAX_GIVEN_EXIT); else if(max_seconds != -1 && seconds >= max_seconds) return(MAX_SECONDS_EXIT); else if (max_gen != -1 && gen >= max_gen) return(MAX_GEN_EXIT); else if (max_kept != -1 && kept >= max_kept) return(MAX_KEPT_EXIT); else return(KEEP_SEARCHING); } /* check_stop */ /************* * * report() -- possibly report statistics and times * *************/ void report(void) { static int next_report; double runtime; if (next_report == 0) next_report = Parms[REPORT].val; runtime = run_time() / 1000.; if (runtime >= next_report) { printf("\n----- report at %9.2f seconds ----- %s", runtime, get_time()); output_stats(stdout, Parms[STATS_LEVEL].val); fprintf(stderr, "%cA report (%.2f seconds) has been sent to the output file.\n", Bell, runtime); while (runtime >= next_report) next_report += Parms[REPORT].val; } } /* report */ /************* * * void control_memory() * *************/ void control_memory(void) { static int next_control_point = 0; int sos_distribution[500]; int i, j, wt, n, control, size; struct clause *c; j = total_mem(); if (Parms[MAX_MEM].val != 0 && j*3 > Parms[MAX_MEM].val) { if (!next_control_point) control = 1; else if (next_control_point == Stats[CL_GIVEN]) control = 1; else control = 0; } else control = 0; if (control) { next_control_point = Stats[CL_GIVEN] + 20; for (i = 0; i < 500; i++) sos_distribution[i] = 0; for (c = Sos->first_cl, size = 0; c; c = c->next_cl, size++) { if (c->pick_weight < 0) wt = 0; else if (c->pick_weight >= 500) wt = 499; else wt = c->pick_weight; sos_distribution[wt]++; } i = 0; n = 0; while (i < 500 && n*20 <= size) { n += sos_distribution[i]; i++; } i--; /* reset weight limit to i */ if (i < Parms[MAX_WEIGHT].val || Parms[MAX_WEIGHT].val == 0) { Parms[MAX_WEIGHT].val = i; fprintf(stderr, "%c\n\nResetting weight limit to %d.\n\n", Bell, i); printf("\nResetting weight limit to %d.\n\n", i); printf("sos_size=%d\n", size); fflush(stdout); #if 0 printf("weight: number of sos clauses with that weight\n"); for (j = 0; j < 100; j++) printf("%d: %d\n", j, sos_distribution[j]); #endif } } } /* control_memory */ /************* * * proof_message(c) - print a message to stderr * * If clause c has any (probably answer) literals, print c. * *************/ static void proof_message(struct clause *c) { char *user = username(); long i = run_time(); /* i is milliseconds */ if (Stats[EMPTY_CLAUSES] == 1) fprintf(stderr, "\n"); if (splitting() && current_case() != NULL) { fprintf(stderr, "%c--- refuted case ", Bell); print_case(stderr); } else if (i > 10000) { /* If more than 10 seconds, print excitedly. */ fprintf(stderr, "%c-- HEY %s, WE HAVE A PROOF!! -- ", Bell, user); } else fprintf(stderr, "%c-------- PROOF -------- ", Bell); if (c->first_lit) print_clause(stderr, c); else fprintf(stderr, "\n"); } /* proof_message */ /************* * * print_proof(fp, c) * *************/ void print_proof(FILE *fp, struct clause *c) { struct clause_ptr *cp1, *cp2, *cp3; struct ilist *ip1, *ip2; int length, level; cp1 = NULL; ip1 = NULL; level = get_ancestors(c, &cp1, &ip1); for (length = 0, cp2 = cp1; cp2; cp2 = cp2->next) if (cp2->c->parents && cp2->c->parents->i != NEW_DEMOD_RULE) { length++; } proof_message(c); /* to stderr */ fprintf(fp, "Length of proof is %d.", length-1); fprintf(fp, " Level of proof is %d.", level-1); if (splitting()) { struct ilist *p = current_case(); if (p != NULL) { fprintf(fp, " Case "); print_case(fp); } } if (Flags[PROOF_WEIGHT].val) fprintf(fp, " Weight of proof is %d.", prf_weight(c)); fprintf(fp, "\n\n---------------- PROOF ----------------\n\n"); cp2 = cp1; while (cp2) { cp3 = cp2->next; if (cp3 && cp3->c->parents && cp3->c->parents->i == NEW_DEMOD_RULE && cp3->c->parents->next->i == cp2->c->id) { /* skip over dynamic demodulator copy */ fprintf(fp, "%d,", cp3->c->id); print_clause(fp, cp2->c); cp2 = cp3->next; } else { print_clause(fp, cp2->c); cp2 = cp2->next; } } fprintf(fp, "\n------------ end of proof -------------\n\n"); fflush(fp); while (cp1 != NULL) { cp2 = cp1; cp1 = cp1->next; free_clause_ptr(cp2); ip2 = ip1; ip1 = ip1->next; free_ilist(ip2); } } /* print_proof */ /************* * * struct clause *check_for_proof(c) * * Check for EMPTY CLAUSE proof and UNIT CONFLICT proof. * *************/ struct clause *check_for_proof(struct clause *c) { struct clause *e; struct clause_ptr *cp1, *cp2; int number_of_lits; e = NULL; number_of_lits = num_literals(c); if (number_of_lits == 0) { printf("\n-----> EMPTY CLAUSE at %6.2f sec ----> ", run_time() / 1000.); print_clause(stdout, c); printf("\n"); Stats[CL_KEPT]--; /* don't count empty clauses */ /* pre_process has already KEPT it */ rem_from_list(c); hide_clause(c); Stats[EMPTY_CLAUSES]++; e = c; if (Flags[PRINT_PROOFS].val) print_proof(stdout, e); if (Flags[BUILD_PROOF_OBJECT_1].val || Flags[BUILD_PROOF_OBJECT_2].val) build_proof_object(e); } else if (number_of_lits == 1) { cp1 = unit_conflict(c); while (cp1) { /* empty clause from unit conflict */ e = cp1->c; cp2 = cp1->next; free_clause_ptr(cp1); cp1 = cp2; cl_integrate(e); printf("\n----> UNIT CONFLICT at %6.2f sec ----> ", run_time() / 1000.); print_clause(stdout, e); printf("\n"); hide_clause(e); if (Flags[PRINT_PROOFS].val) print_proof(stdout, e); if (Flags[BUILD_PROOF_OBJECT_1].val || Flags[BUILD_PROOF_OBJECT_2].val) build_proof_object(e); #if 0 multi_test(e); #endif } } return(e); /* NULL if no proof was found */ } /* check_for_proof */ /************* * * int proper_list(t) * * Is term t a proper list * *************/ int proper_list(struct term *t) { if (t->type == VARIABLE) return(0); else if (t->type == NAME) return(t->sym_num == str_to_sn("$nil", 0)); else if (t->sym_num != str_to_sn("$cons", 2)) return(0); else return(proper_list(t->farg->narg->argval)); } /* proper_list */ /************* * * move_clauses() * * Move clauses satisfying given routine from one list to another. * *************/ void move_clauses(int (*clause_proc)(struct clause *c), struct list *source, struct list *destination) { struct clause *c1, *c2; c1 = source->first_cl; while (c1) { c2 = c1->next_cl; if ((*clause_proc)(c1)) { rem_from_list(c1); append_cl(destination, c1); } c1 = c2; } } /* move_clauses */ /************* * * automatic_1_settings() * * Original version (Otter 3.0.4) * * Do a very simple syntactic analysis of the clauses and decide on * a simple strategy. Print a message about the strategy. * *************/ void automatic_1_settings(void) { if (Passive->first_cl) abend("Passive list not accepted in auto1 mode."); else if (Demodulators->first_cl) abend("Demodulators list not accepted in auto1 mode."); else if (Weight_pick_given || Weight_purge_gen || Weight_terms) abend("Weight lists not accepted in auto1 mode."); else { struct clause *c; int propositional, horn, equality, max_lits, i, symmetry; if (Sos->first_cl) { printf("WARNING: Sos list not accepted in auto1 mode:\n"); printf(" sos clauses are being moved to usable list.\n"); append_lists(Usable, Sos); Sos = get_list(); } /* Find out some basic properties. */ /* All input clauses are in Usable; move to Sos. */ for (c=Usable->first_cl, propositional=1; c&&propositional; c=c->next_cl) propositional = propositional_clause(c); for (c=Usable->first_cl, horn = 1; c && horn; c=c->next_cl) horn = horn_clause(c); for (c=Usable->first_cl, equality = 0; c && !equality; c=c->next_cl) equality = equality_clause(c); for (c=Usable->first_cl, symmetry = 0; c && !symmetry; c=c->next_cl) symmetry = symmetry_clause(c); for (c=Usable->first_cl, max_lits = 0; c; c=c->next_cl) { i = num_literals(c); max_lits = (i > max_lits ? i : max_lits); } printf("\nSCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d.\n", propositional, horn, equality, symmetry, max_lits); if (propositional) { printf("\nThe clause set is propositional; the strategy will be\n"); printf("ordered hyperresolution with the propositional\n"); printf("optimizations, with satellites in sos and nuclei in usable.\n\n"); auto_change_flag(stdout, HYPER_RES, 1); auto_change_flag(stdout, PROPOSITIONAL, 1); move_clauses(pos_clause, Usable, Sos); } else if (equality && max_lits == 1) { printf("\nAll clauses are units, and equality is present; the\n"); printf("strategy will be Knuth-Bendix with positive clauses in sos.\n\n"); auto_change_flag(stdout, KNUTH_BENDIX, 1); for (c = Usable->first_cl; c && pos_clause(c); c = c->next_cl); if (!c) { printf("\nThere is no negative clause, so all clause lists will\n"); printf("be printed at the end of the search.\n\n"); auto_change_flag(stdout, PRINT_LISTS_AT_END, 1); } move_clauses(pos_clause, Usable, Sos); } else if (!horn && !equality) { printf("\nThis is a non-Horn set without equality. The strategy will\n"); printf("be ordered hyper_res, unit deletion, and factoring, with\n"); printf("satellites in sos and with nuclei in usable.\n\n"); auto_change_flag(stdout, HYPER_RES, 1); auto_change_flag(stdout, FACTOR, 1); auto_change_flag(stdout, UNIT_DELETION, 1); move_clauses(pos_clause, Usable, Sos); } else if (horn && !equality) { printf("\nThis is a Horn set without equality. The strategy will\n"); printf("be hyperresolution, with satellites in sos and nuclei\n"); printf("in usable.\n\n"); auto_change_flag(stdout, HYPER_RES, 1); auto_change_flag(stdout, ORDER_HYPER, 0); move_clauses(pos_clause, Usable, Sos); } else if (!horn && equality) { printf("\nThis ia a non-Horn set with equality. The strategy will be\n"); printf("Knuth-Bendix, ordered hyper_res, factoring, and unit\n"); printf("deletion, with positive clauses in sos and nonpositive\n"); printf("clauses in usable.\n\n"); auto_change_flag(stdout, KNUTH_BENDIX, 1); auto_change_flag(stdout, HYPER_RES, 1); auto_change_flag(stdout, UNIT_DELETION, 1); auto_change_flag(stdout, FACTOR, 1); if (symmetry) { printf("\nThere is a clause for symmetry of equality, so it is\n"); printf("assumed that equality is fully axiomatized; therefore,\n"); printf("paramodulation is disabled.\n\n"); auto_change_flag(stdout, PARA_FROM, 0); auto_change_flag(stdout, PARA_INTO, 0); } move_clauses(pos_clause, Usable, Sos); } else if (horn && equality) { printf("\nThis is a Horn set with equality. The strategy will be\n"); printf("Knuth-Bendix and hyper_res, with positive clauses in\n"); printf("sos and nonpositive clauses in usable.\n\n"); auto_change_flag(stdout, KNUTH_BENDIX, 1); auto_change_flag(stdout, HYPER_RES, 1); auto_change_flag(stdout, ORDER_HYPER, 0); if (symmetry) { printf("\nThere is a clause for symmetry of equality is, so it is\n"); printf("assumed that equality is fully axiomatized; therefore,\n"); printf("paramodulation is disabled.\n\n"); auto_change_flag(stdout, PARA_FROM, 0); auto_change_flag(stdout, PARA_INTO, 0); } move_clauses(pos_clause, Usable, Sos); } } } /* automatic_1_settings */ /************* * * sos_has_pos_nonground() * *************/ int sos_has_pos_nonground(void) { struct clause *c; for (c = Sos->first_cl; c; c = c->next_cl) { if (pos_clause(c) && !ground_clause(c)) return(1); } return (0); } /* sos_has_pos_nonground */ /************* * * automatic_2_settings() * * Revised version (Otter 3.0.5) * * Do a very simple syntactic analysis of the clauses and decide on * a simple strategy. Print a message about the strategy. * * This version accepts input sos clauses. Also, input usable clauses * can be moved to sos. See below. * *************/ void automatic_2_settings(void) { if (Passive->first_cl) abend("Passive list not accepted in auto2 mode."); else if (Demodulators->first_cl) abend("Demodulators list not accepted in auto2 mode."); else if (Weight_pick_given || Weight_purge_gen || Weight_terms) abend("Weight lists not accepted in auto2 mode."); else { struct clause *c; int propositional, horn, equality, max_lits, i, symmetry; if (sos_has_pos_nonground()) printf("Sos has positive nonground clause; therefore it is not changed.\n"); else { printf("\nEvery positive clause in sos is ground (or sos is empty);\n"); printf("therefore we move all positive usable clauses to sos.\n"); move_clauses(pos_clause, Usable, Sos); } /* Find out some basic properties. */ for (c=Usable->first_cl, propositional=1; c&&propositional; c=c->next_cl) propositional = propositional_clause(c); for (c=Sos->first_cl; c&&propositional; c=c->next_cl) propositional = propositional_clause(c); for (c=Usable->first_cl, horn = 1; c && horn; c=c->next_cl) horn = horn_clause(c); for (c=Sos->first_cl; c && horn; c=c->next_cl) horn = horn_clause(c); for (c=Usable->first_cl, equality = 0; c && !equality; c=c->next_cl) equality = equality_clause(c); for (c=Sos->first_cl; c && !equality; c=c->next_cl) equality = equality_clause(c); for (c=Usable->first_cl, symmetry = 0; c && !symmetry; c=c->next_cl) symmetry = symmetry_clause(c); for (c=Sos->first_cl; c && !symmetry; c=c->next_cl) symmetry = symmetry_clause(c); for (c=Usable->first_cl, max_lits = 0; c; c=c->next_cl) { i = num_literals(c); max_lits = (i > max_lits ? i : max_lits); } for (c=Sos->first_cl; c; c=c->next_cl) { i = num_literals(c); max_lits = (i > max_lits ? i : max_lits); } printf("\nProperties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d.\n\n", propositional, horn, equality, symmetry, max_lits); if (propositional) { printf("\nAll clauses are propositional; therefore we set the\n"); printf("propositional flag and use ordered hyperresolution.\n"); auto_change_flag(stdout, PROPOSITIONAL, 1); auto_change_flag(stdout, HYPER_RES, 1); } else { /* nonpropositional */ if (max_lits == 1) { printf("Setting pick_given_ratio to 2, because all clauses are units.\n"); auto_change_parm(stdout, PICK_GIVEN_RATIO, 2); } else { /* Nonunit */ printf("Setting hyper_res, because there are nonunits.\n"); auto_change_flag(stdout, HYPER_RES, 1); if (equality || !horn) { printf("Setting ur_res, because this is a nonunit set containing\n"); printf("either equality literals or non-Horn clauses.\n"); auto_change_flag(stdout, UR_RES, 1); } if (horn) { printf("Clearing order_hyper, because all clauses are Horn.\n"); auto_change_flag(stdout, ORDER_HYPER, 0); } else { /* Non-Horn */ printf("Setting factor and unit_deletion, because there are non-Horn clauses.\n"); auto_change_flag(stdout, FACTOR, 1); auto_change_flag(stdout, UNIT_DELETION, 1); } } if (equality) { printf("Equality is present, so we set the knuth_bendix flag.\n"); auto_change_flag(stdout, KNUTH_BENDIX, 1); if (max_lits > 1) { printf("As an incomplete heuristic, we paramodulate with units only.\n"); auto_change_flag(stdout, PARA_FROM_UNITS_ONLY, 1); auto_change_flag(stdout, PARA_INTO_UNITS_ONLY, 1); } if (symmetry) { printf("There is a clause for symmetry of equality, so it is\n"); printf("assumed that equality is fully axiomatized; therefore,\n"); printf("paramodulation is disabled.\n\n"); auto_change_flag(stdout, PARA_FROM, 0); auto_change_flag(stdout, PARA_INTO, 0); } } } } } /* automatic_2_settings */ /************* * * log_for_x_show() * * Print some statistics to a file. This is intended to be used by * some other program that displays statistics about the search in real time. * *************/ void log_for_x_show(FILE *fp) { fprintf(fp, "given %ld\n", Stats[CL_GIVEN]); fprintf(fp, "generated %ld\n", Stats[CL_GENERATED]); fprintf(fp, "kept %ld\n", Stats[CL_KEPT]); fprintf(fp, "usable %ld\n", Stats[USABLE_SIZE]); fprintf(fp, "sos %ld\n", Stats[SOS_SIZE]); fprintf(fp, "demods %ld\n", Stats[DEMODULATORS_SIZE]); fprintf(fp, "passive %ld\n", Stats[PASSIVE_SIZE]); fprintf(fp, "hot %ld\n", Stats[HOT_SIZE]); fprintf(fp, "kbytes %ld\n", Stats[K_MALLOCED]); fprintf(fp, "wall-time %.2f\n", (double) wall_seconds() - Stats[INIT_WALL_SECONDS]); fprintf(fp, "user-time %.2f\n", run_time() / 1000.); fprintf(fp, "sys-time %.2f\n", system_time() / 1000.); fflush(fp); } /* log_for_x_show */ /************* * * int same_structure(t1, t2) * * Similar to lex_order_vars, except that variables are identical. * *************/ int same_structure(struct term *t1, struct term *t2) { struct rel *r1, *r2; int i; if (t1->type == VARIABLE) return(t2->type == VARIABLE); else if (t2->type == VARIABLE) return(0); else if (t1->sym_num == t2->sym_num) { r1 = t1->farg; r2 = t2->farg; i = 1; while (r1 && (i = same_structure(r1->argval,r2->argval))) { r1 = r1->narg; r2 = r2->narg; } return(i); } else return(0); } /* same_structure */ /************* * * void zap_variable_names(t); * *************/ void zap_variable_names(struct term *t) { if (t->type == VARIABLE) t->sym_num = 0; else if (t->type == COMPLEX) { struct rel *r; for (r = t->farg; r != NULL; r = r->narg) zap_variable_names(r->argval); } } /* zap_variable_names */ /************* * * commuted_terms() * *************/ int commuted_terms(struct term *t1, struct term *t2) { if (t1->type == VARIABLE) return (t2->type == VARIABLE && t1->varnum == t2->varnum); else if (t1->type == VARIABLE) return 0; else if (t1->sym_num != t2->sym_num) return 0; else { if (sn_to_arity(t1->sym_num) != 2) { struct rel *r1, *r2; for (r1 = t1->farg, r2 = t2->farg; r1; r1 = r1->narg, r2 = r2->narg) { if (!commuted_terms(r1->argval, r2->argval)) return 0; } return 1; } else { struct term *t1a = t1->farg->argval; struct term *t1b = t1->farg->narg->argval; struct term *t2a = t2->farg->argval; struct term *t2b = t2->farg->narg->argval; return (commuted_terms(t1a, t2a) && commuted_terms(t1b, t2b)) || (commuted_terms(t1a, t2b) && commuted_terms(t1b, t2a)); } } } /* commuted_terms */ /************* * * int symbol_count(t); * *************/ int symbol_count(struct term *t) { if (t->type == VARIABLE || t->type == NAME) return 1; else { struct rel *r; int n = 1; for (r = t->farg; r != NULL; r = r->narg) n += symbol_count(r->argval); return n; } } /* symbol_count */ /************* * * commutativity_consequence(struct clause *c) * *************/ int commutativity_consequence(struct clause *c) { if (!unit_clause(c)) return 0; else { struct term *atom = ith_literal(c,1)->atom; if (atom->varnum != POS_EQ) return 0; else { struct term *alpha = atom->farg->argval; struct term *beta = atom->farg->narg->argval; if (!commuted_terms(alpha, beta)) return 0; else if (symbol_count(alpha) <= 3) { return 0; /* commutativity itself? or x=x */ } else { /* printf("discarding: "); p_clause(c); */ return 1; } } } } /* commutativity_consequence */ otter-3.3f/source/lisp.c0100644000076400007640000001372607343604674014642 0ustar mccunemccune#include "lisp.h" #define MAX_WORD 100 static char Word[MAX_WORD]; static int Gets, Frees; #if 0 NOTE: the purpose of the /**/ comments before the function definitions is to prevent the prototype-making scripts from making prototypes for the functions. #endif /*************************************************************************/ static BOOLEAN str_ident(char *s, char *t) { return (strcmp(s, t) == 0); } /* str_ident */ /*************************************************************************/ static char *new_str_copy(char *str) { char *p = (void *) malloc((size_t) strlen(str)+1); strcpy(p, str); return p; } /* new_str_copy */ /*************************************************************************/ static Bnode get_bnode(void) { Bnode p = (void *) malloc((size_t) sizeof(struct bnode)); Gets++; p->car = NULL; p->cdr = NULL; p->label = NULL; p->atom = TRUE; return p; } /* get_bnode */ /*************************************************************************/ static void free_bnode(Bnode p) { Frees++; if (p->atom) free(p->label); free(p); } /* get_bnode */ /*************************************************************************/ /**/ void zap_btree(Bnode p) { if (!p->atom) { zap_btree(p->car); zap_btree(p->cdr); } free_bnode(p); } /* get_bnode */ /*************************************************************************/ /**/ BOOLEAN true_listp(Bnode p) { if (p->atom) return str_ident(p->label, "nil"); else return true_listp(p->cdr); } /* true_listp */ /*************************************************************************/ /**/ void fprint_btree(FILE *fp, Bnode p) { if (p->atom) fprintf(fp, "%s", p->label); else if (true_listp(p)) { Bnode p2; fprintf(fp,"("); for (p2 = p; p2->cdr != NULL; p2 = p2->cdr) { fprint_btree(fp, p2->car); if (p2->cdr->cdr) fprintf(fp," "); } fprintf(fp,")"); } else { fprintf(fp,"("); fprint_btree(fp, p->car); fprintf(fp," . "); fprint_btree(fp, p->cdr); fprintf(fp,")"); } } /* fprint_btree */ /*************************************************************************/ /**/ void p_btree(Bnode p) { fprint_btree(stdout, p); printf("\n"); fflush(stdout); } /* p_btree */ /*************************************************************************/ static BOOLEAN white_char(char c) { return (c == ' ' || c == '\t' || /* tab */ c == '\n' || /* newline */ c == '\v' || /* vertical tab */ c == '\r' || /* carriage return */ c == '\f'); /* form feed */ } /* white_char */ static BOOLEAN paren(char c) { return (c == '(' || c == ')'); } /* paren */ /*************************************************************************/ static int fill_word(FILE *fp) { int c; int i = 0; c = getc(fp); while (c != EOF && white_char(c)) c = getc(fp); if (c != EOF) { while (c != EOF && !white_char(c) && !paren(c)) { Word[i] = c; i++; if (i == MAX_WORD) { Word[i] = '\0'; fprintf(stderr, "fill_word, word too big: |%s|\n", Word); exit(2); } c = getc(fp); } if (c == ')' || (i != 0 && c == '(')) ungetc(c, fp); } Word[i] = '\0'; return(c); } /* fill_word */ /*************************************************************************/ /**/ BOOLEAN nullp(Bnode p) { return (p->atom && str_ident(p->label,"nil")); } /* nullp */ static BOOLEAN dotp(Bnode p) { return (p->atom && str_ident(p->label,".")); } /* nullp */ /*************************************************************************/ static void dot_trans (Bnode p) { Bnode curr = p; Bnode prev = NULL; while (!curr->atom) { if (dotp(curr->car)) { if (!curr->cdr->atom && nullp(curr->cdr->cdr) && prev != NULL && !dotp(curr->cdr->car)) { prev->cdr = curr->cdr->car; free_bnode(curr->cdr->cdr); free_bnode(curr->cdr); free_bnode(curr->car); free_bnode(curr); } else { fprintf(stderr, "dot_trans, bad dot notation\n"); exit(2); } } prev = curr; curr = curr->cdr; } } /* dot_trans */ /*************************************************************************/ /**/ Bnode parse_lisp(FILE *fp) { int c; c = fill_word(fp); if (!str_ident(Word, "")) { Bnode p = get_bnode(); p->atom = TRUE; p->label = new_str_copy(Word); return p; } else if (c == ')' ) return NULL; else if (c == '(') { Bnode top = get_bnode(); Bnode curr = top; Bnode p = parse_lisp(fp); while (p != NULL) { curr->atom = FALSE; curr->car = p; curr->cdr = get_bnode(); curr = curr->cdr; p = parse_lisp(fp); } c = getc(fp); /* step past ')' */ curr->label = new_str_copy("nil"); curr->atom = TRUE; dot_trans(top); return top; } else return NULL; } /* parse_lisp */ /*************************************************************************/ /**/ int atom(Bnode p) { return p->atom; } /* atom */ /*************************************************************************/ /**/ Bnode car(Bnode p) { return p->car;} /* car */ /*************************************************************************/ /**/ Bnode cdr(Bnode p) { return p->cdr;} /* cdr */ /*************************************************************************/ /**/ Bnode cadr(Bnode p) { return p->cdr->car;} /* cadr */ /*************************************************************************/ /**/ Bnode caddr(Bnode p) { return p->cdr->cdr->car;} /* caddr */ /*************************************************************************/ /**/ int length(Bnode p) { return (atom(p) ? 0 : length(cdr(p)) + 1); } /* length */ /*************************************************************************/ #ifdef SOLO /**/ int main(int argc, char **argv) { Bnode p; p = parse_lisp(stdin); fprint_btree(stdout, p); printf("length = %d\n", length(p)); zap_btree(p); printf("Gets=%d, Frees=%d.\n", Gets, Frees); } /* main */ #endif otter-3.3f/source/types.h0100644000076400007640000002100110037312646015012 0ustar mccunemccune/* * types.h -- type declarations * */ struct term { struct rel *farg; /* subterm list; used for complex only */ union { /* term is atom iff (NAME or COMPLEX) && varnum > 0 */ struct rel *rel; /* superterm list; used for all except atoms */ struct literal *lit; /* containing literal; used for atoms */ } occ; int fpa_id; /* used to order fpa lists */ unsigned short sym_num; /* used for names, complex, and sometimes vars */ VAR_TYPE varnum; /* used for variables */ unsigned char type; /* NAME, VARIABLE, or COMPLEX */ unsigned char bits; /* bit flags (see macros.h) */ }; struct rel { /* relations between terms */ struct term *argval; /* subterm */ struct term *argof; /* superterm */ struct rel *narg; /* rest of subterm list */ struct rel *nocc; /* rest of superterm list */ unsigned char path; /* used in paramod to mark path to into term */ unsigned char clashable; /* paramodclashability flag */ }; struct sym_ent { /* symbol table entry */ struct sym_ent *next; int sym_num; /* unique identifier */ int arity; /* arity 0 for constants, variables */ int lex_val; /* can be used to assign a lexical value */ int eval_code; /* identifies evaluable functors ($ symbols) */ int skolem; /* identifies Skolem constants and functions */ int special_unary; /* identifies special unary symbol for lex check */ int lex_rpo_status; /* status for LRPO */ char name[MAX_NAME]; /* the print symbol */ int special_op; /* for infix/prefix/postfix functors */ int op_type; /* for infix/prefix/postfix functors */ int op_prec; /* for infix/prefix/postfix functors */ }; struct term_ptr { /* for constructing a list of pointers to terms */ struct term *term; struct term_ptr *next; }; struct formula_ptr_2 { /* for many-linked list of pointers to formulas */ struct formula *f; struct formula_ptr_2 *prev, *next, *left, *right, *up, *down; }; struct fpa_tree { /* for constructing fpa path lookup tree */ struct fposition position; /* for leaves only */ struct fpa_tree *left; /* for AND and OR nodes */ struct fpa_tree *right; /* for AND and OR nodes */ struct term *left_term; /* for OR nodes only */ struct term *right_term; /* for OR nodes only */ int type; /* 1 AND, 2 OR, 3 LEAF */ int *path; /* for debugging only */ }; struct fpa_head { /* head of an FPA list */ struct fnode *terms; /* terms with path */ struct fpa_head *next; /* next FPA list */ int *path; }; struct fpa_index { struct fpa_head *table[FPA_SIZE]; }; struct context { /* substitution table */ struct term *terms[MAX_VARS]; struct context *contexts[MAX_VARS]; int status[MAX_VARS]; /* for batch occur check */ int multiplier; /* needed for apply, not for unify or match */ int built_in_multiplier; /* the use of this is optional */ }; struct trail { /* to record an entry in a substitution table */ struct context *context; struct trail *next; int varnum; }; struct imd_tree { /* index/match/demodulate tree */ struct imd_tree *next, *kids; struct term_ptr *atoms; unsigned short lab; /* variable number or symbol number */ unsigned char type; /* VARIABLE, NAME, or COMPLEX */ /* the following are used for leaves only */ VAR_TYPE max_vnum; /* max. variable number, for clearing substitution */ }; struct imd_pos { /* save a stack of states for backtrack in imd indexing */ struct imd_pos *next; struct imd_tree *imd; struct rel *rel_stack[MAX_AL_TERM_DEPTH]; /* save position in given term */ int reset; /* flag for clearing instantiation on backtracking */ int stack_pos; /* for backtracking */ }; struct is_tree { /* index-subsume tree */ struct is_tree *next; /* sibling */ union { struct is_tree *kids; /* for internal nodes */ struct term_ptr *terms; /* for leaves */ } u; unsigned short lab; /* variable number or symbol number */ unsigned char type; /* VARIABLE, NAME, or COMPLEX */ }; struct is_pos { /* save a stack of states for backtrack in is indexing */ struct is_pos *next; struct is_tree *is; struct rel *rel_stack[MAX_FS_TERM_DEPTH]; /* save position in given term */ int reset; /* flag for clearing instantiation on backtracking */ int stack_pos; /* for backtracking */ }; struct fsub_pos { /* to save position in set of subsuming literals */ struct term_ptr *terms; /* list of identical terms from leaf of is tree */ struct is_pos *pos; /* stack of states for backtracking */ }; struct literal { struct clause *container; /* containing clause */ struct literal *next_lit; struct term *atom; char sign; BOOLEAN target; }; struct clause { struct ilist *parents; struct g2list *multi_parents; /* for proof-shortening experiment */ struct list *container; struct clause *prev_cl, *next_cl; /* prev and next clause in list */ struct literal *first_lit; int id; int pick_weight; struct cl_attribute *attributes; short type; /* for linked inf rules */ unsigned char bits; /* for linked inf rules */ char heat_level; }; struct list { /* the primary way to build a list of clauses */ struct clause *first_cl, *last_cl; char name[MAX_NAME]; /* name of list */ }; struct clause_ptr { /* an alternate way to build a list of clauses */ struct clause *c; struct clause_ptr *next; }; struct ilist { /* for building a list of integers */ struct ilist *next; int i; }; struct ci_ptr { /* for building a list of pairs */ struct ci_ptr *next; struct clause *c; struct ilist *v; }; struct clash_nd { /* for hyper and UR--one for each clashable lit of nuc */ struct term *nuc_atom; /* atom from nucleus */ struct fpa_index *db; /* fpa index to use for finding satellites */ struct fpa_tree *u_tree; /* unification path tree (position in sats) */ struct context *subst; /* unifying substitution */ struct trail *tr; /* trail to undo substitution */ struct term *found_atom; /* unifying atom */ int evaluable; /* $ evaluation */ int evaluation; /* $ evaluation */ int already_evaluated; /* $ evaluation */ struct clash_nd *prev, *next; /* links */ }; struct clock { /* for timing operations, see cos.h, macros.h, clocks.c */ long accum_sec; /* accumulated time */ long accum_usec; long curr_sec; /* time since clock has been turned on */ long curr_usec; }; struct ans_lit_node { struct ans_lit_node *next; struct link_node *parent; struct literal *lit; }; struct link_node { struct link_node *parent, *next_sibling, *prev_sibling, *first_child; struct ans_lit_node *child_first_ans, *child_last_ans; BOOLEAN first; BOOLEAN unit_deleted; /* TRUE if goal_to_resolve has been unit deleted */ struct term *goal, *goal_to_resolve; struct clause *current_clause; struct context *subst; struct trail *tr; struct fpa_tree *unif_position; int near_poss_nuc, farthest_sat, target_dist, back_up; }; struct formula_box { /* This is for the "Formed" formula display program. */ int type; /* FORMULA, OPERATOR */ int subtype; /* COMPLEX_FORM, ATOM_FORM */ /* OR_OP, AND_OP, NOT_OP, EXISTS_OP, ALL_OP */ struct formula *f; char str[100]; int length, height; /* size of box */ int x_off, y_off; /* offset from parent */ int abs_x_loc, abs_y_loc; /* absolute location of box in window */ struct formula_box *first_child; struct formula_box *next; struct formula_box *parent; }; struct formula { struct formula *parent, *first_child, *next; struct term *t; /* for atoms and for quantifier variables */ char type; char quant_type; }; struct formula_ptr { struct formula *f; struct formula_ptr *next; }; struct cl_attribute { int name; union { int i; double d; char *s; struct term *t; } u; struct cl_attribute *next; }; struct glist { void *v; struct glist *next; }; struct g2list { void *v1; void *v2; struct g2list *next; }; otter-3.3f/source/fpa2-test0100755000076400007640000004165210041252535015241 0ustar mccunemccuneELFÀ„454 (44€4€ÀÀôô€ô€€€¨¨( ÈÈ /lib/ld-linux.so.2GNU  „„•"+„-~(„u$8„p3H„%" @‘QD‘X„šlh„Ó,x„2Kˆ„gX˜„å]„L¨„š libc.so.6stdout__strtol_internalmallocfprintf__deregister_frame_infosrandstderrexit_IO_stdin_used__libc_start_mainclock__register_frame_info__gmon_start__GLIBC_2.0ii ©$‘@‘D‘øü‘‘‘ ‘‘ ‘ ‘ ‘ ‘U‰åƒìèùèè* ÉÃÿ5ðÿ%ôÿ%øhéàÿÿÿÿ%ühéÐÿÿÿÿ%‘héÀÿÿÿÿ%‘hé°ÿÿÿÿ%‘h é ÿÿÿÿ% ‘h(éÿÿÿÿ%‘h0é€ÿÿÿÿ%‘h8épÿÿÿÿ%‘h@é`ÿÿÿÿ%‘hHéPÿÿÿÿ% ‘hPé@ÿÿÿ1í^‰áƒäðPTRh`hàƒQVhð‹è‡ÿÿÿô‰öU‰åSPè[Ãþ ‹ƒ8…ÀtÿЋ]üÉÉöU‰åƒì‹ …ÒuI‹‹…Àtt&B£ÿ‹‹ …Éuê¸H„…Àtƒì hèìþÿÿƒÄ¸£ ‰ì]ÃvU‰åƒì‰ì]öU¸„‰åƒì…ÀtƒìhH‘hègþÿÿƒÄ‰ì]ô&U‰åƒì‰ì]öU‰åƒìÿd‘ƒ=`‘uƒì h˜è‚‰ÂƒÄëvÿ l‘‹`‘‹‚”£`‘Ç‚”‰ÐÉÃvU‰å‹Uÿh‘ÿl‘¡`‘‰‚”‰`‘]ÃvU‰åWVSƒì ƒ} tƒìh ÿuè½ýÿÿƒÄƒì ‹5h‘‹=d‘‰û)ó‹ l‘iÀ˜ºRPß,$XZÜ hd$øÝ$QSVWh˜hŽÿuèiýÿÿeô[^_]ÃU‰åƒìjÿ5@‘èqÿÿÿÉÃvU‰åWVSƒì ‹u…öu èÛþÿÿ‰Æ‹E ‰†Œdžé¤ƒ¾d…ËU ;–Œ}ƒìRÿ¶”éЋM ;ŽŒuƒìQh@Žé v¸d+†‹U ;†~ƒìRjènÿÿÿ‰°”ë[‰öèOþÿÿ‰Ç¹»2v‹2‰ŸÇ2ACƒù2|åLJ2¸dƒè2‰†‰·”ƒìÿu Wè ÿÿÿ‰ÆƒÄéÔƒ¾”t3‹–”¸d+‚‹M ; ‚ƒìQRèÔþÿÿ‰†”ƒÄ陉ö‹¾¸d‰Ã)ûƒûc‹E ;ž}Cƒûc‹U ;ž|òƒûc!‹M ; žuƒìQh€Žÿ5D‘èÁûÿÿƒÄëG¸d)ø9Ãu ‹E ‰Džüë*¸d‰Á)ù9Ù}v‹2‰DüA9Ù|í‹U ‰TžüG‰†‰ðeô[^_]ÃvU‰åWVSƒì ‹Mƒ¹”tc‹‘”‹‚ƒødL‰Ö»;™}$¿c‰Ø†‰ú)‰ø)Ø‹‰–C;™|዆ƒì Qèðüÿÿ‰ðë‰Èeô[^_]ÉöU‰åWVSƒì ‹u‹U …öuƒìRhÀŽÿ5D‘è½úÿÿé»;–Œ}ƒìRÿ¶”è½ÿÿÿ‰†”陉ö‹¾¸d)øë@ƒøc;†|õ;†tƒìRhÿ5D‘è`úÿÿëa‰ö‰Á¸d)ø9Á~¸d‰Ã)û‰ö‹Dü‰2I9ÙíÇŽGÿ‰†…Àu‹ž”ƒì Vè üÿÿ‰Þë ‰öƒì Vè—þÿÿ‰ÆƒÄ‰ðeô[^_]ÃU‰åVS‹]‹u …öuÇÇCë‰ö‰ð¹d‰Ê+–‰‰S‰Ø[^]ÂU‰åWVSƒì ‹}‹M ‹]sƒþc‰È‰òëUèƒì‰Èÿ°”Rèÿÿÿ‹Eè‹U쉉W‰øeô[^_]ÂU‰åVS‹u…ötOƒìÿ¶Vhxè¨ùÿÿ»ƒÄƒìÿ4žhˆèùÿÿƒÄCƒûc~çƒì h¦èzùÿÿƒÄ‹¶”…öu±eø[^]ÉöU‰åS‹]¸…Ûtƒì ÿ³”èâÿÿÿƒ‹]üÉÃvU‰åƒìèÝøÿÿ‰ÁºÓMb÷êÁú‰ÈÁø)‰ÐÉÉöU‰åƒìÿuèÆøÿÿÉÃU‰åWVSƒì ‹u‹} ¸9ø} džÿÿÿÿ@9ø|ô»9û}Dvèÿøÿÿ™÷ÿƒ<–ÿu‰–ë)Bëv@9ø}ƒ<†ÿuõ9ø|‰ÐvHxƒ<†ÿu÷‰†C9û|¿ƒÄ [^_]ÃvU‰åWVS켿»ƒ}u3jj j‹E ÿpè;øÿÿ‰$ècøÿÿëƒìSWèžúÿÿ‰Ç‰€‘CƒÄûç~áƒì Wè`þÿÿèëþÿÿÝpPÚ<$Ù@ðÿÿƒÄ¡d‘+h‘PÙ…@ðÿÿd$øÝ$jdh@èë÷ÿÿƒÄhè…HðÿÿPèÓþÿÿ»ƒÄµHðÿÿ‹žƒìÿ4…€‘Wèqüÿÿ‰ÇƒÄCûç~ßèjþÿÿÝpPÚ<$XÙDðÿÿÙ…DðÿÿØ¥@ðÿÿd$øÝ$jdhŒèr÷ÿÿè­ùÿÿÇ$è÷ÿÿU‰åSƒì¡Ü»Üƒøÿtv¼'ƒëÿЋƒøÿuôX[]ÃU‰åƒì‰ì]öU‰åSRè[Âvè—÷ÿÿ‹]üÉà type (bytes each) gets frees in use avail bytes fnode (%4d) %11u%11u%11u%11u%9.1f K WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! WARNING: flist_delete, item %d not found (2)! FMAX=%d, insert time: %.2f, chunks=%d P?@@fnode %p, n=%d: %dFMAX=%d, delete time: %.2f è àƒ `(|‚| ³ ìXˆƒpƒþÿÿoPƒÿÿÿoðÿÿo0ƒÿÿÿÿÿÿÿÿ„„.„>„N„^„n„~„Ž„ž„®„¢ƒdä„dä„9<H€r€Œ€»€ó€0€€Ò€ý€,€V€€™€´€Õ€€1€V€€€©‚¢¢ ‚cV$‚ï[L‚b‚y‚¢¢¢‚ØƀǢڀ ñ€!€"€#3€%K€&a€1x€2€3§€4À€5Ø€6ñ€8 €9"€;B€=X€>n€?„€@š€A±€BÉ€C߀Dö€E €F$€G;€HT€Ii€NÏ€Qç€R€S€T9€UU€Vm€X…€[Ÿ€^·€eÍ€hç€l €q €r5 €uP €vm €yˆ €z¥ €}½ €€Ö €ƒñ €„ €‡& €Š@ ‚Ë”t ‚Fœ €¢Ò € €#V €Y €4u €< €Cú €F €S© €Zç €^€Ù€lù€tM€yn€ö€†4€Œ¢¢‚ L€b€8¢w‚Š‚b‚¢œ‚¢É€K¢¢L€€#Ô‚ç‚5ÁLÂwŠ‚Âœ¢Âø€×€€H8€Kg€L˜€UË€Z€^?€aw€b¯€\€€û€r€­¢¢–€5 €7!€89€9S€:¢m dä„init.c/usr/src/build/87998-i386/BUILD/glibc-2.2.5/csu/gcc2_compiled.int:t(0,1)=r(0,1);-2147483648;2147483647;char:t(0,2)=r(0,2);0;127;long int:t(0,3)=r(0,3);-2147483648;2147483647;unsigned int:t(0,4)=r(0,4);0000000000000;0037777777777;long unsigned int:t(0,5)=r(0,5);0000000000000;0037777777777;long long int:t(0,6)=@s64;r(0,6);01000000000000000000000;0777777777777777777777;long long unsigned int:t(0,7)=@s64;r(0,7);0000000000000;01777777777777777777777;short int:t(0,8)=@s16;r(0,8);-32768;32767;short unsigned int:t(0,9)=@s16;r(0,9);0;65535;signed char:t(0,10)=@s8;r(0,10);-128;127;unsigned char:t(0,11)=@s8;r(0,11);0;255;float:t(0,12)=r(0,1);4;0;double:t(0,13)=r(0,1);8;0;long double:t(0,14)=r(0,1);12;0;complex int:t(0,15)=s8real:(0,1),0,32;imag:(0,1),32,32;;complex float:t(0,16)=r(0,16);8;0;complex double:t(0,17)=r(0,17);16;0;complex long double:t(0,18)=r(0,18);24;0;__builtin_va_list:t(0,19)=*(0,20)=(0,20)../include/libc-symbols.h/usr/src/build/87998-i386/BUILD/glibc-2.2.5/build-i386-linux/config.h../sysdeps/gnu/_G_config.h../sysdeps/unix/sysv/linux/bits/types.h../include/features.h../include/sys/cdefs.h../misc/sys/cdefs.h/usr/lib/gcc-lib/i386-redhat-linux/2.96/include/stddef.hsize_t:t(8,1)=(0,4)__u_char:t(4,1)=(0,11)__u_short:t(4,2)=(0,9)__u_int:t(4,3)=(0,4)__u_long:t(4,4)=(0,5)__u_quad_t:t(4,5)=(0,7)__quad_t:t(4,6)=(0,6)__int8_t:t(4,7)=(0,10)__uint8_t:t(4,8)=(0,11)__int16_t:t(4,9)=(0,8)__uint16_t:t(4,10)=(0,9)__int32_t:t(4,11)=(0,1)__uint32_t:t(4,12)=(0,4)__int64_t:t(4,13)=(0,6)__uint64_t:t(4,14)=(0,7)__qaddr_t:t(4,15)=(4,16)=*(4,6)__dev_t:t(4,17)=(4,5)__uid_t:t(4,18)=(4,3)__gid_t:t(4,19)=(4,3)__ino_t:t(4,20)=(4,4)__mode_t:t(4,21)=(4,3)__nlink_t:t(4,22)=(4,3)__off_t:t(4,23)=(0,3)__loff_t:t(4,24)=(4,6)__pid_t:t(4,25)=(0,1)__ssize_t:t(4,26)=(0,1)__rlim_t:t(4,27)=(4,4)__rlim64_t:t(4,28)=(4,5)__id_t:t(4,29)=(4,3)__fsid_t:t(4,30)=(4,31)=s8__val:(4,32)=ar(4,33)=r(4,33);0000000000000;0037777777777;;0;1;(0,1),0,64;;__daddr_t:t(4,34)=(0,1)__caddr_t:t(4,35)=(4,36)=*(0,2)__time_t:t(4,37)=(0,3)__useconds_t:t(4,38)=(0,4)__suseconds_t:t(4,39)=(0,3)__swblk_t:t(4,40)=(0,3)__clock_t:t(4,41)=(0,3)__clockid_t:t(4,42)=(0,1)__timer_t:t(4,43)=(0,1)__key_t:t(4,44)=(0,1)__ipc_pid_t:t(4,45)=(0,9)__blksize_t:t(4,46)=(0,3)__blkcnt_t:t(4,47)=(0,3)__blkcnt64_t:t(4,48)=(4,6)__fsblkcnt_t:t(4,49)=(4,4)__fsblkcnt64_t:t(4,50)=(4,5)__fsfilcnt_t:t(4,51)=(4,4)__fsfilcnt64_t:t(4,52)=(4,5)__ino64_t:t(4,53)=(4,5)__off64_t:t(4,54)=(4,24)__t_scalar_t:t(4,55)=(0,3)__t_uscalar_t:t(4,56)=(0,5)__intptr_t:t(4,57)=(0,1)__socklen_t:t(4,58)=(0,4)../linuxthreads/sysdeps/pthread/bits/pthreadtypes.h../sysdeps/unix/sysv/linux/bits/sched.h__sched_param:T(10,1)=s4__sched_priority:(0,1),0,32;;_pthread_fastlock:T(9,1)=s8__status:(0,3),0,32;__spinlock:(0,1),32,32;;_pthread_descr:t(9,2)=(9,3)=*(9,4)=xs_pthread_descr_struct:__pthread_attr_s:T(9,5)=s36__detachstate:(0,1),0,32;__schedpolicy:(0,1),32,32;__schedparam:(10,1),64,32;__inheritsched:(0,1),96,32;__scope:(0,1),128,32;__guardsize:(8,1),160,32;__stackaddr_set:(0,1),192,32;__stackaddr:(0,19),224,32;__stacksize:(8,1),256,32;;pthread_attr_t:t(9,6)=(9,5)pthread_cond_t:t(9,7)=(9,8)=s12__c_lock:(9,1),0,64;__c_waiting:(9,2),64,32;;pthread_condattr_t:t(9,9)=(9,10)=s4__dummy:(0,1),0,32;;pthread_key_t:t(9,11)=(0,4)pthread_mutex_t:t(9,12)=(9,13)=s24__m_reserved:(0,1),0,32;__m_count:(0,1),32,32;__m_owner:(9,2),64,32;__m_kind:(0,1),96,32;__m_lock:(9,1),128,64;;pthread_mutexattr_t:t(9,14)=(9,15)=s4__mutexkind:(0,1),0,32;;pthread_once_t:t(9,16)=(0,1)_pthread_rwlock_t:T(9,17)=s32__rw_lock:(9,1),0,64;__rw_readers:(0,1),64,32;__rw_writer:(9,2),96,32;__rw_read_waiting:(9,2),128,32;__rw_write_waiting:(9,2),160,32;__rw_kind:(0,1),192,32;__rw_pshared:(0,1),224,32;;pthread_rwlock_t:t(9,18)=(9,17)pthread_rwlockattr_t:t(9,19)=(9,20)=s8__lockkind:(0,1),0,32;__pshared:(0,1),32,32;;pthread_spinlock_t:t(9,21)=(0,1)pthread_barrier_t:t(9,22)=(9,23)=s20__ba_lock:(9,1),0,64;__ba_required:(0,1),64,32;__ba_present:(0,1),96,32;__ba_waiting:(9,2),128,32;;pthread_barrierattr_t:t(9,24)=(9,25)=s4__pshared:(0,1),0,32;;pthread_t:t(9,26)=(0,5)wchar_t:t(11,1)=(0,3)wint_t:t(11,2)=(0,4)../include/wchar.h../wcsmbs/wchar.h../sysdeps/unix/sysv/linux/i386/bits/wchar.h__mbstate_t:t(13,1)=(13,2)=s8__count:(0,1),0,32;__value:(13,3)=u4__wch:(11,2),0,32;__wchb:(13,4)=ar(4,33);0;3;(0,2),0,32;;,32,32;;_G_fpos_t:t(3,1)=(3,2)=s12__pos:(4,23),0,32;__state:(13,1),32,64;;_G_fpos64_t:t(3,3)=(3,4)=s16__pos:(4,54),0,64;__state:(13,1),64,64;;../include/gconv.h../iconv/gconv.h :T(17,1)=e__GCONV_OK:0,__GCONV_NOCONV:1,__GCONV_NODB:2,__GCONV_NOMEM:3,__GCONV_EMPTY_INPUT:4,__GCONV_FULL_OUTPUT:5,__GCONV_ILLEGAL_INPUT:6,__GCONV_INCOMPLETE_INPUT:7,__GCONV_ILLEGAL_DESCRIPTOR:8,__GCONV_INTERNAL_ERROR:9,; :T(17,2)=e__GCONV_IS_LAST:1,__GCONV_IGNORE_ERRORS:2,;__gconv_fct:t(17,3)=(17,4)=*(17,5)=f(0,1)__gconv_init_fct:t(17,6)=(17,7)=*(17,8)=f(0,1)__gconv_end_fct:t(17,9)=(17,10)=*(17,11)=f(0,20)__gconv_trans_fct:t(17,12)=(17,13)=*(17,14)=f(0,1)__gconv_trans_context_fct:t(17,15)=(17,16)=*(17,17)=f(0,1)__gconv_trans_query_fct:t(17,18)=(17,19)=*(17,20)=f(0,1)__gconv_trans_init_fct:t(17,21)=(17,22)=*(17,23)=f(0,1)__gconv_trans_end_fct:t(17,24)=(17,25)=*(17,26)=f(0,20)__gconv_trans_data:T(17,27)=s20__trans_fct:(17,12),0,32;__trans_context_fct:(17,15),32,32;__trans_end_fct:(17,24),64,32;__data:(0,19),96,32;__next:(17,28)=*(17,27),128,32;;__gconv_step:T(17,29)=s56__shlib_handle:(17,30)=*(17,31)=xs__gconv_loaded_object:,0,32;__modname:(17,32)=*(0,2),32,32;__counter:(0,1),64,32;__from_name:(4,36),96,32;__to_name:(4,36),128,32;__fct:(17,3),160,32;__init_fct:(17,6),192,32;__end_fct:(17,9),224,32;__min_needed_from:(0,1),256,32;__max_needed_from:(0,1),288,32;__min_needed_to:(0,1),320,32;__max_needed_to:(0,1),352,32;__stateful:(0,1),384,32;__data:(0,19),416,32;;__gconv_step_data:T(17,33)=s36__outbuf:(17,34)=*(0,11),0,32;__outbufend:(17,34),32,32;__flags:(0,1),64,32;__invocation_counter:(0,1),96,32;__internal_use:(0,1),128,32;__statep:(17,35)=*(13,1),160,32;__state:(13,1),192,64;__trans:(17,28),256,32;;__gconv_info:T(17,36)=s8__nsteps:(8,1),0,32;__steps:(17,37)=*(17,29),32,32;__data:(17,38)=ar(4,33);0;-1;(17,33),64,0;;__gconv_t:t(17,39)=(17,40)=*(17,36)_G_iconv_t:t(3,5)=(3,6)=u44__cd:(17,36),0,64;__combined:(3,7)=s44__cd:(17,36),0,64;__data:(17,33),64,288;;,0,352;;_G_int16_t:t(3,8)=(0,8)_G_int32_t:t(3,9)=(0,1)_G_uint16_t:t(3,10)=(0,9)_G_uint32_t:t(3,11)=(0,4)_IO_stdin_used:G(0,1)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)01.0101.0101.0101.0101.0101.01.symtab.strtab.shstrtab.interp.note.ABI-tag.hash.dynsym.dynstr.gnu.version.gnu.version_r.rel.dyn.rel.plt.init.text.fini.rodata.data.eh_frame.dynamic.ctors.dtors.got.bss.stab.stabstr.comment.noteô€ô# 1((T7 ||?|‚|³Gÿÿÿo0ƒ0 TþÿÿoPƒP c pƒpl ˆƒˆX uàƒàpøƒøÀ{À„À `` ‡€€ ( •ŸÈ¨Üܯää¶ìì<»@‘@à À@¤ ÆäƒÏg2Jر3x)4Þ9€A @šô€(||‚0ƒPƒpƒˆƒ àƒ øƒ À„ ` €Üäì@‘ñÿñÿä„ "ä„ 2ñÿ… =AäO [… q„p… H‘˜€… ¤°… ¯½Ü2ñÿ  Ë  áà¤P ¯îèûñÿ` ñÿÀ… À…Q d‘%`‘1l‘>†% Ih‘U°ˆ‚ a(Š< l¸† x‹) ‰’„•"³€º„-Í(„uÞІÝ ë°Šb óàƒ ùd‹ 8„pt‹y 'H„%"J@‘\D‘n@‹" xdŠK ‚<†{ “À„ šX„š·(‘ñÿÃð‹' Èh„Óå ðx„2` €‘ ˆ„g 4‰ô -˜„å=(‘ñÿDìZ ¡ñÿ_„n{¨„‹ init.cinitfini.cgcc2_compiled.call_gmon_startcrtstuff.cp.0__DTOR_LIST__completed.1__do_global_dtors_aux__EH_FRAME_BEGIN__fini_dummyobject.2frame_dummyinit_dummyforce_to_data__CTOR_LIST____do_global_ctors_aux__CTOR_END____DTOR_END____FRAME_END__fpa2.cget_fnodefnode_getsfnode_availfnode_availsfree_fnodefnode_freesconsolidatefirst_fposp_flist_memflist_population_DYNAMIC__register_frame_info@@GLIBC_2.0_fp_hwfprintf@@GLIBC_2.0clock@@GLIBC_2.0flist_insertp_flist_inittp_allocmalloc@@GLIBC_2.0random_permutation__deregister_frame_info@@GLIBC_2.0stdout@@GLIBC_2.0stderr@@GLIBC_2.0user_timenext_fposfprint_flist_mem_start__strtol_internal@@GLIBC_2.0__bss_startmain__libc_start_main@@GLIBC_2.0data_startprintf@@GLIBC_2.0_finiRecordsrand@@GLIBC_2.0flist_deleteexit@@GLIBC_2.0_edata_GLOBAL_OFFSET_TABLE__end_IO_stdin_used__data_startrand@@GLIBC_2.0__gmon_start__otter-3.3f/source/attrib.c0100644000076400007640000001255307343604667015157 0ustar mccunemccune/* * attrib.c - attributes of clauses * */ #include "header.h" struct { char *name; int type; } Attributes[MAX_ATTRIBUTES]; /************* * * init_attributes() * *************/ void init_attributes(void) { int i; for (i = 0; i < MAX_ATTRIBUTES; i++) Attributes[i].name = ""; Attributes[BSUB_HINT_WT_ATTR].name = "bsub_hint_wt"; Attributes[BSUB_HINT_WT_ATTR].type = INT_ATTR; Attributes[FSUB_HINT_WT_ATTR].name = "fsub_hint_wt"; Attributes[FSUB_HINT_WT_ATTR].type = INT_ATTR; Attributes[EQUIV_HINT_WT_ATTR].name = "equiv_hint_wt"; Attributes[EQUIV_HINT_WT_ATTR].type = INT_ATTR; Attributes[BSUB_HINT_ADD_WT_ATTR].name = "bsub_hint_add_wt"; Attributes[BSUB_HINT_ADD_WT_ATTR].type = INT_ATTR; Attributes[FSUB_HINT_ADD_WT_ATTR].name = "fsub_hint_add_wt"; Attributes[FSUB_HINT_ADD_WT_ATTR].type = INT_ATTR; Attributes[EQUIV_HINT_ADD_WT_ATTR].name = "equiv_hint_add_wt"; Attributes[EQUIV_HINT_ADD_WT_ATTR].type = INT_ATTR; Attributes[LABEL_ATTR].name = "label"; Attributes[LABEL_ATTR].type = STRING_ATTR; } /* init_attributes */ /************* * * get_attribute_index() * * Return -1 if s is not any known attribute. * *************/ int get_attribute_index(char *s) { int i, found; if (str_ident(s, "")) return(-1); else { for (i = 0, found = 0; i < MAX_ATTRIBUTES && !found; i++) found = str_ident(s, Attributes[i].name); return(found ? i-1 : -1); } } /* get_attribute_index */ /************* * * attribute_type() * *************/ int attribute_type(int name) { switch (name) { case BSUB_HINT_WT_ATTR: return(INT_ATTR); case FSUB_HINT_WT_ATTR: return(INT_ATTR); case EQUIV_HINT_WT_ATTR: return(INT_ATTR); case BSUB_HINT_ADD_WT_ATTR: return(INT_ATTR); case FSUB_HINT_ADD_WT_ATTR: return(INT_ATTR); case EQUIV_HINT_ADD_WT_ATTR: return(INT_ATTR); case LABEL_ATTR: return(STRING_ATTR); default: printf("%d ", name); abend("attribute_type: unknown attribute name"); return(-1); } } /* attribute_type */ /************* * * get_attribute() * * Return the attribute (the whole node) associated with an * attribute name. If it does not exist, return NULL. * *************/ struct cl_attribute *get_attribute(struct clause *c, int name) { struct cl_attribute *a; for (a = c->attributes; a && a->name != name; a = a->next); return(a); } /* get_attribute */ /************* * * set_attribute() * *************/ void set_attribute(struct clause *c, int name, void *val_ptr) { struct cl_attribute *a1; a1 = get_cl_attribute(); a1->next = c->attributes; c->attributes = a1; a1->name = name; switch (attribute_type(name)) { case INT_ATTR: case BOOL_ATTR: a1->u.i = *((int *) val_ptr); break; case DOUBLE_ATTR: a1->u.d = *((double *) val_ptr); break; case STRING_ATTR: a1->u.s = (char *) val_ptr; break; case TERM_ATTR: a1->u.t = (struct term *) val_ptr; break; } } /* set_attribute */ /************* * * delete_attributes() * *************/ void delete_attributes(struct clause *c) { struct cl_attribute *a1, *a2; a1 = c->attributes; while (a1) { if (attribute_type(a1->name) == TERM_ATTR) zap_term(a1->u.t); a2 = a1; a1 = a1->next; free_cl_attribute(a2); } } /* delete_attributes */ /************* * * term_to_attributes() * * If error, print message to stdout and return NULL; * *************/ struct cl_attribute *term_to_attributes(struct term *t) { if (!is_symbol(t, "#", 2)) { struct cl_attribute *a = get_cl_attribute(); struct term *attr_val; int i; if (sn_to_arity(t->sym_num) != 1) { printf("attributes must have arity 1: "); p_term(t); return(NULL); } a->name = get_attribute_index(sn_to_str(t->sym_num)); attr_val = t->farg->argval; switch(attribute_type(a->name)) { case INT_ATTR: if (str_int(sn_to_str(attr_val->sym_num), &i)) { a->u.i = i; return(a); } else { printf("attribute value should be integer: "); p_term(t); return(NULL); } case BOOL_ATTR: a->u.i = 0; /* FIX THIS! */ return(a); case DOUBLE_ATTR: a->u.d = 123.4567E89; /* FIX THIS! */ return(a); case STRING_ATTR: a->u.s = sn_to_str(attr_val->sym_num); return(a); case TERM_ATTR: a->u.t = copy_term(attr_val); return(a); default: return(NULL); } } else { struct cl_attribute *a1, *a2, *a3; a1 = term_to_attributes(t->farg->argval); a2 = term_to_attributes(t->farg->narg->argval); if (!a1 || !a2) return(NULL); else { /* Append attribute lists. */ for (a3 = a1; a3->next; a3 = a3->next); a3->next = a2; return(a1); } } } /* term_to_attributes */ /************* * * print_attributes() * *************/ void print_attributes(FILE *fp, struct cl_attribute *a) { for ( ; a; a = a->next) { fprintf(fp, " # %s(", Attributes[a->name].name); switch (attribute_type(a->name)) { case INT_ATTR: fprintf(fp, "%d", a->u.i); break; case BOOL_ATTR: fprintf(fp, "%s", (a->u.i ? "true" : "false")); break; case DOUBLE_ATTR: fprintf(fp, "%f", a->u.d); break; case STRING_ATTR: fprintf(fp, "%s", a->u.s); break; case TERM_ATTR: print_term(fp, a->u.t); break; } fprintf(fp, ")"); } } /* print_attributes */ otter-3.3f/source/Makefile0100644000076400007640000000724010103514533015137 0ustar mccunemccune############################################################################# # # Makefile for building Otter 3.3. There is no configuration script # or higher-level make. Edit this file to configure compilation of # Otter. There are three things you may need to change: # # DFLAGS - to control conditional compilation to enable/disable things # CC - to specify the C compiler (usually cc or gcc) # CFLAGS - to specify optimization, debugging, and profiling # XFLAGS - this can be given on the call to make (see ../Makefile) # # This should work as is for recent versions of Linux. # ############################################################################# ############################################################################# # # The DFLAGS symbol, defined after this section of comments, controls # conditional compilation; it enables or disables various features. # # Enable features: # # -DTP_NAMES will get username, hostname. # Don't use if you get errors about gethostname, getuid, getpwuid. # -DTP_SIGNAL will cause some signals to be caught. # Don't use if you get errors about signal, SIGINT, SIGSEGV. # -DTP_FORK will allow interactive forks and case splitting. # Don't use if you get errors about fork, wait. # -DTP_RUSAGE for calls to getrusage() (user time, system time). # Don't use if you get errors about rusage, getrusage, RUSAGE_SELF. # # Disable features: # # -DTP_ABSOLUTELY_NO_CLOCKS disables all of the timing. # Use this as a last resort for timing or clock errrors. # # To get the full set of features: # # DFLAGS = -DTP_NAMES -DTP_SIGNAL -DTP_FORK -DTP_RUSAGE # ############### # OK, here is where to define the DFLAGS: DFLAGS = -DTP_NAMES -DTP_SIGNAL -DTP_FORK -DTP_RUSAGE $(XFLAGS) ############################################################################# # # Specify the C compiler. I recommend gcc (GNU C Compiler) if you have it. # In many Linux environments, cc is just a symlink to gcc. CC = gcc ############################################################################# # # Specify the compiler flags; include DFLAGS (above) -- Pick one of these # # optimized CFLAGS = -O $(DFLAGS) # # check for strict ANSI conformance with Solaris cc: # # CFLAGS = -Xc $(DFLAGS) # # various checks for gcc: # # CFLAGS = -Wall $(DFLAGS) # CFLAGS = -ansi -pedantic -Wall $(DFLAGS) # CFLAGS = -Wtraditional -Wpointer-arith -Wcast-qual -Wcast-align $(DFLAGS) # CFLAGS = -Wconversion -Wstrict-prototypes -Wmissing-prototypes\ # -Wmissing-declarations -Wredundant-decls -Wnested-externs $(DFLAGS) # # save symbols for debuggers # CFLAGS = -g $(DFLAGS) # # optimized, debugging # CFLAGS = -O -g $(DFLAGS) # # gprof profiling # CFLAGS = -pg -O $(DFLAGS) # ############################################################################# OBJECTS = av.o io.o share.o fpa.o clocks.o unify.o demod.o weight.o\ imd.o is.o clause.o options.o resolve.o index.o paramod.o\ formula.o process.o misc.o lrpo.o linkur.o linkhyp.o foreign.o\ geometry.o hot.o nonport.o check.o hints.o hints2.o attrib.o\ case.o lisp.o ivy.o pickdiff.o overbeek.o multijust.o lists.o\ fpa2.o ############################################################################# all: otter install clean otter: main.o libotter.a $(CC) $(CFLAGS) main.o libotter.a -o otter libotter.a: $(OBJECTS) $(AR) rs libotter.a $(OBJECTS) main.o $(OBJECTS): header.h types.h macros.h cos.h proto.h foreign.h\ lisp.h fpa2.h install: /bin/mv otter ../bin clean: /bin/rm -f *.o realclean: /bin/rm -f *.o *.a otter *~ prototypes: /bin/csh make-prototypes main.c $(OBJECTS) ############################################################################# otter-3.3f/source/formula.c0100644000076400007640000020402707343604672015332 0ustar mccunemccune/* * formula.c * * This file has routines to input and output quantified formulas and * to convert them to lists of clauses (Skolemization and CNF translation). * */ #include "header.h" static int Sk_func_num, Sk_const_num; /* for creating new skolem symbols */ /************* * * print_formula(fp, t) -- print a formula to a file. * *************/ void print_formula(FILE *fp, struct formula *f) { #if 1 struct term *t; t = formula_to_term(f); t = term_fixup_2(t); print_term(fp, t); zap_term(t); #else char op[MAX_NAME]; struct formula *f1; if (f == NULL) fprintf(fp, "(nil)"); else if (f->type == ATOM_FORM) { print_term(fp, f->t); } else if (f->type == NOT_FORM) { fprintf(fp, "-"); print_formula(fp, f->first_child); } else if (f->type == AND_FORM && f->first_child == NULL) fprintf(fp, "TRUE"); else if (f->type == OR_FORM && f->first_child == NULL) fprintf(fp, "FALSE"); else if (f->type == QUANT_FORM) { fprintf(fp, "("); if (f->quant_type == ALL_QUANT) fprintf(fp, "all "); else fprintf(fp, "exists "); print_term(fp, f->t); fprintf(fp, " "); print_formula(fp, f->first_child); fprintf(fp, ")"); } else { if (f->type == AND_FORM) strcpy(op, "& "); else if (f->type == OR_FORM) strcpy(op, "| "); else if (f->type == IMP_FORM) strcpy(op, "-> "); else if (f->type == IFF_FORM) strcpy(op, "<-> "); else op[0] = '\0'; fprintf(fp, "("); for (f1 = f->first_child; f1; f1 = f1->next) { print_formula(fp, f1); if (f1->next) fprintf(fp, " %s", op); } fprintf(fp, ")"); } #endif } /* print_formula */ /************* * * p_formula(f) -- print formula to standard output * *************/ void p_formula(struct formula *f) { print_formula(stdout, f); } /* p_formula */ /************* * * struct term *formula_args_to_term(f, type) * * Conver list of formulas to right-associated term. * Works for AND_FORM, OR_FORM, IMP_FORM, IFF_FORM. * *************/ static struct term *formula_args_to_term(struct formula *f, int type) { struct term *t, *t1, *t2; struct rel *r1, *r2; if (!f) { /* empty disjunction or conjunction */ t = get_term(); t->type = NAME; if (type == AND_FORM) t->sym_num = str_to_sn("TRUE", 0); else t->sym_num = str_to_sn("FALSE", 0); } else { t1 = formula_to_term(f); if (f->next) { t2 = formula_args_to_term(f->next, type); t = get_term(); r1 = get_rel(); r2 = get_rel(); t->farg = r1; r1->narg = r2; r1->argval = t1; r2->argval = t2; t->type = COMPLEX; switch (type) { case AND_FORM: t->sym_num = str_to_sn("&", 2); break; case OR_FORM: t->sym_num = str_to_sn("|", 2); break; case IMP_FORM: t->sym_num = str_to_sn("->", 2); break; case IFF_FORM: t->sym_num = str_to_sn("<->", 2); break; } } else t = t1; } return(t); } /* formula_args_to_term */ /************* * * struct term *formula_to_term(f) * *************/ struct term *formula_to_term(struct formula *f) { struct term *t, *t1; struct rel *r, *r1, *prev_r; int prev_q, i; struct formula *f1; switch (f->type) { case ATOM_FORM: t = copy_term(f->t); break; case IMP_FORM: case IFF_FORM: case AND_FORM: case OR_FORM: t = formula_args_to_term(f->first_child, f->type); break; case NOT_FORM: t = get_term(); t->type = COMPLEX; t->sym_num = str_to_sn("-", 1); r = get_rel(); t->farg = r; r->argval = formula_to_term(f->first_child); break; case QUANT_FORM: t = get_term(); t->type = COMPLEX; i = 0; prev_q = MAX_INT; prev_r = NULL; for (f1 = f; f1->type == QUANT_FORM; f1 = f1->first_child) { if (f1->quant_type != prev_q) { i++; t1 = get_term(); r1 = get_rel(); r1->argval = t1; if (!t->farg) t->farg = r1; else prev_r->narg = r1; prev_r = r1; t1->type = NAME; if (f1->quant_type == ALL_QUANT) t1->sym_num = str_to_sn("all", 0); else t1->sym_num = str_to_sn("exists", 0); prev_q = f1->quant_type; } i++; r1 = get_rel(); r1->argval = copy_term(f1->t); /* variable */ prev_r->narg = r1; prev_r = r1; } t->sym_num = str_to_sn("$Quantified", i); r1 = get_rel(); prev_r->narg = r1; r1->argval = formula_to_term(f1); break; default: t = NULL; } return(t); } /* formula_to_term */ /************* * * struct formula *term_to_formula(t) * *************/ struct formula *term_to_formula(struct term *t) { struct formula *f1, *f2, *f3; struct rel *r; int type; type = MAX_INT; if (is_symbol(t, "&", 2)) type = AND_FORM; else if (is_symbol(t, "|", 2)) type = OR_FORM; else if (is_symbol(t, "->", 2)) type = IMP_FORM; else if (is_symbol(t, "<->", 2)) type = IFF_FORM; if (type != MAX_INT) { f1 = get_formula(); f1->type = type; f1->first_child = term_to_formula(t->farg->argval); f1->first_child->next = term_to_formula(t->farg->narg->argval); if (type == AND_FORM || type == OR_FORM) flatten_top(f1); } else if (is_symbol(t, "-", 1)) { f1 = get_formula(); f1->type = NOT_FORM; f1->first_child = term_to_formula(t->farg->argval); } else if (t->type == COMPLEX && str_ident(sn_to_str(t->sym_num), "$Quantified")) { f3 = f1 = NULL; for (r = t->farg; r->narg; r = r->narg) { if (is_symbol(r->argval, "all", 0)) type = ALL_QUANT; else if (is_symbol(r->argval, "exists", 0)) type = EXISTS_QUANT; else { f2 = get_formula(); if (f3) f3->first_child = f2; else f1 = f2; f2->type = QUANT_FORM; f2->quant_type = type; f2->t = copy_term(r->argval); f3 = f2; } } f3->first_child = term_to_formula(r->argval); } else { /* assume atomic formula */ f1 = get_formula(); f1->type = ATOM_FORM; f1->t = copy_term(t); } return(f1); } /* term_to_formula */ /************* * * struct formula *read_formula(fp, rcp) -- read a formula from a file * * The return code *rcp: * 0 - an error was encountered and reported; NULL is returned. * 1 - OK; if EOF was found instead of a formula, NULL is returned. * *************/ struct formula *read_formula(FILE *fp, int *rcp) { int rc; struct formula *f; struct term *t; t = read_term(fp, &rc); if (!rc) { *rcp = 0; return(NULL); } else if (t == NULL) { *rcp = 1; return(NULL); } else { if (contains_skolem_symbol(t)) { fprintf(stdout, "\nERROR, input formula contains Skolem symbol:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); *rcp = 0; return(NULL); } else { f = term_to_formula(t); zap_term(t); *rcp = 1; return(f); } } } /* read_formula */ /************* * * struct term_ptr *read_formula_list(file_ptr, errors_ptr) * * Read and return a list of quantified formulas. * * The list must be terminated either with the term `end_of_list.' * or with an actual EOF. * Set errors_ptr to point to the number of errors found. * *************/ struct formula_ptr *read_formula_list(FILE *fp, int *ep) { struct formula_ptr *p1, *p2, *p3; struct formula *f; int rc; Internal_flags[REALLY_CHECK_ARITY] = 1; *ep = 0; p3 = NULL; p2 = NULL; f = read_formula(fp, &rc); while (rc == 0) { (*ep)++; f = read_formula(fp, &rc); } /* keep going until f == NULL || f is end marker */ while (f && !(f->type == ATOM_FORM && is_symbol(f->t, "end_of_list", 0))) { p1 = get_formula_ptr(); p1->f = f; if (p2 == NULL) p3 = p1; else p2->next = p1; p2 = p1; f = read_formula(fp, &rc); while (rc == 0) { (*ep)++; f = read_formula(fp, &rc); } } if (f != NULL) zap_formula(f); Internal_flags[REALLY_CHECK_ARITY] = 0; return(p3); } /* read_formula_list */ /************* * * print_formula_list(file_ptr, term_ptr) * * Print a list of quantified formulas. * * The list is printed with periods after each quantified formula, and * the list is terminated with `end_of_list.' so that it can * be read with read_formula_list. * *************/ void print_formula_list(FILE *fp, struct formula_ptr *p) { while (p != NULL) { print_formula(fp, p->f); fprintf(fp, ".\n"); p = p->next; } fprintf(fp, "end_of_list.\n"); } /* print_formula_list */ /************* * * struct formula *copy_formula(f) * * Copy a formula. copy_term is used to copy atoms and quantified vars. * *************/ struct formula *copy_formula(struct formula *f) { struct formula *f_new, *f_sub, *f_prev, *f3; f_new = get_formula(); f_new->type = f->type; if (f->type == ATOM_FORM) f_new->t = copy_term(f->t); else if (f->type == QUANT_FORM) { f_new->quant_type = f->quant_type; f_new->t = copy_term(f->t); f_new->first_child = copy_formula(f->first_child); } else { f_prev = NULL; for (f_sub = f->first_child; f_sub; f_sub = f_sub->next) { f3 = copy_formula(f_sub); if (f_prev) f_prev->next = f3; else f_new->first_child = f3; f_prev = f3; } } return(f_new); } /* copy_formula */ /************* * * void zap_formula(f) * * Free a formula and all of its subformulas and subterms. * *************/ void zap_formula(struct formula *f) { struct formula *f1, *f2; if (f->type == ATOM_FORM) zap_term(f->t); else { f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; zap_formula(f2); } if (f->type == QUANT_FORM) zap_term(f->t); } free_formula(f); } /* zap_formula */ /************* * * struct formula *negate_formula(f) * * f is changed to its negation. (Do not move negation signs inward.) * *************/ struct formula *negate_formula(struct formula *f) { struct formula *f1, *f_save; /* save next pointer */ f_save = f->next; f->next = NULL; if (f->type == NOT_FORM) { f1 = f->first_child; free_formula(f); } else { f1 = get_formula(); f1->type = NOT_FORM; f1->first_child = f; } /* restore next pointer */ f1->next = f_save; return(f1); } /* negate_formula */ /************* * * struct formula *nnf(f) * * f is changed into its negation normal form (NNF) by removing * -> and <-> and moving negation signs all the way in. * * (A <-> B) (not negated) rewrites to ((-a | b) & (-b | a)). * -(A <-> B) rewrites to ((a | b) & (-a | -b)). * * because conjunctions are favored. * *************/ struct formula *nnf(struct formula *f) { struct formula *f1, *f2, *next, *prev, *fn; switch (f->type) { case ATOM_FORM: return(f); /* f is atomic */ case IFF_FORM: f1 = get_formula(); f1->type = AND_FORM; f1->first_child = f; f1->next = f->next; f2 = copy_formula(f); f2->type = OR_FORM; f2->first_child->next = negate_formula(f2->first_child->next); f->type = OR_FORM; f->first_child = negate_formula(f->first_child); f->next = f2; return(nnf(f1)); case IMP_FORM: f->type = OR_FORM; f->first_child = negate_formula(f->first_child); return(nnf(f)); case QUANT_FORM: f->first_child = nnf(f->first_child); return(f); case AND_FORM: case OR_FORM: prev = NULL; f1 = f->first_child; while(f1) { next = f1->next; f1->next = NULL; f2 = nnf(f1); if (prev) prev->next = f2; else f->first_child = f2; prev = f2; f1 = next; } return(f); case NOT_FORM: fn = f->first_child; switch (fn->type) { case ATOM_FORM: return(f); case IFF_FORM: f2 = copy_formula(fn); f2->type = OR_FORM; fn->type = OR_FORM; f2->first_child = negate_formula(f2->first_child); f2->first_child->next = negate_formula(f2->first_child->next); fn->next = f2; f->type = AND_FORM; f->first_child = fn; return(nnf(f)); case IMP_FORM: fn->type = OR_FORM; fn->first_child = negate_formula(fn->first_child); return(nnf(f)); case QUANT_FORM: fn->quant_type = (fn->quant_type == ALL_QUANT ? EXISTS_QUANT : ALL_QUANT); fn->first_child = nnf(negate_formula(fn->first_child)); fn->next = f->next; free_formula(f); return(fn); case AND_FORM: case OR_FORM: prev = NULL; f1 = fn->first_child; while(f1) { next = f1->next; f1->next = NULL; f2 = nnf(negate_formula(f1)); if (prev) prev->next = f2; else fn->first_child = f2; prev = f2; f1 = next; } fn->type = (fn->type == AND_FORM ? OR_FORM : AND_FORM); fn->next = f->next; free_formula(f); return(fn); case NOT_FORM: /* double negation */ f1 = fn->first_child; f1->next = f->next; free_formula(f); free_formula(fn); return(nnf(f1)); } } return(NULL); /* ERROR */ } /* nnf */ /************* * * static void rename_free_formula(f, old_sn, new_sn) * * Rename free occurrences of old_sn in NAMEs to new_sn. * Recall that variables in formulas are really NAMEs. * *************/ static void rename_free_formula(struct formula *f, int old_sn, int new_sn) { struct formula *f1; if (f->type == ATOM_FORM) subst_sn_term(old_sn, f->t, new_sn, NAME); else if (f->type == QUANT_FORM) { if (old_sn != f->t->sym_num) rename_free_formula(f->first_child, old_sn, new_sn); } else { for (f1 = f->first_child; f1; f1 = f1->next) rename_free_formula(f1, old_sn, new_sn); } } /* rename_free_formula */ /************* * * static struct formula *skolem(f, vars) * * Skolemize f w.r.t universally quantified vars. * Called by skolemize. * *************/ static struct formula *skolem(struct formula *f, struct term *vars) { struct formula *f1, *f2, *prev, *next; struct rel *end, *r2; int sn; if (f->type == NOT_FORM && f->first_child->type != ATOM_FORM) { printf("ERROR, skolem gets negated non-atom: "); print_formula(stdout, f); printf("\n"); } else if (f->type == IMP_FORM || f->type == IFF_FORM) { printf("ERROR, skolem gets: "); print_formula(stdout, f); printf("\n"); } else if (f->type == AND_FORM || f->type == OR_FORM) { prev = NULL; f1 = f->first_child; while(f1) { next = f1->next; f1->next = NULL; f2 = skolem(f1, vars); if (prev) prev->next = f2; else f->first_child = f2; prev = f2; f1 = next; } } else if (f->type == QUANT_FORM) { if (f->quant_type == ALL_QUANT) { if (occurs_in(f->t, vars)) { /* rename current variable, because we are already in the scope of a universally quantified var with that name. */ sn = new_var_name(); rename_free_formula(f->first_child, f->t->sym_num, sn); f->t->sym_num = sn; } r2 = get_rel(); r2->argval = f->t; /* Install variable at end of vars. */ for (end = vars->farg; end && end->narg; end = end->narg); if (end) end->narg = r2; else vars->farg = r2; f->first_child = skolem(f->first_child, vars); /* Remove variable from vars. */ free_rel(r2); if (end) end->narg = NULL; else vars->farg = NULL; } else { /* existential quantifier */ /* must skolemize subformula first to avoid problem in Ax...Ey...Ex F(x,y). */ f->first_child = skolem(f->first_child, vars); gen_sk_sym(vars); /* fills in sym_num and assigns type */ subst_free_formula(f->t, f->first_child, vars); vars->type = COMPLEX; /* so that occurs_in above works */ f1 = f->first_child; zap_term(f->t); free_formula(f); f = f1; } } return(f); } /* skolem */ /************* * * struct formula *skolemize(f) -- Skolemize a formula * * This routine assumes that f is in negation normal form. * The existential quantifiers are deleted. * *************/ struct formula *skolemize(struct formula *f) { struct term *vars; vars = get_term(); vars->type = COMPLEX; f = skolem(f, vars); free_term(vars); return(f); } /* skolemize */ /************* * * struct formula *anti_skolemize(f) -- Anti-Skolemize a formula * * The dual of skolemize: universal quantifiers are removed. * *************/ struct formula *anti_skolemize(struct formula *f) { return(nnf(negate_formula(skolemize(nnf(negate_formula(f)))))); } /* anti_skolemize */ /************* * * static void subst_free_term(var, t, sk) * * Substitute free occurrences of var in t with copies of sk. * *************/ static void subst_free_term(struct term *var, struct term *t, struct term *sk) { struct rel *r; if (t->type != COMPLEX) return; else { r = t->farg; for (r = t->farg; r; r = r->narg) { if (term_ident(var, r->argval)) { zap_term(r->argval); r->argval = copy_term(sk); } else subst_free_term(var, r->argval, sk); } } } /* subst_free_term */ /************* * * void subst_free_formula(var, f, sk) * Substitute free occurrences of var in f with copies of sk. * *************/ void subst_free_formula(struct term *var, struct formula *f, struct term *sk) { struct formula *f1; if (f->type == ATOM_FORM) subst_free_term(var, f->t, sk); else if (f->type == QUANT_FORM) { if (!term_ident(f->t, var)) subst_free_formula(var, f->first_child, sk); } else { for (f1 = f->first_child; f1; f1 = f1->next) subst_free_formula(var, f1, sk); } } /* subst_free_formula */ /************* * * gen_sk_sym(t) -- generate a fresh skolem symbol for term t. * * Assign type field as well as sym_num field to term t. * *************/ void gen_sk_sym(struct term *t) { int arity; struct rel *r; char s1[MAX_NAME], s2[MAX_NAME]; arity = 0; r = t->farg; while (r != NULL) { arity++; r = r->narg; } if (arity == 0) { t->type = NAME; int_str(++Sk_const_num, s1); cat_str("$c", s1, s2); } else { t->type = COMPLEX; int_str(++Sk_func_num, s1); cat_str("$f", s1, s2); } t->sym_num = str_to_sn(s2, arity); mark_as_skolem(t->sym_num); } /* gen_sk_sym */ /************* * * int skolem_symbol(sn) -- Is sn the symbol number of a skolem symbol? * * Check if it is "$cn" or "$fn" for integer n. * Do not check the skolem flag in the symbol node. * *************/ int skolem_symbol(int sn) { char *s; int dummy; s = sn_to_str(sn); return(*s == '$' && (*(s+1) == 'c' || *(s+1) == 'f') && str_int(s+2,&dummy)); } /* skolem_symbol */ /************* * * int contains_skolem_symbol(t) * * Check if any of the NAMEs in t are "$cn" or "$fn", for integer n. * *************/ int contains_skolem_symbol(struct term *t) { struct rel *r; if (t->type == VARIABLE) return(0); else if (t->type == NAME) return(skolem_symbol(t->sym_num)); else { /* COMPLEX */ if (skolem_symbol(t->sym_num)) return(1); else { for (r = t->farg; r; r = r->narg) if (contains_skolem_symbol(r->argval)) return(1); return(0); } } } /* contains_skolem_symbol */ /************* * * int new_var_name() -- return a sym_num for a new VARIABLE symbol * * Check and make sure that the new symbol does not occur in the * symbol table. * *************/ int new_var_name(void) { char s1[MAX_NAME], s2[MAX_NAME]; static int var_num; char c[2]; c[0] = (Flags[PROLOG_STYLE_VARIABLES].val ? 'X' : 'x'); c[1] = '\0'; int_str(++var_num, s1); cat_str(c, s1, s2); while (in_sym_tab(s2)) { int_str(++var_num, s1); cat_str(c, s1, s2); } return(str_to_sn(s2, 0)); } /* new_var_name */ /************* * * int new_functor_name(arity) -- return a sym_num for a new symbol. * * Check and make sure that the new symbol does not occur in the symbol table. * *************/ int new_functor_name(int arity) { char s1[MAX_NAME], s2[MAX_NAME]; static int functor_num; int_str(++functor_num, s1); cat_str("k", s1, s2); while (in_sym_tab(s2)) { int_str(++functor_num, s1); cat_str("k", s1, s2); } return(str_to_sn(s2, arity)); } /* new_functor_name */ /************* * * static void uq_all(f, vars) -- called by unique_all * *************/ static void uq_all(struct formula *f, struct term *vars) { struct rel *r1; struct formula *f1; int sn; switch (f->type) { case ATOM_FORM: break; case NOT_FORM: case AND_FORM: case OR_FORM: for (f1 = f->first_child; f1; f1 = f1->next) uq_all(f1, vars); break; case QUANT_FORM: if (occurs_in(f->t, vars)) { /* rename current variable, because already have a quantified var with that name. */ sn = new_var_name(); rename_free_formula(f->first_child, f->t->sym_num, sn); f->t->sym_num = sn; } else { r1 = get_rel(); r1->argval = f->t; r1->narg = vars->farg; vars->farg = r1; } /* recursive call on quantified formula */ uq_all(f->first_child, vars); break; } } /* uq_all */ /************* * * void unique_all(f) -- make all universally quantified variables unique * * It is assumed that f is in negation normal form and is Skolemized (no * existential quantifiers). * *************/ void unique_all(struct formula *f) { struct term *vars; struct rel *r1, *r2; vars = get_term(); vars->type = COMPLEX; uq_all(f, vars); r1 = vars->farg; while (r1 != NULL) { r2 = r1; r1 = r1->narg; free_rel(r2); } free_term(vars); } /* unique_all */ /************* * * static mark_free_var_term(v, t) -- mark free occurrences of v in t * * Each free NAME in t with sym_num == v->sym_num is marked as * a VARIABLE by setting the type field to VARIABLE. * *************/ static void mark_free_var_term(struct term *v, struct term *t) { struct rel *r; struct term *t1; if (t->type != COMPLEX) return; else { r = t->farg; for (r = t->farg; r; r = r->narg) { t1 = r->argval; if (t1->type == NAME) { if (t1->sym_num == v->sym_num) { t1->type = VARIABLE; /* bug fix 31-Jan-91. WWM. The following line was added because term-ident (called if simplify_fol) does not check sym_num field for vars. It is a trick. */ t1->varnum = t1->sym_num; } } else mark_free_var_term(v, t1); } } } /* mark_free_var_term */ /************* * * static void mark_free_var_formula(v, f) * *************/ static void mark_free_var_formula(struct term *v, struct formula *f) { struct formula *f1; if (f->type == ATOM_FORM) mark_free_var_term(v, f->t); else { for (f1 = f->first_child; f1; f1 = f1->next) mark_free_var_formula(v, f1); } } /* mark_free_var_formula */ /************* * * struct term *zap_quant(f) * * Delete quantifiers and mark quantified variables. * * It is assumed that f is skolemized nnf with unique universally * quantified variables. For each universal quantifier, * mark all occurrences of the quantified variable by setting the type field * to VARIABLE, then delete the quantifier. * All QUANT_FORM nodes are deleted as well. * *************/ struct formula *zap_quant(struct formula *f) { struct formula *f1, *f2, *prev, *next; switch (f->type) { case ATOM_FORM: break; case NOT_FORM: case AND_FORM: case OR_FORM: prev = NULL; f1 = f->first_child; while(f1) { next = f1->next; f1->next = NULL; f2 = zap_quant(f1); if (prev) prev->next = f2; else f->first_child = f2; prev = f2; f1 = next; } break; case QUANT_FORM: mark_free_var_formula(f->t, f->first_child); f1 = f->first_child; f1->next = f->next; free_formula(f); f = zap_quant(f1); break; } return(f); } /* zap_quant */ /************* * * static void flatten_top_2(f, start, end_p) -- called by flatten_top. * *************/ static void flatten_top_2(struct formula *f, struct formula *start, struct formula **end_p) { struct formula *f1, *f2; f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; if (f2->type == f->type) { flatten_top_2(f2, start, end_p); free_formula(f2); } else { if (*end_p) (*end_p)->next = f2; else start->first_child = f2; *end_p = f2; } } } /* flatten_top_2 */ /************* * * void flatten_top(f) -- flatten conjunctions or disjunctions * * The top part of f is flattened. Subtrees below * a node of the oppposite type are not flattened. For example, in * (a or (b and (c or (d or e)))), the formula (c or (d or e)) is never * flattened. * *************/ void flatten_top(struct formula *f) { struct formula *end; if (f->type == AND_FORM || f->type == OR_FORM) { end = NULL; flatten_top_2(f, f, &end); if (end) end->next = NULL; else f->first_child = NULL; } } /* flatten_top */ /************* * * static struct formula *distribute(f) -- distribute OR over AND. * * f is an OR node whose subterms are in CNF. This routine returns * a CNF of f. * *************/ static struct formula *distribute(struct formula *f) { struct formula *f_new, *f1, *f2, *f3, *f4, *f_prev, *f_save; int i, j; f_save = f->next; f->next = NULL; if (f->type != OR_FORM) return(f); else { flatten_top(f); if (Flags[SIMPLIFY_FOL].val) { conflict_tautology(f); f = subsume_disj(f); } if (f->type != OR_FORM) return(f); else { /* find first AND subformula */ i = 1; f_prev = NULL; for (f1 = f->first_child; f1 && f1->type != AND_FORM; f1 = f1->next) { i++; f_prev = f1; } if (f1 == NULL) return(f); /* nothing to distribute */ else { /* unhook AND */ if (f_prev) f_prev->next = f1->next; else f->first_child = f1->next; f2 = f1->first_child; f_new = f1; f_prev = NULL; while (f2) { f3 = f2->next; if (f3) f1 = copy_formula(f); else f1 = f; if (i == 1) { f2->next = f1->first_child; f1->first_child = f2; } else { j = 1; for (f4 = f1->first_child; j < i-1; f4 = f4->next) j++; f2->next = f4->next; f4->next = f2; } f1 = distribute(f1); if (f_prev) f_prev->next = f1; else f_new->first_child = f1; f_prev = f1; f2 = f3; } f_new->next = f_save; flatten_top(f_new); if (Flags[SIMPLIFY_FOL].val) { conflict_tautology(f_new); f_new = subsume_conj(f_new); } return(f_new); } } } } /* distribute */ /************* * * struct formula *cnf(f) -- convert nnf f to conjunctive normal form. * *************/ struct formula *cnf(struct formula *f) { struct formula *f1, *f2, *f_prev, *f_next, *f_save; f_save = f->next; f->next = NULL; if (f->type == AND_FORM || f->type == OR_FORM) { /* first convert subterms to CNF */ f_prev = NULL; f1 = f->first_child; while(f1) { f_next = f1->next; f2 = cnf(f1); if (f_prev) f_prev->next = f2; else f->first_child = f2; f_prev = f2; f1 = f_next; } if (f->type == AND_FORM) { flatten_top(f); if (Flags[SIMPLIFY_FOL].val) { conflict_tautology(f); f = subsume_conj(f); } } else f = distribute(f); /* flatten and simplify in distribute */ } f->next = f_save; return(f); } /* cnf */ /************* * * struct formula *dnf(f) -- convert f to disjunctive normal form. * *************/ struct formula *dnf(struct formula *f) { return(nnf(negate_formula(cnf(nnf(negate_formula(f)))))); } /* dnf */ /************* * * static void rename_syms_term(t, fr) * * Called from rename_syms_formula. * *************/ static void rename_syms_term(struct term *t, struct formula *fr) { struct rel *r; int sn; if (t->type == NAME) { if (var_name(sn_to_str(t->sym_num))) { fprintf(stderr,"\nWARNING, the following formula has constant '%s', whose\nname may be misinterpreted by the user as a variable.\n", sn_to_str(t->sym_num)); print_formula(stderr, fr); fprintf(stderr, "\n"); #if 0 /* replaced 18 June 91 WWM */ sn = new_functor_name(0); /* with arity 0 */ subst_sn_formula(t->sym_num, fr, sn, NAME); #endif } } else if (t->type == VARIABLE) { if (!var_name(sn_to_str(t->sym_num))) { sn = new_var_name(); subst_sn_formula(t->sym_num, fr, sn, VARIABLE); } } else { r = t->farg; while(r != NULL) { rename_syms_term(r->argval, fr); r = r->narg; } } } /* rename_syms_term */ /************* * * void rename_syms_formula(f, fr) * * Rename VARIABLEs so that they conform to the rule for clauses. * *************/ void rename_syms_formula(struct formula *f, struct formula *fr) { struct formula *f1; if (f->type == ATOM_FORM) rename_syms_term(f->t, fr); else { for (f1 = f->first_child; f1; f1 = f1->next) rename_syms_formula(f1, fr); } } /* rename_syms_formula */ /************* * * void subst_sn_term(old_sn, t, new_sn, type) * *************/ void subst_sn_term(int old_sn, struct term *t, int new_sn, int type) { struct rel *r; if (t->type == NAME) { if (type == NAME && t->sym_num == old_sn) t->sym_num = new_sn; } else if (t->type == VARIABLE) { if (type == VARIABLE && t->sym_num == old_sn) t->sym_num = new_sn; } else { for (r = t->farg; r; r = r->narg) subst_sn_term(old_sn, r->argval, new_sn, type); } } /* subst_sn_term */ /************* * * void subst_sn_formula(old_sn, f, new_sn, type) * *************/ void subst_sn_formula(int old_sn, struct formula *f, int new_sn, int type) { struct formula *f1; if (f->type == ATOM_FORM) subst_sn_term(old_sn, f->t, new_sn, type); else { for (f1 = f->first_child; f1; f1 = f1->next) subst_sn_formula(old_sn, f1, new_sn, type); } } /* subst_sn_formula */ /************* * * int gen_subsume_prop(c, d) -- does c gen_subsume_prop d? * * This is generalized propositional subsumption. If given * quantified formulas, they are treated as atoms (formula_ident * determines outcome). * *************/ int gen_subsume_prop(struct formula *c, struct formula *d) { struct formula *f; /* The order of these tests is important. For example, if */ /* the last test is moved to the front, c=(p|q) will not */ /* subsume d=(p|q|r). */ if (c->type == OR_FORM) { /* return(each c_i subsumes d) */ for (f = c->first_child; f && gen_subsume_prop(f, d); f = f->next); return(f == NULL); } else if (d->type == AND_FORM) { /* return(c subsumes each d_i) */ for (f = d->first_child; f && gen_subsume_prop(c, f); f = f->next); return(f == NULL); } else if (c->type == AND_FORM) { /* return(one c_i subsumes d) */ for (f = c->first_child; f && ! gen_subsume_prop(f, d); f = f->next); return(f != NULL); } else if (d->type == OR_FORM) { /* return(c subsumes one d_i) */ for (f = d->first_child; f && ! gen_subsume_prop(c, f); f = f->next); return(f != NULL); } else /* c and d are NOT, ATOM, or QUANT */ return(formula_ident(c, d)); } /* gen_subsume_prop */ /************* * * struct formula *subsume_conj(c) * * Given a conjunction, discard weaker conjuncts. * This is like deleting subsumed clauses. * The result is equivalent. * *************/ struct formula *subsume_conj(struct formula *c) { struct formula *f1, *f2, *f3, *prev; if (c->type != AND_FORM || c->first_child == NULL) return(c); else { /* start with second child */ prev = c->first_child; f1 = prev->next; while (f1) { /* first do forward subsumption of part already processed */ f2 = c->first_child; while (f2 != f1 && ! gen_subsume_prop(f2, f1)) f2 = f2->next;; if (f2 != f1) { /* delete f1 */ prev->next = f1->next; zap_formula(f1); f1 = prev; } else { /* back subsumption on part already processed */ /* delete all previous that are subsumed by f1 */ f2 = c->first_child; prev = NULL; while (f2 != f1) { if (gen_subsume_prop(f1, f2)) { if (prev == NULL) c->first_child = f2->next; else prev->next = f2->next; f3 = f2; f2 = f2->next; zap_formula(f3); } else { prev = f2; f2 = f2->next; } } } prev = f1; f1 = f1->next; } /* If just one child left, replace input formula with child. */ if (c->first_child->next == NULL) { f1 = c->first_child; f1->next = c->next; free_formula(c); return(f1); } else return(c); } } /* subsume_conj */ /************* * * struct formula *subsume_disj(c) * * Given a disjunction, discard stronger disjuncts. * The result is equivalent. This the dual of * normal clause subsumption. * *************/ struct formula *subsume_disj(struct formula *c) { struct formula *f1, *f2, *f3, *prev; if (c->type != OR_FORM || c->first_child == NULL) return(c); else { /* start with second child */ prev = c->first_child; f1 = prev->next; while (f1) { /* delete f1 if it subsumes anything previous */ f2 = c->first_child; while (f2 != f1 && ! gen_subsume_prop(f1, f2)) f2 = f2->next;; if (f2 != f1) { /* delete f1 */ prev->next = f1->next; zap_formula(f1); f1 = prev; } else { /* delete all previous that subsume f1 */ f2 = c->first_child; prev = NULL; while (f2 != f1) { if (gen_subsume_prop(f2, f1)) { if (prev == NULL) c->first_child = f2->next; else prev->next = f2->next; f3 = f2; f2 = f2->next; zap_formula(f3); } else { prev = f2; f2 = f2->next; } } } prev = f1; f1 = f1->next; } /* If just one child left, replace input formula with child. */ if (c->first_child->next == NULL) { f1 = c->first_child; f1->next = c->next; free_formula(c); return(f1); } else return(c); } } /* subsume_disj */ /************* * * int formula_ident(f1, f2) * * Do not permute ANDs, ORs, or like quantifiers. * *************/ int formula_ident(struct formula *f, struct formula *g) { struct formula *f1, *g1; if (f->type != g->type) return(0); else if (f->type == ATOM_FORM) return(term_ident(f->t, g->t)); else if (f->type == QUANT_FORM) { if (f->quant_type != g->quant_type || ! term_ident(f->t, g->t)) return(0); else return(formula_ident(f->first_child, g->first_child)); } else { /* AND_FORM || OR_FORM || IFF_FORM || IMP_FORM || NOT_FORM */ for (f1 = f->first_child, g1 = g->first_child; f1 && g1; f1 = f1->next, g1 = g1->next) if (! formula_ident(f1, g1)) return(0); return(f1 == NULL && g1 == NULL); } } /* formula_ident */ /************* * * conflict_tautology(f) * * If f is an AND_FORM, reduce to empty disjunction (FALSE) * if conflicting conjuncts occur. * If f is an OR_FORM, reduce to empty conjunction (TRUE) * if conflicting disjuncts occur. * *************/ void conflict_tautology(struct formula *f) { struct formula *f1, *f2, *a1, *a2; int f1_sign, f2_sign; /* note possible return from inner loop */ if (f->type == AND_FORM || f->type == OR_FORM) { for (f1 = f->first_child; f1; f1 = f1->next) { f1_sign = (f1->type != NOT_FORM); a1 = (f1_sign ? f1 : f1->first_child); for (f2 = f1->next; f2; f2 = f2->next) { f2_sign = (f2->type != NOT_FORM); if (f1_sign != f2_sign) { a2 = (f2_sign ? f2 : f2->first_child); if (formula_ident(a1, a2)) { f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; zap_formula(f2); } f->first_child = NULL; /* switch types */ f->type = (f->type == AND_FORM ? OR_FORM : AND_FORM); return; } } } } } } /* conflict_tautology */ /************* * * void ts_and_fs(f) * * Simplify if f is AND or OR, and an immediate subformula is * TRUE (empty AND) or FALSE (empty OR). * *************/ void ts_and_fs(struct formula *f) { struct formula *f1, *f2, *f_prev; int f_type; f_type = f->type; if (f_type != AND_FORM && f_type != OR_FORM) return; else { f_prev = NULL; f1 = f->first_child; while (f1 != NULL) { if ((f1->type == AND_FORM || f1->type == OR_FORM) && f1->first_child == NULL) { if (f_type != f1->type) { f->type = f1->type; f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; zap_formula(f2); } f->first_child = NULL; /* switch types */ f->type = (f->type == AND_FORM ? OR_FORM : AND_FORM); return; } else { if (f_prev == NULL) f->first_child = f1->next; else f_prev->next = f1->next; f2 = f1; f1 = f1->next; free_formula(f2); } } else { f_prev = f1; f1 = f1->next; } } } } /* ts_and_fs */ /************* * * static int set_vars_term_2(term, sn) * * Called from set_vars_cl_2. * *************/ static int set_vars_term_2(struct term *t, int *sn) { struct rel *r; int i, rc; if (t->type == COMPLEX) { r = t->farg; rc = 1; while (rc && r != NULL) { rc = set_vars_term_2(r->argval, sn); r = r->narg; } return(rc); } else if (t->type == NAME) return(1); else { i = 0; while (i < MAX_VARS && sn[i] != -1 && sn[i] != t->sym_num) i++; if (i == MAX_VARS) return(0); else { if (sn[i] == -1) sn[i] = t->sym_num; t->varnum = i; /* include following to destroy input variable names t->sym_num = 0; */ return(1); } } } /* set_vars_term_2 */ /************* * * static int set_vars_cl_2(cl) -- give variables var_nums * * This is different from set_vars_cl bacause variables have * already been identified: type==VARIABLE. Identical * variables have same sym_num. * *************/ static int set_vars_cl_2(struct clause *cl) { struct literal *lit; int sn[MAX_VARS]; int i; for (i=0; ifirst_lit; while (lit != NULL) { if (set_vars_term_2(lit->atom, sn)) lit = lit->next_lit; else return(0); } return(1); } /* set_vars_cl_2 */ /************* * * static struct clause *disj_to_clause(f) * *************/ static struct clause *disj_to_clause(struct formula *f) { struct formula *f1, *f2; struct clause *c; struct literal *lit, *prev; c = get_clause(); if (f->type == ATOM_FORM || f->type == NOT_FORM) { lit = get_literal(); lit->sign = (f->type == ATOM_FORM); lit->atom = (f->type == ATOM_FORM ? f->t : f->first_child->t); if (f->type == NOT_FORM) free_formula(f->first_child); free_formula(f); lit->atom->occ.lit = lit; lit->container = c; mark_literal(lit); /* atoms have varnum > 0 */ c->first_lit = lit; } else { /* OR_FORM */ prev = NULL; f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; lit = get_literal(); lit->sign = (f2->type == ATOM_FORM); lit->atom = (f2->type == ATOM_FORM ? f2->t : f2->first_child->t); if (f2->type == NOT_FORM) free_formula(f2->first_child); free_formula(f2); lit->atom->occ.lit = lit; lit->container = c; mark_literal(lit); /* atoms have varnum > 0 */ if (prev == NULL) c->first_lit = lit; else prev->next_lit = lit; prev = lit; } free_formula(f); } if (set_vars_cl_2(c) == 0) { char s[500]; print_clause(stdout, c); sprintf(s, "disj_to_clause, too many variables in clause, max is %d.", MAX_VARS); abend(s); } cl_merge(c); /* merge identical literals */ return(c); } /* disj_to_clause */ /************* * * static struct list *cnf_to_list(f) * * Convert a CNF formula to a list of clauses. * This includes assigning variable numbers to the varnum fileds of VARIABLES. * An ABEND occurs if a clause has too many variables. * *************/ static struct list *cnf_to_list(struct formula *f) { struct formula *f1, *f2; struct list *l; struct clause *c; l = get_list(); if (f->type != AND_FORM) { c = disj_to_clause(f); append_cl(l, c); } else { /* OR_FORM || ATOM_FORM || NOT_FORM */ f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; c = disj_to_clause(f2); /* zaps f2 */ append_cl(l, c); } free_formula(f); } return(l); } /* cnf_to_list */ /************* * * struct list *clausify(f) -- Skolem/CNF tranformation. * * Convert a quantified formula to a list of clauses. * *************/ struct list *clausify(struct formula *f) { struct list *l; f = nnf(f); f = skolemize(f); unique_all(f); f = zap_quant(f); rename_syms_formula(f, f); f = cnf(f); l = cnf_to_list(f); return(l); } /* clausify */ /************* * * struct list *clausify_formula_list(fp) * * Clausify a set of formulas, and return a list of clauses. * The set of formulas is deallocated. * *************/ struct list *clausify_formula_list(struct formula_ptr *fp) { struct list *l, *l1; struct formula_ptr *fp1, *fp2; l = get_list(); fp1 = fp; while (fp1 != NULL) { if (Flags[FORMULA_HISTORY].val) { int f_id; struct clause *c = get_clause(); struct literal *lit = get_literal(); struct ilist *ip1 = get_ilist(); struct ilist *ip2 = get_ilist(); c->first_lit = lit; lit->sign = 1; lit->atom = formula_to_term(fp1->f); assign_cl_id(c); f_id = c->id; hide_clause(c); l1 = clausify(fp1->f); for (c = l1->first_cl; c; c = c->next_cl) { ip1 = get_ilist(); ip2 = get_ilist(); c->parents = ip1; ip1->next = ip2; ip1->i = CLAUSIFY_RULE; ip2->i = f_id; } } else l1 = clausify(fp1->f); append_lists(l, l1); fp2 = fp1; fp1 = fp1->next; free_formula_ptr(fp2); } return(l); } /* clausify_formula_list */ /************* * * struct formula *negation_inward(f) * * If f is a negated conjunction, disjunction, or quantified formula, * move the negation sign in one level. * *************/ struct formula *negation_inward(struct formula *f) { struct formula *f1, *f2, *prev, *f_save; if (f->type == NOT_FORM) { f1 = f->first_child; if (f1->type == AND_FORM || f1->type == OR_FORM || f1->type == QUANT_FORM) { f_save = f->next; f = negate_formula(f); f->next = f_save; if (f->type == AND_FORM || f->type == OR_FORM) { /* apply DeMorgan's laws */ f->type = (f->type == AND_FORM ? OR_FORM : AND_FORM); f1 = f->first_child; prev = NULL; while (f1) { f2 = f1; f1 = f1->next; f2 = negate_formula(f2); if (prev) prev->next = f2; else f->first_child = f2; prev = f2; } } else { /* QUANT_FORM */ f->quant_type = (f->quant_type==ALL_QUANT ? EXISTS_QUANT : ALL_QUANT); f->first_child = negate_formula(f->first_child); } } } return(f); } /* negation_inward */ /************* * * struct formula *expand_imp(f) * * Change (P -> Q) to (-P | Q). * *************/ struct formula *expand_imp(struct formula *f) { if (f->type != IMP_FORM) return(f); else { f->type = OR_FORM; f->first_child = negate_formula(f->first_child); return(f); } } /* expand_imp */ /************* * * struct formula *iff_to_conj(f) * * Change (P <-> Q) to ((P -> Q) & (Q -> P)). * *************/ struct formula *iff_to_conj(struct formula *f) { struct formula *f1, *f2, *f_save; if (f->type != IFF_FORM) return(f); else { f_save = f->next; f1 = copy_formula(f); f->type = f1->type = IMP_FORM; /* flip args of f1 */ f2 = f1->first_child; f1->first_child = f2->next; f2->next = NULL; f1->first_child->next = f2; f->next = f1; f1->next = NULL; /* build conjunction */ f2 = get_formula(); f2->type = AND_FORM; f2->first_child = f; f2->next = f_save; return(f2); } } /* iff_to_conj */ /************* * * struct formula *iff_to_disj(f) * * Change (P <-> Q) to ((P & Q) | (-Q & -P)). * *************/ struct formula *iff_to_disj(struct formula *f) { struct formula *f1, *f2, *f_save; if (f->type != IFF_FORM) return(f); else { f_save = f->next; f1 = copy_formula(f); f->type = f1->type = AND_FORM; f1->first_child->next = negate_formula(f1->first_child->next); f1->first_child = negate_formula(f1->first_child); f->next = f1; f1->next = NULL; /* build disjunction */ f2 = get_formula(); f2->type = OR_FORM; f2->first_child = f; f2->next = f_save; return(f2); } } /* iff_to_disj */ /************* * * struct formula *nnf_cnf(f) * *************/ struct formula *nnf_cnf(struct formula *f) { return(cnf(nnf(f))); } /* nnf_cnf */ /************* * * struct formula *nnf_dnf(f) * *************/ struct formula *nnf_dnf(struct formula *f) { return(dnf(nnf(f))); } /* nnf_dnf */ /************* * * struct formula *nnf_skolemize(f) * *************/ struct formula *nnf_skolemize(struct formula *f) { return(skolemize(nnf(f))); } /* nnf_skolemize */ /************* * * struct formula *clausify_formed(f) * *************/ struct formula *clausify_formed(struct formula *f) { f = nnf(f); f = skolemize(f); unique_all(f); f = zap_quant(f); rename_syms_formula(f, f); f = cnf(f); return(f); } /* clausify_formed */ /************* * * rms_conflict_tautology(f) * * If f is an AND_FORM, reduce to empty disjunction (FALSE) * if conflicting conjuncts occur. * If f is an OR_FORM, reduce to empty conjunction (TRUE) * if conflicting disjuncts occur. * *************/ void rms_conflict_tautology(struct formula *f) { struct formula *f1, *f2; /* note possible return from inner loop */ if (f->type == AND_FORM) { for (f1 = f->first_child; f1; f1 = f1->next) { for (f2 = f1->next; f2; f2 = f2->next) { if (gen_conflict(f1, f2)) { f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; zap_formula(f2); } f->first_child = NULL; /* switch types */ f->type = OR_FORM; return; } } } } else if (f->type == OR_FORM) { for (f1 = f->first_child; f1; f1 = f1->next) { for (f2 = f1->next; f2; f2 = f2->next) { if (gen_tautology(f1, f2)) { f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; zap_formula(f2); } f->first_child = NULL; /* switch types */ f->type = AND_FORM; return; } } } } } /* rms_conflict_tautology */ /************* * * struct formula *rms_subsume_conj(c) * * Given a conjunction, discard weaker conjuncts. * This is like deleting subsumed clauses. * The result is equivalent. * *************/ struct formula *rms_subsume_conj(struct formula *c) { struct formula *f1, *f2, *f3, *prev; if (c->type != AND_FORM || c->first_child == NULL) return(c); else { /* start with second child */ prev = c->first_child; f1 = prev->next; while (f1) { /* first do forward subsumption of part already processed */ f2 = c->first_child; while (f2 != f1 && ! gen_subsume(f2, f1)) f2 = f2->next;; if (f2 != f1) { /* delete f1 */ prev->next = f1->next; zap_formula(f1); f1 = prev; } else { /* back subsumption on part already processed */ /* delete all previous that are subsumed by f1 */ f2 = c->first_child; prev = NULL; while (f2 != f1) { if (gen_subsume(f1, f2)) { if (prev == NULL) c->first_child = f2->next; else prev->next = f2->next; f3 = f2; f2 = f2->next; zap_formula(f3); } else { prev = f2; f2 = f2->next; } } } prev = f1; f1 = f1->next; } /* If just one child left, replace input formula with child. */ if (c->first_child->next == NULL) { f1 = c->first_child; f1->next = c->next; free_formula(c); return(f1); } else return(c); } } /* rms_subsume_conj */ /************* * * struct formula *rms_subsume_disj(c) * * Given a disjunction, discard stronger disjuncts. * The result is equivalent. This the dual of * normal clause subsumption. * *************/ struct formula *rms_subsume_disj(struct formula *c) { struct formula *f1, *f2, *f3, *prev; if (c->type != OR_FORM || c->first_child == NULL) return(c); else { /* start with second child */ prev = c->first_child; f1 = prev->next; while (f1) { /* delete f1 if it subsumes anything previous */ f2 = c->first_child; while (f2 != f1 && ! gen_subsume(f1, f2)) f2 = f2->next;; if (f2 != f1) { /* delete f1 */ prev->next = f1->next; zap_formula(f1); f1 = prev; } else { /* delete all previous that subsume f1 */ f2 = c->first_child; prev = NULL; while (f2 != f1) { if (gen_subsume(f2, f1)) { if (prev == NULL) c->first_child = f2->next; else prev->next = f2->next; f3 = f2; f2 = f2->next; zap_formula(f3); } else { prev = f2; f2 = f2->next; } } } prev = f1; f1 = f1->next; } /* If just one child left, replace input formula with child. */ if (c->first_child->next == NULL) { f1 = c->first_child; f1->next = c->next; free_formula(c); return(f1); } else return(c); } } /* rms_subsume_disj */ /************* * * int free_occurrence(v, f) * * Does v have a free occurrence in f? * *************/ int free_occurrence(struct term *v, struct formula *f) { struct formula *f1; int free; switch (f->type) { case ATOM_FORM: free = occurs_in(v, f->t); break; case NOT_FORM: case AND_FORM: case OR_FORM: case IMP_FORM: case IFF_FORM: for (free = 0, f1 = f->first_child; f1 && ! free; f1 = f1->next) free = free_occurrence(v, f1); break; case QUANT_FORM: if (term_ident(v, f->t)) free = 0; else free = free_occurrence(v, f->first_child); break; default: free = 0; } return(free); } /* free_occurrence */ /************* * * struct formula *rms_distribute_quants(f) * * f is universally quantified formula. * Child is conjunction in RMS. * Distribute quantifier to conjuncts. * Return a RMS of f. * *************/ struct formula *rms_distribute_quants(struct formula *f_quant) { struct formula *f_conj, *f1, *f2, *f3; f_conj = f_quant->first_child; f3 = NULL; f1 = f_conj->first_child; while (f1) { f2 = get_formula(); f2->type = QUANT_FORM; f2->quant_type = ALL_QUANT; f2->first_child = f1; f2->t = copy_term(f_quant->t); f1 = f1->next; f2->first_child->next = NULL; f2 = rms_quantifiers(f2); /* indirect recursive call */ if (f3) f3->next = f2; else f_conj->first_child = f2; f3 = f2; } zap_term(f_quant->t); free_formula(f_quant); flatten_top(f_conj); rms_conflict_tautology(f_conj); f_conj = rms_subsume_conj(f_conj); return(f_conj); } /* rms_distribute_quants */ /************* * * void separate_free(v, f, free, not_free) * *************/ static void separate_free(struct term *v, struct formula *f, struct formula **p_free, struct formula **p_not_free) { struct formula *f1, *not_free, *f2, *f3, *prev; not_free = f2 = f3 = prev = NULL; f1 = f->first_child; while (f1) { f2 = f1; f1 = f1->next; if (!free_occurrence(v, f2)) { f2->next = NULL; if (not_free) f3->next = f2; else not_free = f2; f3 = f2; if (prev == NULL) f->first_child = f1; else prev->next = f1; } else prev = f2; } if (f->first_child == NULL) { *p_free = NULL; free_formula(f); } else if (f->first_child->next == NULL) { *p_free = f->first_child; free_formula(f); } else *p_free = f; if (not_free == NULL) *p_not_free = NULL; else if (not_free->next == NULL) *p_not_free = not_free; else { f1 = get_formula(); f1->type = OR_FORM; f1->first_child = not_free; *p_not_free = f1; } } /* separate_free */ /************* * * struct formula *rms_push_free(f) * * f is universally quantifierd formula. * The child of f is a (simple) disjunction in RMS. * Reduce scopes based on free variables. * Result is in RMS, either a quantified formula or a disjunction. * *************/ struct formula *rms_push_free(struct formula *f) { struct formula *f2, *free, *not_free; separate_free(f->t, f->first_child, &free, ¬_free); if (!free) { /* var doesn't occur free in any subformula. */ abend("rms_push_free has extra quantifier."); } if (not_free) { f->first_child = free; f = rms_quantifiers(f); f->next = NULL; if (not_free->type == OR_FORM) { /* Install f as last disjunct. */ for (f2 = not_free->first_child; f2->next; f2 = f2->next); f2->next = f; f2 = not_free; } else { f2 = get_formula(); f2->type = OR_FORM; f2->first_child = not_free; not_free->next = f; } /* f2 is disjunction */ rms_conflict_tautology(f2); f2 = rms_subsume_disj(f2); return(f2); } else return(f); } /* rms_push_free */ /************* * * struct formula *rms_quantifiers(f) * * f is a quantified formula whose child is in RMS. * This function returns a RMS of f. * *************/ struct formula *rms_quantifiers(struct formula *f) { struct formula *f1, *f2, *f_save; int negate_flag; f_save = f->next; f->next = NULL; if (!free_occurrence(f->t, f->first_child)) { f1 = f->first_child; zap_term(f->t); free_formula(f); f1->next = f_save; return(f1); } if (f->quant_type == EXISTS_QUANT) { f = nnf(negate_formula(f)); negate_flag = 1; /* If f is an OR with and AND child, call rms to make conjunction. */ if (f->first_child->type == OR_FORM) { for(f1 = f->first_child->first_child; f1 && f1->type != AND_FORM; f1 = f1->next); if (f1) f->first_child = rms(f->first_child); } } else negate_flag = 0; /* Now, "all" is the quantifier, and child is RMS. */ if (f->first_child->type == AND_FORM) f = rms_distribute_quants(f); else if (f->first_child->type == OR_FORM) f = rms_push_free(f); /* else atomic or negated atomic, so do nothing */ /* f is now not necessarily QUANT_FORM. */ if (negate_flag) { f = nnf(negate_formula(f)); if (f->type == QUANT_FORM) f2 = f->first_child; else f2 = f; /* If f2 is an OR with and AND child, call rms to make conjunction. */ if (f2->type == OR_FORM) { for(f1 = f2->first_child; f1 && f1->type != AND_FORM; f1 = f1->next); if (f1) { if (f == f2) f = rms(f2); else f->first_child = rms(f2); } } } f->next= f_save; return(f); } /* rms_quantifiers */ /************* * * static struct formula *rms_distribute(f) -- rms_distribute OR over AND. * * f is an OR node whose subterms are in Reduced MiniScope (RMS). * This routine returns a RMS of f. * *************/ static struct formula *rms_distribute(struct formula *f) { struct formula *f_new, *f1, *f2, *f3, *f4, *f_prev, *f_save; int i, j; f_save = f->next; f->next = NULL; if (f->type != OR_FORM) return(f); else { flatten_top(f); rms_conflict_tautology(f); f = rms_subsume_disj(f); if (f->type != OR_FORM) return(f); else { /* find first AND subformula */ i = 1; f_prev = NULL; for (f1 = f->first_child; f1 && f1->type != AND_FORM; f1 = f1->next) { i++; f_prev = f1; } if (f1 == NULL) return(f); /* nothing to rms_distribute */ else { /* unhook AND */ if (f_prev) f_prev->next = f1->next; else f->first_child = f1->next; f2 = f1->first_child; f_new = f1; f_prev = NULL; while (f2) { f3 = f2->next; if (f3) f1 = copy_formula(f); else f1 = f; if (i == 1) { f2->next = f1->first_child; f1->first_child = f2; } else { j = 1; for (f4 = f1->first_child; j < i-1; f4 = f4->next) j++; f2->next = f4->next; f4->next = f2; } f1 = rms_distribute(f1); if (f_prev) f_prev->next = f1; else f_new->first_child = f1; f_prev = f1; f2 = f3; } f_new->next = f_save; flatten_top(f_new); rms_conflict_tautology(f_new); f_new = rms_subsume_conj(f_new); return(f_new); } } } } /* rms_distribute */ /************* * * struct formula *rms(f) -- convert f to Reduced MiniScope (RMS) * *************/ struct formula *rms(struct formula *f) { struct formula *f1, *f2, *f_prev, *f_next, *f_save; f_save = f->next; f->next = NULL; if (f->type == AND_FORM || f->type == OR_FORM) { /* first convert subterms to RMS */ f_prev = NULL; f1 = f->first_child; while(f1) { f_next = f1->next; f2 = rms(f1); if (f_prev) f_prev->next = f2; else f->first_child = f2; f_prev = f2; f1 = f_next; } if (f->type == AND_FORM) { flatten_top(f); rms_conflict_tautology(f); f = rms_subsume_conj(f); } else f = rms_distribute(f); /* flatten and simplify in distribute */ } else if (f->type == QUANT_FORM) { f->first_child = rms(f->first_child); f = rms_quantifiers(f); } /* else f is atomic or negated atomic, so do nothing; */ f->next = f_save; return(f); } /* rms */ /************* * * static void introduce_var_term(t, v, vnum) * *************/ static void introduce_var_term(struct term *t, struct term *v, int vnum) { struct rel *r; switch (t->type) { case NAME: if (term_ident(t,v)) { t->type = VARIABLE; t->varnum = vnum; t->sym_num = 0; } break; case VARIABLE: break; case COMPLEX: for (r = t->farg; r; r = r->narg) introduce_var_term(r->argval, v, vnum); break; } } /* introduce_var_term */ /************* * * static void introduce_var(f, t, vnum) * * In formula f, replace all free occurrences of t with a variable * (set type to VARIABLE) with number vnum. * *************/ static void introduce_var(struct formula *f, struct term *t, int vnum) { struct formula *f1; switch (f->type) { case ATOM_FORM: introduce_var_term(f->t, t, vnum); break; case AND_FORM: case OR_FORM: case NOT_FORM: for (f1 = f->first_child; f1; f1 = f1->next) introduce_var(f1, t, vnum); break; case QUANT_FORM: if (!term_ident(t, f->t)) introduce_var(f->first_child, t, vnum); break; default: abend("introduce_var, bad formula."); } } /* introduce_var */ /************* * * struct formula *renumber_unique(f, vnum) * * f is NNF, and all quantifiers are unique. * This function renumbers variables, starting with *vnum_p and * removes quantifiers. * *************/ struct formula *renumber_unique(struct formula *f, int *vnum_p) { struct formula *f1, *f2, *f_prev, *f_next; switch (f->type) { case ATOM_FORM: return(f); case AND_FORM: case OR_FORM: case NOT_FORM: f_prev = NULL; f1 = f->first_child; while(f1) { f_next = f1->next; f2 = renumber_unique(f1, vnum_p); if (f_prev) f_prev->next = f2; else f->first_child = f2; f_prev = f2; f1 = f_next; } return(f); case QUANT_FORM: f1 = f->first_child; introduce_var(f1, f->t, *vnum_p); (*vnum_p)++; if (*vnum_p == MAX_VARS) { abend("renumber_unique, too many vars."); } f1->next = f->next; f->first_child = NULL; zap_formula(f); return(renumber_unique(f1, vnum_p)); } abend("renumber_unique, bad formula."); return(f); /* to quiet lint */ } /* renumber_unique */ /************* * * int gen_subsume_rec(c, cs, d, ds, tr_p) -- does c gen_subsume_rec d? * * This is generalized subsumption on quantified formulas. It is * not as complete as the Prolog version, because there is no * backtracking to try alternatives in cases 3 and 4 below. * *************/ int gen_subsume_rec(struct formula *c, struct context *cs, struct formula *d, struct context *ds, struct trail **tr_p) { struct formula *f; /* The order of these tests is important. For example, if */ /* the last test is moved to the front, c=(p|q) will not */ /* subsume d=(p|q|r). */ if (c->type == OR_FORM) { /* return(each c_i subsumes d) */ for (f = c->first_child; f && gen_subsume_rec(f, cs, d, ds, tr_p); f = f->next); return(f == NULL); } else if (d->type == AND_FORM) { /* return(c subsumes each d_i) */ for (f = d->first_child; f && gen_subsume_rec(c, cs, f, ds, tr_p); f = f->next); return(f == NULL); } else if (c->type == AND_FORM) { /* return(one c_i subsumes d) */ for (f = c->first_child; f && ! gen_subsume_rec(f, cs, d, ds, tr_p); f = f->next); return(f != NULL); } else if (d->type == OR_FORM) { /* return(c subsumes one d_i) */ for (f = d->first_child; f && ! gen_subsume_rec(c, cs, f, ds, tr_p); f = f->next); return(f != NULL); } else if (c->type != d->type) return(0); else if (c->type == NOT_FORM) return(unify(c->first_child->t, cs, d->first_child->t, ds, tr_p)); else /* both ATOMs */ return(unify(c->t, cs, d->t, ds, tr_p)); } /* gen_subsume_rec */ /************* * * int gen_subsume(c, d) -- generalized subsumption on RMS formulas. * * If 1 is returned, (c -> d) holds. * *************/ int gen_subsume(struct formula *c, struct formula *d) { struct formula *c1, *d1; int result, i; struct context *cs, *ds; struct trail *tr; Sk_const_num = Sk_func_num = 0; i = 6; c1 = renumber_unique(skolemize(copy_formula(c)),&i); i = 6; d1 = renumber_unique(anti_skolemize(copy_formula(d)),&i); cs = get_context(); ds = get_context(); tr = NULL; result = gen_subsume_rec(c1, cs, d1, ds, &tr); clear_subst_1(tr); free_context(cs); free_context(ds); zap_formula(c1); zap_formula(d1); return(result); } /* gen_subsume */ /************* * * int gen_conflict(c, d) * * Try to show (c & d) inconsistent by showing (c -> -d). * * If 1 is returned, (c & d) is inconsistent. * *************/ int gen_conflict(struct formula *c, struct formula *d) { struct formula *c1, *d1; int result, i; struct context *cs, *ds; struct trail *tr; Sk_const_num = Sk_func_num = 0; i = 6; c1 = renumber_unique(skolemize(copy_formula(c)),&i); i = 6; /* can skip nnf of negate_formula, because anti-skolemize re-negates */ d1 = renumber_unique(anti_skolemize(negate_formula(copy_formula(d))),&i); cs = get_context(); ds = get_context(); tr = NULL; result = gen_subsume_rec(c1, cs, d1, ds, &tr); clear_subst_1(tr); free_context(cs); free_context(ds); zap_formula(c1); zap_formula(d1); return(result); } /* gen_conflict */ /************* * * int gen_tautology(c, d) * * Try to show (c | d) a tautology by showing (-c -> d). * * If 1 is returned, (c | d) is a tautology. * *************/ int gen_tautology(struct formula *c, struct formula *d) { struct formula *c1, *d1; int result, i; struct context *cs, *ds; struct trail *tr; Sk_const_num = Sk_func_num = 0; i = 6; c1 = renumber_unique(skolemize(nnf(negate_formula(copy_formula(c)))),&i); i = 6; d1 = renumber_unique(anti_skolemize(copy_formula(d)),&i); cs = get_context(); ds = get_context(); tr = NULL; result = gen_subsume_rec(c1, cs, d1, ds, &tr); clear_subst_1(tr); free_context(cs); free_context(ds); zap_formula(c1); zap_formula(d1); return(result); } /* gen_tautology */ /************* * * struct formula *rms_cnf(f) * *************/ struct formula *rms_cnf(struct formula *f) { return(rms(nnf(f))); } /* rms_cnf */ /************* * * struct formula *rms_dnf(f) * *************/ struct formula *rms_dnf(struct formula *f) { return(nnf(negate_formula(rms(nnf(negate_formula(f)))))); } /* rms_dnf */ /************* * * struct formula *push_free(f) * * f is universally quantifierd formula * The child of f is a disjunction. * Reduce scopes 1 level based on free variables. * Result is either a quantified formula or a disjunction. * *************/ static struct formula *push_free(struct formula *f) { struct formula *f2, *free, *not_free; separate_free(f->t, f->first_child, &free, ¬_free); if (!free) { /* var doesn't occur free in any subformula. */ not_free->next = f->next; free_term(f->t); free_formula(f); return(not_free); } else if (!not_free) /* var occurs free in all subformulas */ return(f); else { /* at least one of each */ f->first_child = free; f->next = NULL; if (not_free->type == OR_FORM) { /* Install f as last disjunct. */ for (f2 = not_free->first_child; f2->next; f2 = f2->next); f2->next = f; f2 = not_free; } else { f2 = get_formula(); f2->type = OR_FORM; f2->first_child = not_free; not_free->next = f; } /* f2 is disjunction */ return(f2); } } /* push_free */ /************* * * struct formula *distribute_quantifier(f) * * If f is (all x (f1 & ...)) or (exists x (f1 | ...)), * distribute the quantifier to the subformulas (and delete * the quantifier if the subformula has no free occurrences * of the variable. * *************/ struct formula *distribute_quantifier(struct formula *f) { struct formula *f1, *f2, *f3, *prev, *save_next; if (f->type == QUANT_FORM) { save_next = f->next; f->next = NULL; f1 = f->first_child; if ((f->quant_type == ALL_QUANT && f1->type == AND_FORM) || (f->quant_type == EXISTS_QUANT && f1->type == OR_FORM)) { for (f2=f1->first_child, prev=NULL; f2; prev=f2, f2=f2->next) { if (free_occurrence(f->t, f2)) { f3 = get_formula(); f3->type = QUANT_FORM; f3->quant_type = f->quant_type; f3->t = copy_term(f->t); /* variable */ f3->next = f2->next; f3->first_child = f2; f2->next = NULL; if (prev) prev->next = f3; else f1->first_child = f3; f2 = f3; } } free_term(f->t); free_formula(f); f = f1; } else if (f->quant_type == ALL_QUANT && f1->type == OR_FORM) { f = push_free(f); } else if (f->quant_type == EXISTS_QUANT && f1->type == AND_FORM) { f = nnf(negate_formula(f)); f = push_free(f); f = nnf(negate_formula(f)); } f->next = save_next; } return(f); } /* distribute_quantifier */ otter-3.3f/source/sed.clocks0100644000076400007640000000006307264331220015452 0ustar mccunemccune/CLOCK_START(.*)$/s/)/);/ /CLOCK_STOP(.*)$/s/)/);/ otter-3.3f/source/geometry.c0100644000076400007640000001666007343604672015524 0ustar mccunemccune/* * geometry.c -- Padmanabhan's inference rule * * This is an inference rule of R. Padmanabhan. Assume f is a binary * functor, left and right cancellation hold for f, and the following * axiom holds: f(f(x,y),f(z,u)) = f(f(x,z),f(y,u)). Then the following * inference rule is sound: * * Consider A=B, in which A and B are terms built from f, variables, and * constants. (If other terms appear, we can treat them as constants.) * If A and B have identical terms, say C, in corresponding positions, * then infer A'=B', which is similar to A=B, except that the two occurrences * of C have been replaced with a fresh variable. * * Of course, if two terms in corresponding positions can be made * identical by unification, then we can instantiate that equality * and replace the terms with a fresh variable. * * This file contains several versions of the inference rule. * * 1. As a rewrite rule (separate from demodulation) (without unification). * routine geo_rewrite below. * * 2. As an inference rule (applied to given clause), with unification. * routine geometry_rule_unif below. * */ #include "header.h" #define MAX_DEPTH 50 /************* * * is_geometry_symbol() -- THIS IS LIKELY TO CHANGE!!! * *************/ static int is_geometry_symbol(int sn) { #if 1 /* August 9. make gL apply everywhere. */ return(1); #else return(str_ident(sn_to_str(sn), "f") || str_ident(sn_to_str(sn), "g") || str_ident(sn_to_str(sn), "*")); #endif } /* is_geometry_symbol */ /************* * * geo_rewrite_recurse() * *************/ static int geo_rewrite_recurse(struct rel *a, struct rel *b, struct clause *cl, int *next_var) { #if 0 if (a->argval->type == VARIABLE || b->argval->type == VARIABLE) return(0); else #endif if (term_ident(a->argval, b->argval)) { if (a->argval->type == VARIABLE && occurrences(a->argval, cl->first_lit->atom) == 2) /* a & b are the only occurrences, so there is no point in applying the rule. */ return(0); else { struct term *t; struct ilist *p1, *p2; if (*next_var == MAX_VARS) { abend("geo_rewrite_recurse, too many variables."); } for (p1 = cl->parents; p1 && p1->next; p1 = p1->next); p2 = get_ilist(); p2->i = GEO_ID_RULE; p2->next = NULL; if (p1) p1->next = p2; else cl->parents = p2; zap_term(a->argval); zap_term(b->argval); t = get_term(); t->type = VARIABLE; t->varnum = *next_var; a->argval = t; t = get_term(); t->type = VARIABLE; t->varnum = *next_var; b->argval = t; (*next_var)++; return(1); } } else if (is_geometry_symbol(a->argval->sym_num) && a->argval->sym_num == b->argval->sym_num) { int n; struct rel *a1, *b1; n = 0; for (a1 = a->argval->farg, b1 = b->argval->farg; a1; a1 = a1->narg, b1 = b1->narg) n += geo_rewrite_recurse(a1, b1, cl, next_var); return(n); } else return(0); } /* geo_rewrite_recurse */ /************* * * geo_rewrite() * * This is a rewrite version of Padmanabhan's geometry law. * * When applied, this rule introduces a new variable, and the number * of the new variable is 1 more than the greatest variable already * in the equality. * * This routine applies the rule as much as possible. * *************/ int geo_rewrite(struct clause *c) { if (c->first_lit && !c->first_lit->next_lit && pos_eq_lit(c->first_lit)) { struct rel *a, *b; int next_var, replacements; a = c->first_lit->atom->farg; b = a->narg; next_var = biggest_var(c->first_lit->atom) + 1; replacements = geo_rewrite_recurse(a, b, c, &next_var); return(replacements > 0); } else return(0); } /* geo_rewrite */ /************* * * geo_replace_unif() * *************/ static struct term *geo_replace_unif(struct term *t, int *pos_vec, int depth) { if (depth == 0) { zap_term(t); t = get_term(); t->type = VARIABLE; t->varnum = MAX_VARS+1; } else { struct rel *r; int i; for (i=1, r=t->farg; i < *pos_vec; i++, r = r->narg); r->argval = geo_replace_unif(r->argval, pos_vec+1, depth-1); } return(t); } /* geo_replace_unif */ /************* * * geo_generate_unif() * *************/ static void geo_generate_unif(struct clause *giv_cl, int *pos_vec, int depth, struct context *subst) { struct clause *new_clause; struct ilist *ip; struct literal *lit; new_clause = get_clause(); new_clause->type = giv_cl->type; lit = get_literal(); lit->sign = giv_cl->first_lit->sign; lit->container = new_clause; new_clause->first_lit = lit; lit->atom = apply(giv_cl->first_lit->atom, subst); lit->atom->occ.lit = lit; lit->atom->varnum = giv_cl->first_lit->atom->varnum; /* type of atom */ lit->atom->farg->argval = geo_replace_unif(lit->atom->farg->argval, pos_vec, depth); lit->atom->farg->narg->argval = geo_replace_unif(lit->atom->farg->narg->argval, pos_vec, depth); ip = get_ilist(); ip->i = GEO_RULE; new_clause->parents = ip; ip = get_ilist(); ip->i = giv_cl->id; new_clause->parents->next = ip; Stats[CL_GENERATED]++; Stats[GEO_GEN]++; pre_process(new_clause, 0, Sos); } /* geo_generate_unif */ /************* * * geo_recurse_unif() * *************/ static void geo_recurse_unif(struct term *a, struct term *b, struct clause *giv_cl, int *pos_vec, int depth) { struct context *subst; struct trail *tr; subst = get_context(); subst->multiplier = 0; tr = NULL; if (unify(a, subst, b, subst, &tr)) { geo_generate_unif(giv_cl, pos_vec, depth, subst); clear_subst_1(tr); } if (is_geometry_symbol(a->sym_num) && a->sym_num == b->sym_num) { struct rel *a1, *b1; int i; if (depth == MAX_DEPTH) { abend("geo_recurse, MAX_DEPTH."); } for (i = 1, a1 = a->farg, b1 = b->farg; a1; i++, a1 = a1->narg, b1 = b1->narg) { pos_vec[depth] = i; geo_recurse_unif(a1->argval, b1->argval, giv_cl, pos_vec, depth+1); } pos_vec[depth] = 0; /* not really necessary */ } } /* geo_recurse_unif */ /************* * * geometry_rule_unif() * * As in other inference rules, this rule assumes that the given clause * has variables renumbered, in particular, that all variable numbers * are < MAX_VARS. And as in other inference rules, clauses inferred by * this rule may have variable numbers >= MAX_VARS. * *************/ void geometry_rule_unif(struct clause *giv_cl) { if (giv_cl->first_lit && !giv_cl->first_lit->next_lit && pos_eq_lit(giv_cl->first_lit)) { struct term *a, *b; int pos_vec[MAX_DEPTH]; a = giv_cl->first_lit->atom->farg->argval; b = giv_cl->first_lit->atom->farg->narg->argval; geo_recurse_unif(a, b, giv_cl, pos_vec, 0); } } /* geometry_rule_unif */ /************* * * child_of_geometry() * *************/ int child_of_geometry(struct clause *c) { struct ilist *p; for (p = c->parents; p; p = p->next) { if (p->i == GEO_ID_RULE || p->i == GEO_RULE) return(1); } return(0); } /* child_of_geometry */ /************* * * gl_demod() * * Copy, demodulate, then pre_process. * *************/ void gl_demod(struct clause *c, struct list *lst) { struct clause *d; struct ilist *ip1, *ip2; d = cl_copy(c); ip1 = get_ilist(); ip1->i = COPY_RULE; d->parents = ip1; ip2 = get_ilist(); ip2->i = c->id; ip1->next = ip2; demod_cl(d); pre_process(d, 0, lst); } /* gl_demod */ otter-3.3f/source/linkhyp.c0100644000076400007640000000041007343604673015332 0ustar mccunemccune/* * linkhyp.c -- linked hyperresolution * */ #include "header.h" /************* * * linked_hyper_res(giv_cl) * *************/ void linked_hyper_res(struct clause *giv_cl) { printf("linked hyper not implemented yet.\n"); } /* linked_hyper_res */ otter-3.3f/source/types.h.diffs0100644000076400007640000000037410041245667016121 0ustar mccunemccune54c54 < struct term_ptr *terms; /* for leaves only */ --- > struct fposition position; /* for leaves only */ 64c64 < struct term_ptr *terms; /* list of terms with path */ --- > struct fnode *terms; /* terms with path */ otter-3.3f/source/lisp.h0100644000076400007640000000167107343604666014644 0ustar mccunemccune/* This is a dirty little parser for LISP-like expressions. It is meant to to parse expressions written by machine. * Comments are not recognized. * Almost any token is accepted as an atom. * Dot expressions are ok. * Extra whitespace is ok. * If anything goes wrong, exit with a message goes to stderr. */ #include #include #include /* for malloc, free */ #if 1 #define BOOLEAN char #define FALSE 0 #define TRUE 1 #else typedef enum { FALSE=0, TRUE=1 } BOOL; #endif typedef struct bnode * Bnode; struct bnode { Bnode car; Bnode cdr; BOOLEAN atom; char *label; }; /* Prototypes from lisp.c */ void zap_btree(Bnode p); BOOLEAN true_listp(Bnode p); void fprint_btree(FILE *fp, Bnode p); void p_btree(Bnode p); BOOLEAN nullp(Bnode p); Bnode parse_lisp(FILE *fp); int atom(Bnode p); Bnode car(Bnode p); Bnode cdr(Bnode p); Bnode cadr(Bnode p); Bnode caddr(Bnode p); int length(Bnode p); otter-3.3f/source/io.c0100644000076400007640000017003610012217075014256 0ustar mccunemccune/* * io.c -- input/output routines * */ /* to do for new operator stuff: * * 5. optimize seq_to_term? * 8. can protect cl when in list with parens, but output does not get parens. * 10. -3 should be a number, -(3) should not. Same for unary +. * 11. Check arity problem? * 12. check set_variables? * */ #include "header.h" #define SYM_TAB_SIZE 50 #define MAX_COMPLEX 1000 /* number of operators/terms */ /* Include the following if ' should be a a quote character (like "). Otter has had that behavior since the beginning. But I am changing it today, on Feb 19, 2004, making ' a SYM_SYM. To revert to the old behavior, include the following. */ /* #define SINGLE_QUOTE */ /* Following structure is to store data on symbol that might be special op. */ struct sequence_member { struct term *t; short binary_type; short binary_prec; short unary_type; short unary_prec; }; static struct sym_ent *Sym_tab[SYM_TAB_SIZE]; /* Symbol Table */ /************* * * int str_double(string, double_ptr) -- Translate a string to a double. * * Return(1) iff success. * *************/ int str_double(char *s, double *dp) { char *end; double d; if (*s != '\"') return(0); else if (*(s+1) == '\"') return(0); else { d = strtod(s+1, &end); *dp = d; return (*end == '\"'); } } /* str_double */ /************* * * double_str(double, str) -- translate a double to a string * * Like sprintf, except that format is built in and string is * surrouded by double quotes. * *************/ void double_str(double d, char *s) { int i, n; sprintf(s, Float_format, d); n = strlen(s); for (i=n; i>0; i--) s[i] = s[i-1]; s[0] = '\"'; s[n+1] = '\"'; s[n+2] = '\0'; } /* double_str */ /************* * * int str_int(string, ilist) -- Translate a string to an integer. * * String has optional '+' or '-' as first character. * Return(1) iff success. * *************/ int str_int(char *s, int *np) { int i, sign, n; i = 0; sign = 1; if (s[0] == '+' || s[0] == '-') { if (s[0] == '-') sign = -1; i = 1; } if (s[i] == '\0') return(0); else { n = 0; for( ; s[i] >= '0' && s[i] <= '9'; i++) n = n * 10 + s[i] - '0'; *np = n * sign; return(s[i] == '\0'); } } /* str_int */ /************* * * int_str(int, str) -- translate an integer to a string * *************/ void int_str(int i, char *s) { int j, sign; if ((sign = i) < 0) i = -i; j = 0; if (i == 0) s[j++] = '0'; else { while (i > 0) { s[j++] = i % 10 + '0'; i = i / 10; } } if (sign < 0) s[j++] = '-'; s[j] = '\0'; reverse(s); } /* int_str */ /************* * * int str_long(string, long_ptr) -- Translate a string to a long. * * String has optional '+' or '-' as first character. * Return(1) iff success. * *************/ int str_long(char *s, long int *np) { int i, sign; long n; i = 0; sign = 1; if (s[0] == '+' || s[0] == '-') { if (s[0] == '-') sign = -1; i = 1; } if (s[i] == '\0') return(0); else { n = 0; for( ; s[i] >= '0' && s[i] <= '9'; i++) n = n * 10 + s[i] - '0'; *np = n * sign; return(s[i] == '\0'); } } /* str_long */ /************* * * int bits_ulong(string, long_ptr) -- Translate a string to a long. * * String must consist only of 0's and 1's. * * Return(1) iff success. * *************/ int bits_ulong(char *s, long unsigned int *np) { int i; unsigned long n; n = 0; for(i = 0 ; s[i] == '0' || s[i] == '1'; i++) n = n * 2 + s[i] - '0'; *np = n; return(s[i] == '\0'); } /* bits_ulong */ /************* * * long_str(int, str) -- translate a long to a string * *************/ void long_str(long int i, char *s) { int j; long signd; if ((signd = i) < 0) i = -i; j = 0; if (i == 0) s[j++] = '0'; else { while (i > 0) { s[j++] = i % 10 + '0'; i = i / 10; } } if (signd < 0) s[j++] = '-'; s[j] = '\0'; reverse(s); } /* long_str */ /************* * * ulong_bits(int, str) -- translate a long to a base-2 string. * *************/ void ulong_bits(long unsigned int i, char *s) { unsigned long j; int n, k; /* Set n to the number of places we'll use. */ /* First ignore leading 0's, then increase if necessary. */ for (j = i, n = 0; j > 0; j = j >> 1, n++); n = (n < Parms[MIN_BIT_WIDTH].val ? Parms[MIN_BIT_WIDTH].val : n); /* build the string */ for (k = 0; k < n; k++) s[k] = '0' + ((i >> (n-(k+1))) & 1); s[n] = '\0'; } /* ulong_bits */ /************* * * cat_str(s1, s2, s3) * *************/ void cat_str(char *s1, char *s2, char *s3) { int i, j; for (i = 0; s1[i] != '\0'; i++) s3[i] = s1[i]; for (j = 0; s2[j] != '\0'; j++, i++) s3[i] = s2[j]; s3[i] = '\0'; } /* cat_str */ /************* * * int str_ident(s, t) -- Identity of strings * *************/ int str_ident(char *s, char *t) { for ( ; *s == *t; s++, t++) if (*s == '\0') return(1); return(0); } /* str_ident */ /************* * * reverse(s) -- reverse a string * *************/ void reverse(char *s) { int i, j; char temp; for (i = 0, j = strlen(s)-1; iname, s); p->arity = arity; p->lex_val = (2 * Parms[NEW_SYMBOL_LEX_POSITION].val) - 1; p->sym_num = new_sym_num(); i = p->sym_num % SYM_TAB_SIZE; p->next = Sym_tab[i]; Sym_tab[i] = p; return(p); } /* insert_sym */ /************* * * int str_to_sn(str, arity) -- Return a symbol number for string/arity. * * If the given string/arity is already in the global symbol table, * then return symbol number; else, create a new symbol table entry and * return a new symbol number * *************/ int str_to_sn(char *str, int arity) { struct sym_ent *p, *save; int i; long dummy; save = NULL; for (i = 0; i < SYM_TAB_SIZE; i++) { p = Sym_tab[i]; while (p != NULL) { if (!str_ident(str, p->name)) p = p->next; else if (p->arity != arity) { save = p; p = p->next; } else { if (p->eval_code != 0) /* recall that evaluable symbols are inserted in init */ Internal_flags[DOLLAR_PRESENT] = 1; return(p->sym_num); } } } if (save && !save->special_op && Flags[CHECK_ARITY].val && Internal_flags[REALLY_CHECK_ARITY] && !str_ident(str, "$Quantified") && !str_ident(str, "$Hyps") && !str_ident(str, "$Concs") ) { fprintf(stderr, "%c\n\nWARNING, multiple arity: %s/%d, %s/%d.\n\n", Bell, save->name, save->arity, str, arity); } /* String/arity not in table, so create an entry. */ p = insert_sym(str, arity); if (str[0] == '$' && p->sym_num != Cons_sym_num && /* Lists */ p->sym_num != Nil_sym_num && p->sym_num != Ignore_sym_num && /* Misc */ p->sym_num != Chr_sym_num && p->sym_num != Dots_sym_num && !initial_str("$Quantified", str) && !initial_str("$ANS", str) && /* Answer literals */ !initial_str("$Ans", str) && !initial_str("$ans", str) && !initial_str("$Connect", str) && /* mace2 connection relations */ !str_ident(str, "$NUCLEUS") && /* Linked inference */ !str_ident(str, "$BOTH") && !str_ident(str, "$LINK") && !str_ident(str, "$SATELLITE") && !str_ident(str, "$FSUB") && /* Hints */ !str_ident(str, "$BSUB") && !str_ident(str, "$EQUIV") && !str_ident(str, "$Concs") && /* Sequent i/o */ !str_ident(str, "$Hyps") && !skolem_symbol(p->sym_num) && !str_long(str+1, &dummy)) /* e.g., weight(f($3,a),-2) */ fprintf(stderr, "%c\n\nWARNING, unrecognized $ symbol: %s.\n\n", Bell, str); return(p->sym_num); } /* str_to_sn */ /************* * * print_syms(file_ptr) -- Display the symbol list. * *************/ void print_syms(FILE *fp) { struct sym_ent *p; int i; for (i = 0; i < SYM_TAB_SIZE; i++) { p = Sym_tab[i]; while (p != NULL) { fprintf(fp, "%d %s/%d, lex_val=%d\n", p->sym_num, p->name, p->arity, p->lex_val); p = p->next; } } } /* print_syms */ /************* * * p_syms() * *************/ void p_syms(void) { print_syms(stdout); } /* p_syms */ /************* * * char *sn_to_str(sym_num) -- given a symbol number, return the name * *************/ char *sn_to_str(int sym_num) { struct sym_ent *p; p = Sym_tab[sym_num % SYM_TAB_SIZE]; while (p != NULL && p->sym_num != sym_num) p = p->next; if (p == NULL) return(""); else return(p->name); } /* sn_to_str */ /************* * * int sn_to_arity(sym_num) -- given a symbol number, return the arity * *************/ int sn_to_arity(int sym_num) { struct sym_ent *p; p = Sym_tab[sym_num % SYM_TAB_SIZE]; while (p != NULL && p->sym_num != sym_num) p = p->next; if (p == NULL) return(-1); else return(p->arity); } /* sn_to_arity */ /************* * * int sn_to_node(sym_num) * * Given a symbol number, return the symbol table node. * *************/ struct sym_ent *sn_to_node(int sym_num) { struct sym_ent *p; p = Sym_tab[sym_num % SYM_TAB_SIZE]; while (p != NULL && p->sym_num != sym_num) p = p->next; return(p); /* possibly NULL */ } /* sn_to_node */ /************* * * int sn_to_ec(sym_num) * * Given a symbol number, return the evaluation code. * *************/ int sn_to_ec(int sym_num) { struct sym_ent *p; p = Sym_tab[sym_num % SYM_TAB_SIZE]; while (p != NULL && p->sym_num != sym_num) p = p->next; if (p == NULL) return(-1); else return(p->eval_code); } /* sn_to_ec */ /************* * * sym_tab_member(str, arity) * * Similar to str_to_sn, but do not insert if not there, * and return node instead of sn. * *************/ struct sym_ent *sym_tab_member(char *str, int arity) { struct sym_ent *p; int i; for (i = 0; i < SYM_TAB_SIZE; i++) { p = Sym_tab[i]; while (p != NULL) { if (!str_ident(str, p->name)) p = p->next; else if (p->arity != arity) p = p->next; else return(p); } } return((struct sym_ent *) NULL); } /* sym_tab_member */ /************* * * int in_sym_tab(s) -- is s in the symbol table? * *************/ int in_sym_tab(char *s) { struct sym_ent *p; int i; for (i = 0; i < SYM_TAB_SIZE; i++) { p = Sym_tab[i]; while (p != NULL) { if (str_ident(p->name, s)) return(1); p = p->next; } } return(0); } /* in_sym_tab */ /************* * * free_sym_tab() -- free all symbols in the symbol table * *************/ void free_sym_tab(void) { struct sym_ent *p1, *p2; int i; for (i = 0; i < SYM_TAB_SIZE; i++) { p1 = Sym_tab[i]; while (p1 != NULL) { p2 = p1; p1 = p1->next; free_sym_ent(p2); } Sym_tab[i] = NULL; } } /* free_sym_tab */ /************* * * int is_symbol(t, str, arity) * * Does t have leading function symbol str with arity? * *************/ int is_symbol(struct term *t, char *str, int arity) { return((t->type == COMPLEX || t->type == NAME) && sn_to_arity(t->sym_num) == arity && str_ident(sn_to_str(t->sym_num), str)); } /* is_symbol */ /************* * * mark_as_skolem(sym_num) * *************/ void mark_as_skolem(int sym_num) { struct sym_ent *se; se = sn_to_node(sym_num); if (!se) { char s[500]; sprintf(s, "mark_as_skolem, no symbol for %d.", sym_num); abend(s); } else se->skolem = 1; } /* mark_as_skolem */ /************* * * int is_skolem(sym_num) * *************/ int is_skolem(int sym_num) { struct sym_ent *se; se = sn_to_node(sym_num); if (!se) { char s[500]; sprintf(s, "is_skolem, no symbol for %d.", sym_num); abend(s); return(0); /* to quiet lint */ } else return(se->skolem); } /* is_skolem */ /************* * * int initial_str(s, t) -- Is s an initial substring of t? * *************/ int initial_str(char *s, char *t) { for ( ; *s == *t; s++, t++) if (*s == '\0') return(1); return(*s == '\0'); } /* initial_str */ /************* * * int set_vars(term) * * Decide which of the names are really variables, and make * into variables. (This routine is used only on input terms.) * Preserve the user's variable names by keeping the pointer into * the symbol list. * * If too many variables, return(0); elase return(1). * *************/ int set_vars(struct term *t) { char *varnames[MAX_VARS]; int i; for (i=0; itype == COMPLEX) { r = t->farg; rc = 1; while (rc && r != NULL) { rc = set_vars_term(r->argval, varnames); r = r->narg; } return(rc); } else if (var_name(sn_to_str(t->sym_num)) == 0) return(1); else { i = 0; t->type = VARIABLE; while (i < MAX_VARS && varnames[i] != NULL && varnames[i] != sn_to_str(t->sym_num)) i++; if (i == MAX_VARS) return(0); else { if (varnames[i] == NULL) varnames[i] = sn_to_str(t->sym_num); t->varnum = i; return(1); /* t->sym_num = 0; include this to destroy input variable names */ } } } /* set_vars_term */ /************* * * int var_name(string) -- Decide if a string represents a variable. * * return("string is a variable") * *************/ int var_name(char *s) { if (Flags[PROLOG_STYLE_VARIABLES].val) return((*s >= 'A' && *s <= 'Z') || *s == '_'); else return(*s >= 'u' && *s <= 'z'); } /* var_name */ /************* * * struct term *read_list(file_ptr, errors_ptr, integrate) * * Read and return a list of terms. * * The list must be terminated either with the term `end_of_list.' * or with an actual EOF. * Set errors_ptr to point to the number of errors found. * *************/ struct term_ptr *read_list(FILE *fp, int *ep, int integrate) { struct term_ptr *p1, *p2, *p3; struct term *t; int rc; *ep = 0; p3 = NULL; p2 = NULL; t = read_term(fp, &rc); while (rc == 0) { (*ep)++; t = read_term(fp, &rc); } /* keep going until t == NULL || t is end marker */ while (t != NULL && (t->type != NAME || str_ident(sn_to_str(t->sym_num), "end_of_list") == 0)) { if (integrate) t = integrate_term(t); p1 = get_term_ptr(); p1->term = t; if (p2 == NULL) p3 = p1; else p2->next = p1; p2 = p1; t = read_term(fp, &rc); while (rc == 0) { (*ep)++; t = read_term(fp, &rc); } } if (t == NULL) return(p3); else { zap_term(t); return(p3); } } /* read_list */ /************* * * print_list(file_ptr, term_ptr) -- Print a list of terms. * * The list is printed with periods after each term, and * the list is terminated with `end_of_list.' so that it can * be read with read_list. * *************/ void print_list(FILE *fp, struct term_ptr *p) { while (p != NULL) { print_term(fp, p->term); fprintf(fp, ".\n"); p = p->next; } fprintf(fp, "end_of_list.\n"); } /* print_list */ /************* * * bird_print(fp, t) * *************/ void bird_print(FILE *fp, struct term *t) { struct rel *r; if (t == NULL) fprintf(fp, "(nil)"); else if (!is_symbol(t, "a", 2)) { /* t is not of the form a(_,_), so print in prefix */ if (t->type == NAME) /* name */ fprintf(fp, "%s", sn_to_str(t->sym_num)); else if (t->type == VARIABLE) /* variable */ print_variable(fp, t); else { /* complex */ fprintf(fp, "%s", sn_to_str(t->sym_num)); fprintf(fp, "("); r = t->farg; while(r != NULL) { bird_print(fp, r->argval); r = r->narg; if(r != NULL) fprintf(fp, ","); } fprintf(fp, ")"); } } else { /* t has form a(_,_), so print in bird notation */ if (is_symbol(t->farg->narg->argval, "a", 2)) { bird_print(fp, t->farg->argval); fprintf(fp, " ("); bird_print(fp, t->farg->narg->argval); fprintf(fp, ")"); } else { bird_print(fp, t->farg->argval); fprintf(fp, " "); bird_print(fp, t->farg->narg->argval); } } } /* bird_print */ /**************************************** write_term outputs a term in readable format (w.r.t. infix, prefix, and postfix operators) and without extra parentheses. It it much complicated by one feature: deciding where to omit space around the special operators. For example, just as we can input a+b+c instead of a + b + c, we wish to output without spaces were possible. (I'm sorry the code is so complicated---I couldn't see a simpler way of doing it.) There are 2 types of constant/operator/functor: NAME_SYM: string of alphanumerics, $, and _. Also quoted string. SYM_SYM: string of *+-/\^<>=`~:?@&!;# and sometimes | (if not in list) For completeness, the other characters are ,()[]{} and sometimes | (if in list) puctuation for building terms . end of input term % start of comment "' for quoted strings For this problem, tokens are of 4 types: NAME_SYM SYM_SYM OPEN_PAREN '(' OTHER_PUNC other punctuation (including space) Special ops that are NAME_SYMs are always surrounded by spaces. Here are the space rules for SYM_SYM special ops: infix omit space before if preceding token is NAME_SYM or OTHER_PUNC omit space after if next token is is NAME_SYM or OTHER_PUNC (note that space is included if next is '(') prefix omit space before if preceding token is OTHER_PUNC omit space after if next token is is NAME_SYM or OTHER_PUNC postfix omit space before if preceding token is NAME_SYM or OTHER_PUNC always include space after (could omit if next token is OTHER_PUNC, but current mechanism won't handle that, and it's not that important) *****************************************/ /* Token types */ #define OPEN_PAREN 1 #define OTHER_PUNC 2 #define NAME_SYM 6 #define SYM_SYM 7 /************* * * int next_token_type(t, n) * * Find the next token type that would be output for t. * n is precedence parameter as in write term. * *************/ static int next_token_type(struct term *t, int n) { struct sym_ent *s; int na1; char *str; str = sn_to_str(t->sym_num); if (t->type == NAME) { if (str_ident(str, "$nil")) return(OTHER_PUNC); else return(name_sym(str) ? NAME_SYM : SYM_SYM); } else if (t->type == VARIABLE) { if (t->sym_num == 0) return(NAME_SYM); else return(name_sym(str) ? NAME_SYM : SYM_SYM); } else { /* complex */ if (t->sym_num == str_to_sn("$cons", 2)) return(OTHER_PUNC); else if (str_ident(sn_to_str(t->sym_num), "$Quantified")) { /* parens if parent is special op */ if (n < 1000) return(OPEN_PAREN); else return(next_token_type(t->farg->argval, 0)); } else { s = sn_to_node(t->sym_num); if (s->special_op && s->arity == 2) { na1 = s->op_prec; if (s->op_type == XFX || s->op_type == XFY) na1--; if (s->op_prec > n) return(OPEN_PAREN); else return(next_token_type(t->farg->argval, na1)); } else if (s->special_op && s->arity == 1) { na1 = s->op_prec; if (s->op_type == FX || s->op_type == XF) na1--; if (s->op_prec > n) return(OPEN_PAREN); if (s->op_type == FX || s->op_type == FY) return(name_sym(str) ? NAME_SYM : SYM_SYM); else return(next_token_type(t->farg->argval, na1)); } else return(name_sym(str) ? NAME_SYM : SYM_SYM); } } } /* next_token_type */ /************* * * write_term(file_ptr, term, n, prev) -- print in readable form. * *************/ void write_term(FILE *fp, struct term *t, int n, int *prev) { struct rel *r; struct term *t1; struct sym_ent *s; int na1, na2, next; char *str, *s1, *s2; if (t == NULL) { fprintf(fp, ""); return; } if (t->type == NAME) { str = sn_to_str(t->sym_num); if (str_ident(str, "$nil")) { fprintf(fp, "[]"); *prev = OTHER_PUNC;} else { fprintf(fp, "%s", str); *prev = (name_sym(str) ? NAME_SYM : SYM_SYM); } } else if (t->type == VARIABLE) { print_variable(fp, t); if (t->sym_num == 0) *prev = NAME_SYM; else *prev = (name_sym(sn_to_str(t->sym_num)) ? NAME_SYM : SYM_SYM); } else { /* complex */ str = sn_to_str(t->sym_num); if (str_ident(str, "$Quantified")) { /* Quantified Formula */ /* parens if parent is special op */ if (n < 1000) { fprintf(fp, "("); *prev = OPEN_PAREN; } for (r = t->farg; r; r = r->narg) { /* parens if special op in child */ write_term(fp, r->argval, 0, prev); if (r->narg) { fprintf(fp, " "); *prev = OTHER_PUNC; } } if (n < 1000) { fprintf(fp, ")"); *prev = OTHER_PUNC; } } /* end Formula */ else if (is_symbol(t, "$cons", 2)) { fprintf(fp, "["); *prev = OTHER_PUNC; write_term(fp, t->farg->argval, 1000, prev); t1 = t->farg->narg->argval; while (t1->sym_num == str_to_sn("$cons", 2)) { fprintf(fp, ","); *prev = OTHER_PUNC; write_term(fp, t1->farg->argval, 1000, prev); t1 = t1->farg->narg->argval; } if (t1->sym_num == str_to_sn("$nil", 0)) { fprintf(fp, "]"); *prev = OTHER_PUNC; } else { fprintf(fp, "|"); *prev = OTHER_PUNC; write_term(fp, t1, 1000, prev); fprintf(fp, "]"); *prev = OTHER_PUNC; } } /* end list */ else if (Flags[BIRD_PRINT].val &&is_symbol(t, "a", 2)) bird_print(fp, t); else { s = sn_to_node(t->sym_num); if (s->special_op && s->arity == 2) { /* infix */ na1 = na2 = s->op_prec; if (s->op_type == XFX || s->op_type == XFY) na1--; if (s->op_type == XFX || s->op_type == YFX) na2--; if (s->op_prec > n) { fprintf(fp, "("); *prev = OPEN_PAREN; } write_term(fp, t->farg->argval, na1, prev); /* Decide on spaces around infix op. */ if (name_sym(str)) s1 = s2 = " "; else { if (*prev == OTHER_PUNC || *prev == NAME_SYM) s1 = ""; else s1 = " "; next = next_token_type(t->farg->narg->argval, na2); if (next == OTHER_PUNC || next == NAME_SYM) s2 = ""; else s2 = " "; } fprintf(fp, "%s%s%s", s1,str,s2); if (str_ident(s2, " ")) *prev = OTHER_PUNC; else *prev = (name_sym(str) ? NAME_SYM : SYM_SYM); write_term(fp, t->farg->narg->argval, na2, prev); if (s->op_prec > n) { fprintf(fp, ")"); *prev = OTHER_PUNC; } } else if (s->special_op && s->arity == 1) { /* prefix,postfix */ na1 = s->op_prec; if (s->op_type == FX || s->op_type == XF) na1--; if (s->op_prec > n) { fprintf(fp, "("); *prev = OPEN_PAREN; } if (s->op_type == FX || s->op_type == FY) { /* Decide on spaces around special prefix op. */ if (name_sym(str)) s1 = s2 = " "; else { if (*prev == OTHER_PUNC || *prev == OPEN_PAREN) s1 = ""; else s1 = " "; next = next_token_type(t->farg->argval, na1); if (next == OTHER_PUNC || next == OPEN_PAREN || next == NAME_SYM) s2 = ""; else s2 = " "; } fprintf(fp, "%s%s%s", s1,str,s2); if (str_ident(s2, " ")) *prev = OTHER_PUNC; else *prev = (name_sym(str) ? NAME_SYM : SYM_SYM); write_term(fp, t->farg->argval, na1, prev); } else { write_term(fp, t->farg->argval, na1, prev); /* Decide on spaces around special postfix op. */ if (name_sym(str)) s1 = s2 = " "; else { if (*prev == OTHER_PUNC || *prev == NAME_SYM) s1 = ""; else s1 = " "; /* Can't easily tell next token, so just output space. */ s2 = " "; } fprintf(fp, "%s%s%s", s1,str,s2); *prev = OTHER_PUNC; } if (s->op_prec > n) { fprintf(fp, ")"); *prev = OTHER_PUNC; } } else { /* functor(args) */ fprintf(fp, "%s", str); fprintf(fp, "("); *prev = OPEN_PAREN; r = t->farg; while(r != NULL) { write_term(fp, r->argval, 1000, prev); r = r->narg; if(r != NULL) { fprintf(fp, ","); *prev = OTHER_PUNC; } } fprintf(fp, ")"); *prev = OTHER_PUNC; } } } } /* write_term */ /************* * * display_term(file_ptr, term) -- Display a term in internal form. * *************/ void display_term(FILE *fp, struct term *t) { struct rel *r; if (t == NULL) fprintf(fp, ""); else if (t->type == NAME) { fprintf(fp, "%s", sn_to_str(t->sym_num)); } else if (t->type == VARIABLE) print_variable(fp, t); else { /* complex */ fprintf(fp, "%s", sn_to_str(t->sym_num)); fprintf(fp, "("); r = t->farg; while(r != NULL) { display_term(fp, r->argval); r = r->narg; if(r != NULL) fprintf(fp, ","); } fprintf(fp, ")"); } } /* display_term */ /************* * * print_term(file_ptr, term) -- Print a term to a file. * * Flag determines write_term vs. display_term. * *************/ void print_term(FILE *fp, struct term *t) { int i; if (Flags[DISPLAY_TERMS].val) display_term(fp, t); else { i = OTHER_PUNC; /* Assume previous token is punctuation. */ write_term(fp, t, 1000, &i); } } /* print_term */ /************* * * p_term(term) -- print_term and \n to the standard output. * *************/ void p_term(struct term *t) { print_term(stdout, t); printf("\n"); fflush(stdout); } /* p_term */ /************* * * d_term(term) -- display_term and \n to the standard output. * *************/ void d_term(struct term *t) { display_term(stdout, t); printf("\n"); fflush(stdout); } /* p_term */ /************* * * print_term_nl(fp, term) -- print_term followed by period and newline * *************/ void print_term_nl(FILE *fp, struct term *t) { print_term(fp, t); fprintf(fp,".\n"); } /* print_term_nl */ /************* * * int print_term_length(t) * *************/ int print_term_length(struct term *t) { static FILE *tfp = NULL; int i; char s[MAX_BUF]; if (!tfp) tfp = tmpfile(); rewind(tfp); print_term(tfp, t); fprintf(tfp, "%c", '\0'); /* end marker */ fflush(tfp); rewind(tfp); for (i = 0, s[i]=getc(tfp); s[i] && i < MAX_BUF; s[++i]=getc(tfp)); #if 0 printf("%d: ", i); print_term(stdout, t); #endif return(i == MAX_BUF ? MAX_INT : i); } /* print_term_length */ /************* * * pretty_print_term(fp, t, indents) * *************/ void pretty_print_term(FILE *fp, struct term *t, int indents) { int len, spaces_before_term, i; spaces_before_term = indents * Parms[PRETTY_PRINT_INDENT].val; for (i=0; itype != COMPLEX) print_term(fp, t); else { len = print_term_length(t); if (spaces_before_term + len < 80) print_term(fp, t); else { struct rel *r; fprintf(fp, "%s", sn_to_str(t->sym_num)); fprintf(fp, "(\n"); r = t->farg; while(r) { pretty_print_term(fp, r->argval, indents+1); r = r->narg; if(r != NULL) fprintf(fp, ","); fprintf(fp, "\n"); } for (i=0; isym_num != 0) fprintf(fp, "%s", sn_to_str(t->sym_num)); else if (Flags[PROLOG_STYLE_VARIABLES].val) { fprintf(fp, "%c", (t->varnum % 26) + 'A'); i = t->varnum / 26; if (i > 0) fprintf(fp, "%d", i); } else { if (t->varnum <= 2) fprintf(fp, "%c", 'x'+t->varnum); else if (t->varnum <= 5) fprintf(fp, "%c", 'r'+t->varnum); else fprintf(fp, "%c%d", 'v', t->varnum); } } /* print_variable */ /************* * * void built_in_symbols() * * note: in a similar way, user-defined evaluable functions are declared * in `declare_user_functions'. * *************/ void built_in_symbols(void) { struct sym_ent *p; p = insert_sym("$cons", 2); Cons_sym_num = p->sym_num; p = insert_sym("$nil", 0); Nil_sym_num = p->sym_num; p = insert_sym("$IGNORE", 1); Ignore_sym_num = p->sym_num; p = insert_sym("$CHR", 1); Chr_sym_num = p->sym_num; p = insert_sym("$dots", 1); Dots_sym_num = p->sym_num; p = insert_sym("$", 1); p = insert_sym("$SUM", 2); p->eval_code = SUM_SYM; p = insert_sym("$PROD", 2); p->eval_code = PROD_SYM; p = insert_sym("$DIFF", 2); p->eval_code = DIFF_SYM; p = insert_sym("$DIV", 2); p->eval_code = DIV_SYM; p = insert_sym("$MOD", 2); p->eval_code = MOD_SYM; p = insert_sym("$EQ", 2); p->eval_code = EQ_SYM; p = insert_sym("$NE", 2); p->eval_code = NE_SYM; p = insert_sym("$LT", 2); p->eval_code = LT_SYM; p = insert_sym("$LE", 2); p->eval_code = LE_SYM; p = insert_sym("$GT", 2); p->eval_code = GT_SYM; p = insert_sym("$GE", 2); p->eval_code = GE_SYM; p = insert_sym("$AND", 2); p->eval_code = AND_SYM; p = insert_sym("$OR", 2); p->eval_code = OR_SYM; p = insert_sym("$NOT", 1); p->eval_code = NOT_SYM; p = insert_sym("$TRUE", 1); p->eval_code = TRUE_SYM; p = insert_sym("$T", 0); p->eval_code = T_SYM; p = insert_sym("$F", 0); p->eval_code = F_SYM; p = insert_sym("$ID", 2); p->eval_code = ID_SYM; p = insert_sym("$LNE", 2); p->eval_code = LNE_SYM; p = insert_sym("$LLT", 2); p->eval_code = LLT_SYM; p = insert_sym("$LLE", 2); p->eval_code = LLE_SYM; p = insert_sym("$LGT", 2); p->eval_code = LGT_SYM; p = insert_sym("$LGE", 2); p->eval_code = LGE_SYM; p = insert_sym("$BIT_AND", 2); p->eval_code = BIT_AND_SYM; p = insert_sym("$BIT_OR", 2); p->eval_code = BIT_OR_SYM; p = insert_sym("$BIT_XOR", 2); p->eval_code = BIT_XOR_SYM; p = insert_sym("$BIT_NOT", 1); p->eval_code = BIT_NOT_SYM; p = insert_sym("$SHIFT_LEFT", 2); p->eval_code = SHIFT_LEFT_SYM; p = insert_sym("$SHIFT_RIGHT", 2); p->eval_code = SHIFT_RIGHT_SYM; p = insert_sym("$INT_TO_BITS", 1); p->eval_code = INT_TO_BITS_SYM; p = insert_sym("$BITS_TO_INT", 1); p->eval_code = BITS_TO_INT_SYM; p = insert_sym("$IF", 3); p->eval_code = IF_SYM; p = insert_sym("$NEXT_CL_NUM", 0); p->eval_code = NEXT_CL_NUM_SYM; p = insert_sym("$ATOMIC", 1); p->eval_code = ATOMIC_SYM; p = insert_sym("$INT", 1); p->eval_code = INT_SYM; p = insert_sym("$BITS", 1); p->eval_code = BITS_SYM; p = insert_sym("$VAR", 1); p->eval_code = VAR_SYM; p = insert_sym("$GROUND", 1); p->eval_code = GROUND_SYM; p = insert_sym("$OUT", 1); p->eval_code = OUT_SYM; p = insert_sym("$FSUM", 2); p->eval_code = FSUM_SYM; p = insert_sym("$FPROD", 2); p->eval_code = FPROD_SYM; p = insert_sym("$FDIFF", 2); p->eval_code = FDIFF_SYM; p = insert_sym("$FDIV", 2); p->eval_code = FDIV_SYM; p = insert_sym("$FEQ", 2); p->eval_code = FEQ_SYM; p = insert_sym("$FNE", 2); p->eval_code = FNE_SYM; p = insert_sym("$FLT", 2); p->eval_code = FLT_SYM; p = insert_sym("$FLE", 2); p->eval_code = FLE_SYM; p = insert_sym("$FGT", 2); p->eval_code = FGT_SYM; p = insert_sym("$FGE", 2); p->eval_code = FGE_SYM; p = insert_sym("$COMMON_EXPRESSION", 3); p->eval_code = COMMON_EXPRESSION_SYM; p = insert_sym("$RENAME", 2); p->eval_code = RENAME_SYM; p = insert_sym("$UNIQUE_NUM", 0); p->eval_code = UNIQUE_NUM_SYM; p = insert_sym("$OCCURS", 2); p->eval_code = OCCURS_SYM; p = insert_sym("$VOCCURS", 2); p->eval_code = VOCCURS_SYM; p = insert_sym("$VFREE", 2); p->eval_code = VFREE_SYM; } /* built_in_symbols */ /************* * * int declare_op(prec, type, str) * *************/ int declare_op(int prec, int type, char *str) { int arity, sn, save_flag; struct sym_ent *p; if (prec < 1 || prec > 999) return(0); switch (type) { case FX: case FY: case XF: case YF: arity = 1; break; case XFX: case XFY: case YFX: arity = 2; break; default: return(0); } save_flag = Flags[CHECK_ARITY].val; Flags[CHECK_ARITY].val = 0; sn = str_to_sn(str, arity); Flags[CHECK_ARITY].val = save_flag; p = sn_to_node(sn); /* Don't check if it's already special. Allow it to change. */ p->special_op = 1; p->op_type = type; p->op_prec = prec; return(1); } /* declare_op */ /************* * * init_special_ops() * * Declare the built-in special operators. * *************/ void init_special_ops(void) { int rc; rc = declare_op(800, XFY, "#"); rc = declare_op(800, XFX, "->"); rc = declare_op(800, XFX, "<->"); rc = declare_op(790, XFY, "|"); rc = declare_op(780, XFY, "&"); rc = declare_op(700, XFX, "="); rc = declare_op(700, XFX, "!="); rc = declare_op(700, XFX, "<"); rc = declare_op(700, XFX, ">"); rc = declare_op(700, XFX, "<="); rc = declare_op(700, XFX, ">="); rc = declare_op(700, XFX, "=="); rc = declare_op(700, XFX, "=/="); rc = declare_op(700, XFX, "@<"); rc = declare_op(700, XFX, "@>"); rc = declare_op(700, XFX, "@<="); rc = declare_op(700, XFX, "@>="); rc = declare_op(500, XFY, "+"); rc = declare_op(500, XFX, "-"); rc = declare_op(500, FX, "+"); rc = declare_op(500, FX, "-"); rc = declare_op(400, XFY, "*"); rc = declare_op(400, XFX, "/"); rc = declare_op(300, XFX, "mod"); #ifndef SINGLE_QUOTE rc = declare_op(300, XF, "\'"); #endif } /* init_special_ops */ /************* * * int process_op_command(t) * *************/ int process_op_command(struct term *t) { int type, n, rc; struct term *t1, *t2; char *s; if (sn_to_arity(t->sym_num) != 3) { printf("op command must have arity 3.\n"); return(0); } t1 = t->farg->argval; if (t1->type != NAME || !str_int(sn_to_str(t1->sym_num), &n) || n < 1 || n > 999) { printf("\nERROR: first argument of op command must be 1..999.\n"); return(0); } t1 = t->farg->narg->argval; s = sn_to_str(t1->sym_num); if (str_ident(s, "xfx") || str_ident(s, "infix")) type = XFX; else if (str_ident(s, "xfy") || str_ident(s, "infix_right")) type = XFY; else if (str_ident(s, "yfx") || str_ident(s, "infix_left")) type = YFX; else if (str_ident(s, "fx") || str_ident(s, "prefix")) type = FX; else if (str_ident(s, "xf") || str_ident(s, "postfix")) type = XF; else if (str_ident(s, "fy") || str_ident(s, "prefix_assoc")) type = FY; else if (str_ident(s, "yf") || str_ident(s, "postfix_assoc")) type = YF; else type = MAX_INT; if (type == MAX_INT || t1->type != NAME) { printf("\nERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy.\n"); return(0); } t1 = t->farg->narg->narg->argval; if (t1->type == NAME) rc = declare_op(n, type, sn_to_str(t1->sym_num)); else if (proper_list(t1)) { for ( ; t1->type == COMPLEX; t1 = t1->farg->narg->argval) { t2 = t1->farg->argval; if (t2->type != NAME) { printf("\nERROR: list in op command must be all names.\n"); return(0); } rc = declare_op(n, type, sn_to_str(t2->sym_num)); } } else { printf("\nERROR: third argument of op command must be a name or a list.\n"); return(0); } return(1); } /* process_op_command */ /************* * * void fill_in_op_data(p, t) * *************/ static void fill_in_op_data(struct sequence_member *p, struct term *t) { struct sym_ent *nd; char *str; int i, flag; p->t = t; p->binary_type = p->unary_type = 0; p->binary_prec = p->unary_prec = 0; if (t->type == NAME) { str = sn_to_str(t->sym_num); for (i = flag = 0; i < SYM_TAB_SIZE && flag < 2; i++) { for (nd = Sym_tab[i]; nd && flag < 2; nd = nd->next) { if (str_ident(str, nd->name) && nd->special_op) { if (nd->arity == 1) { p->unary_type = nd->op_type; p->unary_prec = nd->op_prec; } else { /* must be binary */ p->binary_type = nd->op_type; p->binary_prec = nd->op_prec; } } } } } } /* fill_in_op_data */ /************* * * int is_white(c) -- including start-of-comment '%'. * *************/ static int is_white(char c) { return(c == ' ' || c == '\t' || /* tab */ c == '\n' || /* newline */ c == '\v' || /* vertical tab */ c == '\r' || /* carriage return */ c == '\f' || /* form feed */ c == '%'); } /* is_white */ /************* * * skip_white(buffer, position) * * Advance the pointer to the next nonwhite, noncomment position. * *************/ void skip_white(char *buf, int *p) { char c; c = buf[*p]; while (is_white(c)) { if (c == '%') /* skip over comment */ while (buf[++(*p)] != '\n' && buf[*p] != '\0') ; if (buf[*p] == '\0') c = '\0'; else c = buf[++(*p)]; } } /* skip_white */ /************* * * int is_symbol_char(c, in_list) * *************/ static int is_symbol_char(char c, int in_list) { return(c == '+' || c == '-' || c == '*' || c == '/' || c == '\\' || c == '^' || c == '<' || c == '>' || c == '=' || c == '`' || c == '~' || c == ':' || c == '?' || c == '@' || c == '&' || (c == '|' && !in_list) || #ifndef SINGLE_QUOTE c == '\'' || #endif c == '!' || c == '#' || c == ';' ); } /* is_symbol_char */ /************* * * int quote_char(c) * *************/ static int quote_char(char c) { return( #ifdef SINGLE_QUOTE c == '\'' || #endif c == '\"'); } /* quote_char */ /************* * * int is_alpha_numeric(c) -- including _ and $ * *************/ static int is_alpha_numeric(char c) { return((c >= '0' && c <= '9') || (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || c == '_' || c == '$'); } /* is_alpha_numeric */ /************* * * int name_sym(s) * *************/ int name_sym(char *s) { if (quote_char(*s)) return(1); /* quoted string ok */ else { for ( ; *s; s++) if (!is_alpha_numeric(*s)) return(0); return(1); } } /* name_sym */ /************* * * get_name(buffer, position, name, in_list) * *************/ static void get_name(char *buf, int *p, char *name, int in_list) { int i, ok, okq; char c, q; i = 0; ok = 1; okq = 1; skip_white(buf, p); c = buf[*p]; if (is_alpha_numeric(c)) { while ((ok = i < MAX_NAME-1) && is_alpha_numeric(c)) { name[i++] = c; c = buf[++(*p)]; } } else if (is_symbol_char(c, in_list)) { while ((ok = i < MAX_NAME-1) && is_symbol_char(c, in_list)) { name[i++] = c; c = buf[++(*p)]; } } else if (quote_char(c)) { q = c; name[i++] = c; c = buf[++(*p)]; while ((ok = i < MAX_NAME-1) && c != q && (okq = c != '\0')) { name[i++] = c; c = buf[++(*p)]; } if (okq) { name[i++] = c; /* quote char */ ++(*p); } } if (!ok) { fprintf(stdout, "\nERROR, name too big, max is %d; ", MAX_NAME-1); name[0] = '\0'; } else if (!okq) { fprintf(stdout, "\nERROR, quoted name has no end; "); name[0] = '\0'; } else name[i] = '\0'; } /* get_name */ /************* * * print_error(fp, buf, pos) * *************/ void print_error(FILE *fp, char *buf, int pos) { #if 0 int i; fprintf(fp, "%s\n", buf); for (i = 0; i < pos; i++) { if (buf[i] == '\t') fprintf(fp, "--------"); /* doesn't always work */ else if (buf[i] == '\n') fprintf(fp, "\n"); else fprintf(fp, "-"); } fprintf(fp, "^\n"); #else int i; i = 0; if (buf[0] == '\n') i = 1; while (i < pos) { if (buf[i] == '%') /* skip over comment */ while (buf[++i] != '\n') ; fprintf(fp, "%c", buf[i++]); } fprintf(fp, " ***HERE*** "); while (buf[i]) { if (buf[i] == '%') /* skip over comment */ while (buf[++i] != '\n') ; fprintf(fp, "%c", buf[i++]); } fprintf(fp, "\n"); #endif } /* print_error */ /* We need this declaration, because seq_to_term is mutually recursive with seq_to_quant_term */ static struct term *seq_to_term(struct sequence_member *seq, int start, int end, int m); /************* * * struct term *seq_to_quant_term(seq, n) * * Take a sequence of terms t1,...,tn and build term $Quantified(t1,...,tn). * t1 is already known to be a quantifier, and n >= 3. * Check that t2,...,tn-1 are all names. * On success, the resulting term is an entirely new copy. * *************/ static struct term *seq_to_quant_term(struct sequence_member *seq, int n) { struct rel *r_prev, *r_new; struct term *t, *t1; int i; if (n == 1) return(NULL); for (i = 1; i < n-1; i++) if (seq[i].t->type != NAME) return(NULL); /* Special case: negated formula need not be parenthesized. * For example, all x -p(x) is OK. In this case, the sequence is * [all, x, -, p(x)], so we must adjust things. */ if (str_ident(sn_to_str(seq[n-2].t->sym_num), "-")) { if (n == 3) return(NULL); /* all - p */ else { struct term *t; t = seq_to_term(seq, n-2, n-1, 1000); printf("adjusted term: "); p_term(t); if (t) { zap_term(seq[n-2].t); zap_term(seq[n-1].t); fill_in_op_data(&seq[n-2], t); /* caller will still think there are n terms */ seq[n-1].t = NULL; n--; } else return(NULL); } } t = get_term(); t->type = COMPLEX; t->sym_num = str_to_sn("$Quantified", n); for (i = 0, r_prev = NULL; i < n; i++) { r_new = get_rel(); if (!r_prev) t->farg = r_new; else r_prev->narg = r_new; t1 = copy_term(seq[i].t); r_new->argval = t1; r_prev = r_new; } return(t); } /* seq_to_quant_term */ /************* * * struct term *seq_to_term(seq, start, end, m) * * seq is an array of terms/operators, and start and end are * indexes into seq. This routine attempts to construct a term * starting with start, ending with end, with precedence <= m. * On success, the resulting term is an entirely new copy. * *************/ static struct term *seq_to_term(struct sequence_member *seq, int start, int end, int m) { int i, n, type; struct term *t1, *t2, *t3, *t; struct rel *r1, *r2; if (start == end) { t = copy_term(seq[start].t); return(t); } else { /* Check if first is prefix op that applies to rest. */ if (seq[start].t->type == NAME) { type = seq[start].unary_type; n = seq[start].unary_prec; t = seq[start].t; if (type == FX && n <= m) { t1 = seq_to_term(seq, start+1, end, n-1); if (t1) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 1); r1 = get_rel(); t3->farg = r1; r1->argval = t1; return(t3); } } else if (type == FY && n <= m) { t1 = seq_to_term(seq, start+1, end, n); if (t1) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 1); r1 = get_rel(); t3->farg = r1; r1->argval = t1; return(t3); } } } /* Check if last is postfix op that applies to all preceding. */ if (seq[end].t->type == NAME) { type = seq[end].unary_type; n = seq[end].unary_prec; t = seq[end].t; if (type == XF && n <= m) { t1 = seq_to_term(seq, start, end-1, n-1); if (t1) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 1); r1 = get_rel(); t3->farg = r1; r1->argval = t1; return(t3); } } else if (type == YF && n <= m) { t1 = seq_to_term(seq, start, end-1, n); if (t1) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 1); r1 = get_rel(); t3->farg = r1; r1->argval = t1; return(t3); } } } /* Look for an infix operator. */ for (i = start+1; i <= end-1; i++) { if (seq[i].t->type == NAME) { type = seq[i].binary_type; n = seq[i].binary_prec; t = seq[i].t; if (type == XFY && n <= m) { t1 = seq_to_term(seq, start, i-1, n-1); if (t1) { t2 = seq_to_term(seq, i+1, end, n); if (!t2) zap_term(t1); } if (t1 && t2) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 2); r1 = get_rel(); r2 = get_rel(); t3->farg = r1; r1->narg = r2; r1->argval = t1; r2->argval = t2; return(t3); } } else if (type == YFX && n <= m) { t1 = NULL; t2 = seq_to_term(seq, i+1, end, n-1); if (t2) { t1 = seq_to_term(seq, start, i-1, n); if (!t1) zap_term(t2); } if (t1 && t2) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 2); r1 = get_rel(); r2 = get_rel(); t3->farg = r1; r1->narg = r2; r1->argval = t1; r2->argval = t2; return(t3); } } else if (type == XFX && n <= m) { t1 = seq_to_term(seq, start, i-1, n-1); t2 = NULL; if (t1) { t2 = seq_to_term(seq, i+1, end, n-1); if (!t2) zap_term(t1); } if (t1 && t2) { t3 = get_term(); t3->type = COMPLEX; t3->sym_num = str_to_sn(sn_to_str(t->sym_num), 2); r1 = get_rel(); r2 = get_rel(); t3->farg = r1; r1->narg = r2; r1->argval = t1; r2->argval = t2; return(t3); } } } /* name */ } /* loop looking for infix op to apply */ return(NULL); } } /* seq_to_term */ /************* * * struct term_ptr *str_to_args(buffer, position, name) * * name -- the functor. * * start: functor( a1 , a2 , a3 ) * ^ * end: functor( a1 , a2 , a3 ) * ^ *************/ static struct term *str_to_args(char *buf, int *p, char *name) { struct term *t, *t_sub; struct rel *r1, *r2; int i; t = get_term(); t->type = COMPLEX; r1 = NULL; i = 0; /* count subterms to get arity */ while (buf[*p] != ')') { i++; t_sub = str_to_term(buf, p, 0); if (t_sub == NULL) return(NULL); else if (buf[*p] != ',' && buf[*p] != ')') { fprintf(stdout, "\nERROR, comma or ) expected:\n"); print_error(stdout, buf, *p); return(NULL); } else { r2 = get_rel(); r2->argval = t_sub; if (r1 == NULL) t->farg = r2; else r1->narg = r2; r1 = r2; if (buf[*p] == ',') (*p)++; /* step past comma */ } } if (i == 0) { fprintf(stdout, "\nERROR, functor has no arguments:\n"); print_error(stdout, buf, *p); return(NULL); } t->sym_num = str_to_sn(name, i); /* functor */ return(t); } /* str_to_args */ /************* * * struct term_ptr *str_to_list(buffer, position) * * start: [ a1 , a2 , a3 ] * ^ * end: [ a1 , a2 , a3 ] * ^ *************/ static struct term *str_to_list(char *buf, int *p) { struct term *t_cons, *t_head, *t_tail, *t_return; struct rel *r_head, *r_tail; int go; (*p)++; /* step past '[' */ if (buf[*p] == ']') { /* [] */ t_return = get_term(); t_return->type = NAME; t_return->sym_num = str_to_sn("$nil", 0); (*p)++; /* skip "]" */ return(t_return); } else { /* [h|t], [t1,...,tn], or [t1,...,tn|t] */ t_return = NULL; r_tail = NULL; go = 1; while (go) { t_head = str_to_term(buf, p, 1); if (t_head == NULL) return(NULL); /* error */ t_cons = get_term(); if (r_tail == NULL) t_return = t_cons; else r_tail->argval = t_cons; t_cons->type = COMPLEX; t_cons->sym_num = str_to_sn("$cons", 2); r_head = get_rel(); t_cons->farg = r_head; r_head->argval = t_head; r_tail = get_rel(); r_head->narg = r_tail; go = (buf[*p] == ','); if (go) (*p)++; /* step past ',' */ } if (buf[*p] == ']') { t_tail = get_term(); r_tail->argval = t_tail; t_tail->type = NAME; t_tail->sym_num = str_to_sn("$nil", 0); (*p)++; /* step past ']' */ return(t_return); } else if (buf[*p] == '|') { (*p)++; /* step past '|' */ t_tail = str_to_term(buf, p, 1); if (buf[*p] != ']') { fprintf(stdout, "\nERROR, ']' expected in list:\n"); print_error(stdout, buf, *p); return(NULL); } r_tail->argval = t_tail; (*p)++; /* step past ']' */ return(t_return); } else { fprintf(stdout, "\nERROR, ], |, or comma expected in list:\n"); print_error(stdout, buf, *p); return(NULL); } } } /* str_to_list */ /************* * * int str_to_sequence(buffer, position, seq, in_list) * * Read a sequence of operators/terms---It will be parsed into * a term later in str_to_term. * After successful call, position is the delimeter following the term. * * Mutually recursive with str_to_term. * * If success, return the number of terms read. * * If a syntax error is found, print message and return(0). * *************/ static int str_to_sequence(char *buf, int *p, struct sequence_member *seq, int in_list) { char name[MAX_NAME], c; struct term *t; int done, n, white;; done = 0; n = 0; while (!done) { get_name(buf, p, name, in_list); white = is_white(buf[*p]); /* f(a) vs. f (a) */ skip_white(buf, p); if (name[0] == '\0' && buf[*p] != '[' && buf[*p] != '(' && buf[*p] != '{') { fprintf(stdout, "\nERROR, name expected:\n"); print_error(stdout, buf, *p); return(0); } else if (name[0] == '\0' && buf[*p] == '(') { /* (term) */ (*p)++; /* step past '(' */ t = str_to_term(buf, p, 0); if (t == NULL) return(0); if (buf[*p] != ')') { fprintf(stdout, "\nERROR, ')' expected:\n"); print_error(stdout, buf, *p); return(0); } (*p)++; /* step past ')' */ } else if (name[0] == '\0' && buf[*p] == '{') { /* {term} */ (*p)++; /* step past '{' */ t = str_to_term(buf, p, 0); if (t == NULL) return(0); if (buf[*p] != '}') { fprintf(stdout, "\nERROR, '}' expected:\n"); print_error(stdout, buf, *p); return(0); } (*p)++; /* step past '}' */ } else if (name[0] == '\0' && buf[*p] == '[') { /* list */ t = str_to_list(buf, p); if (t == NULL) return(0); } else if (name[0] != '\0' && !white && buf[*p] == '(') /* f(args) */ { (*p)++; /* step past '(' */ t = str_to_args(buf, p, name); if (t == NULL) return(0); (*p)++; /* step past ')' */ } else if (name[0] != '\0') { /* name */ t = get_term(); t->type = NAME; /* If it's an operator, change arity later. */ t->sym_num = str_to_sn(name, 0); } else { fprintf(stdout, "\nERROR, unrecognized error in term:\n"); print_error(stdout, buf, *p); return(0); } /* We have a term t. */ if (n == MAX_COMPLEX) { fprintf(stdout, "\nERROR, term too big:\n"); print_error(stdout, buf, *p); return(0); } else { fill_in_op_data(&seq[n], t); n++; } skip_white(buf, p); c = buf[*p]; done = (c == ',' || c == ')' || c == '}' || c == ']' || c == '.' || c == '\0' || (in_list && c == '|')); } return(n); } /* str_to_sequence */ /************* * * struct term *str_to_term(buffer, position, in_list) * * Parse a string and build a term. * Mutually recursive with str_to_sequence. * After successful call, position is the delimeter following the term. * * If a syntax error is found, print message and return(NULL). * *************/ struct term *str_to_term(char *buf, int *p, int in_list) { struct sequence_member seq[MAX_COMPLEX]; struct term *t; int n, i, save_pos; save_pos = *p; n = str_to_sequence(buf, p, seq, in_list); if (n == 0) return(NULL); else if (seq[0].t->type == NAME && n > 2 && (str_ident(sn_to_str(seq[0].t->sym_num), "all") || str_ident(sn_to_str(seq[0].t->sym_num), "exists"))) { t = seq_to_quant_term(seq, n); if (!t) { fprintf(stdout, "\nERROR in quantifier prefix starting here:\n"); print_error(stdout, buf, save_pos); } } else { t = seq_to_term(seq, 0, n-1, 1000); if (!t) { fprintf(stdout, "\nERROR, the %d terms/operators in the following sequence are OK, but they\ncould not be combined into a single term with special operators.\n", n); for (i = 0; i < n; i++) { p_term(seq[i].t); printf(" ");} printf("\n"); fprintf(stdout, "The context of the bad sequence is:\n"); print_error(stdout, buf, save_pos); } } for (i = 0; i < n; i++) if (seq[i].t != NULL) zap_term(seq[i].t); return(t); } /* str_to_term */ /************* * * int read_buf(file_ptr, buffer) * * Read characters into buffer until one of the following: * 1. '.' is reached ('.' goes into the buffer) * 2. EOF is reached: buf[0] = '\0' (an error occurs if * any nonwhite space precedes EOF) * 3. MAX_BUF characters have been read (an error occurs) * * If error occurs, return(0), else return(1). * *************/ int read_buf(FILE *fp, char *buf) { int c, qc, i, j, ok, eof, eof_q, max, max_q; ok = eof = eof_q = max = max_q = 0; /* stop conditions */ i = 0; while (!ok && !eof && !eof_q && !max && !max_q) { c = getc(fp); if (c == '%') { /* comment--discard rest of line */ while (c != '\n' && c != EOF) c = getc(fp); } if (c =='.') ok = 1; else if (c == EOF) eof = 1; else if (i == MAX_BUF-1) max = 1; else { buf[i++] = c; if (quote_char(c)) { qc = c; c = getc(fp); while (c != qc && c != EOF && i != MAX_BUF-1) { buf[i++] = c; c = getc(fp); } if (i == MAX_BUF-1) max_q = 1; else if (c == EOF) eof_q = 1; else buf[i++] = c; } } } if (ok) { buf[i++] = '.'; buf[i] = '\0'; return(1); } else if (eof) { /* white space at end of file is OK */ j = 0; buf[i] = '\0'; skip_white(buf, &j); if (i != j) { fprintf(stdout, "\nERROR, characters after last period: %s\n", buf); buf[0] = '\0'; return(0); } else { buf[0] = '\0'; return(1); } } else if (eof_q) { char s[500]; buf[i>100 ? 100 : i] = '\0'; sprintf(s, "read_buf, quoted string has no end:%s", buf); abend(s); } else if (max) { char s[500]; buf[i>100 ? 100 : i] = '\0'; sprintf(s, "read_buf, input string has more than %d characters, increase MAX_BUF", MAX_BUF); abend(s); } else { /* max_q */ char s[500]; buf[i>100 ? 100 : i] = '\0'; sprintf(s, "read_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUF", MAX_BUF); abend(s); } return(0); /* to quiet lint */ } /* read_buf */ /************* * * struct term *term_fixup(t) * * change !=(a,b) to -(=(a,b)) * change -(3) to -3 not recursive, -(-(3)) -> -(-3)) * change +(3) to +3 not recursive, +(+(3)) +> +(+3)) * *************/ struct term *term_fixup(struct term *t) { struct rel *r, *r1; struct term *t1; int neg; char *s, str[MAX_NAME]; long l; if (t->type == COMPLEX) { if (is_symbol(t, "!=", 2)) { t1 = get_term(); t1->type = COMPLEX; r1 = get_rel(); t1->farg = r1; r1->argval = t; t1->sym_num = str_to_sn("-", 1); t->sym_num = str_to_sn("=", 2); t = t1; } else if ((neg = is_symbol(t, "-", 1)) || is_symbol(t, "+", 1)) { t1 = t->farg->argval; s = sn_to_str(t1->sym_num); if (t1->type == NAME && str_long(s, &l)) { cat_str((neg ? "-" : "+"), s, str); t1->sym_num = str_to_sn(str, 0); free_rel(t->farg); free_term(t); t = t1; } } for (r = t->farg; r; r = r->narg) r->argval = term_fixup(r->argval); } return(t); } /* term_fixup */ /************* * * struct term *term_fixup_2(t) * * change -(=(a,b)) to !=(a,b) * *************/ struct term *term_fixup_2(struct term *t) { struct term *t1; struct rel *r; if (is_symbol(t, "-", 1) && is_symbol(t->farg->argval, "=", 2)) { t1 = t->farg->argval; t1->sym_num = str_to_sn("!=", 2); free_rel(t->farg); free_term(t); t = t1; } if (t->type == COMPLEX) for (r = t->farg; r; r = r->narg) r->argval = term_fixup_2(r->argval); return(t); } /* term_fixup_2 */ /************* * * struct term *read_term(file_ptr, retcd_ptr) -- * * Read and return then next term. * It is assumed that the next term in the file is terminated * with a period. NULL is returned if EOF is reached first. * * If an error is found, return(0); else return(1). * *************/ struct term *read_term(FILE *fp, int *rcp) { char buf[MAX_BUF+1]; /* one extra for \0 at end */ int p, rc; struct term *t; rc = read_buf(fp, buf); if (rc == 0) { /* error */ *rcp = 0; return(NULL); } else if (buf[0] == '\0') { /* ok. EOF */ *rcp = 1; return(NULL); } else { p = 0; t = str_to_term(buf, &p, 0); if (t == NULL) { *rcp = 0; return(NULL); } else { skip_white(buf, &p); if (buf[p] != '.') { fprintf(stdout, "\nERROR, text after term:\n"); print_error(stdout, buf, p); *rcp = 0; return(NULL); } else { t = term_fixup(t); *rcp = 1; return(t); } } } } /* read_term */ /************* * * merge_sort * *************/ void merge_sort(void **a, void **w, int start, int end, int (*comp_proc)(void *v1, void *v2)) { int mid, i, i1, i2, e1, e2; if (start < end) { mid = (start+end)/2; merge_sort(a, w, start, mid, comp_proc); merge_sort(a, w, mid+1, end, comp_proc); i1 = start; e1 = mid; i2 = mid+1; e2 = end; i = start; while (i1 <= e1 && i2 <= e2) { if ((*comp_proc)(a[i1], a[i2]) == LESS_THAN) w[i++] = a[i1++]; else w[i++] = a[i2++]; } if (i2 > e2) while (i1 <= e1) w[i++] = a[i1++]; else while (i2 <= e2) w[i++] = a[i2++]; for (i = start; i <= end; i++) a[i] = w[i]; } } /* merge_sort */ /************* * * compare_for_auto_lex_order() * * First sort on arity: 0 < MAX_INT < ... < 3 < 2 < 1. * Within arity, use strcmp function * *************/ int compare_for_auto_lex_order(void *d1, void *d2) { struct sym_ent *p1, *p2; int i; p1 = (struct sym_ent *) d1; p2 = (struct sym_ent *) d2; if (p1->arity == p2->arity) { i = strcmp(p1->name, p2->name); if (i < 0) return(LESS_THAN); else if (i > 0) return(GREATER_THAN); else { char s[500]; sprintf(s, "compare_for_auto_lex_order, strings the same: %s.", p1->name); abend(s); return(0); /* to quiet lint */ } } else if (p1->arity == 0) return(LESS_THAN); else if (p2->arity == 0) return(GREATER_THAN); else if (p1->arity < p2->arity) return(GREATER_THAN); else return(LESS_THAN); } /* compare_for_auto_lex_order */ /************* * * auto_lex_order() * * Order the symbols in the symbol table using the lex_val field. * *************/ void auto_lex_order(void) { int i, j, n; struct sym_ent *p; struct sym_ent **a, **w; /* Find an upper limit on the number of symbols. */ n = new_sym_num(); /* don't use this for a sym_num */ /* There should be at most n-1 symbols. */ /* Allocate arrays for storing and for work. */ a = (struct sym_ent **) tp_alloc(n * (int) sizeof(struct sym_ent *)); w = (struct sym_ent **) tp_alloc(n * (int) sizeof(struct sym_ent *)); for (i = j = 0; i < SYM_TAB_SIZE; i++) for (p = Sym_tab[i]; p; p = p->next) a[j++] = p; /* We find j symbols. */ #if 0 printf("\nauto_lex_order: new_sym_num=%d, count=%d.\n\n", n, j); #endif merge_sort((void **) a, (void **) w, 0, j-1, compare_for_auto_lex_order); /* Symbols get lex vals 2, 4, 6, 8, ... . */ for (i = 0; i < j; i++) { a[i]->lex_val = i*2 + 2; #if 0 printf("%7s %d %d\n", a[i]->name, a[i]->arity, i); #endif } } /* auto_lex_order */ otter-3.3f/source/hints.c0100644000076400007640000001735707562242547015024 0ustar mccunemccune/* * hints.c -- routines related to the hints strategy. * */ /* The main purpose of the hints mechanism is to set or adjust the pick-given weight of clauses. A hint H can apply to a clause C in 3 ways: H subsumes C (forward subsume, fsub), C subsumes H (back subsume, bsub), and H is equivalent to C (equiv, which implies fsub and bsub). 2 more ways, which apply to unit clauses only, to be added later: H and C unify H anc C have the same shape (identical-except-variables) Another purpose of hints is to retain clauses that would otherwise be discarded because the purge-gen weight is too high. The Flag KEEP_HINT_SUBSUMERS (default clear) says to skip the purge-gen test on generated clauses that subsume hints (i.e., bsub). The Parms are FSUB_HINT_WT FSUB_HINT_ADD_WT BSUB_HINT_WT BSUB_HINT_ADD_WT EQUIV_HINT_WT EQUIV_HINT_ADD_WT These can be overridden for individual hints with corresponding attributes on the hints, e.g., p0(a,x) # bsub_hint_wt(200) # fsub_hint_wt(100). If the Parms (attributes) are not set, they are not used; if you have a list of hints with no attributes, and you don't set any hint parms, the hints won't be used for anything. If more than Parm (attribute) might apply, equiv is tested first, then fsub, then bsub. If you use both WT and ADD_WT, then BOTH can apply, e.g., when the hint p # bsub_hint_wt(200) # bsub_hint_add_wt(20). applies to a clause, the clause gets pick-given weight 220. The hint attributes and parameters are compiled into a special structure that is attached to the hint clause with the parents pointer. This causes several problems. (1) Compiled hints must be printed with print_hint_clause() instead of print_clause(), and (2) the Parms in effect at the start of the search are compiled in; if the user changes hint parms during the search, this will have no effect. */ #include "header.h" /* Any hint-wt attributes on hints are compiled into a hint_data * structure (attached to the hint with parent pointer) * to avoid costly attribute processing when using the hints. */ struct hint_data { char fsub, bsub, equiv; int fsub_wt, bsub_wt, equiv_wt; int fsub_add_wt, bsub_add_wt, equiv_add_wt; }; /************* * * process_hint_attributes() * * Look for hint-wt attributes, put the data into a hint_data node. * *************/ static void process_hint_attributes(struct clause *c) { struct cl_attribute *a; struct hint_data *hd; hd = (struct hint_data *) tp_alloc((int) sizeof(struct hint_data)); c->parents = (struct ilist *) hd; hd->fsub = 0; hd->fsub_wt = Parms[FSUB_HINT_WT].val; hd->fsub_add_wt = Parms[FSUB_HINT_ADD_WT].val; hd->bsub = 0; hd->bsub_wt = Parms[BSUB_HINT_WT].val; hd->bsub_add_wt = Parms[BSUB_HINT_ADD_WT].val; hd->equiv = 0; hd->equiv_wt = Parms[EQUIV_HINT_WT].val; hd->equiv_add_wt = Parms[EQUIV_HINT_ADD_WT].val; for (a = c->attributes; a; a = a->next) { switch (a->name) { case FSUB_HINT_WT_ATTR: hd->fsub_wt = a->u.i; break; case BSUB_HINT_WT_ATTR: hd->bsub_wt = a->u.i; break; case EQUIV_HINT_WT_ATTR: hd->equiv_wt = a->u.i; break; case FSUB_HINT_ADD_WT_ATTR: hd->fsub_add_wt = a->u.i; break; case BSUB_HINT_ADD_WT_ATTR: hd->bsub_add_wt = a->u.i; break; case EQUIV_HINT_ADD_WT_ATTR: hd->equiv_add_wt = a->u.i; break; } } hd->fsub = !(hd->fsub_wt == MAX_INT && hd->fsub_add_wt == 0); hd->bsub = !(hd->bsub_wt == MAX_INT && hd->bsub_add_wt == 0); hd->equiv = !(hd->equiv_wt == MAX_INT && hd->equiv_add_wt == 0); if (hd->fsub == 0 && hd->bsub == 0 && hd->equiv == 0 && !Flags[KEEP_HINT_SUBSUMERS].val && !Flags[KEEP_HINT_EQUIVALENTS].val) { printf("\n%cWARNING, hint will not be used, because no weights have been\nset for it: ", Bell); print_hint_clause(stdout, c); } } /* process_hint_attributes */ /************* * * compile_hints * *************/ void compile_hints(void) { struct clause *h; for (h = Hints->first_cl; h != NULL; h = h->next_cl) process_hint_attributes(h); } /* compile_hints2 */ /************* * * print_hint_clause() * * (Not in the same form as they were input.) * *************/ void print_hint_clause(FILE *fp, struct clause *c) { struct hint_data *hd; struct term *t; hd = (struct hint_data *) c->parents; fprintf(fp, "%d [", c->id); if (hd && hd->fsub) fprintf(fp, " fsub_wt=%d", hd->fsub_wt); if (hd && hd->bsub) fprintf(fp, " bsub_wt=%d", hd->bsub_wt); if (hd && hd->equiv) fprintf(fp, " equiv_wt=%d", hd->equiv_wt); fprintf(fp, "] "); t = clause_to_term(c); t = term_fixup_2(t); /* Change -(=(a,b)) to !=(a,b). */ print_term(fp, t); zap_term(t); if (c->attributes) print_attributes(fp, c->attributes); fprintf(fp, ".\n"); } /* print_hint_clause */ /************* * * p_hint_clause() * *************/ void p_hint_clause(struct clause *c) { print_hint_clause(stdout, c); } /* p_hint_clause */ /************* * * print_hints_cl_list() * *************/ void print_hints_cl_list(FILE *fp, struct list *lst) { struct clause *cl; if (!lst) fprintf(fp, "(hints list nil)\n"); else { cl = lst->first_cl; while (cl) { print_hint_clause(fp, cl); cl = cl->next_cl; } fprintf(fp, "end_of_list.\n"); } } /* print_hints_cl_list */ /************* * * p_hints_cl_list() * *************/ void p_hints_cl_list(struct list *lst) { print_hints_cl_list(stdout, lst); } /* p_hints_cl_list */ /************* * * adjust_weight_with_hints() * * This routine uses the list Hints to adjust or reset * the pick_weight of a clause. * * Traverse the hints, looking for one that "matches" the * clause. If a match is found, change the pick_weight * of the clause. * *************/ void adjust_weight_with_hints(struct clause *c) { int f_test, b_test, e_test; int fsub, bsub, done; struct hint_data *hd; struct clause *h; CLOCK_START(HINTS_TIME); h = Hints->first_cl; done = 0; while (h && !done) { hd = (struct hint_data *) h->parents; f_test = hd->fsub; b_test = hd->bsub; e_test = hd->equiv; if (f_test || e_test) fsub = subsume(h, c); else fsub = 0; if (b_test || e_test) bsub = subsume(c, h); else bsub = 0; if (e_test && fsub && bsub) { if (hd->equiv_wt != MAX_INT) c->pick_weight = hd->equiv_wt; c->pick_weight += hd->equiv_add_wt; done = 1; } else if (f_test && fsub) { if (hd->fsub_wt != MAX_INT) c->pick_weight = hd->fsub_wt; c->pick_weight += hd->fsub_add_wt; done = 1; } else if (b_test && bsub) { if (hd->bsub_wt != MAX_INT) c->pick_weight = hd->bsub_wt; c->pick_weight += hd->bsub_add_wt; done = 1; } if (!done) h = h->next_cl; } if (done) { /* The clause gets the label of the hint. */ struct cl_attribute *a1; if ((a1 = get_attribute(h, LABEL_ATTR))) { set_attribute(c, LABEL_ATTR, (void *) a1->u.s); } } CLOCK_STOP(HINTS_TIME); } /* adjust_weight_with_hints */ /************* * * hint_keep_test() * * We might want to speed this up with indexing, because it will be * called with all generated clauses (if KEEP_HINT_SUBSUMERS is set). * *************/ int hint_keep_test(struct clause *c) { struct clause *h; int ok = 0; /* Note that KEEP_HINT_SUBSUMERS is ignored when KEEP_HINT_EQUIVALENTS is set. */ CLOCK_START(HINTS_KEEP_TIME) if (Flags[KEEP_HINT_EQUIVALENTS].val) { for (h = Hints->first_cl; h && !ok; h = h->next_cl) ok = subsume(c, h) && subsume(h, c); } else if (Flags[KEEP_HINT_SUBSUMERS].val) { for (h = Hints->first_cl; h && !ok; h = h->next_cl) ok = subsume(c, h); } CLOCK_STOP(HINTS_KEEP_TIME) return(ok); } /* hint_keep_test */ otter-3.3f/source/multijust.c0100644000076400007640000007013607653771547015741 0ustar mccunemccune/* multijust.c -- proof-shortening experiment */ #include "header.h" /* Alists is an array, indexed by true clause IDs. Each entry contains a glist of justification lists. The justification lists contain (true) clause IDs only, no inference rule codes. If an entry is NULL, then that clause is either input or irrelevant to the search for short proofs. Blists is a renumbering of Alists, starting with 0. It is indexed by the renamed Ids. There are no gaps in Blists, that is, Bsize is the number of relevant clauses, including input clauses. Arrays A_to_B and B_to_A give the correspondence. The irrelevant entries in A_to_B are -1. B_to_A is all relevant. */ static int Asize; static int Bsize; static struct glist **Alists; static struct glist **Blists; static int *A_to_B; static int *B_to_A; static struct ilist *Demod_map; /* Those darn "25 [new_demod,24]" clauses. */ /************* * * remove_those_containing() * *************/ static struct glist *remove_those_containing(struct glist *a, int i) { if (a == NULL) return NULL; else if (ilist_member(i, a->v)) { struct glist *b = a->next; free_ilist_list(a->v); free_glist(a); return remove_those_containing(b, i); } else { a->next = remove_those_containing(a->next, i); return a; } } /* remove_those_containing */ /************* * * keep_only() * *************/ struct glist *keep_only(struct glist *a, int i) { if (a == NULL) return NULL; else if (i == 0) { free_glist_of_ilists(a); return NULL; } else { a->next = keep_only(a->next, i-1); return a; } } /* keep_only */ /************* * * remove_supersets() * *************/ struct glist *remove_supersets(struct glist *a, struct ilist *s) { if (a == NULL) return NULL; else if (iset_subset(s, a->v)) { struct glist *b = a->next; free_ilist_list(a->v); free_glist(a); return remove_supersets(b, s); } else { a->next = remove_supersets(a->next, s); return a; } } /* remove_supersets */ /************* * * remove_all_supersets() * *************/ struct glist *remove_all_supersets(struct glist *a, struct glist *b) { if (b == NULL) return a; else if (member_is_subset(a, b->v)) { struct glist *c = b->next; free_ilist_list(b->v); free_glist(b); return remove_all_supersets(a, c); } else { struct glist *c = b->next; a = remove_supersets(a, b->v); b->next = NULL; a = glist_append(a, b); return remove_all_supersets(a, c); } } /* remove_all_supersets */ /************* * * g2_superset() * * Is p a superset of any v2 (second component) of g2? * *************/ static int g2_superset(struct g2list *g2, struct ilist *p) { if (g2 == NULL) return 0; else if (iset_subset(g2->v2, p)) return 1; else return g2_superset(g2->next, p); } /* g2_superset */ /************* * * g2_remove_supersets() * * Foreach v2 (second compnent) of g2, if v2 is a superset of p, * remove the g2 node. * *************/ struct g2list *g2_remove_supersets(struct g2list *g2, struct ilist *p) { if (g2 == NULL) return NULL; else { g2->next = g2_remove_supersets(g2->next, p); if (!iset_subset(p, g2->v2)) return g2; else { struct g2list *h2 = g2->next; free_ilist_list(g2->v1); free_ilist_list(g2->v2); free_g2list(g2); return h2; } } } /* g2_remove_supersets */ /************* * * append_parents() * *************/ static void append_parents(struct clause *c, struct ilist *j1, struct ilist *j2) { /* j1 is an ordinary justification (parent IDs, inf rules, positions) */ /* j2 is a supporters list (parent IDs only) */ if (g2_superset(c->multi_parents, j2)) return; else { struct g2list *p; c->multi_parents = g2_remove_supersets(c->multi_parents, j2); p = get_g2list(); p->v1 = copy_ilist(j1); p->v2 = copy_ilist(j2); if (c->multi_parents == NULL) c->multi_parents = p; else { struct g2list *q = c->multi_parents; while (q->next != NULL) q = q->next; q->next = p; } } } /* append_parents */ /************* * * input_clause() * *************/ int input_clause(int id) { struct clause *c = cl_find(id); if (c == NULL) return 0; else if (c->parents != NULL) return 0; else return 1; } /* input_clause */ /************* * * first_just_input_only() * *************/ int first_just_input_only(struct g2list *p) { struct ilist *b; for (b = p->v2; b != NULL; b = b->next) { if (!input_clause(b->i)) break; /* fail */ } return (b == NULL); } /* first_just_input_only */ /************* * * all_supporters_less_than() * *************/ int all_supporters_less_than(struct clause *c, struct ilist *supporters) { struct ilist *b; for (b = supporters; b != NULL; b = b->next) { if (b->i >= c->id) break; /* fail */ } return (b == NULL); } /* all_supporters_less_than */ /************* * * derived_from_itself() * *************/ int derived_from_itself(struct clause *c, struct ilist *supporters) { return (ilist_member(c->id, supporters)); } /* derived_from_itself */ /************* * * proof_not_longer_than() * *************/ int proof_not_longer_than(struct clause *c, struct ilist *p) { /* Return TRUE if the proof length of some new clauses (justification p) is no longer than the proof length of c (using c->parents). The routine that gets the proof length takes a clause as input, so we construct a dummy clause for the justification p. */ int clen, dlen; struct clause *d = get_clause(); d->parents = p; dlen = proof_length(d); free_clause(d); clen = proof_length(c); return (dlen <= clen); } /* proof_not_longer_than */ /************* * * possibly_append_parents() * * c is a previously kept clause, and ip is the (ordinary) * justification of a newly-derived copy of c. This routine * decides whether to add the new justification to c. * *************/ void possibly_append_parents(struct clause *c, struct ilist *ip) { struct ilist *supporters = just_to_supporters(ip); if (c->parents == NULL) ; /* Don't add the new justification, because c is input. */ else if (c->multi_parents == NULL) append_parents(c, ip, supporters); /* First time we have derived c. */ else if (Parms[MULTI_JUST_MAX].val != -1 && g2list_length(c->multi_parents) >= Parms[MULTI_JUST_MAX].val) ; /* Don't add new justification. */ else if (first_just_input_only(c->multi_parents)) ; /* Don't add new justification, because c can be derived from input. */ else if (derived_from_itself(c, supporters)) ; /* Don't add new justification. */ else if (Flags[MULTI_JUST_LESS].val) { if (all_supporters_less_than(c, supporters)) append_parents(c, ip, supporters); } else if (Flags[MULTI_JUST_SHORTER].val) { if (proof_not_longer_than(c, ip)) append_parents(c, ip, supporters); } else append_parents(c, ip, supporters); free_ilist_list(supporters); } /* possibly_append_parents */ /************* * * print_multi_supporters() * *************/ static void print_multi_supporters(FILE *fp, int id, struct glist *p) { fprintf(fp, "CLAUSE %d", id); for ( ; p != NULL; p = p->next) { struct ilist *ip; fprintf(fp, "\n "); for (ip = p->v; ip != NULL; ip = ip->next) { fprintf(fp, " %d", ip->i); } fprintf(fp, " -1"); } fprintf(fp, " \n-2\n"); } /* print_multi_supporters */ /************* * * just_lists_to_supporters_lists() * *************/ static struct glist *just_lists_to_supporters_lists(struct g2list *p) { if (p == NULL) return NULL; else { struct glist *a = get_glist(); a->v = copy_ilist(p->v2); a->next = just_lists_to_supporters_lists(p->next); return a; } } /* just_lists_to_supporters_lists */ /************* * * build_support_lists() * *************/ static void build_support_lists(struct clause *c) { if (Alists[c->id] == NULL) { struct glist *p; p = just_lists_to_supporters_lists(c->multi_parents); #if 0 /* These operations are now done when adding justifications. */ p = remove_all_supersets(NULL, p); p = remove_those_containing(p, c->id); if (Parms[MULTI_JUST_MAX].val != -1) p = keep_only(p, Parms[MULTI_JUST_MAX].val); #endif Alists[c->id] = p; for (p = Alists[c->id]; p != NULL; p = p->next) { /* foreach just list */ struct ilist *ip; for (ip = p->v; ip != NULL; ip = ip->next) { /* foreach ID */ struct clause *d = cl_find(ip->i); if (d == NULL) abend("build_support_lists: clause not found"); build_support_lists(d); } } } } /* build_support_lists */ /************* * * map_demod() * *************/ int map_demod(struct ilist *p, int i) { if (p == NULL) return 0; else if (p->i == i) return (p->next != NULL ? p->next->i : 0); else return map_demod(p->next->next, i); } /* map_demod */ /************* * * collapse_new_demod2() * * We do this because of the darn "25 [new_demod,24]" clauses. * * We remove clause 25 from Alists; and in the justifications, * change all occurrences of 25 to 24. * *************/ static void collapse_new_demod2(void) { int i; for (i = 0; i < Asize; i++) { if (Alists[i] != NULL) { struct clause *c = cl_find(i); if (c->multi_parents != NULL && c->multi_parents->next == NULL) { struct ilist *p = c->multi_parents->v1; if (p->i == NEW_DEMOD_RULE) { int id = p->next->i; int j; printf("\nremoving %d and changing references to %d\n", i, id); Alists[i] = NULL; for (j = 0; j < Asize; j++) { struct glist *g; for (g = Alists[j]; g != NULL; g = g->next) { struct ilist *p; for (p = g->v; p != NULL; p = p->next) { if (p->i == i) { p->i = id; Demod_map = ilist_tack_on(Demod_map, i); Demod_map = ilist_tack_on(Demod_map, id); } } } } } } } } } /* collapse_new_demod2 */ /************* * * multi_map() * *************/ static void multi_map(void) { int i; struct ilist *inputs = NULL; struct ilist *ip; Bsize = 0; /* Alists has lots of gaps in the numbering. This routine builds Blists, numbered 0,1,2,... Arrays A_to_B and B_to_A give the correspondence. There is ambiguity in Alists: NULL means either "clause is irrelelvant" or "clause is input". In Blists, all are relevant, and NULL means "input". So we go through Alists, finding input clauses (goals without 0 in Alist), and initialize Blists to those. */ for (i = 0; i < Asize; i++) { if (Alists[i] != NULL) { struct glist *d; for (d = Alists[i]; d != NULL; d= d->next) { for (ip = d->v; ip != NULL; ip = ip->next) { if (Alists[ip->i] == NULL) inputs = iset_add(ip->i, inputs); } } } } A_to_B = calloc(Asize, sizeof(int)); for (i = 0; i < Asize; i++) A_to_B[i] = -1; for (ip = inputs; ip != NULL; ip = ip->next) { A_to_B[ip->i] = Bsize++; } free_ilist_list(inputs); /* Finish setting up the A_to_B map. */ for (i = 0; i < Asize; i++) { if (Alists[i] != NULL) { A_to_B[i] = Bsize++; } } /* Now we know how many Bs there are, so allocate the B arrays. */ Blists = calloc(Bsize, sizeof(struct glist *)); B_to_A = calloc(Bsize, sizeof(int)); for (i = 0; i < Asize; i++) { if (Alists[i] != NULL) { struct glist *d; Blists[A_to_B[i]] = copy_glist(Alists[i]); for (d = Blists[A_to_B[i]]; d != NULL; d= d->next) { d->v = copy_ilist(d->v); for (ip = d->v; ip != NULL; ip = ip->next) { ip->i = A_to_B[ip->i]; } } } } /* Finally, set up the B_to_A map. */ for (i = 0; i < Asize; i++) if (A_to_B[i] != -1) B_to_A[A_to_B[i]] = i; } /* multi_map */ /* ====================================================================== SET OPERATIONS ====================================================================== */ #define INT_BIT 32 static int Set_size; /* in integers */ static unsigned Compares; /************* * * set_jset_size() * *************/ void set_jset_size(int n) { Set_size = ((n-1) / INT_BIT) + 1; } /* set_jset_size */ /************* * * get_jset() * *************/ int *get_jset(void) { return calloc(Set_size, sizeof(int)); } /* get_jset */ /************* * * copy_jset() * *************/ int *copy_jset(int *a) { int *b = get_jset(); int i; for (i = 0; i < Set_size;i++) b[i] = a[i]; return b; } /* copy_jset */ /************* * * jset_member() * *************/ int jset_member(int *s, int n) { int i = n / INT_BIT; int j = n % INT_BIT; return s[i] & (1<v, s); if (comp == SAME_AS) return 1; else if (comp == GREATER_THAN) return 0; else { Crashes++; return jhash_member_recurse(s, p->next); } } } /* jhash_member_recurse */ /************* * * jhash_member() * *************/ static int jhash_member(int *s) { int h = jhash(s); Lookups++; return jhash_member_recurse(s, Jhash[h]); } /* jhash_member */ /************* * * jhash_insert_recurse() * *************/ static struct glist *jhash_insert_recurse(int *s, struct glist *p) { if (p == NULL) { p = get_glist(); p->v = s; return p; } else { int comp = j_compare(p->v, s); if (comp == SAME_AS) { abend("jhash_inset_recurse: already there"); return p; /* to avoid compiler warning */ } else if (comp == GREATER_THAN) { struct glist *q = get_glist(); q->v = s; q->next = p; return q; } else { p->next = jhash_insert_recurse(s, p->next); return p; } } } /* jhash_insert_recurse */ /************* * * jhash_insert() * * Do not copy the set. If already there, ABEND. * *************/ static void jhash_insert(int *s) { int h = jhash(s); Jhash[h] = jhash_insert_recurse(s, Jhash[h]); } /* jhash_insert */ /************* * * print_set() * *************/ void print_set(int *s) { int i, j; printf("("); for (i = 0; i < Set_size; i++) { int k = s[i]; for (j = 0; j < INT_BIT; j++) { if ((k>>j) & 1) printf("%d ", (INT_BIT * i) + j); } } printf(") "); } /* print_set */ /************* * * print_set_b_to_a() * *************/ void print_set_b_to_a(int *s) { int i, j; printf("("); for (i = 0; i < Set_size; i++) { int k = s[i]; for (j = 0; j < INT_BIT; j++) { if ((k>>j) & 1) printf("%d ", B_to_A[(INT_BIT * i) + j]); } } printf(") "); } /* print_set_b_to_a */ /************* * * print_jhash() * *************/ static void print_jhash(void) { int i; printf("\n========== Jhash ==========\n"); for (i = 0; i < JHASH_SIZE; i++) { if (Jhash[i] != NULL) { struct glist *p = Jhash[i]; printf("%d: ", i); for (; p != NULL; p = p->next) { print_set(p->v); } printf("\n"); } } } /* print_jhash */ /* ====================================================================== JNODE STRUCTURE ====================================================================== */ struct jnode { int id; /* clause id */ int justification; /* which justification (count from 1) */ int *goals; /* current set of goals */ int *resolved; /* atoms resolved so far */ struct jnode *parent; struct jnode *next; }; static struct jnode *Jstart; static struct jnode *Jend; static struct jnode *Jcurrent; static int Expanded; static int Generated; static int Pruned; static int Subsumed; static int Kept; /************* * * get_jnode() * *************/ static struct jnode *get_jnode(void) { struct jnode *p = (struct jnode *) tp_alloc((int) sizeof(struct jnode)); p->id = -1; p->justification = -1; p->goals = NULL; p->parent = NULL; p->next = NULL; return p; } /* get_jnode */ /************* * * b_input() * *************/ static int b_input(int i) { return Blists[i] == NULL; } /* b_input */ /************* * * a_input() * *************/ static int a_input(int i) { return Blists[A_to_B[i]] == NULL; } /* a_input */ /************* * * print_jnode() * *************/ static void print_jnode(struct jnode *j) { printf("%d ", j->id); printf("[%d] ", j->justification); print_set(j->goals); printf(" resolved: "); print_set(j->resolved); printf("\n"); } /* print_jnode */ /************* * * print_jnode_b_to_a() * *************/ static void print_jnode_b_to_a(struct jnode *j) { printf("%d ", j->id >= 0 ? B_to_A[j->id] : j->id); printf("[%d] ", j->justification); print_set_b_to_a(j->goals); printf(" resolved: "); print_set_b_to_a(j->resolved); printf("\n"); } /* print_jnode_b_to_a */ /************* * * subset_or_input() * *************/ int subset_or_input(struct ilist *a, struct ilist *b) { if (a == NULL) return 1; else if (ilist_member(a->i, b)) return subset_or_input(a->next, b); else if (a_input(a->i)) return subset_or_input(a->next, b); else if (ilist_member(map_demod(Demod_map, a->i), b)) return subset_or_input(a->next, b); else return 0; } /* subset_or_input */ /************* * * jproof() * *************/ static void jproof(struct jnode *j) { struct ilist *ids = NULL; struct glist *derived = NULL; struct glist *justs = NULL; struct ilist *input = NULL; struct glist *p1, *p2; struct ilist *ip1, *ip2; struct clause *c; int n; struct jnode *p; printf("\n=== JPROOF ===\n Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d.\n", Expanded, Generated, Pruned, Subsumed, Kept); #if 0 printf(" Lookups %u, Crashes %u, Compares %u.\n", Lookups, Crashes, Compares); for (p = j; p != NULL; p = p->parent) print_jnode(p); printf("==== unmapped =====\n"); #endif for (p = j; p != NULL; p = p->parent) print_jnode_b_to_a(p); /* For each clause, look through justifications and use the first one all of whose members are previously seen or input. */ ids = NULL; /* List of IDs seen so far. */ for (p = j; p->parent != NULL; p = p->parent) { /* for each jnode */ struct g2list *g; int real_id = B_to_A[p->id]; c = cl_find(real_id); if (c == NULL) abend("jproof: derived clause not found"); for (g = c->multi_parents; g != NULL; g = g->next) { /* for each just */ ip1 = g->v2; if (subset_or_input(ip1, ids)) { /* We found it. Collect any input clauses in the justification. */ for (ip2 = ip1; ip2 != NULL; ip2 = ip2->next) { if (a_input(ip2->i)) input = iset_add(ip2->i, input); } break; } } if (g == NULL) { print_clause(stdout, c); abend("jproof: justification not found"); } derived = glist_tack_on(derived, c); justs = glist_tack_on(justs, g->v1); ids = iset_add(real_id, ids); } /* c now contains the last clause (empty clause) in the original proof. */ n = proof_length(c); /* When printing the proof lengths, don't count the empty clause. */ printf("\n==== SHORT_PROOF ===== Length %d (starting length %d)\n", glist_length(derived)-1, n-1); fprintf(stderr, "\n==== SHORT_PROOF ===== Length %d (starting length %d)\n", glist_length(derived)-1, n-1); for (ip1 = input; ip1 != NULL; ip1 = ip1->next) { struct clause *c = cl_find(ip1->i); if (c == NULL) abend("jproof: input clause not found"); printf("[] "); print_clause_without_just(stdout, c); } for (p1 = derived, p2 = justs; p1 && p2; p1 = p1->next, p2 = p2->next) { print_justification(stdout, p2->v); printf(" "); print_clause_without_just(stdout, p1->v); } free_glist_list(derived); free_glist_list(justs); { struct ilist *id1 = get_ancestors2(c); struct ilist *id2 = iset_sort(ilist_append(input, ids)); struct ilist *id2_id1, *id1_id2; printf("IDs in original proof: "); p_ilist(id1); printf("IDs in short proof: "); p_ilist(id2); id2_id1 = iset_subtract(id2, id1); id1_id2 = iset_subtract(id1, id2); printf("original - short: "); p_ilist(id1_id2); printf("short - original: "); p_ilist(id2_id1); free_ilist_list(id1); free_ilist_list(id2); free_ilist_list(id1_id2); free_ilist_list(id2_id1); } printf("==== end jproof =====\n"); } /* jproof */ /************* * * j_subsumed_recurse() * *************/ static int j_subsumed_recurse(int *s, struct ilist *p) { if (p == NULL) { #if DEBUG printf(" Checking hash membership: "); print_set(s); printf("\n"); #endif return jhash_member(s); } #if 0 /* try empty set first */ else if (j_subsumed_recurse(s, p->next)) return 1; else { int subsumed; add_to_jset(s, p->i); subsumed = j_subsumed_recurse(s, p->next); remove_from_jset(s, p->i); return subsumed; } #else /* try full set first */ else { int subsumed; add_to_jset(s, p->i); subsumed = j_subsumed_recurse(s, p->next); remove_from_jset(s, p->i); if (subsumed) return 1; else if (j_subsumed_recurse(s, p->next)) return 1; else return 0; } #endif } /* j_subsumed_recurse */ /************* * * j_subsumed() * *************/ static int j_subsumed(struct ilist *p, int *s) { /* p has the list (set) of goals. s has been allocated, but it is empty. */ int subsumed; #if DEBUG printf("Subsume check: "); p_ilist(p); #endif subsumed = j_subsumed_recurse(s, p); if (subsumed) return 1; else { struct ilist *q; for (q = p ; q != NULL; q = q->next) add_to_jset(s, q->i); jhash_insert(s); #if DEBUG printf(" KEPT: "); print_set(s); #endif Kept++; return 0; } } /* j_subsumed */ /************* * * jset_to_ilist() * *************/ struct ilist *jset_to_ilist(int *s) { int i, j; struct ilist *p = NULL; for (i = 0; i < Set_size; i++) { int k = s[i]; for (j = 0; j < INT_BIT; j++) { if ((k>>j) & 1) p = iset_add((INT_BIT * i) + j, p); } } return p; } /* jset_to_ilist */ /************* * * ilist_to_jset() * *************/ int *ilist_to_jset(struct ilist *p) { int *s = get_jset(); for ( ; p != NULL; p = p->next) add_to_jset(s, p->i); return s; } /* ilist_to_jset */ /************* * * iset_jset_disjoint() * *************/ static int iset_jset_disjoint(struct ilist *i, int *j) { if (i == NULL) return 1; else if (jset_member(j, i->i)) return 0; else return iset_jset_disjoint(i->next, j); } /* iset_jset_disjoint */ /************* * * j_expand() * *************/ static int j_expand(struct jnode *n) { int proof = 0; struct ilist *g, *igoals; #if DEBUG printf("Expanding: "); print_jnode(n); #endif Expanded++; igoals = jset_to_ilist(n->goals); for (g = igoals; g != NULL; g = g->next) { /* for each goal */ int goal = g->i; struct glist *j; int jcount = 0; for (j = Blists[goal]; j != NULL; j = j->next) { /* for each just */ Generated++; if (0 && !iset_jset_disjoint(j->v, n->resolved)) /* I believe that all nodes pruned here would be subsumed below. But this test is much faster than the subsumption test. */ Pruned++; else { struct ilist *x; struct ilist *new_igoals = copy_ilist(igoals); int *new_jgoals = NULL; jcount++; new_igoals = iset_remove(goal, new_igoals); for (x = j->v; x != NULL; x = x->next) { if (!b_input(x->i)) new_igoals = iset_add(x->i, new_igoals); } /* Check later if new_igoals is empty. */ new_jgoals = get_jset(); if (j_subsumed(new_igoals, new_jgoals)) { Subsumed++; free(new_jgoals); } else { struct jnode *n2 = get_jnode(); n2->id = goal; n2->justification = jcount; n2->goals = new_jgoals; /* set up by j_subsume; shared with hash */ n2->resolved = copy_jset(n->resolved); add_to_jset(n2->resolved, goal); n2->parent = n; Jend->next = n2; Jend = n2; if (new_igoals == NULL) { jproof(n2); proof = 1; return proof; } } free_ilist_list(new_igoals); } } } free_ilist_list(igoals); return proof; } /* j_expand */ /************* * * j_search() * *************/ static int j_search(int b_goal) { int level = 0; int end_of_level = 0; int proof = 0; Kept = 1; jhash_init(); set_jset_size(Bsize); Jstart = get_jnode(); Jstart->goals = get_jset(); Jstart->resolved = get_jset(); add_to_jset(Jstart->goals, b_goal); Jend = Jstart; for (Jcurrent = Jstart; Jcurrent != NULL; Jcurrent = Jcurrent->next) { if (Expanded == end_of_level) { double seconds = run_time() / 1000.; level++; end_of_level = Kept; fprintf(stderr, "Level %d, last kept clause of level %d is %d.\n", level, level-1, end_of_level); printf("\nLevel %d, last kept clause of level %d is %d, %.2f seconds.\n", level, level-1, end_of_level, seconds); fflush(stdout); } if (Expanded % 10000 == 0) { double seconds = run_time() / 1000.; printf("\n expanded %d, generated %d, pruned %d, subsumed %d, kept %d, \n", Expanded, Generated, Pruned, Subsumed, Kept); #if 0 printf(" lookups %u, crashes %u, compares %u,\n", Lookups, Crashes, Compares); #endif printf(" user time %.2f, lookups/second %d\n", seconds, (int) (Lookups / seconds)); fflush(stdout); } if (j_expand(Jcurrent)) { proof = 1; return proof; } } return proof; } /* j_search */ /************* * * multi_just_process() * *************/ void multi_just_process(struct clause *c) { int i; printf("\nLooking through the multi justifications for a short proof.\n"); fprintf(stderr, "\nLooking through the multi justifications for a short proof.\n\n"); Asize = next_cl_num(); Alists = calloc(Asize, sizeof(struct glist *)); build_support_lists(c); collapse_new_demod2(); #if 1 printf("============ MULTIJUST ============\n"); for (i = 0; i < Asize; i++) { if (Alists[i] != NULL) { print_multi_supporters(stdout, i, Alists[i]); } } printf("============ end multijust ============\n"); #endif multi_map(); #if 0 printf("============ MULTI_RENUMBERED_JUST ============\n"); for (i = 0; i < Bsize; i++) { if (Blists[i] != NULL) { print_multi_supporters(stdout, i, Blists[i]); } } printf("============ end multi_renumbered_just ============\n"); #endif i = j_search(A_to_B[c->id]); } /* multi_just_process */ /************* * * multi_justifications() * * Are we keeping multiple justifications? * *************/ int multi_justifications() { return (Flags[MULTI_JUST].val || Flags[MULTI_JUST_LESS].val || Flags[MULTI_JUST_SHORTER].val || Parms[MULTI_JUST_MAX].val != -1); } /* multijust */ otter-3.3f/source/main.c0100644000076400007640000001170210103517270014566 0ustar mccunemccune/* Otter 3.3 * * William McCune * Mathematics and Computer Science Division * Argonne National Laboratory * Argonne, IL 60439 * U.S.A. * * E-mail: mccune@mcs.anl.gov * Web: http://www.mcs.anl.gov/~mccune * http://www.mcs.anl.gov/AR/otter */ #define OTTER_VERSION "3.3f" #define VERSION_DATE "August 2004" #define IN_MAIN /* so that global vars in header.h will not be external */ #include "header.h" /**/ int main(int argc, char **argv) { struct clause *giv_cl; int errors, status, level, first_of_next_level; char *str; FILE *xlog_fp = NULL; non_portable_init(argc, argv); print_banner(argc, argv); init(); read_all_input(argc, argv); errors = Stats[INPUT_ERRORS]; if (errors != 0) { fprintf(stderr, "\n%d input errors were found.%c\n\n", errors, Bell); printf("%d input errors were found.\n", errors); exit(INPUT_ERROR_EXIT); } else { status = check_stop(); if (status == KEEP_SEARCHING && Parms[MAX_LEVELS].val == 0) status = MAX_LEVELS_EXIT; if (status == KEEP_SEARCHING) { if (splitting() && Parms[SPLIT_GIVEN].val == 0) always_split(); /* does not return */ giv_cl = extract_given_clause(); } else giv_cl = NULL; level = 0; first_of_next_level = 0; if (Flags[LOG_FOR_X_SHOW].val) xlog_fp = init_log_for_x_show(); /* --------------------- MAIN LOOP STARTS HERE --------------------- */ printf("\n=========== start of search ===========\n"); fflush(stdout); while (giv_cl != NULL && status == KEEP_SEARCHING) { if (Flags[SOS_QUEUE].val && giv_cl->id >= first_of_next_level) { level++; first_of_next_level = next_cl_num(); printf("\nStarting on level %d, last kept clause of level %d is %d.\n", level, level-1, first_of_next_level-1); fprintf(stderr, "\n%cStarting on level %d, last kept clause " "of level %d is %d.\n", Bell, level, level-1, first_of_next_level-1); } if (Flags[LOG_FOR_X_SHOW].val) log_for_x_show(xlog_fp); Stats[CL_GIVEN]++; if (Flags[PRINT_GIVEN].val) { printf("\ngiven clause #%ld: ", Stats[CL_GIVEN]); printf("(wt=%d) ", giv_cl->pick_weight); print_clause(stdout, giv_cl); fflush(stdout); } index_lits_clash(giv_cl); append_cl(Usable, giv_cl); if (splitting()) possible_given_split(giv_cl); infer_and_process(giv_cl); if (Parms[INTERRUPT_GIVEN].val > 0 && Stats[CL_GIVEN] % Parms[INTERRUPT_GIVEN].val == 0) { fprintf(stderr, "\n%c%ld clauses have been given.\n", Bell, Stats[CL_GIVEN]); interact(); } status = check_stop(); if (status == KEEP_SEARCHING && Flags[SOS_QUEUE].val && level == Parms[MAX_LEVELS].val && Sos->first_cl != NULL && Sos->first_cl->id >= first_of_next_level) status = MAX_LEVELS_EXIT; if (status == KEEP_SEARCHING) { if (Parms[CHANGE_LIMIT_AFTER].val == Stats[CL_GIVEN]) { int new_limit; new_limit = Parms[NEW_MAX_WEIGHT].val; Parms[MAX_WEIGHT].val = new_limit; printf("\nreducing weight limit to %d.\n", new_limit); } if (splitting()) possible_split(); /* parent does not return if successful */ giv_cl = extract_given_clause(); } if (status == KEEP_SEARCHING && giv_cl && Parms[REPORT].val > 0) report(); } /* end of main loop */ /* --------------------- MAIN LOOP ENDS HERE --------------------- */ /* print the reason the search ended */ if (status == KEEP_SEARCHING) { if (splitting() && current_case() != NULL) exit_with_possible_model(); /* this call does not return here */ status = SOS_EMPTY_EXIT; fprintf(stderr, "\n%cSearch stopped because sos empty.\n\n", Bell); printf("\nSearch stopped because sos empty.\n"); } else { switch (status) { case MAX_GIVEN_EXIT: str = "max_given"; break; case MAX_GEN_EXIT: str = "max_gen"; break; case MAX_KEPT_EXIT: str = "max_kept"; break; case MAX_SECONDS_EXIT: str = "max_seconds"; break; case MAX_LEVELS_EXIT: str = "max_levels"; break; default: str = "???"; break; } fprintf(stderr, "\n%cSearch stopped by %s option.\n\n", Bell, str); printf("\nSearch stopped by %s option.\n", str); } cleanup(); if (multi_justifications()) { struct clause *ee = proof_last_hidden_empty(); if (ee != NULL) { multi_just_process(ee); output_stats(stdout, Parms[STATS_LEVEL].val); } } exit(status); } } /* main */ /************* * * void print_banner(argc, argv) * *************/ void print_banner(int argc, char **argv) { int i; int pid = my_process_id(); printf("----- Otter %s, %s -----\n", OTTER_VERSION, VERSION_DATE); printf("The process was started by %s on %s,\n%s", username(), hostname(), get_time()); printf("The command was \""); for(i = 0; i < argc; i++) printf("%s%s", argv[i], (i < argc-1 ? " " : "")); printf("\"."); if (pid != 0) printf(" The process ID is %d.\n\n", pid); else printf("\n\n"); } /* print_banner */ otter-3.3f/source/overbeek.c0100644000076400007640000001212207343604675015463 0ustar mccunemccune/* overbeek.c -- experimental weighting method, Feb 2001. To use this feature, input a list of weight/term pairs like this. overbeek_world(junk). 0 # P(e(e(x,y),e(e(x,z),e(z,y)))). 0 # P(e(e(e(x,y),z),e(z,e(e(x,u),e(u,y))))). 0 # P(e(e(e(x,y),e(y,z)),e(e(x,u),e(u,z)))). 0 # P(e(e(e(x,x),y),e(y,e(z,z)))). 0 # P(e(e(e(x,x),e(y,y)),e(z,z))). 0 # P(e(x,x)). 0 # P(e(e(x,y),e(y,x))). 0 # P(e(e(e(x,y),z),e(z,e(y,x)))). 0 # P(e(e(e(x,y),e(y,z)),e(x,z))). 0 # P(e(e(x,y),e(e(z,y),e(x,z)))). end_of_list. Variable renumbering/renaming is applied to each term before it is inserted into the hash table. The ordinary term weighting routine, weight(t), first calls overbeek_weight(t) below to try to (exact) match a renumberd copy of t with one of the overbeek_world terms. If nothing matches, the ordinary weighting method is applied. Here's an example input file: % % Equivalential calculus (EC): YQF -> YQL (both are single axioms) % set(hyper_res). assign(max_weight, 0). list(usable). -P(e(x,y)) | -P(x) | P(y). % condensed detachment -P(e(e(a,b),e(e(c,b),e(a,c)))). % YQL end_of_list. list(sos). P(e(e(x,y),e(e(x,z),e(z,y)))). % YQF end_of_list. overbeek_world(junk). 0 # P(e(e(x,y),e(e(x,z),e(z,y)))). 0 # P(e(e(e(x,y),z),e(z,e(e(x,u),e(u,y))))). 0 # P(e(e(e(x,y),e(y,z)),e(e(x,u),e(u,z)))). 0 # P(e(e(e(x,x),y),e(y,e(z,z)))). 0 # P(e(e(e(x,x),e(y,y)),e(z,z))). 0 # P(e(x,x)). 0 # P(e(e(x,y),e(y,x))). 0 # P(e(e(e(x,y),z),e(z,e(y,x)))). 0 # P(e(e(e(x,y),e(y,z)),e(x,z))). 0 # P(e(e(x,y),e(e(z,y),e(x,z)))). end_of_list. */ #include "header.h" #define OVERBEEK_WORLD_SIZE 25000 /* size of hash table */ /************* * * hash_term2(term) * * Return a hash value of a term: just a word of bits. * *************/ static unsigned hash_term2(struct term *t) { unsigned hashval = 0; if (t->type == NAME) hashval = t->sym_num; else if (t->type == VARIABLE) hashval = t->varnum; else { /* complex */ struct rel *r; hashval = t->sym_num; for (r = t->farg; r != NULL; r = r->narg) { hashval <<= 1; /* shift left */ hashval ^= hash_term2(r->argval); /* exclusive or */ } } return(hashval); } /* hash_term2 */ /************* * * void overbeek_insert() * *************/ void overbeek_insert(struct term *t) { int i; /* If this is the first call, allocate a hash table. */ if (Overbeek_world == NULL) { int i; Overbeek_world = (void *) malloc((size_t) (OVERBEEK_WORLD_SIZE * sizeof(void *))); for (i = 0; i < OVERBEEK_WORLD_SIZE; i++) Overbeek_world[i] = NULL; } if (!is_symbol(t, "#", 2)) abend("overbeek_insert, bad term"); else if (!str_int(sn_to_str(t->farg->argval->sym_num), &i)) abend("overbeek_insert, bad weight in term"); else { int hashval = abs(hash_term2(t->farg->narg->argval) % OVERBEEK_WORLD_SIZE); struct term_ptr *p = get_term_ptr(); p->term = t; p->next = Overbeek_world[hashval]; Overbeek_world[hashval] = p; } } /* overbeek_insert */ /************* * * int overbeek_weight() * *************/ int overbeek_weight(struct term *t, int *ip) { if (Overbeek_world == NULL) return 0; else { int hashval; struct term_ptr *p; int found = 0; struct term *copy = copy_term(t); renumber_vars_term(copy); hashval = abs(hash_term2(copy) % OVERBEEK_WORLD_SIZE); for (p = Overbeek_world[hashval]; p && !found; p = p->next) { if (term_ident(copy, p->term->farg->narg->argval)) { int rc; found = 1; rc = str_int(sn_to_str(p->term->farg->argval->sym_num), ip); } } zap_term(copy); return found; } } /* overbeek_weight */ /************* * * void print_overbeek_world() * *************/ void print_overbeek_world(void) { if (Overbeek_world == NULL) printf("There is no Overbeek World to print!\n"); else { int i; int terms = 0; int excess = 0; int max = 0; printf("\nstart of Overbeek_world\n\n"); for (i = 0; i < OVERBEEK_WORLD_SIZE; i++) { if (Overbeek_world[i]) { int n = 0; struct term_ptr *p; printf("%d:\n", i); excess--; for (p = Overbeek_world[i]; p; p = p->next) { terms++; excess++; n++; printf(" "); p_term(p->term); } max = (n > max ? n : max); } } printf("\nend of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d.\n\n",terms, excess, max); } } /* print_overbeek_world */ /************* * * void check_overbeek_world() * *************/ void check_overbeek_world(void) { if (Overbeek_world == NULL) printf("There is no Overbeek World to check!\n"); else { int i; for (i = 0; i < OVERBEEK_WORLD_SIZE; i++) { if (Overbeek_world[i]) { struct term_ptr *p; for (p = Overbeek_world[i]; p; p = p->next) { int wt1, wt2, rc; struct term *t = p->term->farg->narg->argval; rc = str_int(sn_to_str(p->term->farg->argval->sym_num), &wt1); if (overbeek_weight(t, &wt2)) { if (wt1 != wt2) { printf("check_overbeek_world, wrong weight: %d %d ", wt1, wt2); p_term(t); } } else { printf("check_overbeek_world, term not found: "); p_term(t); } } } } } } /* check_overbeek_world */ otter-3.3f/source/fpa2.c0100644000076400007640000001064110041261516014473 0ustar mccunemccune/* This if the new code (April 2004) for inserting/deleting/traversing FPA lists. It should function exactly the same as the old code, except that deletions should be much faster, and memory usage will be somewhat different (not much). Instead of a (singly-linked) list of pointers to terms, we have a (singly-linked) list of *arrays* of pointers to terms. As before, the terms are kept in decreasing order. Recall that in practice, terms being inserted will usually be greater than anything already in the list. */ #include "header.h" /* The design is determined by the following properties of the application: (1) items will nearly always be inserted in increasing order, (2) the lists will be traversed, and the items must be kept in decreasing order, and (3) deletions will be arbitrary and occasionally extensive. */ /* First and last items in chunk. Items are right-justified. */ #define FLAST(f) (f)->d[FMAX-1] #define FFIRST(f) (f)->d[FMAX-((f)->n)] /************* * * flist_insert() * * If the item is greater than any in the list, insertion should * be constant time. * *************/ Fnode flist_insert(Fnode f, FTYPE x) { if (f == NULL) { f = get_fnode(); FLAST(f) = x; f->n = 1; } else if (f->n == FMAX) { if (FLT(x,FLAST(f))) f->next = flist_insert(f->next, x); else if (FEQ(x,FLAST(f))) fprintf(stderr, "WARNING: flist_insert, item %d already here (1)!\n", x); else if (FGT(x,FFIRST(f))) { /* This special case isn't necessary. It is to improve performance. The application for which I'm writing this inserts items in increasing order (most of the time), and this prevents a lot of half-empty nodes in that case. */ Fnode f2 = flist_insert(NULL, x); f2->next = f; f = f2; } else { /* split this node in half */ Fnode f2 = get_fnode(); int move = FMAX / 2; int i, j; for (i = 0, j = FMAX-move; i < move; i++, j++) { f2->d[j] = f->d[i]; f->d[i] = FDEFAULT; } f2->n = move; f->n = FMAX - move; f2->next = f; f = flist_insert(f2, x); } } else { if (f->next && FLE(x,FFIRST(f->next))) f->next = flist_insert(f->next, x); else { /* insert into this node */ int n = f->n; int i = FMAX - n; while (i < FMAX && FLT(x,f->d[i])) i++; if (i < FMAX && FEQ(x,f->d[i])) fprintf(stderr, "WARNING: flist_insert, item %d already here (2)!\n", x); else if (i == FMAX - n) { f->d[i-1] = x; f->n = n+1; } else { /* insert at i-1, shifting the rest */ int j; for (j = FMAX-n; j < i; j++) f->d[j-1] = f->d[j]; f->d[i-1] = x; f->n = n+1; } } } return f; } /* flist_insert */ /************* * * consolidate() - try to join f and f->next; not recursive * *************/ static Fnode consolidate(Fnode f) { if (f->next && f->n + f->next->n <= FMAX) { Fnode f2 = f->next; int i; for (i = 0; i < f->n; i++) f2->d[FMAX - (f2->n + i + 1)] = f->d[FMAX - (i+1)]; f2->n = f->n + f2->n; free_fnode(f); return f2; } else return f; } /* consolidate */ /************* * * flist_delete() * *************/ Fnode flist_delete(Fnode f, FTYPE x) { if (f == NULL) fprintf(stderr, "WARNING: flist_delete, item %d not found (1)!\n", x); else if (FLT(x,FLAST(f))) f->next = flist_delete(f->next, x); else { int n = f->n; int i = FMAX - n; while (i < FMAX && FLT(x,f->d[i])) i++; if (FNE(x,f->d[i])) fprintf(stderr, "WARNING: flist_delete, item %d not found (2)!\n", x); else { /* delete and close the hole */ int j; for (j = i; j > FMAX-n; j--) f->d[j] = f->d[j-1]; f->d[j] = FDEFAULT; f->n = n-1; if (f->n == 0) { /* delete this node */ Fnode next = f->next; free_fnode(f); f = next; } else { /* try to join this node with the next */ f = consolidate(f); } } } return f; } /* flist_delete */ /************* * * first_fpos() * *************/ struct fposition first_fpos(Fnode f) { if (f == NULL) return (struct fposition) {NULL, 0}; else return (struct fposition) {f, FMAX - f->n}; } /* first_fpos */ /************* * * next_fpos() * *************/ struct fposition next_fpos(struct fposition p) { int i = p.i+1; if (i < FMAX) return (struct fposition) {p.f, i}; else return first_fpos((p.f)->next); } /* next_fpos */ otter-3.3f/source/lists.c0100644000076400007640000001646407714004014015013 0ustar mccunemccune/* * lists.c -- utilities for ilist, glist, and g2list * */ #include "header.h" /* ============================================================ ilist */ /************* * * free_ilist_list() * *************/ void free_ilist_list(struct ilist *p) { if (p != NULL) { free_ilist_list(p->next); free_ilist(p); } } /* free_ilist_list */ /************* * * ilist_tack_on() * *************/ struct ilist *ilist_tack_on(struct ilist *a, int i) { if (a == NULL) { struct ilist *b = get_ilist(); b->i = i; return b; } else { a->next = ilist_tack_on(a->next, i); return a; } } /* ilist_tack_on */ /************* * * iset_add() * *************/ struct ilist *iset_add(int i, struct ilist *p) { if (p == NULL) { p = get_ilist(); p->i = i; return p; } else if (p->i == i) return p; else if (p->i > i) { struct ilist *q = get_ilist(); q->i = i; q->next = p; return q; } else { p->next = iset_add(i, p->next); return p; } } /* iset_add */ /************* * * iset_remove() -- assume ordered, remove first * *************/ struct ilist *iset_remove(int i, struct ilist *p) { if (p == NULL) { return p; } else if (p->i == i) { struct ilist *q = p; p = p->next; free_ilist(q); return p; } else if (p->i > i) { return p; } else { p->next = iset_remove(i, p->next); return p; } } /* iset_remove */ /************* * * ilist_member() * *************/ int ilist_member(int i, struct ilist *p) { if (p == NULL) return 0; else if (p->i == i) return 1; else return ilist_member(i, p->next); } /* ilist_member */ /************* * * iset_subset() * *************/ int iset_subset(struct ilist *a, struct ilist *b) { if (a == NULL) return 1; else return (ilist_member(a->i, b) && iset_subset(a->next, b)); } /* iset_subset */ /************* * * iset_subtract() * *************/ struct ilist *iset_subtract(struct ilist *a, struct ilist *b) { if (b == NULL) return copy_ilist(a); else { a = iset_subtract(a, b->next); return iset_remove(b->i, a); } } /* iset_subtract */ /************* * * iset_sort() -- insertion sort -- remove duplicates * *************/ struct ilist *iset_sort(struct ilist *a) { if (a == NULL) return NULL; else { int i = a->i; struct ilist *b = iset_sort(a->next); free_ilist(a); return iset_add(i, b); } } /* iset_sort */ /************* * * idempot_ip() * *************/ struct ilist *idempot_ip(struct ilist *a) { if (a == NULL) return NULL; else if (ilist_member(a->i, a->next)) { struct ilist *b = a->next; free_ilist(a); return idempot_ip(b); } else { a->next = idempot_ip(a->next); return a; } } /* idempot_ip */ /************* * * reverse_ip() * *************/ struct ilist *reverse_ip(struct ilist *ip1, struct ilist *ip2) { if (ip1 == NULL) return ip2; else { struct ilist *ip3 = ip1->next; ip1->next = ip2; return reverse_ip(ip3, ip1); } } /* reverse_ip */ /************* * * ilist_append() -- This uses up the two inputs. * *************/ struct ilist *ilist_append(struct ilist *a, struct ilist *b) { if (a == NULL) return b; else { a->next = ilist_append(a->next, b); return a; } } /* ilist_append */ /************* * * copy_ilist() * * Copy and return a list of pointers to integers. * *************/ struct ilist *copy_ilist(struct ilist *p) { if (p == NULL) return NULL; else { struct ilist *q = get_ilist(); q->i = p->i; q->next = copy_ilist(p->next); return q; } } /* copy_ilist */ /************* * * ilist_length() * *************/ int ilist_length(struct ilist *a) { if (a == NULL) return 0; else return 1 + ilist_length(a->next); } /* ilist_length */ /************* * * copy_ilist_segment() -- copy the first n members * *************/ struct ilist *copy_ilist_segment(struct ilist *p, int n) { if (n == 0 || p == NULL) return NULL; else { struct ilist *q = get_ilist(); q->i = p->i; q->next = copy_ilist_segment(p->next, n-1); return q; } } /* copy_ilist_segment */ /************* * * print_ilist(fp, ip) * *************/ void print_ilist(FILE *fp, struct ilist *ip) { struct ilist *p; fprintf(fp, "("); for (p = ip; p; p = p->next) fprintf(fp, "%d%s", p->i, (p->next ? " " : "")); fprintf(fp, ")"); } /* print_ilist */ /************* * * p_ilist(ip) * *************/ void p_ilist(struct ilist *ip) { print_ilist(stdout, ip); printf("\n"); } /* p_ilist */ /* ============================================================ glist */ /************* * * glist_length() * *************/ int glist_length(struct glist *a) { if (a == NULL) return 0; else return 1 + glist_length(a->next); } /* glist_length */ /************* * * copy_glist() -- don't copy objects (how could we??) * *************/ struct glist *copy_glist(struct glist *p) { if (p == NULL) return NULL; else { struct glist *q = get_glist(); q->v = p->v; q->next = copy_glist(p->next); return q; } } /* copy_glist */ /************* * * glist_append() -- this uses up both arguments * *************/ struct glist *glist_append(struct glist *a, struct glist *b) { if (a == NULL) return b; else { a->next = glist_append(a->next, b); return a; } } /* glist_append */ /************* * * glist_prepend() -- put a pointer onto the front. * *************/ struct glist *glist_prepend(void *p, struct glist *a) { struct glist *b = get_glist(); b->v = p; b->next = a; return b; } /* glist_prepend */ /************* * * glist_tack_on() * *************/ struct glist *glist_tack_on(struct glist *a, void *v) { if (a == NULL) { struct glist *b = get_glist(); b->v = v; return b; } else { a->next = glist_tack_on(a->next, v); return a; } } /* glist_tack_on */ /************* * * free_glist_list() * *************/ void free_glist_list(struct glist *p) { if (p != NULL) { free_glist_list(p->next); free_glist(p); } } /* free_glist_list */ /* ============================================================ g2list */ /************* * * g2list_length() * *************/ int g2list_length(struct g2list *a) { if (a == NULL) return 0; else return 1 + g2list_length(a->next); } /* g2list_length */ /* ===================================================== glist and ilist */ /************* * * member_is_subset() * *************/ int member_is_subset(struct glist *a, struct ilist *s) { if (a == NULL) return 0; else if (iset_subset(a->v, s)) return 1; else return member_is_subset(a->next, s); } /* member_is_subset */ /************* * * copy_glist_of_ilists() * *************/ struct glist *copy_glist_of_ilists(struct glist *a) { if (a == NULL) return NULL; else { struct glist *b = get_glist(); b->v = copy_ilist(a->v); b->next = copy_glist_of_ilists(a->next); return b; } } /* copy_glist_of_ilists */ /************* * * free_glist_of_ilists() * *************/ void free_glist_of_ilists(struct glist *p) { if (p != NULL) { free_glist_of_ilists(p->next); free_ilist_list(p->v); free_glist(p); } } /* free_glist_of_ilists */ otter-3.3f/source/resolve.c0100644000076400007640000011057607674160772015356 0ustar mccunemccune/* * resolve.c -- Resolution inference rules. * */ #include "header.h" /************* * * struct clause *build_hyper(clash,nuc_subst,nuc_lits,nuc, * giv_subst,giv_lits,giv_sat,nuc_pos,sat_indexes) * * This routine constructs a hyperresolvent or UR-resolvent. * *************/ static struct clause *build_hyper(struct clash_nd *cla, struct context *nuc_subst, struct literal *nuc_lits, struct clause *nuc, struct context *giv_subst, struct literal *giv_lits, struct clause *giv_sat, int nuc_pos, int sat_indexes) { struct clause *res, *sat; struct literal *lit, *new, *prev; struct clash_nd *c; struct ilist *ip1, *ip2, *ip3, *ip4; int i, j; int n = 0; res = get_clause(); ip1 = get_ilist(); /* to be filled in by caller with name of inference rule */ res->parents = ip1; /* If given clause is satellite, add number to parent list. */ ip3 = NULL; if (giv_sat) { ip2 = get_ilist(); ip2->i = giv_sat->id; if (Flags[ORDER_HISTORY].val && nuc_pos != 0) /* insert later in correct position */ ip3 = ip2; else { ip1->next = ip2; ip1 = ip2; } } ip2 = get_ilist(); ip2->i = nuc->id; ip1->next = ip2; lit = giv_lits; prev = NULL; while (lit != NULL) { new = get_literal(); new->container = res; if (prev == NULL) res->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, giv_subst); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ lit = lit->next_lit; } lit = nuc_lits; while (lit != NULL) { new = get_literal(); new->container = res; if (res->first_lit == NULL) res->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, nuc_subst); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ lit = lit->next_lit; } c = cla; i = 1; while (c != NULL) { if (ip3 && i == nuc_pos) { /* insert given clause (which is satellite) number here */ ip2->next = ip3; ip2 = ip3; } ip1 = get_ilist(); ip2->next = ip1; ip2 = ip1; if (c->evaluable) ip1->i = EVAL_RULE; else { sat = c->found_atom->occ.lit->container; lit = sat->first_lit; j = 0; while (lit != NULL) { j++; if (lit->atom != c->found_atom) { new = get_literal(); new->container = res; if (res->first_lit == NULL) res->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, c->subst); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* type of atom */ } else n = j; lit = lit->next_lit; } ip1->i = sat->id; if (sat_indexes) { ip1 = get_ilist(); ip4 = get_ilist(); ip1->next = ip4; ip2->next = ip1; ip1->i = LIST_RULE-1; ip4->i = n; ip2 = ip4; } } i++; c = c->next; } if (ip3 && i == nuc_pos) { /* insert given clause (which is satellite) number here */ ip2->next = ip3; ip2 = ip3; } if (ip3 && sat_indexes) { struct literal *l1, *l2; ip1 = get_ilist(); ip4 = get_ilist(); ip1->next = ip4; ip4->next = ip3->next; ip3->next = ip1; ip1->i = LIST_RULE-1; /* Need index of clashed literal in given clause (which is satellite). */ l1 = giv_sat->first_lit; l2 = giv_lits; i = 1; while (l2 && l1->sign == l2->sign && l1->atom == l2->atom) { l1 = l1->next_lit; l2 = l2->next_lit; i++; } ip4->i = i; } return(res); } /* build_hyper */ /************* * * maximal_lit() * * true iff no predicate symbol in clause has a higher lex val. * *************/ int maximal_lit(struct literal *l1) { struct literal *l2; int i1; i1 = sn_to_node(l1->atom->sym_num)->lex_val; for (l2 = l1->container->first_lit; l2; l2 = l2->next_lit) { if (l2 != l1 && l2->atom->varnum != ANSWER) { if (l2->sign > l1->sign) return(0); else if (l2->sign == l1->sign && sn_to_node(l2->atom->sym_num)->lex_val > i1) return(0); } } return(1); } /* maximal_lit */ /************* * * clash(c_start, nuc_subst, nuc_lits, nuc, giv_subst, giv_lits, giv_sat, * sat_proc, inf_clock, nuc_pos) * * This routine is called by both hyper and UR to clash away the * marked literals of the given nucleus, and append kept resolvents * to Sos. * * c_start: Start of the clash_structure list. There is one node * for each literal that is to be clashed away. * nuc_subst: Substitution for the nucleus. * nuc_lits: Non-clashed literals of the nucleus. * nuc: The nucleus. * giv_subst: If the given clause is a satellite, then this is its * substitution; else NULL. * giv_lits: If the given clause is a satellite, then these are its * non-clashed literals; else NULL. * giv_sat: If the given clause is a satellite, then this is it; * else NULL. * sat_proc: procedure to identify (other) satellites: `pos_clause' * for hyper, `unit_clause' for UR. * inf_clock: Clock (HYPER_TIME or UR_TIME) to be turned off during * call to `pre_process'. * nuc_pos: If not 0, giv cl is sat, and nuc_pos gives position * of "missing" clash node. To construct history. * ur_box: if not 0, UR is rule, and this is the index of the boxed literal. * *************/ static void clash(struct clash_nd *c_start, struct context *nuc_subst, struct literal *nuc_lits, struct clause *nuc, struct context *giv_subst, struct literal *giv_lits, struct clause *giv_sat, int (*sat_proc)(struct clause *c), int inf_clock, int nuc_pos, int ur_box) { struct clash_nd *c; struct clash_nd *c_end = NULL; int found, backup, fpa_depth, sign; struct term *f_atom, *nuc_atom_instance; struct trail *tr; struct clause *res; char *s; fpa_depth = Parms[FPA_LITERALS].val; c = NULL; backup = 0; while (1) { /* return from within loop */ if (backup == 0) { if (c_start == NULL || (c != NULL && c->next == NULL)) { /* clash is complete */ res = build_hyper(c_start, nuc_subst, nuc_lits, nuc, giv_subst, giv_lits, giv_sat, nuc_pos, (inf_clock == HYPER_TIME || inf_clock == NEG_HYPER_TIME) && (Flags[BUILD_PROOF_OBJECT_1].val || Flags[BUILD_PROOF_OBJECT_2].val)); if (inf_clock == HYPER_TIME) { Stats[HYPER_RES_GEN]++; res->parents->i = HYPER_RES_RULE; } else if (inf_clock == NEG_HYPER_TIME) { Stats[NEG_HYPER_RES_GEN]++; res->parents->i = NEG_HYPER_RES_RULE; } else { Stats[UR_RES_GEN]++; res->parents->i = UR_RES_RULE; if (Flags[BUILD_PROOF_OBJECT_1].val || Flags[BUILD_PROOF_OBJECT_2].val) { /* Insert position of NONclashed nuc literal into history. */ struct ilist *ip1, *ip2; ip1 = get_ilist(); ip2 = get_ilist(); ip1->next = ip2; ip2->next = res->parents->next->next; res->parents->next->next = ip1; ip1->i = LIST_RULE-1; ip2->i = ur_box; } } Stats[CL_GENERATED]++; if (heat_is_on()) { struct clause *giv; giv = (giv_sat ? giv_sat : nuc); res->heat_level = giv->heat_level + 1; } CLOCK_STOP(inf_clock); pre_process(res, 0, Sos); CLOCK_START(inf_clock); backup = 1; c_end = c; c = NULL; } else { if (c == NULL) /* just starting */ c = c_start; else c = c->next; nuc_atom_instance = apply(c->nuc_atom, nuc_subst); if (c->evaluable) { /* evaluate, but don't take any action yet */ nuc_atom_instance = convenient_demod(nuc_atom_instance); s = sn_to_str(nuc_atom_instance->sym_num); sign = c->nuc_atom->occ.lit->sign; if (sign) c->evaluation = str_ident(s, "$F"); else c->evaluation = str_ident(s,"$T"); c->already_evaluated = 0; } else { /* not evaluable */ c->u_tree = build_tree(nuc_atom_instance, UNIFY, fpa_depth, c->db); } zap_term(nuc_atom_instance); } } else { /* backup */ if (c_start == NULL || (c != NULL && c->prev == NULL)) /* done with this nucleus */ return; else { if (c == NULL) c = c_end; else c = c->prev; if (!c->evaluable) clear_subst_1(c->tr); backup = 0; } } if (backup == 0) { found = 0; if (c->evaluable) { if (c->already_evaluated || !c->evaluation) backup = 1; else /* Set flag and proceed. */ c->already_evaluated = 1; } else { f_atom = next_term(c->u_tree, 0); tr = NULL; while (f_atom && !found) { /* Sorry this test is so complicated. */ if ( /* Basic satellite test. */ (*sat_proc)(f_atom->occ.lit->container) && /* order_hyper & !UR -> maximal_lit */ (!Flags[ORDER_HYPER].val || inf_clock == UR_TIME || maximal_lit(f_atom->occ.lit)) && unify(c->nuc_atom,nuc_subst,f_atom,c->subst,&tr) ) { found = 1; } if (!found) f_atom = next_term(c->u_tree, 0); } if (found) { c->found_atom = f_atom; c->tr = tr; } else { backup = 1; } } } } /* while */ } /* clash */ /************* * * hyper_res(c) -- hyperresolution * * Append kept resolvents to Sos. Each kept * clause has already passed the pre_process filter (forward * subsumption, etc.), been integrated, and inserted into * appropriate indexes. * *************/ void hyper_res(struct clause *giv_cl) { struct literal *lit, *nuc_lits, *giv_lits, *l1, *l2, *l3; struct context *nuc_subst, *giv_subst; struct clash_nd *clash_list, *c1, *c2; struct clause *nuc; int m, i, nuc_pos; struct term *f_atom; struct fpa_tree *ut; struct trail *tr; CLOCK_START(HYPER_TIME); if (num_literals(giv_cl) == 0) { CLOCK_STOP(HYPER_TIME); return; } else if (!pos_clause(giv_cl)) { /* given clause is nucleus */ clash_list = NULL; nuc_lits = NULL; nuc_subst = get_context(); nuc_subst->multiplier = 0; m = 1; lit = giv_cl->first_lit; l2 = NULL; c2 = NULL; /* to quiet lint */ while (lit != NULL) { /* positive literal || answer literal */ if (lit->sign || lit->atom->varnum == ANSWER) { l1 = get_literal(); if (nuc_lits == NULL) nuc_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } else { /* put negative literal into clash structure */ c1 = get_clash_nd(); if (clash_list == NULL) clash_list = c1; else { c2->next = c1; c1->prev = c2; } c2 = c1; c2->db = Fpa_clash_pos_lits; c2->subst = get_context(); c2->subst->multiplier = m++; c2->nuc_atom = lit->atom; c2->evaluable = (lit->atom->varnum == EVALUABLE); } lit = lit->next_lit; } clash(clash_list, nuc_subst, nuc_lits, giv_cl, (struct context *) NULL, (struct literal *) NULL, (struct clause *) NULL, pos_clause, HYPER_TIME, 0, 0); c1 = clash_list; while (c1 != NULL) { free_context(c1->subst); c2 = c1; c1 = c1->next; free_clash_nd(c2); } l1 = nuc_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } free_context(nuc_subst); CLOCK_STOP(HYPER_TIME); return; } else { /* given clause is satellite (positive) */ giv_subst = get_context(); /* substitution for given satellite */ giv_subst->multiplier = 0; nuc_subst = get_context(); /* substitution for nucleus */ nuc_subst->multiplier = 1; l3 = giv_cl->first_lit; l2 = NULL; c2 = NULL; while (l3 != NULL) { /* for each literal in given satellite */ if (!Flags[ORDER_HYPER].val || maximal_lit(l3)) { /* collect non-clashed lits (including answers) of given sat*/ giv_lits = NULL; lit = giv_cl->first_lit; while (lit != NULL) { if (lit != l3) { l1 = get_literal(); if (giv_lits == NULL) giv_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } lit = lit->next_lit; } ut = build_tree(l3->atom, UNIFY, Parms[FPA_LITERALS].val, Fpa_clash_neg_lits); f_atom = next_term(ut, 0); while (f_atom != NULL) { /* for each potential nucleus */ tr = NULL; nuc = f_atom->occ.lit->container; if (!pos_clause(nuc) && unify(l3->atom, giv_subst, f_atom, nuc_subst, &tr)) { /* we have a nucleus */ /* there are three kinds of literal in the nucleus: */ /* 1. the clashed literal -> do nothing */ /* 2. positive or answer literals -> collect them */ /* 3. negative literals -> put into clash structure */ nuc_lits = NULL; clash_list = NULL; m = 2; /* multipliers for found sats start with 2 */ lit = nuc->first_lit; i = 1; /* find index of clausable lit that sat clahes with. */ nuc_pos = 0; while (lit != NULL) { if (lit->atom == f_atom) /* save position */ nuc_pos = i; /* positive || answer */ else if (lit->sign || lit->atom->varnum == ANSWER) { l1 = get_literal(); if (nuc_lits == NULL) nuc_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } else { /* put literal into clash structure */ i++; c1 = get_clash_nd(); if (clash_list == NULL) clash_list = c1; else { c2->next = c1; c1->prev = c2; } c2 = c1; c2->db = Fpa_clash_pos_lits; c2->subst = get_context(); c2->subst->multiplier = m++; c2->nuc_atom = lit->atom; c2->evaluable = (lit->atom->varnum == EVALUABLE); } lit = lit->next_lit; } clash(clash_list, nuc_subst, nuc_lits, nuc, giv_subst, giv_lits, giv_cl, pos_clause, HYPER_TIME, nuc_pos, 0); /* now deallocate the clash structure and literal nodes */ c1 = clash_list; while (c1 != NULL) { free_context(c1->subst); c2 = c1; c1 = c1->next; free_clash_nd(c2); } l1 = nuc_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } clear_subst_1(tr); } f_atom = next_term(ut, 0); } l1 = giv_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } } l3 = l3->next_lit; } free_context(giv_subst); free_context(nuc_subst); CLOCK_STOP(HYPER_TIME); return; } } /* hyper_res */ /************* * * neg_hyper_res(c) -- negative hyperresolution * * Append kept resolvents to Sos. Each kept * clause has already passed the pre_process filter (forward * subsumption, etc.), been integrated, and inserted into * appropriate indexes. * *************/ void neg_hyper_res(struct clause *giv_cl) { struct literal *lit, *nuc_lits, *giv_lits, *l1, *l2, *l3; struct context *nuc_subst, *giv_subst; struct clash_nd *clash_list, *c1, *c2; struct clause *nuc; int m, i, nuc_pos; struct term *f_atom; struct fpa_tree *ut; struct trail *tr; /* This code should have been combined with the pos hyper code. */ CLOCK_START(NEG_HYPER_TIME); if (num_literals(giv_cl) == 0) { CLOCK_STOP(NEG_HYPER_TIME); return; } else if (!neg_clause(giv_cl)) { /* given clause is nucleus */ clash_list = NULL; nuc_lits = NULL; nuc_subst = get_context(); nuc_subst->multiplier = 0; m = 1; lit = giv_cl->first_lit; l2 = NULL; c2 = NULL; /* to quiet lint */ while (lit != NULL) { /* negative literal || answer literal */ if (!lit->sign || lit->atom->varnum == ANSWER) { l1 = get_literal(); if (nuc_lits == NULL) nuc_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } else { /* put positive literal into clash structure */ c1 = get_clash_nd(); if (clash_list == NULL) clash_list = c1; else { c2->next = c1; c1->prev = c2; } c2 = c1; c2->db = Fpa_clash_neg_lits; c2->subst = get_context(); c2->subst->multiplier = m++; c2->nuc_atom = lit->atom; c2->evaluable = (lit->atom->varnum == EVALUABLE); } lit = lit->next_lit; } clash(clash_list, nuc_subst, nuc_lits, giv_cl, (struct context *) NULL, (struct literal *) NULL, (struct clause *) NULL, neg_clause, NEG_HYPER_TIME, 0, 0); c1 = clash_list; while (c1 != NULL) { free_context(c1->subst); c2 = c1; c1 = c1->next; free_clash_nd(c2); } l1 = nuc_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } free_context(nuc_subst); CLOCK_STOP(NEG_HYPER_TIME); return; } else { /* given clause is satellite (negative) */ giv_subst = get_context(); /* substitution for given satellite */ giv_subst->multiplier = 0; nuc_subst = get_context(); /* substitution for nucleus */ nuc_subst->multiplier = 1; l3 = giv_cl->first_lit; l2 = NULL; c2 = NULL; while (l3 != NULL) { /* for each literal in given satellite */ if (!Flags[ORDER_HYPER].val || maximal_lit(l3)) { /* collect non-clashed lits (including answers) of given sat*/ giv_lits = NULL; lit = giv_cl->first_lit; while (lit != NULL) { if (lit != l3) { l1 = get_literal(); if (giv_lits == NULL) giv_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } lit = lit->next_lit; } ut = build_tree(l3->atom, UNIFY, Parms[FPA_LITERALS].val, Fpa_clash_pos_lits); f_atom = next_term(ut, 0); while (f_atom != NULL) { /* for each potential nucleus */ tr = NULL; nuc = f_atom->occ.lit->container; if (!neg_clause(nuc) && unify(l3->atom, giv_subst, f_atom, nuc_subst, &tr)) { /* we have a nucleus */ /* there are three kinds of literal in the nucleus: */ /* 1. the clashed literal -> do nothing */ /* 2. negative or answer literals -> collect them */ /* 3. positive literals -> put into clash structure */ nuc_lits = NULL; clash_list = NULL; m = 2; /* multipliers for found sats start with 2 */ lit = nuc->first_lit; i = 1; /* find index of clahsable lit that sat clashes with. */ nuc_pos = 0; while (lit != NULL) { if (lit->atom == f_atom) /* save position */ nuc_pos = i; /* negative || answer */ else if (!lit->sign || lit->atom->varnum == ANSWER) { l1 = get_literal(); if (nuc_lits == NULL) nuc_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } else { /* put literal into clash structure */ i++; c1 = get_clash_nd(); if (clash_list == NULL) clash_list = c1; else { c2->next = c1; c1->prev = c2; } c2 = c1; c2->db = Fpa_clash_neg_lits; c2->subst = get_context(); c2->subst->multiplier = m++; c2->nuc_atom = lit->atom; c2->evaluable = (lit->atom->varnum == EVALUABLE); } lit = lit->next_lit; } clash(clash_list, nuc_subst, nuc_lits, nuc, giv_subst, giv_lits, giv_cl, neg_clause, NEG_HYPER_TIME, nuc_pos, 0); /* now deallocate the clash structure and literal nodes */ c1 = clash_list; while (c1 != NULL) { free_context(c1->subst); c2 = c1; c1 = c1->next; free_clash_nd(c2); } l1 = nuc_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } clear_subst_1(tr); } f_atom = next_term(ut, 0); } l1 = giv_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } } l3 = l3->next_lit; } free_context(giv_subst); free_context(nuc_subst); CLOCK_STOP(NEG_HYPER_TIME); return; } } /* neg_hyper_res */ /************* * * ur_res(c) -- unit resulting (UR) resolution * * Append kept resolvents to Sos. Each kept * clause has already passed the pre_process filter (forward * subsumption, etc.), been integrated, and inserted into * appropriate indexes. * *************/ void ur_res(struct clause *giv_cl) { struct literal *lit, *nuc_lits, *giv_lits; struct literal *l1, *l2, *l3, *box, *f_lit; struct context *nuc_subst, *giv_subst; struct clash_nd *clash_list, *c1, *c2; struct clause *nuc; int m, i, nlits, j, nuc_pos; struct term *f_atom; struct fpa_tree *ut; struct trail *tr; CLOCK_START(UR_TIME); nlits = num_literals(giv_cl); if (nlits == 0) { CLOCK_STOP(UR_TIME); return; } if (nlits > 1) { /* given clause is nucleus (non-unit) */ clash_list = NULL; nuc_subst = get_context(); nuc_subst->multiplier = 0; m = 1; nuc_lits = get_literal(); /* for boxed literal */ l2 = nuc_lits; lit = giv_cl->first_lit; while (lit != NULL) { if (lit->atom->varnum == ANSWER) { /* if answer literal */ l1 = get_literal(); l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } lit = lit->next_lit; } c2 = NULL; /* to quiet lint */ for (i = 1; i < nlits; i++) { /* set up nlits-1 empty clash nodes */ c1 = get_clash_nd(); if (clash_list == NULL) clash_list = c1; else { c2->next = c1; c1->prev = c2; } c2 = c1; c2->subst = get_context(); c2->subst->multiplier = m++; } box = giv_cl->first_lit; if (Flags[UR_LAST].val) { /* boxed literal must be the last literal */ while (box->next_lit) box = box->next_lit; } i = 1; while (box != NULL) { if (box->atom->varnum != ANSWER) { /* if not answer literal */ c1 = clash_list; nuc_lits->sign = box->sign; nuc_lits->atom = box->atom; lit = giv_cl->first_lit; while (lit != NULL) { /* if not boxed or answer literal */ if (lit != box && lit->atom->varnum != ANSWER) { c1->nuc_atom = lit->atom; c1->db = (lit->sign ? Fpa_clash_neg_lits : Fpa_clash_pos_lits); c1 = c1->next; } lit = lit->next_lit; } if (c1 != NULL) { abend("ur_res: too many clash nodes (nuc)."); } clash(clash_list, nuc_subst, nuc_lits, giv_cl, (struct context *) NULL, (struct literal *) NULL, (struct clause *) NULL, unit_clause, UR_TIME, 0, i); } box = box->next_lit; i++; } c1 = clash_list; while (c1 != NULL) { free_context(c1->subst); c2 = c1; c1 = c1->next; free_clash_nd(c2); } l1 = nuc_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } free_context(nuc_subst); CLOCK_STOP(UR_TIME); return; } else { /* given clause is satellite (unit) */ giv_subst = get_context(); /* substitution for given satellite */ giv_subst->multiplier = 0; nuc_subst = get_context(); /* substitution for nucleus */ nuc_subst->multiplier = 1; /* collect any answer literals from given satellite */ /* and get clashable literal (l3) */ giv_lits = NULL; lit = giv_cl->first_lit; l2 = NULL; l3 = NULL; c2 = NULL; while (lit != NULL) { if (lit->atom->varnum != ANSWER) /* if not answer lit */ l3 = lit; /* the only non-answer literal */ else { l1 = get_literal(); if (giv_lits == NULL) giv_lits = l1; else l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } lit = lit->next_lit; } ut = build_tree(l3->atom, UNIFY, Parms[FPA_LITERALS].val, l3->sign ? Fpa_clash_neg_lits : Fpa_clash_pos_lits); f_atom = next_term(ut, 0); while (f_atom != NULL) { /* for each potential nucleus */ tr = NULL; f_lit = f_atom->occ.lit; nuc = f_lit->container; nlits = num_literals(nuc); if (nlits > 1 && (!Flags[UR_LAST].val || f_lit->next_lit) && unify(l3->atom, giv_subst, f_atom, nuc_subst, &tr)) { /* we have a nucleus */ m = 2; nuc_lits = get_literal(); /* for boxed literal */ /* now append any answer literals to nuc_lits */ l2 = nuc_lits; lit = nuc->first_lit; while (lit != NULL) { if (lit->atom->varnum == ANSWER) { /* if answer literal */ l1 = get_literal(); l2->next_lit = l1; l2 = l1; l1->sign = lit->sign; l1->atom = lit->atom; } lit = lit->next_lit; } /* build clash structure for this nucleus */ clash_list = NULL; for (i = 2; i < nlits; i++) { /* nlits-2 empty clash nodes */ c1 = get_clash_nd(); if (clash_list == NULL) clash_list = c1; else { c2->next = c1; c1->prev = c2; } c2 = c1; c2->subst = get_context(); c2->subst->multiplier = m++; } box = nuc->first_lit; if (Flags[UR_LAST].val) { /* boxed literal must be the last literal */ while (box->next_lit) box = box->next_lit; } i = 1; while (box != NULL) { /* if not clashed or answer literal */ if (box != f_lit && box->atom->varnum != ANSWER) { c1 = clash_list; nuc_lits->sign = box->sign; nuc_lits->atom = box->atom; lit = nuc->first_lit; j = 1; nuc_pos = 0; while (lit != NULL) { /* if not boxed or clashed or answer literal */ if (lit != box && lit != f_lit && lit->atom->varnum != ANSWER) { c1->nuc_atom = lit->atom; c1->db = (lit->sign ? Fpa_clash_neg_lits : Fpa_clash_pos_lits); c1 = c1->next; j++; } if (lit == f_lit) nuc_pos = j; /* For ordered history option */ lit = lit->next_lit; } if ( c1 != NULL) { abend("ur_res: too many clash nodes (sat)."); } clash(clash_list, nuc_subst, nuc_lits, nuc, giv_subst, giv_lits, giv_cl, unit_clause, UR_TIME, nuc_pos, i); } box = box->next_lit; i++; } c1 = clash_list; while (c1 != NULL) { free_context(c1->subst); c2 = c1; c1 = c1->next; free_clash_nd(c2); } l1 = nuc_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } clear_subst_1(tr); } f_atom = next_term(ut, 0); } /* free answer literals from given satellite */ l1 = giv_lits; while (l1 != NULL) { l2 = l1; l1 = l1->next_lit; free_literal(l2); } free_context(giv_subst); free_context(nuc_subst); CLOCK_STOP(UR_TIME); return; } } /* ur_res */ /************* * * int one_unary_answer(c) * *************/ int one_unary_answer(struct clause *c) { struct literal *l; for (l = c->first_lit; l != NULL && l->atom->varnum != ANSWER; l = l->next_lit); /* empty body */ if (l == NULL) return(0); else if (sn_to_arity(l->atom->sym_num) != 1) return(0); else { for (l = l->next_lit; l != NULL && l->atom->varnum != ANSWER; l = l->next_lit); /* empty body */ return(l == NULL); } } /* one_unary_answer */ /************* * * struct term *build_term(sn, arg1, arg2, arg3) * *************/ struct term *build_term(int sn, struct term *arg1, struct term *arg2, struct term *arg3) { int arity; struct rel *r1, *r2, *r3; struct term *t; arity = sn_to_arity(sn); if (arity != 3) { abend("build_term, bad arity."); } t = get_term(); t->sym_num = sn; t->type = COMPLEX; r1 = get_rel(); r2 = get_rel(); r3 = get_rel(); t->farg = r1; r1->narg = r2; r2->narg = r3; r1->argval = arg1; r2->argval = arg2; r3->argval = arg3; return(t); } /* build_term */ /************* * * void combine_answers(res, a1, s1, a2, s2) * *************/ void combine_answers(struct clause *res, struct term *a1, struct context *s1, struct term *a2, struct context *s2) { struct clause *par1, *par2; int condition_par1; struct term *condition, *then_part, *else_part; struct literal *lit1, *lit2, *prev_lit; par1 = a1->occ.lit->container; par2 = a2->occ.lit->container; if (one_unary_answer(par1) && one_unary_answer(par2)) { condition_par1 = a2->occ.lit->sign; if (condition_par1) condition = apply(a1, s1); else condition = apply(a2, s2); for (lit1 = res->first_lit, prev_lit = NULL; lit1->atom->varnum != ANSWER; prev_lit = lit1, lit1 = lit1->next_lit); /* empty body */ for (lit2 = lit1->next_lit; lit2->atom->varnum != ANSWER; lit2 = lit2->next_lit); /* empty body */ if (condition_par1) { then_part = lit1->atom->farg->argval; else_part = lit2->atom->farg->argval; } else { then_part = lit2->atom->farg->argval; else_part = lit1->atom->farg->argval; } if (prev_lit == NULL) res->first_lit = lit1->next_lit; else prev_lit->next_lit = lit1->next_lit; free_rel(lit1->atom->farg); free_term(lit1->atom); free_literal(lit1); lit2->atom->farg->argval = build_term(str_to_sn("if",3),condition,then_part,else_part); } } /* combine_answers */ /************* * * struct clause *build_bin_res(a1, s1, a2, s2) * * Build a binary resolvent. a1 and a2 are the clashed literals, * and s1 and s2 are the respective unifying substitutions. * *************/ struct clause *build_bin_res(struct term *a1, struct context *s1, struct term *a2, struct context *s2) { struct clause *res; struct literal *lit, *new, *prev; struct ilist *ip0, *ip1, *ip2; res = get_clause(); prev = NULL; lit = a1->occ.lit->container->first_lit; while (lit != NULL) { if (lit->atom != a1) { new = get_literal(); new->container = res; if (prev == NULL) res->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, s1); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ } lit = lit->next_lit; } lit = a2->occ.lit->container->first_lit; while (lit != NULL) { if (lit->atom != a2) { new = get_literal(); new->container = res; if (res->first_lit == NULL) res->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, s2); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ } lit = lit->next_lit; } ip0 = get_ilist(); ip1 = get_ilist(); ip2 = get_ilist(); ip0->i = BINARY_RES_RULE; ip1->i = a1->occ.lit->container->id; ip2->i = a2->occ.lit->container->id; ip0->next = ip1; ip1->next = ip2; res->parents = ip0; if (Flags[DETAILED_HISTORY].val) { ip0 = get_ilist(); ip1 = get_ilist(); ip0->next = ip1; ip1->next = res->parents->next->next->next; res->parents->next->next->next = ip0; ip0->i = LIST_RULE - 1; ip1->i = literal_number(a2->occ.lit); ip0 = get_ilist(); ip1 = get_ilist(); ip0->next = ip1; ip1->next = res->parents->next->next; res->parents->next->next = ip0; ip0->i = LIST_RULE - 1; ip1->i = literal_number(a1->occ.lit); } if (Flags[PROG_SYNTHESIS].val) combine_answers(res, a1, s1, a2, s2); return(res); } /* build_bin_res */ /************* * * struct clause *apply_clause(c, s) * *************/ struct clause *apply_clause(struct clause *c, struct context *s) { struct clause *d; struct literal *lit, *new, *prev; d = get_clause(); prev = NULL; for (lit = c->first_lit; lit; lit = lit->next_lit) { new = get_literal(); new->container = d; if (!prev) d->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, s); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ } return(d); } /* apply_clause */ /************* * * bin_res(giv_cl) -- binary resolution * *************/ void bin_res(struct clause *giv_cl) { struct literal *g_lit; struct term *g_atom, *f_atom; struct context *gs, *fs; struct trail *tr; struct fpa_tree *ut; struct fpa_index *db; struct clause *resolvent; int given_unit = unit_clause(giv_cl); CLOCK_START(BINARY_TIME); gs = get_context(); gs->multiplier = 0; fs = get_context(); fs->multiplier = 1; g_lit = giv_cl->first_lit; while (g_lit != NULL) { g_atom = g_lit->atom; if (g_atom->varnum != ANSWER) { /* if not answer literal */ if (g_lit->sign) db = Fpa_clash_neg_lits; else db = Fpa_clash_pos_lits; ut = build_tree(g_lit->atom, UNIFY, Parms[FPA_LITERALS].val, db); f_atom = next_term(ut, 0); while (f_atom != NULL) { tr = NULL; if (!Flags[UNIT_RES].val || given_unit || unit_clause(f_atom->occ.lit->container)) { if (unify(g_atom, gs, f_atom, fs, &tr)) { resolvent = build_bin_res(g_atom, gs, f_atom, fs); clear_subst_1(tr); Stats[CL_GENERATED]++; Stats[BINARY_RES_GEN]++; if (heat_is_on()) resolvent->heat_level = giv_cl->heat_level + 1; CLOCK_STOP(BINARY_TIME); pre_process(resolvent, 0, Sos); CLOCK_START(BINARY_TIME); } } f_atom = next_term(ut, 0); } } g_lit = g_lit->next_lit; } free_context(gs); free_context(fs); CLOCK_STOP(BINARY_TIME); } /* bin_res */ /************* * * first_or_next_factor(c, l1p, l2p) * * Generate the first (*l1p == NULL) or next (*l1p and *l2p are the * previously factored literals) factor from c. * *************/ struct clause *first_or_next_factor(struct clause *c, struct literal **l1p, struct literal **l2p) { int factored = 0; struct literal *l1 = *l1p; struct literal *l2 = *l2p; struct context *subst = get_context(); struct trail *tr; struct clause *factor; struct literal *l3, *l4, *l5; if (!l1) l1 = l2 = c->first_lit; while (l1 && !factored) { l2 = l2->next_lit; while (l2 && !factored) { tr = NULL; if (l1->sign == l2->sign && unify(l1->atom, subst, l2->atom, subst, &tr)) { factored = 1; } else l2 = l2->next_lit; } if (!factored) l1 = l2 = l1->next_lit; } if (factored) { subst->multiplier = 0; factor = get_clause(); /* do not fill in parents */ l3 = NULL; l5 = c->first_lit; while (l5 != NULL) { /* l2 is the literal to exclude */ if (l5 != l2) { l4 = get_literal(); l4->sign = l5->sign; l4->container = factor; if (l3 == NULL) factor->first_lit = l4; else l3->next_lit = l4; l4->atom = apply(l5->atom, subst); /* Following is for factor_simp; shouldn't hurt otherwise. */ if (TP_BIT(l5->atom->bits, ORIENTED_EQ_BIT)) SET_BIT(l4->atom->bits, ORIENTED_EQ_BIT); l4->atom->occ.lit = l4; l4->atom->varnum = l5->atom->varnum; /* copy type */ l3 = l4; } l5 = l5->next_lit; } clear_subst_1(tr); *l2p = l2; *l1p = l1; } else factor = NULL; free_context(subst); return(factor); } /* first_or_next_factor */ /************* * * all_factors(c, lst) -- generate and pre_process all binary factors c. * * Indirect recursive calls will get factors of factors, etc. * *************/ void all_factors(struct clause *c, struct list *lst) { struct literal *l1, *l2; struct clause *factor; struct ilist *ip0, *ip1; l1 = NULL; factor = first_or_next_factor(c, &l1, &l2); while (factor) { ip0 = get_ilist(); ip0->i = FACTOR_RULE; ip1 = get_ilist(); ip1->i = c->id; factor->parents = ip0; ip0->next = ip1; if (Flags[DETAILED_HISTORY].val) { /* append list of indexes of factored literals */ struct ilist *ip3, *ip4, *ip5; ip3 = get_ilist(); ip3->i = LIST_RULE-2; ip4 = get_ilist(); ip4->i = literal_number(l1); ip5 = get_ilist(); ip5->i = literal_number(l2); ip1->next = ip3; ip3->next = ip4; ip4->next = ip5; } Stats[CL_GENERATED]++; Stats[FACTOR_GEN]++; CLOCK_STOP(FACTOR_TIME); CLOCK_STOP(POST_PROC_TIME); pre_process(factor, 0, lst); CLOCK_START(POST_PROC_TIME); CLOCK_START(FACTOR_TIME); factor = first_or_next_factor(c, &l1, &l2); } } /* all_factors */ /************* * * factor_simpify(c) * * Return the number of literals removed. * *************/ int factor_simplify(struct clause *c) { struct literal *l1, *l2; struct clause *f; struct ilist *p0, *p1; int n = 0; l1 = NULL; f = first_or_next_factor(c, &l1, &l2); while (f) { if (subsume(f, c)) { n++; /* Swap list of literals. */ l1 = c->first_lit; c->first_lit = f->first_lit; f->first_lit = l1; for (l1 = c->first_lit; l1; l1 = l1->next_lit) l1->container = c; for (l1 = f->first_lit; l1; l1 = l1->next_lit) l1->container = f; cl_del_non(f); if (Flags[DETAILED_HISTORY].val) { for (p1 = c->parents, p0 = NULL; p1; p1 = p1->next) p0 = p1; p1 = get_ilist(); p1->i = FACTOR_SIMP_RULE; if (p0) p0->next = p1; else c->parents = p1; } l1 = NULL; f = first_or_next_factor(c, &l1, &l2); } else { cl_del_non(f); f = first_or_next_factor(c, &l1, &l2); } } return(n); } /* factor_simplify */ otter-3.3f/source/b2.outb0100644000076400007640000307567010012004731014705 0ustar mccunemccune----- Otter 3.3x1, 9 Feb 2004 ----- The process was started by mccune on theorem.mcs.anl.gov, Mon Feb 9 16:28:54 2004 The command was "./otter". The process ID is 32052. lex([h(x,x),f(x,x),g(x)]). assign(bsub_hint_add_wt,-1024). set(keep_hint_subsumers). set(print_proof_as_hints). dependent: set(build_proof_object_1). dependent: set(order_history). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(back_sub). assign(max_mem,750000). assign(max_weight,50). assign(pick_given_ratio,4). set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(input_sos_first). list(usable). 0 [] x=x. end_of_list. list(sos). 0 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("33"). 0 [] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y # label("35"). 0 [] f(f(a,b),c)!=f(a,f(b,c)). end_of_list. list(hints2). 1 [] g(f(f(f(x,x),y),f(g(f(x,y)),g(f(z,x)))))=z # label("1"). 2 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(z),x))))=z # label("2"). 3 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y # label("3"). 4 [] f(f(g(f(x,g(y))),z),f(x,f(g(f(z,x)),x)))=y # label("4"). 5 [] f(g(f(x,y)),g(f(g(f(f(f(x,x),y),z)),x)))=z # label("5"). 6 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z # label("6"). 7 [] f(f(g(x),y),g(f(f(z,g(f(x,f(z,z)))),y)))=z # label("7"). 8 [] g(f(f(x,y),g(f(f(z,f(x,f(g(z),z))),y))))=z # label("8"). 9 [] f(f(g(x),y),g(f(y,f(g(f(f(x,z),y)),y))))=z # label("9"). 10 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("10"). 11 [] f(x,g(f(g(f(f(f(y,g(f(y,x))),y),z)),y)))=z # label("11"). 12 [] g(f(x,f(g(f(f(f(x,y),f(x,g(z))),z)),x)))=y # label("12"). 13 [] f(x,f(g(f(f(f(x,g(y)),f(x,g(z))),z)),x))=y # label("13"). 14 [] g(f(x,f(g(f(f(y,f(f(g(y),x),z)),x)),x)))=z # label("14"). 15 [] f(x,f(g(f(f(y,f(f(g(y),x),g(z))),x)),x))=z # label("15"). 16 [] f(x,f(f(g(f(g(f(y,x)),x)),g(f(z,x))),z))=y # label("16"). 17 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y # label("17"). 18 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y # label("18"). 19 [] f(x,g(f(f(f(y,g(f(y,y))),f(x,g(z))),z)))=y # label("19"). 20 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z # label("20"). 21 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z # label("21"). 22 [] g(f(x,g(f(f(y,g(f(z,x))),f(z,f(x,x))))))=y # label("22"). 23 [] f(x,g(f(f(g(y),g(f(z,x))),f(z,f(x,x)))))=y # label("23"). 24 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("24"). 25 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),y)),y)))=z # label("25"). 26 [] f(x,f(f(g(x),y),g(f(y,f(g(f(z,y)),y)))))=z # label("26"). 27 [] g(f(x,g(f(f(y,z),f(x,f(g(f(z,x)),x))))))=y # label("27"). 28 [] f(x,g(f(f(g(y),z),f(x,f(g(f(z,x)),x)))))=y # label("28"). 29 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("29"). 30 [] f(x,g(f(x,f(g(f(f(y,f(x,g(z))),z)),x))))=y # label("30"). 31 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("31"). 32 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z # label("32"). 33 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("33"). 34 [] g(f(x,f(y,f(f(g(f(x,y)),z),g(f(y,z))))))=y # label("34"). 35 [] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y # label("35"). 36 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z # label("36"). end_of_list. list(hints2). 37 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y # label("Hint 1(3)"). 38 [] f(f(g(f(x,g(y))),z),f(x,f(g(f(z,x)),x)))=y # label("Hint 2(4)"). 39 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z # label("Hint 3(6)"). 40 [] g(f(f(x,y),g(f(f(z,f(x,f(g(z),z))),y))))=z # label("Hint 4(8)"). 41 [] f(f(g(x),y),g(f(y,f(g(f(f(x,z),y)),y))))=z # label("Hint 5(9)"). 42 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 6(10)"). 43 [] g(f(x,f(g(f(f(f(x,y),f(x,g(z))),z)),x)))=y # label("Hint 7(12)"). 44 [] f(x,f(g(f(f(f(x,g(y)),f(x,g(z))),z)),x))=y # label("Hint 8(13)"). 45 [] f(x,g(f(f(f(y,g(f(y,y))),f(x,g(z))),z)))=y # label("Hint 9(19)"). 46 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z # label("Hint 10(21)"). 47 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("Hint 11(24)"). 48 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),y)),y)))=z # label("Hint 12(25)"). 49 [] f(x,f(f(g(x),y),g(f(y,f(g(f(z,y)),y)))))=z # label("Hint 13(26)"). 50 [] f(x,g(f(f(g(y),z),f(x,f(g(f(z,x)),x)))))=y # label("Hint 14(28)"). 51 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("Hint 15(29)"). 52 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 16(31)"). 53 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z # label("Hint 17(32)"). 54 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 18(33)"). 55 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 19(37)"). 56 [] f(f(g(f(x,y)),x),y)=f(x,g(x)) # label("Hint 20(499)"). 57 [] f(f(x,y),f(f(z,f(g(f(f(x,y),z)),u)),f(x,y)))=f(f(u,f(x,f(g(u),u))),y) # label("Hint 21(1288)"). 58 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(y,g(f(y,f(f(z,u),y)))) # label("Hint 22(1733)"). 59 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,g(z))))))))=f(g(f(z,y)),z) # label("Hint 23(4007)"). 60 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(x,g(z))),z))))=f(g(f(y,x)),y) # label("Hint 24(4043)"). 61 [] g(f(x,g(x)))=f(x,f(g(f(x,x)),x)) # label("Hint 25(4065)"). 62 [] f(g(f(x,g(x))),x)=x # label("Hint 26(4107)"). 63 [] f(x,f(f(g(x),y),g(f(y,f(g(y),y)))))=g(f(y,g(y))) # label("Hint 27(4145)"). 64 [] g(f(x,g(f(x,f(f(g(x),x),x)))))=x # label("Hint 28(4183)"). 65 [] f(x,g(f(x,g(x))))=x # label("Hint 29(4207)"). 66 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 30(4702)"). 67 [] g(f(x,g(f(x,x))))=x # label("Hint 31(4704)"). 68 [] f(f(x,y),f(x,f(g(f(y,x)),x)))=f(x,x) # label("Hint 32(4909)"). 69 [] f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y)))=f(z,g(f(z,z))) # label("Hint 33(4913)"). 70 [] f(x,g(f(f(y,f(x,g(z))),z)))=g(y) # label("Hint 34(5001)"). 71 [] f(x,f(g(f(y,x)),y))=f(g(y),y) # label("Hint 35(5366)"). 72 [] f(x,f(f(g(x),x),x))=f(x,x) # label("Hint 36(5388)"). 73 [] f(f(g(x),x),x)=x # label("Hint 37(5434)"). 74 [] g(f(x,g(x)))=f(g(x),x) # label("Hint 38(5448)"). 75 [] f(x,f(g(x),x))=x # label("Hint 39(5535)"). 76 [] f(f(g(x),x),f(g(x),x))=f(x,g(x)) # label("Hint 40(5805)"). 77 [] f(g(x),x)=f(x,g(x)) # label("Hint 41(6060)"). 78 [] f(x,f(x,g(x)))=x # label("Hint 42(6301)"). 79 [] f(f(x,g(x)),x)=x # label("Hint 43(6307)"). 80 [] f(g(f(x,x)),x)=g(x) # label("Hint 44(6351)"). 81 [] f(x,g(f(g(x),x)))=x # label("Hint 45(6461)"). 82 [] f(g(f(g(x),x)),x)=x # label("Hint 46(6463)"). 83 [] g(g(x))=x # label("Hint 47(6765)"). 84 [] f(x,g(f(x,x)))=g(x) # label("Hint 48(6797)"). 85 [] f(f(x,x),g(x))=x # label("Hint 49(7040)"). 86 [] f(f(g(x),g(x)),x)=g(x) # label("Hint 50(7098)"). 87 [] f(x,f(f(g(x),y),y))=f(y,y) # label("Hint 51(7415)"). 88 [] f(f(x,g(y)),y)=x # label("Hint 52(9630)"). 89 [] f(f(g(x),x),y)=y # label("Hint 53(9805)"). 90 [] f(x,f(g(y),y))=x # label("Hint 54(10003)"). 91 [] f(x,f(g(x),y))=y # label("Hint 55(10023)"). 92 [] g(f(x,g(f(x,f(y,x)))))=f(x,y) # label("Hint 56(10060)"). 93 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 57(10097)"). end_of_list. list(hints2). 94 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y # label("Hint 1(1)"). 95 [] f(f(g(f(x,g(y))),z),f(x,f(g(f(z,x)),x)))=y # label("Hint 2(2)"). 96 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z # label("Hint 3(3)"). 97 [] g(f(f(x,y),g(f(f(z,f(x,f(g(z),z))),y))))=z # label("Hint 4(4)"). 98 [] f(f(g(x),y),g(f(y,f(g(f(f(x,z),y)),y))))=z # label("Hint 5(5)"). 99 [] g(f(x,f(g(f(f(f(x,y),f(x,g(z))),z)),x)))=y # label("Hint 6(6)"). 100 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y # label("Hint 7(9)"). 101 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y # label("Hint 8(10)"). 102 [] f(x,g(f(f(f(y,g(f(y,y))),f(x,g(z))),z)))=y # label("Hint 9(11)"). 103 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("Hint 10(14)"). 104 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 11(15)"). 105 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z # label("Hint 12(16)"). 106 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 13(17)"). 107 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 14(18)"). 108 [] f(f(g(f(g(x),y)),z),f(g(f(f(z,g(u)),z)),z))=f(g(f(f(y,g(f(x,u))),y)),y) # label("Hint 15(88)"). 109 [] f(g(f(f(x,g(f(f(y,g(z)),z))),x)),x)=f(y,f(g(f(x,y)),y)) # label("Hint 16(90)"). 110 [] f(f(g(f(x,y)),z),f(g(f(f(z,u),z)),z))=g(f(f(u,f(x,f(g(u),u))),y)) # label("Hint 17(116)"). 111 [] f(f(g(f(x,y)),x),y)=f(x,g(x)) # label("Hint 18(172)"). 112 [] g(f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z)))))=g(f(z,f(g(f(f(y,u),z)),z))) # label("Hint 19(558)"). 113 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 20(828)"). 114 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(x,g(z))),z))))=f(g(f(y,x)),y) # label("Hint 21(936)"). 115 [] g(f(x,g(x)))=f(x,f(g(f(x,x)),x)) # label("Hint 22(976)"). 116 [] f(g(f(x,g(x))),x)=x # label("Hint 23(980)"). 117 [] f(x,g(f(x,g(x))))=x # label("Hint 24(1042)"). 118 [] g(f(x,g(f(x,f(f(g(x),x),x)))))=x # label("Hint 25(1066)"). 119 [] f(f(g(x),x),g(f(x,g(x))))=f(x,g(x)) # label("Hint 26(1082)"). 120 [] f(x,f(f(g(f(x,x)),f(x,g(y))),y))=f(x,g(x)) # label("Hint 27(1122)"). 121 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 28(1150)"). 122 [] g(f(x,g(f(x,x))))=x # label("Hint 29(1152)"). 123 [] g(f(x,f(f(g(x),f(x,g(y))),y)))=f(g(f(x,x)),x) # label("Hint 30(1192)"). 124 [] f(f(g(x),y),f(g(f(f(y,x),y)),y))=g(f(x,x)) # label("Hint 31(1240)"). 125 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))) # label("Hint 32(1250)"). 126 [] f(f(x,y),f(x,f(g(f(y,x)),x)))=f(x,x) # label("Hint 33(1256)"). 127 [] f(x,g(f(f(y,f(x,g(z))),z)))=g(y) # label("Hint 34(1290)"). 128 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)) # label("Hint 35(1314)"). 129 [] f(x,f(f(g(x),x),x))=f(x,x) # label("Hint 36(1350)"). 130 [] f(f(g(x),x),x)=x # label("Hint 37(1392)"). 131 [] g(f(x,f(g(f(f(x,x),x)),x)))=x # label("Hint 38(1401)"). 132 [] g(f(x,g(x)))=f(g(x),x) # label("Hint 39(1408)"). 133 [] f(x,f(g(x),x))=x # label("Hint 40(1456)"). 134 [] f(f(g(x),x),f(g(x),x))=f(x,g(x)) # label("Hint 41(1606)"). 135 [] g(f(f(x,y),g(f(f(x,x),y))))=x # label("Hint 42(1614)"). 136 [] f(g(g(x)),g(f(g(x),x)))=g(g(x)) # label("Hint 43(1676)"). 137 [] g(f(g(f(x,g(y))),f(x,g(y))))=f(x,g(f(f(x,g(y)),y))) # label("Hint 44(1680)"). 138 [] f(g(f(x,g(x))),f(x,x))=f(x,x) # label("Hint 45(1827)"). 139 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 46(2085)"). 140 [] f(g(f(x,y)),g(f(x,g(f(x,f(y,x))))))=f(g(y),y) # label("Hint 47(2159)"). 141 [] f(g(f(f(x,x),x)),x)=g(f(x,x)) # label("Hint 48(2377)"). 142 [] g(f(x,g(f(f(x,g(x)),x))))=f(g(x),x) # label("Hint 49(2393)"). 143 [] f(f(x,y),g(f(f(x,x),y)))=f(x,g(f(x,x))) # label("Hint 50(2477)"). 144 [] f(g(g(f(x,g(x)))),f(x,g(f(f(x,g(x)),x))))=g(g(f(x,g(x)))) # label("Hint 51(2509)"). 145 [] g(g(f(x,g(x))))=g(f(g(x),x)) # label("Hint 52(2523)"). 146 [] f(g(g(g(x))),g(g(x)))=g(f(g(x),x)) # label("Hint 53(2528)"). 147 [] f(g(g(x)),g(g(g(x))))=f(g(f(g(x),x)),g(f(g(x),x))) # label("Hint 54(2542)"). 148 [] f(g(g(x)),g(g(g(x))))=f(g(x),x) # label("Hint 55(2570)"). 149 [] f(g(g(f(x,g(x)))),g(f(g(x),x)))=f(g(x),x) # label("Hint 56(2661)"). 150 [] f(f(x,x),f(x,g(f(x,x))))=x # label("Hint 57(2856)"). 151 [] f(f(g(x),g(x)),x)=g(x) # label("Hint 58(2918)"). 152 [] g(f(g(x),x))=f(x,g(x)) # label("Hint 59(2976)"). 153 [] g(f(g(f(g(x),x)),f(g(x),x)))=f(f(g(x),x),f(x,g(x))) # label("Hint 60(3120)"). 154 [] f(g(g(f(g(x),x))),x)=x # label("Hint 61(3230)"). 155 [] g(g(f(g(x),x)))=f(g(x),x) # label("Hint 62(3238)"). 156 [] f(f(g(x),x),f(x,g(x)))=f(x,g(x)) # label("Hint 63(3286)"). 157 [] f(f(x,g(x)),x)=x # label("Hint 64(3292)"). 158 [] g(g(x))=x # label("Hint 65(3306)"). 159 [] f(x,g(f(x,x)))=g(x) # label("Hint 66(3332)"). 160 [] f(x,g(f(g(x),x)))=x # label("Hint 67(3338)"). 161 [] f(g(f(x,x)),x)=g(x) # label("Hint 68(3398)"). 162 [] g(f(f(x,g(y)),g(f(x,g(y)))))=f(x,g(f(f(x,g(y)),y))) # label("Hint 69(3406)"). 163 [] f(x,f(x,g(x)))=x # label("Hint 70(3553)"). 164 [] f(g(f(x,g(y))),x)=y # label("Hint 71(3633)"). 165 [] f(x,f(y,g(y)))=x # label("Hint 72(3775)"). 166 [] f(x,f(g(y),y))=x # label("Hint 73(4017)"). 167 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 74(4162)"). end_of_list. list(hints2). 168 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y # label("Hint 1(1)"). 169 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z # label("Hint 2(2)"). 170 [] g(f(f(x,y),g(f(f(z,f(x,f(g(z),z))),y))))=z # label("Hint 3(3)"). 171 [] f(f(g(x),y),g(f(y,f(g(f(f(x,z),y)),y))))=z # label("Hint 4(4)"). 172 [] g(f(x,f(g(f(f(f(x,y),f(x,g(z))),z)),x)))=y # label("Hint 5(5)"). 173 [] f(x,f(f(g(f(g(f(y,x)),x)),g(f(z,x))),z))=y # label("Hint 6(6)"). 174 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y # label("Hint 7(7)"). 175 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y # label("Hint 8(8)"). 176 [] f(x,g(f(f(f(y,g(f(y,y))),f(x,g(z))),z)))=y # label("Hint 9(9)"). 177 [] g(f(x,g(f(f(y,g(f(z,x))),f(z,f(x,x))))))=y # label("Hint 10(10)"). 178 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("Hint 11(11)"). 179 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 12(12)"). 180 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 13(13)"). 181 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 14(14)"). 182 [] f(f(g(f(g(x),y)),z),f(g(f(f(z,g(u)),z)),z))=f(g(f(f(y,g(f(x,u))),y)),y) # label("Hint 15(153)"). 183 [] f(f(g(f(x,y)),z),f(g(f(f(z,u),z)),z))=g(f(f(u,f(x,f(g(u),u))),y)) # label("Hint 16(173)"). 184 [] f(f(g(f(x,y)),x),y)=f(x,g(x)) # label("Hint 17(218)"). 185 [] g(f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z)))))=g(f(z,f(g(f(f(y,u),z)),z))) # label("Hint 18(462)"). 186 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 19(603)"). 187 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))) # label("Hint 20(605)"). 188 [] f(x,f(f(x,g(x)),g(f(x,g(x)))))=x # label("Hint 21(704)"). 189 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(x,g(z))),z))))=f(g(f(y,x)),y) # label("Hint 22(706)"). 190 [] f(x,f(g(f(x,x)),g(g(f(x,x)))))=x # label("Hint 23(710)"). 191 [] g(f(x,g(x)))=f(x,f(g(f(x,x)),x)) # label("Hint 24(738)"). 192 [] f(g(f(x,g(x))),x)=x # label("Hint 25(742)"). 193 [] g(f(x,g(f(x,f(f(g(x),x),x)))))=x # label("Hint 26(800)"). 194 [] g(f(x,g(f(x,g(x)))))=g(x) # label("Hint 27(810)"). 195 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 28(814)"). 196 [] g(f(x,f(f(g(x),y),f(g(y),y))))=f(g(f(y,y)),y) # label("Hint 29(816)"). 197 [] g(f(x,f(f(g(x),f(x,g(y))),y)))=f(g(f(x,x)),x) # label("Hint 30(846)"). 198 [] f(x,g(f(f(y,f(x,g(z))),z)))=g(y) # label("Hint 31(904)"). 199 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)) # label("Hint 32(906)"). 200 [] f(x,g(f(x,f(f(g(x),x),x))))=f(x,g(f(x,x))) # label("Hint 33(964)"). 201 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))) # label("Hint 34(980)"). 202 [] g(f(x,g(f(x,x))))=x # label("Hint 35(1063)"). 203 [] f(f(x,x),g(f(x,x)))=f(x,g(x)) # label("Hint 36(1115)"). 204 [] f(f(g(f(x,g(x))),f(g(x),g(y))),y)=g(x) # label("Hint 37(1320)"). 205 [] f(g(f(x,y)),f(f(g(f(z,g(z))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,f(g(f(z,g(f(x,y)))),z)),x)))) # label("Hint 38(1462)"). 206 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 39(1509)"). 207 [] f(g(f(x,f(g(y),z))),g(f(x,g(f(x,f(u,x))))))=g(f(z,f(g(f(f(y,u),z)),z))) # label("Hint 40(1567)"). 208 [] g(f(x,f(f(g(x),f(y,z)),f(g(f(u,f(y,z))),f(y,z)))))=g(f(z,f(g(f(f(f(y,g(f(y,y))),u),z)),z))) # label("Hint 41(2196)"). 209 [] f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z))))=f(z,f(g(f(f(y,u),z)),z)) # label("Hint 42(2327)"). 210 [] f(x,g(f(x,g(x))))=x # label("Hint 43(2398)"). 211 [] f(f(g(x),x),g(f(x,g(x))))=f(x,g(x)) # label("Hint 44(2404)"). 212 [] f(g(f(x,y)),g(f(x,g(f(x,f(y,x))))))=g(f(y,g(y))) # label("Hint 45(2461)"). 213 [] f(x,f(f(g(f(x,x)),f(x,g(y))),y))=f(x,g(x)) # label("Hint 46(2475)"). 214 [] f(f(x,x),g(f(x,g(x))))=f(x,x) # label("Hint 47(2675)"). 215 [] f(g(f(x,x)),f(x,x))=f(g(x),x) # label("Hint 48(2801)"). 216 [] f(f(x,g(x)),g(f(x,g(x))))=g(f(x,g(x))) # label("Hint 49(2928)"). 217 [] f(g(f(x,x)),x)=g(x) # label("Hint 50(2958)"). 218 [] f(x,g(f(x,f(f(x,g(x)),x))))=f(x,g(f(x,x))) # label("Hint 51(3007)"). 219 [] f(g(x),x)=f(x,g(x)) # label("Hint 52(3015)"). 220 [] g(f(g(x),f(x,g(x))))=x # label("Hint 53(3056)"). 221 [] g(f(x,g(x)))=f(f(x,g(x)),f(x,g(x))) # label("Hint 54(3060)"). 222 [] f(x,g(f(x,x)))=g(x) # label("Hint 55(3100)"). 223 [] g(g(x))=x # label("Hint 56(3116)"). 224 [] f(x,f(x,g(x)))=x # label("Hint 57(3180)"). 225 [] f(g(f(g(x),x)),x)=x # label("Hint 58(3203)"). 226 [] f(x,g(f(x,f(f(g(f(g(y),y)),f(x,g(z))),z))))=f(g(f(y,x)),y) # label("Hint 59(3205)"). 227 [] f(f(g(x),x),g(f(g(x),x)))=f(x,g(x)) # label("Hint 60(3224)"). 228 [] f(x,g(f(g(x),x)))=x # label("Hint 61(3226)"). 229 [] f(x,f(f(g(x),f(x,g(y))),y))=x # label("Hint 62(3270)"). 230 [] f(x,f(g(x),x))=x # label("Hint 63(3284)"). 231 [] f(g(f(g(x),y)),g(x))=f(g(f(x,y)),x) # label("Hint 64(3287)"). 232 [] f(g(x),f(x,g(x)))=g(x) # label("Hint 65(3308)"). 233 [] g(f(x,g(x)))=f(g(x),x) # label("Hint 66(3356)"). 234 [] f(f(g(x),x),f(x,g(x)))=f(x,g(x)) # label("Hint 67(3362)"). 235 [] f(g(f(f(x,g(y)),x)),x)=g(f(g(y),x)) # label("Hint 68(3395)"). 236 [] f(f(g(x),y),g(f(g(x),y)))=f(g(x),x) # label("Hint 69(3424)"). 237 [] f(f(g(x),x),x)=x # label("Hint 70(3481)"). 238 [] f(f(g(f(g(x),y)),z),g(f(g(u),z)))=g(f(g(f(x,u)),y)) # label("Hint 71(3491)"). 239 [] f(f(x,g(x)),g(x))=g(x) # label("Hint 72(3495)"). 240 [] f(f(x,g(x)),x)=x # label("Hint 73(3497)"). 241 [] g(f(x,f(g(f(f(x,x),x)),x)))=x # label("Hint 74(3506)"). 242 [] g(f(x,g(x)))=f(f(x,g(x)),f(g(x),x)) # label("Hint 75(3508)"). 243 [] g(f(g(f(x,g(y))),f(x,g(y))))=f(x,g(f(f(x,g(y)),y))) # label("Hint 76(3516)"). 244 [] f(f(x,x),g(x))=x # label("Hint 77(3531)"). 245 [] g(f(x,f(g(f(y,x)),x)))=g(f(g(y),x)) # label("Hint 78(3549)"). 246 [] g(f(f(x,g(y)),g(f(x,g(y)))))=f(x,g(f(f(x,g(y)),y))) # label("Hint 79(3569)"). 247 [] f(f(g(x),g(x)),x)=g(x) # label("Hint 80(3604)"). 248 [] f(g(x),g(f(x,g(x))))=g(x) # label("Hint 81(3726)"). 249 [] f(x,g(f(x,f(f(f(y,g(y)),f(x,g(z))),z))))=f(g(f(f(y,g(y)),x)),f(y,g(y))) # label("Hint 82(3942)"). 250 [] f(g(f(f(x,y),x)),x)=g(f(y,x)) # label("Hint 83(4012)"). 251 [] f(x,f(f(y,f(g(f(x,y)),g(x))),x))=g(f(x,g(x))) # label("Hint 84(4344)"). 252 [] f(f(x,y),g(f(x,y)))=f(x,g(x)) # label("Hint 85(4854)"). 253 [] f(g(f(x,y)),f(x,g(x)))=g(f(x,y)) # label("Hint 86(4968)"). 254 [] f(f(x,y),g(f(g(z),y)))=f(x,z) # label("Hint 87(4991)"). 255 [] f(g(x),f(x,y))=y # label("Hint 88(5005)"). 256 [] g(f(g(f(x,y)),x))=y # label("Hint 89(5009)"). 257 [] f(x,f(g(x),y))=y # label("Hint 90(5052)"). 258 [] g(f(f(x,g(y)),y))=g(x) # label("Hint 91(5070)"). 259 [] f(f(g(f(f(x,y),x)),f(x,g(z))),z)=f(g(x),g(y)) # label("Hint 92(5086)"). 260 [] f(x,f(y,g(y)))=x # label("Hint 93(5090)"). 261 [] f(g(f(x,y)),f(x,y))=g(f(y,g(y))) # label("Hint 94(5103)"). 262 [] f(g(f(x,y)),f(x,z))=g(f(g(z),y)) # label("Hint 95(5105)"). 263 [] f(x,g(f(g(y),y)))=x # label("Hint 96(5119)"). 264 [] g(f(x,g(f(y,x))))=y # label("Hint 97(5130)"). 265 [] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=f(g(y),z) # label("Hint 98(5183)"). 266 [] f(x,f(f(g(f(y,x)),f(x,g(z))),z))=g(f(g(x),y)) # label("Hint 99(5190)"). 267 [] f(x,g(f(y,g(y))))=x # label("Hint 100(5195)"). 268 [] f(x,g(f(y,g(f(y,f(z,y))))))=f(g(f(g(y),g(x))),z) # label("Hint 101(5260)"). 269 [] f(g(f(x,y)),x)=g(y) # label("Hint 102(5303)"). 270 [] g(f(g(f(x,g(f(x,f(y,x))))),f(g(f(g(x),f(g(f(g(x),g(f(f(x,z),u)))),y))),y)))=g(f(g(f(z,u)),y)) # label("Hint 103(5368)"). 271 [] f(g(f(g(x),y)),g(f(z,x)))=g(f(z,y)) # label("Hint 104(5388)"). 272 [] g(f(x,g(f(x,f(y,x)))))=f(x,y) # label("Hint 105(5414)"). 273 [] f(f(x,y),f(g(y),z))=f(x,z) # label("Hint 106(5434)"). 274 [] f(x,g(f(x,f(y,x))))=g(f(x,y)) # label("Hint 107(5455)"). 275 [] f(f(x,y),g(y))=x # label("Hint 108(5461)"). 276 [] f(x,g(x))=f(g(y),y) # label("Hint 109(5549)"). 277 [] f(g(f(x,g(x))),y)=y # label("Hint 110(5661)"). 278 [] f(f(x,g(x)),y)=y # label("Hint 111(5670)"). 279 [] f(f(x,g(y)),y)=x # label("Hint 112(5771)"). 280 [] f(x,f(g(f(y,x)),z))=f(g(y),z) # label("Hint 113(5780)"). 281 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 114(5838)"). end_of_list. list(hints2). 282 [] f(f(g(x),y),g(f(y,f(g(f(f(x,z),y)),y))))=z # label("Hint 1(1)"). 283 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y # label("Hint 2(2)"). 284 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y # label("Hint 3(3)"). 285 [] f(x,g(f(f(f(y,g(f(y,y))),f(x,g(z))),z)))=y # label("Hint 4(4)"). 286 [] g(f(x,g(f(f(y,g(f(z,x))),f(z,f(x,x))))))=y # label("Hint 5(5)"). 287 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("Hint 6(6)"). 288 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 7(7)"). 289 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 8(8)"). 290 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 9(9)"). 291 [] g(f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z)))))=g(f(z,f(g(f(f(y,u),z)),z))) # label("Hint 10(337)"). 292 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 11(417)"). 293 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))) # label("Hint 12(419)"). 294 [] f(x,g(f(x,f(f(f(g(y),z),g(f(z,f(g(f(f(y,u),z)),z)))),x))))=f(x,g(f(x,f(u,x)))) # label("Hint 13(520)"). 295 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 14(534)"). 296 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))) # label("Hint 15(565)"). 297 [] f(g(f(x,f(g(y),z))),g(f(x,g(f(x,f(u,x))))))=g(f(z,f(g(f(f(y,u),z)),z))) # label("Hint 16(571)"). 298 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)) # label("Hint 17(589)"). 299 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z # label("Hint 18(788)"). 300 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))) # label("Hint 19(993)"). 301 [] g(f(x,g(f(x,x))))=x # label("Hint 20(1007)"). 302 [] g(f(x,f(f(g(x),f(y,z)),f(g(f(u,f(y,z))),f(y,z)))))=g(f(z,f(g(f(f(f(y,g(f(y,y))),u),z)),z))) # label("Hint 21(1017)"). 303 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y # label("Hint 22(1025)"). 304 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x)))))=y # label("Hint 23(1029)"). 305 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y # label("Hint 24(1031)"). 306 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))) # label("Hint 25(1035)"). 307 [] f(g(f(x,g(f(x,f(y,x))))),g(g(f(x,g(f(x,f(f(f(y,x),y),x)))))))=f(x,g(f(x,f(y,x)))) # label("Hint 26(1058)"). 308 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 27(1090)"). 309 [] f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z))))=f(z,f(g(f(f(y,u),z)),z)) # label("Hint 28(1125)"). 310 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)) # label("Hint 29(1145)"). 311 [] g(f(g(x),g(f(x,f(g(x),f(g(x),g(x)))))))=g(x) # label("Hint 30(1149)"). 312 [] f(x,g(f(f(y,f(x,g(z))),z)))=g(y) # label("Hint 31(1151)"). 313 [] f(x,g(f(f(y,f(x,z)),f(z,g(f(z,z))))))=g(y) # label("Hint 32(1159)"). 314 [] f(g(x),g(f(f(y,x),f(g(x),g(x)))))=g(y) # label("Hint 33(1167)"). 315 [] f(g(g(x)),g(f(x,f(y,g(y)))))=f(y,g(y)) # label("Hint 34(1195)"). 316 [] f(f(g(f(x,g(x))),f(g(x),g(y))),y)=g(x) # label("Hint 35(1276)"). 317 [] f(f(g(f(x,g(x))),x),f(g(x),g(x)))=g(x) # label("Hint 36(1296)"). 318 [] g(g(f(x,g(x))))=f(g(x),g(g(x))) # label("Hint 37(1312)"). 319 [] g(g(f(f(x,g(f(x,x))),x)))=f(x,g(x)) # label("Hint 38(1489)"). 320 [] g(g(g(g(f(x,g(x))))))=f(g(g(x)),g(g(g(x)))) # label("Hint 39(1497)"). 321 [] f(g(x),g(f(f(y,g(z)),f(f(z,x),f(g(x),g(x))))))=g(y) # label("Hint 40(1701)"). 322 [] g(f(g(f(x,g(x))),x))=f(g(x),g(f(g(x),x))) # label("Hint 41(1826)"). 323 [] g(g(g(g(f(x,g(x))))))=g(g(f(g(x),g(g(x))))) # label("Hint 42(1880)"). 324 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z # label("Hint 43(2682)"). 325 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))) # label("Hint 44(2702)"). 326 [] f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y)))=f(z,g(f(z,z))) # label("Hint 45(2722)"). 327 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z # label("Hint 46(2741)"). 328 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y # label("Hint 47(2803)"). 329 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))) # label("Hint 48(2827)"). 330 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x) # label("Hint 49(2843)"). 331 [] f(f(x,f(g(f(g(f(y,y)),x)),g(f(g(f(y,y)),g(z))))),g(f(y,y)))=f(y,g(f(y,g(f(y,f(z,y)))))) # label("Hint 50(2855)"). 332 [] f(x,f(f(g(x),g(y)),f(g(f(y,g(y))),g(y))))=f(g(y),g(y)) # label("Hint 51(2984)"). 333 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(y,g(f(y,f(f(z,u),y)))) # label("Hint 52(2991)"). 334 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z # label("Hint 53(3375)"). 335 [] f(f(x,f(g(f(y,x)),y)),y)=y # label("Hint 54(3465)"). 336 [] f(f(g(f(x,x)),f(x,x)),x)=x # label("Hint 55(3473)"). 337 [] g(f(x,f(f(g(x),y),f(g(y),y))))=f(g(f(y,y)),y) # label("Hint 56(3581)"). 338 [] g(f(x,f(f(g(x),f(x,g(y))),y)))=f(g(f(x,x)),x) # label("Hint 57(3592)"). 339 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y # label("Hint 58(3747)"). 340 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(x,f(g(f(x,x)),x)) # label("Hint 59(3828)"). 341 [] f(g(f(x,g(x))),g(f(g(f(x,x)),f(x,x))))=f(x,g(x)) # label("Hint 60(3913)"). 342 [] f(x,f(g(x),f(g(x),g(x))))=f(g(x),g(x)) # label("Hint 61(4199)"). 343 [] f(f(x,g(f(x,x))),f(x,f(x,x)))=f(x,x) # label("Hint 62(4223)"). 344 [] f(f(x,f(g(f(y,z)),u)),f(u,g(f(u,u))))=f(y,g(f(y,f(f(z,g(x)),y)))) # label("Hint 63(4501)"). 345 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x)))=y # label("Hint 64(4846)"). 346 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x))=f(y,g(f(y,y))) # label("Hint 65(4953)"). 347 [] f(g(x),f(f(g(f(g(x),g(x))),x),g(x)))=x # label("Hint 66(4962)"). 348 [] f(f(g(f(g(x),g(x))),x),g(x))=g(f(g(x),g(x))) # label("Hint 67(5117)"). 349 [] f(x,f(g(f(x,x)),x))=f(y,f(g(f(x,y)),x)) # label("Hint 68(5283)"). 350 [] f(x,f(g(f(y,x)),y))=f(z,f(g(f(y,z)),y)) # label("Hint 69(5396)"). 351 [] f(x,f(g(f(y,x)),y))=f(g(f(y,y)),f(y,y)) # label("Hint 70(5742)"). 352 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,g(z)),x))))))=g(y) # label("Hint 71(5750)"). 353 [] f(g(f(x,x)),f(x,y))=f(z,f(g(f(x,z)),y)) # label("Hint 72(6178)"). 354 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)) # label("Hint 73(6300)"). 355 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("Hint 74(6301)"). 356 [] f(g(x),f(g(f(x,g(x))),y))=f(g(f(x,x)),f(x,y)) # label("Hint 75(6350)"). 357 [] f(g(f(x,f(g(f(x,x)),x))),f(g(f(x,g(x))),y))=f(x,f(f(g(x),g(f(g(x),x))),y)) # label("Hint 76(6390)"). 358 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,g(z)))))))=f(g(f(z,g(z))),f(g(z),g(y))) # label("Hint 77(6716)"). 359 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(y,f(g(f(z,y)),u))))),x)))=f(g(f(z,x)),u) # label("Hint 78(7803)"). 360 [] f(f(g(x),f(y,z)),f(g(f(u,f(y,z))),f(y,z)))=f(g(f(f(f(y,g(f(y,y))),u),x)),z) # label("Hint 79(7847)"). 361 [] g(g(x))=x # label("Hint 80(8045)"). 362 [] f(g(x),x)=f(x,g(x)) # label("Hint 81(8071)"). 363 [] f(x,g(f(x,x)))=g(x) # label("Hint 82(8085)"). 364 [] f(x,f(f(g(x),y),f(g(y),y)))=g(f(g(f(y,y)),y)) # label("Hint 83(8097)"). 365 [] g(f(g(x),x))=g(f(x,g(x))) # label("Hint 84(8099)"). 366 [] g(f(g(x),g(f(g(x),x))))=f(g(f(x,g(x))),x) # label("Hint 85(8100)"). 367 [] f(g(x),f(x,f(x,x)))=f(x,x) # label("Hint 86(8130)"). 368 [] f(g(f(g(x),g(x))),f(g(x),y))=f(x,f(g(f(x,g(x))),y)) # label("Hint 87(8203)"). 369 [] f(g(f(x,g(x))),g(f(g(x),x)))=f(f(x,g(x)),f(g(f(x,g(x))),f(x,f(g(f(x,x)),x)))) # label("Hint 88(8625)"). 370 [] f(g(f(x,g(x))),g(f(g(x),x)))=f(x,f(g(f(x,x)),x)) # label("Hint 89(8644)"). 371 [] g(f(x,g(x)))=f(x,g(x)) # label("Hint 90(8794)"). 372 [] g(f(g(x),x))=f(x,g(x)) # label("Hint 91(8813)"). 373 [] f(f(x,g(x)),g(f(x,g(x))))=f(x,f(g(f(x,x)),x)) # label("Hint 92(8890)"). 374 [] f(x,f(f(g(x),g(f(g(x),x))),x))=x # label("Hint 93(9023)"). 375 [] f(g(f(x,x)),x)=g(x) # label("Hint 94(9346)"). 376 [] f(x,f(x,g(x)))=x # label("Hint 95(9385)"). 377 [] f(x,g(f(x,g(x))))=x # label("Hint 96(9496)"). 378 [] f(x,f(g(x),x))=x # label("Hint 97(9498)"). 379 [] f(g(f(x,x)),f(x,x))=f(x,g(x)) # label("Hint 98(9523)"). 380 [] f(f(x,g(x)),f(g(x),x))=f(x,g(x)) # label("Hint 99(9545)"). 381 [] f(f(x,g(x)),x)=x # label("Hint 100(9549)"). 382 [] g(f(x,f(g(f(y,x)),x)))=g(f(g(y),x)) # label("Hint 101(9572)"). 383 [] f(f(g(x),y),g(f(g(x),y)))=f(x,g(x)) # label("Hint 102(9602)"). 384 [] f(g(x),g(f(x,g(f(x,f(y,x))))))=g(f(g(f(x,y)),x)) # label("Hint 103(9699)"). 385 [] f(x,f(g(f(y,x)),x))=f(g(y),x) # label("Hint 104(9794)"). 386 [] f(x,f(g(f(y,x)),z))=f(g(y),z) # label("Hint 105(9806)"). 387 [] g(f(g(f(x,y)),x))=y # label("Hint 106(10078)"). 388 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 107(10358)"). end_of_list. list(hints2). 389 [] g(f(x,g(f(f(y,g(f(z,x))),f(z,f(x,x))))))=y # label("Hint 1(1)"). 390 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("Hint 2(2)"). 391 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 3(3)"). 392 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 4(4)"). 393 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 5(5)"). 394 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 6(396)"). 395 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))) # label("Hint 7(398)"). 396 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))) # label("Hint 8(429)"). 397 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 9(457)"). 398 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))) # label("Hint 10(476)"). 399 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)) # label("Hint 11(487)"). 400 [] g(f(x,g(f(x,f(f(g(f(y,x)),f(x,g(x))),x)))))=g(y) # label("Hint 12(523)"). 401 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))) # label("Hint 13(533)"). 402 [] g(f(x,g(f(x,x))))=x # label("Hint 14(541)"). 403 [] f(g(f(x,g(f(f(y,g(f(y,y))),x)))),y)=f(x,g(x)) # label("Hint 15(543)"). 404 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y # label("Hint 16(550)"). 405 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y # label("Hint 17(553)"). 406 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))) # label("Hint 18(555)"). 407 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 19(573)"). 408 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))) # label("Hint 20(610)"). 409 [] f(x,g(f(x,f(f(y,f(x,y)),x))))=f(g(f(x,y)),g(f(x,y))) # label("Hint 21(614)"). 410 [] g(f(g(x),g(f(x,f(g(x),f(g(x),g(x)))))))=g(x) # label("Hint 22(622)"). 411 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))) # label("Hint 23(624)"). 412 [] f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y)))=f(z,g(f(z,z))) # label("Hint 24(626)"). 413 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z # label("Hint 25(634)"). 414 [] f(g(x),g(f(x,f(g(x),f(g(x),g(x))))))=x # label("Hint 26(659)"). 415 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y # label("Hint 27(692)"). 416 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))) # label("Hint 28(698)"). 417 [] f(g(x),f(f(y,f(g(f(g(x),y)),g(x))),g(x)))=f(g(x),g(x)) # label("Hint 29(701)"). 418 [] f(x,f(g(x),f(g(x),g(x))))=f(g(x),g(x)) # label("Hint 30(705)"). 419 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x) # label("Hint 31(707)"). 420 [] f(f(x,f(g(f(g(f(y,y)),x)),g(f(g(f(y,y)),g(z))))),g(f(y,y)))=f(y,g(f(y,g(f(y,f(z,y)))))) # label("Hint 32(712)"). 421 [] f(f(x,g(f(x,x))),f(x,f(x,x)))=f(x,x) # label("Hint 33(733)"). 422 [] f(f(x,f(g(f(y,x)),y)),y)=y # label("Hint 34(786)"). 423 [] f(f(g(f(x,x)),f(x,x)),x)=x # label("Hint 35(810)"). 424 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)) # label("Hint 36(822)"). 425 [] g(f(x,f(f(g(x),y),f(g(y),y))))=f(g(f(y,y)),y) # label("Hint 37(838)"). 426 [] f(g(f(x,g(x))),g(f(g(f(x,x)),f(x,x))))=f(x,g(x)) # label("Hint 38(851)"). 427 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x))=f(y,g(f(y,y))) # label("Hint 39(893)"). 428 [] f(g(x),f(f(g(f(g(x),g(x))),x),g(x)))=x # label("Hint 40(895)"). 429 [] f(f(g(f(g(x),g(x))),x),g(x))=g(f(g(x),g(x))) # label("Hint 41(935)"). 430 [] f(f(g(f(x,x)),f(x,g(f(x,x)))),x)=g(f(x,x)) # label("Hint 42(937)"). 431 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y # label("Hint 43(1028)"). 432 [] f(g(f(x,x)),f(x,x))=f(y,f(g(f(x,y)),x)) # label("Hint 44(1038)"). 433 [] f(g(f(x,x)),f(x,g(y)))=f(z,f(g(f(x,z)),g(y))) # label("Hint 45(1061)"). 434 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x # label("Hint 46(1078)"). 435 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(g(f(x,x)),f(x,x)) # label("Hint 47(1089)"). 436 [] f(g(f(x,g(f(x,f(y,x))))),g(g(f(x,g(f(x,f(f(f(y,x),y),x)))))))=f(x,g(f(x,f(y,x)))) # label("Hint 48(1143)"). 437 [] f(x,f(f(g(x),g(y)),f(g(f(y,g(y))),g(y))))=f(g(y),g(y)) # label("Hint 49(1228)"). 438 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(y,g(f(y,f(f(z,u),y)))) # label("Hint 50(1240)"). 439 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(x,g(z))),z))))=g(f(y,g(f(f(x,g(f(x,x))),y)))) # label("Hint 51(1436)"). 440 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("Hint 52(1675)"). 441 [] f(x,f(g(f(y,x)),y))=f(g(f(y,y)),f(y,y)) # label("Hint 53(1747)"). 442 [] f(x,f(g(f(y,x)),y))=f(z,f(g(f(y,z)),y)) # label("Hint 54(1748)"). 443 [] f(x,f(g(f(y,x)),z))=f(g(f(y,y)),f(y,z)) # label("Hint 55(1780)"). 444 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y # label("Hint 56(1783)"). 445 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(g(f(z,z)),f(z,z)),x))))))=f(g(f(z,y)),z) # label("Hint 57(1902)"). 446 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)) # label("Hint 58(2137)"). 447 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))) # label("Hint 59(2143)"). 448 [] f(f(g(f(x,g(x))),f(g(x),g(y))),y)=g(x) # label("Hint 60(2217)"). 449 [] f(f(g(f(x,g(x))),f(g(x),y)),f(y,g(f(y,y))))=g(x) # label("Hint 61(2227)"). 450 [] f(f(g(f(x,g(x))),x),f(g(x),g(x)))=g(x) # label("Hint 62(2233)"). 451 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,g(z)))))))=f(g(f(z,g(z))),f(g(z),g(y))) # label("Hint 63(2252)"). 452 [] g(f(z,g(f(g(x),f(y,f(z,z))))))=f(g(f(x,g(x))),f(g(x),g(g(f(y,z))))) # label("Hint 64(2308)"). 453 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z # label("Hint 65(2891)"). 454 [] f(g(f(x,g(f(g(y),f(x,f(x,x)))))),g(f(x,x)))=g(y) # label("Hint 66(3100)"). 455 [] f(f(g(f(x,y)),z),f(g(f(g(f(x,x)),f(x,z))),u))=f(g(f(y,y)),f(y,u)) # label("Hint 67(3181)"). 456 [] f(g(f(x,x)),f(x,y))=f(x,f(g(f(x,x)),y)) # label("Hint 68(3224)"). 457 [] f(g(f(x,y)),f(y,g(y)))=f(g(f(y,y)),f(y,g(x))) # label("Hint 69(3280)"). 458 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)) # label("Hint 70(3339)"). 459 [] f(g(f(x,x)),f(x,y))=f(z,f(g(f(x,z)),y)) # label("Hint 71(3499)"). 460 [] f(x,f(y,f(g(f(x,y)),z)))=f(u,f(g(f(x,u)),f(x,z))) # label("Hint 72(3520)"). 461 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),v)))=f(u,f(g(f(z,z)),f(z,v))) # label("Hint 73(3521)"). 462 [] f(g(f(x,y)),f(y,g(y)))=f(z,f(g(f(y,z)),g(x))) # label("Hint 74(3548)"). 463 [] f(x,f(y,f(g(f(z,y)),u)))=f(x,f(g(f(z,z)),f(z,u))) # label("Hint 75(3554)"). 464 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(x))),y))))=x # label("Hint 76(3767)"). 465 [] f(f(x,f(g(f(y,x)),g(f(y,y)))),y)=g(f(y,y)) # label("Hint 77(4003)"). 466 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)) # label("Hint 78(4211)"). 467 [] g(f(g(f(x,x)),f(x,x)))=g(f(y,f(g(f(x,y)),x))) # label("Hint 79(5337)"). 468 [] g(f(x,f(g(f(x,x)),x)))=g(f(y,f(g(f(x,y)),x))) # label("Hint 80(5408)"). 469 [] g(f(g(x),f(g(f(x,g(x))),x)))=g(f(g(f(x,x)),f(x,x))) # label("Hint 81(5410)"). 470 [] f(x,f(f(g(x),f(g(f(x,x)),f(x,x))),x))=x # label("Hint 82(6144)"). 471 [] f(g(f(x,g(f(x,g(x))))),x)=g(f(x,g(x))) # label("Hint 83(6163)"). 472 [] g(g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)))=g(y) # label("Hint 84(6295)"). 473 [] f(x,f(f(g(x),f(x,f(g(f(x,x)),x))),x))=x # label("Hint 85(6313)"). 474 [] f(x,f(f(g(x),f(y,f(g(f(x,y)),x))),x))=x # label("Hint 86(6315)"). 475 [] f(g(f(x,g(f(y,f(x,f(x,x)))))),g(f(x,x)))=y # label("Hint 87(6642)"). 476 [] f(f(g(f(x,f(y,f(y,y)))),x),y)=g(f(y,y)) # label("Hint 88(6767)"). 477 [] f(f(x,f(x,x)),g(f(x,x)))=x # label("Hint 89(6882)"). 478 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y # label("Hint 90(7263)"). 479 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)) # label("Hint 91(7329)"). 480 [] f(x,f(f(g(x),y),f(z,y)))=f(y,f(f(z,f(y,g(y))),y)) # label("Hint 92(7341)"). 481 [] f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)=f(y,g(f(y,y))) # label("Hint 93(7352)"). 482 [] f(f(x,f(y,g(y))),y)=f(f(x,f(y,g(z))),z) # label("Hint 94(11652)"). 483 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y # label("Hint 95(11697)"). 484 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(y))),y) # label("Hint 96(11775)"). 485 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u) # label("Hint 97(11858)"). 486 [] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(f(x,f(y,g(y))),y) # label("Hint 98(11865)"). 487 [] f(f(x,f(g(y),g(g(y)))),g(y))=f(f(x,y),f(g(y),g(y))) # label("Hint 99(11901)"). 488 [] f(f(f(g(f(x,g(x))),x),x),f(g(x),g(x)))=f(g(x),x) # label("Hint 100(11962)"). 489 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,f(z,g(z))),z))))))=f(z,g(x)) # label("Hint 101(12275)"). 490 [] f(f(x,f(f(y,f(y,y)),g(z))),z)=f(f(x,y),f(y,y)) # label("Hint 102(12363)"). 491 [] f(f(x,f(g(y),g(z))),z)=f(f(x,y),f(g(y),g(y))) # label("Hint 103(12377)"). 492 [] f(f(f(g(f(x,g(x))),x),f(g(x),g(y))),y)=f(g(x),x) # label("Hint 104(12424)"). 493 [] f(f(x,f(x,x)),g(f(f(x,f(x,x)),f(f(y,x),f(x,x)))))=f(g(f(x,y)),g(f(x,x))) # label("Hint 105(12757)"). 494 [] f(f(x,f(g(g(y)),g(y))),y)=f(f(x,g(y)),f(g(g(y)),g(g(y)))) # label("Hint 106(14196)"). 495 [] g(f(f(g(f(x,y)),g(f(x,x))),f(x,f(x,x))))=y # label("Hint 107(14302)"). 496 [] g(f(f(f(g(f(x,x)),x),g(f(y,y))),f(y,f(y,y))))=f(f(g(y),x),f(g(x),x)) # label("Hint 108(14580)"). 497 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x) # label("Hint 109(15237)"). 498 [] f(f(g(x),f(x,g(x))),x)=f(f(g(x),x),f(g(x),x)) # label("Hint 110(16042)"). 499 [] f(x,g(f(g(x),x)))=x # label("Hint 111(16645)"). 500 [] f(f(x,g(y)),f(g(g(y)),g(y)))=f(f(x,y),f(g(y),g(y))) # label("Hint 112(16711)"). 501 [] f(g(f(g(x),x)),f(g(x),y))=f(g(f(x,x)),f(x,y)) # label("Hint 113(16772)"). 502 [] f(g(x),g(g(x)))=f(x,g(x)) # label("Hint 114(16818)"). 503 [] f(g(f(g(x),g(x))),f(g(x),g(y)))=f(g(f(y,g(x))),f(x,g(x))) # label("Hint 115(16946)"). 504 [] g(f(g(x),g(f(y,g(x)))))=g(f(x,g(f(y,x)))) # label("Hint 116(16951)"). 505 [] f(g(g(x)),f(g(f(x,g(x))),g(y)))=f(g(f(y,g(x))),f(x,g(x))) # label("Hint 117(16961)"). 506 [] g(f(x,g(x)))=f(x,g(x)) # label("Hint 118(16967)"). 507 [] f(g(g(x)),g(x))=f(g(x),x) # label("Hint 119(16983)"). 508 [] f(g(f(x,g(x))),f(x,g(x)))=f(g(f(x,x)),f(x,x)) # label("Hint 120(16991)"). 509 [] f(f(g(f(x,x)),f(x,x)),g(x))=g(x) # label("Hint 121(17001)"). 510 [] f(x,f(g(f(g(y),x)),g(y)))=f(g(f(y,y)),f(y,y)) # label("Hint 122(17028)"). 511 [] f(g(g(x)),g(f(g(x),x)))=g(g(x)) # label("Hint 123(17030)"). 512 [] f(g(x),g(f(g(x),x)))=g(x) # label("Hint 124(17077)"). 513 [] f(f(x,g(x)),g(f(x,g(x))))=f(g(f(x,x)),f(x,x)) # label("Hint 125(17161)"). 514 [] g(f(f(x,g(x)),f(x,g(x))))=f(g(f(x,x)),f(x,x)) # label("Hint 126(17245)"). 515 [] g(f(g(x),f(x,g(x))))=x # label("Hint 127(17351)"). 516 [] f(g(f(g(x),g(x))),g(x))=x # label("Hint 128(17459)"). 517 [] f(f(g(x),f(x,g(x))),x)=f(x,g(x)) # label("Hint 129(17559)"). 518 [] f(f(g(f(x,g(x))),f(x,g(y))),y)=x # label("Hint 130(17594)"). 519 [] g(f(g(x),x))=f(g(f(x,x)),f(x,x)) # label("Hint 131(17677)"). 520 [] f(g(f(x,g(x))),g(f(g(x),x)))=f(x,g(x)) # label("Hint 132(17680)"). 521 [] f(g(g(g(x))),g(f(g(x),x)))=g(g(g(x))) # label("Hint 133(17700)"). 522 [] g(g(g(f(g(x),x))))=g(f(g(x),x)) # label("Hint 134(17714)"). 523 [] f(f(g(x),x),g(f(g(x),x)))=g(f(g(x),x)) # label("Hint 135(17740)"). 524 [] f(x,f(y,f(g(f(g(g(z)),y)),g(f(g(z),z)))))=f(x,g(z)) # label("Hint 136(17810)"). 525 [] f(g(f(g(x),x)),g(f(g(x),x)))=f(x,g(x)) # label("Hint 137(17824)"). 526 [] g(f(g(x),x))=f(g(x),x) # label("Hint 138(17826)"). 527 [] f(g(g(x)),f(g(x),x))=g(g(x)) # label("Hint 139(17904)"). 528 [] f(g(x),f(g(x),x))=g(x) # label("Hint 140(17921)"). 529 [] g(g(f(g(x),x)))=f(g(x),x) # label("Hint 141(17947)"). 530 [] f(g(x),x)=f(x,g(x)) # label("Hint 142(17957)"). 531 [] f(f(g(x),x),f(g(x),x))=f(g(x),x) # label("Hint 143(17964)"). 532 [] f(x,f(g(f(y,x)),y))=f(g(y),y) # label("Hint 144(17980)"). 533 [] f(x,f(g(x),x))=x # label("Hint 145(17982)"). 534 [] f(f(g(x),x),f(x,g(x)))=f(g(x),x) # label("Hint 146(18006)"). 535 [] f(x,f(f(g(x),x),g(x)))=f(g(x),x) # label("Hint 147(18012)"). 536 [] f(g(g(x)),f(x,g(x)))=x # label("Hint 148(18032)"). 537 [] f(f(g(x),x),g(x))=g(x) # label("Hint 149(18148)"). 538 [] f(x,g(f(x,g(x))))=x # label("Hint 150(18150)"). 539 [] f(g(x),f(x,g(x)))=g(x) # label("Hint 151(18163)"). 540 [] f(f(g(x),x),x)=x # label("Hint 152(18202)"). 541 [] f(x,f(f(g(x),y),g(f(g(y),y))))=y # label("Hint 153(18236)"). 542 [] g(g(x))=f(f(x,g(x)),x) # label("Hint 154(18253)"). 543 [] f(g(f(x,x)),x)=g(x) # label("Hint 155(18263)"). 544 [] g(g(x))=x # label("Hint 156(18287)"). 545 [] f(x,g(f(x,x)))=g(x) # label("Hint 157(18308)"). 546 [] f(g(f(g(x),y)),f(y,g(y)))=f(g(f(y,y)),f(y,x)) # label("Hint 158(18383)"). 547 [] f(f(x,x),g(f(x,x)))=f(x,g(x)) # label("Hint 159(18495)"). 548 [] f(f(x,f(f(g(x),x),g(y))),y)=x # label("Hint 160(18527)"). 549 [] f(g(f(x,g(x))),x)=x # label("Hint 161(18650)"). 550 [] f(x,f(x,g(x)))=x # label("Hint 162(18686)"). 551 [] f(x,f(g(y),y))=f(x,f(y,g(y))) # label("Hint 163(18697)"). 552 [] f(f(g(f(x,x)),f(x,y)),g(y))=g(x) # label("Hint 164(18854)"). 553 [] f(x,f(f(g(x),y),f(y,y)))=f(y,f(y,y)) # label("Hint 165(18903)"). 554 [] g(f(f(x,g(f(x,f(x,x)))),x))=x # label("Hint 166(18906)"). 555 [] f(x,f(f(g(x),f(y,g(y))),y))=y # label("Hint 167(18932)"). 556 [] f(x,g(f(x,f(x,x))))=g(f(x,x)) # label("Hint 168(19219)"). 557 [] g(f(x,g(y)))=f(y,g(x)) # label("Hint 169(25759)"). 558 [] f(x,f(f(g(x),f(y,g(z))),z))=y # label("Hint 170(25770)"). 559 [] g(f(g(x),g(y)))=f(y,x) # label("Hint 171(25948)"). 560 [] f(x,f(g(y),y))=x # label("Hint 172(25988)"). 561 [] f(x,g(f(y,x)))=g(y) # label("Hint 173(26392)"). 562 [] f(x,g(f(y,g(y))))=x # label("Hint 174(26518)"). 563 [] f(f(x,f(y,g(z))),z)=f(x,y) # label("Hint 175(26522)"). 564 [] f(g(x),x)=f(g(y),y) # label("Hint 176(26532)"). 565 [] f(f(g(x),x),y)=y # label("Hint 177(26656)"). 566 [] f(f(x,g(y)),y)=x # label("Hint 178(26660)"). 567 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 179(26717)"). end_of_list. list(hints2). 568 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z # label("Hint 1(1)"). 569 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 2(2)"). 570 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 3(3)"). 571 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 4(4)"). 572 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 5(557)"). 573 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))) # label("Hint 6(559)"). 574 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))) # label("Hint 7(582)"). 575 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 8(605)"). 576 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))) # label("Hint 9(620)"). 577 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)) # label("Hint 10(631)"). 578 [] g(f(x,g(f(x,f(f(g(f(y,x)),f(x,g(x))),x)))))=g(y) # label("Hint 11(657)"). 579 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))) # label("Hint 12(667)"). 580 [] g(f(x,g(f(x,x))))=x # label("Hint 13(671)"). 581 [] f(g(f(x,g(f(f(y,g(f(y,y))),x)))),y)=f(x,g(x)) # label("Hint 14(673)"). 582 [] f(g(f(g(f(x,x)),x)),g(x))=f(g(f(x,x)),g(g(f(x,x)))) # label("Hint 15(675)"). 583 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y # label("Hint 16(680)"). 584 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y # label("Hint 17(683)"). 585 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))) # label("Hint 18(685)"). 586 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 19(701)"). 587 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))) # label("Hint 20(730)"). 588 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))) # label("Hint 21(742)"). 589 [] f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y)))=f(z,g(f(z,z))) # label("Hint 22(744)"). 590 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z # label("Hint 23(750)"). 591 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y # label("Hint 24(781)"). 592 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))) # label("Hint 25(785)"). 593 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x) # label("Hint 26(792)"). 594 [] f(f(x,f(g(f(g(f(y,y)),x)),g(f(g(f(y,y)),g(z))))),g(f(y,y)))=f(y,g(f(y,g(f(y,f(z,y)))))) # label("Hint 27(796)"). 595 [] f(f(x,f(g(f(y,x)),y)),y)=y # label("Hint 28(839)"). 596 [] f(f(g(f(g(x),g(x))),f(g(x),g(x))),g(x))=g(x) # label("Hint 29(847)"). 597 [] f(f(g(f(x,x)),f(x,x)),x)=x # label("Hint 30(861)"). 598 [] f(f(f(f(g(x),y),f(g(f(f(y,z),y)),y)),f(z,x)),x)=x # label("Hint 31(863)"). 599 [] f(f(g(f(x,g(x))),f(g(x),g(g(x)))),g(x))=g(x) # label("Hint 32(865)"). 600 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)) # label("Hint 33(871)"). 601 [] g(f(x,f(f(g(x),y),f(g(y),y))))=f(g(f(y,y)),y) # label("Hint 34(887)"). 602 [] f(g(f(x,g(x))),g(f(g(f(x,x)),f(x,x))))=f(x,g(x)) # label("Hint 35(895)"). 603 [] f(g(x),f(f(g(f(g(x),g(x))),x),g(x)))=x # label("Hint 36(918)"). 604 [] f(f(g(f(g(x),g(x))),x),g(x))=g(f(g(x),g(x))) # label("Hint 37(951)"). 605 [] f(f(g(f(f(x,g(f(x,x))),x)),f(x,g(x))),x)=x # label("Hint 38(1001)"). 606 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(x,g(z))),z))))=g(f(y,g(f(f(x,g(f(x,x))),y)))) # label("Hint 39(1013)"). 607 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y # label("Hint 40(1072)"). 608 [] f(g(f(x,x)),f(x,x))=f(y,f(g(f(x,y)),x)) # label("Hint 41(1082)"). 609 [] f(g(f(x,x)),f(x,g(y)))=f(z,f(g(f(x,z)),g(y))) # label("Hint 42(1103)"). 610 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x # label("Hint 43(1118)"). 611 [] f(x,f(g(f(y,x)),y))=f(z,f(g(f(y,z)),y)) # label("Hint 44(1122)"). 612 [] f(f(f(g(x),y),f(g(f(f(y,z),y)),y)),f(z,x))=f(g(f(x,x)),f(x,x)) # label("Hint 45(1160)"). 613 [] f(g(f(f(x,g(f(x,x))),x)),f(x,g(x)))=f(g(f(x,x)),f(x,x)) # label("Hint 46(1162)"). 614 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z))))=x # label("Hint 47(1273)"). 615 [] f(g(f(x,f(y,f(x,g(f(x,f(y,x))))))),f(g(x),x))=f(g(f(x,x)),f(x,x)) # label("Hint 48(1299)"). 616 [] f(x,f(g(f(y,x)),y))=f(g(f(y,y)),f(y,y)) # label("Hint 49(1334)"). 617 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),u)),x))))))=f(g(f(u,y)),u) # label("Hint 50(1352)"). 618 [] f(g(f(x,x)),f(x,y))=f(z,f(g(f(x,z)),y)) # label("Hint 51(1453)"). 619 [] f(x,f(g(f(y,x)),g(z)))=f(u,f(g(f(y,u)),g(z))) # label("Hint 52(1474)"). 620 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("Hint 53(1475)"). 621 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)) # label("Hint 54(1625)"). 622 [] f(g(x),f(g(f(x,g(x))),y))=f(g(f(x,x)),f(x,y)) # label("Hint 55(1636)"). 623 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(g(f(z,z)),f(z,u)),x))))))=f(g(f(z,y)),u) # label("Hint 56(1736)"). 624 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y # label("Hint 57(1830)"). 625 [] f(g(f(x,y)),f(y,g(y)))=f(g(f(y,y)),f(y,g(x))) # label("Hint 58(1968)"). 626 [] f(g(f(x,y)),f(y,g(y)))=f(z,f(g(f(y,z)),g(x))) # label("Hint 59(1969)"). 627 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)) # label("Hint 60(2006)"). 628 [] f(x,g(f(x,f(g(x),f(x,g(x))))))=x # label("Hint 61(2018)"). 629 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(y,f(g(f(x,y)),x)) # label("Hint 62(2564)"). 630 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(g(f(x,x)),f(x,x)) # label("Hint 63(2610)"). 631 [] f(x,f(f(g(x),f(y,f(g(f(x,y)),x))),x))=x # label("Hint 64(2681)"). 632 [] f(g(f(x,g(f(x,g(x))))),x)=g(f(x,g(x))) # label("Hint 65(2700)"). 633 [] g(g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)))=g(y) # label("Hint 66(2781)"). 634 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y # label("Hint 67(2992)"). 635 [] f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)=f(y,g(f(y,y))) # label("Hint 68(3034)"). 636 [] f(g(f(x,g(f(x,f(y,x))))),g(g(f(x,g(f(x,f(f(f(y,x),y),x)))))))=f(x,g(f(x,f(y,x)))) # label("Hint 69(3117)"). 637 [] f(x,f(g(f(y,x)),z))=f(g(f(y,y)),f(y,z)) # label("Hint 70(3574)"). 638 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(y,g(f(y,f(f(z,u),y)))) # label("Hint 71(3769)"). 639 [] f(x,f(f(g(x),y),f(z,y)))=f(y,f(f(z,f(y,g(y))),y)) # label("Hint 72(3774)"). 640 [] f(x,f(f(g(f(x,f(g(y),x))),f(x,g(x))),x))=f(y,f(g(f(x,x)),f(x,x))) # label("Hint 73(3952)"). 641 [] f(x,f(y,f(g(f(z,y)),z)))=f(x,f(g(f(z,z)),f(z,z))) # label("Hint 74(3960)"). 642 [] f(x,f(f(g(x),y),f(z,y)))=f(u,f(f(g(u),y),f(z,y))) # label("Hint 75(3980)"). 643 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x) # label("Hint 76(4005)"). 644 [] f(x,g(f(y,f(f(g(y),x),f(g(f(x,x)),x)))))=x # label("Hint 77(4059)"). 645 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x))=z # label("Hint 78(4063)"). 646 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z # label("Hint 79(4134)"). 647 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)) # label("Hint 80(6164)"). 648 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))) # label("Hint 81(6170)"). 649 [] f(f(g(f(x,g(x))),f(g(x),g(y))),y)=g(x) # label("Hint 82(6308)"). 650 [] f(f(g(f(f(x,g(f(x,x))),x)),f(x,g(y))),y)=x # label("Hint 83(6312)"). 651 [] f(f(g(f(x,g(x))),x),f(g(x),g(x)))=g(x) # label("Hint 84(6350)"). 652 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)) # label("Hint 85(6710)"). 653 [] f(f(x,f(y,g(y))),y)=f(f(x,f(y,g(z))),z) # label("Hint 86(7005)"). 654 [] g(f(x,f(f(g(x),f(x,g(y))),y)))=f(g(f(x,x)),x) # label("Hint 87(7056)"). 655 [] f(x,f(f(g(x),y),f(z,y)))=f(y,f(f(z,f(y,g(u))),u)) # label("Hint 88(7062)"). 656 [] f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x)=f(y,g(f(y,y))) # label("Hint 89(7065)"). 657 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(y))),y) # label("Hint 90(7109)"). 658 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u) # label("Hint 91(7175)"). 659 [] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(f(x,f(y,g(y))),y) # label("Hint 92(7178)"). 660 [] f(f(x,f(g(y),g(g(y)))),g(y))=f(f(x,y),f(g(y),g(y))) # label("Hint 93(7235)"). 661 [] f(f(f(g(f(x,g(x))),x),x),f(g(x),g(x)))=f(g(x),x) # label("Hint 94(7252)"). 662 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,f(z,g(z))),z))))))=f(z,g(x)) # label("Hint 95(7473)"). 663 [] f(f(x,f(g(g(y)),g(y))),y)=f(f(x,g(y)),f(g(g(y)),g(g(y)))) # label("Hint 96(7799)"). 664 [] f(f(x,f(g(y),g(z))),z)=f(f(x,y),f(g(y),g(y))) # label("Hint 97(8042)"). 665 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,f(z,g(u))),u))))))=f(z,g(x)) # label("Hint 98(8467)"). 666 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(z,f(g(z),u)) # label("Hint 99(10553)"). 667 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),v)))=f(u,f(g(f(z,z)),f(z,v))) # label("Hint 100(10598)"). 668 [] f(x,f(f(y,f(g(f(x,y)),g(x))),x))=f(x,f(g(x),f(x,g(x)))) # label("Hint 101(15396)"). 669 [] g(f(f(x,g(f(y,f(f(g(y),x),x)))),x))=f(g(f(x,x)),f(x,x)) # label("Hint 102(16177)"). 670 [] f(x,f(f(g(x),y),y))=f(z,f(f(g(z),y),y)) # label("Hint 103(18837)"). 671 [] f(x,f(f(g(x),y),z))=f(u,f(f(g(u),y),z)) # label("Hint 104(18850)"). 672 [] f(f(g(f(x,x)),f(x,x)),f(x,g(x)))=f(g(x),x) # label("Hint 105(19311)"). 673 [] f(x,f(f(g(x),g(f(g(y),g(y)))),z))=f(y,f(y,z)) # label("Hint 106(19466)"). 674 [] f(x,f(f(g(x),y),f(g(y),g(y))))=f(f(y,g(y)),g(y)) # label("Hint 107(19549)"). 675 [] f(x,f(f(g(x),f(g(y),g(z))),z))=f(f(y,g(y)),g(y)) # label("Hint 108(19558)"). 676 [] f(x,f(f(g(x),f(y,y)),y))=f(f(y,y),y) # label("Hint 109(19604)"). 677 [] f(f(x,g(f(y,f(f(g(y),f(x,g(z))),z)))),x)=x # label("Hint 110(19646)"). 678 [] g(f(x,f(f(g(x),f(y,g(z))),z)))=f(g(f(y,y)),y) # label("Hint 111(19668)"). 679 [] f(g(f(x,g(x))),g(f(x,g(f(y,f(f(g(y),z),x))))))=z # label("Hint 112(19791)"). 680 [] f(g(f(x,g(x))),g(f(x,f(g(f(y,y)),y))))=f(y,g(x)) # label("Hint 113(19851)"). 681 [] g(f(f(x,g(f(y,f(f(x,x),x)))),x))=f(g(f(g(y),x)),f(x,x)) # label("Hint 114(20752)"). 682 [] f(f(g(f(g(x),x)),f(x,x)),f(x,g(x)))=f(x,x) # label("Hint 115(20918)"). 683 [] f(f(x,f(g(f(y,x)),y)),f(y,g(y)))=f(g(y),y) # label("Hint 116(20956)"). 684 [] f(x,f(f(g(x),f(y,y)),f(y,g(y))))=f(f(y,y),f(g(y),y)) # label("Hint 117(20990)"). 685 [] f(f(f(g(f(x,x)),f(x,x)),f(g(f(x,g(x))),g(y))),y)=f(f(g(x),x),f(g(f(x,x)),f(x,x))) # label("Hint 118(21068)"). 686 [] f(f(g(x),x),f(x,x))=f(f(x,x),f(g(x),x)) # label("Hint 119(22397)"). 687 [] g(f(f(x,g(f(x,f(f(x,x),f(g(x),x))))),x))=x # label("Hint 120(22551)"). 688 [] f(f(x,g(f(x,f(f(x,x),f(g(x),x))))),x)=f(x,g(f(x,x))) # label("Hint 121(23187)"). 689 [] f(x,g(f(y,f(y,f(x,g(f(y,f(y,x))))))))=x # label("Hint 122(23465)"). 690 [] f(x,g(f(f(x,f(g(f(x,x)),x)),f(g(x),x))))=x # label("Hint 123(23555)"). 691 [] f(x,g(f(f(g(f(x,x)),f(x,x)),f(g(x),x))))=x # label("Hint 124(23577)"). 692 [] f(x,g(f(f(y,f(g(f(x,y)),x)),f(g(x),x))))=x # label("Hint 125(23727)"). 693 [] f(f(g(x),x),f(g(f(x,x)),f(x,y)))=f(x,f(g(x),f(g(x),y))) # label("Hint 126(23976)"). 694 [] f(f(g(f(x,x)),f(x,x)),f(g(x),x))=f(x,f(g(x),f(x,g(x)))) # label("Hint 127(24188)"). 695 [] f(x,g(f(g(x),x)))=x # label("Hint 128(26022)"). 696 [] f(f(x,g(y)),f(g(g(y)),g(y)))=f(f(x,y),f(g(y),g(y))) # label("Hint 129(26247)"). 697 [] f(f(x,f(y,g(z))),z)=f(f(x,y),f(g(y),y)) # label("Hint 130(26249)"). 698 [] f(g(f(g(x),x)),f(g(x),y))=f(g(f(x,x)),f(x,y)) # label("Hint 131(26308)"). 699 [] f(x,f(g(x),f(x,g(x))))=f(g(x),x) # label("Hint 132(26310)"). 700 [] f(g(x),g(g(x)))=f(x,g(x)) # label("Hint 133(26357)"). 701 [] f(f(x,g(f(x,x))),x)=f(x,g(x)) # label("Hint 134(26398)"). 702 [] f(g(f(g(x),g(x))),f(g(x),g(y)))=f(g(f(y,g(x))),f(x,g(x))) # label("Hint 135(26513)"). 703 [] g(f(g(x),g(f(y,g(x)))))=g(f(x,g(f(y,x)))) # label("Hint 136(26518)"). 704 [] f(g(g(x)),f(g(f(x,g(x))),g(y)))=f(g(f(y,g(x))),f(x,g(x))) # label("Hint 137(26542)"). 705 [] g(f(x,g(x)))=f(x,g(x)) # label("Hint 138(26556)"). 706 [] f(g(f(x,g(x))),f(x,g(x)))=f(g(f(x,x)),f(x,x)) # label("Hint 139(26573)"). 707 [] f(x,f(g(f(g(y),x)),g(y)))=f(g(f(y,y)),f(y,y)) # label("Hint 140(26575)"). 708 [] f(g(g(x)),g(x))=f(g(x),x) # label("Hint 141(26579)"). 709 [] f(g(x),g(f(g(x),x)))=g(x) # label("Hint 142(26665)"). 710 [] g(g(f(x,g(x))))=f(x,g(x)) # label("Hint 143(26704)"). 711 [] f(f(x,g(x)),g(f(x,g(x))))=f(g(f(x,x)),f(x,x)) # label("Hint 144(26770)"). 712 [] f(f(g(f(g(f(x,x)),f(x,x))),f(x,g(x))),f(x,g(x)))=g(f(g(f(x,x)),f(x,x))) # label("Hint 145(26874)"). 713 [] f(g(f(f(x,x),f(x,x))),f(f(x,x),f(x,x)))=f(g(f(x,x)),f(x,x)) # label("Hint 146(26900)"). 714 [] f(f(g(f(x,x)),f(x,x)),g(f(x,g(x))))=g(f(x,g(x))) # label("Hint 147(26904)"). 715 [] g(f(f(x,g(x)),f(x,g(x))))=f(g(f(x,x)),f(x,x)) # label("Hint 148(26910)"). 716 [] g(f(x,g(x)))=f(x,f(g(x),f(g(x),x))) # label("Hint 149(26943)"). 717 [] f(x,f(f(g(x),f(f(y,g(y)),g(z))),z))=g(f(y,g(y))) # label("Hint 150(27009)"). 718 [] f(x,f(x,g(x)))=x # label("Hint 151(27096)"). 719 [] g(f(x,g(f(x,g(x)))))=g(x) # label("Hint 152(27137)"). 720 [] f(g(x),x)=f(x,g(x)) # label("Hint 153(27187)"). 721 [] f(g(f(g(x),g(x))),g(x))=x # label("Hint 154(27238)"). 722 [] f(g(x),f(x,g(x)))=g(x) # label("Hint 155(27297)"). 723 [] g(f(x,f(g(x),g(x))))=x # label("Hint 156(27310)"). 724 [] f(x,f(f(g(x),f(y,g(y))),z))=f(y,f(g(y),z)) # label("Hint 157(27316)"). 725 [] f(f(x,g(x)),x)=x # label("Hint 158(27362)"). 726 [] f(f(x,g(x)),f(x,g(x)))=f(x,g(x)) # label("Hint 159(27368)"). 727 [] f(g(f(x,x)),f(x,x))=f(x,g(x)) # label("Hint 160(27393)"). 728 [] f(f(x,g(x)),f(g(x),x))=f(x,g(x)) # label("Hint 161(27433)"). 729 [] f(g(f(x,x)),x)=g(x) # label("Hint 162(27463)"). 730 [] f(x,f(g(f(f(y,g(y)),x)),g(y)))=g(y) # label("Hint 163(27471)"). 731 [] f(x,f(g(x),x))=x # label("Hint 164(27476)"). 732 [] f(g(f(x,g(x))),x)=x # label("Hint 165(27525)"). 733 [] f(f(x,g(x)),g(x))=g(x) # label("Hint 166(27527)"). 734 [] f(f(g(x),x),g(f(x,x)))=g(f(x,x)) # label("Hint 167(27529)"). 735 [] g(g(x))=x # label("Hint 168(27537)"). 736 [] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=f(g(f(f(z,g(z)),y)),z) # label("Hint 169(27596)"). 737 [] f(f(x,x),g(x))=x # label("Hint 170(27604)"). 738 [] f(x,f(f(g(x),y),f(g(y),y)))=y # label("Hint 171(27616)"). 739 [] f(x,g(f(x,x)))=g(x) # label("Hint 172(27637)"). 740 [] g(f(g(x),x))=f(g(x),x) # label("Hint 173(27760)"). 741 [] f(g(f(g(x),x)),x)=x # label("Hint 174(28190)"). 742 [] f(x,f(g(y),y))=f(x,f(y,g(y))) # label("Hint 175(28628)"). 743 [] f(x,f(f(g(x),y),g(f(g(y),y))))=y # label("Hint 176(30274)"). 744 [] f(f(x,f(f(g(x),y),g(z))),z)=y # label("Hint 177(33380)"). 745 [] f(f(x,f(f(y,f(g(f(z,y)),u)),g(v))),v)=f(g(f(z,g(x))),u) # label("Hint 178(33610)"). 746 [] g(f(g(x),g(y)))=f(y,x) # label("Hint 179(37155)"). 747 [] f(g(f(g(x),x)),y)=y # label("Hint 180(37368)"). 748 [] g(f(g(f(x,y)),f(x,x)))=f(g(x),y) # label("Hint 181(37414)"). 749 [] f(f(x,f(y,g(z))),z)=f(x,y) # label("Hint 182(37416)"). 750 [] f(x,f(y,g(y)))=x # label("Hint 183(37423)"). 751 [] f(x,f(f(g(x),y),f(z,y)))=f(y,f(z,y)) # label("Hint 184(37458)"). 752 [] f(x,f(g(f(y,x)),z))=f(g(y),z) # label("Hint 185(37461)"). 753 [] f(x,g(f(x,f(f(y,z),x))))=f(g(z),g(f(x,y))) # label("Hint 186(37479)"). 754 [] f(f(x,f(y,z)),g(z))=f(x,y) # label("Hint 187(37493)"). 755 [] f(x,g(f(y,f(z,x))))=f(g(z),g(y)) # label("Hint 188(37754)"). 756 [] f(g(f(x,g(f(y,z)))),f(x,u))=f(f(y,z),u) # label("Hint 189(37788)"). 757 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 190(37790)"). end_of_list. list(hints2). 758 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z. 759 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y. 760 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 761 [] f(f(a,b),c)!=f(a,f(b,c)). 762 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 763 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))). 764 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),g(u))))),g(f(x,y))))=u. 765 [] f(g(f(g(f(x,y)),z)),f(f(u,f(g(f(g(f(g(f(x,y)),z)),u)),g(f(g(f(g(f(x,y)),z)),g(v))))),g(f(g(f(x,y)),z))))=f(g(f(x,y)),g(f(x,g(f(x,f(f(y,v),x)))))). 766 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 767 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 768 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)). 769 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))). 770 [] g(f(x,g(f(x,x))))=x. 771 [] f(g(f(x,g(f(x,x)))),g(f(x,f(f(g(f(y,g(y))),f(g(f(x,g(f(x,x)))),g(z))),z))))=g(f(y,g(f(f(x,g(f(x,x))),y)))). 772 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(g(f(x,g(f(x,x)))),g(z))),z))))=g(f(y,g(f(f(x,g(f(x,x))),y)))). 773 [] f(x,g(f(x,f(f(g(f(y,g(y))),f(x,g(z))),z))))=g(f(y,g(f(f(x,g(f(x,x))),y)))). 774 [] f(g(f(x,g(f(f(y,g(f(y,y))),x)))),y)=f(x,g(x)). 775 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y. 776 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y. 777 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))). 778 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))). 779 [] f(g(f(x,g(f(x,x)))),f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 780 [] f(x,f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 781 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 782 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 783 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y. 784 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))). 785 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x). 786 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,y),x))))))=f(f(z,f(g(f(y,z)),y)),y). 787 [] f(f(x,f(g(f(y,x)),y)),y)=y. 788 [] f(g(x),g(f(g(x),g(x))))=x. 789 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))). 790 [] f(f(g(f(x,x)),f(x,x)),x)=x. 791 [] f(f(g(f(x,g(x))),f(g(x),g(g(x)))),g(x))=g(x). 792 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)). 793 [] g(f(x,f(f(g(x),y),f(g(y),y))))=f(g(f(y,y)),y). 794 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x))=f(y,g(f(y,y))). 795 [] f(f(g(f(f(x,g(f(x,x))),x)),f(g(f(x,g(f(x,x)))),g(g(f(x,g(f(x,x))))))),g(f(x,g(f(x,x)))))=g(f(x,g(f(x,x)))). 796 [] f(f(g(f(f(x,g(f(x,x))),x)),f(x,g(g(f(x,g(f(x,x))))))),g(f(x,g(f(x,x)))))=g(f(x,g(f(x,x)))). 797 [] f(f(g(f(f(x,g(f(x,x))),x)),f(x,g(x))),g(f(x,g(f(x,x)))))=g(f(x,g(f(x,x)))). 798 [] f(f(g(f(f(x,g(f(x,x))),x)),f(x,g(x))),x)=g(f(x,g(f(x,x)))). 799 [] f(f(g(f(f(x,g(f(x,x))),x)),f(x,g(x))),x)=x. 800 [] f(f(x,g(f(y,f(f(g(y),x),f(g(x),x))))),x)=x. 801 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 802 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(g(f(y,g(f(y,f(f(z,f(g(f(y,z)),x)),y))))),u)),x)))))=u. 803 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x)))))=y. 804 [] g(f(g(f(x,g(f(x,x)))),f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,z)))),g(f(x,g(f(x,x)))))))=z. 805 [] g(f(x,f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,z)))),g(f(x,g(f(x,x)))))))=z. 806 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),g(f(x,g(f(x,x)))))))=z. 807 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 808 [] g(f(x,f(f(g(f(x,x)),f(g(f(y,g(f(y,f(f(z,f(g(f(y,z)),x)),y))))),g(f(x,u)))),x)))=u. 809 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x)))=y. 810 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x). 811 [] f(x,f(g(f(y,g(f(x,g(f(x,x)))))),g(f(y,g(f(y,f(z,y)))))))=z. 812 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 813 [] f(g(f(x,x)),f(g(f(y,f(f(g(f(y,y)),f(y,g(f(y,x)))),y))),g(f(x,g(f(x,f(z,x)))))))=z. 814 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y. 815 [] f(x,f(g(f(y,x)),g(f(z,g(f(z,z))))))=f(g(f(y,y)),f(y,z)). 816 [] f(x,f(g(f(y,x)),z))=f(g(f(y,y)),f(y,z)). 817 [] f(g(f(f(g(f(x,g(f(x,f(y,x))))),g(f(g(f(x,g(f(x,f(y,x))))),g(f(x,g(f(x,f(y,x)))))))),x)),f(x,g(x)))=y. 818 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y. 819 [] f(g(f(f(x,g(f(x,x))),y)),f(y,g(y)))=f(g(f(y,y)),f(y,x)). 820 [] f(g(f(x,y)),f(y,g(y)))=f(g(f(y,y)),f(y,g(x))). 821 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z))))=x. 822 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x. 823 [] f(x,g(f(x,f(g(f(x,x)),f(x,g(f(x,g(f(x,f(f(g(x),f(x,g(x))),x))))))))))=x. 824 [] f(x,g(f(x,f(g(x),f(x,g(x))))))=x. 825 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(x))),y))))=x. 826 [] f(g(f(x,f(g(x),f(x,g(x))))),g(f(g(f(x,f(g(x),f(x,g(x))))),g(f(x,f(g(x),f(x,g(x))))))))=f(x,f(f(y,f(g(f(x,y)),g(f(x,g(f(x,f(g(x),f(x,g(x))))))))),x)). 827 [] f(g(f(x,f(g(x),f(x,g(x))))),g(f(g(f(x,f(g(x),f(x,g(x))))),g(f(x,f(g(x),f(x,g(x))))))))=f(x,f(f(y,f(g(f(x,y)),g(x))),x)). 828 [] f(x,f(f(y,f(g(f(x,y)),g(x))),x))=f(x,f(g(x),f(x,g(x)))). 829 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)). 830 [] f(g(f(x,g(f(x,x)))),f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 831 [] f(x,f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 832 [] f(x,f(f(g(f(f(x,y),x)),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 833 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))). 834 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(f(f(x,g(x)),f(x,g(x)))),f(f(x,g(x)),g(y))),f(x,g(x)))))). 835 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y. 836 [] f(x,f(f(g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)),f(x,g(z))),z))=f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(x,f(f(y,f(x,g(x))),x)))))). 837 [] f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(x,f(f(y,f(x,g(x))),x))))))=f(x,f(f(y,f(x,g(z))),z)). 838 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)). 839 [] f(x,g(f(g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)),g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)))))=f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y). 840 [] f(x,g(f(x,g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)))))=f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y). 841 [] f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)=f(y,g(f(y,y))). 842 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,f(f(z,f(x,g(x))),x))))),x)))=f(f(z,f(x,g(u))),u). 843 [] f(f(x,f(y,g(y))),y)=f(f(x,f(y,g(z))),z). 844 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y. 845 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,f(f(z,f(x,g(u))),u))))),x)))=f(f(z,f(x,g(x))),x). 846 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(y))),y). 847 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u). 848 [] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(f(x,f(y,g(u))),u). 849 [] f(x,f(f(y,f(g(f(x,y)),g(z))),z))=f(x,f(g(x),f(x,g(x)))). 850 [] f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x)=f(y,g(f(y,y))). 851 [] f(g(x),f(g(f(y,g(x))),g(f(y,g(f(y,f(x,y)))))))=f(f(z,g(f(z,f(f(g(x),f(z,g(z))),z)))),z). 852 [] f(f(x,g(f(x,f(f(g(y),f(x,g(x))),x)))),x)=y. 853 [] f(g(x),f(g(f(y,g(x))),g(f(y,g(f(y,f(x,y)))))))=f(f(z,g(f(z,f(f(g(x),f(z,g(u))),u)))),z). 854 [] f(f(x,g(f(x,f(f(g(y),f(x,g(z))),z)))),x)=y. 855 [] f(f(x,g(y)),g(f(f(x,g(y)),f(f(g(z),f(f(x,g(y)),g(u))),u))))=g(f(f(x,g(f(x,f(z,y)))),x)). 856 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=y. 857 [] f(g(f(f(x,g(f(x,y))),x)),f(x,g(y)))=f(g(f(y,y)),f(y,y)). 858 [] f(g(f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z)))),x)),f(x,g(f(x,g(x)))))=g(x). 859 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=g(x). 860 [] f(f(g(f(f(y,g(f(y,x))),y)),f(y,g(z))),z)=f(f(g(f(x,x)),f(x,x)),f(g(x),g(f(g(x),g(x))))). 861 [] f(f(g(f(f(x,g(f(x,y))),x)),f(x,g(z))),z)=f(f(g(f(y,y)),f(y,y)),y). 862 [] f(f(g(f(f(x,g(f(x,y))),x)),f(x,g(z))),z)=y. 863 [] f(f(g(x),f(x,g(y))),y)=f(f(g(x),x),f(g(x),x)). 864 [] f(g(x),g(f(g(x),g(x))))=f(x,f(g(x),x)). 865 [] f(x,f(g(x),x))=x. 866 [] f(f(f(g(x),x),f(g(x),x)),x)=x. 867 [] f(f(f(g(x),f(x,g(y))),y),x)=x. 868 [] f(g(f(x,f(g(x),f(x,g(y))))),g(f(x,g(f(x,x)))))=y. 869 [] f(g(f(x,f(g(x),f(x,g(y))))),x)=y. 870 [] f(g(f(x,f(g(x),x))),x)=f(x,f(g(x),f(x,g(x)))). 871 [] f(x,f(g(x),f(x,g(x))))=f(g(x),x). 872 [] f(g(f(g(x),x)),x)=x. 873 [] f(x,g(f(g(x),x)))=x. 874 [] f(g(f(x,g(f(x,f(g(x),f(x,g(x))))))),g(g(x)))=f(x,g(x)). 875 [] f(g(x),g(g(x)))=f(x,g(x)). 876 [] f(f(x,f(y,g(z))),z)=f(f(x,y),f(g(y),y)). 877 [] f(x,g(g(f(x,g(f(x,x))))))=f(f(x,g(f(x,x))),g(f(x,g(f(x,x))))). 878 [] f(f(x,g(f(x,x))),g(f(x,g(f(x,x)))))=f(x,g(x)). 879 [] f(f(x,g(f(x,x))),x)=f(x,g(x)). 880 [] f(g(x),g(f(g(x),f(f(g(f(y,g(x))),f(x,g(x))),g(x)))))=y. 881 [] f(f(g(f(f(x,g(f(x,x))),x)),f(g(x),g(g(x)))),x)=x. 882 [] f(f(g(f(x,g(x))),f(x,g(y))),y)=x. 883 [] f(g(x),g(f(g(x),f(f(g(f(f(x,g(f(x,x))),x)),f(g(x),g(g(x)))),x))))=g(x). 884 [] f(g(x),g(f(g(x),x)))=g(x). 885 [] g(f(g(x),f(f(g(f(g(x),g(x))),g(x)),g(x))))=x. 886 [] f(g(f(g(x),f(g(g(x)),g(x)))),g(x))=f(g(x),x). 887 [] f(g(g(x)),g(x))=f(g(x),x). 888 [] f(g(x),f(g(x),x))=g(x). 889 [] g(f(g(x),g(f(g(x),f(f(g(f(g(x),g(x))),g(x)),g(x))))))=f(g(x),x). 890 [] g(f(g(x),x))=f(g(x),x). 891 [] f(f(g(x),x),x)=x. 892 [] f(g(g(f(g(x),x))),x)=x. 893 [] f(g(f(x,g(x))),g(f(x,g(f(x,x)))))=x. 894 [] f(g(f(x,g(x))),x)=x. 895 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,y))))))=g(f(y,g(y))). 896 [] f(x,f(g(f(y,x)),y))=g(f(y,g(y))). 897 [] g(f(g(f(g(x),x)),f(x,f(g(x),x))))=f(g(f(x,x)),x). 898 [] g(f(g(f(g(x),x)),x))=f(g(f(x,x)),x). 899 [] f(g(f(x,x)),x)=g(x). 900 [] f(x,g(f(x,g(f(x,f(g(x),x))))))=x. 901 [] f(x,g(f(x,g(x))))=x. 902 [] f(x,g(f(f(x,g(f(x,x))),x)))=x. 903 [] f(g(f(x,f(g(x),x))),x)=f(x,g(x)). 904 [] f(g(x),x)=f(x,g(x)). 905 [] f(f(g(f(x,g(x))),f(x,g(y))),y)=f(f(f(x,g(x)),g(f(x,g(x)))),x). 906 [] f(f(f(x,g(x)),g(f(x,g(x)))),x)=x. 907 [] g(f(x,g(f(f(x,g(f(x,x))),x))))=f(x,g(f(x,f(f(f(x,g(x)),g(f(x,g(x)))),x)))). 908 [] g(f(x,g(f(f(x,g(f(x,x))),x))))=f(x,g(f(x,x))). 909 [] f(x,g(f(x,x)))=g(x). 910 [] f(g(g(x)),g(f(g(g(x)),f(f(g(f(g(g(x)),g(g(x)))),f(g(x),g(g(x)))),g(g(x))))))=x. 911 [] g(g(x))=x. 912 [] g(f(g(f(x,x)),x))=x. 913 [] f(x,f(f(g(x),y),f(g(y),y)))=g(f(g(f(y,y)),y)). 914 [] f(x,f(f(g(x),y),f(g(y),y)))=y. 915 [] f(x,f(f(g(x),x),g(f(f(g(x),x),f(g(x),x)))))=x. 916 [] f(x,f(f(g(x),x),g(f(f(g(x),x),f(g(x),x)))))=f(f(y,f(f(g(y),x),g(z))),z). 917 [] f(f(x,f(f(g(x),y),g(z))),z)=y. 918 [] f(x,f(f(g(x),f(y,g(z))),z))=y. 919 [] f(x,f(g(f(g(y),g(g(y)))),y))=g(f(g(y),g(x))). 920 [] f(x,f(g(f(g(y),y)),y))=g(f(g(y),g(x))). 921 [] g(f(g(x),g(y)))=f(y,x). 922 [] f(f(x,g(f(g(g(y)),g(f(g(x),z))))),y)=z. 923 [] f(f(x,g(f(y,g(f(g(x),z))))),y)=z. 924 [] g(f(f(x,g(f(x,g(f(g(x),g(f(y,f(x,g(x))))))))),x))=y. 925 [] g(g(f(x,f(y,g(y)))))=x. 926 [] f(x,f(y,g(y)))=x. 927 [] f(x,g(f(g(g(y)),g(y))))=x. 928 [] f(x,g(f(y,g(y))))=x. 929 [] f(x,f(f(g(x),y),g(f(z,g(z)))))=y. 930 [] f(x,f(g(x),y))=y. 931 [] g(f(f(x,g(x)),f(g(f(x,g(x))),f(f(x,g(x)),g(y)))))=y. 932 [] g(f(f(x,g(x)),g(y)))=y. 933 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(f(x,g(x))))),f(x,g(x))))))=y. 934 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(x,g(x))),f(x,g(x))))))=y. 935 [] f(f(x,g(x)),g(f(f(x,g(x)),f(g(y),f(x,g(x))))))=y. 936 [] f(f(x,g(x)),g(f(f(x,g(x)),g(y))))=y. 937 [] f(f(x,g(x)),y)=y. 938 [] f(x,f(y,g(f(z,g(z)))))=f(f(x,f(y,g(u))),u). 939 [] f(f(x,f(y,g(z))),z)=f(x,y). 940 [] f(g(f(x,g(f(x,x)))),f(f(y,g(y)),g(f(y,g(y)))))=f(g(f(f(y,g(y)),f(y,g(y)))),f(f(y,g(y)),x)). 941 [] f(g(f(f(x,g(x)),f(x,g(x)))),f(f(x,g(x)),y))=f(y,f(f(x,g(x)),g(f(x,g(x))))). 942 [] f(g(f(f(x,g(x)),f(x,g(x)))),f(f(x,g(x)),y))=f(y,f(x,g(x))). 943 [] f(g(f(f(x,g(x)),f(x,g(x)))),f(f(x,g(x)),y))=y. 944 [] f(g(f(x,g(x))),f(f(x,g(x)),y))=y. 945 [] f(g(f(x,g(x))),y)=y. 946 [] f(x,f(g(f(y,g(y))),f(y,g(g(z)))))=f(f(x,y),z). 947 [] f(x,f(g(f(y,g(y))),f(y,z)))=f(f(x,y),z). 948 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 949 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y # label("Hint 1(2)"). 950 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 2(3)"). 951 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 3(4)"). 952 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 4(925)"). 953 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))) # label("Hint 5(926)"). 954 [] f(g(f(g(f(x,y)),z)),f(f(u,f(g(f(g(f(g(f(x,y)),z)),u)),g(f(g(f(g(f(x,y)),z)),g(v))))),g(f(g(f(x,y)),z))))=f(g(f(x,y)),g(f(x,g(f(x,f(f(y,v),x)))))) # label("Hint 6(957)"). 955 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),g(u))))),g(f(x,y))))=u # label("Hint 7(959)"). 956 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 8(963)"). 957 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))) # label("Hint 9(985)"). 958 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)) # label("Hint 10(996)"). 959 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))) # label("Hint 11(1026)"). 960 [] g(f(x,g(f(x,x))))=x # label("Hint 12(1061)"). 961 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y # label("Hint 13(1135)"). 962 [] f(g(f(x,g(f(f(y,g(f(y,y))),x)))),y)=f(x,g(x)) # label("Hint 14(1140)"). 963 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y # label("Hint 15(1143)"). 964 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))) # label("Hint 16(1145)"). 965 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z # label("Hint 17(1187)"). 966 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y # label("Hint 18(1232)"). 967 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))) # label("Hint 19(1236)"). 968 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x) # label("Hint 20(1245)"). 969 [] f(f(x,f(g(f(y,x)),y)),y)=y # label("Hint 21(1296)"). 970 [] f(g(x),g(f(g(x),g(x))))=x # label("Hint 22(1298)"). 971 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))) # label("Hint 23(1312)"). 972 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)) # label("Hint 24(1360)"). 973 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x))=f(y,g(f(y,y))) # label("Hint 25(1386)"). 974 [] f(g(x),f(f(g(f(g(x),g(x))),x),g(x)))=x # label("Hint 26(1402)"). 975 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(y,f(g(f(x,y)),x)) # label("Hint 27(1597)"). 976 [] f(x,f(g(f(y,x)),y))=f(z,f(g(f(y,z)),y)) # label("Hint 28(1746)"). 977 [] f(x,f(f(g(x),f(y,f(g(f(x,y)),x))),x))=x # label("Hint 29(1776)"). 978 [] f(f(g(f(x,g(x))),g(f(x,g(x)))),x)=x # label("Hint 30(1809)"). 979 [] f(g(f(x,x)),f(x,x))=f(y,f(g(f(x,y)),x)) # label("Hint 31(1860)"). 980 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),u)),x))))))=f(g(f(u,y)),u) # label("Hint 32(1870)"). 981 [] f(g(f(x,y)),g(f(x,g(f(x,f(y,x))))))=f(f(g(y),f(z,f(g(f(y,z)),y))),y) # label("Hint 33(1951)"). 982 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(g(f(z,z)),f(z,z)),x))))))=f(g(f(z,y)),z) # label("Hint 34(2032)"). 983 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z # label("Hint 35(2338)"). 984 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x)))))=y # label("Hint 36(2394)"). 985 [] f(g(f(x,g(f(x,g(x))))),x)=g(f(x,g(x))) # label("Hint 37(2459)"). 986 [] f(f(g(f(g(x),g(x))),x),g(x))=g(f(g(x),g(x))) # label("Hint 38(2621)"). 987 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z # label("Hint 39(2637)"). 988 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x)))=y # label("Hint 40(2862)"). 989 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x) # label("Hint 41(2932)"). 990 [] f(g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(x))),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),x)))))=g(f(g(x),g(x))) # label("Hint 42(3803)"). 991 [] f(g(f(x,g(f(x,f(y,x))))),g(g(f(x,g(f(x,f(f(f(y,x),y),x)))))))=f(x,g(f(x,f(y,x)))) # label("Hint 43(5105)"). 992 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("Hint 44(5192)"). 993 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y # label("Hint 45(5332)"). 994 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)) # label("Hint 46(5497)"). 995 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y # label("Hint 47(5506)"). 996 [] f(g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),f(f(g(x),f(y,f(g(f(x,y)),x))),x))),f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),x))))))=x # label("Hint 48(5587)"). 997 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=f(g(x),f(y,f(g(f(x,y)),x))) # label("Hint 49(5656)"). 998 [] f(g(f(x,x)),f(x,y))=f(z,f(g(f(x,z)),y)) # label("Hint 50(5663)"). 999 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x # label("Hint 51(5711)"). 1000 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z))))=x # label("Hint 52(5945)"). 1001 [] f(x,g(f(x,f(g(x),f(x,g(x))))))=x # label("Hint 53(6027)"). 1002 [] g(f(x,f(f(g(f(x,x)),x),x)))=f(y,f(x,g(f(x,f(y,x))))) # label("Hint 54(6128)"). 1003 [] f(x,f(f(y,f(g(f(x,y)),g(x))),x))=f(x,f(g(x),f(x,g(x)))) # label("Hint 55(6247)"). 1004 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=f(g(x),f(y,f(g(f(x,y)),x))) # label("Hint 56(6394)"). 1005 [] f(g(f(x,y)),f(y,g(y)))=f(g(f(y,y)),f(y,g(x))) # label("Hint 57(6402)"). 1006 [] f(g(f(x,y)),f(y,g(y)))=f(z,f(g(f(y,z)),g(x))) # label("Hint 58(6406)"). 1007 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)) # label("Hint 59(6493)"). 1008 [] g(f(x,f(f(g(f(x,x)),x),x)))=f(f(y,f(g(f(x,y)),g(z))),z) # label("Hint 60(6926)"). 1009 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))) # label("Hint 61(7235)"). 1010 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(f(y,g(y)),z)),f(y,g(y)))),x))))))=f(g(f(y,y)),f(y,g(f(y,g(y))))) # label("Hint 62(7257)"). 1011 [] f(f(x,f(g(f(x,x)),f(x,g(f(x,g(x)))))),f(x,g(x)))=f(x,g(x)) # label("Hint 63(7325)"). 1012 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(u,f(g(f(g(f(x,y)),u)),g(y))) # label("Hint 64(7514)"). 1013 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(f(y,g(y)),z)),f(y,g(y)))),x))))))=f(u,f(g(f(y,u)),g(f(y,g(y))))) # label("Hint 65(7536)"). 1014 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)) # label("Hint 66(9701)"). 1015 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y # label("Hint 67(9753)"). 1016 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y # label("Hint 68(9834)"). 1017 [] g(f(x,f(f(g(x),f(x,g(y))),y)))=f(g(f(x,x)),x) # label("Hint 69(10295)"). 1018 [] f(f(g(f(x,g(x))),f(g(x),g(y))),y)=g(x) # label("Hint 70(10974)"). 1019 [] f(f(g(f(x,g(x))),x),f(g(x),g(x)))=g(x) # label("Hint 71(11084)"). 1020 [] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),g(g(f(x,g(f(x,f(f(f(g(f(y,x)),x),g(f(y,x))),x)))))))=f(x,g(f(x,f(g(f(y,x)),x)))) # label("Hint 72(12379)"). 1021 [] f(g(f(g(x),g(f(g(x),f(g(f(y,g(x))),g(x)))))),g(g(f(g(x),g(f(g(x),f(f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))),g(x))))))))=f(g(x),g(f(g(f(x,y)),f(y,g(y))))) # label("Hint 73(12542)"). 1022 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y # label("Hint 74(13350)"). 1023 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)) # label("Hint 75(13809)"). 1024 [] f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)=f(y,g(f(y,y))) # label("Hint 76(13835)"). 1025 [] f(g(x),f(f(f(g(f(x,g(x))),x),f(g(x),g(g(x)))),g(x)))=f(g(x),f(g(x),x)) # label("Hint 77(13996)"). 1026 [] f(f(x,f(y,g(y))),y)=f(f(x,f(y,g(z))),z) # label("Hint 78(14098)"). 1027 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y # label("Hint 79(14195)"). 1028 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(y))),y) # label("Hint 80(14216)"). 1029 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u) # label("Hint 81(14344)"). 1030 [] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(f(x,f(y,g(y))),y) # label("Hint 82(14358)"). 1031 [] f(f(x,f(g(y),g(g(y)))),g(y))=f(f(x,y),f(g(y),g(y))) # label("Hint 83(14388)"). 1032 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(g(f(g(x),g(x))),f(g(x),g(g(x)))),g(x)))))))=f(g(f(g(x),y)),g(x)) # label("Hint 84(14560)"). 1033 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,f(z,g(z))),z))))))=f(z,g(x)) # label("Hint 85(14594)"). 1034 [] f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x)=f(y,g(f(y,y))) # label("Hint 86(14901)"). 1035 [] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(f(x,f(y,g(u))),u) # label("Hint 87(15130)"). 1036 [] f(g(f(f(g(x),g(g(x))),f(f(g(f(g(x),g(g(x)))),f(f(g(x),g(g(x))),g(y))),y))),g(x))=f(f(g(f(f(g(x),g(g(x))),f(g(x),g(g(x))))),x),f(g(x),g(x))) # label("Hint 88(15376)"). 1037 [] f(f(x,f(g(y),g(z))),z)=f(f(x,y),f(g(y),g(y))) # label("Hint 89(15405)"). 1038 [] f(f(x,g(f(x,f(f(g(y),f(x,g(x))),x)))),x)=y # label("Hint 90(15790)"). 1039 [] f(f(x,g(f(x,f(f(g(y),f(x,g(z))),z)))),x)=y # label("Hint 91(15976)"). 1040 [] f(f(x,g(y)),g(f(f(x,g(y)),f(f(g(z),f(f(x,g(y)),g(u))),u))))=g(f(f(x,g(f(x,f(z,y)))),x)) # label("Hint 92(16199)"). 1041 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,f(z,g(u))),u))))))=f(z,g(x)) # label("Hint 93(16406)"). 1042 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(z,f(g(z),u)) # label("Hint 94(18220)"). 1043 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v) # label("Hint 95(18399)"). 1044 [] f(f(f(g(f(x,g(x))),x),f(g(x),g(y))),y)=f(g(x),x) # label("Hint 96(24201)"). 1045 [] f(x,f(f(y,f(g(f(x,y)),g(z))),z))=f(x,f(g(x),f(x,g(x)))) # label("Hint 97(24262)"). 1046 [] f(f(g(f(x,g(x))),x),g(f(f(g(f(x,g(x))),x),f(g(f(x,g(x))),x))))=f(f(g(x),g(f(g(x),f(g(x),x)))),g(x)) # label("Hint 98(24578)"). 1047 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(g(f(x,f(g(x),f(x,g(x)))))))) # label("Hint 99(25487)"). 1048 [] f(f(x,g(f(x,x))),f(g(f(f(y,f(g(f(x,y)),g(z))),z)),u))=f(x,f(g(x),u)) # label("Hint 100(26442)"). 1049 [] f(x,f(f(y,f(z,g(x))),x))=f(x,f(f(y,f(z,g(u))),u)) # label("Hint 101(28318)"). 1050 [] f(x,f(f(y,f(z,g(u))),u))=f(x,f(f(y,f(z,g(v))),v)) # label("Hint 102(29025)"). 1051 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=y # label("Hint 103(32516)"). 1052 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=g(x) # label("Hint 104(33050)"). 1053 [] f(g(f(f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x # label("Hint 105(33126)"). 1054 [] f(f(x,g(x)),f(x,g(x)))=f(x,g(x)) # label("Hint 106(33356)"). 1055 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(f(y,g(y)),z)),f(y,g(y)))),x))))))=g(y) # label("Hint 107(33362)"). 1056 [] f(g(x),f(y,f(g(f(x,y)),x)))=g(x) # label("Hint 108(33366)"). 1057 [] f(x,f(g(f(y,x)),g(f(y,g(y)))))=g(y) # label("Hint 109(33380)"). 1058 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=g(x) # label("Hint 110(33481)"). 1059 [] f(g(f(f(g(x),x),f(g(x),x))),f(f(g(x),x),g(f(f(g(x),x),g(f(f(g(x),x),x))))))=x # label("Hint 111(33487)"). 1060 [] f(g(f(f(g(x),x),g(x))),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))) # label("Hint 112(33503)"). 1061 [] f(g(f(x,y)),g(f(x,g(f(x,f(y,x))))))=f(g(y),y) # label("Hint 113(33537)"). 1062 [] f(x,f(g(x),x))=x # label("Hint 114(33545)"). 1063 [] f(f(x,x),f(y,f(g(f(x,y)),x)))=f(x,x) # label("Hint 115(33791)"). 1064 [] g(f(f(x,g(x)),g(f(x,g(x)))))=f(x,g(x)) # label("Hint 116(34203)"). 1065 [] f(f(g(f(x,x)),f(x,y)),f(y,g(f(y,y))))=f(g(x),f(x,g(x))) # label("Hint 117(34593)"). 1066 [] f(g(g(x)),f(f(g(f(f(g(f(y,g(x))),g(f(y,g(f(y,f(g(x),y)))))),g(g(x)))),f(g(g(x)),g(z))),z))=x # label("Hint 118(35234)"). 1067 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=x # label("Hint 119(36909)"). 1068 [] f(g(f(x,g(x))),f(x,g(x)))=g(f(x,g(x))) # label("Hint 120(36924)"). 1069 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(g(y),x)))))),y)=y # label("Hint 121(37566)"). 1070 [] f(f(g(x),x),f(g(x),g(f(x,g(x)))))=g(x) # label("Hint 122(37732)"). 1071 [] f(f(x,f(g(f(y,x)),z)),f(z,g(f(z,z))))=f(g(y),f(y,g(y))) # label("Hint 123(37966)"). 1072 [] f(x,f(f(y,f(g(f(z,y)),g(u))),u))=f(x,f(g(z),f(z,g(z)))) # label("Hint 124(37967)"). 1073 [] f(f(f(g(f(f(f(x,f(g(f(y,x)),g(z))),z),g(f(f(x,f(g(f(y,x)),g(z))),z)))),f(f(x,f(g(f(y,x)),g(z))),z)),f(g(f(f(x,f(g(f(y,x)),g(z))),z)),g(u))),u)=f(g(f(f(x,f(g(f(y,x)),g(z))),z)),f(g(y),f(y,g(y)))) # label("Hint 125(38320)"). 1074 [] g(f(f(g(x),f(x,g(x))),f(f(g(f(g(x),f(x,g(x)))),f(f(g(x),f(x,g(x))),g(f(g(x),f(x,g(x)))))),f(f(y,f(g(f(x,y)),g(z))),z))))=f(g(f(f(g(x),f(x,g(x))),f(g(x),f(x,g(x))))),f(g(x),f(x,g(x)))) # label("Hint 126(38810)"). 1075 [] f(f(g(x),f(x,g(x))),f(g(f(g(x),f(x,g(x)))),f(f(y,f(g(f(x,y)),g(z))),z)))=f(g(x),f(x,g(x))) # label("Hint 127(38832)"). 1076 [] f(g(g(f(f(x,g(x)),x))),f(f(x,g(x)),f(g(g(x)),g(f(f(x,g(x)),x)))))=g(g(f(f(x,g(x)),x))) # label("Hint 128(39227)"). 1077 [] f(x,f(g(f(y,x)),f(y,g(y))))=f(g(y),g(f(y,g(y)))) # label("Hint 129(41294)"). 1078 [] f(g(f(f(g(f(x,g(x))),g(g(f(x,g(x))))),g(f(x,g(x))))),f(g(f(x,g(x))),g(g(x))))=x # label("Hint 130(41299)"). 1079 [] f(f(f(g(f(x,g(x))),f(x,g(x))),x),f(g(x),g(x)))=g(x) # label("Hint 131(41449)"). 1080 [] f(g(f(x,g(x))),f(g(f(x,g(x))),f(x,g(x))))=f(y,f(g(f(x,y)),x)) # label("Hint 132(41460)"). 1081 [] f(f(g(f(x,g(x))),f(g(f(x,g(x))),f(x,g(x)))),x)=x # label("Hint 133(41462)"). 1082 [] g(f(x,g(x)))=f(x,g(x)) # label("Hint 134(41468)"). 1083 [] f(f(x,x),f(g(x),f(f(g(f(x,g(x))),f(x,g(x))),x)))=f(x,x) # label("Hint 135(41582)"). 1084 [] f(g(x),f(g(x),f(f(g(f(x,g(x))),f(x,g(x))),x)))=g(x) # label("Hint 136(41584)"). 1085 [] f(f(g(x),f(f(g(f(x,g(x))),f(x,g(x))),x)),x)=x # label("Hint 137(41690)"). 1086 [] f(x,f(g(f(y,x)),f(y,g(y))))=g(y) # label("Hint 138(41781)"). 1087 [] f(f(g(f(x,g(x))),f(x,g(x))),x)=x # label("Hint 139(41800)"). 1088 [] g(f(x,f(f(g(x),g(f(x,g(x)))),x)))=f(g(f(x,x)),x) # label("Hint 140(42085)"). 1089 [] f(x,g(f(x,f(g(x),g(f(x,g(x)))))))=x # label("Hint 141(42121)"). 1090 [] f(g(f(g(x),g(x))),f(g(x),g(f(g(x),g(f(g(x),g(f(x,g(x)))))))))=x # label("Hint 142(42264)"). 1091 [] f(g(x),g(f(x,g(x))))=g(x) # label("Hint 143(42288)"). 1092 [] f(f(g(x),x),x)=x # label("Hint 144(42297)"). 1093 [] f(g(x),f(g(x),x))=g(x) # label("Hint 145(42300)"). 1094 [] f(f(x,x),f(g(x),x))=f(x,x) # label("Hint 146(42302)"). 1095 [] f(x,f(g(x),g(x)))=g(x) # label("Hint 147(42306)"). 1096 [] g(g(x))=x # label("Hint 148(42349)"). 1097 [] f(x,g(f(x,g(x))))=x # label("Hint 149(42384)"). 1098 [] f(g(f(x,x)),x)=g(x) # label("Hint 150(42387)"). 1099 [] f(f(g(x),x),g(x))=g(x) # label("Hint 151(42409)"). 1100 [] g(f(g(x),g(x)))=f(x,x) # label("Hint 152(42430)"). 1101 [] f(g(f(f(g(x),x),f(g(x),x))),x)=x # label("Hint 153(42437)"). 1102 [] f(g(f(x,g(x))),x)=x # label("Hint 154(42469)"). 1103 [] f(x,f(g(f(y,x)),y))=g(f(y,g(y))) # label("Hint 155(42471)"). 1104 [] f(x,g(f(x,x)))=g(x) # label("Hint 156(42473)"). 1105 [] f(g(x),f(x,g(x)))=g(x) # label("Hint 157(42477)"). 1106 [] f(g(x),f(x,f(f(y,f(g(f(x,y)),g(z))),z)))=g(x) # label("Hint 158(42572)"). 1107 [] f(f(x,x),g(x))=x # label("Hint 159(42582)"). 1108 [] f(f(x,g(x)),x)=x # label("Hint 160(42863)"). 1109 [] f(x,f(f(x,g(x)),f(x,g(x))))=x # label("Hint 161(43933)"). 1110 [] f(x,f(f(g(x),f(x,g(y))),y))=x # label("Hint 162(44958)"). 1111 [] f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y)))=x # label("Hint 163(45415)"). 1112 [] f(f(x,f(f(x,g(x)),g(y))),y)=x # label("Hint 164(46711)"). 1113 [] f(g(f(g(x),x)),g(x))=g(x) # label("Hint 165(48270)"). 1114 [] f(g(f(g(x),y)),g(x))=f(g(f(x,y)),x) # label("Hint 166(48315)"). 1115 [] f(g(f(g(x),g(f(g(x),f(g(f(y,g(x))),g(x)))))),f(g(x),g(f(g(x),f(f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))),g(x))))))=f(g(x),g(f(g(f(x,y)),f(y,g(y))))) # label("Hint 167(48658)"). 1116 [] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),f(x,g(f(x,f(f(f(g(f(y,x)),x),g(f(y,x))),x)))))=f(x,g(f(x,f(g(f(y,x)),x)))) # label("Hint 168(48764)"). 1117 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(u,f(g(f(g(f(x,y)),u)),g(y))) # label("Hint 169(49475)"). 1118 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=x # label("Hint 170(49546)"). 1119 [] f(f(x,f(g(f(y,x)),g(z))),z)=g(y) # label("Hint 171(50897)"). 1120 [] f(x,f(y,g(f(y,f(x,y)))))=g(y) # label("Hint 172(50908)"). 1121 [] f(f(g(x),f(x,g(y))),y)=f(x,g(x)) # label("Hint 173(53398)"). 1122 [] f(f(x,f(g(f(y,x)),z)),g(z))=g(y) # label("Hint 174(53934)"). 1123 [] f(x,f(y,f(g(f(g(x),y)),g(x))))=x # label("Hint 175(54008)"). 1124 [] f(f(g(f(x,x)),f(x,y)),g(y))=g(x) # label("Hint 176(54186)"). 1125 [] f(g(x),f(x,y))=f(x,f(g(x),y)) # label("Hint 177(55221)"). 1126 [] f(x,f(g(f(g(f(y,z)),x)),g(z)))=y # label("Hint 178(57555)"). 1127 [] f(f(f(g(x),f(x,g(y))),y),x)=x # label("Hint 179(65401)"). 1128 [] f(g(f(x,f(g(x),f(x,g(y))))),x)=y # label("Hint 180(65718)"). 1129 [] f(g(f(x,f(g(x),f(x,y)))),x)=g(y) # label("Hint 181(68393)"). 1130 [] f(f(x,f(f(x,g(x)),y)),g(y))=x # label("Hint 182(98136)"). 1131 [] f(g(f(x,y)),f(y,g(f(g(f(x,x)),f(x,y)))))=g(y) # label("Hint 183(99383)"). 1132 [] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),y)=g(f(z,g(f(z,f(f(u,y),z))))) # label("Hint 184(134583)"). 1133 [] f(g(f(f(x,f(f(x,g(x)),y)),f(g(f(x,f(f(x,g(x)),y))),x))),f(x,f(f(x,g(x)),y)))=y # label("Hint 185(156011)"). 1134 [] f(g(f(g(x),f(x,f(x,f(g(x),y))))),g(x))=g(f(x,y)) # label("Hint 186(156065)"). 1135 [] g(f(y,g(f(y,f(x,y)))))=f(g(f(x,f(g(x),g(y)))),x) # label("Hint 187(156078)"). 1136 [] f(x,f(y,g(f(g(x),f(x,y)))))=x # label("Hint 188(156283)"). 1137 [] f(x,f(y,g(f(x,f(g(x),y)))))=x # label("Hint 189(156730)"). 1138 [] f(x,f(y,g(f(z,f(g(f(f(u,f(g(f(x,u)),x)),z)),y)))))=x # label("Hint 190(157330)"). 1139 [] f(g(x),f(x,f(x,f(g(x),y))))=y # label("Hint 191(157390)"). 1140 [] g(f(y,x))=f(g(x),g(y)) # label("Hint 192(157577)"). 1141 [] f(g(x),f(y,f(g(f(z,y)),z)))=g(f(f(z,g(z)),x)) # label("Hint 193(157725)"). 1142 [] f(x,g(f(g(f(y,y)),f(y,x))))=y # label("Hint 194(157838)"). 1143 [] f(x,g(f(y,f(g(f(z,y)),x))))=z # label("Hint 195(157840)"). 1144 [] g(f(g(f(x,y)),x))=f(x,f(g(x),y)) # label("Hint 196(157858)"). 1145 [] f(g(f(x,y)),x)=g(y) # label("Hint 197(157946)"). 1146 [] f(g(x),f(y,g(f(y,f(f(f(g(f(x,y)),y),g(f(x,y))),y)))))=x # label("Hint 198(157956)"). 1147 [] f(x,f(y,g(y)))=x # label("Hint 199(157975)"). 1148 [] f(g(x),f(x,y))=y # label("Hint 200(157984)"). 1149 [] f(x,f(g(x),y))=y # label("Hint 201(158039)"). 1150 [] g(f(f(x,g(x)),y))=g(y) # label("Hint 202(158042)"). 1151 [] g(f(x,g(f(x,f(y,x)))))=f(x,y) # label("Hint 203(158128)"). 1152 [] f(f(x,g(x)),y)=y # label("Hint 204(158173)"). 1153 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 205(158372)"). end_of_list. list(hints2). 1154 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y. 1155 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 1156 [] f(f(a,b),c)!=f(a,f(b,c)). 1157 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 1158 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))). 1159 [] f(g(f(g(f(x,y)),z)),f(f(u,f(g(f(g(f(g(f(x,y)),z)),u)),g(f(g(f(g(f(x,y)),z)),g(v))))),g(f(g(f(x,y)),z))))=f(g(f(x,y)),g(f(x,g(f(x,f(f(y,v),x)))))). 1160 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),g(u))))),g(f(x,y))))=u. 1161 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 1162 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 1163 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)). 1164 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))). 1165 [] g(f(x,g(f(x,x))))=x. 1166 [] f(g(f(x,g(f(f(y,g(f(y,y))),x)))),y)=f(x,g(x)). 1167 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y. 1168 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y. 1169 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))). 1170 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))). 1171 [] f(g(f(x,g(f(x,x)))),f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 1172 [] f(x,f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 1173 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 1174 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 1175 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y. 1176 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))). 1177 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x). 1178 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,y),x))))))=f(f(z,f(g(f(y,z)),y)),y). 1179 [] f(f(x,f(g(f(y,x)),y)),y)=y. 1180 [] f(g(x),g(f(g(x),g(x))))=x. 1181 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))). 1182 [] f(f(g(f(x,x)),f(x,x)),x)=x. 1183 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)). 1184 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x))=f(y,g(f(y,y))). 1185 [] f(g(x),f(f(g(f(g(x),g(x))),x),g(x)))=x. 1186 [] f(g(f(x,g(x))),f(f(g(f(g(f(x,g(x))),g(f(x,g(x))))),f(g(f(x,g(x))),g(f(x,g(x))))),g(f(x,g(x)))))=f(y,f(g(f(x,y)),x)). 1187 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(y,f(g(f(x,y)),x)). 1188 [] f(x,f(g(f(y,x)),y))=f(z,f(g(f(y,z)),y)). 1189 [] f(x,f(f(g(x),f(y,f(g(f(x,y)),x))),x))=x. 1190 [] f(f(g(f(x,g(x))),g(f(x,g(x)))),x)=x. 1191 [] f(g(f(x,g(f(x,g(x))))),g(f(x,g(f(x,x)))))=g(f(x,g(x))). 1192 [] f(g(f(x,g(f(x,g(x))))),x)=g(f(x,g(x))). 1193 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),u)),x))))))=f(g(f(u,y)),u). 1194 [] f(g(f(x,y)),g(f(x,g(f(x,f(y,x))))))=f(f(g(y),f(z,f(g(f(y,z)),y))),y). 1195 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 1196 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(g(f(y,g(f(y,f(f(z,f(g(f(y,z)),x)),y))))),u)),x)))))=u. 1197 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x)))))=y. 1198 [] g(f(g(x),g(f(g(x),f(f(g(f(g(x),g(x))),x),g(x))))))=f(f(g(f(g(x),g(x))),x),g(x)). 1199 [] f(f(g(f(g(x),g(x))),x),g(x))=g(f(g(x),g(x))). 1200 [] g(f(g(f(x,g(f(x,x)))),f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,z)))),g(f(x,g(f(x,x)))))))=z. 1201 [] g(f(x,f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,z)))),g(f(x,g(f(x,x)))))))=z. 1202 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),g(f(x,g(f(x,x)))))))=z. 1203 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 1204 [] g(f(x,f(f(g(f(x,x)),f(g(f(y,g(f(y,f(f(z,f(g(f(y,z)),x)),y))))),g(f(x,u)))),x)))=u. 1205 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x)))=y. 1206 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x). 1207 [] f(g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(x))),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),x)))))=g(f(g(x),g(x))). 1208 [] f(g(f(x,g(f(x,f(y,x))))),g(g(f(x,g(f(x,f(f(f(y,x),y),x)))))))=f(x,g(f(x,f(y,x)))). 1209 [] f(x,f(g(f(y,g(f(x,g(f(x,x)))))),g(f(y,g(f(y,f(z,y)))))))=z. 1210 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 1211 [] f(g(f(x,x)),f(g(f(y,f(f(g(f(y,y)),f(y,g(f(y,x)))),y))),g(f(x,g(f(x,f(z,x)))))))=z. 1212 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y. 1213 [] f(x,f(g(f(y,x)),g(f(z,g(f(z,z))))))=f(g(f(y,y)),f(y,z)). 1214 [] f(x,f(g(f(y,x)),z))=f(g(f(y,y)),f(y,z)). 1215 [] f(x,f(g(f(y,x)),g(f(z,g(f(z,z))))))=f(u,f(g(f(y,u)),z)). 1216 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 1217 [] f(g(f(f(g(f(x,g(f(x,f(y,x))))),g(f(g(f(x,g(f(x,f(y,x))))),g(f(x,g(f(x,f(y,x)))))))),x)),f(x,g(x)))=y. 1218 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y. 1219 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=f(g(x),f(y,f(g(f(x,y)),x))). 1220 [] f(g(f(x,y)),f(y,g(y)))=f(g(f(y,y)),f(y,g(x))). 1221 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z))))=x. 1222 [] f(g(f(x,x)),f(g(f(y,f(f(g(f(y,y)),f(y,g(f(y,x)))),y))),z))=f(u,f(g(f(x,u)),z)). 1223 [] f(g(f(x,x)),f(x,y))=f(z,f(g(f(x,z)),y)). 1224 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(z,f(g(z),u)). 1225 [] f(g(f(x,y)),f(y,g(y)))=f(z,f(g(f(y,z)),g(x))). 1226 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x. 1227 [] f(x,g(f(x,f(g(f(x,x)),f(x,g(f(x,g(f(x,f(f(g(x),f(x,g(x))),x))))))))))=x. 1228 [] f(x,g(f(x,f(g(x),f(x,g(x))))))=x. 1229 [] g(f(x,f(f(g(f(x,x)),x),x)))=f(y,f(x,g(f(x,f(y,x))))). 1230 [] f(g(f(x,f(g(x),f(x,g(x))))),g(f(g(f(x,f(g(x),f(x,g(x))))),g(f(x,f(g(x),f(x,g(x))))))))=f(x,f(f(y,f(g(f(x,y)),g(f(x,g(f(x,f(g(x),f(x,g(x))))))))),x)). 1231 [] f(g(f(x,f(g(x),f(x,g(x))))),g(f(g(f(x,f(g(x),f(x,g(x))))),g(f(x,f(g(x),f(x,g(x))))))))=f(x,f(f(y,f(g(f(x,y)),g(x))),x)). 1232 [] f(x,f(f(y,f(g(f(x,y)),g(x))),x))=f(x,f(g(x),f(x,g(x)))). 1233 [] f(g(f(f(x,g(f(x,f(g(f(y,x)),g(f(y,g(f(y,f(x,y))))))))),x)),f(x,g(x)))=f(g(x),f(z,f(g(f(x,z)),x))). 1234 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=f(g(x),f(y,f(g(f(x,y)),x))). 1235 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)). 1236 [] g(f(x,f(f(g(f(x,x)),x),x)))=f(f(y,f(g(f(x,y)),g(z))),z). 1237 [] f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y)))=f(g(f(y,g(f(x,y)))),f(g(f(x,y)),g(g(f(x,y))))). 1238 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))). 1239 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(f(y,g(y)),z)),f(y,g(y)))),x))))))=f(g(f(y,y)),f(y,g(f(y,g(y))))). 1240 [] f(f(x,f(g(f(x,x)),f(x,g(f(x,g(x)))))),f(x,g(x)))=f(x,g(x)). 1241 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(u,f(g(f(g(f(x,y)),u)),g(y))). 1242 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(f(y,g(y)),z)),f(y,g(y)))),x))))))=f(u,f(g(f(y,u)),g(f(y,g(y))))). 1243 [] f(g(f(g(x),g(f(g(x),g(x))))),f(f(g(f(x,g(f(g(x),g(f(g(x),g(x))))))),f(g(f(g(x),g(f(g(x),g(x))))),g(y))),y))=f(g(x),g(f(g(x),g(f(g(x),g(x)))))). 1244 [] f(g(x),f(f(g(f(x,g(f(g(x),g(f(g(x),g(x))))))),f(g(f(g(x),g(f(g(x),g(x))))),g(y))),y))=f(g(x),g(f(g(x),g(f(g(x),g(x)))))). 1245 [] f(g(x),f(f(g(f(x,g(x))),f(g(f(g(x),g(f(g(x),g(x))))),g(y))),y))=f(g(x),g(f(g(x),g(f(g(x),g(x)))))). 1246 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(f(g(x),g(f(g(x),g(x)))))). 1247 [] f(g(x),f(f(g(f(x,g(x))),f(g(x),g(y))),y))=f(g(x),g(x)). 1248 [] f(g(f(x,g(f(x,x)))),f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 1249 [] f(x,f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 1250 [] f(x,f(f(g(f(f(x,y),x)),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 1251 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))). 1252 [] g(f(g(x),f(f(y,f(g(f(g(x),y)),g(f(g(x),g(x))))),g(x))))=f(f(g(f(x,g(x))),f(g(x),g(z))),z). 1253 [] f(f(g(f(x,g(x))),f(g(x),g(y))),y)=g(x). 1254 [] f(f(g(f(x,g(x))),f(y,f(f(g(f(y,y)),f(y,g(f(y,g(x))))),y))),f(g(x),g(x)))=g(x). 1255 [] f(f(g(f(x,g(x))),x),f(g(x),g(x)))=g(x). 1256 [] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),g(g(f(x,g(f(x,f(f(f(g(f(y,x)),x),g(f(y,x))),x)))))))=f(x,g(f(x,f(g(f(y,x)),x)))). 1257 [] f(g(x),f(g(f(y,g(x))),g(x)))=f(g(f(x,y)),f(y,g(y))). 1258 [] f(g(f(g(x),g(f(g(x),f(g(f(y,g(x))),g(x)))))),g(g(f(g(x),g(f(g(x),f(f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))),g(x))))))))=f(g(x),g(f(g(f(x,y)),f(y,g(y))))). 1259 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(f(f(x,g(x)),f(x,g(x)))),f(f(x,g(x)),g(y))),f(x,g(x)))))). 1260 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y. 1261 [] f(x,f(f(g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)),f(x,g(z))),z))=f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(x,f(f(y,f(x,g(x))),x)))))). 1262 [] f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(g(f(x,f(f(y,f(x,g(x))),x))),g(f(x,f(f(y,f(x,g(x))),x))))))=f(x,f(f(y,f(x,g(z))),z)). 1263 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)). 1264 [] f(g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)),g(f(g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)),y)))=f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x). 1265 [] f(x,g(f(g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)),x)))=f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y). 1266 [] f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)=f(y,g(f(y,y))). 1267 [] f(g(x),f(f(f(g(f(x,g(x))),x),f(g(x),g(g(x)))),g(x)))=f(g(x),f(f(f(g(f(x,g(x))),x),f(g(x),g(x))),x)). 1268 [] f(g(x),f(f(f(g(f(x,g(x))),x),f(g(x),g(g(x)))),g(x)))=f(g(x),f(g(x),x)). 1269 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,f(f(z,f(x,g(x))),x))))),x)))=f(f(z,f(x,g(u))),u). 1270 [] f(f(x,f(y,g(y))),y)=f(f(x,f(y,g(z))),z). 1271 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y. 1272 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,f(f(z,f(x,g(u))),u))))),x)))=f(f(z,f(x,g(x))),x). 1273 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(y))),y). 1274 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u). 1275 [] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(f(x,f(y,g(u))),u). 1276 [] f(f(x,f(g(y),g(z))),z)=f(f(x,y),f(g(y),g(y))). 1277 [] f(f(f(g(f(x,g(x))),x),f(g(x),g(y))),y)=f(g(x),x). 1278 [] f(x,f(f(y,f(g(f(x,y)),g(z))),z))=f(x,f(g(x),f(x,g(x)))). 1279 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(f(x,g(f(x,f(g(x),f(x,g(x)))))),f(g(g(f(x,f(g(x),f(x,g(x)))))),g(g(f(x,f(g(x),f(x,g(x)))))))). 1280 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(g(f(x,f(g(x),f(x,g(x)))))))). 1281 [] f(f(x,g(f(x,x))),f(g(f(f(y,f(g(f(x,y)),g(z))),z)),u))=f(x,f(g(x),u)). 1282 [] f(f(g(f(x,g(x))),x),g(f(f(g(f(x,g(x))),x),f(g(f(x,g(x))),x))))=f(f(g(x),g(f(g(x),f(g(x),x)))),g(x)). 1283 [] f(f(x,g(f(x,f(f(g(y),f(x,g(x))),x)))),x)=f(g(y),f(f(g(f(g(y),g(y))),y),g(y))). 1284 [] f(f(x,g(f(x,f(f(g(y),f(x,g(x))),x)))),x)=y. 1285 [] f(f(x,g(f(x,f(f(g(y),f(x,g(z))),z)))),x)=y. 1286 [] f(f(x,g(y)),g(f(f(x,g(y)),f(f(g(z),f(f(x,g(y)),g(u))),u))))=g(f(f(x,g(f(x,f(z,y)))),x)). 1287 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=y. 1288 [] f(g(f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z)))),x)),f(x,g(f(x,g(x)))))=g(x). 1289 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=g(x). 1290 [] f(g(f(f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1291 [] f(f(x,g(x)),f(x,g(x)))=f(x,g(x)). 1292 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(f(y,g(y)),z)),f(y,g(y)))),x))))))=g(y). 1293 [] f(g(x),f(y,f(g(f(x,y)),x)))=g(x). 1294 [] f(x,f(g(f(y,x)),g(f(y,g(y)))))=g(y). 1295 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=g(x). 1296 [] f(g(f(f(g(x),x),g(x))),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),x)))))=g(f(g(x),g(x))). 1297 [] f(g(f(f(g(x),x),g(x))),g(f(f(g(x),x),g(f(f(f(g(x),f(y,f(g(f(x,y)),x))),x),x)))))=g(f(g(x),g(x))). 1298 [] f(g(f(f(g(x),x),g(x))),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 1299 [] f(x,f(g(x),x))=x. 1300 [] g(f(f(x,g(x)),g(f(x,g(x)))))=f(x,g(x)). 1301 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=g(f(x,g(f(x,x)))). 1302 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=x. 1303 [] f(g(f(x,g(x))),f(f(x,g(x)),f(g(f(x,g(x))),f(x,g(x)))))=g(f(x,g(x))). 1304 [] f(g(f(x,g(x))),f(x,g(x)))=g(f(x,g(x))). 1305 [] f(f(g(f(x,x)),f(x,g(f(x,g(x))))),f(x,g(x)))=f(f(g(f(x,x)),f(x,y)),f(y,g(f(y,y)))). 1306 [] f(f(g(f(x,x)),f(x,y)),f(y,g(f(y,y))))=f(g(x),f(x,g(x))). 1307 [] f(f(g(x),x),f(g(x),g(f(x,g(x)))))=g(x). 1308 [] f(f(x,f(g(f(y,x)),g(f(y,g(y))))),f(y,g(y)))=f(f(x,f(g(f(y,x)),z)),f(z,g(f(z,z)))). 1309 [] f(f(x,f(g(f(y,x)),z)),f(z,g(f(z,z))))=f(g(y),f(y,g(y))). 1310 [] f(g(g(f(f(x,g(x)),x))),f(f(x,g(x)),f(g(g(x)),g(f(f(x,g(x)),x)))))=g(g(f(f(x,g(x)),x))). 1311 [] f(g(f(f(g(f(x,g(x))),g(g(f(x,g(x))))),g(f(x,g(x))))),f(g(f(x,g(x))),g(g(x))))=x. 1312 [] f(g(x),g(f(x,g(x))))=f(g(f(x,x)),f(x,f(x,g(x)))). 1313 [] g(f(f(x,g(x)),f(g(f(x,g(x))),f(x,g(x)))))=f(x,g(x)). 1314 [] g(f(x,g(x)))=f(x,g(x)). 1315 [] f(f(g(f(x,g(x))),f(g(f(x,g(x))),f(x,g(x)))),x)=x. 1316 [] f(g(f(x,g(x))),f(g(f(x,g(x))),f(x,g(x))))=f(y,f(g(f(x,y)),x)). 1317 [] f(f(g(x),f(f(g(f(x,g(x))),f(x,g(x))),x)),x)=x. 1318 [] f(g(x),f(g(x),f(f(g(f(x,g(x))),f(x,g(x))),x)))=g(x). 1319 [] f(g(f(x,x)),f(x,f(x,g(x))))=g(x). 1320 [] f(f(g(f(x,g(x))),f(x,g(x))),x)=x. 1321 [] f(x,g(f(x,f(g(x),g(f(x,g(x)))))))=x. 1322 [] g(f(x,f(f(g(x),g(f(x,g(x)))),x)))=f(g(f(x,x)),x). 1323 [] f(g(f(g(x),g(x))),f(g(x),g(f(g(x),g(f(g(x),g(f(x,g(x)))))))))=x. 1324 [] f(g(x),g(f(x,g(x))))=g(x). 1325 [] f(g(x),f(g(x),x))=g(x). 1326 [] f(f(g(x),x),x)=x. 1327 [] f(g(f(g(x),g(x))),f(g(x),g(f(g(x),g(g(x))))))=x. 1328 [] g(g(x))=x. 1329 [] g(f(x,f(g(x),x)))=f(g(f(x,x)),x). 1330 [] f(g(f(x,x)),x)=g(x). 1331 [] f(x,g(f(x,g(x))))=x. 1332 [] f(f(g(x),x),g(x))=g(x). 1333 [] f(x,f(g(f(y,x)),y))=g(f(y,g(y))). 1334 [] f(g(f(x,g(x))),x)=x. 1335 [] f(x,g(f(f(g(f(x,g(x))),x),f(g(f(x,g(x))),x))))=f(f(g(x),g(f(g(x),f(g(x),x)))),g(x)). 1336 [] f(x,g(f(x,f(g(f(x,g(x))),x))))=f(f(g(x),g(f(g(x),f(g(x),x)))),g(x)). 1337 [] f(f(g(x),g(f(g(x),f(g(x),x)))),g(x))=f(x,g(f(x,x))). 1338 [] f(f(g(x),g(g(x))),g(x))=f(x,g(f(x,x))). 1339 [] f(x,g(f(x,x)))=f(f(g(x),x),g(x)). 1340 [] f(x,g(f(x,x)))=g(x). 1341 [] f(g(x),f(f(x,f(g(x),g(g(x)))),g(x)))=f(g(x),f(g(x),x)). 1342 [] f(g(x),f(f(x,f(g(x),x)),g(x)))=f(g(x),f(g(x),x)). 1343 [] f(g(x),f(g(x),x))=f(g(x),f(x,g(x))). 1344 [] f(g(x),f(x,g(x)))=g(x). 1345 [] f(g(g(x)),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 1346 [] f(x,g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 1347 [] f(x,g(f(f(g(x),x),g(x))))=g(f(g(x),g(x))). 1348 [] g(f(g(x),g(x)))=f(x,g(g(x))). 1349 [] g(f(g(x),g(x)))=f(x,x). 1350 [] f(g(f(f(g(f(x,g(x))),f(x,g(x))),g(f(x,g(x))))),f(g(f(x,g(x))),g(g(x))))=x. 1351 [] f(g(g(f(x,g(x)))),f(g(f(x,g(x))),g(g(x))))=x. 1352 [] f(f(x,g(x)),f(g(f(x,g(x))),g(g(x))))=x. 1353 [] f(f(x,g(x)),f(g(f(x,g(x))),x))=x. 1354 [] f(f(x,g(x)),x)=x. 1355 [] g(g(f(f(x,g(x)),x)))=f(g(g(x)),f(f(x,g(x)),f(g(g(x)),g(f(f(x,g(x)),x))))). 1356 [] g(g(f(f(x,g(x)),x)))=f(x,f(f(x,g(x)),f(g(g(x)),g(f(f(x,g(x)),x))))). 1357 [] g(g(f(f(x,g(x)),x)))=f(x,f(f(x,g(x)),f(x,g(f(f(x,g(x)),x))))). 1358 [] g(g(f(f(x,g(x)),x)))=f(x,f(f(x,g(x)),f(x,g(x)))). 1359 [] g(g(x))=f(x,f(f(x,g(x)),f(x,g(x)))). 1360 [] f(x,f(f(x,g(x)),f(x,g(x))))=x. 1361 [] f(g(f(f(g(f(x,y)),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1362 [] f(g(f(f(g(f(x,y)),f(f(x,y),g(f(x,y)))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1363 [] f(g(f(g(f(x,y)),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1364 [] f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1365 [] f(f(f(x,y),f(x,y)),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1366 [] f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y)))=x. 1367 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(g(g(f(x,g(x)))),g(g(f(x,f(g(x),f(x,g(x)))))))). 1368 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(f(x,g(x)),g(g(f(x,f(g(x),f(x,g(x)))))))). 1369 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(f(x,g(x)),g(g(f(x,g(x)))))). 1370 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(f(x,g(x)),f(x,g(x)))). 1371 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=x. 1372 [] f(f(x,f(g(g(f(x,g(x)))),g(y))),y)=x. 1373 [] f(f(x,f(f(x,g(x)),g(y))),y)=x. 1374 [] f(g(f(g(x),g(f(g(x),f(g(f(y,g(x))),g(x)))))),f(g(x),g(f(g(x),f(f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))),g(x))))))=f(g(x),g(f(g(f(x,y)),f(y,g(y))))). 1375 [] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),f(x,g(f(x,f(f(f(g(f(y,x)),x),g(f(y,x))),x)))))=f(x,g(f(x,f(g(f(y,x)),x)))). 1376 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(u,f(g(f(g(f(x,y)),u)),g(y))). 1377 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))). 1378 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y))). 1379 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=x. 1380 [] f(f(x,f(g(f(y,x)),g(z))),z)=g(f(y,f(g(y),y))). 1381 [] f(f(x,f(g(f(y,x)),g(z))),z)=g(y). 1382 [] f(x,f(y,g(f(y,f(x,y)))))=g(f(y,f(g(y),y))). 1383 [] f(x,f(y,g(f(y,f(x,y)))))=g(y). 1384 [] f(f(x,f(g(f(y,x)),z)),g(z))=f(g(y),f(y,g(y))). 1385 [] f(f(x,f(g(f(y,x)),z)),g(z))=g(y). 1386 [] f(f(g(f(x,x)),f(x,y)),g(y))=f(g(x),f(x,g(x))). 1387 [] f(f(g(f(x,x)),f(x,y)),g(y))=g(x). 1388 [] f(x,f(y,f(g(f(g(x),y)),f(x,g(f(x,x))))))=x. 1389 [] f(x,f(y,f(g(f(g(x),y)),g(x))))=x. 1390 [] f(g(x),f(g(f(f(y,f(g(f(x,y)),g(z))),z)),u))=f(x,f(g(x),u)). 1391 [] f(g(x),f(g(g(x)),y))=f(x,f(g(x),y)). 1392 [] f(g(x),f(x,y))=f(x,f(g(x),y)). 1393 [] f(x,f(g(f(g(f(y,z)),x)),g(z)))=y. 1394 [] f(f(x,f(f(x,g(x)),y)),g(y))=x. 1395 [] f(g(f(x,y)),f(y,g(f(g(f(x,x)),f(x,y)))))=g(y). 1396 [] f(f(x,f(g(x),g(g(x)))),g(x))=f(f(g(x),f(x,g(y))),y). 1397 [] f(f(g(x),f(x,g(y))),y)=f(f(x,f(g(x),x)),g(x)). 1398 [] f(f(g(x),f(x,g(y))),y)=f(x,g(x)). 1399 [] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(f(x,f(g(f(g(y),x)),g(y))),y)))))=g(f(z,g(f(z,f(f(u,y),z))))). 1400 [] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(f(f(x,f(g(f(g(y),x)),g(y))),g(g(g(y))))))=g(f(z,g(f(z,f(f(u,y),z))))). 1401 [] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(f(f(x,f(g(f(g(y),x)),g(y))),g(y))))=g(f(z,g(f(z,f(f(u,y),z))))). 1402 [] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(g(y)))=g(f(z,g(f(z,f(f(u,y),z))))). 1403 [] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),y)=g(f(z,g(f(z,f(f(u,y),z))))). 1404 [] f(f(f(g(x),f(x,g(y))),y),x)=x. 1405 [] f(g(f(x,f(g(x),f(x,g(y))))),g(f(x,g(f(x,x)))))=y. 1406 [] f(g(f(x,f(g(x),f(x,g(y))))),g(g(x)))=y. 1407 [] f(g(f(x,f(g(x),f(x,g(y))))),x)=y. 1408 [] f(g(f(x,f(g(x),f(x,y)))),x)=g(y). 1409 [] f(g(f(f(x,f(f(x,g(x)),y)),f(g(f(x,f(f(x,g(x)),y))),x))),f(x,f(f(x,g(x)),y)))=y. 1410 [] f(g(f(g(x),f(g(g(x)),f(x,f(g(x),y))))),g(x))=g(f(x,y)). 1411 [] f(g(f(g(x),f(x,f(x,f(g(x),y))))),g(x))=g(f(x,y)). 1412 [] g(f(y,g(f(y,f(x,y)))))=f(g(f(x,f(g(x),g(y)))),x). 1413 [] f(x,f(g(g(y)),g(f(g(x),f(x,y)))))=x. 1414 [] f(x,f(y,g(f(g(x),f(x,y)))))=x. 1415 [] f(x,f(y,g(f(x,f(g(x),y)))))=x. 1416 [] f(x,f(y,g(f(z,f(g(f(f(u,f(g(f(x,u)),x)),z)),y)))))=x. 1417 [] f(g(f(f(x,g(x)),x)),f(x,g(g(f(x,f(g(x),y))))))=y. 1418 [] f(g(x),f(x,g(g(f(x,f(g(x),y))))))=y. 1419 [] f(g(x),f(x,f(x,f(g(x),y))))=y. 1420 [] g(f(y,x))=f(g(x),g(y)). 1421 [] f(g(x),f(y,f(g(f(z,y)),z)))=g(f(f(z,g(z)),x)). 1422 [] g(f(x,f(g(x),y)))=f(g(f(x,y)),g(g(x))). 1423 [] g(f(x,f(g(x),y)))=f(g(f(x,y)),x). 1424 [] f(g(g(x)),g(f(g(f(y,y)),f(y,x))))=g(g(y)). 1425 [] f(x,g(f(g(f(y,y)),f(y,x))))=g(g(y)). 1426 [] f(x,g(f(g(f(y,y)),f(y,x))))=y. 1427 [] f(g(g(x)),g(f(y,f(g(f(z,y)),x))))=g(g(z)). 1428 [] f(x,g(f(y,f(g(f(z,y)),x))))=g(g(z)). 1429 [] f(x,g(f(y,f(g(f(z,y)),x))))=z. 1430 [] f(g(f(x,y)),x)=g(y). 1431 [] f(g(x),f(y,g(f(y,f(f(f(g(f(x,y)),y),g(f(x,y))),y)))))=f(y,g(f(y,f(g(f(x,y)),y)))). 1432 [] f(g(x),f(y,g(f(y,f(f(f(g(f(x,y)),y),g(f(x,y))),y)))))=x. 1433 [] f(x,f(y,g(f(z,f(g(f(f(u,g(u)),z)),y)))))=x. 1434 [] f(x,f(y,g(y)))=x. 1435 [] f(g(x),f(g(y),g(f(g(y),f(f(f(g(f(x,g(y))),g(y)),g(f(x,g(y)))),g(y))))))=f(g(y),g(f(g(f(y,x)),f(x,g(x))))). 1436 [] f(g(x),g(f(g(f(x,y)),f(y,g(y)))))=y. 1437 [] f(g(x),g(g(f(x,y))))=y. 1438 [] f(g(x),f(x,y))=y. 1439 [] g(f(x,f(g(x),y)))=g(y). 1440 [] g(f(f(x,g(x)),y))=f(g(y),f(z,g(z))). 1441 [] g(f(f(x,g(x)),y))=g(y). 1442 [] g(f(x,g(f(x,f(y,x)))))=f(g(g(x)),y). 1443 [] g(f(x,g(f(x,f(y,x)))))=f(x,y). 1444 [] f(g(f(f(x,f(f(x,g(x)),y)),g(f(f(x,g(x)),y)))),f(x,f(f(x,g(x)),y)))=y. 1445 [] f(g(f(f(x,f(f(x,g(x)),y)),g(y))),f(x,f(f(x,g(x)),y)))=y. 1446 [] f(g(x),f(x,f(f(x,g(x)),y)))=y. 1447 [] f(f(x,g(x)),y)=y. 1448 [] f(g(f(f(x,g(x)),g(f(y,z)))),u)=g(f(y,g(f(y,f(f(z,u),y))))). 1449 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(g(g(f(x,y))),z). 1450 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(f(x,y),z). 1451 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 1452 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y. 1453 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 1454 [] f(f(a,b),c)!=f(a,f(b,c)). 1455 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 1456 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))). 1457 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 1458 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 1459 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)). 1460 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))). 1461 [] g(f(x,g(f(x,x))))=x. 1462 [] f(x,g(f(x,g(f(x,f(f(g(f(x,x)),y),x))))))=y. 1463 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y. 1464 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))). 1465 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))). 1466 [] f(g(f(x,g(f(x,x)))),f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 1467 [] f(g(x),g(f(g(x),g(x))))=x. 1468 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 1469 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))). 1470 [] f(x,g(f(x,f(f(y,f(x,y)),x))))=f(g(f(x,y)),g(f(x,y))). 1471 [] g(f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x)))))=y. 1472 [] f(x,f(g(f(y,g(f(x,g(f(x,x)))))),g(f(y,g(f(y,f(z,y)))))))=z. 1473 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 1474 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y. 1475 [] f(x,f(g(f(y,x)),g(z)))=f(g(f(z,y)),f(y,g(y))). 1476 [] f(x,f(g(f(y,x)),z))=f(g(f(y,y)),f(y,z)). 1477 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 1478 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y. 1479 [] f(g(f(x,y)),f(y,g(y)))=f(g(f(y,y)),f(y,g(x))). 1480 [] f(g(f(x,x)),f(x,y))=f(z,f(g(f(x,z)),y)). 1481 [] f(g(f(x,x)),f(x,g(y)))=f(g(f(y,x)),f(x,g(x))). 1482 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x. 1483 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)). 1484 [] f(z,f(g(f(g(f(y,x)),z)),g(x)))=f(g(f(x,g(f(y,x)))),f(g(f(y,x)),g(g(f(y,x))))). 1485 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(u,f(g(f(g(f(x,y)),u)),g(y))). 1486 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))). 1487 [] f(g(f(x,g(f(x,x)))),f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 1488 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y. 1489 [] f(x,g(f(g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)),g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)))))=f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y). 1490 [] f(x,f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 1491 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 1492 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 1493 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y. 1494 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))). 1495 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x). 1496 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,y),x))))))=f(f(z,f(g(f(y,z)),y)),y). 1497 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 1498 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x)))=y. 1499 [] g(f(x,f(f(g(f(x,x)),x),x)))=f(y,f(x,g(f(x,f(y,x))))). 1500 [] f(f(x,f(g(f(y,x)),y)),y)=y. 1501 [] f(f(x,f(g(f(x,x)),f(x,g(f(x,g(x)))))),f(x,g(x)))=f(x,g(x)). 1502 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)). 1503 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(z,f(g(z),u)). 1504 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x). 1505 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(x,f(g(f(x,x)),x)). 1506 [] f(x,g(f(x,f(g(f(x,x)),f(x,g(f(x,g(f(x,f(f(g(x),f(x,g(x))),x))))))))))=x. 1507 [] f(x,f(f(g(x),f(x,f(g(f(x,x)),x))),x))=x. 1508 [] f(x,f(f(g(x),f(y,f(g(f(x,y)),x))),x))=x. 1509 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=f(g(x),f(y,f(g(f(x,y)),x))). 1510 [] f(g(f(x,g(f(x,g(x))))),x)=g(f(x,g(x))). 1511 [] f(x,g(f(x,f(g(x),f(x,g(x))))))=x. 1512 [] f(x,f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 1513 [] f(x,f(f(g(f(f(x,y),x)),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 1514 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))). 1515 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y. 1516 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)). 1517 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,f(f(z,f(x,g(x))),x))))),x)))=f(f(z,f(x,g(u))),u). 1518 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y. 1519 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u). 1520 [] f(f(x,f(g(y),g(z))),z)=f(f(x,y),f(g(y),g(y))). 1521 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(f(x,g(f(x,f(g(x),f(x,g(x)))))),f(g(g(f(x,f(g(x),f(x,g(x)))))),g(g(f(x,f(g(x),f(x,g(x)))))))). 1522 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(g(f(x,f(g(x),f(x,g(x)))))))). 1523 [] f(x,g(f(x,g(f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y)))))=f(f(y,g(f(y,f(f(x,f(y,g(y))),y)))),y). 1524 [] f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x)=f(y,g(f(y,y))). 1525 [] f(f(x,g(f(x,f(f(g(y),f(x,g(x))),x)))),x)=y. 1526 [] f(f(x,g(f(x,f(f(g(y),f(x,g(z))),z)))),x)=y. 1527 [] f(f(x,g(y)),g(f(f(x,g(y)),f(f(g(z),f(f(x,g(y)),g(u))),u))))=g(f(f(x,g(f(x,f(z,y)))),x)). 1528 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=y. 1529 [] f(g(f(f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1530 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=g(x). 1531 [] f(g(x),f(y,f(g(f(x,y)),x)))=g(x). 1532 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=g(x). 1533 [] f(x,f(g(f(y,x)),g(f(y,g(y)))))=g(y). 1534 [] f(f(x,g(x)),f(x,g(x)))=f(x,g(x)). 1535 [] f(x,f(g(x),x))=x. 1536 [] f(g(f(f(g(x),x),g(x))),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 1537 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=g(f(x,g(f(x,x)))). 1538 [] g(f(f(x,g(x)),g(f(x,g(x)))))=f(x,g(x)). 1539 [] f(g(f(x,g(x))),f(x,g(x)))=g(f(x,g(x))). 1540 [] f(f(g(x),x),f(g(x),g(f(x,g(x)))))=g(x). 1541 [] f(g(x),g(f(x,g(x))))=f(g(f(x,x)),f(x,f(x,g(x)))). 1542 [] g(f(f(x,g(x)),f(g(f(x,g(x))),f(x,g(x)))))=f(x,g(x)). 1543 [] g(f(x,g(x)))=f(x,g(x)). 1544 [] g(g(f(x,g(x))))=f(x,g(x)). 1545 [] f(g(f(x,x)),f(x,f(x,g(x))))=g(x). 1546 [] f(g(x),g(f(x,g(x))))=g(x). 1547 [] f(g(x),f(x,g(x)))=g(x). 1548 [] f(f(g(x),x),g(x))=g(x). 1549 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(g(g(f(x,g(x)))),g(g(f(x,f(g(x),f(x,g(x)))))))). 1550 [] f(x,g(f(x,g(x))))=x. 1551 [] f(x,f(x,g(x)))=x. 1552 [] f(g(f(x,x)),x)=g(x). 1553 [] g(f(x,g(x)))=f(g(x),x). 1554 [] f(x,f(f(x,g(x)),f(x,g(x))))=x. 1555 [] f(f(x,g(x)),x)=x. 1556 [] f(x,f(y,g(f(y,f(x,y)))))=g(f(y,f(g(y),y))). 1557 [] f(g(f(x,g(x))),x)=x. 1558 [] f(f(g(x),x),x)=x. 1559 [] f(g(x),x)=f(x,g(x)). 1560 [] g(f(g(x),x))=f(x,g(x)). 1561 [] f(f(g(x),f(x,g(x))),x)=f(x,g(x)). 1562 [] f(f(x,g(x)),g(x))=g(x). 1563 [] f(g(f(g(x),x)),g(x))=g(x). 1564 [] f(f(g(x),f(x,g(y))),y)=f(x,g(x)). 1565 [] f(f(f(g(x),f(x,g(y))),y),x)=x. 1566 [] f(g(f(x,f(g(x),f(x,g(y))))),g(f(x,g(f(x,x)))))=y. 1567 [] f(x,f(y,g(f(y,f(x,y)))))=g(y). 1568 [] f(g(f(x,y)),f(y,g(f(g(f(x,x)),f(x,y)))))=g(y). 1569 [] f(f(x,f(g(f(y,x)),g(z))),z)=g(y). 1570 [] g(g(x))=f(f(x,g(x)),x). 1571 [] g(g(x))=x. 1572 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))). 1573 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(u,f(g(f(g(f(x,y)),u)),g(y))). 1574 [] f(f(x,f(g(f(y,x)),z)),g(z))=g(y). 1575 [] f(g(x),f(g(g(x)),y))=f(x,f(g(x),y)). 1576 [] f(g(x),f(x,y))=f(x,f(g(x),y)). 1577 [] f(g(f(x,f(g(x),f(x,g(y))))),x)=y. 1578 [] f(g(f(x,f(g(x),f(x,y)))),x)=g(y). 1579 [] f(g(f(g(x),f(g(g(x)),f(x,f(g(x),y))))),g(x))=g(f(x,y)). 1580 [] f(g(f(g(x),f(x,f(x,f(g(x),y))))),g(x))=g(f(x,y)). 1581 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=x. 1582 [] f(g(g(x)),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 1583 [] f(x,g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 1584 [] f(x,g(f(f(g(x),x),g(x))))=g(f(g(x),g(x))). 1585 [] g(f(g(x),g(x)))=f(x,g(g(x))). 1586 [] g(f(g(x),g(x)))=f(x,x). 1587 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(f(x,g(x)),g(g(f(x,f(g(x),f(x,g(x)))))))). 1588 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(f(x,g(x)),g(g(f(x,g(x)))))). 1589 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=f(x,f(f(x,g(x)),f(x,g(x)))). 1590 [] f(f(x,f(g(g(f(x,f(g(x),f(x,g(x)))))),g(y))),y)=x. 1591 [] f(f(x,f(g(g(f(x,g(x)))),g(y))),y)=x. 1592 [] f(f(x,f(f(x,g(x)),g(y))),y)=x. 1593 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y))). 1594 [] f(g(f(f(g(f(x,y)),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1595 [] f(g(f(f(g(f(x,y)),f(f(x,y),g(f(x,y)))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1596 [] f(g(f(g(f(x,y)),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1597 [] f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1598 [] f(f(f(x,y),f(x,y)),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 1599 [] f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y)))=x. 1600 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=x. 1601 [] f(x,f(g(f(g(f(y,z)),x)),g(z)))=y. 1602 [] f(x,f(g(f(y,x)),g(g(f(y,y)))))=y. 1603 [] f(x,f(g(g(y)),g(f(g(x),f(x,y)))))=x. 1604 [] f(x,f(y,g(f(g(x),f(x,y)))))=x. 1605 [] f(x,f(y,g(f(x,f(g(x),y)))))=x. 1606 [] f(g(f(f(x,g(x)),x)),f(x,g(g(f(x,f(g(x),y))))))=y. 1607 [] f(g(x),f(x,g(g(f(x,f(g(x),y))))))=y. 1608 [] f(g(x),f(x,f(x,f(g(x),y))))=y. 1609 [] g(f(y,x))=f(g(x),g(y)). 1610 [] f(x,g(f(g(f(y,y)),f(y,x))))=y. 1611 [] f(g(f(x,y)),x)=g(y). 1612 [] f(x,f(y,g(y)))=x. 1613 [] f(f(x,g(x)),y)=y. 1614 [] f(f(x,f(y,g(z))),z)=f(x,y). 1615 [] f(f(x,g(y)),y)=x. 1616 [] f(f(x,f(y,z)),g(z))=f(x,y). 1617 [] f(f(f(a,f(b,x)),g(x)),c)!=f(a,f(b,c)). end_of_list. list(hints2). 1618 [] f(f(g(x),y),g(f(y,f(g(f(f(x,z),y)),y))))=z. 1619 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 1620 [] f(f(a,b),c)!=f(a,f(b,c)). 1621 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 1622 [] f(g(f(g(f(x,y)),z)),f(f(u,f(g(f(g(f(g(f(x,y)),z)),u)),g(f(g(f(g(f(x,y)),z)),g(v))))),g(f(g(f(x,y)),z))))=f(g(f(x,y)),g(f(x,g(f(x,f(f(y,v),x)))))). 1623 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),g(u))))),g(f(x,y))))=u. 1624 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 1625 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 1626 [] f(g(f(x,f(g(y),z))),g(f(x,g(f(x,f(u,x))))))=g(f(z,f(g(f(f(y,u),z)),z))). 1627 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 1628 [] f(f(g(x),g(f(f(x,y),g(f(f(x,y),f(z,f(x,y))))))),g(f(g(f(f(x,y),g(f(f(x,y),f(z,f(x,y)))))),g(f(f(x,y),g(f(f(x,y),f(f(g(f(f(x,y),f(z,f(x,y)))),z),f(x,y)))))))))=y. 1629 [] f(f(g(x),g(f(f(x,y),g(f(f(x,y),f(z,f(x,y))))))),g(z))=y. 1630 [] g(f(x,f(g(f(f(y,f(f(g(y),x),z)),x)),x)))=z. 1631 [] f(x,f(f(y,f(g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),y)),g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),g(v))))),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z)))))))=v. 1632 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),g(v))))),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z)))))))=v. 1633 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),x)),u)))))))=z. 1634 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 1635 [] f(f(g(x),y),g(f(z,f(g(f(f(x,u),z)),y))))=u. 1636 [] g(f(x,f(g(f(f(y,z),x)),x)))=g(f(u,f(g(f(f(y,z),u)),x))). 1637 [] f(g(f(x,f(g(y),z))),g(f(x,g(f(x,f(u,x))))))=g(f(v,f(g(f(f(y,u),v)),z))). 1638 [] g(f(x,f(g(f(f(y,f(f(g(y),z),u)),x)),z)))=u. 1639 [] g(f(x,f(g(f(y,x)),f(g(f(z,g(z))),g(f(z,g(y)))))))=z. 1640 [] f(f(g(x),f(g(f(y,g(y))),g(f(y,g(f(x,z)))))),y)=z. 1641 [] f(f(g(x),f(g(f(x,g(x))),y)),x)=f(f(z,f(g(f(x,z)),y)),x). 1642 [] g(f(x,f(g(f(f(f(g(y),f(g(f(z,g(z))),g(f(z,g(f(y,u)))))),z),x)),v)))=g(f(v,f(g(f(u,v)),v))). 1643 [] g(f(x,f(g(f(y,x)),x)))=g(f(z,f(g(f(y,z)),x))). 1644 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(f(z,f(g(f(u,z)),z))))))),x))=f(v,f(g(f(u,v)),z)). 1645 [] f(x,f(g(f(y,x)),x))=f(z,f(g(f(y,z)),x)). 1646 [] f(g(f(x,g(f(x,f(y,x))))),g(f(x,g(f(x,f(f(g(f(x,f(y,x))),y),x))))))=f(z,f(g(f(x,z)),g(f(x,g(f(x,f(y,x))))))). 1647 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 1648 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 1649 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 1650 [] g(f(x,f(y,f(g(f(f(z,x),y)),g(f(f(z,x),g(z)))))))=f(z,x). 1651 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v). 1652 [] g(f(f(x,f(f(g(x),y),z)),y))=f(u,f(g(f(y,u)),g(f(y,z)))). 1653 [] f(f(g(x),y),f(g(f(z,f(g(x),y))),g(f(z,g(f(z,f(u,z)))))))=g(f(f(v,f(f(g(v),z),g(f(z,f(u,z))))),z)). 1654 [] g(f(f(x,f(f(g(x),y),g(f(y,f(z,y))))),y))=f(f(g(u),v),g(f(w,f(g(f(f(u,z),w)),v)))). 1655 [] g(f(f(x,f(f(g(x),y),g(f(y,f(z,y))))),y))=z. 1656 [] g(f(f(x,f(f(g(x),y),z)),y))=g(f(f(u,f(f(g(u),y),z)),y)). 1657 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 1658 [] f(x,f(g(f(f(y,f(f(g(y),x),g(z))),x)),x))=z. 1659 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(f(z,f(g(f(f(u,f(f(g(u),x),g(v))),z)),x)),y)))))))=v. 1660 [] f(x,f(g(f(f(y,f(f(g(y),z),g(u))),x)),z))=u. 1661 [] f(x,f(g(f(f(y,f(f(g(y),z),g(f(f(u,f(f(g(u),v),w)),v)))),x)),z))=f(f(v6,f(f(g(v6),v),w)),v). 1662 [] f(f(x,f(f(g(x),y),z)),y)=f(f(u,f(f(g(u),y),z)),y). 1663 [] g(f(f(x,f(f(g(x),y),g(f(y,f(f(z,f(f(g(z),y),u)),y))))),y))=f(v,f(f(g(v),y),u)). 1664 [] f(x,f(f(g(x),y),z))=f(u,f(f(g(u),y),z)). 1665 [] f(x,f(f(g(x),y),g(f(z,f(g(f(f(u,v),z)),y)))))=f(u,v). 1666 [] f(g(f(x,g(x))),g(f(x,g(f(y,f(f(g(y),z),x))))))=z. 1667 [] f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),g(z))),x))))=z. 1668 [] g(f(x,f(f(g(x),y),x)))=g(f(z,f(f(g(z),y),x))). 1669 [] g(f(x,f(f(g(x),y),z)))=g(f(u,f(f(g(u),y),z))). 1670 [] f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),g(z))),x))))=f(u,f(f(g(u),v),g(f(w,f(g(f(z,w)),v))))). 1671 [] f(x,f(f(g(x),y),g(f(z,f(g(f(u,z)),y)))))=u. 1672 [] f(x,f(f(g(x),g(f(y,g(f(y,f(z,y)))))),g(f(f(g(u),v),g(f(w,f(g(f(f(u,z),w)),v)))))))=y. 1673 [] f(x,f(f(g(x),g(f(y,g(f(y,f(z,y)))))),g(z)))=y. 1674 [] f(f(x,y),f(z,g(f(y,z))))=x. 1675 [] f(x,f(g(f(y,x)),g(f(z,g(f(y,f(u,z)))))))=u. 1676 [] f(x,f(f(g(x),y),f(z,g(f(y,z)))))=f(u,g(u)). 1677 [] f(x,g(x))=f(y,g(y)). 1678 [] g(f(x,f(f(g(x),y),f(z,g(f(y,z))))))=g(f(u,g(u))). 1679 [] g(f(x,g(x)))=g(f(y,g(y))). 1680 [] f(f(x,f(f(g(x),y),f(z,g(f(y,z))))),y)=f(f(u,g(u)),y). 1681 [] f(f(x,g(x)),y)=f(f(z,g(z)),y). 1682 [] f(g(f(x,g(x))),g(f(y,g(f(z,f(f(g(z),u),y))))))=u. 1683 [] f(f(x,y),f(g(y),g(f(z,g(z)))))=x. 1684 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,g(z)),x))))))=g(y). 1685 [] g(f(g(x),f(y,f(g(f(f(z,g(z)),y)),g(f(f(x,g(x)),g(x)))))))=f(x,g(x)). 1686 [] f(f(x,y),g(f(f(z,g(z)),y)))=x. 1687 [] f(g(f(x,g(f(y,z)))),g(f(u,g(f(x,f(v,u))))))=g(f(y,g(f(y,f(f(z,v),y))))). 1688 [] f(g(f(x,g(x))),g(f(f(g(y),g(f(z,g(z)))),g(f(u,g(u))))))=y. 1689 [] f(g(f(x,g(x))),f(f(y,f(g(f(g(f(x,g(x))),y)),g(z))),g(f(x,g(x)))))=f(u,g(f(v,f(f(g(v),z),u)))). 1690 [] f(g(f(x,g(x))),f(f(g(f(y,g(f(z,f(f(g(z),u),y))))),f(g(u),g(f(g(f(x,g(x))),g(v))))),g(f(x,g(x)))))=v. 1691 [] f(g(f(x,g(x))),g(f(y,g(f(f(z,g(z)),f(f(g(f(u,g(u))),v),y))))))=v. 1692 [] f(g(f(f(x,g(x)),g(f(y,z)))),g(f(u,g(f(f(v,g(v)),f(w,u))))))=g(f(y,g(f(y,f(f(z,w),y))))). 1693 [] f(f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,g(z)),g(f(f(z,g(z)),u)))))),f(z,g(z)))=u. 1694 [] f(f(x,f(g(f(f(y,g(y)),x)),g(f(f(y,g(y)),g(f(f(z,g(z)),u)))))),f(y,g(y)))=u. 1695 [] g(f(f(x,g(x)),f(f(y,f(g(f(f(x,g(x)),y)),g(f(f(z,g(z)),u)))),f(x,g(x)))))=u. 1696 [] f(x,g(f(f(y,g(y)),g(f(f(z,g(z)),u)))))=f(x,u). 1697 [] f(f(x,g(x)),g(f(f(y,g(y)),g(z))))=z. 1698 [] f(f(x,g(f(y,g(y)))),g(f(z,g(z))))=x. 1699 [] f(f(x,g(f(f(y,g(y)),f(f(z,f(g(f(f(y,g(y)),z)),u)),f(y,g(y)))))),u)=x. 1700 [] f(f(x,f(g(f(f(y,g(y)),x)),z)),f(y,g(y)))=z. 1701 [] f(f(x,f(g(f(f(y,g(y)),x)),z)),f(u,g(u)))=z. 1702 [] f(g(f(x,g(x))),g(g(y)))=y. 1703 [] f(f(x,g(f(f(y,g(y)),z))),z)=x. 1704 [] g(f(f(x,g(x)),g(f(f(y,g(y)),z))))=z. 1705 [] f(g(f(x,g(f(y,f(z,g(z)))))),g(f(u,g(f(x,f(g(f(f(v,g(v)),g(w))),u))))))=g(f(y,g(f(y,f(w,y))))). 1706 [] g(f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(f(f(y,g(y)),g(z))),u),f(x,g(x)))))))=f(g(f(v,g(f(f(x,g(x)),g(f(f(y,g(y)),g(z))))))),g(f(w,g(f(v,f(u,w)))))). 1707 [] g(f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(f(f(y,g(y)),g(z))),u),f(x,g(x)))))))=f(g(f(v,g(z))),g(f(w,g(f(v,f(u,w)))))). 1708 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=f(f(g(f(f(v,g(v)),g(y))),u),f(w,g(w))). 1709 [] f(g(f(x,g(x))),f(f(y,f(g(f(g(f(x,g(x))),y)),g(z))),g(f(x,g(x)))))=g(z). 1710 [] f(g(f(x,g(x))),g(f(y,g(f(f(z,g(z)),f(u,y))))))=g(g(u)). 1711 [] f(g(f(x,g(x))),f(f(g(g(y)),f(g(y),g(z))),g(f(x,g(x)))))=f(x,g(f(x,f(f(g(x),z),x)))). 1712 [] f(x,g(f(x,f(f(g(x),y),x))))=g(y). 1713 [] f(x,g(f(y,f(f(g(y),z),x))))=g(z). 1714 [] g(g(f(g(f(x,g(x))),y)))=y. 1715 [] f(g(f(x,g(x))),f(f(g(g(y)),f(g(y),g(z))),g(f(x,g(x)))))=g(z). 1716 [] f(g(f(x,g(x))),f(f(g(g(y)),f(g(y),g(f(g(f(x,g(x))),g(z))))),g(f(x,g(x)))))=z. 1717 [] g(f(g(f(x,g(x))),g(y)))=y. 1718 [] f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,g(z)),g(u)))))=u. 1719 [] g(f(g(x),x))=f(x,g(x)). 1720 [] g(f(g(f(f(x,g(x)),g(f(x,g(x))))),f(f(x,g(x)),g(f(x,g(x))))))=f(x,g(x)). 1721 [] f(f(g(x),x),f(x,g(x)))=f(y,g(y)). 1722 [] f(f(x,g(f(y,g(y)))),g(g(f(g(f(y,g(y))),f(y,g(y))))))=x. 1723 [] f(f(x,g(f(y,g(y)))),f(y,g(y)))=x. 1724 [] f(f(g(g(f(x,g(x)))),g(f(x,g(x)))),f(x,g(x)))=f(y,g(y)). 1725 [] g(g(f(x,g(x))))=f(y,g(y)). 1726 [] f(g(f(f(x,g(x)),g(f(y,z)))),g(f(f(x,g(x)),g(f(f(x,g(x)),f(u,g(u)))))))=g(f(y,g(f(y,f(f(z,f(g(x),x)),y))))). 1727 [] f(g(f(f(x,g(x)),g(f(y,z)))),f(u,g(u)))=g(f(y,g(f(y,f(f(z,f(g(x),x)),y))))). 1728 [] g(g(f(x,g(x))))=g(f(g(y),y)). 1729 [] g(f(g(f(x,g(x))),g(f(g(y),y))))=g(f(z,g(z))). 1730 [] g(f(x,g(x)))=f(g(y),y). 1731 [] g(f(g(f(x,g(x))),g(f(g(y),y))))=f(g(z),z). 1732 [] f(g(x),x)=f(g(y),y). 1733 [] f(f(f(g(x),x),f(g(f(f(y,g(y)),g(f(y,g(y))))),z)),f(y,g(y)))=f(f(u,f(g(f(f(y,g(y)),u)),z)),f(y,g(y))). 1734 [] f(f(f(g(x),x),f(g(f(f(y,g(y)),g(f(y,g(y))))),z)),f(y,g(y)))=z. 1735 [] g(g(f(f(x,g(x)),y)))=f(f(g(z),z),y). 1736 [] g(f(x,g(f(x,f(f(y,f(g(z),z)),x)))))=f(x,y). 1737 [] f(g(f(f(x,g(x)),g(f(y,z)))),f(u,g(u)))=f(y,z). 1738 [] g(f(x,g(x)))=f(x,g(x)). 1739 [] g(f(f(x,g(x)),g(y)))=y. 1740 [] f(g(f(x,f(y,g(y)))),g(f(z,g(f(x,f(u,z))))))=g(f(y,g(f(y,f(f(g(y),u),y))))). 1741 [] f(g(f(x,f(y,g(y)))),g(f(z,g(f(x,f(u,z))))))=g(g(u)). 1742 [] f(f(f(x,g(x)),f(x,g(x))),g(f(f(y,g(y)),g(z))))=z. 1743 [] f(f(f(x,g(x)),f(x,g(x))),y)=y. 1744 [] f(f(f(x,g(x)),f(x,g(x))),y)=f(f(z,g(z)),y). 1745 [] f(f(x,g(x)),y)=y. 1746 [] f(f(x,g(x)),f(f(f(x,g(x)),y),z))=f(u,f(f(g(u),y),z)). 1747 [] f(f(x,g(x)),f(y,z))=f(u,f(f(g(u),y),z)). 1748 [] f(x,f(f(g(x),y),z))=f(y,z). 1749 [] f(g(f(x,g(x))),y)=f(f(z,g(z)),y). 1750 [] f(g(f(x,g(x))),y)=y. 1751 [] f(g(f(x,g(x))),g(f(f(y,g(y)),g(z))))=z. 1752 [] g(g(x))=x. 1753 [] f(g(f(x,g(g(f(y,g(y)))))),g(f(z,g(f(x,f(u,z))))))=g(f(y,g(f(y,f(f(g(y),u),y))))). 1754 [] g(f(x,g(f(x,f(f(g(x),y),x)))))=g(g(y)). 1755 [] g(f(x,g(f(x,f(f(g(x),y),x)))))=y. 1756 [] g(f(x,g(f(y,x))))=y. 1757 [] f(g(f(x,g(x))),f(g(g(x)),g(f(y,g(y)))))=x. 1758 [] f(g(f(x,g(x))),f(x,g(f(y,g(y)))))=x. 1759 [] f(x,g(f(y,g(y))))=x. 1760 [] f(f(g(x),x),y)=g(g(y)). 1761 [] f(f(g(x),x),y)=y. 1762 [] f(f(f(g(x),x),f(g(f(y,g(y))),z)),f(y,g(y)))=z. 1763 [] f(f(f(g(x),x),y),f(z,g(z)))=y. 1764 [] f(x,f(y,g(y)))=x. 1765 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=f(f(g(g(y)),u),f(v,g(v))). 1766 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=f(f(y,u),f(v,g(v))). 1767 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=f(y,u). 1768 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(g(f(f(u,g(u)),g(v))),z))))))=g(f(y,g(f(y,f(v,y))))). 1769 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(g(g(u)),z))))))=g(f(y,g(f(y,f(u,y))))). 1770 [] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=g(f(y,g(f(y,f(u,y))))). 1771 [] g(f(x,g(f(x,f(y,x)))))=f(x,y). 1772 [] f(g(g(f(x,y))),g(f(z,g(f(f(u,g(u)),f(v,z))))))=g(f(x,g(f(x,f(f(y,v),x))))). 1773 [] f(f(x,y),g(f(z,g(f(f(u,g(u)),f(v,z))))))=g(f(x,g(f(x,f(f(y,v),x))))). 1774 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(f(x,y),g(f(u,g(f(z,u))))). 1775 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(f(x,y),z). 1776 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 1777 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y. 1778 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 1779 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 1780 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 1781 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 1782 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 1783 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 1784 [] f(f(a,b),c)!=f(a,f(b,c)). 1785 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 1786 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 1787 [] g(f(f(g(f(g(f(x,g(f(x,f(y,x))))),z)),x),y))=z. 1788 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 1789 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). 1790 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v). 1791 [] g(f(f(g(f(x,y)),z),f(u,f(g(f(z,u)),x))))=y. 1792 [] g(f(x,f(y,f(g(f(g(f(z,g(f(z,f(f(u,x),z))))),y)),z))))=u. 1793 [] g(f(x,f(g(f(y,x)),f(g(f(z,g(f(y,f(g(f(u,v)),z))))),u))))=v. 1794 [] f(x,f(g(f(f(g(f(y,z)),y),x)),g(f(f(g(f(y,z)),y),z))))=z. 1795 [] g(f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x)))))))=g(z). 1796 [] g(f(f(g(f(g(f(f(g(f(x,y)),x),y)),z)),f(g(f(x,y)),x)),y))=z. 1797 [] g(f(x,g(f(x,f(f(g(f(x,f(y,x))),z),x)))))=g(f(f(g(z),x),y)). 1798 [] f(f(x,f(g(f(y,x)),y)),f(z,g(f(f(g(f(y,z)),y),z))))=z. 1799 [] f(f(g(f(x,g(y))),x),f(g(y),f(g(f(x,g(y))),x)))=y. 1800 [] f(f(g(f(x,g(y))),x),f(z,f(g(f(x,z)),x)))=y. 1801 [] f(g(f(x,g(f(y,f(g(f(x,g(z))),x))))),x)=g(f(y,g(f(y,f(z,y))))). 1802 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(y,f(g(f(z,y)),z)),g(f(f(y,f(g(f(z,y)),z)),u))))))=f(g(f(z,g(u))),z). 1803 [] f(f(g(f(f(x,f(g(f(y,x)),y)),g(z))),f(x,f(g(f(y,x)),y))),f(f(u,g(f(f(g(f(y,u)),y),u))),f(g(u),f(x,f(g(f(y,x)),y)))))=z. 1804 [] f(g(f(x,g(f(y,f(z,f(g(f(u,z)),u)))))),g(f(x,g(f(x,f(f(v,g(f(f(g(f(u,v)),u),v))),x))))))=g(f(y,g(f(y,f(v,y))))). 1805 [] g(f(f(x,f(g(f(y,x)),y)),f(f(z,f(g(f(f(x,f(g(f(y,x)),y)),z)),g(u))),f(x,f(g(f(y,x)),y)))))=f(u,g(f(f(g(f(y,u)),y),u))). 1806 [] g(f(f(x,f(g(f(y,x)),y)),g(f(f(x,f(g(f(y,x)),y)),f(f(f(z,g(f(f(g(f(y,z)),y),z))),f(g(z),u)),f(x,f(g(f(y,x)),y)))))))=u. 1807 [] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),g(f(f(z,f(g(f(y,z)),y)),g(f(u,f(g(f(v,u)),f(z,f(g(f(y,z)),y)))))))))=g(f(v,f(z,f(g(f(y,z)),y)))). 1808 [] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))). 1809 [] g(f(x,f(g(f(y,x)),x)))=g(f(z,f(g(f(y,z)),x))). 1810 [] g(f(g(f(x,g(f(x,f(y,x))))),g(f(x,g(f(x,f(f(g(f(x,f(y,x))),y),x)))))))=g(f(z,f(g(f(x,z)),g(f(x,g(f(x,f(y,x)))))))). 1811 [] g(f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y))))))))=g(z). 1812 [] g(f(g(f(x,y)),g(f(x,g(f(x,f(f(y,g(f(z,f(g(f(u,z)),y)))),x)))))))=g(g(f(y,f(g(f(u,y)),y)))). 1813 [] g(g(f(x,f(g(f(y,x)),z))))=g(g(f(z,f(g(f(y,z)),z)))). 1814 [] g(g(f(g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x))))),f(g(f(x,g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x))))))),g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x)))))))))=g(g(f(v,f(g(f(x,v)),g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x))))))))). 1815 [] g(g(f(g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x))))),f(g(f(x,g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x))))))),g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x)))))))))=g(g(f(v,f(g(f(z,v)),u)))). 1816 [] g(g(f(x,f(g(f(y,x)),z))))=g(g(f(u,f(g(f(y,u)),z)))). 1817 [] g(g(f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),z))))=g(g(f(u,f(g(f(f(v,f(g(f(y,v)),y)),u)),z)))). 1818 [] f(g(f(x,g(f(x,f(y,x))))),g(f(f(g(z),x),y)))=z. 1819 [] f(x,g(f(f(g(y),z),f(u,f(g(f(z,u)),x)))))=y. 1820 [] g(f(x,f(g(f(f(g(y),z),f(u,x))),f(g(y),z))))=u. 1821 [] g(f(x,f(g(f(y,f(z,x))),f(g(u),g(f(f(g(y),v),f(w,f(g(f(v,w)),g(u)))))))))=z. 1822 [] g(f(x,f(g(f(y,f(z,x))),y)))=z. 1823 [] g(f(x,f(g(f(y,x)),f(g(f(z,u)),z))))=f(u,y). 1824 [] g(f(x,f(y,f(g(f(z,y)),z))))=f(g(f(u,x)),u). 1825 [] f(g(f(x,f(g(f(y,z)),y))),x)=z. 1826 [] g(f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),f(g(f(u,f(g(f(z,g(v))),z))),u))))=v. 1827 [] g(f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(u))))=u. 1828 [] f(g(f(x,f(g(f(y,x)),y))),z)=z. 1829 [] f(f(x,f(g(f(y,x)),y)),z)=z. 1830 [] f(x,f(g(f(g(f(f(g(f(y,f(g(f(z,u)),z))),y),f(g(f(z,u)),z))),x)),f(g(f(y,f(g(f(z,u)),z))),y)))=u. 1831 [] f(x,f(g(f(g(f(y,f(g(f(z,y)),z))),x)),f(g(f(u,f(g(f(z,y)),z))),u)))=y. 1832 [] f(x,f(g(x),f(g(f(y,f(g(f(z,u)),z))),y)))=u. 1833 [] f(x,f(g(x),y))=y. 1834 [] g(f(x,f(g(x),g(y))))=y. 1835 [] g(g(x))=x. 1836 [] g(g(f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))))=f(f(v,g(f(f(g(f(z,v)),z),v))),f(g(v),u)). 1837 [] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),z))=g(g(f(u,f(g(u),z)))). 1838 [] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),z))=g(g(z)). 1839 [] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),z))=z. 1840 [] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),g(g(f(z,f(g(f(u,z)),f(v,f(g(f(y,v)),y))))))))=g(f(u,f(v,f(g(f(y,v)),y)))). 1841 [] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),f(z,f(g(f(u,z)),f(v,f(g(f(y,v)),y))))))=g(f(u,f(v,f(g(f(y,v)),y)))). 1842 [] f(x,f(g(f(y,x)),f(z,f(g(f(u,z)),u))))=g(f(y,f(z,f(g(f(u,z)),u)))). 1843 [] g(f(f(x,f(g(f(y,x)),y)),g(f(f(x,f(g(f(y,x)),y)),f(z,f(x,f(g(f(y,x)),y)))))))=z. 1844 [] g(f(f(x,f(g(f(y,x)),y)),g(f(z,f(x,f(g(f(y,x)),y))))))=z. 1845 [] g(g(f(x,f(y,f(g(f(z,y)),z)))))=x. 1846 [] f(x,f(y,f(g(f(z,y)),z)))=x. 1847 [] g(f(f(x,f(g(f(y,x)),y)),f(f(z,f(g(z),g(u))),f(x,f(g(f(y,x)),y)))))=f(u,g(f(f(g(f(y,u)),y),u))). 1848 [] g(f(f(x,f(g(f(y,x)),y)),f(g(z),f(x,f(g(f(y,x)),y)))))=f(z,g(f(f(g(f(y,z)),y),z))). 1849 [] g(f(f(x,f(g(f(y,x)),y)),g(z)))=f(z,g(f(f(g(f(y,z)),y),z))). 1850 [] f(x,g(f(f(g(f(y,x)),y),x)))=g(g(x)). 1851 [] f(x,g(f(f(g(f(y,x)),y),x)))=x. 1852 [] f(f(g(g(x)),f(y,f(g(f(z,y)),z))),f(f(u,g(f(f(g(f(z,u)),z),u))),f(g(u),f(y,f(g(f(z,y)),z)))))=x. 1853 [] f(f(x,f(y,f(g(f(z,y)),z))),f(f(u,g(f(f(g(f(z,u)),z),u))),f(g(u),f(y,f(g(f(z,y)),z)))))=x. 1854 [] f(x,f(f(y,g(f(f(g(f(z,y)),z),y))),f(g(y),f(u,f(g(f(z,u)),z)))))=x. 1855 [] f(x,f(y,f(g(y),f(z,f(g(f(u,z)),u)))))=x. 1856 [] f(x,f(y,g(y)))=x. 1857 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(f(f(y,f(g(f(z,y)),z)),u))))))=f(g(f(z,g(u))),z). 1858 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(u)))))=f(g(f(z,g(u))),z). 1859 [] f(x,f(g(x),g(g(y))))=f(g(f(z,g(y))),z). 1860 [] f(g(f(x,g(y))),x)=f(z,f(g(z),y)). 1861 [] f(g(f(x,g(y))),x)=y. 1862 [] g(f(x,g(f(x,f(y,x)))))=f(g(f(z,g(f(x,y)))),z). 1863 [] g(f(x,g(f(x,f(y,x)))))=f(x,y). 1864 [] g(f(x,f(y,f(g(f(z,y)),z))))=f(u,g(f(x,u))). 1865 [] f(x,g(f(y,x)))=g(y). 1866 [] f(g(f(x,y)),x)=g(y). 1867 [] f(g(f(x,g(f(y,f(z,g(z)))))),g(f(x,g(f(x,f(f(u,g(f(f(g(f(v,u)),v),u))),x))))))=g(f(y,g(f(y,f(u,y))))). 1868 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(f(z,g(f(f(g(f(u,z)),u),z))),x))))))=g(f(y,g(f(y,f(z,y))))). 1869 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(f(z,g(f(g(z),z))),x))))))=g(f(y,g(f(y,f(z,y))))). 1870 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(g(g(z)),x))))))=g(f(y,g(f(y,f(z,y))))). 1871 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=g(f(y,g(f(y,f(z,y))))). 1872 [] g(f(x,g(f(x,f(y,x)))))=f(g(f(z,g(x))),f(z,y)). 1873 [] f(g(f(x,g(y))),f(x,z))=f(y,z). 1874 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(g(f(u,g(f(x,y)))),f(u,z)). 1875 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(f(x,y),z). 1876 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 1877 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y. 1878 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 1879 [] f(f(a,b),c)!=f(a,f(b,c)). 1880 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 1881 [] f(g(f(g(f(x,y)),z)),f(f(u,f(g(f(g(f(g(f(x,y)),z)),u)),g(f(g(f(g(f(x,y)),z)),g(v))))),g(f(g(f(x,y)),z))))=f(g(f(x,y)),g(f(x,g(f(x,f(f(y,v),x)))))). 1882 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),g(u))))),g(f(x,y))))=u. 1883 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 1884 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 1885 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 1886 [] g(f(f(g(f(g(f(x,g(f(x,f(y,x))))),z)),x),f(g(f(x,g(f(x,f(y,x))))),g(f(x,g(f(x,f(f(g(f(x,f(y,x))),y),x))))))))=z. 1887 [] g(f(f(g(f(g(f(x,g(f(x,f(y,x))))),z)),x),y))=z. 1888 [] g(f(f(g(f(x,y)),z),f(u,f(g(f(z,u)),x))))=y. 1889 [] g(f(x,g(f(x,f(f(g(f(x,f(y,x))),z),x)))))=g(f(f(g(z),x),y)). 1890 [] g(f(x,f(y,f(g(f(g(f(z,g(f(z,f(f(u,x),z))))),y)),z))))=u. 1891 [] g(f(f(g(f(g(f(f(g(f(x,y)),x),y)),z)),f(g(f(x,y)),x)),y))=z. 1892 [] f(g(f(x,g(f(x,f(y,x))))),g(f(f(g(z),x),y)))=z. 1893 [] f(x,g(f(f(g(y),z),f(u,f(g(f(z,u)),x)))))=y. 1894 [] g(f(x,f(g(f(f(g(y),z),f(u,x))),f(g(y),z))))=u. 1895 [] g(f(x,f(g(f(y,f(z,x))),f(g(u),g(f(f(g(y),v),f(w,f(g(f(v,w)),g(u)))))))))=z. 1896 [] g(f(x,f(g(f(y,f(z,x))),y)))=z. 1897 [] g(f(f(g(f(x,g(f(y,z)))),x),g(f(f(g(f(x,g(f(y,z)))),x),f(u,f(g(f(x,g(f(y,z)))),x))))))=g(f(f(g(g(f(y,g(f(y,f(f(z,u),y)))))),f(g(f(x,g(f(y,z)))),x)),g(f(y,z)))). 1898 [] f(x,f(f(y,f(g(f(g(f(z,f(g(f(u,f(x,z))),u))),y)),g(f(g(f(z,f(g(f(u,f(x,z))),u))),g(v))))),g(f(z,f(g(f(u,f(x,z))),u)))))=v. 1899 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,f(g(f(u,f(x,z))),u))),g(v))))),g(f(z,f(g(f(u,f(x,z))),u)))))=v. 1900 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(u,f(g(f(v,f(x,u))),v)))))=z. 1901 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 1902 [] f(x,f(g(f(y,x)),g(f(y,g(z)))))=g(f(y,f(g(z),y))). 1903 [] g(f(x,f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),x)))=f(u,f(g(f(x,u)),z)). 1904 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 1905 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 1906 [] g(f(x,f(g(f(y,x)),f(g(f(z,g(f(y,f(g(f(u,v)),z))))),u))))=v. 1907 [] f(x,f(g(f(f(g(f(y,z)),y),x)),g(f(f(g(f(y,z)),y),z))))=z. 1908 [] f(f(x,f(g(f(y,x)),y)),f(z,g(f(f(g(f(y,z)),y),z))))=z. 1909 [] f(f(g(f(x,g(y))),x),f(g(y),f(g(f(x,g(y))),x)))=y. 1910 [] f(f(g(f(x,g(y))),x),f(z,f(g(f(x,z)),x)))=y. 1911 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(y,f(g(f(z,y)),z)),g(f(f(y,f(g(f(z,y)),z)),u))))))=f(g(f(z,g(u))),z). 1912 [] f(g(f(x,g(f(y,f(g(f(x,g(z))),x))))),x)=g(f(y,g(f(y,f(z,y))))). 1913 [] f(g(f(f(g(f(x,g(y))),x),g(f(f(g(f(x,g(y))),x),f(f(z,g(f(f(g(f(x,z)),x),z))),f(g(f(x,g(y))),x)))))),g(z))=y. 1914 [] g(f(x,f(g(f(y,x)),f(g(f(z,u)),z))))=f(u,y). 1915 [] f(g(f(x,f(g(f(y,z)),y))),x)=z. 1916 [] g(f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),f(g(f(u,f(g(f(z,g(v))),z))),u))))=v. 1917 [] g(f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(u))))=u. 1918 [] f(g(f(x,f(g(f(y,x)),y))),z)=z. 1919 [] f(f(x,f(g(f(y,x)),y)),z)=z. 1920 [] f(x,f(g(f(g(f(f(g(f(y,f(g(f(z,u)),z))),y),f(g(f(z,u)),z))),x)),f(g(f(y,f(g(f(z,u)),z))),y)))=u. 1921 [] f(x,f(g(f(g(f(y,f(g(f(z,y)),z))),x)),f(g(f(u,f(g(f(z,y)),z))),u)))=y. 1922 [] f(x,f(g(x),f(g(f(y,f(g(f(z,u)),z))),y)))=u. 1923 [] f(x,f(g(x),y))=y. 1924 [] g(f(x,f(g(x),g(y))))=y. 1925 [] g(g(x))=x. 1926 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(f(f(y,f(g(f(z,y)),z)),u))))))=f(g(f(z,g(u))),z). 1927 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(u)))))=f(g(f(z,g(u))),z). 1928 [] f(x,f(g(x),g(g(y))))=f(g(f(z,g(y))),z). 1929 [] f(g(f(x,g(y))),x)=f(z,f(g(z),y)). 1930 [] f(g(f(x,g(y))),x)=y. 1931 [] f(x,g(f(f(g(f(y,x)),y),x)))=x. 1932 [] g(f(f(g(g(f(x,g(f(x,f(f(y,z),x)))))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y))))=g(f(f(x,y),g(f(f(g(f(u,g(f(x,y)))),u),f(z,f(g(f(u,g(f(x,y)))),u)))))). 1933 [] g(f(f(g(g(f(x,g(f(x,f(f(y,z),x)))))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y))))=g(f(f(x,y),g(f(f(x,y),f(z,f(g(f(u,g(f(x,y)))),u)))))). 1934 [] g(f(f(g(g(f(x,g(f(x,f(f(y,z),x)))))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y))))=g(f(f(x,y),g(f(f(x,y),f(z,f(x,y)))))). 1935 [] g(f(f(f(x,g(f(x,f(f(y,z),x)))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y))))=g(f(f(x,y),g(f(f(x,y),f(z,f(x,y)))))). 1936 [] g(f(f(f(x,g(f(x,f(f(y,z),x)))),f(x,y)),g(f(x,y))))=g(f(f(x,y),g(f(f(x,y),f(z,f(x,y)))))). 1937 [] f(g(f(x,g(f(f(g(f(y,g(x))),y),f(f(z,g(f(f(g(f(y,z)),y),z))),f(g(f(y,g(x))),y)))))),g(z))=x. 1938 [] f(g(f(x,g(f(x,f(f(y,g(f(f(g(f(z,y)),z),y))),f(g(f(z,g(x))),z)))))),g(y))=x. 1939 [] f(g(f(x,g(f(x,f(y,f(g(f(z,g(x))),z)))))),g(y))=x. 1940 [] f(g(f(x,g(f(x,f(y,x))))),g(y))=x. 1941 [] g(f(x,g(f(x,f(y,x)))))=f(g(f(z,g(f(x,y)))),z). 1942 [] g(f(x,g(f(x,f(y,x)))))=f(x,y). 1943 [] f(f(x,y),g(y))=x. 1944 [] g(f(f(x,y),g(f(f(x,y),f(z,f(x,y))))))=g(f(x,g(f(x,f(f(y,z),x))))). 1945 [] g(f(f(x,y),g(f(f(x,y),f(z,f(x,y))))))=f(x,f(y,z)). 1946 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 1947 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z. 1948 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 1949 [] f(f(a,b),c)!=f(a,f(b,c)). 1950 [] f(f(g(f(g(x),y)),z),f(g(f(f(z,g(u)),z)),z))=f(g(f(f(y,g(f(x,u))),y)),y). 1951 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 1952 [] f(f(g(x),x),f(g(f(y,x)),x))=f(f(z,f(g(f(x,z)),g(y))),x). 1953 [] f(g(f(f(x,g(f(y,f(f(g(y),x),z)))),x)),x)=z. 1954 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))). 1955 [] f(g(f(g(f(x,y)),z)),f(f(u,f(g(f(g(f(g(f(x,y)),z)),u)),g(f(g(f(g(f(x,y)),z)),g(v))))),g(f(g(f(x,y)),z))))=f(g(f(x,y)),g(f(x,g(f(x,f(f(y,v),x)))))). 1956 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),g(u))))),g(f(x,y))))=u. 1957 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 1958 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 1959 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 1960 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u)),x)))))=u. 1961 [] f(x,g(f(y,g(f(y,f(f(g(f(y,f(f(z,f(g(f(y,z)),x)),y))),u),y))))))=u. 1962 [] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(g(x),u),f(g(f(f(u,z),u)),u)). 1963 [] f(x,f(f(y,f(g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),y)),g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),g(v))))),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z)))))))=v. 1964 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),g(v))))),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z)))))))=v. 1965 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),x)),u)))))))=z. 1966 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 1967 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(f(g(f(x,y)),g(v))))),g(f(x,y))))=v. 1968 [] f(x,f(g(f(f(y,g(f(f(f(y,g(f(z,f(f(g(z),y),x)))),y),u))),y)),y))=u. 1969 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 1970 [] f(x,f(f(g(x),x),f(g(f(f(x,g(y)),x)),x)))=y. 1971 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(f(g(f(x,y)),g(v))))),g(f(x,y))))=f(x,g(f(x,f(f(g(x),x),f(g(f(v,x)),x))))). 1972 [] f(x,g(f(x,f(f(g(x),x),f(g(f(y,x)),x)))))=y. 1973 [] f(f(x,f(g(f(y,x)),z)),y)=f(f(u,f(g(f(y,u)),z)),y). 1974 [] f(x,f(f(g(x),x),y))=f(z,f(f(g(z),x),y)). 1975 [] f(x,f(f(g(x),y),z))=f(u,f(f(g(u),y),z)). 1976 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),y)),y)))=z. 1977 [] f(x,f(f(g(x),x),f(f(g(f(g(y),x)),z),u)))=f(y,f(z,f(f(g(z),z),u))). 1978 [] f(x,f(f(g(x),g(f(y,g(f(y,f(f(z,u),y)))))),v))=f(f(y,z),f(u,v)). 1979 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(y,g(z))))),y))=z. 1980 [] f(x,f(f(g(x),y),f(g(f(z,y)),y)))=f(y,f(f(u,f(g(f(y,u)),g(z))),y)). 1981 [] g(f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),z)),x)))))=z. 1982 [] f(g(f(x,g(x))),g(f(x,g(f(y,f(f(g(y),z),x))))))=z. 1983 [] f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),g(z))),x))))=z. 1984 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(y,g(f(y,f(f(z,u),y)))). 1985 [] f(g(f(x,g(x))),g(f(x,g(f(y,z)))))=f(g(f(x,g(y))),g(f(x,g(f(x,z))))). 1986 [] f(x,g(f(x,f(f(g(x),y),x))))=f(x,g(f(z,f(f(g(z),y),x)))). 1987 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z. 1988 [] f(f(x,f(g(f(y,x)),g(z))),y)=f(f(g(y),y),f(g(f(z,y)),y)). 1989 [] f(f(g(x),f(g(f(y,g(y))),g(z))),y)=f(f(g(x),y),f(g(f(z,y)),y)). 1990 [] f(x,g(f(y,f(f(g(y),x),f(g(f(f(z,f(g(f(x,z)),u)),x)),x)))))=f(v,f(g(f(x,v)),u)). 1991 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 1992 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(f(g(z),u),y)))))))=f(g(y),u). 1993 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=f(u,f(g(f(v,u)),g(f(v,g(f(v,f(z,v))))))). 1994 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 1995 [] f(x,f(g(f(f(y,g(f(z,f(f(g(z),y),u)))),x)),y))=f(y,u). 1996 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v). 1997 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). 1998 [] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))). 1999 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(f(x,g(f(z,f(g(f(u,z)),x))))))),x))))=f(x,g(f(v,f(g(f(u,v)),x)))). 2000 [] f(x,g(f(y,f(g(f(z,y)),x))))=f(x,g(f(u,f(g(f(z,u)),x)))). 2001 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,f(f(z,f(g(f(u,z)),v)),y))))))),y)=f(f(w,f(g(f(u,w)),v)),y). 2002 [] f(f(x,f(g(f(y,x)),z)),u)=f(f(v,f(g(f(y,v)),z)),u). 2003 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,g(f(z,f(f(g(z),u),y)))),x))))))=g(f(y,f(f(g(y),u),y))). 2004 [] g(f(x,f(f(g(x),y),z)))=g(f(z,f(f(g(z),y),z))). 2005 [] g(f(f(g(f(f(x,g(y)),x)),x),f(f(g(f(g(f(f(x,g(y)),x)),x)),x),f(g(f(f(x,g(y)),x)),x))))=g(f(f(g(z),u),f(f(g(f(g(z),u)),x),f(g(f(f(x,g(y)),x)),x)))). 2006 [] g(f(f(g(f(f(x,g(y)),x)),x),f(f(g(f(g(f(f(x,g(y)),x)),x)),x),f(g(f(f(x,g(y)),x)),x))))=g(f(f(g(z),u),f(g(f(f(u,g(f(z,y))),u)),u))). 2007 [] g(f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y)))=g(z). 2008 [] g(f(f(g(x),y),f(g(f(f(y,g(f(x,g(f(z,f(g(f(u,z)),x)))))),y)),y)))=g(g(f(v,f(g(f(u,v)),x)))). 2009 [] g(g(f(x,f(g(f(y,x)),z))))=g(g(f(u,f(g(f(y,u)),z)))). 2010 [] g(f(x,g(f(y,f(f(z,f(g(f(y,z)),g(f(y,g(f(u,f(f(g(u),f(g(f(x,g(x))),v)),y))))))),x)))))=v. 2011 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(f(z,f(f(g(z),f(g(f(u,g(u))),g(f(u,g(v))))),x))))))),u))=v. 2012 [] f(g(f(x,g(x))),g(f(x,g(f(y,f(f(z,f(g(f(y,z)),g(f(y,g(f(u,f(f(g(u),v),y))))))),x))))))=v. 2013 [] f(f(g(f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),z)),x))))),u),f(g(f(v,u)),u))=f(f(z,f(g(f(u,g(u))),g(v))),u). 2014 [] f(f(x,f(g(f(y,g(y))),g(z))),y)=f(f(x,y),f(g(f(z,y)),y)). 2015 [] f(f(g(x),f(g(f(y,g(y))),g(f(y,g(f(x,z)))))),y)=z. 2016 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(z,f(f(g(z),f(g(f(u,g(u))),g(f(u,g(f(y,v)))))),y))))))),u)=v. 2017 [] f(f(x,y),f(g(f(f(y,g(f(z,f(f(g(z),u),y)))),y)),y))=f(f(x,u),y). 2018 [] g(f(x,f(f(g(x),g(f(y,g(f(y,f(f(z,f(g(f(y,z)),u)),y)))))),f(g(f(f(u,v),g(f(y,g(f(y,f(f(z,f(g(f(y,z)),u)),y))))))),g(f(y,g(f(y,f(f(z,f(g(f(y,z)),u)),y)))))))))=v. 2019 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u))))))),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u)))))))))=z. 2020 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u)))))))))=z. 2021 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z. 2022 [] g(f(x,f(f(g(x),y),f(g(z),y))))=f(g(f(y,y)),g(f(y,g(f(y,z))))). 2023 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=f(f(y,g(f(u,f(f(g(u),y),f(g(z),y))))),y). 2024 [] f(f(x,g(f(y,f(f(g(y),x),f(g(z),x))))),x)=z. 2025 [] f(f(g(f(x,g(f(y,f(f(g(y),z),x))))),g(f(u,f(f(g(u),g(f(x,g(f(y,f(f(g(y),z),x)))))),z)))),g(f(x,g(f(y,f(f(g(y),z),x))))))=f(x,g(x)). 2026 [] f(f(x,g(f(y,f(z,f(g(f(u,z)),x))))),x)=f(u,f(g(y),x)). 2027 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),f(u,v))=f(z,f(u,v)). 2028 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),u)=f(z,f(f(v,g(f(w,f(f(g(w),v),f(g(u),v))))),v)). 2029 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),u)=f(z,u). 2030 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),f(u,f(g(v),w)))=f(z,f(f(w,g(f(v,f(v6,f(g(f(u,v6)),w))))),w)). 2031 [] f(x,f(f(y,g(f(z,f(u,f(g(f(v,u)),y))))),y))=f(x,f(v,f(g(z),y))). 2032 [] g(f(f(g(x),y),f(g(f(f(y,g(f(x,f(z,f(g(u),v))))),y)),y)))=g(f(f(v,g(f(u,f(w,f(g(f(z,w)),v))))),v)). 2033 [] g(f(f(x,g(f(y,f(z,f(g(f(u,z)),x))))),x))=g(f(u,f(g(y),x))). 2034 [] f(f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u),x)=f(f(z,u),x). 2035 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(f(z,u),y)))))))=f(g(f(f(y,g(f(v,f(f(g(v),y),f(z,y))))),y)),u). 2036 [] f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u)=f(z,u). 2037 [] f(g(f(f(g(f(x,g(f(y,f(f(g(y),z),x))))),g(f(u,f(f(g(u),g(f(x,g(f(y,f(f(g(y),z),x)))))),z)))),g(f(x,g(f(y,f(f(g(y),z),x))))))),v)=f(g(f(x,g(x))),v). 2038 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x))=f(u,f(g(f(v,u)),g(f(v,g(f(v,f(z,v))))))). 2039 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x))=z. 2040 [] g(f(f(g(f(x,g(f(y,f(f(g(y),z),x))))),g(f(u,f(f(g(u),g(f(x,g(f(y,f(f(g(y),z),x)))))),z)))),g(f(x,g(f(y,f(f(g(y),z),x)))))))=g(f(x,g(x))). 2041 [] g(f(f(x,g(f(y,f(z,f(f(g(z),u),x))))),x))=f(g(f(g(y),x)),u). 2042 [] f(f(g(g(f(x,g(x)))),g(f(x,g(x)))),f(f(g(f(g(y),g(f(x,g(x))))),z),u))=g(f(x,g(f(v,f(f(g(v),f(y,f(z,f(f(g(z),z),u)))),x))))). 2043 [] f(g(x),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))))=g(f(z,x)). 2044 [] f(g(x),f(g(f(y,g(y))),g(f(y,g(f(x,f(z,y)))))))=z. 2045 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(f(g(z),f(g(f(u,g(u))),g(f(u,g(f(y,f(v,u))))))),y)))))))=v. 2046 [] f(g(x),g(f(y,g(f(y,f(f(z,g(f(u,f(y,z)))),y))))))=g(f(u,x)). 2047 [] f(x,g(f(y,f(z,x))))=f(u,g(f(y,f(z,u)))). 2048 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=f(u,g(f(x,f(f(v,f(g(f(x,v)),g(z))),u)))). 2049 [] f(x,g(f(y,f(f(z,f(g(f(y,z)),g(u))),x))))=u. 2050 [] f(x,g(f(y,f(f(g(y),f(g(f(z,g(z))),g(u))),x))))=u. 2051 [] f(g(f(x,g(x))),g(f(y,g(f(z,f(f(g(z),u),y))))))=u. 2052 [] g(f(x,g(f(y,f(f(g(y),f(g(f(z,g(z))),u)),x)))))=u. 2053 [] f(x,f(g(f(y,x)),g(f(z,g(f(y,f(u,z)))))))=u. 2054 [] f(f(x,f(g(f(y,x)),g(f(z,g(f(y,u)))))),z)=u. 2055 [] f(x,f(f(y,f(g(f(x,y)),g(f(z,g(u))))),z))=u. 2056 [] g(f(x,g(f(y,f(f(z,f(g(f(y,z)),u)),x)))))=u. 2057 [] f(g(f(x,y)),g(f(z,g(f(x,f(f(y,u),z))))))=u. 2058 [] f(g(f(f(x,g(f(y,f(f(g(y),z),x)))),z)),z)=z. 2059 [] f(x,f(f(y,f(g(f(x,y)),g(z))),g(f(u,v))))=f(w,g(f(u,f(f(v,z),w)))). 2060 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(z,g(u))))),z))=u. 2061 [] f(g(f(x,g(x))),g(f(f(g(f(f(y,z),y)),y),z)))=y. 2062 [] f(f(g(f(x,g(f(y,f(f(z,u),x))))),g(f(v,f(f(g(v),g(f(x,g(f(y,f(f(z,u),x)))))),u)))),g(f(x,g(f(y,f(f(z,u),x))))))=f(y,z). 2063 [] g(f(x,g(x)))=g(f(y,g(y))). 2064 [] f(g(f(x,g(x))),y)=f(g(f(z,g(z))),y). 2065 [] f(x,g(x))=f(y,g(y)). 2066 [] g(f(g(f(x,f(g(f(y,x)),z))),g(f(y,f(u,g(u))))))=z. 2067 [] f(x,f(f(g(x),y),f(g(f(f(z,g(z)),y)),y)))=y. 2068 [] f(g(x),g(f(y,f(z,g(z)))))=f(u,g(f(y,f(x,u)))). 2069 [] f(g(f(x,y)),g(f(z,g(f(x,f(f(u,g(u)),z))))))=g(y). 2070 [] f(x,f(f(y,f(g(f(x,y)),g(f(z,g(z))))),u))=u. 2071 [] f(f(g(x),y),f(g(f(f(y,g(f(z,g(z)))),y)),y))=g(x). 2072 [] f(f(x,f(g(f(y,x)),g(f(z,g(f(y,f(f(u,g(u)),z))))))),v)=f(f(w,g(w)),v). 2073 [] f(f(x,g(x)),y)=f(f(z,g(z)),y). 2074 [] g(g(f(x,f(g(f(y,x)),g(f(z,g(f(y,f(f(u,g(u)),z)))))))))=g(g(f(v,g(v)))). 2075 [] g(g(f(x,g(x))))=g(g(f(y,g(y)))). 2076 [] f(g(f(x,g(x))),g(g(f(f(y,g(f(z,f(u,f(f(g(u),g(f(v,f(f(g(v),w),g(f(g(z),y)))))),y))))),y))))=w. 2077 [] f(x,f(f(f(f(y,f(g(f(x,y)),g(z))),g(f(u,v))),f(g(f(w,g(f(u,f(f(v,z),w))))),g(v6))),g(f(v7,v8))))=f(v9,g(f(v7,f(f(v8,v6),v9)))). 2078 [] f(f(x,g(x)),g(f(y,g(y))))=f(z,g(z)). 2079 [] f(f(f(x,g(x)),g(f(y,g(y)))),z)=f(f(u,g(u)),z). 2080 [] f(g(f(x,g(x))),g(g(f(y,g(y)))))=f(z,g(z)). 2081 [] f(x,f(g(f(f(y,g(f(g(f(z,g(z))),f(f(g(g(f(u,g(u)))),y),v)))),x)),y))=f(y,v). 2082 [] f(g(f(x,g(x))),f(f(g(g(f(y,g(y)))),z),u))=f(v,f(f(g(v),z),u)). 2083 [] g(f(f(g(g(f(x,g(x)))),g(f(f(y,g(y)),f(z,f(g(f(u,z)),g(g(f(x,g(x))))))))),g(g(f(x,g(x))))))=g(f(u,f(v,g(v)))). 2084 [] f(f(g(g(f(x,g(x)))),g(f(x,g(x)))),f(g(f(y,g(f(x,g(x))))),g(f(x,g(x)))))=f(f(g(g(f(z,g(z)))),f(g(f(u,g(u))),g(y))),g(f(x,g(x)))). 2085 [] g(f(f(g(g(f(x,g(x)))),y),f(g(f(f(y,g(f(z,g(z)))),y)),y)))=g(g(g(f(u,g(u))))). 2086 [] g(g(g(f(x,g(x)))))=g(g(g(f(y,g(y))))). 2087 [] f(f(x,g(x)),f(g(f(f(g(g(f(y,g(y)))),g(f(z,f(f(g(z),u),g(g(f(y,g(y)))))))),g(g(f(y,g(y)))))),g(g(f(y,g(y))))))=f(f(g(f(v,g(v))),u),g(g(f(y,g(y))))). 2088 [] g(f(g(f(x,g(x))),f(f(g(g(f(y,g(y)))),f(g(f(z,g(z))),u)),g(f(x,g(x))))))=f(f(g(g(f(x,g(x)))),v),f(g(f(f(v,u),v)),v)). 2089 [] g(f(f(x,g(x)),f(f(y,g(y)),f(g(f(f(g(g(f(z,g(z)))),u),g(g(f(z,g(z)))))),g(g(f(z,g(z))))))))=u. 2090 [] f(f(x,g(x)),f(f(y,g(y)),f(g(f(f(g(g(f(z,g(z)))),g(u)),g(g(f(z,g(z)))))),g(g(f(z,g(z)))))))=u. 2091 [] f(f(x,g(x)),f(g(f(f(g(g(f(y,g(y)))),g(f(f(z,g(z)),u))),g(g(f(y,g(y)))))),g(g(f(y,g(y))))))=u. 2092 [] f(f(g(g(f(x,g(x)))),g(g(g(f(y,g(y)))))),z)=f(f(u,g(u)),z). 2093 [] f(f(x,f(g(f(y,x)),g(f(z,g(z))))),f(u,g(u)))=g(y). 2094 [] f(f(x,f(g(f(y,x)),g(f(z,g(z))))),f(y,u))=u. 2095 [] f(g(f(f(f(g(f(f(x,y),x)),x),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),y)),z)))))),x)),x)=x. 2096 [] f(g(f(f(f(g(f(f(x,y),x)),x),y),x)),x)=x. 2097 [] f(g(f(f(f(g(f(f(x,g(x)),y)),y),g(y)),y)),y)=y. 2098 [] f(x,f(f(f(f(y,f(g(f(x,y)),g(z))),g(f(u,v))),f(g(f(w,g(f(u,f(f(v,z),w))))),g(v6))),g(f(v7,g(v7)))))=f(f(g(f(f(v8,g(v8)),v6)),v6),g(v6)). 2099 [] f(g(f(f(x,g(x)),x)),x)=f(g(f(f(y,g(y)),x)),x). 2100 [] f(x,f(g(f(f(f(g(f(y,g(y))),g(f(z,g(z)))),g(u)),x)),f(g(f(y,g(y))),g(f(z,g(z))))))=f(f(g(f(y,g(y))),g(f(z,g(z)))),u). 2101 [] f(f(f(g(g(f(x,g(x)))),g(g(g(f(y,g(y)))))),g(f(z,g(z)))),u)=f(f(v,g(v)),u). 2102 [] f(f(f(g(f(f(x,g(x)),g(f(y,g(y))))),g(f(y,g(y)))),g(g(f(y,g(y))))),f(f(g(f(y,g(y))),g(f(y,g(y)))),z))=z. 2103 [] f(g(x),g(f(g(f(f(f(y,g(y)),g(f(y,g(y)))),f(y,g(y)))),f(y,g(y)))))=f(z,g(f(g(f(f(u,g(u)),f(y,g(y)))),f(x,z)))). 2104 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(z))),g(f(u,g(u)))))=f(v,g(f(w,f(f(g(w),z),v)))). 2105 [] f(x,f(f(f(f(y,f(g(f(x,y)),g(z))),g(f(u,v))),f(g(f(w,g(f(u,f(f(v,z),w))))),g(f(g(f(v6,g(v6))),g(v7))))),g(f(v8,g(v8)))))=v7. 2106 [] g(f(f(x,g(f(y,f(z,f(f(g(z),g(f(u,f(f(g(u),f(g(f(v,g(v))),g(w))),g(f(g(y),x)))))),x))))),x))=w. 2107 [] g(g(f(f(x,g(f(y,f(z,f(f(g(z),g(f(u,f(f(g(u),f(g(f(v,g(v))),w)),g(f(g(y),x)))))),x))))),x)))=w. 2108 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(g(f(z,g(z))),g(u))))),g(f(v,g(v)))))=u. 2109 [] g(f(g(f(f(x,y),f(g(y),z))),g(f(f(u,f(g(f(x,u)),g(f(v,g(v))))),f(w,g(w))))))=z. 2110 [] g(f(g(f(f(x,y),f(g(y),z))),g(g(x))))=z. 2111 [] g(f(g(f(f(x,g(x)),f(g(g(y)),z))),g(g(y))))=z. 2112 [] g(f(g(f(f(x,g(x)),f(g(y),z))),g(g(f(g(f(f(u,g(u)),f(g(g(v)),y))),g(g(v)))))))=z. 2113 [] g(f(g(f(f(x,g(x)),f(g(y),z))),g(y)))=z. 2114 [] g(f(g(f(f(x,g(x)),f(y,z))),g(f(g(f(f(u,g(u)),f(g(v),y))),g(v)))))=z. 2115 [] g(f(g(f(f(x,g(x)),f(y,z))),y))=z. 2116 [] g(f(g(f(f(x,g(x)),f(y,g(y)))),z))=g(z). 2117 [] f(x,g(f(g(f(f(y,g(y)),f(z,g(z)))),f(u,x))))=f(g(u),g(f(z,g(z)))). 2118 [] f(g(x),g(f(y,g(y))))=f(z,g(f(x,z))). 2119 [] f(g(f(x,y)),g(f(z,g(f(x,y)))))=f(g(z),g(f(u,g(u)))). 2120 [] f(f(x,f(g(y),g(f(z,g(z))))),y)=x. 2121 [] f(f(x,y),f(g(y),g(f(z,g(z)))))=x. 2122 [] f(x,f(g(f(f(y,z),x)),g(f(g(f(u,g(u))),g(y)))))=g(z). 2123 [] f(g(f(x,g(x))),g(g(f(f(y,f(g(y),g(f(z,g(z))))),y))))=y. 2124 [] f(g(f(x,g(x))),g(g(y)))=y. 2125 [] f(f(x,g(f(y,f(z,f(f(g(z),g(f(u,f(f(g(u),v),g(f(g(y),x)))))),x))))),x)=v. 2126 [] g(g(f(g(f(x,g(x))),y)))=y. 2127 [] g(f(g(f(x,g(x))),g(y)))=y. 2128 [] f(x,f(g(f(f(y,z),x)),y))=g(z). 2129 [] f(x,f(f(g(x),f(g(f(y,g(y))),z)),g(f(u,g(u)))))=z. 2130 [] f(x,f(f(f(f(y,f(g(f(x,y)),g(z))),g(f(u,v))),f(g(f(w,g(f(u,f(f(v,z),w))))),v6)),g(f(v7,g(v7)))))=v6. 2131 [] f(f(g(f(x,g(x))),g(f(y,g(y)))),z)=g(g(z)). 2132 [] g(g(f(g(f(x,g(x))),f(f(g(g(f(y,g(y)))),z),u))))=f(z,u). 2133 [] f(f(g(g(f(x,g(x)))),y),z)=f(y,z). 2134 [] f(x,g(f(y,f(f(g(y),z),x))))=g(z). 2135 [] f(f(g(f(f(x,g(x)),y)),y),g(y))=g(y). 2136 [] f(g(g(f(x,g(x)))),f(f(g(f(x,g(x))),g(f(x,g(x)))),y))=y. 2137 [] f(g(g(f(x,g(x)))),g(g(y)))=y. 2138 [] f(f(g(f(x,g(x))),g(f(y,g(y)))),z)=f(f(u,g(u)),z). 2139 [] f(f(x,g(x)),y)=g(g(y)). 2140 [] f(g(f(x,g(x))),y)=f(f(z,g(z)),y). 2141 [] f(g(f(x,g(x))),y)=g(g(y)). 2142 [] f(f(x,g(x)),f(g(f(f(g(g(f(y,g(y)))),g(g(g(z)))),g(g(f(y,g(y)))))),g(g(f(y,g(y))))))=z. 2143 [] f(f(x,g(x)),f(g(f(g(y),g(g(f(z,g(z)))))),g(g(f(z,g(z))))))=y. 2144 [] g(g(f(g(f(g(x),g(g(f(y,g(y)))))),g(g(f(y,g(y)))))))=x. 2145 [] f(f(x,g(x)),f(f(y,g(y)),f(g(f(g(z),g(g(f(u,g(u)))))),g(g(f(u,g(u)))))))=z. 2146 [] f(f(x,g(x)),g(g(f(g(f(g(y),g(g(f(z,g(z)))))),g(g(f(z,g(z))))))))=y. 2147 [] f(f(x,g(x)),y)=y. 2148 [] g(g(x))=x. 2149 [] g(f(f(x,g(x)),f(f(y,g(y)),f(g(f(f(f(z,g(z)),u),g(g(f(z,g(z)))))),g(g(f(z,g(z))))))))=u. 2150 [] g(f(f(x,g(x)),f(f(y,g(y)),f(g(f(g(g(z)),g(g(f(u,g(u)))))),g(g(f(u,g(u))))))))=z. 2151 [] g(f(f(x,g(x)),f(f(y,g(y)),f(g(f(z,g(g(f(u,g(u)))))),g(g(f(u,g(u))))))))=z. 2152 [] g(f(f(x,g(x)),f(f(y,g(y)),f(g(f(z,f(u,g(u)))),g(g(f(u,g(u))))))))=z. 2153 [] g(f(f(x,g(x)),f(f(y,g(y)),f(g(f(z,f(u,g(u)))),f(u,g(u))))))=z. 2154 [] g(f(f(x,g(x)),g(g(f(g(f(y,f(z,g(z)))),f(z,g(z)))))))=y. 2155 [] g(f(f(x,g(x)),f(g(f(y,f(z,g(z)))),f(z,g(z)))))=y. 2156 [] g(g(g(f(g(f(x,f(y,g(y)))),f(y,g(y))))))=x. 2157 [] g(f(g(f(x,f(y,g(y)))),f(y,g(y))))=x. 2158 [] g(f(g(f(x,g(x))),f(f(f(y,g(y)),f(g(f(z,g(z))),u)),g(f(x,g(x))))))=f(f(g(g(f(x,g(x)))),v),f(g(f(f(v,u),v)),v)). 2159 [] g(f(g(f(x,g(x))),f(f(f(y,g(y)),g(g(z))),g(f(x,g(x))))))=f(f(g(g(f(x,g(x)))),u),f(g(f(f(u,z),u)),u)). 2160 [] g(f(g(f(x,g(x))),f(f(f(y,g(y)),z),g(f(x,g(x))))))=f(f(g(g(f(x,g(x)))),u),f(g(f(f(u,z),u)),u)). 2161 [] f(f(g(g(f(x,g(x)))),y),f(g(f(f(y,z),y)),y))=g(f(g(f(x,g(x))),f(g(g(z)),g(f(x,g(x)))))). 2162 [] f(f(g(g(f(x,g(x)))),y),f(g(f(f(y,z),y)),y))=g(f(g(f(x,g(x))),f(z,g(f(x,g(x)))))). 2163 [] f(f(g(g(f(x,g(x)))),y),f(g(f(f(y,z),y)),y))=g(g(g(f(z,g(f(x,g(x))))))). 2164 [] f(f(g(g(f(x,g(x)))),y),f(g(f(f(y,z),y)),y))=g(f(z,g(f(x,g(x))))). 2165 [] f(f(f(x,g(x)),y),f(g(f(f(y,z),y)),y))=g(f(z,g(f(x,g(x))))). 2166 [] f(g(g(x)),f(g(f(f(x,y),x)),x))=g(f(y,g(f(z,g(z))))). 2167 [] f(x,f(g(f(f(x,y),x)),x))=g(f(y,g(f(z,g(z))))). 2168 [] g(f(x,g(f(y,g(y)))))=g(x). 2169 [] f(f(x,g(x)),f(g(f(f(f(y,g(y)),g(f(z,f(f(g(z),u),g(g(f(y,g(y)))))))),g(g(f(y,g(y)))))),g(g(f(y,g(y))))))=f(f(g(f(v,g(v))),u),g(g(f(y,g(y))))). 2170 [] f(f(x,g(x)),f(g(f(f(f(y,g(y)),g(f(z,f(f(g(z),u),f(y,g(y)))))),g(g(f(y,g(y)))))),g(g(f(y,g(y))))))=f(f(g(f(v,g(v))),u),g(g(f(y,g(y))))). 2171 [] f(f(x,g(x)),f(g(f(g(y),g(g(f(z,g(z)))))),g(g(f(z,g(z))))))=f(f(g(f(u,g(u))),y),g(g(f(z,g(z))))). 2172 [] f(f(x,g(x)),f(g(f(g(y),f(z,g(z)))),g(g(f(z,g(z))))))=f(f(g(f(u,g(u))),y),g(g(f(z,g(z))))). 2173 [] f(f(x,g(x)),f(g(f(g(y),f(z,g(z)))),f(z,g(z))))=f(f(g(f(u,g(u))),y),g(g(f(z,g(z))))). 2174 [] g(g(f(g(f(g(x),f(y,g(y)))),f(y,g(y)))))=f(f(g(f(z,g(z))),x),g(g(f(y,g(y))))). 2175 [] f(f(g(f(x,g(x))),y),g(g(f(z,g(z)))))=g(g(y)). 2176 [] f(f(g(f(x,g(x))),y),g(g(f(z,g(z)))))=y. 2177 [] f(g(g(x)),g(g(f(y,g(y)))))=x. 2178 [] f(x,g(g(f(y,g(y)))))=x. 2179 [] f(x,f(y,g(y)))=x. 2180 [] f(f(f(x,g(x)),g(f(x,g(x)))),f(g(f(y,g(f(x,g(x))))),g(f(x,g(x)))))=f(f(g(g(f(z,g(z)))),f(g(f(u,g(u))),g(y))),g(f(x,g(x)))). 2181 [] f(g(g(g(f(x,g(x))))),f(g(f(y,g(f(x,g(x))))),g(f(x,g(x)))))=f(f(g(g(f(z,g(z)))),f(g(f(u,g(u))),g(y))),g(f(x,g(x)))). 2182 [] f(f(g(g(f(x,g(x)))),f(g(f(y,g(y))),g(z))),g(f(u,g(u))))=f(g(f(u,g(u))),f(g(f(z,g(f(u,g(u))))),g(f(u,g(u))))). 2183 [] f(f(g(g(f(x,g(x)))),f(g(f(y,g(y))),g(z))),g(f(u,g(u))))=f(g(f(u,g(u))),f(g(z),g(f(u,g(u))))). 2184 [] f(f(g(g(f(x,g(x)))),f(g(f(y,g(y))),g(z))),g(f(u,g(u))))=g(g(f(g(z),g(f(u,g(u)))))). 2185 [] f(f(g(g(f(x,g(x)))),f(g(f(y,g(y))),g(z))),g(f(u,g(u))))=g(g(g(z))). 2186 [] f(f(g(g(f(x,g(x)))),f(g(f(y,g(y))),g(z))),g(f(u,g(u))))=g(z). 2187 [] f(f(f(x,g(x)),f(g(f(y,g(y))),g(z))),g(f(u,g(u))))=g(z). 2188 [] f(f(f(x,g(x)),g(g(g(y)))),g(f(z,g(z))))=g(y). 2189 [] f(f(f(x,g(x)),g(y)),g(f(z,g(z))))=g(y). 2190 [] f(g(g(g(x))),g(f(y,g(y))))=g(x). 2191 [] f(g(x),g(f(y,g(y))))=g(x). 2192 [] g(f(f(f(x,g(x)),g(f(f(y,g(y)),f(z,f(g(f(u,z)),g(g(f(x,g(x))))))))),g(g(f(x,g(x))))))=g(f(u,f(v,g(v)))). 2193 [] g(f(f(f(x,g(x)),g(f(f(y,g(y)),f(z,f(g(f(u,z)),f(x,g(x))))))),g(g(f(x,g(x))))))=g(f(u,f(v,g(v)))). 2194 [] g(f(f(f(x,g(x)),g(f(f(y,g(y)),f(z,g(f(u,z)))))),g(g(f(x,g(x))))))=g(f(u,f(v,g(v)))). 2195 [] g(f(f(f(x,g(x)),g(g(g(f(y,g(f(z,y))))))),g(g(f(x,g(x))))))=g(f(z,f(u,g(u)))). 2196 [] g(f(f(f(x,g(x)),g(f(y,g(f(z,y))))),g(g(f(x,g(x))))))=g(f(z,f(u,g(u)))). 2197 [] g(f(g(g(g(f(x,g(f(y,x)))))),g(g(f(z,g(z))))))=g(f(y,f(u,g(u)))). 2198 [] g(f(g(f(x,g(f(y,x)))),g(g(f(z,g(z))))))=g(f(y,f(u,g(u)))). 2199 [] g(f(g(f(x,g(f(y,x)))),f(z,g(z))))=g(f(y,f(u,g(u)))). 2200 [] g(g(f(x,g(f(y,x)))))=g(f(y,f(z,g(z)))). 2201 [] g(f(x,f(y,g(y))))=f(z,g(f(x,z))). 2202 [] f(x,g(f(y,x)))=g(y). 2203 [] f(g(f(x,g(x))),f(f(f(y,g(y)),z),u))=f(v,f(f(g(v),z),u)). 2204 [] f(g(f(x,g(x))),f(g(g(y)),z))=f(u,f(f(g(u),y),z)). 2205 [] f(g(f(x,g(x))),f(y,z))=f(u,f(f(g(u),y),z)). 2206 [] f(x,f(f(g(x),y),z))=g(g(f(y,z))). 2207 [] f(x,f(f(g(x),y),z))=f(y,z). 2208 [] f(f(f(x,g(x)),g(f(x,g(x)))),f(f(g(f(g(y),g(f(x,g(x))))),z),u))=g(f(x,g(f(v,f(f(g(v),f(y,f(z,f(f(g(z),z),u)))),x))))). 2209 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)))))=f(g(g(g(f(x,g(x))))),f(f(g(f(g(z),g(f(x,g(x))))),u),v)). 2210 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)))))=f(g(f(x,g(x))),f(f(g(f(g(z),g(f(x,g(x))))),u),v)). 2211 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)))))=f(g(f(x,g(x))),f(f(g(g(z)),u),v)). 2212 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)))))=f(g(f(x,g(x))),f(f(z,u),v)). 2213 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)))))=g(g(f(f(z,u),v))). 2214 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)))))=f(f(z,u),v). 2215 [] g(f(x,g(f(y,f(f(g(y),f(z,f(u,v))),x)))))=f(f(z,u),v). 2216 [] g(f(x,g(f(f(y,f(z,u)),x))))=f(f(y,z),u). 2217 [] g(g(f(x,f(y,z))))=f(f(x,y),z). 2218 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 2219 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z. 2220 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 2221 [] f(f(a,b),c)!=f(a,f(b,c)). 2222 [] f(f(g(f(g(x),y)),z),f(g(f(f(z,g(u)),z)),z))=f(g(f(f(y,g(f(x,u))),y)),y). 2223 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 2224 [] f(f(g(x),x),f(g(f(y,x)),x))=f(f(z,f(g(f(x,z)),g(y))),x). 2225 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 2226 [] f(x,g(f(x,f(f(g(x),x),f(g(f(y,x)),x)))))=y. 2227 [] f(f(x,f(g(f(y,x)),g(z))),y)=f(f(g(y),y),f(g(f(z,y)),y)). 2228 [] f(g(f(f(x,g(f(y,f(f(g(y),x),z)))),x)),x)=z. 2229 [] f(x,f(g(f(f(y,g(f(f(f(y,g(f(z,f(f(g(z),y),x)))),y),u))),y)),y))=u. 2230 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 2231 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 2232 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 2233 [] f(x,g(f(y,g(f(y,f(f(g(f(y,f(f(z,f(g(f(y,z)),x)),y))),u),y))))))=u. 2234 [] f(f(x,f(g(f(y,x)),z)),y)=f(f(u,f(g(f(y,u)),z)),y). 2235 [] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(g(x),u),f(g(f(f(u,z),u)),u)). 2236 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z. 2237 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),y)),y)))=z. 2238 [] g(f(x,f(f(g(x),y),f(g(z),y))))=f(g(f(y,y)),g(f(y,g(f(y,z))))). 2239 [] g(f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y)))=g(z). 2240 [] f(x,f(f(g(x),y),z))=f(u,f(f(g(u),y),z)). 2241 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 2242 [] f(x,f(f(g(x),g(f(y,g(f(y,f(f(z,u),y)))))),v))=f(f(y,z),f(u,v)). 2243 [] g(f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),z)),x)))))=z. 2244 [] f(g(f(x,g(x))),g(f(x,g(f(y,f(f(g(y),z),x))))))=z. 2245 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z. 2246 [] f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),g(z))),x))))=z. 2247 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(y,g(z))))),y))=z. 2248 [] f(x,g(f(y,f(f(g(y),x),f(g(f(f(z,f(g(f(x,z)),u)),x)),x)))))=f(v,f(g(f(x,v)),u)). 2249 [] f(g(f(x,g(x))),g(f(x,g(f(y,z)))))=f(g(f(x,g(y))),g(f(x,g(f(x,z))))). 2250 [] f(f(g(x),f(g(f(y,g(y))),g(z))),y)=f(f(g(x),y),f(g(f(z,y)),y)). 2251 [] f(f(x,g(f(y,f(f(g(y),x),f(g(z),x))))),x)=z. 2252 [] f(f(g(f(x,g(f(y,f(f(g(y),z),x))))),g(f(u,f(f(g(u),g(f(x,g(f(y,f(f(g(y),z),x)))))),z)))),g(f(x,g(f(y,f(f(g(y),z),x))))))=f(x,g(x)). 2253 [] f(f(g(f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),z)),x))))),u),f(g(f(v,u)),u))=f(f(z,f(g(f(u,g(u))),g(v))),u). 2254 [] f(f(g(x),f(g(f(y,g(y))),g(f(y,g(f(x,z)))))),y)=z. 2255 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),f(u,v))=f(z,f(u,v)). 2256 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),u)=f(z,f(f(v,g(f(w,f(f(g(w),v),f(g(u),v))))),v)). 2257 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 2258 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(f(g(z),u),y)))))))=f(g(y),u). 2259 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=f(u,f(g(f(v,u)),g(f(v,g(f(v,f(z,v))))))). 2260 [] f(x,f(g(f(f(y,g(f(z,f(f(g(z),y),u)))),x)),y))=f(y,u). 2261 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(z,f(f(g(z),f(g(f(u,g(u))),g(f(u,g(f(y,v)))))),y))))))),u)=v. 2262 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 2263 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). 2264 [] f(g(x),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))))=g(f(z,x)). 2265 [] f(g(x),g(f(y,g(f(y,f(f(z,g(f(u,f(y,z)))),y))))))=g(f(u,x)). 2266 [] f(x,g(f(y,f(z,x))))=f(u,g(f(y,f(z,u)))). 2267 [] f(x,g(f(y,f(f(g(y),f(g(f(z,g(z))),g(u))),x))))=u. 2268 [] f(x,f(g(f(y,x)),g(f(z,g(f(y,f(u,z)))))))=u. 2269 [] f(g(f(x,g(x))),g(f(y,g(f(z,f(f(g(z),u),y))))))=u. 2270 [] g(f(x,g(f(y,f(f(g(y),f(g(f(z,g(z))),u)),x)))))=u. 2271 [] g(f(x,g(f(y,f(f(z,f(g(f(y,z)),u)),x)))))=u. 2272 [] f(g(f(x,y)),g(f(z,g(f(x,f(f(y,u),z))))))=u. 2273 [] f(g(f(x,g(x))),y)=f(g(f(z,g(z))),y). 2274 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(z,g(u))))),z))=u. 2275 [] f(g(f(x,g(x))),g(f(f(g(f(f(y,z),y)),y),z)))=y. 2276 [] f(f(g(f(x,g(f(y,f(f(z,u),x))))),g(f(v,f(f(g(v),g(f(x,g(f(y,f(f(z,u),x)))))),u)))),g(f(x,g(f(y,f(f(z,u),x))))))=f(y,z). 2277 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(g(f(z,g(z))),g(u))))),g(f(v,g(v)))))=u. 2278 [] f(x,f(f(y,f(g(f(x,y)),g(f(z,g(u))))),z))=u. 2279 [] f(f(x,f(g(f(y,x)),g(f(z,g(f(y,u)))))),z)=u. 2280 [] f(f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x)))),u)=f(z,u). 2281 [] f(f(x,f(g(f(y,g(y))),g(z))),y)=f(f(x,y),f(g(f(z,y)),y)). 2282 [] f(f(x,y),f(g(f(f(z,g(f(u,f(f(g(u),v),z)))),y)),y))=f(f(x,v),y). 2283 [] f(f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u),x)=f(f(z,u),x). 2284 [] f(x,f(g(f(y,x)),g(f(z,g(f(y,f(f(u,v),z)))))))=f(g(f(f(z,g(f(w,f(f(g(w),z),f(u,z))))),z)),v). 2285 [] f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u)=f(z,f(g(f(v,z)),g(f(x,g(f(v,f(f(z,u),x))))))). 2286 [] f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u)=f(z,u). 2287 [] f(x,g(x))=f(y,g(y)). 2288 [] f(g(f(x,g(x))),g(g(f(y,g(y)))))=f(z,g(z)). 2289 [] f(f(x,f(g(f(y,x)),g(f(z,g(z))))),f(y,u))=u. 2290 [] g(f(g(f(x,f(g(f(y,x)),z))),g(f(y,f(u,g(u))))))=z. 2291 [] f(g(x),g(f(y,f(z,g(z)))))=f(u,g(f(y,f(x,u)))). 2292 [] f(x,f(f(g(x),y),f(g(f(f(z,g(z)),y)),y)))=y. 2293 [] f(x,f(f(y,f(g(f(x,y)),g(f(z,g(z))))),u))=u. 2294 [] f(f(g(x),y),f(g(f(f(y,g(f(z,g(z)))),y)),y))=g(x). 2295 [] g(f(f(g(g(f(x,g(x)))),y),f(g(f(f(y,g(f(z,g(z)))),y)),y)))=g(g(g(f(u,g(u))))). 2296 [] f(f(x,f(g(f(y,x)),g(f(z,g(z))))),f(u,g(u)))=g(y). 2297 [] f(g(f(f(x,g(x)),x)),y)=f(g(f(f(z,g(z)),x)),y). 2298 [] g(f(x,g(x)))=g(f(y,g(y))). 2299 [] f(x,f(g(f(f(f(g(f(y,g(y))),g(f(z,g(z)))),g(u)),x)),f(g(f(y,g(y))),g(f(z,g(z))))))=f(f(g(f(y,g(y))),g(f(z,g(z)))),u). 2300 [] f(f(x,g(x)),y)=f(f(z,g(z)),y). 2301 [] f(f(f(x,g(x)),g(f(y,g(y)))),z)=f(f(u,g(u)),z). 2302 [] f(g(x),g(f(g(f(f(y,g(y)),y)),f(z,g(z)))))=f(u,g(f(g(f(f(v,g(v)),y)),f(x,u)))). 2303 [] g(f(g(f(f(x,y),f(g(y),z))),g(f(f(u,f(g(f(x,u)),g(f(v,g(v))))),f(w,g(w))))))=z. 2304 [] g(g(g(f(x,g(x)))))=g(g(g(f(y,g(y))))). 2305 [] f(f(f(g(g(f(x,g(x)))),g(g(g(f(y,g(y)))))),g(f(z,g(z)))),u)=f(f(v,g(v)),u). 2306 [] g(f(g(f(f(x,y),f(g(y),z))),g(g(x))))=z. 2307 [] g(f(g(f(f(x,g(x)),f(g(g(y)),z))),g(g(y))))=z. 2308 [] g(f(g(f(f(x,g(x)),f(g(y),z))),g(g(f(g(f(f(u,g(u)),f(g(g(v)),y))),g(g(v)))))))=z. 2309 [] g(f(g(f(f(x,g(x)),f(g(y),z))),g(y)))=z. 2310 [] g(f(g(f(f(x,g(x)),f(y,z))),g(f(g(f(f(u,g(u)),f(g(v),y))),g(v)))))=z. 2311 [] g(f(g(f(f(x,g(x)),f(y,z))),y))=z. 2312 [] g(f(g(f(f(x,g(x)),f(y,g(y)))),z))=g(z). 2313 [] f(x,g(f(g(f(f(y,g(y)),f(z,g(z)))),f(u,x))))=f(g(u),g(f(v,g(v)))). 2314 [] f(g(x),g(f(y,g(y))))=f(z,g(f(x,z))). 2315 [] f(g(f(x,y)),g(f(z,g(f(x,y)))))=f(g(z),g(f(u,g(u)))). 2316 [] f(f(x,f(g(y),g(f(z,g(z))))),y)=x. 2317 [] f(f(x,y),f(g(y),g(f(z,g(z)))))=x. 2318 [] f(f(x,f(y,g(f(z,y)))),z)=x. 2319 [] f(f(x,y),f(z,g(f(y,z))))=x. 2320 [] f(g(f(x,g(x))),g(g(f(f(y,f(g(y),g(f(z,g(z))))),y))))=y. 2321 [] f(x,f(g(f(f(y,z),x)),g(f(g(f(u,g(u))),g(y)))))=g(z). 2322 [] f(g(x),f(f(g(f(y,g(y))),x),z))=z. 2323 [] f(f(g(f(x,g(x))),y),f(g(y),z))=z. 2324 [] f(g(f(x,g(x))),g(g(y)))=y. 2325 [] f(x,g(f(y,f(f(g(y),z),x))))=g(z). 2326 [] g(f(g(f(x,g(x))),g(y)))=y. 2327 [] f(x,f(g(f(f(y,z),x)),y))=g(z). 2328 [] f(f(g(f(x,g(x))),g(f(y,g(y)))),z)=g(g(z)). 2329 [] f(g(g(f(x,g(x)))),g(g(y)))=y. 2330 [] f(f(g(f(x,g(x))),g(f(y,g(y)))),z)=f(f(u,g(u)),z). 2331 [] f(f(x,g(x)),y)=g(g(y)). 2332 [] f(g(f(x,g(x))),f(f(y,g(y)),z))=z. 2333 [] f(x,f(g(f(f(y,g(y)),x)),z))=z. 2334 [] g(g(x))=x. 2335 [] f(f(x,g(x)),y)=y. 2336 [] f(f(g(x),x),y)=y. 2337 [] f(x,g(f(g(y),x)))=y. 2338 [] f(x,f(g(x),y))=y. 2339 [] f(x,f(f(g(x),y),z))=f(y,z). 2340 [] g(f(g(x),g(y)))=f(y,x). 2341 [] f(g(f(g(b),g(a))),c)!=f(a,f(b,c)). 2342 [] f(g(f(g(x),g(y))),z)=f(y,f(x,z)). end_of_list. list(hints2). 2343 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y. 2344 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y. 2345 [] f(x,g(f(f(f(y,g(f(y,y))),f(x,g(z))),z)))=y. 2346 [] f(f(a,b),c)!=f(a,f(b,c)). 2347 [] g(f(x,f(f(g(f(y,x)),f(x,g(z))),z)))=f(f(g(f(f(x,g(y)),x)),f(x,g(u))),u). 2348 [] f(x,g(f(f(f(y,g(f(y,y))),z),f(f(f(z,g(f(z,z))),f(x,g(u))),u))))=y. 2349 [] f(f(f(x,g(f(x,x))),f(y,g(z))),z)=f(y,f(f(g(f(x,y)),f(y,g(u))),u)). 2350 [] f(f(f(f(x,g(y)),g(f(f(x,g(y)),f(x,g(y))))),f(x,g(z))),z)=y. 2351 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y. 2352 [] f(f(g(f(f(x,g(f(x,y))),x)),f(x,g(z))),z)=y. 2353 [] f(x,g(f(x,f(f(g(y),f(x,g(z))),z))))=f(g(f(f(u,g(f(u,y))),u)),f(u,g(x))). 2354 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=f(z,g(f(z,f(f(g(f(y,z)),f(z,g(u))),u)))). 2355 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=y. 2356 [] f(f(x,g(f(x,f(f(g(y),f(x,g(z))),z)))),x)=y. 2357 [] f(f(x,g(y)),g(f(f(x,g(y)),f(f(g(z),f(f(x,g(y)),g(u))),u))))=g(f(f(x,g(f(x,f(z,y)))),x)). 2358 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y. 2359 [] g(f(x,f(f(x,g(f(x,x))),y)))=f(y,g(f(y,y))). 2360 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u). 2361 [] f(f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(g(z)))),g(u))),u)=f(y,z). 2362 [] g(f(x,f(g(f(y,f(f(y,g(f(y,y))),x))),z)))=f(z,g(f(z,z))). 2363 [] f(f(x,g(y)),g(f(f(x,g(y)),f(x,g(y)))))=g(f(z,f(f(z,g(f(z,z))),f(x,g(y))))). 2364 [] f(f(g(f(x,f(f(x,g(f(x,x))),f(y,g(z))))),f(y,g(u))),u)=z. 2365 [] f(x,f(f(x,g(f(x,x))),f(y,g(z))))=f(f(y,g(f(y,z))),y). 2366 [] f(g(f(x,f(f(x,g(f(x,x))),f(y,g(f(z,u)))))),f(y,g(u)))=z. 2367 [] g(f(f(x,g(f(z,y))),z))=f(f(x,g(y)),g(f(f(x,g(y)),f(x,g(y))))). 2368 [] f(f(g(f(f(x,g(f(y,z))),y)),f(x,g(u))),u)=z. 2369 [] f(f(x,g(f(x,y))),x)=f(f(x,g(f(z,y))),z). 2370 [] f(f(x,g(f(y,f(f(g(z),f(x,g(u))),u)))),y)=z. 2371 [] f(f(f(f(x,g(y)),g(f(z,f(x,g(y))))),z),y)=y. 2372 [] f(f(f(f(f(g(f(f(x,y),x)),f(x,g(g(z)))),g(z)),y),x),z)=z. 2373 [] f(f(f(x,g(f(y,x))),y),z)=z. 2374 [] f(f(f(x,g(x)),f(f(y,g(f(z,y))),z)),u)=u. 2375 [] f(f(g(f(f(x,g(f(y,z))),y)),f(x,g(z))),u)=u. 2376 [] f(f(x,g(y)),y)=f(f(x,g(z)),z). 2377 [] f(f(f(x,g(f(g(y),x))),g(z)),z)=y. 2378 [] f(f(f(f(f(x,g(f(y,x))),y),g(z)),z),u)=u. 2379 [] f(f(g(x),x),y)=y. 2380 [] f(f(x,g(f(y,z))),y)=f(x,g(z)). 2381 [] f(f(x,g(x)),y)=y. 2382 [] f(f(x,y),g(y))=x. 2383 [] f(x,g(f(g(y),x)))=y. 2384 [] f(f(x,g(y)),y)=x. 2385 [] g(g(x))=x. 2386 [] f(x,g(f(y,x)))=g(y). 2387 [] f(x,f(g(x),y))=y. 2388 [] f(g(x),f(x,y))=y. 2389 [] g(f(g(x),g(y)))=f(y,x). 2390 [] f(g(f(x,g(y))),x)=y. 2391 [] g(f(y,x))=f(g(x),g(y)). 2392 [] f(a,g(f(g(c),g(b))))!=f(f(a,b),c). 2393 [] g(f(x,f(g(x),g(y))))=y. 2394 [] f(x,g(f(g(y),g(z))))=f(f(x,z),y). end_of_list. list(hints2). 2395 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 2396 [] f(x,g(f(x,f(f(g(f(y,x)),f(x,g(z))),z))))=y. 2397 [] f(f(a,b),c)!=f(a,f(b,c)). 2398 [] f(x,f(g(f(y,x)),g(z)))=f(g(f(z,y)),f(y,g(y))). 2399 [] f(g(f(f(x,g(f(x,f(y,x)))),x)),f(x,g(x)))=y. 2400 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 2401 [] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(f(x,g(f(x,f(y,x)))),x)). 2402 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 2403 [] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=f(x,g(f(x,f(f(y,z),x)))). 2404 [] f(g(f(x,y)),f(y,g(y)))=f(z,f(g(f(y,z)),g(x))). 2405 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 2406 [] f(g(f(x,g(f(y,x)))),g(y))=f(x,g(x)). 2407 [] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=g(f(y,g(f(x,y)))). 2408 [] g(f(x,g(f(x,x))))=x. 2409 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),g(g(f(x,y)))))=f(u,f(g(f(g(f(x,y)),u)),g(y))). 2410 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,g(y))),x))))=y. 2411 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(z,z))). 2412 [] f(g(f(x,x)),f(x,g(y)))=f(g(f(y,x)),f(x,g(x))). 2413 [] f(g(f(x,x)),f(x,g(f(x,g(f(x,f(y,x)))))))=y. 2414 [] f(x,g(f(x,f(f(g(f(x,x)),f(x,y)),x))))=f(y,g(f(y,y))). 2415 [] f(g(f(x,g(f(x,x)))),f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 2416 [] f(x,g(f(x,f(y,f(x,g(f(x,f(y,x))))))))=x. 2417 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),z))))=x. 2418 [] f(g(x),g(f(g(x),g(x))))=x. 2419 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 2420 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(y,x))))))=g(f(g(y),g(y))). 2421 [] f(x,g(f(x,f(f(y,f(x,y)),x))))=f(g(f(x,y)),g(f(x,y))). 2422 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 2423 [] f(x,f(g(f(y,x)),z))=f(g(f(y,y)),f(y,z)). 2424 [] f(g(f(x,g(f(x,x)))),f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 2425 [] g(f(f(x,g(f(x,f(f(y,f(x,g(x))),x)))),x))=y. 2426 [] f(x,f(f(y,f(g(f(g(f(x,g(f(x,x)))),y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 2427 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(x,g(f(x,x))))))=z. 2428 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 2429 [] f(x,f(f(g(f(x,x)),f(x,g(f(x,g(y))))),x))=y. 2430 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))=f(z,g(f(z,z))). 2431 [] f(x,f(f(y,f(g(f(x,y)),x)),x))=f(x,x). 2432 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,y),x))))))=f(f(z,f(g(f(y,z)),y)),y). 2433 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 2434 [] g(f(x,f(f(g(f(x,x)),f(x,g(f(x,y)))),x)))=y. 2435 [] g(f(x,f(f(g(f(x,x)),x),x)))=f(y,f(x,g(f(x,f(y,x))))). 2436 [] f(f(x,f(g(f(y,x)),y)),y)=y. 2437 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=f(g(f(x,x)),f(x,g(f(x,g(x))))). 2438 [] f(f(x,f(g(f(x,x)),f(x,g(f(x,g(x)))))),f(x,g(x)))=f(x,g(x)). 2439 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(z,f(g(z),u)). 2440 [] f(g(f(x,g(x))),g(f(y,f(g(f(x,y)),x))))=f(x,g(x)). 2441 [] g(f(x,f(f(g(x),f(x,g(x))),x)))=f(g(f(x,x)),x). 2442 [] f(g(f(x,g(x))),g(f(x,g(x))))=f(x,f(g(f(x,x)),x)). 2443 [] f(x,g(f(x,f(g(f(x,x)),f(x,g(f(x,g(f(x,f(f(g(x),f(x,g(x))),x))))))))))=x. 2444 [] f(x,f(f(g(x),f(x,f(g(f(x,x)),x))),x))=x. 2445 [] f(x,f(f(g(x),f(y,f(g(f(x,y)),x))),x))=x. 2446 [] f(g(f(x,g(f(x,g(x))))),x)=g(f(x,g(x))). 2447 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=f(g(x),f(y,f(g(f(x,y)),x))). 2448 [] f(x,g(f(x,f(g(x),f(x,g(x))))))=x. 2449 [] f(x,f(f(g(f(f(x,y),g(f(x,g(f(x,x)))))),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 2450 [] f(x,f(f(g(f(f(x,y),x)),f(g(f(x,g(f(x,x)))),g(z))),z))=f(y,g(f(y,y))). 2451 [] f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z))=f(y,g(f(y,y))). 2452 [] f(x,f(f(g(f(f(x,g(y)),x)),f(x,g(z))),z))=y. 2453 [] g(f(x,f(f(g(f(f(x,y),x)),f(x,g(z))),z)))=y. 2454 [] f(x,f(f(y,f(x,g(z))),z))=f(x,f(f(y,f(x,g(x))),x)). 2455 [] g(f(x,f(f(g(f(y,x)),f(x,g(z))),z)))=f(f(g(f(f(x,g(y)),x)),f(x,g(u))),u). 2456 [] g(f(f(x,g(f(x,f(f(y,f(x,g(z))),z)))),x))=y. 2457 [] f(f(g(f(f(x,g(f(x,y))),x)),f(x,g(z))),z)=y. 2458 [] f(f(x,f(y,g(z))),z)=f(f(x,f(y,g(u))),u). 2459 [] f(x,g(f(x,f(f(g(y),f(x,g(z))),z))))=f(g(f(f(u,g(f(u,y))),u)),f(u,g(x))). 2460 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=f(z,g(f(z,f(f(g(f(y,z)),f(z,g(u))),u)))). 2461 [] f(g(f(f(x,g(f(x,f(y,z)))),x)),f(x,g(z)))=y. 2462 [] f(g(f(f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 2463 [] f(g(f(x,x)),f(x,g(f(x,g(x)))))=g(x). 2464 [] f(g(x),f(y,f(g(f(x,y)),x)))=g(x). 2465 [] f(x,f(g(f(y,x)),g(f(y,g(y)))))=g(y). 2466 [] f(g(f(f(x,g(x)),x)),f(x,g(x)))=g(x). 2467 [] f(f(x,g(x)),f(x,g(x)))=f(x,g(x)). 2468 [] f(x,f(g(x),x))=x. 2469 [] f(g(f(f(g(x),x),g(x))),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 2470 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=g(f(x,g(f(x,x)))). 2471 [] g(f(f(x,g(x)),g(f(x,g(x)))))=f(x,g(x)). 2472 [] f(f(g(x),x),f(g(x),g(f(x,g(x)))))=g(x). 2473 [] f(g(f(x,g(x))),f(x,g(x)))=g(f(x,g(x))). 2474 [] f(g(x),g(f(x,g(x))))=f(g(f(x,x)),f(x,f(x,g(x)))). 2475 [] g(f(f(x,g(x)),f(g(f(x,g(x))),f(x,g(x)))))=f(x,g(x)). 2476 [] g(f(x,g(x)))=f(x,g(x)). 2477 [] g(g(f(x,g(x))))=f(x,g(x)). 2478 [] f(g(f(x,x)),f(x,f(x,g(x))))=g(x). 2479 [] f(g(x),g(f(x,g(x))))=g(x). 2480 [] f(g(x),f(x,g(x)))=g(x). 2481 [] f(f(g(x),x),g(x))=g(x). 2482 [] f(x,g(f(x,g(x))))=x. 2483 [] f(g(f(x,x)),x)=g(x). 2484 [] g(f(x,g(x)))=f(g(x),x). 2485 [] f(f(x,g(x)),x)=x. 2486 [] f(x,f(y,g(f(y,f(x,y)))))=g(f(y,f(g(y),y))). 2487 [] f(g(f(x,g(x))),x)=x. 2488 [] f(f(g(x),x),x)=x. 2489 [] f(g(x),x)=f(x,g(x)). 2490 [] g(f(g(x),x))=f(x,g(x)). 2491 [] f(f(g(x),f(x,g(x))),x)=f(x,g(x)). 2492 [] f(f(x,g(x)),g(x))=g(x). 2493 [] f(g(f(g(x),x)),g(x))=g(x). 2494 [] f(f(g(x),f(x,g(y))),y)=f(x,g(x)). 2495 [] f(f(f(g(x),f(x,g(y))),y),x)=x. 2496 [] f(g(f(x,f(g(x),f(x,g(y))))),g(f(x,g(f(x,x)))))=y. 2497 [] f(x,f(y,g(f(y,f(x,y)))))=g(y). 2498 [] f(g(f(x,y)),f(y,g(f(g(f(x,x)),f(x,y)))))=g(y). 2499 [] f(f(x,f(g(f(y,x)),g(z))),z)=g(y). 2500 [] g(g(x))=f(f(x,g(x)),x). 2501 [] g(g(x))=x. 2502 [] f(f(x,f(g(f(y,x)),z)),g(z))=g(y). 2503 [] f(g(x),f(g(g(x)),y))=f(x,f(g(x),y)). 2504 [] f(g(x),f(x,y))=f(x,f(g(x),y)). 2505 [] f(g(f(x,f(g(x),f(x,g(y))))),x)=y. 2506 [] f(g(f(x,f(g(x),f(x,y)))),x)=g(y). 2507 [] f(g(f(g(x),f(g(g(x)),f(x,f(g(x),y))))),g(x))=g(f(x,y)). 2508 [] f(g(f(g(x),f(x,f(x,f(g(x),y))))),g(x))=g(f(x,y)). 2509 [] f(x,f(y,f(g(f(f(x,g(f(x,x))),y)),f(x,g(f(x,x))))))=x. 2510 [] f(g(g(x)),g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 2511 [] f(x,g(f(f(g(x),x),g(f(f(g(x),x),x)))))=g(f(g(x),g(x))). 2512 [] f(x,g(f(f(g(x),x),g(x))))=g(f(g(x),g(x))). 2513 [] g(f(g(x),g(x)))=f(x,g(g(x))). 2514 [] g(f(g(x),g(x)))=f(x,x). 2515 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(u,f(g(f(g(f(x,y)),u)),g(y))). 2516 [] f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(g(f(x,y)),g(f(g(f(x,y)),g(f(x,y)))))),g(y)))=f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y))). 2517 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))). 2518 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y))). 2519 [] f(g(f(f(g(f(x,y)),g(g(f(f(x,y),g(f(x,y)))))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 2520 [] f(g(f(f(g(f(x,y)),f(f(x,y),g(f(x,y)))),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 2521 [] f(g(f(g(f(x,y)),g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 2522 [] f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 2523 [] f(f(f(x,y),f(x,y)),f(g(f(f(x,y),g(f(f(x,y),g(f(x,y)))))),g(y)))=x. 2524 [] f(f(f(x,y),f(x,y)),f(g(f(x,y)),g(y)))=x. 2525 [] f(f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z)))),f(g(f(x,y)),f(x,y)))=x. 2526 [] f(x,f(g(f(g(f(y,z)),x)),g(z)))=y. 2527 [] f(x,f(g(f(y,x)),g(g(f(y,y)))))=y. 2528 [] f(x,f(g(g(y)),g(f(g(x),f(x,y)))))=x. 2529 [] f(x,f(y,g(f(g(x),f(x,y)))))=x. 2530 [] f(x,f(y,g(f(x,f(g(x),y)))))=x. 2531 [] f(g(f(f(x,g(x)),x)),f(x,g(g(f(x,f(g(x),y))))))=y. 2532 [] f(g(x),f(x,g(g(f(x,f(g(x),y))))))=y. 2533 [] f(g(x),f(x,f(x,f(g(x),y))))=y. 2534 [] g(f(y,x))=f(g(x),g(y)). 2535 [] f(x,g(f(g(f(y,y)),f(y,x))))=y. 2536 [] g(f(g(x),g(y)))=f(y,x). 2537 [] f(a,g(f(g(c),g(b))))!=f(f(a,b),c). 2538 [] f(g(f(x,y)),x)=g(y). 2539 [] f(g(f(x,g(y))),x)=y. 2540 [] f(x,f(y,g(y)))=x. 2541 [] f(f(x,f(y,g(z))),z)=f(x,y). 2542 [] f(x,g(f(g(y),g(z))))=f(f(x,z),y). end_of_list. list(hints2). 2543 [] g(f(f(f(x,x),y),f(g(f(x,y)),g(f(z,x)))))=z # label("Hint 1(2544)"). 2544 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("Hint 2(2546)"). 2545 [] f(f(a,b),c)!=f(a,f(b,c)) # label("Hint 3(2548)"). 2546 [] f(f(f(x,x),y),g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(z,x))),f(z,g(u))),f(f(x,x),y)))))=u # label("Hint 4(2559)"). 2547 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))) # label("Hint 5(2562)"). 2548 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))) # label("Hint 6(2564)"). 2549 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("Hint 7(2583)"). 2550 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))) # label("Hint 8(2617)"). 2551 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(z),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))) # label("Hint 9(2641)"). 2552 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z # label("Hint 10(2653)"). 2553 [] g(f(f(f(x,x),y),g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(z,x))),f(z,u)),f(f(x,x),y))))))=u # label("Hint 11(2711)"). 2554 [] f(x,f(g(f(g(f(y,z)),x)),g(f(g(f(y,z)),g(f(g(f(y,z)),f(u,g(f(y,z)))))))))=u # label("Hint 12(2727)"). 2555 [] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(u))),x))))=u # label("Hint 13(2730)"). 2556 [] g(f(f(f(x,x),g(f(x,f(f(y,f(g(f(x,y)),z)),x)))),f(z,g(f(u,x)))))=u # label("Hint 14(2732)"). 2557 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z # label("Hint 15(2744)"). 2558 [] f(x,f(g(f(g(f(y,z)),x)),u))=f(v,f(g(f(g(f(y,z)),v)),u)) # label("Hint 16(2777)"). 2559 [] f(x,f(g(f(y,x)),g(z)))=f(u,f(g(f(y,u)),g(z))) # label("Hint 17(2801)"). 2560 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)) # label("Hint 18(2802)"). 2561 [] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u))=f(v,f(g(f(x,v)),u)) # label("Hint 19(2834)"). 2562 [] f(f(g(f(x,y)),g(f(z,x))),f(z,u))=f(v,f(g(f(f(f(x,x),y),v)),u)) # label("Hint 20(2835)"). 2563 [] f(x,f(g(f(y,x)),z))=f(g(f(y,f(f(u,f(g(f(y,u)),v)),y))),f(v,z)) # label("Hint 21(2848)"). 2564 [] f(x,f(g(f(f(f(y,y),z),x)),u))=f(f(g(f(y,z)),g(f(v,y))),f(v,u)) # label("Hint 22(2849)"). 2565 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)) # label("Hint 23(2853)"). 2566 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v) # label("Hint 24(2861)"). 2567 [] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))) # label("Hint 25(2953)"). 2568 [] g(f(x,f(g(f(y,x)),z)))=g(f(z,f(g(f(y,z)),z))) # label("Hint 26(3009)"). 2569 [] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(f(z,u)))),x))),v),x))))=f(z,g(f(z,f(f(u,v),z)))) # label("Hint 27(4182)"). 2570 [] g(f(f(f(f(g(f(f(f(x,x),y),z)),u),f(g(f(f(f(x,x),y),z)),u)),g(f(f(g(f(f(f(x,x),y),z)),u),f(f(v,f(g(f(f(g(f(f(f(x,x),y),z)),u),v)),w)),f(g(f(f(f(x,x),y),z)),u))))),f(w,g(f(f(g(f(x,y)),g(f(v6,x))),f(v6,u))))))=z # label("Hint 28(4326)"). 2571 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(v,z))),f(v,u)) # label("Hint 29(4358)"). 2572 [] g(f(f(f(f(x,y),f(x,y)),g(f(f(x,y),f(f(z,f(g(f(f(x,y),z)),u)),f(x,y))))),f(u,g(f(f(v,g(f(w,v6))),f(w,y))))))=f(v,g(f(x,v6))) # label("Hint 30(4526)"). 2573 [] f(g(f(x,y)),g(f(g(f(f(f(x,x),y),z)),x)))=z # label("Hint 31(4586)"). 2574 [] g(f(f(f(x,x),y),f(f(g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y)))),f(u,g(v))),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(v),x))) # label("Hint 32(4677)"). 2575 [] g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y))))=f(g(f(x,y)),g(f(u,x))) # label("Hint 33(4681)"). 2576 [] g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(z,x))),f(z,g(u))),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(u),x))) # label("Hint 34(4691)"). 2577 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(z),x))))=z # label("Hint 35(4694)"). 2578 [] f(x,f(g(f(y,x)),g(f(g(f(f(f(y,y),z),u)),y))))=f(z,u) # label("Hint 36(4700)"). 2579 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(f(f(x,x),y),z)),x) # label("Hint 37(4744)"). 2580 [] f(g(f(f(f(x,x),y),z)),x)=f(x,g(f(x,f(f(y,z),x)))) # label("Hint 38(4791)"). 2581 [] f(g(f(f(f(x,x),y),f(g(f(x,y)),g(z)))),x)=z # label("Hint 39(4967)"). 2582 [] g(f(g(f(f(f(x,x),y),f(g(f(x,y)),z))),x))=z # label("Hint 40(5011)"). 2583 [] f(f(f(x,x),y),g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(z)),u),f(f(x,x),y)))))=f(g(f(f(f(x,x),y),f(g(f(x,y)),g(z)))),f(f(x,f(g(z),g(u))),g(f(f(f(x,x),y),f(g(f(x,y)),g(z)))))) # label("Hint 41(5260)"). 2584 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z # label("Hint 42(5308)"). 2585 [] f(x,f(g(f(g(f(f(f(y,y),z),f(g(f(y,z)),u))),x)),v))=f(y,f(u,v)) # label("Hint 43(5600)"). 2586 [] f(g(f(x,y)),f(x,z))=f(g(f(u,y)),f(u,z)) # label("Hint 44(5908)"). 2587 [] f(g(f(x,f(f(y,f(g(f(z,y)),g(f(z,u)))),z))),f(x,v))=f(u,f(z,v)) # label("Hint 45(6097)"). 2588 [] f(g(f(g(f(x,g(f(y,z)))),u)),g(f(y,g(f(y,f(f(z,v),y))))))=f(g(f(w,u)),f(w,g(f(x,g(f(x,f(v,x))))))) # label("Hint 46(6123)"). 2589 [] f(x,f(g(f(y,x)),g(f(y,g(f(f(z,u),f(g(f(g(f(v,w)),f(v,u))),y)))))))=g(f(g(f(z,w)),y)) # label("Hint 47(6188)"). 2590 [] f(x,f(g(f(y,x)),f(y,z)))=f(u,f(g(f(v,u)),f(v,z))) # label("Hint 48(6193)"). 2591 [] f(f(x,y),f(g(f(g(f(z,u)),f(z,y))),g(f(g(f(x,u)),g(f(v,f(g(f(w,v)),g(f(x,u)))))))))=g(f(w,g(f(x,u)))) # label("Hint 49(6202)"). 2592 [] g(f(f(f(f(x,y),f(x,y)),g(f(f(x,y),f(f(z,f(g(f(f(x,y),z)),u)),f(x,y))))),f(u,g(f(g(f(v,w)),f(v,y))))))=g(f(x,w)) # label("Hint 50(6211)"). 2593 [] f(x,f(g(f(g(f(y,z)),x)),f(g(f(u,z)),f(u,v))))=f(w,f(g(f(v6,w)),f(v6,f(y,v)))) # label("Hint 51(6342)"). 2594 [] f(x,f(g(y),y))=f(z,f(g(f(u,z)),f(u,x))) # label("Hint 52(6343)"). 2595 [] f(x,f(g(f(g(f(y,g(f(z,u)))),x)),g(f(z,g(f(z,f(f(u,v),z)))))))=f(w,f(g(f(v6,w)),f(v6,g(f(y,g(f(y,f(v,y)))))))) # label("Hint 53(6360)"). 2596 [] f(x,f(g(f(y,x)),f(y,z)))=f(z,f(g(u),u)) # label("Hint 54(6393)"). 2597 [] f(x,f(g(f(y,x)),f(y,g(f(z,g(f(z,f(u,z))))))))=f(v,f(g(f(g(f(z,g(f(w,v6)))),v)),g(f(w,g(f(w,f(f(v6,u),w))))))) # label("Hint 55(6410)"). 2598 [] g(f(g(f(x,f(g(f(y,x)),f(y,f(f(z,z),u))))),z))=f(z,u) # label("Hint 56(6605)"). 2599 [] f(g(f(x,y)),f(x,y))=f(g(z),z) # label("Hint 57(6616)"). 2600 [] f(x,f(g(f(g(f(y,f(g(f(z,y)),f(z,u)))),x)),v))=f(w,f(g(f(g(f(u,f(g(v6),v6))),w)),v)) # label("Hint 58(6673)"). 2601 [] f(g(x),x)=f(g(f(y,z)),f(y,z)) # label("Hint 59(6761)"). 2602 [] f(g(x),x)=f(g(y),y) # label("Hint 60(6826)"). 2603 [] f(f(x,y),f(g(f(g(z),z)),u))=f(g(f(g(f(x,y)),f(f(v,f(g(f(g(f(x,y)),v)),w)),g(f(x,y))))),f(w,u)) # label("Hint 61(6906)"). 2604 [] g(f(x,g(f(x,f(f(y,f(g(z),z)),x)))))=f(x,y) # label("Hint 62(6932)"). 2605 [] f(g(f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))))),f(u,v))=f(f(x,y),f(g(f(g(w),w)),v)) # label("Hint 63(6987)"). 2606 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(f(g(f(z,u)),f(z,u)),x))))))=y # label("Hint 64(7055)"). 2607 [] g(f(x,g(f(x,f(f(g(f(y,z)),f(y,z)),x)))))=f(x,g(f(g(u),u))) # label("Hint 65(7154)"). 2608 [] g(f(x,g(f(x,f(f(g(f(y,z)),f(y,u)),x)))))=f(x,g(f(g(u),z))) # label("Hint 66(7156)"). 2609 [] f(x,g(f(g(y),y)))=f(x,g(f(g(z),z))) # label("Hint 67(7200)"). 2610 [] f(g(f(x,g(y))),f(x,g(f(g(z),z))))=y # label("Hint 68(7203)"). 2611 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(z),z))))=x # label("Hint 69(7332)"). 2612 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(g(z),z)))))))=g(y) # label("Hint 70(7374)"). 2613 [] f(g(f(g(x),x)),f(g(y),y))=f(g(z),z) # label("Hint 71(7379)"). 2614 [] f(g(f(g(x),x)),f(g(y),z))=f(g(f(u,y)),f(u,z)) # label("Hint 72(7380)"). 2615 [] f(g(x),g(f(g(x),f(f(x,f(g(f(g(y),y)),g(z))),g(x)))))=z # label("Hint 73(7409)"). 2616 [] f(g(x),x)=f(g(f(g(y),y)),f(g(z),z)) # label("Hint 74(7438)"). 2617 [] g(f(g(f(g(x),x)),y))=g(f(g(f(g(z),z)),y)) # label("Hint 75(7563)"). 2618 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),g(f(g(f(z,u)),f(z,g(f(g(y),y)))))))))=g(u) # label("Hint 76(7570)"). 2619 [] g(f(g(x),x))=g(f(g(y),y)) # label("Hint 77(7587)"). 2620 [] f(g(f(x,y)),f(f(g(f(z,f(g(f(x,y)),g(f(g(u),u))))),f(z,g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))) # label("Hint 78(7591)"). 2621 [] f(x,g(f(g(y),f(x,g(f(g(z),z))))))=y # label("Hint 79(7604)"). 2622 [] g(f(g(x),g(f(g(x),f(f(x,f(g(f(y,z)),f(y,u))),g(x))))))=f(g(z),u) # label("Hint 80(7615)"). 2623 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(g(f(u,f(g(f(x,y)),g(f(g(v),v))))),f(u,g(z))),g(f(x,y)))) # label("Hint 81(7687)"). 2624 [] g(f(g(f(g(x),x)),f(g(y),y)))=g(f(g(z),z)) # label("Hint 82(7715)"). 2625 [] g(f(g(x),x))=g(f(g(f(g(y),y)),f(g(z),z))) # label("Hint 83(7726)"). 2626 [] f(g(x),x)=f(g(g(f(g(y),y))),g(f(g(z),z))) # label("Hint 84(7763)"). 2627 [] f(g(g(f(g(x),x))),g(f(g(y),y)))=f(g(z),z) # label("Hint 85(7779)"). 2628 [] g(f(g(f(g(x),x)),f(f(y,f(g(f(g(f(g(x),x)),y)),g(f(g(f(g(x),x)),z)))),g(f(g(u),u)))))=z # label("Hint 86(7790)"). 2629 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(f(g(z),z)),f(g(f(u,g(f(g(v),v)))),y)))))))=g(f(u,y)) # label("Hint 87(7811)"). 2630 [] f(g(f(g(x),x)),y)=f(g(f(g(z),z)),y) # label("Hint 88(7830)"). 2631 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),g(f(g(f(g(y),y)),f(z,g(f(g(u),u)))))))))=z # label("Hint 89(7865)"). 2632 [] f(f(g(f(g(f(g(x),x)),y)),g(f(z,g(f(g(u),u))))),f(z,v))=f(w,f(g(f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),w)),v)) # label("Hint 90(7871)"). 2633 [] f(x,f(g(f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),x)),u))=f(f(g(f(g(f(g(y),y)),z)),g(f(v,g(f(g(w),w))))),f(v,u)) # label("Hint 91(7954)"). 2634 [] f(g(f(g(x),x)),f(g(g(y)),g(f(g(z),z))))=y # label("Hint 92(7972)"). 2635 [] f(f(x,g(f(g(f(g(y),y)),f(g(z),z)))),f(g(u),v))=f(f(x,g(f(w,u))),f(w,v)) # label("Hint 93(8388)"). 2636 [] f(g(f(x,y)),f(f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))) # label("Hint 94(8394)"). 2637 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(g(f(g(v),v)),f(g(w),w)))),f(g(z),u)) # label("Hint 95(8462)"). 2638 [] f(g(g(f(g(x),x))),g(f(g(y),f(g(z),z))))=y # label("Hint 96(8516)"). 2639 [] f(x,g(f(g(f(y,z)),f(y,g(f(g(u),u))))))=f(x,z) # label("Hint 97(8525)"). 2640 [] f(f(f(f(x,g(f(g(y),y))),f(x,g(f(g(y),y)))),z),f(g(f(f(x,g(f(g(y),y))),z)),u))=f(x,u) # label("Hint 98(8542)"). 2641 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),z))))=g(z) # label("Hint 99(8555)"). 2642 [] g(g(f(g(f(g(x),x)),f(y,g(f(g(z),z))))))=y # label("Hint 100(8577)"). 2643 [] g(f(g(f(g(x),x)),f(g(y),g(f(g(z),z)))))=y # label("Hint 101(8580)"). 2644 [] g(f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,f(g(u),u)),g(f(g(x),x)))))))=f(g(f(g(x),x)),z) # label("Hint 102(8797)"). 2645 [] f(g(f(g(f(g(x),x)),g(f(y,z)))),g(f(g(f(g(u),u)),g(f(g(f(g(x),x)),f(v,g(f(g(x),x))))))))=g(f(y,g(f(y,f(f(z,v),y))))) # label("Hint 103(8809)"). 2646 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(f(f(g(f(g(z),z)),g(f(g(z),z))),u),v)),g(f(g(z),z))))))=f(u,v) # label("Hint 104(8816)"). 2647 [] g(f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,f(g(f(g(f(g(x),x)),z)),u)),g(f(g(x),x)))))))=u # label("Hint 105(8847)"). 2648 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,f(g(f(g(f(g(x),x)),z)),g(u))),g(f(g(x),x))))))=u # label("Hint 106(8852)"). 2649 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(z),z)),y)),g(f(g(u),g(f(g(x),x))))))=u # label("Hint 107(8857)"). 2650 [] f(g(f(g(f(g(x),x)),y)),g(f(g(f(g(z),z)),g(f(g(f(g(z),z)),f(f(y,u),g(f(g(z),z))))))))=u # label("Hint 108(8862)"). 2651 [] g(f(g(f(g(x),x)),g(f(g(f(g(x),x)),f(f(y,f(g(f(g(f(g(z),z)),y)),u)),g(f(g(x),x)))))))=u # label("Hint 109(8878)"). 2652 [] f(x,f(g(y),y))=f(x,f(g(z),z)) # label("Hint 110(8976)"). 2653 [] f(f(x,g(f(y,z))),f(u,f(g(v),v)))=f(f(x,g(f(w,z))),f(w,f(g(f(v6,y)),f(v6,u)))) # label("Hint 111(9112)"). 2654 [] f(f(x,g(f(y,z))),f(y,f(g(f(u,v)),f(u,w))))=f(f(x,g(f(v,z))),f(w,f(g(v6),v6))) # label("Hint 112(9209)"). 2655 [] f(f(g(x),x),y)=f(f(g(z),z),y) # label("Hint 113(9311)"). 2656 [] f(x,g(f(g(f(g(y),y)),f(g(f(g(z),z)),f(g(u),u)))))=f(x,g(f(g(v),v))) # label("Hint 114(9866)"). 2657 [] f(x,g(f(g(y),f(x,g(f(g(f(g(z),z)),f(g(f(g(u),u)),f(g(v),v))))))))=y # label("Hint 115(9880)"). 2658 [] f(x,g(f(g(y),y)))=f(x,g(f(g(f(g(z),z)),f(g(f(g(u),u)),f(g(v),v))))) # label("Hint 116(9889)"). 2659 [] f(x,f(g(f(g(f(g(y),y)),f(g(z),z))),f(g(u),u)))=f(x,f(g(v),v)) # label("Hint 117(9932)"). 2660 [] f(x,f(g(f(g(f(g(y),y)),f(g(z),z))),f(g(u),u)))=f(v,f(g(f(w,v)),f(w,x))) # label("Hint 118(9936)"). 2661 [] f(f(g(f(g(f(g(x),x)),f(g(y),y))),f(g(z),z)),u)=f(f(g(v),v),u) # label("Hint 119(9940)"). 2662 [] f(x,f(g(y),y))=f(x,f(g(f(g(f(g(z),z)),f(g(u),u))),f(g(v),v))) # label("Hint 120(9956)"). 2663 [] f(x,f(g(f(y,x)),f(y,z)))=f(z,f(g(f(g(f(g(u),u)),f(g(v),v))),f(g(w),w))) # label("Hint 121(9960)"). 2664 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(g(f(g(z),z)),f(g(f(g(u),u)),v)),x))))))=f(g(f(g(g(f(g(w),w))),y)),v) # label("Hint 122(10213)"). 2665 [] f(f(x,g(f(g(f(g(y),y)),z))),u)=f(f(x,g(f(v,z))),f(v,f(g(g(u)),g(f(g(w),w))))) # label("Hint 123(10402)"). 2666 [] f(f(x,g(f(y,z))),f(y,f(g(g(u)),g(f(g(v),v)))))=f(f(x,g(f(g(f(g(w),w)),z))),u) # label("Hint 124(10465)"). 2667 [] f(g(g(f(g(x),x))),g(f(g(y),f(g(f(g(f(g(z),z)),u)),f(g(f(g(v),v)),u)))))=y # label("Hint 125(10762)"). 2668 [] g(g(f(g(f(x,f(g(f(y,x)),f(f(z,f(g(f(y,z)),y)),y)))),f(u,g(f(g(v),v))))))=u # label("Hint 126(10944)"). 2669 [] g(g(f(g(x),g(f(g(x),f(f(x,y),g(x)))))))=f(z,f(g(f(g(f(g(x),x)),z)),g(y))) # label("Hint 127(10986)"). 2670 [] g(f(x,g(f(g(y),y))))=g(f(x,g(f(g(z),z)))) # label("Hint 128(10987)"). 2671 [] f(x,f(g(f(g(f(g(y),y)),x)),g(z)))=g(g(f(g(y),g(f(g(y),f(f(y,z),g(y))))))) # label("Hint 129(10992)"). 2672 [] g(f(g(f(g(x),x)),y))=f(f(f(g(f(g(z),z)),g(f(g(z),z))),u),f(g(f(g(f(g(z),z)),u)),g(y))) # label("Hint 130(11090)"). 2673 [] g(f(g(f(x,y)),f(x,g(f(g(z),z)))))=y # label("Hint 131(11093)"). 2674 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(x),x)),y)),g(z)))=g(f(g(f(g(u),u)),z)) # label("Hint 132(11100)"). 2675 [] f(f(x,y),f(g(f(g(z),z)),u))=f(f(x,g(f(v,f(g(y),g(f(g(w),w)))))),f(v,u)) # label("Hint 133(11131)"). 2676 [] f(f(x,g(f(y,f(g(z),g(f(g(u),u)))))),f(y,v))=f(f(x,z),f(g(f(g(w),w)),v)) # label("Hint 134(11225)"). 2677 [] g(f(g(f(x,f(g(f(y,x)),z))),f(u,g(f(g(v),v)))))=f(g(f(y,u)),z) # label("Hint 135(11288)"). 2678 [] g(f(g(f(g(g(f(g(x),x))),y)),f(g(z),z)))=y # label("Hint 136(11338)"). 2679 [] g(f(g(f(x,y)),f(f(z,f(g(f(x,z)),x)),x)))=y # label("Hint 137(11359)"). 2680 [] f(g(g(f(g(x),x))),y)=f(g(g(f(g(z),z))),y) # label("Hint 138(11370)"). 2681 [] g(f(f(f(f(x,g(f(g(y),y))),f(x,g(f(g(y),y)))),g(f(f(x,g(f(g(y),y))),f(f(z,f(g(f(f(x,g(f(g(y),y))),z)),u)),f(x,g(f(g(y),y))))))),f(u,v)))=g(f(x,v)) # label("Hint 139(11395)"). 2682 [] g(f(g(f(g(g(f(g(x),x))),y)),f(g(f(g(f(g(z),z)),u)),f(g(f(g(v),v)),u))))=y # label("Hint 140(11565)"). 2683 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))))=f(x,g(f(x,f(f(y,f(g(f(g(g(f(g(v),v))),u)),f(g(w),w))),x)))) # label("Hint 141(11664)"). 2684 [] f(x,g(f(x,f(f(y,f(g(f(g(g(f(g(z),z))),u)),f(g(v),v))),x))))=f(g(f(x,y)),f(f(w,f(g(f(g(f(x,y)),w)),u)),g(f(x,y)))) # label("Hint 142(11754)"). 2685 [] f(x,g(g(f(g(y),y))))=f(x,g(g(f(g(z),z)))) # label("Hint 143(11831)"). 2686 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(g(g(f(g(z),z)))),g(g(f(g(u),u)))))))=x # label("Hint 144(13004)"). 2687 [] g(f(g(f(x,y)),g(x)))=f(f(x,x),y) # label("Hint 145(13035)"). 2688 [] f(g(f(x,f(g(f(y,z)),g(f(g(u),u))))),f(x,v))=f(g(y),f(f(f(y,y),z),v)) # label("Hint 146(13057)"). 2689 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))) # label("Hint 147(13117)"). 2690 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))))=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),u)),g(f(x,y)))) # label("Hint 148(13285)"). 2691 [] f(x,f(g(f(g(f(g(y),y)),x)),g(z)))=f(g(g(y)),f(f(f(g(y),g(y)),y),g(z))) # label("Hint 149(13389)"). 2692 [] f(g(f(x,y)),g(f(g(f(x,g(f(g(z),z)))),f(f(g(x),f(f(f(x,x),g(f(g(z),z))),g(f(g(f(g(u),u)),v)))),g(f(x,g(f(g(z),z))))))))=f(g(f(g(g(f(g(w),w))),y)),v) # label("Hint 150(13482)"). 2693 [] g(f(g(f(g(f(g(x),x)),y)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),g(f(g(f(g(f(g(z),z)),y)),u)))),g(f(g(f(g(x),x)),y)))))=u # label("Hint 151(13715)"). 2694 [] f(g(f(g(f(g(x),x)),y)),g(f(g(f(g(f(g(z),z)),y)),f(f(g(g(f(g(z),z))),f(f(f(g(f(g(z),z)),g(f(g(z),z))),y),g(u))),g(f(g(f(g(z),z)),y))))))=u # label("Hint 152(13721)"). 2695 [] f(g(f(g(f(g(x),x)),g(f(y,z)))),g(f(g(f(g(u),u)),g(f(g(f(g(x),x)),f(v,g(f(g(x),x))))))))=g(f(g(f(y,z)),f(f(g(y),f(f(f(y,y),z),g(v))),g(f(y,z))))) # label("Hint 153(13729)"). 2696 [] f(g(f(x,y)),f(f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),g(v))),g(f(x,y))))=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(v))),g(f(x,y)))) # label("Hint 154(13817)"). 2697 [] g(f(g(f(g(x),x)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(y,z)),f(y,u))))),g(f(g(x),x)))))=f(g(z),u) # label("Hint 155(13960)"). 2698 [] f(g(f(g(x),x)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(y),y)),g(z))))),g(f(g(x),x))))=z # label("Hint 156(13998)"). 2699 [] f(x,f(g(f(y,x)),f(y,g(f(z,g(f(z,f(u,z))))))))=f(v,f(g(f(g(f(z,g(f(w,v6)))),v)),g(f(g(f(w,v6)),f(f(g(w),f(f(f(w,w),v6),g(u))),g(f(w,v6))))))) # label("Hint 157(14187)"). 2700 [] f(g(f(g(f(x,g(f(y,z)))),u)),g(f(g(f(y,z)),f(f(g(y),f(f(f(y,y),z),g(v))),g(f(y,z))))))=f(g(f(w,u)),f(w,g(f(x,g(f(x,f(v,x))))))) # label("Hint 158(14243)"). 2701 [] f(g(f(f(f(x,x),y),z)),x)=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))) # label("Hint 159(14575)"). 2702 [] f(g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),z)),g(f(x,y))))),f(z,u))=f(f(x,y),f(g(f(g(v),v)),u)) # label("Hint 160(15309)"). 2703 [] f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(f(g(y),y)),z)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),g(u))),g(f(g(f(g(y),y)),z)))))))=f(z,u) # label("Hint 161(15352)"). 2704 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(z))),g(f(g(x),x))))))=z # label("Hint 162(15370)"). 2705 [] f(g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),z)),g(f(x,y))))),f(z,u))=f(g(x),f(f(f(x,x),y),u)) # label("Hint 163(16121)"). 2706 [] f(x,f(g(f(g(f(y,z)),x)),u))=f(g(y),f(f(f(y,y),z),u)) # label("Hint 164(16123)"). 2707 [] f(f(f(x,x),y),f(g(f(x,y)),g(x)))=f(g(z),z) # label("Hint 165(16130)"). 2708 [] f(x,f(g(f(y,x)),f(y,g(f(z,g(f(z,f(u,z))))))))=f(g(z),f(f(f(z,z),g(f(v,w))),g(f(g(f(v,w)),f(f(g(v),f(f(f(v,v),w),g(u))),g(f(v,w))))))) # label("Hint 166(16235)"). 2709 [] f(g(x),f(f(f(x,x),y),z))=f(f(x,y),f(g(f(g(u),u)),z)) # label("Hint 167(16330)"). 2710 [] g(f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),z)),g(f(g(x),x)))))))=z # label("Hint 168(16449)"). 2711 [] f(g(x),f(f(f(x,x),f(g(f(y,x)),f(y,z))),u))=f(g(z),f(f(f(z,z),f(g(v),v)),u)) # label("Hint 169(16515)"). 2712 [] f(g(x),f(f(f(x,x),y),f(g(f(z,y)),f(z,u))))=f(v,f(g(f(w,v)),f(w,f(x,u)))) # label("Hint 170(16523)"). 2713 [] g(f(g(f(g(f(x,y)),f(x,z))),f(f(g(u),f(f(f(u,u),y),g(f(u,y)))),g(f(u,y)))))=f(u,z) # label("Hint 171(16819)"). 2714 [] f(x,g(f(x,g(f(g(y),y)))))=f(g(z),z) # label("Hint 172(17251)"). 2715 [] g(f(g(x),g(f(g(y),y))))=x # label("Hint 173(17452)"). 2716 [] g(g(f(x,g(f(g(y),y)))))=x # label("Hint 174(17488)"). 2717 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(z),z)),y)),u))=u # label("Hint 175(17563)"). 2718 [] g(f(g(f(g(x),x)),y))=g(y) # label("Hint 176(17616)"). 2719 [] f(g(g(x)),f(f(f(g(x),g(x)),x),y))=y # label("Hint 177(17728)"). 2720 [] f(g(f(g(x),x)),y)=y # label("Hint 178(17762)"). 2721 [] g(f(g(x),f(f(g(g(f(g(y),y))),f(x,g(z))),g(x))))=f(x,z) # label("Hint 179(17768)"). 2722 [] f(g(g(x)),g(f(g(y),y)))=x # label("Hint 180(17775)"). 2723 [] f(g(f(x,y)),f(x,z))=f(g(y),z) # label("Hint 181(17784)"). 2724 [] f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y))))=f(g(f(x,y)),f(f(f(x,y),g(z)),g(f(x,y)))) # label("Hint 182(17816)"). 2725 [] g(f(g(f(x,y)),f(f(f(x,y),g(z)),g(f(x,y)))))=f(g(g(f(x,y))),z) # label("Hint 183(17833)"). 2726 [] f(g(x),f(x,y))=y # label("Hint 184(17838)"). 2727 [] f(x,f(g(x),y))=y # label("Hint 185(17840)"). 2728 [] f(g(f(g(g(f(g(x),x))),y)),z)=f(g(y),z) # label("Hint 186(17860)"). 2729 [] g(f(g(x),f(g(y),y)))=x # label("Hint 187(17897)"). 2730 [] f(g(g(f(g(x),x))),y)=y # label("Hint 188(17947)"). 2731 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(z)),u) # label("Hint 189(17951)"). 2732 [] f(x,f(g(y),y))=x # label("Hint 190(17957)"). 2733 [] f(x,g(g(f(g(y),y))))=x # label("Hint 191(17959)"). 2734 [] f(f(g(x),x),y)=y # label("Hint 192(17964)"). 2735 [] f(x,g(f(g(y),y)))=x # label("Hint 193(17979)"). 2736 [] f(x,g(f(g(y),x)))=y # label("Hint 194(17984)"). 2737 [] g(g(x))=x # label("Hint 195(18015)"). 2738 [] f(f(x,g(y)),z)=f(x,f(g(y),z)) # label("Hint 196(18027)"). 2739 [] f(x,f(g(f(y,x)),z))=f(g(y),z) # label("Hint 197(18053)"). 2740 [] g(f(x,y))=f(g(y),g(x)) # label("Hint 198(18055)"). 2741 [] f(f(f(x,x),y),f(g(y),g(x)))=x # label("Hint 199(18104)"). 2742 [] f(g(x),f(f(f(x,x),y),z))=f(f(x,y),z) # label("Hint 200(18189)"). 2743 [] f(f(x,f(y,g(z))),f(z,u))=f(f(x,y),u) # label("Hint 201(18241)"). 2744 [] f(f(x,y),f(g(y),z))=f(x,z) # label("Hint 202(18291)"). 2745 [] f(g(x),f(f(x,x),y))=f(x,y) # label("Hint 203(18295)"). 2746 [] f(g(x),f(f(x,y),z))=f(y,z) # label("Hint 204(18300)"). 2747 [] f(f(x,f(g(y),g(z))),f(f(z,y),u))=f(x,u) # label("Hint 205(18304)"). 2748 [] f(f(g(x),y),z)=f(g(x),f(y,z)) # label("Hint 206(18339)"). 2749 [] f(f(x,f(g(y),g(z))),u)=f(x,f(g(y),f(g(z),u))) # label("Hint 207(18381)"). 2750 [] f(f(x,y),g(z))=f(x,f(y,g(z))) # label("Hint 208(18399)"). 2751 [] f(f(x,y),z)=f(x,f(y,z)) # label("Hint 209(18411)"). end_of_list. list(hints2). 2752 [] f(x,f(f(y,f(g(f(g(f(f(f(z,z),u),f(g(f(z,u)),g(f(x,z))))),y)),g(f(g(f(f(f(z,z),u),f(g(f(z,u)),g(f(x,z))))),g(v))))),g(f(f(f(z,z),u),f(g(f(z,u)),g(f(x,z)))))))=v # label("cl 2807 demod 0"). 2753 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(f(f(z,z),u),f(g(f(z,u)),g(f(x,z))))),g(v))))),g(f(f(f(z,z),u),f(g(f(z,u)),g(f(x,z)))))))=v # label("cl 2807 demod 1"). 2754 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(v))))),g(f(f(f(z,z),u),f(g(f(z,u)),g(f(x,z)))))))=v # label("cl 2807 demod 2"). 2755 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(v))))),x))=v # label("cl 2807 demod 3"). 2756 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(v))))),x))=v # label("cl 2807 eqord 4"). 2757 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=f(g(f(g(f(x,y)),u)),f(f(v,f(g(f(g(f(g(f(x,y)),u)),v)),g(f(g(f(g(f(x,y)),u)),g(z))))),g(f(g(f(x,y)),u)))) # label("cl 2876 demod 0"). 2758 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("cl 2876 demod 1"). 2759 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z # label("cl 2876 eqord 2"). 2760 [] f(x,g(f(y,g(f(y,f(f(g(f(y,f(f(z,f(g(f(y,z)),x)),y))),u),y))))))=u # label("cl 3060 demod 0"). 2761 [] f(x,f(g(f(g(f(y,z)),x)),g(f(g(f(y,z)),g(f(g(f(y,z)),f(u,g(f(y,z)))))))))=u # label("cl 3060 demod 1"). 2762 [] f(x,f(g(f(g(f(y,z)),x)),g(f(g(f(y,z)),g(f(g(f(y,z)),f(u,g(f(y,z)))))))))=u # label("cl 3060 eqord 2"). 2763 [] f(x,f(g(f(y,x)),g(f(g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))),g(f(g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))),f(w,g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))))))))))=w # label("cl 3224 demod 0"). 2764 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))),f(w,g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))))))))))=w # label("cl 3224 demod 1"). 2765 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(w,g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))))))))))=w # label("cl 3224 demod 2"). 2766 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(w,y)))))))=w # label("cl 3224 demod 3"). 2767 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(w,y)))))))=w # label("cl 3224 eqord 4"). 2768 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,g(f(z,f(g(f(u,z)),y)))),x))))))=g(f(y,f(g(f(u,y)),y))) # label("cl 3618 demod 0"). 2769 [] g(f(z,f(g(f(u,z)),y)))=g(f(y,f(g(f(u,y)),y))) # label("cl 3618 demod 1"). 2770 [] g(f(z,f(g(f(u,z)),y)))=g(f(y,f(g(f(u,y)),y))) # label("cl 3618 eqord 2"). 2771 [] f(f(x,g(f(y,z))),f(y,u))=f(f(g(f(z,g(f(z,f(f(v,f(g(f(z,v)),x)),z))))),g(f(w,z))),f(w,u)) # label("cl 4190 demod 0"). 2772 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(w,z))),f(w,u)) # label("cl 4190 demod 1"). 2773 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(w,z))),f(w,u)) # label("cl 4190 eqord 2"). 2774 [] g(f(f(f(f(g(f(f(f(x,x),y),z)),u),f(g(f(f(f(x,x),y),z)),u)),g(f(f(g(f(f(f(x,x),y),z)),u),f(f(v,f(g(f(f(g(f(f(f(x,x),y),z)),u),v)),w)),f(g(f(f(f(x,x),y),z)),u))))),f(w,g(f(f(g(f(x,y)),g(f(v6,x))),f(v6,u))))))=z # label("cl 4498 demod 0"). 2775 [] f(g(f(x,y)),g(f(g(f(f(f(x,x),y),z)),x)))=z # label("cl 4498 demod 1"). 2776 [] f(g(f(x,y)),g(f(g(f(f(f(x,x),y),z)),x)))=z # label("cl 4498 eqord 2"). 2777 [] g(f(f(f(x,x),y),f(f(g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y)))),f(u,g(v))),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(v),x))) # label("cl 4608 demod 0"). 2778 [] g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(u,x))),f(u,g(v))),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(v),x))) # label("cl 4608 demod 1"). 2779 [] g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(u,x))),f(u,g(v))),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(v),x))) # label("cl 4608 eqord 2"). 2780 [] f(f(f(x,x),y),g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(z,x))),f(z,g(u))),f(f(x,x),y)))))=u # label("cl 4611 demod 0"). 2781 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(u),x))))=u # label("cl 4611 demod 1"). 2782 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(u),x))))=u # label("cl 4611 eqord 2"). 2783 [] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(f(z,u)))),x))),v),x))))=f(g(f(f(f(z,z),u),v)),z) # label("cl 4657 demod 0"). 2784 [] f(z,g(f(z,f(f(u,v),z))))=f(g(f(f(f(z,z),u),v)),z) # label("cl 4657 demod 1"). 2785 [] f(z,g(f(z,f(f(u,v),z))))=f(g(f(f(f(z,z),u),v)),z) # label("cl 4657 eqord 2"). 2786 [] g(f(f(f(x,x),y),g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(z,x))),f(z,u)),f(f(x,x),y))))))=u # label("cl 5179 demod 0"). 2787 [] g(f(g(f(f(f(x,x),y),f(g(f(x,y)),g(f(z,x))))),f(f(x,f(g(f(z,x)),g(f(z,u)))),g(f(f(f(x,x),y),f(g(f(x,y)),g(f(z,x))))))))=u # label("cl 5179 demod 1"). 2788 [] g(f(z,f(f(x,f(g(f(z,x)),g(f(z,u)))),g(f(f(f(x,x),y),f(g(f(x,y)),g(f(z,x))))))))=u # label("cl 5179 demod 2"). 2789 [] g(f(z,f(f(x,f(g(f(z,x)),g(f(z,u)))),z)))=u # label("cl 5179 demod 3"). 2790 [] g(f(z,f(f(x,f(g(f(z,x)),g(f(z,u)))),z)))=u # label("cl 5179 eqord 4"). 2791 [] f(x,f(g(f(y,x)),g(f(g(f(f(f(y,y),g(f(z,u))),f(z,v))),y))))=f(g(f(w,u)),f(w,v)) # label("cl 5731 demod 0"). 2792 [] f(g(f(z,u)),f(z,v))=f(g(f(w,u)),f(w,v)) # label("cl 5731 demod 1"). 2793 [] f(g(f(z,u)),f(z,v))=f(g(f(w,u)),f(w,v)) # label("cl 5731 eqord 2"). 2794 [] f(x,f(g(f(g(f(f(f(y,y),z),f(g(f(y,z)),g(u)))),x)),u))=f(v,f(g(f(w,v)),f(w,y))) # label("cl 6134 demod 0"). 2795 [] f(y,f(g(u),u))=f(v,f(g(f(w,v)),f(w,y))) # label("cl 6134 demod 1"). 2796 [] f(y,f(g(u),u))=f(v,f(g(f(w,v)),f(w,y))) # label("cl 6134 eqord 2"). 2797 [] f(g(f(x,y)),g(f(g(f(z,f(g(f(u,z)),f(u,f(f(x,x),y))))),x)))=f(g(v),v) # label("cl 6387 demod 0"). 2798 [] f(g(f(x,y)),f(x,y))=f(g(v),v) # label("cl 6387 demod 1"). 2799 [] f(g(f(x,y)),f(x,y))=f(g(v),v) # label("cl 6387 eqord 2"). 2800 [] f(x,f(g(f(g(f(f(f(y,y),z),f(g(f(y,z)),g(u)))),x)),u))=f(y,f(g(v),v)) # label("cl 6873 demod 0"). 2801 [] f(y,f(g(u),u))=f(y,f(g(v),v)) # label("cl 6873 demod 1"). 2802 [] f(y,f(g(u),u))=f(y,f(g(v),v)) # label("cl 6873 eqord 2"). 2803 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(f(g(f(g(z),z)),f(g(u),u)),x))))))=y # label("cl 7546 demod 0"). 2804 [] f(g(f(x,g(y))),f(x,g(f(g(z),z))))=y # label("cl 7546 demod 1"). 2805 [] f(g(f(x,g(y))),f(x,g(f(g(z),z))))=y # label("cl 7546 eqord 2"). 2806 [] f(x,f(g(f(y,x)),g(f(y,g(f(f(g(z),z),f(g(f(g(u),u)),y)))))))=g(f(g(f(g(v),v)),y)) # label("cl 7684 demod 0"). 2807 [] g(f(g(f(g(z),z)),y))=g(f(g(f(g(v),v)),y)) # label("cl 7684 demod 1"). 2808 [] g(f(g(f(g(z),z)),y))=g(f(g(f(g(v),v)),y)) # label("cl 7684 eqord 2"). 2809 [] g(f(f(f(f(g(x),x),f(g(x),x)),g(f(f(g(x),x),f(f(y,f(g(f(f(g(x),x),y)),z)),f(g(x),x))))),f(z,g(f(g(u),u)))))=g(f(g(v),v)) # label("cl 7702 demod 0"). 2810 [] g(f(g(x),x))=g(f(g(v),v)) # label("cl 7702 demod 1"). 2811 [] g(f(g(x),x))=g(f(g(v),v)) # label("cl 7702 eqord 2"). 2812 [] f(g(f(x,g(f(g(f(g(y),y)),z)))),f(x,g(f(g(u),u))))=f(g(f(g(v),v)),z) # label("cl 8157 demod 0"). 2813 [] f(g(f(g(y),y)),z)=f(g(f(g(v),v)),z) # label("cl 8157 demod 1"). 2814 [] f(g(f(g(y),y)),z)=f(g(f(g(v),v)),z) # label("cl 8157 eqord 2"). 2815 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),g(f(g(f(g(z),z)),f(u,g(f(g(y),y)))))))))=u # label("cl 8599 demod 0"). 2816 [] g(g(f(g(f(g(z),z)),f(u,g(f(g(y),y))))))=u # label("cl 8599 demod 1"). 2817 [] g(g(f(g(f(g(z),z)),f(u,g(f(g(y),y))))))=u # label("cl 8599 eqord 2"). 2818 [] g(g(f(g(f(g(x),x)),f(g(f(y,g(f(g(x),x)))),g(f(g(x),x))))))=g(f(y,g(f(g(z),z)))) # label("cl 8703 demod 0"). 2819 [] g(f(y,g(f(g(x),x))))=g(f(y,g(f(g(z),z)))) # label("cl 8703 demod 1"). 2820 [] g(f(y,g(f(g(x),x))))=g(f(y,g(f(g(z),z)))) # label("cl 8703 eqord 2"). 2821 [] g(f(g(f(g(x),x)),f(f(y,f(g(f(g(f(g(z),z)),y)),g(f(g(f(g(z),z)),u)))),g(f(g(z),z)))))=u # label("cl 8713 demod 0"). 2822 [] g(f(g(f(g(x),x)),f(g(u),g(f(g(z),z)))))=u # label("cl 8713 demod 1"). 2823 [] g(f(g(f(g(x),x)),f(g(u),g(f(g(z),z)))))=u # label("cl 8713 eqord 2"). 2824 [] g(g(f(g(f(x,f(g(f(y,x)),f(y,g(f(g(z),z)))))),f(u,g(f(g(v),v))))))=u # label("cl 8867 demod 0"). 2825 [] g(f(g(f(y,u)),f(y,g(f(g(z),z)))))=u # label("cl 8867 demod 1"). 2826 [] g(f(g(f(y,u)),f(y,g(f(g(z),z)))))=u # label("cl 8867 eqord 2"). 2827 [] f(x,f(g(f(y,x)),g(f(g(f(f(f(y,y),z),g(f(g(u),u)))),y))))=f(z,g(f(g(v),v))) # label("cl 9186 demod 0"). 2828 [] f(z,g(f(g(u),u)))=f(z,g(f(g(v),v))) # label("cl 9186 demod 1"). 2829 [] f(z,g(f(g(u),u)))=f(z,g(f(g(v),v))) # label("cl 9186 eqord 2"). 2830 [] g(f(f(f(f(g(f(x,y)),g(f(g(z),z))),f(g(f(x,y)),g(f(g(z),z)))),g(f(f(g(f(x,y)),g(f(g(z),z))),f(f(u,f(g(f(f(g(f(x,y)),g(f(g(z),z))),u)),v)),f(g(f(x,y)),g(f(g(z),z))))))),f(v,g(x))))=f(f(x,x),y) # label("cl 10207 demod 0"). 2831 [] g(f(g(f(x,y)),g(x)))=f(f(x,x),y) # label("cl 10207 demod 1"). 2832 [] g(f(g(f(x,y)),g(x)))=f(f(x,x),y) # label("cl 10207 eqord 2"). 2833 [] f(g(f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),v)),g(f(x,y))))),f(v,z))=f(g(x),f(f(f(x,x),y),z)) # label("cl 10773 demod 0"). 2834 [] f(g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),v)),g(f(x,y))))),f(v,z))=f(g(x),f(f(f(x,x),y),z)) # label("cl 10773 demod 1"). 2835 [] f(g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),v)),g(f(x,y))))),f(v,z))=f(g(x),f(f(f(x,x),y),z)) # label("cl 10773 eqord 2"). 2836 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),z))))=g(z) # label("cl 10967 demod 0"). 2837 [] f(g(g(y)),f(f(f(g(y),g(y)),y),g(f(g(f(g(y),y)),z))))=g(z) # label("cl 10967 demod 1"). 2838 [] f(g(g(y)),f(f(f(g(y),g(y)),y),g(f(g(f(g(y),y)),z))))=g(z) # label("cl 10967 eqord 2"). 2839 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(x),x))))))=f(g(f(g(f(g(x),x)),z)),f(f(v,f(g(f(g(f(g(f(g(x),x)),z)),v)),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 11016 demod 0"). 2840 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(x),x))))))=f(g(f(g(f(g(x),x)),z)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 11016 demod 1"). 2841 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(x),x))))))=f(g(f(g(f(g(x),x)),z)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 11016 eqord 2"). 2842 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(z),z)),g(f(g(f(g(y),y)),f(u,g(f(g(y),y)))))))))=u # label("cl 11031 demod 0"). 2843 [] f(g(g(y)),f(f(f(g(y),g(y)),y),g(f(g(f(g(z),z)),g(f(g(f(g(y),y)),f(u,g(f(g(y),y)))))))))=u # label("cl 11031 demod 1"). 2844 [] f(g(g(y)),f(f(f(g(y),g(y)),y),g(f(g(f(g(z),z)),g(f(g(f(g(y),y)),f(u,g(f(g(y),y)))))))))=u # label("cl 11031 eqord 2"). 2845 [] f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),v))=f(w,f(g(f(g(f(x,y)),w)),v)) # label("cl 11075 demod 0"). 2846 [] f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),v))=f(g(x),f(f(f(x,x),y),v)) # label("cl 11075 demod 1"). 2847 [] f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),v))=f(g(x),f(f(f(x,x),y),v)) # label("cl 11075 eqord 2"). 2848 [] g(f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y)))))=g(f(g(f(f(f(x,x),y),u)),x)) # label("cl 11268 demod 0"). 2849 [] g(f(g(f(f(f(x,x),y),u)),x))=g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(u))),g(f(x,y))))) # label("cl 11268 demod 1"). 2850 [] g(f(g(f(f(f(x,x),y),u)),x))=g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(u))),g(f(x,y))))) # label("cl 11268 eqord 2"). 2851 [] f(f(x,f(g(f(g(f(y,z)),x)),g(f(g(f(y,z)),g(u))))),g(f(y,z)))=g(f(g(f(f(f(y,y),z),u)),y)) # label("cl 11270 demod 0"). 2852 [] g(f(g(f(f(f(y,y),z),u)),y))=f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(u))))),g(f(y,z))) # label("cl 11270 demod 1"). 2853 [] g(f(g(f(y,z)),f(f(g(y),f(f(f(y,y),z),g(u))),g(f(y,z)))))=f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(u))))),g(f(y,z))) # label("cl 11270 demod 2"). 2854 [] g(f(g(f(y,z)),f(f(g(y),f(f(f(y,y),z),g(u))),g(f(y,z)))))=f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(u))))),g(f(y,z))) # label("cl 11270 eqord 3"). 2855 [] f(g(f(x,y)),f(f(g(f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))))),f(u,g(v))),g(f(x,y))))=f(g(f(f(f(x,x),y),v)),x) # label("cl 11276 demod 0"). 2856 [] f(g(f(x,y)),f(f(g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),u)),g(f(x,y))))),f(u,g(v))),g(f(x,y))))=f(g(f(f(f(x,x),y),v)),x) # label("cl 11276 demod 1"). 2857 [] f(g(f(f(f(x,x),y),v)),x)=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(v))),g(f(x,y)))) # label("cl 11276 demod 2"). 2858 [] f(g(f(f(f(x,x),y),v)),x)=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(v))),g(f(x,y)))) # label("cl 11276 eqord 3"). 2859 [] g(f(g(f(g(x),x)),f(g(f(g(y),y)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(y),y))))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 11757 demod 0"). 2860 [] g(f(g(f(g(x),x)),f(g(f(g(f(g(y),y)),z)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 11757 demod 1"). 2861 [] g(f(g(f(g(x),x)),f(g(f(g(f(g(y),y)),z)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 11757 eqord 2"). 2862 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),g(f(g(f(g(y),y)),f(f(f(g(z),z),u),g(f(g(y),y))))))))=u # label("cl 11879 demod 0"). 2863 [] f(g(f(g(x),x)),g(f(g(f(g(f(g(y),y)),f(g(z),z))),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(u))),g(f(g(f(g(y),y)),f(g(z),z)))))))=u # label("cl 11879 demod 1"). 2864 [] f(g(f(g(x),x)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(f(g(f(g(f(g(y),y)),f(g(z),z))),g(u))))),g(f(g(f(g(y),y)),f(g(z),z)))))=u # label("cl 11879 demod 2"). 2865 [] f(g(f(g(x),x)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(f(g(f(g(f(g(y),y)),f(g(z),z))),g(u))))),g(f(g(f(g(y),y)),f(g(z),z)))))=u # label("cl 11879 eqord 3"). 2866 [] f(g(f(x,g(f(g(y),y)))),g(f(x,g(f(x,f(z,x))))))=g(f(g(f(g(u),u)),g(f(g(f(g(u),u)),f(f(f(g(v),v),z),g(f(g(u),u))))))) # label("cl 11887 demod 0"). 2867 [] f(g(f(x,g(f(g(y),y)))),g(f(x,g(f(x,f(z,x))))))=g(f(g(f(g(f(g(u),u)),f(g(v),v))),f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(z))),g(f(g(f(g(u),u)),f(g(v),v)))))) # label("cl 11887 demod 1"). 2868 [] f(g(f(x,g(f(g(y),y)))),g(f(x,g(f(x,f(z,x))))))=f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(f(g(f(g(f(g(u),u)),f(g(v),v))),g(z))))),g(f(g(f(g(u),u)),f(g(v),v)))) # label("cl 11887 demod 2"). 2869 [] f(g(f(x,g(f(g(y),y)))),g(f(x,g(f(x,f(z,x))))))=f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(f(g(f(g(f(g(u),u)),f(g(v),v))),g(z))))),g(f(g(f(g(u),u)),f(g(v),v)))) # label("cl 11887 eqord 3"). 2870 [] g(f(g(x),g(f(g(x),f(f(x,y),g(x))))))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(y,z)))))) # label("cl 11893 demod 0"). 2871 [] g(f(g(f(g(x),x)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(y))),g(f(g(x),x)))))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(y,z)))))) # label("cl 11893 demod 1"). 2872 [] f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(x),x)),g(y))))),g(f(g(x),x)))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(y,z)))))) # label("cl 11893 demod 2"). 2873 [] f(g(g(y)),g(f(g(x),x)))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(y,z)))))) # label("cl 11893 demod 3"). 2874 [] f(g(g(y)),g(f(g(x),x)))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(y,z)))))) # label("cl 11893 eqord 4"). 2875 [] g(f(g(x),g(f(g(x),f(f(x,f(g(f(g(f(g(y),y)),f(g(z),z))),u)),g(x))))))=u # label("cl 11898 demod 0"). 2876 [] g(f(g(f(g(x),x)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(f(g(y),y)),f(g(z),z))),u)))),g(f(g(x),x)))))=u # label("cl 11898 demod 1"). 2877 [] f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(x),x)),g(f(g(f(g(f(g(y),y)),f(g(z),z))),u)))))),g(f(g(x),x)))=u # label("cl 11898 demod 2"). 2878 [] f(g(g(f(g(f(g(f(g(y),y)),f(g(z),z))),u))),g(f(g(x),x)))=u # label("cl 11898 demod 3"). 2879 [] f(g(g(f(g(f(g(f(g(y),y)),f(g(z),z))),u))),g(f(g(x),x)))=u # label("cl 11898 eqord 4"). 2880 [] g(f(x,g(f(x,f(f(y,f(g(f(z,f(f(u,f(g(f(z,u)),v)),z))),f(v,w))),x)))))=f(g(f(z,g(f(x,y)))),w) # label("cl 12275 demod 0"). 2881 [] g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(f(g(f(z,f(f(u,f(g(f(z,u)),v)),z))),f(v,w))))),g(f(x,y)))))=f(g(f(z,g(f(x,y)))),w) # label("cl 12275 demod 1"). 2882 [] f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),g(f(g(f(z,f(f(u,f(g(f(z,u)),v)),z))),f(v,w))))))),g(f(x,y)))=f(g(f(z,g(f(x,y)))),w) # label("cl 12275 demod 2"). 2883 [] f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),g(f(g(f(z,f(f(u,f(g(f(z,u)),v)),z))),f(v,w))))))),g(f(x,y)))=f(g(f(z,g(f(x,y)))),w) # label("cl 12275 eqord 3"). 2884 [] g(f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),z)),x),u),x)))))=f(z,g(f(x,g(f(x,f(u,x)))))) # label("cl 12392 demod 0"). 2885 [] g(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(f(g(x),f(f(f(x,x),f(f(y,f(g(f(x,y)),z)),x)),g(u))),g(f(x,f(f(y,f(g(f(x,y)),z)),x))))))=f(z,g(f(x,g(f(x,f(u,x)))))) # label("cl 12392 demod 1"). 2886 [] f(f(g(x),f(f(f(x,x),f(f(y,f(g(f(x,y)),z)),x)),g(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),g(u))))),g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(x,g(f(x,f(u,x)))))) # label("cl 12392 demod 2"). 2887 [] f(f(g(x),f(f(f(x,x),f(f(y,f(g(f(x,y)),z)),x)),g(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),g(u))))),g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(f(x,g(f(x,f(u,x)))))) # label("cl 12392 eqord 3"). 2888 [] g(f(g(f(x,y)),g(z)))=f(f(z,z),f(g(f(u,z)),g(f(g(f(f(f(u,u),x),y)),u)))) # label("cl 12616 demod 0"). 2889 [] g(f(g(f(x,y)),g(z)))=f(f(z,z),f(g(f(u,z)),g(f(g(f(u,x)),f(f(g(u),f(f(f(u,u),x),g(y))),g(f(u,x))))))) # label("cl 12616 demod 1"). 2890 [] g(f(g(f(x,y)),g(z)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 12616 demod 2"). 2891 [] g(f(g(f(x,y)),g(z)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 12616 eqord 3"). 2892 [] f(f(g(f(x,y)),g(f(g(f(f(f(x,x),z),u)),x))),f(g(f(z,u)),g(f(g(f(f(f(y,y),v),w)),y))))=f(v,w) # label("cl 12779 demod 0"). 2893 [] f(f(g(f(x,y)),g(f(g(f(x,z)),f(f(g(x),f(f(f(x,x),z),g(u))),g(f(x,z)))))),f(g(f(z,u)),g(f(g(f(f(f(y,y),v),w)),y))))=f(v,w) # label("cl 12779 demod 1"). 2894 [] f(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),z),g(f(g(f(x,z)),g(u))))),g(f(x,z)))),f(g(f(z,u)),g(f(g(f(f(f(y,y),v),w)),y))))=f(v,w) # label("cl 12779 demod 2"). 2895 [] f(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),z),g(f(g(f(x,z)),g(u))))),g(f(x,z)))),f(g(f(z,u)),g(f(g(f(y,v)),f(f(g(y),f(f(f(y,y),v),g(w))),g(f(y,v)))))))=f(v,w) # label("cl 12779 demod 3"). 2896 [] f(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),z),g(f(g(f(x,z)),g(u))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 12779 demod 4"). 2897 [] f(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),z),g(f(g(f(x,z)),g(u))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 12779 eqord 5"). 2898 [] g(f(g(f(f(f(x,x),y),g(f(z,u)))),x))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 12788 demod 0"). 2899 [] g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(g(f(z,u))))),g(f(x,y)))))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 12788 demod 1"). 2900 [] f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),g(g(f(z,u))))))),g(f(x,y)))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 12788 demod 2"). 2901 [] f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),g(g(f(z,u))))))),g(f(x,y)))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 12788 eqord 3"). 2902 [] f(f(f(f(x,g(f(g(y),y))),f(x,g(f(g(y),y)))),z),f(g(f(f(x,g(f(g(y),y))),z)),g(f(x,g(f(g(u),u))))))=f(g(v),v) # label("cl 13102 demod 0"). 2903 [] f(x,g(f(x,g(f(g(u),u)))))=f(g(v),v) # label("cl 13102 demod 1"). 2904 [] f(x,g(f(x,g(f(g(u),u)))))=f(g(v),v) # label("cl 13102 eqord 2"). 2905 [] f(f(f(g(f(g(x),g(f(g(y),y)))),g(f(g(x),g(f(g(y),y))))),z),f(g(f(g(f(g(x),g(f(g(y),y)))),z)),g(f(g(u),u))))=x # label("cl 13273 demod 0"). 2906 [] g(f(g(x),g(f(g(y),y))))=x # label("cl 13273 demod 1"). 2907 [] g(f(g(x),g(f(g(y),y))))=x # label("cl 13273 eqord 2"). 2908 [] f(x,f(g(f(g(f(y,g(f(g(z),z)))),x)),g(f(g(f(y,g(f(g(z),z)))),g(f(g(f(y,g(f(g(z),z)))),f(g(u),u)))))))=y # label("cl 13304 demod 0"). 2909 [] g(g(f(y,g(f(g(z),z)))))=y # label("cl 13304 demod 1"). 2910 [] g(g(f(y,g(f(g(z),z)))))=y # label("cl 13304 eqord 2"). 2911 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(z),z)),y)),g(f(g(u),g(f(g(x),x))))))=u # label("cl 13356 demod 0"). 2912 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(z),z)),y)),u))=u # label("cl 13356 demod 1"). 2913 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(z),z)),y)),u))=u # label("cl 13356 eqord 2"). 2914 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(f(g(f(g(x),x)),y)),g(z)))=g(f(g(f(g(u),u)),z)) # label("cl 13400 demod 0"). 2915 [] g(f(g(f(g(u),u)),z))=g(z) # label("cl 13400 demod 1"). 2916 [] g(f(g(f(g(u),u)),z))=g(z) # label("cl 13400 eqord 2"). 2917 [] f(f(g(x),x),f(g(f(g(f(g(y),y)),z)),u))=f(v,f(g(f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),v)),u)) # label("cl 13417 demod 0"). 2918 [] f(f(g(x),x),f(g(z),u))=f(v,f(g(f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),v)),u)) # label("cl 13417 demod 1"). 2919 [] f(f(g(x),x),f(g(z),u))=f(v,f(g(f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),v)),u)) # label("cl 13417 eqord 2"). 2920 [] g(f(g(f(g(x),x)),g(y)))=f(f(y,y),g(f(y,g(f(g(z),z))))) # label("cl 13418 demod 0"). 2921 [] g(g(y))=f(f(y,y),g(f(y,g(f(g(z),z))))) # label("cl 13418 demod 1"). 2922 [] g(g(y))=f(f(y,y),g(f(y,g(f(g(z),z))))) # label("cl 13418 eqord 2"). 2923 [] f(g(g(f(g(f(g(f(g(x),x)),f(g(y),y))),z))),g(f(g(u),u)))=z # label("cl 13463 demod 0"). 2924 [] f(g(g(f(g(f(g(y),y)),z))),g(f(g(u),u)))=z # label("cl 13463 demod 1"). 2925 [] f(g(g(z)),g(f(g(u),u)))=z # label("cl 13463 demod 2"). 2926 [] f(g(g(z)),g(f(g(u),u)))=z # label("cl 13463 eqord 3"). 2927 [] f(g(g(x)),g(f(g(y),y)))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(x,z)))))) # label("cl 13467 demod 0"). 2928 [] f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(f(z,g(f(z,f(x,z))))))=x # label("cl 13467 demod 1"). 2929 [] f(g(f(z,g(f(g(v),v)))),g(f(z,g(f(z,f(x,z))))))=x # label("cl 13467 demod 2"). 2930 [] f(g(f(z,g(f(g(v),v)))),g(f(z,g(f(z,f(x,z))))))=x # label("cl 13467 eqord 3"). 2931 [] f(g(f(x,g(f(g(y),y)))),g(f(x,g(f(x,f(z,x))))))=f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(f(g(f(g(f(g(u),u)),f(g(v),v))),g(z))))),g(f(g(f(g(u),u)),f(g(v),v)))) # label("cl 13469 demod 0"). 2932 [] f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(f(g(f(g(f(g(u),u)),f(g(v),v))),g(z))))),g(f(g(f(g(u),u)),f(g(v),v))))=z # label("cl 13469 demod 1"). 2933 [] f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(f(g(f(g(v),v)),g(z))))),g(f(g(f(g(u),u)),f(g(v),v))))=z # label("cl 13469 demod 2"). 2934 [] f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(g(z)))),g(f(g(f(g(u),u)),f(g(v),v))))=z # label("cl 13469 demod 3"). 2935 [] f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(g(z)))),g(f(g(v),v)))=z # label("cl 13469 demod 4"). 2936 [] f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(g(z)))),g(f(g(v),v)))=z # label("cl 13469 eqord 5"). 2937 [] f(g(f(g(x),x)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(f(g(f(g(f(g(y),y)),f(g(z),z))),g(u))))),g(f(g(f(g(y),y)),f(g(z),z)))))=u # label("cl 13471 demod 0"). 2938 [] f(g(f(g(x),x)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(f(g(f(g(z),z)),g(u))))),g(f(g(f(g(y),y)),f(g(z),z)))))=u # label("cl 13471 demod 1"). 2939 [] f(g(f(g(x),x)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(g(u)))),g(f(g(f(g(y),y)),f(g(z),z)))))=u # label("cl 13471 demod 2"). 2940 [] f(g(f(g(x),x)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),z)),g(g(u)))),g(f(g(z),z))))=u # label("cl 13471 demod 3"). 2941 [] f(g(f(g(x),x)),u)=u # label("cl 13471 demod 4"). 2942 [] f(g(f(g(x),x)),u)=u # label("cl 13471 eqord 5"). 2943 [] g(f(g(f(g(x),x)),f(g(f(g(f(g(y),y)),z)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 13497 demod 0"). 2944 [] g(f(g(f(g(x),x)),f(g(z),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 13497 demod 1"). 2945 [] g(f(g(f(g(x),x)),f(g(z),f(f(g(g(f(g(y),y))),f(f(g(f(g(y),y)),z),g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 13497 demod 2"). 2946 [] g(f(g(f(g(x),x)),f(g(z),f(f(g(g(f(g(y),y))),f(z,g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 13497 demod 3"). 2947 [] g(f(g(f(g(x),x)),f(g(z),f(f(g(g(f(g(y),y))),f(z,g(u))),g(z)))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 13497 demod 4"). 2948 [] g(f(g(z),f(f(g(g(f(g(y),y))),f(z,g(u))),g(z))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u) # label("cl 13497 demod 5"). 2949 [] g(f(g(z),f(f(g(g(f(g(y),y))),f(z,g(u))),g(z))))=f(f(g(f(g(y),y)),z),u) # label("cl 13497 demod 6"). 2950 [] g(f(g(z),f(f(g(g(f(g(y),y))),f(z,g(u))),g(z))))=f(z,u) # label("cl 13497 demod 7"). 2951 [] g(f(g(z),f(f(g(g(f(g(y),y))),f(z,g(u))),g(z))))=f(z,u) # label("cl 13497 eqord 8"). 2952 [] f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),v))=f(g(x),f(f(f(x,x),y),v)) # label("cl 13513 demod 0"). 2953 [] f(f(x,y),f(g(f(g(u),u)),v))=f(g(x),f(f(f(x,x),y),v)) # label("cl 13513 demod 1"). 2954 [] f(g(x),f(f(f(x,x),y),v))=f(f(x,y),v) # label("cl 13513 demod 2"). 2955 [] f(g(x),f(f(f(x,x),y),v))=f(f(x,y),v) # label("cl 13513 eqord 3"). 2956 [] f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(y),y)),g(f(g(f(g(x),x)),f(z,g(f(g(x),x)))))))))=z # label("cl 13521 demod 0"). 2957 [] f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(y),y)),g(f(z,g(f(g(x),x))))))))=z # label("cl 13521 demod 1"). 2958 [] f(g(g(x)),f(f(f(g(x),g(x)),x),g(g(f(z,g(f(g(x),x)))))))=z # label("cl 13521 demod 2"). 2959 [] f(g(g(x)),f(f(f(g(x),g(x)),x),z))=z # label("cl 13521 demod 3"). 2960 [] f(f(g(x),x),z)=z # label("cl 13521 demod 4"). 2961 [] f(f(g(x),x),z)=z # label("cl 13521 eqord 5"). 2962 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(x),x))))))=f(g(f(g(f(g(x),x)),z)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 13523 demod 0"). 2963 [] f(g(f(g(x),x)),g(f(f(z,u),g(f(g(x),x)))))=f(g(f(g(f(g(x),x)),z)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 13523 demod 1"). 2964 [] g(f(f(z,u),g(f(g(x),x))))=f(g(f(g(f(g(x),x)),z)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 13523 demod 2"). 2965 [] g(f(f(z,u),g(f(g(x),x))))=f(g(z),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 13523 demod 3"). 2966 [] g(f(f(z,u),g(f(g(x),x))))=f(g(z),f(f(g(g(f(g(x),x))),f(f(g(f(g(x),x)),z),g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 13523 demod 4"). 2967 [] g(f(f(z,u),g(f(g(x),x))))=f(g(z),f(f(g(g(f(g(x),x))),f(z,g(u))),g(f(g(f(g(x),x)),z)))) # label("cl 13523 demod 5"). 2968 [] g(f(f(z,u),g(f(g(x),x))))=f(g(z),f(f(g(g(f(g(x),x))),f(z,g(u))),g(z))) # label("cl 13523 demod 6"). 2969 [] g(f(f(z,u),g(f(g(x),x))))=f(g(z),f(f(g(g(f(g(x),x))),f(z,g(u))),g(z))) # label("cl 13523 eqord 7"). 2970 [] g(f(g(f(g(f(g(x),x)),y)),g(g(f(g(z),z)))))=f(f(g(f(g(z),z)),g(f(g(z),z))),y) # label("cl 13555 demod 0"). 2971 [] g(f(g(y),g(g(f(g(z),z)))))=f(f(g(f(g(z),z)),g(f(g(z),z))),y) # label("cl 13555 demod 1"). 2972 [] g(f(g(y),g(g(f(g(z),z)))))=f(g(f(g(z),z)),y) # label("cl 13555 demod 2"). 2973 [] g(f(g(y),g(g(f(g(z),z)))))=y # label("cl 13555 demod 3"). 2974 [] g(f(g(y),g(g(f(g(z),z)))))=y # label("cl 13555 eqord 4"). 2975 [] g(f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,f(g(u),u)),g(f(g(x),x)))))))=f(g(f(g(x),x)),z) # label("cl 13563 demod 0"). 2976 [] g(f(g(f(g(x),x)),g(f(f(z,f(g(u),u)),g(f(g(x),x))))))=f(g(f(g(x),x)),z) # label("cl 13563 demod 1"). 2977 [] g(f(g(f(g(x),x)),f(g(z),f(f(g(g(f(g(x),x))),f(z,g(f(g(u),u)))),g(z)))))=f(g(f(g(x),x)),z) # label("cl 13563 demod 2"). 2978 [] g(f(g(z),f(f(g(g(f(g(x),x))),f(z,g(f(g(u),u)))),g(z))))=f(g(f(g(x),x)),z) # label("cl 13563 demod 3"). 2979 [] f(z,f(g(u),u))=f(g(f(g(x),x)),z) # label("cl 13563 demod 4"). 2980 [] f(z,f(g(u),u))=z # label("cl 13563 demod 5"). 2981 [] f(z,f(g(u),u))=z # label("cl 13563 eqord 6"). 2982 [] g(f(g(f(g(g(f(g(x),x))),y)),f(g(f(g(f(g(z),z)),f(g(u),u))),f(g(v),v))))=y # label("cl 13583 demod 0"). 2983 [] g(f(g(f(g(g(f(g(x),x))),y)),f(g(g(f(g(z),z))),f(g(v),v))))=y # label("cl 13583 demod 1"). 2984 [] g(f(g(f(g(g(f(g(x),x))),y)),g(g(f(g(z),z)))))=y # label("cl 13583 demod 2"). 2985 [] f(g(g(f(g(x),x))),y)=y # label("cl 13583 demod 3"). 2986 [] f(g(g(f(g(x),x))),y)=y # label("cl 13583 eqord 4"). 2987 [] g(f(g(f(g(g(f(g(f(g(f(g(x),x)),y)),f(g(f(g(z),z)),y)))),u)),f(g(v),v)))=u # label("cl 13587 demod 0"). 2988 [] g(f(g(f(g(g(f(g(y),f(g(f(g(z),z)),y)))),u)),f(g(v),v)))=u # label("cl 13587 demod 1"). 2989 [] g(f(g(f(g(g(f(g(y),y))),u)),f(g(v),v)))=u # label("cl 13587 demod 2"). 2990 [] g(f(g(u),f(g(v),v)))=u # label("cl 13587 demod 3"). 2991 [] g(g(u))=u # label("cl 13587 demod 4"). 2992 [] g(g(u))=u # label("cl 13587 eqord 5"). 2993 [] f(x,g(f(g(y),y)))=f(x,g(f(g(f(g(z),z)),f(g(u),u)))) # label("cl 13624 demod 0"). 2994 [] f(x,g(f(g(y),y)))=f(x,g(g(f(g(z),z)))) # label("cl 13624 demod 1"). 2995 [] f(x,g(f(g(y),y)))=f(x,f(g(z),z)) # label("cl 13624 demod 2"). 2996 [] f(x,g(f(g(y),y)))=x # label("cl 13624 demod 3"). 2997 [] f(x,g(f(g(y),y)))=x # label("cl 13624 eqord 4"). 2998 [] g(f(g(f(g(x),x)),f(y,g(f(g(z),z)))))=f(g(f(u,y)),f(u,g(f(g(v),v)))) # label("cl 13685 demod 0"). 2999 [] g(f(g(f(g(x),x)),y))=f(g(f(u,y)),f(u,g(f(g(v),v)))) # label("cl 13685 demod 1"). 3000 [] f(g(f(u,y)),f(u,g(f(g(v),v))))=g(y) # label("cl 13685 demod 2"). 3001 [] f(g(f(u,y)),u)=g(y) # label("cl 13685 demod 3"). 3002 [] f(g(f(u,y)),u)=g(y) # label("cl 13685 eqord 4"). 3003 [] f(f(x,g(f(y,z))),f(y,f(g(g(u)),g(f(g(v),v)))))=f(f(x,g(f(g(f(g(w),w)),z))),u) # label("cl 13704 demod 0"). 3004 [] f(f(x,g(f(y,z))),f(y,f(u,g(f(g(v),v)))))=f(f(x,g(f(g(f(g(w),w)),z))),u) # label("cl 13704 demod 1"). 3005 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(g(f(g(w),w)),z))),u) # label("cl 13704 demod 2"). 3006 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(z)),u) # label("cl 13704 demod 3"). 3007 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(z)),u) # label("cl 13704 eqord 4"). 3008 [] f(g(f(x,y)),f(x,f(g(g(z)),g(f(g(u),u)))))=f(g(f(g(f(g(v),v)),y)),z) # label("cl 13706 demod 0"). 3009 [] f(g(f(x,y)),f(x,f(z,g(f(g(u),u)))))=f(g(f(g(f(g(v),v)),y)),z) # label("cl 13706 demod 1"). 3010 [] f(g(f(x,y)),f(x,z))=f(g(f(g(f(g(v),v)),y)),z) # label("cl 13706 demod 2"). 3011 [] f(g(f(x,y)),f(x,z))=f(g(y),z) # label("cl 13706 demod 3"). 3012 [] f(g(f(x,y)),f(x,z))=f(g(y),z) # label("cl 13706 eqord 4"). 3013 [] f(x,f(g(f(y,x)),f(y,z)))=f(z,f(g(f(g(f(g(u),u)),f(g(v),v))),f(g(w),w))) # label("cl 13708 demod 0"). 3014 [] f(x,f(g(x),z))=f(z,f(g(f(g(f(g(u),u)),f(g(v),v))),f(g(w),w))) # label("cl 13708 demod 1"). 3015 [] f(x,f(g(x),z))=f(z,f(g(g(f(g(u),u))),f(g(w),w))) # label("cl 13708 demod 2"). 3016 [] f(x,f(g(x),z))=f(z,f(f(g(u),u),f(g(w),w))) # label("cl 13708 demod 3"). 3017 [] f(x,f(g(x),z))=f(z,f(g(u),u)) # label("cl 13708 demod 4"). 3018 [] f(x,f(g(x),z))=z # label("cl 13708 demod 5"). 3019 [] f(x,f(g(x),z))=z # label("cl 13708 eqord 6"). 3020 [] f(g(f(g(f(g(x),x)),y)),g(f(g(f(g(x),x)),g(f(g(f(g(z),z)),f(f(y,u),g(f(g(x),x))))))))=u # label("cl 13715 demod 0"). 3021 [] f(g(y),g(f(g(f(g(x),x)),g(f(g(f(g(z),z)),f(f(y,u),g(f(g(x),x))))))))=u # label("cl 13715 demod 1"). 3022 [] f(g(y),g(f(g(f(g(x),x)),g(f(g(f(g(z),z)),f(y,u))))))=u # label("cl 13715 demod 2"). 3023 [] f(g(y),g(f(g(f(g(x),x)),g(f(y,u)))))=u # label("cl 13715 demod 3"). 3024 [] f(g(y),g(g(f(y,u))))=u # label("cl 13715 demod 4"). 3025 [] f(g(y),f(y,u))=u # label("cl 13715 demod 5"). 3026 [] f(g(y),f(y,u))=u # label("cl 13715 eqord 6"). 3027 [] g(f(g(f(g(x),x)),f(g(f(y,g(f(g(z),z)))),u)))=g(f(v,f(g(f(y,v)),u))) # label("cl 13718 demod 0"). 3028 [] g(f(g(f(g(x),x)),f(g(y),u)))=g(f(v,f(g(f(y,v)),u))) # label("cl 13718 demod 1"). 3029 [] g(f(v,f(g(f(y,v)),u)))=g(f(g(y),u)) # label("cl 13718 demod 2"). 3030 [] g(f(v,f(g(f(y,v)),u)))=g(f(g(y),u)) # label("cl 13718 eqord 3"). 3031 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(g(f(g(v),v)),f(g(w),w)))),f(g(z),u)) # label("cl 13733 demod 0"). 3032 [] f(f(x,g(z)),u)=f(f(x,g(f(g(f(g(v),v)),f(g(w),w)))),f(g(z),u)) # label("cl 13733 demod 1"). 3033 [] f(f(x,g(z)),u)=f(f(x,g(g(f(g(v),v)))),f(g(z),u)) # label("cl 13733 demod 2"). 3034 [] f(f(x,g(z)),u)=f(f(x,f(g(v),v)),f(g(z),u)) # label("cl 13733 demod 3"). 3035 [] f(f(x,g(z)),u)=f(x,f(g(z),u)) # label("cl 13733 demod 4"). 3036 [] f(f(x,g(z)),u)=f(x,f(g(z),u)) # label("cl 13733 eqord 5"). 3037 [] f(f(f(g(x),g(x)),x),f(g(f(g(f(g(y),y)),f(g(z),z))),g(f(g(u),g(x)))))=u # label("cl 13739 demod 0"). 3038 [] f(f(g(x),f(g(x),x)),f(g(f(g(f(g(y),y)),f(g(z),z))),g(f(g(u),g(x)))))=u # label("cl 13739 demod 1"). 3039 [] f(g(x),f(g(f(g(f(g(y),y)),f(g(z),z))),g(f(g(u),g(x)))))=u # label("cl 13739 demod 2"). 3040 [] f(g(x),f(g(g(f(g(y),y))),g(f(g(u),g(x)))))=u # label("cl 13739 demod 3"). 3041 [] f(g(x),f(f(g(y),y),g(f(g(u),g(x)))))=u # label("cl 13739 demod 4"). 3042 [] f(g(x),g(f(g(u),g(x))))=u # label("cl 13739 demod 5"). 3043 [] f(g(x),g(f(g(u),g(x))))=u # label("cl 13739 eqord 6"). 3044 [] f(x,f(g(f(g(f(g(y),y)),f(g(z),z))),g(f(g(x),g(f(u,f(g(f(v,u)),g(x))))))))=g(f(v,g(x))) # label("cl 13743 demod 0"). 3045 [] f(x,f(g(g(f(g(y),y))),g(f(g(x),g(f(u,f(g(f(v,u)),g(x))))))))=g(f(v,g(x))) # label("cl 13743 demod 1"). 3046 [] f(x,f(f(g(y),y),g(f(g(x),g(f(u,f(g(f(v,u)),g(x))))))))=g(f(v,g(x))) # label("cl 13743 demod 2"). 3047 [] f(x,f(f(g(y),y),g(f(g(x),g(f(g(v),g(x)))))))=g(f(v,g(x))) # label("cl 13743 demod 3"). 3048 [] f(x,f(f(g(y),y),g(v)))=g(f(v,g(x))) # label("cl 13743 demod 4"). 3049 [] g(f(v,g(x)))=f(x,g(v)) # label("cl 13743 demod 5"). 3050 [] g(f(v,g(x)))=f(x,g(v)) # label("cl 13743 eqord 6"). 3051 [] f(x,f(g(f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),x)),u))=f(f(g(v),v),f(g(z),u)) # label("cl 13753 demod 0"). 3052 [] f(x,f(g(f(f(g(f(g(y),y)),z),x)),u))=f(f(g(v),v),f(g(z),u)) # label("cl 13753 demod 1"). 3053 [] f(x,f(g(f(z,x)),u))=f(f(g(v),v),f(g(z),u)) # label("cl 13753 demod 2"). 3054 [] f(x,f(g(f(z,x)),u))=f(g(z),u) # label("cl 13753 demod 3"). 3055 [] f(x,f(g(f(z,x)),u))=f(g(z),u) # label("cl 13753 eqord 4"). 3056 [] f(f(x,x),g(f(x,g(f(g(y),y)))))=g(g(x)) # label("cl 13755 demod 0"). 3057 [] g(g(x))=f(f(x,x),g(x)) # label("cl 13755 demod 1"). 3058 [] f(f(x,x),g(x))=x # label("cl 13755 demod 2"). 3059 [] f(f(x,x),g(x))=x # label("cl 13755 eqord 3"). 3060 [] f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),g(g(f(z,u))))))),g(f(x,y)))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 13760 demod 0"). 3061 [] f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),f(z,u))))),g(f(x,y)))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 13760 demod 1"). 3062 [] f(f(f(x,y),g(f(g(f(x,y)),f(z,u)))),g(f(x,y)))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 13760 demod 2"). 3063 [] f(f(x,y),f(g(f(g(f(x,y)),f(z,u))),g(f(x,y))))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u)))))) # label("cl 13760 demod 3"). 3064 [] f(g(f(u,g(f(x,y)))),g(f(u,g(f(v,f(g(f(z,v)),u))))))=f(f(x,y),g(f(z,u))) # label("cl 13760 demod 4"). 3065 [] f(f(f(x,y),g(u)),g(f(u,g(f(v,f(g(f(z,v)),u))))))=f(f(x,y),g(f(z,u))) # label("cl 13760 demod 5"). 3066 [] f(f(f(x,y),g(u)),g(f(u,g(f(g(z),u)))))=f(f(x,y),g(f(z,u))) # label("cl 13760 demod 6"). 3067 [] f(f(x,y),g(f(z,u)))=f(f(f(x,y),g(u)),f(f(g(z),u),g(u))) # label("cl 13760 demod 7"). 3068 [] f(f(x,y),g(f(z,u)))=f(f(x,y),f(g(u),f(f(g(z),u),g(u)))) # label("cl 13760 demod 8"). 3069 [] f(f(x,y),g(f(z,u)))=f(f(x,y),f(g(u),f(f(g(z),u),g(u)))) # label("cl 13760 eqord 9"). 3070 [] g(f(g(x),f(g(g(y)),g(f(g(z),z)))))=f(u,f(g(f(f(g(g(y)),g(f(g(z),z))),u)),g(f(f(g(g(y)),g(f(g(z),z))),g(f(x,y)))))) # label("cl 13780 demod 0"). 3071 [] g(f(g(x),f(y,g(f(g(z),z)))))=f(u,f(g(f(f(g(g(y)),g(f(g(z),z))),u)),g(f(f(g(g(y)),g(f(g(z),z))),g(f(x,y)))))) # label("cl 13780 demod 1"). 3072 [] f(u,f(g(f(f(g(g(y)),g(f(g(z),z))),u)),g(f(f(g(g(y)),g(f(g(z),z))),g(f(x,y))))))=g(f(g(x),y)) # label("cl 13780 demod 2"). 3073 [] f(u,f(g(f(f(y,g(f(g(z),z))),u)),g(f(f(g(g(y)),g(f(g(z),z))),g(f(x,y))))))=g(f(g(x),y)) # label("cl 13780 demod 3"). 3074 [] f(u,f(g(f(y,u)),g(f(f(g(g(y)),g(f(g(z),z))),g(f(x,y))))))=g(f(g(x),y)) # label("cl 13780 demod 4"). 3075 [] f(u,f(g(f(y,u)),g(f(f(y,g(f(g(z),z))),g(f(x,y))))))=g(f(g(x),y)) # label("cl 13780 demod 5"). 3076 [] f(u,f(g(f(y,u)),g(f(y,g(f(x,y))))))=g(f(g(x),y)) # label("cl 13780 demod 6"). 3077 [] g(f(g(x),y))=f(u,f(g(f(y,u)),f(f(x,y),g(y)))) # label("cl 13780 demod 7"). 3078 [] g(f(g(x),y))=f(g(y),f(f(x,y),g(y))) # label("cl 13780 demod 8"). 3079 [] g(f(g(x),y))=f(g(y),f(f(x,y),g(y))) # label("cl 13780 eqord 9"). 3080 [] g(f(f(f(x,x),g(f(x,g(f(g(y),y))))),f(g(f(g(z),z)),g(f(u,x)))))=u # label("cl 13799 demod 0"). 3081 [] g(f(f(f(x,x),g(f(x,f(g(y),f(f(y,y),g(y)))))),f(g(f(g(z),z)),g(f(u,x)))))=u # label("cl 13799 demod 1"). 3082 [] g(f(f(f(x,x),g(f(x,f(g(y),y)))),f(g(f(g(z),z)),g(f(u,x)))))=u # label("cl 13799 demod 2"). 3083 [] g(f(f(f(x,x),g(x)),f(g(f(g(z),z)),g(f(u,x)))))=u # label("cl 13799 demod 3"). 3084 [] g(f(x,f(g(f(g(z),z)),g(f(u,x)))))=u # label("cl 13799 demod 4"). 3085 [] g(f(x,f(f(g(z),f(f(z,z),g(z))),g(f(u,x)))))=u # label("cl 13799 demod 5"). 3086 [] g(f(x,f(f(g(z),z),g(f(u,x)))))=u # label("cl 13799 demod 6"). 3087 [] g(f(x,f(f(g(z),z),f(g(x),f(f(g(u),x),g(x))))))=u # label("cl 13799 demod 7"). 3088 [] g(f(x,f(g(x),f(f(g(u),x),g(x)))))=u # label("cl 13799 demod 8"). 3089 [] g(f(f(g(u),x),g(x)))=u # label("cl 13799 demod 9"). 3090 [] f(x,g(f(g(u),x)))=u # label("cl 13799 demod 10"). 3091 [] f(x,f(g(x),f(f(u,x),g(x))))=u # label("cl 13799 demod 11"). 3092 [] f(f(u,x),g(x))=u # label("cl 13799 demod 12"). 3093 [] f(f(u,x),g(x))=u # label("cl 13799 eqord 13"). 3094 [] f(g(f(x,g(f(g(y),y)))),f(g(f(g(z),z)),g(f(x,g(f(u,f(g(f(v,u)),x)))))))=g(f(v,x)) # label("cl 13801 demod 0"). 3095 [] f(g(f(x,f(g(y),f(f(y,y),g(y))))),f(g(f(g(z),z)),g(f(x,g(f(u,f(g(f(v,u)),x)))))))=g(f(v,x)) # label("cl 13801 demod 1"). 3096 [] f(g(f(x,f(g(y),y))),f(g(f(g(z),z)),g(f(x,g(f(u,f(g(f(v,u)),x)))))))=g(f(v,x)) # label("cl 13801 demod 2"). 3097 [] f(g(x),f(g(f(g(z),z)),g(f(x,g(f(u,f(g(f(v,u)),x)))))))=g(f(v,x)) # label("cl 13801 demod 3"). 3098 [] f(g(x),f(f(g(z),f(f(z,z),g(z))),g(f(x,g(f(u,f(g(f(v,u)),x)))))))=g(f(v,x)) # label("cl 13801 demod 4"). 3099 [] f(g(x),f(f(g(z),z),g(f(x,g(f(u,f(g(f(v,u)),x)))))))=g(f(v,x)) # label("cl 13801 demod 5"). 3100 [] f(g(x),f(f(g(z),z),g(f(x,g(f(g(v),x))))))=g(f(v,x)) # label("cl 13801 demod 6"). 3101 [] f(g(x),f(f(g(z),z),g(f(x,f(g(x),f(f(v,x),g(x)))))))=g(f(v,x)) # label("cl 13801 demod 7"). 3102 [] f(g(x),f(f(g(z),z),g(f(x,f(g(x),v)))))=g(f(v,x)) # label("cl 13801 demod 8"). 3103 [] f(g(x),f(f(g(z),z),g(v)))=g(f(v,x)) # label("cl 13801 demod 9"). 3104 [] g(f(v,x))=f(g(x),g(v)) # label("cl 13801 demod 10"). 3105 [] g(f(v,x))=f(g(x),g(v)) # label("cl 13801 eqord 11"). 3106 [] f(x,f(g(f(f(f(g(f(g(y),y)),g(f(g(y),y))),f(g(z),g(f(g(u),u)))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 0"). 3107 [] f(x,f(g(f(f(f(f(g(y),g(g(y))),g(f(g(y),y))),f(g(z),g(f(g(u),u)))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 1"). 3108 [] f(x,f(g(f(f(f(f(g(y),y),g(f(g(y),y))),f(g(z),g(f(g(u),u)))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 2"). 3109 [] f(x,f(g(f(f(f(f(g(y),y),f(g(y),g(g(y)))),f(g(z),g(f(g(u),u)))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 3"). 3110 [] f(x,f(g(f(f(f(f(g(y),y),f(g(y),y)),f(g(z),g(f(g(u),u)))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 4"). 3111 [] f(x,f(g(f(f(f(g(y),y),f(g(z),g(f(g(u),u)))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 5"). 3112 [] f(x,f(g(f(f(f(g(y),y),f(g(z),f(g(u),g(g(u))))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 6"). 3113 [] f(x,f(g(f(f(f(g(y),y),f(g(z),f(g(u),u))),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 7"). 3114 [] f(x,f(g(f(f(f(g(y),y),g(z)),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 8"). 3115 [] f(x,f(g(f(g(z),x)),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 9"). 3116 [] f(x,f(f(g(x),g(g(z))),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 10"). 3117 [] f(x,f(f(g(x),z),v))=f(f(z,g(f(w,g(f(g(y),y))))),f(w,v)) # label("cl 13875 demod 11"). 3118 [] f(x,f(f(g(x),z),v))=f(f(z,g(f(w,f(g(y),g(g(y)))))),f(w,v)) # label("cl 13875 demod 12"). 3119 [] f(x,f(f(g(x),z),v))=f(f(z,g(f(w,f(g(y),y)))),f(w,v)) # label("cl 13875 demod 13"). 3120 [] f(x,f(f(g(x),z),v))=f(f(z,g(w)),f(w,v)) # label("cl 13875 demod 14"). 3121 [] f(x,f(f(g(x),z),v))=f(z,f(g(w),f(w,v))) # label("cl 13875 demod 15"). 3122 [] f(x,f(f(g(x),z),v))=f(z,v) # label("cl 13875 demod 16"). 3123 [] f(x,f(f(g(x),z),v))=f(z,v) # label("cl 13875 eqord 17"). 3124 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(g(u),z))),f(g(f(g(v),v)),f(g(w),w))) # label("cl 13893 demod 0"). 3125 [] f(f(x,f(g(z),g(y))),f(y,u))=f(f(x,g(f(g(u),z))),f(g(f(g(v),v)),f(g(w),w))) # label("cl 13893 demod 1"). 3126 [] f(f(x,f(g(z),g(y))),f(y,u))=f(f(x,f(g(z),g(g(u)))),f(g(f(g(v),v)),f(g(w),w))) # label("cl 13893 demod 2"). 3127 [] f(f(x,f(g(z),g(y))),f(y,u))=f(f(x,f(g(z),u)),f(g(f(g(v),v)),f(g(w),w))) # label("cl 13893 demod 3"). 3128 [] f(f(x,f(g(z),g(y))),f(y,u))=f(f(x,f(g(z),u)),f(f(g(v),g(g(v))),f(g(w),w))) # label("cl 13893 demod 4"). 3129 [] f(f(x,f(g(z),g(y))),f(y,u))=f(f(x,f(g(z),u)),f(f(g(v),v),f(g(w),w))) # label("cl 13893 demod 5"). 3130 [] f(f(x,f(g(z),g(y))),f(y,u))=f(f(x,f(g(z),u)),f(g(v),v)) # label("cl 13893 demod 6"). 3131 [] f(f(x,f(g(z),g(y))),f(y,u))=f(x,f(g(z),u)) # label("cl 13893 demod 7"). 3132 [] f(f(x,f(g(z),g(y))),f(y,u))=f(x,f(g(z),u)) # label("cl 13893 eqord 8"). 3133 [] f(f(g(g(f(x,y))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 0"). 3134 [] f(f(g(f(g(y),g(x))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 1"). 3135 [] f(f(f(g(g(x)),g(g(y))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 2"). 3136 [] f(f(f(x,g(g(y))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 3"). 3137 [] f(f(f(x,y),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 4"). 3138 [] f(f(f(x,y),f(g(y),g(z))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 5"). 3139 [] f(f(x,y),f(g(y),u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)) # label("cl 13895 demod 6"). 3140 [] f(f(x,y),f(g(y),u))=f(f(f(g(v),g(g(v))),f(g(w),w)),f(x,u)) # label("cl 13895 demod 7"). 3141 [] f(f(x,y),f(g(y),u))=f(f(f(g(v),v),f(g(w),w)),f(x,u)) # label("cl 13895 demod 8"). 3142 [] f(f(x,y),f(g(y),u))=f(f(g(v),v),f(x,u)) # label("cl 13895 demod 9"). 3143 [] f(f(x,y),f(g(y),u))=f(x,u) # label("cl 13895 demod 10"). 3144 [] f(f(x,y),f(g(y),u))=f(x,u) # label("cl 13895 eqord 11"). 3145 [] f(x,g(f(y,g(f(y,f(z,y))))))=f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y)))) # label("cl 13908 demod 0"). 3146 [] f(x,g(f(y,f(g(f(z,y)),g(y)))))=f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y)))) # label("cl 13908 demod 1"). 3147 [] f(x,g(f(y,f(f(g(y),g(z)),g(y)))))=f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y)))) # label("cl 13908 demod 2"). 3148 [] f(x,g(f(y,f(g(y),f(g(z),g(y))))))=f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y)))) # label("cl 13908 demod 3"). 3149 [] f(x,g(f(g(z),g(y))))=f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y)))) # label("cl 13908 demod 4"). 3150 [] f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(g(g(y)),g(g(z)))) # label("cl 13908 demod 5"). 3151 [] f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,g(g(z)))) # label("cl 13908 demod 6"). 3152 [] f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 7"). 3153 [] f(f(g(y),f(f(f(y,y),f(f(u,f(f(g(u),g(y)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 8"). 3154 [] f(f(g(y),f(f(f(y,y),f(f(u,f(g(u),f(g(y),x))),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 9"). 3155 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 10"). 3156 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(g(f(y,f(f(u,f(f(g(u),g(y)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 11"). 3157 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(g(f(y,f(f(u,f(g(u),f(g(y),x))),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 12"). 3158 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(g(f(y,f(f(g(y),x),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 13"). 3159 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(g(f(x,y)),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 14"). 3160 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(f(g(y),g(x)),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 15"). 3161 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),g(f(g(y),f(g(x),g(z)))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 16"). 3162 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),f(g(f(g(x),g(z))),g(g(y))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 17"). 3163 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),f(f(g(g(z)),g(g(x))),g(g(y))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 18"). 3164 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),f(f(z,g(g(x))),g(g(y))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 19"). 3165 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),f(f(z,x),g(g(y))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 20"). 3166 [] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),f(f(z,x),y))),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 21"). 3167 [] f(f(f(y,f(f(g(y),x),y)),f(f(z,x),y)),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 22"). 3168 [] f(f(f(x,y),f(f(z,x),y)),g(f(y,f(f(u,f(g(f(y,u)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 23"). 3169 [] f(f(f(x,y),f(f(z,x),y)),g(f(y,f(f(u,f(f(g(u),g(y)),x)),y))))=f(x,f(y,z)) # label("cl 13908 demod 24"). 3170 [] f(f(f(x,y),f(f(z,x),y)),g(f(y,f(f(u,f(g(u),f(g(y),x))),y))))=f(x,f(y,z)) # label("cl 13908 demod 25"). 3171 [] f(f(f(x,y),f(f(z,x),y)),g(f(y,f(f(g(y),x),y))))=f(x,f(y,z)) # label("cl 13908 demod 26"). 3172 [] f(f(f(x,y),f(f(z,x),y)),g(f(x,y)))=f(x,f(y,z)) # label("cl 13908 demod 27"). 3173 [] f(f(f(x,y),f(f(z,x),y)),f(g(y),g(x)))=f(x,f(y,z)) # label("cl 13908 demod 28"). 3174 [] f(f(f(x,y),f(f(z,x),y)),f(g(y),g(x)))=f(x,f(y,z)) # label("cl 13908 eqord 29"). 3175 [] f(g(f(x,g(f(y,z)))),u)=f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z))) # label("cl 13912 demod 0"). 3176 [] f(g(f(x,f(g(z),g(y)))),u)=f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z))) # label("cl 13912 demod 1"). 3177 [] f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(g(f(g(z),g(y))),g(x)),u) # label("cl 13912 demod 2"). 3178 [] f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(f(g(g(y)),g(g(z))),g(x)),u) # label("cl 13912 demod 3"). 3179 [] f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(f(y,g(g(z))),g(x)),u) # label("cl 13912 demod 4"). 3180 [] f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(f(y,z),g(x)),u) # label("cl 13912 demod 5"). 3181 [] f(f(g(y),f(f(f(y,y),z),g(f(g(f(y,z)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 6"). 3182 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(f(x,f(f(v,f(g(f(x,v)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 7"). 3183 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(f(x,f(f(v,f(f(g(v),g(x)),w)),x))),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 8"). 3184 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(f(x,f(f(v,f(g(v),f(g(x),w))),x))),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 9"). 3185 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(f(x,f(f(g(x),w),x))),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 10"). 3186 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(f(w,x)),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 11"). 3187 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(f(g(x),g(w)),f(w,u))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 12"). 3188 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(x),f(g(w),f(w,u)))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 13"). 3189 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),g(f(g(x),u)))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 14"). 3190 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),f(g(u),g(g(x))))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 15"). 3191 [] f(f(g(y),f(f(f(y,y),z),g(f(f(g(z),g(y)),f(g(u),x))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 16"). 3192 [] f(f(g(y),f(f(f(y,y),z),g(f(g(z),f(g(y),f(g(u),x)))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 17"). 3193 [] f(f(g(y),f(f(f(y,y),z),f(g(f(g(y),f(g(u),x))),g(g(z))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 18"). 3194 [] f(f(g(y),f(f(f(y,y),z),f(f(g(f(g(u),x)),g(g(y))),g(g(z))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 19"). 3195 [] f(f(g(y),f(f(f(y,y),z),f(f(f(g(x),g(g(u))),g(g(y))),g(g(z))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 20"). 3196 [] f(f(g(y),f(f(f(y,y),z),f(f(f(g(x),u),g(g(y))),g(g(z))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 21"). 3197 [] f(f(g(y),f(f(f(y,y),z),f(f(f(g(x),u),y),g(g(z))))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 22"). 3198 [] f(f(g(y),f(f(f(y,y),z),f(f(f(g(x),u),y),z))),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 23"). 3199 [] f(f(f(y,z),f(f(f(g(x),u),y),z)),g(f(y,z)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 24"). 3200 [] f(f(f(y,z),f(f(f(g(x),u),y),z)),f(g(z),g(y)))=f(f(y,z),f(g(x),u)) # label("cl 13912 demod 25"). 3201 [] f(f(y,z),f(g(x),u))=f(y,f(z,f(g(x),u))) # label("cl 13912 demod 26"). 3202 [] f(f(y,z),f(g(x),u))=f(y,f(z,f(g(x),u))) # label("cl 13912 eqord 27"). 3203 [] f(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),z),g(f(g(f(x,z)),g(u))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 0"). 3204 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),g(f(g(f(x,z)),g(u))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 1"). 3205 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),g(f(f(g(z),g(x)),g(u))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 2"). 3206 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),g(f(g(z),f(g(x),g(u)))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 3"). 3207 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),f(g(f(g(x),g(u))),g(g(z))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 4"). 3208 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),f(f(g(g(u)),g(g(x))),g(g(z))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 5"). 3209 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),f(f(u,g(g(x))),g(g(z))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 6"). 3210 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),f(f(u,x),g(g(z))))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 7"). 3211 [] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),f(f(u,x),z))),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 8"). 3212 [] f(f(f(g(y),g(x)),f(f(f(x,z),f(f(u,x),z)),g(f(x,z)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 9"). 3213 [] f(f(f(g(y),g(x)),f(f(f(x,z),f(f(u,x),z)),f(g(z),g(x)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 10"). 3214 [] f(f(f(g(y),g(x)),f(f(x,z),f(f(f(u,x),z),f(g(z),g(x))))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 11"). 3215 [] f(f(f(g(y),g(x)),f(f(x,z),f(f(u,x),g(x)))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 12"). 3216 [] f(f(f(g(y),g(x)),f(f(x,z),u)),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 13"). 3217 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(g(f(z,u)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 14"). 3218 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),g(f(g(f(y,v)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 15"). 3219 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),g(f(f(g(v),g(y)),g(w))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 16"). 3220 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),g(f(g(v),f(g(y),g(w)))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 17"). 3221 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),f(g(f(g(y),g(w))),g(g(v))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 18"). 3222 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),f(f(g(g(w)),g(g(y))),g(g(v))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 19"). 3223 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),f(f(w,g(g(y))),g(g(v))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 20"). 3224 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),f(f(w,y),g(g(v))))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 21"). 3225 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(g(y),f(f(f(y,y),v),f(f(w,y),v))),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 22"). 3226 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(f(y,v),f(f(w,y),v)),g(f(y,v)))))=f(v,w) # label("cl 13931 demod 23"). 3227 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(f(y,v),f(f(w,y),v)),f(g(v),g(y)))))=f(v,w) # label("cl 13931 demod 24"). 3228 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(y,v),f(f(f(w,y),v),f(g(v),g(y))))))=f(v,w) # label("cl 13931 demod 25"). 3229 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(y,v),f(f(w,y),g(y)))))=f(v,w) # label("cl 13931 demod 26"). 3230 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(f(g(u),g(z)),f(f(y,v),w)))=f(v,w) # label("cl 13931 demod 27"). 3231 [] f(f(g(y),f(g(x),f(f(x,z),u))),f(g(u),f(g(z),f(f(y,v),w))))=f(v,w) # label("cl 13931 demod 28"). 3232 [] f(g(y),f(f(g(x),f(f(x,z),u)),f(g(u),f(g(z),f(f(y,v),w)))))=f(v,w) # label("cl 13931 demod 29"). 3233 [] f(g(y),f(g(x),f(f(f(x,z),u),f(g(u),f(g(z),f(f(y,v),w))))))=f(v,w) # label("cl 13931 demod 30"). 3234 [] f(g(y),f(g(x),f(f(x,z),f(g(z),f(f(y,v),w)))))=f(v,w) # label("cl 13931 demod 31"). 3235 [] f(g(y),f(g(x),f(x,f(f(y,v),w))))=f(v,w) # label("cl 13931 demod 32"). 3236 [] f(g(y),f(f(y,v),w))=f(v,w) # label("cl 13931 demod 33"). 3237 [] f(g(y),f(f(y,v),w))=f(v,w) # label("cl 13931 eqord 34"). 3238 [] g(f(g(f(x,y)),g(z)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 0"). 3239 [] g(f(f(g(y),g(x)),g(z)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 1"). 3240 [] g(f(g(y),f(g(x),g(z))))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 2"). 3241 [] f(g(f(g(x),g(z))),g(g(y)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 3"). 3242 [] f(f(g(g(z)),g(g(x))),g(g(y)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 4"). 3243 [] f(f(z,g(g(x))),g(g(y)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 5"). 3244 [] f(f(z,x),g(g(y)))=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 6"). 3245 [] f(f(z,x),y)=f(f(z,z),f(g(f(u,z)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 7"). 3246 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),g(f(g(f(u,x)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 8"). 3247 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),g(f(f(g(x),g(u)),g(y))))),g(f(u,x))))) # label("cl 13972 demod 9"). 3248 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),g(f(g(x),f(g(u),g(y)))))),g(f(u,x))))) # label("cl 13972 demod 10"). 3249 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),f(g(f(g(u),g(y))),g(g(x))))),g(f(u,x))))) # label("cl 13972 demod 11"). 3250 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),f(f(g(g(y)),g(g(u))),g(g(x))))),g(f(u,x))))) # label("cl 13972 demod 12"). 3251 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),f(f(y,g(g(u))),g(g(x))))),g(f(u,x))))) # label("cl 13972 demod 13"). 3252 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),f(f(y,u),g(g(x))))),g(f(u,x))))) # label("cl 13972 demod 14"). 3253 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),x),f(f(y,u),x))),g(f(u,x))))) # label("cl 13972 demod 15"). 3254 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(f(u,x),f(f(y,u),x)),g(f(u,x))))) # label("cl 13972 demod 16"). 3255 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(f(u,x),f(f(y,u),x)),f(g(x),g(u))))) # label("cl 13972 demod 17"). 3256 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(u,x),f(f(f(y,u),x),f(g(x),g(u)))))) # label("cl 13972 demod 18"). 3257 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(u,x),f(f(y,u),g(u))))) # label("cl 13972 demod 19"). 3258 [] f(f(z,x),y)=f(f(z,z),f(f(g(z),g(u)),f(f(u,x),y))) # label("cl 13972 demod 20"). 3259 [] f(f(z,x),y)=f(f(z,z),f(g(z),f(g(u),f(f(u,x),y)))) # label("cl 13972 demod 21"). 3260 [] f(f(z,x),y)=f(f(z,z),f(g(z),f(x,y))) # label("cl 13972 demod 22"). 3261 [] f(f(z,x),y)=f(z,f(x,y)) # label("cl 13972 demod 23"). 3262 [] f(f(z,x),y)=f(z,f(x,y)) # label("cl 13972 eqord 24"). end_of_list. list(hints2). 3263 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(z),x))))=z. 3264 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 3265 [] f(f(a,b),c)!=f(a,f(b,c)). 3266 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). 3267 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 3268 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 3269 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 3270 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). 3271 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(z),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). 3272 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 3273 [] g(f(f(f(x,x),y),g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(g(z),x))),f(g(z),u)),f(f(x,x),y))))))=u. 3274 [] f(x,g(f(y,g(f(y,f(f(g(f(y,f(f(z,f(g(f(y,z)),x)),y))),u),y))))))=u. 3275 [] f(x,f(g(f(g(f(y,z)),x)),g(f(g(f(y,z)),g(f(g(f(y,z)),f(u,g(f(y,z)))))))))=u. 3276 [] f(f(f(x,x),g(f(x,f(f(y,f(g(f(x,y)),z)),x)))),f(z,g(f(g(u),x))))=u. 3277 [] f(x,f(g(f(y,x)),g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),y)),z))))),g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),y)),z))))),f(v,g(f(z,g(f(z,f(f(u,f(g(f(z,u)),y)),z))))))))))))=v. 3278 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),y)),z))))),f(v,g(f(z,g(f(z,f(f(u,f(g(f(z,u)),y)),z))))))))))))=v. 3279 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u))))))))))))=z. 3280 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 3281 [] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,g(f(x,f(u,x)))))))=u. 3282 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 3283 [] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u))=f(v,f(g(f(x,v)),u)). 3284 [] f(x,f(y,f(g(f(z,y)),u)))=f(v,f(g(f(w,v)),f(g(f(z,g(f(w,x)))),u))). 3285 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z))))))))=f(u,v). 3286 [] f(x,f(g(f(y,x)),z))=f(g(f(y,f(f(u,f(g(f(y,u)),v)),y))),f(v,z)). 3287 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),v)))=f(u,f(w,f(g(f(z,w)),v))). 3288 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). 3289 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v). 3290 [] g(f(x,g(f(x,f(g(f(y,x)),x)))))=g(f(x,g(f(z,f(g(f(y,z)),x))))). 3291 [] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))). 3292 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,g(f(z,f(g(f(u,z)),y)))),x))))))=g(f(y,f(g(f(u,y)),y))). 3293 [] g(f(x,f(g(f(y,x)),z)))=g(f(z,f(g(f(y,z)),z))). 3294 [] f(g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(g(z),x))),f(g(z),u)),f(f(x,x),y)))),f(u,v))=f(w,f(g(f(f(f(x,x),y),w)),v)). 3295 [] f(x,f(g(f(f(f(y,y),z),x)),u))=f(g(f(f(f(y,y),z),f(f(f(g(f(y,z)),g(f(g(v),y))),f(g(v),w)),f(f(y,y),z)))),f(w,u)). 3296 [] g(f(x,g(f(y,f(g(f(z,y)),x)))))=g(f(x,g(f(u,f(g(f(z,u)),x))))). 3297 [] f(g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))),u)=f(z,u). 3298 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,u))=f(v,f(g(f(y,v)),u)). 3299 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(u,y)))))))=u. 3300 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=g(f(u,f(f(v,f(g(f(u,v)),g(f(u,z)))),u))). 3301 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 3302 [] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,z)))),x),f(z,g(u))),x))))=u. 3303 [] f(f(f(x,x),f(f(y,f(g(f(x,y)),g(f(x,z)))),x)),f(z,g(f(g(u),x))))=u. 3304 [] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,u)))),x)))=u. 3305 [] f(x,f(y,f(g(f(z,y)),u)))=f(v,f(g(f(w,v)),f(g(f(v6,g(f(w,x)))),g(f(v6,g(f(v6,f(f(v7,f(g(f(z,v7)),u)),v6)))))))). 3306 [] f(x,f(y,f(g(f(z,y)),u)))=f(x,f(v,f(g(f(z,v)),u))). 3307 [] f(f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y),u)=f(z,u). 3308 [] f(f(f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,f(g(f(u,z)),v)))))))),y),w)=f(f(v6,f(g(f(u,v6)),v)),w). 3309 [] f(f(x,f(g(f(y,x)),z)),u)=f(f(v,f(g(f(y,v)),z)),u). 3310 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(u,y)))))))=f(f(v,f(g(f(w,v)),g(f(w,g(f(w,u)))))),w). 3311 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 3312 [] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,g(f(z,u)))))),x),v),x))))=f(z,g(f(z,f(f(u,v),z)))). 3313 [] g(f(f(f(x,x),y),f(f(g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y)))),f(u,g(v))),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(v),x))). 3314 [] g(f(f(f(x,x),y),f(f(g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y)))),f(u,v)),f(f(x,x),y))))=f(g(f(x,y)),g(f(g(f(w,f(f(g(f(w,f(f(v6,f(g(f(w,v6)),v7)),w))),f(v7,g(f(w,v)))),w))),x))). 3315 [] g(f(f(f(x,x),y),f(f(g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y)))),f(u,v)),f(f(x,x),y))))=f(g(f(x,y)),g(f(v,x))). 3316 [] f(g(f(x,y)),g(f(g(f(f(f(x,x),y),z)),x)))=z. 3317 [] g(f(f(f(x,x),y),f(f(z,f(g(f(f(f(x,x),y),z)),u)),f(f(x,x),y))))=f(g(f(x,y)),g(f(u,x))). 3318 [] g(f(f(f(x,x),y),f(f(f(g(f(x,y)),g(f(z,x))),f(z,u)),f(f(x,x),y))))=f(g(f(x,y)),g(f(u,x))). 3319 [] f(x,f(g(f(f(f(y,y),z),x)),u))=f(f(g(f(y,z)),g(f(v,y))),f(v,u)). 3320 [] g(f(f(f(x,x),y),f(g(f(x,y)),g(f(z,x)))))=z. 3321 [] f(x,f(g(f(y,x)),g(f(g(f(f(f(y,y),z),u)),y))))=f(z,u). 3322 [] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,g(f(z,u)))))),x),v),x))))=f(g(f(f(f(z,z),u),v)),z). 3323 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(f(f(x,x),y),z)),x). 3324 [] f(f(x,f(g(f(g(f(y,z)),x)),g(f(g(f(y,z)),g(u))))),g(f(y,z)))=g(f(g(f(f(f(y,y),z),u)),y)). 3325 [] f(g(f(f(f(x,x),y),z)),x)=f(x,g(f(x,f(f(y,z),x)))). 3326 [] g(f(g(f(f(f(x,x),y),z)),x))=f(f(u,f(g(f(g(f(x,y)),u)),g(f(g(f(x,y)),g(z))))),g(f(x,y))). 3327 [] g(f(f(f(x,x),g(f(x,f(f(y,f(g(f(x,y)),z)),x)))),f(z,g(f(u,x)))))=u. 3328 [] f(g(f(f(f(x,x),y),f(g(f(x,y)),g(z)))),x)=z. 3329 [] g(f(g(f(f(f(x,x),y),f(g(f(x,y)),z))),x))=z. 3330 [] f(g(f(f(f(x,x),y),z)),x)=f(g(f(x,y)),f(f(f(f(u,f(g(f(g(f(x,y)),u)),g(f(g(f(x,y)),v)))),g(f(x,y))),f(v,g(z))),g(f(x,y)))). 3331 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(f(g(f(x,y)),u)))),g(f(x,y))),f(u,g(v))),g(f(x,y))))=f(g(f(f(f(x,x),y),v)),x). 3332 [] f(x,f(g(f(g(f(f(f(y,y),z),f(g(f(y,z)),u))),x)),v))=f(y,f(u,v)). 3333 [] f(f(x,g(f(y,z))),f(y,u))=f(f(g(f(z,g(f(z,f(f(v,f(g(f(z,v)),x)),z))))),g(f(w,z))),f(w,u)). 3334 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(v,z))),f(v,u)). 3335 [] f(x,f(g(f(y,x)),g(f(g(f(f(f(y,y),g(f(z,u))),f(z,v))),y))))=f(g(f(w,u)),f(w,v)). 3336 [] f(g(f(x,y)),f(x,z))=f(g(f(u,y)),f(u,z)). 3337 [] f(x,f(g(f(y,x)),f(y,z)))=f(u,f(g(f(v,u)),f(v,z))). 3338 [] f(x,f(g(f(g(f(f(f(y,y),z),f(g(f(y,z)),g(u)))),x)),u))=f(v,f(g(f(w,v)),f(w,y))). 3339 [] f(x,f(g(y),y))=f(z,f(g(f(u,z)),f(u,x))). 3340 [] f(x,f(g(f(y,x)),f(y,z)))=f(z,f(g(u),u)). 3341 [] g(f(g(f(x,f(g(f(y,x)),f(y,f(f(z,z),u))))),z))=f(z,u). 3342 [] f(g(f(x,y)),g(f(g(f(z,f(g(f(u,z)),f(u,f(f(x,x),y))))),x)))=f(g(v),v). 3343 [] f(g(f(x,y)),f(x,y))=f(g(z),z). 3344 [] f(x,f(g(f(y,x)),g(f(y,g(f(f(z,u),f(g(f(g(v),v)),y)))))))=g(f(g(f(z,u)),y)). 3345 [] g(f(x,g(f(x,f(f(y,f(g(z),z)),x)))))=f(x,y). 3346 [] f(x,f(g(f(g(f(f(f(y,y),z),f(g(f(y,z)),g(u)))),x)),u))=f(y,f(g(v),v)). 3347 [] f(x,f(g(y),y))=f(x,f(g(z),z)). 3348 [] f(g(x),x)=f(g(f(g(y),y)),f(g(z),z)). 3349 [] f(g(f(g(x),x)),f(g(y),y))=f(g(z),z). 3350 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(g(u),u)))))))=g(y). 3351 [] f(f(f(f(x,x),y),f(g(f(x,y)),z)),f(g(f(g(f(g(u),u)),f(g(v),v))),w))=f(x,f(z,w)). 3352 [] f(f(g(f(g(x),x)),f(g(y),y)),f(z,u))=f(f(g(g(f(z,v))),g(f(w,v))),f(w,u)). 3353 [] f(f(x,g(f(g(f(g(y),y)),f(g(z),z)))),f(g(u),v))=f(f(x,g(f(w,u))),f(w,v)). 3354 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(f(g(f(g(z),z)),f(g(u),u)),x))))))=y. 3355 [] f(g(f(x,g(y))),f(x,g(f(g(z),z))))=y. 3356 [] f(f(g(g(f(x,y))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)). 3357 [] f(f(x,g(f(y,z))),f(y,u))=f(f(x,g(f(g(f(g(v),v)),f(g(w),w)))),f(g(z),u)). 3358 [] f(f(f(x,f(g(f(f(g(y),y),x)),g(f(f(g(y),y),z)))),f(g(y),y)),f(z,g(f(f(g(y),y),g(f(f(g(y),y),f(g(u),u)))))))=g(f(g(v),v)). 3359 [] g(f(g(x),x))=g(f(g(y),y)). 3360 [] f(x,f(g(f(y,x)),g(f(y,g(f(f(g(z),z),f(g(f(g(u),u)),y)))))))=g(f(g(f(g(v),v)),y)). 3361 [] g(f(g(f(g(x),x)),y))=g(f(g(f(g(z),z)),y)). 3362 [] f(f(g(x),x),f(g(f(g(y),y)),f(g(f(z,g(f(g(f(g(u),u)),v)))),w)))=f(v,f(v6,f(g(f(z,v6)),w))). 3363 [] f(x,f(y,f(g(f(z,y)),u)))=f(f(g(v),v),f(g(f(g(w),w)),f(g(f(z,g(f(g(f(g(v6),v6)),x)))),u))). 3364 [] g(f(g(f(g(x),x)),f(g(y),y)))=g(f(g(z),z)). 3365 [] g(f(g(x),x))=g(f(g(f(g(y),y)),f(g(z),z))). 3366 [] f(f(f(x,x),y),f(g(f(x,y)),g(f(g(z),z))))=x. 3367 [] f(g(f(g(x),x)),f(g(g(y)),g(f(g(z),z))))=y. 3368 [] f(f(f(x,f(g(f(f(y,g(f(g(z),z))),x)),g(f(f(y,g(f(g(z),z))),u)))),f(y,g(f(g(z),z)))),f(u,g(f(f(y,g(f(g(z),z))),g(f(f(y,g(f(g(z),z))),v))))))=g(f(y,g(v))). 3369 [] g(f(g(f(g(x),x)),f(f(g(f(g(f(g(y),y)),f(f(z,f(g(f(g(f(g(y),y)),z)),u)),g(f(g(y),y))))),f(u,g(f(g(f(g(y),y)),v)))),g(f(g(y),y)))))=v. 3370 [] f(g(f(g(f(g(x),x)),y)),g(f(g(f(g(x),x)),g(f(g(f(g(z),z)),f(f(u,f(g(f(v,u)),w)),g(f(g(x),x))))))))=f(g(f(v,y)),w). 3371 [] f(f(f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),z)))),g(f(g(y),y))),f(z,g(f(g(f(g(y),y)),g(f(g(f(g(u),u)),f(v,g(f(g(y),y)))))))))=v. 3372 [] f(g(f(x,g(f(g(f(g(y),y)),z)))),f(x,g(f(g(u),u))))=f(g(f(g(v),v)),z). 3373 [] f(g(f(g(x),x)),y)=f(g(f(g(z),z)),y). 3374 [] f(f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),g(f(g(f(g(z),z)),u)))))),g(f(g(y),y)))=u. 3375 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(x),x))))))=f(g(f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),u)),g(f(g(x),x))). 3376 [] f(g(f(x,y)),z)=f(g(f(g(f(g(u),u)),y)),g(f(g(f(g(u),u)),g(f(g(f(g(v),v)),f(f(w,f(g(f(x,w)),z)),g(f(g(u),u)))))))). 3377 [] f(f(f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),z)))),g(f(g(y),y))),f(z,g(f(g(f(g(y),y)),g(u)))))=g(g(u)). 3378 [] f(x,f(g(f(g(f(g(y),y)),x)),g(f(g(f(g(y),y)),g(z)))))=g(g(z)). 3379 [] g(g(f(g(f(g(x),x)),f(y,g(f(g(z),z))))))=y. 3380 [] f(g(g(f(g(f(g(x),x)),y))),g(f(g(z),z)))=y. 3381 [] g(g(f(g(f(x,f(g(f(y,x)),f(y,g(f(g(z),z)))))),f(u,g(f(g(v),v))))))=u. 3382 [] g(g(f(g(f(x,y)),f(x,g(f(g(z),z))))))=g(y). 3383 [] g(g(f(g(x),g(f(g(x),f(f(x,y),g(x)))))))=f(z,f(g(f(g(f(g(x),x)),z)),g(y))). 3384 [] f(g(f(g(f(g(x),x)),f(f(y,f(g(f(g(f(g(x),x)),y)),z)),g(f(g(x),x))))),f(z,g(f(g(f(g(x),x)),u))))=g(u). 3385 [] g(g(f(g(f(g(x),x)),f(g(f(y,g(f(g(x),x)))),g(f(g(x),x))))))=g(f(y,g(f(g(z),z)))). 3386 [] g(f(x,g(f(g(y),y))))=g(f(x,g(f(g(z),z)))). 3387 [] f(x,f(g(f(g(f(g(y),y)),x)),g(z)))=g(g(f(g(y),g(f(g(y),f(f(y,z),g(y))))))). 3388 [] g(f(g(f(g(x),x)),f(g(y),g(f(g(z),z)))))=y. 3389 [] f(g(g(f(g(x),x))),g(f(g(y),y)))=f(g(z),z). 3390 [] f(g(g(f(g(f(g(x),x)),g(f(y,f(g(f(z,y)),g(f(g(x),x)))))))),g(f(g(u),u)))=g(f(g(f(g(x),x)),f(g(f(z,g(f(g(x),x)))),g(f(g(x),x))))). 3391 [] g(f(x,f(g(f(y,x)),g(f(g(z),z)))))=f(y,g(f(g(z),z))). 3392 [] f(g(g(f(g(f(g(x),x)),g(f(y,f(g(f(z,y)),g(f(g(x),x)))))))),g(f(g(u),u)))=g(f(v,f(g(f(z,v)),g(f(g(x),x))))). 3393 [] f(g(g(f(g(f(g(x),x)),f(y,g(f(g(x),x)))))),g(f(g(z),z)))=g(f(u,f(g(f(y,u)),g(f(g(x),x))))). 3394 [] f(x,g(f(g(y),y)))=g(f(z,f(g(f(x,z)),g(f(g(u),u))))). 3395 [] f(x,g(f(g(y),y)))=f(x,g(f(g(z),z))). 3396 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(f(g(z),z)),f(g(u),y)))))))=g(f(g(g(f(g(f(g(v),v)),u))),y)). 3397 [] f(g(f(g(x),x)),f(g(y),z))=f(u,f(g(f(g(g(f(g(f(g(v),v)),y))),u)),z)). 3398 [] g(f(g(g(f(g(f(g(x),x)),y))),z))=f(u,f(g(f(z,u)),g(f(z,g(f(g(f(g(v),v)),f(g(y),z))))))). 3399 [] f(x,f(g(f(g(g(f(g(f(g(y),y)),z))),x)),u))=f(g(f(g(v),v)),f(g(z),u)). 3400 [] f(g(f(g(x),x)),f(g(g(y)),g(f(g(g(f(g(z),z))),g(f(g(u),u))))))=y. 3401 [] g(g(f(g(f(x,f(g(f(y,x)),z))),f(u,g(f(g(v),v))))))=g(f(g(f(y,u)),z)). 3402 [] g(f(g(f(x,y)),f(x,g(f(g(z),z)))))=y. 3403 [] g(f(g(f(g(g(f(g(x),x))),y)),f(g(z),z)))=y. 3404 [] f(f(f(f(x,g(f(g(y),y))),f(x,g(f(g(y),y)))),g(f(f(x,g(f(g(y),y))),f(f(z,f(g(f(f(x,g(f(g(y),y))),z)),u)),f(x,g(f(g(y),y))))))),f(u,v))=f(x,v). 3405 [] f(f(f(f(x,g(f(g(y),y))),f(x,g(f(g(y),y)))),z),f(g(f(f(x,g(f(g(y),y))),z)),u))=f(x,u). 3406 [] g(f(g(f(g(x),x)),f(g(f(g(y),y)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(y),y))))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u). 3407 [] f(g(f(g(x),x)),f(g(f(g(y),y)),g(f(g(g(f(g(z),z))),g(f(u,f(g(f(v,u)),g(g(f(g(z),z))))))))))=g(f(v,g(g(f(g(z),z))))). 3408 [] f(g(f(g(x),x)),f(g(f(g(y),y)),z))=f(u,f(g(f(g(g(f(g(v),v))),u)),z)). 3409 [] f(x,f(g(f(g(g(f(g(y),y))),x)),z))=f(g(f(g(u),u)),f(g(f(g(v),v)),z)). 3410 [] g(f(g(f(g(g(f(g(f(g(f(g(x),x)),f(g(y),y))),f(g(z),z)))),u)),f(g(v),v)))=u. 3411 [] g(f(g(f(g(g(f(g(f(g(x),x)),f(g(y),y)))),z)),f(g(u),u)))=z. 3412 [] g(f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,f(g(u),u)),g(f(g(x),x)))))))=f(g(f(g(x),x)),z). 3413 [] f(f(f(x,f(g(f(f(g(f(y,z)),g(f(g(u),u))),x)),g(f(f(g(f(y,z)),g(f(g(u),u))),v)))),f(g(f(y,z)),g(f(g(u),u)))),f(v,g(f(f(g(f(y,z)),g(f(g(u),u))),g(f(f(g(f(y,z)),g(f(g(u),u))),y))))))=f(f(y,y),z). 3414 [] g(f(g(f(x,y)),g(x)))=f(f(x,x),y). 3415 [] g(f(g(f(g(f(g(x),x)),f(g(y),y))),g(g(z))))=f(f(g(z),g(z)),z). 3416 [] f(f(x,x),g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=g(f(z,g(x))). 3417 [] f(g(f(x,g(f(y,g(f(g(z),z)))))),f(x,u))=f(y,u). 3418 [] f(f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),z)))),g(f(x,y))),f(z,u))=f(v,f(g(f(g(f(x,y)),v)),u)). 3419 [] f(f(x,f(g(f(g(f(y,z)),x)),u)),v)=f(f(g(y),f(f(f(y,y),z),u)),v). 3420 [] f(g(f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))))),f(u,v))=f(g(x),f(f(f(x,x),y),v)). 3421 [] f(g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),z)),g(f(x,y))))),f(z,u))=f(g(x),f(f(f(x,x),y),u)). 3422 [] f(x,f(g(f(g(f(y,z)),x)),u))=f(g(y),f(f(f(y,y),z),u)). 3423 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))). 3424 [] f(f(f(x,x),y),f(g(f(x,y)),g(x)))=f(g(z),z). 3425 [] f(f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),z)))),g(f(x,y))),f(z,u))=f(g(x),f(f(f(x,x),y),u)). 3426 [] f(g(f(x,y)),f(f(f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),z)))),g(f(x,y))),f(z,g(u))),g(f(x,y))))=f(g(f(f(f(x,x),y),u)),x). 3427 [] f(g(f(f(f(x,x),y),z)),x)=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))). 3428 [] f(g(f(g(f(g(x),x)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),y)),g(f(g(x),x))))),f(y,g(f(g(f(g(x),x)),z))))=g(z). 3429 [] f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(x),x)),y))))=g(y). 3430 [] g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))))=f(f(u,f(g(f(g(f(x,y)),u)),g(f(g(f(x,y)),g(z))))),g(f(x,y))). 3431 [] g(f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))))=f(f(g(x),f(f(f(x,x),y),g(f(g(f(x,y)),g(z))))),g(f(x,y))). 3432 [] g(g(f(g(x),g(f(g(x),f(f(x,y),g(x)))))))=f(g(g(x)),f(f(f(g(x),g(x)),x),g(y))). 3433 [] g(f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(x),x)),g(y))))),g(f(g(x),x))))=f(g(g(x)),f(f(f(g(x),g(x)),x),g(y))). 3434 [] g(f(g(g(x)),g(f(g(y),y))))=f(g(g(y)),f(f(f(g(y),g(y)),y),g(x))). 3435 [] g(f(g(f(g(x),x)),f(g(f(g(f(g(y),y)),z)),f(f(g(g(f(g(y),y))),f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),g(u))),g(f(g(f(g(y),y)),z))))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u). 3436 [] f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(f(z,u),g(f(g(x),x))))))=f(g(f(g(f(g(x),x)),z)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),z),g(u))),g(f(g(f(g(x),x)),z)))). 3437 [] f(g(f(g(x),x)),f(g(g(y)),f(g(g(z)),f(f(f(g(z),g(z)),z),g(f(g(u),u))))))=y. 3438 [] f(f(f(f(x,g(f(g(y),y))),f(x,g(f(g(y),y)))),z),f(g(f(f(x,g(f(g(y),y))),z)),g(f(x,g(f(g(u),u))))))=f(g(v),v). 3439 [] f(x,g(f(x,g(f(g(y),y)))))=f(g(z),z). 3440 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),f(f(y,f(g(f(g(f(g(x),x)),y)),g(f(g(f(g(x),x)),g(z))))),g(f(g(x),x)))),f(g(u),u))=z. 3441 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(x),x)),g(y))))),g(f(g(x),x)))),f(g(z),z))=y. 3442 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),f(g(g(y)),g(f(g(x),x)))),f(g(z),z))=y. 3443 [] f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),f(g(z),z))=f(g(f(g(x),x)),y). 3444 [] f(g(f(g(x),x)),f(y,z))=f(g(f(u,g(f(y,g(f(g(v),v)))))),f(u,z)). 3445 [] f(g(f(g(x),x)),f(y,z))=f(y,z). 3446 [] f(g(g(x)),g(f(g(y),y)))=x. 3447 [] f(g(g(x)),f(f(f(g(x),g(x)),x),g(y)))=g(y). 3448 [] f(g(f(g(x),x)),y)=y. 3449 [] f(g(f(g(x),x)),g(f(f(y,z),g(f(g(x),x)))))=f(g(f(g(f(g(x),x)),y)),f(f(g(g(f(g(x),x))),f(f(f(g(f(g(x),x)),g(f(g(x),x))),y),g(z))),g(f(g(f(g(x),x)),y)))). 3450 [] g(f(f(x,y),g(f(g(z),z))))=f(g(f(g(f(g(z),z)),x)),f(f(g(g(f(g(z),z))),f(f(f(g(f(g(z),z)),g(f(g(z),z))),x),g(y))),g(f(g(f(g(z),z)),x)))). 3451 [] g(f(f(x,y),g(f(g(z),z))))=f(g(x),f(f(g(g(f(g(z),z))),f(f(f(g(f(g(z),z)),g(f(g(z),z))),x),g(y))),g(f(g(f(g(z),z)),x)))). 3452 [] g(f(f(x,y),g(f(g(z),z))))=f(g(x),f(f(g(g(f(g(z),z))),f(f(g(f(g(z),z)),x),g(y))),g(f(g(f(g(z),z)),x)))). 3453 [] g(f(f(x,y),g(f(g(z),z))))=f(g(x),f(f(g(g(f(g(z),z))),f(x,g(y))),g(f(g(f(g(z),z)),x)))). 3454 [] g(f(f(x,y),g(f(g(z),z))))=f(g(x),f(f(g(g(f(g(z),z))),f(x,g(y))),g(x))). 3455 [] g(f(g(f(g(x),x)),f(g(y),f(f(g(g(f(g(z),z))),f(f(f(g(f(g(z),z)),g(f(g(z),z))),y),g(u))),g(f(g(f(g(z),z)),y))))))=f(f(f(g(f(g(z),z)),g(f(g(z),z))),y),u). 3456 [] g(f(g(f(g(x),x)),f(g(y),f(f(g(g(f(g(z),z))),f(f(g(f(g(z),z)),y),g(u))),g(f(g(f(g(z),z)),y))))))=f(f(f(g(f(g(z),z)),g(f(g(z),z))),y),u). 3457 [] g(f(g(f(g(x),x)),f(g(y),f(f(g(g(f(g(z),z))),f(y,g(u))),g(f(g(f(g(z),z)),y))))))=f(f(f(g(f(g(z),z)),g(f(g(z),z))),y),u). 3458 [] g(f(g(f(g(x),x)),f(g(y),f(f(g(g(f(g(z),z))),f(y,g(u))),g(y)))))=f(f(f(g(f(g(z),z)),g(f(g(z),z))),y),u). 3459 [] g(f(g(x),f(f(g(g(f(g(y),y))),f(x,g(z))),g(x))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),x),z). 3460 [] g(f(g(x),f(f(g(g(f(g(y),y))),f(x,g(z))),g(x))))=f(f(g(f(g(y),y)),x),z). 3461 [] g(f(g(x),f(f(g(g(f(g(y),y))),f(x,g(z))),g(x))))=f(x,z). 3462 [] g(f(g(f(g(x),x)),g(g(y))))=f(f(g(y),g(y)),y). 3463 [] g(g(g(x)))=f(f(g(x),g(x)),x). 3464 [] g(f(g(f(g(x),x)),g(f(f(y,f(g(z),z)),g(f(g(x),x))))))=f(g(f(g(x),x)),y). 3465 [] g(f(g(f(g(x),x)),f(g(y),f(f(g(g(f(g(x),x))),f(y,g(f(g(z),z)))),g(y)))))=f(g(f(g(x),x)),y). 3466 [] g(f(g(x),f(f(g(g(f(g(y),y))),f(x,g(f(g(z),z)))),g(x))))=f(g(f(g(y),y)),x). 3467 [] f(x,f(g(y),y))=f(g(f(g(z),z)),x). 3468 [] f(x,f(g(y),y))=x. 3469 [] g(f(g(f(g(g(g(f(g(x),x)))),y)),f(g(z),z)))=y. 3470 [] g(f(g(f(f(f(g(f(g(x),x)),g(f(g(x),x))),f(g(x),x)),y)),f(g(z),z)))=y. 3471 [] g(f(g(f(f(g(f(g(x),x)),f(g(x),x)),y)),f(g(z),z)))=y. 3472 [] g(f(g(f(g(f(g(x),x)),y)),f(g(z),z)))=y. 3473 [] g(f(g(x),f(g(y),y)))=x. 3474 [] g(g(x))=x. 3475 [] g(f(g(f(g(g(f(g(g(f(g(x),x))),f(g(y),y)))),z)),f(g(u),u)))=z. 3476 [] g(f(g(f(g(g(f(f(g(x),x),f(g(y),y)))),z)),f(g(u),u)))=z. 3477 [] g(f(g(f(f(g(x),x),y)),f(g(z),z)))=y. 3478 [] g(g(f(f(g(x),x),y)))=y. 3479 [] f(f(g(x),x),y)=y. 3480 [] f(x,f(g(f(f(g(y),y),x)),z))=f(g(f(g(u),u)),f(g(f(g(v),v)),z)). 3481 [] f(x,f(g(x),y))=f(g(f(g(z),z)),f(g(f(g(u),u)),y)). 3482 [] f(x,f(g(x),y))=f(g(f(g(z),z)),y). 3483 [] f(x,f(g(x),y))=y. 3484 [] f(g(f(g(x),x)),f(g(f(g(y),y)),g(f(f(g(z),z),g(f(u,f(g(f(v,u)),g(g(f(g(z),z))))))))))=g(f(v,g(g(f(g(z),z))))). 3485 [] f(g(f(g(x),x)),f(g(f(g(y),y)),g(f(f(g(z),z),g(f(u,f(g(f(v,u)),f(g(z),z))))))))=g(f(v,g(g(f(g(z),z))))). 3486 [] f(g(f(g(x),x)),f(g(f(g(y),y)),g(f(f(g(z),z),g(f(u,g(f(v,u))))))))=g(f(v,g(g(f(g(z),z))))). 3487 [] f(g(f(g(x),x)),f(g(f(g(y),y)),g(g(f(z,g(f(u,z)))))))=g(f(u,g(g(f(g(v),v))))). 3488 [] f(g(f(g(x),x)),f(g(f(g(y),y)),f(z,g(f(u,z)))))=g(f(u,g(g(f(g(v),v))))). 3489 [] f(g(f(g(x),x)),f(y,g(f(z,y))))=g(f(z,g(g(f(g(u),u))))). 3490 [] f(x,g(f(y,x)))=g(f(y,g(g(f(g(z),z))))). 3491 [] f(x,g(f(y,x)))=g(f(y,f(g(z),z))). 3492 [] f(x,g(f(y,x)))=g(y). 3493 [] f(x,f(g(f(g(g(y)),x)),z))=f(g(f(g(u),u)),f(g(y),z)). 3494 [] f(x,f(g(f(y,x)),z))=f(g(f(g(u),u)),f(g(y),z)). 3495 [] f(x,f(g(f(y,x)),z))=f(g(y),z). 3496 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(f(g(z),z)),f(g(u),y)))))))=g(f(g(g(u)),y)). 3497 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(f(g(z),z)),f(g(u),y)))))))=g(f(u,y)). 3498 [] f(x,f(g(f(y,x)),g(f(y,g(f(g(z),y))))))=g(f(z,y)). 3499 [] g(f(x,y))=f(z,f(g(f(y,z)),g(g(g(x))))). 3500 [] g(f(x,y))=f(z,f(g(f(y,z)),g(x))). 3501 [] g(f(x,y))=f(g(y),g(x)). 3502 [] f(f(g(x),g(g(x))),f(g(y),z))=f(u,f(g(f(g(g(f(g(f(g(v),v)),y))),u)),z)). 3503 [] f(f(g(x),x),f(g(y),z))=f(u,f(g(f(g(g(f(g(f(g(v),v)),y))),u)),z)). 3504 [] f(x,f(g(f(g(g(f(g(f(g(y),y)),z))),x)),u))=f(g(z),u). 3505 [] f(x,f(g(f(g(g(f(f(g(y),g(g(y))),z))),x)),u))=f(g(z),u). 3506 [] f(x,f(g(f(g(g(f(f(g(y),y),z))),x)),u))=f(g(z),u). 3507 [] f(x,f(g(f(g(g(y)),x)),z))=f(g(y),z). 3508 [] f(x,f(f(g(x),g(y)),z))=f(g(y),z). 3509 [] f(f(g(x),g(y)),z)=f(g(f(g(f(g(u),u)),x)),g(f(g(f(g(u),u)),g(f(g(f(g(v),v)),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3510 [] f(f(g(x),g(y)),z)=f(g(f(f(g(u),g(g(u))),x)),g(f(g(f(g(u),u)),g(f(g(f(g(v),v)),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3511 [] f(f(g(x),g(y)),z)=f(g(f(f(g(u),u),x)),g(f(g(f(g(u),u)),g(f(g(f(g(v),v)),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3512 [] f(f(g(x),g(y)),z)=f(g(x),g(f(g(f(g(u),u)),g(f(g(f(g(v),v)),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3513 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),g(g(u))),g(f(g(f(g(v),v)),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3514 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(g(f(g(v),v)),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3515 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),g(g(v))),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3516 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),v),f(f(w,f(g(f(y,w)),z)),g(f(g(u),u)))))))). 3517 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),v),f(f(w,f(f(g(w),g(y)),z)),g(f(g(u),u)))))))). 3518 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),v),f(f(g(y),z),g(f(g(u),u)))))))). 3519 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),v),f(f(g(y),z),f(g(u),g(g(u))))))))). 3520 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),v),f(f(g(y),z),f(g(u),u))))))). 3521 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(f(g(v),v),f(g(y),z)))))). 3522 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),g(f(g(y),z))))). 3523 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),f(g(z),g(g(y)))))). 3524 [] f(f(g(x),g(y)),z)=f(g(x),g(f(f(g(u),u),f(g(z),y)))). 3525 [] f(f(g(x),g(y)),z)=f(g(x),g(f(g(z),y))). 3526 [] f(f(g(x),g(y)),z)=f(g(x),f(g(y),g(g(z)))). 3527 [] f(f(g(x),g(y)),z)=f(g(x),f(g(y),z)). 3528 [] f(x,f(y,f(f(g(y),g(z)),u)))=f(f(g(v),v),f(g(f(g(w),w)),f(g(f(z,g(f(g(f(g(v6),v6)),x)))),u))). 3529 [] f(x,f(y,f(g(y),f(g(z),u))))=f(f(g(v),v),f(g(f(g(w),w)),f(g(f(z,g(f(g(f(g(v6),v6)),x)))),u))). 3530 [] f(f(g(x),x),f(g(f(g(y),y)),f(g(f(z,g(f(g(f(g(u),u)),v)))),w)))=f(v,f(g(z),w)). 3531 [] f(f(g(x),x),f(f(g(y),g(g(y))),f(g(f(z,g(f(g(f(g(u),u)),v)))),w)))=f(v,f(g(z),w)). 3532 [] f(f(g(x),x),f(f(g(y),y),f(g(f(z,g(f(g(f(g(u),u)),v)))),w)))=f(v,f(g(z),w)). 3533 [] f(f(g(x),x),f(f(g(y),y),f(g(f(z,g(f(f(g(u),g(g(u))),v)))),w)))=f(v,f(g(z),w)). 3534 [] f(f(g(x),x),f(f(g(y),y),f(g(f(z,g(f(f(g(u),u),v)))),w)))=f(v,f(g(z),w)). 3535 [] f(f(g(x),x),f(f(g(y),y),f(g(f(z,g(u))),v)))=f(u,f(g(z),v)). 3536 [] f(f(g(x),x),f(f(g(y),y),f(f(g(g(z)),g(u)),v)))=f(z,f(g(u),v)). 3537 [] f(f(g(x),x),f(f(g(y),y),f(f(z,g(u)),v)))=f(z,f(g(u),v)). 3538 [] f(f(g(x),x),f(f(y,g(z)),u))=f(y,f(g(z),u)). 3539 [] f(f(x,g(y)),z)=f(x,f(g(y),z)). 3540 [] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,g(f(g(f(g(v),v)),f(g(w),w)))),f(g(y),u)). 3541 [] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,g(f(f(g(v),g(g(v))),f(g(w),w)))),f(g(y),u)). 3542 [] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,g(f(f(g(v),v),f(g(w),w)))),f(g(y),u)). 3543 [] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,g(f(g(v),v))),f(g(y),u)). 3544 [] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,f(g(v),g(g(v)))),f(g(y),u)). 3545 [] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,f(g(v),v)),f(g(y),u)). 3546 [] f(f(x,f(g(y),g(z))),f(z,u))=f(x,f(g(y),u)). 3547 [] f(f(g(f(g(x),g(y))),g(f(z,x))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(y,u)). 3548 [] f(f(f(g(g(x)),g(g(y))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)). 3549 [] f(f(f(x,g(g(y))),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)). 3550 [] f(f(f(x,y),g(f(z,y))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)). 3551 [] f(f(f(x,y),f(g(y),g(z))),f(z,u))=f(f(g(f(g(v),v)),f(g(w),w)),f(x,u)). 3552 [] f(f(x,y),f(g(y),z))=f(f(g(f(g(u),u)),f(g(v),v)),f(x,z)). 3553 [] f(f(x,y),f(g(y),z))=f(f(f(g(u),g(g(u))),f(g(v),v)),f(x,z)). 3554 [] f(f(x,y),f(g(y),z))=f(f(f(g(u),u),f(g(v),v)),f(x,z)). 3555 [] f(f(x,y),f(g(y),z))=f(f(g(u),u),f(x,z)). 3556 [] f(f(x,y),f(g(y),z))=f(x,z). 3557 [] f(f(f(f(x,x),y),f(f(g(y),g(x)),z)),f(g(f(g(f(g(u),u)),f(g(v),v))),w))=f(x,f(z,w)). 3558 [] f(f(f(f(x,x),y),f(g(y),f(g(x),z))),f(g(f(g(f(g(u),u)),f(g(v),v))),w))=f(x,f(z,w)). 3559 [] f(f(f(x,x),f(g(x),y)),f(g(f(g(f(g(z),z)),f(g(u),u))),v))=f(x,f(y,v)). 3560 [] f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),v))=f(x,f(y,v)). 3561 [] f(f(x,y),f(g(f(f(g(z),g(g(z))),f(g(u),u))),v))=f(x,f(y,v)). 3562 [] f(f(x,y),f(g(f(f(g(z),z),f(g(u),u))),v))=f(x,f(y,v)). 3563 [] f(f(x,y),f(g(f(g(z),z)),u))=f(x,f(y,u)). 3564 [] f(f(x,y),f(f(g(z),g(g(z))),u))=f(x,f(y,u)). 3565 [] f(f(x,y),f(f(g(z),z),u))=f(x,f(y,u)). 3566 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 3567 [] g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x))))=y. 3568 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 3569 [] f(f(a,b),c)!=f(a,f(b,c)). 3570 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u))). 3571 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). 3572 [] f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x)))=f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u)))). 3573 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 3574 [] g(f(f(g(x),y),f(z,f(g(f(y,z)),z))))=g(f(z,f(f(u,f(g(f(z,u)),g(x))),z))). 3575 [] f(x,f(f(y,f(g(f(g(f(f(g(f(z,x)),u),f(z,f(g(f(u,z)),z)))),y)),g(v))),g(f(f(g(f(z,x)),u),f(z,f(g(f(u,z)),z))))))=f(f(g(f(z,x)),u),g(f(f(g(f(z,x)),u),f(f(f(z,f(g(f(u,z)),z)),v),f(g(f(z,x)),u))))). 3576 [] f(x,f(f(y,f(g(f(x,y)),g(z))),g(f(f(g(f(u,x)),v),f(u,f(g(f(v,u)),u))))))=f(f(g(f(u,x)),v),g(f(f(g(f(u,x)),v),f(f(f(u,f(g(f(v,u)),u)),z),f(g(f(u,x)),v))))). 3577 [] f(x,f(f(y,f(g(f(x,y)),g(z))),x))=f(f(g(f(u,x)),v),g(f(f(g(f(u,x)),v),f(f(f(u,f(g(f(v,u)),u)),z),f(g(f(u,x)),v))))). 3578 [] f(f(g(f(x,y)),z),g(f(f(g(f(x,y)),z),f(f(f(x,f(g(f(z,x)),x)),u),f(g(f(x,y)),z)))))=f(y,f(f(v,f(g(f(y,v)),g(u))),y)). 3579 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 3580 [] f(x,g(f(f(g(f(y,x)),z),g(f(f(g(f(y,x)),z),f(f(f(y,f(g(f(z,y)),y)),u),f(g(f(y,x)),z)))))))=u. 3581 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 3582 [] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=g(f(y,f(f(u,f(g(f(y,u)),g(z))),y))). 3583 [] f(g(f(f(g(f(f(x,y),f(x,y))),f(x,y)),x)),g(f(f(g(f(f(x,y),f(x,y))),f(x,y)),f(x,y))))=y. 3584 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). 3585 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(z),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). 3586 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(g(f(f(g(f(z,z)),z),g(f(x,y)))),g(f(f(g(f(z,z)),z),z))). 3587 [] f(g(f(f(g(f(x,x)),x),g(f(y,g(f(y,f(f(z,u),y))))))),g(f(f(g(f(x,x)),x),x)))=f(g(u),g(f(g(f(y,z)),g(f(g(f(y,z)),f(x,g(f(y,z)))))))). 3588 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,y)),y),g(f(z,u)))),g(f(f(g(f(y,y)),y),y))))),g(f(f(g(f(x,x)),x),x)))=f(g(y),g(f(g(f(z,u)),g(f(g(f(z,u)),f(x,g(f(z,u)))))))). 3589 [] f(x,f(g(f(f(g(f(y,y)),y),g(f(f(g(f(z,x)),u),f(z,f(g(f(u,z)),z)))))),g(f(f(g(f(y,y)),y),y))))=y. 3590 [] f(x,f(g(f(f(g(f(y,y)),y),x)),g(f(f(g(f(y,y)),y),y))))=y. 3591 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,y)),y),z)),g(f(f(g(f(y,y)),y),y))))),g(f(f(g(f(x,x)),x),x)))=f(g(y),g(f(g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))),g(f(g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))),f(x,g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))))))))). 3592 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,y)),y),z)),g(f(f(g(f(y,y)),y),y))))),g(f(f(g(f(x,x)),x),x)))=f(g(y),g(f(z,g(f(g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))),f(x,g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))))))))). 3593 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,y)),y),z)),g(f(f(g(f(y,y)),y),y))))),g(f(f(g(f(x,x)),x),x)))=f(g(y),g(f(z,g(f(z,f(x,g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))))))))). 3594 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,y)),y),z)),g(f(f(g(f(y,y)),y),y))))),g(f(f(g(f(x,x)),x),x)))=f(g(y),g(f(z,g(f(z,f(x,z)))))). 3595 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 3596 [] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(u,f(g(f(x,u)),g(f(x,z)))),x). 3597 [] g(f(f(x,y),f(z,f(g(f(y,z)),z))))=f(f(u,f(g(f(z,u)),g(f(z,x)))),z). 3598 [] f(f(x,f(g(f(y,x)),g(f(y,z)))),y)=g(f(f(z,u),f(y,f(g(f(u,y)),y)))). 3599 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=f(f(g(f(u,g(z))),v),f(u,f(g(f(v,u)),u))). 3600 [] f(g(f(x,y)),f(g(f(f(g(f(z,z)),z),g(f(x,y)))),g(f(f(g(f(z,z)),z),z))))=f(f(g(f(u,g(z))),v),f(u,f(g(f(v,u)),u))). 3601 [] f(f(g(f(x,g(y))),z),f(x,f(g(f(z,x)),x)))=y. 3602 [] f(f(g(f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x)))),u),f(v,f(g(f(u,v)),v)))=f(v,f(f(w,f(g(f(v,w)),y)),v)). 3603 [] f(f(x,y),f(z,f(g(f(y,z)),z)))=f(z,f(f(u,f(g(f(z,u)),x)),z)). 3604 [] f(x,f(f(y,f(g(f(x,y)),z)),x))=f(f(z,u),f(x,f(g(f(u,x)),x))). 3605 [] f(x,f(f(y,f(g(f(x,y)),z)),x))=f(x,f(f(u,f(g(f(x,u)),z)),x)). 3606 [] f(f(x,y),f(z,f(g(f(y,z)),z)))=f(f(x,u),f(z,f(g(f(u,z)),z))). 3607 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,f(f(z,f(g(f(x,z)),u)),x))))),x)))=f(f(v,f(g(f(x,v)),u)),x). 3608 [] f(f(x,f(g(f(y,x)),z)),y)=f(f(u,f(g(f(y,u)),z)),y). 3609 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 3610 [] g(f(x,g(f(f(y,z),f(x,f(g(f(z,x)),x))))))=y. 3611 [] g(f(x,g(f(f(f(y,f(g(f(z,y)),u)),z),f(x,f(g(f(z,x)),x))))))=f(v,f(g(f(z,v)),u)). 3612 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 3613 [] f(f(x,f(g(f(y,x)),x)),f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),v)),z))))),w))=f(v6,f(g(f(f(g(f(x,v)),y),v6)),w)). 3614 [] f(f(x,f(g(f(y,x)),x)),f(f(g(f(f(g(f(f(g(f(z,u)),v),f(g(f(z,u)),v))),f(g(f(z,u)),v)),g(f(z,u)))),g(f(f(g(f(f(g(f(z,u)),v),f(g(f(z,u)),v))),f(g(f(z,u)),v)),f(g(f(z,u)),v)))),w))=f(v6,f(g(f(f(g(f(x,v)),y),v6)),w)). 3615 [] f(x,f(g(f(f(g(f(y,z)),u),x)),v))=f(f(y,f(g(f(u,y)),y)),f(z,v)). 3616 [] f(x,f(y,f(g(f(z,y)),u)))=f(v,f(g(f(w,v)),f(g(f(z,g(f(w,x)))),u))). 3617 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),v)))=f(u,f(w,f(g(f(z,w)),v))). 3618 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(z,f(g(f(u,z)),v))))),x)))=f(g(f(u,x)),v). 3619 [] g(f(x,g(f(f(y,z),f(u,f(g(f(z,u)),x))))))=y. 3620 [] f(f(g(f(x,g(y))),z),f(u,f(g(f(z,u)),x)))=y. 3621 [] g(f(f(g(f(x,y)),z),f(u,f(g(f(z,u)),x))))=y. 3622 [] g(f(x,f(g(f(y,x)),f(g(f(z,g(f(y,f(g(f(u,v)),z))))),u))))=v. 3623 [] g(f(x,g(f(y,f(z,f(g(f(f(u,f(g(f(v,u)),w)),z)),x))))))=f(g(f(w,g(y))),v). 3624 [] g(f(x,g(f(f(y,f(z,f(g(f(u,z)),v))),f(u,f(g(f(f(w,f(g(f(u,w)),v)),u)),x))))))=y. 3625 [] f(g(f(x,g(f(y,f(z,f(g(f(u,z)),x)))))),u)=y. 3626 [] f(g(f(x,g(f(y,f(g(f(z,f(u,f(g(f(x,u)),v)))),z))))),v)=y. 3627 [] f(x,f(g(f(f(y,f(g(f(z,y)),u)),x)),g(f(f(y,f(g(f(z,y)),u)),g(f(f(y,f(g(f(z,y)),u)),v))))))=f(g(f(u,g(v))),z). 3628 [] f(g(f(x,f(y,f(g(f(z,y)),u)))),x)=f(v,f(g(f(u,v)),z)). 3629 [] f(x,f(g(f(y,x)),z))=f(g(f(u,f(v,f(g(f(z,v)),y)))),u). 3630 [] f(x,f(g(f(f(y,f(g(f(z,y)),u)),x)),g(f(f(v,f(g(f(z,v)),u)),g(f(f(v,f(g(f(z,v)),u)),w))))))=f(g(f(u,g(w))),z). 3631 [] f(x,f(g(f(f(y,f(g(f(z,y)),u)),x)),g(f(f(v,f(g(f(z,v)),u)),g(f(f(w,f(g(f(z,w)),u)),v6))))))=f(g(f(u,g(v6))),z). 3632 [] g(f(x,f(g(f(y,x)),y)))=f(z,f(g(f(u,z)),u)). 3633 [] f(x,f(g(f(y,x)),y))=f(z,f(g(f(u,z)),u)). 3634 [] f(x,f(g(f(f(f(g(f(y,z)),y),f(f(u,f(g(f(v,u)),v)),w)),x)),g(f(f(v6,f(g(f(z,v6)),w)),g(f(f(v7,f(g(f(z,v7)),w)),v8))))))=f(g(f(w,g(v8))),z). 3635 [] f(f(g(f(x,y)),x),f(f(z,f(g(f(u,z)),u)),f(g(f(v,g(f(y,w)))),v6)))=f(w,f(v7,f(g(f(v,v7)),v6))). 3636 [] f(x,f(y,f(g(f(z,y)),u)))=f(f(g(f(v,w)),v),f(f(v6,f(g(f(v7,v6)),v7)),f(g(f(z,g(f(w,x)))),u))). 3637 [] f(g(f(x,g(f(y,f(z,f(g(f(u,z)),u)))))),x)=y. 3638 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(f(f(v,f(g(f(w,v)),w)),v6))))))=f(g(f(z,g(v6))),z). 3639 [] f(f(g(f(x,g(y))),x),f(z,f(g(f(u,z)),u)))=y. 3640 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(z,f(g(f(u,z)),u))))),x)))=f(g(f(v,x)),v). 3641 [] f(g(f(x,y)),x)=f(g(f(z,y)),z). 3642 [] f(x,f(y,f(g(f(z,y)),z)))=f(g(f(u,f(v,f(g(f(f(g(f(w,g(f(v6,x)))),w),v)),v6)))),u). 3643 [] f(x,f(y,f(g(f(z,y)),z)))=f(g(f(u,f(f(v,f(g(f(v,v)),v)),f(g(f(w,x)),w)))),u). 3644 [] f(f(g(f(x,y)),z),g(f(f(g(f(x,y)),z),f(f(u,f(g(f(v,u)),v)),f(g(f(x,y)),z)))))=f(y,f(f(w,f(g(f(y,w)),g(f(g(f(v6,f(x,f(g(f(z,x)),x)))),v6)))),y)). 3645 [] f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z))))=f(f(g(f(z,y)),z),f(f(w,f(g(f(f(g(f(z,y)),z),w)),x)),f(g(f(z,y)),z))). 3646 [] f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z))))=f(f(g(f(z,y)),z),f(f(f(z,f(g(f(z,z)),z)),f(y,x)),f(g(f(z,y)),z))). 3647 [] g(f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z)))))=f(f(w,f(g(f(f(g(f(z,y)),z),w)),g(f(f(g(f(z,y)),z),x)))),f(g(f(z,y)),z)). 3648 [] g(f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z)))))=f(f(f(z,f(g(f(z,z)),z)),f(y,g(f(f(g(f(z,y)),z),x)))),f(g(f(z,y)),z)). 3649 [] f(f(g(f(x,f(g(f(y,x)),y))),z),g(f(f(g(f(u,f(g(f(v,u)),v))),z),f(f(f(u,f(g(f(z,u)),u)),w),f(g(f(u,f(g(f(v,u)),v))),z)))))=f(f(g(f(v,u)),v),f(f(v6,f(g(f(f(g(f(v,u)),v),v6)),g(w))),f(g(f(v,u)),v))). 3650 [] f(f(g(f(x,f(g(f(y,x)),y))),z),g(f(f(g(f(u,f(g(f(v,u)),v))),z),f(f(f(u,f(g(f(z,u)),u)),w),f(g(f(u,f(g(f(v,u)),v))),z)))))=f(f(g(f(v,u)),v),f(f(f(v,f(g(f(v,v)),v)),f(u,g(w))),f(g(f(v,u)),v))). 3651 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,f(u,f(g(f(v,u)),u)))),z)))),x))=f(f(g(f(u,x)),v),g(f(f(g(f(u,x)),v),f(f(w,f(g(f(v6,w)),v6)),f(g(f(u,x)),v))))). 3652 [] f(f(g(f(x,y)),x),f(f(f(x,f(g(f(x,x)),x)),f(y,z)),f(g(f(x,y)),x)))=f(f(z,y),f(f(g(f(x,y)),x),f(g(f(u,f(g(f(v,u)),v))),f(g(f(x,y)),x)))). 3653 [] f(f(f(x,f(g(f(x,x)),x)),f(y,g(f(f(g(f(x,y)),x),z)))),f(g(f(x,y)),x))=g(f(f(z,y),f(f(g(f(x,y)),x),f(g(f(u,f(g(f(v,u)),v))),f(g(f(x,y)),x))))). 3654 [] f(f(x,f(g(f(y,x)),y)),z)=f(g(f(u,f(g(f(v,z)),v))),u). 3655 [] f(g(f(x,f(g(f(y,z)),y))),x)=f(f(u,f(g(f(v,u)),v)),z). 3656 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,z)),y),u)),g(f(f(g(f(z,z)),z),z))))),g(f(f(g(f(x,x)),x),x)))=f(g(z),g(f(u,g(f(u,f(x,u)))))). 3657 [] f(f(g(f(x,g(y))),x),f(f(g(f(z,u)),z),f(f(v,f(g(f(w,v)),w)),u)))=y. 3658 [] f(g(f(x,f(y,f(g(f(f(g(f(z,g(f(u,f(g(f(v,g(w))),v))))),z),y)),u)))),x)=w. 3659 [] f(g(f(x,f(f(y,f(g(f(y,y)),y)),f(g(f(z,f(g(f(u,g(v))),u))),z)))),x)=v. 3660 [] f(g(f(x,y)),x)=f(z,f(g(f(f(g(f(u,g(f(v,f(g(f(w,g(y))),w))))),u),z)),v)). 3661 [] f(g(f(x,y)),x)=f(f(z,f(g(f(z,z)),z)),f(g(f(u,f(g(f(v,g(y))),v))),u)). 3662 [] f(f(g(f(f(x,f(g(f(y,x)),y)),z)),f(g(f(u,g(v))),u)),f(f(x,f(g(f(y,x)),y)),f(g(v),f(x,f(g(f(y,x)),y)))))=f(w,g(f(w,f(f(v6,f(g(f(w,v6)),z)),w)))). 3663 [] f(x,f(y,f(g(f(f(z,f(g(f(u,z)),u)),y)),y)))=f(f(f(g(f(v,g(x))),v),w),f(y,f(g(f(w,y)),y))). 3664 [] f(x,f(y,f(g(f(f(z,f(g(f(u,z)),u)),y)),y)))=f(y,f(f(v,f(g(f(y,v)),f(g(f(w,g(x))),w))),y)). 3665 [] f(f(x,f(g(f(x,x)),x)),f(g(f(y,f(g(f(z,g(u))),z))),y))=f(g(f(v,u)),v). 3666 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(f(g(f(f(u,f(g(f(v,u)),v)),z)),f(g(f(w,g(v6))),w)),f(f(u,f(g(f(v,u)),v)),f(g(v6),f(u,f(g(f(v,u)),v))))). 3667 [] f(f(f(g(f(x,g(y))),x),z),f(u,f(g(f(z,u)),u)))=f(y,f(u,f(g(f(f(v,f(g(f(w,v)),w)),u)),u))). 3668 [] f(x,f(f(y,f(g(f(x,y)),f(g(f(z,g(u))),z))),x))=f(u,f(x,f(g(f(f(v,f(g(f(w,v)),w)),x)),x))). 3669 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(f(g(f(f(g(f(w,u)),w),f(g(f(w,u)),w))),f(g(f(w,u)),w)),f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(f(v,g(f(v,f(x,v)))))). 3670 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(f(g(f(v,g(w))),v))))))=f(g(f(z,g(f(g(f(f(v6,f(g(f(v,v6)),v)),f(v7,f(g(f(v8,v7)),v8)))),g(f(f(v9,f(g(f(v,v9)),v)),g(f(f(v10,f(g(f(v11,v10)),v11)),w)))))))),z). 3671 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(f(g(f(v,f(w,f(g(f(v6,w)),v7)))),v))))))=f(g(f(z,g(f(g(f(v7,f(v8,f(g(f(v9,v8)),v9)))),v6)))),z). 3672 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(v)))))=f(g(f(z,g(f(w,f(g(f(f(g(f(v6,g(f(v7,g(v))))),v6),w)),v7))))),z). 3673 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(v)))))=f(g(f(z,g(f(f(w,f(g(f(w,w)),w)),f(g(f(v6,g(v))),v6))))),z). 3674 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(f(v,f(g(f(w,v)),v6)))))))=f(g(f(z,g(f(g(f(w,f(v7,f(g(f(v8,v7)),v8)))),v6)))),z). 3675 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(f(f(v,w),f(f(v6,f(g(f(v7,v6)),v7)),f(g(f(w,f(v6,f(g(f(v7,v6)),v7)))),f(v6,f(g(f(v7,v6)),v7))))))))))=f(g(f(z,g(f(f(v8,f(g(f(f(v6,f(g(f(v7,v6)),v7)),v8)),v)),f(v6,f(g(f(v7,v6)),v7)))))),z). 3676 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(f(f(v,w),f(f(v6,f(g(f(v7,v6)),v7)),f(g(f(w,f(v6,f(g(f(v7,v6)),v7)))),f(v6,f(g(f(v7,v6)),v7))))))))))=f(v8,f(g(f(f(v6,f(g(f(v7,v6)),v7)),v8)),v)). 3677 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(g(f(z,g(f(v,f(g(f(f(g(f(w,u)),w),v)),f(v6,f(g(f(z,v6)),z))))))),z). 3678 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),u))=f(g(f(z,g(f(f(v,f(g(f(v,v)),v)),f(u,f(w,f(g(f(z,w)),z))))))),z). 3679 [] f(g(f(x,g(f(g(f(f(y,f(g(f(z,y)),z)),f(u,f(g(f(v,u)),v)))),g(f(f(w,f(g(f(z,w)),z)),g(f(f(v6,f(g(f(v7,v6)),v7)),v8)))))))),x)=f(v9,f(g(f(f(v10,f(g(f(x,v10)),x)),v9)),g(f(f(v11,f(g(f(x,v11)),x)),g(f(g(f(z,g(v8))),z)))))). 3680 [] f(g(f(x,g(f(f(y,f(g(f(y,y)),y)),f(g(f(z,g(u))),z))))),x)=f(v,f(g(f(f(w,f(g(f(x,w)),x)),v)),g(f(f(v6,f(g(f(x,v6)),x)),g(u))))). 3681 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=f(u,f(g(f(v,u)),g(f(v,g(f(v,f(z,v))))))). 3682 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 3683 [] f(f(x,f(g(f(y,x)),y)),f(g(z),g(f(f(g(f(u,g(z))),u),g(f(f(g(f(u,g(z))),u),f(v,f(g(f(u,g(z))),u))))))))=v. 3684 [] f(f(g(f(x,y)),x),f(f(z,f(g(f(u,z)),u)),g(f(y,g(f(y,f(v,y)))))))=v. 3685 [] f(g(f(x,f(g(f(y,f(z,f(g(f(u,z)),g(f(u,g(f(u,f(v,u))))))))),y))),x)=v. 3686 [] f(g(f(x,f(g(f(y,z)),y))),x)=z. 3687 [] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(f(v,g(f(v,f(x,v)))))). 3688 [] f(f(x,f(g(f(x,x)),x)),g(y))=f(g(f(z,y)),z). 3689 [] f(g(f(x,y)),x)=f(f(z,f(g(f(z,z)),z)),g(y)). 3690 [] f(g(f(x,f(f(y,f(g(f(y,y)),y)),g(z)))),x)=z. 3691 [] f(f(x,f(g(f(y,x)),y)),z)=z. 3692 [] f(g(f(x,y)),x)=g(y). 3693 [] f(f(x,g(x)),g(y))=g(y). 3694 [] f(g(f(x,f(f(y,g(y)),g(z)))),x)=z. 3695 [] f(g(f(x,g(y))),x)=y. 3696 [] g(g(x))=x. 3697 [] f(g(x),f(f(y,f(g(f(z,y)),z)),g(f(x,g(f(x,f(u,x)))))))=u. 3698 [] f(g(x),f(f(y,g(y)),g(f(x,g(f(x,f(z,x)))))))=z. 3699 [] f(g(x),g(f(x,g(f(x,f(y,x))))))=y. 3700 [] f(f(x,g(x)),f(g(y),g(f(f(g(f(z,g(y))),z),g(f(f(g(f(z,g(y))),z),f(u,f(g(f(z,g(y))),z))))))))=u. 3701 [] f(f(x,g(x)),f(g(y),g(f(g(g(y)),g(f(f(g(f(z,g(y))),z),f(u,f(g(f(z,g(y))),z))))))))=u. 3702 [] f(f(x,g(x)),f(g(y),g(f(y,g(f(f(g(f(z,g(y))),z),f(u,f(g(f(z,g(y))),z))))))))=u. 3703 [] f(f(x,g(x)),f(g(y),g(f(y,g(f(g(g(y)),f(z,f(g(f(u,g(y))),u))))))))=z. 3704 [] f(f(x,g(x)),f(g(y),g(f(y,g(f(y,f(z,f(g(f(u,g(y))),u))))))))=z. 3705 [] f(f(x,g(x)),f(g(y),g(f(y,g(f(y,f(z,g(g(y)))))))))=z. 3706 [] f(f(x,g(x)),f(g(y),g(f(y,g(f(y,f(z,y)))))))=z. 3707 [] f(f(x,g(x)),y)=y. 3708 [] f(g(f(x,g(f(f(y,g(y)),f(g(f(z,g(u))),z))))),x)=f(v,f(g(f(f(w,f(g(f(x,w)),x)),v)),g(f(f(v6,f(g(f(x,v6)),x)),g(u))))). 3709 [] f(g(f(x,g(f(f(y,g(y)),g(g(z)))))),x)=f(u,f(g(f(f(v,f(g(f(x,v)),x)),u)),g(f(f(w,f(g(f(x,w)),x)),g(z))))). 3710 [] f(g(f(x,g(f(f(y,g(y)),z)))),x)=f(u,f(g(f(f(v,f(g(f(x,v)),x)),u)),g(f(f(w,f(g(f(x,w)),x)),g(z))))). 3711 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(v)))))=f(g(f(z,g(v))),z). 3712 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(v)))))=g(g(v)). 3713 [] f(x,f(g(f(f(y,f(g(f(z,y)),z)),x)),g(f(f(u,f(g(f(z,u)),z)),g(v)))))=v. 3714 [] f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,f(g(f(u,z)),u)),g(v)))))=v. 3715 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(u)))))=u. 3716 [] f(x,f(g(x),g(f(f(y,g(y)),g(z)))))=z. 3717 [] f(x,f(g(x),g(g(y))))=y. 3718 [] f(x,f(g(x),y))=y. 3719 [] f(g(f(x,g(f(g(f(f(y,g(y)),f(z,f(g(f(u,z)),u)))),g(f(f(v,f(g(f(w,v)),w)),g(f(f(v6,f(g(f(v7,v6)),v7)),v8)))))))),x)=f(v9,f(g(f(f(v10,f(g(f(x,v10)),x)),v9)),g(f(f(v11,f(g(f(x,v11)),x)),g(f(g(f(w,g(v8))),w)))))). 3720 [] f(g(f(x,g(f(g(f(f(y,g(y)),f(z,g(z)))),g(f(f(u,f(g(f(v,u)),v)),g(f(f(w,f(g(f(v6,w)),v6)),v7)))))))),x)=f(v8,f(g(f(f(v9,f(g(f(x,v9)),x)),v8)),g(f(f(v10,f(g(f(x,v10)),x)),g(f(g(f(v,g(v7))),v)))))). 3721 [] f(g(f(x,g(f(g(f(y,g(y))),g(f(f(z,f(g(f(u,z)),u)),g(f(f(v,f(g(f(w,v)),w)),v6)))))))),x)=f(v7,f(g(f(f(v8,f(g(f(x,v8)),x)),v7)),g(f(f(v9,f(g(f(x,v9)),x)),g(f(g(f(u,g(v6))),u)))))). 3722 [] f(g(f(x,g(f(g(f(y,g(y))),g(f(f(z,g(z)),g(f(f(u,f(g(f(v,u)),v)),w)))))))),x)=f(v6,f(g(f(f(v7,f(g(f(x,v7)),x)),v6)),g(f(f(v8,f(g(f(x,v8)),x)),g(f(g(f(v9,g(w))),v9)))))). 3723 [] f(g(f(x,g(f(g(f(y,g(y))),g(f(f(z,g(z)),g(f(f(u,g(u)),v)))))))),x)=f(w,f(g(f(f(v6,f(g(f(x,v6)),x)),w)),g(f(f(v7,f(g(f(x,v7)),x)),g(f(g(f(v8,g(v))),v8)))))). 3724 [] f(g(f(x,g(f(g(f(y,g(y))),g(f(f(z,g(z)),g(u))))))),x)=f(v,f(g(f(f(w,f(g(f(x,w)),x)),v)),g(f(f(v6,f(g(f(x,v6)),x)),g(f(g(f(v7,g(u))),v7)))))). 3725 [] f(g(f(x,g(f(g(f(y,g(y))),g(g(z)))))),x)=f(u,f(g(f(f(v,f(g(f(x,v)),x)),u)),g(f(f(w,f(g(f(x,w)),x)),g(f(g(f(v6,g(z))),v6)))))). 3726 [] f(g(f(x,g(f(g(f(y,g(y))),z)))),x)=f(u,f(g(f(f(v,f(g(f(x,v)),x)),u)),g(f(f(w,f(g(f(x,w)),x)),g(f(g(f(v6,g(z))),v6)))))). 3727 [] g(g(f(g(f(x,g(x))),y)))=f(z,f(g(f(f(u,f(g(f(v,u)),v)),z)),g(f(f(w,f(g(f(v,w)),v)),g(f(g(f(v6,g(y))),v6)))))). 3728 [] f(g(f(x,g(x))),y)=f(z,f(g(f(f(u,f(g(f(v,u)),v)),z)),g(f(f(w,f(g(f(v,w)),v)),g(f(g(f(v6,g(y))),v6)))))). 3729 [] f(g(f(x,g(x))),y)=f(z,f(g(f(f(u,g(u)),z)),g(f(f(v,f(g(f(w,v)),w)),g(f(g(f(v6,g(y))),v6)))))). 3730 [] f(g(f(x,g(x))),y)=f(z,f(g(z),g(f(f(u,f(g(f(v,u)),v)),g(f(g(f(w,g(y))),w)))))). 3731 [] f(g(f(x,g(x))),y)=f(z,f(g(z),g(f(f(u,g(u)),g(f(g(f(v,g(y))),v)))))). 3732 [] f(g(f(x,g(x))),y)=f(z,f(g(z),g(f(f(u,g(u)),g(g(g(y))))))). 3733 [] f(g(f(x,g(x))),y)=f(z,f(g(z),g(f(f(u,g(u)),g(y))))). 3734 [] f(g(f(x,g(x))),y)=f(z,f(g(z),g(g(y)))). 3735 [] f(g(f(x,g(x))),y)=f(z,f(g(z),y)). 3736 [] f(g(f(x,g(x))),y)=y. 3737 [] f(x,f(g(f(f(y,g(y)),x)),z))=f(g(f(u,g(f(f(v,f(g(f(v,v)),v)),f(z,f(w,f(g(f(u,w)),u))))))),u). 3738 [] f(x,f(g(x),y))=f(g(f(z,g(f(f(u,f(g(f(u,u)),u)),f(y,f(v,f(g(f(z,v)),z))))))),z). 3739 [] f(g(f(x,g(f(f(y,f(g(f(y,y)),y)),f(z,f(u,f(g(f(x,u)),x))))))),x)=z. 3740 [] f(g(f(x,g(f(f(y,g(y)),f(z,f(u,f(g(f(x,u)),x))))))),x)=z. 3741 [] f(g(f(x,g(f(f(y,g(y)),f(z,f(u,g(u))))))),x)=z. 3742 [] f(g(f(x,g(f(y,f(z,g(z)))))),x)=y. 3743 [] g(g(f(x,f(y,g(y)))))=x. 3744 [] f(x,f(y,g(y)))=x. 3745 [] f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,f(g(f(u,z)),u)),g(f(f(v,w),f(f(v6,f(g(f(v7,v6)),v7)),f(g(f(w,f(v6,f(g(f(v7,v6)),v7)))),f(v6,f(g(f(v7,v6)),v7))))))))))=f(v8,f(g(f(f(v6,f(g(f(v7,v6)),v7)),v8)),v)). 3746 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(f(f(u,v),f(f(w,f(g(f(v6,w)),v6)),f(g(f(v,f(w,f(g(f(v6,w)),v6)))),f(w,f(g(f(v6,w)),v6))))))))))=f(v7,f(g(f(f(w,f(g(f(v6,w)),v6)),v7)),u)). 3747 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),f(f(v,f(g(f(w,v)),w)),f(g(f(u,f(v,f(g(f(w,v)),w)))),f(v,f(g(f(w,v)),w))))))))))=f(v6,f(g(f(f(v,f(g(f(w,v)),w)),v6)),z)). 3748 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),f(f(v,g(v)),f(g(f(u,f(v,f(g(f(w,v)),w)))),f(v,f(g(f(w,v)),w))))))))))=f(v6,f(g(f(f(v,f(g(f(w,v)),w)),v6)),z)). 3749 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),f(f(v,g(v)),f(g(f(u,f(v,g(v)))),f(v,f(g(f(w,v)),w))))))))))=f(v6,f(g(f(f(v,f(g(f(w,v)),w)),v6)),z)). 3750 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),f(f(v,g(v)),f(g(u),f(v,f(g(f(w,v)),w))))))))))=f(v6,f(g(f(f(v,f(g(f(w,v)),w)),v6)),z)). 3751 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),f(f(v,g(v)),f(g(u),f(v,g(v))))))))))=f(w,f(g(f(f(v,f(g(f(v6,v)),v6)),w)),z)). 3752 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),f(f(v,g(v)),g(u))))))))=f(w,f(g(f(f(v,f(g(f(v6,v)),v6)),w)),z)). 3753 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(f(z,u),g(u)))))))=f(v,f(g(f(f(w,f(g(f(v6,w)),v6)),v)),z)). 3754 [] f(x,f(g(x),g(g(f(f(y,z),g(z))))))=f(u,f(g(f(f(v,f(g(f(w,v)),w)),u)),y)). 3755 [] f(x,f(g(x),f(f(y,z),g(z))))=f(u,f(g(f(f(v,f(g(f(w,v)),w)),u)),y)). 3756 [] f(f(x,y),g(y))=f(z,f(g(f(f(u,f(g(f(v,u)),v)),z)),x)). 3757 [] f(f(x,y),g(y))=f(z,f(g(f(f(u,g(u)),z)),x)). 3758 [] f(f(x,y),g(y))=f(z,f(g(z),x)). 3759 [] f(f(x,y),g(y))=x. 3760 [] f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,f(g(f(u,z)),u)),g(f(v,f(g(f(w,v)),v6)))))))=f(g(f(u,g(f(g(f(w,f(v7,f(g(f(v8,v7)),v8)))),v6)))),u). 3761 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(f(u,f(g(f(v,u)),w)))))))=f(g(f(z,g(f(g(f(v,f(v6,f(g(f(v7,v6)),v7)))),w)))),z). 3762 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(z,f(g(f(u,z)),v)))))))=f(g(f(w,g(f(g(f(u,f(v6,f(g(f(v7,v6)),v7)))),v)))),w). 3763 [] f(x,f(g(x),g(g(f(y,f(g(f(z,y)),u))))))=f(g(f(v,g(f(g(f(z,f(w,f(g(f(v6,w)),v6)))),u)))),v). 3764 [] f(x,f(g(x),f(y,f(g(f(z,y)),u))))=f(g(f(v,g(f(g(f(z,f(w,f(g(f(v6,w)),v6)))),u)))),v). 3765 [] f(x,f(g(f(y,x)),z))=f(g(f(u,g(f(g(f(y,f(v,f(g(f(w,v)),w)))),z)))),u). 3766 [] f(x,f(g(f(y,x)),z))=f(g(f(u,g(f(g(f(y,f(v,g(v)))),z)))),u). 3767 [] f(x,f(g(f(y,x)),z))=f(g(f(u,g(f(g(y),z)))),u). 3768 [] f(x,f(g(f(y,x)),z))=g(g(f(g(y),z))). 3769 [] f(x,f(g(f(y,x)),z))=f(g(y),z). 3770 [] f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,f(g(f(u,z)),u)),g(f(g(f(v,f(w,f(g(f(v6,w)),v7)))),v))))))=f(g(f(u,g(f(g(f(v7,f(v8,f(g(f(v9,v8)),v9)))),v6)))),u). 3771 [] f(x,f(g(x),g(f(f(y,f(g(f(z,y)),z)),g(f(g(f(u,f(v,f(g(f(w,v)),v6)))),u))))))=f(g(f(z,g(f(g(f(v6,f(v7,f(g(f(v8,v7)),v8)))),w)))),z). 3772 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(g(f(z,f(u,f(g(f(v,u)),w)))),z))))))=f(g(f(v6,g(f(g(f(w,f(v7,f(g(f(v8,v7)),v8)))),v)))),v6). 3773 [] f(x,f(g(x),g(f(f(y,g(y)),g(f(g(f(z,f(g(u),v))),z))))))=f(g(f(w,g(f(g(f(v,f(v6,f(g(f(v7,v6)),v7)))),u)))),w). 3774 [] f(x,f(g(x),g(f(f(y,g(y)),g(g(f(g(z),u)))))))=f(g(f(v,g(f(g(f(u,f(w,f(g(f(v6,w)),v6)))),z)))),v). 3775 [] f(x,f(g(x),g(f(f(y,g(y)),f(g(z),u)))))=f(g(f(v,g(f(g(f(u,f(w,f(g(f(v6,w)),v6)))),z)))),v). 3776 [] f(x,f(g(x),g(f(g(y),z))))=f(g(f(u,g(f(g(f(z,f(v,f(g(f(w,v)),w)))),y)))),u). 3777 [] f(g(f(x,g(f(g(f(y,f(z,f(g(f(u,z)),u)))),v)))),x)=g(f(g(v),y)). 3778 [] f(g(f(x,g(f(g(f(y,f(z,g(z)))),u)))),x)=g(f(g(u),y)). 3779 [] f(g(f(x,g(f(g(y),z)))),x)=g(f(g(z),y)). 3780 [] g(g(f(g(x),y)))=g(f(g(y),x)). 3781 [] g(f(g(x),y))=f(g(y),x). 3782 [] f(x,f(f(y,f(g(f(x,y)),g(g(z)))),x))=f(z,f(x,f(g(f(f(u,f(g(f(v,u)),v)),x)),x))). 3783 [] f(x,f(f(y,f(g(f(x,y)),z)),x))=f(z,f(x,f(g(f(f(u,f(g(f(v,u)),v)),x)),x))). 3784 [] f(x,f(f(g(x),y),x))=f(y,f(x,f(g(f(f(z,f(g(f(u,z)),u)),x)),x))). 3785 [] f(x,f(f(g(x),y),x))=f(y,f(x,f(g(f(f(z,g(z)),x)),x))). 3786 [] f(x,f(f(g(x),y),x))=f(y,f(x,f(g(x),x))). 3787 [] f(x,f(f(g(x),y),x))=f(y,x). 3788 [] f(f(g(g(x)),y),f(z,f(g(f(y,z)),z)))=f(x,f(z,f(g(f(f(u,f(g(f(v,u)),v)),z)),z))). 3789 [] f(f(x,y),f(z,f(g(f(y,z)),z)))=f(x,f(z,f(g(f(f(u,f(g(f(v,u)),v)),z)),z))). 3790 [] f(f(x,y),f(g(y),z))=f(x,f(z,f(g(f(f(u,f(g(f(v,u)),v)),z)),z))). 3791 [] f(f(x,y),f(g(y),z))=f(x,f(z,f(g(f(f(u,g(u)),z)),z))). 3792 [] f(f(x,y),f(g(y),z))=f(x,f(z,f(g(z),z))). 3793 [] f(f(x,y),f(g(y),z))=f(x,z). 3794 [] f(x,g(f(x,f(f(g(x),y),x))))=f(f(g(f(f(z,f(g(f(u,z)),u)),y)),f(g(f(v,g(w))),v)),f(f(z,f(g(f(u,z)),u)),f(g(w),f(z,f(g(f(u,z)),u))))). 3795 [] f(x,g(f(y,x)))=f(f(g(f(f(z,f(g(f(u,z)),u)),y)),f(g(f(v,g(w))),v)),f(f(z,f(g(f(u,z)),u)),f(g(w),f(z,f(g(f(u,z)),u))))). 3796 [] f(x,g(f(y,x)))=f(f(g(f(f(z,g(z)),y)),f(g(f(u,g(v))),u)),f(f(z,f(g(f(w,z)),w)),f(g(v),f(z,f(g(f(w,z)),w))))). 3797 [] f(x,g(f(y,x)))=f(f(g(y),f(g(f(z,g(u))),z)),f(f(v,f(g(f(w,v)),w)),f(g(u),f(v,f(g(f(w,v)),w))))). 3798 [] f(x,g(f(y,x)))=f(f(g(y),g(g(z))),f(f(u,f(g(f(v,u)),v)),f(g(z),f(u,f(g(f(v,u)),v))))). 3799 [] f(x,g(f(y,x)))=f(f(g(y),z),f(f(u,f(g(f(v,u)),v)),f(g(z),f(u,f(g(f(v,u)),v))))). 3800 [] f(x,g(f(y,x)))=f(f(g(y),z),f(f(u,g(u)),f(g(z),f(u,f(g(f(v,u)),v))))). 3801 [] f(x,g(f(y,x)))=f(f(g(y),z),f(f(u,g(u)),f(g(z),f(u,g(u))))). 3802 [] f(x,g(f(y,x)))=f(f(g(y),z),f(f(u,g(u)),g(z))). 3803 [] f(x,g(f(y,x)))=f(f(g(y),z),g(z)). 3804 [] f(x,g(f(y,x)))=g(y). 3805 [] f(g(g(x)),f(f(g(f(y,z)),y),f(f(u,f(g(f(v,u)),v)),z)))=x. 3806 [] f(x,f(f(g(f(y,z)),y),f(f(u,f(g(f(v,u)),v)),z)))=x. 3807 [] f(x,f(g(y),f(f(z,f(g(f(u,z)),u)),y)))=x. 3808 [] f(x,f(g(y),f(f(z,g(z)),y)))=x. 3809 [] f(x,f(g(y),y))=x. 3810 [] f(f(f(x,g(x)),f(y,g(f(f(g(f(x,y)),x),z)))),f(g(f(x,y)),x))=g(f(f(z,y),f(f(g(f(x,y)),x),f(g(f(u,f(g(f(v,u)),v))),f(g(f(x,y)),x))))). 3811 [] f(f(f(x,g(x)),f(y,g(f(g(y),z)))),f(g(f(x,y)),x))=g(f(f(z,y),f(f(g(f(x,y)),x),f(g(f(u,f(g(f(v,u)),v))),f(g(f(x,y)),x))))). 3812 [] g(f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z)))))=f(f(f(z,g(z)),f(y,f(g(x),y))),f(g(f(z,y)),z)). 3813 [] g(f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z)))))=f(f(y,f(g(x),y)),f(g(f(z,y)),z)). 3814 [] g(f(f(x,y),f(f(g(f(z,y)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,y)),z)))))=f(f(y,f(g(x),y)),g(y)). 3815 [] g(f(f(x,y),f(g(y),f(g(f(z,f(g(f(u,z)),u))),f(g(f(v,y)),v)))))=f(f(y,f(g(x),y)),g(y)). 3816 [] g(f(f(x,y),f(g(y),f(g(f(z,g(z))),f(g(f(u,y)),u)))))=f(f(y,f(g(x),y)),g(y)). 3817 [] g(f(f(x,y),f(g(y),f(g(f(z,g(z))),g(y)))))=f(f(y,f(g(x),y)),g(y)). 3818 [] g(f(f(x,y),f(g(y),g(y))))=f(f(y,f(g(x),y)),g(y)). 3819 [] g(f(x,g(y)))=f(f(y,f(g(x),y)),g(y)). 3820 [] f(g(x),f(f(f(y,f(g(f(y,y)),y)),f(x,z)),f(g(f(y,x)),y)))=f(f(z,x),f(f(g(f(y,x)),y),f(g(f(u,f(g(f(v,u)),v))),f(g(f(y,x)),y)))). 3821 [] f(g(x),f(f(f(y,g(y)),f(x,z)),f(g(f(y,x)),y)))=f(f(z,x),f(f(g(f(y,x)),y),f(g(f(u,f(g(f(v,u)),v))),f(g(f(y,x)),y)))). 3822 [] f(g(x),f(f(x,y),f(g(f(z,x)),z)))=f(f(y,x),f(f(g(f(z,x)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,x)),z)))). 3823 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(f(g(f(z,x)),z),f(g(f(u,f(g(f(v,u)),v))),f(g(f(z,x)),z)))). 3824 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),f(g(f(z,f(g(f(u,z)),u))),f(g(f(v,x)),v)))). 3825 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),f(g(f(z,g(z))),f(g(f(u,x)),u)))). 3826 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),f(f(f(z,f(g(z),z)),g(z)),f(g(f(u,x)),u)))). 3827 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),f(f(z,g(z)),f(g(f(u,x)),u)))). 3828 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),f(f(z,g(z)),g(x)))). 3829 [] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),g(x))). 3830 [] f(g(x),f(f(x,y),g(x)))=f(y,g(x)). 3831 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,f(g(u),v))),z)))),x))=f(f(g(f(v,x)),u),g(f(f(g(f(v,x)),u),f(f(w,f(g(f(v6,w)),v6)),f(g(f(v,x)),u))))). 3832 [] f(x,f(f(y,f(g(f(x,y)),g(g(f(g(z),u))))),x))=f(f(g(f(u,x)),z),g(f(f(g(f(u,x)),z),f(f(v,f(g(f(w,v)),w)),f(g(f(u,x)),z))))). 3833 [] f(x,f(f(y,f(g(f(x,y)),g(f(g(z),u)))),x))=f(f(g(f(z,x)),u),g(f(f(g(f(z,x)),u),f(f(v,f(g(f(w,v)),w)),f(g(f(z,x)),u))))). 3834 [] f(x,f(f(y,f(g(f(x,y)),f(g(z),u))),x))=f(f(g(f(u,x)),z),g(f(f(g(f(u,x)),z),f(f(v,f(g(f(w,v)),w)),f(g(f(u,x)),z))))). 3835 [] f(f(g(f(x,y)),z),g(f(f(g(f(x,y)),z),f(f(u,f(g(f(v,u)),v)),f(g(f(x,y)),z)))))=f(y,f(f(g(y),f(g(z),x)),y)). 3836 [] f(f(g(f(x,y)),z),g(f(f(g(f(x,y)),z),f(f(u,f(g(f(v,u)),v)),f(g(f(x,y)),z)))))=f(f(g(z),x),y). 3837 [] f(f(g(f(x,y)),z),g(f(f(g(f(x,y)),z),f(f(u,g(u)),f(g(f(x,y)),z)))))=f(f(g(z),x),y). 3838 [] f(f(g(f(x,y)),z),g(f(f(g(f(x,y)),z),f(g(f(x,y)),z))))=f(f(g(z),x),y). 3839 [] g(f(g(f(x,y)),z))=f(f(g(z),x),y). 3840 [] f(f(g(x),y),z)=f(g(x),f(y,z)). 3841 [] f(f(g(f(x,g(x))),y),g(f(f(g(f(z,f(g(f(u,z)),u))),y),f(f(f(z,f(g(f(y,z)),z)),v),f(g(f(z,f(g(f(u,z)),u))),y)))))=f(f(g(f(u,z)),u),f(f(f(u,f(g(f(u,u)),u)),f(z,g(v))),f(g(f(u,z)),u))). 3842 [] f(f(f(f(x,f(g(x),x)),g(x)),y),g(f(f(g(f(z,f(g(f(u,z)),u))),y),f(f(f(z,f(g(f(y,z)),z)),v),f(g(f(z,f(g(f(u,z)),u))),y)))))=f(f(g(f(u,z)),u),f(f(f(u,f(g(f(u,u)),u)),f(z,g(v))),f(g(f(u,z)),u))). 3843 [] f(f(f(x,g(x)),y),g(f(f(g(f(z,f(g(f(u,z)),u))),y),f(f(f(z,f(g(f(y,z)),z)),v),f(g(f(z,f(g(f(u,z)),u))),y)))))=f(f(g(f(u,z)),u),f(f(f(u,f(g(f(u,u)),u)),f(z,g(v))),f(g(f(u,z)),u))). 3844 [] f(x,g(f(f(g(f(y,f(g(f(z,y)),z))),x),f(f(f(y,f(g(f(x,y)),y)),u),f(g(f(y,f(g(f(z,y)),z))),x)))))=f(f(g(f(z,y)),z),f(f(f(z,f(g(f(z,z)),z)),f(y,g(u))),f(g(f(z,y)),z))). 3845 [] f(x,g(f(f(g(f(y,g(y))),x),f(f(f(y,f(g(f(x,y)),y)),z),f(g(f(y,f(g(f(u,y)),u))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3846 [] f(x,g(f(f(f(f(y,f(g(y),y)),g(y)),x),f(f(f(y,f(g(f(x,y)),y)),z),f(g(f(y,f(g(f(u,y)),u))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3847 [] f(x,g(f(f(f(y,g(y)),x),f(f(f(y,f(g(f(x,y)),y)),z),f(g(f(y,f(g(f(u,y)),u))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3848 [] f(x,g(f(x,f(f(f(y,f(g(f(x,y)),y)),z),f(g(f(y,f(g(f(u,y)),u))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3849 [] f(x,g(f(x,f(f(f(g(x),y),z),f(g(f(y,f(g(f(u,y)),u))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3850 [] f(x,g(f(x,f(f(g(x),f(y,z)),f(g(f(y,f(g(f(u,y)),u))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3851 [] f(x,g(f(x,f(f(g(x),f(y,z)),f(g(f(y,g(y))),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3852 [] f(x,g(f(x,f(f(g(x),f(y,z)),f(f(f(y,f(g(y),y)),g(y)),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3853 [] f(x,g(f(x,f(f(g(x),f(y,z)),f(f(y,g(y)),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3854 [] f(x,g(f(x,f(f(g(x),f(y,z)),x))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3855 [] f(x,g(f(x,f(g(x),f(f(y,z),x)))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3856 [] f(x,g(f(f(y,z),x)))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). 3857 [] g(f(x,y))=f(f(g(f(z,x)),z),f(f(f(z,f(g(f(z,z)),z)),f(x,g(y))),f(g(f(z,x)),z))). 3858 [] g(f(x,y))=f(g(x),f(f(f(z,f(g(f(z,z)),z)),f(x,g(y))),f(g(f(z,x)),z))). 3859 [] g(f(x,y))=f(g(x),f(f(f(z,g(z)),f(x,g(y))),f(g(f(z,x)),z))). 3860 [] g(f(x,y))=f(g(x),f(f(x,g(y)),f(g(f(z,x)),z))). 3861 [] g(f(x,y))=f(g(x),f(f(x,g(y)),g(x))). 3862 [] g(f(x,y))=f(g(y),g(x)). 3863 [] f(x,f(y,f(f(g(y),g(z)),z)))=f(g(f(u,f(f(v,f(g(f(v,v)),v)),f(g(f(w,x)),w)))),u). 3864 [] f(x,f(y,f(g(y),f(g(z),z))))=f(g(f(u,f(f(v,f(g(f(v,v)),v)),f(g(f(w,x)),w)))),u). 3865 [] f(x,f(y,g(y)))=f(g(f(z,f(f(u,f(g(f(u,u)),u)),f(g(f(v,x)),v)))),z). 3866 [] f(g(f(x,f(f(y,f(g(f(y,y)),y)),f(g(f(z,u)),z)))),x)=u. 3867 [] f(g(f(x,f(f(y,f(f(g(y),g(y)),y)),f(g(f(z,u)),z)))),x)=u. 3868 [] f(g(f(x,f(f(y,f(g(y),f(g(y),y))),f(g(f(z,u)),z)))),x)=u. 3869 [] f(g(f(x,f(f(y,g(y)),f(g(f(z,u)),z)))),x)=u. 3870 [] f(g(f(x,f(f(y,g(y)),f(f(g(z),g(u)),u)))),x)=z. 3871 [] f(g(f(x,f(f(y,g(y)),f(g(z),f(g(u),u))))),x)=z. 3872 [] f(f(g(g(x)),g(y)),y)=x. 3873 [] f(f(x,g(y)),y)=x. 3874 [] f(x,f(y,f(f(g(y),g(z)),u)))=f(f(g(f(v,w)),v),f(f(v6,f(g(f(v7,v6)),v7)),f(g(f(z,g(f(w,x)))),u))). 3875 [] f(x,f(y,f(g(y),f(g(z),u))))=f(f(g(f(v,w)),v),f(f(v6,f(g(f(v7,v6)),v7)),f(g(f(z,g(f(w,x)))),u))). 3876 [] f(f(g(f(x,y)),x),f(f(z,f(g(f(u,z)),u)),f(g(f(v,g(f(y,w)))),v6)))=f(w,f(g(v),v6)). 3877 [] f(f(f(g(x),g(y)),y),f(f(z,f(g(f(u,z)),u)),f(g(f(v,g(f(x,w)))),v6)))=f(w,f(g(v),v6)). 3878 [] f(g(x),f(f(y,f(g(f(z,y)),z)),f(g(f(u,g(f(x,v)))),w)))=f(v,f(g(u),w)). 3879 [] f(g(x),f(f(y,f(f(g(y),g(z)),z)),f(g(f(u,g(f(x,v)))),w)))=f(v,f(g(u),w)). 3880 [] f(g(x),f(f(y,g(y)),f(g(f(z,g(f(x,u)))),v)))=f(u,f(g(z),v)). 3881 [] f(g(x),f(f(y,g(y)),f(g(f(z,f(g(u),g(x)))),v)))=f(u,f(g(z),v)). 3882 [] f(g(x),f(f(y,g(y)),f(f(g(f(g(z),g(x))),g(u)),v)))=f(z,f(g(u),v)). 3883 [] f(g(x),f(f(y,g(y)),f(f(f(g(g(x)),g(g(z))),g(u)),v)))=f(z,f(g(u),v)). 3884 [] f(g(x),f(f(y,g(y)),f(f(f(x,g(g(z))),g(u)),v)))=f(z,f(g(u),v)). 3885 [] f(g(x),f(f(y,g(y)),f(f(f(x,z),g(u)),v)))=f(z,f(g(u),v)). 3886 [] f(g(x),f(f(f(x,y),g(z)),u))=f(y,f(g(z),u)). 3887 [] f(x,f(g(f(f(f(f(g(y),g(z)),z),f(f(u,f(g(f(v,u)),v)),w)),x)),g(f(f(v6,f(g(f(y,v6)),w)),g(f(f(v7,f(g(f(y,v7)),w)),v8))))))=f(g(f(w,g(v8))),y). 3888 [] f(x,f(g(f(f(g(y),f(f(z,f(g(f(u,z)),u)),v)),x)),g(f(f(w,f(g(f(y,w)),v)),g(f(f(v6,f(g(f(y,v6)),v)),v7))))))=f(g(f(v,g(v7))),y). 3889 [] f(x,f(g(f(f(g(y),f(f(z,f(f(g(z),g(u)),u)),v)),x)),g(f(f(w,f(g(f(y,w)),v)),g(f(f(v6,f(g(f(y,v6)),v)),v7))))))=f(g(f(v,g(v7))),y). 3890 [] f(x,f(g(f(f(g(y),f(f(z,g(z)),u)),x)),g(f(f(v,f(g(f(y,v)),u)),g(f(f(w,f(g(f(y,w)),u)),v6))))))=f(g(f(u,g(v6))),y). 3891 [] f(x,f(g(f(f(g(y),z),x)),g(f(f(u,f(g(f(y,u)),z)),g(f(f(v,f(g(f(y,v)),z)),w))))))=f(g(f(z,g(w))),y). 3892 [] f(x,f(g(f(g(y),f(z,x))),g(f(f(u,f(g(f(y,u)),z)),g(f(f(v,f(g(f(y,v)),z)),w))))))=f(g(f(z,g(w))),y). 3893 [] f(x,f(f(g(f(y,x)),g(g(z))),g(f(f(u,f(g(f(z,u)),y)),g(f(f(v,f(g(f(z,v)),y)),w))))))=f(g(f(y,g(w))),z). 3894 [] f(x,f(f(f(g(x),g(y)),g(g(z))),g(f(f(u,f(g(f(z,u)),y)),g(f(f(v,f(g(f(z,v)),y)),w))))))=f(g(f(y,g(w))),z). 3895 [] f(x,f(f(f(g(x),g(y)),z),g(f(f(u,f(g(f(z,u)),y)),g(f(f(v,f(g(f(z,v)),y)),w))))))=f(g(f(y,g(w))),z). 3896 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(u,f(g(f(z,u)),y)),g(f(f(v,f(g(f(z,v)),y)),w))))))=f(g(f(y,g(w))),z). 3897 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(u,f(f(g(u),g(z)),y)),g(f(f(v,f(g(f(z,v)),y)),w))))))=f(g(f(y,g(w))),z). 3898 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(u,f(g(u),f(g(z),y))),g(f(f(v,f(g(f(z,v)),y)),w))))))=f(g(f(y,g(w))),z). 3899 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),g(f(f(u,f(g(f(z,u)),y)),v))))))=f(g(f(y,g(v))),z). 3900 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),g(f(f(u,f(f(g(u),g(z)),y)),v))))))=f(g(f(y,g(v))),z). 3901 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),g(f(f(u,f(g(u),f(g(z),y))),v))))))=f(g(f(y,g(v))),z). 3902 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),g(f(f(g(z),y),u))))))=f(g(f(y,g(u))),z). 3903 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),g(f(g(z),f(y,u)))))))=f(g(f(y,g(u))),z). 3904 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),f(g(f(y,u)),g(g(z)))))))=f(g(f(y,g(u))),z). 3905 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),f(f(g(u),g(y)),g(g(z)))))))=f(g(f(y,g(u))),z). 3906 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),f(f(g(u),g(y)),z)))))=f(g(f(y,g(u))),z). 3907 [] f(x,f(f(g(x),f(g(y),z)),g(f(f(g(z),y),f(g(u),f(g(y),z))))))=f(g(f(y,g(u))),z). 3908 [] f(x,f(f(g(x),f(g(y),z)),g(f(g(z),f(y,f(g(u),f(g(y),z)))))))=f(g(f(y,g(u))),z). 3909 [] f(x,f(f(g(x),f(g(y),z)),f(g(f(y,f(g(u),f(g(y),z)))),g(g(z)))))=f(g(f(y,g(u))),z). 3910 [] f(x,f(f(g(x),f(g(y),z)),f(f(g(f(g(u),f(g(y),z))),g(y)),g(g(z)))))=f(g(f(y,g(u))),z). 3911 [] f(x,f(f(g(x),f(g(y),z)),f(f(f(g(f(g(y),z)),g(g(u))),g(y)),g(g(z)))))=f(g(f(y,g(u))),z). 3912 [] f(x,f(f(g(x),f(g(y),z)),f(f(f(f(g(z),g(g(y))),g(g(u))),g(y)),g(g(z)))))=f(g(f(y,g(u))),z). 3913 [] f(x,f(f(g(x),f(g(y),z)),f(f(f(f(g(z),y),g(g(u))),g(y)),g(g(z)))))=f(g(f(y,g(u))),z). 3914 [] f(x,f(f(g(x),f(g(y),z)),f(f(f(f(g(z),y),u),g(y)),g(g(z)))))=f(g(f(y,g(u))),z). 3915 [] f(x,f(f(g(x),f(g(y),z)),f(f(f(g(z),f(y,u)),g(y)),g(g(z)))))=f(g(f(y,g(u))),z). 3916 [] f(x,f(f(g(x),f(g(y),z)),f(f(g(z),f(f(y,u),g(y))),g(g(z)))))=f(g(f(y,g(u))),z). 3917 [] f(x,f(f(g(x),f(g(y),z)),f(f(g(z),f(f(y,u),g(y))),z)))=f(g(f(y,g(u))),z). 3918 [] f(x,f(f(g(x),f(g(y),z)),f(g(z),f(f(f(y,u),g(y)),z))))=f(g(f(y,g(u))),z). 3919 [] f(x,f(g(x),f(f(g(y),z),f(g(z),f(f(f(y,u),g(y)),z)))))=f(g(f(y,g(u))),z). 3920 [] f(x,f(g(x),f(g(y),f(f(f(y,z),g(y)),u))))=f(g(f(y,g(z))),u). 3921 [] f(x,f(g(x),f(y,f(g(z),u))))=f(g(f(z,g(y))),u). 3922 [] f(g(f(x,g(y))),z)=f(y,f(g(x),z)). 3923 [] f(f(g(g(x)),g(y)),z)=f(x,f(g(y),z)). 3924 [] f(f(x,g(y)),z)=f(x,f(g(y),z)). 3925 [] f(g(f(f(f(g(x),g(x)),x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(f(v,g(f(v,f(x,v)))))). 3926 [] f(g(f(g(x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(f(v,g(f(v,f(x,v)))))). 3927 [] f(g(f(g(x),f(g(f(f(g(f(y,f(f(g(y),g(z)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(f(v,g(f(v,f(x,v)))))). 3928 [] f(g(f(g(x),f(g(f(f(g(f(y,g(y))),z),u)),g(f(z,f(g(f(v,z)),v)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(v,z)),v)),g(f(u,g(f(u,f(x,u)))))). 3929 [] f(g(f(g(x),f(g(f(f(f(g(g(y)),g(y)),z),u)),g(f(z,f(g(f(v,z)),v)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(v,z)),v)),g(f(u,g(f(u,f(x,u)))))). 3930 [] f(g(f(g(x),f(g(f(f(f(y,g(y)),z),u)),g(f(z,f(g(f(v,z)),v)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(v,z)),v)),g(f(u,g(f(u,f(x,u)))))). 3931 [] f(g(f(g(x),f(g(f(y,z)),g(f(y,f(g(f(u,y)),u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,y)),u)),g(f(z,g(f(z,f(x,z)))))). 3932 [] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,f(g(f(u,z)),u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(f(y,g(f(y,f(x,y)))))). 3933 [] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,f(f(g(z),g(u)),u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(f(y,g(f(y,f(x,y)))))). 3934 [] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,g(z)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(f(y,g(f(y,f(x,y)))))). 3935 [] f(g(f(g(x),f(f(g(y),g(z)),f(g(g(z)),g(z))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(f(y,g(f(y,f(x,y)))))). 3936 [] f(g(f(g(x),f(f(g(y),g(z)),f(z,g(z))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(f(y,g(f(y,f(x,y)))))). 3937 [] f(g(f(g(x),f(g(y),g(z)))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(f(y,g(f(y,f(x,y)))))). 3938 [] f(f(g(f(g(x),g(y))),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,y)),u)),g(f(x,g(f(x,f(z,x)))))). 3939 [] f(f(f(g(g(x)),g(g(y))),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3940 [] f(f(f(x,g(g(y))),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3941 [] f(f(f(x,y),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3942 [] f(f(f(x,y),z),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3943 [] f(f(f(x,y),z),g(f(f(f(g(z),g(z)),z),z)))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3944 [] f(f(f(x,y),z),g(f(g(z),z)))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3945 [] f(f(f(x,y),z),f(g(z),g(g(z))))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3946 [] f(f(f(x,y),z),f(g(z),z))=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3947 [] f(f(x,y),z)=f(g(f(g(f(u,x)),u)),g(f(y,g(f(y,f(z,y)))))). 3948 [] f(f(x,y),z)=f(g(f(f(g(x),g(u)),u)),g(f(y,g(f(y,f(z,y)))))). 3949 [] f(f(x,y),z)=f(g(g(x)),g(f(y,g(f(y,f(z,y)))))). 3950 [] f(f(x,y),z)=f(x,g(f(y,g(f(y,f(z,y)))))). 3951 [] f(f(x,y),z)=f(x,g(f(y,f(g(f(z,y)),g(y))))). 3952 [] f(f(x,y),z)=f(x,g(f(y,f(f(g(y),g(z)),g(y))))). 3953 [] f(f(x,y),z)=f(x,g(f(y,f(g(y),f(g(z),g(y)))))). 3954 [] f(f(x,y),z)=f(x,g(f(g(z),g(y)))). 3955 [] f(f(x,y),z)=f(x,f(g(g(y)),g(g(z)))). 3956 [] f(f(x,y),z)=f(x,f(y,g(g(z)))). 3957 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. list(hints2). 3958 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. 3959 [] f(x,g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))))=z. 3960 [] f(f(a,b),c)!=f(a,f(b,c)). 3961 [] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))),f(g(z),g(u))),x))))=u. 3962 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). 3963 [] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 3964 [] f(x,g(f(x,f(f(y,z),x))))=f(u,f(f(g(u),g(f(x,y))),f(g(f(z,g(f(x,y)))),g(f(x,y))))). 3965 [] f(x,g(f(x,f(f(g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))),f(g(z),g(u))),x))))=u. 3966 [] f(g(x),f(f(y,f(g(f(g(f(z,g(f(u,f(f(g(u),z),f(g(f(x,z)),z)))))),y)),g(v))),g(f(z,g(f(u,f(f(g(u),z),f(g(f(x,z)),z))))))))=f(z,g(f(z,f(f(g(f(u,f(f(g(u),z),f(g(f(x,z)),z)))),v),z)))). 3967 [] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(f(u,g(f(v,f(f(g(v),u),f(g(f(x,u)),u))))))))=f(u,g(f(u,f(f(g(f(v,f(f(g(v),u),f(g(f(x,u)),u)))),z),u)))). 3968 [] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(x)))=f(u,g(f(u,f(f(g(f(v,f(f(g(v),u),f(g(f(x,u)),u)))),z),u)))). 3969 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))). 3970 [] f(g(f(x,y)),f(f(g(f(z,f(f(g(z),g(f(x,y))),f(g(f(u,g(f(x,y)))),g(f(x,y)))))),f(g(u),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))). 3971 [] f(x,g(f(x,f(f(g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))),u),x))))=f(g(z),f(f(v,f(g(f(g(z),v)),g(u))),g(z))). 3972 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(f(f(u,f(g(f(g(f(x,y)),u)),g(v))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,v),x))))),g(z))),g(f(x,y)))). 3973 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y)))))),f(g(v),g(z))),g(f(x,y)))). 3974 [] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 3975 [] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 3976 [] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=g(f(u,f(f(g(u),y),f(g(f(z,y)),y)))). 3977 [] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=g(f(y,f(f(u,f(g(f(y,u)),g(z))),y))). 3978 [] g(f(x,g(f(x,f(f(y,z),x)))))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(u,f(z,u)))))). 3979 [] g(f(x,f(f(g(x),y),f(g(f(z,y)),y))))=f(g(f(u,y)),g(f(u,g(f(u,f(z,u)))))). 3980 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=g(f(u,g(f(u,f(f(g(f(u,f(f(g(f(u,f(f(v,f(g(f(u,v)),g(w))),u))),f(g(w),g(y))),u))),z),u))))). 3981 [] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(z),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). 3982 [] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 3983 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=f(g(f(g(u),g(y))),g(f(g(f(v,g(f(v,f(f(w,f(g(f(v,w)),g(u))),v))))),g(f(g(f(v,g(f(v,f(f(w,f(g(f(v,w)),g(u))),v))))),f(z,g(f(v,g(f(v,f(f(w,f(g(f(v,w)),g(u))),v))))))))))). 3984 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=f(g(f(g(u),g(y))),g(f(g(u),g(f(g(f(v,g(f(v,f(f(w,f(g(f(v,w)),g(u))),v))))),f(z,g(f(v,g(f(v,f(f(w,f(g(f(v,w)),g(u))),v))))))))))). 3985 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=f(g(f(g(u),g(y))),g(f(g(u),g(f(g(u),f(z,g(f(v,g(f(v,f(f(w,f(g(f(v,w)),g(u))),v))))))))))). 3986 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=f(g(f(g(u),g(y))),g(f(g(u),g(f(g(u),f(z,g(u))))))). 3987 [] f(g(f(g(x),g(y))),g(f(g(x),g(f(g(x),f(z,g(x)))))))=f(g(f(u,g(y))),g(f(u,g(f(u,f(z,u)))))). 3988 [] g(f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),z)),x),u),x)))))=f(z,g(f(x,g(f(x,f(u,x)))))). 3989 [] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),v)),z))))))),x))),f(v,g(w))),x))))=w. 3990 [] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(u))),x))))=u. 3991 [] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 3992 [] f(g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))),f(f(u,f(g(f(g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x))))),u)),g(f(z,g(v))))),g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))))=v. 3993 [] f(x,f(f(y,f(g(f(g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z))))),y)),g(f(x,g(v))))),g(f(z,g(f(z,f(f(u,f(g(f(z,u)),x)),z)))))))=v. 3994 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),x)),u)))))))=z. 3995 [] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 3996 [] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,u)))),x)))=u. 3997 [] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(u,f(g(f(x,u)),g(f(x,z)))),x). 3998 [] f(x,g(f(y,g(f(y,f(f(f(f(z,f(g(f(y,z)),g(f(y,x)))),y),u),y))))))=u. 3999 [] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 4000 [] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,z)))),x),f(z,g(u))),x))))=u. 4001 [] f(x,f(f(y,f(g(f(x,y)),g(z))),x))=f(u,f(f(g(u),x),f(g(f(z,x)),x))). 4002 [] f(x,f(f(g(x),y),f(g(f(z,y)),y)))=f(y,f(f(u,f(g(f(y,u)),g(z))),y)). 4003 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(u,y)))))))=u. 4004 [] f(x,f(g(f(g(f(y,g(f(y,f(f(z,u),y))))),x)),g(f(g(f(y,g(f(y,f(f(z,u),y))))),g(f(g(f(y,g(f(y,f(f(z,u),y))))),u))))))=g(f(y,z)). 4005 [] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 4006 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,u))=f(v,f(g(f(y,v)),u)). 4007 [] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u))=f(v,f(g(f(x,v)),u)). 4008 [] f(x,f(y,f(g(f(z,y)),u)))=f(v,f(g(f(w,v)),f(g(f(z,g(f(w,x)))),u))). 4009 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z))))))))=f(u,v). 4010 [] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),v)))=f(u,f(w,f(g(f(z,w)),v))). 4011 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). 4012 [] f(x,f(g(f(g(f(y,g(f(z,f(g(f(u,z)),y))))),x)),g(f(g(f(y,g(f(z,f(g(f(u,z)),y))))),g(g(f(u,y)))))))=g(f(y,g(f(y,g(f(z,f(g(f(u,z)),y))))))). 4013 [] g(f(x,g(f(x,f(g(f(y,x)),x)))))=g(f(x,g(f(z,f(g(f(y,z)),x))))). 4014 [] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))). 4015 [] g(f(x,g(f(y,f(g(f(z,y)),x)))))=g(f(x,g(f(u,f(g(f(z,u)),x))))). 4016 [] f(g(f(x,g(f(y,g(f(z,f(g(f(u,z)),y))))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),v),y))))). 4017 [] f(x,g(f(x,f(f(g(f(y,f(g(f(z,y)),x))),f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(v))),x))))=v. 4018 [] f(g(f(x,f(f(g(f(y,f(g(f(z,y)),x))),f(g(f(x,g(f(u,f(g(f(z,u)),x))))),v)),x))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4019 [] f(x,f(f(g(x),g(f(y,g(f(y,f(f(z,f(g(f(y,z)),u)),y)))))),f(g(f(f(u,g(v)),g(f(y,g(f(y,f(f(z,f(g(f(y,z)),u)),y))))))),g(f(y,g(f(y,f(f(z,f(g(f(y,z)),u)),y))))))))=v. 4020 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u))))))),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u))))))))=z. 4021 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),y)),g(f(u,g(f(u,f(f(v,f(g(f(u,v)),y)),u))))))))=z. 4022 [] f(x,f(f(g(x),y),f(g(f(f(y,g(z)),y)),y)))=z. 4023 [] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u)),x)))=g(f(x,f(f(v,f(g(f(x,v)),u)),x))). 4024 [] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),u),x)))=f(f(g(x),z),f(g(f(u,z)),z)). 4025 [] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),x)),x))),z),x)))=f(f(u,f(g(f(x,u)),g(z))),x). 4026 [] f(f(g(x),x),f(g(f(y,x)),x))=f(f(z,f(g(f(x,z)),g(y))),x). 4027 [] f(f(g(x),y),f(g(f(f(y,z),y)),y))=g(f(x,f(f(u,f(g(f(x,u)),z)),x))). 4028 [] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(g(x),u),f(g(f(f(u,z),u)),u)). 4029 [] f(f(g(x),y),f(g(f(f(y,g(f(x,z))),y)),y))=z. 4030 [] f(f(x,f(g(f(y,x)),g(z))),y)=f(f(g(y),y),f(g(f(z,y)),y)). 4031 [] f(f(g(f(g(x),y)),z),f(g(f(f(z,g(u)),z)),z))=f(g(f(f(y,g(f(x,u))),y)),y). 4032 [] g(f(f(g(x),y),f(f(z,f(g(f(f(g(x),y),z)),g(u))),f(g(x),y))))=f(g(f(f(y,g(f(x,u))),y)),y). 4033 [] f(g(f(f(x,g(f(y,z))),x)),x)=g(f(f(g(y),x),f(f(u,f(g(f(f(g(y),x),u)),g(z))),f(g(y),x)))). 4034 [] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 4035 [] f(x,g(f(x,f(f(g(f(y,f(f(g(y),x),f(g(f(f(z,u),x)),x)))),v),x))))=f(z,g(f(z,f(f(u,v),z)))). 4036 [] f(f(x,f(g(f(y,x)),g(f(z,f(g(f(y,z)),g(f(y,g(f(y,u))))))))),y)=f(f(g(y),y),f(g(u),y)). 4037 [] f(x,f(f(g(x),y),f(g(z),y)))=f(y,f(f(u,f(g(f(y,u)),g(f(v,f(g(f(y,v)),g(f(y,g(f(y,z))))))))),y)). 4038 [] f(x,f(f(g(x),y),f(g(z),y)))=f(y,f(f(g(y),y),f(g(z),y))). 4039 [] f(x,f(f(g(x),x),f(g(y),x)))=f(z,f(f(g(z),x),f(g(y),x))). 4040 [] f(f(g(x),y),f(g(f(f(y,f(f(z,f(g(f(g(f(x,u)),z)),g(f(g(f(x,u)),g(v))))),g(f(x,u)))),y)),y))=g(f(x,f(f(u,v),x))). 4041 [] g(f(x,f(f(y,f(z,g(f(z,f(f(g(f(u,f(f(g(u),z),f(g(f(f(x,y),z)),z)))),v),z))))),x)))=f(f(g(x),w),f(g(f(f(w,f(f(v6,f(g(f(g(f(x,y)),v6)),g(v))),g(f(x,y)))),w)),w)). 4042 [] g(f(x,f(f(y,f(x,g(f(x,f(f(y,z),x))))),x)))=f(f(g(x),u),f(g(f(f(u,f(f(v,f(g(f(g(f(x,y)),v)),g(z))),g(f(x,y)))),u)),u)). 4043 [] f(f(g(x),y),f(g(f(f(y,f(f(z,f(g(f(g(f(x,u)),z)),g(v))),g(f(x,u)))),y)),y))=g(f(x,f(f(u,f(x,g(f(x,f(f(u,v),x))))),x))). 4044 [] g(f(x,f(f(g(x),y),f(g(f(f(y,z),y)),y))))=z. 4045 [] g(f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z)))))=f(g(f(f(z,g(f(y,u))),z)),z). 4046 [] g(f(x,f(f(g(x),y),f(g(f(z,y)),y))))=g(f(u,f(f(g(u),y),f(g(f(z,y)),y)))). 4047 [] f(g(f(f(x,g(f(y,z))),x)),x)=g(f(u,f(f(g(u),f(g(y),x)),f(g(f(z,f(g(y),x))),f(g(y),x))))). 4048 [] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). 4049 [] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(u,v),y),w). 4050 [] f(f(f(x,y),z),f(u,f(g(f(z,u)),v)))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(f(v6,g(f(v6,f(y,v6)))))),v))). 4051 [] f(g(f(f(x,g(f(y,f(f(g(y),x),z)))),x)),x)=z. 4052 [] f(x,f(f(g(x),y),z))=f(u,f(f(g(u),y),z)). 4053 [] f(x,f(g(f(f(y,g(f(z,f(f(g(z),y),u)))),x)),y))=f(y,u). 4054 [] f(x,f(g(f(f(y,g(f(f(f(y,g(f(z,f(f(g(z),y),x)))),y),u))),y)),y))=u. 4055 [] f(x,f(f(g(x),f(g(f(y,g(z))),g(f(y,g(f(y,f(u,y))))))),v))=f(z,f(u,v)). 4056 [] f(x,f(f(g(x),g(f(y,g(f(y,f(f(z,u),y)))))),v))=f(f(y,z),f(u,v)). 4057 [] f(x,f(f(g(x),y),g(f(f(g(z),y),f(f(u,f(g(f(f(g(z),y),u)),g(v))),f(g(z),y))))))=f(z,v). 4058 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(y,g(z))))),y))=z. 4059 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(f(g(z),u),y)))))))=f(g(y),u). 4060 [] g(f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),z)),x)))))=z. 4061 [] g(f(x,g(f(f(f(g(y),z),u),f(g(f(v,f(f(g(v),z),u))),x)))))=g(f(x,g(f(w,f(g(f(y,w)),x))))). 4062 [] f(g(f(x,g(x))),g(f(x,g(f(y,f(f(g(y),z),x))))))=z. 4063 [] f(x,g(f(y,f(f(g(y),f(g(f(x,g(x))),g(z))),x))))=z. 4064 [] f(g(f(x,g(x))),g(f(x,g(f(y,z)))))=f(g(f(x,g(y))),g(f(x,g(f(x,z))))). 4065 [] f(x,f(g(f(g(f(y,g(f(z,f(f(g(z),u),y))))),x)),g(f(g(f(y,g(f(z,f(f(g(z),u),y))))),g(f(g(f(y,g(f(z,f(f(g(z),u),y))))),u))))))=g(f(y,g(y))). 4066 [] f(f(x,g(f(y,f(g(f(z,y)),x)))),g(f(u,f(f(g(u),f(g(f(f(x,g(f(y,f(g(f(z,y)),x)))),g(f(x,g(f(v,f(g(f(z,v)),x))))))),g(w))),f(x,g(f(y,f(g(f(z,y)),x))))))))=w. 4067 [] f(f(g(x),y),f(g(f(z,y)),y))=f(f(g(x),f(g(f(y,g(y))),g(z))),y). 4068 [] g(f(x,f(f(y,z),x)))=f(f(g(x),f(g(f(g(f(x,y)),g(g(f(x,y))))),g(z))),g(f(x,y))). 4069 [] f(f(g(x),f(g(f(y,g(y))),g(z))),y)=f(f(g(x),y),f(g(f(z,y)),y)). 4070 [] f(f(g(x),f(g(f(g(f(x,y)),g(g(f(x,y))))),g(z))),g(f(x,y)))=g(f(x,f(f(y,z),x))). 4071 [] f(x,f(g(f(f(y,g(f(z,f(f(g(z),y),g(f(u,f(g(f(v,u)),f(g(z),y)))))))),x)),y))=f(y,g(f(f(g(z),y),f(g(f(v,f(g(z),y))),f(g(z),y))))). 4072 [] f(x,g(f(y,f(g(f(z,y)),f(g(u),x)))))=f(x,g(f(f(g(u),x),f(g(f(z,f(g(u),x))),f(g(u),x))))). 4073 [] f(x,g(f(f(g(y),x),f(g(f(z,f(g(y),x))),f(g(y),x)))))=f(x,g(f(u,f(g(f(z,u)),f(g(y),x))))). 4074 [] f(g(f(x,f(g(f(y,x)),z))),f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(f(z,g(f(v,f(f(g(v),w),z)))))))=f(g(z),w). 4075 [] f(f(x,f(g(f(y,g(y))),g(z))),y)=f(f(g(f(u,g(f(v,f(f(g(v),f(g(f(u,g(u))),x)),u))))),y),f(g(f(z,y)),y)). 4076 [] f(f(x,f(g(f(y,g(y))),g(z))),y)=f(f(x,y),f(g(f(z,y)),y)). 4077 [] f(f(x,y),f(g(f(z,y)),y))=f(f(x,f(g(f(y,g(y))),g(z))),y). 4078 [] f(f(x,y),z)=f(f(x,z),f(g(f(f(z,g(f(u,f(f(g(u),y),z)))),z)),z)). 4079 [] f(f(x,y),f(g(f(f(y,g(f(z,f(f(g(z),u),y)))),y)),y))=f(f(x,u),y). 4080 [] f(f(g(x),f(g(f(y,g(y))),g(f(y,g(f(x,z)))))),y)=z. 4081 [] f(f(g(x),f(g(f(y,g(y))),g(f(y,g(f(z,f(f(u,f(g(f(z,u)),g(v))),z))))))),y)=f(f(g(x),z),f(g(f(v,z)),z)). 4082 [] f(f(g(x),f(g(f(g(f(x,g(x))),g(g(f(x,g(x)))))),g(y))),g(f(x,g(x))))=g(f(z,f(f(g(z),y),x))). 4083 [] f(f(g(x),f(g(f(y,g(y))),g(f(y,g(f(g(z),f(f(u,f(g(f(g(z),u)),g(v))),g(z)))))))),y)=g(f(x,f(f(g(f(w,f(f(g(w),x),f(g(f(z,x)),x)))),v),x))). 4084 [] g(f(x,f(f(g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))),u),x)))=f(f(g(x),g(z)),f(g(f(u,g(z))),g(z))). 4085 [] f(f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u),x)=f(f(z,u),x). 4086 [] f(f(x,f(f(g(x),y),z)),u)=f(f(v,f(f(g(g(f(f(u,g(f(w,f(f(g(w),u),f(v,u))))),u))),y),z)),u). 4087 [] f(f(x,f(f(g(g(f(f(y,g(f(z,f(f(g(z),y),f(x,y))))),y))),u),v)),y)=f(f(w,f(f(g(w),u),v)),y). 4088 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(f(u,v),y)))))))=f(g(f(f(y,g(f(w,f(f(g(w),y),f(u,y))))),y)),v). 4089 [] f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),u)=f(z,u). 4090 [] f(x,f(g(f(f(y,g(f(z,f(f(g(z),y),f(u,y))))),x)),v))=f(y,f(u,v)). 4091 [] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(u,y)))))))=g(f(f(v,g(f(w,f(f(g(w),v),f(u,v))))),v)). 4092 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x))=z. 4093 [] f(g(f(x,y)),f(f(g(f(z,f(f(g(z),g(f(x,y))),f(g(f(f(f(u,g(f(v,f(f(g(v),u),f(w,u))))),u),g(f(x,y)))),g(f(x,y)))))),f(w,g(v6))),g(f(x,y))))=f(x,g(f(x,f(f(y,v6),x)))). 4094 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),f(f(x,f(z,u)),f(x,g(f(y,f(f(g(y),x),f(z,x))))))))=f(f(v,f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),v)),g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),u)))),f(x,g(f(y,f(f(g(y),x),f(z,x)))))). 4095 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),f(f(x,f(z,u)),f(x,g(f(y,f(f(g(y),x),f(z,x))))))))=f(f(x,f(z,g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),u)))),f(x,g(f(y,f(f(g(y),x),f(z,x)))))). 4096 [] f(f(x,f(f(g(x),y),z)),u)=f(f(v,f(f(g(v),y),z)),u). 4097 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(f(f(v,g(f(w,f(f(g(w),v),f(v6,v))))),v),g(f(x,y)))),g(f(x,y)))))),f(v6,g(z))),g(f(x,y)))). 4098 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(g(f(y,z)),f(f(f(f(v,f(g(f(g(f(y,z)),v)),g(w))),g(f(y,z))),f(g(f(y,g(f(y,f(f(z,w),y))))),g(u))),g(f(y,z)))). 4099 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y))))=f(w,f(f(g(w),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y))))). 4100 [] f(f(g(x),x),f(g(f(f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y)))),x)),x))=f(f(y,v),x). 4101 [] f(x,f(f(g(x),y),f(g(f(f(g(f(y,z)),f(f(f(f(u,f(g(f(g(f(y,z)),u)),g(v))),g(f(y,z))),f(g(f(y,g(f(y,f(f(z,v),y))))),g(w))),g(f(y,z)))),y)),y)))=f(y,f(f(z,w),y)). 4102 [] g(f(f(x,g(f(y,f(f(z,u),f(v,x))))),x))=f(g(f(g(y),x)),g(f(z,g(f(z,f(f(u,v),z)))))). 4103 [] g(f(f(x,g(f(y,f(z,f(g(f(u,z)),x))))),x))=g(f(u,f(g(y),x))). 4104 [] f(g(f(g(x),y)),g(f(z,g(f(z,f(f(u,v),z))))))=g(f(f(y,g(f(x,f(f(z,u),f(v,y))))),y)). 4105 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),f(f(u,f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),u)),z)),f(x,g(f(y,f(f(g(y),x),f(z,x))))))))=x. 4106 [] g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),f(f(x,f(z,z)),f(x,g(f(y,f(f(g(y),x),f(z,x))))))))=x. 4107 [] f(f(x,f(y,g(f(f(x,g(f(z,f(f(g(z),x),f(y,x))))),y)))),f(x,g(f(z,f(f(g(z),x),f(y,x))))))=x. 4108 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,f(f(v,g(f(w,f(f(g(w),v),f(u,v))))),v)),x))))),g(v6))),g(f(x,y))))=f(x,g(f(x,f(f(y,v6),x)))). 4109 [] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(f(f(u,f(g(f(g(f(x,y)),u)),v)),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,f(f(w,g(f(v6,f(f(g(v6),w),f(v,w))))),w)),x))))),g(z))),g(f(x,y)))). 4110 [] f(g(f(x,f(f(y,z),x))),f(g(f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y)))))),f(g(v),g(z))),g(f(x,y))))),g(f(x,g(f(w,f(f(g(w),v6),x)))))))=f(g(x),v6). 4111 [] f(g(f(x,f(f(y,z),x))),f(f(f(g(g(f(x,y))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),g(f(x,g(f(v,f(f(g(v),w),x)))))))=f(g(x),w). 4112 [] f(g(f(x,f(f(y,z),x))),f(g(f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y)))))),f(g(v),g(z))),g(f(x,y))))),f(g(f(w,g(f(x,v6)))),g(f(w,g(f(w,f(v7,w))))))))=f(v6,v7). 4113 [] f(g(f(x,f(f(y,z),x))),f(f(f(g(g(f(x,y))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4114 [] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,z)))),x),f(z,g(f(u,f(g(v),w))))),x))))=f(f(w,g(f(v,f(v6,f(g(f(u,v6)),w))))),w). 4115 [] f(f(x,g(f(y,f(z,f(g(f(u,z)),x))))),x)=f(u,f(g(y),x)). 4116 [] f(f(x,g(f(y,f(g(f(z,f(f(u,v),z))),f(g(f(g(f(z,u)),f(f(g(f(w,f(f(g(w),g(f(z,u))),f(g(f(v6,g(f(z,u)))),g(f(z,u)))))),f(g(v6),g(v))),g(f(z,u))))),x))))),x)=f(z,f(g(y),x)). 4117 [] f(f(x,g(f(y,f(g(f(z,f(f(u,v),z))),f(f(f(g(g(f(z,u))),g(w)),f(g(f(f(g(w),g(v)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4118 [] f(f(g(f(x,g(f(y,f(g(f(z,y)),x))))),g(f(u,g(f(z,x))))),g(f(x,g(f(y,f(g(f(z,y)),x))))))=f(x,f(g(u),g(f(x,g(f(y,f(g(f(z,y)),x))))))). 4119 [] f(f(x,g(f(y,f(g(f(z,y)),f(g(f(u,g(f(z,v)))),x))))),x)=f(u,f(g(v),x)). 4120 [] f(g(x),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))))=g(f(z,x)). 4121 [] f(x,f(y,f(g(f(f(z,u),y)),g(f(f(z,u),g(f(f(z,u),f(g(f(v,f(z,x))),f(z,u)))))))))=f(u,g(f(v,f(z,u)))). 4122 [] f(x,g(f(y,f(z,x))))=f(u,g(f(y,f(z,u)))). 4123 [] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=f(g(y),f(g(f(z,g(v))),g(f(z,g(f(z,f(g(f(u,v)),z))))))). 4124 [] g(f(x,y))=f(g(y),f(g(f(z,g(u))),g(f(z,g(f(z,f(g(f(x,u)),z))))))). 4125 [] f(f(f(x,f(g(f(y,x)),g(f(y,g(z))))),y),g(f(u,z)))=f(v,f(g(f(y,v)),f(g(f(z,g(w))),g(f(z,g(f(z,f(g(f(u,w)),z)))))))). 4126 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))),g(f(u,f(f(g(u),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x))))))),f(g(g(f(z,x))),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))))))))=g(x). 4127 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))),g(f(y,f(g(f(z,y)),f(g(g(f(z,x))),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))))))))=g(x). 4128 [] f(g(f(x,g(f(x,f(y,x))))),g(y))=f(z,g(f(u,f(g(f(x,u)),z)))). 4129 [] f(g(f(x,y)),f(f(g(f(z,f(f(g(z),g(f(x,y))),f(g(f(u,g(f(x,y)))),g(f(x,y)))))),f(g(u),g(v))),g(f(x,y))))=f(w,g(f(x,f(f(y,v),w)))). 4130 [] f(x,g(f(y,f(f(z,f(g(f(y,z)),g(u))),x))))=u. 4131 [] f(x,g(f(y,f(g(f(z,y)),x))))=f(g(f(z,g(f(z,f(u,z))))),g(u)). 4132 [] f(x,g(f(y,f(f(z,u),x))))=f(g(f(y,z)),f(f(g(f(v,f(f(g(v),g(f(y,z))),f(g(f(w,g(f(y,z)))),g(f(y,z)))))),f(g(w),g(u))),g(f(y,z)))). 4133 [] g(f(x,f(f(y,f(z,g(f(x,f(u,z))))),x)))=f(u,g(f(x,y))). 4134 [] f(x,f(g(f(y,x)),g(f(z,g(f(y,f(u,z)))))))=u. 4135 [] f(f(g(x),y),f(g(f(f(y,f(f(z,f(g(f(g(f(x,u)),z)),g(v))),g(f(x,u)))),y)),y))=f(f(u,v),g(f(x,u))). 4136 [] g(f(x,f(f(y,z),x)))=f(f(y,f(g(f(x,y)),g(z))),g(f(x,y))). 4137 [] f(f(x,g(f(y,f(f(f(z,f(g(f(u,z)),g(v))),g(f(u,z))),f(f(f(g(g(f(u,z))),g(w)),f(g(f(f(g(w),g(v)),g(w))),g(w))),x))))),x)=f(u,f(g(y),x)). 4138 [] f(f(f(x,f(g(f(y,x)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(y,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4139 [] f(f(f(x,f(g(f(y,x)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),g(f(y,g(f(v,f(f(g(v),w),y)))))))=f(g(y),w). 4140 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,f(f(v,g(f(w,f(f(g(w),v),f(u,v))))),v)),x))))),g(v6))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(v6))),g(f(x,y)))). 4141 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))),f(g(f(x,f(f(y,f(g(f(x,y)),g(f(f(v,g(f(w,f(f(g(w),v),f(u,v))))),v)))),g(f(x,y))))),g(v6))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(v6))),g(f(x,y)))). 4142 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))),f(g(f(x,f(f(y,f(g(f(x,y)),u)),g(f(x,y))))),g(v))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(v))),g(f(x,y)))). 4143 [] g(f(f(x,g(f(y,f(f(z,u),f(v,x))))),x))=f(g(f(g(y),x)),g(f(z,f(f(u,f(g(f(z,u)),g(v))),g(f(z,u)))))). 4144 [] f(x,f(f(g(x),y),f(g(f(f(g(f(y,z)),f(f(f(f(u,f(g(f(g(f(y,z)),u)),g(v))),g(f(y,z))),f(g(f(y,f(f(z,f(g(f(y,z)),g(v))),g(f(y,z))))),g(w))),g(f(y,z)))),y)),y)))=f(y,f(f(z,w),y)). 4145 [] f(x,f(f(g(x),y),f(g(f(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z)))),y)),y)))=f(y,f(f(z,u),y)). 4146 [] f(f(g(x),x),f(g(f(f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,f(f(y,f(g(f(x,y)),g(u))),g(f(x,y))))),g(v))),g(f(x,y)))),x)),x))=f(f(y,v),x). 4147 [] f(f(g(x),x),f(g(f(f(x,f(f(y,f(g(f(x,y)),g(z))),g(f(x,y)))),x)),x))=f(f(y,z),x). 4148 [] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,f(f(y,f(g(f(x,y)),g(u))),g(f(x,y))))),g(v))),g(f(x,y))))=f(w,f(f(g(w),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y))))). 4149 [] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z)))). 4150 [] f(g(f(x,y)),f(f(g(f(z,f(f(g(z),g(f(x,y))),f(g(f(f(f(u,g(f(v,f(f(g(v),u),f(w,u))))),u),g(f(x,y)))),g(f(x,y)))))),f(w,g(v6))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(v6))),g(f(x,y)))). 4151 [] f(g(f(x,y)),f(f(g(f(x,f(f(y,f(g(f(x,y)),g(f(f(z,g(f(u,f(f(g(u),z),f(v,z))))),z)))),g(f(x,y))))),f(v,g(w))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(w))),g(f(x,y)))). 4152 [] f(g(f(x,y)),f(f(g(f(x,f(f(y,f(g(f(x,y)),f(g(f(g(z),u)),g(f(g(z),f(f(u,f(g(f(g(z),u)),g(v))),g(f(g(z),u)))))))),g(f(x,y))))),f(v,g(w))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(w))),g(f(x,y)))). 4153 [] f(g(f(x,y)),f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),g(f(x,y))))),f(z,g(u))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(u))),g(f(x,y)))). 4154 [] f(f(x,f(g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)),g(f(z,u)))),g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)))=f(f(x,f(z,g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),u)))),f(x,g(f(y,f(f(g(y),x),f(z,x)))))). 4155 [] f(f(x,f(f(g(f(g(y),x)),g(f(g(y),f(f(x,f(g(f(g(y),x)),g(z))),g(f(g(y),x)))))),g(f(z,u)))),g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),x)))=f(f(x,f(z,g(f(f(x,g(f(y,f(f(g(y),x),f(z,x))))),u)))),f(x,g(f(y,f(f(g(y),x),f(z,x)))))). 4156 [] f(f(x,f(y,g(f(y,z)))),g(f(f(x,g(f(u,f(f(g(u),x),f(y,x))))),x)))=f(f(x,f(y,g(f(f(x,g(f(u,f(f(g(u),x),f(y,x))))),z)))),f(x,g(f(u,f(f(g(u),x),f(y,x)))))). 4157 [] f(f(x,f(y,g(f(f(x,g(f(z,f(f(g(z),x),f(y,x))))),u)))),f(x,g(f(z,f(f(g(z),x),f(y,x))))))=f(f(x,f(y,g(f(y,u)))),f(g(f(g(z),x)),g(f(g(z),f(f(x,f(g(f(g(z),x)),g(y))),g(f(g(z),x))))))). 4158 [] f(f(x,f(y,g(f(f(x,g(f(z,f(f(g(z),x),f(y,x))))),u)))),f(x,g(f(z,f(f(g(z),x),f(y,x))))))=f(f(x,f(y,g(f(y,u)))),y). 4159 [] f(f(g(x),f(g(f(g(f(x,y)),g(g(f(x,y))))),g(z))),g(f(x,y)))=f(f(y,f(g(f(x,y)),g(z))),g(f(x,y))). 4160 [] f(x,f(f(g(x),y),f(f(z,f(g(f(f(g(u),y),z)),g(f(g(f(f(g(u),y),z)),g(v))))),g(f(f(g(u),y),z)))))=f(u,v). 4161 [] f(g(f(f(x,g(f(y,z))),x)),x)=f(f(u,f(g(f(f(g(y),x),u)),g(f(g(f(f(g(y),x),u)),g(z))))),g(f(f(g(y),x),u))). 4162 [] f(f(f(g(f(x,f(g(f(y,x)),z))),f(g(f(z,g(f(x,f(g(f(y,x)),z))))),g(f(g(f(z,g(f(u,f(g(f(y,u)),z))))),v)))),g(f(z,g(f(x,f(g(f(y,x)),z)))))),f(v,w))=f(v6,f(g(f(z,v6)),w)). 4163 [] f(x,f(f(g(f(y,f(g(f(z,y)),x))),f(g(f(x,g(f(y,f(g(f(z,y)),x))))),g(f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(v))))),g(f(x,g(f(y,f(g(f(z,y)),x)))))))=v. 4164 [] f(g(f(x,g(f(y,g(f(z,f(g(f(u,z)),y))))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). 4165 [] f(x,f(g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),x)),g(f(g(f(y,g(f(y,f(f(z,u),y))))),g(f(g(f(y,g(f(y,f(f(z,u),y))))),u))))))=g(f(y,z)). 4166 [] f(x,f(g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),x)),g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),g(f(g(f(y,g(f(y,f(f(z,u),y))))),u))))))=g(f(y,z)). 4167 [] f(x,f(g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),x)),g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),u))))))=g(f(y,z)). 4168 [] f(x,g(f(y,f(f(z,u),x))))=f(g(f(y,z)),f(f(g(f(y,f(f(z,f(g(f(y,z)),g(v))),g(f(y,z))))),f(g(v),g(u))),g(f(y,z)))). 4169 [] f(x,g(f(y,f(f(z,u),x))))=f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z)))). 4170 [] f(f(x,f(y,g(f(y,y)))),y)=x. 4171 [] f(f(g(x),f(g(f(x,g(x))),g(y))),g(f(x,g(x))))=g(f(z,f(f(g(z),y),x))). 4172 [] f(f(f(x,f(g(f(y,x)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(y),w). 4173 [] f(g(f(x,f(g(f(y,x)),z))),f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(z),w). 4174 [] f(x,f(f(g(x),f(g(f(x,g(x))),g(f(g(f(f(y,g(f(z,f(g(f(u,z)),y)))),g(f(y,g(f(v,f(g(f(u,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4175 [] f(x,f(g(f(g(f(y,f(f(g(y),f(g(f(y,g(y))),g(z))),g(f(y,g(y)))))),x)),g(f(g(f(u,g(f(y,f(f(g(y),z),u))))),g(f(g(f(u,g(f(y,f(f(g(y),z),u))))),z))))))=g(f(u,g(u))). 4176 [] f(x,f(g(f(g(f(y,f(f(g(y),f(g(f(y,g(y))),g(z))),g(f(y,g(y)))))),x)),g(f(g(f(y,f(f(g(y),f(g(f(y,g(y))),g(z))),g(f(y,g(y)))))),g(f(g(f(u,g(f(y,f(f(g(y),z),u))))),z))))))=g(f(u,g(u))). 4177 [] f(x,f(g(f(g(f(y,f(f(g(y),f(g(f(y,g(y))),g(z))),g(f(y,g(y)))))),x)),g(f(g(f(y,f(f(g(y),f(g(f(y,g(y))),g(z))),g(f(y,g(y)))))),g(f(g(f(y,f(f(g(y),f(g(f(y,g(y))),g(z))),g(f(y,g(y)))))),z))))))=g(f(u,g(u))). 4178 [] g(f(x,g(x)))=g(f(y,g(y))). 4179 [] f(x,f(f(g(x),f(g(f(y,g(y))),g(f(z,g(u))))),z))=u. 4180 [] f(f(g(x),y),f(g(f(f(y,g(f(z,g(z)))),y)),y))=g(x). 4181 [] f(x,f(f(g(x),y),f(g(f(f(y,g(f(z,g(z)))),y)),y)))=f(u,g(u)). 4182 [] f(x,g(x))=f(y,g(y)). 4183 [] f(f(x,g(x)),g(f(y,g(y))))=f(z,g(z)). 4184 [] f(f(x,f(y,g(y))),z)=f(f(g(z),z),f(g(f(g(f(z,x)),z)),z)). 4185 [] f(x,f(f(g(x),y),f(g(f(f(z,g(z)),y)),y)))=y. 4186 [] f(g(x),g(f(y,f(z,g(z)))))=f(u,g(f(y,f(x,u)))). 4187 [] f(f(x,g(x)),y)=f(f(z,f(f(g(z),f(u,g(f(u,u)))),u)),y). 4188 [] f(f(x,g(x)),y)=f(f(z,g(z)),y). 4189 [] g(f(x,f(f(g(x),y),f(g(y),y))))=f(y,g(f(y,y))). 4190 [] f(x,g(f(y,f(f(g(y),x),f(g(z),x)))))=f(z,f(x,g(f(x,x)))). 4191 [] f(f(x,y),f(y,g(f(y,y))))=x. 4192 [] g(f(x,f(f(g(x),f(y,g(f(y,y)))),f(g(f(y,g(f(y,y)))),f(y,g(f(y,y)))))))=y. 4193 [] f(f(x,g(f(x,x))),g(f(f(x,g(f(x,x))),f(x,g(f(x,x))))))=x. 4194 [] f(x,f(g(f(f(y,z),x)),u))=f(f(z,g(f(z,z))),f(g(y),u)). 4195 [] g(f(x,f(f(g(x),f(y,z)),f(g(f(y,f(y,z))),f(y,z)))))=f(z,g(f(z,z))). 4196 [] f(g(f(f(x,g(f(y,z))),x)),x)=f(f(f(x,g(f(x,x))),f(g(g(y)),g(f(g(f(f(g(y),x),u)),g(z))))),g(f(f(g(y),x),u))). 4197 [] f(x,f(f(g(x),y),f(f(f(y,g(f(y,y))),f(g(g(z)),g(f(g(f(f(g(z),y),u)),g(v))))),g(f(f(g(z),y),u)))))=f(z,v). 4198 [] f(f(f(x,g(x)),g(f(y,g(y)))),z)=f(f(u,g(u)),z). 4199 [] f(g(f(x,g(x))),f(g(f(y,g(y))),z))=f(u,f(g(f(f(v,g(v)),u)),z)). 4200 [] f(g(f(x,g(x))),f(g(f(y,g(y))),z))=f(f(g(u),g(f(g(u),g(u)))),f(g(u),z)). 4201 [] f(f(g(x),g(f(g(x),g(x)))),f(g(x),y))=f(g(f(z,g(z))),f(g(f(u,g(u))),y)). 4202 [] f(x,f(f(g(x),y),f(g(f(f(f(z,g(z)),g(f(u,g(u)))),y)),y)))=y. 4203 [] f(x,f(f(g(x),y),f(g(f(f(f(z,f(f(g(z),u),f(g(f(f(u,v),u)),u))),v),y)),y)))=y. 4204 [] f(g(f(x,f(y,g(y)))),f(g(f(z,g(f(x,f(u,z))))),g(f(g(u),g(f(v,f(g(f(w,v)),g(u))))))))=g(f(w,g(u))). 4205 [] f(x,f(g(f(f(y,g(y)),x)),g(f(f(f(z,g(z)),g(f(u,g(u)))),g(f(v,f(g(f(w,v)),f(f(z,g(z)),g(f(u,g(u)))))))))))=g(f(w,f(f(z,g(z)),g(f(u,g(u)))))). 4206 [] f(f(g(x),g(f(g(x),g(x)))),f(g(x),g(f(f(f(y,g(y)),g(f(z,g(z)))),g(f(u,f(g(f(v,u)),f(f(y,g(y)),g(f(z,g(z)))))))))))=g(f(v,f(f(y,g(y)),g(f(z,g(z)))))). 4207 [] f(f(f(x,f(g(f(f(y,g(y)),x)),g(f(f(f(z,g(z)),g(f(u,g(u)))),v)))),f(f(z,g(z)),g(f(u,g(u))))),f(v,w))=f(v6,f(g(f(f(f(z,g(z)),g(f(u,g(u)))),v6)),w)). 4208 [] f(f(f(f(g(x),g(f(g(x),g(x)))),f(g(x),g(f(f(f(y,g(y)),g(f(z,g(z)))),u)))),f(f(y,g(y)),g(f(z,g(z))))),f(u,v))=f(w,f(g(f(f(f(y,g(y)),g(f(z,g(z)))),w)),v)). 4209 [] f(f(f(f(g(x),g(f(g(x),g(x)))),f(g(x),g(f(f(f(y,g(y)),g(f(z,g(z)))),u)))),f(f(y,g(y)),g(f(z,g(z))))),f(u,v))=f(f(g(f(z,g(z))),g(f(g(f(z,g(z))),g(f(z,g(z)))))),f(g(f(y,g(y))),v)). 4210 [] f(f(x,g(x)),f(f(g(f(y,g(y))),f(g(f(z,g(z))),g(f(u,g(v))))),u))=v. 4211 [] g(f(f(x,f(f(g(x),y),f(g(f(z,y)),y))),f(f(f(g(f(u,y)),g(f(u,g(f(u,f(z,u)))))),v),f(g(f(f(v,w),v)),v))))=w. 4212 [] f(f(g(x),f(g(f(x,g(x))),g(f(y,g(f(z,f(g(f(u,z)),y))))))),g(f(x,g(x))))=g(f(v,f(f(g(v),f(y,g(f(w,f(g(f(u,w)),y))))),x))). 4213 [] g(f(x,f(f(g(x),f(y,g(f(z,f(g(f(u,z)),y))))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(u,w)),y))))))),g(f(v,g(v)))). 4214 [] g(f(f(x,f(f(g(x),y),f(g(f(z,y)),y))),f(f(f(g(f(u,y)),g(f(u,g(f(u,f(z,u)))))),v),f(g(f(w,v)),v))))=g(f(v6,f(f(g(v6),v),f(g(f(w,v)),v)))). 4215 [] g(f(x,f(f(g(x),y),f(g(f(z,y)),y))))=g(f(f(u,f(f(g(u),v),f(g(f(w,v)),v))),f(f(f(g(f(v6,v)),g(f(v6,g(f(v6,f(w,v6)))))),y),f(g(f(z,y)),y)))). 4216 [] f(g(f(x,g(x))),f(g(f(y,g(y))),g(f(z,g(f(f(u,g(u)),f(v,z)))))))=v. 4217 [] f(x,f(g(f(f(y,f(f(z,u),g(f(f(z,u),f(z,u))))),x)),g(f(u,g(y)))))=z. 4218 [] f(f(f(f(x,y),g(f(f(x,y),f(x,y)))),g(f(f(f(x,y),g(f(f(x,y),f(x,y)))),f(f(x,y),g(f(f(x,y),f(x,y))))))),f(g(z),g(f(y,g(z)))))=x. 4219 [] f(f(x,y),f(g(z),g(f(y,g(z)))))=x. 4220 [] f(x,f(g(f(f(g(y),z),x)),g(f(z,g(u)))))=g(f(f(z,g(f(y,u))),z)). 4221 [] g(f(f(x,g(f(y,z))),x))=f(f(x,g(f(x,x))),f(g(g(y)),g(f(x,g(z))))). 4222 [] f(x,f(g(f(y,x)),g(f(g(f(z,g(f(u,f(g(f(v,u)),z))))),g(g(f(v,z)))))))=g(f(z,y)). 4223 [] f(f(f(x,g(f(x,x))),f(g(g(y)),g(f(g(f(f(g(y),x),z)),g(u))))),g(f(f(g(y),x),z)))=f(f(f(x,g(f(x,x))),f(g(g(y)),g(f(x,g(u))))),x). 4224 [] g(f(x,f(f(g(x),f(g(y),z)),f(g(f(u,f(g(y),z))),f(g(y),z)))))=f(f(f(z,g(f(z,z))),f(g(g(y)),g(f(z,g(u))))),z). 4225 [] g(f(x,y))=f(z,f(g(f(y,z)),g(f(g(f(x,g(f(u,f(g(f(v,u)),x))))),g(g(f(v,x))))))). 4226 [] f(x,f(f(g(x),y),f(f(f(y,g(f(y,y))),f(g(g(z)),g(f(y,g(u))))),y)))=f(z,u). 4227 [] f(f(x,y),f(z,g(f(y,g(f(u,f(f(g(u),v),f(g(f(f(v,z),v)),v))))))))=x. 4228 [] f(f(x,y),f(z,g(f(y,z))))=x. 4229 [] f(f(x,y),f(g(y),g(f(z,g(z)))))=x. 4230 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=g(f(g(v),g(y))). 4231 [] f(x,f(f(g(x),y),g(f(z,f(g(f(u,z)),y)))))=u. 4232 [] g(f(g(x),g(y)))=f(f(g(f(z,g(y))),g(f(z,g(f(z,f(u,z)))))),f(v,g(f(g(f(g(x),g(f(g(x),f(u,g(x)))))),v)))). 4233 [] f(x,g(f(f(y,z),f(u,x))))=f(g(f(z,u)),g(y)). 4234 [] f(g(f(x,g(x))),f(g(f(y,g(y))),g(f(g(f(g(z),u)),g(z)))))=u. 4235 [] g(f(g(f(x,g(f(y,f(f(g(y),z),x))))),g(f(g(u),z))))=g(f(v,g(f(w,f(g(f(u,w)),v))))). 4236 [] g(f(g(f(x,f(f(g(x),f(g(f(x,g(x))),g(y))),g(f(x,g(x)))))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4237 [] f(x,f(g(f(y,z)),g(f(u,f(g(f(v,u)),f(g(f(z,g(x))),g(f(z,g(f(w,f(g(f(y,w)),z)))))))))))=v. 4238 [] f(x,f(f(g(x),y),g(f(f(z,g(f(u,z))),f(g(v),y)))))=f(v,u). 4239 [] f(x,f(f(g(x),g(f(y,g(f(z,f(u,y)))))),g(u)))=z. 4240 [] f(x,f(g(f(y,z)),g(f(f(u,g(f(v,u))),f(g(w),f(g(f(z,g(x))),g(f(z,g(f(v6,f(g(f(y,v6)),z)))))))))))=f(w,v). 4241 [] f(x,f(f(g(x),g(f(y,g(f(z,f(u,y)))))),g(u)))=f(f(z,f(v,g(f(w,v)))),w). 4242 [] f(f(x,f(y,g(f(z,y)))),z)=x. 4243 [] f(f(x,f(g(y),g(f(z,g(z))))),y)=x. 4244 [] f(f(x,f(g(f(y,x)),g(f(z,g(z))))),f(y,u))=u. 4245 [] g(f(x,f(f(g(x),f(y,f(g(z),g(f(u,g(u)))))),f(g(f(y,f(y,f(g(z),g(f(u,g(u))))))),f(y,f(g(z),g(f(u,g(u)))))))))=z. 4246 [] f(f(g(x),g(f(y,g(y)))),g(f(f(g(x),g(f(y,g(y)))),f(g(x),g(f(y,g(y)))))))=x. 4247 [] f(f(f(x,y),f(g(y),g(f(z,g(z))))),f(f(u,f(g(f(x,u)),g(f(v,g(v))))),w))=w. 4248 [] f(x,f(f(y,f(g(f(x,y)),g(f(z,g(z))))),u))=u. 4249 [] f(f(x,f(g(f(y,x)),g(f(z,g(z))))),f(u,g(u)))=g(y). 4250 [] f(g(f(x,y)),x)=f(z,f(g(f(y,z)),g(f(u,g(u))))). 4251 [] f(f(x,y),f(g(y),z))=f(u,f(g(f(f(v,f(g(f(x,v)),g(f(w,g(w))))),u)),z)). 4252 [] f(f(x,y),f(g(y),z))=f(f(f(g(f(x,u)),g(f(v,g(v)))),g(f(f(g(f(x,u)),g(f(v,g(v)))),f(g(f(x,u)),g(f(v,g(v))))))),f(g(u),z)). 4253 [] f(f(x,y),f(g(y),z))=f(f(x,u),f(g(u),z)). 4254 [] f(x,f(g(f(y,x)),g(f(z,g(z)))))=f(g(f(u,y)),u). 4255 [] f(f(f(x,f(g(y),g(f(z,g(z))))),u),f(g(u),v))=f(x,f(g(y),v)). 4256 [] f(g(f(x,f(y,f(g(f(z,y)),g(f(u,g(u))))))),x)=z. 4257 [] f(f(f(x,f(g(f(y,x)),g(f(z,g(z))))),u),f(g(f(g(f(u,g(u))),u)),u))=f(g(y),u). 4258 [] f(f(g(x),x),f(g(f(g(f(x,f(y,f(g(f(z,y)),g(f(u,g(u))))))),x)),x))=f(g(z),x). 4259 [] f(f(g(x),x),f(g(y),x))=f(g(y),x). 4260 [] f(f(x,f(y,g(y))),z)=f(g(f(g(f(z,x)),z)),z). 4261 [] f(g(f(f(x,f(f(y,f(g(f(x,y)),g(z))),g(f(x,y)))),x)),x)=f(f(y,z),x). 4262 [] f(x,f(f(g(x),y),f(g(z),y)))=f(y,f(g(z),y)). 4263 [] f(x,f(f(g(x),y),f(f(z,u),y)))=f(y,f(f(z,u),y)). 4264 [] g(f(f(g(x),y),f(g(f(z,f(g(x),y))),f(g(x),y))))=f(f(f(y,g(f(y,y))),f(g(g(x)),g(f(y,g(z))))),y). 4265 [] g(f(f(x,f(f(g(x),y),f(g(f(z,y)),y))),f(f(f(g(f(u,y)),g(f(u,g(f(u,f(z,u)))))),v),f(g(f(w,v)),v))))=g(f(v,f(g(f(w,v)),v))). 4266 [] g(f(f(x,f(g(f(y,x)),x)),f(f(f(g(f(z,x)),g(f(z,g(f(z,f(y,z)))))),u),f(g(f(v,u)),u))))=g(f(u,f(g(f(v,u)),u))). 4267 [] g(f(f(x,f(g(f(y,x)),x)),f(f(f(g(f(z,x)),g(f(z,g(f(z,f(y,z)))))),u),f(g(f(f(u,v),u)),u))))=v. 4268 [] g(f(x,f(g(f(f(x,y),x)),x)))=y. 4269 [] g(f(f(x,g(f(x,x))),f(g(y),y)))=x. 4270 [] f(x,f(f(g(x),y),f(g(f(f(f(z,f(g(f(f(z,u),z)),z)),u),y)),y)))=y. 4271 [] f(x,f(f(g(x),y),f(g(f(f(f(f(z,g(f(z,z))),f(g(u),u)),z),y)),y)))=y. 4272 [] f(x,f(g(f(f(f(f(y,g(f(y,y))),f(g(z),z)),y),x)),x))=x. 4273 [] f(f(x,g(f(x,x))),f(g(f(f(x,g(f(x,x))),f(g(y),y))),z))=z. 4274 [] f(f(x,g(f(x,x))),f(x,y))=y. 4275 [] f(x,f(g(f(f(f(y,g(y)),g(f(z,g(z)))),x)),x))=x. 4276 [] f(f(g(f(x,g(x))),g(f(g(f(x,g(x))),g(f(x,g(x)))))),f(g(f(y,g(y))),z))=z. 4277 [] f(x,g(f(x,f(g(y),x))))=f(y,f(x,g(f(x,x)))). 4278 [] f(x,f(f(f(x,g(f(x,x))),f(g(g(y)),g(f(x,g(z))))),x))=f(y,z). 4279 [] f(x,f(f(f(x,g(f(x,x))),f(g(g(y)),g(f(x,g(z))))),x))=f(x,g(f(u,f(g(f(z,u)),f(g(y),x))))). 4280 [] f(x,g(f(y,f(g(f(z,y)),f(g(u),x)))))=f(u,z). 4281 [] f(f(g(f(f(f(x,g(x)),g(f(y,g(y)))),z)),f(f(x,g(x)),g(f(y,g(y))))),f(z,u))=f(f(g(f(y,g(y))),g(f(g(f(y,g(y))),g(f(y,g(y)))))),f(g(f(x,g(x))),u)). 4282 [] f(f(g(f(f(f(x,g(x)),g(f(y,g(y)))),z)),f(f(x,g(x)),g(f(y,g(y))))),f(z,u))=u. 4283 [] g(f(f(f(x,g(x)),g(f(y,g(y)))),g(f(z,f(g(f(u,z)),f(f(x,g(x)),g(f(y,g(y)))))))))=g(f(u,f(f(x,g(x)),g(f(y,g(y)))))). 4284 [] f(g(f(x,g(x))),f(g(f(y,g(y))),z))=z. 4285 [] f(f(g(f(x,g(y))),g(f(f(z,y),f(x,g(f(x,x)))))),g(f(y,f(g(f(z,y)),f(g(g(f(z,x))),f(g(f(x,g(y))),g(f(x,g(f(x,f(g(f(z,y)),x)))))))))))=g(x). 4286 [] f(f(g(f(x,g(y))),g(f(f(z,y),f(x,g(f(x,x)))))),g(f(y,f(g(f(z,y)),f(g(g(f(z,x))),f(g(f(x,g(y))),g(f(f(z,y),f(x,g(f(x,x)))))))))))=g(x). 4287 [] f(g(f(x,y)),x)=g(y). 4288 [] f(f(f(x,f(g(f(y,x)),g(f(y,g(z))))),y),g(f(u,z)))=f(v,f(g(f(y,v)),f(g(f(z,g(w))),g(f(f(u,w),f(z,g(f(z,z)))))))). 4289 [] g(f(x,y))=f(g(y),f(g(f(z,g(u))),g(f(f(x,u),f(z,g(f(z,z))))))). 4290 [] f(f(f(x,g(f(y,z))),y),u)=f(x,f(g(z),u)). 4291 [] f(g(f(x,g(x))),f(g(f(y,g(y))),g(g(z))))=z. 4292 [] g(g(x))=x. 4293 [] f(f(x,g(x)),f(g(f(y,g(z))),y))=z. 4294 [] f(f(x,g(x)),g(g(y)))=y. 4295 [] f(f(x,g(x)),y)=y. 4296 [] f(f(g(f(g(f(x,g(x))),y)),f(f(z,g(z)),g(f(x,g(x))))),f(y,u))=u. 4297 [] f(f(g(f(g(f(x,g(x))),y)),g(f(x,g(x)))),f(y,z))=z. 4298 [] f(g(x),f(x,y))=y. 4299 [] f(f(x,f(y,g(y))),z)=f(g(g(x)),z). 4300 [] f(f(x,f(y,g(y))),z)=f(x,z). 4301 [] f(f(f(x,f(g(f(y,x)),g(f(z,g(z))))),u),f(g(g(g(u))),u))=f(g(y),u). 4302 [] f(f(f(x,f(g(f(y,x)),g(f(z,g(z))))),u),f(g(u),u))=f(g(y),u). 4303 [] f(x,f(g(f(y,x)),z))=f(g(y),z). 4304 [] f(g(x),g(f(y,g(y))))=f(g(f(z,x)),z). 4305 [] f(g(x),g(f(y,g(y))))=g(x). 4306 [] f(x,f(g(f(y,x)),g(f(z,g(z)))))=g(y). 4307 [] f(x,g(f(y,x)))=g(y). 4308 [] f(f(f(x,f(g(f(y,x)),g(f(y,g(z))))),y),g(f(u,z)))=f(v,f(g(f(y,v)),f(g(f(z,g(w))),g(f(f(u,w),g(z)))))). 4309 [] f(f(f(g(x),g(f(x,g(y)))),x),g(f(z,y)))=f(u,f(g(f(x,u)),f(g(f(y,g(v))),g(f(f(z,v),g(y)))))). 4310 [] f(f(f(g(x),g(f(x,g(y)))),x),g(f(z,y)))=f(g(x),f(g(f(y,g(u))),g(f(f(z,u),g(y))))). 4311 [] f(g(x),f(g(f(y,g(z))),g(f(f(u,z),g(y)))))=f(g(x),f(g(g(y)),g(f(u,y)))). 4312 [] f(g(x),f(g(f(y,g(z))),g(f(f(u,z),g(y)))))=f(g(x),f(y,g(f(u,y)))). 4313 [] f(g(x),f(g(f(y,g(z))),g(f(f(u,z),g(y)))))=f(g(x),g(u)). 4314 [] g(f(x,y))=f(g(y),f(g(f(z,g(u))),g(f(f(x,u),g(z))))). 4315 [] g(f(x,y))=f(g(y),g(x)). 4316 [] g(f(f(f(x,g(x)),f(g(g(y)),g(y))),g(f(z,f(g(f(u,z)),f(f(x,g(x)),g(f(y,g(y)))))))))=g(f(u,f(f(x,g(x)),g(f(y,g(y)))))). 4317 [] g(f(f(f(x,g(x)),f(y,g(y))),g(f(z,f(g(f(u,z)),f(f(x,g(x)),g(f(y,g(y)))))))))=g(f(u,f(f(x,g(x)),g(f(y,g(y)))))). 4318 [] g(f(f(x,g(x)),g(f(y,f(g(f(z,y)),f(f(u,g(u)),g(f(x,g(x)))))))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4319 [] g(f(f(x,g(x)),g(f(y,f(f(g(y),g(z)),f(f(u,g(u)),g(f(x,g(x)))))))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4320 [] g(f(f(x,g(x)),g(f(y,f(f(g(y),g(z)),f(f(u,g(u)),f(g(g(x)),g(x))))))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4321 [] g(f(f(x,g(x)),g(f(y,f(f(g(y),g(z)),f(f(u,g(u)),f(x,g(x))))))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4322 [] g(f(f(x,g(x)),g(f(y,f(f(g(y),g(z)),f(x,g(x)))))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4323 [] g(f(f(x,g(x)),f(g(f(f(g(y),g(z)),f(x,g(x)))),g(y))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4324 [] g(f(f(x,g(x)),f(f(g(f(x,g(x))),g(f(g(y),g(z)))),g(y))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4325 [] g(f(f(x,g(x)),f(f(f(g(g(x)),g(x)),g(f(g(y),g(z)))),g(y))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4326 [] g(f(f(x,g(x)),f(f(f(x,g(x)),g(f(g(y),g(z)))),g(y))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). 4327 [] g(f(f(x,g(x)),f(f(f(x,g(x)),f(g(g(y)),g(g(z)))),g(z))))=g(f(y,f(f(u,g(u)),g(f(x,g(x)))))). 4328 [] g(f(f(x,g(x)),f(f(f(x,g(x)),f(y,g(g(z)))),g(z))))=g(f(y,f(f(u,g(u)),g(f(x,g(x)))))). 4329 [] g(f(f(x,g(x)),f(f(f(x,g(x)),f(y,z)),g(z))))=g(f(y,f(f(u,g(u)),g(f(x,g(x)))))). 4330 [] g(f(f(x,g(x)),f(f(y,z),g(z))))=g(f(y,f(f(u,g(u)),g(f(x,g(x)))))). 4331 [] g(f(f(x,y),g(y)))=g(f(x,f(f(z,g(z)),g(f(u,g(u)))))). 4332 [] f(g(g(x)),g(f(y,x)))=g(f(y,f(f(z,g(z)),g(f(u,g(u)))))). 4333 [] f(x,g(f(y,x)))=g(f(y,f(f(z,g(z)),g(f(u,g(u)))))). 4334 [] f(x,f(g(x),g(y)))=g(f(y,f(f(z,g(z)),g(f(u,g(u)))))). 4335 [] f(x,f(g(x),g(y)))=g(f(y,f(f(z,g(z)),f(g(g(u)),g(u))))). 4336 [] f(x,f(g(x),g(y)))=g(f(y,f(f(z,g(z)),f(u,g(u))))). 4337 [] f(x,f(g(x),g(y)))=g(f(y,f(z,g(z)))). 4338 [] f(x,f(g(x),g(y)))=f(g(f(z,g(z))),g(y)). 4339 [] f(x,f(g(x),g(y)))=f(f(g(g(z)),g(z)),g(y)). 4340 [] f(x,f(g(x),g(y)))=f(f(z,g(z)),g(y)). 4341 [] f(x,f(g(x),g(y)))=g(y). 4342 [] f(x,f(f(g(y),g(z)),g(f(f(u,g(f(v,u))),f(g(w),f(g(f(y,g(x))),g(f(y,g(f(v6,f(g(f(z,v6)),y)))))))))))=f(w,v). 4343 [] f(x,f(f(g(y),g(z)),g(f(f(u,f(g(u),g(v))),f(g(w),f(g(f(y,g(x))),g(f(y,g(f(v6,f(g(f(z,v6)),y)))))))))))=f(w,v). 4344 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(g(f(y,g(x))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=f(v,u). 4345 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(g(g(x)),g(y)),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=f(v,u). 4346 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=f(v,u). 4347 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,g(f(w,f(f(g(w),g(z)),y)))))))))))=f(v,u). 4348 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,f(g(f(f(g(w),g(z)),y)),g(w))))))))))=f(v,u). 4349 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,f(f(g(y),g(f(g(w),g(z)))),g(w))))))))))=f(v,u). 4350 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,f(f(g(y),f(g(g(z)),g(g(w)))),g(w))))))))))=f(v,u). 4351 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,f(f(g(y),f(z,g(g(w)))),g(w))))))))))=f(v,u). 4352 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),g(f(y,f(f(g(y),f(z,w)),g(w))))))))))=f(v,u). 4353 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),f(g(f(f(g(y),f(z,w)),g(w))),g(y))))))))=f(v,u). 4354 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),f(f(g(g(w)),g(f(g(y),f(z,w)))),g(y))))))))=f(v,u). 4355 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),f(f(w,g(f(g(y),f(z,w)))),g(y))))))))=f(v,u). 4356 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),f(f(w,f(g(f(z,w)),g(g(y)))),g(y))))))))=f(v,u). 4357 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),f(f(w,f(f(g(w),g(z)),g(g(y)))),g(y))))))))=f(v,u). 4358 [] f(x,f(f(g(y),g(z)),g(f(g(u),f(g(v),f(f(x,g(y)),f(f(w,f(f(g(w),g(z)),y)),g(y))))))))=f(v,u). 4359 [] f(x,f(f(g(y),g(z)),f(g(f(g(u),f(f(x,g(y)),f(f(v,f(f(g(v),g(z)),y)),g(y))))),g(g(w)))))=f(u,w). 4360 [] f(x,f(f(g(y),g(z)),f(f(g(f(f(x,g(y)),f(f(u,f(f(g(u),g(z)),y)),g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4361 [] f(x,f(f(g(y),g(z)),f(f(f(g(f(f(u,f(f(g(u),g(z)),y)),g(y))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4362 [] f(x,f(f(g(y),g(z)),f(f(f(f(g(g(y)),g(f(u,f(f(g(u),g(z)),y)))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4363 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,g(f(u,f(f(g(u),g(z)),y)))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4364 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(g(f(f(g(u),g(z)),y)),g(u))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4365 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),g(f(g(u),g(z)))),g(u))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4366 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(g(g(z)),g(g(u)))),g(u))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4367 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,g(g(u)))),g(u))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4368 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(x,g(y)))),g(g(v))),g(g(w)))))=f(v,w). 4369 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(g(g(y)),g(x))),g(g(v))),g(g(w)))))=f(v,w). 4370 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),g(g(v))),g(g(w)))))=f(v,w). 4371 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),v),g(g(w)))))=f(v,w). 4372 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),v),w)))=f(v,w). 4373 [] f(x,f(f(g(y),g(z)),g(f(u,f(g(f(v,u)),f(g(f(y,g(x))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=v. 4374 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(g(f(y,g(x))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=v. 4375 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(g(g(x)),g(y)),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=v. 4376 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,g(f(w,f(g(f(z,w)),y)))))))))))=v. 4377 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,g(f(w,f(f(g(w),g(z)),y)))))))))))=v. 4378 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,f(g(f(f(g(w),g(z)),y)),g(w))))))))))=v. 4379 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,f(f(g(y),g(f(g(w),g(z)))),g(w))))))))))=v. 4380 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,f(f(g(y),f(g(g(z)),g(g(w)))),g(w))))))))))=v. 4381 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,f(f(g(y),f(z,g(g(w)))),g(w))))))))))=v. 4382 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),g(f(y,f(f(g(y),f(z,w)),g(w))))))))))=v. 4383 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),f(g(f(f(g(y),f(z,w)),g(w))),g(y))))))))=v. 4384 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),f(f(g(g(w)),g(f(g(y),f(z,w)))),g(y))))))))=v. 4385 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),f(f(w,g(f(g(y),f(z,w)))),g(y))))))))=v. 4386 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),f(f(w,f(g(f(z,w)),g(g(y)))),g(y))))))))=v. 4387 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),f(f(w,f(f(g(w),g(z)),g(g(y)))),g(y))))))))=v. 4388 [] f(x,f(f(g(y),g(z)),g(f(u,f(f(g(u),g(v)),f(f(x,g(y)),f(f(w,f(f(g(w),g(z)),y)),g(y))))))))=v. 4389 [] f(x,f(f(g(y),g(z)),f(g(f(f(g(u),g(v)),f(f(x,g(y)),f(f(w,f(f(g(w),g(z)),y)),g(y))))),g(u))))=v. 4390 [] f(x,f(f(g(y),g(z)),f(f(g(f(f(x,g(y)),f(f(u,f(f(g(u),g(z)),y)),g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4391 [] f(x,f(f(g(y),g(z)),f(f(f(g(f(f(u,f(f(g(u),g(z)),y)),g(y))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4392 [] f(x,f(f(g(y),g(z)),f(f(f(f(g(g(y)),g(f(u,f(f(g(u),g(z)),y)))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4393 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,g(f(u,f(f(g(u),g(z)),y)))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4394 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(g(f(f(g(u),g(z)),y)),g(u))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4395 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),g(f(g(u),g(z)))),g(u))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4396 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(g(g(z)),g(g(u)))),g(u))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4397 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,g(g(u)))),g(u))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4398 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(x,g(y)))),g(f(g(v),g(w)))),g(v))))=w. 4399 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(g(g(y)),g(x))),g(f(g(v),g(w)))),g(v))))=w. 4400 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),g(f(g(v),g(w)))),g(v))))=w. 4401 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),f(g(g(v)),g(g(w)))),g(w))))=v. 4402 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),f(v,g(g(w)))),g(w))))=v. 4403 [] f(x,f(f(g(y),g(z)),f(f(f(f(y,f(f(g(y),f(z,u)),g(u))),f(y,g(x))),f(v,w)),g(w))))=v. 4404 [] f(f(x,y),g(y))=x. 4405 [] g(f(g(f(x,f(f(g(x),f(f(g(g(x)),g(x)),g(y))),g(f(x,g(x)))))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4406 [] g(f(g(f(x,f(f(g(x),f(f(x,g(x)),g(y))),g(f(x,g(x)))))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4407 [] g(f(g(f(x,f(f(g(x),g(y)),g(f(x,g(x)))))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4408 [] g(f(g(f(x,f(f(g(x),g(y)),f(g(g(x)),g(x))))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4409 [] g(f(g(f(x,f(f(g(x),g(y)),f(x,g(x))))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4410 [] g(f(f(g(f(f(g(x),g(y)),f(x,g(x)))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4411 [] g(f(f(f(g(f(x,g(x))),g(f(g(x),g(y)))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4412 [] g(f(f(f(f(g(g(x)),g(x)),g(f(g(x),g(y)))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4413 [] g(f(f(f(f(x,g(x)),g(f(g(x),g(y)))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4414 [] g(f(f(f(f(x,g(x)),f(g(g(y)),g(g(x)))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4415 [] g(f(f(f(f(x,g(x)),f(y,g(g(x)))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4416 [] g(f(f(f(f(x,g(x)),f(y,x)),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4417 [] g(f(f(f(x,y),g(y)),g(f(g(z),x))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). 4418 [] g(f(x,g(f(g(y),x))))=g(f(z,g(f(u,f(g(f(y,u)),z))))). 4419 [] g(f(x,f(g(x),g(g(y)))))=g(f(z,g(f(u,f(g(f(y,u)),z))))). 4420 [] g(f(x,f(g(x),y)))=g(f(z,g(f(u,f(g(f(y,u)),z))))). 4421 [] f(g(f(g(x),y)),g(x))=g(f(z,g(f(u,f(g(f(y,u)),z))))). 4422 [] f(f(g(x),g(g(y))),g(y))=g(f(z,g(f(u,f(g(f(x,u)),z))))). 4423 [] f(f(g(x),y),g(y))=g(f(z,g(f(u,f(g(f(x,u)),z))))). 4424 [] g(f(x,g(f(y,f(g(f(z,y)),x)))))=g(z). 4425 [] g(f(x,g(f(y,f(f(g(y),g(z)),x)))))=g(z). 4426 [] g(f(x,f(g(f(f(g(y),g(z)),x)),g(y))))=g(z). 4427 [] g(f(x,f(f(g(x),g(f(g(y),g(z)))),g(y))))=g(z). 4428 [] g(f(x,f(f(g(x),f(g(g(y)),g(g(z)))),g(z))))=g(y). 4429 [] g(f(x,f(f(g(x),f(y,g(g(z)))),g(z))))=g(y). 4430 [] g(f(x,f(f(g(x),f(y,z)),g(z))))=g(y). 4431 [] f(g(f(f(g(x),f(y,z)),g(z))),g(x))=g(y). 4432 [] f(f(g(g(x)),g(f(g(y),f(z,x)))),g(y))=g(z). 4433 [] f(f(x,g(f(g(y),f(z,x)))),g(y))=g(z). 4434 [] f(f(x,f(g(f(y,x)),g(g(z)))),g(z))=g(y). 4435 [] f(f(x,f(f(g(x),g(y)),g(g(z)))),g(z))=g(y). 4436 [] f(f(x,f(f(g(x),g(y)),z)),g(z))=g(y). 4437 [] f(x,f(g(f(y,x)),g(f(g(f(z,g(f(u,f(g(f(v,u)),z))))),g(g(f(v,z)))))))=f(g(y),g(z)). 4438 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,g(f(u,f(g(f(v,u)),z))))),g(g(f(v,z)))))))=f(g(y),g(z)). 4439 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,g(f(u,f(f(g(u),g(v)),z))))),g(g(f(v,z)))))))=f(g(y),g(z)). 4440 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,f(g(f(f(g(u),g(v)),z)),g(u)))),g(g(f(v,z)))))))=f(g(y),g(z)). 4441 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,f(f(g(z),g(f(g(u),g(v)))),g(u)))),g(g(f(v,z)))))))=f(g(y),g(z)). 4442 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,f(f(g(z),f(g(g(u)),g(g(v)))),g(v)))),g(g(f(u,z)))))))=f(g(y),g(z)). 4443 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,f(f(g(z),f(u,g(g(v)))),g(v)))),g(g(f(u,z)))))))=f(g(y),g(z)). 4444 [] f(x,f(f(g(x),g(y)),g(f(g(f(z,f(f(g(z),f(u,v)),g(v)))),g(g(f(u,z)))))))=f(g(y),g(z)). 4445 [] f(x,f(f(g(x),g(y)),g(f(f(g(f(f(g(z),f(u,v)),g(v))),g(z)),g(g(f(u,z)))))))=f(g(y),g(z)). 4446 [] f(x,f(f(g(x),g(y)),g(f(f(f(g(g(z)),g(f(g(u),f(v,z)))),g(u)),g(g(f(v,u)))))))=f(g(y),g(u)). 4447 [] f(x,f(f(g(x),g(y)),g(f(f(f(z,g(f(g(u),f(v,z)))),g(u)),g(g(f(v,u)))))))=f(g(y),g(u)). 4448 [] f(x,f(f(g(x),g(y)),g(f(f(f(z,f(g(f(u,z)),g(g(v)))),g(v)),g(g(f(u,v)))))))=f(g(y),g(v)). 4449 [] f(x,f(f(g(x),g(y)),g(f(f(f(z,f(f(g(z),g(u)),g(g(v)))),g(v)),g(g(f(u,v)))))))=f(g(y),g(v)). 4450 [] f(x,f(f(g(x),g(y)),g(f(f(f(z,f(f(g(z),g(u)),v)),g(v)),g(g(f(u,v)))))))=f(g(y),g(v)). 4451 [] f(x,f(f(g(x),g(y)),g(f(g(z),g(g(f(z,u)))))))=f(g(y),g(u)). 4452 [] f(x,f(f(g(x),g(y)),g(f(g(z),g(f(g(u),g(z)))))))=f(g(y),g(u)). 4453 [] f(x,f(f(g(x),g(y)),g(f(g(z),f(g(g(z)),g(g(u)))))))=f(g(y),g(u)). 4454 [] f(x,f(f(g(x),g(y)),g(f(g(z),f(z,g(g(u)))))))=f(g(y),g(u)). 4455 [] f(x,f(f(g(x),g(y)),g(f(g(z),f(z,u)))))=f(g(y),g(u)). 4456 [] f(x,f(f(g(x),g(y)),g(z)))=f(g(y),g(z)). 4457 [] g(f(x,f(f(g(x),f(y,g(f(z,f(f(g(z),g(u)),y))))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(u,w)),y))))))),g(f(v,g(v)))). 4458 [] g(f(x,f(f(g(x),f(y,f(g(f(f(g(z),g(u)),y)),g(z)))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(u,w)),y))))))),g(f(v,g(v)))). 4459 [] g(f(x,f(f(g(x),f(y,f(f(g(y),g(f(g(z),g(u)))),g(z)))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(u,w)),y))))))),g(f(v,g(v)))). 4460 [] g(f(x,f(f(g(x),f(y,f(f(g(y),f(g(g(z)),g(g(u)))),g(u)))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(z,w)),y))))))),g(f(v,g(v)))). 4461 [] g(f(x,f(f(g(x),f(y,f(f(g(y),f(z,g(g(u)))),g(u)))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(z,w)),y))))))),g(f(v,g(v)))). 4462 [] g(f(x,f(f(g(x),f(y,f(f(g(y),f(z,u)),g(u)))),v)))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(z,w)),y))))))),g(f(v,g(v)))). 4463 [] f(g(f(f(g(x),f(y,f(f(g(y),f(z,u)),g(u)))),v)),g(x))=f(f(g(v),f(g(f(v,g(v))),g(f(y,g(f(w,f(g(f(z,w)),y))))))),g(f(v,g(v)))). 4464 [] f(f(g(x),g(f(g(y),f(z,f(f(g(z),f(u,v)),g(v)))))),g(y))=f(f(g(x),f(g(f(x,g(x))),g(f(z,g(f(w,f(g(f(u,w)),z))))))),g(f(x,g(x)))). 4465 [] f(f(g(x),f(g(f(y,f(f(g(y),f(z,u)),g(u)))),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(y,g(f(w,f(g(f(z,w)),y))))))),g(f(x,g(x)))). 4466 [] f(f(g(x),f(f(g(f(f(g(y),f(z,u)),g(u))),g(y)),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(y,g(f(w,f(g(f(z,w)),y))))))),g(f(x,g(x)))). 4467 [] f(f(g(x),f(f(f(g(g(y)),g(f(g(z),f(u,y)))),g(z)),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(z,g(f(w,f(g(f(u,w)),z))))))),g(f(x,g(x)))). 4468 [] f(f(g(x),f(f(f(y,g(f(g(z),f(u,y)))),g(z)),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(z,g(f(w,f(g(f(u,w)),z))))))),g(f(x,g(x)))). 4469 [] f(f(g(x),f(f(f(y,f(g(f(z,y)),g(g(u)))),g(u)),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(u,g(f(w,f(g(f(z,w)),u))))))),g(f(x,g(x)))). 4470 [] f(f(g(x),f(f(f(y,f(f(g(y),g(z)),g(g(u)))),g(u)),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(u,g(f(w,f(g(f(z,w)),u))))))),g(f(x,g(x)))). 4471 [] f(f(g(x),f(f(f(y,f(f(g(y),g(z)),u)),g(u)),g(g(v)))),g(v))=f(f(g(x),f(g(f(x,g(x))),g(f(u,g(f(w,f(g(f(z,w)),u))))))),g(f(x,g(x)))). 4472 [] f(f(g(x),f(g(y),g(g(z)))),g(z))=f(f(g(x),f(g(f(x,g(x))),g(f(u,g(f(v,f(g(f(y,v)),u))))))),g(f(x,g(x)))). 4473 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(g(f(x,g(x))),g(f(u,g(f(v,f(g(f(y,v)),u))))))),g(f(x,g(x)))). 4474 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(g(g(x)),g(x)),g(f(u,g(f(v,f(g(f(y,v)),u))))))),g(f(x,g(x)))). 4475 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,g(f(v,f(g(f(y,v)),u))))))),g(f(x,g(x)))). 4476 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,g(f(v,f(f(g(v),g(y)),u))))))),g(f(x,g(x)))). 4477 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,f(g(f(f(g(v),g(y)),u)),g(v)))))),g(f(x,g(x)))). 4478 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,f(f(g(u),g(f(g(v),g(y)))),g(v)))))),g(f(x,g(x)))). 4479 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,f(f(g(u),f(g(g(y)),g(g(v)))),g(v)))))),g(f(x,g(x)))). 4480 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,f(f(g(u),f(y,g(g(v)))),g(v)))))),g(f(x,g(x)))). 4481 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(f(u,f(f(g(u),f(y,v)),g(v)))))),g(f(x,g(x)))). 4482 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),f(g(f(f(g(u),f(y,v)),g(v))),g(u)))),g(f(x,g(x)))). 4483 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),f(f(g(g(u)),g(f(g(v),f(y,u)))),g(v)))),g(f(x,g(x)))). 4484 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),f(f(u,g(f(g(v),f(y,u)))),g(v)))),g(f(x,g(x)))). 4485 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),f(f(u,f(g(f(y,u)),g(g(v)))),g(v)))),g(f(x,g(x)))). 4486 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),f(f(u,f(f(g(u),g(y)),g(g(v)))),g(v)))),g(f(x,g(x)))). 4487 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),f(f(u,f(f(g(u),g(y)),v)),g(v)))),g(f(x,g(x)))). 4488 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(x,g(x)),g(y))),g(f(x,g(x)))). 4489 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),g(y)),g(f(x,g(x)))). 4490 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),g(y)),f(g(g(x)),g(x))). 4491 [] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),g(y)),f(x,g(x))). 4492 [] f(f(g(f(x,g(x))),g(y)),f(g(f(z,g(f(y,f(u,z))))),g(f(g(u),g(f(v,f(g(f(w,v)),g(u))))))))=g(f(w,g(u))). 4493 [] f(f(f(g(g(x)),g(x)),g(y)),f(g(f(z,g(f(y,f(u,z))))),g(f(g(u),g(f(v,f(g(f(w,v)),g(u))))))))=g(f(w,g(u))). 4494 [] f(f(f(x,g(x)),g(y)),f(g(f(z,g(f(y,f(u,z))))),g(f(g(u),g(f(v,f(g(f(w,v)),g(u))))))))=g(f(w,g(u))). 4495 [] f(g(x),f(g(f(y,g(f(x,f(z,y))))),g(f(g(z),g(f(u,f(g(f(v,u)),g(z))))))))=g(f(v,g(z))). 4496 [] f(g(x),f(g(f(y,f(g(f(z,y)),g(x)))),g(f(g(z),g(f(u,f(g(f(v,u)),g(z))))))))=g(f(v,g(z))). 4497 [] f(g(x),f(g(f(y,f(f(g(y),g(z)),g(x)))),g(f(g(z),g(f(u,f(g(f(v,u)),g(z))))))))=g(f(v,g(z))). 4498 [] f(g(x),f(f(g(g(x)),g(g(y))),g(f(g(y),g(f(z,f(g(f(u,z)),g(y))))))))=g(f(u,g(y))). 4499 [] f(g(x),f(f(x,g(g(y))),g(f(g(y),g(f(z,f(g(f(u,z)),g(y))))))))=g(f(u,g(y))). 4500 [] f(g(x),f(f(x,y),g(f(g(y),g(f(z,f(g(f(u,z)),g(y))))))))=g(f(u,g(y))). 4501 [] f(g(x),f(f(x,y),g(f(g(y),g(f(z,f(f(g(z),g(u)),g(y))))))))=g(f(u,g(y))). 4502 [] f(g(x),f(f(x,y),g(f(g(y),g(f(g(z),g(y)))))))=g(f(z,g(y))). 4503 [] f(g(x),f(f(x,y),g(f(g(y),f(g(g(y)),g(g(z)))))))=g(f(z,g(y))). 4504 [] f(g(x),f(f(x,y),g(f(g(y),f(y,g(g(z)))))))=g(f(z,g(y))). 4505 [] f(g(x),f(f(x,y),g(f(g(y),f(y,z)))))=g(f(z,g(y))). 4506 [] f(g(x),f(f(x,y),g(z)))=g(f(z,g(y))). 4507 [] f(g(x),f(f(x,y),g(z)))=f(g(g(y)),g(z)). 4508 [] f(g(x),f(f(x,y),g(z)))=f(y,g(z)). 4509 [] f(x,f(f(g(x),f(f(g(g(x)),g(x)),g(f(g(f(f(y,g(f(z,f(g(f(u,z)),y)))),g(f(y,g(f(v,f(g(f(u,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4510 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,g(f(z,f(g(f(u,z)),y)))),g(f(y,g(f(v,f(g(f(u,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4511 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,g(f(z,f(f(g(z),g(u)),y)))),g(f(y,g(f(v,f(g(f(u,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4512 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(g(f(f(g(z),g(u)),y)),g(z))),g(f(y,g(f(v,f(g(f(u,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4513 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),g(f(g(z),g(u)))),g(z))),g(f(y,g(f(v,f(g(f(u,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4514 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(g(g(z)),g(g(u)))),g(u))),g(f(y,g(f(v,f(g(f(z,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4515 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,g(g(u)))),g(u))),g(f(y,g(f(v,f(g(f(z,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4516 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,g(f(v,f(g(f(z,v)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4517 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,g(f(v,f(f(g(v),g(z)),y))))))),g(w))))),g(f(x,g(x)))))=w. 4518 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,f(g(f(f(g(v),g(z)),y)),g(v)))))),g(w))))),g(f(x,g(x)))))=w. 4519 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,f(f(g(y),g(f(g(v),g(z)))),g(v)))))),g(w))))),g(f(x,g(x)))))=w. 4520 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,f(f(g(y),f(g(g(z)),g(g(v)))),g(v)))))),g(w))))),g(f(x,g(x)))))=w. 4521 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,f(f(g(y),f(z,g(g(v)))),g(v)))))),g(w))))),g(f(x,g(x)))))=w. 4522 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(f(y,f(f(g(y),f(z,v)),g(v)))))),g(w))))),g(f(x,g(x)))))=w. 4523 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),f(g(f(f(g(y),f(z,v)),g(v))),g(y)))),g(w))))),g(f(x,g(x)))))=w. 4524 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),f(f(g(g(v)),g(f(g(y),f(z,v)))),g(y)))),g(w))))),g(f(x,g(x)))))=w. 4525 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),f(f(v,g(f(g(y),f(z,v)))),g(y)))),g(w))))),g(f(x,g(x)))))=w. 4526 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),f(f(v,f(g(f(z,v)),g(g(y)))),g(y)))),g(w))))),g(f(x,g(x)))))=w. 4527 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),f(f(v,f(f(g(v),g(z)),g(g(y)))),g(y)))),g(w))))),g(f(x,g(x)))))=w. 4528 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),f(f(v,f(f(g(v),g(z)),y)),g(y)))),g(w))))),g(f(x,g(x)))))=w. 4529 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(g(f(f(y,f(f(g(y),f(z,u)),g(u))),g(z))),g(v))))),g(f(x,g(x)))))=v. 4530 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(g(g(y)),g(f(z,f(f(g(z),f(y,u)),g(u))))),g(v))))),g(f(x,g(x)))))=v. 4531 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,g(f(z,f(f(g(z),f(y,u)),g(u))))),g(v))))),g(f(x,g(x)))))=v. 4532 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,f(g(f(f(g(z),f(y,u)),g(u))),g(z))),g(v))))),g(f(x,g(x)))))=v. 4533 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,f(f(g(g(z)),g(f(g(u),f(y,z)))),g(u))),g(v))))),g(f(x,g(x)))))=v. 4534 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,f(f(z,g(f(g(u),f(y,z)))),g(u))),g(v))))),g(f(x,g(x)))))=v. 4535 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,f(f(z,f(g(f(y,z)),g(g(u)))),g(u))),g(v))))),g(f(x,g(x)))))=v. 4536 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,f(f(z,f(f(g(z),g(y)),g(g(u)))),g(u))),g(v))))),g(f(x,g(x)))))=v. 4537 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,f(f(z,f(f(g(z),g(y)),u)),g(u))),g(v))))),g(f(x,g(x)))))=v. 4538 [] f(x,f(f(g(x),f(f(x,g(x)),g(f(f(y,g(y)),g(z))))),g(f(x,g(x)))))=z. 4539 [] f(x,f(f(g(x),f(f(x,g(x)),g(g(y)))),g(f(x,g(x)))))=y. 4540 [] f(x,f(f(g(x),f(f(x,g(x)),y)),g(f(x,g(x)))))=y. 4541 [] f(x,f(f(g(x),y),g(f(x,g(x)))))=y. 4542 [] f(x,f(f(g(x),y),f(g(g(x)),g(x))))=y. 4543 [] f(x,f(f(g(x),y),f(x,g(x))))=y. 4544 [] f(g(f(x,f(f(g(x),g(y)),z))),f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(z),w). 4545 [] f(f(g(f(f(g(x),g(y)),z)),g(x)),f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(z),w). 4546 [] f(f(f(g(x),g(f(g(y),g(z)))),g(y)),f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4547 [] f(f(f(g(x),f(g(g(y)),g(g(z)))),g(z)),f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4548 [] f(f(f(g(x),f(y,g(g(z)))),g(z)),f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4549 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4550 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,g(f(u,f(f(g(u),g(y)),x))))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4551 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(g(f(f(g(u),g(y)),x)),g(u)))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4552 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),g(f(g(u),g(y)))),g(u)))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4553 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(g(g(y)),g(g(u)))),g(u)))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4554 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(y,g(g(u)))),g(u)))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4555 [] f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(y,u)),g(u)))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4556 [] f(f(f(g(x),f(y,z)),g(z)),f(f(g(f(f(g(x),f(y,u)),g(u))),g(x)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4557 [] f(f(f(g(x),f(y,z)),g(z)),f(f(f(g(g(u)),g(f(g(x),f(y,u)))),g(x)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4558 [] f(f(f(g(x),f(y,z)),g(z)),f(f(f(u,g(f(g(x),f(y,u)))),g(x)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4559 [] f(f(f(g(x),f(y,z)),g(z)),f(f(f(u,f(g(f(y,u)),g(g(x)))),g(x)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4560 [] f(f(f(g(x),f(y,z)),g(z)),f(f(f(u,f(f(g(u),g(y)),g(g(x)))),g(x)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4561 [] f(f(f(g(x),f(y,z)),g(z)),f(f(f(u,f(f(g(u),g(y)),x)),g(x)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4562 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(f(g(u),f(g(f(u,g(u))),g(v))),g(f(u,g(u))))))))=f(g(x),v). 4563 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(f(g(u),f(f(g(g(u)),g(u)),g(v))),g(f(u,g(u))))))))=f(g(x),v). 4564 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(f(g(u),f(f(u,g(u)),g(v))),g(f(u,g(u))))))))=f(g(x),v). 4565 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(f(g(u),g(v)),g(f(u,g(u))))))))=f(g(x),v). 4566 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(f(g(u),g(v)),f(g(g(u)),g(u)))))))=f(g(x),v). 4567 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(f(g(u),g(v)),f(u,g(u)))))))=f(g(x),v). 4568 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(g(u))))=f(g(x),u). 4569 [] f(f(f(g(x),f(y,z)),g(z)),f(g(y),u))=f(g(x),u). 4570 [] f(g(f(x,g(f(y,g(f(z,f(f(g(z),g(u)),y))))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). 4571 [] f(g(f(x,g(f(y,f(g(f(f(g(z),g(u)),y)),g(z)))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). 4572 [] f(g(f(x,g(f(y,f(f(g(y),g(f(g(z),g(u)))),g(z)))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). 4573 [] f(g(f(x,g(f(y,f(f(g(y),f(g(g(z)),g(g(u)))),g(u)))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). 4574 [] f(g(f(x,g(f(y,f(f(g(y),f(z,g(g(u)))),g(u)))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). 4575 [] f(g(f(x,g(f(y,f(f(g(y),f(z,u)),g(u)))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). 4576 [] f(g(f(x,f(g(f(f(g(y),f(z,u)),g(u))),g(y)))),g(f(x,g(f(x,f(v,x))))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). 4577 [] f(g(f(x,f(f(g(g(y)),g(f(g(z),f(u,y)))),g(z)))),g(f(x,g(f(x,f(v,x))))))=g(f(z,f(f(g(f(w,f(g(f(u,w)),z))),f(g(f(z,g(f(w,f(g(f(u,w)),z))))),g(v))),g(f(z,g(f(w,f(g(f(u,w)),z)))))))). 4578 [] f(g(f(x,f(f(y,g(f(g(z),f(u,y)))),g(z)))),g(f(x,g(f(x,f(v,x))))))=g(f(z,f(f(g(f(w,f(g(f(u,w)),z))),f(g(f(z,g(f(w,f(g(f(u,w)),z))))),g(v))),g(f(z,g(f(w,f(g(f(u,w)),z)))))))). 4579 [] f(g(f(x,f(f(y,f(g(f(z,y)),g(g(u)))),g(u)))),g(f(x,g(f(x,f(v,x))))))=g(f(u,f(f(g(f(w,f(g(f(z,w)),u))),f(g(f(u,g(f(w,f(g(f(z,w)),u))))),g(v))),g(f(u,g(f(w,f(g(f(z,w)),u)))))))). 4580 [] f(g(f(x,f(f(y,f(f(g(y),g(z)),g(g(u)))),g(u)))),g(f(x,g(f(x,f(v,x))))))=g(f(u,f(f(g(f(w,f(g(f(z,w)),u))),f(g(f(u,g(f(w,f(g(f(z,w)),u))))),g(v))),g(f(u,g(f(w,f(g(f(z,w)),u)))))))). 4581 [] f(g(f(x,f(f(y,f(f(g(y),g(z)),u)),g(u)))),g(f(x,g(f(x,f(v,x))))))=g(f(u,f(f(g(f(w,f(g(f(z,w)),u))),f(g(f(u,g(f(w,f(g(f(z,w)),u))))),g(v))),g(f(u,g(f(w,f(g(f(z,w)),u)))))))). 4582 [] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=g(f(u,f(f(g(f(v,f(g(f(y,v)),u))),f(g(f(u,g(f(v,f(g(f(y,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(y,v)),u)))))))). 4583 [] f(f(g(g(x)),g(y)),g(f(y,g(f(y,f(z,y))))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4584 [] f(f(x,g(y)),g(f(y,g(f(y,f(z,y))))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4585 [] f(f(x,g(y)),g(f(y,f(g(f(z,y)),g(y)))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4586 [] f(f(x,g(y)),g(f(y,f(f(g(y),g(z)),g(y)))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4587 [] f(f(x,g(y)),g(f(g(z),g(y))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4588 [] f(f(x,g(y)),f(g(g(y)),g(g(z))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4589 [] f(f(x,g(y)),f(y,g(g(z))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4590 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4591 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(f(v,f(f(g(v),g(x)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4592 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(g(f(f(g(v),g(x)),u)),g(v)),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4593 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),g(f(g(v),g(x)))),g(v)),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4594 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(g(g(x)),g(g(v)))),g(v)),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4595 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,g(g(v)))),g(v)),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4596 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4597 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,g(f(v,f(f(g(v),g(x)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4598 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,f(g(f(f(g(v),g(x)),u)),g(v)))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4599 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,f(f(g(u),g(f(g(v),g(x)))),g(v)))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4600 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,f(f(g(u),f(g(g(x)),g(g(v)))),g(v)))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4601 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,f(f(g(u),f(x,g(g(v)))),g(v)))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4602 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(f(u,f(f(g(u),f(x,v)),g(v)))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4603 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(f(g(f(f(g(u),f(x,v)),g(v))),g(u)),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4604 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(f(f(g(g(v)),g(f(g(u),f(x,v)))),g(u)),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4605 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(f(f(v,g(f(g(u),f(x,v)))),g(u)),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4606 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(f(f(v,f(g(f(x,v)),g(g(u)))),g(u)),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4607 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(f(f(v,f(f(g(v),g(x)),g(g(u)))),g(u)),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4608 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(f(f(v,f(f(g(v),g(x)),u)),g(u)),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4609 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(f(f(g(u),f(x,v)),g(v)),f(g(x),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4610 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). 4611 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,g(f(v,f(f(g(v),g(x)),u)))))))). 4612 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,f(g(f(f(g(v),g(x)),u)),g(v))))))). 4613 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,f(f(g(u),g(f(g(v),g(x)))),g(v))))))). 4614 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,f(f(g(u),f(g(g(x)),g(g(v)))),g(v))))))). 4615 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,f(f(g(u),f(x,g(g(v)))),g(v))))))). 4616 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(f(u,f(f(g(u),f(x,v)),g(v))))))). 4617 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),f(g(f(f(g(u),f(x,v)),g(v))),g(u))))). 4618 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),f(f(g(g(v)),g(f(g(u),f(x,v)))),g(u))))). 4619 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),f(f(v,g(f(g(u),f(x,v)))),g(u))))). 4620 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),f(f(v,f(g(f(x,v)),g(g(u)))),g(u))))). 4621 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),f(f(v,f(f(g(v),g(x)),g(g(u)))),g(u))))). 4622 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),f(f(v,f(f(g(v),g(x)),u)),g(u))))). 4623 [] f(f(x,g(y)),f(y,z))=g(f(u,f(f(g(u),g(z)),g(x)))). 4624 [] f(f(x,g(y)),f(y,z))=g(f(g(z),g(x))). 4625 [] f(f(x,g(y)),f(y,z))=f(g(g(x)),g(g(z))). 4626 [] f(f(x,g(y)),f(y,z))=f(x,g(g(z))). 4627 [] f(f(x,g(y)),f(y,z))=f(x,z). 4628 [] f(x,f(f(g(f(y,f(f(g(y),g(z)),x))),f(g(f(x,g(f(y,f(g(f(z,y)),x))))),g(f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(v))))),g(f(x,g(f(y,f(g(f(z,y)),x)))))))=v. 4629 [] f(x,f(f(f(g(f(f(g(y),g(z)),x)),g(y)),f(g(f(x,g(f(y,f(g(f(z,y)),x))))),g(f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(v))))),g(f(x,g(f(y,f(g(f(z,y)),x)))))))=v. 4630 [] f(x,f(f(f(f(g(x),g(f(g(y),g(z)))),g(y)),f(g(f(x,g(f(y,f(g(f(z,y)),x))))),g(f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(v))))),g(f(x,g(f(y,f(g(f(z,y)),x)))))))=v. 4631 [] f(x,f(f(f(f(g(x),f(g(g(y)),g(g(z)))),g(z)),f(g(f(x,g(f(z,f(g(f(y,z)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4632 [] f(x,f(f(f(f(g(x),f(y,g(g(z)))),g(z)),f(g(f(x,g(f(z,f(g(f(y,z)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4633 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,g(f(z,f(g(f(y,z)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4634 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,g(f(z,f(f(g(z),g(y)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4635 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(g(f(f(g(z),g(y)),x)),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4636 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),g(f(g(z),g(y)))),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4637 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(g(g(y)),g(g(z)))),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4638 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(y,g(g(z)))),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4639 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(y,z)),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4640 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(g(f(f(g(x),f(y,z)),g(z))),g(x)),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4641 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(g(g(z)),g(f(g(x),f(y,z)))),g(x)),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4642 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(z,g(f(g(x),f(y,z)))),g(x)),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4643 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(z,f(g(f(y,z)),g(g(x)))),g(x)),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4644 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(z,f(f(g(z),g(y)),g(g(x)))),g(x)),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4645 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(z,f(f(g(z),g(y)),x)),g(x)),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4646 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4647 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,g(f(u,f(f(g(u),g(y)),x))))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4648 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(g(f(f(g(u),g(y)),x)),g(u)))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4649 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),g(f(g(u),g(y)))),g(u)))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4650 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),f(g(g(y)),g(g(u)))),g(u)))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4651 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),f(y,g(g(u)))),g(u)))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4652 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),f(y,u)),g(u)))),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4653 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(f(g(f(f(g(x),f(y,u)),g(u))),g(x)),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4654 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(f(f(g(g(u)),g(f(g(x),f(y,u)))),g(x)),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4655 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(f(f(u,g(f(g(x),f(y,u)))),g(x)),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4656 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(f(f(u,f(g(f(y,u)),g(g(x)))),g(x)),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4657 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(f(f(u,f(f(g(u),g(y)),g(g(x)))),g(x)),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4658 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(f(f(u,f(f(g(u),g(y)),x)),g(x)),g(v))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=v. 4659 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(y),g(u))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=u. 4660 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(g(g(u)),g(g(y))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=u. 4661 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(u,g(g(y))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=u. 4662 [] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(u,y))),g(f(x,g(f(z,f(g(f(y,z)),x)))))))=u. 4663 [] f(x,f(f(g(x),f(y,z)),g(f(x,g(f(u,f(g(f(z,u)),x)))))))=y. 4664 [] f(x,f(f(g(x),f(y,z)),g(f(x,g(f(u,f(f(g(u),g(z)),x)))))))=y. 4665 [] f(x,f(f(g(x),f(y,z)),g(f(x,f(g(f(f(g(u),g(z)),x)),g(u))))))=y. 4666 [] f(x,f(f(g(x),f(y,z)),g(f(x,f(f(g(x),g(f(g(u),g(z)))),g(u))))))=y. 4667 [] f(x,f(f(g(x),f(y,z)),g(f(x,f(f(g(x),f(g(g(z)),g(g(u)))),g(u))))))=y. 4668 [] f(x,f(f(g(x),f(y,z)),g(f(x,f(f(g(x),f(z,g(g(u)))),g(u))))))=y. 4669 [] f(x,f(f(g(x),f(y,z)),g(f(x,f(f(g(x),f(z,u)),g(u))))))=y. 4670 [] f(x,f(f(g(x),f(y,z)),f(g(f(f(g(x),f(z,u)),g(u))),g(x))))=y. 4671 [] f(x,f(f(g(x),f(y,z)),f(f(g(g(u)),g(f(g(x),f(z,u)))),g(x))))=y. 4672 [] f(x,f(f(g(x),f(y,z)),f(f(u,g(f(g(x),f(z,u)))),g(x))))=y. 4673 [] f(x,f(f(g(x),f(y,z)),f(f(u,f(g(f(z,u)),g(g(x)))),g(x))))=y. 4674 [] f(x,f(f(g(x),f(y,z)),f(f(u,f(f(g(u),g(z)),g(g(x)))),g(x))))=y. 4675 [] f(x,f(f(g(x),f(y,z)),f(f(u,f(f(g(u),g(z)),x)),g(x))))=y. 4676 [] f(x,f(f(g(x),f(y,z)),g(z)))=y. 4677 [] f(f(f(g(f(x,f(f(g(x),g(y)),z))),f(g(f(z,g(f(x,f(g(f(y,x)),z))))),g(f(g(f(z,g(f(u,f(g(f(y,u)),z))))),v)))),g(f(z,g(f(x,f(g(f(y,x)),z)))))),f(v,w))=f(v6,f(g(f(z,v6)),w)). 4678 [] f(f(f(f(g(f(f(g(x),g(y)),z)),g(x)),f(g(f(z,g(f(x,f(g(f(y,x)),z))))),g(f(g(f(z,g(f(u,f(g(f(y,u)),z))))),v)))),g(f(z,g(f(x,f(g(f(y,x)),z)))))),f(v,w))=f(v6,f(g(f(z,v6)),w)). 4679 [] f(f(f(f(f(g(x),g(f(g(y),g(z)))),g(y)),f(g(f(x,g(f(y,f(g(f(z,y)),x))))),g(f(g(f(x,g(f(u,f(g(f(z,u)),x))))),v)))),g(f(x,g(f(y,f(g(f(z,y)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4680 [] f(f(f(f(f(g(x),f(g(g(y)),g(g(z)))),g(z)),f(g(f(x,g(f(z,f(g(f(y,z)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4681 [] f(f(f(f(f(g(x),f(y,g(g(z)))),g(z)),f(g(f(x,g(f(z,f(g(f(y,z)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4682 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,g(f(z,f(g(f(y,z)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4683 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,g(f(z,f(f(g(z),g(y)),x))))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4684 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(g(f(f(g(z),g(y)),x)),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4685 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),g(f(g(z),g(y)))),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4686 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(g(g(y)),g(g(z)))),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4687 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(y,g(g(z)))),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4688 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(f(x,f(f(g(x),f(y,z)),g(z)))),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4689 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,g(f(u,f(g(f(y,u)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4690 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,g(f(u,f(f(g(u),g(y)),x))))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4691 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(g(f(f(g(u),g(y)),x)),g(u)))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4692 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),g(f(g(u),g(y)))),g(u)))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4693 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),f(g(g(y)),g(g(u)))),g(u)))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4694 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),f(y,g(g(u)))),g(u)))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4695 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(f(g(x),f(y,u)),g(u)))),v)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(v,w))=f(v6,f(g(f(x,v6)),w)). 4696 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(y),u)))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(u,v))=f(w,f(g(f(x,w)),v)). 4697 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(g(u),g(g(y))))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(u,v))=f(w,f(g(f(x,w)),v)). 4698 [] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(g(u),y))),g(f(x,g(f(z,f(g(f(y,z)),x)))))),f(u,v))=f(w,f(g(f(x,w)),v)). 4699 [] f(f(f(g(x),f(g(y),z)),g(f(x,g(f(u,f(g(f(z,u)),x)))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4700 [] f(f(f(g(x),f(g(y),z)),g(f(x,g(f(u,f(f(g(u),g(z)),x)))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4701 [] f(f(f(g(x),f(g(y),z)),g(f(x,f(g(f(f(g(u),g(z)),x)),g(u))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4702 [] f(f(f(g(x),f(g(y),z)),g(f(x,f(f(g(x),g(f(g(u),g(z)))),g(u))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4703 [] f(f(f(g(x),f(g(y),z)),g(f(x,f(f(g(x),f(g(g(z)),g(g(u)))),g(u))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4704 [] f(f(f(g(x),f(g(y),z)),g(f(x,f(f(g(x),f(z,g(g(u)))),g(u))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4705 [] f(f(f(g(x),f(g(y),z)),g(f(x,f(f(g(x),f(z,u)),g(u))))),f(y,v))=f(w,f(g(f(x,w)),v)). 4706 [] f(f(f(g(x),f(g(y),z)),g(z)),f(y,u))=f(v,f(g(f(x,v)),u)). 4707 [] f(f(f(g(x),g(y)),f(x,g(x))),f(y,z))=f(u,f(g(f(x,u)),z)). 4708 [] f(f(g(x),g(y)),f(y,z))=f(u,f(g(f(x,u)),z)). 4709 [] f(x,f(f(g(x),g(y)),z))=f(g(y),z). 4710 [] f(x,g(f(y,f(f(g(y),g(z)),x))))=f(g(f(z,g(f(z,f(u,z))))),g(u)). 4711 [] f(x,g(f(g(y),x)))=f(g(f(y,g(f(y,f(z,y))))),g(z)). 4712 [] f(x,f(g(x),g(g(y))))=f(g(f(y,g(f(y,f(z,y))))),g(z)). 4713 [] f(x,f(g(x),y))=f(g(f(y,g(f(y,f(z,y))))),g(z)). 4714 [] f(x,f(g(x),y))=f(g(f(y,f(g(f(z,y)),g(y)))),g(z)). 4715 [] f(x,f(g(x),y))=f(g(f(y,f(f(g(y),g(z)),g(y)))),g(z)). 4716 [] f(x,f(g(x),y))=f(g(f(g(z),g(y))),g(z)). 4717 [] f(x,f(g(x),y))=f(f(g(g(y)),g(g(z))),g(z)). 4718 [] f(x,f(g(x),y))=f(f(y,g(g(z))),g(z)). 4719 [] f(x,f(g(x),y))=f(f(y,z),g(z)). 4720 [] f(x,f(g(x),y))=y. 4721 [] f(f(g(f(x,g(f(y,f(f(g(y),g(z)),x))))),g(f(u,g(f(z,x))))),g(f(x,g(f(y,f(g(f(z,y)),x))))))=f(x,f(g(u),g(f(x,g(f(y,f(g(f(z,y)),x))))))). 4722 [] f(f(g(f(x,g(f(g(y),x)))),g(f(z,g(f(y,x))))),g(f(x,g(f(u,f(g(f(y,u)),x))))))=f(x,f(g(z),g(f(x,g(f(u,f(g(f(y,u)),x))))))). 4723 [] f(f(g(f(x,f(g(x),g(g(y))))),g(f(z,g(f(y,x))))),g(f(x,g(f(u,f(g(f(y,u)),x))))))=f(x,f(g(z),g(f(x,g(f(u,f(g(f(y,u)),x))))))). 4724 [] f(f(g(f(x,f(g(x),y))),g(f(z,g(f(y,x))))),g(f(x,g(f(u,f(g(f(y,u)),x))))))=f(x,f(g(z),g(f(x,g(f(u,f(g(f(y,u)),x))))))). 4725 [] f(f(g(x),g(f(y,g(f(x,z))))),g(f(z,g(f(u,f(g(f(x,u)),z))))))=f(z,f(g(y),g(f(z,g(f(u,f(g(f(x,u)),z))))))). 4726 [] f(f(g(x),g(f(y,f(g(z),g(x))))),g(f(z,g(f(u,f(g(f(x,u)),z))))))=f(z,f(g(y),g(f(z,g(f(u,f(g(f(x,u)),z))))))). 4727 [] f(f(g(x),f(g(f(g(y),g(x))),g(z))),g(f(y,g(f(u,f(g(f(x,u)),y))))))=f(y,f(g(z),g(f(y,g(f(u,f(g(f(x,u)),y))))))). 4728 [] f(f(g(x),f(f(g(g(x)),g(g(y))),g(z))),g(f(y,g(f(u,f(g(f(x,u)),y))))))=f(y,f(g(z),g(f(y,g(f(u,f(g(f(x,u)),y))))))). 4729 [] f(f(g(x),f(f(x,g(g(y))),g(z))),g(f(y,g(f(u,f(g(f(x,u)),y))))))=f(y,f(g(z),g(f(y,g(f(u,f(g(f(x,u)),y))))))). 4730 [] f(f(g(x),f(f(x,y),g(z))),g(f(y,g(f(u,f(g(f(x,u)),y))))))=f(y,f(g(z),g(f(y,g(f(u,f(g(f(x,u)),y))))))). 4731 [] f(f(x,g(y)),g(f(x,g(f(z,f(g(f(u,z)),x))))))=f(x,f(g(y),g(f(x,g(f(z,f(g(f(u,z)),x))))))). 4732 [] f(f(x,g(y)),g(f(x,g(f(z,f(f(g(z),g(u)),x))))))=f(x,f(g(y),g(f(x,g(f(z,f(g(f(u,z)),x))))))). 4733 [] f(f(x,g(y)),g(f(x,g(f(g(z),x)))))=f(x,f(g(y),g(f(x,g(f(u,f(g(f(z,u)),x))))))). 4734 [] f(f(x,g(y)),g(f(x,f(g(x),g(g(z))))))=f(x,f(g(y),g(f(x,g(f(u,f(g(f(z,u)),x))))))). 4735 [] f(f(x,g(y)),g(f(x,f(g(x),z))))=f(x,f(g(y),g(f(x,g(f(u,f(g(f(z,u)),x))))))). 4736 [] f(f(x,g(y)),g(z))=f(x,f(g(y),g(f(x,g(f(u,f(g(f(z,u)),x))))))). 4737 [] f(f(x,g(y)),g(z))=f(x,f(g(y),g(f(x,g(f(u,f(f(g(u),g(z)),x))))))). 4738 [] f(f(x,g(y)),g(z))=f(x,f(g(y),g(f(x,g(f(g(z),x)))))). 4739 [] f(f(x,g(y)),g(z))=f(x,f(g(y),g(f(x,f(g(x),g(g(z))))))). 4740 [] f(f(x,g(y)),g(z))=f(x,f(g(y),g(f(x,f(g(x),z))))). 4741 [] f(f(x,g(y)),g(z))=f(x,f(g(y),g(z))). 4742 [] f(x,f(g(f(g(f(y,g(f(z,f(f(g(z),g(u)),y))))),x)),g(f(g(f(y,g(f(z,f(g(f(u,z)),y))))),g(g(f(u,y)))))))=g(f(y,g(f(y,g(f(z,f(g(f(u,z)),y))))))). 4743 [] f(x,f(g(f(g(f(y,g(f(g(z),y)))),x)),g(f(g(f(y,g(f(u,f(g(f(z,u)),y))))),g(g(f(z,y)))))))=g(f(y,g(f(y,g(f(u,f(g(f(z,u)),y))))))). 4744 [] f(x,f(g(f(g(f(y,f(g(y),g(g(z))))),x)),g(f(g(f(y,g(f(u,f(g(f(z,u)),y))))),g(g(f(z,y)))))))=g(f(y,g(f(y,g(f(u,f(g(f(z,u)),y))))))). 4745 [] f(x,f(g(f(g(f(y,f(g(y),z))),x)),g(f(g(f(y,g(f(u,f(g(f(z,u)),y))))),g(g(f(z,y)))))))=g(f(y,g(f(y,g(f(u,f(g(f(z,u)),y))))))). 4746 [] f(x,f(g(f(g(y),x)),g(f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4747 [] f(x,f(f(g(x),g(g(y))),g(f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4748 [] f(x,f(f(g(x),y),g(f(g(f(z,g(f(u,f(g(f(y,u)),z))))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4749 [] f(x,f(f(g(x),y),g(f(g(f(z,g(f(u,f(f(g(u),g(y)),z))))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4750 [] f(x,f(f(g(x),y),g(f(g(f(z,g(f(g(y),z)))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4751 [] f(x,f(f(g(x),y),g(f(g(f(z,f(g(z),g(g(y))))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4752 [] f(x,f(f(g(x),y),g(f(g(f(z,f(g(z),y))),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4753 [] f(x,f(f(g(x),y),g(f(g(y),g(g(f(y,z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4754 [] f(x,f(f(g(x),y),g(f(g(y),g(f(g(z),g(y)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4755 [] f(x,f(f(g(x),y),g(f(g(y),f(g(g(y)),g(g(z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4756 [] f(x,f(f(g(x),y),g(f(g(y),f(y,g(g(z)))))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4757 [] f(x,f(f(g(x),y),g(f(g(y),f(y,z)))))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4758 [] f(x,f(f(g(x),y),g(z)))=g(f(z,g(f(z,g(f(u,f(g(f(y,u)),z))))))). 4759 [] f(x,f(f(g(x),y),g(z)))=g(f(z,g(f(z,g(f(u,f(f(g(u),g(y)),z))))))). 4760 [] f(x,f(f(g(x),y),g(z)))=g(f(z,g(f(z,g(f(g(y),z)))))). 4761 [] f(x,f(f(g(x),y),g(z)))=g(f(z,g(f(z,f(g(z),g(g(y))))))). 4762 [] f(x,f(f(g(x),y),g(z)))=g(f(z,g(f(z,f(g(z),y))))). 4763 [] f(x,f(f(g(x),y),g(z)))=g(f(z,g(y))). 4764 [] f(x,f(f(g(x),y),g(z)))=f(g(g(y)),g(z)). 4765 [] f(x,f(f(g(x),y),g(z)))=f(y,g(z)). 4766 [] f(f(f(x,f(f(g(x),g(y)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(y),w). 4767 [] f(f(f(x,f(g(x),f(g(y),g(z)))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(y),w). 4768 [] f(f(f(g(x),g(y)),g(f(x,z))),f(f(f(g(g(f(x,z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4769 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(g(g(f(x,z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4770 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(g(f(g(z),g(x))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4771 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(g(g(x)),g(g(z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4772 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,g(g(z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4773 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4774 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(g(f(g(u),f(g(y),g(u)))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4775 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(g(f(g(y),g(u))),g(g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4776 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(g(g(u)),g(g(y))),g(g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4777 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,g(g(y))),g(g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4778 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,y),g(g(u))),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4779 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,y),u),g(u))),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4780 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(u,y)),g(f(v,f(f(g(v),f(g(f(v,g(v))),g(w))),g(f(v,g(v))))))))=f(g(x),w). 4781 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(f(g(u),f(g(f(u,g(u))),g(v))),g(f(u,g(u))))))))=f(g(x),v). 4782 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(f(g(u),f(f(g(g(u)),g(u)),g(v))),g(f(u,g(u))))))))=f(g(x),v). 4783 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(f(g(u),f(f(u,g(u)),g(v))),g(f(u,g(u))))))))=f(g(x),v). 4784 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(f(g(u),g(v)),g(f(u,g(u))))))))=f(g(x),v). 4785 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(f(g(u),g(v)),f(g(g(u)),g(u)))))))=f(g(x),v). 4786 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(f(g(u),g(v)),f(u,g(u)))))))=f(g(x),v). 4787 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(g(u))))=f(g(x),u). 4788 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),u))=f(g(x),u). 4789 [] f(f(f(x,f(f(g(x),g(y)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(y,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4790 [] f(f(f(x,f(g(x),f(g(y),g(z)))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(y,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4791 [] f(f(f(g(x),g(y)),g(f(x,z))),f(f(f(g(g(f(x,z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4792 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(g(g(f(x,z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4793 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(g(f(g(z),g(x))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4794 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(g(g(x)),g(g(z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4795 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,g(g(z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4796 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4797 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(g(f(g(u),f(g(y),g(u)))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4798 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(g(f(g(y),g(u))),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4799 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(g(g(u)),g(g(y))),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4800 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,g(g(y))),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4801 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,y),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4802 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,y),u),g(u))),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4803 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(u,y)),f(g(f(v,g(f(x,w)))),g(f(v,g(f(v,f(v6,v))))))))=f(w,v6). 4804 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(g(f(u,g(f(x,v)))),g(f(u,g(f(u,f(w,u))))))))=f(v,w). 4805 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(g(f(u,f(g(v),g(x)))),g(f(u,g(f(u,f(w,u))))))))=f(v,w). 4806 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(g(f(g(u),g(x))),g(v)),g(f(v,g(f(v,f(w,v))))))))=f(u,w). 4807 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(g(g(x)),g(g(u))),g(v)),g(f(v,g(f(v,f(w,v))))))))=f(u,w). 4808 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,g(g(u))),g(v)),g(f(v,g(f(v,f(w,v))))))))=f(u,w). 4809 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),g(f(v,g(f(v,f(w,v))))))))=f(u,w). 4810 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),g(f(v,f(g(f(w,v)),g(v)))))))=f(u,w). 4811 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),g(f(v,f(f(g(v),g(w)),g(v)))))))=f(u,w). 4812 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),g(f(v,f(g(v),f(g(w),g(v))))))))=f(u,w). 4813 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),g(f(g(w),g(v))))))=f(u,w). 4814 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),f(g(g(v)),g(g(w))))))=f(u,w). 4815 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),f(v,g(g(w))))))=f(u,w). 4816 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),f(v,w))))=f(u,w). 4817 [] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(x,u),v)))=f(u,v). 4818 [] f(g(x),f(f(x,y),z))=f(y,z). 4819 [] f(f(x,g(f(y,f(f(f(z,f(f(g(z),g(u)),g(v))),g(f(u,z))),f(f(f(g(g(f(u,z))),g(w)),f(g(f(f(g(w),g(v)),g(w))),g(w))),x))))),x)=f(u,f(g(y),x)). 4820 [] f(f(x,g(f(y,f(f(f(z,f(g(z),f(g(u),g(v)))),g(f(u,z))),f(f(f(g(g(f(u,z))),g(w)),f(g(f(f(g(w),g(v)),g(w))),g(w))),x))))),x)=f(u,f(g(y),x)). 4821 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),g(f(z,v))),f(f(f(g(g(f(z,v))),g(w)),f(g(f(f(g(w),g(u)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4822 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(g(g(f(z,v))),g(w)),f(g(f(f(g(w),g(u)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4823 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(g(f(g(v),g(z))),g(w)),f(g(f(f(g(w),g(u)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4824 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(g(g(z)),g(g(v))),g(w)),f(g(f(f(g(w),g(u)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4825 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,g(g(v))),g(w)),f(g(f(f(g(w),g(u)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4826 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(g(f(f(g(w),g(u)),g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4827 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(g(f(g(w),f(g(u),g(w)))),g(w))),x))))),x)=f(z,f(g(y),x)). 4828 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(f(g(f(g(u),g(w))),g(g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4829 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(f(f(g(g(w)),g(g(u))),g(g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4830 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(f(f(w,g(g(u))),g(g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4831 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(f(f(w,u),g(g(w))),g(w))),x))))),x)=f(z,f(g(y),x)). 4832 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(f(f(w,u),w),g(w))),x))))),x)=f(z,f(g(y),x)). 4833 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(f(z,v),g(w)),f(w,u)),x))))),x)=f(z,f(g(y),x)). 4834 [] f(f(x,g(f(y,f(f(f(g(z),g(u)),f(g(v),g(z))),f(f(f(z,v),u),x))))),x)=f(z,f(g(y),x)). 4835 [] f(f(x,g(f(y,f(g(z),x)))),x)=f(z,f(g(y),x)). 4836 [] f(f(x,f(g(f(g(y),x)),g(z))),x)=f(y,f(g(z),x)). 4837 [] f(f(x,f(f(g(x),g(g(y))),g(z))),x)=f(y,f(g(z),x)). 4838 [] f(f(x,f(f(g(x),y),g(z))),x)=f(y,f(g(z),x)). 4839 [] f(f(x,g(y)),z)=f(x,f(g(y),z)). 4840 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(g(g(y)),g(g(v))). 4841 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(y,g(g(v))). 4842 [] f(f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(y,v). 4843 [] f(f(f(g(g(x)),g(y)),g(f(y,g(f(y,f(z,y)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4844 [] f(f(f(x,g(y)),g(f(y,g(f(y,f(z,y)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4845 [] f(f(f(x,g(y)),g(f(y,f(g(f(z,y)),g(y))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4846 [] f(f(f(x,g(y)),g(f(y,f(f(g(y),g(z)),g(y))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4847 [] f(f(f(x,g(y)),g(f(y,f(g(y),f(g(z),g(y)))))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4848 [] f(f(f(x,g(y)),g(f(g(z),g(y)))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4849 [] f(f(f(x,g(y)),f(g(g(y)),g(g(z)))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4850 [] f(f(f(x,g(y)),f(y,g(g(z)))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4851 [] f(f(f(x,g(y)),f(y,z)),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4852 [] f(f(x,f(g(y),f(y,z))),f(u,g(f(g(f(g(v),g(f(g(v),f(z,g(v)))))),u))))=f(x,v). 4853 [] f(f(x,y),f(z,g(f(g(f(g(u),g(f(g(u),f(y,g(u)))))),z))))=f(x,u). 4854 [] f(f(x,y),f(z,g(f(g(f(g(u),f(g(f(y,g(u))),g(g(u))))),z))))=f(x,u). 4855 [] f(f(x,y),f(z,g(f(g(f(g(u),f(f(g(g(u)),g(y)),g(g(u))))),z))))=f(x,u). 4856 [] f(f(x,y),f(z,g(f(g(f(g(u),f(f(u,g(y)),g(g(u))))),z))))=f(x,u). 4857 [] f(f(x,y),f(z,g(f(g(f(g(u),f(f(u,g(y)),u))),z))))=f(x,u). 4858 [] f(f(x,y),f(z,g(f(g(f(g(u),f(u,f(g(y),u)))),z))))=f(x,u). 4859 [] f(f(x,y),f(z,g(f(g(f(g(y),u)),z))))=f(x,u). 4860 [] f(f(x,y),f(z,g(f(f(g(u),g(g(y))),z))))=f(x,u). 4861 [] f(f(x,y),f(z,g(f(f(g(u),y),z))))=f(x,u). 4862 [] f(f(x,y),f(z,f(g(z),g(f(g(u),y)))))=f(x,u). 4863 [] f(f(x,y),f(z,f(g(z),f(g(y),g(g(u))))))=f(x,u). 4864 [] f(f(x,y),f(z,f(g(z),f(g(y),u))))=f(x,u). 4865 [] f(f(x,y),f(g(y),z))=f(x,z). 4866 [] f(f(f(x,y),z),f(u,f(f(g(u),g(z)),v)))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(f(v6,g(f(v6,f(y,v6)))))),v))). 4867 [] f(f(f(x,y),z),f(u,f(g(u),f(g(z),v))))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(f(v6,g(f(v6,f(y,v6)))))),v))). 4868 [] f(f(f(x,y),z),f(g(z),u))=f(v,f(g(f(z,v)),f(f(g(f(w,g(f(z,x)))),g(f(w,g(f(w,f(y,w)))))),u))). 4869 [] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(u,v),w). 4870 [] f(x,f(f(g(x),g(y)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(u,v),w). 4871 [] f(x,f(f(g(x),g(y)),f(f(g(f(z,f(g(u),g(y)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(u,v),w). 4872 [] f(x,f(f(g(x),g(y)),f(f(f(g(f(g(z),g(y))),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(z,v),w). 4873 [] f(x,f(f(g(x),g(y)),f(f(f(f(g(g(y)),g(g(z))),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(z,v),w). 4874 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,g(g(z))),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(z,v),w). 4875 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(z,v),w). 4876 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(f(v,u)),g(u))))),w)))=f(f(z,v),w). 4877 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(f(g(u),g(v)),g(u))))),w)))=f(f(z,v),w). 4878 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(u),f(g(v),g(u)))))),w)))=f(f(z,v),w). 4879 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(g(v),g(u)))),w)))=f(f(z,v),w). 4880 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(g(g(u)),g(g(v)))),w)))=f(f(z,v),w). 4881 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,g(g(v)))),w)))=f(f(z,v),w). 4882 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,v)),w)))=f(f(z,v),w). 4883 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),f(g(u),f(u,v))),w)))=f(f(z,v),w). 4884 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),v)))=f(f(z,u),v). 4885 [] f(x,f(g(x),f(g(y),f(f(f(y,z),u),v))))=f(f(z,u),v). 4886 [] f(g(x),f(f(f(x,y),z),u))=f(f(y,z),u). 4887 [] f(x,f(f(g(x),g(y)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(u,v),y),w). 4888 [] f(x,f(f(g(x),g(y)),f(f(g(f(z,f(g(u),g(y)))),g(f(z,g(f(z,f(v,z)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(u,v),y),w). 4889 [] f(x,f(f(g(x),g(y)),f(f(f(g(f(g(z),g(y))),g(u)),g(f(u,g(f(u,f(v,u)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4890 [] f(x,f(f(g(x),g(y)),f(f(f(f(g(g(y)),g(g(z))),g(u)),g(f(u,g(f(u,f(v,u)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4891 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,g(g(z))),g(u)),g(f(u,g(f(u,f(v,u)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4892 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,g(f(u,f(v,u)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4893 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(f(v,u)),g(u))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4894 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(f(g(u),g(v)),g(u))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4895 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(u),f(g(v),g(u)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4896 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(g(v),g(u)))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4897 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(g(g(u)),g(g(v)))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4898 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,g(g(v)))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4899 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,v)),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4900 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),f(g(u),f(u,v))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(z,v),y),w). 4901 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),g(f(y,g(f(y,f(v,y))))))))=f(f(f(z,u),y),v). 4902 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),g(f(y,f(g(f(v,y)),g(y)))))))=f(f(f(z,u),y),v). 4903 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),g(f(y,f(f(g(y),g(v)),g(y)))))))=f(f(f(z,u),y),v). 4904 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),g(f(y,f(g(y),f(g(v),g(y))))))))=f(f(f(z,u),y),v). 4905 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),g(f(g(v),g(y))))))=f(f(f(z,u),y),v). 4906 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),f(g(g(y)),g(g(v))))))=f(f(f(z,u),y),v). 4907 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),f(y,g(g(v))))))=f(f(f(z,u),y),v). 4908 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),f(y,v))))=f(f(f(z,u),y),v). 4909 [] f(x,f(g(x),f(g(y),f(f(f(y,z),u),f(y,v)))))=f(f(f(z,u),y),v). 4910 [] f(x,f(g(x),f(f(y,z),f(u,v))))=f(f(f(y,z),u),v). 4911 [] f(f(f(x,y),z),u)=f(f(x,y),f(z,u)). 4912 [] f(x,f(f(g(x),g(y)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). 4913 [] f(x,f(f(g(x),g(y)),f(f(g(f(z,f(g(u),g(y)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). 4914 [] f(x,f(f(g(x),g(y)),f(f(f(g(f(g(z),g(y))),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4915 [] f(x,f(f(g(x),g(y)),f(f(f(f(g(g(y)),g(g(z))),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4916 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,g(g(z))),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4917 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,g(f(u,f(v,u)))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4918 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(f(v,u)),g(u))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4919 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(f(g(u),g(v)),g(u))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4920 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(u),f(g(v),g(u)))))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4921 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(g(v),g(u)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4922 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(g(g(u)),g(g(v)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4923 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,g(g(v)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4924 [] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,v)),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4925 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),f(g(u),f(u,v))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). 4926 [] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),v)))=f(f(f(z,u),y),f(w,f(g(f(y,w)),v))). 4927 [] f(x,f(f(g(x),g(y)),f(f(y,z),f(u,v))))=f(f(f(z,u),y),f(w,f(g(f(y,w)),v))). 4928 [] f(x,f(g(x),f(g(y),f(f(y,z),f(u,v)))))=f(f(f(z,u),y),f(w,f(g(f(y,w)),v))). 4929 [] f(x,f(g(x),f(y,f(z,u))))=f(f(f(y,z),v),f(w,f(g(f(v,w)),u))). 4930 [] f(f(f(x,y),z),f(u,f(g(f(z,u)),v)))=f(x,f(y,v)). 4931 [] f(f(f(x,y),z),f(u,f(f(g(u),g(z)),v)))=f(x,f(y,v)). 4932 [] f(f(f(x,y),z),f(u,f(g(u),f(g(z),v))))=f(x,f(y,v)). 4933 [] f(f(f(x,y),z),f(g(z),u))=f(x,f(y,u)). 4934 [] f(f(x,y),z)=f(x,f(y,z)). 4935 [] $F. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 4936 [] x=x. Following clause subsumed by 4936 during input processing: 0 [copy,4936,flip.1] x=x. ------------> process sos: ** KEPT (pick-wt=-1006): 4937 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("33"). ---> New Demodulator: 4938 [new_demod,4937] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. ** KEPT (pick-wt=-1006): 4939 [] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y # label("35") # label("35"). ---> New Demodulator: 4940 [new_demod,4939] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y. ** KEPT (pick-wt=-1013): 4941 [] f(f(a,b),c)!=f(a,f(b,c)). >>>> Starting back demodulation with 4938. >> BACK DEMODULATING HINT 3985 WITH 4938. >> BACK DEMODULATING HINT 3984 WITH 4938. >> BACK DEMODULATING HINT 3983 WITH 4938. >> BACK DEMODULATING HINT 3958 WITH 4938. >> BACK DEMODULATING HINT 3681 WITH 4938. >> BACK DEMODULATING HINT 3568 WITH 4938. >> BACK DEMODULATING HINT 3264 WITH 4938. >> BACK DEMODULATING HINT 2544 WITH 4938. >> BACK DEMODULATING HINT 2400 WITH 4938. >> BACK DEMODULATING HINT 2280 WITH 4938. >> BACK DEMODULATING HINT 2256 WITH 4938. NEW HINT: 4942 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(f(v,g(f(w,f(f(g(w),v),f(g(u),v))))),v))=f(z,u). >> BACK DEMODULATING HINT 2255 WITH 4938. >> BACK DEMODULATING HINT 2220 WITH 4938. >> BACK DEMODULATING HINT 2030 WITH 4938. >> BACK DEMODULATING HINT 2029 WITH 4938. >> BACK DEMODULATING HINT 2028 WITH 4938. >> BACK DEMODULATING HINT 2027 WITH 4938. >> BACK DEMODULATING HINT 1999 WITH 4938. >> BACK DEMODULATING HINT 1948 WITH 4938. >> BACK DEMODULATING HINT 1878 WITH 4938. >> BACK DEMODULATING HINT 1783 WITH 4938. >> BACK DEMODULATING HINT 1619 WITH 4938. >> BACK DEMODULATING HINT 1453 WITH 4938. >> BACK DEMODULATING HINT 1155 WITH 4938. >> BACK DEMODULATING HINT 950 WITH 4938. >> BACK DEMODULATING HINT 760 WITH 4938. >> BACK DEMODULATING HINT 570 WITH 4938. >> BACK DEMODULATING HINT 392 WITH 4938. >> BACK DEMODULATING HINT 289 WITH 4938. >> BACK DEMODULATING HINT 180 WITH 4938. >> BACK DEMODULATING HINT 106 WITH 4938. >> BACK DEMODULATING HINT 54 WITH 4938. >> BACK DEMODULATING HINT 33 WITH 4938. >>>> Starting back demodulation with 4940. >> BACK DEMODULATING HINT 35 WITH 4940. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=-2147483647) 4937 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("33"). >> BACK DEMODULATING HINT 3961 WITH 4944. given clause #2: (wt=-2147483647) 4939 [] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y # label("35") # label("35"). given clause #3: (wt=-2147483647) 4941 [] f(f(a,b),c)!=f(a,f(b,c)). given clause #4: (wt=-995) 4943 [para_into,4937.1.1.2.1.2.1.2.1.1,4937.1.1] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))),f(g(z),g(u))),x))))=u. given clause #5: (wt=-991) 4945 [para_into,4937.1.1.2.1.2.1.2,4937.1.1] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 2757 WITH 4973. >> BACK DEMODULATING HINT 1956 WITH 4973. >> BACK DEMODULATING HINT 1955 WITH 4973. >> BACK DEMODULATING HINT 1882 WITH 4973. >> BACK DEMODULATING HINT 1881 WITH 4973. >> BACK DEMODULATING HINT 1623 WITH 4973. >> BACK DEMODULATING HINT 1622 WITH 4973. >> BACK DEMODULATING HINT 1252 WITH 4973. >> BACK DEMODULATING HINT 1160 WITH 4973. >> BACK DEMODULATING HINT 1159 WITH 4973. >> BACK DEMODULATING HINT 955 WITH 4973. >> BACK DEMODULATING HINT 954 WITH 4973. >> BACK DEMODULATING HINT 765 WITH 4973. >> BACK DEMODULATING HINT 764 WITH 4973. given clause #6: (wt=-991) 4946 [copy,4945,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). >> BACK DEMODULATING HINT 3974 WITH 4985. >> BACK DEMODULATING HINT 3599 WITH 4985. >> BACK DEMODULATING HINT 3584 WITH 4985. >> BACK DEMODULATING HINT 3579 WITH 4985. >> BACK DEMODULATING HINT 3292 WITH 4985. >> BACK DEMODULATING HINT 3270 WITH 4985. >> BACK DEMODULATING HINT 3268 WITH 4985. >> BACK DEMODULATING HINT 2768 WITH 4985. >> BACK DEMODULATING HINT 2759 WITH 4985. >> BACK DEMODULATING HINT 2758 WITH 4985. >> BACK DEMODULATING HINT 2757 WITH 4985. >> BACK DEMODULATING HINT 2549 WITH 4985. >> BACK DEMODULATING HINT 2432 WITH 4985. >> BACK DEMODULATING HINT 2405 WITH 4985. >> BACK DEMODULATING HINT 2259 WITH 4985. >> BACK DEMODULATING HINT 2230 WITH 4985. >> BACK DEMODULATING HINT 2003 WITH 4985. >> BACK DEMODULATING HINT 1993 WITH 4985. >> BACK DEMODULATING HINT 1957 WITH 4985. >> BACK DEMODULATING HINT 1955 WITH 4985. >> BACK DEMODULATING HINT 1886 WITH 4985. >> BACK DEMODULATING HINT 1883 WITH 4985. >> BACK DEMODULATING HINT 1881 WITH 4985. >> BACK DEMODULATING HINT 1812 WITH 4985. >> BACK DEMODULATING HINT 1810 WITH 4985. >> BACK DEMODULATING HINT 1795 WITH 4985. >> BACK DEMODULATING HINT 1778 WITH 4985. >> BACK DEMODULATING HINT 1646 WITH 4985. >> BACK DEMODULATING HINT 1628 WITH 4985. >> BACK DEMODULATING HINT 1624 WITH 4985. >> BACK DEMODULATING HINT 1622 WITH 4985. >> BACK DEMODULATING HINT 1496 WITH 4985. >> BACK DEMODULATING HINT 1457 WITH 4985. >> BACK DEMODULATING HINT 1178 WITH 4985. >> BACK DEMODULATING HINT 1161 WITH 4985. >> BACK DEMODULATING HINT 1159 WITH 4985. >> BACK DEMODULATING HINT 956 WITH 4985. >> BACK DEMODULATING HINT 954 WITH 4985. >> BACK DEMODULATING HINT 786 WITH 4985. >> BACK DEMODULATING HINT 766 WITH 4985. >> BACK DEMODULATING HINT 765 WITH 4985. >> BACK DEMODULATING HINT 575 WITH 4985. >> BACK DEMODULATING HINT 397 WITH 4985. >> BACK DEMODULATING HINT 295 WITH 4985. >> BACK DEMODULATING HINT 206 WITH 4985. >> BACK DEMODULATING HINT 139 WITH 4985. >> BACK DEMODULATING HINT 42 WITH 4985. >> BACK DEMODULATING HINT 10 WITH 4985. given clause #7: (wt=-1006) 4984 [para_from,4946.1.1,4945.1.1.2.1,demod,4973] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. >> BACK DEMODULATING HINT 3989 WITH 5020. >> BACK DEMODULATING HINT 2783 WITH 5020. >> BACK DEMODULATING HINT 2569 WITH 5020. given clause #8: (wt=-1002) 4972 [para_into,4945.1.1,4943.1.1,demod,4938,4938,4938,flip.1] f(g(x),f(f(y,f(g(f(g(x),y)),g(f(g(x),g(z))))),g(x)))=z. >> BACK DEMODULATING HINT 1971 WITH 5037. >> BACK DEMODULATING HINT 1967 WITH 5037. given clause #9: (wt=-995) 5006 [para_into,4984.1.1.2.1.2.1.2.1,4984.1.1] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). >> BACK DEMODULATING HINT 3981 WITH 5073. >> BACK DEMODULATING HINT 3980 WITH 5073. >> BACK DEMODULATING HINT 3585 WITH 5073. >> BACK DEMODULATING HINT 3584 WITH 5073. >> BACK DEMODULATING HINT 3274 WITH 5073. >> BACK DEMODULATING HINT 3271 WITH 5073. >> BACK DEMODULATING HINT 3270 WITH 5073. >> BACK DEMODULATING HINT 2760 WITH 5073. >> BACK DEMODULATING HINT 2551 WITH 5073. >> BACK DEMODULATING HINT 2233 WITH 5073. >> BACK DEMODULATING HINT 1961 WITH 5073. >> BACK DEMODULATING HINT 1960 WITH 5073. >> BACK DEMODULATING HINT 3998 WITH 5078. >> BACK DEMODULATING HINT 4021 WITH 5089. >> BACK DEMODULATING HINT 4020 WITH 5089. >> BACK DEMODULATING HINT 4019 WITH 5089. >> BACK DEMODULATING HINT 3994 WITH 5089. >> BACK DEMODULATING HINT 3993 WITH 5089. >> BACK DEMODULATING HINT 3992 WITH 5089. >> BACK DEMODULATING HINT 3989 WITH 5089. >> BACK DEMODULATING HINT 3985 WITH 5089. >> BACK DEMODULATING HINT 3984 WITH 5089. >> BACK DEMODULATING HINT 3983 WITH 5089. >> BACK DEMODULATING HINT 3982 WITH 5089. >> BACK DEMODULATING HINT 3613 WITH 5089. >> BACK DEMODULATING HINT 3333 WITH 5089. >> BACK DEMODULATING HINT 3279 WITH 5089. >> BACK DEMODULATING HINT 3278 WITH 5089. >> BACK DEMODULATING HINT 3277 WITH 5089. >> BACK DEMODULATING HINT 3272 WITH 5089. >> BACK DEMODULATING HINT 2771 WITH 5089. >> BACK DEMODULATING HINT 2552 WITH 5089. >> BACK DEMODULATING HINT 2419 WITH 5089. >> BACK DEMODULATING HINT 2232 WITH 5089. >> BACK DEMODULATING HINT 2095 WITH 5089. >> BACK DEMODULATING HINT 2020 WITH 5089. >> BACK DEMODULATING HINT 2019 WITH 5089. >> BACK DEMODULATING HINT 2018 WITH 5089. >> BACK DEMODULATING HINT 1965 WITH 5089. >> BACK DEMODULATING HINT 1964 WITH 5089. >> BACK DEMODULATING HINT 1963 WITH 5089. >> BACK DEMODULATING HINT 1959 WITH 5089. >> BACK DEMODULATING HINT 1885 WITH 5089. >> BACK DEMODULATING HINT 1782 WITH 5089. >> BACK DEMODULATING HINT 1633 WITH 5089. >> BACK DEMODULATING HINT 1632 WITH 5089. >> BACK DEMODULATING HINT 1631 WITH 5089. >> BACK DEMODULATING HINT 1627 WITH 5089. >> BACK DEMODULATING HINT 1468 WITH 5089. >> BACK DEMODULATING HINT 1204 WITH 5089. >> BACK DEMODULATING HINT 1196 WITH 5089. >> BACK DEMODULATING HINT 1195 WITH 5089. >> BACK DEMODULATING HINT 983 WITH 5089. >> BACK DEMODULATING HINT 808 WITH 5089. >> BACK DEMODULATING HINT 802 WITH 5089. >> BACK DEMODULATING HINT 801 WITH 5089. >> BACK DEMODULATING HINT 299 WITH 5089. >> BACK DEMODULATING HINT 105 WITH 5089. >> BACK DEMODULATING HINT 53 WITH 5089. >> BACK DEMODULATING HINT 32 WITH 5089. given clause #10: (wt=-1006) 5088 [para_into,5006.1.1,4984.1.1,flip.1] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. >> BACK DEMODULATING HINT 3998 WITH 5130. >> BACK DEMODULATING HINT 3988 WITH 5130. >> BACK DEMODULATING HINT 2884 WITH 5130. >> BACK DEMODULATING HINT 3995 WITH 5136. >> BACK DEMODULATING HINT 2757 WITH 5136. >> BACK DEMODULATING HINT 2756 WITH 5136. >> BACK DEMODULATING HINT 2755 WITH 5136. >> BACK DEMODULATING HINT 2428 WITH 5136. >> BACK DEMODULATING HINT 2241 WITH 5136. >> BACK DEMODULATING HINT 1999 WITH 5136. >> BACK DEMODULATING HINT 1966 WITH 5136. >> BACK DEMODULATING HINT 1956 WITH 5136. >> BACK DEMODULATING HINT 1955 WITH 5136. >> BACK DEMODULATING HINT 1901 WITH 5136. >> BACK DEMODULATING HINT 1882 WITH 5136. >> BACK DEMODULATING HINT 1881 WITH 5136. >> BACK DEMODULATING HINT 1780 WITH 5136. >> BACK DEMODULATING HINT 1644 WITH 5136. >> BACK DEMODULATING HINT 1634 WITH 5136. >> BACK DEMODULATING HINT 1623 WITH 5136. >> BACK DEMODULATING HINT 1622 WITH 5136. >> BACK DEMODULATING HINT 1492 WITH 5136. >> BACK DEMODULATING HINT 1252 WITH 5136. >> BACK DEMODULATING HINT 1230 WITH 5136. >> BACK DEMODULATING HINT 1174 WITH 5136. >> BACK DEMODULATING HINT 1160 WITH 5136. >> BACK DEMODULATING HINT 1159 WITH 5136. >> BACK DEMODULATING HINT 965 WITH 5136. >> BACK DEMODULATING HINT 955 WITH 5136. >> BACK DEMODULATING HINT 954 WITH 5136. >> BACK DEMODULATING HINT 826 WITH 5136. >> BACK DEMODULATING HINT 782 WITH 5136. >> BACK DEMODULATING HINT 765 WITH 5136. >> BACK DEMODULATING HINT 764 WITH 5136. >> BACK DEMODULATING HINT 590 WITH 5136. >> BACK DEMODULATING HINT 413 WITH 5136. >> BACK DEMODULATING HINT 327 WITH 5136. >> BACK DEMODULATING HINT 46 WITH 5136. >> BACK DEMODULATING HINT 21 WITH 5136. >> BACK DEMODULATING HINT 3990 WITH 5144. >> BACK DEMODULATING HINT 3961 WITH 5144. >> BACK DEMODULATING HINT 2555 WITH 5144. >> BACK DEMODULATING HINT 3275 WITH 5147. >> BACK DEMODULATING HINT 2762 WITH 5147. >> BACK DEMODULATING HINT 2761 WITH 5147. >> BACK DEMODULATING HINT 2554 WITH 5147. given clause #11: (wt=29) 4947 [para_into,4939.1.1.2.2.1,4939.1.1] f(x,f(y,f(z,g(f(g(y),f(z,f(f(g(f(g(f(x,y)),z)),u),g(f(g(z),u)))))))))=y. given clause #12: (wt=-1006) 5135 [para_from,5088.1.1,4972.1.1.2.2,demod,5089,5089,5089] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. >> BACK DEMODULATING HINT 1815 WITH 5207. >> BACK DEMODULATING HINT 1814 WITH 5207. NEW HINT: 5213 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(v,f(g(f(x,v)),g(f(x,g(f(x,f(f(y,f(g(f(z,y)),u)),x)))))))))=g(g(f(y,f(g(f(z,y)),u)))). >> BACK DEMODULATING HINT 853 WITH 5207. >> BACK DEMODULATING HINT 851 WITH 5207. given clause #13: (wt=-999) 5199 [para_into,5135.1.1.2.1.2.2,5088.1.1] f(x,f(f(y,f(g(f(x,y)),z)),x))=f(x,f(f(u,f(g(f(x,u)),z)),x)). >> BACK DEMODULATING HINT 3281 WITH 5246. given clause #14: (wt=-1003) 5238 [para_from,5199.1.1,4984.1.1.2.1.2.1.2.1,demod,4985] f(f(x,f(g(f(y,x)),z)),y)=f(f(u,f(g(f(y,u)),z)),y). >> BACK DEMODULATING HINT 2001 WITH 5262. given clause #15: (wt=-997) 5143 [para_from,5088.1.1,4943.1.1.2.1.2.1.2.1,demod,5089] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(u))),x))))=u. given clause #16: (wt=35) 4949 [para_into,4939.1.1.2.2.1,4937.1.1] f(x,f(y,f(z,g(f(g(y),g(f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y))))))))))=y. given clause #17: (wt=-997) 5245 [para_from,5199.1.1,4984.1.1.1.1,demod,5130] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,g(f(x,f(u,x)))))))=u. >> BACK DEMODULATING HINT 3297 WITH 5399. given clause #18: (wt=-1002) 5398 [para_into,5245.1.1.2,4984.1.1] f(g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))),u)=f(z,u). >> BACK DEMODULATING HINT 3314 WITH 5432. >> BACK DEMODULATING HINT 5213 WITH 5449. >> BACK DEMODULATING HINT 4121 WITH 5449. >> BACK DEMODULATING HINT 3999 WITH 5449. >> BACK DEMODULATING HINT 3685 WITH 5449. >> BACK DEMODULATING HINT 3682 WITH 5449. >> BACK DEMODULATING HINT 3681 WITH 5449. >> BACK DEMODULATING HINT 3300 WITH 5449. >> BACK DEMODULATING HINT 3280 WITH 5449. >> BACK DEMODULATING HINT 3275 WITH 5449. >> BACK DEMODULATING HINT 2767 WITH 5449. >> BACK DEMODULATING HINT 2766 WITH 5449. >> BACK DEMODULATING HINT 2762 WITH 5449. >> BACK DEMODULATING HINT 2761 WITH 5449. >> BACK DEMODULATING HINT 2557 WITH 5449. >> BACK DEMODULATING HINT 2554 WITH 5449. >> BACK DEMODULATING HINT 2395 WITH 5449. >> BACK DEMODULATING HINT 2262 WITH 5449. >> BACK DEMODULATING HINT 2259 WITH 5449. >> BACK DEMODULATING HINT 2038 WITH 5449. >> BACK DEMODULATING HINT 2035 WITH 5449. >> BACK DEMODULATING HINT 2001 WITH 5449. >> BACK DEMODULATING HINT 1994 WITH 5449. >> BACK DEMODULATING HINT 1993 WITH 5449. >> BACK DEMODULATING HINT 1905 WITH 5449. >> BACK DEMODULATING HINT 1815 WITH 5449. >> BACK DEMODULATING HINT 1814 WITH 5449. >> BACK DEMODULATING HINT 1811 WITH 5449. >> BACK DEMODULATING HINT 1810 WITH 5449. >> BACK DEMODULATING HINT 1781 WITH 5449. >> BACK DEMODULATING HINT 1659 WITH 5449. >> BACK DEMODULATING HINT 1653 WITH 5449. >> BACK DEMODULATING HINT 1647 WITH 5449. >> BACK DEMODULATING HINT 1646 WITH 5449. >> BACK DEMODULATING HINT 1473 WITH 5449. >> BACK DEMODULATING HINT 1233 WITH 5449. >> BACK DEMODULATING HINT 1210 WITH 5449. >> BACK DEMODULATING HINT 992 WITH 5449. >> BACK DEMODULATING HINT 853 WITH 5449. >> BACK DEMODULATING HINT 851 WITH 5449. >> BACK DEMODULATING HINT 812 WITH 5449. >> BACK DEMODULATING HINT 620 WITH 5449. >> BACK DEMODULATING HINT 440 WITH 5449. >> BACK DEMODULATING HINT 355 WITH 5449. >> BACK DEMODULATING HINT 51 WITH 5449. >> BACK DEMODULATING HINT 29 WITH 5449. >> BACK DEMODULATING HINT 4114 WITH 5470. >> BACK DEMODULATING HINT 4000 WITH 5470. >> BACK DEMODULATING HINT 3302 WITH 5470. >> BACK DEMODULATING HINT 3991 WITH 5485. >> BACK DEMODULATING HINT 3607 WITH 5485. >> BACK DEMODULATING HINT 3595 WITH 5485. >> BACK DEMODULATING HINT 3301 WITH 5485. >> BACK DEMODULATING HINT 3300 WITH 5485. >> BACK DEMODULATING HINT 3297 WITH 5485. >> BACK DEMODULATING HINT 2790 WITH 5485. >> BACK DEMODULATING HINT 2789 WITH 5485. >> BACK DEMODULATING HINT 2584 WITH 5485. >> BACK DEMODULATING HINT 2433 WITH 5485. >> BACK DEMODULATING HINT 1999 WITH 5485. >> BACK DEMODULATING HINT 1779 WITH 5485. >> BACK DEMODULATING HINT 1657 WITH 5485. >> BACK DEMODULATING HINT 1517 WITH 5485. >> BACK DEMODULATING HINT 1497 WITH 5485. >> BACK DEMODULATING HINT 1272 WITH 5485. >> BACK DEMODULATING HINT 1269 WITH 5485. >> BACK DEMODULATING HINT 1252 WITH 5485. >> BACK DEMODULATING HINT 1203 WITH 5485. >> BACK DEMODULATING HINT 987 WITH 5485. >> BACK DEMODULATING HINT 845 WITH 5485. >> BACK DEMODULATING HINT 842 WITH 5485. >> BACK DEMODULATING HINT 807 WITH 5485. >> BACK DEMODULATING HINT 324 WITH 5485. >> BACK DEMODULATING HINT 20 WITH 5485. given clause #19: (wt=-1006) 5448 [para_into,5398.1.1,5245.1.1,flip.1] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. >> BACK DEMODULATING HINT 4004 WITH 5517. given clause #20: (wt=-1007) 5515 [para_into,5448.1.1.2.2.1.2.1.2,5238.1.1,demod,5089] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). >> BACK DEMODULATING HINT 4009 WITH 5579. >> BACK DEMODULATING HINT 3305 WITH 5579. >> BACK DEMODULATING HINT 3285 WITH 5579. >> BACK DEMODULATING HINT 4123 WITH 5610. >> BACK DEMODULATING HINT 4011 WITH 5610. >> BACK DEMODULATING HINT 3288 WITH 5610. >> BACK DEMODULATING HINT 2565 WITH 5610. >> BACK DEMODULATING HINT 2263 WITH 5610. >> BACK DEMODULATING HINT 1999 WITH 5610. >> BACK DEMODULATING HINT 1997 WITH 5610. >> BACK DEMODULATING HINT 1789 WITH 5610. given clause #21: (wt=29) 4951 [para_into,4939.1.1.2.2.2.1,4939.1.1] f(x,f(y,f(f(g(f(x,y)),f(z,f(f(g(f(g(y),z)),u),g(f(g(z),u))))),g(z))))=y. given clause #22: (wt=-1006) 5484 [para_from,5398.1.1,5245.1.1.2.2.1.2.1.2,demod,5246,flip.1] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. >> BACK DEMODULATING HINT 3996 WITH 5768. >> BACK DEMODULATING HINT 3314 WITH 5768. >> BACK DEMODULATING HINT 3304 WITH 5768. >> BACK DEMODULATING HINT 3640 WITH 5770. >> BACK DEMODULATING HINT 3618 WITH 5770. >> BACK DEMODULATING HINT 4091 WITH 5792. >> BACK DEMODULATING HINT 4088 WITH 5792. >> BACK DEMODULATING HINT 4003 WITH 5792. >> BACK DEMODULATING HINT 3310 WITH 5792. >> BACK DEMODULATING HINT 3299 WITH 5792. given clause #23: (wt=-1000) 5609 [para_from,5515.1.1,5448.1.1.2.2.1.2.1] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). >> BACK DEMODULATING HINT 4012 WITH 5869. given clause #24: (wt=-1005) 5871 [para_from,5609.1.1,5484.1.1.1.2.1] g(f(x,f(g(f(y,x)),x)))=g(f(z,f(g(f(y,z)),x))). given clause #25: (wt=-1005) 5922 [copy,5871,flip.1] g(f(x,f(g(f(y,x)),z)))=g(f(z,f(g(f(y,z)),z))). given clause #26: (wt=29) 4955 [para_from,4939.1.1,4937.1.1.2.1.2.1.2.1.1] f(x,g(f(x,f(f(f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))),f(g(y),g(u))),x))))=u. given clause #27: (wt=-1005) 5936 [para_into,5871.1.1.1,5515.1.1] g(f(x,f(g(f(y,x)),z)))=g(f(u,f(g(f(y,u)),z))). given clause #28: (wt=-1001) 5906 [para_from,5609.1.1,4937.1.1.2.1.2.1] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))). given clause #29: (wt=-1001) 6115 [para_into,5906.1.1.2.1,5515.1.1] f(x,g(f(y,f(g(f(z,y)),x))))=f(x,g(f(u,f(g(f(z,u)),x)))). >> BACK DEMODULATING HINT 4017 WITH 6248. given clause #30: (wt=-999) 5876 [para_from,5609.1.1,5088.1.1.1.2.1.2.1] g(f(x,g(f(x,f(g(f(y,x)),x)))))=g(f(x,g(f(z,f(g(f(y,z)),x))))). given clause #31: (wt=44) 4961 [para_into,4943.1.1.2.1.2.1.1.1.2.1.2,4937.1.1] f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),f(g(f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y))))),g(v))),x))))=v. given clause #32: (wt=-999) 6260 [para_into,5876.1.1.1.2.1,5515.1.1] g(f(x,g(f(y,f(g(f(z,y)),x)))))=g(f(x,g(f(u,f(g(f(z,u)),x))))). given clause #33: (wt=-998) 5394 [para_into,5245.1.1.2.2.1.2.1.2,5238.1.1,demod,5089] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u))=f(v,f(g(f(x,v)),u)). given clause #34: (wt=-998) 5400 [copy,5394,flip.1] f(x,f(g(f(y,x)),z))=f(g(f(y,f(f(u,f(g(f(y,u)),v)),y))),f(v,z)). >> BACK DEMODULATING HINT 2880 WITH 6538. given clause #35: (wt=-998) 5793 [para_from,5484.1.1,5515.1.1.2.1] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,u))=f(v,f(g(f(y,v)),u)). given clause #36: (wt=40) 4963 [para_into,4943.1.1.2.1.2.1.2,4937.1.1] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))),u),x))))=f(g(z),f(f(v,f(g(f(g(z),v)),g(u))),g(z))). given clause #37: (wt=-997) 5469 [para_from,5398.1.1,5143.1.1.2.1.2.1.2,demod,5020] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,z)))),x),f(z,g(u))),x))))=u. >> BACK DEMODULATING HINT 3322 WITH 6781. >> BACK DEMODULATING HINT 3312 WITH 6781. given clause #38: (wt=-997) 5577 [para_into,5515.1.1.2,5515.1.1] f(x,f(y,f(g(f(z,y)),u)))=f(v,f(g(f(w,v)),f(g(f(z,g(f(w,x)))),u))). given clause #39: (wt=-997) 5605 [copy,5577,flip.1] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),v)))=f(u,f(w,f(g(f(z,w)),v))). given clause #40: (wt=-1003) 7074 [para_into,5605.1.1.2,5515.1.1] f(x,f(y,f(g(f(z,y)),u)))=f(x,f(v,f(g(f(z,v)),u))). given clause #41: (wt=40) 4964 [copy,4963,flip.1] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(x)))=f(u,g(f(u,f(f(g(f(u,f(f(v,f(g(f(u,v)),g(x))),u))),z),u)))). given clause #42: (wt=-997) 5767 [para_into,5484.1.1.1.2.1.2.1,5088.1.1] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,u)))),x)))=u. given clause #43: (wt=-997) 5781 [para_into,5484.1.1.1.2.1.2.2,5484.1.1] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(u,f(g(f(x,u)),g(f(x,z)))),x). >> BACK DEMODULATING HINT 4034 WITH 7613. >> BACK DEMODULATING HINT 3609 WITH 7613. >> BACK DEMODULATING HINT 3311 WITH 7613. >> BACK DEMODULATING HINT 3310 WITH 7613. >> BACK DEMODULATING HINT 3308 WITH 7613. >> BACK DEMODULATING HINT 3307 WITH 7613. >> BACK DEMODULATING HINT 2225 WITH 7613. >> BACK DEMODULATING HINT 2023 WITH 7613. >> BACK DEMODULATING HINT 2001 WITH 7613. >> BACK DEMODULATING HINT 1969 WITH 7613. >> BACK DEMODULATING HINT 1649 WITH 7613. >> BACK DEMODULATING HINT 1230 WITH 7613. >> BACK DEMODULATING HINT 826 WITH 7613. given clause #44: (wt=-1006) 7612 [para_into,5781.1.1,5484.1.1,flip.1] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. given clause #45: (wt=-997) 5791 [para_from,5484.1.1,5448.1.1.2.1] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,g(f(y,g(f(y,f(u,y)))))))=u. given clause #46: (wt=50) 4967 [para_from,4943.1.1,4937.1.1.2.1.2.1.2] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(g(f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(v))),g(f(x,y))))),f(g(v),g(z))),g(f(x,y)))). given clause #47: (wt=-996) 5578 [para_into,5515.1.1.2,5448.1.1,flip.1] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z))))))))=f(u,v). given clause #48: (wt=-1003) 7983 [para_into,5578.1.1.2.2.1.1.2.1,7074.1.1,demod,5579] f(f(x,f(g(f(y,x)),z)),u)=f(f(v,f(g(f(y,v)),z)),u). given clause #49: (wt=-996) 5636 [para_from,5515.1.1,4984.1.1.2.1.2.1.2.1] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v). given clause #50: (wt=-999) 8442 [para_from,5636.1.1,5135.1.1.2.1.2] f(x,f(f(y,f(g(f(z,y)),u)),x))=f(x,f(f(v,f(g(f(z,v)),u)),x)). given clause #51: (wt=50) 4968 [copy,4967,flip.1] f(g(f(x,y)),f(f(g(f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))),f(g(u),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))). given clause #52: (wt=-996) 5769 [para_into,5484.1.1.1.2.1.2.2.1,5515.1.1] g(f(x,f(f(y,f(g(f(x,y)),g(f(z,f(g(f(u,z)),v))))),x)))=f(g(f(u,x)),v). given clause #53: (wt=-995) 5012 [para_into,4984.1.1.2.1.2.1.2.1,4937.1.1] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=g(f(y,f(f(u,f(g(f(y,u)),g(z))),y))). given clause #54: (wt=-995) 5013 [copy,5006,flip.1] g(f(x,g(f(x,f(f(y,z),x)))))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(u,f(z,u)))))). given clause #55: (wt=-995) 5532 [para_from,5448.1.1,4984.1.1.2.1.2.1.2.1] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=f(g(f(u,y)),g(f(u,g(f(u,f(z,u)))))). given clause #56: (wt=44) 4969 [para_into,4945.1.1.2.1.2.1,4939.1.1] f(x,g(f(x,f(y,x))))=f(g(f(x,z)),f(f(u,f(g(f(g(f(x,z)),u)),g(f(y,f(f(g(f(z,y)),v),g(f(g(y),v))))))),g(f(x,z)))). given clause #57: (wt=-993) 5203 [para_from,5135.1.1,5006.1.1.1.1.2.1,demod,5130] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=f(g(f(u,g(y))),g(f(u,g(f(u,f(z,u)))))). given clause #58: (wt=-992) 5129 [para_from,5088.1.1,5006.1.1.1,flip.1] g(f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),z)),x),u),x)))))=f(z,g(f(x,g(f(x,f(u,x)))))). given clause #59: (wt=-992) 7489 [para_into,5767.1.1.1.2.1.2,4937.1.1] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),x)),x))),z),x)))=f(f(u,f(g(f(x,u)),g(z))),x). given clause #60: (wt=-990) 6247 [para_from,6115.1.1,4937.1.1.2.1.2.1.2.1.1] f(x,g(f(x,f(f(g(f(y,f(g(f(z,y)),x))),f(g(f(x,g(f(u,f(g(f(z,u)),x))))),g(v))),x))))=v. given clause #61: (wt=44) 4970 [para_into,4945.1.1.2.1.2.1,4937.1.1] f(x,g(f(x,f(y,x))))=f(g(f(x,z)),f(f(u,f(g(f(g(f(x,z)),u)),g(g(f(z,f(f(v,f(g(f(z,v)),g(y))),z)))))),g(f(x,z)))). given clause #62: (wt=-989) 5091 [copy,5068,flip.1,demod,5078] f(g(f(g(x),g(y))),g(f(g(x),g(f(g(x),f(z,g(x)))))))=f(g(f(u,g(y))),g(f(u,g(f(u,f(z,u)))))). given clause #63: (wt=-989) 5094 [back_demod,5069,demod,5073,4938,4938,4938] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=f(g(f(g(u),g(y))),g(f(g(u),g(f(g(u),f(z,g(u))))))). given clause #64: (wt=-988) 5019 [para_from,4984.1.1,4943.1.1.2.1.2.1.2] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(f(z,u)))),x))),v),x))))=f(z,g(f(z,f(f(u,v),z)))) # label("Hint 27(4182)"). given clause #65: (wt=-988) 6780 [para_into,5469.1.1.2.1.2.1.2,4984.1.1] f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),g(f(x,g(f(z,u)))))),x),v),x))))=f(z,g(f(z,f(f(u,v),z)))). given clause #66: (wt=45) 4971 [para_into,4945.1.1,4945.1.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(g(f(x,y)),f(f(v,f(g(f(g(f(x,y)),v)),g(u))),g(f(x,y)))). given clause #67: (wt=-988) 7483 [para_into,5767.1.1.1.2.1.2.2,5088.1.1] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u)),x)))=g(f(x,f(f(v,f(g(f(x,v)),u)),x))). given clause #68: (wt=-987) 6537 [para_from,5400.1.1,5088.1.1.1.2.1.2.1.2] g(f(x,g(f(x,f(f(y,f(g(f(z,f(f(u,f(g(f(z,u)),v)),z))),f(v,w))),x)))))=f(g(f(z,g(f(x,y)))),w) # label("cl 12275 demod 0"). given clause #69: (wt=-984) 5072 [para_into,5006.1.1.1.1,4984.1.1,flip.1] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(z),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). >> BACK DEMODULATING HINT 2880 WITH 9889. given clause #70: (wt=-983) 9024 [para_from,5013.1.1,5605.1.1.2.2.1] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). given clause #71: (wt=44) 4974 [copy,4969,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(u,f(f(g(f(y,u)),v),g(f(g(u),v))))))),g(f(x,y))))=f(x,g(f(x,f(u,x)))). given clause #72: (wt=-983) 9073 [copy,9024,flip.1] f(f(f(x,y),z),f(u,f(g(f(z,u)),v)))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(f(v6,g(f(v6,f(y,v6)))))),v))). given clause #73: (wt=-982) 6304 [para_into,5394.1.1.1.1.2.1.2.1.1,6115.1.1] f(g(f(x,f(f(g(f(y,f(g(f(z,y)),x))),f(g(f(x,g(f(u,f(g(f(z,u)),x))))),v)),x))),f(v,w))=f(v6,f(g(f(x,v6)),w)). given clause #74: (wt=-982) 9025 [para_from,5013.1.1,5578.1.1.2.2.1] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z)))))),g(f(y,g(f(y,f(w,y))))))))=f(f(f(u,v),y),w). given clause #75: (wt=-979) 6223 [para_from,6115.1.1,5006.1.1.1.1.2.1] f(g(f(x,g(f(y,g(f(z,f(g(f(u,z)),y))))))),g(f(x,g(f(x,f(v,x))))))=g(f(y,g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),v),y))))). given clause #76: (wt=44) 4975 [copy,4970,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(g(f(y,f(f(u,f(g(f(y,u)),g(v))),y)))))),g(f(x,y))))=f(x,g(f(x,f(v,x)))). given clause #77: (wt=-975) 5516 [para_into,5448.1.1.2.2.1.2.1.2,4984.1.1] f(x,f(g(f(g(f(y,g(f(y,f(f(z,u),y))))),x)),g(f(g(f(y,g(f(y,f(f(z,u),y))))),g(f(g(f(y,g(f(y,f(f(z,u),y))))),u))))))=g(f(y,z)). given clause #78: (wt=-974) 5036 [para_into,4972.1.1.2.1.2.1.1,4946.1.1] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(f(g(f(x,y)),g(v))))),g(f(x,y))))=v. given clause #79: (wt=-973) 9875 [para_into,5072.1.1.1.2.1.2.1.1.1.2.1,5448.1.1] g(f(x,g(f(x,f(f(g(f(x,f(y,x))),z),x)))))=f(g(f(g(f(u,v)),g(f(u,g(f(u,f(y,u))))))),g(f(g(f(x,v)),g(f(g(f(x,v)),f(z,g(f(x,v)))))))). given clause #80: (wt=-971) 4979 [para_into,4946.1.1.2.1.2.1.1,4946.1.1] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,u),x))))),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))). given clause #81: (wt=48) 4976 [para_from,4945.1.1,4939.1.1.2.2.2.1] f(x,f(y,f(f(g(f(x,y)),g(f(g(y),f(f(z,u),g(y))))),g(f(g(f(g(y),z)),f(f(v,f(g(f(g(f(g(y),z)),v)),g(u))),g(f(g(y),z))))))))=y. given clause #82: (wt=-971) 4982 [copy,4979,flip.1] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(f(f(u,f(g(f(g(f(x,y)),u)),g(v))),g(f(x,y))),f(g(f(x,g(f(x,f(f(y,v),x))))),g(z))),g(f(x,y)))). given clause #83: (wt=-971) 5868 [para_into,5609.1.1.2.2.1.2.1,5609.1.1] f(x,f(g(f(g(f(y,g(f(z,f(g(f(u,z)),y))))),x)),g(f(g(f(y,g(f(z,f(g(f(u,z)),y))))),g(g(f(u,y)))))))=g(f(y,g(f(y,g(f(z,f(g(f(u,z)),y))))))). >> BACK DEMODULATING HINT 4012 WITH 10061. given clause #84: (wt=-971) 10060 [para_into,5868.1.1.2.1.1.1.1.2.1,5515.1.1] f(x,f(g(f(g(f(y,g(f(z,f(g(f(u,z)),y))))),x)),g(f(g(f(y,g(f(v,f(g(f(u,v)),y))))),g(g(f(u,y)))))))=g(f(y,g(f(y,g(f(v,f(g(f(u,v)),y))))))). given clause #85: (wt=23) 5024 [para_from,4984.1.1,4939.1.1.2.2.1] f(x,f(y,f(z,g(f(g(y),g(f(x,g(f(x,f(f(y,z),x))))))))))=y. given clause #86: (wt=40) 4978 [para_into,4946.1.1.1.1,4939.1.1,demod,4940,4940] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(x)))=f(u,g(f(u,f(f(f(x,f(f(g(f(u,x)),v),g(f(g(x),v)))),z),u)))). given clause #87: (wt=23) 5839 [para_into,5609.1.1.2.2.1.2.1.2.1.1,5238.1.1,demod,5610] g(f(f(x,f(g(f(y,x)),z)),u))=g(f(f(v,f(g(f(y,v)),z)),u)). given clause #88: (wt=23) 5931 [copy,5906,flip.1] f(x,g(f(y,f(g(f(z,y)),x))))=f(x,g(f(x,f(g(f(z,x)),x)))). given clause #89: (wt=23) 7984 [para_into,5578.1.1.2.2.1.1.2.1,6115.1.1,demod,5579] f(g(f(x,f(g(f(y,x)),z))),u)=f(g(f(v,f(g(f(y,v)),z))),u). >> BACK DEMODULATING HINT 4017 WITH 10645. given clause #90: (wt=-1001) 10581 [para_from,7984.1.1,5578.1.1.2.2.2.1.2.1.2,demod,5579] f(x,g(f(y,f(g(f(z,y)),u))))=f(x,g(f(v,f(g(f(z,v)),u)))). given clause #91: (wt=44) 4980 [para_into,4946.1.1.2.1.2.1.1,4939.1.1] f(g(f(x,y)),f(f(f(z,f(f(g(f(g(f(x,y)),z)),u),g(f(g(z),u)))),f(g(z),g(v))),g(f(x,y))))=f(x,g(f(x,f(f(y,v),x)))). given clause #92: (wt=-990) 10644 [para_from,7984.1.1,4937.1.1.2.1.2.1] f(x,g(f(x,f(f(g(f(y,f(g(f(z,y)),u))),f(g(f(x,g(f(v,f(g(f(z,v)),u))))),g(w))),x))))=w. given clause #93: (wt=-999) 10914 [para_from,10644.1.1,5516.1.1.2.2.1.1.1,demod,10645,10645,5449] g(f(x,g(f(y,f(g(f(z,y)),u)))))=g(f(x,g(f(v,f(g(f(z,v)),u))))). given clause #94: (wt=-982) 10591 [para_from,7984.1.1,5394.1.1.1.1.2.1] f(g(f(x,f(f(g(f(y,f(g(f(z,y)),u))),f(g(f(x,g(f(v,f(g(f(z,v)),u))))),w)),x))),f(w,v6))=f(v7,f(g(f(x,v7)),v6)). given clause #95: (wt=-979) 10675 [copy,10637,flip.1] f(g(f(x,g(f(y,g(f(z,f(g(f(u,z)),v))))))),g(f(x,g(f(x,f(w,x))))))=g(f(y,g(f(y,f(f(g(f(v6,f(g(f(u,v6)),v))),w),y))))). given clause #96: (wt=40) 4981 [copy,4978,flip.1] f(x,g(f(x,f(f(f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))),u),x))))=f(g(y),f(f(v,f(g(f(g(y),v)),g(u))),g(y))). given clause #97: (wt=25) 5435 [para_into,5398.1.1.1.1.2.1.2.2.1,5199.1.1,demod,5399] f(f(f(x,f(g(f(y,x)),z)),y),u)=f(f(f(v,f(g(f(y,v)),z)),y),u). given clause #98: (wt=-999) 11232 [para_from,5435.1.1,5578.1.1.2.2.2.1.2.1.2,demod,5579] f(x,f(f(y,f(g(f(z,y)),u)),z))=f(x,f(f(v,f(g(f(z,v)),u)),z)). given clause #99: (wt=-999) 11336 [para_into,11232.1.1.2.1.2,5636.1.1,demod,5449] f(x,f(f(y,f(g(f(z,y)),u)),v))=f(x,f(f(w,f(g(f(z,w)),u)),v)). given clause #100: (wt=25) 5923 [copy,5876,flip.1] g(f(x,g(f(y,f(g(f(z,y)),x)))))=g(f(x,g(f(x,f(g(f(z,x)),x))))). given clause #101: (wt=44) 4983 [copy,4980,flip.1] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(f(u,f(f(g(f(g(f(x,y)),u)),v),g(f(g(u),v)))),f(g(u),g(z))),g(f(x,y)))). given clause #102: (wt=25) 8631 [para_from,8442.1.1,5578.1.1.2.2.1.1.2.1,demod,5579] f(f(f(x,f(g(f(y,x)),z)),u),v)=f(f(f(w,f(g(f(y,w)),z)),u),v). given clause #103: (wt=25) 10598 [para_from,7984.1.1,5609.1.1.2.2.1.2.1.2.1.1,demod,5610] g(f(g(f(x,f(g(f(y,x)),z))),u))=g(f(g(f(v,f(g(f(y,v)),z))),u)). given clause #104: (wt=26) 5805 [copy,5793,flip.1] f(x,f(g(f(y,x)),z))=f(f(f(u,f(g(f(y,u)),g(f(y,v)))),y),f(v,z)). given clause #105: (wt=26) 10105 [para_into,5024.1.1.2.2.2.1,5636.1.1] f(x,f(f(x,y),f(f(g(f(z,f(x,y))),u),g(f(g(f(z,y)),u)))))=f(x,y). given clause #106: (wt=46) 4986 [para_from,4946.1.1,4939.1.1.2.2.2.1] f(x,f(f(y,z),f(f(g(f(x,f(y,z))),f(f(u,f(g(f(g(f(y,z)),u)),g(v))),g(f(y,z)))),g(f(y,g(f(y,f(f(z,v),y))))))))=f(y,z). given clause #107: (wt=22) 12353 [para_from,10105.1.1,5767.1.1.1.2.1.2.2.1,demod,5768,flip.1] f(f(x,y),f(f(g(f(z,f(x,y))),u),g(f(g(f(z,y)),u))))=y. given clause #108: (wt=18) 12367 [para_into,12353.1.1.1,7612.1.1,demod,7613] f(x,f(f(g(f(y,x)),z),g(f(g(f(y,u)),z))))=u. given clause #109: (wt=23) 12665 [para_into,12367.1.1.2.1,5024.1.1,demod,10214] f(x,f(y,g(f(g(f(z,u)),g(f(z,g(f(z,f(f(x,y),z)))))))))=u. >> BACK DEMODULATING HINT 4786 WITH 13187. NEW HINT: 13223 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),g(f(u,f(g(u),g(v))))))=f(g(x),v). >> BACK DEMODULATING HINT 4707 WITH 13187. >> BACK DEMODULATING HINT 4567 WITH 13187. NEW HINT: 13224 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(u,f(g(u),g(v))))))=f(g(x),v). >> BACK DEMODULATING HINT 4543 WITH 13187. >> BACK DEMODULATING HINT 4491 WITH 13187. >> BACK DEMODULATING HINT 4410 WITH 13187. NEW HINT: 13225 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(g(x),g(y))),g(x)),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). >> BACK DEMODULATING HINT 4409 WITH 13187. NEW HINT: 13226 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,f(g(x),g(y)))),g(f(g(z),y))))=g(f(u,g(f(v,f(g(f(z,v)),u))))). >> BACK DEMODULATING HINT 4337 WITH 13187. >> BACK DEMODULATING HINT 4336 WITH 13187. >> BACK DEMODULATING HINT 4323 WITH 13187. NEW HINT: 13227 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),f(g(f(g(y),g(z))),g(y))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). >> BACK DEMODULATING HINT 4322 WITH 13187. NEW HINT: 13228 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),g(f(y,f(g(y),g(z))))))=g(f(z,f(f(u,g(u)),g(f(x,g(x)))))). >> BACK DEMODULATING HINT 4321 WITH 13187. >> BACK DEMODULATING HINT 4317 WITH 13187. NEW HINT: 13229 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),g(f(z,f(g(f(u,z)),f(f(x,g(x)),g(f(y,g(y)))))))))=g(f(u,f(f(x,g(x)),g(f(y,g(y)))))). >> BACK DEMODULATING HINT 4300 WITH 13187. >> BACK DEMODULATING HINT 4299 WITH 13187. NEW HINT: 13230 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(x)),z)=f(x,z). >> BACK DEMODULATING HINT 4260 WITH 13187. NEW HINT: 13231 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(z,x)),z)),z)=f(x,z). >> BACK DEMODULATING HINT 4249 WITH 13187. >> BACK DEMODULATING HINT 4204 WITH 13187. >> BACK DEMODULATING HINT 4186 WITH 13187. >> BACK DEMODULATING HINT 4184 WITH 13187. NEW HINT: 13232 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),z),f(g(f(g(f(z,x)),z)),z))=f(x,z). >> BACK DEMODULATING HINT 3945 WITH 13187. >> BACK DEMODULATING HINT 3936 WITH 13187. >> BACK DEMODULATING HINT 3865 WITH 13187. >> BACK DEMODULATING HINT 3801 WITH 13187. >> BACK DEMODULATING HINT 3778 WITH 13187. >> BACK DEMODULATING HINT 3766 WITH 13187. >> BACK DEMODULATING HINT 3751 WITH 13187. >> BACK DEMODULATING HINT 3749 WITH 13187. >> BACK DEMODULATING HINT 3744 WITH 13187. >> BACK DEMODULATING HINT 3743 WITH 13187. >> BACK DEMODULATING HINT 3742 WITH 13187. >> BACK DEMODULATING HINT 3741 WITH 13187. NEW HINT: 13233 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(f(y,g(y)),z)))),x)=z. >> BACK DEMODULATING HINT 3720 WITH 13187. >> BACK DEMODULATING HINT 3544 WITH 13187. >> BACK DEMODULATING HINT 3519 WITH 13187. >> BACK DEMODULATING HINT 3118 WITH 13187. >> BACK DEMODULATING HINT 3112 WITH 13187. >> BACK DEMODULATING HINT 3109 WITH 13187. >> BACK DEMODULATING HINT 2540 WITH 13187. >> BACK DEMODULATING HINT 2520 WITH 13187. >> BACK DEMODULATING HINT 2491 WITH 13187. >> BACK DEMODULATING HINT 2480 WITH 13187. >> BACK DEMODULATING HINT 2478 WITH 13187. >> BACK DEMODULATING HINT 2475 WITH 13187. >> BACK DEMODULATING HINT 2474 WITH 13187. >> BACK DEMODULATING HINT 2473 WITH 13187. >> BACK DEMODULATING HINT 2467 WITH 13187. >> BACK DEMODULATING HINT 2466 WITH 13187. >> BACK DEMODULATING HINT 2454 WITH 13187. NEW HINT: 13234 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(x,g(z))),z))=f(x,f(y,x)). >> BACK DEMODULATING HINT 2448 WITH 13187. >> BACK DEMODULATING HINT 2443 WITH 13187. NEW HINT: 13235 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,f(g(f(x,x)),f(x,g(f(x,g(f(x,f(g(x),x))))))))))=x. >> BACK DEMODULATING HINT 2441 WITH 13187. >> BACK DEMODULATING HINT 2438 WITH 13187. NEW HINT: 13236 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(x,x)),f(x,g(f(x,g(x))))))=f(x,g(x)). >> BACK DEMODULATING HINT 2437 WITH 13187. NEW HINT: 13237 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),x))=f(g(f(x,x)),f(x,g(f(x,g(x))))). >> BACK DEMODULATING HINT 2425 WITH 13187. NEW HINT: 13238 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(f(x,f(y,x)))),x))=y. >> BACK DEMODULATING HINT 2412 WITH 13187. NEW HINT: 13239 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,x)),f(x,g(y)))=g(f(y,x)). >> BACK DEMODULATING HINT 2409 WITH 13187. NEW HINT: 13240 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=f(u,f(g(f(g(f(x,y)),u)),g(y))). >> BACK DEMODULATING HINT 2404 WITH 13187. >> BACK DEMODULATING HINT 2399 WITH 13187. >> BACK DEMODULATING HINT 2398 WITH 13187. NEW HINT: 13241 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),g(z)))=g(f(z,y)). >> BACK DEMODULATING HINT 2313 WITH 13187. NEW HINT: 13242 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(g(f(y,g(y))),f(u,x))))=f(g(u),g(f(v,g(v)))). >> BACK DEMODULATING HINT 2312 WITH 13187. NEW HINT: 13243 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,g(x))),z))=g(z). >> BACK DEMODULATING HINT 2303 WITH 13187. NEW HINT: 13244 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(f(x,y),f(g(y),z))),g(f(u,f(g(f(x,u)),g(f(v,g(v))))))))=z. >> BACK DEMODULATING HINT 2302 WITH 13187. NEW HINT: 13245 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(g(f(f(y,g(y)),y))))=f(u,g(f(g(f(f(v,g(v)),y)),f(x,u)))). >> BACK DEMODULATING HINT 2296 WITH 13187. >> BACK DEMODULATING HINT 2291 WITH 13187. >> BACK DEMODULATING HINT 2290 WITH 13187. NEW HINT: 13246 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,f(g(f(y,x)),z))),g(y)))=z. >> BACK DEMODULATING HINT 2201 WITH 13187. >> BACK DEMODULATING HINT 2200 WITH 13187. NEW HINT: 13247 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,g(f(y,x)))))=g(y). >> BACK DEMODULATING HINT 2199 WITH 13187. >> BACK DEMODULATING HINT 2198 WITH 13187. NEW HINT: 13248 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,g(f(y,x)))),g(g(f(z,g(z))))))=g(y). >> BACK DEMODULATING HINT 2197 WITH 13187. NEW HINT: 13249 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(g(g(f(x,g(f(y,x)))))),g(g(f(z,g(z))))))=g(y). >> BACK DEMODULATING HINT 2196 WITH 13187. NEW HINT: 13250 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(x,g(x)),g(f(y,g(f(z,y))))),g(g(f(x,g(x))))))=g(z). >> BACK DEMODULATING HINT 2195 WITH 13187. NEW HINT: 13251 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(x,g(x)),g(g(g(f(y,g(f(z,y))))))),g(g(f(x,g(x))))))=g(z). >> BACK DEMODULATING HINT 2194 WITH 13187. NEW HINT: 13252 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(x,g(x)),g(f(f(y,g(y)),f(z,g(f(u,z)))))),g(g(f(x,g(x))))))=g(u). >> BACK DEMODULATING HINT 2193 WITH 13187. >> BACK DEMODULATING HINT 2192 WITH 13187. NEW HINT: 13253 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(x,g(x)),g(f(f(y,g(y)),f(z,f(g(f(u,z)),g(g(f(x,g(x))))))))),g(g(f(x,g(x))))))=g(u). >> BACK DEMODULATING HINT 2179 WITH 13187. >> BACK DEMODULATING HINT 2174 WITH 13187. NEW HINT: 13254 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(g(g(x))))=f(f(g(f(z,g(z))),x),g(g(f(y,g(y))))). >> BACK DEMODULATING HINT 2173 WITH 13187. NEW HINT: 13255 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(x)),g(g(y)))=f(f(g(f(u,g(u))),y),g(g(f(z,g(z))))). >> BACK DEMODULATING HINT 2172 WITH 13187. NEW HINT: 13256 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(x)),f(g(g(y)),g(g(f(z,g(z))))))=f(f(g(f(u,g(u))),y),g(g(f(z,g(z))))). >> BACK DEMODULATING HINT 2170 WITH 13187. NEW HINT: 13257 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(x)),f(g(f(f(f(y,g(y)),g(f(z,f(g(z),u)))),g(g(f(y,g(y)))))),g(g(f(y,g(y))))))=f(f(g(f(v,g(v))),u),g(g(f(y,g(y))))). >> BACK DEMODULATING HINT 2157 WITH 13187. >> BACK DEMODULATING HINT 2156 WITH 13187. NEW HINT: 13258 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(g(g(x))))=x. >> BACK DEMODULATING HINT 2155 WITH 13187. >> BACK DEMODULATING HINT 2154 WITH 13187. NEW HINT: 13259 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),g(g(g(y)))))=y. >> BACK DEMODULATING HINT 2153 WITH 13187. NEW HINT: 13260 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),f(f(y,g(y)),g(z))))=z. >> BACK DEMODULATING HINT 2152 WITH 13187. NEW HINT: 13261 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),f(f(y,g(y)),f(g(z),g(g(f(u,g(u))))))))=z. >> BACK DEMODULATING HINT 2117 WITH 13187. >> BACK DEMODULATING HINT 2116 WITH 13187. >> BACK DEMODULATING HINT 2109 WITH 13187. >> BACK DEMODULATING HINT 2103 WITH 13187. NEW HINT: 13262 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(g(f(f(y,g(y)),g(f(y,g(y)))))))=f(z,g(f(g(f(u,g(u))),f(x,z)))). >> BACK DEMODULATING HINT 2093 WITH 13187. >> BACK DEMODULATING HINT 2083 WITH 13187. NEW HINT: 13263 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(g(f(x,g(x)))),g(f(f(y,g(y)),f(z,f(g(f(u,z)),g(g(f(x,g(x))))))))),g(g(f(x,g(x))))))=g(u). >> BACK DEMODULATING HINT 2068 WITH 13187. >> BACK DEMODULATING HINT 2066 WITH 13187. >> BACK DEMODULATING HINT 1867 WITH 13187. >> BACK DEMODULATING HINT 1856 WITH 13187. >> BACK DEMODULATING HINT 1766 WITH 13187. >> BACK DEMODULATING HINT 1765 WITH 13187. NEW HINT: 13264 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=f(g(g(y)),u). >> BACK DEMODULATING HINT 1764 WITH 13187. >> BACK DEMODULATING HINT 1763 WITH 13187. >> BACK DEMODULATING HINT 1762 WITH 13187. NEW HINT: 13265 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(g(f(y,g(y))),z))=z. >> BACK DEMODULATING HINT 1744 WITH 13187. >> BACK DEMODULATING HINT 1743 WITH 13187. >> BACK DEMODULATING HINT 1742 WITH 13187. >> BACK DEMODULATING HINT 1741 WITH 13187. NEW HINT: 13266 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(z,g(f(x,f(u,z))))))=g(g(u)). >> BACK DEMODULATING HINT 1740 WITH 13187. NEW HINT: 13267 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(z,g(f(x,f(u,z))))))=g(f(y,g(f(y,f(f(g(y),u),y))))). >> BACK DEMODULATING HINT 1737 WITH 13187. >> BACK DEMODULATING HINT 1734 WITH 13187. >> BACK DEMODULATING HINT 1733 WITH 13187. NEW HINT: 13268 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(g(f(f(y,g(y)),g(f(y,g(y))))),z))=f(u,f(g(f(f(y,g(y)),u)),z)). >> BACK DEMODULATING HINT 1727 WITH 13187. NEW HINT: 13269 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(y,g(f(y,f(f(z,f(g(x),x)),y)))))=g(f(f(x,g(x)),g(f(y,z)))). >> BACK DEMODULATING HINT 1726 WITH 13187. NEW HINT: 13270 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(y,g(f(y,f(f(z,f(g(x),x)),y)))))=f(g(f(f(x,g(x)),g(f(y,z)))),g(f(f(x,g(x)),g(f(x,g(x)))))). >> BACK DEMODULATING HINT 1724 WITH 13187. NEW HINT: 13271 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,g(x)))),g(f(x,g(x))))=f(y,g(y)). >> BACK DEMODULATING HINT 1723 WITH 13187. >> BACK DEMODULATING HINT 1722 WITH 13187. NEW HINT: 13272 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(f(y,g(y)))),g(g(g(f(y,g(y))))))=x. >> BACK DEMODULATING HINT 1721 WITH 13187. NEW HINT: 13273 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),x)=f(y,g(y)). >> BACK DEMODULATING HINT 1720 WITH 13187. >> BACK DEMODULATING HINT 1708 WITH 13187. NEW HINT: 13274 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=f(g(f(f(v,g(v)),g(y))),u). >> BACK DEMODULATING HINT 1707 WITH 13187. NEW HINT: 13275 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),g(f(f(x,g(x)),f(g(f(f(y,g(y)),g(z))),u)))))=f(g(f(v,g(z))),g(f(w,g(f(v,f(u,w)))))). >> BACK DEMODULATING HINT 1706 WITH 13187. NEW HINT: 13276 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),g(f(f(x,g(x)),f(g(f(f(y,g(y)),g(z))),u)))))=f(g(f(v,g(f(f(x,g(x)),g(f(f(y,g(y)),g(z))))))),g(f(w,g(f(v,f(u,w)))))). >> BACK DEMODULATING HINT 1705 WITH 13187. >> BACK DEMODULATING HINT 1701 WITH 13187. >> BACK DEMODULATING HINT 1700 WITH 13187. >> BACK DEMODULATING HINT 1699 WITH 13187. NEW HINT: 13277 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(f(f(y,g(y)),f(z,f(g(f(f(y,g(y)),z)),u))))),u)=x. >> BACK DEMODULATING HINT 1695 WITH 13187. NEW HINT: 13278 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),f(y,f(g(f(f(x,g(x)),y)),g(f(f(z,g(z)),u))))))=u. >> BACK DEMODULATING HINT 1694 WITH 13187. NEW HINT: 13279 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(f(y,g(y)),x)),g(f(f(y,g(y)),g(f(f(z,g(z)),u))))))=u. >> BACK DEMODULATING HINT 1693 WITH 13187. NEW HINT: 13280 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(f(y,g(y)),x)),g(f(f(z,g(z)),g(f(f(z,g(z)),u))))))=u. >> BACK DEMODULATING HINT 1612 WITH 13187. >> BACK DEMODULATING HINT 1595 WITH 13187. >> BACK DEMODULATING HINT 1590 WITH 13187. >> BACK DEMODULATING HINT 1589 WITH 13187. >> BACK DEMODULATING HINT 1588 WITH 13187. NEW HINT: 13281 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(g(f(x,g(x)))),g(y))),y)=f(x,f(f(x,g(x)),g(g(f(x,g(x)))))). >> BACK DEMODULATING HINT 1587 WITH 13187. >> BACK DEMODULATING HINT 1561 WITH 13187. >> BACK DEMODULATING HINT 1554 WITH 13187. >> BACK DEMODULATING HINT 1551 WITH 13187. >> BACK DEMODULATING HINT 1549 WITH 13187. NEW HINT: 13282 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(g(f(x,g(x)))),g(y))),y)=f(x,f(g(g(f(x,g(x)))),g(g(f(x,g(x)))))). >> BACK DEMODULATING HINT 1547 WITH 13187. >> BACK DEMODULATING HINT 1545 WITH 13187. >> BACK DEMODULATING HINT 1542 WITH 13187. >> BACK DEMODULATING HINT 1541 WITH 13187. >> BACK DEMODULATING HINT 1539 WITH 13187. >> BACK DEMODULATING HINT 1534 WITH 13187. >> BACK DEMODULATING HINT 1532 WITH 13187. >> BACK DEMODULATING HINT 1525 WITH 13187. NEW HINT: 13283 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(f(x,f(g(y),x)))),x)=y. >> BACK DEMODULATING HINT 1524 WITH 13187. NEW HINT: 13284 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(f(x,f(y,x)))),x)=f(y,g(f(y,y))). >> BACK DEMODULATING HINT 1523 WITH 13187. NEW HINT: 13285 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,g(f(f(y,g(f(y,f(x,y)))),y)))))=f(f(y,g(f(y,f(x,y)))),y). >> BACK DEMODULATING HINT 1522 WITH 13187. >> BACK DEMODULATING HINT 1521 WITH 13187. >> BACK DEMODULATING HINT 1517 WITH 13187. >> BACK DEMODULATING HINT 1516 WITH 13187. >> BACK DEMODULATING HINT 1511 WITH 13187. >> BACK DEMODULATING HINT 1506 WITH 13187. >> BACK DEMODULATING HINT 1504 WITH 13187. >> BACK DEMODULATING HINT 1501 WITH 13187. >> BACK DEMODULATING HINT 1489 WITH 13187. NEW HINT: 13286 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(g(f(f(y,g(f(y,f(x,y)))),y)),g(f(f(y,g(f(y,f(x,y)))),y)))))=f(f(y,g(f(y,f(x,y)))),y). >> BACK DEMODULATING HINT 1488 WITH 13187. >> BACK DEMODULATING HINT 1486 WITH 13187. NEW HINT: 13287 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(g(x),f(f(g(f(y,g(y))),f(g(x),g(z))),z))))=f(g(f(g(f(x,y)),g(f(x,y)))),f(g(f(x,y)),g(y))). >> BACK DEMODULATING HINT 1485 WITH 13187. >> BACK DEMODULATING HINT 1484 WITH 13187. >> BACK DEMODULATING HINT 1481 WITH 13187. >> BACK DEMODULATING HINT 1479 WITH 13187. NEW HINT: 13288 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,y))=f(g(f(y,y)),f(y,g(x))). >> BACK DEMODULATING HINT 1478 WITH 13187. >> BACK DEMODULATING HINT 1475 WITH 13187. >> BACK DEMODULATING HINT 1440 WITH 13187. >> BACK DEMODULATING HINT 1436 WITH 13187. >> BACK DEMODULATING HINT 1435 WITH 13187. NEW HINT: 13289 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(g(y),g(f(g(y),f(f(f(g(f(x,g(y))),g(y)),g(f(x,g(y)))),g(y))))))=f(g(y),g(g(f(y,x)))). >> BACK DEMODULATING HINT 1434 WITH 13187. >> BACK DEMODULATING HINT 1396 WITH 13187. >> BACK DEMODULATING HINT 1386 WITH 13187. >> BACK DEMODULATING HINT 1384 WITH 13187. >> BACK DEMODULATING HINT 1374 WITH 13187. NEW HINT: 13290 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),g(f(g(x),f(g(f(y,g(x))),g(x)))))),f(g(x),g(f(g(x),f(f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))),g(x))))))=f(g(x),g(g(f(x,y)))). >> BACK DEMODULATING HINT 1371 WITH 13187. >> BACK DEMODULATING HINT 1370 WITH 13187. >> BACK DEMODULATING HINT 1369 WITH 13187. >> BACK DEMODULATING HINT 1368 WITH 13187. >> BACK DEMODULATING HINT 1367 WITH 13187. >> BACK DEMODULATING HINT 1362 WITH 13187. >> BACK DEMODULATING HINT 1360 WITH 13187. >> BACK DEMODULATING HINT 1359 WITH 13187. >> BACK DEMODULATING HINT 1358 WITH 13187. NEW HINT: 13291 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,g(x)),x)))=x. >> BACK DEMODULATING HINT 1350 WITH 13187. NEW HINT: 13292 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,g(x))),g(f(x,g(x))))),f(g(f(x,g(x))),g(g(x))))=x. >> BACK DEMODULATING HINT 1344 WITH 13187. >> BACK DEMODULATING HINT 1343 WITH 13187. >> BACK DEMODULATING HINT 1341 WITH 13187. >> BACK DEMODULATING HINT 1320 WITH 13187. >> BACK DEMODULATING HINT 1319 WITH 13187. >> BACK DEMODULATING HINT 1318 WITH 13187. >> BACK DEMODULATING HINT 1317 WITH 13187. >> BACK DEMODULATING HINT 1316 WITH 13187. >> BACK DEMODULATING HINT 1315 WITH 13187. >> BACK DEMODULATING HINT 1313 WITH 13187. >> BACK DEMODULATING HINT 1312 WITH 13187. >> BACK DEMODULATING HINT 1309 WITH 13187. NEW HINT: 13293 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(f(y,x)),z)),f(z,g(f(z,z))))=g(y). >> BACK DEMODULATING HINT 1308 WITH 13187. NEW HINT: 13294 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),g(f(y,g(y)))))=f(f(x,f(g(f(y,x)),z)),f(z,g(f(z,z)))). >> BACK DEMODULATING HINT 1306 WITH 13187. NEW HINT: 13295 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,x)),f(x,y)),f(y,g(f(y,y))))=g(x). >> BACK DEMODULATING HINT 1305 WITH 13187. NEW HINT: 13296 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,x)),f(x,g(f(x,g(x)))))=f(f(g(f(x,x)),f(x,y)),f(y,g(f(y,y)))). >> BACK DEMODULATING HINT 1304 WITH 13187. >> BACK DEMODULATING HINT 1303 WITH 13187. >> BACK DEMODULATING HINT 1295 WITH 13187. >> BACK DEMODULATING HINT 1292 WITH 13187. NEW HINT: 13297 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,g(f(f(y,g(y)),z))),x))))))=g(y). >> BACK DEMODULATING HINT 1291 WITH 13187. >> BACK DEMODULATING HINT 1284 WITH 13187. >> BACK DEMODULATING HINT 1283 WITH 13187. NEW HINT: 13298 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(f(x,f(g(y),x)))),x)=f(g(y),f(f(g(f(g(y),g(y))),y),g(y))). >> BACK DEMODULATING HINT 1280 WITH 13187. >> BACK DEMODULATING HINT 1279 WITH 13187. >> BACK DEMODULATING HINT 1278 WITH 13187. NEW HINT: 13299 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(z))),z))=f(x,g(x)). >> BACK DEMODULATING HINT 1273 WITH 13187. >> BACK DEMODULATING HINT 1272 WITH 13187. >> BACK DEMODULATING HINT 1270 WITH 13187. >> BACK DEMODULATING HINT 1269 WITH 13187. >> BACK DEMODULATING HINT 1268 WITH 13187. NEW HINT: 13300 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(g(f(x,g(x))),x),g(x)))=f(g(x),f(g(x),x)). >> BACK DEMODULATING HINT 1267 WITH 13187. >> BACK DEMODULATING HINT 1266 WITH 13187. >> BACK DEMODULATING HINT 1265 WITH 13187. >> BACK DEMODULATING HINT 1264 WITH 13187. NEW HINT: 13301 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,g(f(x,f(y,x)))),x)),g(f(g(f(f(x,g(f(x,f(y,x)))),x)),y)))=f(f(x,g(f(x,f(y,x)))),x). >> BACK DEMODULATING HINT 1263 WITH 13187. >> BACK DEMODULATING HINT 1262 WITH 13187. NEW HINT: 13302 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(y,x))),g(f(g(f(x,f(y,x))),g(f(x,f(y,x))))))=f(x,f(f(y,f(x,g(z))),z)). >> BACK DEMODULATING HINT 1261 WITH 13187. >> BACK DEMODULATING HINT 1260 WITH 13187. >> BACK DEMODULATING HINT 1259 WITH 13187. NEW HINT: 13303 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(f(x,f(y,x)))),x))=f(f(x,g(x)),g(f(f(x,g(x)),f(g(f(x,g(x))),f(f(x,g(x)),g(y)))))). >> BACK DEMODULATING HINT 1258 WITH 13187. NEW HINT: 13304 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),g(f(g(x),f(g(f(y,g(x))),g(x)))))),g(g(f(g(x),g(f(g(x),f(f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))),g(x))))))))=f(g(x),g(g(f(x,y)))). >> BACK DEMODULATING HINT 1257 WITH 13187. >> BACK DEMODULATING HINT 1242 WITH 13187. NEW HINT: 13305 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,g(f(f(y,g(y)),z))),x))))))=f(u,f(g(f(y,u)),g(f(y,g(y))))). >> BACK DEMODULATING HINT 1241 WITH 13187. >> BACK DEMODULATING HINT 1240 WITH 13187. >> BACK DEMODULATING HINT 1239 WITH 13187. NEW HINT: 13306 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,g(f(f(y,g(y)),z))),x))))))=f(g(f(y,y)),f(y,g(f(y,g(y))))). >> BACK DEMODULATING HINT 1238 WITH 13187. >> BACK DEMODULATING HINT 1237 WITH 13187. >> BACK DEMODULATING HINT 1234 WITH 13187. NEW HINT: 13307 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(x)),x))=f(g(x),f(y,f(g(f(x,y)),x))). >> BACK DEMODULATING HINT 1233 WITH 13187. >> BACK DEMODULATING HINT 1232 WITH 13187. >> BACK DEMODULATING HINT 1231 WITH 13187. NEW HINT: 13308 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(x))),g(f(g(f(x,g(x))),g(f(x,g(x))))))=f(x,f(f(y,f(g(f(x,y)),g(x))),x)). >> BACK DEMODULATING HINT 1230 WITH 13187. >> BACK DEMODULATING HINT 1228 WITH 13187. >> BACK DEMODULATING HINT 1227 WITH 13187. >> BACK DEMODULATING HINT 1225 WITH 13187. >> BACK DEMODULATING HINT 1220 WITH 13187. >> BACK DEMODULATING HINT 1218 WITH 13187. >> BACK DEMODULATING HINT 1217 WITH 13187. NEW HINT: 13309 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(x,g(f(x,f(y,x))))),g(f(g(f(x,g(f(x,f(y,x))))),g(f(x,g(f(x,f(y,x)))))))),x))=y. >> BACK DEMODULATING HINT 1206 WITH 13187. >> BACK DEMODULATING HINT 1147 WITH 13187. >> BACK DEMODULATING HINT 1115 WITH 13187. >> BACK DEMODULATING HINT 1109 WITH 13187. >> BACK DEMODULATING HINT 1105 WITH 13187. >> BACK DEMODULATING HINT 1087 WITH 13187. >> BACK DEMODULATING HINT 1086 WITH 13187. >> BACK DEMODULATING HINT 1085 WITH 13187. >> BACK DEMODULATING HINT 1084 WITH 13187. >> BACK DEMODULATING HINT 1083 WITH 13187. >> BACK DEMODULATING HINT 1081 WITH 13187. >> BACK DEMODULATING HINT 1080 WITH 13187. >> BACK DEMODULATING HINT 1079 WITH 13187. >> BACK DEMODULATING HINT 1077 WITH 13187. NEW HINT: 13310 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(y,x)))=f(g(y),g(f(y,g(y)))) # label(bd). >> BACK DEMODULATING HINT 1075 WITH 13187. NEW HINT: 13311 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(g(g(x)),f(f(y,f(g(f(x,y)),g(z))),z)))=g(x) # label(bd). >> BACK DEMODULATING HINT 1074 WITH 13187. NEW HINT: 13312 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(x),f(g(g(x)),f(f(y,f(g(f(x,y)),g(z))),z))))=f(g(f(g(x),g(x))),g(x)) # label(bd). >> BACK DEMODULATING HINT 1073 WITH 13187. NEW HINT: 13313 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(f(f(f(x,f(g(f(y,x)),g(z))),z),g(f(f(x,f(g(f(y,x)),g(z))),z)))),f(f(x,f(g(f(y,x)),g(z))),z)),f(g(f(f(x,f(g(f(y,x)),g(z))),z)),g(u))),u)=f(g(f(f(x,f(g(f(y,x)),g(z))),z)),g(y)) # label(bd). >> BACK DEMODULATING HINT 1072 WITH 13187. NEW HINT: 13314 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(z,y)),g(u))),u))=f(x,g(z)) # label(bd). >> BACK DEMODULATING HINT 1071 WITH 13187. >> BACK DEMODULATING HINT 1068 WITH 13187. >> BACK DEMODULATING HINT 1065 WITH 13187. >> BACK DEMODULATING HINT 1058 WITH 13187. >> BACK DEMODULATING HINT 1055 WITH 13187. >> BACK DEMODULATING HINT 1054 WITH 13187. >> BACK DEMODULATING HINT 1047 WITH 13187. >> BACK DEMODULATING HINT 1045 WITH 13187. >> BACK DEMODULATING HINT 1038 WITH 13187. >> BACK DEMODULATING HINT 1036 WITH 13187. NEW HINT: 13315 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(g(x),g(g(x))),f(f(g(f(g(x),g(g(x)))),f(f(g(x),g(g(x))),g(y))),y))),g(x))=f(f(g(f(g(x),g(g(x)))),x),f(g(x),g(x))) # label(bd). >> BACK DEMODULATING HINT 1033 WITH 13187. NEW HINT: 13316 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(f(x,g(f(x,f(y,z))))))=f(z,g(x)) # label(bd). >> BACK DEMODULATING HINT 1032 WITH 13187. NEW HINT: 13317 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(f(x,g(f(x,f(g(f(g(x),g(x))),g(x)))))))=f(g(f(g(x),y)),g(x)) # label(bd). >> BACK DEMODULATING HINT 1031 WITH 13187. >> BACK DEMODULATING HINT 1030 WITH 13187. NEW HINT: 13318 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(y,z)),f(z,g(f(z,z))))=f(x,y) # label(bd). >> BACK DEMODULATING HINT 1028 WITH 13187. >> BACK DEMODULATING HINT 1026 WITH 13187. >> BACK DEMODULATING HINT 1025 WITH 13187. >> BACK DEMODULATING HINT 1024 WITH 13187. >> BACK DEMODULATING HINT 1023 WITH 13187. >> BACK DEMODULATING HINT 1022 WITH 13187. >> BACK DEMODULATING HINT 1021 WITH 13187. >> BACK DEMODULATING HINT 1013 WITH 13187. >> BACK DEMODULATING HINT 1012 WITH 13187. >> BACK DEMODULATING HINT 1011 WITH 13187. >> BACK DEMODULATING HINT 1010 WITH 13187. >> BACK DEMODULATING HINT 1009 WITH 13187. >> BACK DEMODULATING HINT 1006 WITH 13187. >> BACK DEMODULATING HINT 1005 WITH 13187. >> BACK DEMODULATING HINT 1004 WITH 13187. >> BACK DEMODULATING HINT 1003 WITH 13187. >> BACK DEMODULATING HINT 1001 WITH 13187. >> BACK DEMODULATING HINT 995 WITH 13187. >> BACK DEMODULATING HINT 989 WITH 13187. >> BACK DEMODULATING HINT 943 WITH 13187. >> BACK DEMODULATING HINT 942 WITH 13187. >> BACK DEMODULATING HINT 941 WITH 13187. >> BACK DEMODULATING HINT 940 WITH 13187. NEW HINT: 13319 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,g(f(x,x))))=f(g(f(y,g(y))),f(f(y,g(y)),x)). >> BACK DEMODULATING HINT 935 WITH 13187. >> BACK DEMODULATING HINT 934 WITH 13187. >> BACK DEMODULATING HINT 933 WITH 13187. >> BACK DEMODULATING HINT 926 WITH 13187. >> BACK DEMODULATING HINT 925 WITH 13187. >> BACK DEMODULATING HINT 924 WITH 13187. NEW HINT: 13320 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(f(x,g(f(g(x),g(y)))))),x))=y. >> BACK DEMODULATING HINT 910 WITH 13187. NEW HINT: 13321 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(x)),g(f(g(g(x)),f(g(f(g(g(x)),g(g(x)))),g(g(x))))))=x. >> BACK DEMODULATING HINT 883 WITH 13187. NEW HINT: 13322 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(g(x),f(g(f(f(x,g(f(x,x))),x)),x))))=g(x). >> BACK DEMODULATING HINT 881 WITH 13187. NEW HINT: 13323 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,g(f(x,x))),x)),x)=x. >> BACK DEMODULATING HINT 880 WITH 13187. >> BACK DEMODULATING HINT 874 WITH 13187. NEW HINT: 13324 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(x,g(x))))),g(g(x)))=f(x,g(x)). >> BACK DEMODULATING HINT 871 WITH 13187. >> BACK DEMODULATING HINT 870 WITH 13187. >> BACK DEMODULATING HINT 852 WITH 13187. >> BACK DEMODULATING HINT 851 WITH 13187. >> BACK DEMODULATING HINT 849 WITH 13187. >> BACK DEMODULATING HINT 846 WITH 13187. >> BACK DEMODULATING HINT 845 WITH 13187. >> BACK DEMODULATING HINT 843 WITH 13187. >> BACK DEMODULATING HINT 842 WITH 13187. >> BACK DEMODULATING HINT 841 WITH 13187. >> BACK DEMODULATING HINT 840 WITH 13187. >> BACK DEMODULATING HINT 839 WITH 13187. >> BACK DEMODULATING HINT 838 WITH 13187. >> BACK DEMODULATING HINT 837 WITH 13187. >> BACK DEMODULATING HINT 836 WITH 13187. >> BACK DEMODULATING HINT 835 WITH 13187. >> BACK DEMODULATING HINT 834 WITH 13187. >> BACK DEMODULATING HINT 828 WITH 13187. >> BACK DEMODULATING HINT 827 WITH 13187. >> BACK DEMODULATING HINT 826 WITH 13187. >> BACK DEMODULATING HINT 825 WITH 13187. NEW HINT: 13325 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,f(g(f(y,x)),y))))=x. >> BACK DEMODULATING HINT 824 WITH 13187. >> BACK DEMODULATING HINT 823 WITH 13187. >> BACK DEMODULATING HINT 820 WITH 13187. >> BACK DEMODULATING HINT 819 WITH 13187. NEW HINT: 13326 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,g(f(x,x))),y))=f(g(f(y,y)),f(y,x)). >> BACK DEMODULATING HINT 818 WITH 13187. >> BACK DEMODULATING HINT 817 WITH 13187. >> BACK DEMODULATING HINT 810 WITH 13187. >> BACK DEMODULATING HINT 799 WITH 13187. >> BACK DEMODULATING HINT 798 WITH 13187. NEW HINT: 13327 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,g(f(x,x))),x)),x)=g(f(x,g(f(x,x)))). >> BACK DEMODULATING HINT 797 WITH 13187. NEW HINT: 13328 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,g(f(x,x))),x)),g(f(x,g(f(x,x)))))=g(f(x,g(f(x,x)))). >> BACK DEMODULATING HINT 795 WITH 13187. >> BACK DEMODULATING HINT 791 WITH 13187. >> BACK DEMODULATING HINT 750 WITH 13187. >> BACK DEMODULATING HINT 742 WITH 13187. >> BACK DEMODULATING HINT 726 WITH 13187. >> BACK DEMODULATING HINT 724 WITH 13187. NEW HINT: 13329 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(x),z))=f(y,f(g(y),z)) # label(bd). >> BACK DEMODULATING HINT 722 WITH 13187. >> BACK DEMODULATING HINT 718 WITH 13187. >> BACK DEMODULATING HINT 715 WITH 13187. >> BACK DEMODULATING HINT 712 WITH 13187. >> BACK DEMODULATING HINT 706 WITH 13187. >> BACK DEMODULATING HINT 704 WITH 13187. NEW HINT: 13330 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(x)),f(g(f(x,g(x))),g(y)))=g(f(y,g(x))) # label(bd). >> BACK DEMODULATING HINT 702 WITH 13187. >> BACK DEMODULATING HINT 699 WITH 13187. >> BACK DEMODULATING HINT 694 WITH 13187. NEW HINT: 13331 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,x)),f(x,x)),f(g(x),x))=f(x,g(x)) # label(bd). >> BACK DEMODULATING HINT 684 WITH 13187. >> BACK DEMODULATING HINT 683 WITH 13187. >> BACK DEMODULATING HINT 682 WITH 13187. >> BACK DEMODULATING HINT 672 WITH 13187. >> BACK DEMODULATING HINT 668 WITH 13187. >> BACK DEMODULATING HINT 662 WITH 13187. >> BACK DEMODULATING HINT 660 WITH 13187. >> BACK DEMODULATING HINT 659 WITH 13187. >> BACK DEMODULATING HINT 657 WITH 13187. >> BACK DEMODULATING HINT 653 WITH 13187. >> BACK DEMODULATING HINT 652 WITH 13187. >> BACK DEMODULATING HINT 643 WITH 13187. >> BACK DEMODULATING HINT 640 WITH 13187. NEW HINT: 13332 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(x,f(g(y),x))),x))=f(y,f(g(f(x,x)),f(x,x))) # label(bd). >> BACK DEMODULATING HINT 639 WITH 13187. >> BACK DEMODULATING HINT 635 WITH 13187. >> BACK DEMODULATING HINT 634 WITH 13187. >> BACK DEMODULATING HINT 633 WITH 13187. NEW HINT: 13333 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,g(f(x,f(y,x)))),x)))=g(y) # label(bd). >> BACK DEMODULATING HINT 628 WITH 13187. >> BACK DEMODULATING HINT 626 WITH 13187. >> BACK DEMODULATING HINT 625 WITH 13187. >> BACK DEMODULATING HINT 624 WITH 13187. >> BACK DEMODULATING HINT 613 WITH 13187. >> BACK DEMODULATING HINT 605 WITH 13187. >> BACK DEMODULATING HINT 599 WITH 13187. >> BACK DEMODULATING HINT 578 WITH 13187. >> BACK DEMODULATING HINT 555 WITH 13187. >> BACK DEMODULATING HINT 551 WITH 13187. >> BACK DEMODULATING HINT 550 WITH 13187. >> BACK DEMODULATING HINT 546 WITH 13187. NEW HINT: 13334 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(x),y))=f(g(f(y,y)),f(y,x)) # label(bd). >> BACK DEMODULATING HINT 539 WITH 13187. >> BACK DEMODULATING HINT 536 WITH 13187. >> BACK DEMODULATING HINT 534 WITH 13187. >> BACK DEMODULATING HINT 517 WITH 13187. >> BACK DEMODULATING HINT 515 WITH 13187. >> BACK DEMODULATING HINT 514 WITH 13187. >> BACK DEMODULATING HINT 508 WITH 13187. >> BACK DEMODULATING HINT 505 WITH 13187. >> BACK DEMODULATING HINT 503 WITH 13187. >> BACK DEMODULATING HINT 498 WITH 13187. >> BACK DEMODULATING HINT 497 WITH 13187. >> BACK DEMODULATING HINT 489 WITH 13187. >> BACK DEMODULATING HINT 487 WITH 13187. >> BACK DEMODULATING HINT 486 WITH 13187. >> BACK DEMODULATING HINT 484 WITH 13187. >> BACK DEMODULATING HINT 482 WITH 13187. >> BACK DEMODULATING HINT 481 WITH 13187. >> BACK DEMODULATING HINT 480 WITH 13187. >> BACK DEMODULATING HINT 479 WITH 13187. >> BACK DEMODULATING HINT 478 WITH 13187. >> BACK DEMODULATING HINT 472 WITH 13187. >> BACK DEMODULATING HINT 464 WITH 13187. >> BACK DEMODULATING HINT 462 WITH 13187. >> BACK DEMODULATING HINT 457 WITH 13187. >> BACK DEMODULATING HINT 444 WITH 13187. >> BACK DEMODULATING HINT 400 WITH 13187. >> BACK DEMODULATING HINT 376 WITH 13187. >> BACK DEMODULATING HINT 315 WITH 13187. >> BACK DEMODULATING HINT 260 WITH 13187. >> BACK DEMODULATING HINT 253 WITH 13187. >> BACK DEMODULATING HINT 249 WITH 13187. NEW HINT: 13335 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,f(f(f(y,g(y)),f(x,g(z))),z))))=g(f(f(y,g(y)),x)) # label(bd). >> BACK DEMODULATING HINT 234 WITH 13187. >> BACK DEMODULATING HINT 232 WITH 13187. >> BACK DEMODULATING HINT 224 WITH 13187. >> BACK DEMODULATING HINT 221 WITH 13187. >> BACK DEMODULATING HINT 220 WITH 13187. >> BACK DEMODULATING HINT 190 WITH 13187. >> BACK DEMODULATING HINT 188 WITH 13187. >> BACK DEMODULATING HINT 165 WITH 13187. >> BACK DEMODULATING HINT 163 WITH 13187. >> BACK DEMODULATING HINT 156 WITH 13187. >> BACK DEMODULATING HINT 153 WITH 13187. >> BACK DEMODULATING HINT 78 WITH 13187. >> BACK DEMODULATING HINT 59 WITH 13187. given clause #110: (wt=-1016) 13186 [para_into,12665.1.1.2.2.1,4984.1.1] f(x,f(y,g(y)))=x. >> BACK DEMODULATING HINT 2527 WITH 13621. >> BACK DEMODULATING HINT 1602 WITH 13621. >> BACK DEMODULATING HINT 190 WITH 13621. >> BACK DEMODULATING HINT 13304 WITH 13744. NEW HINT: 14136 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(g(x),g(f(y,g(x)))))),f(g(g(f(y,g(x)))),f(g(g(x)),g(g(g(f(g(x),g(f(y,g(x))))))))))=f(g(x),g(g(f(x,y)))). >> BACK DEMODULATING HINT 3998 WITH 13744. >> BACK DEMODULATING HINT 3988 WITH 13744. >> BACK DEMODULATING HINT 2884 WITH 13744. >> BACK DEMODULATING HINT 1258 WITH 13744. >> BACK DEMODULATING HINT 1256 WITH 13744. NEW HINT: 14137 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),f(g(g(f(y,x))),f(g(x),g(g(g(f(x,g(f(y,x)))))))))=g(f(x,g(f(y,x)))). >> BACK DEMODULATING HINT 1208 WITH 13744. NEW HINT: 14138 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,y))),f(g(y),f(g(x),g(g(g(f(x,y)))))))=g(f(x,y)). >> BACK DEMODULATING HINT 1021 WITH 13744. >> BACK DEMODULATING HINT 1020 WITH 13744. >> BACK DEMODULATING HINT 991 WITH 13744. >> BACK DEMODULATING HINT 636 WITH 13744. >> BACK DEMODULATING HINT 436 WITH 13744. >> BACK DEMODULATING HINT 307 WITH 13744. >> BACK DEMODULATING HINT 13309 WITH 13756. NEW HINT: 16718 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(g(f(x,y))),g(f(g(g(f(x,y))),g(g(f(x,y)))))),x))=y. >> BACK DEMODULATING HINT 13306 WITH 13756. NEW HINT: 16719 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(z,g(f(f(y,g(y)),z)))))))=f(g(f(y,y)),f(y,g(f(y,g(y))))). >> BACK DEMODULATING HINT 13305 WITH 13756. NEW HINT: 16720 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(z,g(f(f(y,g(y)),z)))))))=f(u,f(g(f(y,u)),g(f(y,g(y))))). >> BACK DEMODULATING HINT 13304 WITH 13756. NEW HINT: 16721 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(g(x),g(f(y,g(x)))))),g(f(g(g(f(g(x),g(f(y,g(x)))))),g(g(f(g(x),g(f(y,g(x)))))))))=f(g(x),g(g(f(x,y)))). >> BACK DEMODULATING HINT 13297 WITH 13756. NEW HINT: 16722 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(z,g(f(f(y,g(y)),z)))))))=g(y). >> BACK DEMODULATING HINT 13290 WITH 13756. NEW HINT: 16723 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(g(x),g(f(y,g(x)))))),g(f(g(x),f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))))))=f(g(x),g(g(f(x,y)))). >> BACK DEMODULATING HINT 13270 WITH 13756. NEW HINT: 16724 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(y,f(z,f(g(x),x)))))=f(g(f(f(x,g(x)),g(f(y,z)))),g(f(f(x,g(x)),g(f(x,g(x)))))). >> BACK DEMODULATING HINT 13269 WITH 13756. NEW HINT: 16725 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(y,f(z,f(g(x),x)))))=g(f(f(x,g(x)),g(f(y,z)))). >> BACK DEMODULATING HINT 13267 WITH 13756. NEW HINT: 16726 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(z,g(f(x,f(u,z))))))=g(g(f(y,f(g(y),u)))). >> BACK DEMODULATING HINT 13235 WITH 13756. NEW HINT: 16727 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,f(g(f(x,x)),f(x,g(g(f(x,g(x)))))))))=x. >> BACK DEMODULATING HINT 5213 WITH 13756. >> BACK DEMODULATING HINT 4917 WITH 13756. NEW HINT: 16728 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(g(f(u,v)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4916 WITH 13756. NEW HINT: 16729 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,g(g(z))),g(u)),g(g(f(u,v)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4915 WITH 13756. NEW HINT: 16730 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(g(g(y)),g(g(z))),g(u)),g(g(f(u,v)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4914 WITH 13756. NEW HINT: 16731 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(g(f(g(z),g(y))),g(u)),g(g(f(u,v)))),w)))=f(f(f(z,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4913 WITH 13756. NEW HINT: 16732 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(f(z,f(g(u),g(y)))),g(g(f(z,v)))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4912 WITH 13756. NEW HINT: 16733 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(f(z,g(f(y,u)))),g(g(f(z,v)))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4901 WITH 13756. NEW HINT: 16734 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(y,z),u),g(g(f(y,v))))))=f(f(f(z,u),y),v). >> BACK DEMODULATING HINT 4900 WITH 13756. NEW HINT: 16735 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(y,z),f(g(u),f(u,v))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4899 WITH 13756. NEW HINT: 16736 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,v)),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4898 WITH 13756. NEW HINT: 16737 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(u,g(g(v)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4897 WITH 13756. NEW HINT: 16738 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),f(g(g(u)),g(g(v)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4896 WITH 13756. NEW HINT: 16739 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(g(v),g(u)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4895 WITH 13756. NEW HINT: 16740 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(u),f(g(v),g(u)))))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4894 WITH 13756. NEW HINT: 16741 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(f(g(u),g(v)),g(u))))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4893 WITH 13756. NEW HINT: 16742 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(f(u,f(g(f(v,u)),g(u))))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4892 WITH 13756. NEW HINT: 16743 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(g(f(u,v)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4891 WITH 13756. NEW HINT: 16744 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,g(g(z))),g(u)),g(g(f(u,v)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4890 WITH 13756. NEW HINT: 16745 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(g(g(y)),g(g(z))),g(u)),g(g(f(u,v)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4889 WITH 13756. NEW HINT: 16746 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(g(f(g(z),g(y))),g(u)),g(g(f(u,v)))),g(g(f(y,w))))))=f(f(f(z,v),y),w). >> BACK DEMODULATING HINT 4888 WITH 13756. NEW HINT: 16747 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(f(z,f(g(u),g(y)))),g(g(f(z,v)))),g(g(f(y,w))))))=f(f(f(u,v),y),w). >> BACK DEMODULATING HINT 4887 WITH 13756. NEW HINT: 16748 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(f(z,g(f(y,u)))),g(g(f(z,v)))),g(g(f(y,w))))))=f(f(f(u,v),y),w). >> BACK DEMODULATING HINT 4875 WITH 13756. NEW HINT: 16749 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(u)),g(g(f(u,v)))),w)))=f(f(z,v),w). >> BACK DEMODULATING HINT 4874 WITH 13756. NEW HINT: 16750 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,g(g(z))),g(u)),g(g(f(u,v)))),w)))=f(f(z,v),w). >> BACK DEMODULATING HINT 4873 WITH 13756. NEW HINT: 16751 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(g(g(y)),g(g(z))),g(u)),g(g(f(u,v)))),w)))=f(f(z,v),w). >> BACK DEMODULATING HINT 4872 WITH 13756. NEW HINT: 16752 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(g(f(g(z),g(y))),g(u)),g(g(f(u,v)))),w)))=f(f(z,v),w). >> BACK DEMODULATING HINT 4871 WITH 13756. NEW HINT: 16753 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(f(z,f(g(u),g(y)))),g(g(f(z,v)))),w)))=f(f(u,v),w). >> BACK DEMODULATING HINT 4870 WITH 13756. NEW HINT: 16754 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(f(z,g(f(y,u)))),g(g(f(z,v)))),w)))=f(f(u,v),w). >> BACK DEMODULATING HINT 4869 WITH 13756. NEW HINT: 16755 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(g(f(z,v)))),w)))=f(f(u,v),w). >> BACK DEMODULATING HINT 4868 WITH 13756. NEW HINT: 16756 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(g(z),u))=f(v,f(g(f(z,v)),f(f(g(f(w,g(f(z,x)))),g(g(f(w,y)))),u))). >> BACK DEMODULATING HINT 4867 WITH 13756. NEW HINT: 16757 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(u,f(g(u),f(g(z),v))))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(g(f(v6,y)))),v))). >> BACK DEMODULATING HINT 4866 WITH 13756. NEW HINT: 16758 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(u,f(f(g(u),g(z)),v)))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(g(f(v6,y)))),v))). >> BACK DEMODULATING HINT 4853 WITH 13756. NEW HINT: 16759 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(z,g(f(g(g(f(g(u),y))),z))))=f(x,u). >> BACK DEMODULATING HINT 4852 WITH 13756. NEW HINT: 16760 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(y),f(y,z))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4851 WITH 13756. NEW HINT: 16761 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),f(y,z)),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4850 WITH 13756. NEW HINT: 16762 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),f(y,g(g(z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4849 WITH 13756. NEW HINT: 16763 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),f(g(g(y)),g(g(z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4848 WITH 13756. NEW HINT: 16764 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),g(f(g(z),g(y)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4847 WITH 13756. NEW HINT: 16765 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),g(f(y,f(g(y),f(g(z),g(y)))))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4846 WITH 13756. NEW HINT: 16766 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),g(f(y,f(f(g(y),g(z)),g(y))))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4845 WITH 13756. NEW HINT: 16767 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),g(f(y,f(g(f(z,y)),g(y))))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4844 WITH 13756. NEW HINT: 16768 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(y)),g(g(f(y,z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4843 WITH 13756. NEW HINT: 16769 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(g(x)),g(y)),g(g(f(y,z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(x,v). >> BACK DEMODULATING HINT 4842 WITH 13756. NEW HINT: 16770 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(g(f(x,z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(y,v). >> BACK DEMODULATING HINT 4841 WITH 13756. NEW HINT: 16771 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(g(f(x,z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(y,g(g(v))). >> BACK DEMODULATING HINT 4840 WITH 13756. NEW HINT: 16772 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(g(f(x,z)))),f(u,g(f(g(g(f(g(v),z))),u))))=f(g(g(y)),g(g(v))). >> BACK DEMODULATING HINT 4809 WITH 13756. NEW HINT: 16773 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,u),g(v)),g(g(f(v,w))))))=f(u,w). >> BACK DEMODULATING HINT 4808 WITH 13756. NEW HINT: 16774 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(x,g(g(u))),g(v)),g(g(f(v,w))))))=f(u,w). >> BACK DEMODULATING HINT 4807 WITH 13756. NEW HINT: 16775 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(f(g(g(x)),g(g(u))),g(v)),g(g(f(v,w))))))=f(u,w). >> BACK DEMODULATING HINT 4806 WITH 13756. NEW HINT: 16776 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(f(g(f(g(u),g(x))),g(v)),g(g(f(v,w))))))=f(u,w). >> BACK DEMODULATING HINT 4805 WITH 13756. NEW HINT: 16777 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(g(f(u,f(g(v),g(x)))),g(g(f(u,w))))))=f(v,w). >> BACK DEMODULATING HINT 4804 WITH 13756. NEW HINT: 16778 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(x,z),y),f(g(f(u,g(f(x,v)))),g(g(f(u,w))))))=f(v,w). >> BACK DEMODULATING HINT 4803 WITH 13756. NEW HINT: 16779 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(u,y)),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4802 WITH 13756. NEW HINT: 16780 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,y),u),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4801 WITH 13756. NEW HINT: 16781 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,y),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4800 WITH 13756. NEW HINT: 16782 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(u,g(g(y))),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4799 WITH 13756. NEW HINT: 16783 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(f(g(g(u)),g(g(y))),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4798 WITH 13756. NEW HINT: 16784 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(g(f(g(y),g(u))),g(g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4797 WITH 13756. NEW HINT: 16785 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(g(f(g(u),f(g(y),g(u)))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4796 WITH 13756. NEW HINT: 16786 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4795 WITH 13756. NEW HINT: 16787 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,g(g(z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4794 WITH 13756. NEW HINT: 16788 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(g(g(x)),g(g(z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4793 WITH 13756. NEW HINT: 16789 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(g(f(g(z),g(x))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4792 WITH 13756. NEW HINT: 16790 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(g(g(f(x,z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4791 WITH 13756. NEW HINT: 16791 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),g(f(x,z))),f(f(f(g(g(f(x,z))),g(u)),f(g(f(f(g(u),g(y)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4790 WITH 13756. NEW HINT: 16792 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(g(x),f(g(y),g(z)))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(y,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4789 WITH 13756. NEW HINT: 16793 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(y,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4713 WITH 13756. NEW HINT: 16794 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(x),y))=f(g(g(f(y,z))),g(z)). >> BACK DEMODULATING HINT 4712 WITH 13756. NEW HINT: 16795 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(x),g(g(y))))=f(g(g(f(y,z))),g(z)). >> BACK DEMODULATING HINT 4711 WITH 13756. NEW HINT: 16796 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(g(y),x)))=f(g(g(f(y,z))),g(z)). >> BACK DEMODULATING HINT 4710 WITH 13756. NEW HINT: 16797 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(y,f(f(g(y),g(z)),x))))=f(g(g(f(z,u))),g(u)). >> BACK DEMODULATING HINT 4584 WITH 13756. NEW HINT: 16798 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(y)),g(g(f(y,z))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). >> BACK DEMODULATING HINT 4583 WITH 13756. NEW HINT: 16799 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(g(x)),g(y)),g(g(f(y,z))))=g(f(u,f(f(g(f(v,f(g(f(x,v)),u))),f(g(f(u,g(f(v,f(g(f(x,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(x,v)),u)))))))). >> BACK DEMODULATING HINT 4582 WITH 13756. NEW HINT: 16800 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,z))))=g(f(u,f(f(g(f(v,f(g(f(y,v)),u))),f(g(f(u,g(f(v,f(g(f(y,v)),u))))),g(z))),g(f(u,g(f(v,f(g(f(y,v)),u)))))))). >> BACK DEMODULATING HINT 4581 WITH 13756. NEW HINT: 16801 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(y,f(f(g(y),g(z)),u)),g(u)))),g(g(f(x,v))))=g(f(u,f(f(g(f(w,f(g(f(z,w)),u))),f(g(f(u,g(f(w,f(g(f(z,w)),u))))),g(v))),g(f(u,g(f(w,f(g(f(z,w)),u)))))))). >> BACK DEMODULATING HINT 4580 WITH 13756. NEW HINT: 16802 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(y,f(f(g(y),g(z)),g(g(u)))),g(u)))),g(g(f(x,v))))=g(f(u,f(f(g(f(w,f(g(f(z,w)),u))),f(g(f(u,g(f(w,f(g(f(z,w)),u))))),g(v))),g(f(u,g(f(w,f(g(f(z,w)),u)))))))). >> BACK DEMODULATING HINT 4579 WITH 13756. NEW HINT: 16803 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(y,f(g(f(z,y)),g(g(u)))),g(u)))),g(g(f(x,v))))=g(f(u,f(f(g(f(w,f(g(f(z,w)),u))),f(g(f(u,g(f(w,f(g(f(z,w)),u))))),g(v))),g(f(u,g(f(w,f(g(f(z,w)),u)))))))). >> BACK DEMODULATING HINT 4578 WITH 13756. NEW HINT: 16804 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(y,g(f(g(z),f(u,y)))),g(z)))),g(g(f(x,v))))=g(f(z,f(f(g(f(w,f(g(f(u,w)),z))),f(g(f(z,g(f(w,f(g(f(u,w)),z))))),g(v))),g(f(z,g(f(w,f(g(f(u,w)),z)))))))). >> BACK DEMODULATING HINT 4577 WITH 13756. NEW HINT: 16805 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(g(g(y)),g(f(g(z),f(u,y)))),g(z)))),g(g(f(x,v))))=g(f(z,f(f(g(f(w,f(g(f(u,w)),z))),f(g(f(z,g(f(w,f(g(f(u,w)),z))))),g(v))),g(f(z,g(f(w,f(g(f(u,w)),z)))))))). >> BACK DEMODULATING HINT 4576 WITH 13756. NEW HINT: 16806 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(g(f(f(g(y),f(z,u)),g(u))),g(y)))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). >> BACK DEMODULATING HINT 4575 WITH 13756. NEW HINT: 16807 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(f(g(y),f(z,u)),g(u)))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). >> BACK DEMODULATING HINT 4574 WITH 13756. NEW HINT: 16808 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(f(g(y),f(z,g(g(u)))),g(u)))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). >> BACK DEMODULATING HINT 4573 WITH 13756. NEW HINT: 16809 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(f(g(y),f(g(g(z)),g(g(u)))),g(u)))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(z,w)),y))),f(g(f(y,g(f(w,f(g(f(z,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(z,w)),y)))))))). >> BACK DEMODULATING HINT 4572 WITH 13756. NEW HINT: 16810 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(f(g(y),g(f(g(z),g(u)))),g(z)))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). >> BACK DEMODULATING HINT 4571 WITH 13756. NEW HINT: 16811 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(g(f(f(g(z),g(u)),y)),g(z)))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). >> BACK DEMODULATING HINT 4570 WITH 13756. NEW HINT: 16812 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,g(f(z,f(f(g(z),g(u)),y))))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). >> BACK DEMODULATING HINT 4285 WITH 13756. NEW HINT: 16813 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(f(f(z,y),f(x,g(f(x,x)))))),g(f(y,f(g(f(z,y)),f(g(g(f(z,x))),f(g(f(x,g(y))),g(g(f(x,g(f(z,y)))))))))))=g(x). >> BACK DEMODULATING HINT 4267 WITH 13756. NEW HINT: 16814 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,f(g(f(y,x)),x)),f(f(f(g(f(z,x)),g(g(f(z,y)))),u),f(g(f(f(u,v),u)),u))))=v. >> BACK DEMODULATING HINT 4266 WITH 13756. NEW HINT: 16815 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,f(g(f(y,x)),x)),f(f(f(g(f(z,x)),g(g(f(z,y)))),u),f(g(f(v,u)),u))))=g(f(u,f(g(f(v,u)),u))). >> BACK DEMODULATING HINT 4265 WITH 13756. NEW HINT: 16816 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,f(f(g(x),y),f(g(f(z,y)),y))),f(f(f(g(f(u,y)),g(g(f(u,z)))),v),f(g(f(w,v)),v))))=g(f(v,f(g(f(w,v)),v))). >> BACK DEMODULATING HINT 4232 WITH 13756. NEW HINT: 16817 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(x),g(y)))=f(f(g(f(z,g(y))),g(g(f(z,u)))),f(v,g(f(g(g(f(g(x),u))),v)))). >> BACK DEMODULATING HINT 4230 WITH 13756. NEW HINT: 16818 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(g(f(x,z)))),f(u,g(f(g(g(f(g(v),z))),u))))=g(f(g(v),g(y))). >> BACK DEMODULATING HINT 4215 WITH 13756. NEW HINT: 16819 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(g(x),y),f(g(f(z,y)),y))))=g(f(f(u,f(f(g(u),v),f(g(f(w,v)),v))),f(f(f(g(f(v6,v)),g(g(f(v6,w)))),y),f(g(f(z,y)),y)))). >> BACK DEMODULATING HINT 4214 WITH 13756. NEW HINT: 16820 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,f(f(g(x),y),f(g(f(z,y)),y))),f(f(f(g(f(u,y)),g(g(f(u,z)))),v),f(g(f(w,v)),v))))=g(f(v6,f(f(g(v6),v),f(g(f(w,v)),v)))). >> BACK DEMODULATING HINT 4211 WITH 13756. NEW HINT: 16821 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,f(f(g(x),y),f(g(f(z,y)),y))),f(f(f(g(f(u,y)),g(g(f(u,z)))),v),f(g(f(f(v,w),v)),v))))=w. >> BACK DEMODULATING HINT 4166 WITH 13756. NEW HINT: 16822 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),x)),g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),g(f(g(g(f(y,f(z,u)))),u))))))=g(f(y,z)). >> BACK DEMODULATING HINT 4165 WITH 13756. NEW HINT: 16823 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(g(f(y,f(f(z,f(g(f(y,z)),g(u))),g(f(y,z))))),x)),g(f(g(g(f(y,f(z,u)))),g(f(g(g(f(y,f(z,u)))),u))))))=g(f(y,z)). >> BACK DEMODULATING HINT 4164 WITH 13756. NEW HINT: 16824 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,g(f(z,f(g(f(u,z)),y))))))),g(g(f(x,v))))=g(f(y,f(f(g(f(w,f(g(f(u,w)),y))),f(g(f(y,g(f(w,f(g(f(u,w)),y))))),g(v))),g(f(y,g(f(w,f(g(f(u,w)),y)))))))). >> BACK DEMODULATING HINT 4140 WITH 13756. NEW HINT: 16825 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))),f(g(g(f(x,f(y,f(f(v,g(f(w,f(f(g(w),v),f(u,v))))),v))))),g(v6))),g(f(x,y))))=f(x,f(f(y,f(g(f(x,y)),g(v6))),g(f(x,y)))). >> BACK DEMODULATING HINT 4138 WITH 13756. NEW HINT: 16826 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(g(f(y,x)),g(z))),g(f(y,x))),f(f(f(g(g(f(y,x))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(y,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4131 WITH 13756. NEW HINT: 16827 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(y,f(g(f(z,y)),x))))=f(g(g(f(z,u))),g(u)). >> BACK DEMODULATING HINT 4128 WITH 13756. NEW HINT: 16828 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,y))),g(y))=f(z,g(f(u,f(g(f(x,u)),z)))). >> BACK DEMODULATING HINT 4127 WITH 13756. NEW HINT: 16829 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(g(f(x,g(f(z,y)))))),g(f(y,f(g(f(z,y)),f(g(g(f(z,x))),f(g(f(x,g(y))),g(g(f(x,g(f(z,y)))))))))))=g(x). >> BACK DEMODULATING HINT 4126 WITH 13756. NEW HINT: 16830 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,g(y))),g(g(f(x,g(f(z,y)))))),g(f(u,f(f(g(u),f(g(f(x,g(y))),g(g(f(x,g(f(z,y))))))),f(g(g(f(z,x))),f(g(f(x,g(y))),g(g(f(x,g(f(z,y)))))))))))=g(x). >> BACK DEMODULATING HINT 4125 WITH 13756. NEW HINT: 16831 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(g(f(y,x)),g(f(y,g(z))))),y),g(f(u,z)))=f(v,f(g(f(y,v)),f(g(f(z,g(w))),g(g(f(z,g(f(u,w)))))))). >> BACK DEMODULATING HINT 4124 WITH 13756. NEW HINT: 16832 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,y))=f(g(y),f(g(f(z,g(u))),g(g(f(z,g(f(x,u))))))). >> BACK DEMODULATING HINT 4123 WITH 13756. >> BACK DEMODULATING HINT 4121 WITH 13756. >> BACK DEMODULATING HINT 4120 WITH 13756. NEW HINT: 16833 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(g(f(x,g(y))),g(g(f(x,g(f(z,y)))))))=g(f(z,x)). >> BACK DEMODULATING HINT 4113 WITH 13756. NEW HINT: 16834 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(y,z),x))),f(f(f(g(g(f(x,y))),g(u)),f(g(f(f(g(u),g(z)),g(u))),g(u))),f(g(f(v,g(f(x,w)))),g(g(f(v,v6))))))=f(w,v6). >> BACK DEMODULATING HINT 4112 WITH 13756. NEW HINT: 16835 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(f(y,z),x))),f(g(f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y)))))),f(g(v),g(z))),g(f(x,y))))),f(g(f(w,g(f(x,v6)))),g(g(f(w,v7))))))=f(v6,v7). >> BACK DEMODULATING HINT 4109 WITH 13756. NEW HINT: 16836 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(f(f(u,f(g(f(g(f(x,y)),u)),v)),g(f(x,y))),f(g(g(f(x,f(y,f(f(w,g(f(v6,f(f(g(v6),w),f(v,w))))),w))))),g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 4108 WITH 13756. NEW HINT: 16837 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))),f(g(g(f(x,f(y,f(f(v,g(f(w,f(f(g(w),v),f(u,v))))),v))))),g(v6))),g(f(x,y))))=g(f(x,f(y,v6))). >> BACK DEMODULATING HINT 4104 WITH 13756. NEW HINT: 16838 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(y,g(f(x,f(f(z,u),f(v,y))))),y))=f(g(f(g(x),y)),g(g(f(z,f(u,v))))). >> BACK DEMODULATING HINT 4102 WITH 13756. >> BACK DEMODULATING HINT 4101 WITH 13756. NEW HINT: 16839 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(g(f(f(g(f(y,z)),f(f(f(f(u,f(g(f(g(f(y,z)),u)),g(v))),g(f(y,z))),f(g(g(f(y,f(z,v)))),g(w))),g(f(y,z)))),y)),y)))=f(y,f(f(z,w),y)). >> BACK DEMODULATING HINT 4100 WITH 13756. NEW HINT: 16840 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(g(f(f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(g(f(x,f(y,u)))),g(v))),g(f(x,y)))),x)),x))=f(f(y,v),x). >> BACK DEMODULATING HINT 4099 WITH 13756. NEW HINT: 16841 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(g(f(x,f(y,u)))),g(v))),g(f(x,y))))=f(w,f(f(g(w),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y))))). >> BACK DEMODULATING HINT 4098 WITH 13756. NEW HINT: 16842 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=f(g(f(y,z)),f(f(f(f(v,f(g(f(g(f(y,z)),v)),g(w))),g(f(y,z))),f(g(g(f(y,f(z,w)))),g(u))),g(f(y,z)))). >> BACK DEMODULATING HINT 4091 WITH 13756. >> BACK DEMODULATING HINT 4088 WITH 13756. >> BACK DEMODULATING HINT 4056 WITH 13756. NEW HINT: 16843 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(g(f(y,f(z,u))))),v))=f(f(y,z),f(u,v)). >> BACK DEMODULATING HINT 4055 WITH 13756. NEW HINT: 16844 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(f(y,g(z))),g(g(f(y,u))))),v))=f(z,f(u,v)). >> BACK DEMODULATING HINT 4050 WITH 13756. NEW HINT: 16845 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(u,f(g(f(z,u)),v)))=f(w,f(g(f(z,w)),f(f(g(f(v6,g(f(z,x)))),g(g(f(v6,y)))),v))). >> BACK DEMODULATING HINT 4049 WITH 13756. NEW HINT: 16846 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(g(f(z,v)))),g(g(f(y,w))))))=f(f(f(u,v),y),w). >> BACK DEMODULATING HINT 4048 WITH 13756. NEW HINT: 16847 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),f(f(g(f(z,g(f(y,u)))),g(g(f(z,v)))),w)))=f(f(f(u,v),y),f(v6,f(g(f(y,v6)),w))). >> BACK DEMODULATING HINT 4021 WITH 13756. >> BACK DEMODULATING HINT 4020 WITH 13756. >> BACK DEMODULATING HINT 4019 WITH 13756. >> BACK DEMODULATING HINT 4016 WITH 13756. NEW HINT: 16848 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,g(f(z,f(g(f(u,z)),y))))))),g(g(f(x,v))))=g(g(f(y,f(g(f(w,f(g(f(u,w)),y))),v)))). >> BACK DEMODULATING HINT 4013 WITH 13756. NEW HINT: 16849 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,g(f(y,x)))))=g(f(x,g(f(z,f(g(f(y,z)),x))))). >> BACK DEMODULATING HINT 4009 WITH 13756. >> BACK DEMODULATING HINT 4004 WITH 13756. >> BACK DEMODULATING HINT 4003 WITH 13756. >> BACK DEMODULATING HINT 3999 WITH 13756. >> BACK DEMODULATING HINT 3998 WITH 13756. >> BACK DEMODULATING HINT 3994 WITH 13756. >> BACK DEMODULATING HINT 3993 WITH 13756. >> BACK DEMODULATING HINT 3992 WITH 13756. >> BACK DEMODULATING HINT 3989 WITH 13756. NEW HINT: 16850 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(f(x,f(f(y,f(g(f(x,y)),v)),x))),f(v,g(w)))))=w. >> BACK DEMODULATING HINT 3988 WITH 13756. >> BACK DEMODULATING HINT 3987 WITH 13756. NEW HINT: 16851 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),g(y))),g(g(f(g(x),z))))=f(g(f(u,g(y))),g(g(f(u,z)))). >> BACK DEMODULATING HINT 3986 WITH 13756. NEW HINT: 16852 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,z))))=f(g(f(g(u),g(y))),g(g(f(g(u),z)))). >> BACK DEMODULATING HINT 3985 WITH 13756. >> BACK DEMODULATING HINT 3984 WITH 13756. >> BACK DEMODULATING HINT 3983 WITH 13756. >> BACK DEMODULATING HINT 3982 WITH 13756. >> BACK DEMODULATING HINT 3981 WITH 13756. >> BACK DEMODULATING HINT 3980 WITH 13756. >> BACK DEMODULATING HINT 3979 WITH 13756. NEW HINT: 16853 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(g(x),y),f(g(f(z,y)),y))))=f(g(f(u,y)),g(g(f(u,z)))). >> BACK DEMODULATING HINT 3978 WITH 13756. NEW HINT: 16854 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(y,z))))=f(g(f(u,g(f(x,y)))),g(g(f(u,z)))). >> BACK DEMODULATING HINT 3977 WITH 13756. NEW HINT: 16855 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,z))))=g(f(y,f(f(u,f(g(f(y,u)),g(z))),y))). >> BACK DEMODULATING HINT 3976 WITH 13756. NEW HINT: 16856 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,z))))=g(f(u,f(f(g(u),y),f(g(f(z,y)),y)))). >> BACK DEMODULATING HINT 3975 WITH 13756. NEW HINT: 16857 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,z)))),g(g(f(x,u))))=g(g(f(y,f(z,u)))). >> BACK DEMODULATING HINT 3974 WITH 13756. >> BACK DEMODULATING HINT 3972 WITH 13756. NEW HINT: 16858 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(f(f(u,f(g(f(g(f(x,y)),u)),g(v))),g(f(x,y))),f(g(g(f(x,f(y,v)))),g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 3969 WITH 13756. NEW HINT: 16859 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))),f(g(g(f(x,f(y,u)))),g(v))),g(f(x,y))))=g(f(x,f(y,v))). >> BACK DEMODULATING HINT 3950 WITH 13756. NEW HINT: 16860 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(x,g(g(f(y,z)))). >> BACK DEMODULATING HINT 3949 WITH 13756. NEW HINT: 16861 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(g(g(x)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3948 WITH 13756. NEW HINT: 16862 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(g(f(f(g(x),g(u)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3947 WITH 13756. NEW HINT: 16863 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3946 WITH 13756. NEW HINT: 16864 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(g(z),z))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3945 WITH 13756. >> BACK DEMODULATING HINT 3944 WITH 13756. NEW HINT: 16865 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),g(f(g(z),z)))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3943 WITH 13756. NEW HINT: 16866 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),g(f(f(f(g(z),g(z)),z),z)))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3942 WITH 13756. NEW HINT: 16867 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3941 WITH 13756. NEW HINT: 16868 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3940 WITH 13756. NEW HINT: 16869 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(g(y))),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3939 WITH 13756. NEW HINT: 16870 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(g(x)),g(g(y))),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,x)),u)),g(g(f(y,z)))). >> BACK DEMODULATING HINT 3938 WITH 13756. NEW HINT: 16871 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(g(x),g(y))),g(g(z))),g(f(f(g(f(z,z)),z),z)))=f(g(f(g(f(u,y)),u)),g(g(f(x,z)))). >> BACK DEMODULATING HINT 3937 WITH 13756. NEW HINT: 16872 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(y),g(z)))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(g(f(y,x)))). >> BACK DEMODULATING HINT 3936 WITH 13756. >> BACK DEMODULATING HINT 3935 WITH 13756. NEW HINT: 16873 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),f(g(g(z)),g(z))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(g(f(y,x)))). >> BACK DEMODULATING HINT 3934 WITH 13756. NEW HINT: 16874 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,g(z)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(g(f(y,x)))). >> BACK DEMODULATING HINT 3933 WITH 13756. NEW HINT: 16875 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,f(f(g(z),g(u)),u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(g(f(y,x)))). >> BACK DEMODULATING HINT 3932 WITH 13756. NEW HINT: 16876 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,f(g(f(u,z)),u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,z)),u)),g(g(f(y,x)))). >> BACK DEMODULATING HINT 3931 WITH 13756. NEW HINT: 16877 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(y,z)),g(f(y,f(g(f(u,y)),u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(u,y)),u)),g(g(f(z,x)))). >> BACK DEMODULATING HINT 3930 WITH 13756. NEW HINT: 16878 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(f(f(y,g(y)),z),u)),g(f(z,f(g(f(v,z)),v)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(v,z)),v)),g(g(f(u,x)))). >> BACK DEMODULATING HINT 3929 WITH 13756. NEW HINT: 16879 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(f(f(g(g(y)),g(y)),z),u)),g(f(z,f(g(f(v,z)),v)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(v,z)),v)),g(g(f(u,x)))). >> BACK DEMODULATING HINT 3928 WITH 13756. NEW HINT: 16880 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(f(g(f(y,g(y))),z),u)),g(f(z,f(g(f(v,z)),v)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(v,z)),v)),g(g(f(u,x)))). >> BACK DEMODULATING HINT 3927 WITH 13756. NEW HINT: 16881 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(f(g(f(y,f(f(g(y),g(z)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(g(f(v,x)))). >> BACK DEMODULATING HINT 3926 WITH 13756. NEW HINT: 16882 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(g(f(v,x)))). >> BACK DEMODULATING HINT 3925 WITH 13756. NEW HINT: 16883 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(f(g(x),g(x)),x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(g(f(v,x)))). >> BACK DEMODULATING HINT 3706 WITH 13756. >> BACK DEMODULATING HINT 3700 WITH 13756. NEW HINT: 16884 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(x)),f(g(y),g(g(f(f(g(f(z,g(y))),z),u)))))=u. >> BACK DEMODULATING HINT 3699 WITH 13756. >> BACK DEMODULATING HINT 3698 WITH 13756. NEW HINT: 16885 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,g(y)),g(g(f(x,z)))))=z. >> BACK DEMODULATING HINT 3697 WITH 13756. NEW HINT: 16886 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(g(f(z,y)),z)),g(g(f(x,u)))))=u. >> BACK DEMODULATING HINT 3687 WITH 13756. NEW HINT: 16887 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(u,f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(g(f(v,x)))). >> BACK DEMODULATING HINT 3685 WITH 13756. >> BACK DEMODULATING HINT 3684 WITH 13756. NEW HINT: 16888 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,y)),x),f(f(z,f(g(f(u,z)),u)),g(g(f(y,v)))))=v. >> BACK DEMODULATING HINT 3683 WITH 13756. NEW HINT: 16889 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(f(y,x)),y)),f(g(z),g(g(f(f(g(f(u,g(z))),u),v)))))=v. >> BACK DEMODULATING HINT 3682 WITH 13756. >> BACK DEMODULATING HINT 3681 WITH 13756. NEW HINT: 16890 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(g(f(x,y)),g(z)))))=z. >> BACK DEMODULATING HINT 3669 WITH 13756. NEW HINT: 16891 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,f(g(f(z,y)),z))),u),v)),g(f(f(g(f(f(g(f(w,u)),w),f(g(f(w,u)),w))),f(g(f(w,u)),w)),f(g(f(w,u)),w)))))),g(f(f(g(f(x,x)),x),x)))=f(g(f(g(f(w,u)),w)),g(g(f(v,x)))). >> BACK DEMODULATING HINT 3656 WITH 13756. NEW HINT: 16892 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,z)),y),u)),g(f(f(g(f(z,z)),z),z))))),g(f(f(g(f(x,x)),x),x)))=f(g(z),g(g(f(u,x)))). >> BACK DEMODULATING HINT 3613 WITH 13756. >> BACK DEMODULATING HINT 3599 WITH 13756. >> BACK DEMODULATING HINT 3594 WITH 13756. >> BACK DEMODULATING HINT 3591 WITH 13756. NEW HINT: 16893 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(g(f(x,x)),x),f(g(f(f(g(f(y,y)),y),z)),g(f(f(g(f(y,y)),y),y))))),g(f(f(g(f(x,x)),x),x)))=f(g(y),g(g(f(g(f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u)))),x)))). >> BACK DEMODULATING HINT 3588 WITH 13756. >> BACK DEMODULATING HINT 3587 WITH 13756. NEW HINT: 16894 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(g(f(x,x)),x),g(g(f(y,f(z,u)))))),g(f(f(g(f(x,x)),x),x)))=f(g(u),g(g(f(g(f(y,z)),x)))). >> BACK DEMODULATING HINT 3586 WITH 13756. NEW HINT: 16895 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(y,z))))=f(g(f(f(g(f(z,z)),z),g(f(x,y)))),g(f(f(g(f(z,z)),z),z))). >> BACK DEMODULATING HINT 3585 WITH 13756. >> BACK DEMODULATING HINT 3584 WITH 13756. >> BACK DEMODULATING HINT 3582 WITH 13756. >> BACK DEMODULATING HINT 3581 WITH 13756. >> BACK DEMODULATING HINT 3580 WITH 13756. NEW HINT: 16896 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(g(f(f(g(f(y,x)),z),f(f(y,f(g(f(z,y)),y)),u)))))=u. >> BACK DEMODULATING HINT 3579 WITH 13756. >> BACK DEMODULATING HINT 3432 WITH 13756. NEW HINT: 16897 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),g(g(g(f(g(x),x)))))=f(g(g(x)),f(f(f(g(x),g(x)),x),g(y))). >> BACK DEMODULATING HINT 3387 WITH 13756. NEW HINT: 16898 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(g(f(g(y),y)),x)),g(z)))=f(g(z),g(g(g(f(g(y),y))))). >> BACK DEMODULATING HINT 3383 WITH 13756. NEW HINT: 16899 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),g(g(g(f(g(x),x)))))=f(z,f(g(f(g(f(g(x),x)),z)),g(y))). >> BACK DEMODULATING HINT 3354 WITH 13756. NEW HINT: 16900 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,f(g(f(g(z),z)),f(g(u),u))))))=y. >> BACK DEMODULATING HINT 3345 WITH 13756. NEW HINT: 16901 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(y,f(g(z),z)))))=f(x,y). >> BACK DEMODULATING HINT 3333 WITH 13756. >> BACK DEMODULATING HINT 3310 WITH 13756. >> BACK DEMODULATING HINT 3305 WITH 13756. >> BACK DEMODULATING HINT 3300 WITH 13756. >> BACK DEMODULATING HINT 3299 WITH 13756. >> BACK DEMODULATING HINT 3292 WITH 13756. >> BACK DEMODULATING HINT 3290 WITH 13756. >> BACK DEMODULATING HINT 3289 WITH 13756. NEW HINT: 16902 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(z,f(g(f(u,z)),v))))))=f(g(f(u,y)),v). >> BACK DEMODULATING HINT 3285 WITH 13756. >> BACK DEMODULATING HINT 3281 WITH 13756. >> BACK DEMODULATING HINT 3280 WITH 13756. >> BACK DEMODULATING HINT 3279 WITH 13756. >> BACK DEMODULATING HINT 3278 WITH 13756. >> BACK DEMODULATING HINT 3277 WITH 13756. >> BACK DEMODULATING HINT 3275 WITH 13756. >> BACK DEMODULATING HINT 3274 WITH 13756. >> BACK DEMODULATING HINT 3273 WITH 13756. NEW HINT: 16903 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(f(x,x),y),f(f(g(f(x,y)),g(f(g(z),x))),f(g(z),u)))))=u. >> BACK DEMODULATING HINT 3272 WITH 13756. >> BACK DEMODULATING HINT 3271 WITH 13756. >> BACK DEMODULATING HINT 3270 WITH 13756. >> BACK DEMODULATING HINT 3269 WITH 13756. >> BACK DEMODULATING HINT 3268 WITH 13756. >> BACK DEMODULATING HINT 3145 WITH 13756. NEW HINT: 16904 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(g(f(y,z))))=f(f(g(y),f(f(f(y,y),f(f(u,f(g(f(y,u)),x)),y)),g(f(g(f(y,f(f(u,f(g(f(y,u)),x)),y))),g(z))))),g(f(y,f(f(u,f(g(f(y,u)),x)),y)))) # label(bd). >> BACK DEMODULATING HINT 2931 WITH 13756. NEW HINT: 16905 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(y),y)))),g(g(f(x,z))))=f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(f(g(f(g(f(g(u),u)),f(g(v),v))),g(z))))),g(f(g(f(g(u),u)),f(g(v),v)))) # label(bd). >> BACK DEMODULATING HINT 2930 WITH 13756. NEW HINT: 16906 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(y),y)))),g(g(f(x,z))))=z # label(bd). >> BACK DEMODULATING HINT 2929 WITH 13756. >> BACK DEMODULATING HINT 2928 WITH 13756. NEW HINT: 16907 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(y,g(f(g(f(g(z),z)),f(g(u),u))))),g(g(f(y,x))))=x # label(bd). >> BACK DEMODULATING HINT 2927 WITH 13756. NEW HINT: 16908 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(x)),g(f(g(y),y)))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(g(f(z,x)))) # label(bd). >> BACK DEMODULATING HINT 2887 WITH 13756. NEW HINT: 16909 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,x),f(f(y,f(g(f(x,y)),z)),x)),g(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),g(u))))),g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(g(f(x,u)))) # label(bd). >> BACK DEMODULATING HINT 2886 WITH 13756. >> BACK DEMODULATING HINT 2885 WITH 13756. NEW HINT: 16910 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(f(g(x),f(f(f(x,x),f(f(y,f(g(f(x,y)),z)),x)),g(u))),g(f(x,f(f(y,f(g(f(x,y)),z)),x))))))=f(z,g(g(f(x,u)))) # label(bd). >> BACK DEMODULATING HINT 2884 WITH 13756. >> BACK DEMODULATING HINT 2880 WITH 13756. >> BACK DEMODULATING HINT 2875 WITH 13756. NEW HINT: 16911 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(x),f(x,f(g(f(g(f(g(y),y)),f(g(z),z))),u)))))=u # label(bd). >> BACK DEMODULATING HINT 2874 WITH 13756. >> BACK DEMODULATING HINT 2873 WITH 13756. >> BACK DEMODULATING HINT 2872 WITH 13756. NEW HINT: 16912 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(f(g(f(g(x),x)),g(y))))),g(f(g(x),x)))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(g(f(z,y)))) # label(bd). >> BACK DEMODULATING HINT 2871 WITH 13756. NEW HINT: 16913 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(g(x),x)),f(f(g(g(x)),f(f(f(g(x),g(x)),x),g(y))),g(f(g(x),x)))))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(g(f(z,y)))) # label(bd). >> BACK DEMODULATING HINT 2870 WITH 13756. NEW HINT: 16914 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(x),f(x,y))))=f(g(f(z,g(f(g(f(g(u),u)),f(g(v),v))))),g(g(f(z,y)))) # label(bd). >> BACK DEMODULATING HINT 2869 WITH 13756. >> BACK DEMODULATING HINT 2868 WITH 13756. >> BACK DEMODULATING HINT 2867 WITH 13756. NEW HINT: 16915 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(y),y)))),g(g(f(x,z))))=g(f(g(f(g(f(g(u),u)),f(g(v),v))),f(f(g(g(f(g(u),u))),f(f(f(g(f(g(u),u)),g(f(g(u),u))),f(g(v),v)),g(z))),g(f(g(f(g(u),u)),f(g(v),v)))))) # label(bd). >> BACK DEMODULATING HINT 2866 WITH 13756. NEW HINT: 16916 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(y),y)))),g(g(f(x,z))))=g(g(f(g(f(g(u),u)),f(f(g(v),v),z)))) # label(bd). >> BACK DEMODULATING HINT 2862 WITH 13756. NEW HINT: 16917 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),x)),g(g(f(g(f(g(y),y)),f(f(g(z),z),u)))))=u # label(bd). >> BACK DEMODULATING HINT 2803 WITH 13756. >> BACK DEMODULATING HINT 2786 WITH 13756. NEW HINT: 16918 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(f(x,x),y),f(f(g(f(x,y)),g(f(z,x))),f(z,u)))))=u # label(bd). >> BACK DEMODULATING HINT 2771 WITH 13756. >> BACK DEMODULATING HINT 2768 WITH 13756. >> BACK DEMODULATING HINT 2767 WITH 13756. >> BACK DEMODULATING HINT 2766 WITH 13756. >> BACK DEMODULATING HINT 2763 WITH 13756. NEW HINT: 16919 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),g(g(f(g(f(f(f(z,z),g(f(z,f(f(u,f(g(f(z,u)),v)),z)))),f(v,g(f(y,z))))),w)))))=w # label(bd). >> BACK DEMODULATING HINT 2762 WITH 13756. >> BACK DEMODULATING HINT 2761 WITH 13756. >> BACK DEMODULATING HINT 2760 WITH 13756. >> BACK DEMODULATING HINT 2759 WITH 13756. >> BACK DEMODULATING HINT 2758 WITH 13756. >> BACK DEMODULATING HINT 2757 WITH 13756. >> BACK DEMODULATING HINT 2708 WITH 13756. NEW HINT: 16920 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),f(y,g(g(f(z,u))))))=f(g(z),f(f(f(z,z),g(f(v,w))),g(f(g(f(v,w)),f(f(g(v),f(f(f(v,v),w),g(u))),g(f(v,w))))))) # label(bd). >> BACK DEMODULATING HINT 2700 WITH 13756. NEW HINT: 16921 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,g(f(y,z)))),u)),g(f(g(f(y,z)),f(f(g(y),f(f(f(y,y),z),g(v))),g(f(y,z))))))=f(g(f(w,u)),f(w,g(g(f(x,v))))) # label(bd). >> BACK DEMODULATING HINT 2699 WITH 13756. NEW HINT: 16922 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),f(y,g(g(f(z,u))))))=f(v,f(g(f(g(f(z,g(f(w,v6)))),v)),g(f(g(f(w,v6)),f(f(g(w),f(f(f(w,w),v6),g(u))),g(f(w,v6))))))) # label(bd). >> BACK DEMODULATING HINT 2671 WITH 13756. >> BACK DEMODULATING HINT 2669 WITH 13756. >> BACK DEMODULATING HINT 2664 WITH 13756. NEW HINT: 16923 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(g(f(g(z),z)),f(g(f(g(u),u)),v))))))=f(g(f(g(g(f(g(w),w))),y)),v) # label(bd). >> BACK DEMODULATING HINT 2651 WITH 13756. NEW HINT: 16924 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(f(g(x),x)),f(y,f(g(f(g(f(g(z),z)),y)),u)))))=u # label(bd). >> BACK DEMODULATING HINT 2650 WITH 13756. NEW HINT: 16925 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(g(x),x)),y)),g(g(f(g(f(g(z),z)),f(y,u)))))=u # label(bd). >> BACK DEMODULATING HINT 2645 WITH 13756. NEW HINT: 16926 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(g(x),x)),g(f(y,z)))),g(f(g(f(g(u),u)),g(f(g(f(g(x),x)),f(v,g(f(g(x),x))))))))=g(g(f(y,f(z,v)))) # label(bd). >> BACK DEMODULATING HINT 2622 WITH 13756. NEW HINT: 16927 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(x),f(x,f(g(f(y,z)),f(y,u))))))=f(g(z),u) # label(bd). >> BACK DEMODULATING HINT 2608 WITH 13756. NEW HINT: 16928 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(g(f(y,z)),f(y,u)))))=f(x,g(f(g(u),z))) # label(bd). >> BACK DEMODULATING HINT 2607 WITH 13756. NEW HINT: 16929 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(g(f(y,z)),f(y,z)))))=f(x,g(f(g(u),u))) # label(bd). >> BACK DEMODULATING HINT 2606 WITH 13756. NEW HINT: 16930 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,f(g(f(z,u)),f(z,u))))))=y # label(bd). >> BACK DEMODULATING HINT 2604 WITH 13756. >> BACK DEMODULATING HINT 2597 WITH 13756. NEW HINT: 16931 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,x)),f(y,g(g(f(z,u))))))=f(v,f(g(f(g(f(z,g(f(w,v6)))),v)),g(g(f(w,f(v6,u)))))) # label(bd). >> BACK DEMODULATING HINT 2595 WITH 13756. NEW HINT: 16932 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(g(f(y,g(f(z,u)))),x)),g(g(f(z,f(u,v))))))=f(w,f(g(f(v6,w)),f(v6,g(g(f(y,v)))))) # label(bd). >> BACK DEMODULATING HINT 2588 WITH 13756. NEW HINT: 16933 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,g(f(y,z)))),u)),g(g(f(y,f(z,v)))))=f(g(f(w,u)),f(w,g(g(f(x,v))))) # label(bd). >> BACK DEMODULATING HINT 2566 WITH 13756. >> BACK DEMODULATING HINT 2557 WITH 13756. >> BACK DEMODULATING HINT 2554 WITH 13756. >> BACK DEMODULATING HINT 2553 WITH 13756. >> BACK DEMODULATING HINT 2552 WITH 13756. >> BACK DEMODULATING HINT 2551 WITH 13756. >> BACK DEMODULATING HINT 2550 WITH 13756. >> BACK DEMODULATING HINT 2549 WITH 13756. >> BACK DEMODULATING HINT 2443 WITH 13756. >> BACK DEMODULATING HINT 2432 WITH 13756. >> BACK DEMODULATING HINT 2420 WITH 13756. NEW HINT: 16934 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,y))))=g(f(g(y),g(y))). >> BACK DEMODULATING HINT 2419 WITH 13756. >> BACK DEMODULATING HINT 2413 WITH 13756. NEW HINT: 16935 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,x)),f(x,g(g(f(x,y)))))=y. >> BACK DEMODULATING HINT 2405 WITH 13756. >> BACK DEMODULATING HINT 2395 WITH 13756. >> BACK DEMODULATING HINT 2265 WITH 13756. NEW HINT: 16936 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(g(f(y,f(z,g(f(u,f(y,z))))))))=g(f(u,x)). >> BACK DEMODULATING HINT 2264 WITH 13756. >> BACK DEMODULATING HINT 2262 WITH 13756. >> BACK DEMODULATING HINT 2259 WITH 13756. >> BACK DEMODULATING HINT 2242 WITH 13756. >> BACK DEMODULATING HINT 2233 WITH 13756. >> BACK DEMODULATING HINT 2232 WITH 13756. >> BACK DEMODULATING HINT 2231 WITH 13756. >> BACK DEMODULATING HINT 2230 WITH 13756. >> BACK DEMODULATING HINT 2095 WITH 13756. >> BACK DEMODULATING HINT 2046 WITH 13756. >> BACK DEMODULATING HINT 2043 WITH 13756. >> BACK DEMODULATING HINT 2038 WITH 13756. >> BACK DEMODULATING HINT 2035 WITH 13756. >> BACK DEMODULATING HINT 2020 WITH 13756. >> BACK DEMODULATING HINT 2019 WITH 13756. >> BACK DEMODULATING HINT 2018 WITH 13756. >> BACK DEMODULATING HINT 2003 WITH 13756. >> BACK DEMODULATING HINT 2001 WITH 13756. >> BACK DEMODULATING HINT 1996 WITH 13756. >> BACK DEMODULATING HINT 1994 WITH 13756. >> BACK DEMODULATING HINT 1993 WITH 13756. >> BACK DEMODULATING HINT 1978 WITH 13756. >> BACK DEMODULATING HINT 1971 WITH 13756. >> BACK DEMODULATING HINT 1967 WITH 13756. >> BACK DEMODULATING HINT 1965 WITH 13756. >> BACK DEMODULATING HINT 1964 WITH 13756. >> BACK DEMODULATING HINT 1963 WITH 13756. >> BACK DEMODULATING HINT 1961 WITH 13756. >> BACK DEMODULATING HINT 1960 WITH 13756. >> BACK DEMODULATING HINT 1959 WITH 13756. >> BACK DEMODULATING HINT 1958 WITH 13756. >> BACK DEMODULATING HINT 1957 WITH 13756. >> BACK DEMODULATING HINT 1955 WITH 13756. >> BACK DEMODULATING HINT 1954 WITH 13756. >> BACK DEMODULATING HINT 1945 WITH 13756. NEW HINT: 16937 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,y),z)))=f(x,f(y,z)). >> BACK DEMODULATING HINT 1944 WITH 13756. NEW HINT: 16938 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,y),z)))=g(g(f(x,f(y,z)))). >> BACK DEMODULATING HINT 1942 WITH 13756. >> BACK DEMODULATING HINT 1941 WITH 13756. >> BACK DEMODULATING HINT 1940 WITH 13756. NEW HINT: 16939 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,y))),g(y))=x. >> BACK DEMODULATING HINT 1936 WITH 13756. NEW HINT: 16940 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,y),z)))=g(f(f(g(f(x,f(y,z))),f(x,y)),g(f(x,y)))). >> BACK DEMODULATING HINT 1935 WITH 13756. NEW HINT: 16941 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(x,f(y,z))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y))))=g(g(f(f(x,y),z))). >> BACK DEMODULATING HINT 1934 WITH 13756. NEW HINT: 16942 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(g(z),g(g(g(f(x,y))))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y))))=g(g(f(f(x,y),z))). >> BACK DEMODULATING HINT 1933 WITH 13756. NEW HINT: 16943 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,y),g(f(f(x,y),f(z,f(g(f(u,g(f(x,y)))),u))))))=g(f(f(f(g(z),g(g(g(f(x,y))))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y)))). >> BACK DEMODULATING HINT 1932 WITH 13756. NEW HINT: 16944 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(x,y),g(f(f(g(f(u,g(f(x,y)))),u),f(z,f(g(f(u,g(f(x,y)))),u))))))=g(f(f(f(g(z),g(g(g(f(x,y))))),f(g(f(u,g(f(x,y)))),u)),g(f(x,y)))). >> BACK DEMODULATING HINT 1913 WITH 13756. NEW HINT: 16945 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(f(g(f(x,g(y))),x),f(z,g(f(f(g(f(x,z)),x),z)))))),g(z))=y. >> BACK DEMODULATING HINT 1912 WITH 13756. NEW HINT: 16946 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(g(f(x,g(z))),x))))),x)=g(g(f(y,z))). >> BACK DEMODULATING HINT 1905 WITH 13756. >> BACK DEMODULATING HINT 1897 WITH 13756. NEW HINT: 16947 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(g(f(x,g(f(y,z)))),x),u)))=g(f(f(f(g(u),g(g(g(f(y,z))))),f(g(f(x,g(f(y,z)))),x)),g(f(y,z)))). >> BACK DEMODULATING HINT 1892 WITH 13756. NEW HINT: 16948 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,y))),g(f(f(g(z),x),y)))=z. >> BACK DEMODULATING HINT 1890 WITH 13756. NEW HINT: 16949 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(g(f(g(g(f(z,f(u,x)))),y)),z))))=u. >> BACK DEMODULATING HINT 1889 WITH 13756. NEW HINT: 16950 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(g(f(x,f(y,x))),z))))=g(f(f(g(z),x),y)). >> BACK DEMODULATING HINT 1887 WITH 13756. NEW HINT: 16951 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(g(g(f(x,y))),z)),x),y))=z. >> BACK DEMODULATING HINT 1886 WITH 13756. NEW HINT: 16952 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(g(g(f(x,y))),z)),x),f(g(g(f(x,y))),g(g(f(x,f(g(f(x,f(y,x))),y)))))))=z. >> BACK DEMODULATING HINT 1885 WITH 13756. >> BACK DEMODULATING HINT 1884 WITH 13756. >> BACK DEMODULATING HINT 1883 WITH 13756. >> BACK DEMODULATING HINT 1881 WITH 13756. >> BACK DEMODULATING HINT 1875 WITH 13756. >> BACK DEMODULATING HINT 1874 WITH 13756. NEW HINT: 16953 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(y,z))))=f(g(f(u,g(f(x,y)))),f(u,z)). >> BACK DEMODULATING HINT 1872 WITH 13756. NEW HINT: 16954 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,y)))=f(g(f(z,g(x))),f(z,y)). >> BACK DEMODULATING HINT 1871 WITH 13756. NEW HINT: 16955 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,z))))=g(g(f(y,z))). >> BACK DEMODULATING HINT 1870 WITH 13756. NEW HINT: 16956 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,g(g(z))))))=g(g(f(y,z))). >> BACK DEMODULATING HINT 1869 WITH 13756. NEW HINT: 16957 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,f(z,g(f(g(z),z)))))))=g(g(f(y,z))). >> BACK DEMODULATING HINT 1868 WITH 13756. NEW HINT: 16958 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(g(f(x,f(z,g(f(f(g(f(u,z)),u),z)))))))=g(g(f(y,z))). >> BACK DEMODULATING HINT 1867 WITH 13756. >> BACK DEMODULATING HINT 1863 WITH 13756. >> BACK DEMODULATING HINT 1862 WITH 13756. >> BACK DEMODULATING HINT 1843 WITH 13756. NEW HINT: 16959 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,f(g(f(y,x)),y)),z)))=z. >> BACK DEMODULATING HINT 1818 WITH 13756. >> BACK DEMODULATING HINT 1815 WITH 13756. >> BACK DEMODULATING HINT 1814 WITH 13756. >> BACK DEMODULATING HINT 1812 WITH 13756. >> BACK DEMODULATING HINT 1811 WITH 13756. >> BACK DEMODULATING HINT 1810 WITH 13756. NEW HINT: 16960 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(g(f(x,y))),g(g(f(x,f(g(f(x,f(y,x))),y))))))=g(y). >> BACK DEMODULATING HINT 1806 WITH 13756. NEW HINT: 16961 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(f(x,f(g(f(y,x)),y)),f(f(z,g(f(f(g(f(y,z)),y),z))),f(g(z),u)))))=u. >> BACK DEMODULATING HINT 1804 WITH 13756. NEW HINT: 16962 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,f(z,f(g(f(u,z)),u)))))),g(g(f(x,f(v,g(f(f(g(f(u,v)),u),v)))))))=g(g(f(y,v))). >> BACK DEMODULATING HINT 1801 WITH 13756. >> BACK DEMODULATING HINT 1797 WITH 13756. >> BACK DEMODULATING HINT 1795 WITH 13756. >> BACK DEMODULATING HINT 1792 WITH 13756. >> BACK DEMODULATING HINT 1790 WITH 13756. >> BACK DEMODULATING HINT 1787 WITH 13756. >> BACK DEMODULATING HINT 1785 WITH 13756. >> BACK DEMODULATING HINT 1782 WITH 13756. >> BACK DEMODULATING HINT 1781 WITH 13756. >> BACK DEMODULATING HINT 1778 WITH 13756. >> BACK DEMODULATING HINT 1775 WITH 13756. >> BACK DEMODULATING HINT 1774 WITH 13756. NEW HINT: 16963 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(y,z))))=f(f(x,y),g(f(u,g(f(z,u))))). >> BACK DEMODULATING HINT 1773 WITH 13756. NEW HINT: 16964 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),g(f(z,g(f(f(u,g(u)),f(v,z))))))=g(g(f(x,f(y,v)))). >> BACK DEMODULATING HINT 1772 WITH 13756. NEW HINT: 16965 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,y))),g(f(z,g(f(f(u,g(u)),f(v,z))))))=g(g(f(x,f(y,v)))). >> BACK DEMODULATING HINT 1771 WITH 13756. >> BACK DEMODULATING HINT 1770 WITH 13756. NEW HINT: 16966 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(f(z,g(f(x,f(u,z))))))=g(g(f(y,u))). >> BACK DEMODULATING HINT 1769 WITH 13756. NEW HINT: 16967 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(f(z,g(f(x,f(g(g(u)),z))))))=g(g(f(y,u))). >> BACK DEMODULATING HINT 1768 WITH 13756. NEW HINT: 16968 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),g(f(z,g(f(x,f(g(f(f(u,g(u)),g(v))),z))))))=g(g(f(y,v))). >> BACK DEMODULATING HINT 1755 WITH 13756. NEW HINT: 16969 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(g(x),y))))=y. >> BACK DEMODULATING HINT 1754 WITH 13756. NEW HINT: 16970 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(g(x),y))))=g(g(y)). >> BACK DEMODULATING HINT 1753 WITH 13756. NEW HINT: 16971 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(g(f(y,g(y)))))),g(f(z,g(f(x,f(u,z))))))=g(g(f(y,f(g(y),u)))). >> BACK DEMODULATING HINT 1740 WITH 13756. >> BACK DEMODULATING HINT 1736 WITH 13756. >> BACK DEMODULATING HINT 1727 WITH 13756. >> BACK DEMODULATING HINT 1726 WITH 13756. >> BACK DEMODULATING HINT 1707 WITH 13756. >> BACK DEMODULATING HINT 1706 WITH 13756. >> BACK DEMODULATING HINT 1705 WITH 13756. >> BACK DEMODULATING HINT 1692 WITH 13756. NEW HINT: 16972 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,g(x)),g(f(y,z)))),g(f(u,g(f(f(v,g(v)),f(w,u))))))=g(g(f(y,f(z,w)))). >> BACK DEMODULATING HINT 1687 WITH 13756. NEW HINT: 16973 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(y,z)))),g(f(u,g(f(x,f(v,u))))))=g(g(f(y,f(z,v)))). >> BACK DEMODULATING HINT 1684 WITH 13756. NEW HINT: 16974 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(x)))=g(y). >> BACK DEMODULATING HINT 1673 WITH 13756. NEW HINT: 16975 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(g(f(y,z)))),g(z)))=y. >> BACK DEMODULATING HINT 1672 WITH 13756. NEW HINT: 16976 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(g(f(y,z)))),g(f(f(g(u),v),g(f(w,f(g(f(f(u,z),w)),v)))))))=y. >> BACK DEMODULATING HINT 1659 WITH 13756. >> BACK DEMODULATING HINT 1653 WITH 13756. >> BACK DEMODULATING HINT 1651 WITH 13756. >> BACK DEMODULATING HINT 1647 WITH 13756. >> BACK DEMODULATING HINT 1646 WITH 13756. NEW HINT: 16977 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(f(x,y))),g(g(f(x,f(g(f(x,f(y,x))),y)))))=y. >> BACK DEMODULATING HINT 1637 WITH 13756. NEW HINT: 16978 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(g(y),z))),g(g(f(x,u))))=g(f(v,f(g(f(f(y,u),v)),z))). >> BACK DEMODULATING HINT 1633 WITH 13756. >> BACK DEMODULATING HINT 1632 WITH 13756. >> BACK DEMODULATING HINT 1631 WITH 13756. >> BACK DEMODULATING HINT 1629 WITH 13756. NEW HINT: 16979 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(g(f(f(x,y),z)))),g(z))=y. >> BACK DEMODULATING HINT 1628 WITH 13756. NEW HINT: 16980 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(g(f(f(x,y),z)))),g(f(g(g(f(f(x,y),z))),g(g(f(f(x,y),f(g(f(f(x,y),f(z,f(x,y)))),z)))))))=y. >> BACK DEMODULATING HINT 1627 WITH 13756. >> BACK DEMODULATING HINT 1626 WITH 13756. >> BACK DEMODULATING HINT 1625 WITH 13756. >> BACK DEMODULATING HINT 1624 WITH 13756. >> BACK DEMODULATING HINT 1622 WITH 13756. >> BACK DEMODULATING HINT 1506 WITH 13756. >> BACK DEMODULATING HINT 1496 WITH 13756. >> BACK DEMODULATING HINT 1474 WITH 13756. >> BACK DEMODULATING HINT 1473 WITH 13756. >> BACK DEMODULATING HINT 1472 WITH 13756. NEW HINT: 16981 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(y,g(f(x,g(f(x,x)))))),g(g(f(y,z)))))=z. >> BACK DEMODULATING HINT 1471 WITH 13756. NEW HINT: 16982 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(g(f(x,x)),f(x,y)))))=y. >> BACK DEMODULATING HINT 1469 WITH 13756. >> BACK DEMODULATING HINT 1468 WITH 13756. >> BACK DEMODULATING HINT 1462 WITH 13756. NEW HINT: 16983 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(g(f(x,f(g(f(x,x)),y)))))=y. >> BACK DEMODULATING HINT 1458 WITH 13756. >> BACK DEMODULATING HINT 1457 WITH 13756. >> BACK DEMODULATING HINT 1450 WITH 13756. >> BACK DEMODULATING HINT 1449 WITH 13756. NEW HINT: 16984 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,f(y,z))))=f(g(g(f(x,y))),z). >> BACK DEMODULATING HINT 1448 WITH 13756. NEW HINT: 16985 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,g(x)),g(f(y,z)))),u)=g(g(f(y,f(z,u)))). >> BACK DEMODULATING HINT 1443 WITH 13756. >> BACK DEMODULATING HINT 1442 WITH 13756. NEW HINT: 16986 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(x,y)))=f(g(g(x)),y). >> BACK DEMODULATING HINT 1412 WITH 13756. NEW HINT: 16987 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(y,x)))=f(g(f(x,f(g(x),g(y)))),x). >> BACK DEMODULATING HINT 1403 WITH 13756. NEW HINT: 16988 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),y)=g(g(f(z,f(u,y)))). >> BACK DEMODULATING HINT 1402 WITH 13756. NEW HINT: 16989 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(g(y)))=g(g(f(z,f(u,y)))). >> BACK DEMODULATING HINT 1401 WITH 13756. NEW HINT: 16990 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(f(f(x,f(g(f(g(y),x)),g(y))),g(y))))=g(g(f(z,f(u,y)))). >> BACK DEMODULATING HINT 1400 WITH 13756. NEW HINT: 16991 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(f(f(x,f(g(f(g(y),x)),g(y))),g(g(g(y))))))=g(g(f(z,f(u,y)))). >> BACK DEMODULATING HINT 1399 WITH 13756. NEW HINT: 16992 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(z,u)))),g(f(f(x,f(g(f(g(y),x)),g(y))),g(f(f(x,f(g(f(g(y),x)),g(y))),y)))))=g(g(f(z,f(u,y)))). >> BACK DEMODULATING HINT 1374 WITH 13756. >> BACK DEMODULATING HINT 1292 WITH 13756. >> BACK DEMODULATING HINT 1258 WITH 13756. >> BACK DEMODULATING HINT 1256 WITH 13756. NEW HINT: 16993 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),g(f(g(g(f(x,g(f(y,x))))),g(g(f(x,g(f(y,x))))))))=g(f(x,g(f(y,x)))). >> BACK DEMODULATING HINT 1242 WITH 13756. >> BACK DEMODULATING HINT 1239 WITH 13756. >> BACK DEMODULATING HINT 1233 WITH 13756. >> BACK DEMODULATING HINT 1227 WITH 13756. >> BACK DEMODULATING HINT 1217 WITH 13756. >> BACK DEMODULATING HINT 1212 WITH 13756. >> BACK DEMODULATING HINT 1211 WITH 13756. NEW HINT: 16994 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,x)),f(g(f(y,f(f(g(f(y,y)),f(y,g(f(y,x)))),y))),g(g(f(x,z)))))=z. >> BACK DEMODULATING HINT 1210 WITH 13756. >> BACK DEMODULATING HINT 1209 WITH 13756. >> BACK DEMODULATING HINT 1208 WITH 13756. >> BACK DEMODULATING HINT 1204 WITH 13756. >> BACK DEMODULATING HINT 1198 WITH 13756. NEW HINT: 16995 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(x),f(g(f(g(x),g(x))),x))))=f(f(g(f(g(x),g(x))),x),g(x)). >> BACK DEMODULATING HINT 1197 WITH 13756. >> BACK DEMODULATING HINT 1196 WITH 13756. >> BACK DEMODULATING HINT 1195 WITH 13756. >> BACK DEMODULATING HINT 1194 WITH 13756. NEW HINT: 16996 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,y))))=f(f(g(y),f(z,f(g(f(y,z)),y))),y). >> BACK DEMODULATING HINT 1193 WITH 13756. >> BACK DEMODULATING HINT 1181 WITH 13756. >> BACK DEMODULATING HINT 1178 WITH 13756. >> BACK DEMODULATING HINT 1167 WITH 13756. >> BACK DEMODULATING HINT 1162 WITH 13756. >> BACK DEMODULATING HINT 1161 WITH 13756. >> BACK DEMODULATING HINT 1159 WITH 13756. >> BACK DEMODULATING HINT 1151 WITH 13756. >> BACK DEMODULATING HINT 1135 WITH 13756. >> BACK DEMODULATING HINT 1132 WITH 13756. >> BACK DEMODULATING HINT 1115 WITH 13756. >> BACK DEMODULATING HINT 1069 WITH 13756. >> BACK DEMODULATING HINT 1066 WITH 13756. NEW HINT: 16997 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(g(x)),f(f(g(f(f(g(f(y,g(x))),g(g(f(y,g(x))))),g(g(x)))),f(g(g(x)),g(z))),z))=x # label(bd). >> BACK DEMODULATING HINT 1061 WITH 13756. >> BACK DEMODULATING HINT 1055 WITH 13756. >> BACK DEMODULATING HINT 1043 WITH 13756. >> BACK DEMODULATING HINT 1021 WITH 13756. >> BACK DEMODULATING HINT 1020 WITH 13756. >> BACK DEMODULATING HINT 1013 WITH 13756. >> BACK DEMODULATING HINT 1010 WITH 13756. >> BACK DEMODULATING HINT 993 WITH 13756. >> BACK DEMODULATING HINT 992 WITH 13756. >> BACK DEMODULATING HINT 991 WITH 13756. >> BACK DEMODULATING HINT 984 WITH 13756. >> BACK DEMODULATING HINT 983 WITH 13756. >> BACK DEMODULATING HINT 982 WITH 13756. NEW HINT: 16998 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(g(f(z,z)),f(z,z))))))=f(g(f(z,y)),z) # label(bd). >> BACK DEMODULATING HINT 981 WITH 13756. >> BACK DEMODULATING HINT 980 WITH 13756. >> BACK DEMODULATING HINT 971 WITH 13756. >> BACK DEMODULATING HINT 961 WITH 13756. >> BACK DEMODULATING HINT 957 WITH 13756. >> BACK DEMODULATING HINT 956 WITH 13756. >> BACK DEMODULATING HINT 954 WITH 13756. >> BACK DEMODULATING HINT 900 WITH 13756. >> BACK DEMODULATING HINT 889 WITH 13756. NEW HINT: 16999 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(x),f(g(f(g(x),g(x))),g(x)))))=f(g(x),x). >> BACK DEMODULATING HINT 853 WITH 13756. >> BACK DEMODULATING HINT 851 WITH 13756. >> BACK DEMODULATING HINT 823 WITH 13756. >> BACK DEMODULATING HINT 817 WITH 13756. >> BACK DEMODULATING HINT 814 WITH 13756. >> BACK DEMODULATING HINT 813 WITH 13756. >> BACK DEMODULATING HINT 812 WITH 13756. >> BACK DEMODULATING HINT 811 WITH 13756. >> BACK DEMODULATING HINT 808 WITH 13756. >> BACK DEMODULATING HINT 803 WITH 13756. >> BACK DEMODULATING HINT 802 WITH 13756. >> BACK DEMODULATING HINT 801 WITH 13756. >> BACK DEMODULATING HINT 789 WITH 13756. >> BACK DEMODULATING HINT 786 WITH 13756. >> BACK DEMODULATING HINT 775 WITH 13756. >> BACK DEMODULATING HINT 767 WITH 13756. >> BACK DEMODULATING HINT 766 WITH 13756. >> BACK DEMODULATING HINT 765 WITH 13756. >> BACK DEMODULATING HINT 736 WITH 13756. NEW HINT: 17000 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,z))))=f(g(f(f(z,g(z)),y)),z) # label(bd). >> BACK DEMODULATING HINT 636 WITH 13756. >> BACK DEMODULATING HINT 623 WITH 13756. NEW HINT: 17001 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,f(g(f(z,z)),f(z,u))))))=f(g(f(z,y)),u) # label(bd). >> BACK DEMODULATING HINT 620 WITH 13756. >> BACK DEMODULATING HINT 617 WITH 13756. >> BACK DEMODULATING HINT 607 WITH 13756. >> BACK DEMODULATING HINT 594 WITH 13756. NEW HINT: 17002 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(f(g(f(y,y)),x)),g(f(g(f(y,y)),g(z))))),g(f(y,y)))=f(y,g(g(f(y,z)))) # label(bd). >> BACK DEMODULATING HINT 587 WITH 13756. >> BACK DEMODULATING HINT 583 WITH 13756. >> BACK DEMODULATING HINT 578 WITH 13756. >> BACK DEMODULATING HINT 576 WITH 13756. >> BACK DEMODULATING HINT 575 WITH 13756. >> BACK DEMODULATING HINT 574 WITH 13756. >> BACK DEMODULATING HINT 445 WITH 13756. >> BACK DEMODULATING HINT 440 WITH 13756. >> BACK DEMODULATING HINT 436 WITH 13756. >> BACK DEMODULATING HINT 431 WITH 13756. >> BACK DEMODULATING HINT 420 WITH 13756. >> BACK DEMODULATING HINT 408 WITH 13756. >> BACK DEMODULATING HINT 404 WITH 13756. >> BACK DEMODULATING HINT 400 WITH 13756. >> BACK DEMODULATING HINT 398 WITH 13756. >> BACK DEMODULATING HINT 397 WITH 13756. >> BACK DEMODULATING HINT 396 WITH 13756. >> BACK DEMODULATING HINT 384 WITH 13756. >> BACK DEMODULATING HINT 355 WITH 13756. >> BACK DEMODULATING HINT 352 WITH 13756. >> BACK DEMODULATING HINT 339 WITH 13756. >> BACK DEMODULATING HINT 331 WITH 13756. >> BACK DEMODULATING HINT 307 WITH 13756. >> BACK DEMODULATING HINT 304 WITH 13756. >> BACK DEMODULATING HINT 303 WITH 13756. >> BACK DEMODULATING HINT 299 WITH 13756. >> BACK DEMODULATING HINT 297 WITH 13756. >> BACK DEMODULATING HINT 296 WITH 13756. >> BACK DEMODULATING HINT 295 WITH 13756. >> BACK DEMODULATING HINT 272 WITH 13756. >> BACK DEMODULATING HINT 270 WITH 13756. NEW HINT: 17003 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(g(f(x,y))),f(g(f(g(x),f(g(f(g(x),g(f(f(x,z),u)))),y))),y)))=g(f(g(f(z,u)),y)) # label(bd). >> BACK DEMODULATING HINT 268 WITH 13756. NEW HINT: 17004 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(g(f(y,z))))=f(g(f(g(y),g(x))),z) # label(bd). >> BACK DEMODULATING HINT 265 WITH 13756. NEW HINT: 17005 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,z))))=f(g(y),z) # label(bd). >> BACK DEMODULATING HINT 212 WITH 13756. NEW HINT: 17006 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(g(f(x,y))))=g(f(y,g(y))) # label(bd). >> BACK DEMODULATING HINT 207 WITH 13756. >> BACK DEMODULATING HINT 206 WITH 13756. >> BACK DEMODULATING HINT 193 WITH 13756. >> BACK DEMODULATING HINT 140 WITH 13756. >> BACK DEMODULATING HINT 139 WITH 13756. >> BACK DEMODULATING HINT 118 WITH 13756. >> BACK DEMODULATING HINT 105 WITH 13756. >> BACK DEMODULATING HINT 92 WITH 13756. >> BACK DEMODULATING HINT 64 WITH 13756. >> BACK DEMODULATING HINT 53 WITH 13756. >> BACK DEMODULATING HINT 51 WITH 13756. >> BACK DEMODULATING HINT 42 WITH 13756. >> BACK DEMODULATING HINT 32 WITH 13756. >> BACK DEMODULATING HINT 29 WITH 13756. >> BACK DEMODULATING HINT 10 WITH 13756. >> BACK DEMODULATING HINT 2156 WITH 13767. >> BACK DEMODULATING HINT 13333 WITH 13770. NEW HINT: 17587 [bsub_wt=2147483647, bsub_add_wt=-1024] g(g(f(g(f(x,y)),x)))=g(y) # label(bd). >> BACK DEMODULATING HINT 13321 WITH 13770. NEW HINT: 17588 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(g(x)),g(f(g(g(x)),g(g(x))))))=x. >> BACK DEMODULATING HINT 13309 WITH 13770. >> BACK DEMODULATING HINT 13306 WITH 13770. >> BACK DEMODULATING HINT 13305 WITH 13770. >> BACK DEMODULATING HINT 13304 WITH 13770. >> BACK DEMODULATING HINT 13303 WITH 13770. NEW HINT: 17589 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,y)),x))=f(f(x,g(x)),g(f(f(x,g(x)),f(g(f(x,g(x))),f(f(x,g(x)),g(y)))))). >> BACK DEMODULATING HINT 13301 WITH 13770. NEW HINT: 17590 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,y)),x)),g(f(g(f(g(f(x,y)),x)),y)))=f(g(f(x,y)),x). >> BACK DEMODULATING HINT 13298 WITH 13770. NEW HINT: 17591 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(y))),x)=f(g(y),f(f(g(f(g(y),g(y))),y),g(y))). >> BACK DEMODULATING HINT 13297 WITH 13770. >> BACK DEMODULATING HINT 13290 WITH 13770. >> BACK DEMODULATING HINT 13289 WITH 13770. NEW HINT: 17592 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(g(y),f(f(g(f(x,g(y))),g(y)),g(f(x,g(y)))))))=f(g(y),g(g(f(y,x)))). >> BACK DEMODULATING HINT 13286 WITH 13770. NEW HINT: 17593 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(g(f(g(f(y,x)),y)),g(f(g(f(y,x)),y)))))=f(g(f(y,x)),y). >> BACK DEMODULATING HINT 13285 WITH 13770. NEW HINT: 17594 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,g(f(g(f(y,x)),y)))))=f(g(f(y,x)),y). >> BACK DEMODULATING HINT 13284 WITH 13770. NEW HINT: 17595 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),x)=f(y,g(f(y,y))). >> BACK DEMODULATING HINT 13283 WITH 13770. >> BACK DEMODULATING HINT 13270 WITH 13770. >> BACK DEMODULATING HINT 13269 WITH 13770. >> BACK DEMODULATING HINT 13267 WITH 13770. >> BACK DEMODULATING HINT 13238 WITH 13770. >> BACK DEMODULATING HINT 13235 WITH 13770. >> BACK DEMODULATING HINT 5213 WITH 13770. >> BACK DEMODULATING HINT 4917 WITH 13770. >> BACK DEMODULATING HINT 4916 WITH 13770. >> BACK DEMODULATING HINT 4915 WITH 13770. >> BACK DEMODULATING HINT 4914 WITH 13770. >> BACK DEMODULATING HINT 4913 WITH 13770. >> BACK DEMODULATING HINT 4912 WITH 13770. >> BACK DEMODULATING HINT 4901 WITH 13770. >> BACK DEMODULATING HINT 4900 WITH 13770. >> BACK DEMODULATING HINT 4899 WITH 13770. >> BACK DEMODULATING HINT 4898 WITH 13770. >> BACK DEMODULATING HINT 4897 WITH 13770. >> BACK DEMODULATING HINT 4896 WITH 13770. >> BACK DEMODULATING HINT 4895 WITH 13770. >> BACK DEMODULATING HINT 4894 WITH 13770. >> BACK DEMODULATING HINT 4893 WITH 13770. >> BACK DEMODULATING HINT 4892 WITH 13770. >> BACK DEMODULATING HINT 4891 WITH 13770. >> BACK DEMODULATING HINT 4890 WITH 13770. >> BACK DEMODULATING HINT 4889 WITH 13770. >> BACK DEMODULATING HINT 4888 WITH 13770. >> BACK DEMODULATING HINT 4887 WITH 13770. >> BACK DEMODULATING HINT 4875 WITH 13770. >> BACK DEMODULATING HINT 4874 WITH 13770. >> BACK DEMODULATING HINT 4873 WITH 13770. >> BACK DEMODULATING HINT 4872 WITH 13770. >> BACK DEMODULATING HINT 4871 WITH 13770. >> BACK DEMODULATING HINT 4870 WITH 13770. >> BACK DEMODULATING HINT 4869 WITH 13770. >> BACK DEMODULATING HINT 4868 WITH 13770. >> BACK DEMODULATING HINT 4867 WITH 13770. >> BACK DEMODULATING HINT 4866 WITH 13770. >> BACK DEMODULATING HINT 4853 WITH 13770. >> BACK DEMODULATING HINT 4852 WITH 13770. >> BACK DEMODULATING HINT 4851 WITH 13770. >> BACK DEMODULATING HINT 4850 WITH 13770. >> BACK DEMODULATING HINT 4849 WITH 13770. >> BACK DEMODULATING HINT 4848 WITH 13770. >> BACK DEMODULATING HINT 4847 WITH 13770. >> BACK DEMODULATING HINT 4846 WITH 13770. >> BACK DEMODULATING HINT 4845 WITH 13770. >> BACK DEMODULATING HINT 4844 WITH 13770. >> BACK DEMODULATING HINT 4843 WITH 13770. >> BACK DEMODULATING HINT 4842 WITH 13770. >> BACK DEMODULATING HINT 4841 WITH 13770. >> BACK DEMODULATING HINT 4840 WITH 13770. >> BACK DEMODULATING HINT 4809 WITH 13770. >> BACK DEMODULATING HINT 4808 WITH 13770. >> BACK DEMODULATING HINT 4807 WITH 13770. >> BACK DEMODULATING HINT 4806 WITH 13770. >> BACK DEMODULATING HINT 4805 WITH 13770. >> BACK DEMODULATING HINT 4804 WITH 13770. >> BACK DEMODULATING HINT 4803 WITH 13770. >> BACK DEMODULATING HINT 4802 WITH 13770. >> BACK DEMODULATING HINT 4801 WITH 13770. >> BACK DEMODULATING HINT 4800 WITH 13770. >> BACK DEMODULATING HINT 4799 WITH 13770. >> BACK DEMODULATING HINT 4798 WITH 13770. >> BACK DEMODULATING HINT 4797 WITH 13770. >> BACK DEMODULATING HINT 4796 WITH 13770. >> BACK DEMODULATING HINT 4795 WITH 13770. >> BACK DEMODULATING HINT 4794 WITH 13770. >> BACK DEMODULATING HINT 4793 WITH 13770. >> BACK DEMODULATING HINT 4792 WITH 13770. >> BACK DEMODULATING HINT 4791 WITH 13770. >> BACK DEMODULATING HINT 4790 WITH 13770. >> BACK DEMODULATING HINT 4789 WITH 13770. >> BACK DEMODULATING HINT 4713 WITH 13770. >> BACK DEMODULATING HINT 4712 WITH 13770. >> BACK DEMODULATING HINT 4711 WITH 13770. >> BACK DEMODULATING HINT 4710 WITH 13770. >> BACK DEMODULATING HINT 4584 WITH 13770. >> BACK DEMODULATING HINT 4583 WITH 13770. >> BACK DEMODULATING HINT 4582 WITH 13770. >> BACK DEMODULATING HINT 4581 WITH 13770. >> BACK DEMODULATING HINT 4580 WITH 13770. >> BACK DEMODULATING HINT 4579 WITH 13770. >> BACK DEMODULATING HINT 4578 WITH 13770. >> BACK DEMODULATING HINT 4577 WITH 13770. >> BACK DEMODULATING HINT 4576 WITH 13770. >> BACK DEMODULATING HINT 4575 WITH 13770. >> BACK DEMODULATING HINT 4574 WITH 13770. >> BACK DEMODULATING HINT 4573 WITH 13770. >> BACK DEMODULATING HINT 4572 WITH 13770. >> BACK DEMODULATING HINT 4571 WITH 13770. >> BACK DEMODULATING HINT 4570 WITH 13770. >> BACK DEMODULATING HINT 4285 WITH 13770. >> BACK DEMODULATING HINT 4277 WITH 13770. NEW HINT: 17596 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,g(y)))=f(y,f(x,g(f(x,x)))). >> BACK DEMODULATING HINT 4267 WITH 13770. >> BACK DEMODULATING HINT 4266 WITH 13770. >> BACK DEMODULATING HINT 4265 WITH 13770. >> BACK DEMODULATING HINT 4232 WITH 13770. >> BACK DEMODULATING HINT 4230 WITH 13770. >> BACK DEMODULATING HINT 4215 WITH 13770. >> BACK DEMODULATING HINT 4214 WITH 13770. >> BACK DEMODULATING HINT 4211 WITH 13770. >> BACK DEMODULATING HINT 4166 WITH 13770. >> BACK DEMODULATING HINT 4165 WITH 13770. >> BACK DEMODULATING HINT 4164 WITH 13770. >> BACK DEMODULATING HINT 4140 WITH 13770. >> BACK DEMODULATING HINT 4138 WITH 13770. >> BACK DEMODULATING HINT 4131 WITH 13770. >> BACK DEMODULATING HINT 4128 WITH 13770. >> BACK DEMODULATING HINT 4127 WITH 13770. >> BACK DEMODULATING HINT 4126 WITH 13770. >> BACK DEMODULATING HINT 4125 WITH 13770. >> BACK DEMODULATING HINT 4124 WITH 13770. >> BACK DEMODULATING HINT 4123 WITH 13770. >> BACK DEMODULATING HINT 4121 WITH 13770. >> BACK DEMODULATING HINT 4120 WITH 13770. >> BACK DEMODULATING HINT 4114 WITH 13770. >> BACK DEMODULATING HINT 4113 WITH 13770. >> BACK DEMODULATING HINT 4112 WITH 13770. >> BACK DEMODULATING HINT 4109 WITH 13770. >> BACK DEMODULATING HINT 4108 WITH 13770. >> BACK DEMODULATING HINT 4104 WITH 13770. >> BACK DEMODULATING HINT 4102 WITH 13770. >> BACK DEMODULATING HINT 4101 WITH 13770. >> BACK DEMODULATING HINT 4100 WITH 13770. >> BACK DEMODULATING HINT 4099 WITH 13770. >> BACK DEMODULATING HINT 4098 WITH 13770. >> BACK DEMODULATING HINT 4097 WITH 13770. NEW HINT: 17597 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(f(f(v,g(f(w,f(f(g(w),v),f(v6,v))))),v),g(f(x,y)))),g(f(x,y)))))),f(v6,g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 4093 WITH 13770. NEW HINT: 17598 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(g(f(z,f(f(g(z),g(f(x,y))),f(g(f(f(f(u,g(f(v,f(f(g(v),u),f(w,u))))),u),g(f(x,y)))),g(f(x,y)))))),f(w,g(v6))),g(f(x,y))))=g(f(x,f(y,v6))). >> BACK DEMODULATING HINT 4091 WITH 13770. >> BACK DEMODULATING HINT 4088 WITH 13770. >> BACK DEMODULATING HINT 4056 WITH 13770. >> BACK DEMODULATING HINT 4055 WITH 13770. >> BACK DEMODULATING HINT 4050 WITH 13770. >> BACK DEMODULATING HINT 4049 WITH 13770. >> BACK DEMODULATING HINT 4048 WITH 13770. >> BACK DEMODULATING HINT 4043 WITH 13770. NEW HINT: 17599 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(g(f(f(y,f(f(z,f(g(f(g(f(x,u)),z)),g(v))),g(f(x,u)))),y)),y))=g(f(x,f(f(u,g(f(x,f(u,v)))),x))). >> BACK DEMODULATING HINT 4042 WITH 13770. NEW HINT: 17600 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(y,g(f(x,f(y,z)))),x)))=f(f(g(x),u),f(g(f(f(u,f(f(v,f(g(f(g(f(x,y)),v)),g(z))),g(f(x,y)))),u)),u)). >> BACK DEMODULATING HINT 4041 WITH 13770. NEW HINT: 17601 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(y,g(f(z,f(g(f(u,f(f(g(u),z),f(g(f(f(x,y),z)),z)))),v)))),x)))=f(f(g(x),w),f(g(f(f(w,f(f(v6,f(g(f(g(f(x,y)),v6)),g(v))),g(f(x,y)))),w)),w)). >> BACK DEMODULATING HINT 4035 WITH 13770. NEW HINT: 17602 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(f(y,f(f(g(y),x),f(g(f(f(z,u),x)),x)))),v)))=g(f(z,f(u,v))). >> BACK DEMODULATING HINT 4021 WITH 13770. >> BACK DEMODULATING HINT 4020 WITH 13770. >> BACK DEMODULATING HINT 4019 WITH 13770. >> BACK DEMODULATING HINT 4017 WITH 13770. >> BACK DEMODULATING HINT 4016 WITH 13770. >> BACK DEMODULATING HINT 4014 WITH 13770. NEW HINT: 17603 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,g(f(y,x))))=f(x,g(f(z,f(g(f(y,z)),x)))). >> BACK DEMODULATING HINT 4013 WITH 13770. >> BACK DEMODULATING HINT 4009 WITH 13770. >> BACK DEMODULATING HINT 4004 WITH 13770. >> BACK DEMODULATING HINT 4003 WITH 13770. >> BACK DEMODULATING HINT 4000 WITH 13770. >> BACK DEMODULATING HINT 3999 WITH 13770. >> BACK DEMODULATING HINT 3998 WITH 13770. >> BACK DEMODULATING HINT 3994 WITH 13770. >> BACK DEMODULATING HINT 3993 WITH 13770. >> BACK DEMODULATING HINT 3992 WITH 13770. >> BACK DEMODULATING HINT 3990 WITH 13770. >> BACK DEMODULATING HINT 3989 WITH 13770. >> BACK DEMODULATING HINT 3988 WITH 13770. >> BACK DEMODULATING HINT 3987 WITH 13770. >> BACK DEMODULATING HINT 3986 WITH 13770. >> BACK DEMODULATING HINT 3985 WITH 13770. >> BACK DEMODULATING HINT 3984 WITH 13770. >> BACK DEMODULATING HINT 3983 WITH 13770. >> BACK DEMODULATING HINT 3982 WITH 13770. >> BACK DEMODULATING HINT 3981 WITH 13770. >> BACK DEMODULATING HINT 3980 WITH 13770. >> BACK DEMODULATING HINT 3979 WITH 13770. >> BACK DEMODULATING HINT 3978 WITH 13770. >> BACK DEMODULATING HINT 3977 WITH 13770. >> BACK DEMODULATING HINT 3976 WITH 13770. >> BACK DEMODULATING HINT 3975 WITH 13770. >> BACK DEMODULATING HINT 3974 WITH 13770. >> BACK DEMODULATING HINT 3973 WITH 13770. NEW HINT: 17604 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(g(f(u,f(f(g(u),g(f(x,y))),f(g(f(v,g(f(x,y)))),g(f(x,y)))))),f(g(v),g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 3972 WITH 13770. >> BACK DEMODULATING HINT 3971 WITH 13770. NEW HINT: 17605 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))),u)))=f(g(z),f(f(v,f(g(f(g(z),v)),g(u))),g(z))). >> BACK DEMODULATING HINT 3970 WITH 13770. NEW HINT: 17606 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(g(f(z,f(f(g(z),g(f(x,y))),f(g(f(u,g(f(x,y)))),g(f(x,y)))))),f(g(u),g(v))),g(f(x,y))))=g(f(x,f(y,v))). >> BACK DEMODULATING HINT 3969 WITH 13770. >> BACK DEMODULATING HINT 3968 WITH 13770. NEW HINT: 17607 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(x)))=g(f(u,f(g(f(v,f(f(g(v),u),f(g(f(x,u)),u)))),z))). >> BACK DEMODULATING HINT 3967 WITH 13770. NEW HINT: 17608 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(f(u,g(f(v,f(f(g(v),u),f(g(f(x,u)),u))))))))=g(f(u,f(g(f(v,f(f(g(v),u),f(g(f(x,u)),u)))),z))). >> BACK DEMODULATING HINT 3966 WITH 13770. NEW HINT: 17609 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(g(f(g(f(z,g(f(u,f(f(g(u),z),f(g(f(x,z)),z)))))),y)),g(v))),g(f(z,g(f(u,f(f(g(u),z),f(g(f(x,z)),z))))))))=g(f(z,f(g(f(u,f(f(g(u),z),f(g(f(x,z)),z)))),v))). >> BACK DEMODULATING HINT 3965 WITH 13770. NEW HINT: 17610 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(f(y,f(f(g(y),x),f(g(f(z,x)),x)))),f(g(z),g(u)))))=u. >> BACK DEMODULATING HINT 3964 WITH 13770. NEW HINT: 17611 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(u,f(f(g(u),g(f(x,y))),f(g(f(z,g(f(x,y)))),g(f(x,y))))). >> BACK DEMODULATING HINT 3963 WITH 13770. NEW HINT: 17612 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=g(f(x,f(y,u))). >> BACK DEMODULATING HINT 3962 WITH 13770. NEW HINT: 17613 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 3961 WITH 13770. >> BACK DEMODULATING HINT 3958 WITH 13770. >> BACK DEMODULATING HINT 3950 WITH 13770. >> BACK DEMODULATING HINT 3949 WITH 13770. >> BACK DEMODULATING HINT 3948 WITH 13770. >> BACK DEMODULATING HINT 3947 WITH 13770. >> BACK DEMODULATING HINT 3946 WITH 13770. >> BACK DEMODULATING HINT 3945 WITH 13770. >> BACK DEMODULATING HINT 3944 WITH 13770. >> BACK DEMODULATING HINT 3943 WITH 13770. >> BACK DEMODULATING HINT 3942 WITH 13770. >> BACK DEMODULATING HINT 3941 WITH 13770. >> BACK DEMODULATING HINT 3940 WITH 13770. >> BACK DEMODULATING HINT 3939 WITH 13770. >> BACK DEMODULATING HINT 3938 WITH 13770. >> BACK DEMODULATING HINT 3937 WITH 13770. >> BACK DEMODULATING HINT 3936 WITH 13770. >> BACK DEMODULATING HINT 3935 WITH 13770. >> BACK DEMODULATING HINT 3934 WITH 13770. >> BACK DEMODULATING HINT 3933 WITH 13770. >> BACK DEMODULATING HINT 3932 WITH 13770. >> BACK DEMODULATING HINT 3931 WITH 13770. >> BACK DEMODULATING HINT 3930 WITH 13770. >> BACK DEMODULATING HINT 3929 WITH 13770. >> BACK DEMODULATING HINT 3928 WITH 13770. >> BACK DEMODULATING HINT 3927 WITH 13770. >> BACK DEMODULATING HINT 3926 WITH 13770. >> BACK DEMODULATING HINT 3925 WITH 13770. >> BACK DEMODULATING HINT 3854 WITH 13770. NEW HINT: 17614 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(x),f(y,z))))=f(f(g(f(u,y)),u),f(f(f(u,f(g(f(u,u)),u)),f(y,g(z))),f(g(f(u,y)),u))). >> BACK DEMODULATING HINT 3837 WITH 13770. >> BACK DEMODULATING HINT 3836 WITH 13770. NEW HINT: 17615 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(x,y)),z),f(u,f(g(f(v,u)),v))))=f(f(g(z),x),y). >> BACK DEMODULATING HINT 3835 WITH 13770. NEW HINT: 17616 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(x,y)),z),f(u,f(g(f(v,u)),v))))=f(y,f(f(g(y),f(g(z),x)),y)). >> BACK DEMODULATING HINT 3834 WITH 13770. NEW HINT: 17617 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),f(g(z),u))),x))=g(f(f(g(f(u,x)),z),f(v,f(g(f(w,v)),w)))). >> BACK DEMODULATING HINT 3833 WITH 13770. NEW HINT: 17618 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(f(g(z),u)))),x))=g(f(f(g(f(z,x)),u),f(v,f(g(f(w,v)),w)))). >> BACK DEMODULATING HINT 3832 WITH 13770. NEW HINT: 17619 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(g(f(g(z),u))))),x))=g(f(f(g(f(u,x)),z),f(v,f(g(f(w,v)),w)))). >> BACK DEMODULATING HINT 3831 WITH 13770. NEW HINT: 17620 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,f(g(u),v))),z)))),x))=g(f(f(g(f(v,x)),u),f(w,f(g(f(v6,w)),v6)))). >> BACK DEMODULATING HINT 3794 WITH 13770. NEW HINT: 17621 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(x),y)))=f(f(g(f(f(z,f(g(f(u,z)),u)),y)),f(g(f(v,g(w))),v)),f(f(z,f(g(f(u,z)),u)),f(g(w),f(z,f(g(f(u,z)),u))))). >> BACK DEMODULATING HINT 3706 WITH 13770. >> BACK DEMODULATING HINT 3700 WITH 13770. >> BACK DEMODULATING HINT 3699 WITH 13770. >> BACK DEMODULATING HINT 3698 WITH 13770. >> BACK DEMODULATING HINT 3697 WITH 13770. >> BACK DEMODULATING HINT 3687 WITH 13770. >> BACK DEMODULATING HINT 3685 WITH 13770. >> BACK DEMODULATING HINT 3684 WITH 13770. >> BACK DEMODULATING HINT 3683 WITH 13770. >> BACK DEMODULATING HINT 3682 WITH 13770. >> BACK DEMODULATING HINT 3681 WITH 13770. >> BACK DEMODULATING HINT 3669 WITH 13770. >> BACK DEMODULATING HINT 3666 WITH 13770. NEW HINT: 17622 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(g(f(x,y)),z))))=f(f(g(f(f(u,f(g(f(v,u)),v)),z)),f(g(f(w,g(v6))),w)),f(f(u,f(g(f(v,u)),v)),f(g(v6),f(u,f(g(f(v,u)),v))))). >> BACK DEMODULATING HINT 3662 WITH 13770. NEW HINT: 17623 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(f(x,f(g(f(y,x)),y)),z)),f(g(f(u,g(v))),u)),f(f(x,f(g(f(y,x)),y)),f(g(v),f(x,f(g(f(y,x)),y)))))=g(f(w,f(v6,f(g(f(w,v6)),z)))). >> BACK DEMODULATING HINT 3656 WITH 13770. >> BACK DEMODULATING HINT 3651 WITH 13770. NEW HINT: 17624 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(f(g(f(z,f(u,f(g(f(v,u)),u)))),z)))),x))=g(f(f(g(f(u,x)),v),f(w,f(g(f(v6,w)),v6)))). >> BACK DEMODULATING HINT 3644 WITH 13770. NEW HINT: 17625 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(x,y)),z),f(u,f(g(f(v,u)),v))))=f(y,f(f(w,f(g(f(y,w)),g(f(g(f(v6,f(x,f(g(f(z,x)),x)))),v6)))),y)). >> BACK DEMODULATING HINT 3613 WITH 13770. >> BACK DEMODULATING HINT 3599 WITH 13770. >> BACK DEMODULATING HINT 3594 WITH 13770. >> BACK DEMODULATING HINT 3591 WITH 13770. >> BACK DEMODULATING HINT 3588 WITH 13770. >> BACK DEMODULATING HINT 3587 WITH 13770. >> BACK DEMODULATING HINT 3586 WITH 13770. >> BACK DEMODULATING HINT 3585 WITH 13770. >> BACK DEMODULATING HINT 3584 WITH 13770. >> BACK DEMODULATING HINT 3582 WITH 13770. >> BACK DEMODULATING HINT 3581 WITH 13770. >> BACK DEMODULATING HINT 3580 WITH 13770. >> BACK DEMODULATING HINT 3579 WITH 13770. >> BACK DEMODULATING HINT 3578 WITH 13770. NEW HINT: 17626 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(g(f(x,y)),z),f(f(x,f(g(f(z,x)),x)),u)))=f(y,f(f(v,f(g(f(y,v)),g(u))),y)). >> BACK DEMODULATING HINT 3577 WITH 13770. NEW HINT: 17627 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(z))),x))=g(f(f(g(f(u,x)),v),f(f(u,f(g(f(v,u)),u)),z))). >> BACK DEMODULATING HINT 3576 WITH 13770. NEW HINT: 17628 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(x,y)),g(z))),g(f(f(g(f(u,x)),v),f(u,f(g(f(v,u)),u))))))=g(f(f(g(f(u,x)),v),f(f(u,f(g(f(v,u)),u)),z))). >> BACK DEMODULATING HINT 3575 WITH 13770. NEW HINT: 17629 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(g(f(g(f(f(g(f(z,x)),u),f(z,f(g(f(u,z)),z)))),y)),g(v))),g(f(f(g(f(z,x)),u),f(z,f(g(f(u,z)),z))))))=g(f(f(g(f(z,x)),u),f(f(z,f(g(f(u,z)),z)),v))). >> BACK DEMODULATING HINT 3573 WITH 13770. >> BACK DEMODULATING HINT 3572 WITH 13770. NEW HINT: 17630 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(x,y)),z),f(x,f(g(f(z,x)),x)))=g(f(u,f(v,f(g(f(u,v)),y)))). >> BACK DEMODULATING HINT 3571 WITH 13770. >> BACK DEMODULATING HINT 3570 WITH 13770. NEW HINT: 17631 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(g(f(x,y)),z))))=f(f(g(f(u,z)),v),f(u,f(g(f(v,u)),u))). >> BACK DEMODULATING HINT 3568 WITH 13770. >> BACK DEMODULATING HINT 3432 WITH 13770. >> BACK DEMODULATING HINT 3423 WITH 13770. NEW HINT: 17632 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(g(x),f(f(f(x,x),y),g(z))),g(f(x,y)))). >> BACK DEMODULATING HINT 3406 WITH 13770. NEW HINT: 17633 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(g(x),x)),g(f(g(f(g(y),y)),f(z,u)))))=f(f(f(g(f(g(y),y)),g(f(g(y),y))),z),u). >> BACK DEMODULATING HINT 3387 WITH 13770. >> BACK DEMODULATING HINT 3383 WITH 13770. >> BACK DEMODULATING HINT 3354 WITH 13770. >> BACK DEMODULATING HINT 3345 WITH 13770. >> BACK DEMODULATING HINT 3333 WITH 13770. >> BACK DEMODULATING HINT 3325 WITH 13770. NEW HINT: 17634 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(f(f(x,x),y),z)),x)=g(f(x,f(y,z))). >> BACK DEMODULATING HINT 3323 WITH 13770. >> BACK DEMODULATING HINT 3322 WITH 13770. >> BACK DEMODULATING HINT 3312 WITH 13770. >> BACK DEMODULATING HINT 3310 WITH 13770. >> BACK DEMODULATING HINT 3305 WITH 13770. >> BACK DEMODULATING HINT 3302 WITH 13770. >> BACK DEMODULATING HINT 3300 WITH 13770. >> BACK DEMODULATING HINT 3299 WITH 13770. >> BACK DEMODULATING HINT 3292 WITH 13770. >> BACK DEMODULATING HINT 3291 WITH 13770. >> BACK DEMODULATING HINT 3290 WITH 13770. >> BACK DEMODULATING HINT 3289 WITH 13770. >> BACK DEMODULATING HINT 3285 WITH 13770. >> BACK DEMODULATING HINT 3281 WITH 13770. >> BACK DEMODULATING HINT 3280 WITH 13770. >> BACK DEMODULATING HINT 3279 WITH 13770. >> BACK DEMODULATING HINT 3278 WITH 13770. >> BACK DEMODULATING HINT 3277 WITH 13770. >> BACK DEMODULATING HINT 3275 WITH 13770. >> BACK DEMODULATING HINT 3274 WITH 13770. >> BACK DEMODULATING HINT 3273 WITH 13770. >> BACK DEMODULATING HINT 3272 WITH 13770. >> BACK DEMODULATING HINT 3271 WITH 13770. >> BACK DEMODULATING HINT 3270 WITH 13770. >> BACK DEMODULATING HINT 3269 WITH 13770. >> BACK DEMODULATING HINT 3268 WITH 13770. >> BACK DEMODULATING HINT 3267 WITH 13770. >> BACK DEMODULATING HINT 3266 WITH 13770. >> BACK DEMODULATING HINT 3264 WITH 13770. >> BACK DEMODULATING HINT 3145 WITH 13770. >> BACK DEMODULATING HINT 2931 WITH 13770. >> BACK DEMODULATING HINT 2930 WITH 13770. >> BACK DEMODULATING HINT 2929 WITH 13770. >> BACK DEMODULATING HINT 2928 WITH 13770. >> BACK DEMODULATING HINT 2927 WITH 13770. >> BACK DEMODULATING HINT 2887 WITH 13770. >> BACK DEMODULATING HINT 2886 WITH 13770. >> BACK DEMODULATING HINT 2885 WITH 13770. >> BACK DEMODULATING HINT 2884 WITH 13770. >> BACK DEMODULATING HINT 2880 WITH 13770. >> BACK DEMODULATING HINT 2875 WITH 13770. >> BACK DEMODULATING HINT 2874 WITH 13770. >> BACK DEMODULATING HINT 2873 WITH 13770. >> BACK DEMODULATING HINT 2872 WITH 13770. >> BACK DEMODULATING HINT 2871 WITH 13770. >> BACK DEMODULATING HINT 2870 WITH 13770. >> BACK DEMODULATING HINT 2869 WITH 13770. >> BACK DEMODULATING HINT 2868 WITH 13770. >> BACK DEMODULATING HINT 2867 WITH 13770. >> BACK DEMODULATING HINT 2866 WITH 13770. >> BACK DEMODULATING HINT 2862 WITH 13770. >> BACK DEMODULATING HINT 2859 WITH 13770. >> BACK DEMODULATING HINT 2803 WITH 13770. >> BACK DEMODULATING HINT 2786 WITH 13770. >> BACK DEMODULATING HINT 2785 WITH 13770. >> BACK DEMODULATING HINT 2784 WITH 13770. >> BACK DEMODULATING HINT 2783 WITH 13770. >> BACK DEMODULATING HINT 2780 WITH 13770. NEW HINT: 17635 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(x,x),y),f(f(g(f(x,y)),g(f(z,x))),f(z,g(u)))))=u # label(bd). >> BACK DEMODULATING HINT 2771 WITH 13770. >> BACK DEMODULATING HINT 2768 WITH 13770. >> BACK DEMODULATING HINT 2767 WITH 13770. >> BACK DEMODULATING HINT 2766 WITH 13770. >> BACK DEMODULATING HINT 2763 WITH 13770. >> BACK DEMODULATING HINT 2762 WITH 13770. >> BACK DEMODULATING HINT 2761 WITH 13770. >> BACK DEMODULATING HINT 2760 WITH 13770. >> BACK DEMODULATING HINT 2759 WITH 13770. >> BACK DEMODULATING HINT 2758 WITH 13770. >> BACK DEMODULATING HINT 2757 WITH 13770. >> BACK DEMODULATING HINT 2708 WITH 13770. >> BACK DEMODULATING HINT 2700 WITH 13770. >> BACK DEMODULATING HINT 2699 WITH 13770. >> BACK DEMODULATING HINT 2689 WITH 13770. >> BACK DEMODULATING HINT 2684 WITH 13770. NEW HINT: 17636 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(g(f(g(g(f(g(z),z))),u)),f(g(v),v)))))=f(g(f(x,y)),f(f(w,f(g(f(g(f(x,y)),w)),u)),g(f(x,y)))) # label(bd). >> BACK DEMODULATING HINT 2683 WITH 13770. NEW HINT: 17637 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),u)),g(f(x,y))))=g(f(x,f(y,f(g(f(g(g(f(g(v),v))),u)),f(g(w),w))))) # label(bd). >> BACK DEMODULATING HINT 2671 WITH 13770. >> BACK DEMODULATING HINT 2669 WITH 13770. >> BACK DEMODULATING HINT 2664 WITH 13770. >> BACK DEMODULATING HINT 2651 WITH 13770. >> BACK DEMODULATING HINT 2650 WITH 13770. >> BACK DEMODULATING HINT 2645 WITH 13770. >> BACK DEMODULATING HINT 2636 WITH 13770. NEW HINT: 17638 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(f(x,y),f(g(f(g(f(g(z),z)),f(g(u),u))),g(v))),g(f(x,y))))=g(f(x,f(y,v))) # label(bd). >> BACK DEMODULATING HINT 2623 WITH 13770. NEW HINT: 17639 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(f(x,y)),f(f(g(f(u,f(g(f(x,y)),g(f(g(v),v))))),f(u,g(z))),g(f(x,y)))) # label(bd). >> BACK DEMODULATING HINT 2622 WITH 13770. >> BACK DEMODULATING HINT 2620 WITH 13770. NEW HINT: 17640 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(g(f(z,f(g(f(x,y)),g(f(g(u),u))))),f(z,g(v))),g(f(x,y))))=g(f(x,f(y,v))) # label(bd). >> BACK DEMODULATING HINT 2615 WITH 13770. NEW HINT: 17641 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(x),f(x,f(g(f(g(y),y)),g(z)))))=z # label(bd). >> BACK DEMODULATING HINT 2608 WITH 13770. >> BACK DEMODULATING HINT 2607 WITH 13770. >> BACK DEMODULATING HINT 2606 WITH 13770. >> BACK DEMODULATING HINT 2604 WITH 13770. >> BACK DEMODULATING HINT 2597 WITH 13770. >> BACK DEMODULATING HINT 2595 WITH 13770. >> BACK DEMODULATING HINT 2588 WITH 13770. >> BACK DEMODULATING HINT 2583 WITH 13770. NEW HINT: 17642 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(f(f(x,x),y),f(f(g(f(x,y)),g(z)),u)))=f(g(f(f(f(x,x),y),f(g(f(x,y)),g(z)))),f(f(x,f(g(z),g(u))),g(f(f(f(x,x),y),f(g(f(x,y)),g(z)))))) # label(bd). >> BACK DEMODULATING HINT 2580 WITH 13770. >> BACK DEMODULATING HINT 2579 WITH 13770. >> BACK DEMODULATING HINT 2569 WITH 13770. >> BACK DEMODULATING HINT 2567 WITH 13770. >> BACK DEMODULATING HINT 2566 WITH 13770. >> BACK DEMODULATING HINT 2557 WITH 13770. >> BACK DEMODULATING HINT 2555 WITH 13770. >> BACK DEMODULATING HINT 2554 WITH 13770. >> BACK DEMODULATING HINT 2553 WITH 13770. >> BACK DEMODULATING HINT 2552 WITH 13770. >> BACK DEMODULATING HINT 2551 WITH 13770. >> BACK DEMODULATING HINT 2550 WITH 13770. >> BACK DEMODULATING HINT 2549 WITH 13770. >> BACK DEMODULATING HINT 2548 WITH 13770. >> BACK DEMODULATING HINT 2547 WITH 13770. >> BACK DEMODULATING HINT 2546 WITH 13770. >> BACK DEMODULATING HINT 2544 WITH 13770. >> BACK DEMODULATING HINT 2497 WITH 13770. >> BACK DEMODULATING HINT 2486 WITH 13770. >> BACK DEMODULATING HINT 2443 WITH 13770. >> BACK DEMODULATING HINT 2435 WITH 13770. NEW HINT: 17643 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(g(f(x,x)),x),x)))=f(y,g(f(x,y))). >> BACK DEMODULATING HINT 2432 WITH 13770. >> BACK DEMODULATING HINT 2425 WITH 13770. >> BACK DEMODULATING HINT 2421 WITH 13770. NEW HINT: 17644 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(x,y))))=f(g(f(x,y)),g(f(x,y))). >> BACK DEMODULATING HINT 2420 WITH 13770. >> BACK DEMODULATING HINT 2419 WITH 13770. >> BACK DEMODULATING HINT 2416 WITH 13770. NEW HINT: 17645 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,f(y,g(f(x,y))))))=x. >> BACK DEMODULATING HINT 2414 WITH 13770. NEW HINT: 17646 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(f(x,x)),f(x,y))))=f(y,g(f(y,y))). >> BACK DEMODULATING HINT 2413 WITH 13770. >> BACK DEMODULATING HINT 2411 WITH 13770. NEW HINT: 17647 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(g(f(x,y)),z))))=f(z,g(f(z,z))). >> BACK DEMODULATING HINT 2410 WITH 13770. NEW HINT: 17648 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(f(x,x)),f(x,g(y)))))=y. >> BACK DEMODULATING HINT 2405 WITH 13770. >> BACK DEMODULATING HINT 2403 WITH 13770. NEW HINT: 17649 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(g(f(z,g(f(x,y)))),f(g(f(x,y)),g(u))),u))=g(f(x,f(y,z))). >> BACK DEMODULATING HINT 2402 WITH 13770. >> BACK DEMODULATING HINT 2401 WITH 13770. NEW HINT: 17650 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(x)),g(f(f(x,g(x)),f(f(g(y),f(f(x,g(x)),g(z))),z))))=g(f(g(f(x,y)),x)). >> BACK DEMODULATING HINT 2400 WITH 13770. >> BACK DEMODULATING HINT 2399 WITH 13770. >> BACK DEMODULATING HINT 2395 WITH 13770. >> BACK DEMODULATING HINT 2280 WITH 13770. >> BACK DEMODULATING HINT 2265 WITH 13770. >> BACK DEMODULATING HINT 2264 WITH 13770. >> BACK DEMODULATING HINT 2262 WITH 13770. >> BACK DEMODULATING HINT 2259 WITH 13770. >> BACK DEMODULATING HINT 2256 WITH 13770. >> BACK DEMODULATING HINT 2255 WITH 13770. >> BACK DEMODULATING HINT 2242 WITH 13770. >> BACK DEMODULATING HINT 2233 WITH 13770. >> BACK DEMODULATING HINT 2232 WITH 13770. >> BACK DEMODULATING HINT 2231 WITH 13770. >> BACK DEMODULATING HINT 2230 WITH 13770. >> BACK DEMODULATING HINT 2223 WITH 13770. >> BACK DEMODULATING HINT 2220 WITH 13770. >> BACK DEMODULATING HINT 2095 WITH 13770. >> BACK DEMODULATING HINT 2046 WITH 13770. >> BACK DEMODULATING HINT 2043 WITH 13770. >> BACK DEMODULATING HINT 2038 WITH 13770. >> BACK DEMODULATING HINT 2035 WITH 13770. >> BACK DEMODULATING HINT 2030 WITH 13770. >> BACK DEMODULATING HINT 2029 WITH 13770. >> BACK DEMODULATING HINT 2028 WITH 13770. >> BACK DEMODULATING HINT 2027 WITH 13770. >> BACK DEMODULATING HINT 2020 WITH 13770. >> BACK DEMODULATING HINT 2019 WITH 13770. >> BACK DEMODULATING HINT 2018 WITH 13770. >> BACK DEMODULATING HINT 2003 WITH 13770. >> BACK DEMODULATING HINT 2001 WITH 13770. >> BACK DEMODULATING HINT 1999 WITH 13770. >> BACK DEMODULATING HINT 1998 WITH 13770. >> BACK DEMODULATING HINT 1996 WITH 13770. >> BACK DEMODULATING HINT 1994 WITH 13770. >> BACK DEMODULATING HINT 1993 WITH 13770. >> BACK DEMODULATING HINT 1986 WITH 13770. NEW HINT: 17651 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(x),y)))=f(x,g(f(z,f(f(g(z),y),x)))). >> BACK DEMODULATING HINT 1984 WITH 13770. NEW HINT: 17652 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,z))),f(g(f(u,g(f(y,z)))),g(f(y,z)))))=g(f(y,f(z,u))). >> BACK DEMODULATING HINT 1978 WITH 13770. >> BACK DEMODULATING HINT 1971 WITH 13770. >> BACK DEMODULATING HINT 1967 WITH 13770. >> BACK DEMODULATING HINT 1965 WITH 13770. >> BACK DEMODULATING HINT 1964 WITH 13770. >> BACK DEMODULATING HINT 1963 WITH 13770. >> BACK DEMODULATING HINT 1961 WITH 13770. >> BACK DEMODULATING HINT 1960 WITH 13770. >> BACK DEMODULATING HINT 1959 WITH 13770. >> BACK DEMODULATING HINT 1958 WITH 13770. >> BACK DEMODULATING HINT 1957 WITH 13770. >> BACK DEMODULATING HINT 1955 WITH 13770. >> BACK DEMODULATING HINT 1954 WITH 13770. >> BACK DEMODULATING HINT 1951 WITH 13770. >> BACK DEMODULATING HINT 1948 WITH 13770. >> BACK DEMODULATING HINT 1945 WITH 13770. >> BACK DEMODULATING HINT 1944 WITH 13770. >> BACK DEMODULATING HINT 1942 WITH 13770. >> BACK DEMODULATING HINT 1941 WITH 13770. >> BACK DEMODULATING HINT 1940 WITH 13770. >> BACK DEMODULATING HINT 1936 WITH 13770. >> BACK DEMODULATING HINT 1935 WITH 13770. >> BACK DEMODULATING HINT 1934 WITH 13770. >> BACK DEMODULATING HINT 1933 WITH 13770. >> BACK DEMODULATING HINT 1932 WITH 13770. >> BACK DEMODULATING HINT 1913 WITH 13770. >> BACK DEMODULATING HINT 1912 WITH 13770. >> BACK DEMODULATING HINT 1905 WITH 13770. >> BACK DEMODULATING HINT 1897 WITH 13770. >> BACK DEMODULATING HINT 1892 WITH 13770. >> BACK DEMODULATING HINT 1890 WITH 13770. >> BACK DEMODULATING HINT 1889 WITH 13770. >> BACK DEMODULATING HINT 1887 WITH 13770. >> BACK DEMODULATING HINT 1886 WITH 13770. >> BACK DEMODULATING HINT 1885 WITH 13770. >> BACK DEMODULATING HINT 1884 WITH 13770. >> BACK DEMODULATING HINT 1883 WITH 13770. >> BACK DEMODULATING HINT 1881 WITH 13770. >> BACK DEMODULATING HINT 1880 WITH 13770. >> BACK DEMODULATING HINT 1878 WITH 13770. >> BACK DEMODULATING HINT 1875 WITH 13770. >> BACK DEMODULATING HINT 1874 WITH 13770. >> BACK DEMODULATING HINT 1872 WITH 13770. >> BACK DEMODULATING HINT 1871 WITH 13770. >> BACK DEMODULATING HINT 1870 WITH 13770. >> BACK DEMODULATING HINT 1869 WITH 13770. >> BACK DEMODULATING HINT 1868 WITH 13770. >> BACK DEMODULATING HINT 1867 WITH 13770. >> BACK DEMODULATING HINT 1863 WITH 13770. >> BACK DEMODULATING HINT 1862 WITH 13770. >> BACK DEMODULATING HINT 1843 WITH 13770. >> BACK DEMODULATING HINT 1818 WITH 13770. >> BACK DEMODULATING HINT 1815 WITH 13770. >> BACK DEMODULATING HINT 1814 WITH 13770. >> BACK DEMODULATING HINT 1812 WITH 13770. >> BACK DEMODULATING HINT 1811 WITH 13770. >> BACK DEMODULATING HINT 1810 WITH 13770. >> BACK DEMODULATING HINT 1808 WITH 13770. >> BACK DEMODULATING HINT 1806 WITH 13770. >> BACK DEMODULATING HINT 1804 WITH 13770. >> BACK DEMODULATING HINT 1801 WITH 13770. >> BACK DEMODULATING HINT 1797 WITH 13770. >> BACK DEMODULATING HINT 1795 WITH 13770. >> BACK DEMODULATING HINT 1792 WITH 13770. >> BACK DEMODULATING HINT 1790 WITH 13770. >> BACK DEMODULATING HINT 1787 WITH 13770. >> BACK DEMODULATING HINT 1786 WITH 13770. >> BACK DEMODULATING HINT 1785 WITH 13770. >> BACK DEMODULATING HINT 1783 WITH 13770. >> BACK DEMODULATING HINT 1782 WITH 13770. >> BACK DEMODULATING HINT 1781 WITH 13770. >> BACK DEMODULATING HINT 1778 WITH 13770. >> BACK DEMODULATING HINT 1775 WITH 13770. >> BACK DEMODULATING HINT 1774 WITH 13770. >> BACK DEMODULATING HINT 1773 WITH 13770. >> BACK DEMODULATING HINT 1772 WITH 13770. >> BACK DEMODULATING HINT 1771 WITH 13770. >> BACK DEMODULATING HINT 1770 WITH 13770. >> BACK DEMODULATING HINT 1769 WITH 13770. >> BACK DEMODULATING HINT 1768 WITH 13770. >> BACK DEMODULATING HINT 1755 WITH 13770. >> BACK DEMODULATING HINT 1754 WITH 13770. >> BACK DEMODULATING HINT 1753 WITH 13770. >> BACK DEMODULATING HINT 1740 WITH 13770. >> BACK DEMODULATING HINT 1736 WITH 13770. >> BACK DEMODULATING HINT 1727 WITH 13770. >> BACK DEMODULATING HINT 1726 WITH 13770. >> BACK DEMODULATING HINT 1712 WITH 13770. >> BACK DEMODULATING HINT 1711 WITH 13770. NEW HINT: 17653 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(x))),f(f(g(g(y)),f(g(y),g(z))),g(f(x,g(x)))))=g(f(x,f(g(x),z))). >> BACK DEMODULATING HINT 1707 WITH 13770. >> BACK DEMODULATING HINT 1706 WITH 13770. >> BACK DEMODULATING HINT 1705 WITH 13770. >> BACK DEMODULATING HINT 1692 WITH 13770. >> BACK DEMODULATING HINT 1687 WITH 13770. >> BACK DEMODULATING HINT 1684 WITH 13770. >> BACK DEMODULATING HINT 1673 WITH 13770. >> BACK DEMODULATING HINT 1672 WITH 13770. >> BACK DEMODULATING HINT 1659 WITH 13770. >> BACK DEMODULATING HINT 1653 WITH 13770. >> BACK DEMODULATING HINT 1651 WITH 13770. >> BACK DEMODULATING HINT 1647 WITH 13770. >> BACK DEMODULATING HINT 1646 WITH 13770. >> BACK DEMODULATING HINT 1637 WITH 13770. >> BACK DEMODULATING HINT 1633 WITH 13770. >> BACK DEMODULATING HINT 1632 WITH 13770. >> BACK DEMODULATING HINT 1631 WITH 13770. >> BACK DEMODULATING HINT 1629 WITH 13770. >> BACK DEMODULATING HINT 1628 WITH 13770. >> BACK DEMODULATING HINT 1627 WITH 13770. >> BACK DEMODULATING HINT 1626 WITH 13770. >> BACK DEMODULATING HINT 1625 WITH 13770. >> BACK DEMODULATING HINT 1624 WITH 13770. >> BACK DEMODULATING HINT 1622 WITH 13770. >> BACK DEMODULATING HINT 1621 WITH 13770. >> BACK DEMODULATING HINT 1619 WITH 13770. >> BACK DEMODULATING HINT 1567 WITH 13770. >> BACK DEMODULATING HINT 1556 WITH 13770. >> BACK DEMODULATING HINT 1525 WITH 13770. >> BACK DEMODULATING HINT 1524 WITH 13770. >> BACK DEMODULATING HINT 1523 WITH 13770. >> BACK DEMODULATING HINT 1506 WITH 13770. >> BACK DEMODULATING HINT 1499 WITH 13770. >> BACK DEMODULATING HINT 1496 WITH 13770. >> BACK DEMODULATING HINT 1489 WITH 13770. >> BACK DEMODULATING HINT 1488 WITH 13770. >> BACK DEMODULATING HINT 1483 WITH 13770. >> BACK DEMODULATING HINT 1482 WITH 13770. >> BACK DEMODULATING HINT 1478 WITH 13770. >> BACK DEMODULATING HINT 1474 WITH 13770. >> BACK DEMODULATING HINT 1473 WITH 13770. >> BACK DEMODULATING HINT 1472 WITH 13770. >> BACK DEMODULATING HINT 1471 WITH 13770. >> BACK DEMODULATING HINT 1470 WITH 13770. >> BACK DEMODULATING HINT 1469 WITH 13770. >> BACK DEMODULATING HINT 1468 WITH 13770. >> BACK DEMODULATING HINT 1465 WITH 13770. >> BACK DEMODULATING HINT 1464 WITH 13770. >> BACK DEMODULATING HINT 1463 WITH 13770. >> BACK DEMODULATING HINT 1462 WITH 13770. >> BACK DEMODULATING HINT 1458 WITH 13770. >> BACK DEMODULATING HINT 1457 WITH 13770. >> BACK DEMODULATING HINT 1456 WITH 13770. >> BACK DEMODULATING HINT 1455 WITH 13770. >> BACK DEMODULATING HINT 1453 WITH 13770. >> BACK DEMODULATING HINT 1450 WITH 13770. >> BACK DEMODULATING HINT 1449 WITH 13770. >> BACK DEMODULATING HINT 1448 WITH 13770. >> BACK DEMODULATING HINT 1443 WITH 13770. >> BACK DEMODULATING HINT 1442 WITH 13770. >> BACK DEMODULATING HINT 1435 WITH 13770. >> BACK DEMODULATING HINT 1432 WITH 13770. NEW HINT: 17654 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(y,f(f(g(f(x,y)),y),g(f(x,y))))))=x. >> BACK DEMODULATING HINT 1431 WITH 13770. NEW HINT: 17655 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),g(f(y,f(f(g(f(x,y)),y),g(f(x,y))))))=g(f(y,g(f(x,y)))). >> BACK DEMODULATING HINT 1412 WITH 13770. >> BACK DEMODULATING HINT 1403 WITH 13770. >> BACK DEMODULATING HINT 1402 WITH 13770. >> BACK DEMODULATING HINT 1401 WITH 13770. >> BACK DEMODULATING HINT 1400 WITH 13770. >> BACK DEMODULATING HINT 1399 WITH 13770. >> BACK DEMODULATING HINT 1383 WITH 13770. >> BACK DEMODULATING HINT 1382 WITH 13770. >> BACK DEMODULATING HINT 1375 WITH 13770. NEW HINT: 17656 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(y,y)),f(y,x))))),g(f(x,f(f(g(f(y,x)),x),g(f(y,x))))))=g(f(x,g(f(y,x)))). >> BACK DEMODULATING HINT 1374 WITH 13770. >> BACK DEMODULATING HINT 1336 WITH 13770. NEW HINT: 17657 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,g(f(x,g(x)))))=f(f(g(x),g(f(g(x),f(g(x),x)))),g(x)). >> BACK DEMODULATING HINT 1292 WITH 13770. >> BACK DEMODULATING HINT 1284 WITH 13770. >> BACK DEMODULATING HINT 1283 WITH 13770. >> BACK DEMODULATING HINT 1266 WITH 13770. >> BACK DEMODULATING HINT 1265 WITH 13770. >> BACK DEMODULATING HINT 1264 WITH 13770. >> BACK DEMODULATING HINT 1261 WITH 13770. NEW HINT: 17658 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(f(g(f(x,y)),x)),f(x,g(z))),z))=f(g(f(x,f(y,x))),g(f(g(f(x,f(y,x))),g(f(x,f(y,x)))))). >> BACK DEMODULATING HINT 1260 WITH 13770. >> BACK DEMODULATING HINT 1259 WITH 13770. >> BACK DEMODULATING HINT 1258 WITH 13770. >> BACK DEMODULATING HINT 1256 WITH 13770. >> BACK DEMODULATING HINT 1242 WITH 13770. >> BACK DEMODULATING HINT 1239 WITH 13770. >> BACK DEMODULATING HINT 1235 WITH 13770. >> BACK DEMODULATING HINT 1233 WITH 13770. >> BACK DEMODULATING HINT 1229 WITH 13770. >> BACK DEMODULATING HINT 1227 WITH 13770. >> BACK DEMODULATING HINT 1226 WITH 13770. >> BACK DEMODULATING HINT 1218 WITH 13770. >> BACK DEMODULATING HINT 1217 WITH 13770. >> BACK DEMODULATING HINT 1212 WITH 13770. >> BACK DEMODULATING HINT 1211 WITH 13770. >> BACK DEMODULATING HINT 1210 WITH 13770. >> BACK DEMODULATING HINT 1209 WITH 13770. >> BACK DEMODULATING HINT 1208 WITH 13770. >> BACK DEMODULATING HINT 1204 WITH 13770. >> BACK DEMODULATING HINT 1198 WITH 13770. >> BACK DEMODULATING HINT 1197 WITH 13770. >> BACK DEMODULATING HINT 1196 WITH 13770. >> BACK DEMODULATING HINT 1195 WITH 13770. >> BACK DEMODULATING HINT 1194 WITH 13770. >> BACK DEMODULATING HINT 1193 WITH 13770. >> BACK DEMODULATING HINT 1181 WITH 13770. >> BACK DEMODULATING HINT 1178 WITH 13770. >> BACK DEMODULATING HINT 1170 WITH 13770. >> BACK DEMODULATING HINT 1169 WITH 13770. >> BACK DEMODULATING HINT 1168 WITH 13770. >> BACK DEMODULATING HINT 1167 WITH 13770. >> BACK DEMODULATING HINT 1162 WITH 13770. >> BACK DEMODULATING HINT 1161 WITH 13770. >> BACK DEMODULATING HINT 1159 WITH 13770. >> BACK DEMODULATING HINT 1158 WITH 13770. >> BACK DEMODULATING HINT 1157 WITH 13770. >> BACK DEMODULATING HINT 1155 WITH 13770. >> BACK DEMODULATING HINT 1151 WITH 13770. >> BACK DEMODULATING HINT 1146 WITH 13770. >> BACK DEMODULATING HINT 1135 WITH 13770. >> BACK DEMODULATING HINT 1132 WITH 13770. >> BACK DEMODULATING HINT 1120 WITH 13770. >> BACK DEMODULATING HINT 1116 WITH 13770. >> BACK DEMODULATING HINT 1115 WITH 13770. >> BACK DEMODULATING HINT 1069 WITH 13770. >> BACK DEMODULATING HINT 1066 WITH 13770. >> BACK DEMODULATING HINT 1061 WITH 13770. >> BACK DEMODULATING HINT 1055 WITH 13770. >> BACK DEMODULATING HINT 1043 WITH 13770. >> BACK DEMODULATING HINT 1038 WITH 13770. >> BACK DEMODULATING HINT 1024 WITH 13770. >> BACK DEMODULATING HINT 1022 WITH 13770. >> BACK DEMODULATING HINT 1021 WITH 13770. >> BACK DEMODULATING HINT 1020 WITH 13770. >> BACK DEMODULATING HINT 1013 WITH 13770. >> BACK DEMODULATING HINT 1010 WITH 13770. >> BACK DEMODULATING HINT 1007 WITH 13770. >> BACK DEMODULATING HINT 1002 WITH 13770. >> BACK DEMODULATING HINT 999 WITH 13770. >> BACK DEMODULATING HINT 995 WITH 13770. >> BACK DEMODULATING HINT 993 WITH 13770. >> BACK DEMODULATING HINT 992 WITH 13770. >> BACK DEMODULATING HINT 991 WITH 13770. >> BACK DEMODULATING HINT 984 WITH 13770. >> BACK DEMODULATING HINT 983 WITH 13770. >> BACK DEMODULATING HINT 982 WITH 13770. >> BACK DEMODULATING HINT 981 WITH 13770. >> BACK DEMODULATING HINT 980 WITH 13770. >> BACK DEMODULATING HINT 971 WITH 13770. >> BACK DEMODULATING HINT 964 WITH 13770. >> BACK DEMODULATING HINT 963 WITH 13770. >> BACK DEMODULATING HINT 961 WITH 13770. >> BACK DEMODULATING HINT 957 WITH 13770. >> BACK DEMODULATING HINT 956 WITH 13770. >> BACK DEMODULATING HINT 954 WITH 13770. >> BACK DEMODULATING HINT 953 WITH 13770. >> BACK DEMODULATING HINT 952 WITH 13770. >> BACK DEMODULATING HINT 950 WITH 13770. >> BACK DEMODULATING HINT 935 WITH 13770. >> BACK DEMODULATING HINT 934 WITH 13770. >> BACK DEMODULATING HINT 933 WITH 13770. >> BACK DEMODULATING HINT 910 WITH 13770. >> BACK DEMODULATING HINT 907 WITH 13770. NEW HINT: 17659 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,g(f(f(x,g(f(x,x))),x))))=g(x). >> BACK DEMODULATING HINT 900 WITH 13770. >> BACK DEMODULATING HINT 889 WITH 13770. >> BACK DEMODULATING HINT 880 WITH 13770. >> BACK DEMODULATING HINT 853 WITH 13770. >> BACK DEMODULATING HINT 852 WITH 13770. >> BACK DEMODULATING HINT 851 WITH 13770. >> BACK DEMODULATING HINT 841 WITH 13770. >> BACK DEMODULATING HINT 840 WITH 13770. >> BACK DEMODULATING HINT 839 WITH 13770. >> BACK DEMODULATING HINT 836 WITH 13770. >> BACK DEMODULATING HINT 835 WITH 13770. >> BACK DEMODULATING HINT 834 WITH 13770. >> BACK DEMODULATING HINT 829 WITH 13770. >> BACK DEMODULATING HINT 823 WITH 13770. >> BACK DEMODULATING HINT 822 WITH 13770. >> BACK DEMODULATING HINT 818 WITH 13770. >> BACK DEMODULATING HINT 817 WITH 13770. >> BACK DEMODULATING HINT 814 WITH 13770. >> BACK DEMODULATING HINT 813 WITH 13770. >> BACK DEMODULATING HINT 812 WITH 13770. >> BACK DEMODULATING HINT 811 WITH 13770. >> BACK DEMODULATING HINT 808 WITH 13770. >> BACK DEMODULATING HINT 803 WITH 13770. >> BACK DEMODULATING HINT 802 WITH 13770. >> BACK DEMODULATING HINT 801 WITH 13770. >> BACK DEMODULATING HINT 789 WITH 13770. >> BACK DEMODULATING HINT 786 WITH 13770. >> BACK DEMODULATING HINT 778 WITH 13770. >> BACK DEMODULATING HINT 777 WITH 13770. >> BACK DEMODULATING HINT 776 WITH 13770. >> BACK DEMODULATING HINT 775 WITH 13770. >> BACK DEMODULATING HINT 767 WITH 13770. >> BACK DEMODULATING HINT 766 WITH 13770. >> BACK DEMODULATING HINT 765 WITH 13770. >> BACK DEMODULATING HINT 763 WITH 13770. >> BACK DEMODULATING HINT 762 WITH 13770. >> BACK DEMODULATING HINT 760 WITH 13770. >> BACK DEMODULATING HINT 753 WITH 13770. NEW HINT: 17660 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,z)))=f(g(z),g(f(x,y))) # label(bd). >> BACK DEMODULATING HINT 736 WITH 13770. >> BACK DEMODULATING HINT 638 WITH 13770. >> BACK DEMODULATING HINT 636 WITH 13770. >> BACK DEMODULATING HINT 635 WITH 13770. >> BACK DEMODULATING HINT 634 WITH 13770. >> BACK DEMODULATING HINT 633 WITH 13770. >> BACK DEMODULATING HINT 627 WITH 13770. >> BACK DEMODULATING HINT 624 WITH 13770. >> BACK DEMODULATING HINT 623 WITH 13770. >> BACK DEMODULATING HINT 620 WITH 13770. >> BACK DEMODULATING HINT 617 WITH 13770. >> BACK DEMODULATING HINT 615 WITH 13770. NEW HINT: 17661 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,f(y,g(f(x,y))))),f(g(x),x))=f(g(f(x,x)),f(x,x)) # label(bd). >> BACK DEMODULATING HINT 610 WITH 13770. >> BACK DEMODULATING HINT 607 WITH 13770. >> BACK DEMODULATING HINT 594 WITH 13770. >> BACK DEMODULATING HINT 588 WITH 13770. >> BACK DEMODULATING HINT 587 WITH 13770. >> BACK DEMODULATING HINT 585 WITH 13770. >> BACK DEMODULATING HINT 584 WITH 13770. >> BACK DEMODULATING HINT 583 WITH 13770. >> BACK DEMODULATING HINT 578 WITH 13770. >> BACK DEMODULATING HINT 576 WITH 13770. >> BACK DEMODULATING HINT 575 WITH 13770. >> BACK DEMODULATING HINT 574 WITH 13770. >> BACK DEMODULATING HINT 573 WITH 13770. >> BACK DEMODULATING HINT 572 WITH 13770. >> BACK DEMODULATING HINT 570 WITH 13770. >> BACK DEMODULATING HINT 556 WITH 13770. >> BACK DEMODULATING HINT 554 WITH 13770. >> BACK DEMODULATING HINT 481 WITH 13770. >> BACK DEMODULATING HINT 478 WITH 13770. >> BACK DEMODULATING HINT 472 WITH 13770. >> BACK DEMODULATING HINT 466 WITH 13770. >> BACK DEMODULATING HINT 445 WITH 13770. >> BACK DEMODULATING HINT 444 WITH 13770. >> BACK DEMODULATING HINT 440 WITH 13770. >> BACK DEMODULATING HINT 438 WITH 13770. >> BACK DEMODULATING HINT 436 WITH 13770. >> BACK DEMODULATING HINT 434 WITH 13770. >> BACK DEMODULATING HINT 431 WITH 13770. >> BACK DEMODULATING HINT 420 WITH 13770. >> BACK DEMODULATING HINT 411 WITH 13770. >> BACK DEMODULATING HINT 409 WITH 13770. >> BACK DEMODULATING HINT 408 WITH 13770. >> BACK DEMODULATING HINT 406 WITH 13770. >> BACK DEMODULATING HINT 405 WITH 13770. >> BACK DEMODULATING HINT 404 WITH 13770. >> BACK DEMODULATING HINT 400 WITH 13770. >> BACK DEMODULATING HINT 398 WITH 13770. >> BACK DEMODULATING HINT 397 WITH 13770. >> BACK DEMODULATING HINT 396 WITH 13770. >> BACK DEMODULATING HINT 395 WITH 13770. >> BACK DEMODULATING HINT 394 WITH 13770. >> BACK DEMODULATING HINT 392 WITH 13770. >> BACK DEMODULATING HINT 384 WITH 13770. >> BACK DEMODULATING HINT 355 WITH 13770. >> BACK DEMODULATING HINT 352 WITH 13770. >> BACK DEMODULATING HINT 344 WITH 13770. NEW HINT: 17662 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(f(y,z)),u)),f(u,g(f(u,u))))=g(f(y,f(z,g(x)))) # label(bd). >> BACK DEMODULATING HINT 339 WITH 13770. >> BACK DEMODULATING HINT 333 WITH 13770. >> BACK DEMODULATING HINT 331 WITH 13770. >> BACK DEMODULATING HINT 325 WITH 13770. >> BACK DEMODULATING HINT 307 WITH 13770. >> BACK DEMODULATING HINT 305 WITH 13770. >> BACK DEMODULATING HINT 304 WITH 13770. >> BACK DEMODULATING HINT 303 WITH 13770. >> BACK DEMODULATING HINT 299 WITH 13770. >> BACK DEMODULATING HINT 297 WITH 13770. >> BACK DEMODULATING HINT 296 WITH 13770. >> BACK DEMODULATING HINT 295 WITH 13770. >> BACK DEMODULATING HINT 294 WITH 13770. NEW HINT: 17663 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(g(y),z),g(f(z,f(g(f(f(y,u),z)),z))))))=g(f(x,u)) # label(bd). >> BACK DEMODULATING HINT 293 WITH 13770. >> BACK DEMODULATING HINT 292 WITH 13770. >> BACK DEMODULATING HINT 289 WITH 13770. >> BACK DEMODULATING HINT 274 WITH 13770. >> BACK DEMODULATING HINT 272 WITH 13770. >> BACK DEMODULATING HINT 270 WITH 13770. >> BACK DEMODULATING HINT 268 WITH 13770. >> BACK DEMODULATING HINT 265 WITH 13770. >> BACK DEMODULATING HINT 218 WITH 13770. >> BACK DEMODULATING HINT 212 WITH 13770. >> BACK DEMODULATING HINT 207 WITH 13770. >> BACK DEMODULATING HINT 206 WITH 13770. >> BACK DEMODULATING HINT 205 WITH 13770. NEW HINT: 17664 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),f(f(g(f(z,g(z))),f(g(f(x,y)),g(u))),u))=g(f(x,f(y,f(g(f(z,g(f(x,y)))),z)))) # label(bd). >> BACK DEMODULATING HINT 200 WITH 13770. NEW HINT: 17665 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(g(x),x)))=f(x,g(f(x,x))) # label(bd). >> BACK DEMODULATING HINT 193 WITH 13770. >> BACK DEMODULATING HINT 187 WITH 13770. >> BACK DEMODULATING HINT 186 WITH 13770. >> BACK DEMODULATING HINT 180 WITH 13770. >> BACK DEMODULATING HINT 140 WITH 13770. >> BACK DEMODULATING HINT 139 WITH 13770. >> BACK DEMODULATING HINT 118 WITH 13770. >> BACK DEMODULATING HINT 113 WITH 13770. >> BACK DEMODULATING HINT 106 WITH 13770. >> BACK DEMODULATING HINT 105 WITH 13770. >> BACK DEMODULATING HINT 92 WITH 13770. >> BACK DEMODULATING HINT 64 WITH 13770. >> BACK DEMODULATING HINT 58 WITH 13770. >> BACK DEMODULATING HINT 54 WITH 13770. >> BACK DEMODULATING HINT 53 WITH 13770. >> BACK DEMODULATING HINT 51 WITH 13770. >> BACK DEMODULATING HINT 42 WITH 13770. >> BACK DEMODULATING HINT 33 WITH 13770. >> BACK DEMODULATING HINT 32 WITH 13770. >> BACK DEMODULATING HINT 30 WITH 13770. NEW HINT: 17666 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,g(f(f(y,f(x,g(z))),z))))=y # label(bd). >> BACK DEMODULATING HINT 29 WITH 13770. >> BACK DEMODULATING HINT 10 WITH 13770. >> BACK DEMODULATING HINT 13324 WITH 13945. >> BACK DEMODULATING HINT 874 WITH 13945. >> BACK DEMODULATING HINT 4159 WITH 15210. NEW HINT: 18071 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(y),g(g(y))),g(z))),g(f(x,y)))=f(f(y,f(g(f(x,y)),g(z))),g(f(x,y))). >> BACK DEMODULATING HINT 4082 WITH 15210. NEW HINT: 18072 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(g(x)),g(g(g(x)))),g(y))),g(f(x,g(x))))=g(f(z,f(f(g(z),y),x))). >> BACK DEMODULATING HINT 4070 WITH 15210. NEW HINT: 18073 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(y),g(g(y))),g(z))),g(f(x,y)))=g(f(x,f(f(y,z),x))). >> BACK DEMODULATING HINT 4068 WITH 15210. NEW HINT: 18074 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(y,z),x)))=f(f(g(x),f(f(g(y),g(g(y))),g(z))),g(f(x,y))). >> BACK DEMODULATING HINT 1840 WITH 16656. NEW HINT: 18080 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(f(f(g(f(y,x)),y),x))),f(g(x),f(g(f(y,g(f(z,g(f(u,z)))))),y)))=g(f(u,f(v,f(g(f(y,v)),y)))). >> BACK DEMODULATING HINT 16850 WITH 17568. >> BACK DEMODULATING HINT 16890 WITH 17586. >> BACK DEMODULATING HINT 13278 WITH 17586. >> BACK DEMODULATING HINT 17592 WITH 17748. >> BACK DEMODULATING HINT 16723 WITH 17748. NEW HINT: 18161 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(f(g(g(y)),g(x)))),g(f(g(x),f(f(g(f(y,g(x))),g(x)),g(f(y,g(x)))))))=y. >> BACK DEMODULATING HINT 16721 WITH 17748. NEW HINT: 18162 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(f(g(g(y)),g(x)))),g(f(g(g(g(y))),f(g(x),g(f(g(g(y)),g(x)))))))=y. >> BACK DEMODULATING HINT 14136 WITH 17748. NEW HINT: 18163 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(f(g(g(y)),g(x)))),f(f(g(g(y)),g(g(g(x)))),f(g(g(x)),f(g(x),g(f(g(g(g(y))),g(x)))))))=y. >> BACK DEMODULATING HINT 13304 WITH 17748. >> BACK DEMODULATING HINT 13290 WITH 17748. >> BACK DEMODULATING HINT 13289 WITH 17748. >> BACK DEMODULATING HINT 4753 WITH 17748. NEW HINT: 18164 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),g(z)))=g(f(z,f(z,g(f(g(g(y)),z))))). >> BACK DEMODULATING HINT 4451 WITH 17748. >> BACK DEMODULATING HINT 3024 WITH 17748. >> BACK DEMODULATING HINT 2519 WITH 17748. NEW HINT: 18165 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,y)),f(f(g(g(x)),f(y,g(f(g(g(x)),y)))),g(f(x,f(y,g(f(x,f(y,g(f(x,y))))))))))),f(g(f(x,f(y,g(f(x,f(y,g(f(x,y)))))))),g(y)))=x. >> BACK DEMODULATING HINT 1594 WITH 17748. >> BACK DEMODULATING HINT 1437 WITH 17748. >> BACK DEMODULATING HINT 1361 WITH 17748. >> BACK DEMODULATING HINT 17658 WITH 18061. NEW HINT: 18268 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(x,g(z))),z))=f(g(f(x,f(y,x))),g(f(g(f(x,f(y,x))),g(f(x,f(y,x)))))). >> BACK DEMODULATING HINT 17650 WITH 18061. >> BACK DEMODULATING HINT 17625 WITH 18061. NEW HINT: 18269 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(x,y)),f(z,f(g(v),v))))=f(y,f(f(g(y),f(g(z),x)),y)). >> BACK DEMODULATING HINT 17624 WITH 18061. >> BACK DEMODULATING HINT 17620 WITH 18061. >> BACK DEMODULATING HINT 17594 WITH 18061. NEW HINT: 18270 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,x)))=f(g(f(y,x)),y). >> BACK DEMODULATING HINT 17593 WITH 18061. >> BACK DEMODULATING HINT 17590 WITH 18061. >> BACK DEMODULATING HINT 17589 WITH 18061. >> BACK DEMODULATING HINT 17587 WITH 18061. >> BACK DEMODULATING HINT 16891 WITH 18061. NEW HINT: 18271 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,x)),f(x,f(g(f(g(f(g(z),z)),f(u,v))),g(f(g(f(g(f(w,u)),f(w,f(g(f(w,u)),w)))),f(f(g(f(w,u)),w),f(g(f(w,u)),w)))))))),g(f(g(f(x,x)),f(x,x))))=f(u,f(g(g(v)),g(g(x)))). >> BACK DEMODULATING HINT 16887 WITH 18061. NEW HINT: 18272 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(f(x,x)),f(x,f(g(f(g(f(g(z),z)),f(u,v))),g(f(g(w),w)))))),g(f(g(f(x,x)),f(x,x))))=f(u,f(g(g(v)),g(g(x)))). >> BACK DEMODULATING HINT 16883 WITH 18061. NEW HINT: 18273 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(g(f(g(z),z)),f(u,v))),g(f(g(w),w))))),g(f(g(f(x,x)),f(x,x))))=f(u,f(g(g(v)),g(g(x)))). >> BACK DEMODULATING HINT 16882 WITH 18061. >> BACK DEMODULATING HINT 16881 WITH 18061. NEW HINT: 18274 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(g(f(y,f(f(g(y),g(z)),z))),f(u,v))),g(f(g(w),w))))),g(f(g(f(x,x)),f(x,x))))=f(u,f(g(g(v)),g(g(x)))). >> BACK DEMODULATING HINT 16880 WITH 18061. NEW HINT: 18275 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(g(f(y,g(y))),f(z,u))),g(f(g(v),v))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(u)),g(g(x)))). >> BACK DEMODULATING HINT 16879 WITH 18061. NEW HINT: 18276 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(g(g(y)),f(g(y),f(z,u)))),g(f(g(v),v))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(u)),g(g(x)))). >> BACK DEMODULATING HINT 16878 WITH 18061. NEW HINT: 18277 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(f(z,u)),g(f(g(v),v))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(u)),g(g(x)))). >> BACK DEMODULATING HINT 16877 WITH 18061. >> BACK DEMODULATING HINT 16876 WITH 18061. NEW HINT: 18278 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),g(f(g(u),u))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(y)),g(g(x)))). >> BACK DEMODULATING HINT 16875 WITH 18061. NEW HINT: 18279 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,f(f(g(z),g(u)),u)))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(y)),g(g(x)))). >> BACK DEMODULATING HINT 16874 WITH 18061. NEW HINT: 18280 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),g(f(z,g(z)))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(y)),g(g(x)))). >> BACK DEMODULATING HINT 16873 WITH 18061. NEW HINT: 18281 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(f(g(y),g(z)),f(g(g(z)),g(z))))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(y)),g(g(x)))). >> BACK DEMODULATING HINT 16872 WITH 18061. NEW HINT: 18282 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(x),f(g(y),g(z)))),g(f(g(f(x,x)),f(x,x))))=f(z,f(g(g(y)),g(g(x)))). >> BACK DEMODULATING HINT 16871 WITH 18061. NEW HINT: 18283 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(g(x),g(y))),g(g(z))),g(f(g(f(z,z)),f(z,z))))=f(y,f(g(g(x)),g(g(z)))). >> BACK DEMODULATING HINT 16870 WITH 18061. NEW HINT: 18284 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(g(x)),f(g(g(y)),g(g(z)))),g(f(g(f(z,z)),f(z,z))))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 16869 WITH 18061. NEW HINT: 18285 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,g(g(y))),g(g(z))),g(f(g(f(z,z)),f(z,z))))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 16868 WITH 18061. NEW HINT: 18286 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),g(g(z))),g(f(g(f(z,z)),f(z,z))))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 16867 WITH 18061. NEW HINT: 18287 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),g(f(g(f(z,z)),f(z,z))))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 16866 WITH 18061. NEW HINT: 18288 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),g(f(g(z),z)))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 16865 WITH 18061. >> BACK DEMODULATING HINT 16864 WITH 18061. NEW HINT: 18289 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(g(z),z))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 16863 WITH 18061. >> BACK DEMODULATING HINT 13232 WITH 18061. >> BACK DEMODULATING HINT 13231 WITH 18061. >> BACK DEMODULATING HINT 4260 WITH 18061. >> BACK DEMODULATING HINT 4258 WITH 18061. NEW HINT: 18290 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(z),g(f(u,g(u)))),x))=f(g(z),x). >> BACK DEMODULATING HINT 4257 WITH 18061. NEW HINT: 18291 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(f(z,g(z)))),u),f(g(u),u))=f(g(y),u). >> BACK DEMODULATING HINT 4234 WITH 18061. >> BACK DEMODULATING HINT 4184 WITH 18061. >> BACK DEMODULATING HINT 3947 WITH 18061. >> BACK DEMODULATING HINT 3946 WITH 18061. >> BACK DEMODULATING HINT 3945 WITH 18061. NEW HINT: 18292 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(z,f(f(g(z),g(z)),z)))=f(x,f(g(g(y)),g(g(z)))). >> BACK DEMODULATING HINT 3944 WITH 18061. >> BACK DEMODULATING HINT 3943 WITH 18061. >> BACK DEMODULATING HINT 3942 WITH 18061. >> BACK DEMODULATING HINT 3941 WITH 18061. >> BACK DEMODULATING HINT 3940 WITH 18061. >> BACK DEMODULATING HINT 3939 WITH 18061. >> BACK DEMODULATING HINT 3938 WITH 18061. >> BACK DEMODULATING HINT 3937 WITH 18061. >> BACK DEMODULATING HINT 3936 WITH 18061. >> BACK DEMODULATING HINT 3935 WITH 18061. >> BACK DEMODULATING HINT 3934 WITH 18061. >> BACK DEMODULATING HINT 3933 WITH 18061. >> BACK DEMODULATING HINT 3932 WITH 18061. >> BACK DEMODULATING HINT 3931 WITH 18061. >> BACK DEMODULATING HINT 3930 WITH 18061. >> BACK DEMODULATING HINT 3929 WITH 18061. >> BACK DEMODULATING HINT 3928 WITH 18061. >> BACK DEMODULATING HINT 3927 WITH 18061. >> BACK DEMODULATING HINT 3926 WITH 18061. >> BACK DEMODULATING HINT 3925 WITH 18061. >> BACK DEMODULATING HINT 3831 WITH 18061. NEW HINT: 18293 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(f(v,x)),u),g(f(g(f(v,x)),f(u,f(f(g(v6),v6),f(g(f(v,x)),u))))))=f(x,f(f(g(x),f(g(u),v)),x)). >> BACK DEMODULATING HINT 3773 WITH 18061. NEW HINT: 18294 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(x),g(f(g(u),v))))=f(g(f(w,g(f(g(f(v,f(g(v7),v7))),u)))),w). >> BACK DEMODULATING HINT 3772 WITH 18061. >> BACK DEMODULATING HINT 3771 WITH 18061. NEW HINT: 18295 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(x),g(f(g(z),f(z,f(g(w),v6))))))=f(g(f(z,g(f(g(f(v6,f(g(v8),v8))),w)))),z). >> BACK DEMODULATING HINT 3770 WITH 18061. >> BACK DEMODULATING HINT 3731 WITH 18061. >> BACK DEMODULATING HINT 3730 WITH 18061. NEW HINT: 18296 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(x))),y)=f(z,f(g(z),g(f(g(v),f(v,g(y)))))). >> BACK DEMODULATING HINT 3729 WITH 18061. >> BACK DEMODULATING HINT 3728 WITH 18061. NEW HINT: 18297 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(x))),y)=f(z,f(g(f(g(v),f(v,z))),g(f(g(v),f(v,g(y)))))). >> BACK DEMODULATING HINT 3727 WITH 18061. NEW HINT: 18298 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(g(x)),f(x,f(f(g(x),g(x)),x))),g(x)),g(g(y)))=f(z,f(g(f(g(v),f(v,z))),g(f(g(v),f(v,g(y)))))). >> BACK DEMODULATING HINT 3726 WITH 18061. NEW HINT: 18299 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(y,g(y))),z)))),x)=f(u,f(g(f(g(x),f(x,u))),g(f(g(x),f(x,g(z)))))). >> BACK DEMODULATING HINT 3725 WITH 18061. NEW HINT: 18300 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(y,g(y))),g(g(z)))))),x)=f(u,f(g(f(g(x),f(x,u))),g(f(g(x),f(x,g(z)))))). >> BACK DEMODULATING HINT 3724 WITH 18061. >> BACK DEMODULATING HINT 3723 WITH 18061. >> BACK DEMODULATING HINT 3722 WITH 18061. >> BACK DEMODULATING HINT 3721 WITH 18061. NEW HINT: 18301 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(y,g(y))),g(f(g(u),f(u,g(f(g(w),f(w,v6)))))))))),x)=f(v7,f(g(f(g(x),f(x,v7))),g(f(g(x),f(x,g(v6)))))). >> BACK DEMODULATING HINT 3720 WITH 18061. >> BACK DEMODULATING HINT 3719 WITH 18061. NEW HINT: 18302 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(g(u),u)),g(f(g(w),f(w,g(f(g(v7),f(v7,v8)))))))))),x)=f(v9,f(g(f(g(x),f(x,v9))),g(f(g(x),f(x,g(v8)))))). >> BACK DEMODULATING HINT 3687 WITH 18061. >> BACK DEMODULATING HINT 3679 WITH 18061. NEW HINT: 18303 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,g(f(g(f(g(z),f(z,f(g(v),v)))),g(f(g(z),f(z,g(f(g(v7),f(v7,v8)))))))))),x)=f(v9,f(g(f(g(x),f(x,v9))),g(f(g(x),f(x,g(v8)))))). >> BACK DEMODULATING HINT 3671 WITH 18061. NEW HINT: 18304 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(g(z),f(z,x))),g(f(g(z),f(z,f(g(v6),v7))))))=f(g(f(z,g(f(g(f(v7,f(g(v9),v9))),v6)))),z). >> BACK DEMODULATING HINT 3670 WITH 18061. NEW HINT: 18305 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(f(g(z),f(z,x))),g(f(g(z),f(z,g(w))))))=f(g(f(z,g(f(g(f(g(v),f(v,f(g(v8),v8)))),g(f(g(v),f(v,g(f(g(v11),f(v11,w)))))))))),z). >> BACK DEMODULATING HINT 3669 WITH 18061. >> BACK DEMODULATING HINT 3651 WITH 18061. >> BACK DEMODULATING HINT 3644 WITH 18061. >> BACK DEMODULATING HINT 1144 WITH 18061. >> BACK DEMODULATING HINT 913 WITH 18061. >> BACK DEMODULATING HINT 912 WITH 18061. >> BACK DEMODULATING HINT 582 WITH 18061. NEW HINT: 18306 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(x)),x))=f(x,g(x)) # label(bd). >> BACK DEMODULATING HINT 387 WITH 18061. >> BACK DEMODULATING HINT 384 WITH 18061. >> BACK DEMODULATING HINT 364 WITH 18061. >> BACK DEMODULATING HINT 322 WITH 18061. >> BACK DEMODULATING HINT 256 WITH 18061. >> BACK DEMODULATING HINT 13246 WITH 18068. >> BACK DEMODULATING HINT 4854 WITH 18068. NEW HINT: 18377 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(z,g(f(g(f(g(y),g(g(u)))),z))))=f(x,u). >> BACK DEMODULATING HINT 4691 WITH 18068. NEW HINT: 18378 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(g(f(g(u),f(g(y),x))),g(u)))),v)))),f(x,g(f(g(g(y)),x)))),f(v,w))=f(g(x),w). >> BACK DEMODULATING HINT 4648 WITH 18068. NEW HINT: 18379 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),g(f(g(f(x,f(g(f(g(u),f(g(y),x))),g(u)))),g(v))))),f(x,g(f(g(g(y)),x)))))=v. >> BACK DEMODULATING HINT 4440 WITH 18068. NEW HINT: 18380 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),g(f(g(f(z,f(g(f(g(u),f(g(v),z))),g(u)))),f(g(g(v)),g(g(z)))))))=f(g(y),g(z)). >> BACK DEMODULATING HINT 3401 WITH 18068. NEW HINT: 18381 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(g(g(y))),g(g(z)))),f(g(g(u)),g(f(g(g(g(v))),g(g(v))))))=g(f(g(f(y,u)),z)). >> BACK DEMODULATING HINT 3381 WITH 18068. NEW HINT: 18382 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(g(g(g(y))),f(g(g(y)),g(f(g(g(g(z))),g(g(z))))))),f(g(g(u)),g(f(g(g(g(v))),g(g(v))))))=u. >> BACK DEMODULATING HINT 3342 WITH 18068. NEW HINT: 18383 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(f(x,y)),g(f(g(f(g(u),f(u,f(f(x,x),y)))),x)))=f(g(v),v). >> BACK DEMODULATING HINT 3341 WITH 18068. NEW HINT: 18384 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(g(y),f(y,f(f(z,z),u)))),z))=f(z,u). >> BACK DEMODULATING HINT 2824 WITH 18068. >> BACK DEMODULATING HINT 2797 WITH 18068. >> BACK DEMODULATING HINT 2677 WITH 18068. NEW HINT: 18385 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(f(g(y),z)),f(u,g(f(g(v),v)))))=f(g(f(y,u)),z) # label(bd). >> BACK DEMODULATING HINT 2668 WITH 18068. >> BACK DEMODULATING HINT 2600 WITH 18068. NEW HINT: 18386 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(g(g(z))),f(g(g(z)),g(g(u)))),v)=f(f(g(g(u)),f(g(g(g(v6))),g(g(v6)))),v) # label(bd). >> BACK DEMODULATING HINT 2598 WITH 18068. >> BACK DEMODULATING HINT 2290 WITH 18068. >> BACK DEMODULATING HINT 2066 WITH 18068. >> BACK DEMODULATING HINT 1921 WITH 18068. NEW HINT: 18387 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(g(g(z))),g(g(z))),f(g(f(u,f(g(f(z,y)),z))),u))=y. >> BACK DEMODULATING HINT 1831 WITH 18068. >> BACK DEMODULATING HINT 18074 WITH 18084. NEW HINT: 18487 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(y,z),x)))=f(f(g(x),f(f(g(y),y),g(z))),g(f(x,y))). >> BACK DEMODULATING HINT 18073 WITH 18084. >> BACK DEMODULATING HINT 18072 WITH 18084. NEW HINT: 18488 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),g(f(x,g(x))))=g(f(z,f(f(g(z),y),x))). >> BACK DEMODULATING HINT 18071 WITH 18084. NEW HINT: 18489 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(y),y),g(z))),g(f(x,y)))=f(f(g(x),g(z)),g(f(x,y))). >> BACK DEMODULATING HINT 17650 WITH 18084. NEW HINT: 18490 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(y),f(g(z),z)))=g(f(g(y),f(g(x),x))). >> BACK DEMODULATING HINT 17589 WITH 18084. >> BACK DEMODULATING HINT 17000 WITH 18084. >> BACK DEMODULATING HINT 16997 WITH 18084. >> BACK DEMODULATING HINT 16985 WITH 18084. >> BACK DEMODULATING HINT 16972 WITH 18084. >> BACK DEMODULATING HINT 16968 WITH 18084. NEW HINT: 18491 [bsub_wt=2147483647, bsub_add_wt=-1024] f(y,f(g(x),g(f(z,g(f(x,f(v,z)))))))=f(y,v). >> BACK DEMODULATING HINT 16965 WITH 18084. >> BACK DEMODULATING HINT 16964 WITH 18084. >> BACK DEMODULATING HINT 16885 WITH 18084. >> BACK DEMODULATING HINT 16884 WITH 18084. >> BACK DEMODULATING HINT 16878 WITH 18084. NEW HINT: 18492 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(v),v),f(z,f(u,f(x,g(f(g(x),f(f(g(x),x),x)))))))=f(z,f(u,x)). >> BACK DEMODULATING HINT 16725 WITH 18084. NEW HINT: 18493 [bsub_wt=2147483647, bsub_add_wt=-1024] f(y,f(z,f(g(x),x)))=f(y,z). >> BACK DEMODULATING HINT 16724 WITH 18084. >> BACK DEMODULATING HINT 16722 WITH 18084. >> BACK DEMODULATING HINT 16720 WITH 18084. NEW HINT: 18494 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(g(x),x))=f(g(y),g(f(y,g(y)))). >> BACK DEMODULATING HINT 16719 WITH 18084. >> BACK DEMODULATING HINT 13335 WITH 18084. NEW HINT: 18495 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(x,f(f(x,g(z)),z))))=g(x) # label(bd). >> BACK DEMODULATING HINT 13319 WITH 18084. >> BACK DEMODULATING HINT 13315 WITH 18084. >> BACK DEMODULATING HINT 13307 WITH 18084. >> BACK DEMODULATING HINT 13306 WITH 18084. >> BACK DEMODULATING HINT 13305 WITH 18084. >> BACK DEMODULATING HINT 13303 WITH 18084. >> BACK DEMODULATING HINT 13297 WITH 18084. >> BACK DEMODULATING HINT 13291 WITH 18084. >> BACK DEMODULATING HINT 13281 WITH 18084. >> BACK DEMODULATING HINT 13280 WITH 18084. >> BACK DEMODULATING HINT 13279 WITH 18084. >> BACK DEMODULATING HINT 13278 WITH 18084. >> BACK DEMODULATING HINT 13277 WITH 18084. >> BACK DEMODULATING HINT 13276 WITH 18084. >> BACK DEMODULATING HINT 13275 WITH 18084. >> BACK DEMODULATING HINT 13274 WITH 18084. >> BACK DEMODULATING HINT 13270 WITH 18084. >> BACK DEMODULATING HINT 13269 WITH 18084. >> BACK DEMODULATING HINT 13268 WITH 18084. >> BACK DEMODULATING HINT 13263 WITH 18084. >> BACK DEMODULATING HINT 13262 WITH 18084. >> BACK DEMODULATING HINT 13261 WITH 18084. >> BACK DEMODULATING HINT 13260 WITH 18084. >> BACK DEMODULATING HINT 13259 WITH 18084. >> BACK DEMODULATING HINT 13257 WITH 18084. >> BACK DEMODULATING HINT 13256 WITH 18084. >> BACK DEMODULATING HINT 13255 WITH 18084. >> BACK DEMODULATING HINT 13253 WITH 18084. >> BACK DEMODULATING HINT 13252 WITH 18084. >> BACK DEMODULATING HINT 13251 WITH 18084. >> BACK DEMODULATING HINT 13250 WITH 18084. >> BACK DEMODULATING HINT 13245 WITH 18084. NEW HINT: 18496 [bsub_wt=2147483647, bsub_add_wt=-1024] f(u,g(f(g(y),f(x,u))))=f(g(x),y). >> BACK DEMODULATING HINT 13237 WITH 18084. >> BACK DEMODULATING HINT 13233 WITH 18084. >> BACK DEMODULATING HINT 13229 WITH 18084. NEW HINT: 18497 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(u,g(f(y,g(y)))))=f(g(u),g(f(y,g(y)))). >> BACK DEMODULATING HINT 13228 WITH 18084. >> BACK DEMODULATING HINT 13227 WITH 18084. >> BACK DEMODULATING HINT 4783 WITH 18084. >> BACK DEMODULATING HINT 4564 WITH 18084. >> BACK DEMODULATING HINT 4540 WITH 18084. >> BACK DEMODULATING HINT 4539 WITH 18084. >> BACK DEMODULATING HINT 4538 WITH 18084. >> BACK DEMODULATING HINT 4537 WITH 18084. NEW HINT: 18498 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,f(f(f(z,f(f(g(z),g(y)),u)),g(u)),g(v))))),g(f(x,g(x)))))=v. >> BACK DEMODULATING HINT 4536 WITH 18084. >> BACK DEMODULATING HINT 4535 WITH 18084. NEW HINT: 18499 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,f(f(f(g(y),u),g(u)),g(v))))),g(f(x,g(x)))))=v. >> BACK DEMODULATING HINT 4534 WITH 18084. NEW HINT: 18500 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,f(f(f(z,g(f(g(u),f(y,z)))),g(u)),g(v))))),g(f(x,g(x)))))=v. >> BACK DEMODULATING HINT 4533 WITH 18084. >> BACK DEMODULATING HINT 4532 WITH 18084. >> BACK DEMODULATING HINT 4531 WITH 18084. >> BACK DEMODULATING HINT 4530 WITH 18084. >> BACK DEMODULATING HINT 4529 WITH 18084. >> BACK DEMODULATING HINT 4528 WITH 18084. >> BACK DEMODULATING HINT 4527 WITH 18084. >> BACK DEMODULATING HINT 4526 WITH 18084. >> BACK DEMODULATING HINT 4525 WITH 18084. >> BACK DEMODULATING HINT 4524 WITH 18084. >> BACK DEMODULATING HINT 4523 WITH 18084. >> BACK DEMODULATING HINT 4522 WITH 18084. NEW HINT: 18501 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,f(f(f(g(y),f(z,v)),g(v)),f(g(z),g(w)))))),g(f(x,g(x)))))=w. >> BACK DEMODULATING HINT 4521 WITH 18084. >> BACK DEMODULATING HINT 4520 WITH 18084. >> BACK DEMODULATING HINT 4519 WITH 18084. NEW HINT: 18502 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(y,f(f(f(g(y),g(f(g(v),g(z)))),g(v)),f(g(z),g(w)))))),g(f(x,g(x)))))=w. >> BACK DEMODULATING HINT 4518 WITH 18084. >> BACK DEMODULATING HINT 4517 WITH 18084. >> BACK DEMODULATING HINT 4516 WITH 18084. >> BACK DEMODULATING HINT 4515 WITH 18084. >> BACK DEMODULATING HINT 4514 WITH 18084. >> BACK DEMODULATING HINT 4513 WITH 18084. >> BACK DEMODULATING HINT 4512 WITH 18084. >> BACK DEMODULATING HINT 4511 WITH 18084. >> BACK DEMODULATING HINT 4510 WITH 18084. >> BACK DEMODULATING HINT 4494 WITH 18084. NEW HINT: 18503 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(y,f(u,z)),f(g(z),g(w))))=g(f(w,g(u))). >> BACK DEMODULATING HINT 4488 WITH 18084. >> BACK DEMODULATING HINT 4487 WITH 18084. NEW HINT: 18504 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(u,f(f(g(u),g(y)),v)),g(v))),g(f(x,g(x)))). >> BACK DEMODULATING HINT 4486 WITH 18084. >> BACK DEMODULATING HINT 4485 WITH 18084. NEW HINT: 18505 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(g(y),v),g(v))),g(f(x,g(x)))). >> BACK DEMODULATING HINT 4484 WITH 18084. NEW HINT: 18506 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),f(f(u,g(f(g(v),f(y,u)))),g(v))),g(f(x,g(x)))). >> BACK DEMODULATING HINT 4483 WITH 18084. >> BACK DEMODULATING HINT 4482 WITH 18084. >> BACK DEMODULATING HINT 4481 WITH 18084. NEW HINT: 18507 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),g(f(u,f(f(g(u),f(y,v)),g(v))))),g(f(x,g(x)))). >> BACK DEMODULATING HINT 4480 WITH 18084. >> BACK DEMODULATING HINT 4479 WITH 18084. >> BACK DEMODULATING HINT 4478 WITH 18084. NEW HINT: 18508 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),g(f(u,f(f(g(u),g(f(g(v),g(y)))),g(v))))),g(f(x,g(x)))). >> BACK DEMODULATING HINT 4477 WITH 18084. >> BACK DEMODULATING HINT 4476 WITH 18084. NEW HINT: 18509 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(f(g(x),g(f(u,g(f(v,f(f(g(v),g(y)),u)))))),g(f(x,g(x)))). >> BACK DEMODULATING HINT 4475 WITH 18084. >> BACK DEMODULATING HINT 4416 WITH 18084. >> BACK DEMODULATING HINT 4415 WITH 18084. >> BACK DEMODULATING HINT 4414 WITH 18084. >> BACK DEMODULATING HINT 4413 WITH 18084. >> BACK DEMODULATING HINT 4406 WITH 18084. >> BACK DEMODULATING HINT 4340 WITH 18084. >> BACK DEMODULATING HINT 4336 WITH 18084. >> BACK DEMODULATING HINT 4335 WITH 18084. >> BACK DEMODULATING HINT 4334 WITH 18084. >> BACK DEMODULATING HINT 4333 WITH 18084. NEW HINT: 18510 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(y,x)))=g(f(y,g(f(u,g(u))))). >> BACK DEMODULATING HINT 4332 WITH 18084. >> BACK DEMODULATING HINT 4331 WITH 18084. >> BACK DEMODULATING HINT 4330 WITH 18084. >> BACK DEMODULATING HINT 4329 WITH 18084. >> BACK DEMODULATING HINT 4328 WITH 18084. >> BACK DEMODULATING HINT 4327 WITH 18084. >> BACK DEMODULATING HINT 4326 WITH 18084. >> BACK DEMODULATING HINT 4325 WITH 18084. >> BACK DEMODULATING HINT 4324 WITH 18084. >> BACK DEMODULATING HINT 4323 WITH 18084. >> BACK DEMODULATING HINT 4322 WITH 18084. >> BACK DEMODULATING HINT 4321 WITH 18084. >> BACK DEMODULATING HINT 4320 WITH 18084. >> BACK DEMODULATING HINT 4319 WITH 18084. NEW HINT: 18511 [bsub_wt=2147483647, bsub_add_wt=-1024] f(y,f(f(g(y),g(z)),g(f(x,g(x)))))=g(f(z,g(f(x,g(x))))). >> BACK DEMODULATING HINT 4318 WITH 18084. >> BACK DEMODULATING HINT 4317 WITH 18084. >> BACK DEMODULATING HINT 4316 WITH 18084. >> BACK DEMODULATING HINT 4296 WITH 18084. NEW HINT: 18512 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(f(x,g(x)))),f(y,u))=u. >> BACK DEMODULATING HINT 4295 WITH 18084. >> BACK DEMODULATING HINT 4294 WITH 18084. >> BACK DEMODULATING HINT 4293 WITH 18084. >> BACK DEMODULATING HINT 4283 WITH 18084. >> BACK DEMODULATING HINT 4282 WITH 18084. >> BACK DEMODULATING HINT 4281 WITH 18084. >> BACK DEMODULATING HINT 4275 WITH 18084. >> BACK DEMODULATING HINT 4216 WITH 18084. >> BACK DEMODULATING HINT 4210 WITH 18084. >> BACK DEMODULATING HINT 4209 WITH 18084. >> BACK DEMODULATING HINT 4208 WITH 18084. >> BACK DEMODULATING HINT 4207 WITH 18084. >> BACK DEMODULATING HINT 4206 WITH 18084. >> BACK DEMODULATING HINT 4205 WITH 18084. >> BACK DEMODULATING HINT 4202 WITH 18084. >> BACK DEMODULATING HINT 4199 WITH 18084. >> BACK DEMODULATING HINT 4198 WITH 18084. >> BACK DEMODULATING HINT 4188 WITH 18084. >> BACK DEMODULATING HINT 4187 WITH 18084. NEW HINT: 18513 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(z,f(f(g(z),f(u,g(f(u,u)))),u)),y)=y. >> BACK DEMODULATING HINT 4185 WITH 18084. >> BACK DEMODULATING HINT 4183 WITH 18084. NEW HINT: 18514 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(y,g(y)))=f(z,g(z)). >> BACK DEMODULATING HINT 3930 WITH 18084. >> BACK DEMODULATING HINT 3890 WITH 18084. NEW HINT: 18515 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(u),f(y,g(f(g(y),f(u,g(f(g(y),f(u,v6))))))))=f(v6,f(g(u),y)). >> BACK DEMODULATING HINT 3885 WITH 18084. >> BACK DEMODULATING HINT 3884 WITH 18084. >> BACK DEMODULATING HINT 3883 WITH 18084. >> BACK DEMODULATING HINT 3882 WITH 18084. NEW HINT: 18516 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,f(z,g(u))),v))=f(z,f(g(u),v)). >> BACK DEMODULATING HINT 3881 WITH 18084. >> BACK DEMODULATING HINT 3880 WITH 18084. >> BACK DEMODULATING HINT 3871 WITH 18084. >> BACK DEMODULATING HINT 3870 WITH 18084. >> BACK DEMODULATING HINT 3869 WITH 18084. >> BACK DEMODULATING HINT 3859 WITH 18084. NEW HINT: 18517 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,y))=f(g(x),f(f(x,g(y)),f(g(x),f(g(z),z)))). >> BACK DEMODULATING HINT 3853 WITH 18084. NEW HINT: 18518 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(f(x,f(y,z)))),x))=f(f(g(y),f(g(u),u)),f(f(f(g(u),u),f(y,g(z))),f(g(y),f(g(u),u)))). >> BACK DEMODULATING HINT 3847 WITH 18084. NEW HINT: 18519 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(f(g(x),y),z)))=f(f(g(y),f(g(u),u)),f(f(f(g(u),u),f(y,g(z))),f(g(y),f(g(u),u)))). >> BACK DEMODULATING HINT 3843 WITH 18084. >> BACK DEMODULATING HINT 3837 WITH 18084. NEW HINT: 18520 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(g(x),z)),g(f(g(y),f(f(g(x),z),f(g(y),f(g(x),z))))))=f(f(g(z),x),y). >> BACK DEMODULATING HINT 3828 WITH 18084. >> BACK DEMODULATING HINT 3827 WITH 18084. NEW HINT: 18521 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,y),g(x)))=f(f(y,x),f(g(x),f(g(x),f(g(u),u)))). >> BACK DEMODULATING HINT 3821 WITH 18084. NEW HINT: 18522 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,z),f(g(x),f(g(y),y))))=f(f(z,x),f(f(g(x),f(g(y),y)),f(g(x),f(g(y),y)))). >> BACK DEMODULATING HINT 3812 WITH 18084. NEW HINT: 18523 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(x,f(y,f(f(g(y),f(g(z),z)),f(g(y),f(g(z),z))))))=f(f(y,f(g(x),y)),f(g(y),f(g(z),z))). >> BACK DEMODULATING HINT 3811 WITH 18084. NEW HINT: 18524 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,g(f(g(y),z))),f(g(y),f(g(x),x)))=g(f(z,f(y,f(f(g(y),f(g(x),x)),f(g(y),f(g(x),x)))))). >> BACK DEMODULATING HINT 3810 WITH 18084. NEW HINT: 18525 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,g(f(g(y),f(f(g(x),x),z)))),f(g(y),f(g(x),x)))=g(f(z,f(y,f(f(g(y),f(g(x),x)),f(g(y),f(g(x),x)))))). >> BACK DEMODULATING HINT 3808 WITH 18084. >> BACK DEMODULATING HINT 3802 WITH 18084. >> BACK DEMODULATING HINT 3801 WITH 18084. >> BACK DEMODULATING HINT 3800 WITH 18084. NEW HINT: 18526 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(y,x)))=f(f(g(y),z),f(g(z),f(g(v),v))). >> BACK DEMODULATING HINT 3796 WITH 18084. NEW HINT: 18527 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(y,x)))=f(f(g(y),f(v,f(g(u),u))),f(f(g(w),w),f(g(v),f(g(w),w)))). >> BACK DEMODULATING HINT 3791 WITH 18084. >> BACK DEMODULATING HINT 3785 WITH 18084. >> BACK DEMODULATING HINT 3775 WITH 18084. NEW HINT: 18528 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(z),u))=f(f(g(u),z),f(g(v),v)). >> BACK DEMODULATING HINT 3774 WITH 18084. >> BACK DEMODULATING HINT 3773 WITH 18084. NEW HINT: 18529 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(v),f(u,f(g(z),z)))=f(f(g(v),u),f(g(w),w)). >> BACK DEMODULATING HINT 3772 WITH 18084. >> BACK DEMODULATING HINT 3770 WITH 18084. >> BACK DEMODULATING HINT 3762 WITH 18084. >> BACK DEMODULATING HINT 3760 WITH 18084. >> BACK DEMODULATING HINT 3757 WITH 18084. >> BACK DEMODULATING HINT 3753 WITH 18084. >> BACK DEMODULATING HINT 3752 WITH 18084. >> BACK DEMODULATING HINT 3751 WITH 18084. >> BACK DEMODULATING HINT 3750 WITH 18084. >> BACK DEMODULATING HINT 3749 WITH 18084. >> BACK DEMODULATING HINT 3748 WITH 18084. >> BACK DEMODULATING HINT 3747 WITH 18084. NEW HINT: 18530 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(u,f(f(g(w),w),f(g(u),f(g(w),w)))))=z. >> BACK DEMODULATING HINT 3745 WITH 18084. >> BACK DEMODULATING HINT 3741 WITH 18084. >> BACK DEMODULATING HINT 3740 WITH 18084. NEW HINT: 18531 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(z,f(g(x),x)),f(g(x),x))=z. >> BACK DEMODULATING HINT 3737 WITH 18084. >> BACK DEMODULATING HINT 3733 WITH 18084. >> BACK DEMODULATING HINT 3732 WITH 18084. >> BACK DEMODULATING HINT 3731 WITH 18084. >> BACK DEMODULATING HINT 3729 WITH 18084. >> BACK DEMODULATING HINT 3724 WITH 18084. >> BACK DEMODULATING HINT 3723 WITH 18084. >> BACK DEMODULATING HINT 3722 WITH 18084. >> BACK DEMODULATING HINT 3720 WITH 18084. >> BACK DEMODULATING HINT 3719 WITH 18084. >> BACK DEMODULATING HINT 3716 WITH 18084. >> BACK DEMODULATING HINT 3714 WITH 18084. >> BACK DEMODULATING HINT 3710 WITH 18084. >> BACK DEMODULATING HINT 3709 WITH 18084. >> BACK DEMODULATING HINT 3708 WITH 18084. NEW HINT: 18532 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(u,f(g(z),z)),f(g(x),x))=u. >> BACK DEMODULATING HINT 3707 WITH 18084. >> BACK DEMODULATING HINT 3706 WITH 18084. >> BACK DEMODULATING HINT 3705 WITH 18084. >> BACK DEMODULATING HINT 3704 WITH 18084. NEW HINT: 18533 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),g(f(y,g(f(y,f(z,f(y,f(g(u),u))))))))=z. >> BACK DEMODULATING HINT 3703 WITH 18084. >> BACK DEMODULATING HINT 3702 WITH 18084. NEW HINT: 18534 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),g(f(y,g(f(y,f(f(g(z),z),f(u,f(y,f(g(z),z)))))))))=u. >> BACK DEMODULATING HINT 3701 WITH 18084. >> BACK DEMODULATING HINT 3700 WITH 18084. NEW HINT: 18535 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),g(f(y,f(f(g(z),z),g(f(y,f(f(g(z),z),f(u,f(y,f(g(z),z))))))))))=u. >> BACK DEMODULATING HINT 3698 WITH 18084. >> BACK DEMODULATING HINT 3694 WITH 18084. >> BACK DEMODULATING HINT 3693 WITH 18084. >> BACK DEMODULATING HINT 3564 WITH 18084. >> BACK DEMODULATING HINT 3561 WITH 18084. >> BACK DEMODULATING HINT 3553 WITH 18084. >> BACK DEMODULATING HINT 3541 WITH 18084. >> BACK DEMODULATING HINT 3533 WITH 18084. NEW HINT: 18536 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(y),y),f(v,f(g(z),w))))=f(v,f(g(z),w)). >> BACK DEMODULATING HINT 3531 WITH 18084. >> BACK DEMODULATING HINT 3515 WITH 18084. NEW HINT: 18537 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),z)=f(g(x),f(g(y),f(z,g(f(g(u),u))))). >> BACK DEMODULATING HINT 3513 WITH 18084. >> BACK DEMODULATING HINT 3510 WITH 18084. >> BACK DEMODULATING HINT 3505 WITH 18084. >> BACK DEMODULATING HINT 3502 WITH 18084. >> BACK DEMODULATING HINT 3140 WITH 18084. >> BACK DEMODULATING HINT 3128 WITH 18084. >> BACK DEMODULATING HINT 3108 WITH 18084. NEW HINT: 18538 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(z,g(f(w,g(f(g(y),y))))),f(w,v))=f(z,v) # label(bd). >> BACK DEMODULATING HINT 3107 WITH 18084. >> BACK DEMODULATING HINT 2531 WITH 18084. >> BACK DEMODULATING HINT 2500 WITH 18084. >> BACK DEMODULATING HINT 2492 WITH 18084. >> BACK DEMODULATING HINT 2485 WITH 18084. >> BACK DEMODULATING HINT 2475 WITH 18084. >> BACK DEMODULATING HINT 2471 WITH 18084. >> BACK DEMODULATING HINT 2467 WITH 18084. >> BACK DEMODULATING HINT 2466 WITH 18084. >> BACK DEMODULATING HINT 2437 WITH 18084. >> BACK DEMODULATING HINT 2401 WITH 18084. >> BACK DEMODULATING HINT 2381 WITH 18084. >> BACK DEMODULATING HINT 2374 WITH 18084. >> BACK DEMODULATING HINT 2335 WITH 18084. >> BACK DEMODULATING HINT 2333 WITH 18084. >> BACK DEMODULATING HINT 2332 WITH 18084. >> BACK DEMODULATING HINT 2331 WITH 18084. >> BACK DEMODULATING HINT 2330 WITH 18084. >> BACK DEMODULATING HINT 2313 WITH 18084. NEW HINT: 18539 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,g(f(u,x)))=f(g(u),g(f(v,g(v)))). >> BACK DEMODULATING HINT 2312 WITH 18084. >> BACK DEMODULATING HINT 2311 WITH 18084. >> BACK DEMODULATING HINT 2310 WITH 18084. >> BACK DEMODULATING HINT 2309 WITH 18084. >> BACK DEMODULATING HINT 2308 WITH 18084. >> BACK DEMODULATING HINT 2307 WITH 18084. >> BACK DEMODULATING HINT 2305 WITH 18084. >> BACK DEMODULATING HINT 2302 WITH 18084. >> BACK DEMODULATING HINT 2301 WITH 18084. >> BACK DEMODULATING HINT 2300 WITH 18084. >> BACK DEMODULATING HINT 2297 WITH 18084. >> BACK DEMODULATING HINT 2292 WITH 18084. >> BACK DEMODULATING HINT 2208 WITH 18084. >> BACK DEMODULATING HINT 2203 WITH 18084. >> BACK DEMODULATING HINT 2196 WITH 18084. >> BACK DEMODULATING HINT 2195 WITH 18084. >> BACK DEMODULATING HINT 2194 WITH 18084. >> BACK DEMODULATING HINT 2193 WITH 18084. >> BACK DEMODULATING HINT 2192 WITH 18084. >> BACK DEMODULATING HINT 2189 WITH 18084. >> BACK DEMODULATING HINT 2188 WITH 18084. >> BACK DEMODULATING HINT 2187 WITH 18084. >> BACK DEMODULATING HINT 2180 WITH 18084. >> BACK DEMODULATING HINT 2173 WITH 18084. >> BACK DEMODULATING HINT 2172 WITH 18084. >> BACK DEMODULATING HINT 2171 WITH 18084. >> BACK DEMODULATING HINT 2170 WITH 18084. >> BACK DEMODULATING HINT 2169 WITH 18084. >> BACK DEMODULATING HINT 2165 WITH 18084. NEW HINT: 18540 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(z),f(g(y),y))=g(f(z,g(f(x,g(x))))). >> BACK DEMODULATING HINT 2160 WITH 18084. NEW HINT: 18541 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(z,g(f(x,g(x)))))=f(g(z),f(g(u),u)). >> BACK DEMODULATING HINT 2159 WITH 18084. >> BACK DEMODULATING HINT 2158 WITH 18084. >> BACK DEMODULATING HINT 2155 WITH 18084. >> BACK DEMODULATING HINT 2154 WITH 18084. >> BACK DEMODULATING HINT 2153 WITH 18084. >> BACK DEMODULATING HINT 2152 WITH 18084. >> BACK DEMODULATING HINT 2151 WITH 18084. >> BACK DEMODULATING HINT 2150 WITH 18084. >> BACK DEMODULATING HINT 2149 WITH 18084. >> BACK DEMODULATING HINT 2147 WITH 18084. >> BACK DEMODULATING HINT 2146 WITH 18084. >> BACK DEMODULATING HINT 2145 WITH 18084. >> BACK DEMODULATING HINT 2143 WITH 18084. >> BACK DEMODULATING HINT 2142 WITH 18084. >> BACK DEMODULATING HINT 2140 WITH 18084. >> BACK DEMODULATING HINT 2139 WITH 18084. >> BACK DEMODULATING HINT 2138 WITH 18084. >> BACK DEMODULATING HINT 2135 WITH 18084. >> BACK DEMODULATING HINT 2117 WITH 18084. >> BACK DEMODULATING HINT 2116 WITH 18084. >> BACK DEMODULATING HINT 2115 WITH 18084. >> BACK DEMODULATING HINT 2114 WITH 18084. >> BACK DEMODULATING HINT 2113 WITH 18084. >> BACK DEMODULATING HINT 2112 WITH 18084. >> BACK DEMODULATING HINT 2111 WITH 18084. >> BACK DEMODULATING HINT 2103 WITH 18084. >> BACK DEMODULATING HINT 2102 WITH 18084. >> BACK DEMODULATING HINT 2101 WITH 18084. >> BACK DEMODULATING HINT 2099 WITH 18084. >> BACK DEMODULATING HINT 2098 WITH 18084. NEW HINT: 18542 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(f(g(x),g(z)),g(f(u,v))),f(f(u,f(f(v,z),w)),f(g(w),g(v6)))),g(f(v7,g(v7)))))=f(f(g(v6),v6),g(v6)). >> BACK DEMODULATING HINT 2097 WITH 18084. >> BACK DEMODULATING HINT 2092 WITH 18084. >> BACK DEMODULATING HINT 2091 WITH 18084. >> BACK DEMODULATING HINT 2090 WITH 18084. >> BACK DEMODULATING HINT 2089 WITH 18084. >> BACK DEMODULATING HINT 2087 WITH 18084. >> BACK DEMODULATING HINT 2083 WITH 18084. >> BACK DEMODULATING HINT 2079 WITH 18084. >> BACK DEMODULATING HINT 2078 WITH 18084. >> BACK DEMODULATING HINT 2074 WITH 18084. >> BACK DEMODULATING HINT 2073 WITH 18084. >> BACK DEMODULATING HINT 2072 WITH 18084. >> BACK DEMODULATING HINT 2069 WITH 18084. >> BACK DEMODULATING HINT 2067 WITH 18084. >> BACK DEMODULATING HINT 1773 WITH 18084. >> BACK DEMODULATING HINT 1772 WITH 18084. >> BACK DEMODULATING HINT 1768 WITH 18084. >> BACK DEMODULATING HINT 1751 WITH 18084. >> BACK DEMODULATING HINT 1749 WITH 18084. >> BACK DEMODULATING HINT 1747 WITH 18084. >> BACK DEMODULATING HINT 1746 WITH 18084. >> BACK DEMODULATING HINT 1745 WITH 18084. >> BACK DEMODULATING HINT 1744 WITH 18084. >> BACK DEMODULATING HINT 1743 WITH 18084. >> BACK DEMODULATING HINT 1742 WITH 18084. >> BACK DEMODULATING HINT 1739 WITH 18084. >> BACK DEMODULATING HINT 1737 WITH 18084. >> BACK DEMODULATING HINT 1735 WITH 18084. >> BACK DEMODULATING HINT 1734 WITH 18084. >> BACK DEMODULATING HINT 1733 WITH 18084. >> BACK DEMODULATING HINT 1727 WITH 18084. >> BACK DEMODULATING HINT 1726 WITH 18084. >> BACK DEMODULATING HINT 1720 WITH 18084. >> BACK DEMODULATING HINT 1718 WITH 18084. >> BACK DEMODULATING HINT 1710 WITH 18084. >> BACK DEMODULATING HINT 1708 WITH 18084. >> BACK DEMODULATING HINT 1707 WITH 18084. >> BACK DEMODULATING HINT 1706 WITH 18084. >> BACK DEMODULATING HINT 1705 WITH 18084. >> BACK DEMODULATING HINT 1704 WITH 18084. >> BACK DEMODULATING HINT 1703 WITH 18084. >> BACK DEMODULATING HINT 1701 WITH 18084. >> BACK DEMODULATING HINT 1700 WITH 18084. >> BACK DEMODULATING HINT 1699 WITH 18084. >> BACK DEMODULATING HINT 1697 WITH 18084. >> BACK DEMODULATING HINT 1696 WITH 18084. >> BACK DEMODULATING HINT 1695 WITH 18084. >> BACK DEMODULATING HINT 1694 WITH 18084. >> BACK DEMODULATING HINT 1693 WITH 18084. >> BACK DEMODULATING HINT 1692 WITH 18084. >> BACK DEMODULATING HINT 1691 WITH 18084. >> BACK DEMODULATING HINT 1686 WITH 18084. >> BACK DEMODULATING HINT 1685 WITH 18084. >> BACK DEMODULATING HINT 1684 WITH 18084. >> BACK DEMODULATING HINT 1681 WITH 18084. >> BACK DEMODULATING HINT 1680 WITH 18084. NEW HINT: 18543 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),y),f(z,g(f(y,z))))),y)=y. >> BACK DEMODULATING HINT 1613 WITH 18084. >> BACK DEMODULATING HINT 1606 WITH 18084. >> BACK DEMODULATING HINT 1592 WITH 18084. >> BACK DEMODULATING HINT 1589 WITH 18084. >> BACK DEMODULATING HINT 1588 WITH 18084. >> BACK DEMODULATING HINT 1587 WITH 18084. >> BACK DEMODULATING HINT 1570 WITH 18084. >> BACK DEMODULATING HINT 1562 WITH 18084. >> BACK DEMODULATING HINT 1555 WITH 18084. >> BACK DEMODULATING HINT 1554 WITH 18084. >> BACK DEMODULATING HINT 1542 WITH 18084. >> BACK DEMODULATING HINT 1538 WITH 18084. >> BACK DEMODULATING HINT 1534 WITH 18084. >> BACK DEMODULATING HINT 1532 WITH 18084. >> BACK DEMODULATING HINT 1483 WITH 18084. >> BACK DEMODULATING HINT 1448 WITH 18084. >> BACK DEMODULATING HINT 1447 WITH 18084. >> BACK DEMODULATING HINT 1446 WITH 18084. >> BACK DEMODULATING HINT 1445 WITH 18084. >> BACK DEMODULATING HINT 1444 WITH 18084. >> BACK DEMODULATING HINT 1441 WITH 18084. >> BACK DEMODULATING HINT 1440 WITH 18084. >> BACK DEMODULATING HINT 1433 WITH 18084. >> BACK DEMODULATING HINT 1421 WITH 18084. >> BACK DEMODULATING HINT 1417 WITH 18084. >> BACK DEMODULATING HINT 1409 WITH 18084. >> BACK DEMODULATING HINT 1394 WITH 18084. >> BACK DEMODULATING HINT 1373 WITH 18084. >> BACK DEMODULATING HINT 1370 WITH 18084. >> BACK DEMODULATING HINT 1369 WITH 18084. >> BACK DEMODULATING HINT 1368 WITH 18084. >> BACK DEMODULATING HINT 1360 WITH 18084. >> BACK DEMODULATING HINT 1359 WITH 18084. >> BACK DEMODULATING HINT 1358 WITH 18084. >> BACK DEMODULATING HINT 1357 WITH 18084. >> BACK DEMODULATING HINT 1356 WITH 18084. >> BACK DEMODULATING HINT 1355 WITH 18084. >> BACK DEMODULATING HINT 1354 WITH 18084. >> BACK DEMODULATING HINT 1353 WITH 18084. >> BACK DEMODULATING HINT 1352 WITH 18084. >> BACK DEMODULATING HINT 1338 WITH 18084. >> BACK DEMODULATING HINT 1313 WITH 18084. >> BACK DEMODULATING HINT 1311 WITH 18084. >> BACK DEMODULATING HINT 1310 WITH 18084. >> BACK DEMODULATING HINT 1303 WITH 18084. >> BACK DEMODULATING HINT 1300 WITH 18084. >> BACK DEMODULATING HINT 1295 WITH 18084. >> BACK DEMODULATING HINT 1292 WITH 18084. >> BACK DEMODULATING HINT 1291 WITH 18084. >> BACK DEMODULATING HINT 1259 WITH 18084. >> BACK DEMODULATING HINT 1242 WITH 18084. >> BACK DEMODULATING HINT 1239 WITH 18084. >> BACK DEMODULATING HINT 1235 WITH 18084. >> BACK DEMODULATING HINT 1234 WITH 18084. >> BACK DEMODULATING HINT 1152 WITH 18084. >> BACK DEMODULATING HINT 1150 WITH 18084. >> BACK DEMODULATING HINT 1141 WITH 18084. >> BACK DEMODULATING HINT 1133 WITH 18084. >> BACK DEMODULATING HINT 1130 WITH 18084. >> BACK DEMODULATING HINT 1112 WITH 18084. >> BACK DEMODULATING HINT 1109 WITH 18084. >> BACK DEMODULATING HINT 1108 WITH 18084. >> BACK DEMODULATING HINT 1078 WITH 18084. >> BACK DEMODULATING HINT 1076 WITH 18084. >> BACK DEMODULATING HINT 1064 WITH 18084. >> BACK DEMODULATING HINT 1058 WITH 18084. >> BACK DEMODULATING HINT 1055 WITH 18084. >> BACK DEMODULATING HINT 1054 WITH 18084. >> BACK DEMODULATING HINT 1036 WITH 18084. >> BACK DEMODULATING HINT 1013 WITH 18084. >> BACK DEMODULATING HINT 1010 WITH 18084. >> BACK DEMODULATING HINT 1007 WITH 18084. >> BACK DEMODULATING HINT 1004 WITH 18084. >> BACK DEMODULATING HINT 944 WITH 18084. >> BACK DEMODULATING HINT 943 WITH 18084. >> BACK DEMODULATING HINT 942 WITH 18084. >> BACK DEMODULATING HINT 941 WITH 18084. >> BACK DEMODULATING HINT 940 WITH 18084. >> BACK DEMODULATING HINT 937 WITH 18084. >> BACK DEMODULATING HINT 936 WITH 18084. >> BACK DEMODULATING HINT 935 WITH 18084. >> BACK DEMODULATING HINT 934 WITH 18084. >> BACK DEMODULATING HINT 933 WITH 18084. NEW HINT: 18544 [bsub_wt=2147483647, bsub_add_wt=-1024] g(f(g(y),g(f(x,g(x)))))=y. >> BACK DEMODULATING HINT 932 WITH 18084. >> BACK DEMODULATING HINT 931 WITH 18084. >> BACK DEMODULATING HINT 907 WITH 18084. >> BACK DEMODULATING HINT 906 WITH 18084. >> BACK DEMODULATING HINT 905 WITH 18084. >> BACK DEMODULATING HINT 834 WITH 18084. >> BACK DEMODULATING HINT 829 WITH 18084. >> BACK DEMODULATING HINT 736 WITH 18084. >> BACK DEMODULATING HINT 733 WITH 18084. >> BACK DEMODULATING HINT 730 WITH 18084. >> BACK DEMODULATING HINT 728 WITH 18084. >> BACK DEMODULATING HINT 726 WITH 18084. >> BACK DEMODULATING HINT 725 WITH 18084. >> BACK DEMODULATING HINT 717 WITH 18084. NEW HINT: 18545 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(z)),z))=g(f(y,g(y))) # label(bd). >> BACK DEMODULATING HINT 715 WITH 18084. >> BACK DEMODULATING HINT 711 WITH 18084. >> BACK DEMODULATING HINT 675 WITH 18084. >> BACK DEMODULATING HINT 674 WITH 18084. NEW HINT: 18546 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(g(y),g(y))))=g(y) # label(bd). >> BACK DEMODULATING HINT 627 WITH 18084. >> BACK DEMODULATING HINT 542 WITH 18084. >> BACK DEMODULATING HINT 514 WITH 18084. >> BACK DEMODULATING HINT 513 WITH 18084. >> BACK DEMODULATING HINT 466 WITH 18084. >> BACK DEMODULATING HINT 381 WITH 18084. >> BACK DEMODULATING HINT 380 WITH 18084. >> BACK DEMODULATING HINT 373 WITH 18084. >> BACK DEMODULATING HINT 369 WITH 18084. >> BACK DEMODULATING HINT 352 WITH 18084. >> BACK DEMODULATING HINT 278 WITH 18084. >> BACK DEMODULATING HINT 249 WITH 18084. >> BACK DEMODULATING HINT 242 WITH 18084. >> BACK DEMODULATING HINT 240 WITH 18084. >> BACK DEMODULATING HINT 239 WITH 18084. >> BACK DEMODULATING HINT 221 WITH 18084. >> BACK DEMODULATING HINT 218 WITH 18084. >> BACK DEMODULATING HINT 216 WITH 18084. >> BACK DEMODULATING HINT 188 WITH 18084. >> BACK DEMODULATING HINT 157 WITH 18084. >> BACK DEMODULATING HINT 144 WITH 18084. >> BACK DEMODULATING HINT 142 WITH 18084. >> BACK DEMODULATING HINT 79 WITH 18084. >> BACK DEMODULATING HINT 16987 WITH 18088. >> BACK DEMODULATING HINT 13228 WITH 18088. >> BACK DEMODULATING HINT 13226 WITH 18088. >> BACK DEMODULATING HINT 13224 WITH 18088. >> BACK DEMODULATING HINT 13223 WITH 18088. >> BACK DEMODULATING HINT 4761 WITH 18088. >> BACK DEMODULATING HINT 4755 WITH 18088. >> BACK DEMODULATING HINT 4751 WITH 18088. >> BACK DEMODULATING HINT 4744 WITH 18088. >> BACK DEMODULATING HINT 4739 WITH 18088. >> BACK DEMODULATING HINT 4734 WITH 18088. >> BACK DEMODULATING HINT 4723 WITH 18088. NEW HINT: 18549 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(f(z,g(f(y,x))))),g(y))=f(x,f(g(z),g(y))). >> BACK DEMODULATING HINT 4503 WITH 18088. >> BACK DEMODULATING HINT 4453 WITH 18088. >> BACK DEMODULATING HINT 4419 WITH 18088. >> BACK DEMODULATING HINT 2393 WITH 18088. >> BACK DEMODULATING HINT 1924 WITH 18088. >> BACK DEMODULATING HINT 1834 WITH 18088. >> BACK DEMODULATING HINT 1412 WITH 18088. >> BACK DEMODULATING HINT 1321 WITH 18088. >> BACK DEMODULATING HINT 1135 WITH 18088. >> BACK DEMODULATING HINT 1089 WITH 18088. >> BACK DEMODULATING HINT 886 WITH 18088. >> BACK DEMODULATING HINT 723 WITH 18088. >> BACK DEMODULATING HINT 18080 WITH 18090. >> BACK DEMODULATING HINT 17666 WITH 18090. NEW HINT: 19396 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(x,g(z))),z),g(x))=y # label(bd). >> BACK DEMODULATING HINT 17663 WITH 18090. NEW HINT: 19397 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(z,f(f(g(z),f(g(u),g(y))),z)),f(g(z),y)),g(x))=f(g(u),g(x)) # label(bd). >> BACK DEMODULATING HINT 17659 WITH 18090. >> BACK DEMODULATING HINT 17650 WITH 18090. >> BACK DEMODULATING HINT 17642 WITH 18090. NEW HINT: 19398 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(u),f(z,f(x,y))),f(g(y),f(g(x),g(x))))=f(f(f(z,f(x,y)),f(g(y),f(g(x),g(x)))),f(f(x,f(g(z),g(u))),f(f(z,f(x,y)),f(g(y),f(g(x),g(x)))))) # label(bd). >> BACK DEMODULATING HINT 17635 WITH 18090. NEW HINT: 19399 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(u,g(z)),f(f(z,x),f(x,y))),f(g(y),f(g(x),g(x))))=u # label(bd). >> BACK DEMODULATING HINT 17634 WITH 18090. NEW HINT: 19400 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(g(y),f(g(x),g(x)))),x)=f(f(g(z),g(y)),g(x)). >> BACK DEMODULATING HINT 17629 WITH 18090. NEW HINT: 19401 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),f(f(f(g(x),g(z)),u),f(z,f(f(g(z),g(u)),z)))),g(v))),f(f(f(g(z),f(u,z)),g(z)),f(g(u),f(z,x)))))=f(f(g(v),f(f(g(z),f(u,z)),g(z))),f(g(u),f(z,x))). >> BACK DEMODULATING HINT 17628 WITH 18090. NEW HINT: 19402 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),g(z))),f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,x)))))=f(f(g(z),f(f(g(u),f(v,u)),g(u))),f(g(v),f(u,x))). >> BACK DEMODULATING HINT 17627 WITH 18090. NEW HINT: 19403 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),g(z))),x))=f(f(g(z),f(f(g(u),f(v,u)),g(u))),f(g(v),f(u,x))). >> BACK DEMODULATING HINT 17626 WITH 18090. NEW HINT: 19404 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(u),f(f(g(x),f(z,x)),g(x))),f(g(z),f(x,y)))=f(y,f(f(v,f(f(g(v),g(y)),g(u))),y)). >> BACK DEMODULATING HINT 17625 WITH 18090. NEW HINT: 19405 [bsub_wt=2147483647, bsub_add_wt=-1024] f(y,f(f(w,f(f(g(w),g(y)),f(x,f(f(g(x),g(z)),x)))),y))=f(g(z),f(x,y)). >> BACK DEMODULATING HINT 17624 WITH 18090. >> BACK DEMODULATING HINT 17623 WITH 18090. NEW HINT: 19406 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(f(v,g(u)),u)),f(f(x,f(f(g(x),g(y)),y)),f(g(v),f(x,f(f(g(x),g(y)),y)))))=f(f(f(g(z),f(w,v6)),g(v6)),g(w)). >> BACK DEMODULATING HINT 17622 WITH 18090. NEW HINT: 19407 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(z),f(x,y)),g(y)),g(x))=f(f(g(z),f(f(v6,g(w)),w)),f(f(u,f(f(g(u),g(v)),v)),f(g(v6),f(u,f(f(g(u),g(v)),v))))). >> BACK DEMODULATING HINT 17621 WITH 18090. NEW HINT: 19408 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(f(w,g(v)),v)),f(f(z,f(f(g(z),g(u)),u)),f(g(w),f(z,f(f(g(z),g(u)),u)))))=g(y). >> BACK DEMODULATING HINT 17620 WITH 18090. NEW HINT: 19409 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),f(g(u),v))),x))=f(g(u),f(v,x)). >> BACK DEMODULATING HINT 17619 WITH 18090. >> BACK DEMODULATING HINT 17618 WITH 18090. >> BACK DEMODULATING HINT 17617 WITH 18090. >> BACK DEMODULATING HINT 17616 WITH 18090. NEW HINT: 19410 [bsub_wt=2147483647, bsub_add_wt=-1024] f(y,f(f(g(y),f(g(z),x)),y))=f(g(z),f(x,y)). >> BACK DEMODULATING HINT 17615 WITH 18090. >> BACK DEMODULATING HINT 17602 WITH 18090. NEW HINT: 19411 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(v),f(y,f(f(g(y),x),f(f(g(x),f(g(u),g(z))),x)))),g(x))=f(f(g(v),g(u)),g(z)). >> BACK DEMODULATING HINT 17601 WITH 18090. NEW HINT: 19412 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(z,f(f(f(f(g(z),f(f(x,y),z)),f(g(z),u)),g(u)),v)),g(y))),g(x))=f(f(g(x),w),f(f(g(w),f(f(f(x,y),f(f(v,f(f(g(y),g(x)),v6)),g(v6))),g(w))),w)). >> BACK DEMODULATING HINT 17600 WITH 18090. NEW HINT: 19413 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),u),f(f(g(u),f(f(f(x,y),f(f(z,f(f(g(y),g(x)),v)),g(v))),g(u))),u))=f(f(g(x),f(f(x,f(y,z)),g(y))),g(x)). >> BACK DEMODULATING HINT 17599 WITH 18090. >> BACK DEMODULATING HINT 17598 WITH 18090. NEW HINT: 19414 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(f(f(x,y),f(f(f(u,f(f(f(g(u),g(w)),f(g(u),v)),g(v))),u),f(g(y),g(x)))),f(f(x,y),z)),g(z)),f(w,g(v6))),f(g(y),g(x))))=f(f(g(v6),g(y)),g(x)). >> BACK DEMODULATING HINT 17597 WITH 18090. NEW HINT: 19415 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),g(y)),g(x))=f(f(g(y),g(x)),f(f(f(f(f(f(x,y),f(f(f(v,f(f(f(g(v),g(v6)),f(g(v),w)),g(w))),v),f(g(y),g(x)))),f(f(x,y),u)),g(u)),f(v6,g(z))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 17589 WITH 18090. >> BACK DEMODULATING HINT 17003 WITH 18090. NEW HINT: 19416 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(g(x),f(f(f(f(x,z),u),x),y))),f(g(y),g(x)))=f(g(y),f(z,u)) # label(bd). >> BACK DEMODULATING HINT 17000 WITH 18090. >> BACK DEMODULATING HINT 16997 WITH 18090. NEW HINT: 19417 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),f(f(x,g(y)),f(y,g(x)))),f(x,g(z))),z))=x # label(bd). >> BACK DEMODULATING HINT 16992 WITH 18090. >> BACK DEMODULATING HINT 16991 WITH 18090. >> BACK DEMODULATING HINT 16990 WITH 18090. >> BACK DEMODULATING HINT 16989 WITH 18090. >> BACK DEMODULATING HINT 16988 WITH 18090. >> BACK DEMODULATING HINT 16985 WITH 18090. >> BACK DEMODULATING HINT 16980 WITH 18090. NEW HINT: 19418 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,y),z)),f(f(f(g(z),f(f(x,y),f(z,f(x,y)))),f(g(y),g(x))),f(g(z),f(g(y),g(x)))))=y. >> BACK DEMODULATING HINT 16979 WITH 18090. NEW HINT: 19419 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,y),z)),g(z))=y. >> BACK DEMODULATING HINT 16978 WITH 18090. NEW HINT: 19420 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(z),y),g(x)),f(x,u))=f(f(g(z),f(f(y,u),v)),g(v)). >> BACK DEMODULATING HINT 16976 WITH 18090. NEW HINT: 19421 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(y,z)),f(f(w,f(f(g(w),f(g(z),g(u))),v)),f(g(v),u))))=y. >> BACK DEMODULATING HINT 16972 WITH 18090. >> BACK DEMODULATING HINT 16968 WITH 18090. NEW HINT: 19422 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,g(x)),f(f(x,f(v,z)),g(z)))=f(y,v). >> BACK DEMODULATING HINT 16965 WITH 18090. >> BACK DEMODULATING HINT 16964 WITH 18090. >> BACK DEMODULATING HINT 16962 WITH 18090. >> BACK DEMODULATING HINT 16961 WITH 18090. >> BACK DEMODULATING HINT 16959 WITH 18090. >> BACK DEMODULATING HINT 16958 WITH 18090. >> BACK DEMODULATING HINT 16952 WITH 18090. NEW HINT: 19423 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),f(x,f(y,x))),g(x)),f(g(y),g(x))),f(g(x),f(f(x,y),z)))=z. >> BACK DEMODULATING HINT 16951 WITH 18090. NEW HINT: 19424 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(g(x),f(f(x,y),z)))=z. >> BACK DEMODULATING HINT 16950 WITH 18090. NEW HINT: 19425 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),g(y)),g(x)),z))=f(g(y),f(g(x),z)). >> BACK DEMODULATING HINT 16948 WITH 18090. NEW HINT: 19426 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(g(y),f(g(x),z)))=z. >> BACK DEMODULATING HINT 16947 WITH 18090. NEW HINT: 19427 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,z),f(f(g(z),g(y)),f(f(y,z),u)))=f(f(y,z),u). >> BACK DEMODULATING HINT 16945 WITH 18090. >> BACK DEMODULATING HINT 16944 WITH 18090. NEW HINT: 19428 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),f(z,f(x,y))),f(g(y),g(x)))=f(f(x,y),f(f(g(y),g(x)),f(f(x,y),z))). >> BACK DEMODULATING HINT 16943 WITH 18090. >> BACK DEMODULATING HINT 16942 WITH 18090. >> BACK DEMODULATING HINT 16941 WITH 18090. NEW HINT: 19429 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(g(y),g(x)),f(x,f(y,z))))=f(f(x,y),z). >> BACK DEMODULATING HINT 16940 WITH 18090. >> BACK DEMODULATING HINT 16938 WITH 18090. >> BACK DEMODULATING HINT 16937 WITH 18090. >> BACK DEMODULATING HINT 16919 WITH 18090. NEW HINT: 19430 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(y,z),g(v)),f(f(z,f(f(u,f(f(g(u),g(z)),v)),z)),f(g(z),g(z)))),w)))=w # label(bd). >> BACK DEMODULATING HINT 16918 WITH 18090. NEW HINT: 19431 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,x),y),f(f(f(g(y),g(x)),f(g(x),g(z))),f(z,u)))=u # label(bd). >> BACK DEMODULATING HINT 16903 WITH 18090. NEW HINT: 19432 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,x),y),f(f(f(g(y),g(x)),f(g(x),z)),f(g(z),u)))=u. >> BACK DEMODULATING HINT 16896 WITH 18090. NEW HINT: 19433 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),g(y)),z),f(f(y,f(f(g(y),g(z)),y)),u)))=u. >> BACK DEMODULATING HINT 16895 WITH 18090. >> BACK DEMODULATING HINT 16894 WITH 18090. NEW HINT: 19434 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(u),g(z)),g(y)),x),f(g(x),x))=f(g(u),f(f(g(z),g(y)),x)). >> BACK DEMODULATING HINT 16893 WITH 18090. NEW HINT: 19435 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),y),f(g(y),z)),x),f(g(x),x))=f(g(y),f(f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,z))),x)). >> BACK DEMODULATING HINT 16892 WITH 18090. NEW HINT: 19436 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(z),z),f(g(z),u)),x),f(g(x),x))=f(g(z),f(u,x)). >> BACK DEMODULATING HINT 16891 WITH 18090. >> BACK DEMODULATING HINT 16889 WITH 18090. NEW HINT: 19437 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),g(y)),y)),v)=v. >> BACK DEMODULATING HINT 16887 WITH 18090. >> BACK DEMODULATING HINT 16884 WITH 18090. >> BACK DEMODULATING HINT 16883 WITH 18090. >> BACK DEMODULATING HINT 16882 WITH 18090. >> BACK DEMODULATING HINT 16881 WITH 18090. >> BACK DEMODULATING HINT 16880 WITH 18090. >> BACK DEMODULATING HINT 16879 WITH 18090. >> BACK DEMODULATING HINT 16878 WITH 18090. >> BACK DEMODULATING HINT 16877 WITH 18090. >> BACK DEMODULATING HINT 16876 WITH 18090. >> BACK DEMODULATING HINT 16875 WITH 18090. >> BACK DEMODULATING HINT 16874 WITH 18090. >> BACK DEMODULATING HINT 16873 WITH 18090. >> BACK DEMODULATING HINT 16872 WITH 18090. >> BACK DEMODULATING HINT 16871 WITH 18090. >> BACK DEMODULATING HINT 16870 WITH 18090. >> BACK DEMODULATING HINT 16869 WITH 18090. >> BACK DEMODULATING HINT 16868 WITH 18090. >> BACK DEMODULATING HINT 16867 WITH 18090. >> BACK DEMODULATING HINT 16866 WITH 18090. >> BACK DEMODULATING HINT 16862 WITH 18090. >> BACK DEMODULATING HINT 16840 WITH 18090. NEW HINT: 19438 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(x),f(f(f(x,y),f(f(v,f(f(g(u),g(y)),g(x))),f(f(x,y),f(f(u,f(f(g(y),g(x)),z)),g(z))))),f(x,y))),x))=f(f(y,v),x). >> BACK DEMODULATING HINT 16839 WITH 18090. NEW HINT: 19439 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(f(f(y,z),f(f(w,f(f(g(v),g(z)),g(y))),f(f(y,z),f(f(v,f(f(g(z),g(y)),u)),g(u))))),f(y,z))),y)))=f(y,f(f(z,w),y)). >> BACK DEMODULATING HINT 16838 WITH 18090. NEW HINT: 19440 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(x,f(f(z,u),f(v,y))),g(y)))=f(f(g(y),x),f(z,f(u,v))). >> BACK DEMODULATING HINT 16834 WITH 18090. NEW HINT: 19441 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(g(z),g(y))),g(x)),f(f(f(f(x,y),g(u)),f(f(u,f(z,u)),g(u))),f(f(f(x,w),g(v)),f(v,v6))))=f(w,v6). >> BACK DEMODULATING HINT 16826 WITH 18090. NEW HINT: 19442 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),g(z))),f(g(x),g(y))),f(f(f(f(y,x),g(u)),f(f(u,f(z,u)),g(u))),f(f(f(y,w),g(v)),f(v,v6))))=f(w,v6). >> BACK DEMODULATING HINT 16821 WITH 18090. NEW HINT: 19443 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(v),f(f(v,w),v)),f(g(v),f(f(g(z),g(u)),f(u,y)))),f(f(f(g(y),f(z,y)),f(g(y),x)),g(x)))=w. >> BACK DEMODULATING HINT 16820 WITH 18090. NEW HINT: 19444 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(v),f(w,v)),f(g(v),f(f(g(z),g(u)),f(u,y)))),f(f(f(g(y),f(z,y)),f(g(y),x)),g(x)))=f(f(f(g(v),f(w,v)),f(g(v),v6)),g(v6)). >> BACK DEMODULATING HINT 16819 WITH 18090. NEW HINT: 19445 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(z,y)),f(g(y),x)),g(x))=f(f(f(g(y),f(z,y)),f(g(y),f(f(g(w),g(v6)),f(v6,v)))),f(f(f(g(v),f(w,v)),f(g(v),u)),g(u))). >> BACK DEMODULATING HINT 16816 WITH 18090. NEW HINT: 19446 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(v),f(w,v)),f(g(v),f(f(g(z),g(u)),f(u,y)))),f(f(f(g(y),f(z,y)),f(g(y),x)),g(x)))=f(f(g(v),f(w,v)),g(v)). >> BACK DEMODULATING HINT 16815 WITH 18090. NEW HINT: 19447 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(u),f(v,u)),f(g(u),f(f(g(y),g(z)),f(z,x)))),f(f(g(x),f(y,x)),g(x)))=f(f(g(u),f(v,u)),g(u)). >> BACK DEMODULATING HINT 16814 WITH 18090. NEW HINT: 19448 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(u),f(f(u,v),u)),f(g(u),f(f(g(y),g(z)),f(z,x)))),f(f(g(x),f(y,x)),g(x)))=v. >> BACK DEMODULATING HINT 16813 WITH 18090. NEW HINT: 19449 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,g(x)),f(x,f(g(y),g(z)))),f(f(f(f(f(f(z,y),g(x)),f(x,g(y))),f(g(x),g(z))),f(z,y)),g(y)))=g(x). >> BACK DEMODULATING HINT 16811 WITH 18090. NEW HINT: 19450 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(f(g(y),f(u,z)),g(z))),g(x)),f(x,v))=f(f(f(y,f(f(g(y),f(u,w)),g(w))),f(f(v,f(y,f(f(g(y),f(u,w)),g(w)))),f(w,f(f(g(w),g(u)),y)))),g(y)). >> BACK DEMODULATING HINT 16806 WITH 18090. >> BACK DEMODULATING HINT 16793 WITH 18090. >> BACK DEMODULATING HINT 16792 WITH 18090. NEW HINT: 19451 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(z)),f(g(x),g(y))),f(f(f(f(y,x),g(u)),f(f(u,f(z,u)),g(u))),f(f(f(y,w),g(v)),f(v,v6))))=f(w,v6). >> BACK DEMODULATING HINT 16791 WITH 18090. >> BACK DEMODULATING HINT 16790 WITH 18090. >> BACK DEMODULATING HINT 16789 WITH 18090. >> BACK DEMODULATING HINT 16788 WITH 18090. >> BACK DEMODULATING HINT 16787 WITH 18090. >> BACK DEMODULATING HINT 16786 WITH 18090. >> BACK DEMODULATING HINT 16725 WITH 18090. >> BACK DEMODULATING HINT 16724 WITH 18090. >> BACK DEMODULATING HINT 16722 WITH 18090. >> BACK DEMODULATING HINT 16720 WITH 18090. >> BACK DEMODULATING HINT 16719 WITH 18090. >> BACK DEMODULATING HINT 16718 WITH 18090. NEW HINT: 19452 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(x,y),f(x,y)),f(g(y),g(x))))=y. >> BACK DEMODULATING HINT 13335 WITH 18090. >> BACK DEMODULATING HINT 13333 WITH 18090. >> BACK DEMODULATING HINT 13328 WITH 18090. >> BACK DEMODULATING HINT 13327 WITH 18090. >> BACK DEMODULATING HINT 13326 WITH 18090. >> BACK DEMODULATING HINT 13323 WITH 18090. >> BACK DEMODULATING HINT 13322 WITH 18090. NEW HINT: 19453 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(g(x),f(g(x),x)),x))=g(x). >> BACK DEMODULATING HINT 13320 WITH 18090. NEW HINT: 19454 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,f(y,x)),g(x)))=y. >> BACK DEMODULATING HINT 13315 WITH 18090. NEW HINT: 19455 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(f(y,f(g(x),x)),f(g(x),x))),f(g(x),x)),g(x))=f(f(f(g(x),x),x),f(g(x),g(x))) # label(bd). >> BACK DEMODULATING HINT 13313 WITH 18090. NEW HINT: 19456 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(f(x,f(f(g(x),g(y)),g(z))),z),f(g(z),f(f(z,f(y,x)),g(x)))),f(f(x,f(f(g(x),g(y)),g(z))),z)),f(f(g(z),f(f(z,f(y,x)),g(x))),g(u))),u)=f(f(g(z),f(f(z,f(y,x)),g(x))),g(y)) # label(bd). >> BACK DEMODULATING HINT 13309 WITH 18090. NEW HINT: 19457 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(f(x,f(y,x)),g(x)),f(f(x,f(y,x)),g(x))),f(x,f(f(g(x),g(y)),g(x)))))=y. >> BACK DEMODULATING HINT 13307 WITH 18090. NEW HINT: 19458 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(y,f(f(g(y),g(x)),x)))=g(x). >> BACK DEMODULATING HINT 13306 WITH 18090. >> BACK DEMODULATING HINT 13305 WITH 18090. >> BACK DEMODULATING HINT 13303 WITH 18090. >> BACK DEMODULATING HINT 13301 WITH 18090. NEW HINT: 19459 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,f(y,x)),g(x))),f(g(y),f(f(x,f(f(g(x),g(y)),g(x))),x)))=f(f(x,f(f(g(x),g(y)),g(x))),x). >> BACK DEMODULATING HINT 13297 WITH 18090. >> BACK DEMODULATING HINT 13291 WITH 18090. >> BACK DEMODULATING HINT 13286 WITH 18090. NEW HINT: 19460 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(y,f(f(g(y),g(x)),g(y))),y),f(f(y,f(f(g(y),g(x)),g(y))),y)))=f(f(y,f(f(g(y),g(x)),g(y))),y). >> BACK DEMODULATING HINT 13285 WITH 18090. NEW HINT: 19461 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(y,f(f(g(y),g(x)),g(y))),y),g(x)))=f(f(y,f(f(g(y),g(x)),g(y))),y). >> BACK DEMODULATING HINT 13280 WITH 18090. >> BACK DEMODULATING HINT 13279 WITH 18090. >> BACK DEMODULATING HINT 13278 WITH 18090. >> BACK DEMODULATING HINT 13277 WITH 18090. >> BACK DEMODULATING HINT 13276 WITH 18090. >> BACK DEMODULATING HINT 13275 WITH 18090. >> BACK DEMODULATING HINT 13274 WITH 18090. >> BACK DEMODULATING HINT 13270 WITH 18090. NEW HINT: 19462 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,f(f(z,f(g(x),x)),y)),g(y))=f(y,z). >> BACK DEMODULATING HINT 13269 WITH 18090. >> BACK DEMODULATING HINT 13268 WITH 18090. >> BACK DEMODULATING HINT 13263 WITH 18090. >> BACK DEMODULATING HINT 13262 WITH 18090. >> BACK DEMODULATING HINT 13261 WITH 18090. >> BACK DEMODULATING HINT 13260 WITH 18090. >> BACK DEMODULATING HINT 13259 WITH 18090. >> BACK DEMODULATING HINT 13257 WITH 18090. >> BACK DEMODULATING HINT 13253 WITH 18090. >> BACK DEMODULATING HINT 13252 WITH 18090. >> BACK DEMODULATING HINT 13251 WITH 18090. >> BACK DEMODULATING HINT 13250 WITH 18090. >> BACK DEMODULATING HINT 13245 WITH 18090. >> BACK DEMODULATING HINT 13244 WITH 18090. NEW HINT: 19463 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,y),f(g(y),z)))=z. >> BACK DEMODULATING HINT 13238 WITH 18090. >> BACK DEMODULATING HINT 13237 WITH 18090. >> BACK DEMODULATING HINT 13233 WITH 18090. >> BACK DEMODULATING HINT 13229 WITH 18090. >> BACK DEMODULATING HINT 13228 WITH 18090. >> BACK DEMODULATING HINT 13227 WITH 18090. >> BACK DEMODULATING HINT 13225 WITH 18090. NEW HINT: 19464 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),y),g(y))=f(f(v,f(f(g(v),g(z)),u)),g(u)). >> BACK DEMODULATING HINT 4861 WITH 18090. >> BACK DEMODULATING HINT 4860 WITH 18090. >> BACK DEMODULATING HINT 4826 WITH 18090. NEW HINT: 19465 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(g(x),f(f(w,f(f(g(w),g(u)),g(w))),f(w,f(g(v),g(z))))),f(f(z,v),f(u,z))),g(y))),x)=f(z,f(g(y),x)). >> BACK DEMODULATING HINT 4825 WITH 18090. >> BACK DEMODULATING HINT 4824 WITH 18090. >> BACK DEMODULATING HINT 4823 WITH 18090. >> BACK DEMODULATING HINT 4822 WITH 18090. >> BACK DEMODULATING HINT 4821 WITH 18090. >> BACK DEMODULATING HINT 4820 WITH 18090. >> BACK DEMODULATING HINT 4819 WITH 18090. NEW HINT: 19466 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(g(x),f(f(w,f(f(g(w),g(v)),g(w))),f(w,f(g(z),g(u))))),f(f(u,z),f(f(v,f(u,z)),g(z)))),g(y))),x)=f(u,f(g(y),x)). >> BACK DEMODULATING HINT 4796 WITH 18090. NEW HINT: 19467 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(u,f(y,u)),g(u))),f(f(f(x,w),g(v)),f(f(v,f(v6,v)),g(v)))))=f(w,v6). >> BACK DEMODULATING HINT 4795 WITH 18090. >> BACK DEMODULATING HINT 4794 WITH 18090. >> BACK DEMODULATING HINT 4793 WITH 18090. >> BACK DEMODULATING HINT 4792 WITH 18090. >> BACK DEMODULATING HINT 4791 WITH 18090. >> BACK DEMODULATING HINT 4790 WITH 18090. >> BACK DEMODULATING HINT 4789 WITH 18090. NEW HINT: 19468 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),g(z))),f(g(x),g(y))),f(f(f(f(y,x),g(u)),f(f(u,f(z,u)),g(u))),f(f(f(y,w),g(v)),f(f(v,f(v6,v)),g(v)))))=f(w,v6). >> BACK DEMODULATING HINT 4773 WITH 18090. NEW HINT: 19469 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(g(z),g(x))),f(f(f(f(x,z),g(u)),f(f(u,f(y,u)),g(u))),w))=f(g(x),w). >> BACK DEMODULATING HINT 4772 WITH 18090. >> BACK DEMODULATING HINT 4771 WITH 18090. >> BACK DEMODULATING HINT 4770 WITH 18090. >> BACK DEMODULATING HINT 4769 WITH 18090. >> BACK DEMODULATING HINT 4768 WITH 18090. >> BACK DEMODULATING HINT 4767 WITH 18090. >> BACK DEMODULATING HINT 4766 WITH 18090. NEW HINT: 19470 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),g(z))),f(g(x),g(y))),f(f(f(f(y,x),g(u)),f(f(u,f(z,u)),g(u))),w))=f(g(y),w). >> BACK DEMODULATING HINT 4701 WITH 18090. NEW HINT: 19471 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(g(y),z)),f(f(u,f(f(g(u),g(z)),x)),g(x))),f(y,v))=f(w,f(f(g(w),g(x)),v)). >> BACK DEMODULATING HINT 4691 WITH 18090. NEW HINT: 19472 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(g(v),f(x,f(f(g(x),f(y,u)),g(u)))))),f(f(z,f(f(g(z),g(y)),x)),g(x))),f(v,w))=f(v6,f(f(g(v6),g(x)),w)). >> BACK DEMODULATING HINT 4684 WITH 18090. NEW HINT: 19473 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(z,f(f(g(z),g(y)),x)),g(x)),f(g(v),f(x,f(f(g(x),f(y,u)),g(u)))))),f(f(z,f(f(g(z),g(y)),x)),g(x))),f(v,w))=f(v6,f(f(g(v6),g(x)),w)). >> BACK DEMODULATING HINT 4678 WITH 18090. >> BACK DEMODULATING HINT 4670 WITH 18090. >> BACK DEMODULATING HINT 4665 WITH 18090. >> BACK DEMODULATING HINT 4658 WITH 18090. NEW HINT: 19474 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(g(y),f(v,f(x,f(f(g(x),f(y,u)),g(u)))))),f(f(z,f(f(g(z),g(y)),x)),g(x))))=v. >> BACK DEMODULATING HINT 4657 WITH 18090. >> BACK DEMODULATING HINT 4656 WITH 18090. >> BACK DEMODULATING HINT 4655 WITH 18090. >> BACK DEMODULATING HINT 4654 WITH 18090. >> BACK DEMODULATING HINT 4653 WITH 18090. >> BACK DEMODULATING HINT 4648 WITH 18090. >> BACK DEMODULATING HINT 4640 WITH 18090. NEW HINT: 19475 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(f(g(x),f(y,z)),g(z)),f(f(f(z,f(f(g(z),g(y)),x)),g(x)),f(v,f(x,f(f(g(x),f(y,u)),g(u)))))),f(f(z,f(f(g(z),g(y)),x)),g(x))))=v. >> BACK DEMODULATING HINT 4635 WITH 18090. >> BACK DEMODULATING HINT 4629 WITH 18090. >> BACK DEMODULATING HINT 4617 WITH 18090. NEW HINT: 19476 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(y)),f(y,z))=f(f(f(u,f(f(g(u),f(x,v)),g(v))),f(z,u)),g(u)). >> BACK DEMODULATING HINT 4612 WITH 18090. >> BACK DEMODULATING HINT 4603 WITH 18090. NEW HINT: 19477 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(y)),f(y,z))=f(f(f(u,f(f(g(u),f(x,v)),g(v))),f(f(z,f(u,f(f(g(u),f(x,v)),g(v)))),f(v,f(f(g(v),g(x)),u)))),g(u)). >> BACK DEMODULATING HINT 4598 WITH 18090. >> BACK DEMODULATING HINT 4592 WITH 18090. >> BACK DEMODULATING HINT 4576 WITH 18090. NEW HINT: 19478 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(f(g(y),f(z,u)),g(u))),g(x)),f(f(x,f(v,x)),g(x)))=f(f(f(y,f(f(g(y),f(z,w)),g(w))),f(f(v,f(y,f(f(g(y),f(z,w)),g(w)))),f(w,f(f(g(w),g(z)),y)))),g(y)). >> BACK DEMODULATING HINT 4571 WITH 18090. >> BACK DEMODULATING HINT 4556 WITH 18090. NEW HINT: 19479 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(y,z)),g(z)),f(f(f(u,f(f(g(u),g(y)),x)),g(x)),w))=f(g(x),w). >> BACK DEMODULATING HINT 4551 WITH 18090. >> BACK DEMODULATING HINT 4545 WITH 18090. >> BACK DEMODULATING HINT 4538 WITH 18090. >> BACK DEMODULATING HINT 4537 WITH 18090. NEW HINT: 19480 [bsub_wt=2147483647, bsub_add_wt=-1024] f(v,f(f(u,f(f(g(u),f(y,z)),g(z))),g(y)))=v. >> BACK DEMODULATING HINT 4536 WITH 18090. >> BACK DEMODULATING HINT 4535 WITH 18090. >> BACK DEMODULATING HINT 4534 WITH 18090. >> BACK DEMODULATING HINT 4533 WITH 18090. >> BACK DEMODULATING HINT 4532 WITH 18090. >> BACK DEMODULATING HINT 4531 WITH 18090. >> BACK DEMODULATING HINT 4530 WITH 18090. >> BACK DEMODULATING HINT 4529 WITH 18090. >> BACK DEMODULATING HINT 4528 WITH 18090. NEW HINT: 19481 [bsub_wt=2147483647, bsub_add_wt=-1024] f(w,f(f(y,f(f(g(y),f(z,u)),g(u))),f(f(v,f(f(g(v),g(z)),y)),g(y))))=w. >> BACK DEMODULATING HINT 4527 WITH 18090. >> BACK DEMODULATING HINT 4526 WITH 18090. >> BACK DEMODULATING HINT 4525 WITH 18090. >> BACK DEMODULATING HINT 4524 WITH 18090. >> BACK DEMODULATING HINT 4523 WITH 18090. >> BACK DEMODULATING HINT 4522 WITH 18090. >> BACK DEMODULATING HINT 4521 WITH 18090. >> BACK DEMODULATING HINT 4520 WITH 18090. >> BACK DEMODULATING HINT 4519 WITH 18090. >> BACK DEMODULATING HINT 4518 WITH 18090. >> BACK DEMODULATING HINT 4517 WITH 18090. >> BACK DEMODULATING HINT 4516 WITH 18090. >> BACK DEMODULATING HINT 4515 WITH 18090. >> BACK DEMODULATING HINT 4514 WITH 18090. >> BACK DEMODULATING HINT 4513 WITH 18090. >> BACK DEMODULATING HINT 4512 WITH 18090. >> BACK DEMODULATING HINT 4511 WITH 18090. >> BACK DEMODULATING HINT 4510 WITH 18090. >> BACK DEMODULATING HINT 4509 WITH 18090. >> BACK DEMODULATING HINT 4482 WITH 18090. NEW HINT: 19482 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),z)),g(z))=f(g(x),f(f(v,f(f(g(v),g(y)),u)),g(u))). >> BACK DEMODULATING HINT 4477 WITH 18090. >> BACK DEMODULATING HINT 4466 WITH 18090. NEW HINT: 19483 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(u,f(f(g(u),g(z)),y)),g(y)),v)),g(v))=f(g(x),f(f(w,f(f(g(w),g(z)),y)),g(y))). >> BACK DEMODULATING HINT 4463 WITH 18090. >> BACK DEMODULATING HINT 4458 WITH 18090. >> BACK DEMODULATING HINT 4450 WITH 18090. NEW HINT: 19484 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(g(v),g(u)),f(v,f(f(g(v),f(u,z)),g(z))))))=f(g(y),g(v)). >> BACK DEMODULATING HINT 4449 WITH 18090. >> BACK DEMODULATING HINT 4448 WITH 18090. >> BACK DEMODULATING HINT 4447 WITH 18090. >> BACK DEMODULATING HINT 4446 WITH 18090. >> BACK DEMODULATING HINT 4445 WITH 18090. >> BACK DEMODULATING HINT 4440 WITH 18090. >> BACK DEMODULATING HINT 4431 WITH 18090. >> BACK DEMODULATING HINT 4426 WITH 18090. >> BACK DEMODULATING HINT 4417 WITH 18090. >> BACK DEMODULATING HINT 4416 WITH 18090. >> BACK DEMODULATING HINT 4415 WITH 18090. >> BACK DEMODULATING HINT 4414 WITH 18090. >> BACK DEMODULATING HINT 4413 WITH 18090. >> BACK DEMODULATING HINT 4412 WITH 18090. >> BACK DEMODULATING HINT 4411 WITH 18090. >> BACK DEMODULATING HINT 4410 WITH 18090. >> BACK DEMODULATING HINT 4394 WITH 18090. >> BACK DEMODULATING HINT 4391 WITH 18090. >> BACK DEMODULATING HINT 4390 WITH 18090. >> BACK DEMODULATING HINT 4389 WITH 18090. >> BACK DEMODULATING HINT 4383 WITH 18090. >> BACK DEMODULATING HINT 4378 WITH 18090. >> BACK DEMODULATING HINT 4364 WITH 18090. >> BACK DEMODULATING HINT 4361 WITH 18090. >> BACK DEMODULATING HINT 4360 WITH 18090. >> BACK DEMODULATING HINT 4353 WITH 18090. >> BACK DEMODULATING HINT 4348 WITH 18090. >> BACK DEMODULATING HINT 4343 WITH 18090. >> BACK DEMODULATING HINT 4342 WITH 18090. >> BACK DEMODULATING HINT 4331 WITH 18090. >> BACK DEMODULATING HINT 4330 WITH 18090. >> BACK DEMODULATING HINT 4329 WITH 18090. >> BACK DEMODULATING HINT 4328 WITH 18090. >> BACK DEMODULATING HINT 4327 WITH 18090. >> BACK DEMODULATING HINT 4326 WITH 18090. >> BACK DEMODULATING HINT 4325 WITH 18090. >> BACK DEMODULATING HINT 4324 WITH 18090. >> BACK DEMODULATING HINT 4323 WITH 18090. >> BACK DEMODULATING HINT 4322 WITH 18090. >> BACK DEMODULATING HINT 4321 WITH 18090. >> BACK DEMODULATING HINT 4320 WITH 18090. >> BACK DEMODULATING HINT 4319 WITH 18090. >> BACK DEMODULATING HINT 4318 WITH 18090. >> BACK DEMODULATING HINT 4317 WITH 18090. >> BACK DEMODULATING HINT 4316 WITH 18090. >> BACK DEMODULATING HINT 4314 WITH 18090. NEW HINT: 19485 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(u,g(z)),f(z,f(g(u),g(x)))))=f(g(y),g(x)). >> BACK DEMODULATING HINT 4313 WITH 18090. >> BACK DEMODULATING HINT 4312 WITH 18090. >> BACK DEMODULATING HINT 4311 WITH 18090. >> BACK DEMODULATING HINT 4310 WITH 18090. NEW HINT: 19486 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(y,g(x))),x),f(g(y),g(z)))=f(g(x),f(f(u,g(y)),f(y,f(g(u),g(z))))). >> BACK DEMODULATING HINT 4309 WITH 18090. NEW HINT: 19487 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(y,g(x))),x),f(g(y),g(z)))=f(u,f(f(g(u),g(x)),f(f(v,g(y)),f(y,f(g(v),g(z)))))). >> BACK DEMODULATING HINT 4308 WITH 18090. NEW HINT: 19488 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),f(z,g(y)))),y),f(g(z),g(u)))=f(v,f(f(g(v),g(y)),f(f(w,g(z)),f(z,f(g(w),g(u)))))). >> BACK DEMODULATING HINT 4289 WITH 18090. >> BACK DEMODULATING HINT 4288 WITH 18090. >> BACK DEMODULATING HINT 4286 WITH 18090. >> BACK DEMODULATING HINT 4285 WITH 18090. NEW HINT: 19489 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,g(x)),f(x,f(g(y),g(z)))),f(f(f(f(f(x,f(f(g(x),f(z,y)),g(x))),f(x,g(y))),f(g(x),g(z))),f(z,y)),g(y)))=g(x). >> BACK DEMODULATING HINT 4283 WITH 18090. >> BACK DEMODULATING HINT 4282 WITH 18090. >> BACK DEMODULATING HINT 4281 WITH 18090. >> BACK DEMODULATING HINT 4275 WITH 18090. >> BACK DEMODULATING HINT 4273 WITH 18090. NEW HINT: 19490 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(g(y),y),x),z))=z. >> BACK DEMODULATING HINT 4272 WITH 18090. NEW HINT: 19491 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),f(f(g(z),z),y))),x))=x. >> BACK DEMODULATING HINT 4271 WITH 18090. NEW HINT: 19492 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(g(z),f(f(g(u),u),z))),y)))=y. >> BACK DEMODULATING HINT 4270 WITH 18090. NEW HINT: 19493 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(g(u),f(f(g(z),f(f(z,u),z)),g(z)))),y)))=y. >> BACK DEMODULATING HINT 4269 WITH 18090. >> BACK DEMODULATING HINT 4268 WITH 18090. >> BACK DEMODULATING HINT 4267 WITH 18090. NEW HINT: 19494 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(u),f(f(u,v),u)),f(g(u),f(f(z,f(f(g(z),g(y)),g(z))),f(z,x)))),f(f(g(x),f(y,x)),g(x)))=v. >> BACK DEMODULATING HINT 4266 WITH 18090. NEW HINT: 19495 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(u),f(v,u)),f(g(u),f(f(z,f(f(g(z),g(y)),g(z))),f(z,x)))),f(f(g(x),f(y,x)),g(x)))=f(f(g(u),f(v,u)),g(u)). >> BACK DEMODULATING HINT 4265 WITH 18090. NEW HINT: 19496 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(v),f(w,v)),f(g(v),f(f(u,f(f(g(u),g(z)),g(u))),f(u,y)))),f(f(f(g(y),f(z,y)),f(g(y),x)),g(x)))=f(f(g(v),f(w,v)),g(v)). >> BACK DEMODULATING HINT 4264 WITH 18090. NEW HINT: 19497 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),x),f(z,f(g(x),y))),f(g(y),x))=f(f(g(y),f(x,f(z,g(y)))),y). >> BACK DEMODULATING HINT 4261 WITH 18090. NEW HINT: 19498 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,y),f(f(z,f(x,y)),g(y))),g(x))),x)=f(f(y,z),x). >> BACK DEMODULATING HINT 4252 WITH 18090. NEW HINT: 19499 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(g(y),z))=f(f(f(g(u),g(x)),f(f(x,u),f(x,u))),f(g(u),z)). >> BACK DEMODULATING HINT 4251 WITH 18090. NEW HINT: 19500 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(g(y),z))=f(u,f(f(g(u),x),z)). >> BACK DEMODULATING HINT 4246 WITH 18090. >> BACK DEMODULATING HINT 4240 WITH 18090. >> BACK DEMODULATING HINT 4238 WITH 18090. NEW HINT: 19501 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),v),u)))=f(v,u). >> BACK DEMODULATING HINT 4233 WITH 18090. NEW HINT: 19502 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(u)),f(g(z),g(y))))=f(f(g(u),g(z)),g(y)). >> BACK DEMODULATING HINT 4227 WITH 18090. NEW HINT: 19503 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(z,f(f(u,f(f(g(u),v),f(f(g(v),f(g(z),g(v))),v))),g(y))))=x. >> BACK DEMODULATING HINT 4223 WITH 18090. NEW HINT: 19504 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(y,f(u,f(f(g(y),x),z)))),f(g(z),f(g(x),y)))=f(f(g(x),f(y,f(u,g(x)))),x). >> BACK DEMODULATING HINT 4221 WITH 18090. NEW HINT: 19505 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,z),g(x)))=f(g(x),f(y,f(z,g(x)))). >> BACK DEMODULATING HINT 4220 WITH 18090. NEW HINT: 19506 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),y)),f(u,g(z))))=f(g(z),f(f(y,u),g(z))). >> BACK DEMODULATING HINT 4218 WITH 18090. NEW HINT: 19507 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,y),f(f(g(y),g(x)),f(g(y),g(x)))),f(f(f(f(x,y),f(x,y)),f(g(y),g(x))),f(f(f(x,y),f(x,y)),f(g(y),g(x))))),g(y))=x. >> BACK DEMODULATING HINT 4217 WITH 18090. NEW HINT: 19508 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(f(z,u),f(z,u)),f(g(u),g(z))),g(y))),f(y,g(u))))=z. >> BACK DEMODULATING HINT 4216 WITH 18090. >> BACK DEMODULATING HINT 4215 WITH 18090. NEW HINT: 19509 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(z,y)),f(g(y),x)),g(x))=f(f(f(g(y),f(z,y)),f(g(y),f(f(v6,f(f(g(v6),g(w)),g(v6))),f(v6,v)))),f(f(f(g(v),f(w,v)),f(g(v),u)),g(u))). >> BACK DEMODULATING HINT 4214 WITH 18090. NEW HINT: 19510 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(v),f(w,v)),f(g(v),f(f(u,f(f(g(u),g(z)),g(u))),f(u,y)))),f(f(f(g(y),f(z,y)),f(g(y),x)),g(x)))=f(f(f(g(v),f(w,v)),f(g(v),v6)),g(v6)). >> BACK DEMODULATING HINT 4211 WITH 18090. NEW HINT: 19511 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(v),f(f(v,w),v)),f(g(v),f(f(u,f(f(g(u),g(z)),g(u))),f(u,y)))),f(f(f(g(y),f(z,y)),f(g(y),x)),g(x)))=w. >> BACK DEMODULATING HINT 4209 WITH 18090. >> BACK DEMODULATING HINT 4208 WITH 18090. >> BACK DEMODULATING HINT 4207 WITH 18090. >> BACK DEMODULATING HINT 4206 WITH 18090. >> BACK DEMODULATING HINT 4205 WITH 18090. >> BACK DEMODULATING HINT 4203 WITH 18090. NEW HINT: 19512 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(g(v),f(f(f(g(u),f(f(u,v),u)),f(g(u),z)),g(z)))),y)))=y. >> BACK DEMODULATING HINT 4202 WITH 18090. >> BACK DEMODULATING HINT 4199 WITH 18090. >> BACK DEMODULATING HINT 4197 WITH 18090. NEW HINT: 19513 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(z,f(v,f(f(g(z),y),u)))),f(g(u),f(g(y),z)))))=f(z,v). >> BACK DEMODULATING HINT 4196 WITH 18090. NEW HINT: 19514 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,z),g(x))),x)=f(f(g(x),f(y,f(z,f(f(g(y),x),u)))),f(g(u),f(g(x),y))). >> BACK DEMODULATING HINT 4194 WITH 18090. NEW HINT: 19515 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),g(y))),u))=f(g(z),f(g(y),u)). >> BACK DEMODULATING HINT 4193 WITH 18090. >> BACK DEMODULATING HINT 4185 WITH 18090. >> BACK DEMODULATING HINT 4181 WITH 18090. NEW HINT: 19516 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),g(y)),y)))=f(u,g(u)). >> BACK DEMODULATING HINT 4180 WITH 18090. NEW HINT: 19517 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),g(y)),y))=g(x). >> BACK DEMODULATING HINT 4174 WITH 18090. >> BACK DEMODULATING HINT 4172 WITH 18090. >> BACK DEMODULATING HINT 4161 WITH 18090. NEW HINT: 19518 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,z),g(x))),x)=f(f(u,f(f(g(u),f(g(x),y)),f(z,f(f(g(y),x),u)))),f(g(u),f(g(x),y))). >> BACK DEMODULATING HINT 4160 WITH 18090. NEW HINT: 19519 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(z,f(f(g(z),f(g(y),u)),f(v,f(f(g(u),y),z)))),f(g(z),f(g(y),u)))))=f(u,v). >> BACK DEMODULATING HINT 4158 WITH 18090. NEW HINT: 19520 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(y,f(g(u),f(f(z,f(f(g(z),x),f(y,x))),g(x))))),f(x,f(f(f(g(x),g(y)),f(g(x),z)),g(z))))=f(f(x,f(y,f(g(u),g(y)))),y). >> BACK DEMODULATING HINT 4157 WITH 18090. NEW HINT: 19521 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(y,f(g(u),f(f(z,f(f(g(z),x),f(y,x))),g(x))))),f(x,f(f(f(g(x),g(y)),f(g(x),z)),g(z))))=f(f(x,f(y,f(g(u),g(y)))),f(f(g(x),z),f(f(f(g(z),x),f(f(y,f(g(z),x)),g(x))),z))). >> BACK DEMODULATING HINT 4156 WITH 18090. NEW HINT: 19522 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(y,f(g(z),g(y)))),f(g(x),f(f(u,f(f(g(u),x),f(y,x))),g(x))))=f(f(x,f(y,f(g(z),f(f(u,f(f(g(u),x),f(y,x))),g(x))))),f(x,f(f(f(g(x),g(y)),f(g(x),u)),g(u)))). >> BACK DEMODULATING HINT 4155 WITH 18090. NEW HINT: 19523 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(g(x),y),f(f(f(g(y),x),f(f(z,f(g(y),x)),g(x))),y)),f(g(u),g(z)))),f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x))))=f(f(x,f(z,f(g(u),f(f(y,f(f(g(y),x),f(z,x))),g(x))))),f(x,f(f(f(g(x),g(z)),f(g(x),y)),g(y)))). >> BACK DEMODULATING HINT 4154 WITH 18090. NEW HINT: 19524 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x))),f(g(u),g(z)))),f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x))))=f(f(x,f(z,f(g(u),f(f(y,f(f(g(y),x),f(z,x))),g(x))))),f(x,f(f(f(g(x),g(z)),f(g(x),y)),g(y)))). >> BACK DEMODULATING HINT 4151 WITH 18090. NEW HINT: 19525 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(f(x,y),f(f(f(f(z,f(f(f(g(z),g(v)),f(g(z),u)),g(u))),z),f(x,y)),g(y))),g(x)),f(v,g(w))),f(g(y),g(x))))=f(x,f(f(y,f(f(g(y),g(x)),g(w))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 4150 WITH 18090. NEW HINT: 19526 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(f(f(x,y),f(f(f(u,f(f(f(g(u),g(w)),f(g(u),v)),g(v))),u),f(g(y),g(x)))),f(f(x,y),z)),g(z)),f(w,g(v6))),f(g(y),g(x))))=f(x,f(f(y,f(f(g(y),g(x)),g(v6))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 4147 WITH 18090. NEW HINT: 19527 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(x),f(f(f(x,y),f(f(z,f(x,y)),g(y))),g(x))),x))=f(f(y,z),x). >> BACK DEMODULATING HINT 4146 WITH 18090. NEW HINT: 19528 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(x),f(f(f(x,y),f(f(v,f(x,f(f(y,f(f(g(y),g(x)),g(u))),f(g(y),g(x))))),f(f(x,y),f(f(u,f(f(g(y),g(x)),z)),g(z))))),f(x,y))),x))=f(f(y,v),x). >> BACK DEMODULATING HINT 4145 WITH 18090. NEW HINT: 19529 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(f(f(y,z),f(f(u,f(y,z)),g(z))),g(y))),y)))=f(y,f(f(z,u),y)). >> BACK DEMODULATING HINT 4144 WITH 18090. NEW HINT: 19530 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(f(f(y,z),f(f(w,f(y,f(f(z,f(f(g(z),g(y)),g(v))),f(g(z),g(y))))),f(f(y,z),f(f(v,f(f(g(z),g(y)),u)),g(u))))),f(y,z))),y)))=f(y,f(f(z,w),y)). >> BACK DEMODULATING HINT 4143 WITH 18090. NEW HINT: 19531 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(f(z,u),f(v,x))),g(x)))=f(f(g(x),y),f(f(f(z,u),f(f(v,f(z,u)),g(u))),g(z))). >> BACK DEMODULATING HINT 4141 WITH 18090. NEW HINT: 19532 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(z,f(f(g(z),f(x,y)),u)),f(g(y),g(x))),f(f(f(f(x,y),f(f(f(f(v,f(f(f(g(v),g(u)),f(g(v),w)),g(w))),v),f(x,y)),g(y))),g(x)),g(v6))),f(g(y),g(x))))=f(x,f(f(y,f(f(g(y),g(x)),g(v6))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 4139 WITH 18090. NEW HINT: 19533 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),g(z))),f(g(x),g(y))),f(f(f(f(y,x),g(u)),f(f(u,f(z,u)),g(u))),f(f(v,f(f(g(v),w),y)),g(y))))=f(g(y),w). >> BACK DEMODULATING HINT 4138 WITH 18090. >> BACK DEMODULATING HINT 4137 WITH 18090. >> BACK DEMODULATING HINT 4135 WITH 18090. NEW HINT: 19534 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(f(f(x,u),f(f(v,f(f(g(u),g(x)),z)),g(z))),g(y))),y))=f(f(u,v),f(g(u),g(x))). >> BACK DEMODULATING HINT 4121 WITH 18090. NEW HINT: 19535 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(y,f(f(g(y),f(g(u),g(z))),f(f(f(z,u),f(f(f(g(x),g(z)),g(v)),f(z,u))),f(g(u),g(z))))))=f(u,f(f(g(u),g(z)),g(v))). >> BACK DEMODULATING HINT 4117 WITH 18090. NEW HINT: 19536 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(g(x),f(f(w,f(f(g(w),g(v)),g(w))),f(w,f(g(u),g(z))))),f(z,f(f(u,v),z))),g(y))),x)=f(z,f(g(y),x)). >> BACK DEMODULATING HINT 4113 WITH 18090. NEW HINT: 19537 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(g(z),g(y))),g(x)),f(f(f(f(x,y),g(u)),f(f(u,f(z,u)),g(u))),f(f(f(x,w),g(v)),f(f(v,f(v6,v)),g(v)))))=f(w,v6). >> BACK DEMODULATING HINT 4111 WITH 18090. NEW HINT: 19538 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(g(z),g(y))),g(x)),f(f(f(f(x,y),g(u)),f(f(u,f(z,u)),g(u))),f(f(v,f(f(g(v),w),x)),g(x))))=f(g(x),w). >> BACK DEMODULATING HINT 4107 WITH 18090. NEW HINT: 19539 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(z,f(f(g(z),x),f(y,x))),g(x))),f(x,f(f(f(g(x),g(y)),f(g(x),z)),g(z))))=x. >> BACK DEMODULATING HINT 4106 WITH 18090. NEW HINT: 19540 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,f(f(g(y),x),f(z,x))),g(x)),f(f(g(z),g(z)),g(x))),f(f(y,f(f(g(y),x),f(z,x))),g(x)))=x. >> BACK DEMODULATING HINT 4105 WITH 18090. NEW HINT: 19541 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,f(f(g(y),x),f(z,x))),g(x)),f(f(g(z),f(f(x,f(f(f(g(x),g(z)),f(g(x),y)),g(y))),u)),g(u))),f(f(y,f(f(g(y),x),f(z,x))),g(x)))=x. >> BACK DEMODULATING HINT 4104 WITH 18090. NEW HINT: 19542 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),x),f(f(z,f(f(u,v),z)),g(z)))=f(g(y),f(f(x,f(f(z,u),f(v,y))),g(y))). >> BACK DEMODULATING HINT 4103 WITH 18090. NEW HINT: 19543 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(z,f(f(g(z),g(u)),x))),g(x)))=f(f(g(x),y),g(u)). >> BACK DEMODULATING HINT 4102 WITH 18090. NEW HINT: 19544 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(f(z,u),f(v,x))),g(x)))=f(f(g(x),y),f(f(z,f(f(u,v),z)),g(z))). >> BACK DEMODULATING HINT 4101 WITH 18090. NEW HINT: 19545 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(f(f(y,z),f(f(w,f(y,f(f(g(y),f(g(v),g(z))),g(y)))),f(f(y,z),f(f(v,f(f(g(z),g(y)),u)),g(u))))),f(y,z))),y)))=f(y,f(f(z,w),y)). >> BACK DEMODULATING HINT 4100 WITH 18090. NEW HINT: 19546 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(x),f(f(f(x,y),f(f(v,f(x,f(f(g(x),f(g(u),g(y))),g(x)))),f(f(x,y),f(f(u,f(f(g(y),g(x)),z)),g(z))))),f(x,y))),x))=f(f(y,v),x). >> BACK DEMODULATING HINT 4097 WITH 18090. NEW HINT: 19547 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),g(y))),g(x)))=f(f(g(y),g(x)),f(f(f(f(f(f(x,y),f(f(f(v,f(f(f(g(v),g(v6)),f(g(v),w)),g(w))),v),f(g(y),g(x)))),f(f(x,y),u)),g(u)),f(v6,g(z))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 4095 WITH 18090. NEW HINT: 19548 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,f(f(g(y),x),f(z,x))),g(x)),f(f(g(u),g(z)),g(x))),f(f(y,f(f(g(y),x),f(z,x))),g(x)))=f(f(x,f(z,f(g(u),f(f(y,f(f(g(y),x),f(z,x))),g(x))))),f(x,f(f(f(g(x),g(z)),f(g(x),y)),g(y)))). >> BACK DEMODULATING HINT 4094 WITH 18090. NEW HINT: 19549 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,f(f(g(y),x),f(z,x))),g(x)),f(f(g(u),g(z)),g(x))),f(f(y,f(f(g(y),x),f(z,x))),g(x)))=f(f(v,f(f(g(v),f(f(y,f(f(g(y),x),f(z,x))),g(x))),f(g(u),f(f(y,f(f(g(y),x),f(z,x))),g(x))))),f(x,f(f(f(g(x),g(z)),f(g(x),y)),g(y)))). >> BACK DEMODULATING HINT 4093 WITH 18090. NEW HINT: 19550 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(f(f(x,y),f(f(f(u,f(f(f(g(u),g(w)),f(g(u),v)),g(v))),u),f(g(y),g(x)))),f(f(x,y),z)),g(z)),f(w,g(v6))),f(g(y),g(x))))=f(x,f(f(g(x),f(g(v6),g(y))),g(x))). >> BACK DEMODULATING HINT 4092 WITH 18090. NEW HINT: 19551 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x)))=z. >> BACK DEMODULATING HINT 4091 WITH 18090. NEW HINT: 19552 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),f(g(z),g(y)))),y),f(z,f(f(y,f(u,y)),g(y))))=f(g(v),f(f(w,f(f(g(w),v),f(u,v))),g(v))). >> BACK DEMODULATING HINT 4090 WITH 18090. NEW HINT: 19553 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(z,f(f(g(z),y),f(u,y))),g(y))),v))=f(y,f(u,v)). >> BACK DEMODULATING HINT 4089 WITH 18090. NEW HINT: 19554 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x))),u)=f(z,u). >> BACK DEMODULATING HINT 4088 WITH 18090. NEW HINT: 19555 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(y)),f(g(z),g(y)))),y),f(z,f(f(y,f(f(u,v),y)),g(y))))=f(f(g(y),f(f(w,f(f(g(w),y),f(u,y))),g(y))),v). >> BACK DEMODULATING HINT 4087 WITH 18090. NEW HINT: 19556 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(f(y,f(f(f(g(y),g(x)),f(g(y),z)),g(z))),y),u),v)),y)=f(f(w,f(f(g(w),u),v)),y). >> BACK DEMODULATING HINT 4086 WITH 18090. NEW HINT: 19557 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),y),z)),u)=f(f(v,f(f(f(f(u,f(f(f(g(u),g(v)),f(g(u),w)),g(w))),u),y),z)),u). >> BACK DEMODULATING HINT 4085 WITH 18090. NEW HINT: 19558 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x))),u),x)=f(f(z,u),x). >> BACK DEMODULATING HINT 4079 WITH 18090. NEW HINT: 19559 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(g(y),f(f(z,f(f(g(z),u),y)),g(y))),y))=f(f(x,u),y). >> BACK DEMODULATING HINT 4078 WITH 18090. NEW HINT: 19560 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(f(x,z),f(f(g(z),f(f(u,f(f(g(u),y),z)),g(z))),z)). >> BACK DEMODULATING HINT 4073 WITH 18090. NEW HINT: 19561 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),y),f(z,f(g(y),x))),f(g(x),y)))=f(x,f(f(f(g(x),y),f(z,u)),g(u))). >> BACK DEMODULATING HINT 4072 WITH 18090. NEW HINT: 19562 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),u),f(z,y)),g(y)))=f(x,f(f(f(g(x),u),f(z,f(g(u),x))),f(g(x),u))). >> BACK DEMODULATING HINT 4071 WITH 18090. NEW HINT: 19563 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(z,f(f(g(z),y),f(f(f(g(y),z),f(v,u)),g(u)))),g(y))),y))=f(y,f(f(f(g(y),z),f(v,f(g(z),y))),f(g(y),z))). >> BACK DEMODULATING HINT 4066 WITH 18090. NEW HINT: 19564 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),f(z,y)),g(y))),f(f(f(f(y,f(f(g(y),g(z)),x)),g(x)),f(f(w,f(f(x,f(f(g(x),f(z,y)),g(y))),f(f(v,f(f(g(v),g(z)),x)),g(x)))),u)),g(u)))=w. >> BACK DEMODULATING HINT 4061 WITH 18090. NEW HINT: 19565 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),z),u),f(f(f(g(u),f(g(z),v)),g(v)),x)),g(x))=f(f(w,f(f(g(w),g(y)),x)),g(x)). >> BACK DEMODULATING HINT 4057 WITH 18090. NEW HINT: 19566 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(f(g(y),z),f(f(v,f(f(g(z),y),u)),g(u))),f(g(y),z))))=f(z,v). >> BACK DEMODULATING HINT 4054 WITH 18090. NEW HINT: 19567 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(y),f(f(f(f(y,f(f(g(x),f(g(y),z)),g(z))),y),u),g(y))),y))=u. >> BACK DEMODULATING HINT 4053 WITH 18090. NEW HINT: 19568 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(z,f(f(g(z),y),u)),g(y))),y))=f(y,u). >> BACK DEMODULATING HINT 4051 WITH 18090. NEW HINT: 19569 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,f(f(g(y),x),z)),g(x))),x)=z. >> BACK DEMODULATING HINT 4047 WITH 18090. NEW HINT: 19570 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(x),y),f(z,f(g(y),x))),f(f(g(x),y),u)),g(u))=f(f(g(x),f(f(y,z),g(x))),x). >> BACK DEMODULATING HINT 4045 WITH 18090. >> BACK DEMODULATING HINT 4044 WITH 18090. NEW HINT: 19571 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(f(y,z),y)),f(g(y),x)),g(x))=z. >> BACK DEMODULATING HINT 4043 WITH 18090. NEW HINT: 19572 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(f(f(x,u),f(f(v,f(f(g(u),g(x)),z)),g(z))),g(y))),y))=f(f(g(x),f(f(f(x,f(f(u,v),x)),g(x)),g(u))),g(x)). >> BACK DEMODULATING HINT 4042 WITH 18090. NEW HINT: 19573 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,f(f(y,z),x)),g(x)),g(y))),g(x))=f(f(g(x),u),f(f(g(u),f(f(f(x,y),f(f(z,f(f(g(y),g(x)),v)),g(v))),g(u))),u)). >> BACK DEMODULATING HINT 4041 WITH 18090. NEW HINT: 19574 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(z,f(f(f(f(f(g(z),f(f(x,y),z)),f(g(z),u)),g(u)),v),z)),g(z)),g(y))),g(x))=f(f(g(x),w),f(f(g(w),f(f(f(x,y),f(f(v,f(f(g(y),g(x)),v6)),g(v6))),g(w))),w)). >> BACK DEMODULATING HINT 4040 WITH 18090. NEW HINT: 19575 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(f(f(x,u),f(f(f(f(g(u),g(x)),g(v)),f(f(g(u),g(x)),z)),g(z))),g(y))),y))=f(f(g(x),f(g(v),g(u))),g(x)). >> BACK DEMODULATING HINT 4035 WITH 18090. NEW HINT: 19576 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(v),f(y,f(f(g(y),x),f(f(g(x),f(g(u),g(z))),x))))),g(x)))=f(z,f(f(g(z),f(g(v),g(u))),g(z))). >> BACK DEMODULATING HINT 4033 WITH 18090. NEW HINT: 19577 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,z),g(x))),x)=f(f(f(g(x),y),f(f(z,f(f(g(y),x),u)),g(u))),f(g(x),y)). >> BACK DEMODULATING HINT 4032 WITH 18090. NEW HINT: 19578 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),x),f(f(u,f(f(g(x),y),z)),g(z))),f(g(y),x))=f(f(g(y),f(f(x,u),g(y))),y). >> BACK DEMODULATING HINT 4031 WITH 18090. NEW HINT: 19579 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),x),z),f(f(g(z),f(u,g(z))),z))=f(f(g(y),f(f(x,u),g(y))),y). >> BACK DEMODULATING HINT 4029 WITH 18090. NEW HINT: 19580 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(f(x,z),g(y))),y))=z. >> BACK DEMODULATING HINT 4028 WITH 18090. NEW HINT: 19581 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(z),f(x,y)),g(y))),g(x))=f(f(g(x),u),f(f(g(u),f(g(z),g(u))),u)). >> BACK DEMODULATING HINT 4027 WITH 18090. NEW HINT: 19582 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(g(z),g(y))),y))=f(f(g(x),f(f(g(z),f(x,u)),g(u))),g(x)). >> BACK DEMODULATING HINT 4022 WITH 18090. NEW HINT: 19583 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(z,g(y))),y)))=z. >> BACK DEMODULATING HINT 4021 WITH 18090. NEW HINT: 19584 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(z,g(y))),f(f(u,f(f(v,f(f(g(v),g(u)),y)),u)),g(u)))))=z. >> BACK DEMODULATING HINT 4020 WITH 18090. NEW HINT: 19585 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(f(u,f(f(g(u),f(f(g(y),f(u,v)),g(v))),g(u))),f(z,g(y))),f(f(u,f(f(v,f(f(g(v),g(u)),y)),u)),g(u)))))=z. >> BACK DEMODULATING HINT 4019 WITH 18090. NEW HINT: 19586 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(y,f(f(z,f(f(g(z),g(y)),u)),y)),g(y))),f(f(f(y,f(f(g(y),f(f(g(u),f(y,z)),g(z))),g(y))),f(v,g(u))),f(f(y,f(f(z,f(f(g(z),g(y)),u)),y)),g(y)))))=v. >> BACK DEMODULATING HINT 3948 WITH 18090. NEW HINT: 19587 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(x,f(f(y,f(z,y)),g(y))). >> BACK DEMODULATING HINT 3943 WITH 18090. NEW HINT: 19588 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),z),f(g(z),z))=f(x,f(f(y,f(z,y)),g(y))). >> BACK DEMODULATING HINT 3942 WITH 18090. >> BACK DEMODULATING HINT 3941 WITH 18090. >> BACK DEMODULATING HINT 3940 WITH 18090. >> BACK DEMODULATING HINT 3939 WITH 18090. >> BACK DEMODULATING HINT 3938 WITH 18090. >> BACK DEMODULATING HINT 3937 WITH 18090. >> BACK DEMODULATING HINT 3936 WITH 18090. >> BACK DEMODULATING HINT 3935 WITH 18090. >> BACK DEMODULATING HINT 3934 WITH 18090. >> BACK DEMODULATING HINT 3933 WITH 18090. >> BACK DEMODULATING HINT 3932 WITH 18090. >> BACK DEMODULATING HINT 3931 WITH 18090. >> BACK DEMODULATING HINT 3930 WITH 18090. >> BACK DEMODULATING HINT 3929 WITH 18090. >> BACK DEMODULATING HINT 3928 WITH 18090. >> BACK DEMODULATING HINT 3927 WITH 18090. >> BACK DEMODULATING HINT 3926 WITH 18090. >> BACK DEMODULATING HINT 3925 WITH 18090. >> BACK DEMODULATING HINT 3907 WITH 18090. NEW HINT: 19589 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),z)),f(f(f(g(z),y),u),f(g(y),z))))=f(f(u,g(y)),z). >> BACK DEMODULATING HINT 3906 WITH 18090. NEW HINT: 19590 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),z)),f(f(g(z),f(y,u)),f(g(y),z))))=f(f(u,g(y)),z). >> BACK DEMODULATING HINT 3905 WITH 18090. >> BACK DEMODULATING HINT 3904 WITH 18090. >> BACK DEMODULATING HINT 3903 WITH 18090. >> BACK DEMODULATING HINT 3902 WITH 18090. >> BACK DEMODULATING HINT 3901 WITH 18090. >> BACK DEMODULATING HINT 3900 WITH 18090. NEW HINT: 19591 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),z)),f(f(f(u,f(f(g(u),g(z)),y)),v),f(g(y),z))))=f(f(v,g(y)),z). >> BACK DEMODULATING HINT 3899 WITH 18090. >> BACK DEMODULATING HINT 3898 WITH 18090. >> BACK DEMODULATING HINT 3897 WITH 18090. NEW HINT: 19592 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),z)),f(f(f(v,f(f(g(v),g(z)),y)),w),f(f(g(y),f(z,u)),g(u)))))=f(f(w,g(y)),z). >> BACK DEMODULATING HINT 3896 WITH 18090. >> BACK DEMODULATING HINT 3895 WITH 18090. NEW HINT: 19593 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),g(y)),z),f(f(f(v,f(f(g(v),g(z)),y)),w),f(f(g(y),f(z,u)),g(u)))))=f(f(w,g(y)),z). >> BACK DEMODULATING HINT 3894 WITH 18090. >> BACK DEMODULATING HINT 3893 WITH 18090. >> BACK DEMODULATING HINT 3892 WITH 18090. >> BACK DEMODULATING HINT 3891 WITH 18090. >> BACK DEMODULATING HINT 3890 WITH 18090. >> BACK DEMODULATING HINT 3889 WITH 18090. >> BACK DEMODULATING HINT 3888 WITH 18090. >> BACK DEMODULATING HINT 3887 WITH 18090. >> BACK DEMODULATING HINT 3856 WITH 18090. NEW HINT: 19594 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(u)),u),f(f(f(u,f(f(g(u),g(u)),u)),f(y,g(z))),f(f(g(y),g(u)),u)))=f(g(z),g(y)). >> BACK DEMODULATING HINT 3847 WITH 18090. NEW HINT: 19595 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(f(g(y),f(x,y)),g(y)))),g(x)))=f(f(f(g(y),g(u)),u),f(f(f(u,f(f(g(u),g(u)),u)),f(y,g(z))),f(f(g(y),g(u)),u))). >> BACK DEMODULATING HINT 3846 WITH 18090. >> BACK DEMODULATING HINT 3845 WITH 18090. >> BACK DEMODULATING HINT 3844 WITH 18090. >> BACK DEMODULATING HINT 3843 WITH 18090. >> BACK DEMODULATING HINT 3842 WITH 18090. >> BACK DEMODULATING HINT 3841 WITH 18090. >> BACK DEMODULATING HINT 3838 WITH 18090. NEW HINT: 19596 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),z),f(f(g(z),f(x,y)),f(g(z),f(x,y))))=f(f(g(z),x),y). >> BACK DEMODULATING HINT 3837 WITH 18090. >> BACK DEMODULATING HINT 3836 WITH 18090. >> BACK DEMODULATING HINT 3835 WITH 18090. NEW HINT: 19597 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),z),f(f(g(z),f(x,y)),f(g(z),f(x,y))))=f(y,f(f(g(y),f(g(z),x)),y)). >> BACK DEMODULATING HINT 3834 WITH 18090. NEW HINT: 19598 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),f(g(z),u))),x))=f(f(f(g(x),g(u)),z),f(f(g(z),f(u,x)),f(g(z),f(u,x)))). >> BACK DEMODULATING HINT 3833 WITH 18090. >> BACK DEMODULATING HINT 3832 WITH 18090. >> BACK DEMODULATING HINT 3831 WITH 18090. >> BACK DEMODULATING HINT 3818 WITH 18090. NEW HINT: 19599 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,y),f(g(y),g(x)))=f(f(y,f(g(x),y)),g(y)). >> BACK DEMODULATING HINT 3817 WITH 18090. >> BACK DEMODULATING HINT 3816 WITH 18090. >> BACK DEMODULATING HINT 3815 WITH 18090. >> BACK DEMODULATING HINT 3814 WITH 18090. >> BACK DEMODULATING HINT 3813 WITH 18090. NEW HINT: 19600 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,y),f(g(y),g(x)))=f(f(y,f(g(x),y)),f(f(g(y),g(z)),z)). >> BACK DEMODULATING HINT 3812 WITH 18090. >> BACK DEMODULATING HINT 3811 WITH 18090. NEW HINT: 19601 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,f(g(z),y)),f(f(g(y),g(x)),x))=f(f(y,y),f(g(y),g(z))). >> BACK DEMODULATING HINT 3810 WITH 18090. >> BACK DEMODULATING HINT 3796 WITH 18090. >> BACK DEMODULATING HINT 3795 WITH 18090. >> BACK DEMODULATING HINT 3794 WITH 18090. NEW HINT: 19602 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),x)),g(x)))=f(f(g(y),f(f(w,g(v)),v)),f(f(z,f(f(g(z),g(u)),u)),f(g(w),f(z,f(f(g(z),g(u)),u))))). >> BACK DEMODULATING HINT 3791 WITH 18090. >> BACK DEMODULATING HINT 3790 WITH 18090. >> BACK DEMODULATING HINT 3789 WITH 18090. NEW HINT: 19603 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(z,f(f(g(z),g(y)),z)))=f(x,z). >> BACK DEMODULATING HINT 3788 WITH 18090. >> BACK DEMODULATING HINT 3785 WITH 18090. >> BACK DEMODULATING HINT 3784 WITH 18090. >> BACK DEMODULATING HINT 3783 WITH 18090. NEW HINT: 19604 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),z)),x))=f(z,x). >> BACK DEMODULATING HINT 3782 WITH 18090. >> BACK DEMODULATING HINT 3775 WITH 18090. >> BACK DEMODULATING HINT 3774 WITH 18090. >> BACK DEMODULATING HINT 3773 WITH 18090. >> BACK DEMODULATING HINT 3772 WITH 18090. NEW HINT: 19605 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(w),f(v,u)),g(u))=f(f(f(g(w),v),g(v6)),v6). >> BACK DEMODULATING HINT 3771 WITH 18090. >> BACK DEMODULATING HINT 3770 WITH 18090. >> BACK DEMODULATING HINT 3762 WITH 18090. NEW HINT: 19606 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(f(g(z),g(u)),v))=f(f(f(g(u),v),g(w)),w). >> BACK DEMODULATING HINT 3761 WITH 18090. >> BACK DEMODULATING HINT 3760 WITH 18090. >> BACK DEMODULATING HINT 3757 WITH 18090. >> BACK DEMODULATING HINT 3756 WITH 18090. >> BACK DEMODULATING HINT 3755 WITH 18090. >> BACK DEMODULATING HINT 3754 WITH 18090. >> BACK DEMODULATING HINT 3753 WITH 18090. >> BACK DEMODULATING HINT 3752 WITH 18090. >> BACK DEMODULATING HINT 3751 WITH 18090. >> BACK DEMODULATING HINT 3750 WITH 18090. >> BACK DEMODULATING HINT 3749 WITH 18090. >> BACK DEMODULATING HINT 3748 WITH 18090. >> BACK DEMODULATING HINT 3747 WITH 18090. >> BACK DEMODULATING HINT 3746 WITH 18090. >> BACK DEMODULATING HINT 3745 WITH 18090. >> BACK DEMODULATING HINT 3741 WITH 18090. >> BACK DEMODULATING HINT 3740 WITH 18090. >> BACK DEMODULATING HINT 3739 WITH 18090. >> BACK DEMODULATING HINT 3738 WITH 18090. >> BACK DEMODULATING HINT 3737 WITH 18090. >> BACK DEMODULATING HINT 3733 WITH 18090. >> BACK DEMODULATING HINT 3732 WITH 18090. >> BACK DEMODULATING HINT 3731 WITH 18090. >> BACK DEMODULATING HINT 3730 WITH 18090. >> BACK DEMODULATING HINT 3729 WITH 18090. >> BACK DEMODULATING HINT 3728 WITH 18090. >> BACK DEMODULATING HINT 3727 WITH 18090. >> BACK DEMODULATING HINT 3726 WITH 18090. >> BACK DEMODULATING HINT 3725 WITH 18090. >> BACK DEMODULATING HINT 3724 WITH 18090. >> BACK DEMODULATING HINT 3723 WITH 18090. >> BACK DEMODULATING HINT 3722 WITH 18090. >> BACK DEMODULATING HINT 3721 WITH 18090. >> BACK DEMODULATING HINT 3720 WITH 18090. >> BACK DEMODULATING HINT 3719 WITH 18090. >> BACK DEMODULATING HINT 3716 WITH 18090. >> BACK DEMODULATING HINT 3715 WITH 18090. >> BACK DEMODULATING HINT 3714 WITH 18090. >> BACK DEMODULATING HINT 3713 WITH 18090. >> BACK DEMODULATING HINT 3712 WITH 18090. >> BACK DEMODULATING HINT 3711 WITH 18090. >> BACK DEMODULATING HINT 3710 WITH 18090. >> BACK DEMODULATING HINT 3709 WITH 18090. >> BACK DEMODULATING HINT 3708 WITH 18090. >> BACK DEMODULATING HINT 3702 WITH 18090. >> BACK DEMODULATING HINT 3701 WITH 18090. >> BACK DEMODULATING HINT 3700 WITH 18090. >> BACK DEMODULATING HINT 3687 WITH 18090. >> BACK DEMODULATING HINT 3683 WITH 18090. NEW HINT: 19607 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),g(y)),y)),f(g(z),f(f(z,f(v,z)),g(z))))=v. >> BACK DEMODULATING HINT 3680 WITH 18090. >> BACK DEMODULATING HINT 3679 WITH 18090. >> BACK DEMODULATING HINT 3678 WITH 18090. >> BACK DEMODULATING HINT 3677 WITH 18090. >> BACK DEMODULATING HINT 3676 WITH 18090. >> BACK DEMODULATING HINT 3675 WITH 18090. >> BACK DEMODULATING HINT 3674 WITH 18090. >> BACK DEMODULATING HINT 3673 WITH 18090. >> BACK DEMODULATING HINT 3672 WITH 18090. NEW HINT: 19608 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(w,f(f(g(w),f(v,g(v7))),v7)),g(z)),z)=v. >> BACK DEMODULATING HINT 3671 WITH 18090. >> BACK DEMODULATING HINT 3670 WITH 18090. >> BACK DEMODULATING HINT 3669 WITH 18090. >> BACK DEMODULATING HINT 3668 WITH 18090. NEW HINT: 19609 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),f(f(u,g(z)),z))),x))=f(u,x). >> BACK DEMODULATING HINT 3667 WITH 18090. NEW HINT: 19610 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,g(x)),x),z),f(u,f(f(g(u),g(z)),u)))=f(y,u). >> BACK DEMODULATING HINT 3666 WITH 18090. NEW HINT: 19611 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(g(z),f(x,y)),g(y))),g(x)))=f(f(g(z),f(f(v6,g(w)),w)),f(f(u,f(f(g(u),g(v)),v)),f(g(v6),f(u,f(f(g(u),g(v)),v))))). >> BACK DEMODULATING HINT 3664 WITH 18090. >> BACK DEMODULATING HINT 3663 WITH 18090. >> BACK DEMODULATING HINT 3662 WITH 18090. NEW HINT: 19612 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(f(v,g(u)),u)),f(f(x,f(f(g(x),g(y)),y)),f(g(v),f(x,f(f(g(x),g(y)),y)))))=f(w,f(f(g(w),f(f(g(z),f(w,v6)),g(v6))),g(w))). >> BACK DEMODULATING HINT 3660 WITH 18090. NEW HINT: 19613 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),x)=f(z,f(f(g(z),f(g(y),g(v))),v)). >> BACK DEMODULATING HINT 3658 WITH 18090. NEW HINT: 19614 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(u),f(f(u,w),y)),g(y)),g(x)),x)=w. >> BACK DEMODULATING HINT 3656 WITH 18090. NEW HINT: 19615 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(z),z),f(g(z),u)),x),f(g(x),x))=f(g(z),f(f(u,f(x,u)),g(u))). >> BACK DEMODULATING HINT 3653 WITH 18090. NEW HINT: 19616 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),g(x)),x)),f(y,f(g(z),y))),f(f(g(y),g(x)),x))=f(f(y,y),f(g(y),g(z))). >> BACK DEMODULATING HINT 3651 WITH 18090. NEW HINT: 19617 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),f(u,f(f(g(u),g(v)),u)))),x))=f(f(f(g(x),g(u)),v),f(f(g(v),f(u,x)),f(g(v),f(u,x)))). >> BACK DEMODULATING HINT 3650 WITH 18090. >> BACK DEMODULATING HINT 3649 WITH 18090. NEW HINT: 19618 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(f(g(z),f(g(w),f(f(g(u),f(z,u)),g(u)))),g(z)))=f(f(f(g(u),g(v)),v),f(f(v6,f(f(g(v6),u),g(w))),f(f(g(u),g(v)),v))). >> BACK DEMODULATING HINT 3648 WITH 18090. NEW HINT: 19619 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,y),f(g(y),g(x)))=f(f(f(z,f(f(g(z),g(z)),z)),f(y,f(g(x),y))),f(f(g(y),g(z)),z)). >> BACK DEMODULATING HINT 3647 WITH 18090. NEW HINT: 19620 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,y),f(g(y),g(x)))=f(f(w,f(f(g(w),y),f(g(x),y))),f(f(g(y),g(z)),z)). >> BACK DEMODULATING HINT 3645 WITH 18090. NEW HINT: 19621 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(f(g(y),g(z)),z),f(f(g(y),g(z)),z)))=f(f(f(g(y),g(z)),z),f(f(w,f(f(g(w),y),x)),f(f(g(y),g(z)),z))). >> BACK DEMODULATING HINT 3644 WITH 18090. NEW HINT: 19622 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),z),f(f(g(z),f(x,y)),f(g(z),f(x,y))))=f(y,f(f(w,f(f(g(w),g(y)),f(x,f(f(g(x),g(z)),x)))),y)). >> BACK DEMODULATING HINT 3642 WITH 18090. NEW HINT: 19623 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(y,f(f(g(y),g(z)),z)))=f(f(f(f(g(v6),f(f(v6,x),v)),g(v)),g(u)),u). >> BACK DEMODULATING HINT 3638 WITH 18090. >> BACK DEMODULATING HINT 3634 WITH 18090. >> BACK DEMODULATING HINT 3631 WITH 18090. NEW HINT: 19624 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(g(u),f(z,y)),g(y))),f(f(f(w,f(f(g(w),g(z)),u)),v6),f(f(g(u),f(z,v)),g(v)))))=f(f(v6,g(u)),z). >> BACK DEMODULATING HINT 3630 WITH 18090. >> BACK DEMODULATING HINT 3627 WITH 18090. >> BACK DEMODULATING HINT 3624 WITH 18090. NEW HINT: 19625 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(z,f(f(g(z),g(u)),v))),f(u,f(f(g(u),f(f(g(v),f(u,w)),g(w))),x))),g(x))=y. >> BACK DEMODULATING HINT 3623 WITH 18090. NEW HINT: 19626 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,f(z,f(f(g(z),f(f(g(w),f(v,u)),g(u))),x))),g(x))=f(f(y,g(w)),v). >> BACK DEMODULATING HINT 3621 WITH 18090. NEW HINT: 19627 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(z,u)),g(u)),f(g(z),f(x,y)))=y. >> BACK DEMODULATING HINT 3619 WITH 18090. NEW HINT: 19628 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,z),f(u,f(f(g(u),g(z)),x))),g(x))=y. >> BACK DEMODULATING HINT 3615 WITH 18090. NEW HINT: 19629 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(u),f(y,z))),v))=f(f(y,f(f(g(y),g(u)),y)),f(z,v)). >> BACK DEMODULATING HINT 3614 WITH 18090. NEW HINT: 19630 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),g(y)),x)),f(f(f(f(z,u),f(f(g(v),f(z,u)),f(f(f(g(u),g(z)),v),f(f(g(u),g(z)),v)))),f(f(g(v),f(z,u)),f(f(g(v),f(z,u)),f(f(f(g(u),g(z)),v),f(f(g(u),g(z)),v))))),w))=f(v6,f(f(g(v6),f(g(y),f(x,v))),w)). >> BACK DEMODULATING HINT 3613 WITH 18090. NEW HINT: 19631 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),g(y)),x)),f(f(f(z,f(f(u,f(f(g(u),g(z)),v)),z)),g(z)),w))=f(v6,f(f(g(v6),f(g(y),f(x,v))),w)). >> BACK DEMODULATING HINT 3611 WITH 18090. NEW HINT: 19632 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,f(f(g(y),g(z)),u)),z),f(x,f(f(g(x),g(z)),x))),g(x))=f(v,f(f(g(v),g(z)),u)). >> BACK DEMODULATING HINT 3610 WITH 18090. >> BACK DEMODULATING HINT 3602 WITH 18090. NEW HINT: 19633 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(g(x),f(z,x)),g(x)),f(g(z),f(x,y))),u),f(v,f(f(g(v),g(u)),v)))=f(v,f(f(w,f(f(g(w),g(v)),y)),v)). >> BACK DEMODULATING HINT 3600 WITH 18090. NEW HINT: 19634 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(x,y),z),f(g(z),z)))=f(f(f(z,g(u)),v),f(u,f(f(g(u),g(v)),u))). >> BACK DEMODULATING HINT 3598 WITH 18090. NEW HINT: 19635 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),g(y)),f(g(z),g(y)))),y)=f(f(f(g(y),f(u,y)),g(y)),f(g(u),g(z))). >> BACK DEMODULATING HINT 3597 WITH 18090. NEW HINT: 19636 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(z),f(y,z)),g(z)),f(g(y),g(x)))=f(f(u,f(f(g(u),g(z)),f(g(x),g(z)))),z). >> BACK DEMODULATING HINT 3594 WITH 18090. >> BACK DEMODULATING HINT 3593 WITH 18090. NEW HINT: 19637 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),y),f(g(y),z)),x),f(g(x),x))=f(g(y),f(f(z,f(x,f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,z))))),g(z))). >> BACK DEMODULATING HINT 3592 WITH 18090. NEW HINT: 19638 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),y),f(g(y),z)),x),f(g(x),x))=f(g(y),f(f(f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,z))),f(x,f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,z))))),g(z))). >> BACK DEMODULATING HINT 3591 WITH 18090. NEW HINT: 19639 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),y),f(g(y),z)),x),f(g(x),x))=f(g(y),f(f(f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,z))),f(x,f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,z))))),f(f(f(g(z),g(u)),v),f(u,f(f(g(u),g(v)),u))))). >> BACK DEMODULATING HINT 3590 WITH 18090. >> BACK DEMODULATING HINT 3589 WITH 18090. NEW HINT: 19640 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(f(f(g(x),g(z)),u),f(z,f(f(g(z),g(u)),z))),y),f(g(y),y)))=y. >> BACK DEMODULATING HINT 3588 WITH 18090. NEW HINT: 19641 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),y),f(g(y),f(g(u),g(z)))),x),f(g(x),x))=f(g(y),f(f(f(g(u),g(z)),f(x,f(g(u),g(z)))),f(z,u))). >> BACK DEMODULATING HINT 3587 WITH 18090. NEW HINT: 19642 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(f(g(y),f(g(u),g(z))),g(y))),x),f(g(x),x))=f(g(u),f(f(f(g(z),g(y)),f(x,f(g(z),g(y)))),f(y,z))). >> BACK DEMODULATING HINT 3586 WITH 18090. NEW HINT: 19643 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(y,z),x)),g(x))=f(f(f(x,y),z),f(g(z),z)). >> BACK DEMODULATING HINT 3583 WITH 18090. NEW HINT: 19644 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(y),g(x)),f(f(x,y),f(x,y)))),f(f(g(y),g(x)),f(f(g(y),g(x)),f(f(x,y),f(x,y)))))=y. >> BACK DEMODULATING HINT 3580 WITH 18090. NEW HINT: 19645 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(f(g(x),g(y)),z),f(f(f(y,f(f(g(y),g(z)),y)),u),f(f(g(x),g(y)),z))),f(g(z),f(y,x))))=u. >> BACK DEMODULATING HINT 3578 WITH 18090. NEW HINT: 19646 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),z),f(f(f(g(z),f(x,y)),f(g(u),f(f(g(x),f(z,x)),g(x)))),f(g(z),f(x,y))))=f(y,f(f(v,f(f(g(v),g(y)),g(u))),y)). >> BACK DEMODULATING HINT 3577 WITH 18090. NEW HINT: 19647 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),g(z))),x))=f(f(f(g(x),g(u)),v),f(f(f(g(v),f(u,x)),f(g(z),f(f(g(u),f(v,u)),g(u)))),f(g(v),f(u,x)))). >> BACK DEMODULATING HINT 3576 WITH 18090. NEW HINT: 19648 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),g(z))),f(f(f(g(u),f(v,u)),g(u)),f(g(v),f(u,x)))))=f(f(f(g(x),g(u)),v),f(f(f(g(v),f(u,x)),f(g(z),f(f(g(u),f(v,u)),g(u)))),f(g(v),f(u,x)))). >> BACK DEMODULATING HINT 3575 WITH 18090. NEW HINT: 19649 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),f(f(f(g(x),g(z)),u),f(z,f(f(g(z),g(u)),z)))),g(v))),f(f(f(g(z),f(u,z)),g(z)),f(g(u),f(z,x)))))=f(f(f(g(x),g(z)),u),f(f(f(g(u),f(z,x)),f(g(v),f(f(g(z),f(u,z)),g(z)))),f(g(u),f(z,x)))). >> BACK DEMODULATING HINT 3574 WITH 18090. NEW HINT: 19650 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(z),f(y,z)),g(z)),f(g(y),x))=f(f(g(z),f(f(x,f(z,u)),g(u))),g(z)). >> BACK DEMODULATING HINT 3567 WITH 18090. >> BACK DEMODULATING HINT 3562 WITH 18090. NEW HINT: 19651 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(f(g(u),u),f(g(z),z)),v))=f(x,f(y,v)). >> BACK DEMODULATING HINT 3561 WITH 18090. >> BACK DEMODULATING HINT 3542 WITH 18090. NEW HINT: 19652 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(g(y),g(z))),f(z,u))=f(f(x,f(f(g(w),w),f(g(v),v))),f(g(y),u)). >> BACK DEMODULATING HINT 3541 WITH 18090. >> BACK DEMODULATING HINT 3534 WITH 18090. NEW HINT: 19653 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(y),y),f(f(f(f(g(u),u),v),g(z)),w)))=f(v,f(g(z),w)). >> BACK DEMODULATING HINT 3533 WITH 18090. >> BACK DEMODULATING HINT 3524 WITH 18090. NEW HINT: 19654 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),z)=f(g(x),f(f(g(y),z),f(g(u),u))). >> BACK DEMODULATING HINT 3523 WITH 18090. >> BACK DEMODULATING HINT 3522 WITH 18090. >> BACK DEMODULATING HINT 3521 WITH 18090. NEW HINT: 19655 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),z)=f(g(x),f(f(f(g(v),v),f(g(y),z)),f(g(u),u))). >> BACK DEMODULATING HINT 3520 WITH 18090. NEW HINT: 19656 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),z)=f(g(x),f(f(f(g(v),v),f(f(g(y),z),f(g(u),u))),f(g(u),u))). >> BACK DEMODULATING HINT 3519 WITH 18090. >> BACK DEMODULATING HINT 3518 WITH 18090. >> BACK DEMODULATING HINT 3517 WITH 18090. NEW HINT: 19657 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),z)=f(g(x),f(f(f(g(v),v),f(f(w,f(f(g(w),g(y)),z)),f(g(u),u))),f(g(u),u))). >> BACK DEMODULATING HINT 3516 WITH 18090. >> BACK DEMODULATING HINT 3515 WITH 18090. >> BACK DEMODULATING HINT 3514 WITH 18090. >> BACK DEMODULATING HINT 3513 WITH 18090. >> BACK DEMODULATING HINT 3511 WITH 18090. NEW HINT: 19658 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(y)),z)=f(f(g(x),f(g(u),u)),f(f(f(g(v),v),f(f(w,f(f(g(w),g(y)),z)),f(g(u),u))),f(g(u),u))). >> BACK DEMODULATING HINT 3510 WITH 18090. >> BACK DEMODULATING HINT 3506 WITH 18090. NEW HINT: 19659 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(g(y),y))),u))=f(g(z),u). >> BACK DEMODULATING HINT 3505 WITH 18090. >> BACK DEMODULATING HINT 3486 WITH 18090. NEW HINT: 19660 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(y),y),f(g(v),f(g(z),z))))=f(f(g(z),z),g(v)). >> BACK DEMODULATING HINT 3485 WITH 18090. NEW HINT: 19661 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(y),y),f(f(u,f(f(g(u),g(v)),f(g(z),z))),f(g(z),z))))=f(f(g(z),z),g(v)). >> BACK DEMODULATING HINT 3484 WITH 18090. >> BACK DEMODULATING HINT 3480 WITH 18090. NEW HINT: 19662 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),y)),z))=f(f(g(u),u),f(f(g(v),v),z)). >> BACK DEMODULATING HINT 3478 WITH 18090. >> BACK DEMODULATING HINT 3477 WITH 18090. NEW HINT: 19663 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),z),f(f(g(x),x),y))=y. >> BACK DEMODULATING HINT 3476 WITH 18090. NEW HINT: 19664 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(u),u),f(f(f(g(x),x),f(g(y),y)),z))=z. >> BACK DEMODULATING HINT 3471 WITH 18090. >> BACK DEMODULATING HINT 3470 WITH 18090. NEW HINT: 19665 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),z),f(f(f(f(g(x),x),f(g(x),x)),f(g(x),x)),y))=y. >> BACK DEMODULATING HINT 3464 WITH 18090. NEW HINT: 19666 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(g(z),z)),f(g(x),x)),f(g(x),x))=f(f(g(x),x),y). >> BACK DEMODULATING HINT 3454 WITH 18090. NEW HINT: 19667 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(g(z),z),f(x,g(y))),g(x)))=f(f(g(z),z),f(g(y),g(x))). >> BACK DEMODULATING HINT 3453 WITH 18090. NEW HINT: 19668 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(g(z),z),f(x,g(y))),f(g(x),f(g(z),z))))=f(f(g(z),z),f(g(y),g(x))). >> BACK DEMODULATING HINT 3452 WITH 18090. NEW HINT: 19669 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(g(z),z),f(f(f(g(z),z),x),g(y))),f(g(x),f(g(z),z))))=f(f(g(z),z),f(g(y),g(x))). >> BACK DEMODULATING HINT 3451 WITH 18090. NEW HINT: 19670 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(g(z),z),f(f(f(f(g(z),z),f(g(z),z)),x),g(y))),f(g(x),f(g(z),z))))=f(f(g(z),z),f(g(y),g(x))). >> BACK DEMODULATING HINT 3450 WITH 18090. NEW HINT: 19671 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(z),z)),f(f(f(g(z),z),f(f(f(f(g(z),z),f(g(z),z)),x),g(y))),f(g(x),f(g(z),z))))=f(f(g(z),z),f(g(y),g(x))). >> BACK DEMODULATING HINT 3449 WITH 18090. NEW HINT: 19672 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(g(x),x)),f(f(f(g(x),x),f(f(f(f(g(x),x),f(g(x),x)),y),g(z))),f(g(y),f(g(x),x))))=f(f(g(x),x),f(f(g(x),x),f(g(z),g(y)))). >> BACK DEMODULATING HINT 3438 WITH 18090. NEW HINT: 19673 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,f(g(y),y)),f(x,f(g(y),y))),z),f(f(g(z),f(f(g(y),y),g(x))),f(f(g(u),u),g(x))))=f(g(v),v). >> BACK DEMODULATING HINT 3433 WITH 18090. >> BACK DEMODULATING HINT 3427 WITH 18090. NEW HINT: 19674 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(g(y),f(g(x),g(x)))),x)=f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),y),g(z))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 3426 WITH 18090. NEW HINT: 19675 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(g(x),f(f(f(x,x),y),f(g(z),f(x,y)))),f(g(y),g(x))),f(z,g(u))),f(g(y),g(x))))=f(f(g(u),f(g(y),f(g(x),g(x)))),x). >> BACK DEMODULATING HINT 3413 WITH 18090. NEW HINT: 19676 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),f(f(g(u),u),f(y,z))),f(g(v),f(f(g(u),u),f(y,z))))),f(f(g(z),g(y)),f(g(u),u))),f(v,f(f(f(f(g(z),g(y)),f(g(u),u)),y),f(f(g(u),u),f(y,z)))))=f(f(y,y),z). >> BACK DEMODULATING HINT 3405 WITH 18090. NEW HINT: 19677 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,f(g(y),y)),f(x,f(g(y),y))),z),f(f(g(z),f(f(g(y),y),g(x))),u))=f(x,u). >> BACK DEMODULATING HINT 3404 WITH 18090. NEW HINT: 19678 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,f(g(y),y)),f(x,f(g(y),y))),f(f(f(f(g(y),y),g(x)),f(f(g(u),f(f(x,f(g(y),y)),z)),g(z))),f(f(g(y),y),g(x)))),f(u,v))=f(x,v). >> BACK DEMODULATING HINT 3375 WITH 18090. NEW HINT: 19679 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(f(g(x),x),f(g(u),g(z))),f(g(y),y)))=f(f(g(u),f(g(z),f(f(g(x),x),f(g(x),x)))),f(g(x),x)). >> BACK DEMODULATING HINT 3368 WITH 18090. NEW HINT: 19680 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),f(f(g(z),z),g(y))),f(g(u),f(f(g(z),z),g(y))))),f(y,f(g(z),z))),f(u,f(f(f(y,f(g(z),z)),v),f(f(g(z),z),g(y)))))=f(v,g(y)). >> BACK DEMODULATING HINT 3360 WITH 18090. NEW HINT: 19681 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(g(z),z),f(f(g(u),u),y)),g(y))))=f(g(y),f(g(v),v)). >> BACK DEMODULATING HINT 3358 WITH 18090. NEW HINT: 19682 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),f(g(y),y)),f(g(z),f(g(y),y)))),f(g(y),y)),f(z,f(f(f(g(y),y),f(g(u),u)),f(g(y),y))))=f(g(v),v). >> BACK DEMODULATING HINT 3346 WITH 18090. NEW HINT: 19683 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(y,y),z),f(f(g(z),g(y)),g(u)))),u))=f(y,f(g(v),v)). >> BACK DEMODULATING HINT 3344 WITH 18090. NEW HINT: 19684 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(z,u),f(f(g(v),v),y)),g(y))))=f(g(y),f(z,u)). >> BACK DEMODULATING HINT 3338 WITH 18090. NEW HINT: 19685 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(y,y),z),f(f(g(z),g(y)),g(u)))),u))=f(v,f(f(g(v),g(w)),f(w,y))). >> BACK DEMODULATING HINT 3335 WITH 18090. NEW HINT: 19686 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(g(y),f(f(f(y,y),f(g(u),g(z))),f(z,v)))))=f(f(g(u),g(w)),f(w,v)). >> BACK DEMODULATING HINT 3332 WITH 18090. NEW HINT: 19687 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(y,y),z),f(f(g(z),g(y)),u))),v))=f(y,f(u,v)). >> BACK DEMODULATING HINT 3331 WITH 18090. NEW HINT: 19688 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(z,f(f(g(z),f(x,y)),f(g(u),f(x,y)))),f(g(y),g(x))),f(u,g(v))),f(g(y),g(x))))=f(f(g(v),f(g(y),f(g(x),g(x)))),x). >> BACK DEMODULATING HINT 3330 WITH 18090. NEW HINT: 19689 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(g(y),f(g(x),g(x)))),x)=f(f(g(y),g(x)),f(f(f(f(u,f(f(g(u),f(x,y)),f(g(v),f(x,y)))),f(g(y),g(x))),f(v,g(z))),f(g(y),g(x)))). >> BACK DEMODULATING HINT 3329 WITH 18090. NEW HINT: 19690 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(x,x),y),f(f(g(y),g(x)),z)))=z. >> BACK DEMODULATING HINT 3328 WITH 18090. NEW HINT: 19691 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(z,f(x,y)),f(g(y),f(g(x),g(x)))),x)=z. >> BACK DEMODULATING HINT 3327 WITH 18090. NEW HINT: 19692 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(u,x),g(z)),f(f(x,f(f(y,f(f(g(y),g(x)),z)),x)),f(g(x),g(x))))=u. >> BACK DEMODULATING HINT 3326 WITH 18090. NEW HINT: 19693 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(x,x),y),z))=f(f(u,f(f(g(u),f(x,y)),f(z,f(x,y)))),f(g(y),g(x))). >> BACK DEMODULATING HINT 3325 WITH 18090. NEW HINT: 19694 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(g(y),f(g(x),g(x)))),x)=f(x,f(f(g(x),f(g(z),g(y))),g(x))). >> BACK DEMODULATING HINT 3324 WITH 18090. NEW HINT: 19695 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),f(y,z)),f(u,f(y,z)))),f(g(z),g(y)))=f(g(y),f(f(f(y,y),z),u)). >> BACK DEMODULATING HINT 3323 WITH 18090. NEW HINT: 19696 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),g(y))),g(x)))=f(f(g(z),f(g(y),f(g(x),g(x)))),x). >> BACK DEMODULATING HINT 3322 WITH 18090. NEW HINT: 19697 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(v),f(g(x),f(f(f(x,f(g(u),g(z))),f(x,y)),g(y))))),g(x)))=f(f(g(v),f(g(u),f(g(z),g(z)))),z). >> BACK DEMODULATING HINT 3321 WITH 18090. NEW HINT: 19698 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(g(y),f(f(f(y,y),z),u))))=f(z,u). >> BACK DEMODULATING HINT 3320 WITH 18090. NEW HINT: 19699 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(z,x),f(x,y)),f(g(y),f(g(x),g(x))))=z. >> BACK DEMODULATING HINT 3319 WITH 18090. NEW HINT: 19700 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(g(y),g(y)))),u))=f(f(f(g(z),g(y)),f(g(y),g(v))),f(v,u)). >> BACK DEMODULATING HINT 3318 WITH 18090. NEW HINT: 19701 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),g(x))),f(f(g(u),g(z)),f(f(z,x),f(x,y)))),f(g(y),f(g(x),g(x))))=f(f(g(y),g(x)),f(g(x),g(u))). >> BACK DEMODULATING HINT 3317 WITH 18090. NEW HINT: 19702 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),g(x))),f(f(g(u),f(f(f(x,x),y),z)),g(z))),f(g(y),f(g(x),g(x))))=f(f(g(y),g(x)),f(g(x),g(u))). >> BACK DEMODULATING HINT 3316 WITH 18090. NEW HINT: 19703 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(g(x),f(f(f(x,x),y),z)))=z. >> BACK DEMODULATING HINT 3315 WITH 18090. NEW HINT: 19704 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),g(x))),f(f(g(v),g(u)),f(f(f(x,x),y),f(f(z,f(f(g(z),f(g(y),f(g(x),g(x)))),u)),f(f(x,x),y))))),f(g(y),f(g(x),g(x))))=f(f(g(y),g(x)),f(g(x),g(v))). >> BACK DEMODULATING HINT 3314 WITH 18090. NEW HINT: 19705 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),g(x))),f(f(g(v),g(u)),f(f(f(x,x),y),f(f(z,f(f(g(z),f(g(y),f(g(x),g(x)))),u)),f(f(x,x),y))))),f(g(y),f(g(x),g(x))))=f(f(g(y),g(x)),f(g(x),f(w,f(f(f(f(g(w),f(f(g(v7),f(w,v6)),g(v6))),g(w)),f(v7,f(g(v),g(w)))),w)))). >> BACK DEMODULATING HINT 3313 WITH 18090. NEW HINT: 19706 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),g(x))),f(f(v,g(u)),f(f(f(x,x),y),f(f(z,f(f(g(z),f(g(y),f(g(x),g(x)))),u)),f(f(x,x),y))))),f(g(y),f(g(x),g(x))))=f(f(g(y),g(x)),f(g(x),v)). >> BACK DEMODULATING HINT 3295 WITH 18090. NEW HINT: 19707 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(g(y),g(y)))),u))=f(f(f(f(g(z),f(g(y),g(y))),f(f(g(w),v),f(f(g(v),y),f(y,z)))),f(g(z),f(g(y),g(y)))),f(w,u)). >> BACK DEMODULATING HINT 3294 WITH 18090. NEW HINT: 19708 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(y),f(g(x),g(x))),f(f(g(u),z),f(f(g(z),x),f(x,y)))),f(g(y),f(g(x),g(x)))),f(u,v))=f(w,f(f(g(w),f(g(y),f(g(x),g(x)))),v)). >> BACK DEMODULATING HINT 3273 WITH 18090. NEW HINT: 19709 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,x),y),f(f(f(f(g(y),g(x)),f(g(x),z)),f(g(z),u)),f(f(x,x),y))),f(g(y),f(g(x),g(x))))=u. >> BACK DEMODULATING HINT 3247 WITH 18090. NEW HINT: 19710 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),z)=f(f(x,x),f(f(g(x),g(u)),f(f(g(u),f(f(f(u,u),y),f(z,f(u,y)))),f(g(y),g(u))))) # label(bd). >> BACK DEMODULATING HINT 3239 WITH 18090. NEW HINT: 19711 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(z,z),f(f(g(z),g(u)),f(f(g(u),f(f(f(u,u),y),f(x,f(u,y)))),f(g(y),g(u)))))=f(z,f(y,x)) # label(bd). >> BACK DEMODULATING HINT 3219 WITH 18090. NEW HINT: 19712 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),f(f(y,z),u))),f(f(g(u),g(z)),f(f(g(x),f(f(f(x,x),v),f(w,f(x,v)))),f(g(v),g(x)))))=f(v,w) # label(bd). >> BACK DEMODULATING HINT 3205 WITH 18090. NEW HINT: 19713 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(y)),f(f(g(y),f(f(f(y,y),z),f(u,f(y,z)))),f(g(z),g(y)))),f(f(g(u),g(z)),f(f(g(x),f(f(f(x,x),v),f(w,f(x,v)))),f(g(v),g(x)))))=f(v,w) # label(bd). >> BACK DEMODULATING HINT 3191 WITH 18090. NEW HINT: 19714 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,x),y),f(f(g(z),u),f(x,y)))),f(g(y),g(x)))=f(f(x,y),f(g(z),u)) # label(bd). >> BACK DEMODULATING HINT 3190 WITH 18090. >> BACK DEMODULATING HINT 3189 WITH 18090. >> BACK DEMODULATING HINT 3188 WITH 18090. >> BACK DEMODULATING HINT 3187 WITH 18090. NEW HINT: 19715 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,x),y),f(f(f(g(z),g(v)),f(v,u)),f(x,y)))),f(g(y),g(x)))=f(f(x,y),f(g(z),u)) # label(bd). >> BACK DEMODULATING HINT 3186 WITH 18090. >> BACK DEMODULATING HINT 3185 WITH 18090. NEW HINT: 19716 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,x),y),f(f(f(f(g(z),f(g(v),z)),g(z)),f(v,u)),f(x,y)))),f(g(y),g(x)))=f(f(x,y),f(g(z),u)) # label(bd). >> BACK DEMODULATING HINT 3184 WITH 18090. >> BACK DEMODULATING HINT 3183 WITH 18090. NEW HINT: 19717 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,x),y),f(f(f(f(g(z),f(f(g(w),f(z,v)),g(v))),g(z)),f(w,u)),f(x,y)))),f(g(y),g(x)))=f(f(x,y),f(g(z),u)) # label(bd). >> BACK DEMODULATING HINT 3182 WITH 18090. >> BACK DEMODULATING HINT 3160 WITH 18090. NEW HINT: 19718 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(f(f(y,y),f(f(g(y),x),y)),f(z,f(x,y)))),f(f(g(y),f(f(g(x),f(y,u)),g(u))),g(y)))=f(x,f(y,z)) # label(bd). >> BACK DEMODULATING HINT 3114 WITH 18090. NEW HINT: 19719 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(z,f(g(y),y))),u))=f(f(z,f(f(g(y),y),g(v))),f(v,u)) # label(bd). >> BACK DEMODULATING HINT 3113 WITH 18090. NEW HINT: 19720 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(g(u),u),z),f(g(y),y))),v))=f(f(z,f(f(g(y),y),g(w))),f(w,v)) # label(bd). >> BACK DEMODULATING HINT 3112 WITH 18090. >> BACK DEMODULATING HINT 3111 WITH 18090. >> BACK DEMODULATING HINT 3110 WITH 18090. NEW HINT: 19721 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(g(u),u),z),f(f(g(y),y),f(g(y),y)))),v))=f(f(z,f(f(g(y),y),g(w))),f(w,v)) # label(bd). >> BACK DEMODULATING HINT 3109 WITH 18090. >> BACK DEMODULATING HINT 3108 WITH 18090. >> BACK DEMODULATING HINT 3107 WITH 18090. >> BACK DEMODULATING HINT 3106 WITH 18090. >> BACK DEMODULATING HINT 3089 WITH 18090. >> BACK DEMODULATING HINT 3083 WITH 18090. NEW HINT: 19722 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(z,x),f(g(y),y)),g(x))=z # label(bd). >> BACK DEMODULATING HINT 3082 WITH 18090. NEW HINT: 19723 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(u,x),f(g(z),z)),f(f(x,f(g(y),y)),f(g(x),g(x))))=u # label(bd). >> BACK DEMODULATING HINT 3081 WITH 18090. >> BACK DEMODULATING HINT 3080 WITH 18090. >> BACK DEMODULATING HINT 3075 WITH 18090. NEW HINT: 19724 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(f(g(z),g(y)),f(f(x,y),f(f(g(u),u),g(y)))))=f(g(y),x) # label(bd). >> BACK DEMODULATING HINT 3074 WITH 18090. >> BACK DEMODULATING HINT 3073 WITH 18090. NEW HINT: 19725 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(f(g(z),f(f(g(u),u),g(y))),f(f(x,y),f(f(g(u),u),g(y)))))=f(g(y),x) # label(bd). >> BACK DEMODULATING HINT 3072 WITH 18090. >> BACK DEMODULATING HINT 3071 WITH 18090. NEW HINT: 19726 [bsub_wt=2147483647, bsub_add_wt=-1024] f(u,f(f(g(u),f(f(g(z),z),g(y))),f(f(x,y),f(f(g(z),z),g(y)))))=f(f(f(g(z),z),g(y)),x) # label(bd). >> BACK DEMODULATING HINT 3070 WITH 18090. >> BACK DEMODULATING HINT 3052 WITH 18090. NEW HINT: 19727 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(g(y),y))),u))=f(f(g(v),v),f(g(z),u)) # label(bd). >> BACK DEMODULATING HINT 3051 WITH 18090. NEW HINT: 19728 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(f(g(y),y),f(g(y),y)))),u))=f(f(g(v),v),f(g(z),u)) # label(bd). >> BACK DEMODULATING HINT 2976 WITH 18090. >> BACK DEMODULATING HINT 2969 WITH 18090. >> BACK DEMODULATING HINT 2968 WITH 18090. >> BACK DEMODULATING HINT 2967 WITH 18090. >> BACK DEMODULATING HINT 2966 WITH 18090. >> BACK DEMODULATING HINT 2965 WITH 18090. >> BACK DEMODULATING HINT 2964 WITH 18090. >> BACK DEMODULATING HINT 2963 WITH 18090. >> BACK DEMODULATING HINT 2919 WITH 18090. NEW HINT: 19729 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(g(y),z))=f(u,f(f(g(u),f(g(y),f(f(g(v),v),f(g(v),v)))),z)) # label(bd). >> BACK DEMODULATING HINT 2918 WITH 18090. >> BACK DEMODULATING HINT 2917 WITH 18090. NEW HINT: 19730 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),x),f(f(g(z),f(g(y),y)),u))=f(v,f(f(g(v),f(g(z),f(f(g(y),y),f(g(y),y)))),u)) # label(bd). >> BACK DEMODULATING HINT 2902 WITH 18090. >> BACK DEMODULATING HINT 2898 WITH 18090. NEW HINT: 19731 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(x,x),y),f(g(u),g(z))))=f(f(f(x,y),g(u)),f(f(v,f(f(g(v),g(z)),u)),g(u))) # label(bd). >> BACK DEMODULATING HINT 2894 WITH 18090. NEW HINT: 19732 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),f(f(g(x),f(f(f(x,x),z),f(u,f(x,z)))),f(g(z),g(x)))),f(f(g(u),g(z)),f(g(y),f(f(f(y,y),v),w))))=f(v,w) # label(bd). >> BACK DEMODULATING HINT 2893 WITH 18090. NEW HINT: 19733 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),f(f(f(x,z),f(f(u,f(g(z),f(g(x),g(x)))),x)),f(x,z))),f(f(g(u),g(z)),f(g(y),f(f(f(y,y),v),w))))=f(v,w) # label(bd). >> BACK DEMODULATING HINT 2892 WITH 18090. NEW HINT: 19734 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),f(g(x),f(f(f(x,x),z),u))),f(f(g(u),g(z)),f(g(y),f(f(f(y,y),v),w))))=f(v,w) # label(bd). >> BACK DEMODULATING HINT 2888 WITH 18090. NEW HINT: 19735 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(z,z),f(f(g(z),g(u)),f(g(u),f(f(f(u,u),x),y))))=f(z,f(x,y)) # label(bd). >> BACK DEMODULATING HINT 2858 WITH 18090. >> BACK DEMODULATING HINT 2857 WITH 18090. >> BACK DEMODULATING HINT 2856 WITH 18090. NEW HINT: 19736 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(f(x,y),f(f(g(z),f(g(y),f(g(x),g(x)))),x)),f(x,y)),f(z,g(u))),f(g(y),g(x))))=f(f(g(u),f(g(y),f(g(x),g(x)))),x) # label(bd). >> BACK DEMODULATING HINT 2855 WITH 18090. NEW HINT: 19737 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),g(x)),f(f(f(f(f(x,y),f(f(g(u),f(f(g(y),g(x)),z)),g(z))),f(x,y)),f(u,g(v))),f(g(y),g(x))))=f(f(g(v),f(g(y),f(g(x),g(x)))),x) # label(bd). >> BACK DEMODULATING HINT 2852 WITH 18090. NEW HINT: 19738 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,x),y),f(z,f(x,y)))),f(g(y),g(x)))=f(g(x),f(f(f(x,x),y),z)) # label(bd). >> BACK DEMODULATING HINT 2851 WITH 18090. >> BACK DEMODULATING HINT 2850 WITH 18090. NEW HINT: 19739 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),f(f(z,f(g(y),f(g(x),g(x)))),x)),f(x,y))=f(g(x),f(f(f(x,x),y),z)) # label(bd). >> BACK DEMODULATING HINT 2849 WITH 18090. >> BACK DEMODULATING HINT 2848 WITH 18090. NEW HINT: 19740 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),f(f(u,f(f(g(y),g(x)),z)),g(z))),f(x,y))=f(g(x),f(f(f(x,x),y),u)) # label(bd). >> BACK DEMODULATING HINT 2830 WITH 18090. NEW HINT: 19741 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(v)),f(f(f(f(g(y),g(x)),f(g(z),z)),f(f(u,f(f(g(u),f(f(g(z),z),f(x,y))),v)),f(f(g(y),g(x)),f(g(z),z)))),f(f(f(g(z),z),f(x,y)),f(f(g(z),z),f(x,y)))))=f(f(x,x),y) # label(bd). >> BACK DEMODULATING HINT 2827 WITH 18090. NEW HINT: 19742 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(g(y),f(f(f(y,y),z),f(g(u),u)))))=f(z,f(g(v),v)) # label(bd). >> BACK DEMODULATING HINT 2809 WITH 18090. NEW HINT: 19743 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(u),u),g(z)),f(f(f(g(x),x),f(f(y,f(f(g(y),f(g(x),x)),z)),f(g(x),x))),f(f(g(x),x),f(g(x),x))))=f(g(v),v) # label(bd). >> BACK DEMODULATING HINT 2806 WITH 18090. >> BACK DEMODULATING HINT 2800 WITH 18090. >> BACK DEMODULATING HINT 2794 WITH 18090. >> BACK DEMODULATING HINT 2791 WITH 18090. >> BACK DEMODULATING HINT 2788 WITH 18090. NEW HINT: 19744 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(y,y),u),f(f(g(u),g(y)),f(g(y),g(x)))),f(f(f(x,z),f(x,y)),g(y))),g(x))=z # label(bd). >> BACK DEMODULATING HINT 2787 WITH 18090. NEW HINT: 19745 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(x,x),y),f(f(g(y),g(x)),f(g(x),g(z)))),f(f(f(z,u),f(z,x)),g(x))),f(f(f(x,x),y),f(f(g(y),g(x)),f(g(x),g(z)))))=u # label(bd). >> BACK DEMODULATING HINT 2786 WITH 18090. NEW HINT: 19746 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,x),y),f(f(f(f(g(y),g(x)),f(g(x),g(z))),f(z,u)),f(f(x,x),y))),f(g(y),f(g(x),g(x))))=u # label(bd). >> BACK DEMODULATING HINT 2785 WITH 18090. >> BACK DEMODULATING HINT 2784 WITH 18090. >> BACK DEMODULATING HINT 2783 WITH 18090. NEW HINT: 19747 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(v),f(x,f(f(y,f(f(g(y),g(x)),f(g(u),g(z)))),x)))),g(x)))=f(f(g(v),f(g(u),f(g(z),g(z)))),z) # label(bd). >> BACK DEMODULATING HINT 2780 WITH 18090. NEW HINT: 19748 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,x),y),f(f(f(g(y),f(g(x),g(x))),f(f(u,g(z)),f(f(z,x),f(x,y)))),f(g(y),f(g(x),g(x)))))=u # label(bd). >> BACK DEMODULATING HINT 2779 WITH 18090. NEW HINT: 19749 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),g(x))),f(f(u,g(z)),f(f(z,x),f(x,y)))),f(g(y),f(g(x),g(x))))=f(f(g(y),g(x)),f(g(x),u)) # label(bd). >> BACK DEMODULATING HINT 2778 WITH 18090. >> BACK DEMODULATING HINT 2777 WITH 18090. >> BACK DEMODULATING HINT 2776 WITH 18090. >> BACK DEMODULATING HINT 2775 WITH 18090. >> BACK DEMODULATING HINT 2774 WITH 18090. NEW HINT: 19750 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(g(y),g(x)),f(g(x),g(v6))),f(v6,u)),g(w)),f(f(f(f(g(z),f(g(y),f(g(x),g(x)))),u),f(f(v,f(f(g(v),f(g(u),f(f(f(x,x),y),z))),w)),f(f(g(z),f(g(y),f(g(x),g(x)))),u))),f(f(g(u),f(f(f(x,x),y),z)),f(g(u),f(f(f(x,x),y),z)))))=z # label(bd). >> BACK DEMODULATING HINT 2765 WITH 18090. NEW HINT: 19751 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(y,f(z,f(f(f(y,u),g(w)),f(f(u,f(f(v,f(f(g(v),g(u)),w)),u)),f(g(u),g(u)))))),g(y))))=z # label(bd). >> BACK DEMODULATING HINT 2764 WITH 18090. NEW HINT: 19752 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(f(y,z),g(v)),f(f(z,f(f(u,f(f(g(u),g(z)),v)),z)),f(g(z),g(z)))),f(w,f(f(f(y,z),g(v)),f(f(z,f(f(u,f(f(g(u),g(z)),v)),z)),f(g(z),g(z)))))),g(y))))=w # label(bd). >> BACK DEMODULATING HINT 2763 WITH 18090. NEW HINT: 19753 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(f(f(y,z),g(v)),f(f(z,f(f(u,f(f(g(u),g(z)),v)),z)),f(g(z),g(z)))),f(w,f(f(f(y,z),g(v)),f(f(z,f(f(u,f(f(g(u),g(z)),v)),z)),f(g(z),g(z)))))),f(f(f(z,z),f(f(g(z),f(f(g(v),f(z,u)),g(u))),g(z))),f(v,f(g(z),g(y)))))))=w # label(bd). >> BACK DEMODULATING HINT 2754 WITH 18090. NEW HINT: 19754 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),f(z,g(x)))),f(f(f(x,u),f(u,v)),f(g(v),f(g(u),g(u))))))=z # label(bd). >> BACK DEMODULATING HINT 2753 WITH 18090. NEW HINT: 19755 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),g(x)),f(v,f(f(f(z,z),u),f(f(g(u),g(z)),f(g(z),g(x))))))),f(f(f(x,z),f(z,u)),f(g(u),f(g(z),g(z))))))=v # label(bd). >> BACK DEMODULATING HINT 2752 WITH 18090. NEW HINT: 19756 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(y,f(f(g(y),f(f(f(z,z),u),f(f(g(u),g(z)),f(g(z),g(x))))),f(v,f(f(f(z,z),u),f(f(g(u),g(z)),f(g(z),g(x))))))),f(f(f(x,z),f(z,u)),f(g(u),f(g(z),g(z))))))=v # label(bd). >> BACK DEMODULATING HINT 2701 WITH 18090. >> BACK DEMODULATING HINT 2681 WITH 18090. NEW HINT: 19757 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(v),g(u)),f(f(f(x,f(g(y),y)),f(f(z,f(f(g(z),f(f(g(y),y),g(x))),u)),f(x,f(g(y),y)))),f(f(f(g(y),y),g(x)),f(f(g(y),y),g(x)))))=f(g(v),g(x)) # label(bd). >> BACK DEMODULATING HINT 2646 WITH 18090. NEW HINT: 19758 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),y)),f(f(g(z),z),f(f(f(f(g(z),z),f(g(z),z)),u),v))))=f(u,v) # label(bd). >> BACK DEMODULATING HINT 2640 WITH 18090. >> BACK DEMODULATING HINT 2633 WITH 18090. NEW HINT: 19759 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(z),f(f(g(y),y),f(g(y),y)))),u))=f(f(f(g(z),f(g(y),y)),f(f(g(w),w),g(v))),f(v,u)) # label(bd). >> BACK DEMODULATING HINT 2632 WITH 18090. NEW HINT: 19760 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(g(x),x)),f(f(g(u),u),g(z))),f(z,v))=f(w,f(f(g(w),f(g(y),f(f(g(x),x),f(g(x),x)))),v)) # label(bd). >> BACK DEMODULATING HINT 2592 WITH 18090. NEW HINT: 19761 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(w),g(v)),f(v,y)),g(u)),f(f(f(x,y),f(f(z,f(f(g(z),f(g(y),g(x))),u)),f(x,y))),f(f(g(y),g(x)),f(g(y),g(x)))))=f(g(w),g(x)) # label(bd). >> BACK DEMODULATING HINT 2589 WITH 18090. NEW HINT: 19762 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(f(z,u),f(f(f(g(u),g(v)),f(v,w)),y)),g(y))))=f(g(y),f(z,w)) # label(bd). >> BACK DEMODULATING HINT 2585 WITH 18090. >> BACK DEMODULATING HINT 2583 WITH 18090. NEW HINT: 19763 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,x),y),f(f(f(g(y),f(g(x),g(x))),f(g(u),f(z,f(x,y)))),f(g(y),f(g(x),g(x)))))=f(f(f(z,f(x,y)),f(g(y),f(g(x),g(x)))),f(f(x,f(g(z),g(u))),f(f(z,f(x,y)),f(g(y),f(g(x),g(x)))))) # label(bd). >> BACK DEMODULATING HINT 2582 WITH 18090. >> BACK DEMODULATING HINT 2581 WITH 18090. >> BACK DEMODULATING HINT 2580 WITH 18090. >> BACK DEMODULATING HINT 2579 WITH 18090. >> BACK DEMODULATING HINT 2578 WITH 18090. >> BACK DEMODULATING HINT 2576 WITH 18090. >> BACK DEMODULATING HINT 2575 WITH 18090. >> BACK DEMODULATING HINT 2574 WITH 18090. >> BACK DEMODULATING HINT 2573 WITH 18090. >> BACK DEMODULATING HINT 2572 WITH 18090. NEW HINT: 19764 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(v,f(g(v6),g(w))),f(w,y)),g(u)),f(f(f(x,y),f(f(z,f(f(g(z),f(g(y),g(x))),u)),f(x,y))),f(f(g(y),g(x)),f(g(y),g(x)))))=f(v,f(g(v6),g(x))) # label(bd). >> BACK DEMODULATING HINT 2570 WITH 18090. >> BACK DEMODULATING HINT 2564 WITH 18090. >> BACK DEMODULATING HINT 2562 WITH 18090. NEW HINT: 19765 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),f(g(x),g(z))),f(z,u))=f(v,f(f(g(v),f(g(y),f(g(x),g(x)))),u)) # label(bd). >> BACK DEMODULATING HINT 2556 WITH 18090. >> BACK DEMODULATING HINT 2553 WITH 18090. >> BACK DEMODULATING HINT 2546 WITH 18090. >> BACK DEMODULATING HINT 2543 WITH 18090. >> BACK DEMODULATING HINT 2531 WITH 18090. >> BACK DEMODULATING HINT 2523 WITH 18090. NEW HINT: 19766 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(g(y),g(x))),f(g(y),g(x))),g(y)))=x. >> BACK DEMODULATING HINT 2522 WITH 18090. >> BACK DEMODULATING HINT 2521 WITH 18090. NEW HINT: 19767 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,y),f(f(x,y),f(g(y),g(x)))),f(x,y)),f(f(f(f(x,y),f(g(y),g(x))),f(g(y),g(x))),g(y)))=x. >> BACK DEMODULATING HINT 2520 WITH 18090. NEW HINT: 19768 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,y),f(f(x,y),f(g(y),g(x)))),f(f(f(x,y),f(g(y),g(x))),f(x,y))),f(f(f(f(x,y),f(g(y),g(x))),f(g(y),g(x))),g(y)))=x. >> BACK DEMODULATING HINT 2519 WITH 18090. >> BACK DEMODULATING HINT 2512 WITH 18090. >> BACK DEMODULATING HINT 2511 WITH 18090. NEW HINT: 19769 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),x),x),f(g(x),x)))=f(x,x). >> BACK DEMODULATING HINT 2510 WITH 18090. >> BACK DEMODULATING HINT 2509 WITH 18090. NEW HINT: 19770 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(y,f(f(g(y),x),g(x))))=x. >> BACK DEMODULATING HINT 2475 WITH 18090. >> BACK DEMODULATING HINT 2471 WITH 18090. >> BACK DEMODULATING HINT 2470 WITH 18090. >> BACK DEMODULATING HINT 2469 WITH 18090. >> BACK DEMODULATING HINT 2466 WITH 18090. >> BACK DEMODULATING HINT 2462 WITH 18090. NEW HINT: 19771 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,y),f(f(x,y),f(g(y),g(x)))),f(f(f(x,y),f(g(y),g(x))),f(f(x,y),f(f(x,y),f(g(y),g(x)))))),f(f(f(f(x,y),f(g(y),g(x))),f(g(y),g(x))),g(y)))=x. >> BACK DEMODULATING HINT 2461 WITH 18090. NEW HINT: 19772 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,f(y,z)),g(x))),f(x,g(z)))=y. >> BACK DEMODULATING HINT 2460 WITH 18090. NEW HINT: 19773 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,f(y,z)),g(x))),f(x,g(z)))=f(z,f(f(g(u),f(f(u,g(z)),f(y,z))),g(z))). >> BACK DEMODULATING HINT 2459 WITH 18090. NEW HINT: 19774 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(z),f(f(z,g(x)),y)),g(x)))=f(f(g(u),f(f(u,y),g(u))),f(u,g(x))). >> BACK DEMODULATING HINT 2457 WITH 18090. NEW HINT: 19775 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(f(x,y),g(x))),f(x,g(z))),z)=y. >> BACK DEMODULATING HINT 2456 WITH 18090. NEW HINT: 19776 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,f(f(y,f(x,g(z))),z)),g(x)))=y. >> BACK DEMODULATING HINT 2455 WITH 18090. NEW HINT: 19777 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(f(z,g(x)),f(y,x))),g(x))=f(f(f(g(x),f(y,g(x))),f(x,g(u))),u). >> BACK DEMODULATING HINT 2453 WITH 18090. NEW HINT: 19778 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(f(z,g(x)),f(f(x,y),x))),g(x))=y. >> BACK DEMODULATING HINT 2452 WITH 18090. NEW HINT: 19779 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),f(y,g(x))),f(x,g(z))),z))=y. >> BACK DEMODULATING HINT 2451 WITH 18090. >> BACK DEMODULATING HINT 2450 WITH 18090. >> BACK DEMODULATING HINT 2449 WITH 18090. >> BACK DEMODULATING HINT 2439 WITH 18090. >> BACK DEMODULATING HINT 2437 WITH 18090. >> BACK DEMODULATING HINT 2425 WITH 18090. >> BACK DEMODULATING HINT 2424 WITH 18090. >> BACK DEMODULATING HINT 2401 WITH 18090. >> BACK DEMODULATING HINT 2399 WITH 18090. >> BACK DEMODULATING HINT 2375 WITH 18090. NEW HINT: 19780 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(f(y,z),g(x))),f(x,g(z))),u)=u. >> BACK DEMODULATING HINT 2372 WITH 18090. NEW HINT: 19781 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(f(g(x),f(g(y),g(x))),f(x,z)),g(z)),y),x),z)=z. >> BACK DEMODULATING HINT 2368 WITH 18090. NEW HINT: 19782 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(f(y,z),g(x))),f(x,g(u))),u)=z. >> BACK DEMODULATING HINT 2367 WITH 18090. NEW HINT: 19783 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(z),f(f(z,y),g(x)))=f(f(x,g(y)),f(f(y,g(x)),f(y,g(x)))). >> BACK DEMODULATING HINT 2363 WITH 18090. NEW HINT: 19784 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(y)),f(f(y,g(x)),f(y,g(x))))=f(y,g(x)). >> BACK DEMODULATING HINT 2361 WITH 18090. NEW HINT: 19785 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(g(x),f(y,g(x))),f(x,z)),g(u))),u)=f(y,z). >> BACK DEMODULATING HINT 2358 WITH 18090. >> BACK DEMODULATING HINT 2357 WITH 18090. NEW HINT: 19786 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,g(y)),f(f(g(u),f(f(u,f(y,g(x))),z)),f(y,g(x))))=f(g(x),f(f(x,f(z,y)),g(x))). >> BACK DEMODULATING HINT 2355 WITH 18090. >> BACK DEMODULATING HINT 2354 WITH 18090. >> BACK DEMODULATING HINT 2353 WITH 18090. >> BACK DEMODULATING HINT 2352 WITH 18090. >> BACK DEMODULATING HINT 2350 WITH 18090. NEW HINT: 19787 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(x,g(y)),f(f(y,g(x)),f(y,g(x)))),f(x,g(z))),z)=y. >> BACK DEMODULATING HINT 2348 WITH 18090. NEW HINT: 19788 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(u),f(f(u,g(x)),z)),f(g(z),y)))=y. >> BACK DEMODULATING HINT 2347 WITH 18090. >> BACK DEMODULATING HINT 2345 WITH 18090. NEW HINT: 19789 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(z),f(f(z,g(x)),y)))=y. >> BACK DEMODULATING HINT 2344 WITH 18090. >> BACK DEMODULATING HINT 2343 WITH 18090. >> BACK DEMODULATING HINT 2333 WITH 18090. >> BACK DEMODULATING HINT 2327 WITH 18090. >> BACK DEMODULATING HINT 2321 WITH 18090. >> BACK DEMODULATING HINT 2320 WITH 18090. >> BACK DEMODULATING HINT 2313 WITH 18090. >> BACK DEMODULATING HINT 2312 WITH 18090. >> BACK DEMODULATING HINT 2311 WITH 18090. >> BACK DEMODULATING HINT 2310 WITH 18090. >> BACK DEMODULATING HINT 2309 WITH 18090. >> BACK DEMODULATING HINT 2308 WITH 18090. >> BACK DEMODULATING HINT 2307 WITH 18090. >> BACK DEMODULATING HINT 2306 WITH 18090. >> BACK DEMODULATING HINT 2303 WITH 18090. >> BACK DEMODULATING HINT 2302 WITH 18090. >> BACK DEMODULATING HINT 2299 WITH 18090. >> BACK DEMODULATING HINT 2297 WITH 18090. >> BACK DEMODULATING HINT 2295 WITH 18090. >> BACK DEMODULATING HINT 2294 WITH 18090. >> BACK DEMODULATING HINT 2292 WITH 18090. >> BACK DEMODULATING HINT 2286 WITH 18090. >> BACK DEMODULATING HINT 2285 WITH 18090. NEW HINT: 19790 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x))),u)=f(z,f(f(g(z),g(v)),f(f(v,f(f(z,u),x)),g(x)))). >> BACK DEMODULATING HINT 2284 WITH 18090. NEW HINT: 19791 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(y,f(f(u,v),z)),g(z))))=f(f(g(z),f(f(w,f(f(g(w),z),f(u,z))),g(z))),v). >> BACK DEMODULATING HINT 2283 WITH 18090. >> BACK DEMODULATING HINT 2282 WITH 18090. NEW HINT: 19792 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(g(y),f(f(u,f(f(g(u),v),z)),g(z))),y))=f(f(x,v),y). >> BACK DEMODULATING HINT 2275 WITH 18090. >> BACK DEMODULATING HINT 2260 WITH 18090. >> BACK DEMODULATING HINT 2248 WITH 18090. NEW HINT: 19793 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),f(f(z,f(f(g(z),g(x)),u)),x)),f(g(x),y)),g(y)))=f(v,f(f(g(v),g(x)),u)). >> BACK DEMODULATING HINT 2239 WITH 18090. NEW HINT: 19794 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(f(y,f(g(z),g(x))),y)),f(g(y),x))=g(z). >> BACK DEMODULATING HINT 2237 WITH 18090. >> BACK DEMODULATING HINT 2236 WITH 18090. >> BACK DEMODULATING HINT 2235 WITH 18090. >> BACK DEMODULATING HINT 2229 WITH 18090. >> BACK DEMODULATING HINT 2228 WITH 18090. >> BACK DEMODULATING HINT 2222 WITH 18090. >> BACK DEMODULATING HINT 2219 WITH 18090. >> BACK DEMODULATING HINT 2216 WITH 18090. >> BACK DEMODULATING HINT 2213 WITH 18090. NEW HINT: 19795 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,f(f(g(y),f(z,f(u,f(f(g(u),u),v)))),x)),g(x))=f(f(z,u),v). >> BACK DEMODULATING HINT 2196 WITH 18090. >> BACK DEMODULATING HINT 2195 WITH 18090. >> BACK DEMODULATING HINT 2194 WITH 18090. >> BACK DEMODULATING HINT 2193 WITH 18090. >> BACK DEMODULATING HINT 2192 WITH 18090. >> BACK DEMODULATING HINT 2170 WITH 18090. >> BACK DEMODULATING HINT 2169 WITH 18090. >> BACK DEMODULATING HINT 2167 WITH 18090. >> BACK DEMODULATING HINT 2166 WITH 18090. >> BACK DEMODULATING HINT 2165 WITH 18090. >> BACK DEMODULATING HINT 2164 WITH 18090. >> BACK DEMODULATING HINT 2163 WITH 18090. >> BACK DEMODULATING HINT 2162 WITH 18090. >> BACK DEMODULATING HINT 2161 WITH 18090. >> BACK DEMODULATING HINT 2160 WITH 18090. >> BACK DEMODULATING HINT 2159 WITH 18090. >> BACK DEMODULATING HINT 2158 WITH 18090. >> BACK DEMODULATING HINT 2155 WITH 18090. >> BACK DEMODULATING HINT 2154 WITH 18090. >> BACK DEMODULATING HINT 2153 WITH 18090. >> BACK DEMODULATING HINT 2152 WITH 18090. >> BACK DEMODULATING HINT 2151 WITH 18090. >> BACK DEMODULATING HINT 2150 WITH 18090. >> BACK DEMODULATING HINT 2149 WITH 18090. >> BACK DEMODULATING HINT 2142 WITH 18090. >> BACK DEMODULATING HINT 2135 WITH 18090. >> BACK DEMODULATING HINT 2128 WITH 18090. >> BACK DEMODULATING HINT 2123 WITH 18090. >> BACK DEMODULATING HINT 2122 WITH 18090. >> BACK DEMODULATING HINT 2117 WITH 18090. >> BACK DEMODULATING HINT 2116 WITH 18090. >> BACK DEMODULATING HINT 2115 WITH 18090. >> BACK DEMODULATING HINT 2114 WITH 18090. >> BACK DEMODULATING HINT 2113 WITH 18090. >> BACK DEMODULATING HINT 2112 WITH 18090. >> BACK DEMODULATING HINT 2111 WITH 18090. >> BACK DEMODULATING HINT 2110 WITH 18090. >> BACK DEMODULATING HINT 2109 WITH 18090. >> BACK DEMODULATING HINT 2107 WITH 18090. NEW HINT: 19796 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(g(x),f(f(u,f(f(g(u),w),f(g(x),y))),z)),g(z)),g(y))),x)=w. >> BACK DEMODULATING HINT 2106 WITH 18090. NEW HINT: 19797 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(z,f(f(g(z),f(f(f(g(y),x),f(w,u)),g(u))),x))),g(x)))=w. >> BACK DEMODULATING HINT 2103 WITH 18090. >> BACK DEMODULATING HINT 2102 WITH 18090. >> BACK DEMODULATING HINT 2100 WITH 18090. >> BACK DEMODULATING HINT 2099 WITH 18090. >> BACK DEMODULATING HINT 2098 WITH 18090. NEW HINT: 19798 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(y,f(f(g(y),g(x)),g(z))),f(g(v),g(u))),f(f(f(u,f(f(v,z),w)),g(w)),g(v6))))=f(f(g(v6),v6),g(v6)). >> BACK DEMODULATING HINT 2097 WITH 18090. >> BACK DEMODULATING HINT 2096 WITH 18090. NEW HINT: 19799 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(g(y),f(g(x),f(f(x,y),x)))),x)=x. >> BACK DEMODULATING HINT 2095 WITH 18090. NEW HINT: 19800 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(z,f(f(g(z),f(f(g(y),f(z,u)),g(u))),g(z))),f(g(x),f(f(x,y),x)))),x)=x. >> BACK DEMODULATING HINT 2091 WITH 18090. >> BACK DEMODULATING HINT 2090 WITH 18090. >> BACK DEMODULATING HINT 2089 WITH 18090. >> BACK DEMODULATING HINT 2088 WITH 18090. >> BACK DEMODULATING HINT 2087 WITH 18090. >> BACK DEMODULATING HINT 2085 WITH 18090. >> BACK DEMODULATING HINT 2083 WITH 18090. >> BACK DEMODULATING HINT 2081 WITH 18090. >> BACK DEMODULATING HINT 2076 WITH 18090. >> BACK DEMODULATING HINT 2071 WITH 18090. >> BACK DEMODULATING HINT 2067 WITH 18090. >> BACK DEMODULATING HINT 2061 WITH 18090. >> BACK DEMODULATING HINT 2058 WITH 18090. NEW HINT: 19801 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(f(y,f(f(g(y),z),x)),g(x))),z)=z. >> BACK DEMODULATING HINT 2041 WITH 18090. NEW HINT: 19802 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(z,f(f(g(z),u),x))),g(x)))=f(f(g(x),y),u). >> BACK DEMODULATING HINT 2040 WITH 18090. NEW HINT: 19803 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(g(x),f(g(z),y)),g(y))),f(f(u,f(f(g(u),f(f(y,f(f(g(y),z),x)),g(x))),z)),f(x,f(f(g(x),f(g(z),y)),g(y)))))=f(x,g(x)). >> BACK DEMODULATING HINT 2039 WITH 18090. >> BACK DEMODULATING HINT 2038 WITH 18090. NEW HINT: 19804 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(f(g(y),x),f(z,x))),g(x)))=f(u,f(f(g(u),g(v)),f(f(v,f(z,v)),g(v)))). >> BACK DEMODULATING HINT 2037 WITH 18090. NEW HINT: 19805 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),f(g(z),y)),g(y))),f(f(u,f(f(g(u),f(f(y,f(f(g(y),z),x)),g(x))),z)),f(x,f(f(g(x),f(g(z),y)),g(y))))),v)=v. >> BACK DEMODULATING HINT 2036 WITH 18090. >> BACK DEMODULATING HINT 2035 WITH 18090. >> BACK DEMODULATING HINT 2034 WITH 18090. >> BACK DEMODULATING HINT 2033 WITH 18090. >> BACK DEMODULATING HINT 2032 WITH 18090. NEW HINT: 19806 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(f(y,f(f(f(g(v),u),g(z)),g(x))),y)),f(g(y),x))=f(g(v),f(f(u,f(w,f(f(g(w),g(z)),v))),g(v))). >> BACK DEMODULATING HINT 2021 WITH 18090. >> BACK DEMODULATING HINT 2020 WITH 18090. NEW HINT: 19807 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(u,f(f(g(u),f(f(g(y),f(u,v)),g(v))),g(u))),f(f(y,z),y)),f(g(y),x)),g(x))=z. >> BACK DEMODULATING HINT 2019 WITH 18090. NEW HINT: 19808 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(u,f(f(g(u),f(f(g(y),f(u,v)),g(v))),g(u))),f(f(y,z),f(f(u,f(f(v,f(f(g(v),g(u)),y)),u)),g(u)))),f(g(y),x)),g(x))=z. >> BACK DEMODULATING HINT 2018 WITH 18090. NEW HINT: 19809 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(y,f(f(g(y),f(f(g(u),f(y,z)),g(z))),g(y))),f(f(u,v),f(f(y,f(f(z,f(f(g(z),g(y)),u)),y)),g(y)))),f(f(y,f(f(g(y),f(f(g(u),f(y,z)),g(z))),g(y))),x)),g(x))=v. >> BACK DEMODULATING HINT 2017 WITH 18090. >> BACK DEMODULATING HINT 2008 WITH 18090. NEW HINT: 19810 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(f(y,f(f(z,f(f(g(z),g(u)),x)),g(x))),y)),f(g(y),x))=f(v,f(f(g(v),g(u)),x)). >> BACK DEMODULATING HINT 2007 WITH 18090. >> BACK DEMODULATING HINT 2006 WITH 18090. NEW HINT: 19811 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(f(x,g(y)),x)),f(g(x),f(f(g(x),f(y,g(x))),x))),f(g(x),f(f(x,g(y)),x)))=f(f(g(u),f(f(u,f(g(y),g(z))),u)),f(g(u),z)). >> BACK DEMODULATING HINT 2005 WITH 18090. NEW HINT: 19812 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(f(x,g(y)),x)),f(g(x),f(f(g(x),f(y,g(x))),x))),f(g(x),f(f(x,g(y)),x)))=f(f(f(g(x),f(f(x,g(y)),x)),f(g(x),f(g(z),u))),f(g(u),z)). >> BACK DEMODULATING HINT 1995 WITH 18090. >> BACK DEMODULATING HINT 1990 WITH 18090. >> BACK DEMODULATING HINT 1976 WITH 18090. >> BACK DEMODULATING HINT 1970 WITH 18090. >> BACK DEMODULATING HINT 1968 WITH 18090. >> BACK DEMODULATING HINT 1962 WITH 18090. >> BACK DEMODULATING HINT 1953 WITH 18090. >> BACK DEMODULATING HINT 1950 WITH 18090. >> BACK DEMODULATING HINT 1947 WITH 18090. >> BACK DEMODULATING HINT 1945 WITH 18090. NEW HINT: 19813 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),f(z,f(x,y))),f(g(y),g(x)))=f(x,f(y,z)). >> BACK DEMODULATING HINT 1944 WITH 18090. NEW HINT: 19814 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,y),f(z,f(x,y))),f(g(y),g(x)))=f(f(x,f(f(y,z),x)),g(x)). >> BACK DEMODULATING HINT 1938 WITH 18090. NEW HINT: 19815 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(y,x)),g(x)),g(y))=x. >> BACK DEMODULATING HINT 1937 WITH 18090. >> BACK DEMODULATING HINT 1936 WITH 18090. NEW HINT: 19816 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(g(y),g(x)),f(f(x,f(f(y,z),x)),g(x))))=f(f(f(x,y),f(z,f(x,y))),f(g(y),g(x))). >> BACK DEMODULATING HINT 1935 WITH 18090. >> BACK DEMODULATING HINT 1934 WITH 18090. >> BACK DEMODULATING HINT 1933 WITH 18090. >> BACK DEMODULATING HINT 1932 WITH 18090. >> BACK DEMODULATING HINT 1931 WITH 18090. >> BACK DEMODULATING HINT 1927 WITH 18090. >> BACK DEMODULATING HINT 1926 WITH 18090. >> BACK DEMODULATING HINT 1920 WITH 18090. >> BACK DEMODULATING HINT 1917 WITH 18090. >> BACK DEMODULATING HINT 1916 WITH 18090. >> BACK DEMODULATING HINT 1913 WITH 18090. >> BACK DEMODULATING HINT 1911 WITH 18090. >> BACK DEMODULATING HINT 1908 WITH 18090. >> BACK DEMODULATING HINT 1907 WITH 18090. >> BACK DEMODULATING HINT 1897 WITH 18090. NEW HINT: 19817 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,z),f(u,f(y,z))),f(g(z),g(y)))=f(f(y,z),f(f(g(z),g(y)),f(f(y,f(f(z,u),y)),g(y)))). >> BACK DEMODULATING HINT 1895 WITH 18090. NEW HINT: 19818 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(g(y),v),f(w,f(f(g(w),g(v)),g(u)))),u),f(y,f(z,x))),g(x))=z. >> BACK DEMODULATING HINT 1894 WITH 18090. NEW HINT: 19819 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(z),y),f(f(g(y),z),f(u,x))),g(x))=u. >> BACK DEMODULATING HINT 1893 WITH 18090. NEW HINT: 19820 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),f(z,u)),g(u)),f(g(z),y)))=y. >> BACK DEMODULATING HINT 1892 WITH 18090. NEW HINT: 19821 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(y,x)),g(x)),f(g(y),f(g(x),z)))=z. >> BACK DEMODULATING HINT 1891 WITH 18090. >> BACK DEMODULATING HINT 1889 WITH 18090. NEW HINT: 19822 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(f(f(g(x),g(y)),g(x)),z),x)),g(x))=f(g(y),f(g(x),z)). >> BACK DEMODULATING HINT 1888 WITH 18090. >> BACK DEMODULATING HINT 1887 WITH 18090. NEW HINT: 19823 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(g(x),f(f(f(x,f(y,x)),g(x)),z)))=z. >> BACK DEMODULATING HINT 1886 WITH 18090. NEW HINT: 19824 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(x,f(f(g(x),f(g(y),f(x,f(y,x)))),g(x))),f(x,f(f(g(x),g(y)),g(x)))),f(g(x),f(f(f(x,f(y,x)),g(x)),z)))=z. >> BACK DEMODULATING HINT 1877 WITH 18090. >> BACK DEMODULATING HINT 1868 WITH 18090. NEW HINT: 19825 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,g(x)),f(f(x,f(z,x)),g(x)))=f(f(y,f(z,y)),g(y)). >> BACK DEMODULATING HINT 1867 WITH 18090. >> BACK DEMODULATING HINT 1858 WITH 18090. >> BACK DEMODULATING HINT 1857 WITH 18090. >> BACK DEMODULATING HINT 1854 WITH 18090. NEW HINT: 19826 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(u,f(f(g(u),g(z)),z)))=x. >> BACK DEMODULATING HINT 1853 WITH 18090. NEW HINT: 19827 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(y,f(f(g(y),g(z)),z))),f(y,f(f(g(y),g(z)),z)))=x. >> BACK DEMODULATING HINT 1852 WITH 18090. >> BACK DEMODULATING HINT 1851 WITH 18090. >> BACK DEMODULATING HINT 1850 WITH 18090. >> BACK DEMODULATING HINT 1849 WITH 18090. >> BACK DEMODULATING HINT 1848 WITH 18090. >> BACK DEMODULATING HINT 1847 WITH 18090. >> BACK DEMODULATING HINT 1844 WITH 18090. >> BACK DEMODULATING HINT 1843 WITH 18090. >> BACK DEMODULATING HINT 1841 WITH 18090. NEW HINT: 19828 [bsub_wt=2147483647, bsub_add_wt=-1024] f(z,f(f(g(z),g(u)),f(v,f(f(g(v),g(y)),y))))=g(u). >> BACK DEMODULATING HINT 1840 WITH 18090. >> BACK DEMODULATING HINT 1839 WITH 18090. >> BACK DEMODULATING HINT 1838 WITH 18090. >> BACK DEMODULATING HINT 1837 WITH 18090. >> BACK DEMODULATING HINT 1836 WITH 18090. >> BACK DEMODULATING HINT 1830 WITH 18090. >> BACK DEMODULATING HINT 1827 WITH 18090. >> BACK DEMODULATING HINT 1826 WITH 18090. >> BACK DEMODULATING HINT 1821 WITH 18090. >> BACK DEMODULATING HINT 1820 WITH 18090. >> BACK DEMODULATING HINT 1819 WITH 18090. >> BACK DEMODULATING HINT 1818 WITH 18090. >> BACK DEMODULATING HINT 1817 WITH 18090. >> BACK DEMODULATING HINT 1807 WITH 18090. >> BACK DEMODULATING HINT 1806 WITH 18090. >> BACK DEMODULATING HINT 1805 WITH 18090. >> BACK DEMODULATING HINT 1804 WITH 18090. >> BACK DEMODULATING HINT 1803 WITH 18090. >> BACK DEMODULATING HINT 1802 WITH 18090. >> BACK DEMODULATING HINT 1798 WITH 18090. >> BACK DEMODULATING HINT 1797 WITH 18090. >> BACK DEMODULATING HINT 1796 WITH 18090. >> BACK DEMODULATING HINT 1794 WITH 18090. >> BACK DEMODULATING HINT 1791 WITH 18090. >> BACK DEMODULATING HINT 1787 WITH 18090. >> BACK DEMODULATING HINT 1777 WITH 18090. >> BACK DEMODULATING HINT 1773 WITH 18090. NEW HINT: 19829 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(f(y,v),x)),g(x))=f(f(x,y),v). >> BACK DEMODULATING HINT 1772 WITH 18090. >> BACK DEMODULATING HINT 1768 WITH 18090. NEW HINT: 19830 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,g(x)),f(f(x,f(v,z)),g(z)))=f(f(y,f(v,y)),g(y)). >> BACK DEMODULATING HINT 1751 WITH 18090. >> BACK DEMODULATING HINT 1742 WITH 18090. >> BACK DEMODULATING HINT 1739 WITH 18090. >> BACK DEMODULATING HINT 1737 WITH 18090. >> BACK DEMODULATING HINT 1735 WITH 18090. >> BACK DEMODULATING HINT 1734 WITH 18090. >> BACK DEMODULATING HINT 1733 WITH 18090. >> BACK DEMODULATING HINT 1727 WITH 18090. >> BACK DEMODULATING HINT 1726 WITH 18090. >> BACK DEMODULATING HINT 1720 WITH 18090. >> BACK DEMODULATING HINT 1718 WITH 18090. >> BACK DEMODULATING HINT 1710 WITH 18090. >> BACK DEMODULATING HINT 1708 WITH 18090. >> BACK DEMODULATING HINT 1707 WITH 18090. >> BACK DEMODULATING HINT 1706 WITH 18090. >> BACK DEMODULATING HINT 1705 WITH 18090. >> BACK DEMODULATING HINT 1704 WITH 18090. >> BACK DEMODULATING HINT 1703 WITH 18090. >> BACK DEMODULATING HINT 1701 WITH 18090. >> BACK DEMODULATING HINT 1700 WITH 18090. >> BACK DEMODULATING HINT 1699 WITH 18090. >> BACK DEMODULATING HINT 1697 WITH 18090. >> BACK DEMODULATING HINT 1696 WITH 18090. >> BACK DEMODULATING HINT 1695 WITH 18090. >> BACK DEMODULATING HINT 1694 WITH 18090. >> BACK DEMODULATING HINT 1693 WITH 18090. >> BACK DEMODULATING HINT 1692 WITH 18090. >> BACK DEMODULATING HINT 1691 WITH 18090. >> BACK DEMODULATING HINT 1688 WITH 18090. >> BACK DEMODULATING HINT 1686 WITH 18090. >> BACK DEMODULATING HINT 1685 WITH 18090. >> BACK DEMODULATING HINT 1672 WITH 18090. NEW HINT: 19831 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(y,f(z,y)),g(y))),f(f(w,f(f(g(w),f(g(z),g(u))),v)),f(g(v),u))))=y. >> BACK DEMODULATING HINT 1665 WITH 18090. NEW HINT: 19832 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),y),f(f(g(y),f(f(u,v),z)),g(z))))=f(u,v). >> BACK DEMODULATING HINT 1663 WITH 18090. NEW HINT: 19833 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(f(y,f(f(z,f(f(g(z),y),u)),y)),f(g(y),x)),g(x)))=f(v,f(f(g(v),y),u)). >> BACK DEMODULATING HINT 1661 WITH 18090. NEW HINT: 19834 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(f(f(u,f(f(g(u),v),w)),v),f(g(z),y)),g(y))),z))=f(f(v6,f(f(g(v6),v),w)),v). >> BACK DEMODULATING HINT 1660 WITH 18090. NEW HINT: 19835 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(u,f(g(z),y)),g(y))),z))=u. >> BACK DEMODULATING HINT 1659 WITH 18090. NEW HINT: 19836 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),g(y)),f(f(y,f(f(z,f(f(g(z),f(f(v,f(g(x),u)),g(u))),x)),y)),g(y))))=v. >> BACK DEMODULATING HINT 1658 WITH 18090. >> BACK DEMODULATING HINT 1656 WITH 18090. NEW HINT: 19837 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(g(z),f(g(y),x)),g(x)))=f(g(y),f(f(g(z),f(g(y),u)),g(u))). >> BACK DEMODULATING HINT 1655 WITH 18090. NEW HINT: 19838 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(f(y,f(z,y)),f(g(y),x)),g(x)))=z. >> BACK DEMODULATING HINT 1654 WITH 18090. NEW HINT: 19839 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(f(y,f(z,y)),f(g(y),x)),g(x)))=f(f(g(u),v),f(f(g(v),f(f(u,z),w)),g(w))). >> BACK DEMODULATING HINT 1653 WITH 18090. NEW HINT: 19840 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(f(g(y),x),g(z)),f(f(z,f(u,z)),g(z))))=f(g(z),f(f(f(z,f(u,z)),f(g(z),v)),g(v))). >> BACK DEMODULATING HINT 1652 WITH 18090. NEW HINT: 19841 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(y),f(f(g(z),f(g(y),x)),g(x)))=f(u,f(f(g(u),g(y)),f(g(z),g(y)))). >> BACK DEMODULATING HINT 1650 WITH 18090. NEW HINT: 19842 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(f(z,x),g(z)),f(f(z,x),y)),g(y)),g(x))=f(z,x). >> BACK DEMODULATING HINT 1642 WITH 18090. NEW HINT: 19843 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(v),f(f(f(g(y),f(f(y,u),g(z))),z),x)),g(x))=f(f(g(v),f(u,v)),g(v)). >> BACK DEMODULATING HINT 1638 WITH 18090. NEW HINT: 19844 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(z),f(f(y,f(f(g(y),z),u)),x)),g(x))=u. >> BACK DEMODULATING HINT 1637 WITH 18090. NEW HINT: 19845 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(z),y),g(x)),f(f(x,f(u,x)),g(x)))=f(f(g(z),f(f(y,u),v)),g(v)). >> BACK DEMODULATING HINT 1636 WITH 18090. NEW HINT: 19846 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(y,z),x)),g(x))=f(f(g(x),f(f(y,z),u)),g(u)). >> BACK DEMODULATING HINT 1635 WITH 18090. NEW HINT: 19847 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(f(x,u),z)),g(z)))=u. >> BACK DEMODULATING HINT 1630 WITH 18090. >> BACK DEMODULATING HINT 1629 WITH 18090. NEW HINT: 19848 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,y),f(z,f(x,y))),f(g(y),g(x)))),g(z))=y. >> BACK DEMODULATING HINT 1628 WITH 18090. NEW HINT: 19849 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,y),f(z,f(x,y))),f(g(y),g(x)))),f(f(f(x,y),f(f(f(g(y),g(x)),f(g(z),f(f(x,y),f(z,f(x,y))))),f(g(y),g(x)))),f(f(x,y),f(f(f(g(y),g(x)),g(z)),f(g(y),g(x))))))=y. >> BACK DEMODULATING HINT 1626 WITH 18090. >> BACK DEMODULATING HINT 1618 WITH 18090. >> BACK DEMODULATING HINT 1606 WITH 18090. >> BACK DEMODULATING HINT 1598 WITH 18090. >> BACK DEMODULATING HINT 1597 WITH 18090. >> BACK DEMODULATING HINT 1596 WITH 18090. >> BACK DEMODULATING HINT 1595 WITH 18090. >> BACK DEMODULATING HINT 1594 WITH 18090. >> BACK DEMODULATING HINT 1584 WITH 18090. >> BACK DEMODULATING HINT 1583 WITH 18090. >> BACK DEMODULATING HINT 1582 WITH 18090. >> BACK DEMODULATING HINT 1581 WITH 18090. >> BACK DEMODULATING HINT 1542 WITH 18090. >> BACK DEMODULATING HINT 1538 WITH 18090. >> BACK DEMODULATING HINT 1537 WITH 18090. >> BACK DEMODULATING HINT 1536 WITH 18090. >> BACK DEMODULATING HINT 1532 WITH 18090. >> BACK DEMODULATING HINT 1529 WITH 18090. >> BACK DEMODULATING HINT 1528 WITH 18090. >> BACK DEMODULATING HINT 1527 WITH 18090. >> BACK DEMODULATING HINT 1523 WITH 18090. >> BACK DEMODULATING HINT 1518 WITH 18090. >> BACK DEMODULATING HINT 1515 WITH 18090. >> BACK DEMODULATING HINT 1514 WITH 18090. >> BACK DEMODULATING HINT 1513 WITH 18090. >> BACK DEMODULATING HINT 1512 WITH 18090. >> BACK DEMODULATING HINT 1503 WITH 18090. >> BACK DEMODULATING HINT 1489 WITH 18090. >> BACK DEMODULATING HINT 1488 WITH 18090. >> BACK DEMODULATING HINT 1487 WITH 18090. >> BACK DEMODULATING HINT 1483 WITH 18090. >> BACK DEMODULATING HINT 1478 WITH 18090. >> BACK DEMODULATING HINT 1448 WITH 18090. >> BACK DEMODULATING HINT 1445 WITH 18090. >> BACK DEMODULATING HINT 1444 WITH 18090. >> BACK DEMODULATING HINT 1441 WITH 18090. >> BACK DEMODULATING HINT 1440 WITH 18090. >> BACK DEMODULATING HINT 1433 WITH 18090. >> BACK DEMODULATING HINT 1421 WITH 18090. >> BACK DEMODULATING HINT 1417 WITH 18090. >> BACK DEMODULATING HINT 1416 WITH 18090. >> BACK DEMODULATING HINT 1409 WITH 18090. >> BACK DEMODULATING HINT 1403 WITH 18090. >> BACK DEMODULATING HINT 1402 WITH 18090. >> BACK DEMODULATING HINT 1401 WITH 18090. >> BACK DEMODULATING HINT 1400 WITH 18090. >> BACK DEMODULATING HINT 1399 WITH 18090. >> BACK DEMODULATING HINT 1390 WITH 18090. NEW HINT: 19850 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(g(z),f(f(z,f(x,y)),g(y))),u))=u. >> BACK DEMODULATING HINT 1365 WITH 18090. >> BACK DEMODULATING HINT 1364 WITH 18090. >> BACK DEMODULATING HINT 1363 WITH 18090. >> BACK DEMODULATING HINT 1362 WITH 18090. >> BACK DEMODULATING HINT 1361 WITH 18090. >> BACK DEMODULATING HINT 1358 WITH 18090. >> BACK DEMODULATING HINT 1357 WITH 18090. >> BACK DEMODULATING HINT 1356 WITH 18090. >> BACK DEMODULATING HINT 1355 WITH 18090. >> BACK DEMODULATING HINT 1350 WITH 18090. >> BACK DEMODULATING HINT 1347 WITH 18090. >> BACK DEMODULATING HINT 1346 WITH 18090. >> BACK DEMODULATING HINT 1345 WITH 18090. >> BACK DEMODULATING HINT 1335 WITH 18090. NEW HINT: 19851 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(g(x),x),x)),g(x))=g(x). >> BACK DEMODULATING HINT 1313 WITH 18090. >> BACK DEMODULATING HINT 1311 WITH 18090. >> BACK DEMODULATING HINT 1310 WITH 18090. >> BACK DEMODULATING HINT 1302 WITH 18090. >> BACK DEMODULATING HINT 1301 WITH 18090. >> BACK DEMODULATING HINT 1300 WITH 18090. >> BACK DEMODULATING HINT 1298 WITH 18090. >> BACK DEMODULATING HINT 1297 WITH 18090. >> BACK DEMODULATING HINT 1296 WITH 18090. >> BACK DEMODULATING HINT 1295 WITH 18090. >> BACK DEMODULATING HINT 1292 WITH 18090. >> BACK DEMODULATING HINT 1290 WITH 18090. >> BACK DEMODULATING HINT 1288 WITH 18090. NEW HINT: 19852 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,f(f(y,f(f(g(y),g(x)),g(z))),z)),g(x))),x)=g(x). >> BACK DEMODULATING HINT 1287 WITH 18090. >> BACK DEMODULATING HINT 1286 WITH 18090. >> BACK DEMODULATING HINT 1282 WITH 18090. >> BACK DEMODULATING HINT 1281 WITH 18090. >> BACK DEMODULATING HINT 1271 WITH 18090. >> BACK DEMODULATING HINT 1265 WITH 18090. >> BACK DEMODULATING HINT 1264 WITH 18090. >> BACK DEMODULATING HINT 1261 WITH 18090. NEW HINT: 19853 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),f(f(x,f(y,x)),g(x))),f(x,g(z))),z))=f(f(f(g(x),g(y)),g(x)),f(f(x,f(y,x)),f(x,f(y,x)))). >> BACK DEMODULATING HINT 1260 WITH 18090. >> BACK DEMODULATING HINT 1259 WITH 18090. >> BACK DEMODULATING HINT 1251 WITH 18090. >> BACK DEMODULATING HINT 1250 WITH 18090. >> BACK DEMODULATING HINT 1249 WITH 18090. >> BACK DEMODULATING HINT 1248 WITH 18090. >> BACK DEMODULATING HINT 1242 WITH 18090. >> BACK DEMODULATING HINT 1239 WITH 18090. >> BACK DEMODULATING HINT 1235 WITH 18090. >> BACK DEMODULATING HINT 1234 WITH 18090. >> BACK DEMODULATING HINT 1233 WITH 18090. NEW HINT: 19854 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,f(f(g(x),g(y)),f(f(y,f(x,y)),g(y)))),g(x)))=f(g(x),f(z,f(f(g(z),g(x)),x))). >> BACK DEMODULATING HINT 1224 WITH 18090. >> BACK DEMODULATING HINT 1218 WITH 18090. >> BACK DEMODULATING HINT 1217 WITH 18090. >> BACK DEMODULATING HINT 1207 WITH 18090. >> BACK DEMODULATING HINT 1166 WITH 18090. >> BACK DEMODULATING HINT 1150 WITH 18090. >> BACK DEMODULATING HINT 1141 WITH 18090. >> BACK DEMODULATING HINT 1138 WITH 18090. >> BACK DEMODULATING HINT 1133 WITH 18090. >> BACK DEMODULATING HINT 1132 WITH 18090. >> BACK DEMODULATING HINT 1101 WITH 18090. >> BACK DEMODULATING HINT 1078 WITH 18090. >> BACK DEMODULATING HINT 1076 WITH 18090. >> BACK DEMODULATING HINT 1074 WITH 18090. NEW HINT: 19855 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(z),f(f(z,f(x,y)),g(y)))=f(f(x,x),g(x)) # label(bd). >> BACK DEMODULATING HINT 1073 WITH 18090. >> BACK DEMODULATING HINT 1067 WITH 18090. >> BACK DEMODULATING HINT 1066 WITH 18090. NEW HINT: 19856 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),f(f(y,f(f(g(y),x),g(y))),f(y,g(x)))),f(x,g(z))),z))=x # label(bd). >> BACK DEMODULATING HINT 1064 WITH 18090. >> BACK DEMODULATING HINT 1060 WITH 18090. >> BACK DEMODULATING HINT 1059 WITH 18090. NEW HINT: 19857 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),x),f(g(x),x)),f(f(g(x),x),f(f(f(g(x),x),x),f(g(x),x))))=x # label(bd). >> BACK DEMODULATING HINT 1058 WITH 18090. >> BACK DEMODULATING HINT 1055 WITH 18090. >> BACK DEMODULATING HINT 1053 WITH 18090. >> BACK DEMODULATING HINT 1051 WITH 18090. >> BACK DEMODULATING HINT 1048 WITH 18090. >> BACK DEMODULATING HINT 1046 WITH 18090. >> BACK DEMODULATING HINT 1042 WITH 18090. >> BACK DEMODULATING HINT 1040 WITH 18090. >> BACK DEMODULATING HINT 1036 WITH 18090. NEW HINT: 19858 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),f(f(y,f(g(x),x)),f(g(x),x))),f(g(x),x)),g(x))=f(f(f(f(g(x),x),f(g(x),x)),x),f(g(x),g(x))) # label(bd). >> BACK DEMODULATING HINT 1027 WITH 18090. >> BACK DEMODULATING HINT 1022 WITH 18090. >> BACK DEMODULATING HINT 1016 WITH 18090. >> BACK DEMODULATING HINT 1015 WITH 18090. >> BACK DEMODULATING HINT 1013 WITH 18090. >> BACK DEMODULATING HINT 1010 WITH 18090. >> BACK DEMODULATING HINT 1007 WITH 18090. >> BACK DEMODULATING HINT 1004 WITH 18090. >> BACK DEMODULATING HINT 996 WITH 18090. NEW HINT: 19859 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),x),f(g(x),x)),f(f(f(g(x),f(y,f(f(g(y),g(x)),x))),x),f(f(f(g(x),x),x),f(g(x),x))))=x # label(bd). >> BACK DEMODULATING HINT 995 WITH 18090. >> BACK DEMODULATING HINT 990 WITH 18090. >> BACK DEMODULATING HINT 962 WITH 18090. >> BACK DEMODULATING HINT 943 WITH 18090. >> BACK DEMODULATING HINT 942 WITH 18090. >> BACK DEMODULATING HINT 941 WITH 18090. >> BACK DEMODULATING HINT 940 WITH 18090. >> BACK DEMODULATING HINT 936 WITH 18090. >> BACK DEMODULATING HINT 935 WITH 18090. >> BACK DEMODULATING HINT 934 WITH 18090. >> BACK DEMODULATING HINT 933 WITH 18090. >> BACK DEMODULATING HINT 932 WITH 18090. >> BACK DEMODULATING HINT 931 WITH 18090. >> BACK DEMODULATING HINT 924 WITH 18090. >> BACK DEMODULATING HINT 916 WITH 18090. NEW HINT: 19860 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),x),f(f(g(x),x),f(g(x),x))))=f(f(y,f(f(g(y),x),g(z))),z). >> BACK DEMODULATING HINT 915 WITH 18090. NEW HINT: 19861 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),x),f(f(g(x),x),f(g(x),x))))=x. >> BACK DEMODULATING HINT 908 WITH 18090. >> BACK DEMODULATING HINT 907 WITH 18090. >> BACK DEMODULATING HINT 902 WITH 18090. >> BACK DEMODULATING HINT 883 WITH 18090. NEW HINT: 19862 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(g(x),f(f(g(x),x),f(g(x),x))),x))=g(x). >> BACK DEMODULATING HINT 881 WITH 18090. >> BACK DEMODULATING HINT 862 WITH 18090. >> BACK DEMODULATING HINT 861 WITH 18090. NEW HINT: 19863 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(f(x,y),g(x))),f(x,g(z))),z)=f(f(f(g(y),g(y)),f(y,y)),y). >> BACK DEMODULATING HINT 860 WITH 18090. >> BACK DEMODULATING HINT 858 WITH 18090. >> BACK DEMODULATING HINT 857 WITH 18090. NEW HINT: 19864 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(x,y),g(x))),f(x,g(y)))=f(f(g(y),g(y)),f(y,y)). >> BACK DEMODULATING HINT 856 WITH 18090. >> BACK DEMODULATING HINT 855 WITH 18090. >> BACK DEMODULATING HINT 844 WITH 18090. >> BACK DEMODULATING HINT 840 WITH 18090. >> BACK DEMODULATING HINT 839 WITH 18090. >> BACK DEMODULATING HINT 836 WITH 18090. >> BACK DEMODULATING HINT 835 WITH 18090. >> BACK DEMODULATING HINT 834 WITH 18090. >> BACK DEMODULATING HINT 833 WITH 18090. >> BACK DEMODULATING HINT 832 WITH 18090. >> BACK DEMODULATING HINT 831 WITH 18090. >> BACK DEMODULATING HINT 830 WITH 18090. >> BACK DEMODULATING HINT 829 WITH 18090. >> BACK DEMODULATING HINT 819 WITH 18090. >> BACK DEMODULATING HINT 818 WITH 18090. >> BACK DEMODULATING HINT 817 WITH 18090. >> BACK DEMODULATING HINT 799 WITH 18090. >> BACK DEMODULATING HINT 798 WITH 18090. >> BACK DEMODULATING HINT 797 WITH 18090. >> BACK DEMODULATING HINT 796 WITH 18090. >> BACK DEMODULATING HINT 795 WITH 18090. >> BACK DEMODULATING HINT 774 WITH 18090. >> BACK DEMODULATING HINT 773 WITH 18090. >> BACK DEMODULATING HINT 772 WITH 18090. >> BACK DEMODULATING HINT 771 WITH 18090. >> BACK DEMODULATING HINT 758 WITH 18090. >> BACK DEMODULATING HINT 736 WITH 18090. >> BACK DEMODULATING HINT 730 WITH 18090. >> BACK DEMODULATING HINT 715 WITH 18090. NEW HINT: 19865 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),g(x)),f(x,x))=f(x,g(x)) # label(bd). >> BACK DEMODULATING HINT 713 WITH 18090. >> BACK DEMODULATING HINT 692 WITH 18090. >> BACK DEMODULATING HINT 691 WITH 18090. NEW HINT: 19866 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),x),f(f(g(x),g(x)),f(x,x))))=x # label(bd). >> BACK DEMODULATING HINT 690 WITH 18090. >> BACK DEMODULATING HINT 687 WITH 18090. NEW HINT: 19867 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(x,f(f(x,x),f(g(x),x))),g(x)))=x # label(bd). >> BACK DEMODULATING HINT 681 WITH 18090. NEW HINT: 19868 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(f(x,x),x)),g(x)))=f(f(g(x),y),f(x,x)) # label(bd). >> BACK DEMODULATING HINT 669 WITH 18090. NEW HINT: 19869 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(y,f(f(g(y),x),x)),g(x)))=f(f(g(x),g(x)),f(x,x)) # label(bd). >> BACK DEMODULATING HINT 666 WITH 18090. >> BACK DEMODULATING HINT 650 WITH 18090. NEW HINT: 19870 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),x),f(x,g(y))),y)=x # label(bd). >> BACK DEMODULATING HINT 648 WITH 18090. >> BACK DEMODULATING HINT 645 WITH 18090. >> BACK DEMODULATING HINT 634 WITH 18090. >> BACK DEMODULATING HINT 633 WITH 18090. >> BACK DEMODULATING HINT 627 WITH 18090. >> BACK DEMODULATING HINT 624 WITH 18090. >> BACK DEMODULATING HINT 613 WITH 18090. >> BACK DEMODULATING HINT 612 WITH 18090. NEW HINT: 19871 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),y),f(f(g(y),f(g(z),g(y))),y)),f(z,x))=f(f(g(x),g(x)),f(x,x)) # label(bd). >> BACK DEMODULATING HINT 606 WITH 18090. >> BACK DEMODULATING HINT 605 WITH 18090. >> BACK DEMODULATING HINT 598 WITH 18090. NEW HINT: 19872 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(x),y),f(f(g(y),f(g(z),g(y))),y)),f(z,x)),x)=x # label(bd). >> BACK DEMODULATING HINT 589 WITH 18090. >> BACK DEMODULATING HINT 581 WITH 18090. >> BACK DEMODULATING HINT 568 WITH 18090. >> BACK DEMODULATING HINT 554 WITH 18090. >> BACK DEMODULATING HINT 514 WITH 18090. >> BACK DEMODULATING HINT 496 WITH 18090. NEW HINT: 19873 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(y)),g(y)),f(f(y,y),x))=f(f(g(y),x),f(g(x),x)) # label(bd). >> BACK DEMODULATING HINT 495 WITH 18090. NEW HINT: 19874 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),g(x)),g(x)),f(f(x,x),f(x,y)))=y # label(bd). >> BACK DEMODULATING HINT 493 WITH 18090. NEW HINT: 19875 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,f(x,x)),f(f(f(g(x),g(x)),f(g(x),g(y))),f(f(g(x),g(x)),g(x))))=f(f(g(y),g(x)),f(g(x),g(x))) # label(bd). >> BACK DEMODULATING HINT 483 WITH 18090. >> BACK DEMODULATING HINT 478 WITH 18090. >> BACK DEMODULATING HINT 472 WITH 18090. >> BACK DEMODULATING HINT 466 WITH 18090. >> BACK DEMODULATING HINT 447 WITH 18090. >> BACK DEMODULATING HINT 444 WITH 18090. >> BACK DEMODULATING HINT 439 WITH 18090. >> BACK DEMODULATING HINT 412 WITH 18090. >> BACK DEMODULATING HINT 403 WITH 18090. >> BACK DEMODULATING HINT 390 WITH 18090. >> BACK DEMODULATING HINT 389 WITH 18090. NEW HINT: 19876 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(y,f(g(x),g(z))),f(z,f(x,x))),g(x))=y # label(bd). >> BACK DEMODULATING HINT 360 WITH 18090. NEW HINT: 19877 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(y,z)),f(f(f(g(z),g(y)),g(u)),f(y,z)))=f(f(g(x),f(g(u),y)),z) # label(bd). >> BACK DEMODULATING HINT 326 WITH 18090. >> BACK DEMODULATING HINT 321 WITH 18090. NEW HINT: 19878 [bsub_wt=2147483647, bsub_add_wt=-1024] f(g(x),f(f(f(x,x),f(g(x),g(z))),f(z,g(y))))=g(y) # label(bd). >> BACK DEMODULATING HINT 319 WITH 18090. >> BACK DEMODULATING HINT 314 WITH 18090. >> BACK DEMODULATING HINT 313 WITH 18090. NEW HINT: 19879 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(z,f(f(g(z),g(x)),g(y))))=g(y) # label(bd). >> BACK DEMODULATING HINT 312 WITH 18090. >> BACK DEMODULATING HINT 309 WITH 18090. NEW HINT: 19880 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(g(y),z)),f(f(f(g(z),y),g(u)),f(g(y),z))))=f(z,f(f(g(z),f(g(u),g(y))),z)) # label(bd). >> BACK DEMODULATING HINT 306 WITH 18090. >> BACK DEMODULATING HINT 302 WITH 18090. NEW HINT: 19881 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(z),g(y)),f(u,f(y,z))),f(f(g(z),g(y)),x)),g(x))=f(f(g(z),f(f(g(y),u),z)),g(z)) # label(bd). >> BACK DEMODULATING HINT 297 WITH 18090. >> BACK DEMODULATING HINT 294 WITH 18090. NEW HINT: 19882 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(z,f(f(g(z),f(g(u),g(y))),z)),f(g(z),y))),g(x)))=f(x,f(f(g(x),g(u)),g(x))) # label(bd). >> BACK DEMODULATING HINT 291 WITH 18090. NEW HINT: 19883 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(f(g(z),y),f(u,f(g(y),z))),f(f(g(z),y),x)),g(x))=f(f(g(z),f(f(y,u),z)),g(z)) # label(bd). >> BACK DEMODULATING HINT 287 WITH 18090. >> BACK DEMODULATING HINT 286 WITH 18090. >> BACK DEMODULATING HINT 285 WITH 18090. >> BACK DEMODULATING HINT 284 WITH 18090. >> BACK DEMODULATING HINT 283 WITH 18090. >> BACK DEMODULATING HINT 282 WITH 18090. >> BACK DEMODULATING HINT 270 WITH 18090. NEW HINT: 19884 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(y),f(g(x),f(f(f(f(x,z),u),x),y))),f(x,f(f(g(x),g(y)),g(x))))=f(g(y),f(z,u)) # label(bd). >> BACK DEMODULATING HINT 259 WITH 18090. NEW HINT: 19885 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(x),f(g(y),g(x))),f(x,g(z))),z)=f(g(x),g(y)) # label(bd). >> BACK DEMODULATING HINT 258 WITH 18090. >> BACK DEMODULATING HINT 250 WITH 18090. >> BACK DEMODULATING HINT 249 WITH 18090. >> BACK DEMODULATING HINT 246 WITH 18090. >> BACK DEMODULATING HINT 243 WITH 18090. NEW HINT: 19886 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(y,g(x)),f(x,g(y)))=f(x,g(x)) # label(bd). >> BACK DEMODULATING HINT 241 WITH 18090. >> BACK DEMODULATING HINT 235 WITH 18090. >> BACK DEMODULATING HINT 209 WITH 18090. >> BACK DEMODULATING HINT 208 WITH 18090. >> BACK DEMODULATING HINT 207 WITH 18090. >> BACK DEMODULATING HINT 201 WITH 18090. >> BACK DEMODULATING HINT 198 WITH 18090. >> BACK DEMODULATING HINT 185 WITH 18090. >> BACK DEMODULATING HINT 183 WITH 18090. NEW HINT: 19887 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(g(y),g(x)),z),f(f(g(z),f(g(u),g(z))),z))=f(g(y),f(f(f(g(u),u),g(x)),g(u))) # label(bd). >> BACK DEMODULATING HINT 182 WITH 18090. >> BACK DEMODULATING HINT 178 WITH 18090. >> BACK DEMODULATING HINT 177 WITH 18090. >> BACK DEMODULATING HINT 176 WITH 18090. >> BACK DEMODULATING HINT 175 WITH 18090. >> BACK DEMODULATING HINT 174 WITH 18090. >> BACK DEMODULATING HINT 172 WITH 18090. NEW HINT: 19888 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(f(f(x,y),f(x,g(z))),z)),g(x))=y # label(bd). >> BACK DEMODULATING HINT 171 WITH 18090. >> BACK DEMODULATING HINT 170 WITH 18090. NEW HINT: 19889 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(f(z,f(x,f(g(z),z))),y),f(g(y),g(x)))=z # label(bd). >> BACK DEMODULATING HINT 169 WITH 18090. >> BACK DEMODULATING HINT 168 WITH 18090. >> BACK DEMODULATING HINT 162 WITH 18090. >> BACK DEMODULATING HINT 144 WITH 18090. >> BACK DEMODULATING HINT 143 WITH 18090. >> BACK DEMODULATING HINT 142 WITH 18090. >> BACK DEMODULATING HINT 141 WITH 18090. >> BACK DEMODULATING HINT 137 WITH 18090. >> BACK DEMODULATING HINT 135 WITH 18090. >> BACK DEMODULATING HINT 131 WITH 18090. >> BACK DEMODULATING HINT 127 WITH 18090. >> BACK DEMODULATING HINT 125 WITH 18090. >> BACK DEMODULATING HINT 124 WITH 18090. NEW HINT: 19890 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(f(g(y),f(g(x),g(y))),y))=f(g(x),g(x)) # label(bd). >> BACK DEMODULATING HINT 112 WITH 18090. >> BACK DEMODULATING HINT 110 WITH 18090. >> BACK DEMODULATING HINT 109 WITH 18090. NEW HINT: 19891 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),f(y,g(x))),x)=f(y,f(f(g(y),g(x)),y)) # label(bd). >> BACK DEMODULATING HINT 108 WITH 18090. >> BACK DEMODULATING HINT 103 WITH 18090. >> BACK DEMODULATING HINT 102 WITH 18090. >> BACK DEMODULATING HINT 101 WITH 18090. >> BACK DEMODULATING HINT 100 WITH 18090. >> BACK DEMODULATING HINT 99 WITH 18090. >> BACK DEMODULATING HINT 98 WITH 18090. >> BACK DEMODULATING HINT 97 WITH 18090. >> BACK DEMODULATING HINT 96 WITH 18090. >> BACK DEMODULATING HINT 94 WITH 18090. >> BACK DEMODULATING HINT 70 WITH 18090. >> BACK DEMODULATING HINT 69 WITH 18090. >> BACK DEMODULATING HINT 57 WITH 18090. NEW HINT: 19892 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(x,y),f(f(z,f(f(g(z),f(g(y),g(x))),u)),f(x,y)))=f(f(u,f(x,f(g(u),u))),y) # label(bd). >> BACK DEMODULATING HINT 50 WITH 18090. >> BACK DEMODULATING HINT 48 WITH 18090. >> BACK DEMODULATING HINT 47 WITH 18090. >> BACK DEMODULATING HINT 45 WITH 18090. >> BACK DEMODULATING HINT 44 WITH 18090. NEW HINT: 19893 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(z),f(f(z,g(x)),f(y,g(x)))),x))=y # label(bd). >> BACK DEMODULATING HINT 43 WITH 18090. >> BACK DEMODULATING HINT 41 WITH 18090. >> BACK DEMODULATING HINT 40 WITH 18090. >> BACK DEMODULATING HINT 39 WITH 18090. >> BACK DEMODULATING HINT 37 WITH 18090. >> BACK DEMODULATING HINT 30 WITH 18090. NEW HINT: 19894 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(g(x),f(f(y,f(x,g(z))),z)),g(x)))=y # label(bd). >> BACK DEMODULATING HINT 28 WITH 18090. >> BACK DEMODULATING HINT 27 WITH 18090. >> BACK DEMODULATING HINT 25 WITH 18090. >> BACK DEMODULATING HINT 24 WITH 18090. >> BACK DEMODULATING HINT 23 WITH 18090. NEW HINT: 19895 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(f(f(g(x),g(x)),g(z)),f(f(z,x),y)))=y # label(bd). >> BACK DEMODULATING HINT 22 WITH 18090. >> BACK DEMODULATING HINT 19 WITH 18090. >> BACK DEMODULATING HINT 18 WITH 18090. >> BACK DEMODULATING HINT 17 WITH 18090. >> BACK DEMODULATING HINT 15 WITH 18090. >> BACK DEMODULATING HINT 14 WITH 18090. >> BACK DEMODULATING HINT 13 WITH 18090. >> BACK DEMODULATING HINT 12 WITH 18090. >> BACK DEMODULATING HINT 11 WITH 18090. NEW HINT: 19896 [bsub_wt=2147483647, bsub_add_wt=-1024] f(x,f(g(y),f(f(f(y,f(g(x),g(y))),y),z)))=z # label(bd). >> BACK DEMODULATING HINT 9 WITH 18090. >> BACK DEMODULATING HINT 8 WITH 18090. >> BACK DEMODULATING HINT 7 WITH 18090. NEW HINT: 19897 [bsub_wt=2147483647, bsub_add_wt=-1024] f(f(g(x),y),f(g(y),f(f(x,f(z,z)),g(z))))=z # label(bd). >> BACK DEMODULATING HINT 6 WITH 18090. >> BACK DEMODULATING HINT 5 WITH 18090. >> BACK DEMODULATING HINT 3 WITH 18090. >> BACK DEMODULATING HINT 1 WITH 18090. ----> UNIT CONFLICT at 48.86 sec ----> 20305 [binary,20303.1,4941.1] $F. Length of proof is 141. Level of proof is 39. ---------------- PROOF ---------------- 4938,4937 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("33"). 4939 [] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y # label("35") # label("35"). 4941 [] f(f(a,b),c)!=f(a,f(b,c)). 4943 [para_into,4937.1.1.2.1.2.1.2.1.1,4937.1.1] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))),f(g(z),g(u))),x))))=u. 4945 [para_into,4937.1.1.2.1.2.1.2,4937.1.1] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). 4946 [copy,4945,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). 4955 [para_from,4939.1.1,4937.1.1.2.1.2.1.2.1.1] f(x,g(f(x,f(f(f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))),f(g(y),g(u))),x))))=u. 4969 [para_into,4945.1.1.2.1.2.1,4939.1.1] f(x,g(f(x,f(y,x))))=f(g(f(x,z)),f(f(u,f(g(f(g(f(x,z)),u)),g(f(y,f(f(g(f(z,y)),v),g(f(g(y),v))))))),g(f(x,z)))). 4970 [para_into,4945.1.1.2.1.2.1,4937.1.1] f(x,g(f(x,f(y,x))))=f(g(f(x,z)),f(f(u,f(g(f(g(f(x,z)),u)),g(g(f(z,f(f(v,f(g(f(z,v)),g(y))),z)))))),g(f(x,z)))). 4973,4972 [para_into,4945.1.1,4943.1.1,demod,4938,4938,4938,flip.1] f(g(x),f(f(y,f(g(f(g(x),y)),g(f(g(x),g(z))))),g(x)))=z. 4974 [copy,4969,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(f(u,f(f(g(f(y,u)),v),g(f(g(u),v))))))),g(f(x,y))))=f(x,g(f(x,f(u,x)))). 4975 [copy,4970,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(g(f(y,f(f(u,f(g(f(y,u)),g(v))),y)))))),g(f(x,y))))=f(x,g(f(x,f(v,x)))). 4985,4984 [para_from,4946.1.1,4945.1.1.2.1,demod,4973] f(g(f(x,y)),g(f(x,g(f(x,f(f(y,z),x))))))=z. 5006 [para_into,4984.1.1.2.1.2.1.2.1,4984.1.1] f(g(f(x,g(f(y,z)))),g(f(x,g(f(x,f(u,x))))))=g(f(y,g(f(y,f(f(z,u),y))))). 5013 [copy,5006,flip.1] g(f(x,g(f(x,f(f(y,z),x)))))=f(g(f(u,g(f(x,y)))),g(f(u,g(f(u,f(z,u)))))). 5019 [para_from,4984.1.1,4943.1.1.2.1.2.1.2] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(f(z,u)))),x))),v),x))))=f(z,g(f(z,f(f(u,v),z)))) # label("Hint 27(4182)"). 5024 [para_from,4984.1.1,4939.1.1.2.2.1] f(x,f(y,f(z,g(f(g(y),g(f(x,g(f(x,f(f(y,z),x))))))))))=y. 5073,5072 [para_into,5006.1.1.1.1,4984.1.1,flip.1] g(f(x,g(f(x,f(f(g(f(x,f(f(y,z),x))),u),x)))))=f(g(z),g(f(g(f(x,y)),g(f(g(f(x,y)),f(u,g(f(x,y)))))))). 5089,5088 [para_into,5006.1.1,4984.1.1,flip.1] g(f(x,g(f(x,f(f(y,f(g(f(x,y)),z)),x)))))=z. 5130,5129 [para_from,5088.1.1,5006.1.1.1,flip.1] g(f(x,g(f(x,f(f(f(f(y,f(g(f(x,y)),z)),x),u),x)))))=f(z,g(f(x,g(f(x,f(u,x)))))). 5135 [para_from,5088.1.1,4972.1.1.2.2,demod,5089,5089,5089] f(x,f(f(y,f(g(f(x,y)),g(f(x,g(z))))),x))=z. 5143 [para_from,5088.1.1,4943.1.1.2.1.2.1.2.1,demod,5089] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(u))),x))))=u. 5199 [para_into,5135.1.1.2.1.2.2,5088.1.1] f(x,f(f(y,f(g(f(x,y)),z)),x))=f(x,f(f(u,f(g(f(x,u)),z)),x)). 5237 [para_from,5199.1.1,5006.1.1.1.1.2.1,demod,5130] f(g(f(x,g(f(y,f(f(z,f(g(f(y,z)),u)),y))))),g(f(x,g(f(x,f(v,x))))))=f(u,g(f(y,g(f(y,f(v,y)))))). 5238 [para_from,5199.1.1,4984.1.1.2.1.2.1.2.1,demod,4985] f(f(x,f(g(f(y,x)),z)),y)=f(f(u,f(g(f(y,u)),z)),y). 5246,5245 [para_from,5199.1.1,4984.1.1.1.1,demod,5130] f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,g(f(x,f(u,x)))))))=u. 5398 [para_into,5245.1.1.2,4984.1.1] f(g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x))),u)=f(z,u). 5449,5448 [para_into,5398.1.1,5245.1.1,flip.1] f(x,f(g(f(y,x)),g(f(y,g(f(y,f(z,y)))))))=z. 5484 [para_from,5398.1.1,5245.1.1.2.2.1.2.1.2,demod,5246,flip.1] g(f(x,f(f(y,f(g(f(x,y)),g(f(x,z)))),x)))=z. 5515 [para_into,5448.1.1.2.2.1.2.1.2,5238.1.1,demod,5089] f(x,f(g(f(y,x)),z))=f(u,f(g(f(y,u)),z)). 5532 [para_from,5448.1.1,4984.1.1.2.1.2.1.2.1] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=f(g(f(u,y)),g(f(u,g(f(u,f(z,u)))))). 5579,5578 [para_into,5515.1.1.2,5448.1.1,flip.1] f(x,f(g(f(y,x)),f(g(f(z,g(f(y,u)))),g(f(z,g(f(z,f(v,z))))))))=f(u,v). 5609 [para_from,5515.1.1,5448.1.1.2.2.1.2.1] f(x,f(g(f(y,x)),g(f(y,g(f(z,f(g(f(u,z)),y)))))))=g(f(u,y)). 5636 [para_from,5515.1.1,4984.1.1.2.1.2.1.2.1] f(g(f(x,y)),g(f(x,g(f(x,f(f(z,f(g(f(u,z)),v)),x))))))=f(g(f(u,y)),v). 5768,5767 [para_into,5484.1.1.1.2.1.2.1,5088.1.1] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(f(x,u)))),x)))=u. 5769 [para_into,5484.1.1.1.2.1.2.2.1,5515.1.1] g(f(x,f(f(y,f(g(f(x,y)),g(f(z,f(g(f(u,z)),v))))),x)))=f(g(f(u,x)),v). 5781 [para_into,5484.1.1.1.2.1.2.2,5484.1.1] g(f(x,f(f(y,f(g(f(x,y)),z)),x)))=f(f(u,f(g(f(x,u)),g(f(x,z)))),x). 5793 [para_from,5484.1.1,5515.1.1.2.1] f(f(f(x,f(g(f(y,x)),g(f(y,z)))),y),f(z,u))=f(v,f(g(f(y,v)),u)). 5871 [para_from,5609.1.1,5484.1.1.1.2.1] g(f(x,f(g(f(y,x)),x)))=g(f(z,f(g(f(y,z)),x))). 5906 [para_from,5609.1.1,4937.1.1.2.1.2.1] f(x,g(f(x,f(g(f(y,x)),x))))=f(x,g(f(z,f(g(f(y,z)),x)))). 5922 [copy,5871,flip.1] g(f(x,f(g(f(y,x)),z)))=g(f(z,f(g(f(y,z)),z))). 5931 [copy,5906,flip.1] f(x,g(f(y,f(g(f(z,y)),x))))=f(x,g(f(x,f(g(f(z,x)),x)))). 6115 [para_into,5906.1.1.2.1,5515.1.1] f(x,g(f(y,f(g(f(z,y)),x))))=f(x,g(f(u,f(g(f(z,u)),x)))). 7483 [para_into,5767.1.1.1.2.1.2.2,5088.1.1] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,u)),x)))=g(f(x,f(f(v,f(g(f(x,v)),u)),x))). 7613,7612 [para_into,5781.1.1,5484.1.1,flip.1] f(f(x,f(g(f(y,x)),g(f(y,g(f(y,z)))))),y)=z. 7984 [para_into,5578.1.1.2.2.1.1.2.1,6115.1.1,demod,5579] f(g(f(x,f(g(f(y,x)),z))),u)=f(g(f(v,f(g(f(y,v)),z))),u). 9956 [para_from,4974.1.1,5129.1.1.1.2.1,demod,5073,5449] g(f(g(f(x,y)),g(f(x,g(f(x,f(z,x)))))))=g(f(z,f(f(g(f(y,z)),u),g(f(g(z),u))))). 9977 [copy,9956,flip.1] g(f(x,f(f(g(f(y,x)),z),g(f(g(x),z)))))=g(f(g(f(u,y)),g(f(u,g(f(u,f(x,u))))))). 10035 [para_from,4975.1.1,5129.1.1.1.2.1,demod,5073,5449] g(f(g(f(x,y)),g(f(x,g(f(x,f(z,x)))))))=g(g(f(y,f(f(u,f(g(f(y,u)),g(z))),y)))). 10042 [copy,10035,flip.1] g(g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=g(f(g(f(u,x)),g(f(u,g(f(u,f(z,u))))))). 10105 [para_into,5024.1.1.2.2.2.1,5636.1.1] f(x,f(f(x,y),f(f(g(f(z,f(x,y))),u),g(f(g(f(z,y)),u)))))=f(x,y). 10214,10213 [para_from,5024.1.1,5088.1.1.1.2.1.2.1.2,flip.1] f(x,f(y,g(f(g(x),g(f(g(f(z,u)),g(f(g(f(z,u)),f(f(x,y),g(f(z,u)))))))))))=g(f(z,g(f(z,f(f(u,x),z))))). 10644 [para_from,7984.1.1,4937.1.1.2.1.2.1] f(x,g(f(x,f(f(g(f(y,f(g(f(z,y)),u))),f(g(f(x,g(f(v,f(g(f(z,v)),u))))),g(w))),x))))=w. 12353 [para_from,10105.1.1,5767.1.1.1.2.1.2.2.1,demod,5768,flip.1] f(f(x,y),f(f(g(f(z,f(x,y))),u),g(f(g(f(z,y)),u))))=y. 12367 [para_into,12353.1.1.1,7612.1.1,demod,7613] f(x,f(f(g(f(y,x)),z),g(f(g(f(y,u)),z))))=u. 12666,12665 [para_into,12367.1.1.2.1,5024.1.1,demod,10214] f(x,f(y,g(f(g(f(z,u)),g(f(z,g(f(z,f(f(x,y),z)))))))))=u. 13187,13186 [para_into,12665.1.1.2.2.1,4984.1.1] f(x,f(y,g(y)))=x. 13377 [para_from,12665.1.1,5769.1.1.1.2.1.2.2.1.2] g(f(x,f(f(y,f(g(f(x,y)),g(f(z,u)))),x)))=f(g(f(v,x)),f(w,g(f(g(f(v6,u)),g(f(v6,g(f(v6,f(f(g(f(v,z)),w),v6))))))))). 13391 [para_from,12665.1.1,5609.1.1.2.2.1.2.1.2.1.1] f(x,f(g(f(y,x)),g(f(y,g(f(f(z,g(f(g(f(u,v)),g(f(u,g(f(u,f(f(w,z),u)))))))),f(g(v),y)))))))=g(f(w,y)). 13399 [para_from,12665.1.1,5767.1.1.1.2.1.2.2.1] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(u))),x)))=f(v,g(f(g(f(w,u)),g(f(w,g(f(w,f(f(x,v),w)))))))). 13471 [para_from,12665.1.1,5006.1.1.1.1.2.1] f(g(f(x,g(y))),g(f(x,g(f(x,f(z,x))))))=g(f(u,g(f(u,f(f(f(v,g(f(g(f(w,y)),g(f(w,g(f(w,f(f(u,v),w)))))))),z),u))))). 13475 [para_from,12665.1.1,4984.1.1.2.1.2.1.2.1] f(g(f(x,y)),g(f(x,g(f(x,f(z,x))))))=f(u,g(f(g(f(v,z)),g(f(v,g(f(v,f(f(y,u),v)))))))). 13491 [para_from,12665.1.1,5088.1.1.1.2.1.2.1.2] g(f(x,g(f(x,f(f(y,z),x)))))=f(u,g(f(g(f(v,z)),g(f(v,g(f(v,f(f(g(f(x,y)),u),v)))))))). 13501 [para_from,12665.1.1,5532.1.1.1.1] f(g(x),g(f(y,g(f(y,f(z,y))))))=f(g(f(u,f(v,g(f(g(f(w,x)),g(f(w,g(f(w,f(f(y,v),w)))))))))),g(f(u,g(f(u,f(z,u)))))). 13511 [para_from,12665.1.1,4946.1.1.2.2.1,demod,12666,12666] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(x)))=f(u,g(f(u,f(f(f(v,g(f(g(f(w,x)),g(f(w,g(f(w,f(f(u,v),w)))))))),z),u)))). 13531 [copy,13377,flip.1] f(g(f(x,y)),f(z,g(f(g(f(u,v)),g(f(u,g(f(u,f(f(g(f(x,w)),z),u)))))))))=g(f(y,f(f(v6,f(g(f(y,v6)),g(f(w,v)))),y))). 13539 [copy,13399,flip.1] f(x,g(f(g(f(y,z)),g(f(y,g(f(y,f(f(u,x),y))))))))=g(f(u,f(f(g(f(u,f(f(v,f(g(f(u,v)),w)),u))),f(w,g(z))),u))). 13567 [copy,13471,flip.1] g(f(x,g(f(x,f(f(f(y,g(f(g(f(z,u)),g(f(z,g(f(z,f(f(x,y),z)))))))),v),x)))))=f(g(f(w,g(u))),g(f(w,g(f(w,f(v,w)))))). 13569 [copy,13475,flip.1] f(x,g(f(g(f(y,z)),g(f(y,g(f(y,f(f(u,x),y))))))))=f(g(f(v,u)),g(f(v,g(f(v,f(z,v)))))). 13573 [copy,13491,flip.1] f(x,g(f(g(f(y,z)),g(f(y,g(f(y,f(f(g(f(u,v)),x),y))))))))=g(f(u,g(f(u,f(f(v,z),u))))). 13577 [copy,13501,flip.1] f(g(f(x,f(y,g(f(g(f(z,u)),g(f(z,g(f(z,f(f(v,y),z)))))))))),g(f(x,g(f(x,f(w,x))))))=f(g(u),g(f(v,g(f(v,f(w,v)))))). 13634 [para_from,13186.1.1,10644.1.1.2.1.2] f(f(x,g(x)),g(f(f(x,g(x)),f(g(f(y,f(g(f(z,y)),u))),f(g(f(f(x,g(x)),g(f(v,f(g(f(z,v)),u))))),g(w))))))=w. 13663 [para_from,13186.1.1,5769.1.1.1.2,demod,13187] g(f(f(x,g(x)),f(y,f(g(f(f(x,g(x)),y)),g(f(z,f(g(f(u,z)),v)))))))=f(g(u),v). 13667 [para_from,13186.1.1,5636.1.1.2.1.2.1.2] f(g(f(f(x,g(x)),y)),g(f(f(x,g(x)),g(f(f(x,g(x)),f(z,f(g(f(u,z)),v)))))))=f(g(f(u,y)),v). 13693 [para_from,13186.1.1,5767.1.1.1.2,demod,13187] g(f(f(x,g(x)),f(g(f(f(x,g(x)),f(y,f(g(f(f(x,g(x)),y)),z)))),f(z,g(f(f(x,g(x)),u))))))=u. 13703 [para_from,13186.1.1,7483.1.1.1.2,demod,13187,13187] g(f(f(x,g(x)),f(g(f(f(x,g(x)),f(y,f(g(f(f(x,g(x)),y)),z)))),f(z,u))))=g(f(f(x,g(x)),f(v,f(g(f(f(x,g(x)),v)),u)))). 13720,13719 [para_from,13186.1.1,5143.1.1.2.1.2.1] f(x,g(f(x,f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),x))))=z. 13721 [para_from,13186.1.1,5135.1.1.2] f(f(x,g(x)),f(y,f(g(f(f(x,g(x)),y)),g(f(f(x,g(x)),g(z))))))=z. 13723 [para_from,13186.1.1,5129.1.1.1.2.1.2,demod,13187,13187] g(f(f(x,g(x)),g(f(f(x,g(x)),f(f(y,f(g(f(f(x,g(x)),y)),z)),u)))))=f(z,g(f(f(x,g(x)),g(f(f(x,g(x)),u))))). 13725 [para_from,13186.1.1,5129.1.1.1.2.1.2.1] g(f(x,g(f(x,f(f(f(y,f(g(f(x,y)),z)),x),x)))))=f(z,g(f(x,g(f(x,f(f(u,g(u)),x)))))). 13734 [para_from,13186.1.1,5578.1.1.2.2.2.1.2.1.2] f(x,f(g(f(y,x)),f(g(f(f(z,g(z)),g(f(y,u)))),g(f(f(z,g(z)),g(f(f(z,g(z)),v)))))))=f(u,v). 13770,13769 [para_from,13186.1.1,5019.1.1.2.1.2.1,demod,13720,13187,flip.1] f(x,g(f(x,f(y,x))))=g(f(x,y)) # label("Hint 168(19219)"). 13771 [para_from,13186.1.1,5019.1.1.2.1.2.1.1.1.2,demod,13187,13770] f(f(x,g(x)),g(f(f(x,g(x)),f(g(f(f(x,g(x)),f(y,f(g(f(f(x,g(x)),y)),g(f(z,u)))))),v))))=g(f(z,f(u,v))). 13780 [para_from,13186.1.1,5922.1.1.1.2,demod,13187,13187] g(f(x,g(f(y,x))))=g(f(f(z,g(z)),g(y))). 13785 [para_from,13186.1.1,5532.1.1.2.1.2.1.2,demod,13770] f(g(f(f(x,g(x)),y)),g(f(f(x,g(x)),g(f(f(x,g(x)),z)))))=f(g(f(u,y)),g(g(f(u,z)))). 13828 [para_from,13186.1.1,5931.1.1.2.1.2.1.1,demod,13770] f(x,g(f(f(y,g(y)),f(g(z),x))))=g(f(x,g(f(z,x)))). 13857 [para_from,13186.1.1,5793.1.1.1.1.2.1.1] f(f(f(f(x,g(x)),f(g(y),g(f(y,z)))),y),f(z,u))=f(v,f(g(f(y,v)),u)). 13886 [para_from,13186.1.1,4955.1.1.2.1.2] f(f(x,g(x)),g(f(f(x,g(x)),f(f(y,f(f(g(f(f(x,g(x)),y)),z),g(f(g(y),z)))),f(g(y),g(u))))))=u. 13930 [para_from,13186.1.1,5013.1.1.1.2.1.2,demod,13770] g(f(f(x,g(x)),g(f(f(x,g(x)),f(y,z)))))=f(g(f(u,g(f(f(x,g(x)),y)))),g(g(f(u,z)))). 14017 [para_from,13186.1.1,4974.1.1.2.2.1,demod,13187,13187,13770] f(g(x),f(f(y,f(g(f(g(x),y)),g(f(z,f(f(g(f(f(u,g(u)),z)),v),g(f(g(z),v))))))),g(x)))=g(f(x,z)). 14028 [para_from,13186.1.1,5781.1.1.1.2.1.2.1.1] g(f(x,f(f(f(y,g(y)),f(g(x),z)),x)))=f(f(u,f(g(f(x,u)),g(f(x,z)))),x). 14070,14069 [copy,13725,flip.1,demod,13770,13187,13770,flip.1] g(g(f(x,f(f(y,f(g(f(x,y)),z)),x))))=f(z,g(g(x))). 14171 [back_demod,13577,demod,13770,13770,13770] f(g(f(x,f(y,g(f(g(f(z,u)),g(g(f(z,f(v,y))))))))),g(g(f(x,w))))=f(g(u),g(g(f(v,w)))). 14174 [back_demod,13573,demod,13770,13770] f(x,g(f(g(f(y,z)),g(g(f(y,f(g(f(u,v)),x)))))))=g(g(f(u,f(v,z)))). 14177 [back_demod,13569,demod,13770,13770] f(x,g(f(g(f(y,z)),g(g(f(y,f(u,x)))))))=f(g(f(v,u)),g(g(f(v,z)))). 14179 [back_demod,13567,demod,13770,13770,13770] g(g(f(x,f(f(y,g(f(g(f(z,u)),g(g(f(z,f(x,y))))))),v))))=f(g(f(w,g(u))),g(g(f(w,v)))). 14205 [back_demod,13539,demod,13770] f(x,g(f(g(f(y,z)),g(g(f(y,f(u,x)))))))=g(f(u,f(f(g(f(u,f(f(v,f(g(f(u,v)),w)),u))),f(w,g(z))),u))). 14212 [back_demod,13531,demod,13770] f(g(f(x,y)),f(z,g(f(g(f(u,v)),g(g(f(u,f(g(f(x,w)),z))))))))=g(f(y,f(f(v6,f(g(f(y,v6)),g(f(w,v)))),y))). 14230 [back_demod,13511,demod,13770,13770] f(g(x),f(f(y,f(g(f(g(x),y)),g(z))),g(x)))=g(f(u,f(f(v,g(f(g(f(w,x)),g(g(f(w,f(u,v))))))),z))). 14345 [back_demod,13391,demod,13770] f(x,f(g(f(y,x)),g(f(y,g(f(f(z,g(f(g(f(u,v)),g(g(f(u,f(w,z))))))),f(g(v),y)))))))=g(f(w,y)). 15210,15209 [back_demod,10042,demod,14070,13770,flip.1] g(f(g(f(x,y)),g(g(f(x,z)))))=f(g(z),g(g(y))). 15241,15240 [back_demod,9977,demod,13770,15210] g(f(x,f(f(g(f(y,x)),z),g(f(g(x),z)))))=f(g(x),g(g(y))). 16640 [back_demod,5237,demod,13770,13770] f(g(f(x,g(f(y,f(f(z,f(g(f(y,z)),u)),y))))),g(g(f(x,v))))=f(u,g(g(f(y,v)))). 17172,17171 [back_demod,10644,demod,13770] g(f(x,f(g(f(y,f(g(f(z,y)),u))),f(g(f(x,g(f(v,f(g(f(z,v)),u))))),g(w)))))=w. 17670 [copy,13785,flip.1] f(g(f(x,y)),g(g(f(x,z))))=f(g(f(f(u,g(u)),y)),g(f(f(u,g(u)),g(f(f(u,g(u)),z))))). 17690 [copy,13828,flip.1] g(f(x,g(f(y,x))))=f(x,g(f(f(z,g(z)),f(g(y),x)))). 17703 [copy,13857,flip.1] f(x,f(g(f(y,x)),z))=f(f(f(f(u,g(u)),f(g(y),g(f(y,v)))),y),f(v,z)). 17726 [copy,13930,flip.1] f(g(f(x,g(f(f(y,g(y)),z)))),g(g(f(x,u))))=g(f(f(y,g(y)),g(f(f(y,g(y)),f(z,u))))). 17754 [copy,14028,flip.1] f(f(x,f(g(f(y,x)),g(f(y,z)))),y)=g(f(y,f(f(f(u,g(u)),f(g(y),z)),y))). 17795 [copy,14171,flip.1,demod,15210] f(g(x),g(g(f(y,z))))=f(g(f(u,f(v,f(g(f(y,v)),g(g(x)))))),g(g(f(u,z)))). 17798 [copy,14174,flip.1,demod,15210] g(g(f(x,f(y,z))))=f(u,f(g(f(g(f(x,y)),u)),g(g(z)))). 17801 [copy,14177,flip.1,demod,15210] f(g(f(x,y)),g(g(f(x,z))))=f(u,f(g(f(y,u)),g(g(z)))). 17803 [copy,14179,flip.1,demod,15210] f(g(f(x,g(y))),g(g(f(x,z))))=g(g(f(u,f(f(v,f(g(f(u,v)),g(g(y)))),z)))). 17826 [copy,14205,flip.1,demod,15210] g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),z)),x))),f(z,g(u))),x)))=f(v,f(g(f(x,v)),g(g(u)))). 17832 [copy,14212,flip.1,demod,15210] g(f(x,f(f(y,f(g(f(x,y)),g(f(z,u)))),x)))=f(g(f(v,x)),f(w,f(g(f(g(f(v,z)),w)),g(g(u))))). 17837 [copy,14230,flip.1,demod,15210] g(f(x,f(f(y,f(g(f(x,y)),g(g(z)))),u)))=f(g(z),f(f(v,f(g(f(g(z),v)),g(u))),g(z))). 17981 [back_demod,14345,demod,15210] f(x,f(g(f(y,x)),g(f(y,g(f(f(z,f(g(f(u,z)),g(g(v)))),f(g(v),y)))))))=g(f(u,y)). 18075 [back_demod,14017,demod,15241] f(g(x),f(f(y,f(g(f(g(x),y)),f(g(z),g(g(f(u,g(u))))))),g(x)))=g(f(x,z)). 18084,18083 [back_demod,13634,demod,17172] f(f(x,g(x)),y)=y. 18088,18087 [back_demod,13886,demod,18084,13187,18084,18084] g(f(x,f(g(x),g(y))))=y. 18090,18089 [back_demod,13771,demod,18084,18084,18088,18084,18084] g(f(f(x,y),z))=g(f(x,f(y,z))). 18092,18091 [back_demod,13663,demod,18084,18084,18088] f(x,f(g(f(y,x)),z))=f(g(y),z). 18096,18095 [copy,17670,flip.1,demod,18084,18084,18084,flip.1] f(g(f(x,y)),g(g(f(x,z))))=f(g(y),g(g(z))). 18118,18117 [copy,17690,flip.1,demod,18084,flip.1] g(f(x,g(f(y,x))))=f(x,g(f(g(y),x))). 18125,18124 [copy,17703,flip.1,demod,18084,18092] f(f(f(g(x),g(f(x,y))),x),f(y,z))=f(g(x),z). 18136,18135 [copy,17726,flip.1,demod,18084,18084,18084,18096] g(g(f(x,y)))=f(g(g(x)),g(g(y))). 18170,18169 [copy,17754,flip.1,demod,18084,18092] g(f(x,f(f(g(x),y),x)))=f(f(g(x),g(f(x,y))),x). 18207,18206 [copy,17798,flip.1,demod,18092,18136,18136,18136] f(f(g(g(x)),g(g(y))),g(g(z)))=f(g(g(x)),f(g(g(y)),g(g(z)))). 18235,18234 [copy,17826,flip.1,demod,18092,18092,18170,18125,18170,flip.1] f(f(g(x),g(f(x,g(y)))),x)=f(g(x),g(g(y))). 18245,18244 [copy,17832,flip.1,demod,18092,18136,18207,18092,18170,18235,18136] f(g(f(x,y)),f(g(g(x)),f(g(g(z)),g(g(u)))))=f(g(y),f(g(g(z)),g(g(u)))). 18463,18462 [back_demod,13780,demod,18118,18084] f(x,g(f(g(y),x)))=g(g(y)). 18470,18469 [back_demod,13734,demod,18084,18136,18084,18084,18207,18245] f(x,f(g(x),f(g(g(y)),g(g(z)))))=f(y,z). 18472,18471 [back_demod,13723,demod,18084,18084,18090,18084,18136,18090,18136,18136,18470,18084,18084,flip.1] f(x,g(g(y)))=f(x,y). 18474,18473 [back_demod,13721,demod,18084,18084,18472,18084] f(x,f(g(x),y))=y. 18478,18477 [back_demod,13703,demod,18084,18474,18084,18084,18084,18474,18084] g(f(g(x),f(x,y)))=g(y). 18480,18479 [back_demod,13693,demod,18084,18474,18084,18084,18084,18478] g(g(x))=x. 18484,18483 [back_demod,13667,demod,18084,18092,18084,18084,18480,flip.1] f(g(f(x,y)),z)=f(g(y),f(g(x),z)). 18552,18551 [back_demod,17981,demod,18480,18484,18474,18090,18474,18463,18480,18484,18474,flip.1] g(f(x,y))=f(g(y),g(x)). 19905,19904 [back_demod,18075,demod,18552,18480,18552,18480,18552,18480,13187,18552] f(g(x),f(f(y,f(f(g(y),x),g(z))),g(x)))=f(g(z),g(x)). 20075,20074 [back_demod,17837,demod,18552,18480,18552,18552,18552,18552,18552,18480,18480,18552,18480,19905] f(f(g(x),f(f(g(y),f(z,u)),g(u))),g(z))=f(g(x),g(y)). 20102,20101 [back_demod,17803,demod,18552,18480,18552,18552,18480,18480,18552,18480,18552,18552,18552,18552,18552,18480,18480,20075,18552,18480,18480] f(f(x,g(y)),f(y,z))=f(x,z). 20106,20105 [back_demod,17801,demod,18552,18552,18552,18480,18480,20102,18552,18480,flip.1] f(x,f(f(g(x),g(y)),z))=f(g(y),z). 20115,20114 [back_demod,17795,demod,18552,18552,18480,18480,18552,18480,20106,18552,18552,18480,18552,18552,18480,18480,20102,flip.1] f(f(g(x),y),z)=f(g(x),f(y,z)). 20303 [back_demod,16640,demod,18552,20115,18474,20115,18474,18552,18552,18552,18480,18480,18552,18552,18480,18480,20102,18552,18552,18480,18480] f(f(x,y),z)=f(x,f(y,z)). 20305 [binary,20303.1,4941.1] $F. ------------ end of proof ------------- translating: 4937 [] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z # label("33"). translating: 4938 [new_demod,4937] f(x,g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))))=z. translating: 4939 [] f(x,f(y,f(f(g(f(x,y)),z),g(f(g(y),z)))))=y # label("35") # label("35"). translating: 4941 [] f(f(a,b),c)!=f(a,f(b,c)). translating: 4943 [para_into,4937.1.1.2.1.2.1.2.1.1,4937.1.1] f(x,g(f(x,f(f(g(f(x,f(f(y,f(g(f(x,y)),g(z))),x))),f(g(z),g(u))),x))))=u. translating: 4945 [para_into,4937.1.1.2.1.2.1.2,4937.1.1] f(x,g(f(x,f(f(y,z),x))))=f(g(f(x,y)),f(f(u,f(g(f(g(f(x,y)),u)),g(z))),g(f(x,y)))). translating: 4946 [copy,4945,flip.1] f(g(f(x,y)),f(f(z,f(g(f(g(f(x,y)),z)),g(u))),g(f(x,y))))=f(x,g(f(x,f(f(y,u),x)))). -------------- statistics ------------- clauses given 110 clauses generated 38762 para_from generated 18143 para_into generated 20619 demod & eval rewrites 106691 clauses wt,lit,sk delete 25734 tautologies deleted 0 clauses forward subsumed 14590 (subsumed by sos) 7458 unit deletions 0 factor simplifications 0 clauses kept 10866 new demodulators 3393 empty clauses 1 clauses back demodulated 5632 clauses back subsumed 0 usable size 46 sos size 5188 demodulators size 1403 passive size 0 hot size 0 Kbytes malloced 26367 ----------- times (seconds) ----------- user CPU time 48.90 (0 hr, 0 min, 48 sec) system CPU time 0.39 (0 hr, 0 min, 0 sec) wall-clock time 51 (0 hr, 0 min, 51 sec) input time 12.47 clausify time 0.00 process input 0.02 pick given time 0.09 para_into time 0.49 para_from time 0.44 pre_process time 18.11 renumber time 0.56 demod time 11.33 order equalities 0.81 unit deleletion 0.00 factor simplify 0.00 weigh cl time 0.37 hints keep time 0.38 sort lits time 0.00 forward subsume 0.60 delete cl time 0.14 keep cl time 3.40 hints time 0.33 print_cl time 0.00 conflict time 0.13 new demod time 0.25 post_process time 17.17 back demod time 17.04 back subsume 0.00 factor time 0.00 unindex time 10.75 SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. The job finished Mon Feb 9 16:29:45 2004 otter-3.3f/source/is.c0100644000076400007640000002605707653773062014311 0ustar mccunemccune/* * is.c -- This file contains routines for discrimination tree * indexing for forward subsumption. * */ #include "header.h" /************* * * struct is_tree *insert_is_tree(t, is) * *************/ static struct is_tree *insert_is_tree(struct term *t, struct is_tree *is) { struct rel *r; struct is_tree *i1, *prev, *i3; int varnum, sym; if (t->type == VARIABLE) { i1 = is->u.kids; prev = NULL; varnum = t->varnum; while (i1 != NULL && i1->type == VARIABLE && (int) i1->lab < varnum) { prev = i1; i1 = i1->next; } if (i1 == NULL || i1->type != VARIABLE || i1->lab != varnum) { i3 = get_is_tree(); i3->type = VARIABLE; i3->lab = t->varnum; i3->next = i1; if (prev == NULL) is->u.kids = i3; else prev->next = i3; return(i3); } else /* found node */ return(i1); } else { /* NAME || COMPLEX */ i1 = is->u.kids; prev = NULL; /* arities fixed: handle both NAME and COMPLEX */ sym = t->sym_num; while (i1 != NULL && i1->type == VARIABLE) { /* skip variables */ prev = i1; i1 = i1->next; } while (i1 != NULL && (int) i1->lab < sym) { prev = i1; i1 = i1->next; } if (i1 == NULL || i1->lab != sym) { i3 = get_is_tree(); i3->type = t->type; i3->lab = sym; i3->next = i1; i1 = i3; } else i3 = NULL; /* new node not required at this level */ if (t->type == COMPLEX && t->sym_num != Ignore_sym_num) { r = t->farg; while (r != NULL) { i1 = insert_is_tree(r->argval, i1); r = r->narg; } } if (i3 != NULL) { /* link in new subtree (possibly a leaf) */ if (prev == NULL) is->u.kids = i3; else prev->next = i3; } return(i1); /* i1 is leaf corresp. to end of input term */ } } /* insert_is_tree */ /************* * * is_insert(t, root_is) * * Insert a term into the discrimination tree index for * forward subsumption. (for finding more general terms) * *************/ void is_insert(struct term *t, struct is_tree *root_is) { struct is_tree *i1; struct term_ptr *tp; i1 = insert_is_tree(t, root_is); tp = get_term_ptr(); tp->term = t; tp->next = i1->u.terms; i1->u.terms = tp; } /* is_insert */ /************* * * struct is_tree *end_term_is(t, is, path_p) * * Given a discrimination tree (or a subtree) and a term, return the * node in the tree that corresponds to the last symbol in t (or NULL * if the node doesn't exist). *path_p is a list that is extended by * this routine. It is a list of pointers to the * nodes in path from the parent of the returned node up to imd. * (It is needed for deletions, because nodes do not have pointers to * parents.) * *************/ static struct is_tree *end_term_is(struct term *t, struct is_tree *is, struct term_ptr **path_p) { struct rel *r; struct is_tree *i1; struct term_ptr *isp; int varnum, sym; /* add current node to the front of the path list. */ isp = get_term_ptr(); isp->term = (struct term *) is; isp->next = *path_p; *path_p = isp; if (t->type == VARIABLE) { i1 = is->u.kids; varnum = t->varnum; while (i1 != NULL && i1->type == VARIABLE && (int) i1->lab < varnum) i1 = i1->next; if (i1 == NULL || i1->type != VARIABLE || i1->lab != varnum) return(NULL); else /* found node */ return(i1); } else { /* NAME || COMPLEX */ i1 = is->u.kids; sym = t->sym_num; /* arities fixed: handle both NAME and COMPLEX */ while (i1 != NULL && i1->type == VARIABLE) /* skip variables */ i1 = i1->next; while (i1 != NULL && (int) i1->lab < sym) i1 = i1->next; if (i1 == NULL || i1->lab != sym) return(NULL); else { if (t->type == NAME || t->sym_num == Ignore_sym_num) return(i1); else { r = t->farg; while (r != NULL && i1 != NULL) { i1 = end_term_is(r->argval, i1, path_p); r = r->narg; } return(i1); } } } } /* end_term_is */ /************* * * is_delete(t, root_is) * *************/ void is_delete(struct term *t, struct is_tree *root_is) { struct is_tree *end, *i2, *i3, *parent; struct term_ptr *tp1, *tp2; struct term_ptr *isp1, *path; /* First find the correct leaf. path is used to help with */ /* freeing nodes, because nodes don't have parent pointers. */ path = NULL; end = end_term_is(t, root_is, &path); if (end == NULL) { print_term_nl(stdout, t); abend("is_delete, can't find end."); } /* Free the pointer in the leaf-list */ tp1 = end->u.terms; tp2 = NULL; while(tp1 != NULL && tp1->term != t) { tp2 = tp1; tp1 = tp1->next; } if (tp1 == NULL) { print_term_nl(stdout, t); abend("is_delete, can't find term."); } if (tp2 == NULL) end->u.terms = tp1->next; else tp2->next = tp1->next; free_term_ptr(tp1); if (end->u.terms == NULL) { /* free tree nodes from bottom up, using path to get parents */ end->u.kids = NULL; /* probably not necessary */ isp1 = path; while (end->u.kids == NULL && end != root_is) { parent = (struct is_tree *) isp1->term; isp1 = isp1->next; i2 = parent->u.kids; i3 = NULL; while (i2 != end) { i3 = i2; i2 = i2->next; } if (i3 == NULL) parent->u.kids = i2->next; else i3->next = i2->next; free_is_tree(i2); end = parent; } } /* free path list */ while (path != NULL) { isp1 = path; path = path->next; free_term_ptr(isp1); } } /* is_delete */ /************* * * struct term *is_retrieve(term, subst, index_tree, position) * * Return the first or next list of terms that subsumes `term'. * Also return the substitution. Return NULL if there are * none or no more. All terms in the returned list of terms * are identical. * * if (term != NULL) * {This is the first call, so return the first, and also * return a position for subsequent calls} * else if (position != NULL) * {return the next term, and update the position} * else * {there are no more terms that subsume} * * If you don't want the entire set of subsuming terms, then * cancel the position with `free_is_pos_list(position)'. * *************/ struct term_ptr *is_retrieve(struct term *t, struct context *subst, struct is_tree *is, struct is_pos **is_pos) { struct rel *rel_stack[MAX_FS_TERM_DEPTH]; struct is_tree *i1 = NULL; struct is_pos *pos, *ip2; int found, backup, varnum, j, reset, sym; int top = 0; if (t != NULL) { /* first call */ pos = NULL; top = -1; i1 = is->u.kids; backup = 0; } else if (*is_pos != NULL) { /* continuation with more to try */ pos = *is_pos; /* must remember to set is_pos on return */ backup = 1; } else /* continuation with nothing more to try */ return(NULL); while (1) { /* loop until a leaf is found or done with tree */ if (backup) { if (pos == NULL) return(NULL); else { /* pop top of stack (most recent variable node) and restore state */ top = pos->stack_pos; for (j = 0; j <= top; j++) rel_stack[j] = pos->rel_stack[j]; i1 = pos->is; t = subst->terms[i1->lab]; if (pos->reset) /* undo variable binding */ subst->terms[i1->lab] = NULL; i1 = i1->next; ip2 = pos; pos = pos->next; free_is_pos(ip2); } } /* at this point, i1 is the next node to try */ found = 0; /* first try to match input term t with a variable node */ while (found == 0 && i1 != NULL && i1->type == VARIABLE) { varnum = i1->lab; if (subst->terms[varnum] == NULL) { /*if not bound, bind it */ subst->terms[varnum] = t; subst->contexts[varnum] = NULL; found = 1; reset = 1; } else { /* bound variable, succeed iff identical */ found = term_ident(subst->terms[varnum], t); reset = 0; } if (found) { /* save state */ ip2 = get_is_pos(); ip2->next = pos; pos = ip2; pos->is = i1; pos->reset = reset; for (j = 0; j <= top; j++) pos->rel_stack[j] = rel_stack[j]; pos->stack_pos = top; } else /* try next variable */ i1 = i1->next; } backup = 0; if (found == 0) { /* couldn't match t with (another) variable */ if (t->type == VARIABLE) backup = 1; /* because we can't instantiate given term */ else { /* NAME or COMPLEX */ sym = t->sym_num; while (i1 != NULL && (int) i1->lab < sym) i1 = i1->next; if (i1 == NULL || i1->lab != sym) backup = 1; else if (t->type == COMPLEX && t->sym_num != Ignore_sym_num) { top++; if (top >= MAX_FS_TERM_DEPTH) abend("is_retrieve, increase MAX_FS_TERM_DEPTH."); rel_stack[top] = t->farg; /* save pointer to subterms */ } } } if (backup == 0) { /* get next term from rel_stack */ while (top >= 0 && rel_stack[top] == NULL) top--; if (top == -1) { /* found a term */ *is_pos = pos; return(i1->u.terms); } else { /* pop a term and continue */ t = rel_stack[top]->argval; rel_stack[top] = rel_stack[top]->narg; i1 = i1->u.kids; } } } /* end of while(1) loop */ } /* is_retrieve */ /************* * * struct term *fs_retrieve(t, c, is, fs_pos) * * Get the first or next term that subsumes t. (t != NULL) * for first call, and (t == NULL) for subsequent calls. * * If you want to stop calls before a NULL is returned, * call canc_fs_pos(fs_pos, context) to reclaim memory. * *************/ struct term *fs_retrieve(struct term *t, struct context *subst, struct is_tree *is, struct fsub_pos **fs_pos) { struct term_ptr *tp; struct is_pos *i_pos; struct fsub_pos *f_pos; if (t != NULL) { /* if first call */ tp = is_retrieve(t, subst, is, &i_pos); if (tp == NULL) return(NULL); else { f_pos = get_fsub_pos(); f_pos->pos = i_pos; f_pos->terms = tp; *fs_pos = f_pos; return(tp->term); } } else { /* subsequent call */ f_pos = *fs_pos; tp = f_pos->terms->next; if (tp != NULL) { /* if any more terms in current leaf */ f_pos->terms = tp; return(tp->term); } else { /* try for another leaf */ tp = is_retrieve((struct term *) NULL, subst, is, &(f_pos->pos)); if (tp == NULL) { free_fsub_pos(f_pos); return(NULL); } else { f_pos->terms = tp; return(tp->term); } } } } /* fs_retrieve */ /************* * * canc_fs_pos(pos, subst) * *************/ void canc_fs_pos(struct fsub_pos *pos, struct context *subst) { int i; if (pos->pos != NULL) { for (i = 0; i < MAX_VARS; i++) subst->terms[i] = NULL; } free_is_pos_list(pos->pos); free_fsub_pos(pos); } /* canc_fs_pos */ /************* * * print_is_tree(fp, is) * * Display an index-subsumption tree. * *************/ void print_is_tree(FILE *fp, struct is_tree *is) { fprintf(fp, "don't know how to print is tree %p\n", (void *) is); } /* print_is_tree */ /************* * * p_is_tree(is) * *************/ void p_is_tree(struct is_tree *is) { print_is_tree(stdout, is); } /* p_is_tree */ otter-3.3f/source/linkur.c0100644000076400007640000022201307676400202015154 0ustar mccunemccune/* * linkur.c -- Linked hyperresolution inference rule. * */ #include "header.h" /* * As modified by SKW Apr 10 90 and May 15 90, * from "release 2" Otter with linking. * Added routines: subsumable_unit, linked_unit_del. * To see the changes, search for SKW. */ /* When I changed to new-style function prototypes (May 2000), * I put all of these static declarations here, because the * corresponding definitions aren't ordered nicely. Not all * of these are necessary. */ static void construct_children_nodes(struct link_node *curr_node, struct term *tp, struct link_node **target, char target_here); static struct clause *subsumable_unit(char sign, struct term *d); static struct clause *linked_unit_del(char sign, struct term *d); static struct link_node *backward(struct link_node **tree, struct link_node *node, struct link_node **target, int *nopen, int *nres); static struct ilist *build_parental_chain(struct link_node *node, struct link_node *target); static struct clause *build_ur_resolvent(struct link_node *target, struct link_node *tree); static BOOLEAN check_down_tree(struct link_node *node, int my_depth); static BOOLEAN check_up_tree(struct link_node *node, int my_depth); static struct term *first_unifiable(struct term *t, struct fpa_index *index, struct context *subst_t, struct context *subst_ret, struct fpa_tree **pos_ptr, struct trail **tr_ptr, struct link_node *curr_node, struct link_node *target, char *target_here, int *hit_dp_count); static struct link_node *forward(struct link_node *cn, struct link_node *target); static struct link_node *forward_from_resolved_tree(struct link_node *curr_node, struct link_node **target, int *nres, int *nopen); static void free_linked_node_tree(struct link_node *tree, struct link_node **target); static struct term *generate_resolvent(struct link_node *curr_node, struct link_node *target, char *target_here, int *hit_dp_count); static struct link_node *initialize_tree(struct clause *giv_cl); static BOOLEAN is_in_ancestry(struct link_node *curr_node, struct link_node *inf_tree); static BOOLEAN keep_clause(struct link_node *node, struct link_node **target, char *target_here, int *nopen); static void linked_print_clause(struct clause *cp); static void linked_print_link_node(struct link_node *lnp, int lvl); static void linked_print_link_node_tree(struct link_node *lnp, int lvl); static BOOLEAN more_targets_here(struct term *tp); static struct term *next_unifiable(struct term *t, struct context *subst_t, struct context *subst_ret, struct fpa_tree **pos_ptr, struct trail **tr_ptr, struct link_node *curr_node, struct link_node *target, char *target_here, int *hit_dp_count); static BOOLEAN poss_nuc_link(struct link_node *lnp); static BOOLEAN pass_parms_check(struct link_node *curr_node, int nres, int nopen, int *depth_count, int *ded_count, struct link_node *tar); static BOOLEAN pass_target_depth_check(struct link_node *curr_node); static BOOLEAN process_this_resolution(struct link_node *curr_node, struct link_node *target, struct term *tp, char *target_here, int *hit_dp_count); static int term_ident_subst(struct term *t1, struct context *c1, struct term *t2, struct context *c2); static void write_down_tree(struct link_node *node, int my_depth); static void write_up_tree(struct link_node *node, int my_depth); static void write_target_distances(struct link_node *curr_node); /************************************************************ * * void construct_children_nodes(curr_node,tp, target, target_here) * struct link_node *curr_node; * struct term *tp; * struct link_node **target; * BOOLEAN target_here; * * It is assumed that the clause linked to tp may be added as children * to the curr_node. This function writes the new depths in the inference * tree. If target_here then re-writes the whole tree accordingly (the * test for that was done in process_this_resolution()), otherwise it * just writes the depths for the children nodes. * ************************************************************/ static void construct_children_nodes(struct link_node *curr_node, struct term *tp, struct link_node **target, char target_here) { struct link_node *lnp; struct literal *lp; if (Flags[LINKED_UR_TRACE].val == 1) printf("constructing nodes for remaining lits:\n"); if (target_here && *target) { printf("ERROR: constructing children told target here with already target set\n"); exit(ABEND_EXIT); } /* endif */ /* constructing first child node of curr_node */ if ((lnp = get_link_node()) == NULL) { printf("couldn't get link_node\n"); exit(ABEND_EXIT); } /* endif */ curr_node->first_child = lnp; lnp->parent = curr_node; lnp->prev_sibling = NULL; lnp->first = TRUE; /* loop to find first literal other than the one */ /* that linked into this clause */ for (lp = (curr_node->current_clause)->first_lit; lp && lp == tp->occ.lit; lp = lp->next_lit) ; if (!lp) { printf("ERROR ... non UNIT clause looks UNIT\n"); exit(ABEND_EXIT); } /* endif */ if (target_here && lp->target) *target = lnp; lnp->goal = lp->atom; if ((lnp->subst = get_context()) == NULL) { printf("couldn't get context\n"); exit(ABEND_EXIT); } /* endif */ (lnp->subst)->multiplier = lnp->subst->built_in_multiplier; if (Flags[LINKED_UR_TRACE].val == 1) { if (!(((lnp->goal)->occ.lit)->sign)) printf("-"); print_term(stdout, lnp->goal); printf(" from clause "); linked_print_clause(((lnp->goal)->occ.lit)->container); printf("\n"); } /* endif */ /* loop to construct link_node for */ /* remaining lits in new clause */ for (lp = lp->next_lit; lp; lp = lp->next_lit) { if (lp != tp->occ.lit) { if ((lnp->next_sibling = get_link_node()) == NULL) { printf("couldn't get link_node\n"); exit(ABEND_EXIT); } /* endif */ (lnp->next_sibling)->prev_sibling = lnp; lnp = lnp->next_sibling; lnp->parent = curr_node; lnp->first = TRUE; if (target_here && lp->target && !(*target)) *target = lnp; lnp->goal = lp->atom; if ((lnp->subst = get_context()) == NULL) { printf("couldn't get context node\n"); exit(ABEND_EXIT); } /* endif */ (lnp->subst)->multiplier = lnp->subst->built_in_multiplier; if (Flags[LINKED_UR_TRACE].val == 1) { if (!(((lnp->goal)->occ.lit)->sign)) printf("-"); print_term(stdout, lnp->goal); printf(" from clause "); fflush(stdout); linked_print_clause(((lnp->goal)->occ.lit)->container); printf("\n"); } /* endif */ } /* endif */ } /* endfor */ lnp->next_sibling = NULL; if (target_here && !(*target)) { printf("ERROR: constructing children told target here and target not found here\n"); exit(ABEND_EXIT); } /* endif */ /* loop to establish distances for the new clause */ for (lnp = (lnp->parent)->first_child; lnp; lnp = lnp->next_sibling) { if (target_here) lnp->target_dist = -1; else { /* target not in this clause */ if (*target) /* target is elsewhere */ lnp->target_dist = (lnp->parent)->target_dist + 1; } /* endif */ lnp->farthest_sat = (lnp->parent)->farthest_sat + 1; lnp->back_up = UNDEFINED; if (poss_nuc_link(lnp)) lnp->near_poss_nuc = 0; else { if (poss_nuc_link(lnp->parent)) lnp->near_poss_nuc = 1; else { if ((lnp->parent)->near_poss_nuc == UNDEFINED) lnp->near_poss_nuc = UNDEFINED; else lnp->near_poss_nuc = (lnp->parent)->near_poss_nuc + 1; } /* endif */ } /* endif */ } /* endfor */ if (target_here) { write_target_distances(curr_node); } } /* end construct_children_nodes() */ /********************************************************************* * * struct clause *subsumable_unit(sign,d) * * Attempt to find a unit clause that subsumes the (unsigned) literal * (atom) d with sign "sign". * * SKW - Apr 11 90 - This entire routine added to do subsumable unit * checking in linked resolution. * **********************************************************************/ static struct clause *subsumable_unit(char sign, struct term *d) { int subsumed; /* flag set to 1 if literal is subsumed */ struct clause *c = NULL; /* c is a ptr to a (possible) subsuming cl */ struct term *c_atom, *d_atom; /* c_atom and d_atom are ptrs to */ /* atoms (unsigned literals) for */ /* literal c and clause d resp. */ struct context *s; /* a context is a substitution */ struct is_tree *is_db; /* This is the index that we use. */ /* This will be set either to */ /* Is_pos_lits (global variable indicating */ /* index for positive literals) or to */ /* Is_neg_lits (index for neg literals). */ struct fsub_pos *pos; /* Maintains a position in the sequence of */ /* subsuming literals. fsub position. */ /* Maintained from one call to the next of */ /* the indexing routine. */ /* BEGIN DEBUG SKW print out passed term (and possibly sign) */ /* printf("entering subsumable_unit, passed term follows\n"); */ /* print_term(stdout,d); printf("\n"); */ /* END DEBUG SKW */ subsumed = 0; /* initially flag says not subsumed */ s = get_context(); /* s is initially a null context, void subst */ /* The following code checks for subsumption of the passed literal "d" * by a clause in the list or lists selected by option flags. * If Flags[LINKED_SUB_UNIT_USABLE].val is 1, * via set(linked_sub_unit_usable), then subsumption by Usable list * clauses is checked. * If Flags[LINKED_SUB_UNIT_SOS].val is 1, * via set(linked_sub_unit_sos), then subsumption by Sos list * clauses is checked. * If BOTH flags are one, subsumption by both lists is checked. * The necessary flags are set up in "cos.h" and in "options.c", * in the standard manner used throughout Otter. */ /* The following code for subsumable unit assumes that the option * "clear(for_sub_fpa)" is in effect, that is, that forward subsumption * by FPA is not in use. * In fact, forward subsumption by FPA has simply not been used * in the recent past, so this assumption is not a limiting one. */ if (Flags[FOR_SUB_FPA].val == 0) { /* if `is' indexing */ /* d_lit = d; *//* this setting allows the code in "forward_subsume" */ d_atom = d; /* this setting allows the code in "forward_subsume" */ /* in "clause.c" to be copied in here. */ /* Is_pos_lits and Is_neg_lits are global variables */ is_db = sign ? Is_pos_lits : Is_neg_lits; c_atom = fs_retrieve(d_atom, s, is_db, &pos); /* &pos is position returned for subsequent calls. */ while (c_atom != NULL && subsumed == 0) { c = c_atom->occ.lit->container; /* want to get the clause that contains "c_atom". */ /* if c is a unit, in the right list (usable or sos or either), * then set subsumed to 1. */ if (num_literals(c) == 1 && ( (c->container == Usable && Flags[LINKED_SUB_UNIT_USABLE].val == 1) || (c->container == Sos && Flags[LINKED_SUB_UNIT_SOS].val == 1))) subsumed = 1; if (subsumed == 0) c_atom = fs_retrieve((struct term *) NULL, s, is_db, &pos); else { /* clear_subst_1(tr); ** Apr 12 90 SKW */ /* ("tr" is not being used in this simple application ** of subsumption testing for unit clauses. ** We don't need to do additional unifies on additional ** literals. Therefore there is no need to keep a trail ** (tr) of what we did. ** Therefore we never initialized "tr" to NIL. ** Therefore we can't pass "tr" to clear_subst_1, ** and this is all right because we don't need to clear. */ canc_fs_pos(pos, s); } } } else printf("FPA indexing not supported for linked res subsumable unit"); /* endif */ free_context(s); /* BEGIN DEBUG SKW ** if (subsumed) { ** printf("exiting subsumable_unit, subsuming clause c follows\n"); ** print_clause(stdout,c); printf("\n"); ** } ** else ** printf("exiting subsumable_unit, not subsumed\n"); ** END DEBUG SKW */ if (subsumed) return(c); else return(NULL); } /* end of subsumable_unit */ /********************************************************************* * * struct clause *linked_unit_del(sign,d) * * Attempt to find a unit clause that resolves the (unsigned) literal * (atom) d with sign "sign", without instantiating "d". * * SKW - Apr 11 90 - This entire routine added to do unit deletion * checking in linked resolution. * * This routine will not update the link_node data structure. * This routine simply returns a pointer to a clause with sign opposite * to the passed "sign". The clause can be used to unit-delete "d". * * If no unit deletion clause is found, a NULL pointer is returned. * * A literal L can be unit deleted if and only if -L * (L with sign reversed) is subsumed by a unit clause C. * If such a clause C is found, it can be used to resolve off L without * instantiating L. * Hence the use of the forward subsumption routine "fs_retrieve". * The subsuming unit clause C, or "NULL" if none, is returned. * * Essentially the same subsumption logic is used as in "subsumable_unit". * **********************************************************************/ static struct clause *linked_unit_del(char sign, struct term *d) { int subsumed; /* flag set to 1 if negation of * literal is subsumed */ BOOLEAN print_ud_trace; /* Hard-code this to TRUE to print */ /* linked unit deletion trace msgs */ struct clause *c = NULL; /* c is a ptr to a (possible) subsuming cl */ struct term *c_atom, *d_atom; /* c_atom and d_atom are ptrs to */ /* atoms (unsigned literals) for */ /* clause c and literal d resp. */ struct context *s; /* a context is a substitution */ struct is_tree *is_db; /* This is the index that we use. */ /* This will be set either to */ /* Is_pos_lits (global variable indicating */ /* index for positive literals) or to */ /* Is_neg_lits (index for neg literals). */ struct fsub_pos *pos; /* Maintains a position in the sequence of */ /* subsuming literals. fsub position. */ /* Maintained from one call to the next of */ /* the indexing routine. */ print_ud_trace = FALSE; /* Turn off trace */ /* BEGIN DEBUG SKW print out passed term (and possibly sign) */ if (print_ud_trace) { printf("UD entering linked_unit_del, passed term follows\n"); printf("UD "); print_term(stdout,d); printf("\n"); } /* endif */ /* END DEBUG SKW */ subsumed = 0; /* initially flag says not subsumed */ s = get_context(); /* s is initially a null context, void subst */ /* The following code checks for subsumption * of the negation of the passed literal "d" * by a unit clause in any list. */ /* The following code for unit deletion assumes that the option * "clear(for_sub_fpa)" is in effect, that is, that forward subsumption * by FPA is not in use. * In fact, forward subsumption by FPA has simply not been used * in the recent past, so this assumption is not a limiting one. */ if (Flags[FOR_SUB_FPA].val == 0) { /* if `is' indexing */ d_atom = d; /* this setting allows the code in "forward_subsume" */ /* in "clause.c" to be copied in here. */ /* Is_pos_lits and Is_neg_lits are global variables */ /* that point to indexes for positive literals and */ /* negative literals respectively. */ is_db = sign ? Is_neg_lits : Is_pos_lits ; /* Note that if "sign" is positive, use NEGATIVE literal index, * if "sign" is negative, use POSITIVE literal index, * So that in fact a subsumer of the NEGATION * of the passed literal is sought. */ c_atom = fs_retrieve(d_atom, s, is_db, &pos); /* &pos is position returned for subsequent calls. */ while (c_atom != NULL && subsumed == 0) { c = c_atom->occ.lit->container; /* want to get the clause that contains "c_atom". */ /* if c is a unit, * then set subsumed to 1. */ if (num_literals(c) == 1) subsumed = 1; if (subsumed == 0) c_atom = fs_retrieve((struct term *) NULL, s, is_db, &pos); else { /* No need to clear_subst_1(tr); ** Apr 12 90 SKW */ /* ("tr" is not being used in this simple application ** of subsumption testing for unit clauses. ** We don't need to do additional unifies on additional ** literals. Therefore there is no need to keep a trail ** (tr) of what we did. ** Therefore we never initialized "tr" to NIL. ** Therefore we can't pass "tr" to clear_subst_1, ** and this is all right because we don't need to clear.) */ canc_fs_pos(pos, s); } } } else printf("FPA indexing not supported for linked res linked_unit_del"); /* endif */ free_context(s); /* BEGIN DEBUG SKW */ if (print_ud_trace) { if (subsumed) { printf("UD exiting linked_unit_del, subsuming clause c follows\n"); printf("UD "); print_clause(stdout,c); printf("\n"); } /* endif */ else printf("UD exiting linked_unit_del, not subsumed\n"); } /* endif */ /* END DEBUG SKW */ if (subsumed) { Stats[UNIT_DELETES]++; return(c); } else return(NULL); } /* end of linked_unit_del */ /************************************************************ * * struct link_node *backward(tree, node, target, nopen, nres) * struct link_node **tree, *node, **target; * int *nopen, *nres; * ************************************************************/ static struct link_node *backward(struct link_node **tree, struct link_node *node, struct link_node **target, int *nopen, int *nres) { struct link_node *p, *start, *temp_p; BOOLEAN left_most, target_here; if (node->first_child) { printf("attempted to back up from a node with a child\n"); exit(ABEND_EXIT); } /* endif */ clear_subst_1(node->tr); node->first = TRUE; node->current_clause = NULL; /* At the time that you back up away from this node, * all information as to how the node's literal was instantiated, * and all information as to how this literal was resolved, * must be reset to NULL, unknown, etc. * In particular, unit deletion of the node no longer holds good. */ node->unit_deleted = FALSE; if (node->goal_to_resolve) { zap_term(node->goal_to_resolve); /* SKW This is where the instantiated goal_to_resolve */ /* is zapped (deleted from memory) when the backtracking process */ /* is done with it. */ node->goal_to_resolve = NULL; } /* endif */ if (node->prev_sibling) { if (node->prev_sibling == *target) { if ((*target)->prev_sibling) { left_most = FALSE; start = node; } else { left_most = TRUE; start = *target; } /* endif */ } else { left_most = FALSE; start = node; } /* endif */ } else { left_most = TRUE; start = node; } /* endif */ if (!left_most) { /* node has left sibling */ node->farthest_sat = (node->parent)->farthest_sat + 1; p = start->prev_sibling; if (p == *target) p = p->prev_sibling; while (p->first_child) { p = p->first_child; /* loop to get the rightmost sibling at this level */ while (p->next_sibling) p = p->next_sibling; } /* endwhile */ if (p == *target) /* backed up to the target ... must back up again */ p = backward(tree, p, target, nopen, nres); else { *nopen = *nopen + 1; *nres = *nres - 1; p->current_clause = NULL; } /* endif */ } else { /* node is leftmost sibling ... if the target clause is in here */ /* an attempt must be made to re-position the target. if the */ /* target cannot be re-postioned and this is NOT a BOTH clause */ /* it is trashed. if the target is not in this clause then it */ /* is trashed. */ if (keep_clause(start, target, &target_here, nopen)) p = start; else { /* node is leftmost sibling ... must */ /* remove himself and all his siblings. */ /* this simply means returning the nodes */ /* as the clear_subst have been done all */ /* along. */ p = start->parent; /* removing nodes of deleted clause from open lit count */ if (target_here) *nopen = *nopen - (num_literals(p->current_clause) - 2); else *nopen = *nopen - (num_literals(p->current_clause) - 1); while (p->first_child) { temp_p = p->first_child; p->first_child = temp_p->next_sibling; free_context(temp_p->subst); free_link_node(temp_p); } /* endwhile */ if (p == *tree) { /* have removed all the nodes of the tree */ free_context(p->subst); free_link_node(p); p = NULL; *tree = NULL; *nopen = *nopen - 1; } else { /* p now points to a newly acquired open node */ *nres = *nres - 1; *nopen = *nopen + 1; p->current_clause = NULL; } /* endif */ } /* endif */ } /* endif */ return p; } /* end backward() */ /************* * * linked_ur_res(giv_cl) * *************/ void linked_ur_res(struct clause *giv_cl) { struct link_node *inf_tree, *curr_node, *target, *lnp; struct term *tp, *temp_term; int hit_ur_limit_count, open_lit_count, res_count, i; int hit_ur_ded_count; struct clause *resolvent, *unit_cl; BOOLEAN target_here; BOOLEAN subsumable_unit_here; tp = NULL; /* to quite -Wall */ /* subsumable_unit_here is TRUE if the current * literal "curr_node->goal_to_resolve" * has been found to be a subsumable unit. * Otherwise subsumable_unit_here is FALSE. */ /* only process given clauses that are unit */ if (num_literals(giv_cl) > 1) return; CLOCK_START(LINKED_UR_TIME); if (Flags[LINKED_UR_TRACE].val == 1) { printf("********entering Linked UR\n"); print_linked_ur_mem_stats(); printf("***********\n"); } /* endif */ if ((inf_tree = initialize_tree(giv_cl)) == NULL) { printf("ERROR: unable to initialize linked UR inference tree\n"); exit(ABEND_EXIT); } /* endif */ hit_ur_limit_count = hit_ur_ded_count = 0; res_count = 0; open_lit_count = 1; if (Flags[LINKED_UR_TRACE].val == 1) { printf("********tree before BIG loop open lit %d nres %d\n", open_lit_count, res_count); linked_print_link_node_tree(inf_tree, 0); printf("***********\n"); } /* endif */ /* BIG loop to process whole tree */ target = NULL; curr_node = inf_tree->first_child; while (curr_node) { /* assumed that curr_node is correctly positioned */ /* Print trace information if trace flag is turned on */ if (Flags[LINKED_UR_TRACE].val == 1) { printf("attempting to find clash for term "); if (!(((curr_node->goal)->occ.lit)->sign)) printf("-"); fflush(stdout); print_term(stdout, curr_node->goal); fflush(stdout); printf(" in clause "); fflush(stdout); linked_print_clause(((curr_node->goal)->occ.lit)->container); printf(" first time = %c res_count = %d\n", (curr_node->first ? 'T' : 'F'), res_count); } /* endif */ /* Modifications by SKW Apr 10 90 and May 15 90 follow */ subsumable_unit_here = FALSE; /* If the current node's literal has not been unit-deleted away, * and the various parameters say OK to continue linking, * find a first way or an additional way to resolve * this node's literal. */ if ( ! (curr_node->unit_deleted) && pass_parms_check(curr_node, res_count, open_lit_count, &hit_ur_limit_count, &hit_ur_ded_count, target)) { /* Apply: ** Do the apply here so that goal_to_resolve will be correctly ** set to the instantiated form of the current (unsigned) literal ** before "subsumable_unit" (which uses this instantiated term) ** is called. */ if (curr_node->first) { curr_node->goal_to_resolve = apply(curr_node->goal, (curr_node->parent)->subst); curr_node->unit_deleted = FALSE; } /* endif */ /* Subsumable Unit Test: ** If this is the first time that this node of the linked ** inference tree is being examined (after all, we only need ** to check once whether the unit is subsumable) ** and no target has been chosen yet ** (subsumable unit is only applicable if there is just one ** open (unresolved) literal and it is NOT the target) ** and, finally, there is indeed exactly one open literal, ** then perform the subsumable unit test. */ if (curr_node->first && !target && open_lit_count == 1 && res_count >= 1) { /* SKW DEBUG BEGIN - SHOW WHAT res_count IS */ /* printf("ready to test for calling subsumable_unit\n"); */ /* printf("res_count = %d\n",res_count); */ /* SKW DEBUG END */ if ((Flags[LINKED_SUB_UNIT_USABLE].val == 1 || Flags[LINKED_SUB_UNIT_SOS].val == 1) && subsumable_unit(curr_node->goal->occ.lit->sign, curr_node->goal_to_resolve)) { subsumable_unit_here = TRUE; tp = NULL; /* If the unit is indeed subsumable, set tp = NULL ** which essentially means a "FAIL" has occurred ** at this node, that is no linked resolvent can be ** completed when this node is involved. ** ** The sign of the literal is found by tracing the chain ** of pointers "curr_node->goal->occ.lit->sign". ** Here "goal" points to the UNINSTANTIATED and unsigned ** form of the literal to be resolved. ** The pointer "goal_to_resolve" points to the ** INSTANTIATED unsigned form of the literal to be ** resolved. That is, "goal_to_resolve" is ** "goal"/(current unifying substitution so far). */ } } /* The following nested "if" statement has the following effect. * If a resolving clause can be found, point "tp" to * the resolving unsigned literal (struct term) in that clause. * Otherwise, set "tp" to NULL. */ if ( ! subsumable_unit_here) { /* goal_to_resolve is not subsumable */ /* So, test for unit deletion of goal_to_resolve */ /* Note that we only test for unit deletion if at least * one resolution has occurred. * That is, we don't test the unit "given clause" for * unit deletion. */ if ((Flags[LINKED_UNIT_DEL].val) && (res_count >= 1) && (unit_cl = linked_unit_del(curr_node->goal->occ.lit->sign, curr_node->goal_to_resolve))) { /* unit deletion succeeded */ curr_node->unit_deleted = TRUE; tp = unit_cl->first_lit->atom; target_here = FALSE; /* new resolving clause is a unit, and so * does not contain the target */ } else tp = generate_resolvent(curr_node, target, &target_here, &hit_ur_limit_count); } /* endif */ } /* endif */ else /* did not pass parms check */ tp = NULL; /* At this point, "tp" is either a pointer to a clause, that will * resolve the literal "curr_node->goal_to_resolve", * or is "NULL" indicating that no resolving clause could be found. * * If "curr_node->unit_deleted" is TRUE, then the resolving clause * is a unit, the resolution is a "unit deletion", * and the resolution does not instantiate the literal * "curr_node->goal_to_resolve". * In this case there is no need to try any additional ways of * resolving the literal. * * Otherwise ("curr_node->unit_deleted" is FALSE), * other possible resolutions will need to be tried. */ if (tp) { /* found (another) resolvent */ if (Flags[LINKED_UR_TRACE].val == 1) { printf("clashed against term: "); if (!((tp->occ.lit)->sign)) printf("-"); print_term(stdout, tp); printf(" in clause "); linked_print_clause((tp->occ.lit)->container); printf("\n"); } /* endif */ /* this resolution may be added to the inference tree */ res_count ++; open_lit_count --; curr_node->current_clause = (tp->occ.lit)->container; i = num_literals(curr_node->current_clause); if (target_here) open_lit_count = open_lit_count + (i - 2); else open_lit_count = open_lit_count + (i - 1); if (i == 1) /* new clause is UNIT */ curr_node->first_child = NULL; else { /* new clause is non-UNIT */ construct_children_nodes(curr_node, tp, &target, target_here); } /* endif */ if ((lnp = forward(curr_node, target)) != NULL) { /* was able to move forward */ if (!(lnp->first)) { printf("ERROR: moved forward to %p first = FALSE\n", (void *) lnp); exit(ABEND_EXIT); } /* endif */ curr_node = lnp; /* was able to move forward to select new goal */ /* must check that new goal is not in ancestry */ if (is_in_ancestry(curr_node, inf_tree)) { /* literal in curr_node is in ancestry */ /* attempting to resolve it away would */ /* start a loop. must back up. */ if (Flags[LINKED_UR_TRACE].val == 1) { printf("did not attempt to resolve "); if (!(((curr_node->goal)->occ.lit)->sign)) printf("-"); fflush(stdout); print_term(stdout, curr_node->goal); printf(" ... appears in ancestry\n"); } /* endif */ curr_node = backward(&inf_tree, curr_node, &target, &open_lit_count, &res_count); } else { /* literal in curr_node is not in ancestry */ /* and may be chosen as the next literal */ /* to be resolved away. */ /* have moved forward and there's no target */ /* this node's farthest_sat must be */ /* re-calculated as MAX(his farthest_sat, */ /* all left siblings' back_up distances) */ i = curr_node->farthest_sat; for (lnp = (curr_node->parent)->first_child; lnp && lnp != curr_node; lnp = lnp->next_sibling) { if (lnp->back_up == UNDEFINED && lnp != target) { printf("ERROR: found non_target back_up < 0\n"); exit(ABEND_EXIT); } else { if (i < lnp->back_up) i = lnp->back_up; } /* endif */ } /* endfor */ if (!lnp) { printf("ERROR: left_sibling chain to NULL\n"); exit(ABEND_EXIT); } /* endif */ curr_node->farthest_sat = i; } /* endif */ } else { /* resolved away whole tree */ if (Flags[LINKED_UR_TRACE].val == 1) { printf("***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d\n", (void *) curr_node, (void *) target, open_lit_count, res_count); linked_print_link_node_tree(inf_tree, 0); printf("***********\n"); printf("resolvent = "); fflush(stdout); if (target) { if (!(((target->goal)->occ.lit)->sign)) printf("-"); fflush(stdout); temp_term = apply(target->goal, (target->parent)->subst); print_term(stdout, temp_term); printf("\n"); zap_term(temp_term); } else printf("[]\n"); } /* endif */ resolvent = build_ur_resolvent(target, inf_tree->first_child); Stats[CL_GENERATED]++; Stats[LINKED_UR_RES_GEN]++; CLOCK_STOP(LINKED_UR_TIME); pre_process(resolvent, 0, Sos); CLOCK_START(LINKED_UR_TIME); curr_node = forward_from_resolved_tree(curr_node, &target, &res_count, &open_lit_count); } /* endif */ } else { /* couldn't find anything (else) to unify */ /* or failed parms check */ if (Flags[LINKED_UR_TRACE].val == 1) printf("-- FAIL --\n"); /* must back up from curr_node ... when */ /* trying this node again it will be */ /* the first time. */ curr_node = backward(&inf_tree, curr_node, &target, &open_lit_count, &res_count); } /* endif */ if (Flags[LINKED_UR_TRACE].val == 1) { printf("***tree end BIG loop curr_node %p tar %p open lit %d\n", (void *) curr_node, (void *) target, open_lit_count); linked_print_link_node_tree(inf_tree, 0); printf("***********\n"); } /* endif */ } /* endwhile */ if (Flags[LINKED_UR_TRACE].val == 1) { printf("********tree leaving linked UR open lit %d nres %d\n", open_lit_count, res_count); linked_print_link_node_tree(inf_tree, 0); printf("***********\n"); print_linked_ur_mem_stats(); printf("***********\n"); } /* endif */ if (hit_ur_limit_count) printf("** HIT maximum linked UR depth %d times\n", hit_ur_limit_count); if (hit_ur_ded_count) printf("** HIT maximum linked UR deduction size %d times\n", hit_ur_ded_count); Stats[LINKED_UR_DEPTH_HITS] += hit_ur_limit_count; Stats[LINKED_UR_DED_HITS] += hit_ur_ded_count; CLOCK_STOP(LINKED_UR_TIME); } /* end linked_ur_res() */ /************************************************************ * * struct ilist *build_parental_chain(node, target) * struct link_node *node, *target; * ************************************************************/ static struct ilist *build_parental_chain(struct link_node *node, struct link_node *target) { struct ilist *chain_head, *last_one, *tail, *unit_del_flag_node; struct link_node *lnp; chain_head = get_ilist(); chain_head->i = (((node->goal)->occ.lit)->container)->id; chain_head->next = NULL; last_one = chain_head; for (lnp = node; lnp; lnp = lnp->next_sibling) { if (lnp->first_child) tail = build_parental_chain(lnp->first_child, target); else { if (lnp != target) { tail = get_ilist(); tail->i = (lnp->current_clause)->id; if (lnp->unit_deleted) { unit_del_flag_node = get_ilist(); unit_del_flag_node->i = UNIT_DEL_RULE; unit_del_flag_node->next = tail; tail = unit_del_flag_node; } } else tail = NULL; } /* endif */ last_one->next = tail; while (last_one->next) last_one = last_one->next; } /* endfor */ return chain_head; } /* end build_parental_chain() */ /************************************************************ * * struct clause *build_ur_resolvent(target, tree) * struct link_node *target, *tree; * ************************************************************/ static struct clause *build_ur_resolvent(struct link_node *target, struct link_node *tree) { struct clause *resolvent; struct literal *from_lit, *to_lit; resolvent = get_clause(); if (target) { /* linked ur generated a unit clause */ resolvent->first_lit = to_lit = get_literal(); from_lit = (target->goal)->occ.lit; to_lit->container = resolvent; to_lit->sign = from_lit->sign; to_lit->atom = apply(target->goal, (target->parent)->subst); (to_lit->atom)->occ.lit = to_lit; (to_lit->atom)->varnum = (from_lit->atom)->varnum; } else /* linked ur generated the empty clause */ resolvent->first_lit = NULL; resolvent->parents = get_ilist(); (resolvent->parents)->i = LINKED_UR_RES_RULE; (resolvent->parents)->next = build_parental_chain(tree, target); return resolvent; } /* end build_ur_resolvent() */ /************************************************************ * * BOOLEAN check_down_tree(node, my_depth) * struct link_node *node; * int my_depth; * * This function assumes the target rests above node in the tree * at a distance of my_depth. * * if (node) * if (my_depth is OK) * for (each of my left siblings SIB && still OK) * OK = check_down_tree(SIB->first_child, my_depth+1) * endfor * else * OK = FALSE * endif * else * if (mydepth is OK) * OK = TRUE * else * OK = FALSE * endif * endif * * return OK * ************************************************************/ static BOOLEAN check_down_tree(struct link_node *node, int my_depth) { BOOLEAN rc; struct link_node *lnp; if (my_depth <= Parms[MAX_UR_DEPTH].val) { rc = TRUE; if (node) { /* I am not a SATELLITE with no link node */ for (lnp = node; rc && lnp; lnp = lnp->next_sibling) rc = check_down_tree(lnp->first_child, my_depth+1); } /* endif */ } else rc = FALSE; return rc; } /* end check_down_tree */ /************************************************************ * * BOOLEAN check_up_tree(node, my_depth) * struct link_node *node; * int my_depth; * * This function assumes the target has been brought into node * from below at a distance of my_depth. * * if (i am not the dummy node) * if (my_depth is OK) * OK = TRUE * for (each of my siblings to the left && still OK) * OK = check the depth of their children (my_depth+1) * endfor * if (still OK) * OK = check_up_tree(leftmost sibling parent, my_depth+1) * endif * else * OK = FALSE * endif * else * OK = TRUE * endif * * return OK * ************************************************************/ static BOOLEAN check_up_tree(struct link_node *node, int my_depth) { BOOLEAN rc; struct link_node *lnp; if (node->parent) { /* I am NOT the dummy node at the top of the inference tree */ if (my_depth <= Parms[MAX_UR_DEPTH].val) { /* this level clause is OK ... must check */ /* all the children of the siblings to my */ /* left (the ones to the right have not */ /* been processed yet) then go UP on my */ /* leftmost sibling. */ rc = TRUE; lnp = node; while (rc && lnp->prev_sibling) { lnp = lnp->prev_sibling; rc = check_down_tree(lnp->first_child, my_depth+1); } /* endwhile */ if (rc) rc = check_up_tree(lnp->parent, my_depth+1); } else rc = FALSE; } else /* I am the dummy node at the top of the inference tree */ rc = TRUE; return rc; } /* end check_up_tree() */ /************* * * struct term *first_unifiable(t,index,subst_t,subst_ret,pos_ptr,tr_ptr, * curr_node, target, target_here) * struct term *t; * struct fpa_head **index; * struct context *subst_t, *subst_ret; * struct fpa_tree **pos_ptr; * struct trail **tr_ptr; * struct link_node *curr_node, *target; * BOOLEAN *target_here; * * This function finds the first term that can resolve away the literal * pointed at by curr_node. * *************/ static struct term *first_unifiable(struct term *t, struct fpa_index *index, struct context *subst_t, struct context *subst_ret, struct fpa_tree **pos_ptr, struct trail **tr_ptr, struct link_node *curr_node, struct link_node *target, char *target_here, int *hit_dp_count) { int var_nums[MAX_VARS], i; /* curr_node->goal_to_resolve = apply(t, subst_t); ** SKW Apr 12 90 */ for (i = 0; i < MAX_VARS; i ++) var_nums[i] = -1; if (!(renum_vars_term(curr_node->goal_to_resolve, var_nums))) { printf("unable to renumber vas in fist_unifiable()\n"); exit(ABEND_EXIT); } /* endif */ *pos_ptr = build_tree(curr_node->goal_to_resolve, UNIFY, Parms[FPA_LITERALS].val, index); return(next_unifiable(t, subst_t, subst_ret, pos_ptr, tr_ptr, curr_node, target, target_here, hit_dp_count)); } /* first_unifiable */ /************************************************************ * * struct link_node *forward(cn, target) * struct link_node *cn, *target; * ************************************************************/ static struct link_node *forward(struct link_node *cn, struct link_node *target) { struct link_node *p, *lnp; BOOLEAN done; int max_back_up; done = FALSE; p = NULL; /* to quite -Wall */ if (cn->first_child) { /* has a first child */ if (cn->first_child != target) { /* first child is not the target */ p = cn->first_child; done = TRUE; } else { /* has first child that is the target */ if ((cn->first_child)->next_sibling) { /* target has a next_sibling */ p = (cn->first_child)->next_sibling; done = TRUE; } /* endif */ } /* endif */ } /* endif */ if (!done) { /* cn picked off by SATELLITE */ cn->back_up = 0; if (cn->next_sibling) { /* has a next sibling */ if (cn->next_sibling != target) { /* the next_sibling is not the target */ p = cn->next_sibling; done = TRUE; } else { /* the next_sibling is the target */ if ((cn->next_sibling)->next_sibling) { /* the target has a next_sibling */ p = (cn->next_sibling)->next_sibling; done = TRUE; } /* endif */ } /* endif */ } /* endif */ } /* endif */ if (!done) { /* time to go back up in the tree */ /* must traverse up tree until I find a parent that has */ /* a sibling to the right that is NOT the target */ p = cn->parent; while (!done && p) { /* must find the longest back_up value from */ /* all my children to establish my back_up */ for (max_back_up = -1, lnp = p->first_child; lnp; lnp = lnp->next_sibling) if (max_back_up < lnp->back_up) max_back_up = lnp->back_up; p->back_up = max_back_up + 1; if (p->next_sibling) { /* has a next_sibling */ if (p->next_sibling != target) { /* the next sibling is NOT the target */ p = p->next_sibling; done = TRUE; } else { /* the next_sibling is the target */ if ((p->next_sibling)->next_sibling) { /* the target has a next_sibling */ p = (p->next_sibling)->next_sibling; done = TRUE; } else { /* the target does not have a next_sibling */ p = p->parent; } /* endif */ } /* endif */ } else p = p->parent; } /* endwhile */ } /* endif */ return p; } /* end forward() */ /************************************************************ * * struct link_node *forward_from_resolved_tree(curr_node, target, nres, nopen) * struct link_node *curr_node, **target; * int *nres, *nopen; * * The inference tree has been resolved away and curr_node points * to the last node that was resolved away. There is a special case * that must be considered. It is in fact possible for curr_node * to have a first_child. This occurs when the target is in a * two literal clause and that clause was just brought in as the * child of curr_node. * * When this happens, the target must be removed and one of two * things must occur: * 1) The first_child is of type BOTH. The first child must be converted * to a link. The first_child is then chosen as the curr_node first = T. * 2) The first_child is of type NUCLEUS. It must be removed from the * inference tree and the curr_node becomes the curr_node first = F. * ************************************************************/ static struct link_node *forward_from_resolved_tree(struct link_node *curr_node, struct link_node **target, int *nres, int *nopen) { struct link_node *lnp; lnp = curr_node; if (lnp->first_child) { /* the current node has a child ... better be the only */ /* sibling at that level and it better be the target */ if (lnp->first_child != *target) { printf("ERROR: forward failed, has first_child that's NOT tar\n"); exit(ABEND_EXIT); } else { /* this target node better not have any */ /* children or siblings */ if ((lnp->first_child)->next_sibling || (lnp->first_child)->first_child) { printf("ERROR: forward failed with target child (has sibs)\n"); exit(ABEND_EXIT); } else { /* the target must be cleared ... either */ /* tossing this nucleus or both is */ /* converted from a nuclues to a link. */ *target = NULL; if ((lnp->current_clause)->type == BOTH) { /* bottom node is BOTH and must */ /* converted from a nucleus to */ /* a link. */ lnp = lnp->first_child; *nopen = *nopen + 1; } else { /* bottom node is NUCLEUS and must be tossed */ free_linked_node_tree(lnp->first_child, target); lnp->first_child = NULL; *nres = *nres - 1; *nopen = *nopen + 1; lnp->current_clause = NULL; } /* endif */ } /* endif */ } /* endif */ } else { /* curr_node has no children */ *nres = *nres - 1; *nopen = *nopen + 1; lnp->current_clause = NULL; } /* endif */ return lnp; } /* end forward_from_resolved_tree() */ /************************************************************ * * void free_linked_node_tree(tree, target) * struct link_node *tree, **target; * ************************************************************/ static void free_linked_node_tree(struct link_node *tree, struct link_node **target) { if (tree) { free_linked_node_tree(tree->next_sibling, target); free_linked_node_tree(tree->first_child, target); if (tree == *target) *target = NULL; if (tree->subst) free_context(tree->subst); free_link_node(tree); } /* endif */ } /* end free_linked_node_tree() */ /************************************************************ * * struct term *generate_resolvent(curr_node, target, target_here) * struct link_node *curr_node, *target; * BOOLEAN *target_here; * * This function attempts to find the next term that can resolve against * the goal term in the node pointed at by curr_node. If there are * no more terms that resolve against this given term, the NULL pointer * is returned. * ************************************************************/ static struct term *generate_resolvent(struct link_node *curr_node, struct link_node *target, char *target_here, int *hit_dp_count) { struct term *tp; struct fpa_index *db; if ((((curr_node->goal)->occ.lit)->sign)) db = Fpa_clash_neg_lits; else db = Fpa_clash_pos_lits; if (curr_node->first) { curr_node->first = FALSE; tp = first_unifiable(curr_node->goal, db, (curr_node->parent)->subst, curr_node->subst, &(curr_node->unif_position), &(curr_node->tr), curr_node, target, target_here, hit_dp_count); } else { clear_subst_1(curr_node->tr); tp = next_unifiable(curr_node->goal, (curr_node->parent)->subst, curr_node->subst, &(curr_node->unif_position), &(curr_node->tr), curr_node, target, target_here, hit_dp_count); } /* endif */ return tp; } /* end generate_resolvent() */ /************************************************************ * * struct link_node *initialize_tree(giv_cl) * struct clause *giv_cl; * ************************************************************/ static struct link_node *initialize_tree(struct clause *giv_cl) { struct link_node *tree, *given, *dummy_target; dummy_target = NULL; if ((tree = get_link_node()) != NULL) { /* initializing top dummy node */ tree->parent = NULL; tree->next_sibling = NULL; tree->prev_sibling = NULL; tree->near_poss_nuc = UNDEFINED; tree->farthest_sat = -2; tree->target_dist = 0; tree->back_up = UNDEFINED; tree->goal = NULL; tree->current_clause = giv_cl; tree->tr = NULL; tree->first = TRUE; tree->unif_position = NULL; if ((tree->subst = get_context()) != NULL) (tree->subst)->multiplier = tree->subst->built_in_multiplier; else { printf("ERROR: couldn't get context for dummy node\n"); free_linked_node_tree(tree, &dummy_target); tree = NULL; } /* endif */ } else printf("ERROR: couldn't get link node for dummy\n"); if (tree) { /* getting node that represents given clause */ if ((given = get_link_node()) != NULL) { /* initializing node that represents given clause */ given->parent = tree; tree->first_child = given; given->next_sibling = NULL; given->prev_sibling = NULL; given->near_poss_nuc = UNDEFINED; given->farthest_sat = -1; given->target_dist = 0; given->back_up = UNDEFINED; given->goal = (giv_cl->first_lit)->atom; given->current_clause = NULL; given->tr = NULL; given->first = TRUE; given->unif_position = NULL; if ((given->subst = get_context()) != NULL) (given->subst)->multiplier = given->subst->built_in_multiplier; else { printf("ERROR: couldn't get context for given node\n"); free_linked_node_tree(tree, &dummy_target); tree = NULL; } /* endif */ } else { printf("couldn't get given link_node\n"); free_linked_node_tree(tree, &dummy_target); tree = NULL; } /* endif */ } /* endif */ return tree; } /* end initialize_tree() */ /************************************************************ * * BOOLEAN is_in_ancestry(curr_node, inf_tree) * struct link_node *curr_node, *inf_tree; * ************************************************************/ static BOOLEAN is_in_ancestry(struct link_node *curr_node, struct link_node *inf_tree) { struct link_node *lnp; struct term *cand; struct context *cand_subst; BOOLEAN rc; char sign; sign = ((curr_node->goal)->occ.lit)->sign; cand = curr_node->goal; cand_subst = (curr_node->parent)->subst; if (Flags[LINKED_UR_TRACE].val == 1) { printf("checking is_in_ancestry on lit "); if (!sign) printf("-"); fflush(stdout); print_term(stdout, cand); printf("\n"); } /* endif */ for (lnp = curr_node->parent, rc = FALSE; !rc && lnp != inf_tree; lnp = lnp->parent) rc = ( (sign == ((lnp->goal)->occ.lit)->sign) && term_ident_subst(lnp->goal, (lnp->parent)->subst, cand, cand_subst) ); return rc; } /* end is_in_ancestry() */ /************************************************************ * * BOOLEAN keep_clause(node, target, target_here, nopen) * struct link_node *node, **target; * BOOLEAN *target_here; * int *nopen; * * This function is called by backward() when the node that is * being backed up from is the leftmost sibling. A decision must * be made whether to keep the clause represented by this node and * its siblings. * * if (target in this clause) * if (there is another target candidate literal to the right) * re-define the target as the next target literal candidate * keep clause * else * clear target pointer (target = NULL) * if (clause is of type BOTH) * keep clause (BOTH from NUCLEUS to LINK) * else * don't keep clause * endif * endif * else * don't keep clause * endif * ************************************************************/ static BOOLEAN keep_clause(struct link_node *node, struct link_node **target, char *target_here, int *nopen) { BOOLEAN keep, both_to_link; struct link_node *temp_p; if (*target) { /* the target has been established ... may be here */ /* loop to determine if target is in this clause */ for (temp_p = node; temp_p && temp_p != *target; temp_p = temp_p->next_sibling) ; if (temp_p) { /* target is in this clause */ *target_here = TRUE; both_to_link = FALSE; /* loop to find another target in this clause */ for (temp_p = temp_p->next_sibling; temp_p && !(((temp_p->goal)->occ.lit)->target); temp_p = temp_p->next_sibling) ; if (temp_p) { /* there is another target */ *target = temp_p; keep = TRUE; } else { /* there are no other targets */ if (((((*target)->goal)->occ.lit)->container)->type == BOTH) { /* clause is of type BOTH and may */ /* now be treated as a LINK */ keep = TRUE; both_to_link = TRUE; } else /* clause is of type NUC with no more targets */ keep = FALSE; *target = NULL; } /* endif */ if (both_to_link) *nopen = *nopen + 1; } else { /* target is not in this clause */ keep = FALSE; *target_here = FALSE; } /* endif */ } else { /* the target has not been established anywhere */ keep = FALSE; *target_here = FALSE; } /* endif */ return keep; } /* end keep_clause() */ /************************************************************ * * void linked_print_clause(cp) * struct clause *cp; * ************************************************************/ static void linked_print_clause(struct clause *cp) { struct literal *lp; printf("at %p >>", (void *) cp); fflush(stdout); switch (cp->type) { case NOT_SPECIFIED: printf("NOT_SPECIFIED: "); break; case NUCLEUS: printf("NUCLEUS: "); break; case LINK: printf("LINK: "); break; case BOTH: printf("BOTH: "); break; case SATELLITE: printf("SATELLITE: "); break; default: printf("** UNKNOWN **: "); break; } /* end switch() */ fflush(stdout); for (lp = cp->first_lit; lp; lp = lp->next_lit) { if (lp->target) printf("**"); fflush(stdout); printf("-"); fflush(stdout); print_term(stdout, lp->atom); fflush(stdout); if (lp->target) printf("**"); fflush(stdout); printf(" "); fflush(stdout); } /* endfor */ printf("<< "); } /* end linked_print_clause() */ /************************************************************ * * void linked_print_link_node(lnp, lvl) * struct link_node *lnp; * int lvl; * ************************************************************/ static void linked_print_link_node(struct link_node *lnp, int lvl) { int i; for (i = 0; i < lvl; i ++) printf(" "); printf("-----start node at %p------\n", (void *) lnp); for (i = 0; i < lvl; i ++) printf(" "); printf("parent = %p prev_sibling = %p next_sibling = %p first_child = %p\n", (void *) lnp->parent, (void *) lnp->prev_sibling, (void *) lnp->next_sibling, (void *) lnp->first_child); for (i = 0; i < lvl; i ++) printf(" "); printf("current_clause >> "); if (lnp->current_clause) linked_print_clause(lnp->current_clause); else printf("(NIL)"); printf(" <<\n"); for (i = 0; i < lvl; i ++) printf(" "); printf("first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d\n", (lnp->first ? 'T' : 'F'), (lnp->unit_deleted ? 'T' : 'F'), lnp->near_poss_nuc, lnp->farthest_sat, lnp->target_dist, lnp->back_up); for (i = 0; i < lvl; i ++) printf(" "); printf("goal to resolve "); if (lnp->goal_to_resolve) { if (!(((lnp->goal)->occ.lit)->sign)) printf("-"); print_term(stdout, lnp->goal_to_resolve); } else printf("(NIL)"); printf(" ... from literal "); if (lnp->goal) { if (!(((lnp->goal)->occ.lit)->sign)) printf("-"); print_term(stdout, lnp->goal); } else printf("(NIL)"); printf("\n"); if (lnp->goal) { for (i = 0; i < lvl; i ++) printf(" "); printf("from clause "); fflush(stdout); linked_print_clause(((lnp->goal)->occ.lit)->container); printf("\n"); } /* endif */ for (i = 0; i < lvl; i ++) printf(" "); printf("subst = %p subst->multiplier = %d tr = %p unif_position = %p\n", (void *) lnp->subst, (lnp->subst)->multiplier, (void *) lnp->tr, (void *) lnp->unif_position); for (i = 0; i < lvl; i ++) printf(" "); printf("-----end node at %p------\n", (void *) lnp); } /* end linked_print_link_node() */ /************************************************************ * * void linked_print_link_node_tree(lnp, lvl) * struct link_node *lnp; * int lvl; * ************************************************************/ static void linked_print_link_node_tree(struct link_node *lnp, int lvl) { struct link_node *l; for (l = lnp; l; l = l->next_sibling) { linked_print_link_node(l, lvl); linked_print_link_node_tree(l->first_child, lvl+1); } /* endfor */ } /* end linked_print_link_node_tree() */ /************************************************************ * * BOOLEAN more_targets_here(tp) * struct term *tp; * * This function returns TRUE iff there exists a target literal in * the clause that contains tp OTHER than the literal that * contains tp. * ************************************************************/ static BOOLEAN more_targets_here(struct term *tp) { BOOLEAN more; struct literal *lp; for (more = FALSE, lp = ((tp->occ.lit)->container)->first_lit; !more && lp; lp = lp->next_lit) if (lp != (tp->occ.lit) && lp->target) more = TRUE; return more; } /* end more_targets_here() */ /************* * * struct term *next_unifiable(t, subst_t, subst_ret, pos_ptr, tr_ptr, * curr_node, target, target_here) * struct term *t; * struct context *subst_t, *subst_ret; * struct fpa_tree **pos_ptr; * struct trail **tr_ptr; * struct link_node *curr_node, *target; * BOOLEAN *target_here; * * This function finds a term that can be used to resolve away the node * pointed at by curr_node. * *************/ static struct term *next_unifiable(struct term *t, struct context *subst_t, struct context *subst_ret, struct fpa_tree **pos_ptr, struct trail **tr_ptr, struct link_node *curr_node, struct link_node *target, char *target_here, int *hit_dp_count) { struct term *term_to_return; int rc; BOOLEAN try_find_another; term_to_return = next_term(*pos_ptr, 0); *tr_ptr = NULL; /* while (term_to_return != NULL && (!process_this_resolution(curr_node, target, term_to_return, target_here) || unify(t, subst_t, term_to_return, subst_ret, tr_ptr) == 0)) term_to_return = next_term(*pos_ptr, 0); */ if (term_to_return == NULL) try_find_another = FALSE; else { if (process_this_resolution(curr_node, target, term_to_return, target_here, hit_dp_count)) { rc = unify(t, subst_t, term_to_return, subst_ret, tr_ptr); if (rc == 0) { try_find_another = TRUE; } else { try_find_another = FALSE; } /* endif */ } else try_find_another = TRUE; } /* endif */ while (try_find_another) { term_to_return = next_term(*pos_ptr, 0); if (term_to_return == NULL) try_find_another = FALSE; else { if (process_this_resolution(curr_node, target, term_to_return, target_here, hit_dp_count)) { rc = unify(t, subst_t, term_to_return, subst_ret, tr_ptr); if (rc == 0) { try_find_another = TRUE; } else { try_find_another = FALSE; } /* endif */ } else try_find_another = TRUE; } /* endif */ } /* endwhile */ return(term_to_return); } /* next_unifiable */ /************************************************************ * * BOOLEAN poss_nuc_link(lnp) * struct link_node *lnp; * * This function tests the clause associated with the node pointed * at by lnp. It tests whether this clause has the potential to * bring in a NUCLEUS somewhere to the right of lnp. This is * TRUE if lnp has a right sibling and the farthest satellite * from lnp is < max link depth away. * ************************************************************/ static BOOLEAN poss_nuc_link(struct link_node *lnp) { BOOLEAN rc; if (lnp->next_sibling) { if (lnp->farthest_sat < Parms[MAX_UR_DEPTH].val) rc = TRUE; else rc = FALSE; } else rc = FALSE; return rc; } /* end poss_nuc_link() */ /************************************************************ * * BOOLEAN pass_parms_check(curr_node, nres, nopen, depth_count, ded_count, tar) * struct link_node *curr_node; * int nres, nopen, *depth_count, *ded_count; * struct link_node tar; * * Just about to resolve away the node pointed at by curr_node. * Checking the parms set for linked UR deduction. Currently checks * depth of tree and deduction size (number of resolutions). * ************************************************************/ static BOOLEAN pass_parms_check(struct link_node *curr_node, int nres, int nopen, int *depth_count, int *ded_count, struct link_node *tar) { BOOLEAN ok_to_resolve; ok_to_resolve = TRUE; /* check maximum linked UR depth */ if (tar) { /* a target has been established somewhere */ if (curr_node->target_dist >= Parms[MAX_UR_DEPTH].val) { ok_to_resolve = FALSE; *depth_count = *depth_count + 1; if (Flags[LINKED_UR_TRACE].val == 1) printf("max ur depth hit # %d ", *depth_count); } } else { /* a target has not been established yet */ if (curr_node->near_poss_nuc != UNDEFINED) { if (curr_node->near_poss_nuc >= Parms[MAX_UR_DEPTH].val) { ok_to_resolve = FALSE; *depth_count = *depth_count + 1; if (Flags[LINKED_UR_TRACE].val == 1) printf("max ur depth hit # %d ", *depth_count); } /* endif */ } else { if (curr_node->farthest_sat >= Parms[MAX_UR_DEPTH].val) { ok_to_resolve = FALSE; *depth_count = *depth_count + 1; if (Flags[LINKED_UR_TRACE].val == 1) printf("max ur depth hit # %d ", *depth_count); } /* endif */ } /* endif */ } /* endif */ /* check maximum linked UR deduction size */ if (ok_to_resolve) { if ((nres + nopen) > Parms[MAX_UR_DEDUCTION_SIZE].val) /* SKW DEBUG COMMENT HERE IN pass_parms_check, */ /* SKW DEBUG COMMENT "nres + nopen" IS COMPARED TO MAX DEDUCT SIZE */ { ok_to_resolve = FALSE; *ded_count = *ded_count + 1; if (Flags[LINKED_UR_TRACE].val == 1) printf("max ur ded size hit # %d ", *ded_count); } /* endif */ } /* endif */ return ok_to_resolve; } /* end pass_parms_check() */ /************************************************************ * * BOOLEAN pass_target_depth_check(curr_node) * struct link_node *curr_node; * * A potential target has been brought in as a child of this curr_node. * This function returns TRUE iff bringing in this target as a child to * curr_node is consistent with the depth check relative to the existing * inference tree. * ************************************************************/ static BOOLEAN pass_target_depth_check(struct link_node *curr_node) { return (curr_node->farthest_sat < Parms[MAX_UR_DEPTH].val); /* return check_up_tree(curr_node, 0); */ } /* end pass_target_depth_check() */ /************************************************************ * * int process_linked_tags(cp) * struct clause *cp; * ************************************************************/ int process_linked_tags(struct clause *cp) { struct literal *lp, *tag; struct term *tp; int errors, i, rc, num_lits, j; struct rel *r; if (cp->first_lit == NULL) return(0); /* first set target field to the default value */ for (lp = cp->first_lit, num_lits = 0; lp; lp = lp->next_lit, num_lits++) lp->target = Flags[LINKED_TARGET_ALL].val; tp = cp->first_lit->atom; if (str_ident("$NUCLEUS", sn_to_str(tp->sym_num))) cp->type = NUCLEUS; else if (str_ident("$LINK", sn_to_str(tp->sym_num))) cp->type = LINK; else if (str_ident("$BOTH", sn_to_str(tp->sym_num))) cp->type = BOTH; else if (str_ident("$SATELLITE", sn_to_str(tp->sym_num))) cp->type = SATELLITE; else { cp->type = SATELLITE; return(0); } errors = 0; if (tp->farg == NULL || tp->farg->narg != NULL || proper_list(tp->farg->argval) == 0) { printf("ERROR, argument of link tag is not a list: "); print_term_nl(stdout, tp); errors++; } else { /* remove tag literal */ tag = cp->first_lit; cp->first_lit = tag->next_lit; num_lits--; /* process tag list */ for (r = tag->atom->farg; r->argval->sym_num != Nil_sym_num; r = r->argval->farg->narg) { rc = str_int(sn_to_str(r->argval->farg->argval->sym_num), &i); if (rc == 0 || i > num_lits || i < 1) { printf("ERROR, list member has bad literal number: %s\n", sn_to_str(r->argval->farg->argval->sym_num)); errors++; } else { for (lp=cp->first_lit, j = 1; j != i; lp = lp->next_lit, j++) ; /* empty body */ lp->target = (Flags[LINKED_TARGET_ALL].val ? 0 : 1); } } /* delete tag literal */ tag->atom->occ.lit = NULL; zap_term(tag->atom); free_literal(tag); } return(errors); } /* end process_linked_tags() */ /************************************************************ * * BOOLEAN process_this_resolution(curr_node, target, tp, target_here) * struct link_node *curr_node, *target; * struct term *tp; * BOOLEAN *target_here * * The node pointed at by curr_node can be resolved away by the term * pointed at by tp. This function primarily checks that constructing * nodes for the remaining literals in the clause that holds tp doesn't * violate any of the rules associated with the choice of the target ... i.e. * bringing in a nucleus when the target is chosen, choosing the target * here violates the depth check, etc. * * if (clause type is LINK) * target_here = FALSE * process = TRUE; * else * if (target has been chosen) * target_here = FALSE * if (clause type is NUCLEUS) * process = FALSE * else * process = TRUE * endif * else * if (clause type is NUCLEUS) * if (candidate targets left in this clause) * if (pass target depth check) * target_here = TRUE * process = TRUE * else * target_here = FALSE * process = FASLE * endif * else * target_here = FALSE * process = FALSE * endif * else * process = TRUE * if (candidate targets left in this clause) * if (pass target depth check) * target_here = TRUE * else * target_here = FALSE * endif * else * target_here = FALSE * endif * endif * endif * endif * * ------------------------------------------------------------------ * Here is an alternate logic. ### represents a boolean expression. * ### iff bringing in this clause and attempting to resolve away its * other literals will NOT violate the depth check nor the deduction size. * Very much like conducting pass_parms_check() on the clause first. * * switch (tp type) * case NUCLEUS: * if (!(target has been chosen) * && candidate targets left in this clause * && pass target depth check) * target_here = FALSE * process = FALSE * else * target_here = FALSE * process = FALSE * endif * case LINK: * target_here = FALSE * if (###) * process = TRUE * else * process = FALSE * endif * case BOTH: * if (!(target has been chosen) && pass target depth check) * target_here = TRUE * process = TRUE * else * target_here = FALSE * if (###) * process = TRUE * else * process = FALSE * endif * endif * case SATELLITE: * target_here = FALSE * process = TRUE * end switch * ************************************************************/ static BOOLEAN process_this_resolution(struct link_node *curr_node, struct link_node *target, struct term *tp, char *target_here, int *hit_dp_count) { BOOLEAN process, temp; if (((tp->occ.lit)->container)->type == LINK) { process = TRUE; *target_here = FALSE; } else { if (target) { /* the target has been previously chosen */ *target_here = FALSE; if (((tp->occ.lit)->container)->type == NUCLEUS) { /* clause type is NUCLEUS */ process = FALSE; if (Flags[LINKED_UR_TRACE].val == 1) printf("brought NUC is TRASHED .. already have tar\n"); } else /* clause type is BOTH */ process = TRUE; } else { /* the target has not been previously chosen */ if (((tp->occ.lit)->container)->type == NUCLEUS) { /* clause type is NUCLEUS */ if (more_targets_here(tp)) { temp = pass_target_depth_check(curr_node); if (temp) { *target_here = TRUE; process = TRUE; } else { *target_here = FALSE; process = FALSE; *hit_dp_count = *hit_dp_count + 1; if (Flags[LINKED_UR_TRACE].val == 1) printf("NUC failed depth check TRASHED\n"); } /* endif */ } else { /* NUCLEUS brought in on only target */ *target_here = FALSE; process = FALSE; if (Flags[LINKED_UR_TRACE].val == 1) printf("NUC in on only tar TRASHED\n"); } /* endif */ } else { /* clause type is BOTH */ process = TRUE; if (more_targets_here(tp)) { temp = pass_target_depth_check(curr_node); if (temp) *target_here = TRUE; else { *target_here = FALSE; *hit_dp_count = *hit_dp_count + 1; } /* endif */ } else *target_here = FALSE; } /* endif */ } /* endif */ } /* endif */ return process; } /* end process_this_resolution() */ /************* * * int term_ident_subst(t1, c1, t2, c2) * * Is t1 under substitution c1 identical to t2 under substitution c2? * *************/ static int term_ident_subst(struct term *t1, struct context *c1, struct term *t2, struct context *c2) { struct rel *r1, *r2; int vn1, vn2; /* dereference if variables */ while (t1->type == VARIABLE && c1->terms[t1->varnum] != NULL) { vn1 = t1->varnum; t1 = c1->terms[vn1]; c1 = c1->contexts[vn1]; } while (t2->type == VARIABLE && c2->terms[t2->varnum] != NULL) { vn2 = t2->varnum; t2 = c2->terms[vn2]; c2 = c2->contexts[vn2]; } if (t1->type == VARIABLE) return(t2->type == VARIABLE && t1->varnum == t2->varnum && c1 == c2); else if (t2->type == VARIABLE) return(0); else { /* neither term is a variable */ if (t1->sym_num != t2->sym_num) return(0); /* fail because of symbol clash */ else { /* following handles both names and complex terms */ r1 = t1->farg; r2 = t2->farg; /* arities are the same, becuase sym_num's are the same */ while (r1 != NULL && term_ident_subst(r1->argval, c1, r2->argval, c2)) { r1 = r1->narg; r2 = r2->narg; } if (r1 == NULL) return(1); else return(0); } } } /* term_ident_subst */ /************************************************************ * * void write_down_tree(node, my_depth) * struct link_node *node; * int my_depth; * * The target has been brought in somewhere above node in the * inference tree. I must write my_depth into target_dist * of all the nodes at my level and process the child of * myself and all my siblings' children. * ************************************************************/ static void write_down_tree(struct link_node *node, int my_depth) { struct link_node *lnp; if (node) { for (lnp = node; lnp; lnp = lnp->next_sibling) { lnp->target_dist = my_depth; write_down_tree(lnp->first_child, my_depth+1); } /* endfor */ } /* endif */ } /* write_down_tree */ /************************************************************ * * void write_up_tree(node, my_depth) * struct link_node *node; * int my_depth; * * The target has been brought into a node below this one at * a distance of my_depth. I must write my_depth into all the * siblings' target_dist at this level, write all the depths * of all the children of the siblings to my left, and go up * the inference tree at the left_most sibling. * ************************************************************/ static void write_up_tree(struct link_node *node, int my_depth) { struct link_node *lnp; if (node->parent) { /* I am not the dummy node at the top of the inference tree */ /* ... writing my_depth to myself and all to right */ for (lnp = node; lnp; lnp = lnp->next_sibling) lnp->target_dist = my_depth; /* writing my_depth to all my left siblings and */ /* writing depths to their children */ lnp = node; while (lnp->prev_sibling) { lnp = lnp->prev_sibling; lnp->target_dist = my_depth; write_down_tree(lnp->first_child, my_depth+1); } /* endwhile */ write_up_tree(lnp->parent, my_depth+1); } /* endif */ } /* end write_up_tree() */ /************************************************************ * * void write_target_distances(curr_node) * struct link_node *curr_node; * * curr_node has resolved with a clause that has the target. * The acquitistion of this target has passed all the depth * and legality checks and now the entire inference tree * must have all their target_dist updated. * ************************************************************/ static void write_target_distances(struct link_node *curr_node) { write_up_tree(curr_node, 0); } /* end write_target_distances() */ otter-3.3f/source/process.c0100644000076400007640000004430210014505721015321 0ustar mccunemccune/* * process.c -- Routines to handle the processing of generated clauses. * */ #include "header.h" /************* * * post_process(c, input, lst) -- finish processing a clause * * The clause has already been integrated, indexed, appended to * Sos. This routine does back subsumption, * and possibly generates more clauses (factoring, back demod, hot * lists, etc.). Any newly generated and kept clauses will be * appended to lst and will wait their turn to be post_processed. * *************/ static void post_process(struct clause *c, int input, struct list *lst) { struct clause *d, *e; struct clause_ptr *cp1, *cp2; struct literal *lit; #if 0 printf("Starting post: "); p_clause(c); #endif if (Flags[EQ_UNITS_BOTH_WAYS].val && unit_clause(c)) { /* * Generate a flipped copy if * 1. it's a (pos or neg) eq unit, and * 2. either * a. order_eq is clear, or * b. order_eq is set, and it couldn't be oriented. */ lit = ith_literal(c, 1); if (eq_lit(lit) && (!Flags[ORDER_EQ].val || !TP_BIT(lit->atom->bits, ORIENTED_EQ_BIT))) { struct term *t; struct clause *c2; struct ilist *ip1, *ip2, *ip3, *ip4, *ip5; c2 = cl_copy(c); ip1 = get_ilist(); ip1->i = COPY_RULE; c2->parents = ip1; ip2 = get_ilist(); ip2->i = c->id; ip1->next = ip2; ip3 = get_ilist(); ip3->i = FLIP_EQ_RULE; ip2->next = ip3; ip4 = get_ilist(); ip4->i = LIST_RULE-1; ip3->next = ip4; ip5 = get_ilist(); ip5->i = 1; ip4->next = ip5; lit = ith_literal(c2, 1); t = lit->atom->farg->argval; lit->atom->farg->argval = lit->atom->farg->narg->argval; lit->atom->farg->narg->argval = t; CLOCK_STOP(POST_PROC_TIME); pre_process(c2, input, lst); CLOCK_START(POST_PROC_TIME); } } if (Flags[BACK_DEMOD].val && unit_clause(c)) { struct term *atom; atom = ith_literal(c,1)->atom; if (c->first_lit && TP_BIT(atom->bits, SCRATCH_BIT)) { /* c was made into a new demodulator */ CLEAR_BIT(atom->bits, SCRATCH_BIT); d = cl_find(c->id + 1); /* demod id is 1 more than clause id */ if (Flags[PRINT_BACK_DEMOD].val || input) printf(">>>> Starting back demodulation with %d.\n", d->id); CLOCK_START(BACK_DEMOD_TIME); back_demod(d, c, input, lst); back_demod_hints(d); CLOCK_STOP(BACK_DEMOD_TIME); } } if (Flags[BACK_SUB].val) { CLOCK_START(BACK_SUB_TIME); cp1 = back_subsume(c); CLOCK_STOP(BACK_SUB_TIME); while (cp1 != NULL) { e = cp1->c; if (e->container != Passive) { Stats[CL_BACK_SUB]++; if (Flags[PRINT_BACK_SUB].val || input) printf("%d back subsumes %d.\n", c->id, e->id); CLOCK_START(UN_INDEX_TIME); un_index_lits_all(e); if (e->container == Usable) un_index_lits_clash(e); CLOCK_STOP(UN_INDEX_TIME); rem_from_list(e); hide_clause(e); } cp2 = cp1; cp1 = cp1->next; free_clause_ptr(cp2); } } if (Flags[FACTOR].val) { CLOCK_START(FACTOR_TIME); all_factors(c, lst); CLOCK_STOP(FACTOR_TIME); } if (Flags[GL_DEMOD].val) { gl_demod(c, lst); } if (Hot->first_cl && !input) { /* Don't hot-list input clauses. */ CLOCK_STOP(POST_PROC_TIME); hot_inference(c); CLOCK_START(POST_PROC_TIME); } if (Flags[BACK_UNIT_DELETION].val && unit_clause(c)) { if (Flags[PRINT_BACK_DEMOD].val || input) printf(">>>> Starting back unit deletion with %d.\n", c->id); CLOCK_START(BACK_UNIT_DEL_TIME); back_unit_deletion(c, input); CLOCK_STOP(BACK_UNIT_DEL_TIME); } } /* post_process */ /************* * * post_proc_all(lst_pos, input, lst) * *************/ void post_proc_all(struct clause *lst_pos, int input, struct list *lst) { struct clause *c; CLOCK_START(POST_PROC_TIME); if (lst_pos == NULL) c = lst->first_cl; else c = lst_pos->next_cl; while (c != NULL) { struct clause *d; post_process(c, input, lst); /* this may alter c->next_cl */ d = c; c = c->next_cl; #if 1 if (TP_BIT(d->bits, SCRATCH_BIT)) { CLEAR_BIT(d->bits, SCRATCH_BIT); rem_from_list(d); index_lits_clash(d); append_cl(Usable, d); /* printf("Clause %d moved to Usable.\n", d->id); */ } #endif /* following moved from end of infer_and_process 19 Jan 90 */ if (Flags[REALLY_DELETE_CLAUSES].val) /* clauses hidden by back demod, back subsumption */ /* also empty clauses are hidden */ del_hidden_clauses(); } CLOCK_STOP(POST_PROC_TIME); } /* post_proc_all */ /************* * * given_clause_ok(id) * *************/ static int given_clause_ok(int id) { struct clause *c; c = cl_find(id); if (c) return(c->container != NULL); else return(0); } /* given_clause_ok */ /************* * * infer_and_process(giv_cl) * * The inference rules append kept clauses to Sos. After each * inference rule is finished, the newly kept clauses are * `post_process'ed (back subsump, back demod, etc.). * *************/ void infer_and_process(struct clause *giv_cl) { struct clause *c, *sos_pos; struct ilist *ip; int given_id; if (Flags[CONTROL_MEMORY].val) { control_memory(); } if (Parms[WARN_MEM].val != -1 && total_mem() > Parms[WARN_MEM].val) { int i = Parms[WARN_MEM_MAX_WEIGHT].val; if (Parms[MAX_WEIGHT].val != i) { Parms[MAX_WEIGHT].val = i; fprintf(stderr,"\nMemory warning: resetting max_weight to %d.\n\n",i); fprintf(stdout,"\nMemory warning: resetting max_weight to %d.\n\n",i); fflush(stdout); } } given_id = giv_cl->id; if (Flags[BINARY_RES].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; /* Save position of last clauses in Sos. */ bin_res(giv_cl); /* Inf rule appends newly kept clauses to Sos. */ /* Now post_process new clauses in Sos. */ /* (Post_process may append even more clauses to Sos. Do them all.) */ /* (ROO does not do this.) */ post_proc_all(sos_pos, 0, Sos); } /* For subsequent inference rules, check that the given clause */ /* has not back demodulated or back subsumed. */ if (Flags[HYPER_RES].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; hyper_res(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[NEG_HYPER_RES].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; neg_hyper_res(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[UR_RES].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; ur_res(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[PARA_INTO].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; para_into(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[PARA_FROM].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; para_from(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[LINKED_UR_RES].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; linked_ur_res(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[LINKED_HYPER_RES].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; linked_hyper_res(giv_cl); post_proc_all(sos_pos, 0, Sos); } if (Flags[DEMOD_INF].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; c = cl_copy(giv_cl); ip = get_ilist(); ip->i = giv_cl->id; c->parents = ip; Stats[CL_GENERATED]++; Stats[DEMOD_INF_GEN]++; pre_process(c, 0, Sos); post_proc_all(sos_pos, 0, Sos); } if (Flags[GEOMETRIC_RULE].val && given_clause_ok(given_id)) { sos_pos = Sos->last_cl; geometry_rule_unif(giv_cl); post_proc_all(sos_pos, 0, Sos); } } /* infer_and_process */ /************* * * int proc_gen(c, input) * * This is the main processing applied to generated clauses. * * If (input), c is an input clause, and some tests should not be performed. * * This routine takes a generated clause and (* means optional): * * renumber variables * * print the clause * * gL rewriting * demodulate, including $evaluation * * gL rewriting * handle evaluable literals * * order equalities * * unit_deletion * * factor-simplify * merge identical literals * * max literals test (if not input) * * max_distinct_vars check (if not input) * tautology check * * max weight test (if not input) * * delete_identical_nested_skolems (if not input) * * sort literals * * forward subsumption * renumber variables (again) * * Return 0 if clause should be deleted. * *************/ int proc_gen(struct clause *c, int input) { struct clause *e; int wt, i; /* Renumbering variables: Some of the processing requires variables to be in range (< MAX_VARS), so we renumber first. Any of the processing that might introduce variables out of range should renumber again. Some provessing can remove or reorder variables, so we renumber again at the end. Renumbering can be slow, so this could be improved. */ CLOCK_START(RENUMBER_TIME); if (renumber_vars(c) == 0) { Stats[CL_VAR_DELETES]++; CLOCK_STOP(RENUMBER_TIME); return(0); } CLOCK_STOP(RENUMBER_TIME); if (Flags[VERY_VERBOSE].val) { printf("\n "); CLOCK_START(PRINT_CL_TIME); print_clause(stdout, c); CLOCK_STOP(PRINT_CL_TIME); } if (Flags[GEOMETRIC_REWRITE_BEFORE].val) i = geo_rewrite(c); if ((Demodulators->first_cl || Internal_flags[DOLLAR_PRESENT]) && !Flags[GL_DEMOD].val) { CLOCK_START(DEMOD_TIME); demod_cl(c); CLOCK_STOP(DEMOD_TIME); if (Flags[VERY_VERBOSE].val) { printf(" after demodulation: "); CLOCK_START(PRINT_CL_TIME); print_clause(stdout, c); CLOCK_STOP(PRINT_CL_TIME); } /* If demodulation introduced new variables, the clause was renumbered, so so all vars are still < MAX_VARS. However, they might no longer be in order. */ } if (Flags[GEOMETRIC_REWRITE_AFTER].val) i = geo_rewrite(c); /* False lits of c may be deleted even if test fails. */ if (Internal_flags[DOLLAR_PRESENT] && lit_t_f_reduce(c)) { Stats[CL_TAUTOLOGY]++; return(0); } if (Flags[ORDER_EQ].val) { CLOCK_START(ORDER_EQ_TIME); if (Flags[LRPO].val) order_equalities_lrpo(c); else order_equalities(c); CLOCK_STOP(ORDER_EQ_TIME); if (!input && Flags[DISCARD_NON_ORIENTABLE_EQ].val && unit_clause(c) && num_literals_including_answers(c) == 1 && pos_eq_lit(ith_literal(c, 1)) && !TP_BIT(ith_literal(c, 1)->atom->bits, ORIENTED_EQ_BIT)) return(0); } if (Flags[UNIT_DELETION].val && num_literals(c) > 1) { CLOCK_START(UNIT_DEL_TIME); i = unit_del(c); CLOCK_STOP(UNIT_DEL_TIME); } if (Flags[FACTOR].val) { CLOCK_START(FACTOR_SIMP_TIME); i = factor_simplify(c); CLOCK_STOP(FACTOR_SIMP_TIME); Stats[FACTOR_SIMPLIFICATIONS] += i; } /* I had to move cl_merge() after factor_simplify, because * build_proof_object() wants cl_merge() to be the last operation. */ cl_merge(c); if (!input && Parms[MAX_LITERALS].val != -1) { if (num_literals(c) > Parms[MAX_LITERALS].val) { Stats[CL_WT_DELETE]++; return(0); } } if (!input && Parms[MAX_ANSWERS].val != -1) { if (num_answers(c) > Parms[MAX_ANSWERS].val) { Stats[CL_WT_DELETE]++; return(0); } } if (!input && Parms[MAX_DISTINCT_VARS].val != -1) { if (distinct_vars(c) > Parms[MAX_DISTINCT_VARS].val) { Stats[CL_WT_DELETE]++; return(0); } } if (!input && Flags[DISCARD_XX_RESOLVABLE].val && xx_resolvable(c)) { Stats[CL_WT_DELETE]++; return(0); } if (tautology(c)) { Stats[CL_TAUTOLOGY]++; return(0); } if (!input && Parms[MAX_WEIGHT].val != MAX_INT) { CLOCK_START(WEIGH_CL_TIME); wt = weight_cl(c, Weight_purge_gen_index); CLOCK_STOP(WEIGH_CL_TIME); if (wt > Parms[MAX_WEIGHT].val) { /* Do not delete if it hint_keep_test() says to keep it. */ int hint_keep = 0; if (Internal_flags[HINTS_PRESENT]) hint_keep = hint_keep_test(c); else if (Internal_flags[HINTS2_PRESENT]) hint_keep = hint2_keep_test(c); if (hint_keep) { if (Flags[VERY_VERBOSE].val) printf(" keeping clause because it matches a hint.\n"); } else { if (Flags[VERY_VERBOSE].val) printf(" deleted because weight=%d.\n", wt); Stats[CL_WT_DELETE]++; return(0); } } } if (!input && Flags[DELETE_IDENTICAL_NESTED_SKOLEM].val) { if (ident_nested_skolems(c)) { Stats[CL_WT_DELETE]++; return(0); } } if (Flags[SORT_LITERALS].val) { CLOCK_START(SORT_LITS_TIME); if (sort_lits(c) && input) { /* If an input clause is changed by sorting, make a note in the justification. */ struct ilist *p; struct ilist *ip = get_ilist(); ip->i = PROPOSITIONAL_RULE; p = c->parents; if (p == NULL) c->parents = ip; else { while (p->next) p = p->next; p->next = ip; } } CLOCK_STOP(SORT_LITS_TIME); } if (Flags[ORDER_EQ].val) { /* For each eq literal that has been flipped, add an entry to * the history. To make sense, this has to be done after sort_lits. */ struct ilist *ip1, *ip2, *ip3; struct literal *lit; int i; for(lit = c->first_lit, i = 1; lit; lit = lit->next_lit, i++) { if (TP_BIT(lit->atom->bits, SCRATCH_BIT)) { CLEAR_BIT(lit->atom->bits, SCRATCH_BIT); ip1 = get_ilist(); ip1->i = FLIP_EQ_RULE; ip2 = get_ilist(); ip2->i = LIST_RULE-1; ip1->next = ip2; ip3 = get_ilist(); ip3->i = i; ip2->next = ip3; if (c->parents) { for (ip3 = c->parents; ip3->next; ip3 = ip3->next); ip3->next = ip1; } else c->parents = ip1; } } } if (Flags[FOR_SUB].val) { CLOCK_START(FOR_SUB_TIME); e = forward_subsume(c); CLOCK_STOP(FOR_SUB_TIME); if (e) { if (Flags[VERY_VERBOSE].val) printf(" Subsumed by %d.\n", e->id); else if (input) { printf(" Following clause subsumed by %d during input processing: ", e->id); print_clause(stdout, c); } Stats[CL_FOR_SUB]++; if (e->container == Sos) Stats[FOR_SUB_SOS]++; if (e->id < 100) Subsume_count[e->id]++; else Subsume_count[0]++; return(0); } } if (Flags[DISCARD_COMMUTATIVITY_CONSEQUENCES].val && commutativity_consequence(c)) { Stats[CL_WT_DELETE]++; return(0); } CLOCK_START(RENUMBER_TIME); if (renumber_vars(c) == 0) { Stats[CL_VAR_DELETES]++; CLOCK_STOP(RENUMBER_TIME); return(0); } CLOCK_STOP(RENUMBER_TIME); return(1); } /* proc_gen */ /************* * * pre_process(c, input, lst) * *************/ void pre_process(struct clause *c, int input, struct list *lst) { int i; struct clause *e, *original_input; CLOCK_START(PRE_PROC_TIME); if (heat_is_on()) /* if c was generated by hot inference */ Stats[HOT_GENERATED]++; if (!c->parents) original_input = cl_copy(c); else original_input = NULL; i = proc_gen(c, input); if (!i) { CLOCK_START(DEL_CL_TIME); cl_del_non(c); if (original_input) cl_del_non(original_input); CLOCK_STOP(DEL_CL_TIME); CLOCK_STOP(PRE_PROC_TIME); return; } if (original_input && c->parents) { /* When input clauses are changed (demod, unit_del, factor_simp, * sort_lits) during pre_process, we keep the original so that proofs * make sense (in particular, so that proof_objects make sense). */ struct ilist *ip1, *ip2; cl_integrate(original_input); hide_clause(original_input); ip1 = get_ilist(); ip2 = get_ilist(); ip1->i = COPY_RULE; ip2->i = original_input->id; ip1->next = ip2; ip2->next = c->parents; c->parents = ip1; } CLOCK_START(KEEP_CL_TIME); cl_integrate(c); index_lits_all(c); if (lst == Usable) index_lits_clash(c); append_cl(lst, c); c->pick_weight = weight_cl(c, Weight_pick_given_index); if (Internal_flags[HINTS_PRESENT]) adjust_weight_with_hints(c); else if (Internal_flags[HINTS2_PRESENT]) adjust_weight_with_hints2(c); if (Parms[AGE_FACTOR].val != 0) c->pick_weight += (Stats[CL_GIVEN] / Parms[AGE_FACTOR].val); if (Parms[DISTINCT_VARS_FACTOR].val != 0) c->pick_weight += distinct_vars(c) * Parms[DISTINCT_VARS_FACTOR].val; Stats[CL_KEPT]++; if (c->heat_level > 0) Stats[HOT_KEPT]++; CLOCK_STOP(KEEP_CL_TIME); if (input || Flags[PRINT_KEPT].val) { printf("** KEPT (pick-wt=%d): ", c->pick_weight); CLOCK_START(PRINT_CL_TIME); print_clause(stdout, c); CLOCK_STOP(PRINT_CL_TIME); } if (Flags[DYNAMIC_DEMOD].val && unit_clause(c) && num_literals_including_answers(c) == 1 && pos_eq_lit(ith_literal(c, 1))) { int demod_flag; CLOCK_START(NEW_DEMOD_TIME); demod_flag = dynamic_demodulator(c); if (demod_flag != 0) { /* make sure there are no calls to cl_integrate between * KEEP and here, because new_demod ID must be one more * than KEPT copy. In particular, check_for_proof. */ struct clause *d; d = new_demod(c, demod_flag); if (Flags[PRINT_NEW_DEMOD].val || input) { printf("---> New Demodulator: "); if (demod_flag == 2) printf("(lex-dependent) "); print_clause(stdout, d); } } CLOCK_STOP(NEW_DEMOD_TIME); } CLOCK_START(CONFLICT_TIME); e = check_for_proof(c); CLOCK_STOP(CONFLICT_TIME); if (Parms[MAX_PROOFS].val != -1 && Stats[EMPTY_CLAUSES] >= Parms[MAX_PROOFS].val) { if (!splitting() || current_case() == NULL) { fprintf(stderr, "\n%cSearch stopped by max_proofs option.\n\n", Bell); printf("\nSearch stopped by max_proofs option.\n"); cleanup(); } else { /* This is a case. */ if (!Flags[REALLY_DELETE_CLAUSES].val) { /* Send assumptions used for refutation to the parent. */ assumps_to_parent(e); } output_stats(stdout, Parms[STATS_LEVEL].val); printf("\nProcess %d finished %s", my_process_id(), get_time()); } if (multi_justifications()) { struct clause *ee = proof_last_hidden_empty(); multi_just_process(ee); output_stats(stdout, Parms[STATS_LEVEL].val); } exit(PROOF_EXIT); } if (!input && c->pick_weight <= Parms[DYNAMIC_HEAT_WEIGHT].val) hot_dynamic(c); /* add to the hot list */ CLOCK_STOP(PRE_PROC_TIME); } /* pre_process */ otter-3.3f/source/main.c.diffs0100644000076400007640000000022610041245672015664 0ustar mccunemccune14,15c14,15 < #define OTTER_VERSION "3.3c" < #define VERSION_DATE "Feb 2004" --- > #define OTTER_VERSION "3.3d" > #define VERSION_DATE "April 2004" otter-3.3f/source/case.c0100644000076400007640000010255007343605232014567 0ustar mccunemccune/* * case.c - case splitting * */ #include "header.h" #ifdef TP_FORK /* for calls to fork() and wait() */ # include # include # include #endif #define MAX_SPLIT_DEPTH 255 /* see SPLIT_DEPTH in options.c */ #define POS_CLAUSE 1 #define NEG_CLAUSE 2 #define MIX_CLAUSE 3 #define FORK_FAIL 0 #define PARENT 1 #define CHILD 2 #define CHILD_FAIL 3 /* Current_case is a sequence of integers, e.g., Case [2.1.3.2]. */ struct ilist *Current_case = NULL; /* The literal_data structure is used for atom splitting. When * deciding which atom to split, all ground literal occurrences * are considered, and for each, the data in the structure is * collected. See routines get_literal_data(), compare_literal_data(), * find_atom_to_split(). */ struct literal_data { struct term *atom; int sign; int equality; int atom_weight; int clause_id; int clause_weight; int clause_type; int clause_variables; int pos_occurrences; int neg_occurrences; int pos_binary_occurrences; int neg_binary_occurrences; }; /* These are file descriptors (from pipe()), which are used to * communicate with child and parent processes. The main use is * for a child to tell its parent what case assumptions were * used for a refutation, which allows ancestors to sometimes * skip further cases. See assumps_to_parent(), prover_forks(). */ int To_parent, From_parent; /* pipe for communicating with parent */ int To_children, From_children; /* pipe for communicating with children */ /************* * * splitting() -- Is slitting enabled? * *************/ int splitting(void) { return(Flags[SPLIT_CLAUSE].val || Flags[SPLIT_ATOM].val || Flags[SPLIT_WHEN_GIVEN].val); } /* splitting */ /************* * * max_split_depth() -- Return the maximum depth allowed for splitting. * *************/ int max_split_depth(void) { return(MAX_SPLIT_DEPTH); } /* max_split_depth */ /************* * * splitable_literal(clause, lit) -- Is the atom splittable? * * The test is done on an occurrence of a literal. * *************/ int splitable_literal(struct clause *c, struct literal *l) { if (num_literals(c) < 2 || !ground(l->atom)) return 0; else { int ok = 1; if (ok && Flags[SPLIT_POS].val) ok = pos_clause(c); if (ok && Flags[SPLIT_NEG].val) ok = neg_clause(c); if (ok && Flags[SPLIT_NONHORN].val) ok = l->sign && !horn_clause(c); return ok; } } /* splitable_literal */ /************* * * compare_literal_data(d1, d2) -- Compare two splittable literal occurrences. * * Return the better literal_data. If neither is better, return d1. * *************/ static struct literal_data compare_literal_data(struct literal_data d1, struct literal_data d2) { if (d1.atom == NULL) return d2; else if (d2.atom == NULL) return d1; else if (Flags[SPLIT_POPULAR].val) { if (d2.pos_occurrences + d2.neg_occurrences > d1.pos_occurrences + d1.neg_occurrences) return d2; else return d1; } else { if (d2.clause_weight < d1.clause_weight) return d2; else if (d1.clause_weight < d2.clause_weight) return d1; else if (d2.atom_weight < d1.atom_weight) return d2; else return d1; } } /* compare_literal_data */ /************* * * splitable_clause(c) -- Is this clause splittable? * *************/ int splitable_clause(struct clause *c) { if (!ground_clause(c)) return 0; else if (num_literals(c) < 2) return 0; else { int ok = 1; if (ok && Flags[SPLIT_POS].val) ok = pos_clause(c); if (ok && Flags[SPLIT_NEG].val) ok = neg_clause(c); if (ok && Flags[SPLIT_NONHORN].val) ok = !horn_clause(c); return ok; } } /* splitable_clause */ /************* * * compare_splitable_clauses(c, d) -- Compare two splittable clauses. * * Return the better clause. If neither is better, return c. * *************/ struct clause *compare_splitable_clauses(struct clause *c, struct clause *d) { if (c == NULL) return d; else if (d == NULL) return c; else if (Flags[SPLIT_MIN_MAX].val) { /* Return the clause with the smaller maximum literal. * If maxes are the same, return the smaller clause * if clauses are the same weight, return c. */ int cm = max_literal_weight(c, Weight_pick_given_index); int dm = max_literal_weight(c, Weight_pick_given_index); /* printf("maxes: %4d=%4d, %4d=%4d\n", c->id, cm, d->id, dm); */ if (cm < dm) { return c; } else if (dm < cm) { return d; } else return (d->pick_weight < c->pick_weight ? d : c); } else { /* Return smaller clause; if clauses are the same weight, return c. */ return (d->pick_weight < c->pick_weight ? d : c); } } /* compare_splitable_clauses */ /************* * * init_literal_data(p) -- Initialize a literal_data structure. * *************/ static void init_literal_data(struct literal_data *p) { p->atom = NULL; } /* init_literal_data */ /************* * * p_literal_data(data) -- Print a literal_data structure to stdout. * *************/ static void p_literal_data(struct literal_data data) { printf("Atom: "); print_term(stdout, data.atom); printf(" sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d\n", data.sign,data.equality,data.atom_weight,data.clause_id, data.clause_weight, data.clause_type,data.clause_variables, data.pos_occurrences,data.neg_occurrences, data.pos_binary_occurrences,data.neg_binary_occurrences); } /* p_literal_data */ /************* * * get_literal_data(lit, p) * * Given a ground literal occurrence, fill in the data. * *************/ static void get_literal_data(struct literal *lit, struct literal_data *p) { struct clause *c = lit->container; struct term *a; struct fpa_tree *ut; int n, m; p->atom = lit->atom; p->sign = lit->sign; p->equality = is_eq(lit->atom->sym_num); p->atom_weight = weight(lit->atom, Weight_pick_given_index); p->clause_id = c->id; p->clause_weight = weight_cl(c, Weight_pick_given_index); p->clause_variables = distinct_vars(c); if (pos_clause(c)) p->clause_type = POS_CLAUSE; else if (neg_clause(c)) p->clause_type = NEG_CLAUSE; else p->clause_type = MIX_CLAUSE; if (!Flags[SPLIT_POPULAR].val) { p->pos_occurrences = 0; p->neg_occurrences = 0; p->pos_binary_occurrences = 0; p->neg_binary_occurrences = 0; } else { ut = build_tree(lit->atom, INSTANCE, Parms[FPA_LITERALS].val, Fpa_pos_lits); n = 0; m = 0; a = next_term(ut, 0); while (a != NULL) { n++; if (num_literals(a->occ.lit->container) == 2) m++; a = next_term(ut, 0); } p->pos_occurrences = n; p->pos_binary_occurrences = m; ut = build_tree(lit->atom, INSTANCE, Parms[FPA_LITERALS].val, Fpa_neg_lits); n = 0; m = 0; a = next_term(ut, 0); while (a != NULL) { n++; if (num_literals(a->occ.lit->container) == 2) m++; a = next_term(ut, 0); } p->neg_occurrences = n; p->neg_binary_occurrences = m; } } /* get_literal_data */ /************* * * print_case() -- print the current case, e.g., [2.1.3], to a file * *************/ void print_case(FILE *fp) { struct ilist *ip; fprintf(fp, "["); for (ip = Current_case; ip; ip = ip->next) fprintf(fp, "%d%s", ip->i, ip->next == NULL ? "" : "."); fprintf(fp, "]"); } /* print_case */ /************* * * p_case() * *************/ void p_case(void) { print_case(stdout); } /* p_case */ /************* * * print_case_n() -- Like print_case, but add the argument. * *************/ void print_case_n(FILE *fp, int n) { struct ilist *ip; fprintf(fp, "["); for (ip = Current_case; ip; ip = ip->next) fprintf(fp, "%d.", ip->i); fprintf(fp, "%d]", n); } /* print_case_n */ /************* * * p_case_n() * *************/ void p_case_n(int n) { print_case_n(stdout, n); } /* p_case_n */ /************* * * p_assumption_depths() * *************/ void p_assumption_depths(char assumptions[]) { #if 0 int i; printf("Assumptions at the following depths were used to refute this branch:"); for (i = 0; i <= MAX_SPLIT_DEPTH; i++) { if (assumptions[i]) printf(" %d", i); } printf(".\n"); #endif } /* p_assumption_depths */ /************* * * current_case() -- Return Current_case. * *************/ struct ilist *current_case(void) { return(Current_case); } /* current_case */ /************* * * add_subcase(i) -- Append an integer to Current_case. * *************/ void add_subcase(int i) { struct ilist *p1, *p2; p1 = get_ilist(); p1->i = i; if (Current_case == NULL) Current_case = p1; else { for (p2 = Current_case; p2->next != NULL; p2 = p2->next); p2->next = p1; } } /* add_subcase */ /************* * * case_depth() -- What is the depth of the current case? * *************/ int case_depth(void) { return ilist_length(Current_case); } /* case_depth */ /************* * * find_clause_to_split() * * Go through Usable, then Sos, and find the best splittable clause. * *************/ struct clause *find_clause_to_split(void) { struct clause *c; struct clause *best_so_far = NULL; for (c = Usable->first_cl; c != NULL; c = c->next_cl) { if (splitable_clause(c)) { best_so_far = compare_splitable_clauses(best_so_far, c); } } for (c = Sos->first_cl; c != NULL; c = c->next_cl) { if (splitable_clause(c)) { best_so_far = compare_splitable_clauses(best_so_far, c); } } return(best_so_far); /* may be NULL */ } /* find_clause_to_split */ /************* * * find_atom_to_split() * * Go through all literal occurrences in Usable+Sos, and return * the atom of the best splittable literal occurrence. * *************/ struct term *find_atom_to_split(void) { if (Split_atoms != NULL) { int i; struct term *t; /* Split_atoms is a proper list. If the case_depth is n, * return the n-th member of split_atoms. */ for (t = Split_atoms, i = 0; t->sym_num != Nil_sym_num && i < case_depth(); t = t->farg->narg->argval, i++); return (t->sym_num == Nil_sym_num ? NULL : t->farg->argval); } else { struct clause *c; struct literal *lit; struct literal_data min, curr; init_literal_data(&min); for (c = Usable->first_cl; c != NULL; c = c->next_cl) { for (lit = c->first_lit; lit != NULL; lit = lit->next_lit) { if (splitable_literal(c, lit)) { get_literal_data(lit, &curr); min = compare_literal_data(min, curr); } } } for (c = Sos->first_cl; c != NULL; c = c->next_cl) { for (lit = c->first_lit; lit != NULL; lit = lit->next_lit) { if (splitable_literal(c, lit)) { get_literal_data(lit, &curr); min = compare_literal_data(min, curr); } } } return min.atom; /* NULL if no ground lits found */ } } /* find_atom_to_split */ /************* * * prover_forks(int n, int *ip, char assumptions[]) * * This is the guts of the splitting. It is used for both clause * splitting and atom splitting. Parameter n tells how many cases * to do. This routine also takes care of skipping redundant cases * when assumptions are not used. For example, if we split on * clause p|q, and the p case is refuted without using p, then we * skip the q case. * * This routine does not return when a child returns without * a proof. When this happens, we just exit, * sending the same exit code to the parent. * * When this routine does return to its caller, the return value is: * * CHILD Return as child process ready to do its case. * Also, integer *ip is set to the case number. * PARENT Return as parent process---all children succeeded. * Also, fill in the Boolean array assumptions, which * tells which ancestor case assumptions were used to * refute the child cases. * FORK_FAIL Operating system would not allow process to fork. * CHILD_FAIL A child did not exit normally (WIFEXITED(status) nonzero). * *************/ int prover_forks(int n, int *ip, char assumptions[]) { #ifndef TP_FORK return FORK_FAIL; #else int child_status, rc; int parent = 1; int i = 1; int fd[2]; char assumptions_descendents[MAX_SPLIT_DEPTH+1]; int j; for (j = 0; j <= MAX_SPLIT_DEPTH; j++) assumptions[j] = 0; /* Set up pipe for communicating with children. The child processes * will inherit these values and immediately use them to set up a * pipe to the parent (that is, copy them to To_parent and From_parent). */ rc = pipe(fd); From_children = fd[0]; To_children = fd[1]; if (rc != 0) { return FORK_FAIL; } while (i <= n && parent) { fflush(stdout); fflush(stderr); rc = fork(); if (rc < 0) { return FORK_FAIL; } else if (rc > 0) { /* This is the parent process */ int depth = case_depth(); wait(&child_status); if (WIFEXITED(child_status)) { int child_exit_code = WEXITSTATUS(child_status); if (child_exit_code==PROOF_EXIT) { /* all is well---the child proved its case */ printf("Refuted case "); p_case_n(i); printf(".\n"); fflush(stdout); if (Flags[REALLY_DELETE_CLAUSES].val) { /* Really_delete_clauses is incompatable with the assumption redundancy check. We'll just go on to the next case in stead of checking if the assumption for the previous case was used for the refutation. */ i++; } else { rc = read(From_children, assumptions_descendents,MAX_SPLIT_DEPTH+1); if (assumptions_descendents[depth+1]) i++; else if (i == n) i++; /* assumption for last case was not used */ else { printf("\nThe Assumption for case "); p_case_n(i); printf(" was not used;\n"); printf("therefore we skip case%s", (i == n-1 ? ": " : "s:")); for (j = i+1; j <= n; j++) { printf(" "); p_case_n(j); } printf(".\n"); i = n+1; } /* "or" in the assumptions used. */ for (j = 0; j <= depth; j++) assumptions[j] = (assumptions[j] | assumptions_descendents[j]); } } /* child found proof */ else { /* Child exited without a proof. Exit with same code to parent. */ output_stats(stdout, Parms[STATS_LEVEL].val); printf("\nProcess %d finished %s", my_process_id(), get_time()); exit(child_exit_code); } } /* WIFEXITED */ else { /* Child fails for some other reason. */ return CHILD_FAIL; } } /* if parent */ else { /* This is the child process. */ /* Set up pipe to parent. */ To_parent = To_children; From_parent = From_children; /* Exit loop and do the case. */ parent = 0; } } /* while */ *ip = i; return (parent ? PARENT : CHILD); #endif } /* prover_forks */ /************* * * split_clause(c) * * If (c == NULL), look for a clause to split. * If (c != NULL), split on c. * * If success (i.e., split, and each child refutes its case), exit process. * * Return value: * 0: no split * 1: split, child returns * 2: split, parent returns failure (this might not be used) * *************/ int split_clause(struct clause *giv_cl) { #ifndef TP_FORK return 0; #else struct clause *c; char assumptions[MAX_SPLIT_DEPTH+1]; if (giv_cl == NULL) c = find_clause_to_split(); else c = giv_cl; if (c == NULL) { printf("\nI tried to split, but I could not find a suitable clause.\n"); return 0; } else { int rc, n, case_number; printf("\nSplitting on clause "); p_clause(c); n = num_literals(c); rc = prover_forks(n, &case_number, assumptions); if (rc == FORK_FAIL) { printf("Case splitting (fork) failed. Returning to search.\n"); return 0; } else if (rc == PARENT) { if (Current_case == NULL) { printf("\nThat finishes the proof of the theorem.\n"); fprintf(stderr, "%c\nThat finishes the proof of the theorem.\n", Bell); } else { /* Tell the parent the assumptions used to refute this * branch. We don't send the actual assumptions; instead, * we send a set of integers giving the depths of the * assumptions. This is implemented as a Boolean array * indexed by depth. */ rc = write(To_parent, assumptions, MAX_SPLIT_DEPTH+1); p_assumption_depths(assumptions); } output_stats(stdout, Parms[STATS_LEVEL].val); printf("\nProcess %d finished %s", my_process_id(), get_time()); exit(PROOF_EXIT); } else if (rc == CHILD) { /* We are the child. Assert units for this case, then continue search. */ int j; struct literal *c_lit, *d_lit; struct clause *d, *sos_pos; clock_init(); /* reset all clocks to 0 */ add_subcase(case_number); /* Update the case vector. */ printf("\nCase "); p_case(); printf(" (process %d):\n", my_process_id()); /* Disable the clause being split. */ un_index_lits_all(c); if (c->container == Usable) un_index_lits_clash(c); rem_from_list(c); hide_clause(c); /* Add negated units for cases already done. */ /* Then add the unit for this case. */ sos_pos = Sos->last_cl; /* save position for post processing */ for (j = 1; j <= case_number; j++) { c_lit = ith_literal(c, j); d = get_clause(); d_lit = get_literal(); d->first_lit = d_lit; d_lit->container = d; d_lit->atom = copy_term(c_lit->atom); d_lit->atom->occ.lit = d_lit; d_lit->sign = c_lit->sign; d_lit->atom->varnum = c_lit->atom->varnum; /* copy type of atom */ if (j != case_number) { /* negate literal */ d_lit->sign = !d_lit->sign; if (d_lit->atom->varnum == POS_EQ) d_lit->atom->varnum = NEG_EQ; else if (d_lit->atom->varnum == NEG_EQ) d_lit->atom->varnum = POS_EQ; } d->parents = get_ilist(); d->parents->i = c->id; d->parents->next = get_ilist(); d->parents->next->i = (j == case_number ? SPLIT_RULE : SPLIT_NEG_RULE); d->parents->next->next = get_ilist(); d->parents->next->next->i = LIST_RULE - ilist_length(Current_case);; d->parents->next->next->next = copy_ilist(Current_case); pre_process(d, 0, Sos); if (j == case_number && d->container == Sos) { printf("Assumption: "); p_clause(d); } } post_proc_all(sos_pos, 0, Sos); return 1; } else { /* rc == CHILD_FAIL */ abend("case failure"); return -1; } } #endif } /* split_clause */ /************* * * split_atom() * * If success (i.e., split, and each child refutes its case), exit process. * * Return value: * 0: no split * 1: split, child returns * 2: split, parent returns failure (this might not be used) * *************/ int split_atom(void) { #ifndef TP_FORK return 0; #else struct term *atom; char assumptions[MAX_SPLIT_DEPTH+1]; atom = find_atom_to_split(); if (atom == NULL) { printf("\nI tried to split, but I could not find a suitable atom.\n"); return 0; } else { int rc, case_number; printf("\nSplitting on atom "); p_term(atom); rc = prover_forks(2, &case_number, assumptions); if (rc == FORK_FAIL) { printf("Case splitting (fork) failed. Returning to search.\n"); return 0; } else if (rc == PARENT) { if (Current_case == NULL) { printf("\nThat finishes the proof of the theorem.\n"); fprintf(stderr, "%c\nThat finishes the proof of the theorem.\n", Bell); } else { rc = write(To_parent, assumptions, MAX_SPLIT_DEPTH+1); p_assumption_depths(assumptions); } output_stats(stdout, Parms[STATS_LEVEL].val); printf("\nProcess %d finished %s", my_process_id(), get_time()); exit(PROOF_EXIT); } /* parent */ else if (rc == CHILD) { /* We are the child. Assert units for this case, then continue search. */ struct literal *d_lit; struct clause *d, *sos_pos; clock_init(); /* reset all clocks to 0 */ add_subcase(case_number); /* Update the case vector. */ printf("\nCase "); p_case(); printf(" (process %d):\n", my_process_id()); sos_pos = Sos->last_cl; /* save position for post processing */ d = get_clause(); d_lit = get_literal(); d->first_lit = d_lit; d_lit->container = d; d_lit->atom = copy_term(atom); d_lit->atom->occ.lit = d_lit; d_lit->sign = (case_number == 1 ? 1 : 0); if (is_eq(atom->sym_num)) d_lit->atom->varnum = d_lit->sign ? POS_EQ : NEG_EQ; else d_lit->atom->varnum = NORM_ATOM; d->parents = get_ilist(); d->parents->i = SPLIT_RULE; d->parents->next = get_ilist(); d->parents->next->i = LIST_RULE - ilist_length(Current_case); d->parents->next->next = copy_ilist(Current_case); pre_process(d, 0, Sos); if (d->container == Sos) { printf("Assumption: "); p_clause(d); } post_proc_all(sos_pos, 0, Sos); return 1; } /* child */ else { /* rc == CHILD_FAIL */ abend("case failure"); return -1; } } #endif } /* split_atom */ /************* * * possible_split() * * Check if it is time to split, and if so, try to split. * * If a split occurs, children return to continue searching. * If all children find proofs, parent calls exit(PROOF_EXIT). * If any child fails, parent abends. (This may change.) * *************/ void possible_split(void) { static int next_attempt = 0; int ok = 0; #ifndef TP_FORK abend("case splitting is not compiled into this Otter"); #endif if (Flags[SPLIT_CLAUSE].val || Flags[SPLIT_ATOM].val) { if (Parms[SPLIT_SECONDS].val != -1) { int runtime = run_time() / 1000; if (next_attempt == 0) next_attempt = Parms[SPLIT_SECONDS].val; if (runtime >= next_attempt) { ok = 1; next_attempt += Parms[SPLIT_SECONDS].val; } } else if (Parms[SPLIT_GIVEN].val != -1) { int n = Parms[SPLIT_GIVEN].val; if (n == 0 || Stats[CL_GIVEN] % n == 0) { ok = 1; } } if (ok) { int rc; if (case_depth() < Parms[SPLIT_DEPTH].val) { if (Flags[SPLIT_ATOM].val) rc = split_atom(); else rc = split_clause((struct clause *) NULL); } } } } /* possible_split */ /************* * * always_split() * * Unconditional splitting, and keep splitting as long as possible. * *************/ void always_split(void) { int rc; #ifndef TP_FORK abend("case splitting is not compiled into this Otter"); #endif if (Flags[SPLIT_ATOM].val) rc = split_atom(); else rc = split_clause((struct clause *) NULL); if (rc == 1) always_split(); /* We are the child; all is well; split again. */ else { printf("\nalways_split: returning because no splitting is possible at this time.\n"); return; } } /* always_split */ /************* * * possible_given_split(c) * * c has just been selected as the given clause. * *************/ void possible_given_split(struct clause *c) { #ifndef TP_FORK abend("case splitting is not compiled into this Otter"); #endif if (Flags[SPLIT_WHEN_GIVEN].val && ground_clause(c) && num_literals(c) > 1) { int ok = 1; if (ok && Flags[SPLIT_POS].val) ok = pos_clause(c); if (ok && Flags[SPLIT_NEG].val) ok = neg_clause(c); if (ok && Flags[SPLIT_NONHORN].val) ok = !horn_clause(c); if (ok) { int rc; if (case_depth() < Parms[SPLIT_DEPTH].val) { if (Flags[SPLIT_ATOM].val) { /* This is a little strange. We're allowing splitting on an atom. We'll first move the clause back to Sos. */ un_index_lits_clash(c); rem_from_list(c); append_cl(Sos, c); rc = split_atom(); } else rc = split_clause(c); } } } } /* possible_given_split */ /************* * * assumps_to_parent() * * This routine is called when a proof is found during case splitting. * * Tell the parent the assumptions used to refute this * leaf. We don't send the actual assumptions; instead, * we send a set of integers giving the depths of the * assumptions. This is implemented as a Boolean array * indexed by depth. * *************/ void assumps_to_parent(struct clause *e) { struct clause_ptr *p, *q; struct ilist *r; int i; char assumptions[MAX_SPLIT_DEPTH+1]; p = NULL; i = get_ancestors(e, &p, &r); /* i (level), r (level list) won't be used */ for (i = 0; i <= MAX_SPLIT_DEPTH; i++) assumptions[i] = 0; for (q = p; q != NULL; q = q->next) { r = q->c->parents; /* SPLIT_RULE code is either first (atom split) or second (clause split) */ if (r != NULL && r->i == SPLIT_RULE) { i = LIST_RULE - r->next->i; } else if (r!= NULL && r->next != NULL && r->next->i == SPLIT_RULE) { i = LIST_RULE - r->next->next->i; } else i = 0; if (i != 0) { /* The current clause is a split assumption, and i is the * depth. This does not include SPLIT_NEG assumptions from * previous sibling cases. */ assumptions[i] = 1; } } i = write(To_parent, assumptions, MAX_SPLIT_DEPTH+1); printf("\n\n"); p_assumption_depths(assumptions); } /* assumps_to_parent */ /************* * * exit_with_possible_model() * *************/ void exit_with_possible_model(void) { printf("\nPossible model detected on branch "); p_case(); printf(".\n"); fprintf(stderr, "\n%cPossible model detected on branch ", Bell); print_case(stderr); fprintf(stderr, ".\n"); printf("\nHere are the clauses in Usable and SoS. It seems that no more\n"); printf("inferences or splitting can be done. If the search strategy is\n"); printf("complete, these clauses should lead to a model of the input.\n"); printf("\nlist(usable).\n"); print_cl_list(stdout, Usable); printf("\nlist(sos).\n"); print_cl_list(stdout, Sos); output_stats(stdout, Parms[STATS_LEVEL].val); printf("\nProcess %d finished %s", my_process_id(), get_time()); exit(POSSIBLE_MODEL_EXIT); } /* exit_with_possible_model */ /*************************************************************************/ /* The rest of this file is some documentation on the code in this file. */ /*************************************************************************/ /* CASE SPLITTING IN OTTER William McCune, Dale Myers, Rusty Lusk, Mohammed Alumlla December 1997 This implementation uses the UNIX fork() command to make copies of the current state of the process for the cases. This avoids having to explicitly save the state and restore it for the next case. (That is, it was easy to implement.) When enabled, splitting occurs periodically during the search. The default is to split after every 5 given clauses. This can be changed to some other number of given clauses, say 10, with the command assign(split_given, 10). % default 5 Instead, one can split after a specified number of seconds, with a command such as assign(split_seconds, 10). % default infinity which asks Otter to attempt a split every (approximately) 10 seconds. (Jobs that use split_seconds are usually not repeatable.) A third method is to split when a nonunit ground clause is selected as the given clause. This option is specified with the command set(split_when_given). which causes splitting on the given clause if (1) it is ground, (2) it is within the split_depth bound (see below), and (3) it satisfies the split_pos and split_neg flags (see below). If you wish to limit the depth of splitting, use a command such as assign(split_depth, 3). % default 256 (which is also the maximum) which will not allow a case such as "Case [1.1.1.1]". There are two kinds of splitting: on ground clauses and on ground atoms. Clause splitting constructs one case for each literal, and atom splitting, say on p, constructs two cases: p is true; p is false (or, as Larry Wos says, splitting on a tautology). Sequence of Splitting Processes Say Otter decides to split the search into n cases. For each case, the fork() command creates a child process for the case, then the parent process waits for the child to exit. If any child fails to refute its case, the parent exits in failure (causing all ancestor processes to fail as well). If each child refutes its case, the parent exits with success. The Output File Various messages about the splitting events are sent to the output file. To get an overview of the search from an output file, say problem.out, one can use the following command. egrep "Splitting|Assumption|Refuted|skip|That" problem.out Splitting Clauses The following commands enables splitting on clauses after some number of given clauses have been used (see split_given), or after some number of seconds (see split_seconds). set(split_clause). % default clear The following command simply asks Otter to split on ground given clauses. set(split_when_given). % default clear (I suppose one could use both of the preceding commands at the same time---I haven't tried it.) If Otter finds a suitable (see flags below) nonunit ground clause for splitting, say "p | q | r", the assumptions for three cases are Case 1: p. Case 2: -p & q. Case 3: -p & -q & r. Eligible Clauses for Splitting Otter splits on ground nonunit clauses only. They can occur in Usable or in Sos. The following commands can be used to specify the type of clause to split. set(split_pos). % split on positive clauses only (default clear) set(split_neg). % split on negative clauses only (default clear) set(split_nonhorn). % split on nonhorn clauses only (default clear) If none of the preceding flags are set, all ground clauses are eligible. Selecting the Best Eligible Clause The default method for selecting the best eligible clause for splitting is simply to take the first, lowest weight (using the pick_given scale) clause from Usable+Sos. Instead, one can use The command set(split_min_max). % default clear which says to use the following method to compare two eligible clauses C and D. Prefer the clause with the lighter heaviest literal (pick_given scale); if the heaviest literals have the same weight, use the lighter clause; if the clauses have the same weight, use the first in Usable+Sos. Splitting Atoms The following commands enables splitting on atoms after some number of given clauses have been used (see split_given), or after some number of seconds (see split_seconds). set(split_atom). (For propositional problems with assign(split_given, 0), this will cause Otter to perform a (not very speedy) Davis-Putnam search.) To select an atom for splitting, we consider OCCURRENCES of atoms within clauses. Eligible Atoms Otter splits on atoms that occur in nonunit ground clauses. The command set(split_pos). % default clear says to split on atoms the occur only in positive clauses, set(split_neg). % default clear says to split on atoms the occur only in negative clauses, and set(split_nonhorn). % default clear says to split on atoms that occur positively in nonHorn clauses. Selecting the Best Eligible Atom Default method for comparing two eligible atom-occurrences: Prefer the atom that occurs in the lower weight clause. If the clauses have the same weight, prefer the atom with the lower weight. An optional method for selecting an atom considers the number of occurrences of the atom. The command set(split_popular). % default clear says to prefer the atom that occurs in the greatest number of clauses. All clauses in Usable+Sos containing the atom are counted. Another Way to Split Atoms If the user has an idea of how atom splitting should occur, he/she can give a sequence of atoms in the input file, and Otter will split accordingly. (As above, the TIME of splitting is determined as above with the split_given and split_seconds parameters.) For example, with the commands set(split_atom). split_atoms([P, a=b, R]). assign(split_given, 0). Otter will immediately (because of split_given) split the search into 8 cases (because there are 3 atoms), then do no more splitting. Problems With This Implementation Splitting is permanent. That is, if a case fails, the whole search fails (no backing up to try a different split). If Otter fails to find a proof for a particular case (e.g., the Sos empties or some limit is reached), the whole attempt fails. If the search strategy is complete, then an empty Sos indicates satisfiability, and the set of assumptions introduced by splitting give you a partial model; however, it is up to the user to figure this out. When splitting is enabled, max_seconds (for the initial process and all descendent processes) is checked against the wall clock (from the start of the initial process) instead of against the process clock. This is problematic if the computer is busy with other processes. Getting the Total Process Time The process clock ("user CPU" statistic) is initialized at the start of the process, and each process prints statistics once at the end of its life. Therefore, one can get the total process by summing all of the "user CPU" times in the output file. The command grep "user CPU" problem.out | awk '{sum += $4}END{print sum}' can be used to get the approximate total process time from an output file problem.out. Advice on Using Otter's Splitting (from McCune) At this time, we don't have much data. A general strategy for nonground problems is the following. set(split_when_given). set(split_pos). % Also try it without this command. assign(split_depth, 10). For ground (propositional) problems, try the following, which is essentially a Davis-Putnam procedure. set(split_atom). set(split_pos). assign(split_given, 0). */ otter-3.3f/source/paramod.c0100644000076400007640000002727307343604675015321 0ustar mccunemccune/* * paramod.c -- Paramodulation inference rules. * */ #include "header.h" /************* * * struct term *apply_substitute(t, into_term, into_subst, beta, from_subst) * * This routine is similar to apply, except that when it reaches the into * term, the appropriate instance of beta is returned. * *************/ static struct term *apply_substitute(struct term *t, struct term *into_term, struct context *into_subst, struct term *beta, struct context *from_subst, int *pos_vec, int *pi) { struct term *t2; struct rel *r1, *r2, *r3; if (t == into_term) return(apply(beta, from_subst)); else if (t->type != COMPLEX) { if (Flags[PARA_ALL].val == 0) { print_term_nl(stdout, t); abend("apply_substitute, term not COMPLEX."); } return(apply(t, into_subst)); } else { int i; t2 = get_term(); t2->type = COMPLEX; t2->sym_num = t->sym_num; r3 = NULL; for(r1 = t->farg, i = 1; r1; r1 = r1->narg, i++) { r2 = get_rel(); if (r3 == NULL) t2->farg = r2; else r3->narg = r2; /* if we are on the path to the into term || PARA_ALL */ if (r1->path || Flags[PARA_ALL].val) { if (*pi == MAX_FS_TERM_DEPTH) abend("apply_substitute: term too deep."); pos_vec[*pi] = i; (*pi)++; r2->argval = apply_substitute(r1->argval, into_term, into_subst, beta, from_subst, pos_vec, pi); } else r2->argval = apply(r1->argval, into_subst); r3 = r2; } return(t2); } } /* apply_substitute */ /************* * * struct clause *build_bin_para(alpha, from_subst, into_term, into_lit, into_subst) * * Construct a binary paramodulant. * *************/ static struct clause *build_bin_para(struct term *alpha, struct context *from_subst, struct term *into_term, struct literal *into_lit, struct context *into_subst, int *pos_vec, int *pi) { struct clause *paramodulant; struct literal *lit, *new, *prev; struct term *from_atom, *beta; struct ilist *ip0, *ip1, *ip2; int i; paramodulant = get_clause(); prev = NULL; from_atom = alpha->occ.rel->argof; /* find beta */ if (from_atom->farg->argval == alpha) beta = from_atom->farg->narg->argval; /* beta is second arg */ else beta = from_atom->farg->argval; /* beta is first arg */ *pi = 1; /* go through literals of into clause */ for (lit = into_lit->container->first_lit, i = 1; lit; lit = lit->next_lit, i++) { new = get_literal(); new->container = paramodulant; if (prev == NULL) paramodulant->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; if (lit == into_lit || Flags[PARA_ALL].val) { pos_vec[0] = i; new->atom = apply_substitute(lit->atom, into_term, into_subst, beta, from_subst, pos_vec, pi); } else new->atom = apply(lit->atom, into_subst); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ } /* go through literals of from clause */ for (lit = from_atom->occ.lit->container->first_lit; lit; lit = lit->next_lit) { if (lit->atom != from_atom) { /* omit instance of from literal */ new = get_literal(); new->container = paramodulant; if (paramodulant->first_lit == NULL) paramodulant->first_lit = new; else prev->next_lit = new; prev = new; new->sign = lit->sign; new->atom = apply(lit->atom, from_subst); new->atom->occ.lit = new; new->atom->varnum = lit->atom->varnum; /* copy type of atom */ } } ip0 = get_ilist(); /* rule and parents: to be filled in by caller */ ip1 = get_ilist(); ip2 = get_ilist(); ip0->next = ip1; ip1->next = ip2; paramodulant->parents = ip0; return(paramodulant); } /* build_bin_para */ /************* * * insert_detailed_para_history() * *************/ static void insert_detailed_para_history(struct ilist *ip_from, struct ilist *ip_into, struct term *alpha, int *pos_vec, int pos_vec_size) { struct ilist *ip2, *ip3, *ip4; int i; /* Insert position of into term */ ip2 = get_ilist(); ip2->i = LIST_RULE - pos_vec_size; ip4 = ip_into->next; ip_into->next = ip2; for (i = 0; i < pos_vec_size; i++) { ip3 = get_ilist(); ip3->i = pos_vec[i]; ip2->next = ip3; ip2 = ip3; } ip2->next = ip4; /* Insert position of alpha. */ ip2 = get_ilist(); ip3 = get_ilist(); ip4 = get_ilist(); ip2->next = ip3; ip3->next = ip4; ip2->i = LIST_RULE - 2; ip3->i = literal_number(alpha->occ.rel->argof->occ.lit); ip4->i = (alpha->occ.rel->argof->farg->argval == alpha ? 1 : 2); ip4->next = ip_from->next; ip_from->next = ip2; } /* insert_detailed_para_history */ /************* * * para_from_up(t, into_term, into_subst, alpha, from_subst) * * We are paramodulating from the given clause, and a clashable into term * has been found. This routine recursively goes through the clashable * superterms of the into term. * *************/ static void para_from_up(struct term *t, struct term *into_term, struct context *into_subst, struct term *alpha, struct context *from_subst) { struct clause *paramodulant, *from_parent; struct rel *r; struct ilist *ip; int pos_vec[MAX_FS_TERM_DEPTH]; int pos_vec_size; from_parent = alpha->occ.rel->argof->occ.lit->container; if (t->type == COMPLEX && t->varnum != 0) { /* it's an atom */ if (Flags[PARA_INTO_UNITS_ONLY].val == 0 || unit_clause(t->occ.lit->container)) { paramodulant = build_bin_para(alpha, from_subst, into_term, t->occ.lit, into_subst, pos_vec, &pos_vec_size); /* fill in derivation info */ ip = paramodulant->parents; ip->i = PARA_FROM_RULE; ip->next->i = from_parent->id; ip->next->next->i = t->occ.lit->container->id; if (Flags[DETAILED_HISTORY].val) { insert_detailed_para_history(ip->next, ip->next->next, alpha, pos_vec, pos_vec_size); } Stats[CL_GENERATED]++; Stats[PARA_FROM_GEN]++; if (heat_is_on()) paramodulant->heat_level = from_parent->heat_level + 1; CLOCK_STOP(PARA_FROM_TIME); pre_process(paramodulant, 0, Sos); CLOCK_START(PARA_FROM_TIME); } } else { r = t->occ.rel; while (r != NULL) { if (r->clashable) { r->path = 1; /* mark path from into_term up to atom */ para_from_up(r->argof, into_term, into_subst, alpha, from_subst); r->path = 0; /* remove mark */ } r = r->nocc; } } } /* para_from_up */ /************* * * para_from_alpha(alpha) * * We are paramodulating from the given clause. This routine * paramodulates from an alpha. * *************/ static void para_from_alpha(struct term *alpha) { struct context *into_subst, *from_subst; struct term *into_term; struct fpa_tree *ut; struct trail *tr; into_subst = get_context(); into_subst->multiplier = 0; from_subst = get_context(); from_subst->multiplier = 1; if (alpha->type == VARIABLE && Flags[PARA_FROM_VARS].val == 0) ; /* do nothing */ else { if (alpha->type == VARIABLE) ut = build_for_all(Fpa_clash_terms); /* get all terms in index */ else ut = build_tree(alpha, UNIFY, Parms[FPA_TERMS].val, Fpa_clash_terms); into_term = next_term(ut, 0); while (into_term != NULL) { tr = NULL; if (unify(into_term, into_subst, alpha, from_subst, &tr)) { para_from_up(into_term, into_term, into_subst, alpha, from_subst); clear_subst_1(tr); } into_term = next_term(ut, 0); } } free_context(into_subst); free_context(from_subst); } /* para_from_alpha */ /************* * * para_from(giv_cl) -- binary paramodulation from the given clause * * Paramodulants are given to the routine pre_process. * *************/ void para_from(struct clause *giv_cl) { struct literal *from_lit; struct term *atom; CLOCK_START(PARA_FROM_TIME); if (!Flags[PARA_FROM_UNITS_ONLY].val || unit_clause(giv_cl)) { from_lit = giv_cl->first_lit; while (from_lit) { atom = from_lit->atom; if (pos_eq_lit(from_lit) && !term_ident(atom->farg->argval, atom->farg->narg->argval)) { if (Flags[PARA_FROM_LEFT].val) para_from_alpha(atom->farg->argval); if (Flags[PARA_FROM_RIGHT].val) para_from_alpha(atom->farg->narg->argval); } from_lit = from_lit->next_lit; } } CLOCK_STOP(PARA_FROM_TIME); } /* para_from */ /************* * * para_into_terms(t, into_lit, from_subst, into_subst) * * We are paramodulating into the given clause. This routine recursively * goes through the clashable subterms of the given literal. * *************/ static void para_into_terms(struct term *into_term, struct literal *into_lit, struct context *from_subst, struct context *into_subst) { struct term *alpha; struct trail *tr; struct fpa_tree *ut; struct clause *paramodulant; struct rel *r; struct ilist *ip; int pos_vec[MAX_FS_TERM_DEPTH]; int pos_vec_size; if (into_term->type == COMPLEX) { r = into_term->farg; while (r != NULL) { if (r->clashable) { r->path = 1; /* mark path to into term */ para_into_terms(r->argval, into_lit, from_subst, into_subst); r->path = 0; /* remove mark */ } r = r->narg; } } /* no need to check if variable and `no para into vars' */ /* because the clashability flag handles it */ if (into_term->type == VARIABLE) ut = build_for_all(Fpa_alphas); /* get all terms in index */ else ut = build_tree(into_term, UNIFY, Parms[FPA_TERMS].val, Fpa_alphas); alpha = next_term(ut, 0); while (alpha != NULL) { tr = NULL; if (unify(into_term, into_subst, alpha, from_subst, &tr)) { paramodulant = build_bin_para(alpha, from_subst, into_term, into_lit, into_subst, pos_vec, &pos_vec_size); /* fill in derivation info */ ip = paramodulant->parents; ip->i = PARA_INTO_RULE; ip->next->i = into_lit->container->id; ip->next->next->i = alpha->occ.rel->argof->occ.lit->container->id; if (Flags[DETAILED_HISTORY].val) { insert_detailed_para_history(ip->next->next, ip->next, alpha, pos_vec, pos_vec_size); } clear_subst_1(tr); Stats[CL_GENERATED]++; Stats[PARA_INTO_GEN]++; if (heat_is_on()) paramodulant->heat_level = into_lit->container->heat_level + 1; CLOCK_STOP(PARA_INTO_TIME); pre_process(paramodulant, 0, Sos); CLOCK_START(PARA_INTO_TIME); } alpha = next_term(ut, 0); } } /* para_into_terms */ /************* * * para_into(giv_cl) -- binary paramodulation into the given clause * * Paramodulants are given to the routine pre_process. * *************/ void para_into(struct clause *giv_cl) { struct literal *into_lit; struct context *into_subst, *from_subst; struct rel *r; CLOCK_START(PARA_INTO_TIME); if (!Flags[PARA_INTO_UNITS_ONLY].val || unit_clause(giv_cl)) { /* Substitutions are allocated here instead of in */ /* para_into_terms to save procedure calls. */ into_subst = get_context(); into_subst->multiplier = 0; from_subst = get_context(); from_subst->multiplier = 1; into_lit = giv_cl->first_lit; while (into_lit != NULL) { if (into_lit->atom->varnum != ANSWER) { /* if not answer literal */ r = into_lit->atom->farg; while (r != NULL) { if (r->clashable) { r->path = 1; /* mark path to into term */ para_into_terms(r->argval, into_lit, from_subst, into_subst); r->path = 0; /* remove mark */ } r = r->narg; } } into_lit = into_lit->next_lit; } free_context(into_subst); free_context(from_subst); } CLOCK_STOP(PARA_INTO_TIME); } /* para_into */ otter-3.3f/source/cos.h0100644000076400007640000003344510103511130014430 0ustar mccunemccune/* * cos.h -- preprocessor definitions of indices for arrays of * flags, parameters, statistics, clocks, and internal flags. * */ /************* * * Flags are boolean valued options. To install a new flag, append * a new name and index to the end of this list, then insert code to * initialize it in the routine `init_options'. * Example access: if (Flags[PARA_FROM_LEFT].val) { * See routine `init_options' for defaults. * *************/ #define MAX_FLAGS 200 /* This must hold the following list! */ enum { SOS_QUEUE, /* pick first clause on sos as given clause */ SOS_STACK, /* pick last sos clause as given clause */ INPUT_SOS_FIRST, /* use input sos before generated sos */ INTERACTIVE_GIVEN, /* user selects given clause interactively */ PRINT_GIVEN, /* print given clauses */ PRINT_LISTS_AT_END, /* print clause lists at end of run */ BINARY_RES, /* binary resolution */ HYPER_RES, /* hyperresolution */ NEG_HYPER_RES, /* negatve hyperresolution inference rule */ UR_RES, /* UR-resolution */ PARA_INTO, /* `into' paramodulation inference rule */ PARA_FROM, /* `from' paramodulation inference rule */ DEMOD_INF, /* apply demodulation as an inference rule */ ORDER_HYPER, /* ordered hyperresolution (satellites) */ UNIT_RES, /* Unit resolution restriction */ UR_LAST, /* restrict UR: target literal is last */ PARA_FROM_LEFT, /* allow paramodulation from left sides */ PARA_FROM_RIGHT, /* allow paramodulation from right sides */ PARA_INTO_LEFT, /* allow paramodulation into left args of = */ PARA_INTO_RIGHT, /* allow paramodulation into right args of = */ PARA_FROM_VARS, /* allow paramodulation from variables */ PARA_INTO_VARS, /* allow paramodulation into variables */ PARA_FROM_UNITS_ONLY, /* from clause must be unit */ PARA_INTO_UNITS_ONLY, /* into clause must be unit */ PARA_SKIP_SKOLEM, /* Skolem function restriction strategy */ PARA_ONES_RULE, /* paramod only into first args of terms */ PARA_ALL, /* paramodulate all occurrences of into term */ DETAILED_HISTORY, /* store literal numbers and position vectors */ ORDER_HISTORY, /* Nucleus number first for hyper, UR. */ UNIT_DELETION, /* unit deletion processing */ BACK_UNIT_DELETION, /* like back demodulation, but for literals */ DELETE_IDENTICAL_NESTED_SKOLEM, /* delete clauses containing */ SORT_LITERALS, /* sort literals in pre_process */ FOR_SUB, /* forward subsumption */ BACK_SUB, /* back subsumption */ FACTOR, /* factor during post_process */ DEMOD_HISTORY, /* build history in demodulation */ ORDER_EQ, /* flip equalities (+ and -) if right arg heavier */ EQ_UNITS_BOTH_WAYS, /* nonoriented eq units both ways */ DEMOD_LINEAR, /* use linear search instead of index tree */ DEMOD_OUT_IN, /* demodulate outside-in, (leftmost) */ DYNAMIC_DEMOD, /* dynamic addition of demodulators */ DYNAMIC_DEMOD_ALL, /* try to make all equalities into demodulators */ DYNAMIC_DEMOD_LEX_DEP, /* allow lex-dep dynamic demodulators */ BACK_DEMOD, /* back demodulation */ ANL_EQ, /* meta-option for standard equational strategy */ KNUTH_BENDIX, /* Alias for ANL_EQ */ LRPO, /* lexicographic recursive path ordering */ LEX_ORDER_VARS, /* consider variables when lex_checking terms */ SYMBOL_ELIM, /* orient equalities to eliminate symbols */ REWRITER, /* meta-option for demodulation only */ CHECK_ARITY, /* require symbols to have fixed arities */ PROLOG_STYLE_VARIABLES, /* vars start with A-Z */ ECHO_INCLUDED_FILES, /* echo input from included files */ SIMPLIFY_FOL, /* attempt to simplify during cnf translation */ PROCESS_INPUT, /* process input usable and sos */ TPTP_EQ, /* for TPTP: "equal" is the one and only equality */ VERY_VERBOSE, /* print generated clauses */ PRINT_KEPT, /* print kept clauses */ PRINT_PROOFS, /* print all proofs found */ BUILD_PROOF_OBJECT, /* alias to build_proof_object_1 */ BUILD_PROOF_OBJECT_1, /* build proof to be checked elsewhere */ BUILD_PROOF_OBJECT_2, /* build new kind of proof object */ PRINT_NEW_DEMOD, /* print new demodultors */ PRINT_BACK_DEMOD, /* print back demodulated clauses */ PRINT_BACK_SUB, /* print back subsumed clauses */ DISPLAY_TERMS, /* print terms in internal format */ PRETTY_PRINT, /* Pretty print requested by Boyle */ BIRD_PRINT, /* output a(_,_) terms in combinatory logic notation */ INDEX_FOR_BACK_DEMOD, /* index (FPA) all terms for back demod */ FOR_SUB_FPA, /* forward subsump with FPA, not discrim. tree */ NO_FAPL, /* don't FPA index all positive literals */ NO_FANL, /* don't FPA index all negative literals */ /* misc 1 */ CONTROL_MEMORY, /* automatically adjust max_weight */ PROPOSITIONAL, /* some propositional optimizations */ REALLY_DELETE_CLAUSES, /* delete back demod and back_subed cls */ ATOM_WT_MAX_ARGS, /* weight of atom is max of weights of arguments */ TERM_WT_MAX_ARGS, /* weight of term is max of weights of arguments */ FREE_ALL_MEM, /* free all memory to avail lists at end of run */ /*********************** Fringe ******************************/ KEEP_HINT_SUBSUMERS, /* do not delete if it subsumes a hint */ KEEP_HINT_EQUIVALENTS, /* see hint_keep_test() */ PRINT_PROOF_AS_HINTS, /* constructd from proof object */ DEGRADE_HINTS2, /* Bob's Hint degradation */ INPUT_SEQUENT, /* input clauses in sequent notation */ OUTPUT_SEQUENT, /* output clauses in sequent notation */ SIGINT_INTERACT, /* interact on SIGINT */ ANCESTOR_SUBSUME, /* ancestor subsumption */ AUTO, /* select the current AUTO mode (see AUTO*) (sets auto1) */ AUTO1, /* original AUTO mode (3.0.4) */ AUTO2, /* revised AUTO mode (3.0.5) */ GEOMETRIC_RULE, /* RP's inference rule, with unification */ GEOMETRIC_REWRITE_BEFORE, /* RP's inference rule as a rewrite */ GEOMETRIC_REWRITE_AFTER, /* RP's inference rule as a rewrite */ GL_DEMOD, /* Delay demodulation. */ SPLIT_CLAUSE, /* case splitting with fork */ SPLIT_WHEN_GIVEN, /* Split clauses when given */ SPLIT_ATOM, /* Split on atoms instead of clauses */ SPLIT_POS, /* Split on positive clauses only */ SPLIT_NEG, /* Split on negatvie clauses only */ SPLIT_NONHORN, /* Split on negatvie clauses only */ SPLIT_MIN_MAX, /* Split on clause with min max-literal */ SPLIT_POPULAR, /* Split on most popular atoms */ LINKED_UR_RES, /* linked UR resolution inference rule */ LINKED_UR_TRACE, /* trace linked UR res inference rule */ LINKED_SUB_UNIT_USABLE, /* use Usable list to subsume subsumable */ LINKED_SUB_UNIT_SOS, /* use Sos list to subsume subsumable */ LINKED_UNIT_DEL, /* use Unit Deletion during linked UR resolution. */ LINKED_TARGET_ALL, /* If set, all literals are targets. */ LINKED_HYPER_RES, /* Linked hyper inference rule */ /* not documented */ FOR_SUB_EQUIVALENTS_ONLY, /* forward subsumption iff equivalent */ PROOF_WEIGHT, /* Calculate proof weight (ancestor bag). */ FORMULA_HISTORY, /* Make input clauses point at formula parent */ BELL, /* Ring the bell for important events? */ DISCARD_COMMUTATIVITY_CONSEQUENCES, /* experimental */ LITERALS_WEIGH_ONE, HYPER_SYMMETRY_KLUDGE, /* secret flag */ DISCARD_NON_ORIENTABLE_EQ, /* secret flag */ DISCARD_XX_RESOLVABLE, /* secret flag */ LOG_FOR_X_SHOW, /* log some events for X display */ PICK_DIFF_SIM, /* selection of given clause */ PICK_RANDOM_LIGHTEST, /* selection of given clause */ PICK_LAST_LIGHTEST, /* selection of given clause */ PICK_MID_LIGHTEST, /* selection of given clause */ MULTI_JUST, /* for proof-shortening experiment */ MULTI_JUST_LESS, /* for proof-shortening experiment */ MULTI_JUST_SHORTER, /* for proof-shortening experiment */ PROG_SYNTHESIS, /* program synthesis mode */ CLOCKS /* detailed timing */ }; /* end of Flags */ /************* * * Parms are integer valued options. To install a new parm, append * a new name and index to the end of this list, then insert code to * initialize it in the routine `init_options'. * Example access: if (Parms[FPA_LITERALS].val == 4) { * See routine `init_options' for defaults. * *************/ #define MAX_PARMS 100 /* This must hold the following list! */ enum { REPORT, /* output stats and times every n seconds */ MAX_SECONDS, /* stop search after this many seconds */ MAX_GEN, /* stop search after this many generated clauses */ MAX_KEPT, /* stop search after this many kept clauses */ MAX_GIVEN, /* stop search after this many given clauses */ MAX_LEVELS, /* with sos_queue, stop after this many levels */ MAX_MEM, /* stop search after this many K bytes allocated */ MAX_LITERALS, /* max # of lits in kept clause (0 -> no limit) */ MAX_WEIGHT, /* maximum weight of kept clauses */ MAX_DISTINCT_VARS, /* max # of variables in kept clause */ MAX_ANSWERS, /* maximum number of answer literals */ FPA_LITERALS, /* FPA indexing depth for literals */ FPA_TERMS, /* FPA indexing depth for terms */ PICK_GIVEN_RATIO, /* pick lightest n times, then pick first */ AGE_FACTOR, /* to adjust the pick-given weight */ DISTINCT_VARS_FACTOR, /* to adjust the pick-given weight */ INTERRUPT_GIVEN, /* call interact after this many given cls */ DEMOD_LIMIT, /* Limit on number of rewrites per clause */ MAX_PROOFS, /* stop search after this many empty clauses */ MIN_BIT_WIDTH, /* minimum field for bit strings */ NEG_WEIGHT, /* add this value to wight of negative literals */ PRETTY_PRINT_INDENT, /* indent for pretty print */ STATS_LEVEL, /* higher stats_level -> output more statistics */ DYNAMIC_DEMOD_DEPTH, /* deciding dynamic demoulators (ad hoc) */ DYNAMIC_DEMOD_RHS, /* deciding dynamic demoulators (ad hoc) */ FSUB_HINT_ADD_WT, /* add to pick-given wt */ BSUB_HINT_ADD_WT, /* add to pick-given wt */ EQUIV_HINT_ADD_WT, /* add to pick-given wt */ FSUB_HINT_WT, /* pick-given wt */ BSUB_HINT_WT, /* pick-given wt */ EQUIV_HINT_WT, /* pick-given wt */ /* fringe */ CHANGE_LIMIT_AFTER, /* replace reduce_weight_limit */ NEW_MAX_WEIGHT, /* replace reduce_weight_limit */ GEO_GIVEN_RATIO, /* like pick_given_ratio, for geo children */ DEBUG_FIRST, /* turn debugging on */ DEBUG_LAST, /* turn debugging off */ VERBOSE_DEMOD_SKIP, /* debugging option */ HEAT, /* maximum heat level */ DYNAMIC_HEAT_WEIGHT, /* max weigth of dynamic hot clause */ MAX_UR_DEPTH, /* max depth for linked UR (normal depth = 0) */ MAX_UR_DEDUCTION_SIZE, /* max resolutions in a single linked UR */ SPLIT_SECONDS, /* time to search before splitting */ SPLIT_GIVEN, /* given clauses before splitting */ SPLIT_DEPTH, /* maximum splitting depth */ /* not documented */ NEW_SYMBOL_LEX_POSITION, WARN_MEM, /* reset max_weight at this memory usage */ WARN_MEM_MAX_WEIGHT, /* new max_weight */ PICK_DIFF, /* selection of given clause */ PICK_DIFF_RANGE, /* selection of given clause */ MULTI_JUST_MAX /* for proof-shortening experiment */ }; /* end of Parms */ /************* * * Statistics. To install a new statistic, append a new name and index * to the end of this list, then insert the code to output it in the * routine `print_stats'. * Example access: Stats[INPUT_ERRORS]++; * *************/ #define MAX_STATS 50 /* This must hold the following list! */ enum { INPUT_ERRORS, CL_INPUT, CL_GENERATED, CL_KEPT, CL_FOR_SUB, CL_BACK_SUB, CL_TAUTOLOGY, CL_GIVEN, CL_WT_DELETE, REWRITES, UNIT_DELETES, EMPTY_CLAUSES, FPA_OVERLOADS, /* not output if 0 */ FPA_UNDERLOADS, /* not output if 0 */ CL_VAR_DELETES, /* not output if 0 */ FOR_SUB_SOS, NEW_DEMODS, CL_BACK_DEMOD, LINKED_UR_DEPTH_HITS, LINKED_UR_DED_HITS, SOS_SIZE, K_MALLOCED, CL_NOT_ANC_SUBSUMED, USABLE_SIZE, DEMODULATORS_SIZE, DEMOD_LIMITS, /* not output if 0 */ INIT_WALL_SECONDS, BINARY_RES_GEN, HYPER_RES_GEN, NEG_HYPER_RES_GEN, UR_RES_GEN, PARA_INTO_GEN, PARA_FROM_GEN, LINKED_UR_RES_GEN, GEO_GEN, DEMOD_INF_GEN, FACTOR_GEN, HOT_GENERATED, HOT_KEPT, FACTOR_SIMPLIFICATIONS, HOT_SIZE, PASSIVE_SIZE, BACK_UNIT_DEL_GEN }; /* end of Stats */ /************* * * Clocks. To install a new clock, append a new name and index * to the end of this list, then insert the code to output it in the * routine `print_times'. Example of use: CLOCK_START(INPUT_TIME), * CLOCK_STOP(INPUT_TIME), micro_sec = clock_val(INPUT_TIME);. * See files macros.h and clocks.c. * *************/ #define MAX_CLOCKS 50 /* This must hold the following list! */ enum { INPUT_TIME, CLAUSIFY_TIME, PROCESS_INPUT_TIME, BINARY_TIME, HYPER_TIME, NEG_HYPER_TIME, UR_TIME, PARA_INTO_TIME, PARA_FROM_TIME, LINKED_UR_TIME, PRE_PROC_TIME, RENUMBER_TIME, DEMOD_TIME, ORDER_EQ_TIME, UNIT_DEL_TIME, WEIGH_CL_TIME, SORT_LITS_TIME, FOR_SUB_TIME, DEL_CL_TIME, KEEP_CL_TIME, PRINT_CL_TIME, CONFLICT_TIME, NEW_DEMOD_TIME, POST_PROC_TIME, BACK_DEMOD_TIME, BACK_SUB_TIME, FACTOR_TIME, UN_INDEX_TIME, HOT_TIME, FACTOR_SIMP_TIME, HINTS_TIME, HINTS_KEEP_TIME, BACK_UNIT_DEL_TIME, PICK_GIVEN_TIME }; /* end of Clocks */ /************* * * internal flags--invisible to users * *************/ #define MAX_INTERNAL_FLAGS 10 /* This must hold the following list! */ enum { SPECIAL_UNARY_PRESENT, DOLLAR_PRESENT, LEX_VALS_SET, REALLY_CHECK_ARITY, FOREACH_SOS, HINTS_PRESENT, HINTS2_PRESENT }; /************* * * clause attributes * *************/ /* attribute types */ enum { INT_ATTR, BOOL_ATTR, DOUBLE_ATTR, STRING_ATTR, TERM_ATTR }; /* attributes */ #define MAX_ATTRIBUTES 20 /* This must hold the following list! */ enum { BSUB_HINT_WT_ATTR, FSUB_HINT_WT_ATTR, EQUIV_HINT_WT_ATTR, BSUB_HINT_ADD_WT_ATTR, FSUB_HINT_ADD_WT_ATTR, EQUIV_HINT_ADD_WT_ATTR, LABEL_ATTR }; otter-3.3f/source/clause.c0100644000076400007640000022337107713552752015146 0ustar mccunemccune/* * clause.c -- This file has routines associated with the clause data type. * */ #include "header.h" #define CLAUSE_TAB_SIZE 3793 /* hash table for accessing clauses by ID */ static struct clause_ptr *Clause_tab[CLAUSE_TAB_SIZE]; /* clause ID counter */ static int Clause_id_count; /* back subsumed, demodulated put here, not deleted */ static struct clause *Hidden_clauses; /* array to mark mapped literals during subsumption */ #define MAX_LITS 100 static char Map_array[MAX_LITS]; /************* * * reset_clause_counter() * *************/ void reset_clause_counter(void) { Clause_id_count = 0; } /* reset_clause_counter */ /************* * * int next_cl_num() * * What is the next clause number? Do not increment the count. * *************/ int next_cl_num(void) { return(Clause_id_count + 1); } /* next_cl_num */ /************* * * assign_cl_id() * * Assign a unique clause identifier and insert into the clause table. * *************/ void assign_cl_id(struct clause *c) { c->id = ++Clause_id_count; cl_insert_tab(c); /* Turn debugging mode on when DEBUG_FIRST - 1 is assigned. */ if ( (c->id == (Parms[DEBUG_FIRST].val - 1)) && !Flags[VERY_VERBOSE].val) { Flags[VERY_VERBOSE].val = 1; fprintf(stdout, "\n\n***** Turn Debugging Mode ON *****\n\n"); } /* Turn debugging mode off when DEBUG_LAST + 1 is assigned. */ if ( (c->id == (Parms[DEBUG_LAST].val + 1)) && Flags[VERY_VERBOSE].val) { Flags[VERY_VERBOSE].val = 0; fprintf(stdout, "\n\n***** Turn Debugging Mode OFF *****\n\n"); } } /* assign_cl_id */ /************* * * hot_cl_integrate(c) * * Integrate a hot-list clause. All this does is assign a clause ID. * The subterms are not put into the shared data structures, because * this interferes with the kludgy way I implemented hot-list inference. * In particular, hot paramoudlation from the new clause can't * handle going into hot-list clauses that are integrated in the * normal way. * *************/ void hot_cl_integrate(struct clause *c) { struct literal *lit; assign_cl_id(c); for (lit = c->first_lit; lit; lit = lit->next_lit) { set_up_pointers(lit->atom); lit->atom->occ.lit = lit; } } /* hot_cl_integrate */ /************* * * cl_integrate(c) -- integrate a clause * * This routine integrates most subterms of the atoms. (Incoming clause must * already have back pointers from literal to clause and atom to literal.) * * The atoms are not shared, and arguments of positive equality literals * are not shared. * * A clause is integrated iff its ID is > 0. * *************/ void cl_integrate(struct clause *c) { struct literal *lit; struct term *atom; struct rel *r, *r1; if (c->id != 0) { fprintf(stdout, "WARNING, cl_integrate gets clause with ID: "); print_clause(stdout, c); } else { if (multi_justifications()) { /* for proof-shortening experiment */ possibly_append_parents(c, c->parents); } assign_cl_id(c); lit = c->first_lit; while (lit) { atom = lit->atom; if (atom->varnum == POS_EQ || atom->varnum == LEX_DEP_DEMOD || atom->varnum == CONDITIONAL_DEMOD) { /* do not share (condition), alpha, beta */ r1 = atom->farg; while (r1) { /* for alpha and beta */ if (Flags[BACK_DEMOD].val) /* put it where back demod can find it */ bd_kludge_insert(r1->argval); if (r1->argval->type == COMPLEX) { r = r1->argval->farg; while (r) { r->argval = integrate_term(r->argval); r->argof = r1->argval; r->nocc = r->argval->occ.rel; r->argval->occ.rel = r; r = r->narg; } } r1->argof = atom; r1->argval->occ.rel = r1; r1 = r1->narg; } } else if (atom->type == COMPLEX) { r = atom->farg; while (r) { r->argval = integrate_term(r->argval); r->argof = atom; r->nocc = r->argval->occ.rel; r->argval->occ.rel = r; r = r->narg; } } lit = lit->next_lit; } } } /* cl_integrate */ /************* * * cl_del_int(c) -- deallocate an integrated clause. * *************/ void cl_del_int(struct clause *c) { struct literal *lit, *plit; struct rel *r, *r2, *pr, *r1; struct term *atom; struct ilist *ip1, *ip2; lit = c->first_lit; while (lit) { atom = lit->atom; if (atom->varnum == POS_EQ || atom->varnum == LEX_DEP_DEMOD || atom->varnum == CONDITIONAL_DEMOD) { /* (condition), alpha, beta not shared */ r1 = atom->farg; while(r1) { /* for alpha and beta */ if (Flags[BACK_DEMOD].val) bd_kludge_delete(r1->argval); /* back demod kludge */ r = r1->argval->farg; while (r) { r2 = r->argval->occ.rel; pr = NULL; while (r2 && r2 != r) { pr = r2; r2 = r2->nocc; } if (!r2) { print_clause(stdout, c); abend("cl_del_int, bad equality clause."); } if (pr) pr->nocc = r->nocc; else r->argval->occ.rel = r->nocc; if (!r->argval->occ.rel) disintegrate_term(r->argval); pr = r; r = r->narg; free_rel(pr); } free_term(r1->argval); /* alpha or beta */ pr = r1; r1 = r1->narg; free_rel(pr); } } else if (atom->type == COMPLEX) { r = atom->farg; while (r) { r2 = r->argval->occ.rel; pr = NULL; while (r2 && r2 != r) { pr = r2; r2 = r2->nocc; } if (!r2) { print_clause(stdout, c); abend("cl_del_int, bad clause."); } if (!pr) r->argval->occ.rel = r->nocc; else pr->nocc = r->nocc; if (!r->argval->occ.rel) disintegrate_term(r->argval); pr = r; r = r->narg; free_rel(pr); } } free_term(atom); plit = lit; lit = lit->next_lit; free_literal(plit); } ip1 = c->parents; while (ip1) { ip2 = ip1; ip1 = ip1->next; free_ilist(ip2); } cl_delete_tab(c); /* If there is other memory associated with clause, free it here */ delete_attributes(c); free_clause(c); } /* cl_del_int */ /************* * * cl_del_non(c) -- deallocate a nonintegrated clause. * *************/ void cl_del_non(struct clause *c) { struct literal *lit, *plit; struct ilist *ip1, *ip2; lit = c->first_lit; while (lit) { lit->atom->occ.lit = NULL; zap_term(lit->atom); plit = lit; lit = lit->next_lit; free_literal(plit); } ip1 = c->parents; while (ip1) { ip2 = ip1; ip1 = ip1->next; free_ilist(ip2); } /* If there is other memory associated with clause, free it here */ delete_attributes(c); free_clause(c); } /* cl_del_non */ /************* * * cl_int_chk(c) -- check structure of clause -- for debugging * *************/ void cl_int_chk(struct clause *c) { struct literal *lit; printf("checking clause, address:%p " , (void *) c); print_clause(stdout, c); lit = c->first_lit; while (lit) { printf(" literal, address:%p sign:%d type:%d; atom:", (void *) lit, lit->sign, lit->atom->varnum); print_term(stdout, lit->atom); printf("\n"); printf(" cont_cl:%p, atom container:%p\n", (void *) lit->container, (void *) lit->atom->occ.lit); lit = lit->next_lit; } } /* cl_int_chk */ /************* * * struct term *literals_to_term(l) * * Conver list of literals to right-associated "|" term. * *************/ static struct term *literals_to_term(struct literal *l) { struct term *t, *t1, *t2; struct rel *r1, *r2; if (l->sign) t1 = copy_term(l->atom); else { t1 = get_term(); r1 = get_rel(); t1->farg = r1; t1->type = COMPLEX; t1->sym_num = str_to_sn("-", 1); r1->argval = copy_term(l->atom); } if (l->next_lit) { t2 = literals_to_term(l->next_lit); t = get_term(); r1 = get_rel(); r2 = get_rel(); t->farg = r1; r1->narg = r2; r1->argval = t1; r2->argval = t2; t->type = COMPLEX; t->sym_num = str_to_sn("|", 2); } else t = t1; return(t); } /* literals_to_term */ /************* * * struct term *clause_to_term(c) * *************/ struct term *clause_to_term(struct clause *c) { struct term *t; if (c->first_lit) t = literals_to_term(c->first_lit); else { t = get_term(); t->type = NAME; t->sym_num = str_to_sn("$F", 0); } return(t); } /* clause_to_term */ /************* * * struct literal *term_to_literals(t, lits) * *************/ static struct literal *term_to_literals(struct term *t, struct literal *lits) { struct literal *l; if (!is_symbol(t, "|", 2)) { l = get_literal(); l->next_lit = lits; l->sign = !is_symbol(t, "-", 1); if (l->sign) l->atom = copy_term(t); else l->atom = copy_term(t->farg->argval); return(l); } else { l = term_to_literals(t->farg->narg->argval, lits); l = term_to_literals(t->farg->argval, l); return(l); } } /* term_to_literals */ /************* * * struct clause *term_to_clause(t) * * If error found, print message and return NULL. * *************/ struct clause *term_to_clause(struct term *t) { struct clause *c; struct literal *l; c = get_clause(); if (is_symbol(t, "#", 2)) { /* Right arg is attributes, left arg is clause. */ c->attributes = term_to_attributes(t->farg->narg->argval); if (!c->attributes) return(NULL); else t = t->farg->argval; } c->first_lit = term_to_literals(t, (struct literal *) NULL); for (l = c->first_lit; l; l = l->next_lit) { if (l->atom->type == VARIABLE) { fprintf(stdout, "\nERROR, clause contains variable literal:\n"); print_term(stdout, t); printf(".\n\n"); return(NULL); } else { l->container = c; l->atom->occ.lit = l; mark_literal(l); } } return(c); } /* term_to_clause */ /************* * * struct clause *read_sequent_clause(fp, retcd_ptr) * * retcd - 0: error (NULL returned) * 1: ok (NULL returned if EOF encountered) * * a,b,c->d,e,f. * ->d,e,f. * a,b,c->. * ->. * * This is really ugly, kludgey code. * *************/ struct clause *read_sequent_clause(FILE *fp, int *rcp) { struct clause *c; struct literal *l, *prev; struct rel *r1, *r2; char buf1[MAX_BUF+1]; char buf2[MAX_BUF+6]; int rc, i1, i2; struct term *hyps, *concs, *t; rc = read_buf(fp, buf1); if (rc == 0) { /* error */ *rcp = 0; return(NULL); } if (buf1[0] == '\0') { /* ok. EOF */ *rcp = 1; return(NULL); } /* Kludge - make it into a string readable by regular parser. */ /* "a,b,c->d,e,f" becomes "$Hyps(a,b,c)->$Concs(d,e,f)" */ /* "->d,e,f" becomes "$Hyps->$Concs(d,e,f)" */ /* "a,b,c->" becomes "$Hyps(a,b,c)->$Concs" */ /* "->" becomes "$Hyps->$Concs" */ i1 = 0; skip_white(buf1, &i1); /* first check for "end_of_list" */ if (initial_str("end_of_list", buf1+i1)) { i1 += 11; skip_white(buf1, &i1); if (buf1[i1] == '.') { t = get_term(); t->type = NAME; t->sym_num = str_to_sn("end_of_list", 0); c = get_clause(); l = get_literal(); c->first_lit = l; l->atom = t; *rcp = 1; return(c); } } /* now reset and start again */ i1 = 0; skip_white(buf1, &i1); i2 = 0; buf2[i2++] = '$'; buf2[i2++] = 'H'; buf2[i2++] = 'y'; buf2[i2++] = 'p'; buf2[i2++] = 's'; if (buf1[i1] != '-' || buf1[i1+1] != '>') { /* Hyps not empty */ buf2[i2++] = '('; while (buf1[i1] != '-' || buf1[i1+1] != '>') { if (buf1[i1] == '.') { fprintf(stdout, "\nERROR, arrow not found in sequent:\n"); print_error(stdout, buf1, i1); *rcp = 0; return(NULL); } buf2[i2++] = buf1[i1++]; } buf2[i2++] = ')'; } buf2[i2++] = '-'; buf2[i2++] = '>'; buf2[i2++] = '$'; buf2[i2++] = 'C'; buf2[i2++] = 'o'; buf2[i2++] = 'n'; buf2[i2++] = 'c'; buf2[i2++] = 's'; i1 += 2; /* skip over "->" */ skip_white(buf1, &i1); if (buf1[i1] != '.') { /* concs not empty */ buf2[i2++] = '('; while (buf1[i1] != '.') { buf2[i2++] = buf1[i1++]; } buf2[i2++] = ')'; } buf2[i2++] = '.'; buf2[i2++] = '\0'; #if 0 printf("before: %s\n", buf1); printf("after: %s\n", buf2); #endif i2 = 0; t = str_to_term(buf2, &i2, 0); if (!t) { *rcp = 0; return(NULL); } else { skip_white(buf2, &i2); if (buf2[i2] != '.') { fprintf(stdout, "\nERROR, text after term:\n"); print_error(stdout, buf2, i2); *rcp = 0; return(NULL); } } t = term_fixup(t); if (!set_vars(t)) { fprintf(stdout, "\nERROR, input clause contains too many variables:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); *rcp = 0; return(NULL); /* error */ } else if (contains_skolem_symbol(t)) { fprintf(stdout, "\nERROR, input clause contains Skolem symbol:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); *rcp = 0; return(NULL); /* error */ } hyps = t->farg->argval; concs = t->farg->narg->argval; free_rel(t->farg->narg); free_rel(t->farg); free_term(t); /* ok, now we have hypotheses and conclusion */ c = get_clause(); r1 = hyps->farg; prev = NULL; while (r1) { l = get_literal(); if (prev) prev->next_lit = l; else c->first_lit = l; prev = l; l->sign = 0; l->atom = r1->argval; r2 = r1; r1 = r1->narg; free_rel(r2); } free_term(hyps); r1 = concs->farg; while (r1) { l = get_literal(); if (prev) prev->next_lit = l; else c->first_lit = l; prev = l; l->sign = 1; l->atom = r1->argval; r2 = r1; r1 = r1->narg; free_rel(r2); } free_term(concs); for (l = c->first_lit; l; l = l->next_lit) { l->container = c; l->atom->occ.lit = l; mark_literal(l); if (contains_skolem_symbol(l->atom)) { fprintf(stdout,"\nERROR, input literal contains Skolem symbol:\n"); print_term(stdout, l->atom); printf(".\n\n"); *rcp = 0; return(NULL); } } *rcp = 1; return(c); } /* read_sequent_clause */ /************* * * struct clause *read_clause(fp, retcd_ptr) * * retcd - 0: error (NULL returned) * 1: ok (NULL returned if EOF encountered) * *************/ struct clause *read_clause(FILE *fp, int *rcp) { struct term *t; struct clause *cl; int rc; if (Flags[INPUT_SEQUENT].val) return(read_sequent_clause(fp, rcp)); t = read_term(fp, &rc); if (!rc) { *rcp = 0; return(NULL); /* error reading term */ } else if (!t) { *rcp = 1; return(NULL); /* EOF */ } else if (!set_vars(t)) { fprintf(stdout, "\nERROR, input clause contains too many variables:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); *rcp = 0; return(NULL); /* error */ } else if (contains_skolem_symbol(t)) { fprintf(stdout, "\nERROR, input clause contains Skolem symbol:\n"); print_term(stdout, t); printf(".\n\n"); zap_term(t); *rcp = 0; return(NULL); /* error */ } else { cl = term_to_clause(t); zap_term(t); if (cl) *rcp = 1; else *rcp = 0; /* error */ return(cl); } } /* read_clause */ /************* * * struct list *read_cl_list(fp, errors_ptr) * * Read clauses until EOF or the term `end_of_list' is reached. * *************/ struct list *read_cl_list(FILE *fp, int *ep) { struct list *lst; struct clause *cl, *pcl; int rc; Internal_flags[REALLY_CHECK_ARITY] = 1; *ep = 0; lst = get_list(); pcl = NULL; cl = read_clause(fp, &rc); while (rc == 0) { /* while errors */ (*ep)++; cl = read_clause(fp, &rc); } while (cl && !(cl->first_lit && is_symbol(cl->first_lit->atom, "end_of_list", 0))) { if (!pcl) lst->first_cl = cl; else pcl->next_cl = cl; cl->prev_cl = pcl; cl->container = lst; pcl = cl; cl = read_clause(fp, &rc); while (rc == 0) { /* while errors */ (*ep)++; cl = read_clause(fp, &rc); } } if (cl) cl_del_non(cl); /* "end_of_list" term */ lst->last_cl = pcl; Internal_flags[REALLY_CHECK_ARITY] = 0; return(lst); } /* read_cl_list */ /************* * * int set_vars_cl(cl) -- decide which terms are variables * *************/ int set_vars_cl(struct clause *cl) { struct literal *lit; char *varnames[MAX_VARS]; int i; for (i=0; ifirst_lit; while (lit) { if (set_vars_term(lit->atom, varnames)) lit = lit->next_lit; else return(0); } return(1); } /* set_vars_cl */ /************* * * print_sequent_clause() * * Clause number and parents have already been printed. * *************/ void print_sequent_clause(FILE *fp, struct clause *c) { struct literal *l; int first; for (l = c->first_lit, first = 1; l; l = l->next_lit) { if (!l->sign) { if (!first) fprintf(fp, ", "); print_term(fp, l->atom); first = 0; } } fprintf(fp, " -> "); for (l = c->first_lit, first = 1; l; l = l->next_lit) { if (l->sign) { if (!first) fprintf(fp, ", "); print_term(fp, l->atom); first = 0; } } } /* print_sequent_clause */ /************* * * print_justification(fp, clause) * *************/ void print_justification(FILE *fp, struct ilist *just) { struct ilist *ip; fprintf(fp,"["); for (ip = just; ip; ip = ip->next) { if (ip->i <= LIST_RULE) { /* LIST_RULE is a large negative number. If ip->i is less than LIST_RULE, then a list of length LIST_RULE-ip->i follows. */ int i; int j = LIST_RULE - ip->i; for (i = 1; i <= j; i++) { ip = ip->next; fprintf(fp, ".%d", ip->i); } } else { if (ip != just) fprintf(fp, ","); switch (ip->i) { case BINARY_RES_RULE : fprintf(fp, "binary"); break; case HYPER_RES_RULE : fprintf(fp, "hyper"); break; case NEG_HYPER_RES_RULE : fprintf(fp, "neg_hyper"); break; case UR_RES_RULE : fprintf(fp, "ur"); break; case PARA_INTO_RULE : fprintf(fp, "para_into"); break; case PARA_FROM_RULE : fprintf(fp, "para_from"); break; case FACTOR_RULE : fprintf(fp, "factor"); break; case FACTOR_SIMP_RULE : fprintf(fp, "factor_simp"); break; case NEW_DEMOD_RULE : fprintf(fp, "new_demod"); break; case BACK_DEMOD_RULE : fprintf(fp, "back_demod"); break; case DEMOD_RULE : fprintf(fp, "demod"); break; case UNIT_DEL_RULE : fprintf(fp, "unit_del"); break; case LINKED_UR_RES_RULE : fprintf(fp, "linked_ur"); break; case EVAL_RULE : fprintf(fp, "eval"); break; case GEO_ID_RULE : fprintf(fp, "gL-id"); break; case GEO_RULE : fprintf(fp, "gL"); break; case COPY_RULE : fprintf(fp, "copy"); break; case FLIP_EQ_RULE : fprintf(fp, "flip"); break; case CLAUSIFY_RULE : fprintf(fp, "clausify"); break; case BACK_UNIT_DEL_RULE : fprintf(fp, "back_unit_del"); break; case SPLIT_RULE : fprintf(fp, "split"); break; case SPLIT_NEG_RULE : fprintf(fp, "split_neg"); break; case PROPOSITIONAL_RULE : fprintf(fp, "propositional"); break; default : fprintf(fp, "%d", ip->i); break; } } } fprintf(fp, "]"); } /* print_justification */ /************* * * print_clause_bare(fp, clause) * * No ID, justification, period, or newline. * *************/ void print_clause_bare(FILE *fp, struct clause *cl) { struct term *t = clause_to_term(cl); t = term_fixup_2(t); /* Change -(=(a,b)) to !=(a,b). */ print_term(fp, t); zap_term(t); } /* print_clause_bare */ /************* * * print_clause(fp, clause) * *************/ void print_clause(FILE *fp, struct clause *cl) { struct literal *lit; struct term *t; fprintf(fp, "%d ", cl->id); if (cl->heat_level > 0) fprintf(fp, "(heat=%d) ", (int) (cl->heat_level)); if (! multi_justifications()) { print_justification(fp, cl->parents); fprintf(fp, " "); } else { if (cl->multi_parents == NULL) fprintf(fp, " [] "); else { struct g2list *p; for (p = cl->multi_parents; p != NULL; p = p->next) { if (p == cl->multi_parents) fprintf(fp, " "); else fprintf(fp, "\n "); print_justification(fp, p->v1); } fprintf(fp, " "); } } if (Flags[PRETTY_PRINT].val) { int parens; fprintf(fp, "\n"); lit = cl->first_lit; while (lit) { parens = !lit->sign && sn_to_node(lit->atom->sym_num)->special_op; if (!lit->sign) fprintf(fp, "-"); if (parens) fprintf(fp, "("); pretty_print_term(fp, lit->atom, 0); if (parens) fprintf(fp, ")"); lit = lit->next_lit; if (lit) fprintf(fp, " |\n"); } } else if (Flags[OUTPUT_SEQUENT].val) { print_sequent_clause(fp, cl); } else { #if 0 struct rel *r; lit = cl->first_lit; while (lit) { if (!lit->sign) { /* This is so that lit gets correctly parenthesized. */ t = get_term(); r = get_rel(); t->farg = r; t->type = COMPLEX; r->argval = lit->atom; t->sym_num = str_to_sn("-", 1); print_term(fp, t); free_rel(r); free_term(t); } else print_term(fp, lit->atom); lit = lit->next_lit; if (lit) fprintf(fp, " | "); } #else t = clause_to_term(cl); t = term_fixup_2(t); /* Change -(=(a,b)) to !=(a,b). */ print_term(fp, t); zap_term(t); #endif } if (cl->attributes) print_attributes(fp, cl->attributes); fprintf(fp, ".\n"); } /* print_clause */ /************* * * print_clause_without_just(fp, clause) * *************/ void print_clause_without_just(FILE *fp, struct clause *cl) { struct literal *lit; struct term *t; fprintf(fp, "%d ", cl->id); if (cl->heat_level > 0) fprintf(fp, "(heat=%d) ", (int) (cl->heat_level)); if (Flags[PRETTY_PRINT].val) { int parens; fprintf(fp, "\n"); lit = cl->first_lit; while (lit) { parens = !lit->sign && sn_to_node(lit->atom->sym_num)->special_op; if (!lit->sign) fprintf(fp, "-"); if (parens) fprintf(fp, "("); pretty_print_term(fp, lit->atom, 0); if (parens) fprintf(fp, ")"); lit = lit->next_lit; if (lit) fprintf(fp, " |\n"); } } else if (Flags[OUTPUT_SEQUENT].val) { print_sequent_clause(fp, cl); } else { #if 0 struct rel *r; lit = cl->first_lit; while (lit) { if (!lit->sign) { /* This is so that lit gets correctly parenthesized. */ t = get_term(); r = get_rel(); t->farg = r; t->type = COMPLEX; r->argval = lit->atom; t->sym_num = str_to_sn("-", 1); print_term(fp, t); free_rel(r); free_term(t); } else print_term(fp, lit->atom); lit = lit->next_lit; if (lit) fprintf(fp, " | "); } #else t = clause_to_term(cl); t = term_fixup_2(t); /* Change -(=(a,b)) to !=(a,b). */ print_term(fp, t); zap_term(t); #endif } if (cl->attributes) print_attributes(fp, cl->attributes); fprintf(fp, ".\n"); } /* print_clause_without_just */ /************* * * p_clause(clause) * *************/ void p_clause(struct clause *cl) { print_clause(stdout, cl); } /* p_clause */ /************* * * print_cl_list(fp, lst) * *************/ void print_cl_list(FILE *fp, struct list *lst) { struct clause *cl; if (!lst) fprintf(fp, "(list nil)\n"); else { cl = lst->first_cl; while (cl) { print_clause(fp, cl); cl = cl->next_cl; } fprintf(fp, "end_of_list.\n"); } } /* print_cl_list */ /************* * * cl_merge(cl) -- merge identical literals (keep leftmost occurrence) * *************/ void cl_merge(struct clause *c) { struct literal *l1, *l2, *l_prev; l1 = c->first_lit; while (l1) { l2 = l1->next_lit; l_prev = l1; while (l2) if (l1->sign == l2->sign && term_ident(l1->atom, l2->atom)) { l_prev->next_lit = l2->next_lit; l2->atom->occ.lit = NULL; zap_term(l2->atom); free_literal(l2); l2 = l_prev->next_lit; } else { l_prev = l2; l2 = l2->next_lit; } l1 = l1->next_lit; } } /* cl_merge */ /*************0 * * int tautology(c) -- Is clause c a tautology? * *************/ int tautology(struct clause *c) { struct literal *l1, *l2; int taut; taut = 0; l1 = c->first_lit; while (l1 && !taut) { l2 = l1->next_lit; while (l2 && !taut) { taut = (l1->sign != l2->sign && term_ident(l1->atom, l2->atom)); l2 = l2->next_lit; } l1 = l1->next_lit; } return(taut); } /* tautology */ /************* * * prf_weight() * * Return the number of leaves (i.e., occurrences of input clauses) * in the proof tree. * *************/ int prf_weight(struct clause *c) { struct ilist *ip; struct clause *d; int sum = 0; for (ip = c->parents; ip; ip = ip->next) { if (ip->i <= LIST_RULE) { /* LIST_RULE is a large negative number. */ /* If ip->i is less than LIST_RULE, then a list follows. */ int i; int j = LIST_RULE - ip->i; /* size of list */ /* Make ip point at the last element of the list. */ for (i = 1; i <= j; i++) ip = ip->next; } else if (ip->i >= 0) { d = cl_find(ip->i); if (d) sum += prf_weight(d); } } return(sum == 0 ? 1 : sum); } /* prf_weight */ /************* * * int proof_length(c) * * Return length of proof. If demod_history is clear, demodulation * steps are not counted. "new_demod" steps are not counted. * *************/ int proof_length(struct clause *c) { struct clause_ptr *cp1, *cp2; struct ilist *ip1, *ip2; int count, level; cp1 = NULL; ip1 = NULL; level = get_ancestors(c, &cp1, &ip1); for (count = 0; cp1; ) { if (cp1->c->parents && cp1->c->parents->i != NEW_DEMOD_RULE) count++; cp2 = cp1; cp1 = cp1->next; free_clause_ptr(cp2); ip2 = ip1; ip1 = ip1->next; free_ilist(ip2); } return(count); } /* proof_length */ /************* * * int subsume(c, d) -- does clause c subsume clause d? * *************/ int subsume(struct clause *c, struct clause *d) { struct context *s; struct trail *tr; int subsumed; s = get_context(); tr = NULL; subsumed = map_rest(c, d, s, &tr); if (subsumed) clear_subst_1(tr); free_context(s); return(subsumed); } /* subsume */ /************* * * int map_rest(c, d, s, trp) - map rest of literals - for subsumption * *************/ int map_rest(struct clause *c, struct clause *d, struct context *s, struct trail **trp) { struct literal *c_lit, *d_lit; struct term *c_atom, *d_atom; struct trail *t_pos; int subsumed, i; /* get the first unmarked literal */ c_lit = c->first_lit; i = 0; while (c_lit && Map_array[i] == 1) { c_lit = c_lit->next_lit; i++; } if (!c_lit) return(1); /* all lits of c mapped, so c subsumes d */ else if (answer_lit(c_lit)) { /* if answer literal, skip it */ c_atom = c_lit->atom; Map_array[i] = 1; /* mark as mapped */ subsumed = map_rest(c, d, s, trp); Map_array[i] = 0; /* remove mark */ return(subsumed); } else { c_atom = c_lit->atom; Map_array[i] = 1; /* mark as mapped */ d_lit = d->first_lit; subsumed = 0; while (d_lit && !subsumed) { d_atom = d_lit->atom; t_pos = *trp; /* save position in trail in case of failure */ if (c_lit->sign == d_lit->sign && match(c_atom, s, d_atom, trp)) { if (map_rest(c, d, s, trp)) subsumed = 1; else { clear_subst_2(*trp, t_pos); *trp = t_pos; } } d_lit = d_lit->next_lit; } Map_array[i] = 0; /* remove mark */ return(subsumed); } } /* map_rest */ /************* * * int anc_subsume(c, d) * * We already know that c subsumes d. Check if d subsumes c and * ancestors(c) <= ancestors(d). * *************/ int anc_subsume(struct clause *c, struct clause *d) { if (subsume(d,c)) { if (Flags[PROOF_WEIGHT].val) return(prf_weight(c) <= prf_weight(d)); else return(proof_length(c) <= proof_length(d)); } else return(1); } /* anc_subsume */ /************* * * struct clause *for_sub_prop(d) * * Attempt to find a clause that propositionally subsumes d. * *************/ struct clause *for_sub_prop(struct clause *d) { struct clause *c; for (c = Usable->first_cl; c; c = c->next_cl) if (ordered_sub_clause(c, d)) return(c); for (c = Sos->first_cl; c; c = c->next_cl) if (ordered_sub_clause(c, d)) return(c); return(NULL); } /* for_sub_prop */ /************* * * struct clause *forward_subsume(d) * * Attempt to find a clause that subsumes d. * *************/ struct clause *forward_subsume(struct clause *d) { int subsumed; struct literal *d_lit; struct clause *c = NULL; struct term *c_atom, *d_atom; struct context *s; struct trail *tr; struct is_tree *is_db; struct fsub_pos *pos; struct fpa_index *fpa_db; struct fpa_tree *ut; int c_size, factor, i; int d_size = -1; struct literal *lit; if (Flags[PROPOSITIONAL].val) return(for_sub_prop(d)); subsumed = 0; s = get_context(); factor = Flags[FACTOR].val; if (factor) /* if factor don't let long clauses subsume short */ d_size = num_literals(d); if (!Flags[FOR_SUB_FPA].val) { /* if `is' indexing */ d_lit = d->first_lit; while (d_lit && !subsumed) { /* Is_pos_lits and Is_neg_lits are global variables */ is_db = d_lit->sign ? Is_pos_lits : Is_neg_lits; c_atom = fs_retrieve(d_lit->atom, s, is_db, &pos); while (c_atom && !subsumed) { c = c_atom->occ.lit->container; c_size = num_literals(c); if (c_size > MAX_LITS) { abend("forward_subsume, MAX_LITS too small."); } if (literal_number(c_atom->occ.lit) == 1 && (!factor || c_size <= d_size)) { for (i = 0, lit = c->first_lit; lit->atom != c_atom; i++, lit = lit->next_lit); /* empty body */ Map_array[i] = 1; /* mark as mapped*/ tr = NULL; subsumed = map_rest(c, d, s, &tr); Map_array[i] = 0; /* remove mark */ clear_subst_1(tr); } if (subsumed && multi_justifications()) { if (subsume(d,c)) { /* c (old) and d (new) are equivalent, so add d's just to c. */ if (d->parents != NULL) possibly_append_parents(c, d->parents); } } if (subsumed && Flags[ANCESTOR_SUBSUME].val) { /* Removed variable renumbering 4/4/2001; shouldn't be necessary */ subsumed = anc_subsume(c,d); if (!subsumed) Stats[CL_NOT_ANC_SUBSUMED]++; } /* BV(970327) : forward sub only if sub goes both ways */ if (subsumed && Flags[FOR_SUB_EQUIVALENTS_ONLY].val) subsumed = subsume(d,c); if (!subsumed) c_atom = fs_retrieve((struct term *) NULL, s, is_db, &pos); else canc_fs_pos(pos, s); } d_lit = d_lit->next_lit; } } else { /* fpa indexing */ d_lit = d->first_lit; while (d_lit && !subsumed) { fpa_db = (d_lit->sign ? Fpa_pos_lits : Fpa_neg_lits); d_atom = d_lit->atom; ut = build_tree(d_atom, MORE_GEN, Parms[FPA_LITERALS].val, fpa_db); c_atom = next_term(ut, 0); while (c_atom && !subsumed) { tr = NULL; c = c_atom->occ.lit->container; c_size = num_literals(c); if (c_size > MAX_LITS) { abend("forward_subsume, MAX_LITS too small."); } if (literal_number(c_atom->occ.lit) == 1 && (!factor || c_size <= d_size) && match(c_atom, s, d_atom, &tr)) { for (i = 0, lit = c->first_lit; lit->atom != c_atom; i++, lit = lit->next_lit); /* empty body */ Map_array[i] = 1; /* mark as mapped*/ subsumed = map_rest(c, d, s, &tr); Map_array[i] = 0; /* remove mark */ clear_subst_1(tr); } if (subsumed && Flags[ANCESTOR_SUBSUME].val) { /* Removed variable renumbering 4/4/2001; shouldn't be necessary */ subsumed = anc_subsume(c,d); if (!subsumed) Stats[CL_NOT_ANC_SUBSUMED]++; } /* BV(970327) : forward sub only if sub goes both ways */ if (subsumed && Flags[FOR_SUB_EQUIVALENTS_ONLY].val) subsumed = subsume(d,c); if (!subsumed) c_atom = next_term(ut, 0); else zap_prop_tree(ut); } d_lit = d_lit->next_lit; } } free_context(s); if (subsumed) return(c); else return(NULL); } /* forward_subsume */ /************* * * struct clause_ptr *back_subsume(c) * * Get the list of clauses subsumed by c. * *************/ struct clause_ptr *back_subsume(struct clause *c) { int subsumed, c_size, factor, i; struct literal *c_lit; struct clause *d; struct clause_ptr *subsumed_clauses; struct term *c_atom, *d_atom; struct context *s; struct fpa_tree *ut; struct trail *tr; factor = Flags[FACTOR].val; c_size = num_literals(c); if (c_size > MAX_LITS) { abend("back_subsume, MAX_LITS too small."); } s = get_context(); c_lit = c->first_lit; /* get first non-answer literal */ i = 0; while (c_lit && answer_lit(c_lit)) { c_lit = c_lit->next_lit; i++; } if (!c_lit) { fprintf(stdout, "\nNOTE: back_subsume called with empty clause.\n"); return(NULL); } c_atom = c_lit->atom; ut = build_tree(c_atom, INSTANCE, Parms[FPA_LITERALS].val, c_lit->sign ? Fpa_pos_lits : Fpa_neg_lits); /* Fpa_pos_lits and Fpa_neg_lits are global variables */ subsumed_clauses = NULL; d_atom = next_term(ut, 0); while (d_atom) { d = d_atom->occ.lit->container; tr = NULL; if (c != d && (!factor || c_size <= num_literals(d)) && match(c_atom, s, d_atom, &tr)) { Map_array[i] = 1; /* mark as mapped */ subsumed = map_rest(c, d, s, &tr); Map_array[i] = 0; /* remove mark */ clear_subst_1(tr); if (subsumed && Flags[ANCESTOR_SUBSUME].val) subsumed = anc_subsume(c, d); if (subsumed) insert_clause(d, &subsumed_clauses); } d_atom = next_term(ut, 0); } free_context(s); return(subsumed_clauses); } /* back_subsume */ /************* * * struct clause_ptr *unit_conflict(c) * * Search for unit conflict. Return empty clause if found, * return NULL if not found. * * IT IS ASSUMED THAT c IS A UNIT CLAUSE!! * *************/ struct clause_ptr *unit_conflict(struct clause *c) { struct clause *d, *e; struct fpa_tree *ut; struct term *f_atom; struct literal *lit; int go, mp, ec; struct context *c1, *c2; struct trail *tr; struct clause_ptr *cp_return, *cp_prev, *cp_curr; c1 = get_context(); c1->multiplier = 0; c2 = get_context(); c2->multiplier = 1; lit = c->first_lit; while (answer_lit(lit)) /* skip answer literals */ lit = lit->next_lit; ut = build_tree(lit->atom, UNIFY, Parms[FPA_LITERALS].val, lit->sign ? Fpa_neg_lits : Fpa_pos_lits); f_atom = next_term(ut, 0); go = 1; cp_return = cp_prev = NULL; while (go && f_atom) { tr = NULL; d = f_atom->occ.lit->container; if (num_literals(d) == 1 && unify(lit->atom, c1, f_atom, c2, &tr)) { e = build_bin_res(lit->atom, c1, f_atom, c2); clear_subst_1(tr); cl_merge(e); /* answer literals */ cp_curr = get_clause_ptr(); cp_curr->c = e; if (cp_prev) cp_prev->next = cp_curr; else cp_return = cp_curr; cp_prev = cp_curr; ec = ++Stats[EMPTY_CLAUSES]; mp = Parms[MAX_PROOFS].val; if (mp != -1 && ec >= mp) /* do not look for more proofs */ go = 0; } if (go) f_atom = next_term(ut, 0); else zap_prop_tree(ut); } free_context(c1); free_context(c2); return(cp_return); } /* unit_conflict */ /************* * * int propositional_clause(c) * * Is this a propositional clause? * *************/ int propositional_clause(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit) if (lit->atom->type != NAME) return(0); else lit = lit->next_lit; return(1); } /* propositional_clause */ /************* * * int xx_resolvable(c) * * Does the nonunit clause c have a literal that can resolve with x = x? * *************/ int xx_resolvable(struct clause *c) { if (unit_clause(c)) return(0); else { struct literal *lit; lit = c->first_lit; while (lit) { if (!lit->sign && is_eq(lit->atom->sym_num)) { struct term *a1 = lit->atom->farg->argval; struct term *a2 = lit->atom->farg->narg->argval; if (a1->type == VARIABLE && !occurs_in(a1, a2)) return(1); else if (a2->type == VARIABLE && !occurs_in(a2, a1)) return(1); } lit = lit->next_lit; } return(0); } } /* xx_resolvable */ /************* * * int pos_clause(c) * * Is this a positive clause (excluding answer lits) ? * *************/ int pos_clause(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit) if (!lit->sign && !answer_lit(lit)) return(0); /* fail because found negative non-anser literal */ else lit = lit->next_lit; return(1); } /* pos_clause */ /************* * * int answer_lit(lit) -- Is this an answer literal? * *************/ int answer_lit(struct literal *lit) { return(lit->atom->varnum == ANSWER); } /* answer_lit */ /************* * * int pos_eq_lit(lit) -- Is this a positive equality literal? * *************/ int pos_eq_lit(struct literal *lit) { return(lit->atom->varnum == POS_EQ); } /* pos_eq_lit */ /************* * * int neg_eq_lit(lit) -- Is this a negative equality literal? * *************/ int neg_eq_lit(struct literal *lit) { return(lit->atom->varnum == NEG_EQ); } /* neg_eq_lit */ /************* * * int eq_lit(lit) -- Is this an equality literal (pos or neg)? * *************/ int eq_lit(struct literal *lit) { return(pos_eq_lit(lit) || neg_eq_lit(lit)); } /* eq_lit */ /************* * * int neg_clause(c) * * Is this a negative clause (excluding answer lits) ? * *************/ int neg_clause(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit) if (lit->sign && !answer_lit(lit)) return(0); /* fail because found positive non-answer literal */ else lit = lit->next_lit; return(1); } /* neg_clause */ /************* * * int num_literals(c) -- How many literals (excluding answer literals)? * *************/ int num_literals(struct clause *c) { int i; struct literal *lit; i = 0; lit = c->first_lit; while (lit) { if (!answer_lit(lit)) /* if not answer literal */ i++; lit = lit->next_lit; } return(i); } /* num_literals */ /************* * * int num_answers(c) -- How many answer literals? * *************/ int num_answers(struct clause *c) { int i; struct literal *lit; i = 0; lit = c->first_lit; while (lit) { if (answer_lit(lit)) i++; lit = lit->next_lit; } return(i); } /* num_answers */ /************* * * int num_literals_including_answers(c) -- How many literals? * *************/ int num_literals_including_answers(struct clause *c) { int i; struct literal *lit; for (i = 0, lit = c->first_lit; lit; i++, lit = lit->next_lit); return(i); } /* num_literals_including_answers */ /************* * * int literal_number(lit) * * lit is which literal (excluding answers) in the clause that contains it. * *************/ int literal_number(struct literal *lit) { int i; struct literal *l; i = 1; l = lit->container->first_lit; while (l != lit) { if (!answer_lit(l)) i++; l = l->next_lit; } return(i); } /* literal_number */ /************* * * int unit_clause(c) -- Is it a unit clause (don't count answers)? * *************/ int unit_clause(struct clause *c) { return(num_literals(c) == 1); } /* unit_clause */ /************* * * int horn_clause(c) * * Is c a Horn clause (at most one positive literal)? * * Ignore answer literals. * *************/ int horn_clause(struct clause *c) { struct literal *lit; int i; for (lit = c->first_lit, i = 0; lit; lit = lit->next_lit) if (lit->sign && !answer_lit(lit)) i++; return(i <= 1); } /* horn_clause */ /************* * * int equality_clause(c) * * Does c contain any equality literals (pos or neg)? * *************/ int equality_clause(struct clause *c) { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) if (pos_eq_lit(lit) || neg_eq_lit(lit)) return(1); return(0); } /* equality_clause */ /************* * * int symmetry_clause(c) * * Is c a clause for symmetry of equality? * *************/ int symmetry_clause(struct clause *c) { struct literal *l1, *l2; if (num_literals(c) != 2) return(0); else { l1 = c->first_lit; l2 = l1->next_lit; if (l1->sign == l2->sign) return(0); else if (!eq_lit(l1) || l1->atom->sym_num != l2->atom->sym_num) return(0); else if (l1->atom->farg->argval->type != VARIABLE) return(0); else if (l2->atom->farg->argval->type != VARIABLE) return(0); else if (!term_ident(l1->atom->farg->argval, l2->atom->farg->narg->argval)) return(0); else if (!term_ident(l1->atom->farg->narg->argval, l2->atom->farg->argval)) return(0); else return(1); } } /* symmetry_clause */ /************* * * struct literal *ith_literal(c, n) * * Return the i-th (non-answer) literal. * *************/ struct literal *ith_literal(struct clause *c, int n) { int i; struct literal *lit; lit = c->first_lit; i = 0; while(lit) { if (!answer_lit(lit)) i++; if (i == n) return(lit); else lit = lit->next_lit; } return(lit); } /* ith_literal */ /************* * * append_cl(lst, cl) * *************/ void append_cl(struct list *l, struct clause *c) { c->next_cl = NULL; c->prev_cl = l->last_cl; if (!l->first_cl) l->first_cl = c; else l->last_cl->next_cl = c; l->last_cl = c; c->container = l; if (l == Usable) Stats[USABLE_SIZE]++; else if (l == Sos) Stats[SOS_SIZE]++; else if (l == Demodulators) Stats[DEMODULATORS_SIZE]++; } /* append_cl */ /************* * * prepend_cl(lst, cl) * *************/ void prepend_cl(struct list *l, struct clause *c) { c->prev_cl = NULL; c->next_cl = l->first_cl; if (!l->last_cl) l->last_cl = c; else l->first_cl->prev_cl = c; l->first_cl = c; c->container = l; if (l == Usable) Stats[USABLE_SIZE]++; else if (l == Sos) Stats[SOS_SIZE]++; else if (l == Demodulators) Stats[DEMODULATORS_SIZE]++; } /* prepend_cl */ /************* * * insert_before_cl(c, c_new) * *************/ void insert_before_cl(struct clause *c, struct clause *c_new) { struct list *l; l = c->container; c_new->next_cl = c; c_new->prev_cl = c->prev_cl; c->prev_cl = c_new; if (!c_new->prev_cl) l->first_cl = c_new; else c_new->prev_cl->next_cl = c_new; c_new->container = l; if (l == Usable) Stats[USABLE_SIZE]++; else if (l == Sos) Stats[SOS_SIZE]++; else if (l == Demodulators) Stats[DEMODULATORS_SIZE]++; } /* insert_before_cl */ /************* * * insert_after_cl(c, c_new) * *************/ void insert_after_cl(struct clause *c, struct clause *c_new) { struct list *l; l = c->container; c_new->prev_cl = c; c_new->next_cl = c->next_cl; c->next_cl = c_new; if (!c_new->next_cl) l->last_cl = c_new; else c_new->next_cl->prev_cl = c_new; c_new->container = l; if (l == Usable) Stats[USABLE_SIZE]++; else if (l == Sos) Stats[SOS_SIZE]++; else if (l == Demodulators) Stats[DEMODULATORS_SIZE]++; } /* insert_after_cl */ /************* * * rem_from_list(c) * *************/ void rem_from_list(struct clause *c) { struct clause *p, *n; p = c->prev_cl; n = c->next_cl; if (!n) c->container->last_cl = p; else n->prev_cl = p; if (!p) c->container->first_cl = n; else p->next_cl = n; if (c->container == Usable) Stats[USABLE_SIZE]--; else if (c->container == Sos) Stats[SOS_SIZE]--; else if (c->container == Demodulators) Stats[DEMODULATORS_SIZE]--; c->container = NULL; c->prev_cl = NULL; c->next_cl = NULL; } /* rem_from_list */ /************* * * insert_clause(clause, *clause_ptr) * * If not already there, insert clause into list of clause pointers. * *************/ void insert_clause(struct clause *c, struct clause_ptr **cpp) { struct clause_ptr *curr, *prev, *new; curr = *cpp; prev = NULL; while (curr && curr->c->id > c->id) { prev = curr; curr = curr->next; } if (!curr || curr->c->id != c->id) { new = get_clause_ptr(); new->c = c; new->next = curr; if (prev) prev->next = new; else *cpp = new; } } /* insert_clause */ /************* * * max_literal_weight() * *************/ int max_literal_weight(struct clause *c, struct is_tree *wt_index) { struct literal *lit; int wt, max; max = -INT_MAX; for (lit = c->first_lit; lit != NULL; lit = lit->next_lit) { if (!answer_lit(lit)) { wt = weight(lit->atom, wt_index); max = (wt > max ? wt : max); } } return(max); } /* max_literal_weight */ /************* * * int weight_cl(c, wt_index) -- Weigh a clause. * * Also weigh answer lits, which have default weight 0. * *************/ int weight_cl(struct clause *c, struct is_tree *wt_index) { if (Flags[LITERALS_WEIGH_ONE].val) return num_literals(c); else { int w, neg_weight; struct literal *lit; neg_weight = Parms[NEG_WEIGHT].val; w = 0; lit = c->first_lit; while (lit) { w += weight(lit->atom, wt_index); if (!answer_lit(lit) && !lit->sign) w += neg_weight; lit = lit->next_lit; } return(w); } } /* weight_cl */ /************* * * hide_clause(c) -- c must be integrated * * Clauses can be hidden instead of deallocated so that they can * be printed later on (mostly so that a child can know its parent). * *************/ void hide_clause(struct clause *c) { c->next_cl = Hidden_clauses; Hidden_clauses = c; } /* hide_clause */ /************* * * proof_last_hidden_empty() * *************/ struct clause *proof_last_hidden_empty(void) { struct clause *c; struct clause *e = NULL; for (c = Hidden_clauses; c != NULL; c = c->next_cl) { if (num_literals(c) == 0) e = c; } #if 0 if (e != NULL) { printf("\n=========== HIDDEN PROOF ===========\n"); print_proof(stdout, e); printf("\n=========== end hidden proof ===========\n"); } #endif return e; } /* proof_last_hidden_empty */ /************* * * del_hidden_clauses() -- deallocate all hidden clauses * *************/ void del_hidden_clauses(void) { struct clause *c; while (Hidden_clauses) { c = Hidden_clauses; Hidden_clauses = Hidden_clauses->next_cl; cl_del_int(c); } } /* del_hidden_clauses */ /************* * * struct clause *cl_copy(c) * * Do not copy the list of parents. * *************/ struct clause *cl_copy(struct clause *c) { struct clause *d; struct literal *l, *l1, *l2; d = get_clause(); d->type = c->type; l = c->first_lit; l2 = NULL; while (l) { l1 = get_literal(); l1->target = l->target; l1->container = d; l1->sign = l->sign; l1->atom = copy_term(l->atom); remove_var_syms(l1->atom); /* nullify variable symbols (if present) */ l1->atom->occ.lit = l1; if (!l2) d->first_lit = l1; else l2->next_lit = l1; l2 = l1; l = l->next_lit; } return(d); } /* cl_copy */ /************* * * clause_ident(c1, c2) * * Don't check permutations. * *************/ int clause_ident(struct clause *c1, struct clause *c2) { struct literal *l1, *l2; int ok; for (l1 = c1->first_lit, l2 = c2->first_lit, ok = 1; l1 && l2 && ok; l1 = l1->next_lit, l2 = l2->next_lit) ok = (l1->sign == l2->sign && term_ident(l1->atom, l2->atom)); return(ok && l1 == NULL && l2 == NULL); } /* cl_ident */ /************* * * remove_var_syms(t) * * Variable terms normally do not have sym_nums. This * routine removes any that are present. * *************/ void remove_var_syms(struct term *t) { struct rel *r; if (t->type == VARIABLE) t->sym_num = 0; else if (t->type == COMPLEX) for (r = t->farg; r; r = r->narg) remove_var_syms(r->argval); } /* remove_var_syms */ /************* * * cl_insert_tab(c) * *************/ void cl_insert_tab(struct clause *c) { struct clause_ptr *cp1, *cp2, *cp3; int hashval, id; id = c->id; hashval = id % CLAUSE_TAB_SIZE; cp1 = Clause_tab[hashval]; cp2 = NULL; /* keep the chains ordered--increasing id */ while (cp1 && cp1->c->id < id) { cp2 = cp1; cp1 = cp1->next; } if (cp1 && cp1->c->id == id) { print_clause(stdout, c); abend("cl_insert_tab, clause already there."); } else { cp3 = get_clause_ptr(); cp3->c = c; cp3->next = cp1; if (!cp2) Clause_tab[hashval] = cp3; else cp2->next = cp3; } } /* cl_insert_tab */ /************* * * cl_delete_tab(c) * *************/ void cl_delete_tab(struct clause *c) { struct clause_ptr *cp1, *cp2; int hashval, id; id = c->id; hashval = id % CLAUSE_TAB_SIZE; cp1 = Clause_tab[hashval]; cp2 = NULL; /* chains are ordered--increasing id */ while (cp1 && cp1->c->id < id) { cp2 = cp1; cp1 = cp1->next; } if (!cp1 || cp1->c->id != id) { print_clause(stdout, c); abend("cl_delete_tab, clause not found."); } else { if (!cp2) Clause_tab[hashval] = cp1->next; else cp2->next = cp1->next; free_clause_ptr(cp1); } } /* cl_delete_tab */ /************* * * struct clause *cl_find(id) * *************/ struct clause *cl_find(int id) { struct clause_ptr *cp1; int hashval; hashval = id % CLAUSE_TAB_SIZE; cp1 = Clause_tab[hashval]; /* lists are ordered--increasing id */ while (cp1 && cp1->c->id < id) cp1 = cp1->next; if (!cp1 || cp1->c->id != id) return(NULL); else return(cp1->c); } /* cl_find */ /************* * * int lit_compare(l1, l2) * * 1. positive > negative * 2. answer > nonanswer * 3. lex * *************/ int lit_compare(struct literal *l1, struct literal *l2) { if (l1->sign > l2->sign) return(GREATER_THAN); else if (l1->sign < l2->sign) return(LESS_THAN); else if (answer_lit(l1) && !answer_lit(l2)) return(GREATER_THAN); else if (!answer_lit(l1) && answer_lit(l2)) return(LESS_THAN); else { if (Flags[PROPOSITIONAL].val) { if (l1->atom->sym_num == l2->atom->sym_num) return(SAME_AS); else if (l1->atom->sym_num > l2->atom->sym_num) return(GREATER_THAN); else return(LESS_THAN); } else return(lex_order_vars(l1->atom, l2->atom)); } } /* lit_compare */ /************* * * int ordered_sub_clause(c, d) * * True iff each literal of c occurs in d. * Literals assumed to be ordered by lit_compare. * * This routine treats any answer literals as ordinary literals. * Although this might be considered a bug, I decided to write it * this way, because it is designed for propositional clauses * which usually don't have answer literals, and checking for * answer literals will slow it too much. * *************/ int ordered_sub_clause(struct clause *c1, struct clause *c2) { struct literal *l1, *l2; int i; l1 = c1->first_lit; l2 = c2->first_lit; while (l1 && l2) { i = lit_compare(l1, l2); if (i == SAME_AS) { l1 = l1->next_lit; l2 = l2->next_lit; } else if (i == GREATER_THAN) l2 = l2->next_lit; else if (i == LESS_THAN) l2 = NULL; else abend("ordered_sub_clause: not total."); } #if 0 printf("\n c1:%d ", l1 == NULL); p_clause(c1); printf("\n c2: "); p_clause(c2); #endif return(l1 == NULL); } /* ordered_sub_clause */ /************* * * int sub_clause(c, d) * * True iff each literal of c occurs in d. * Literals are not assumed to be ordered. * * This routine treats any answer literals as ordinary literals. * Although this might be considered a bug, I decided to write it * this way, because it is designed for propositional clauses * which usually don't have answer literals, and checking for * answer literals will slow it too much. * *************/ int sub_clause(struct clause *c1, struct clause *c2) { struct literal *l1, *l2; int found; for(l1 = c1->first_lit; l1; l1 = l1->next_lit) { l2 = c2->first_lit; found = 0; while (l2 && !found) { if (l1->sign == l2->sign && l1->atom->sym_num == l2->atom->sym_num) found = 1; else l2 = l2->next_lit; } if (!found) return(0); } return(1); } /* sub_clause */ /************* * * sort_lits(c) -- sort literals * *************/ int sort_lits(struct clause *c) { struct literal *sorted, *prev, *curr, *next, *insert; int changed = 0; /* This is an insertion sort. Use lit_compare */ if (c->first_lit) { sorted = c->first_lit; insert = sorted->next_lit; sorted->next_lit = NULL; while(insert) { prev = NULL; curr = sorted; while (curr && lit_compare(insert, curr) == GREATER_THAN) { prev = curr; curr = curr->next_lit; } if (curr != NULL) changed = 1; next = insert->next_lit; insert->next_lit = curr; if (prev) prev->next_lit = insert; else sorted = insert; insert = next; } c->first_lit = sorted; } return changed; } /* sort lits */ /************* * * all_cont_cl(t, cpp) - insert containing clauses of t into *cpp * *************/ void all_cont_cl(struct term *t, struct clause_ptr **cpp) { struct rel *r; struct clause *c; struct list *l; if (t->type != VARIABLE && t->varnum != 0) { /* atom */ c = t->occ.lit->container; l = c->container; if (l == Usable || l == Sos || l == Demodulators) insert_clause(c, cpp); } else { /* term */ r = t->occ.rel; while (r) { all_cont_cl(r->argof, cpp); r = r->nocc; } } } /* all_cont_cl */ /************* * * zap_cl_list(lst) * *************/ void zap_cl_list(struct list *lst) { struct clause *c1, *c2; c1 = lst->first_cl; while (c1) { c2 = c1; c1 = c1->next_cl; cl_del_non(c2); } free_list(lst); } /* zap_cl_list */ /************* * * is_eq() * *************/ int is_eq(int sym_num) { char *name; name = sn_to_str(sym_num); if (Flags[TPTP_EQ].val) return(sn_to_arity(sym_num) == 2 && str_ident("equal", name)); else return(sn_to_arity(sym_num) == 2 && (initial_str("EQ", name) || initial_str("Eq", name) || initial_str("eq", name) || str_ident("=", name))); } /* is_eq */ /************* * * mark_literal(lit) * * Atoms have varnum > 0. This routine inserts the appropriate code. * *************/ void mark_literal(struct literal *lit) { char *name; struct term *a; a = lit->atom; name = sn_to_str(a->sym_num); if (initial_str("$ANS", name) || initial_str("$Ans", name) || initial_str("$ans", name)) a->varnum = ANSWER; /* answer literal */ else if (is_eq(a->sym_num)) { if (lit->sign) a->varnum = POS_EQ; /* positive equality */ else a->varnum = NEG_EQ; /* negative equality */ } else if (sn_to_ec(a->sym_num) > 0) a->varnum = EVALUABLE; /* $ID, $LE, $AND, ... */ else if (is_symbol(a, "->", 2) && is_eq(a->farg->narg->argval->sym_num)) a->varnum = CONDITIONAL_DEMOD; else a->varnum = NORM_ATOM; /* normal atom */ } /* mark_literal */ /************* * * int get_ancestors(c, cpp, ipp) * * cpp is the list under construction, sorted by ID. * ipp is a corresponding list of the level of each clause. * * Return the level of the proof. * * The justification list of a clause (c->parents) is a list * of integers. Usually, negative integers represent inference * rules, and positive integers are the IDs of parent clauses. * Exception: LIST_RULE is a large negative integer. If a member * is <= LIST_RULE, then a list of length (LIST_RULE-member) follows * (and typically represents a position in a clause). * *************/ int get_ancestors(struct clause *c, struct clause_ptr **cpp, struct ilist **ipp) { struct clause_ptr *cp1, *cp2, *cp3; struct ilist *ip1, *ip2, *ip3; struct ilist *ip; struct clause *d; int max, lev, n; cp1 = *cpp; ip1 = *ipp; cp3 = NULL; ip3 = NULL; /* First check to see if the clause has already been processed. */ while (cp1 && cp1->c->id < c->id) { cp3 = cp1; cp1 = cp1->next; ip3 = ip1; ip1 = ip1->next; } if (!cp1 || cp1->c->id > c->id) { /* Process the clause. */ cp2 = get_clause_ptr(); ip2 = get_ilist(); cp2->c = c; if (!cp3) { cp2->next = *cpp; *cpp = cp2; ip2->next = *ipp; *ipp = ip2; } else { cp2->next = cp3->next; cp3->next = cp2; ip2->next = ip3->next; ip3->next = ip2; } max = -1; for (ip = c->parents; ip; ip = ip->next) { if (ip->i <= LIST_RULE) { /* LIST_RULE is a large negative number. */ /* If ip->i is less than LIST_RULE, then a list follows. */ int i; int j = LIST_RULE - ip->i; /* size of list */ /* Make ip point at the last element of the list. */ for (i = 1; i <= j; i++) ip = ip->next; } else if (ip->i >= 0) { /* < 0 means it's a code for an inference rule */ d = cl_find(ip->i); if (!d) printf("WARNING, clause %d not found, proof is incomplete.\n", ip->i); else { n = get_ancestors(d, cpp, ipp); max = (n > max ? n : max); } } } if (!c->parents) lev = 0; else if (c->parents->i == NEW_DEMOD_RULE) lev = max; else lev = max + 1; ip2->i = lev; #if 0 printf("level %d: ", lev); p_clause(c); #endif return(lev); } else { /* The clause has already been processed, so just return its level. */ return(ip1->i); } } /* get_ancestors */ /************* * * clauses_to_ids() * *************/ struct ilist *clauses_to_ids(struct clause_ptr *p) { if (p == NULL) return NULL; else { struct ilist *ip = get_ilist(); ip->i = p->c->id; ip->next = clauses_to_ids(p->next); return ip; } } /* clauses_to_ids */ /************* * * free_clause_ptr_list() * *************/ void free_clause_ptr_list(struct clause_ptr *p) { if (p != NULL) { free_clause_ptr_list(p->next); free_clause_ptr(p); } } /* free_clause_ptr_list */ /************* * * get_ancestors2(c) * * This is a more convenient version of get_ancestors. * *************/ struct ilist *get_ancestors2(struct clause *c) { struct clause_ptr *cp = NULL; struct ilist *ip = NULL; int level; level = get_ancestors(c, &cp, &ip); free_ilist_list(ip); ip = clauses_to_ids(cp); free_clause_ptr_list(cp); return ip; } /* get_ancestors2 */ /************* * * int just_to_supporters(ip) * * Given a justification list, return a set of the parents. * *************/ struct ilist *just_to_supporters(struct ilist *ip) { struct ilist *ip_construct = NULL; for ( ; ip; ip = ip->next) { if (ip->i <= LIST_RULE) { /* LIST_RULE is a large negative number. */ /* If ip->i is less than LIST_RULE, then a list follows. */ int i; int j = LIST_RULE - ip->i; /* size of list */ /* Make ip point at the last element of the list. */ for (i = 1; i <= j; i++) ip = ip->next; } else if (ip->i >= 0) { /* < 0 means it's a code for an inference rule */ #if 1 ip_construct = iset_add(ip->i, ip_construct); #else struct ilist *ip_new = get_ilist(); ip_new->i = ip->i; ip_new->next = ip_construct; ip_construct = ip_new; #endif } } #if 1 return ip_construct; #else return reverse_ip(ip_construct, NULL); #endif } /* just_to_supporters */ /************* * * int renumber_vars_term(c) * * Renumber the variables of a term, starting with 0. `c' must * be nonintegrated. return(0) if more than MAXVARS distinct variables. * * This is very special-purpose. Ordinarily, you'll call renumber_vars(c) * on clauses. * *************/ int renumber_vars_term(struct term *t) { int varnums[MAX_VARS]; int i; for (i = 0; i < MAX_VARS; i++) varnums[i] = -1; return renum_vars_term(t, varnums); } /* renumber_vars_term */ /************* * * int renumber_vars(c) * * Renumber the variables of a clause, starting with 0. `c' must * be nonintegrated. return(0) if more than MAXVARS distinct variables. * *************/ int renumber_vars(struct clause *c) { struct literal *lit; int varnums[MAX_VARS]; int i, ok; ok = 1; for (i = 0; i < MAX_VARS; i++) varnums[i] = -1; lit = c->first_lit; while (lit) { if (renum_vars_term(lit->atom, varnums) == 0) ok = 0; lit = lit->next_lit; } return(ok); } /* renumber_vars */ /************* * * int renum_vars_term(term, varnums) -- called from renumber_vars. * *************/ int renum_vars_term(struct term *t, int *varnums) { struct rel *r; int i, ok; if (t->type == NAME) return(1); else if (t->type == COMPLEX) { ok = 1; r = t->farg; while (r) { if (renum_vars_term(r->argval, varnums) == 0) ok = 0; r = r->narg; } return(ok); } else { i = 0; while (i < MAX_VARS && varnums[i] != -1 && varnums[i] != t->varnum) i++; if (i == MAX_VARS) return(0); else { if (varnums[i] == -1) { varnums[i] = t->varnum; t->varnum = i; } else t->varnum = i; return(1); } } } /* renum_vars_term */ /************* * * clear_var_names(t) -- set sym_num field of all variables to NULL * *************/ void clear_var_names(struct term *t) { struct rel *r; if (t->type == VARIABLE) t->sym_num = 0; else { for (r = t->farg; r; r = r->narg) clear_var_names(r->argval); } } /* clear_var_names */ /************* * * cl_clear_vars(c) * *************/ void cl_clear_vars(struct clause *c) { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) clear_var_names(lit->atom); } /************* * * void distinct_vars_rec(t, a, max) -- called by distinct_vars * *************/ static void distinct_vars_rec(struct term *t, int *a, int *max) { struct rel *r; int i, vn; if (t->type == VARIABLE) { vn = t->varnum; for (i = 0; i < MAX_VARS && a[i] != -1 && a[i] != vn; i++); if (i != MAX_VARS && a[i] == -1) { a[i] = vn; *max = i+1; } } else if (t->type == COMPLEX) { for (r = t->farg; r && *max < MAX_VARS; r = r->narg) distinct_vars_rec(r->argval, a, max); } } /* distinct_vars_rec */ /************* * * int distinct_vars(c) -- number of variables in a clause. * * if >= MAX_VARS, return MAX_VARS. * *************/ int distinct_vars(struct clause *c) { struct literal *lit; int a[MAX_VARS], i, max; for (i = 0; i < MAX_VARS; i++) a[i] = -1; for (lit = c->first_lit, max = 0; lit; lit = lit->next_lit) distinct_vars_rec(lit->atom, a, &max); return(max); } /* distinct_vars */ /************* * * struct clause *find_first_cl(l) * *************/ struct clause *find_first_cl(struct list *l) { struct clause *c; if (!l->first_cl) return(NULL); else { c = l->first_cl; return(c); } } /* find_first_cl */ /************* * * struct clause *find_last_cl(l) * *************/ struct clause *find_last_cl(struct list *l) { struct clause *c; if (!l->last_cl) return(NULL); else { c = l->last_cl; return(c); } } /* find_last_cl */ /************* * * struct clause *find_random_cl(l) * *************/ struct clause *find_random_cl(struct list *l) { struct clause *c; int i, j; if (l->first_cl == NULL) return(NULL); else { j = (rand() % Stats[SOS_SIZE]) + 1; c = l->first_cl; i = 1; while (i < j && c != NULL) { c = c->next_cl; i++; } if (c == NULL) abend("find_random_cl, sos bad."); return(c); } } /* find_random_cl */ /************* * * get_clauses_of_wt_range() * *************/ struct clause_ptr *get_clauses_of_wt_range(struct clause *c, int min, int max) { if (c == NULL) return NULL; else if (c->pick_weight >= min && c->pick_weight <= max) { struct clause_ptr *p = get_clause_ptr(); p->c = c; p->next = get_clauses_of_wt_range(c->next_cl, min, max); return p; } else return get_clauses_of_wt_range(c->next_cl, min, max); } /* get_clauses_of_wt_range */ /************* * * clause_ptr_list_size() * *************/ int clause_ptr_list_size(struct clause_ptr *p) { if (p == NULL) return 0; else return (1 + clause_ptr_list_size(p->next)); } /* clause_ptr_list_size */ /************* * * nth_clause() -- this counts from 1. * *************/ struct clause *nth_clause(struct clause_ptr *p, int n) { if (p == NULL) return NULL; else if (n == 1) return p->c; else return nth_clause(p->next, n-1); } /* nth_clause */ /************* * * zap_clause_ptr_list(p) * * Free the nodes, but not the clauses they point to. * *************/ void zap_clause_ptr_list(struct clause_ptr *p) { if (p != NULL) { zap_clause_ptr_list(p->next); free_clause_ptr(p); } } /* zap_clause_ptr_list */ /************* * * struct clause *find_random_lightest_cl(l) * *************/ struct clause *find_random_lightest_cl(struct list *l) { struct clause *c = find_lightest_cl(l); if (c == NULL) return NULL; else { int wt = c->pick_weight; struct clause_ptr *p = get_clauses_of_wt_range(l->first_cl, wt, wt); int n = clause_ptr_list_size(p); int j = (rand() % n) + 1; c = nth_clause(p, j); zap_clause_ptr_list(p); return c; } } /* find_random_lightest_cl */ /************* * * struct clause *find_mid_lightest_cl(l) * *************/ struct clause *find_mid_lightest_cl(struct list *l) { struct clause *c = find_lightest_cl(l); if (c == NULL) return NULL; else { int wt = c->pick_weight; struct clause_ptr *p = get_clauses_of_wt_range(l->first_cl, wt, wt); int n = clause_ptr_list_size(p); int j = (n / 2) + 1; c = nth_clause(p, j); zap_clause_ptr_list(p); return c; } } /* find_mid_lightest_cl */ /************* * * struct clause *find_lightest_cl(l) * * If more than one of mimimum weight, return first or last of those, * according to the flag PICK_LAST_LIGHTEST. * * Input sos clauses might have weight field set to -MAX_INT so that * they are returned first (in order). * *************/ struct clause *find_lightest_cl(struct list *l) { if (l->first_cl == NULL) return NULL; else { struct clause *cm = l->first_cl; int wm = cm->pick_weight; struct clause *c = cm->next_cl; while (c) { int w = c->pick_weight; if (Flags[PICK_LAST_LIGHTEST].val ? (w <= wm) : (w < wm)) { wm = w; cm = c; } c = c->next_cl; } return cm; } } /* find_lightest_cl */ /************* * * struct clause *find_lightest_geo_child(l) * * Find the lightest clause c for which child_of_geometry(c) holds. * If there are no children of geometry, return NULL. * If more than one of mimimum weight, return first of those. * *************/ struct clause *find_lightest_geo_child(struct list *l) { struct clause *c, *cmin; int w, wmin; for (c = l->first_cl, cmin = NULL, wmin = MAX_INT; c; c = c->next_cl) { if (child_of_geometry(c)) { w = c->pick_weight; if (!cmin || w < wmin) { wmin = w; cmin = c; } } } return(cmin); } /* find_lightest_geo_child */ /************* * * struct clause *find_interactive_cl() * *************/ struct clause *find_interactive_cl(void) { FILE *fin, *fout; fin = fopen("/dev/tty", "r"); fout = fopen("/dev/tty", "w"); if (!fin || !fout) { printf("interaction failure: cannot find tty.\n"); fprintf(stderr, "interaction failure: cannot find tty.\n"); return(NULL); } else { int id; struct clause *c = NULL; int done = 0; char s[256]; while (!done) { fprintf(fout,"\nEnter clause number of next given clause, or 0 to terminate\ninteractive_given mode, or -1 to print list sos.\n? "); fscanf(fin, "%s", s); if (!str_int(s, &id)) { fprintf(fout, "%c\nNot an integer: \"%s\", try again.\n", Bell, s); } else if (id == 0) { printf("\nTurning off interactive_given mode.\n"); fprintf(fout, "\nTurning off interactive_given mode.\n"); Flags[INTERACTIVE_GIVEN].val = 0; c = NULL; done = 1; } else if (id == -1) { struct clause *c; for (c = Sos->first_cl; c; c = c->next_cl) print_clause(fout, c); } else { c = cl_find(id); if (!c) fprintf(fout, "%c\nClause %d not found.\n", Bell, id); else if (c->container != Sos) fprintf(fout, "%c\nClause %d not in sos.\n", Bell, id); else { done = 1; fprintf(fout, "\nOk, clause %d will be given.\n", id); } } } fclose(fin); fclose(fout); return(c); } } /* find_interactive_cl */ /************* * * struct clause *find_given_clause() * *************/ struct clause *find_given_clause(void) { struct clause *giv_cl; if (Flags[INTERACTIVE_GIVEN].val) { giv_cl = find_interactive_cl(); if (giv_cl) return(giv_cl); } if (Flags[SOS_QUEUE].val) giv_cl = find_first_cl(Sos); else if (Flags[SOS_STACK].val) giv_cl = find_last_cl(Sos); else if (Parms[PICK_GIVEN_RATIO].val != -1 && Stats[CL_GIVEN] % (Parms[PICK_GIVEN_RATIO].val + 1) == 0) giv_cl = find_first_cl(Sos); else if (Parms[PICK_DIFF].val != -1) giv_cl = find_pickdiff_cl(Sos, Usable); else if (Flags[PICK_RANDOM_LIGHTEST].val) giv_cl = find_random_lightest_cl(Sos); else if (Flags[PICK_MID_LIGHTEST].val) giv_cl = find_mid_lightest_cl(Sos); else if (Parms[GEO_GIVEN_RATIO].val != -1) { if (Stats[CL_GIVEN] % (Parms[GEO_GIVEN_RATIO].val + 1) == 0) { giv_cl = find_lightest_geo_child(Sos); if (!giv_cl) giv_cl = find_lightest_cl(Sos); } else giv_cl = find_lightest_cl(Sos); } else /* this is the default */ giv_cl = find_lightest_cl(Sos); return(giv_cl); } /* find_given_clause */ /************* * * struct clause *extract_given_clause() * *************/ struct clause *extract_given_clause(void) { struct clause *giv_cl; CLOCK_START(PICK_GIVEN_TIME); giv_cl = find_given_clause(); if (giv_cl) { rem_from_list(giv_cl); } CLOCK_STOP(PICK_GIVEN_TIME); return(giv_cl); } /* extract_given_clause */ /************* * * int unit_del(c) -- unit deletion * * Delete any literals that are subsumed by a unit with opposite sign. * * Answer literals on the units complicate things. In particular, * if they contain variables not in the regular literal. * * This assumes that FOR_SUB_FPA is clear, because the discrimination * index is used. * * Return 1 if any deletions occur. * *************/ int unit_del(struct clause *c) { struct clause *d; struct literal *prev, *curr, *next, *answers, *l1, *l2; struct term *d_atom; struct context *s; struct is_tree *is_db; struct fsub_pos *pos; struct ilist *ip0, *ip, *lp; int deleted, return_val; return_val = 0; s = get_context(); s->multiplier = 1; /* first get last parent */ lp = c->parents; if (lp) while (lp->next) lp = lp->next; ip0 = lp; /* save position to insert "ud" if any deleted */ answers = NULL; prev = NULL; next = c->first_lit; while (next) { curr = next; next = next->next_lit; is_db = curr->sign ? Is_neg_lits : Is_pos_lits; d_atom = fs_retrieve(curr->atom, s, is_db, &pos); deleted = 0; while (d_atom && !deleted) { d = d_atom->occ.lit->container; if (d->container != Passive && num_literals(d) == 1) { return_val = 1; if (prev) prev->next_lit = next; else c->first_lit = next; ip = get_ilist(); /* append to history */ ip->i = d->id; if (!lp) c->parents = ip; else lp->next = ip; lp = ip; l2 = d->first_lit; /* now append any answer literals */ while (l2) { if (answer_lit(l2)) { l1 = get_literal(); l1->container = c; l1->sign = l2->sign; l1->atom = apply(l2->atom, s); s->multiplier++; /* in case answer has lone vars */ l1->atom->varnum = ANSWER; l1->atom->occ.lit = l1; l1->next_lit = answers; answers = l1; } l2 = l2->next_lit; } curr->atom->occ.lit = NULL; /* so zap_term won't complain */ zap_term(curr->atom); free_literal(curr); canc_fs_pos(pos, s); Stats[UNIT_DELETES]++; deleted = 1; } else d_atom = fs_retrieve((struct term *) NULL, s, is_db, &pos); } if (!deleted) prev = curr; } if (!prev) c->first_lit = answers; else prev->next_lit = answers; if (lp != ip0) { /* at least one deletion occurred */ if (s->multiplier != 1) { /* Answer lits added; renumber in case new vars introduced. */ if (renumber_vars(c) == 0) { print_clause(stdout, c); abend("unit_del, too many variables introduced."); } } ip = get_ilist(); ip->i = UNIT_DEL_RULE; if (!ip0) { ip->next = c->parents; c->parents = ip; } else { ip->next = ip0->next; ip0->next = ip; } } free_context(s); return(return_val); } /* unit_del */ /************* * * back_unit_deletion() * *************/ void back_unit_deletion(struct clause *c, int input) { struct clause *d, *resolvent; struct literal *c_lit; struct term *c_atom, *d_atom; struct context *c_subst, *d_subst; struct fpa_tree *ut; struct trail *tr; struct list *source_list; c_lit = ith_literal(c,1); c_atom = c_lit->atom; ut = build_tree(c_lit->atom, INSTANCE, Parms[FPA_LITERALS].val, c_lit->sign ? Fpa_neg_lits : Fpa_pos_lits); d_atom = next_term(ut, 0); c_subst = get_context(); d_subst = get_context(); /* This will stay empty */ while (d_atom) { d = d_atom->occ.lit->container; source_list = d->container; tr = NULL; if (source_list == Usable || source_list == Sos) { if (match(c_atom, c_subst, d_atom, &tr)) { resolvent = build_bin_res(c_atom, c_subst, d_atom, d_subst); resolvent->parents->i = BACK_UNIT_DEL_RULE; clear_subst_1(tr); Stats[CL_GENERATED]++; Stats[BACK_UNIT_DEL_GEN]++; #if 1 if (source_list == Usable) { SET_BIT(resolvent->bits, SCRATCH_BIT); /* printf("Clause destined for Usable:\n"); */ p_clause(resolvent); } #endif CLOCK_STOP(BACK_UNIT_DEL_TIME); pre_process(resolvent, input, Sos); CLOCK_START(BACK_UNIT_DEL_TIME); } } d_atom = next_term(ut, 0); } free_context(c_subst); free_context(d_subst); } /* back_unit_deletion */ otter-3.3f/source/hot.c0100644000076400007640000001537007343605232014451 0ustar mccunemccune/* * hot.c -- This file has routines hot-list inference. * */ #include "header.h" /* There are separate indexes for hot-list inference. They are analogous to * the ordinary FPA indexes defined in header.h. They are used in * a kludgey way. * * The indexing and inference operations refer to global pointers * to the FPA indexes. (The indexes should be parameters, but they aren't.) * * In init_hot_list, pointers to the real FPA indexes are saved. * During hot-list operations (index and inference) the ordinary * indexes are temporarily replaced with the hot-list indexes; * after the operation, the real fpa indexes are restored. */ /* These are the hot-list indexes. */ static struct fpa_index *Hot_clash_pos_lits; static struct fpa_index *Hot_clash_neg_lits; static struct fpa_index *Hot_alphas; static struct fpa_index *Hot_clash_terms; /* These are the ordinary indexes. */ static struct fpa_index *Ordinary_clash_pos_lits; static struct fpa_index *Ordinary_clash_neg_lits; static struct fpa_index *Ordinary_alphas; static struct fpa_index *Ordinary_clash_terms; /************* * * init_hot() -- initialize for hot-list inference. * *************/ void init_hot(void) { Ordinary_clash_pos_lits = Fpa_clash_pos_lits; Ordinary_clash_neg_lits = Fpa_clash_neg_lits; Ordinary_clash_terms = Fpa_clash_terms; Ordinary_alphas = Fpa_alphas; Hot_clash_pos_lits = alloc_fpa_index(); Hot_clash_neg_lits = alloc_fpa_index(); Hot_clash_terms = alloc_fpa_index(); Hot_alphas = alloc_fpa_index(); } /* init_hot */ /************* * * heat_is_on() * * Inference rules need to know if they are doing hot inference * so that they can set the heat level of generated clauses. * This kludgy routine is used instead of passing a parameter * to all the inference routines. * *************/ int heat_is_on(void) { /* just check any one of the indexes */ return(Fpa_alphas == Hot_alphas); } /* heat_is_on */ /************* * * switch_to_hot_index() * *************/ void switch_to_hot_index(void) { Fpa_clash_pos_lits = Hot_clash_pos_lits; Fpa_clash_neg_lits = Hot_clash_neg_lits; Fpa_clash_terms = Hot_clash_terms; Fpa_alphas = Hot_alphas; } /* switch_to_hot_index */ /************* * * switch_to_ordinary_index() * *************/ void switch_to_ordinary_index(void) { Fpa_clash_pos_lits = Ordinary_clash_pos_lits; Fpa_clash_neg_lits = Ordinary_clash_neg_lits; Fpa_clash_terms = Ordinary_clash_terms; Fpa_alphas = Ordinary_alphas; } /* switch_to_ordinary_index */ /************* * * hot_index_clause(c) * * Index a clause for hot inference. * *************/ void hot_index_clause(struct clause *c) { int already_hot = heat_is_on(); if (!already_hot) switch_to_hot_index(); index_lits_clash(c); if (!already_hot) switch_to_ordinary_index(); } /* hot_index_clause */ /************* * * hot_dynamic(c) * * Insert a copy of c into the hot list. * *************/ void hot_dynamic(struct clause *c) { struct clause *hc; hc = cl_copy(c); hc->parents = copy_ilist(c->parents); hc->heat_level = c->heat_level; hot_cl_integrate(hc); if (!Hot->first_cl) init_hot(); hot_index_clause(hc); append_cl(Hot, hc); Stats[HOT_SIZE]++; printf("\nHOT NEW CLAUSE!: "); print_clause(stdout, hc); printf("\n"); } /* hot_dynamic */ /************* * * hot_mark_clash(r) * * See hot_mark_clash_cl below. * *************/ static void hot_mark_clash(struct rel *r) { struct term *t; struct rel *r1; t = r->argval; if (t->type == VARIABLE && Flags[PARA_INTO_VARS].val == 0) return; else { r1 = t->occ.rel; while (r1 != NULL && r1->clashable == 0) r1 = r1->nocc; r->clashable = 1; if (r1 != NULL) return; /* becuase t is already clashable */ else { if (t->type == COMPLEX) { if (Flags[PARA_SKIP_SKOLEM].val == 0 || is_skolem(t->sym_num) == 0) { r = t->farg; while (r != NULL) { hot_mark_clash(r); if (Flags[PARA_ONES_RULE].val) r = NULL; else r = r->narg; } } } } } } /* hot_mark_clash */ /************* * * hot_unmark_clash(r) * * See hot_mark_clash_cl below. * *************/ static void hot_unmark_clash(struct rel *r) { struct term *t; struct rel *r1; t = r->argval; if (t->type == VARIABLE && Flags[PARA_INTO_VARS].val == 0) return; else { r->clashable = 0; r1 = t->occ.rel; while (r1 != NULL && r1->clashable == 0) r1 = r1->nocc; if (r1 != NULL) return; /* becuase t is clashable from another containing term */ else { if (t->type == COMPLEX) { if (Flags[PARA_SKIP_SKOLEM].val == 0 || is_skolem(t->sym_num) == 0) { r = t->farg; while (r != NULL) { hot_unmark_clash(r); if (Flags[PARA_ONES_RULE].val) r = NULL; else r = r->narg; } } } } } } /* hot_unmark_clash */ /************* * * hot_mark_clash_cl(c, mark) * * This is used for hot paramoudulation into the new clause. * The clashable subterms have to be marked so that the ordinary * para_into will work. This is similar to (un)index_mark_clash * in index.c, but it marks/unmarks only---no indexing is done. * *************/ void hot_mark_clash_cl(struct clause *c, int mark) { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) { if (!Flags[PARA_INTO_UNITS_ONLY].val || unit_clause(c)) { if (eq_lit(lit)) { if (Flags[PARA_INTO_LEFT].val) { if (mark) hot_mark_clash(lit->atom->farg); else hot_unmark_clash(lit->atom->farg); } if (Flags[PARA_INTO_RIGHT].val) { if (mark) hot_mark_clash(lit->atom->farg->narg); else hot_unmark_clash(lit->atom->farg->narg); } } else { struct rel *r; for (r = lit->atom->farg; r; r = r->narg) if (mark) hot_mark_clash(r); else hot_unmark_clash(r); } } } } /* hot_mark_clash_cl */ /************* * * hot_inference(new_cl) * *************/ void hot_inference(struct clause *new_cl) { if (new_cl->heat_level < Parms[HEAT].val) { CLOCK_START(HOT_TIME); switch_to_hot_index(); /* Swap in hot indexes. */ if (Flags[BINARY_RES].val) bin_res(new_cl); if (Flags[HYPER_RES].val) hyper_res(new_cl); if (Flags[NEG_HYPER_RES].val) neg_hyper_res(new_cl); if (Flags[UR_RES].val) ur_res(new_cl); if (Flags[PARA_INTO].val) { /* only need the clash marks, not the indexing */ hot_mark_clash_cl(new_cl, 1); para_into(new_cl); hot_mark_clash_cl(new_cl, 0); } if (Flags[PARA_FROM].val) para_from(new_cl); switch_to_ordinary_index(); /* Restore the ordinary indexes. */ CLOCK_STOP(HOT_TIME); } } /* hot_inference */ otter-3.3f/source/imd.c0100644000076400007640000002756107653773062014450 0ustar mccunemccune/* * * imd.c -- This file contains routines for discrimination * tree indexing for demodulation. * */ #include "header.h" /************* * * struct imd_tree *insert_imd_tree(t, imd) -- called by imd_insert * *************/ static struct imd_tree *insert_imd_tree(struct term *t, struct imd_tree *imd) { struct rel *r; struct imd_tree *i1, *i2, *i3; int varnum, sym; if (t->type == VARIABLE) { i1 = imd->kids; i2 = NULL; varnum = t->varnum; while (i1 != NULL && i1->type == VARIABLE && (int) i1->lab < varnum) { i2 = i1; i1 = i1->next; } if (i1 == NULL || i1->type != VARIABLE || i1->lab != varnum) { i3 = get_imd_tree(); i3->type = VARIABLE; i3->lab = varnum; i3->next = i1; if (i2 == NULL) imd->kids = i3; else i2->next = i3; return(i3); } else /* found node */ return(i1); } else { /* NAME || COMPLEX */ i1 = imd->kids; i2 = NULL; sym = t->sym_num; /* arities fixed: handle both NAME and COMPLEX */ while (i1 != NULL && i1->type == VARIABLE) { /* skip variables */ i2 = i1; i1 = i1->next; } while (i1 != NULL && (int) i1->lab < sym) { i2 = i1; i1 = i1->next; } if (i1 == NULL || i1->lab != sym) { i3 = get_imd_tree(); i3->type = t->type; i3->lab = sym; i3->next = i1; i1 = i3; } else i3 = NULL; /* new node not required at this level */ if (t->type == COMPLEX) { r = t->farg; while (r != NULL) { i1 = insert_imd_tree(r->argval, i1); r = r->narg; } } if (i3 != NULL) { /* link in new subtree (possibly a leaf) */ if (i2 == NULL) imd->kids = i3; else i2->next = i3; } return(i1); /* i1 is leaf corresp. to end of input term */ } } /* insert_imd_tree */ /************* * * imd_insert(demod, imd) * * Insert the left argument of demod into the discrimination * tree index for demodulation. * *************/ void imd_insert(struct clause *demod, struct imd_tree *imd) { struct imd_tree *i1; struct term *atom, *alpha, *beta; struct term_ptr *tp; int max; atom = ith_literal(demod,1)->atom; if (atom->varnum != CONDITIONAL_DEMOD) { alpha = atom->farg->argval; beta = atom->farg->narg->argval; } else { /* CONDITIONAL(cond, alpha, beta) */ alpha = atom->farg->narg->argval->farg->argval; beta = atom->farg->narg->argval->farg->narg->argval; } if (term_ident(alpha, beta)) { fprintf(stderr, "\nWARNING, instance of x=x cannot be inserted into demod_imd index: "); print_clause(stderr, demod); printf("\nWARNING, instance of x=x cannot be inserted into demod_imd index: "); print_clause(stdout, demod); } else { i1 = insert_imd_tree(alpha, imd); tp = get_term_ptr(); tp->term = atom; tp->next = i1->atoms; if ((max = biggest_var(alpha)) == -1) i1->max_vnum = 0; /* in case i->max_vnum is an unsigned char */ else i1->max_vnum = max; i1->atoms = tp; } } /* imd_insert */ /************* * * struct imd_tree *end_term_imd(t, imd, path_p) * * Given a discrimination tree (or a subtree) and a term, return the * node in the tree that corresponds to the last symbol in t (or NULL * if the node doesn't exist). *path_p is a list that is extended by * this routine. It is a list of pointers to the * nodes in path from the parent of the returned node up to imd. * (It is needed for deletions, because nodes do not have pointers to * parents.) * *************/ static struct imd_tree *end_term_imd(struct term *t, struct imd_tree *imd, struct term_ptr **path_p) { struct rel *r; struct imd_tree *i1; struct term_ptr *imdp; int varnum, sym; /* add current node to the front of the path list. */ imdp = get_term_ptr(); imdp->term = (struct term *) imd; imdp->next = *path_p; *path_p = imdp; if (t->type == VARIABLE) { i1 = imd->kids; varnum = t->varnum; while (i1 != NULL && i1->type == VARIABLE && (int) i1->lab < varnum) i1 = i1->next; if (i1 == NULL || i1->type != VARIABLE || i1->lab != varnum) return(NULL); else /* found node */ return(i1); } else { /* NAME || COMPLEX */ i1 = imd->kids; sym = t->sym_num; /* arities fixed: handle both NAME and COMPLEX */ while (i1 != NULL && i1->type == VARIABLE) /* skip variables */ i1 = i1->next; while (i1 != NULL && (int) i1->lab < sym) i1 = i1->next; if (i1 == NULL || i1->lab != sym) return(NULL); else { if (t->type == NAME) return(i1); else { r = t->farg; while (r != NULL && i1 != NULL) { i1 = end_term_imd(r->argval, i1, path_p); r = r->narg; } return(i1); } } } } /* end_term_imd */ /************* * * imd_delete(demod, root_imd) * * Delete the left argument of demod from the demodulation discrimination tree. * *************/ void imd_delete(struct clause *demod, struct imd_tree *root_imd) { struct imd_tree *end, *i2, *i3, *parent; struct term_ptr *tp1, *tp2; struct term_ptr *imdp, *path; struct term *atom, *alpha; /* First find the correct leaf. path is used to help with */ /* freeing nodes, because nodes don't have parent pointers. */ path = NULL; atom = ith_literal(demod,1)->atom; if (atom->varnum == CONDITIONAL_DEMOD) alpha = atom->farg->narg->argval->farg->argval; else alpha = atom->farg->argval; end = end_term_imd(alpha, root_imd, &path); if (end == NULL) { print_term_nl(stdout, alpha); abend("imd_delete, can't find alpha."); } tp1 = end->atoms; tp2 = NULL; while (tp1 != NULL && tp1->term != atom) { tp2 = tp1; tp1 = tp1->next; } if (tp1 == NULL) { print_term_nl(stdout, atom); abend("imd_delete, can't find atom."); } if (tp2 == NULL) end->atoms = tp1->next; else tp2->next = tp1->next; free_term_ptr(tp1); if (end->atoms == NULL) { /* free tree nodes from bottom up, using path to get parents */ imdp = path; while (end->kids == NULL && end != root_imd) { parent = (struct imd_tree *) imdp->term; imdp = imdp->next; i2 = parent->kids; i3 = NULL; while (i2 != end) { i3 = i2; i2 = i2->next; } if (i3 == NULL) parent->kids = i2->next; else i3->next = i2->next; free_imd_tree(i2); end = parent; } } /* free path list */ while (path != NULL) { imdp = path; path = path->next; free_term_ptr(imdp); } } /* imd_delete */ /************* * * struct term *contract_imd(t_in, demods, subst, demod_id_p) * * Attempt to contract (rewrite one step) a term (t_in) using demodulators * in a disckrimination tree index (demods). NULL is returned if t_in * cannot be contracted. subst is an empty substitution. * If success, *demod_id_p is set to the ID of the rewrite rule. * *************/ struct term *contract_imd(struct term *t_in, int *demods, struct context *subst, int *demod_id_p) { struct rel *rel_stack[MAX_AL_TERM_DEPTH]; struct imd_tree *imd, *i1; struct imd_pos *pos, *ip2; struct term *t, *t2, *t3, *atom; struct term *replacement = NULL; struct term_ptr *tp; int top, found, backup, varnum, j, reset, mult_flag, sym, ok, dummy; imd = (struct imd_tree *) demods; if (imd == NULL) return(NULL); pos = NULL; top = -1; backup = 0; i1 = imd->kids; t = t_in; while(1) { if (backup) { if (pos == NULL) return(NULL); else { /* pop top of stack (most recent variable node) and restore state */ top = pos->stack_pos; for (j = 0; j <= top; j++) rel_stack[j] = pos->rel_stack[j]; i1 = pos->imd; t = subst->terms[i1->lab]; if (pos->reset) /* undo variable binding */ subst->terms[i1->lab] = NULL; i1 = i1->next; ip2 = pos; pos = pos->next; free_imd_pos(ip2); } } /* at this point, i1 is the next node to try */ found = 0; /* first try to match input term t with a variable node */ while (found == 0 && i1 != NULL && i1->type == VARIABLE) { varnum = i1->lab; if (subst->terms[varnum] == NULL) { /*if not bound, bind it */ subst->terms[varnum] = t; subst->contexts[varnum] = NULL; found = 1; reset = 1; } else { /* bound variable, succeed iff identical */ found = term_ident(subst->terms[varnum], t); reset = 0; } if (found) { /* save state */ ip2 = get_imd_pos(); ip2->next = pos; pos = ip2; pos->imd = i1; pos->reset = reset; for (j = 0; j <= top; j++) pos->rel_stack[j] = rel_stack[j]; pos->stack_pos = top; } else /* try next variable */ i1 = i1->next; } backup = 0; if (found == 0) { /* couldn't match t with (another) variable */ if (t->type == VARIABLE) backup = 1; /* because we can't instantiate given term */ else { /* NAME or COMPLEX */ sym = t->sym_num; while (i1 != NULL && (int) i1->lab < sym) i1 = i1->next; if (i1 == NULL || i1->lab != sym) backup = 1; else if (t->type == COMPLEX) { top++; if (top >= MAX_AL_TERM_DEPTH) { abend("contract_imd, increase MAX_AL_TERM_DEPTH."); return(NULL); /* to quiet lint */ } rel_stack[top] = t->farg; /* save pointer to subterms */ } } } if (backup == 0) { /* get next term from rel_stack */ while (top >= 0 && rel_stack[top] == NULL) top--; if (top == -1) { /* found potential demods */ tp = i1->atoms; ok = 0; while(tp != NULL && ok == 0) { atom = tp->term; mult_flag = 0; if (atom->varnum == LEX_DEP_DEMOD) { replacement = apply_demod(atom->farg->narg->argval, subst, &mult_flag); if (Flags[LRPO].val) ok = lrpo_greater(t_in, replacement); else ok = lex_check(replacement, t_in) == LESS_THAN; if (ok == 0) { zap_term_special(replacement); tp = tp->next; } } else if (atom->varnum == CONDITIONAL_DEMOD) { /* apply subst to condition, then demodulate */ t2 = apply_demod(atom->farg->argval, subst, &dummy); un_share_special(t2); t3 = convenient_demod(t2); ok = is_symbol(t3, "$T", 0); zap_term_special(t3); if (ok) replacement = apply_demod(atom->farg->narg->argval->farg->narg->argval, subst, &mult_flag); else tp = tp->next; } else { /* redular demoulator */ replacement = apply_demod(atom->farg->narg->argval, subst, &mult_flag); ok = 1; } } if (ok) { if (mult_flag) subst->multiplier++; for (j = 0; j <= (int) i1->max_vnum; j++) /* clear substitution */ subst->terms[j] = NULL; free_imd_pos_list(pos); zap_term_special(t_in); *demod_id_p = tp->term->occ.lit->container->id; return(replacement); } else /* failed lex_checks, so prepare to back up */ backup = 1; } else { /* pop a term and continue */ t = rel_stack[top]->argval; rel_stack[top] = rel_stack[top]->narg; i1 = i1->kids; } } } /* end of while(1) loop */ } /* contract_imd */ /************* * * print_imd_tree(file_pointer, imd_tree, level) * * Display an imd tree. Level == 0 on initial call. * *************/ void print_imd_tree(FILE *fp, struct imd_tree *imd, int level) { struct imd_tree *i1; int i; fprintf(fp, "%p ", (void *) imd); for (i = 0; i < level; i++) fprintf(fp, " "); if (imd->type == 0) fprintf(fp, "start of index-match-demodulate tree"); else if (imd->type == VARIABLE) fprintf(fp, "v%d ", imd->lab); else fprintf(fp, "%s ", sn_to_str((int) imd->lab)); if (imd->atoms != NULL) { fprintf(fp, " demod="); print_term(fp, imd->atoms->term); } fprintf(fp, "\n"); i1 = imd->kids; while (i1 != NULL) { print_imd_tree(fp, i1, level + 1); i1 = i1->next; } } /* print_imd_tree */ /************* * * p_imd_tree(imd_tree) * * Display an imd tree. Level == 0 on initial call. * *************/ void p_imd_tree(struct imd_tree *imd) { print_imd_tree(stdout, imd, 0); } /* p_imd_tree */ otter-3.3f/source/fpa2.h0100644000076400007640000000242410041261435014500 0ustar mccunemccune#ifndef TP_FPA2_H #define TP_FPA2_H /* The objects in FPA lists are pointers to terms, and the lists are ordered (decreasing) by fpa_id field in terms. The code was originally written and debugged with integers instead; hence, the following, which makes it easy to change back to ints. */ #define FTYPE struct term * #define FDEFAULT NULL #define FLT(x,y) ((x)->fpa_id < (y)->fpa_id) #define FGT(x,y) ((x)->fpa_id > (y)->fpa_id) #define FLE(x,y) ((x)->fpa_id <= (y)->fpa_id) #define FGE(x,y) ((x)->fpa_id >= (y)->fpa_id) #define FEQ(x,y) ((x) == (y)) #define FNE(x,y) ((x) != (y)) #define FTERM(p) ((p).f == NULL ? NULL : (p).f->d[(p).i]) /* A chunk of an FPA list */ #define FMAX 400 /* maximum number of items per chunk */ typedef struct fnode *Fnode; struct fnode { FTYPE d[FMAX]; /* array for chunk */ int n; /* current size of chunk (right justified in array) */ Fnode next; /* list of chunks is singly-linked */ }; /* to maintain a position in an FPA list */ struct fposition { Fnode f; int i; }; /* function prototypes */ Fnode flist_insert(Fnode f, FTYPE x); Fnode flist_delete(Fnode f, FTYPE x); struct fposition first_fpos(Fnode f); struct fposition next_fpos(struct fposition p); #endif /* conditional compilation of whole file */ otter-3.3f/source/options.c0100644000076400007640000010005110103511210015315 0ustar mccunemccune/* * options.c -- Routines to manage flags and parameters. * */ #include "header.h" /************* * * init_options() * *************/ void init_options(void) { int i; for (i = 0; i < MAX_FLAGS; i++) Flags[i].name = ""; for (i = 0; i < MAX_PARMS; i++) Parms[i].name = ""; /* flags are boolean valued options */ Flags[BINARY_RES].name = "binary_res"; Flags[BINARY_RES].val = 0; Flags[HYPER_RES].name = "hyper_res"; Flags[HYPER_RES].val = 0; Flags[NEG_HYPER_RES].name = "neg_hyper_res"; Flags[NEG_HYPER_RES].val = 0; Flags[UR_RES].name = "ur_res"; Flags[UR_RES].val = 0; Flags[PARA_FROM].name = "para_from"; Flags[PARA_FROM].val = 0; Flags[PARA_INTO].name = "para_into"; Flags[PARA_INTO].val = 0; Flags[PARA_FROM_LEFT].name = "para_from_left"; Flags[PARA_FROM_LEFT].val = 1; Flags[PARA_FROM_RIGHT].name = "para_from_right"; Flags[PARA_FROM_RIGHT].val = 1; Flags[PARA_FROM_VARS].name = "para_from_vars"; Flags[PARA_FROM_VARS].val = 0; Flags[PARA_INTO_VARS].name = "para_into_vars"; Flags[PARA_INTO_VARS].val = 0; Flags[PARA_INTO_LEFT].name = "para_into_left"; Flags[PARA_INTO_LEFT].val = 1; Flags[PARA_INTO_RIGHT].name = "para_into_right"; Flags[PARA_INTO_RIGHT].val = 1; Flags[PARA_ONES_RULE].name = "para_ones_rule"; Flags[PARA_ONES_RULE].val = 0; Flags[PARA_ALL].name = "para_all"; Flags[PARA_ALL].val = 0; Flags[DEMOD_INF].name = "demod_inf"; Flags[DEMOD_INF].val = 0; Flags[DEMOD_LINEAR].name = "demod_linear"; Flags[DEMOD_LINEAR].val = 0; Flags[VERY_VERBOSE].name = "very_verbose"; Flags[VERY_VERBOSE].val = 0; Flags[FOR_SUB_FPA].name = "for_sub_fpa"; Flags[FOR_SUB_FPA].val = 0; Flags[FOR_SUB].name = "for_sub"; Flags[FOR_SUB].val = 1; Flags[BACK_SUB].name = "back_sub"; Flags[BACK_SUB].val = 1; Flags[FREE_ALL_MEM].name = "free_all_mem"; Flags[FREE_ALL_MEM].val = 0; Flags[NO_FAPL].name = "no_fapl"; Flags[NO_FAPL].val = 0; Flags[NO_FANL].name = "no_fanl"; Flags[NO_FANL].val = 0; Flags[FACTOR].name = "factor"; Flags[FACTOR].val = 0; Flags[PRINT_KEPT].name = "print_kept"; Flags[PRINT_KEPT].val = 1; Flags[DEMOD_HISTORY].name = "demod_history"; Flags[DEMOD_HISTORY].val = 1; Flags[UNIT_DELETION].name = "unit_deletion"; Flags[UNIT_DELETION].val = 0; Flags[SORT_LITERALS].name = "sort_literals"; Flags[SORT_LITERALS].val = 0; Flags[PRINT_GIVEN].name = "print_given"; Flags[PRINT_GIVEN].val = 1; Flags[PRINT_BACK_SUB].name = "print_back_sub"; Flags[PRINT_BACK_SUB].val = 1; Flags[CHECK_ARITY].name = "check_arity"; Flags[CHECK_ARITY].val = 1; Flags[SOS_QUEUE].name = "sos_queue"; Flags[SOS_QUEUE].val = 0; Flags[ATOM_WT_MAX_ARGS].name = "atom_wt_max_args"; Flags[ATOM_WT_MAX_ARGS].val = 0; Flags[TERM_WT_MAX_ARGS].name = "term_wt_max_args"; Flags[TERM_WT_MAX_ARGS].val = 0; Flags[PRINT_LISTS_AT_END].name = "print_lists_at_end"; Flags[PRINT_LISTS_AT_END].val = 0; Flags[ORDER_EQ].name = "order_eq"; Flags[ORDER_EQ].val = 0; Flags[DYNAMIC_DEMOD].name = "dynamic_demod"; Flags[DYNAMIC_DEMOD].val = 0; Flags[BACK_DEMOD].name = "back_demod"; Flags[BACK_DEMOD].val = 0; Flags[PRINT_NEW_DEMOD].name = "print_new_demod"; Flags[PRINT_NEW_DEMOD].val = 1; Flags[PRINT_BACK_DEMOD].name = "print_back_demod"; Flags[PRINT_BACK_DEMOD].val = 1; Flags[DEMOD_OUT_IN].name = "demod_out_in"; Flags[DEMOD_OUT_IN].val = 0; Flags[PROCESS_INPUT].name = "process_input"; Flags[PROCESS_INPUT].val = 0; Flags[SIMPLIFY_FOL].name = "simplify_fol"; Flags[SIMPLIFY_FOL].val = 1; Flags[ANL_EQ].name = "anl_eq"; Flags[ANL_EQ].val = 0; Flags[KNUTH_BENDIX].name = "knuth_bendix"; Flags[KNUTH_BENDIX].val = 0; Flags[REWRITER].name = "rewriter"; Flags[REWRITER].val = 0; Flags[PRINT_PROOFS].name = "print_proofs"; Flags[PRINT_PROOFS].val = 1; Flags[SYMBOL_ELIM].name = "symbol_elim"; Flags[SYMBOL_ELIM].val = 0; Flags[LEX_ORDER_VARS].name = "lex_order_vars"; Flags[LEX_ORDER_VARS].val = 0; Flags[DYNAMIC_DEMOD_ALL].name = "dynamic_demod_all"; Flags[DYNAMIC_DEMOD_ALL].val = 0; Flags[DELETE_IDENTICAL_NESTED_SKOLEM].name = "delete_identical_nested_skolem"; Flags[DELETE_IDENTICAL_NESTED_SKOLEM].val = 0; Flags[PARA_FROM_UNITS_ONLY].name = "para_from_units_only"; Flags[PARA_FROM_UNITS_ONLY].val = 0; Flags[PARA_INTO_UNITS_ONLY].name = "para_into_units_only"; Flags[PARA_INTO_UNITS_ONLY].val = 0; Flags[REALLY_DELETE_CLAUSES].name = "really_delete_clauses"; Flags[REALLY_DELETE_CLAUSES].val = 0; Flags[LRPO].name = "lrpo"; Flags[LRPO].val = 0; Flags[PROLOG_STYLE_VARIABLES].name = "prolog_style_variables"; Flags[PROLOG_STYLE_VARIABLES].val = 0; Flags[SOS_STACK].name = "sos_stack"; Flags[SOS_STACK].val = 0; Flags[DYNAMIC_DEMOD_LEX_DEP].name = "dynamic_demod_lex_dep"; Flags[DYNAMIC_DEMOD_LEX_DEP].val = 0; Flags[PROG_SYNTHESIS].name = "prog_synthesis"; Flags[PROG_SYNTHESIS].val = 0; Flags[ANCESTOR_SUBSUME].name = "ancestor_subsume"; Flags[ANCESTOR_SUBSUME].val = 0; Flags[INPUT_SOS_FIRST].name = "input_sos_first"; Flags[INPUT_SOS_FIRST].val = 0; Flags[LINKED_UR_RES].name = "linked_ur_res"; Flags[LINKED_UR_RES].val = 0; Flags[LINKED_UR_TRACE].name = "linked_ur_trace"; Flags[LINKED_UR_TRACE].val = 0; Flags[PARA_SKIP_SKOLEM].name = "para_skip_skolem"; Flags[PARA_SKIP_SKOLEM].val = 0; Flags[INDEX_FOR_BACK_DEMOD].name = "index_for_back_demod"; Flags[INDEX_FOR_BACK_DEMOD].val = 1; Flags[LINKED_SUB_UNIT_USABLE].name = "linked_sub_unit_usable"; Flags[LINKED_SUB_UNIT_USABLE].val = 0; Flags[LINKED_SUB_UNIT_SOS].name = "linked_sub_unit_sos"; Flags[LINKED_SUB_UNIT_SOS].val = 0; Flags[LINKED_UNIT_DEL].name = "linked_unit_del"; Flags[LINKED_UNIT_DEL].val = 0; Flags[LINKED_TARGET_ALL].name = "linked_target_all"; Flags[LINKED_TARGET_ALL].val = 0; Flags[LINKED_HYPER_RES].name = "linked_hyper_res"; Flags[LINKED_HYPER_RES].val = 0; Flags[CONTROL_MEMORY].name = "control_memory"; Flags[CONTROL_MEMORY].val = 0; Flags[ORDER_HISTORY].name = "order_history"; Flags[ORDER_HISTORY].val = 0; Flags[DISPLAY_TERMS].name = "display_terms"; Flags[DISPLAY_TERMS].val = 0; Flags[GEOMETRIC_RULE].name = "geometric_rule"; Flags[GEOMETRIC_RULE].val = 0; Flags[GEOMETRIC_REWRITE_BEFORE].name = "geometric_rewrite_before"; Flags[GEOMETRIC_REWRITE_BEFORE].val = 0; Flags[GEOMETRIC_REWRITE_AFTER].name = "geometric_rewrite_after"; Flags[GEOMETRIC_REWRITE_AFTER].val = 0; Flags[PRETTY_PRINT].name = "pretty_print"; Flags[PRETTY_PRINT].val = 0; Flags[INPUT_SEQUENT].name = "input_sequent"; Flags[INPUT_SEQUENT].val = 0; Flags[OUTPUT_SEQUENT].name = "output_sequent"; Flags[OUTPUT_SEQUENT].val = 0; Flags[ECHO_INCLUDED_FILES].name = "echo_included_files"; Flags[ECHO_INCLUDED_FILES].val = 1; Flags[INTERACTIVE_GIVEN].name = "interactive_given"; Flags[INTERACTIVE_GIVEN].val = 0; Flags[DETAILED_HISTORY].name = "detailed_history"; Flags[DETAILED_HISTORY].val = 1; Flags[ORDER_HYPER].name = "order_hyper"; Flags[ORDER_HYPER].val = 1; Flags[PROPOSITIONAL].name = "propositional"; Flags[PROPOSITIONAL].val = 0; Flags[AUTO].name = "auto"; Flags[AUTO].val = 0; Flags[AUTO1].name = "auto1"; Flags[AUTO1].val = 0; Flags[AUTO2].name = "auto2"; Flags[AUTO2].val = 0; Flags[EQ_UNITS_BOTH_WAYS].name = "eq_units_both_ways"; Flags[EQ_UNITS_BOTH_WAYS].val = 0; Flags[BIRD_PRINT].name = "bird_print"; Flags[BIRD_PRINT].val = 0; Flags[BUILD_PROOF_OBJECT].name = "build_proof_object"; Flags[BUILD_PROOF_OBJECT].val = 0; Flags[BUILD_PROOF_OBJECT_1].name = "build_proof_object_1"; Flags[BUILD_PROOF_OBJECT_1].val = 0; Flags[BUILD_PROOF_OBJECT_2].name = "build_proof_object_2"; Flags[BUILD_PROOF_OBJECT_2].val = 0; Flags[LOG_FOR_X_SHOW].name = "log_for_x_show"; Flags[LOG_FOR_X_SHOW].val = 0; Flags[FORMULA_HISTORY].name = "formula_history"; Flags[FORMULA_HISTORY].val = 0; Flags[KEEP_HINT_SUBSUMERS].name = "keep_hint_subsumers"; Flags[KEEP_HINT_SUBSUMERS].val = 0; Flags[KEEP_HINT_EQUIVALENTS].name = "keep_hint_equivalents"; Flags[KEEP_HINT_EQUIVALENTS].val = 0; Flags[PROOF_WEIGHT].name = "proof_weight"; Flags[PROOF_WEIGHT].val = 0; Flags[HYPER_SYMMETRY_KLUDGE].name = "hyper_symmetry_kludge"; Flags[HYPER_SYMMETRY_KLUDGE].val = 0; Flags[GL_DEMOD].name = "gl_demod"; Flags[GL_DEMOD].val = 0; Flags[DISCARD_NON_ORIENTABLE_EQ].name = "discard_non_orientable_eq"; Flags[DISCARD_NON_ORIENTABLE_EQ].val = 0; Flags[DISCARD_XX_RESOLVABLE].name = "discard_xx_resolvable"; Flags[DISCARD_XX_RESOLVABLE].val = 0; Flags[TPTP_EQ].name = "tptp_eq"; Flags[TPTP_EQ].val = 0; Flags[BELL].name = "bell"; Flags[BELL].val = 1; /* Do not set default to 0 */ Flags[BACK_UNIT_DELETION].name = "back_unit_deletion"; Flags[BACK_UNIT_DELETION].val = 0; Flags[SPLIT_CLAUSE].name = "split_clause"; Flags[SPLIT_CLAUSE].val = 0; Flags[SPLIT_POS].name = "split_pos"; Flags[SPLIT_POS].val = 0; Flags[SPLIT_NEG].name = "split_neg"; Flags[SPLIT_NEG].val = 0; Flags[SPLIT_NONHORN].name = "split_nonhorn"; Flags[SPLIT_NONHORN].val = 0; Flags[SPLIT_MIN_MAX].name = "split_min_max"; Flags[SPLIT_MIN_MAX].val = 0; Flags[SPLIT_ATOM].name = "split_atom"; Flags[SPLIT_ATOM].val = 0; Flags[SPLIT_POPULAR].name = "split_popular"; Flags[SPLIT_POPULAR].val = 0; Flags[SPLIT_WHEN_GIVEN].name = "split_when_given"; Flags[SPLIT_WHEN_GIVEN].val = 0; Flags[UNIT_RES].name = "unit_res"; Flags[UNIT_RES].val = 0; Flags[SIGINT_INTERACT].name = "sigint_interact"; Flags[SIGINT_INTERACT].val = 1; Flags[UR_LAST].name = "ur_last"; Flags[UR_LAST].val = 0; Flags[LITERALS_WEIGH_ONE].name = "literals_weigh_one"; Flags[LITERALS_WEIGH_ONE].val = 0; Flags[PICK_DIFF_SIM].name = "pick_diff_sim"; Flags[PICK_DIFF_SIM].val = 0; Flags[PICK_RANDOM_LIGHTEST].name = "pick_random_lightest"; Flags[PICK_RANDOM_LIGHTEST].val = 0; Flags[PICK_LAST_LIGHTEST].name = "pick_last_lightest"; Flags[PICK_LAST_LIGHTEST].val = 0; Flags[PICK_MID_LIGHTEST].name = "pick_mid_lightest"; Flags[PICK_MID_LIGHTEST].val = 0; Flags[FOR_SUB_EQUIVALENTS_ONLY].name = "for_sub_equivalents_only"; Flags[FOR_SUB_EQUIVALENTS_ONLY].val = 0; Flags[MULTI_JUST].name = "multi_just"; Flags[MULTI_JUST].val = 0; Flags[MULTI_JUST_LESS].name = "multi_just_less"; Flags[MULTI_JUST_LESS].val = 0; Flags[MULTI_JUST_SHORTER].name = "multi_just_shorter"; Flags[MULTI_JUST_SHORTER].val = 0; Flags[PRINT_PROOF_AS_HINTS].name = "print_proof_as_hints"; Flags[PRINT_PROOF_AS_HINTS].val = 0; Flags[DISCARD_COMMUTATIVITY_CONSEQUENCES].name = "discard_commutativity_consequences"; Flags[DISCARD_COMMUTATIVITY_CONSEQUENCES].val = 0; Flags[DEGRADE_HINTS2].name = "degrade_hints2"; Flags[DEGRADE_HINTS2].val = 0; Flags[CLOCKS].name = "clocks"; Flags[CLOCKS].val = 0; /* parms are integer valued options */ Parms[FPA_LITERALS].name = "fpa_literals"; Parms[FPA_LITERALS].val = 8; Parms[FPA_LITERALS].min = 0; Parms[FPA_LITERALS].max = 100; /* check MAX_PATH before increasing */ Parms[FPA_TERMS].name = "fpa_terms"; Parms[FPA_TERMS].val = 8; Parms[FPA_TERMS].min = 0; Parms[FPA_TERMS].max = 100; /* check MAX_PATH before increasing */ Parms[DEMOD_LIMIT].name = "demod_limit"; Parms[DEMOD_LIMIT].val = 1000; Parms[DEMOD_LIMIT].min = -1; Parms[DEMOD_LIMIT].max = MAX_INT; Parms[MAX_WEIGHT].name = "max_weight"; Parms[MAX_WEIGHT].val = MAX_INT; Parms[MAX_WEIGHT].min = -MAX_INT; Parms[MAX_WEIGHT].max = MAX_INT; Parms[MAX_GIVEN].name = "max_given"; Parms[MAX_GIVEN].val = -1; Parms[MAX_GIVEN].min = -1; Parms[MAX_GIVEN].max = MAX_INT; Parms[MAX_LEVELS].name = "max_levels"; Parms[MAX_LEVELS].val = -1; Parms[MAX_LEVELS].min = -1; Parms[MAX_LEVELS].max = MAX_INT; Parms[MAX_SECONDS].name = "max_seconds"; Parms[MAX_SECONDS].val = -1; Parms[MAX_SECONDS].min = -1; Parms[MAX_SECONDS].max = MAX_INT; Parms[NEG_WEIGHT].name = "neg_weight"; Parms[NEG_WEIGHT].val = 0; Parms[NEG_WEIGHT].min = -MAX_INT; Parms[NEG_WEIGHT].max = MAX_INT; Parms[MAX_KEPT].name = "max_kept"; Parms[MAX_KEPT].val = -1; Parms[MAX_KEPT].min = -1; Parms[MAX_KEPT].max = MAX_INT; Parms[MAX_GEN].name = "max_gen"; Parms[MAX_GEN].val = -1; Parms[MAX_GEN].min = -1; Parms[MAX_GEN].max = MAX_INT; Parms[MAX_MEM].name = "max_mem"; Parms[MAX_MEM].val = -1; Parms[MAX_MEM].min = -1; Parms[MAX_MEM].max = MAX_INT; Parms[MAX_LITERALS].name = "max_literals"; Parms[MAX_LITERALS].val = -1; Parms[MAX_LITERALS].min = -1; Parms[MAX_LITERALS].max = MAX_INT; Parms[REPORT].name = "report"; Parms[REPORT].val = -1; Parms[REPORT].min = -1; Parms[REPORT].max = MAX_INT; Parms[MAX_PROOFS].name = "max_proofs"; Parms[MAX_PROOFS].val = 1; Parms[MAX_PROOFS].min = -1; Parms[MAX_PROOFS].max = MAX_INT; Parms[STATS_LEVEL].name = "stats_level"; Parms[STATS_LEVEL].val = 2; Parms[STATS_LEVEL].min = 0; Parms[STATS_LEVEL].max = 4; Parms[MAX_UR_DEPTH].name = "max_ur_depth"; Parms[MAX_UR_DEPTH].val = 5; Parms[MAX_UR_DEPTH].min = 0; Parms[MAX_UR_DEPTH].max = 100; Parms[MAX_UR_DEDUCTION_SIZE].name = "max_ur_deduction_size"; Parms[MAX_UR_DEDUCTION_SIZE].val = 20; Parms[MAX_UR_DEDUCTION_SIZE].min = 0; Parms[MAX_UR_DEDUCTION_SIZE].max = 100; Parms[MAX_DISTINCT_VARS].name = "max_distinct_vars"; Parms[MAX_DISTINCT_VARS].val = -1; Parms[MAX_DISTINCT_VARS].min = -1; Parms[MAX_DISTINCT_VARS].max = MAX_INT; Parms[PICK_GIVEN_RATIO].name = "pick_given_ratio"; Parms[PICK_GIVEN_RATIO].val = -1; Parms[PICK_GIVEN_RATIO].min = -1; Parms[PICK_GIVEN_RATIO].max = MAX_INT; Parms[CHANGE_LIMIT_AFTER].name = "change_limit_after"; Parms[CHANGE_LIMIT_AFTER].val = 0; Parms[CHANGE_LIMIT_AFTER].min = 0; Parms[CHANGE_LIMIT_AFTER].max = MAX_INT; Parms[NEW_MAX_WEIGHT].name = "new_max_weight"; Parms[NEW_MAX_WEIGHT].val = MAX_INT; Parms[NEW_MAX_WEIGHT].min = -MAX_INT; Parms[NEW_MAX_WEIGHT].max = MAX_INT; Parms[GEO_GIVEN_RATIO].name = "geo_given_ratio"; Parms[GEO_GIVEN_RATIO].val = 1; Parms[GEO_GIVEN_RATIO].min = -1; Parms[GEO_GIVEN_RATIO].max = MAX_INT; Parms[PRETTY_PRINT_INDENT].name = "pretty_print_indent"; Parms[PRETTY_PRINT_INDENT].val = 4; Parms[PRETTY_PRINT_INDENT].min = 0; Parms[PRETTY_PRINT_INDENT].max = 16; Parms[MIN_BIT_WIDTH].name = "min_bit_width"; Parms[MIN_BIT_WIDTH].val = sizeof(unsigned long) * CHAR_BIT; Parms[MIN_BIT_WIDTH].min = 1; Parms[MIN_BIT_WIDTH].max = sizeof(unsigned long) * CHAR_BIT; Parms[INTERRUPT_GIVEN].name = "interrupt_given"; Parms[INTERRUPT_GIVEN].val = -1; Parms[INTERRUPT_GIVEN].min = -1; Parms[INTERRUPT_GIVEN].max = MAX_INT; Parms[HEAT].name = "heat"; Parms[HEAT].val = 1; Parms[HEAT].min = 0; Parms[HEAT].max = 100; Parms[DYNAMIC_HEAT_WEIGHT].name = "dynamic_heat_weight"; Parms[DYNAMIC_HEAT_WEIGHT].val = -MAX_INT; Parms[DYNAMIC_HEAT_WEIGHT].min = -MAX_INT; Parms[DYNAMIC_HEAT_WEIGHT].max = MAX_INT; Parms[MAX_ANSWERS].name = "max_answers"; Parms[MAX_ANSWERS].val = -1; Parms[MAX_ANSWERS].min = -1; Parms[MAX_ANSWERS].max = MAX_INT; Parms[DEBUG_FIRST].name = "debug_first"; Parms[DEBUG_FIRST].val = 0; Parms[DEBUG_FIRST].min = 0; Parms[DEBUG_FIRST].max = MAX_INT; Parms[DEBUG_LAST].name = "debug_last"; Parms[DEBUG_LAST].val = -1; Parms[DEBUG_LAST].min = -1; Parms[DEBUG_LAST].max = MAX_INT; Parms[FSUB_HINT_ADD_WT].name = "fsub_hint_add_wt"; Parms[FSUB_HINT_ADD_WT].val = 0; Parms[FSUB_HINT_ADD_WT].min = -MAX_INT; Parms[FSUB_HINT_ADD_WT].max = MAX_INT; Parms[BSUB_HINT_ADD_WT].name = "bsub_hint_add_wt"; Parms[BSUB_HINT_ADD_WT].val = 0; Parms[BSUB_HINT_ADD_WT].min = -MAX_INT; Parms[BSUB_HINT_ADD_WT].max = MAX_INT; Parms[EQUIV_HINT_ADD_WT].name = "equiv_hint_add_wt"; Parms[EQUIV_HINT_ADD_WT].val = 0; Parms[EQUIV_HINT_ADD_WT].min = -MAX_INT; Parms[EQUIV_HINT_ADD_WT].max = MAX_INT; Parms[FSUB_HINT_WT].name = "fsub_hint_wt"; Parms[FSUB_HINT_WT].val = MAX_INT; Parms[FSUB_HINT_WT].min = -MAX_INT; Parms[FSUB_HINT_WT].max = MAX_INT; Parms[BSUB_HINT_WT].name = "bsub_hint_wt"; Parms[BSUB_HINT_WT].val = MAX_INT; Parms[BSUB_HINT_WT].min = -MAX_INT; Parms[BSUB_HINT_WT].max = MAX_INT; Parms[EQUIV_HINT_WT].name = "equiv_hint_wt"; Parms[EQUIV_HINT_WT].val = MAX_INT; Parms[EQUIV_HINT_WT].min = -MAX_INT; Parms[EQUIV_HINT_WT].max = MAX_INT; Parms[VERBOSE_DEMOD_SKIP].name = "verbose_demod_skip"; Parms[VERBOSE_DEMOD_SKIP].val = 0; Parms[VERBOSE_DEMOD_SKIP].min = 0; Parms[VERBOSE_DEMOD_SKIP].max = MAX_INT; Parms[DYNAMIC_DEMOD_DEPTH].name = "dynamic_demod_depth"; Parms[DYNAMIC_DEMOD_DEPTH].val = -1; Parms[DYNAMIC_DEMOD_DEPTH].min = -1; Parms[DYNAMIC_DEMOD_DEPTH].max = MAX_INT; Parms[DYNAMIC_DEMOD_RHS].name = "dynamic_demod_rhs"; Parms[DYNAMIC_DEMOD_RHS].val = 1; Parms[DYNAMIC_DEMOD_RHS].min = -MAX_INT; Parms[DYNAMIC_DEMOD_RHS].max = MAX_INT; Parms[AGE_FACTOR].name = "age_factor"; Parms[AGE_FACTOR].val = 0; Parms[AGE_FACTOR].min = -MAX_INT; Parms[AGE_FACTOR].max = MAX_INT; Parms[DISTINCT_VARS_FACTOR].name = "distinct_vars_factor"; Parms[DISTINCT_VARS_FACTOR].val = 0; Parms[DISTINCT_VARS_FACTOR].min = -MAX_INT; Parms[DISTINCT_VARS_FACTOR].max = MAX_INT; Parms[NEW_SYMBOL_LEX_POSITION].name = "new_symbol_lex_position"; Parms[NEW_SYMBOL_LEX_POSITION].val = MAX_INT / 2; Parms[NEW_SYMBOL_LEX_POSITION].min = 1; Parms[NEW_SYMBOL_LEX_POSITION].max = MAX_INT / 2; Parms[WARN_MEM].name = "warn_mem"; Parms[WARN_MEM].val = -1; Parms[WARN_MEM].min = -1; Parms[WARN_MEM].max = MAX_INT; Parms[WARN_MEM_MAX_WEIGHT].name = "warn_mem_max_weight"; Parms[WARN_MEM_MAX_WEIGHT].val = MAX_INT; Parms[WARN_MEM_MAX_WEIGHT].min = -MAX_INT; Parms[WARN_MEM_MAX_WEIGHT].max = MAX_INT; Parms[SPLIT_SECONDS].name = "split_seconds"; Parms[SPLIT_SECONDS].val = -1; Parms[SPLIT_SECONDS].min = -1; Parms[SPLIT_SECONDS].max = MAX_INT; Parms[SPLIT_GIVEN].name = "split_given"; Parms[SPLIT_GIVEN].val = 5; Parms[SPLIT_GIVEN].min = -1; Parms[SPLIT_GIVEN].max = MAX_INT; Parms[SPLIT_DEPTH].name = "split_depth"; Parms[SPLIT_DEPTH].val = max_split_depth(); Parms[SPLIT_DEPTH].min = 1; Parms[SPLIT_DEPTH].max = max_split_depth(); Parms[PICK_DIFF].name = "pick_diff"; Parms[PICK_DIFF].val = -1; Parms[PICK_DIFF].min = -1; Parms[PICK_DIFF].max = MAX_INT; Parms[PICK_DIFF_RANGE].name = "pick_diff_range"; Parms[PICK_DIFF_RANGE].val = 0; Parms[PICK_DIFF_RANGE].min = 0; Parms[PICK_DIFF_RANGE].max = MAX_INT; Parms[MULTI_JUST_MAX].name = "multi_just_max"; Parms[MULTI_JUST_MAX].val = -1; Parms[MULTI_JUST_MAX].min = -1; Parms[MULTI_JUST_MAX].max = MAX_INT; } /* init_options */ /************* * * print_options(fp) * *************/ void print_options(FILE *fp) { int i, j; fprintf(fp, "\n--------------- options ---------------\n"); j = 0; for (i = 0; i < MAX_FLAGS; i++) /* print set flags */ if (Flags[i].name[0] != '\0') { fprintf(fp, "%s", Flags[i].val ? "set(" : "clear("); fprintf(fp, "%s). ", Flags[i].name); j++; if (j % 3 == 0) fprintf(fp, "\n"); } fprintf(fp, "\n\n"); j = 0; for (i = 0; i < MAX_PARMS; i++) /* print parms */ if (Parms[i].name[0] != '\0') { fprintf(fp, "assign("); fprintf(fp, "%s, %d). ", Parms[i].name, Parms[i].val); j++; if (j % 3 == 0) fprintf(fp, "\n"); } fprintf(fp, "\n"); } /* print_options */ /************* * * p_options() * *************/ void p_options(void) { print_options(stdout); } /* p_options */ /************* * * auto_change_flag() * *************/ void auto_change_flag(FILE *fp, int index, int val) { if (Flags[index].val != val) { fprintf(fp, " dependent: %s(%s).\n", val ? "set" : "clear", Flags[index].name); Flags[index].val = val; dependent_flags(fp, index); } } /* auto_change_flag */ /************* * * void dependent_flags(FILE *fp, int index) * * Flag[index] has just been changed. Change any flags or parms that * depend on it. Write actions to *fp. * * Mutually recursive with auto_change_flag and auto_change_parm. * *************/ void dependent_flags(FILE *fp, int index) { /* This part handles flags that have just been set. */ if (Flags[index].val) { switch (index) { case KNUTH_BENDIX: auto_change_flag(fp, ANL_EQ, 1); break; case ANL_EQ: auto_change_flag(fp, PARA_FROM, 1); auto_change_flag(fp, PARA_INTO, 1); auto_change_flag(fp, PARA_FROM_LEFT, 1); auto_change_flag(fp, PARA_FROM_RIGHT, 0); auto_change_flag(fp, PARA_INTO_LEFT, 1); auto_change_flag(fp, PARA_INTO_RIGHT, 0); auto_change_flag(fp, PARA_FROM_VARS, 1); auto_change_flag(fp, EQ_UNITS_BOTH_WAYS, 1); auto_change_flag(fp, DYNAMIC_DEMOD_ALL, 1); auto_change_flag(fp, BACK_DEMOD, 1); auto_change_flag(fp, PROCESS_INPUT, 1); auto_change_flag(fp, LRPO, 1); break; case BACK_DEMOD: auto_change_flag(fp, DYNAMIC_DEMOD, 1); break; case DYNAMIC_DEMOD_ALL: auto_change_flag(fp, DYNAMIC_DEMOD, 1); break; case DYNAMIC_DEMOD: auto_change_flag(fp, ORDER_EQ, 1); break; case BINARY_RES: auto_change_flag(fp, FACTOR, 1); auto_change_flag(fp, UNIT_DELETION, 1); break; case UNIT_RES: auto_change_flag(fp, BINARY_RES, 1); break; case VERY_VERBOSE: auto_change_flag(fp, PRINT_KEPT, 1); break; case PARA_ALL: auto_change_flag(fp, DETAILED_HISTORY, 0); break; case PROPOSITIONAL: auto_change_flag(fp, SORT_LITERALS, 1); auto_change_flag(fp, PROCESS_INPUT, 1); break; case AUTO1: /* original auto mode (version 3.0.4) */ auto_change_flag(fp, PROCESS_INPUT, 1); auto_change_flag(fp, PRINT_KEPT, 0); auto_change_flag(fp, PRINT_NEW_DEMOD, 0); auto_change_flag(fp, PRINT_BACK_DEMOD, 0); auto_change_flag(fp, PRINT_BACK_SUB, 0); auto_change_flag(fp, CONTROL_MEMORY, 1); auto_change_parm(fp, MAX_MEM, 12000); auto_change_parm(fp, PICK_GIVEN_RATIO, 4); auto_change_parm(fp, STATS_LEVEL, 1); auto_change_parm(fp, MAX_SECONDS, 10800); /* other options are set after clauses are read */ break; case AUTO2: /* revised auto mode (version 3.0.5) */ auto_change_flag(fp, PROCESS_INPUT, 1); auto_change_flag(fp, PRINT_KEPT, 0); auto_change_flag(fp, PRINT_NEW_DEMOD, 0); auto_change_flag(fp, PRINT_BACK_DEMOD, 0); auto_change_flag(fp, PRINT_BACK_SUB, 0); auto_change_flag(fp, CONTROL_MEMORY, 1); auto_change_parm(fp, MAX_MEM, 20000); auto_change_parm(fp, PICK_GIVEN_RATIO, 4); auto_change_parm(fp, STATS_LEVEL, 1); auto_change_parm(fp, MAX_SECONDS, 10800); /* other options are set after clauses are read */ break; case AUTO: /* selects current auto mode */ auto_change_flag(fp, AUTO1, 1); break; case BUILD_PROOF_OBJECT_1: case BUILD_PROOF_OBJECT_2: auto_change_flag(fp, ORDER_HISTORY, 1); auto_change_flag(fp, DETAILED_HISTORY, 1); break; case BUILD_PROOF_OBJECT: auto_change_flag(fp, BUILD_PROOF_OBJECT_1, 1); break; case SPLIT_CLAUSE: case SPLIT_ATOM: case SPLIT_WHEN_GIVEN: auto_change_flag(fp, BACK_UNIT_DELETION, 1); auto_change_parm(fp, REPORT, -1); break; case BACK_UNIT_DELETION: auto_change_flag(fp, UNIT_DELETION, 1); break; case PRINT_PROOF_AS_HINTS: auto_change_flag(fp, BUILD_PROOF_OBJECT_1, 1); break; case REWRITER: auto_change_flag(fp, DEMOD_INF, 1); auto_change_parm(fp, MAX_LEVELS, 1); auto_change_flag(fp, FOR_SUB, 0); auto_change_flag(fp, BACK_SUB, 0); auto_change_parm(fp, STATS_LEVEL, 0); break; } } /* This part handles flags that have just been cleared. */ if (!Flags[index].val) { switch (index) { } } /* This part handles flags that have just been cleared. */ } /* dependent_flags */ /************* * * auto_change_parm() * *************/ void auto_change_parm(FILE *fp, int index, int val) { if (Parms[index].val != val) { fprintf(fp, " dependent: assign(%s, %d).\n", Parms[index].name, val); Parms[index].val = val; dependent_parms(fp, index); } } /* auto_change_parm */ /************* * * void dependent_parms(FILE *fp, int index) * * Parms[index] has just been changed. Change any flags or parms that * depend on it. Write actions to *fp. * * Mutually recursive with auto_change_flag and auto_change_parm. * * This routine may be empty. * *************/ void dependent_parms(FILE *fp, int index) { switch (index) { case MAX_LEVELS: auto_change_flag(fp, SOS_QUEUE, 1); break; } } /* dependent_parms */ /************* * * int change_flag(fp, term, set) * * Assume term is COMPLEX, with either `set' or `clear' as functor. * * If success, return index of flag, if fail, return -1. * Warning and error messages go to file fp. * *************/ int change_flag(FILE *fp, struct term *t, int set) { char *flag_name; int index, found; if (t->farg == NULL || t->farg->narg != NULL || t->farg->argval->type == COMPLEX) { fprintf(fp, "ERROR: "); print_term(fp, t); fprintf(fp, " must have one simple argument.\n"); Stats[INPUT_ERRORS]++; return(-1); } else { flag_name = sn_to_str(t->farg->argval->sym_num); found = 0; index = 0; while (index < MAX_FLAGS && !found) if (str_ident(flag_name, Flags[index].name)) found = 1; else index++; if (!found) { fprintf(fp, "ERROR: "); print_term(fp, t); fprintf(fp, " flag name not found.\n"); Stats[INPUT_ERRORS]++; if (str_ident(flag_name, "lex_rpo")) fprintf(stderr, "\nERROR, flag `lex_rpo\' has been changed to `lrpo\'.\n"); else if (str_ident(flag_name, "print_level")) fprintf(stderr, "\nERROR, flag `print_level\' no longer exists.\n"); else if (str_ident(flag_name, "new_functions")) fprintf(stderr, "\nERROR, flag `new_functions\' no longer exists.\n"); else if (str_ident(flag_name, "bird_print")) fprintf(stderr, "\nERROR, flag `bird_print\' no longer exists.\n"); return(-1); } else if (Flags[index].val == set) { fprintf(fp, "WARNING: "); print_term(fp, t); if (set) fprintf(fp, " flag already set.\n"); else fprintf(fp, " flag already clear.\n"); return(index); } else { Flags[index].val = set; if (index == BELL) Bell = set ? '\007' : '\000'; return(index); } } } /* change_flag */ /************* * * int change_parm(fp, term) * * Assume term is COMPLEX, with either `assign' as functor. * * If success, return index of parm, if fail, return -1. * Warning and error messages go to file fp. * *************/ int change_parm(FILE *fp, struct term *t) { char *parm_name, *int_name; int index, found, new_val, rc; if (t->farg == NULL || t->farg->narg == NULL || t->farg->narg->narg != NULL || t->farg->argval->type == COMPLEX || t->farg->narg->argval->type == COMPLEX) { fprintf(fp, "ERROR: "); print_term(fp, t); fprintf(fp, " must have two simple arguments.\n"); Stats[INPUT_ERRORS]++; return(-1); } else { parm_name = sn_to_str(t->farg->argval->sym_num); found = 0; index = 0; while (index < MAX_PARMS && !found) if (str_ident(parm_name, Parms[index].name)) found = 1; else index++; if (!found) { fprintf(fp, "ERROR: "); print_term(fp, t); fprintf(fp, " parameter name not found.\n"); Stats[INPUT_ERRORS]++; if (str_ident(parm_name, "reduce_weight_limit")) { fprintf(stderr, "\nERROR, parameter `reduce_weight_limit\' has been changed to\n"); fprintf(stderr, "the pair `change_limit_after\' and `new_max_weight\'.\n"); } return(-1); } else { int_name = sn_to_str(t->farg->narg->argval->sym_num); rc = str_int(int_name, &new_val); if (rc == 0) { fprintf(fp, "ERROR: "); print_term(fp, t); fprintf(fp, " second argument must be integer.\n"); Stats[INPUT_ERRORS]++; return(-1); } else if (new_val < Parms[index].min || new_val > Parms[index].max) { fprintf(fp, "ERROR: "); print_term(fp, t); fprintf(fp, " integer must be in range [%d,%d].\n", Parms[index].min, Parms[index].max); Stats[INPUT_ERRORS]++; return(-1); } else if (new_val == Parms[index].val) { fprintf(fp, "WARNING: "); print_term(fp, t); fprintf(fp, " already has that value.\n"); return(index); } else { Parms[index].val = new_val; return(index); } } } } /* change_parm */ /************* * * check_options() -- check for inconsistent or odd settings * * If a bad combination of settings is found, either a warning * message is printed, or an ABEND occurs. * *************/ void check_options(void) { if (Flags[BINARY_RES].val == 0 && Flags[HYPER_RES].val == 0 && Flags[NEG_HYPER_RES].val == 0 && Flags[UR_RES].val == 0 && Flags[PARA_FROM].val == 0 && Flags[PARA_INTO].val == 0 && Flags[DEMOD_INF].val == 0 && Flags[GEOMETRIC_RULE].val == 0 && Flags[LINKED_UR_RES].val == 0 ) fprintf(stderr, "\nWARNING: no inference rules are set.\n"); if (Flags[PARA_FROM].val && Flags[PARA_FROM_RIGHT].val == 0 && Flags[PARA_FROM_LEFT].val == 0) { fprintf(stderr, "\nWARNING: PARA_FROM is set, but PARA_FROM_LEFT and\nPARA_FROM_RIGHT are both clear.\n"); } if (Flags[PARA_INTO].val && Flags[PARA_FROM_RIGHT].val == 0 && Flags[PARA_FROM_LEFT].val == 0) { fprintf(stderr, "\nWARNING: PARA_INTO is set, but PARA_FROM_LEFT and\n"); fprintf(stderr, "PARA_FROM_RIGHT are both clear.\n"); } if (Flags[PARA_FROM].val == 0 && Flags[PARA_INTO].val == 0 && Flags[PARA_ONES_RULE].val) fprintf(stderr, "\nWARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set.\n"); if (Flags[NO_FAPL].val && Flags[HYPER_RES].val == 0) fprintf(stderr, "\nWARNING: NO_FAPL is set, but HYPER_RES is clear.\n"); if (Flags[NO_FAPL].val && Flags[FOR_SUB_FPA].val) fprintf(stderr, "\nWARNING: NO_FAPL and FOR_SUB_FPA are both set.\n"); if (Flags[NO_FAPL].val && Flags[BACK_SUB].val) fprintf(stderr, "\nWARNING: NO_FAPL and BACK_SUB are both set.\n"); if (Flags[ANL_EQ].val && Flags[LRPO].val == 0) fprintf(stderr, "\nWARNING: ANL_EQ is set and LRPO is clear.\n"); if (Parms[DEMOD_LIMIT].val == 0) fprintf(stderr, "\nWARNING: demod_limit=0; set it to -1 for no limit.\n"); if (Parms[MAX_LITERALS].val == 0) fprintf(stderr, "\nWARNING: max_literals=0; set it to -1 for no limit.\n"); if (Parms[MAX_PROOFS].val == 0) fprintf(stderr, "\nWARNING: max_proofs=0; set it to -1 for no limit.\n"); /* selecting the given clause */ if (Flags[INTERACTIVE_GIVEN].val) { if ( (Parms[PICK_GIVEN_RATIO].val != -1) || (Flags[SOS_STACK].val) || (Flags[SOS_QUEUE].val) ) { fprintf(stderr,"WARNING: INTERACTIVE_GIVEN has highest precedence\n"); fprintf(stderr," for picking given clause.\n"); } } if (Parms[PICK_GIVEN_RATIO].val != -1) { if (Flags[SOS_STACK].val) fprintf(stderr,"\nWARNING: SOS_STACK has priority over PICK_GIVEN_RATIO.\n"); else if (Flags[SOS_QUEUE].val) fprintf(stderr,"\nWARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO.\n"); } if (Flags[SOS_STACK].val && Flags[SOS_QUEUE].val) fprintf(stderr, "\nWARNING, SOS_QUEUE has priority over SOS_STACK.\n"); if (Flags[SOS_STACK].val && Flags[INPUT_SOS_FIRST].val) fprintf(stderr, "\nWARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set.\n"); if (Flags[PARA_ALL].val && Flags[DETAILED_HISTORY].val) fprintf(stderr, "\nWARNING, detailed paramod history is ignored when para_all is set.\n"); if ((Flags[SPLIT_CLAUSE].val || Flags[SPLIT_ATOM].val || Flags[SPLIT_WHEN_GIVEN].val) && Parms[MAX_SECONDS].val != -1) fprintf(stderr, "\nWARNING, with splitting, max_seconds is checked against the wall clock.\n"); /* BV(970327) */ if (Flags[KEEP_HINT_SUBSUMERS].val && Flags[KEEP_HINT_EQUIVALENTS].val) fprintf(stderr, "\nWARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set.\n"); if (Flags[ANCESTOR_SUBSUME].val && Flags[MULTI_JUST].val) abend("ancestor_subsume and multi_just are incompatible"); } /* check_options */ otter-3.3f/source/nonport.c0100644000076400007640000002161307711040533015347 0ustar mccunemccune/* * nonport.c -- nonportable features; see unix makefile. * */ #include "header.h" #ifdef TP_SIGNAL /* for call to signal() */ # include #endif #ifdef TP_FORK /* for calls to fork() and wait() */ # include # include # include #endif #ifdef TP_NAMES /* for calls to getpwuid() and gethostname() */ # include # include # include #endif /************* * * non_portable_init() * *************/ void non_portable_init(int argc, char **argv) { #ifdef TP_SIGNAL signal(SIGINT, sig_handler); signal(SIGSEGV, sig_handler); signal(SIGUSR1, sig_handler); #endif } /* non_portable_init */ #ifdef TP_SIGNAL /************* * * sig_handler() * *************/ void sig_handler(int condition) { if (condition == SIGSEGV) { char message[] = "\nSEGMENTATION FAULT!! This is probably caused by a\n" "bug in Otter. Please send copy of the input file to\n" "otter@mcs.anl.gov, let us know what version of Otter you are\n" "using, and send any other info that might be useful.\n\n"; output_stats(stdout, Parms[STATS_LEVEL].val); fprintf(stdout, "%s", message); fprintf(stderr, "%s%c", message, Bell); printf("\nThe job finished %s", get_time()); exit(SEGV_EXIT); } else if (condition == SIGINT) { signal(SIGINT, sig_handler); /* for subsequent interrupts */ interact(); } else if (condition == SIGUSR1) { output_stats(stdout, Parms[STATS_LEVEL].val); printf("\nOtter killed by SIGUSR1 signal.\n"); fprintf(stderr, "\nOtter killed by SIGUSR1 signal.\n"); exit(USR1_EXIT); } else { char s[100]; sprintf(s, "sig_handler, cannot handle signal %d.\n", condition); abend(s); } } /* sig_handler */ #endif /* TP_SIGNAL */ /************* * * username() * *************/ char *username(void) { #ifdef TP_NAMES /* cuserid is not on some machines; * getlogin doesn't always work if user is not logged in; * getlogin broken on Linux. Following seems to be ok. */ struct passwd *p; p = getpwuid(getuid()); return(p ? p->pw_name : "???"); #else return("???"); #endif } /* username */ /************* * * hostname() * *************/ char *hostname(void) { static char host[64]; #ifdef TP_NAMES if (gethostname(host, 64) != 0) strcpy(host, "???"); #else strcpy(host, "???"); #endif return(host); } /* hostname */ /************* * * void interact() * * This routine provides some primitive interaction with the user. * *************/ void interact(void) { FILE *fin, *fout; struct term *t; int rc, go_back; char *help_string; static int fork_level = 0; if (!Flags[SIGINT_INTERACT].val) { fprintf(stderr, "\n%cSearch stopped by SIGINT.\n\n", Bell); fprintf(stdout, "\nSearch stopped by SIGINT.\n"); exit(INTERACTIVE_EXIT); } fin = fopen("/dev/tty", "r"); fout = fopen("/dev/tty", "w"); help_string = "Commands are help, kill, continue, set(_), clear(_), assign(_,_),\n usable, sos, demodulators, passive, stats, fork, and options.\n All commands end with a period.\n"; if (!fin || !fout) { printf("interaction failure: cannot find tty.\n"); fprintf(stderr, "interaction failure: cannot find tty.\n"); } else { printf("\n--- Begin interaction (level %d) ---\n\n", fork_level); fprintf(fout, "\n--- Begin interaction (level %d) ---\n\n", fork_level); fprintf(fout, "Type `help.' for the list of commands.\n> "); fflush(fout); t = read_term(fin, &rc); go_back = 0; while (!go_back) { if (!t) { if (rc == 1) { fprintf(fout, " Received end-of-file character.\n"); go_back = 1; } else fprintf(fout, " Malformed term.\n"); } else if (t->type == NAME) { if (str_ident("help", sn_to_str(t->sym_num))) { fprintf(fout, "%s", help_string); } else if (str_ident("fork", sn_to_str(t->sym_num))) { #ifdef TP_FORK int fork_status; fflush(stdout); fflush(fout); fork_status = fork(); if (fork_status < 0) { fprintf(fout, "%c\nFork failed.\n", Bell); printf("\nFork failed.\n"); } else if (fork_status == 0) { /* child process */ fork_level++; fprintf(fout, "\nLevel %d process started and running (waiting for commands);\nlevel %d process will resume when %d finishes.\n", fork_level, fork_level-1, fork_level); printf("\nLevel %d process started and running.\n", fork_level); } else { /* parent process */ #ifdef TP_SIGNAL /* Ignore interrupt while waiting. This is necessary * because interrupting a child also interrupts * the parent. */ signal(SIGINT, SIG_IGN); #endif wait(0); /* for child process to finish */ #ifdef TP_SIGNAL signal(SIGINT, sig_handler); #endif printf("\n--- Continue interaction at level %d ---\n\n", fork_level); fprintf(fout, "\n--- Continue interaction at level %d ---\n\n", fork_level); fflush(fout); } #else /* TP_FORK not defined */ fprintf(fout,"The fork operation is not available, because" " TP_FORK was not defined during compilation.\n"); #endif } else if (str_ident("stats", sn_to_str(t->sym_num))) { output_stats(fout, Parms[STATS_LEVEL].val); output_stats(stdout, Parms[STATS_LEVEL].val); fflush(stdout); } else if (str_ident("kill", sn_to_str(t->sym_num))) { printf("\nkilled level %d search during interaction.\n", fork_level); fprintf(fout, "killed level %d search during interaction.\n", fork_level); fprintf(fout, " ok.\n"); fclose(fin); fclose(fout); cleanup(); exit(INTERACTIVE_EXIT); } else if (str_ident("continue", sn_to_str(t->sym_num))) { fprintf(fout, " ok."); go_back = 1; } else if (str_ident("sos", sn_to_str(t->sym_num))) { struct clause *c; for (c = Sos->first_cl; c; c = c->next_cl) print_clause(fout, c); } else if (str_ident("usable", sn_to_str(t->sym_num))) { struct clause *c; for (c = Usable->first_cl; c; c = c->next_cl) print_clause(fout, c); } else if (str_ident("demodulators", sn_to_str(t->sym_num))) { struct clause *c; for (c = Demodulators->first_cl; c; c = c->next_cl) print_clause(fout, c); } else if (str_ident("passive", sn_to_str(t->sym_num))) { struct clause *c; for (c = Passive->first_cl; c; c = c->next_cl) print_clause(fout, c); } else if (str_ident("options", sn_to_str(t->sym_num))) { print_options(stdout); print_options(fout); } else if (str_ident("symbols", sn_to_str(t->sym_num))) { print_syms(stdout); print_syms(fout); } else fprintf(fout, " command not understood.\n"); } else if (str_ident("set", sn_to_str(t->sym_num))) { if (change_flag(fout, t, 1)) { print_term(stdout, t); printf(".\n"); } } else if (str_ident("clear", sn_to_str(t->sym_num))) { if (change_flag(fout, t, 0)) { print_term(stdout, t); printf(".\n"); } } else if (str_ident("assign", sn_to_str(t->sym_num))) { if (change_parm(fout, t)) { print_term(stdout, t); printf(".\n"); } } else fprintf(fout, " Command not understood.\n"); if (t) zap_term(t); if (!go_back) { fprintf(fout, " ok.\n> "); fflush(fout); t = read_term(fin, &rc); } } printf("\n--- End interaction, continue search at level %d ---\n\n", fork_level); fprintf(fout,"\n--- End interaction, continue search at level %d ---\n", fork_level); fclose(fin); fclose(fout); fflush(stdout); } } /* interact */ /************* * * foreach_sos() * *************/ void foreach_sos(void) { int parent = 1; int fork_status; struct clause *c; int rc; int count = 0; while(parent) { c = read_clause(stdin, &rc); count++; if (rc == 0) Stats[INPUT_ERRORS]++; /* ok to fork in this case */ else if (c == NULL || (c->first_lit && is_symbol(c->first_lit->atom,"end_of_list",0))) exit(0); else { /* set up for child */ if (Flags[PROCESS_INPUT].val == 0) cl_integrate(c); append_cl(Sos, c); print_clause_bare(stdout, c); printf(". %s Job %d\n", "%", count); fflush(stdout); Stats[SOS_SIZE]++; } fork_status = fork(); if (fork_status < 0) abend("Fork failed"); else if (fork_status == 0) /* child process */ parent = 0; else { /* undo child setup */ if (rc == 0) Stats[INPUT_ERRORS]--; else { rem_from_list(c); Stats[SOS_SIZE]--; if (Flags[PROCESS_INPUT].val == 0) cl_del_int(c); else cl_del_non(c); } wait(0); } } } /* foreach_sos */ /************* * * init_log_for_x_show() * *************/ FILE *init_log_for_x_show(void) { char s[20]; int ppid = 0; #ifdef TP_NAMES ppid = getppid(); /* parent PID */ #endif sprintf(s, "Xlog_%d", ppid); return(fopen(s, "w")); } /* init_log_for_x_show */ /************* * * my_process_id() * *************/ int my_process_id(void) { #ifdef TP_FORK return getpid(); #else return 0; #endif } /* my_process_id */ otter-3.3f/source/make-prototypes0100754000076400007640000000064207705537651016612 0ustar mccunemccune#!/bin/csh /bin/mv proto.h proto.h~ echo "/* proto.h made " > proto.h date >> proto.h echo "*/" >> proto.h foreach i ($argv) set source=$i:r.c echo "" >> proto.h echo "/* $source */" >> proto.h echo "" >> proto.h awk -f awk.prototypes < $source | sed -f sed.prototypes >> proto.h end otter-3.3f/source/ivy.c0100644000076400007640000001243207343604673014472 0ustar mccunemccune/* * ivy.c - part of the otter/ivy interface. * */ #include "header.h" #include "lisp.h" #include "check.h" static struct proof_object *Initial_proof_object = NULL; /*************************************************************************/ static int bnode_to_natural(Bnode b) { if (!atom(b)) return -1; else { int i; if (str_int(b->label, &i)) return (i < 0 ? -1 : i); else return -1; } } /* bnode_to_natural */ /*************************************************************************/ static struct term *bnode_to_otterterm(Bnode b, char **varnames) { if (atom(b)) { int i = 0; char *str; struct term *t = get_term(); t->type = VARIABLE; t->sym_num = str_to_sn(b->label, 0); str = sn_to_str(t->sym_num); while (i < MAX_VARS && varnames[i] != NULL && varnames[i] != sn_to_str(t->sym_num)) i++; if (i == MAX_VARS) return NULL; else { if (varnames[i] == NULL) varnames[i] = sn_to_str(t->sym_num); t->varnum = i; } return t; } else if (length(b) == 1) { struct term *t = get_term(); t->type = NAME; t->sym_num = str_to_sn(car(b)->label, 0); return t; } else { struct rel *r1, *r2; char *label = car(b)->label; int arity = length(b) - 1; struct term *t = get_term(); t->type = COMPLEX; t->sym_num = str_to_sn(label, arity); r2 = NULL; for (b = cdr(b) ; !atom(b); b = cdr(b)) { r1 = get_rel(); r1->argval = bnode_to_otterterm(b->car, varnames); if (r2 == NULL) t->farg = r1; else r2->narg = r1; r2 = r1; } return t; } } /* bnode_to_otterterm */ /*************************************************************************/ /* This is different from is_symbol in that it works for variables. */ int special_is_symbol(struct term *t, char *str, int arity) { return(sn_to_arity(t->sym_num) == arity && str_ident(sn_to_str(t->sym_num), str)); } /* special_is_symbol */ /*************************************************************************/ void trans_logic_symbols(struct term *t) { if (special_is_symbol(t, "TRUE", 0)) { t->sym_num = str_to_sn("$T", 0); t->type = NAME; } else if (special_is_symbol(t, "FALSE", 0)) { t->sym_num = str_to_sn("$F", 0); t->type = NAME; } else if (is_symbol(t, "NOT", 1)) { t->sym_num = str_to_sn("-", 1); trans_logic_symbols(t->farg->argval); } else if (is_symbol(t, "OR", 2)) { t->sym_num = str_to_sn("|", 2); trans_logic_symbols(t->farg->argval); trans_logic_symbols(t->farg->narg->argval); } } /* trans_logic_symbols */ /*************************************************************************/ static struct clause *bnode_to_clause(Bnode b) { struct term *t; char *varnames[MAX_VARS]; int i; for (i=0; icdr) { struct proof_object_node *pn = connect_new_node(po); Bnode e1, e2, e3; char *label; lisp_step = b->car; if (length(lisp_step) < 3) abend("parse_proof_object: step length < 3"); e1 = car(lisp_step); e2 = cadr(lisp_step); e3 = caddr(lisp_step); pn->id = bnode_to_natural(e1); if (length(e2) < 1 || !atom(car(e2))) abend("parse_proof_object: bad justification (1)"); label = car(e2)->label; if (str_ident(label, "INPUT")) pn->rule = P_RULE_INPUT; else if (str_ident(label, "EQ-AXIOM")) pn->rule = P_RULE_EQ_AXIOM; else abend("parse_proof_object: bad justification (2)"); pn->c = bnode_to_clause(e3); if (!pn->c) abend("parse_proof_object: NULL clause"); } /* for each step */ return po; } /* parse_proof_object */ /*************************************************************************/ struct list *init_proof_object(FILE *fin, FILE *fout) { struct proof_object *obj; init_proof_object_environment(); obj = parse_initial_proof_object(fin); if (obj == NULL) { fprintf(fout, "error parsing initial proof object\n"); return NULL; } else { struct proof_object_node *pn; struct list *lst = get_list(); print_proof_object(fout, obj); for (pn = obj->first; pn != NULL; pn = pn->next) append_cl(lst, cl_copy(pn->c)); /* this gets rid of variable names */ Initial_proof_object = obj; /* save it for construction of final version */ return lst; } } /* init_proof_object */ /*************************************************************************/ struct proof_object *retrieve_initial_proof_object(void) { return Initial_proof_object; } /* retrieve_initial_proof_object */ otter-3.3f/source/awk.prototypes0100644000076400007640000000020107264331220016425 0ustar mccunemccune/^long .*\(/,/^{/ /^int .*\(/,/^{/ /^double .*\(/,/^{/ /^char .*\(/,/^{/ /^struct .*\(/,/^{/ /^void .*\(/,/^{/ /^FILE .*\(/,/^{/ otter-3.3f/source/fpa.c0100644000076400007640000004663610037323673014436 0ustar mccunemccune/* * fpa.c * * This file has the routines for FPA-path indexing. The indexing is * similar to the FPA indexing in LMA/ITP, except that the properties * are Stickel's "path properties". (An old property is something like * "the term has symbol b in position 2 1 3", and a path property is * something like * "the term has a path p 2 h 1 f 3 b".) * * FPA indexing is used when searching for unifiable terms, as in inference * rules and in unit conflict, and it is used when searching for instances, * as in back subsumption. (It can also be used when searching for * more general terms, as in forward subsumption, demodulation, * and unit_deletion, but discrimination tree indexing is usually better.) * */ /* * * A property is a sequence of integers which alternate between symbol * identifiers and argument positions: * * * * The last sym_num can be 0, indicating a variable. * * For example, the a in p(g(b),f(g(a),c)) has property

. * */ /* * * MESSY IMPLEMENTATION DETAIL: Paths have one byte per member, plus * a word of 0s to mark the end. When accessing members of a path, * we treat a path as an array of unsigned chars. When comparing, * copying, and hashing paths, we treat them as arrays of ints (for * speed). The "official" form (argument passing, etc) is as an array * of ints, because lint complains about possible alignment errors when * casting (unsigned char *) to (int *). * * The current position in the path (usually variable j) counts in bytes. * */ #include "header.h" #define AND 1 #define OR 2 #define LEAF 3 /* MAX_PATH is in ints. Overflow is not checked. If fpa_depth is n, */ /* paths can be 2n+1 bytes. */ #define MAX_PATH 110 /************* * * alloc_fpa_index() * *************/ struct fpa_index *alloc_fpa_index(void) { struct fpa_index *p; int i; p = (struct fpa_index *) tp_alloc((int) sizeof(struct fpa_index)); for (i = 0; i < FPA_SIZE; i++) p->table[i] = NULL; return(p); } /* alloc_fpa_index */ /************* * * static void path_mark_end(path, j) * * j (which counts bytes) is one past last entry. * *************/ static void path_mark_end(int *path, int j) { int i, k, m; unsigned char *cpath; cpath = (unsigned char *) path; /* make sure the rest of the integer, starting with j, and the */ /* whole next integer (unless j is at beginning) are all 0. */ m = j % sizeof(int); /* position of j in an int */ if (m == 0) i = sizeof(int); /* just fill int with 0s */ else i = (2 * sizeof(int)) - m; /* 0 rest of int and next int */ for (k = 0; k < i; k++) cpath[j++] = 0; } /* path_mark_end */ /************* * * static int hash_path(path) * *************/ static int hash_path(int *path) { int i, val; val = 0; for (i = 0; path[i] != 0; i++) val += path[i]; return((unsigned) val % FPA_SIZE); } /* hash_path */ /************* * * static int path_comp(p1, p2) * *************/ static int path_comp(int *p1, int *p2) { while (*p1 == *p2 && *p1 != 0 && *p2 != 0) { p1++; p2++; } if (*p1 < *p2) return(-1); else if (*p1 > *p2) return(1); else return(0); } /* path_comp */ /************* * * static int path_size(path) -- in ints, including 0 word at end * *************/ static int path_size(int *path) { int i; int *p1; for (i = 1, p1 = path; *p1 != 0; p1++, i++); return(i); } /* path_size */ /************* * * static int *path_copy(path) * *************/ static int *path_copy(int *path) { int i, j; int *p2; i = path_size(path); p2 = (int *) tp_alloc(i * (int) sizeof(int)); for (j = 0; j < i; j++) p2[j] = path[j]; return(p2); } /* path_copy */ /************* * * static insert_fpa_tab(term, path, index) * * Insert a term into an FPA indexing list. Create a new list * if necessary. The path is something like "1 f 2 g 4 h 3 a". * *************/ static void insert_fpa_tab(struct term *t, int *path, struct fpa_index *index) { int hashval, c; struct term_ptr *tp1, *tp2, *tp3; struct fpa_head *fp1, *fp2, *fp3; /* Treat path as integers here. */ hashval = hash_path(path); fp1 = index->table[hashval]; fp2 = NULL; while (fp1 != NULL && (c = path_comp(fp1->path, path)) == -1) { fp2 = fp1; fp1 = fp1->next; } if (fp1 == NULL || c != 0) { /* need new fpa_head */ fp3 = get_fpa_head(); fp3->path = path_copy(path); fp3->terms = flist_insert(NULL, t); if (fp2 == NULL) { /* insert at beginning */ fp3->next = index->table[hashval]; index->table[hashval] = fp3; } else { /* insert after fp2 */ fp3->next = fp1; fp2->next = fp3; } } else { /* we have a matching fpa_head, so insert t in its list */ fp1->terms = flist_insert(fp1->terms, t); } } /* insert_fpa_tab */ /************* * * static delete_fpa_tab(term, path, database) * * Delete a term from an FPA indexing list. It is assumed that * the corresponding `insert_fpa_tab' was previously made. * *************/ static void delete_fpa_tab(struct term *t, int *path, struct fpa_index *index) { int hashval; struct term_ptr *tp1, *tp2; struct fpa_head *fp1, *fp2; /* Treat path as integers here. */ hashval = hash_path(path); fp1 = index->table[hashval]; fp2 = NULL; while (fp1 != NULL && path_comp(fp1->path, path) != 0) { fp2 = fp1; fp1 = fp1->next; } if (fp1 == NULL) Stats[FPA_UNDERLOADS]++; /* fpa list not found */ else { /* we have a matching fpa_head, so look for t in its list */ fp1->terms = flist_delete(fp1->terms, t); if (fp1->terms == NULL) { /* delete fpa_head also */ if (fp2 == NULL) index->table[hashval] = fp1->next; else fp2->next = fp1->next; free_fpa_head(fp1); /* don't worry about fp1->path; let it be lost forever */ } } } /* delete_fpa_tab */ /************* * * void term_fpa_rec * * Recursive procedure called by fpa_insert and fpa_delete. * *************/ void term_fpa_rec(int insert, struct term *t, struct term *super_term, struct fpa_index *index, int *path, int j, int bound) { int i; struct rel *r; unsigned char *cpath; cpath = (unsigned char *) path; /* `path' has the path from super_term to t */ if (t->type == VARIABLE) /* variable contributes nothing */ cpath[j++] = 0; else cpath[j++] = t->sym_num; /* insert or delete path */ path_mark_end(path, j); if (insert) insert_fpa_tab(super_term, path, index); else delete_fpa_tab(super_term, path, index); if (t->type == COMPLEX && bound > 0) { i = 1; r = t->farg; while (r != NULL) { cpath[j] = i++; term_fpa_rec(insert, r->argval, super_term, index, path, j+1, bound-1); r = r->narg; } } } /* term_fpa_rec */ /************* * * void fpa_insert(term, level, database) * * Insert a term into an FPA indexing database. Level == 0 * gives indexing on functor only. With the term f(a,x,g(b)), * Level == 1 gives indexing on f, a, x, and g. * *************/ void fpa_insert(struct term *t, int level, struct fpa_index *index) { static int atom_count, term_count; int path[MAX_PATH]; /* t->fpa_id is used to order FPA lists. Assign one if necessary. */ if (t->fpa_id == 0) { if (t->type != VARIABLE && t->varnum != 0) t->fpa_id = ++atom_count; else t->fpa_id = ++term_count; } term_fpa_rec(1, t, t, index, path, 0, level); } /* fpa_insert */ /************* * * void fpa_delete(term, level, database) * * Delete a term from an FPA indexing database. The level * must be the same as when the term was given to fpa_insert. * *************/ void fpa_delete(struct term *t, int level, struct fpa_index *index) { int path[MAX_PATH]; term_fpa_rec(0, t, t, index, path, 0, level); } /* fpa_delete */ /************* * * static struct fpa_tree *get_leaf_node(path, index) * * Given a path, if an FPA list exists, then return it in a * leaf node; else return(NULL). * *************/ static struct fpa_tree *get_leaf_node(int *path, struct fpa_index *index) { struct fpa_head *fp; struct fpa_tree *pp; int c; fp = index->table[hash_path(path)]; while (fp && (c = path_comp(fp->path,path)) == -1) fp = fp->next; if (!fp || c != 0) return(NULL); else { pp = get_fpa_tree(); pp->type = LEAF; pp->path = path; /* Note that whole path is not being copied. */ pp->position = first_fpos(fp->terms); return(pp); } } /* get_leaf_node */ /************* * * static int all_args_vars(t) -- are all subterms variables? * *************/ static int all_args_vars(struct term *t) { struct rel *r; if (t->type != COMPLEX) return(0); else { r = t->farg; while (r != NULL) { if (r->argval->type != VARIABLE) return(0); r = r->narg; } return(1); } } /* all_args_vars */ /************* * * static struct fpa_tree *build_tree_local(term, unif_type, path, bound, database) * * Return an FPA indexing tree--to be used with a sequence * of get_next calls. * * term: An error if (term->type == VARIABLE && unif_type != 3) * because everything satisfies that query. * unif_type: UNIFY, INSTANCE, MORE_GEN * path: must be 0 on initial call * bound: indexing bound (must be <= fpa_insert bound) * database: * * Note: If an appathriate fpa list does not exit, then part of * the tree can sometimes be deleted. For example, if you want * a tree to find unifiers for p(a), then normally, the tree will be * * OR * / \ * `variable' \ * AND * / \ * / \ * `p a' \ * `p variable' * * But if the fpa list for `variable' does not exist, then this * routine will produce * * AND * / \ * / \ * `p a' \ * `p variable' * *************/ static struct fpa_tree *build_tree_local(struct term *t, int u_type, int *path, int j, int bound, struct fpa_index *index) { int i, empty; struct rel *r; struct fpa_tree *p1, *p2, *p3; unsigned char *cpath; cpath = (unsigned char *) path; /* `path' has the path to `t' */ if (t->type == VARIABLE) { /* variable */ if (u_type != MORE_GEN) { /* error if not "more general" */ abend("build_tree_local, var and not more general."); return(NULL); /* to quiet lint */ } else { cpath[j++] = 0; path_mark_end(path, j); p1 = get_leaf_node(path, index); return(p1); } } else { /* NAME or COMPLEX */ cpath[j++] = t->sym_num; if (t->type == NAME || bound == 0 || (u_type != MORE_GEN && all_args_vars(t))) { path_mark_end(path, j); p2 = get_leaf_node(path, index); } else { i = 1; empty = 0; p2 = NULL; r = t->farg; while (r != NULL && empty == 0) { cpath[j] = i++; /* skip this arg if var and "unify" or "instance" */ if (r->argval->type != VARIABLE || u_type == MORE_GEN) { p3 = build_tree_local(r->argval, u_type, path, j+1, bound-1, index); if (p3 == NULL) { if (p2 != NULL) { zap_prop_tree(p2); p2 = NULL; } empty = 1; } else if (p2 == NULL) p2 = p3; else { p1 = get_fpa_tree(); p1->type = AND; /* and */ p1->left = p2; p1->right = p3; p2 = p1; } } r = r->narg; } } if (u_type != INSTANCE) { /* if we don't want instances only, */ cpath[j-1] = 0; path_mark_end(path, j); p3 = get_leaf_node(path, index); /* variable */ } else p3 = NULL; if (p2 == NULL) return(p3); else if (p3 == NULL) return(p2); else { /* OR them together */ p1 = get_fpa_tree(); p1->type = OR; /* OR */ p1->left = p2; p1->right = p3; return(p1); } } } /* build_tree_local */ /************* * * struct fpa_tree *build_tree(t, u_type, bound, index) * *************/ struct fpa_tree *build_tree(struct term *t, int u_type, int bound, struct fpa_index *index) { int path[MAX_PATH]; return(build_tree_local(t, u_type, path, 0, bound, index)); } /* build_tree */ /************* * * struct term *next_term(tree, maximum) * * Get the first or next term that satisfies a unification condition. * (Unification conditions are provided by `build_tree'.) * `maximum' must be 0 on nonresursive calls. A return of NULL indicates * that there are none or no more terms that satisfy (and the tree has * been deallocated). If you want to stop getting terms before a NULL * is returned, then please deallocate the tree with zap_prop_tree(tree). * * Warning: a return of NULL means that the tree has been deallocated * *************/ struct term *next_term(struct fpa_tree *n, int max) { struct term_ptr *tp; struct term *t1, *t2; if (n == NULL) return(NULL); else if (n->type == LEAF) { /* LEAF node */ struct term *t = FTERM(n->position); while (t != NULL && max != 0 && t->fpa_id > max) { n->position = next_fpos(n->position); t = FTERM(n->position); } if (t == NULL) { zap_prop_tree(n); return(NULL); } else { n->position = next_fpos(n->position); return(t); } } else if (n->type == AND) { /* AND node */ t1 = next_term(n->left, max); if (t1 != NULL) t2 = next_term(n->right, t1->fpa_id); else t2 = (struct term *) 1; /* anything but NULL */ while (t1 != t2 && t1 != NULL && t2 != NULL) { if (t1->fpa_id > t2->fpa_id) t1 = next_term(n->left, t2->fpa_id); else t2 = next_term(n->right, t1->fpa_id); } if (t1 == NULL || t2 == NULL) { if (t1 == NULL) n->left = NULL; if (t2 == NULL) n->right = NULL; zap_prop_tree(n); return(NULL); } else return(t1); } else { /* OR node */ /* first get the left term */ t1 = n->left_term; if (t1 == NULL) { /* it must be brought up */ if (n->left != NULL) { t1 = next_term(n->left, max); if (t1 == NULL) n->left = NULL; } } else /* it was saved from a previous call */ n->left_term = NULL; /* at this point, n->left_term == NULL */ /* now do the same for the right side */ t2 = n->right_term; if (t2 == NULL) { if (n->right != NULL) { t2 = next_term(n->right, max); if (t2 == NULL) n->right = NULL; } } else n->right_term = NULL; /* now decide which of of t1 and t2 to return */ if (t1 == NULL) { if (t2 == NULL) { zap_prop_tree(n); return(NULL); } else return(t2); } else if (t2 == NULL) return(t1); else if (t1 == t2) return(t1); else if (t1->fpa_id > t2->fpa_id) { n->right_term = t2; /* save t2 for next time */ return(t1); } else { n->left_term = t1; /* save t1 for next time */ return(t2); } } } /* next_term */ /************* * * struct fpa_tree *build_for_all(db) * * For those times when one must have everything (paramodulation * from a variable, and paramodulation into a variable). * (Build a tree that OR's together all of the FPA lists in db.) * *************/ struct fpa_tree *build_for_all(struct fpa_index *index) { struct fpa_head *h; struct fpa_tree *p1, *p2, *p3; int i; p1 = NULL; for (i = 0; i < FPA_SIZE; i++) { h = index->table[i]; while (h != NULL) { p2 = get_fpa_tree(); p2->type = LEAF; p2->path = h->path; p2->position = first_fpos(h->terms); if (p1 == NULL) p1 = p2; else { p3 = get_fpa_tree(); p3->type = OR; p3->left = p1; p3->right = p2; p1 = p3; } h = h->next; } } return(p1); } /* build_for_all */ /************* * * zap_prop_tree(tree) -- Dealocate an FPA indexing tree. * * `next_term' deallocates the tree as it proceeds, so it is not * necessary to call zap_prop_tree if the most recent call to * `next_term' returned NULL. * *************/ void zap_prop_tree(struct fpa_tree *n) { if (n != NULL) { zap_prop_tree(n->left); zap_prop_tree(n->right); free_fpa_tree(n); } } /* zap_prop_tree */ /************* * * print_fpa_tab(file_ptr, database) -- Display all FPA lists in database. * *************/ void print_fpa_tab(FILE *fp, struct fpa_index *index) { int i; struct fpa_head *f; fprintf(fp, "\nfpa index %p\n", (void *) index); for (i=0; itable[i] != NULL) { fprintf(fp, "bucket %d\n", i); f = index->table[i]; while (f != NULL) { struct fposition fpos; struct term *t; print_path(fp, f->path); fpos = first_fpos(f->terms); t = FTERM(fpos); while (t != NULL) { fprintf(fp, " "); print_term(fp, t); fpos = first_fpos(f->terms); t = FTERM(fpos); } fprintf(fp, "\n"); f = f->next; } } } /* print_fpa_tab */ /************* * * p_fpa_tab(index) * *************/ void p_fpa_tab(struct fpa_index *index) { print_fpa_tab(stdout, index); } /* p_fpa_tab */ /************* * * print_prop_tree(file_ptr, tree, level) * * Display an FPA lookup tree that has been returned from * build_tree. Level should be 0 on initial call. * *************/ void print_prop_tree(FILE *fp, struct fpa_tree *n, int level) { int i; if (n != NULL) { for (i=0; itype == AND) fprintf(fp, "and\n"); else if (n->type == OR) fprintf(fp, "or\n"); else print_path(fp, n->path); print_prop_tree(fp, n->left, level+1); print_prop_tree(fp, n->right, level+1); } } /* print_prop_tree */ /************* * * p_prop_tree(t) * *************/ void p_prop_tree(struct fpa_tree *n) { print_prop_tree(stdout, n, 0); } /* p_prop_tree */ /************* * * print_path(fp, path) -- print an fpa path to a file * *************/ void print_path(FILE *fp, int *path) { int i; char *sym; unsigned char *cpath; cpath = (unsigned char *) path; /* example [f,2,g,1,f,1,h,1,a] */ fprintf(fp, "["); for (i = 0; cpath[i] != 0 || cpath[i+1] != 0 ; i++) { if (i % 2 == 0) { sym = sn_to_str( (short) cpath[i]); if (sym[0] == '\0') sym = "*"; fprintf(fp, "%s", sym); } else fprintf(fp, "%d", cpath[i]); if (cpath[i+1] != 0 || cpath[i+1] != 0) fprintf(fp, ","); else fprintf(fp, "]\n"); } } /* print_path */ /************* * * p_path(path) -- print an fpa path * *************/ void p_path(int *path) { print_path(stdout, path); } /* p_path */ /************* * * int new_sym_num() * * Return the next available symbol number. * * The rightmost 8 bits will not be all zero. * This is so that fpa will not map sym_nums to 0 (the * code for variables). * *************/ int new_sym_num(void) { static int sym_ent_count; sym_ent_count++; if (sym_ent_count % 256 == 0) sym_ent_count++; if (sym_ent_count > MAX_UNSIGNED_SHORT) abend("new_sym_num: too many symbols requested."); return(sym_ent_count); } /* new_sym_num */ otter-3.3f/source/check.h0100644000076400007640000000144207343604666014746 0ustar mccunemccune#define MAX_LITS 10 /* Types of step in the proof object */ #define P_RULE_UNDEFINED 0 #define P_RULE_INPUT 1 #define P_RULE_EQ_AXIOM 2 #define P_RULE_INSTANTIATE 3 #define P_RULE_PROPOSITIONAL 4 #define P_RULE_RESOLVE 5 #define P_RULE_PARAMOD 6 #define P_RULE_FLIP 7 struct proof_object_node { int id; int rule; int parent1, parent2; struct ilist *position1, *position2; BOOLEAN backward_subst; struct term *subst[2*MAX_VARS]; struct clause *c; int old_id; /* id of original clause */ struct ilist *map; /* position of literals in original clause */ struct proof_object_node *next; }; struct proof_object { int steps; struct proof_object_node *first; struct proof_object_node *last; }; otter-3.3f/source/demod.c0100644000076400007640000011132607575716034014757 0ustar mccunemccune/* * demod.c -- Demodulation (rewriting) routines. * */ #include "header.h" /************* * * struct term *contract_lin(term, demods, context, demod_id_p) * * Attempt to rewrite the top level of `term', using a * sequential search of `demods'. If success, term is freed; if fail, * NULL is returned. * *************/ static struct term *contract_lin(struct term *t, int *demods, struct context *c, int *demod_id_p) { struct term *atom, *contractum, *t2, *t3, *beta; struct rel *alpha_rel; struct trail *tr; struct clause *p; struct list *d; int mult_flag, dummy, ok; tr = NULL; d = (struct list *) demods; if (d == NULL) return(NULL); p = d->first_cl; contractum = NULL; while (p && contractum == NULL) { atom = ith_literal(p,1)->atom; alpha_rel = (atom->varnum == CONDITIONAL_DEMOD ? atom->farg->narg->argval->farg : atom->farg); tr = NULL; if (match(alpha_rel->argval, c, t, &tr)) { if (atom->varnum == CONDITIONAL_DEMOD) { /* rewrite instantiated condition */ t2 = apply_demod(atom->farg->argval, c, &dummy); un_share_special(t2); t3 = convenient_demod(t2); ok = is_symbol(t3, "$T", 0); zap_term(t3); } else ok = 1; if (ok) { beta = alpha_rel->narg->argval; mult_flag = 0; contractum = apply_demod(beta, c, &mult_flag); if (mult_flag) c->multiplier++; /* varnum == LEX_DEP_DEMOD means it's lex-dependent */ if (atom->varnum != LEX_DEP_DEMOD) ok = 1; else if (Flags[LRPO].val) ok = lrpo_greater(t, contractum); else ok = lex_check(contractum, t) == LESS_THAN; if (ok) { zap_term_special(t); *demod_id_p = p->id; } else { zap_term_special(contractum); contractum = NULL; } } clear_subst_1(tr); } p = p->next_cl; } return(contractum); /* may be NULL */ } /* contract_lin */ /************* * * dollar_out_non_list(t) - Process $OUT(t). * *************/ static void dollar_out_non_list(struct term *t) { int i; if (t->sym_num == Chr_sym_num && str_int(sn_to_str(t->farg->argval->sym_num), &i)) printf("%c", i); else print_term(stdout, t); } /* dollar_out_non_list */ /************* * * dollar_out(t) - Process $OUT(t) or $OUT([t1,...,tn]). * *************/ static void dollar_out(struct term *t) { struct term *t1; if (proper_list(t)) { printf("\n"); for (t1 = t; t1->sym_num != Nil_sym_num; t1 = t1->farg->narg->argval) { if (t != t1) printf(" "); dollar_out_non_list(t1->farg->argval); } printf(".\n\n"); } else dollar_out_non_list(t); } /* dollar_out */ /************* * * struct term *dollar_contract(t) - evaluate $EQ, $SUM, ... * * If t is evaluated, it is deallocated and the result is returned. * If t cannot be evaluated, it is left alone and NULL is returned. * * Here are the current built-ins. (int is actually long, and * float is actually double. Recall that floats are always * surrouded by double quotes.) * * int x int -> int $SUM, $PROD, $DIFF, $DIV, $MOD * int x int -> bool $EQ, $NE, $LT, $LE, $GT, $GE * float x float -> float $FSUM, $FPROD, $FDIFF, $FDIV * float x float -> bool $FEQ, $FNE, $FLT, $FLE, $FGT, $FGE * term x term -> bool $ID, $LNE, $LLT, $LLE, $LGT, $LGE, * $OCCURS, $VOCCURS, VFREE * bool x bool -> bool $AND, $OR * bool -> bool $TRUE, $NOT * -> bool $T, $F * term -> bool $ATOMIC, $INT, $BITS, $VAR * -> int $NEXT_CL_NUM * bool x term x term -> term $IF * term -> bool $GROUND * bits x bits -> bits $BIT_AND, $BIT_OR, $BIT_XOR * bits x int -> bits $SHIFT_LEFT, $SHIFT_RIGHT * bits -> bits $BIT_NOT * bits -> int $BITS_OT_INT * int -> bits $INT_TO_BITS * *************/ static struct term *dollar_contract(struct term *t) { static int unique_num = 0; long i1, i2; long i3 = 0; unsigned long u1, u2; unsigned long u3 = 0; int b1, op_code, op_type, s1t, s1f, s2t, s2f; int b3 = 0; double d1, d2; double d3 = 0.0; char *s1, *s2, str[MAX_NAME]; struct term *t1, *ta, *tb; op_code = sn_to_ec(t->sym_num); /* get eval code */ if (op_code < 1) return(NULL); else if (op_code <= MAX_USER_EVALUABLE) return(evaluate_user_function(t, op_code)); else { switch(op_code) { case SUM_SYM: case PROD_SYM: case DIFF_SYM: case DIV_SYM: case MOD_SYM: op_type = 1; break; /* int x int -> int */ case EQ_SYM: case NE_SYM: case LT_SYM: case LE_SYM: case GT_SYM: case GE_SYM: op_type = 2; break; /* int x int -> bool */ case AND_SYM: case OR_SYM: op_type = 3; break; /* bool x bool -> bool */ case TRUE_SYM: case NOT_SYM: op_type = 4; break; /* bool -> bool */ case IF_SYM: op_type = 5; break; /* bool x term x term -> term */ case LLT_SYM: case LLE_SYM: case LGT_SYM: case LGE_SYM: case LNE_SYM: case ID_SYM: op_type = 6; break; /* term x term -> bool (lex) */ case NEXT_CL_NUM_SYM: op_type = 7; break; /* -> int */ case ATOMIC_SYM: case BITS_SYM: case INT_SYM: case GROUND_SYM: case VAR_SYM: op_type = 8; break; /* term -> bool */ case T_SYM: return(NULL); case F_SYM: return(NULL); case OUT_SYM: op_type = 9; break; /* term -> same_term_with_output */ case BIT_NOT_SYM: op_type = 10; break; /* bits -> bits */ case FSUM_SYM: case FPROD_SYM: case FDIFF_SYM: case FDIV_SYM: op_type = 11; break; /* float x float -> float */ case FEQ_SYM: case FNE_SYM: case FLT_SYM: case FLE_SYM: case FGT_SYM: case FGE_SYM: op_type = 12; break; /* float x float -> bool */ case BIT_AND_SYM: case BIT_OR_SYM: case BIT_XOR_SYM: op_type = 13; break; /* bits x bits -> bits */ case SHIFT_RIGHT_SYM: case SHIFT_LEFT_SYM: op_type = 14; break; /* bits x int -> bits */ case INT_TO_BITS_SYM: op_type = 15; break; /* int -> bits */ case BITS_TO_INT_SYM: op_type = 16; break; /* bits -> int */ case OCCURS_SYM: case VOCCURS_SYM: case VFREE_SYM: case RENAME_SYM: op_type = 17; break; /* term x term -> bool (misc) */ case UNIQUE_NUM_SYM: op_type = 18; break; /* -> int */ default: printf("ERROR, dollar_contract, bad op_code: %d.\n", op_code); return(NULL); } switch (op_type) { case 1: /* int x int -> int */ ta = t->farg->argval; tb = t->farg->narg->argval; if (ta->type != NAME || tb->type != NAME) return(NULL); s1 = sn_to_str(ta->sym_num); s2 = sn_to_str(tb->sym_num); if (str_long(s1, &i1) == 0 || str_long(s2, &i2) == 0) return(NULL); if ((op_code == DIV_SYM || op_code == MOD_SYM) && i2 == 0) { print_term_nl(stdout, t); abend("integer divide by 0."); } switch (op_code) { case SUM_SYM: i3 = i1 + i2; break; case PROD_SYM: i3 = i1 * i2; break; case DIFF_SYM: i3 = i1 - i2; break; case DIV_SYM: i3 = i1 / i2; break; case MOD_SYM: i3 = i1 % i2; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; long_str(i3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 2: /* int x int -> bool */ ta = t->farg->argval; tb = t->farg->narg->argval; if (ta->type != NAME || tb->type != NAME) return(NULL); s1 = sn_to_str(ta->sym_num); s2 = sn_to_str(tb->sym_num); if (str_long(s1, &i1) == 0 || str_long(s2, &i2) == 0) return(NULL); switch (op_code) { case EQ_SYM: b3 = i1 == i2; break; case NE_SYM: b3 = i1 != i2; break; case LT_SYM: b3 = i1 < i2; break; case LE_SYM: b3 = i1 <= i2; break; case GT_SYM: b3 = i1 > i2; break; case GE_SYM: b3 = i1 >= i2; break; } t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn(b3 ? "$T" : "$F", 0); return(t1); case 3: /* bool x bool -> bool */ s1 = sn_to_str(t->farg->argval->sym_num); s2 = sn_to_str(t->farg->narg->argval->sym_num); s1t = str_ident(s1,"$T"); s1f = str_ident(s1,"$F"); s2t = str_ident(s2,"$T"); s2f = str_ident(s2,"$F"); if ((s1t == 0 && s1f == 0) || (s2t == 0 && s2f == 0)) return(NULL); switch (op_code) { case AND_SYM: b3 = s1t && s2t; break; case OR_SYM: b3 = s1t || s2t; break; } t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn(b3 ? "$T" : "$F", 0); return(t1); case 4: /* bool -> bool $NOT(x), $TRUE(x) */ s1 = sn_to_str(t->farg->argval->sym_num); s1t = str_ident(s1,"$T"); s1f = str_ident(s1,"$F"); if (s1t == 0 && s1f == 0) return(NULL); t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; switch (op_code) { case NOT_SYM: t1->sym_num = str_to_sn(s1t ? "$F" : "$T", 0); break; case TRUE_SYM: t1->sym_num = str_to_sn(s1t ? "$T" : "$F", 0); break; } return(t1); case 5: /* bool x term x term -> term $IF(x,y,z) */ s1 = sn_to_str(t->farg->argval->sym_num); s1t = str_ident(s1,"$T"); s1f = str_ident(s1,"$F"); if (s1t == 0 && s1f == 0) return(NULL); if (s1t) t1 = t->farg->narg->argval; else t1 = t->farg->narg->narg->argval; t1->fpa_id++; /* one more pointer to t1 */ zap_term_special(t); /* one less pointer to t */ return(t1); case 6: /* term x term -> bool (lexical comparisons) */ ta = t->farg->argval; tb = t->farg->narg->argval; b1 = lex_check(ta, tb); switch (op_code) { case ID_SYM: b3 = (b1 == SAME_AS); break; case LNE_SYM: b3 = (b1 != SAME_AS); break; case LLT_SYM: b3 = (b1 == LESS_THAN); break; case LLE_SYM: b3 = (b1 == LESS_THAN || b1 == SAME_AS); break; case LGT_SYM: b3 = (b1 == GREATER_THAN); break; case LGE_SYM: b3 = (b1 == GREATER_THAN || b1 == SAME_AS); break; } t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn(b3 ? "$T" : "$F", 0); return(t1); case 7: /* -> int */ int_str(next_cl_num(), str); t->sym_num = str_to_sn(str, 0); return(t); case 8: /* term -> bool (metalogical properties) */ ta = t->farg->argval; switch (op_code) { case ATOMIC_SYM: b3 = ta->type == NAME; break; case INT_SYM: b3 = ( ta->type == NAME && str_long(sn_to_str(ta->sym_num), &i1)); break; case BITS_SYM: b3 = ( ta->type == NAME && bits_ulong(sn_to_str(ta->sym_num), &u1)); break; case VAR_SYM: b3 = ta->type == VARIABLE; break; case GROUND_SYM: b3 = ground(ta); break; } t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn(b3 ? "$T" : "$F", 0); return(t1); case 9: /* term -> same_term_with_output */ dollar_out(t->farg->argval); return(NULL); case 10: /* bits -> bits */ s1 = sn_to_str(t->farg->argval->sym_num); if (bits_ulong(s1, &u1) == 0) return(NULL); switch (op_code) { case BIT_NOT_SYM: u3 = ~u1; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; ulong_bits(u3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 11: /* float x float -> float */ ta = t->farg->argval; tb = t->farg->narg->argval; if (ta->type != NAME || tb->type != NAME) return(NULL); s1 = sn_to_str(ta->sym_num); s2 = sn_to_str(tb->sym_num); if (str_double(s1, &d1) == 0 || str_double(s2, &d2) == 0) return(NULL); if (op_code == FDIV_SYM && d2 == 0) { print_term_nl(stdout, t); abend("float divide by 0."); } switch (op_code) { case FSUM_SYM: d3 = d1 + d2; break; case FPROD_SYM: d3 = d1 * d2; break; case FDIFF_SYM: d3 = d1 - d2; break; case FDIV_SYM: d3 = d1 / d2; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; double_str(d3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 12: /* float x float -> bool */ ta = t->farg->argval; tb = t->farg->narg->argval; if (ta->type != NAME || tb->type != NAME) return(NULL); s1 = sn_to_str(ta->sym_num); s2 = sn_to_str(tb->sym_num); if (str_double(s1, &d1) == 0 || str_double(s2, &d2) == 0) return(NULL); switch (op_code) { case FEQ_SYM: b3 = d1 == d2; break; case FNE_SYM: b3 = d1 != d2; break; case FLT_SYM: b3 = d1 < d2; break; case FLE_SYM: b3 = d1 <= d2; break; case FGT_SYM: b3 = d1 > d2; break; case FGE_SYM: b3 = d1 >= d2; break; } t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn(b3 ? "$T" : "$F", 0); return(t1); case 13: /* bits x bits -> bits */ ta = t->farg->argval; tb = t->farg->narg->argval; if (ta->type != NAME || tb->type != NAME) return(NULL); s1 = sn_to_str(ta->sym_num); s2 = sn_to_str(tb->sym_num); if (bits_ulong(s1, &u1) == 0 || bits_ulong(s2, &u2) == 0) return(NULL); switch (op_code) { case BIT_AND_SYM: u3 = u1 & u2; break; case BIT_OR_SYM: u3 = u1 | u2; break; case BIT_XOR_SYM: u3 = u1 ^ u2; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; ulong_bits(u3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 14: /* bits x int -> bits */ ta = t->farg->argval; tb = t->farg->narg->argval; if (ta->type != NAME || tb->type != NAME) return(NULL); s1 = sn_to_str(ta->sym_num); s2 = sn_to_str(tb->sym_num); if (bits_ulong(s1, &u1) == 0 || str_long(s2, &i2) == 0) return(NULL); switch (op_code) { case SHIFT_RIGHT_SYM: u3 = u1 >> i2; break; case SHIFT_LEFT_SYM: u3 = u1 << i2; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; ulong_bits(u3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 15: /* int -> bits */ s1 = sn_to_str(t->farg->argval->sym_num); if (str_long(s1, &i1) == 0) return(NULL); switch (op_code) { case INT_TO_BITS_SYM: u3 = i1; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; ulong_bits(u3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 16: /* bits -> int */ s1 = sn_to_str(t->farg->argval->sym_num); if (bits_ulong(s1, &u1) == 0) return(NULL); switch (op_code) { case BITS_TO_INT_SYM: i3 = u1; break; } zap_term_special(t); t1 = get_term(); t1->type = NAME; long_str(i3, str); t1->sym_num = str_to_sn(str, 0); return(t1); case 17: /* term x term -> bool (misc) */ ta = t->farg->argval; tb = t->farg->narg->argval; switch (op_code) { case RENAME_SYM: b3 = same_structure(ta, tb); break; case OCCURS_SYM: b3 = occurs_in(ta, tb); break; case VOCCURS_SYM: b3 = ta->type == VARIABLE && occurs_in(ta, tb); break; case VFREE_SYM: b3 = ta->type == VARIABLE && !occurs_in(ta, tb); break; default: b3 = 0; } t->occ.lit = NULL; /* in case t is a literal */ zap_term_special(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn(b3 ? "$T" : "$F", 0); return(t1); case 18: /* -> int */ unique_num++; int_str(unique_num, str); t->sym_num = str_to_sn(str, 0); return(t); } printf("ERROR, dollar_contract, bad op_type: %d.\n", op_type); return(NULL); } } /* dollar_contract */ /************* * * * *************/ static struct term *replace_special(struct term *t, struct term *target, struct term *replacement) { struct rel *r; if (term_ident(t, target)) { zap_term_special(t); replacement->fpa_id++; return(replacement); } else if (t->type == COMPLEX) { for (r = t->farg; r; r = r->narg) r->argval = replace_special(r->argval, target, replacement); return(t); } else return(t); } /* replace_special */ /************* * * struct term *demod(term, contract_proc, demods, count, context, histp) * * Demodulate a term. * * The demodulated term is returned, and the given term * becomes garbage, so a good way to invoke is `t = demod(t, demods, ...'. * A context must be allocated before the call--the same one is used * for all subterms--this saves allocating and deallocating at * each subterm. `count' is pointer to the maximum number of * rewrites that will be applied. `contract_proc' is a pointer to the * routine that looks for demodulators and does the rewriting. * The type of `demods' depends on `contract_proc'. * *************/ static struct term *demod(struct term *t, struct term *(*contract_proc)(struct term *t, int *demods, struct context *c, int *demod_id_p), int *demods, long int *count, struct context *c, struct ilist **histp) { struct rel *r; struct term *t1; struct ilist *ip; int demod_id; if (t->type == VARIABLE || TP_BIT(t->bits, SCRATCH_BIT) || *count <= 0) /* don't try to demodulate if a var or if already fully demodulated */ return(t); else if (t->type == COMPLEX) { /* if $IF, evaulate right now! */ if (Internal_flags[DOLLAR_PRESENT] && sn_to_ec(t->sym_num) == IF_SYM) { /* first reduce condition */ t->farg->argval = demod(t->farg->argval, contract_proc, demods, count, c, histp); /* now evaluate $IF */ t1 = dollar_contract(t); if (t1 != NULL) { (*count)--; return(demod(t1, contract_proc, demods, count, c, histp)); } } #if 0 else if (Internal_flags[DOLLAR_PRESENT] && sn_to_ec(t->sym_num) == COMMON_EXPRESSION_SYM) { t->farg->narg->argval = demod(t->farg->narg->argval, contract_proc, demods, count, c, histp); t->farg->narg->narg->argval = replace_special(t->farg->narg->narg->argval, t->farg->argval, t->farg->narg->argval); t1 = t->farg->narg->narg->argval; t1->fpa_id++; zap_term_special(t); return(demod(t1, contract_proc, demods, count, c, histp)); } #endif /* Fully demodulate subterms. Do not demod subterms of $RENAME(_,_). */ if (!Internal_flags[DOLLAR_PRESENT] || sn_to_ec(t->sym_num) != RENAME_SYM) { r = t->farg; while (r && *count > 0) { r->argval = demod(r->argval, contract_proc, demods, count, c, histp); r = r->narg; } } } if (*count > 0) { int debug = Flags[VERY_VERBOSE].val && (Parms[DEMOD_LIMIT].val - *count) >= Parms[VERBOSE_DEMOD_SKIP].val; if (debug) { fprintf(stdout, " demod term: "); print_term_nl(stdout, t); fflush(stdout); } t1 = (*contract_proc)(t, demods, c, &demod_id); if (t1 != NULL) { if (debug) { fprintf(stdout, " --> result: "); print_term(stdout, t1); fprintf(stdout, " demod<%d>\n", demod_id); fflush(stdout); } (*count)--; if (*histp != NULL) { ip = get_ilist(); ip->i = demod_id; (*histp)->next = ip; *histp = ip; } t = demod(t1, contract_proc, demods, count, c, histp); } else if (Internal_flags[DOLLAR_PRESENT]) { t1 = dollar_contract(t); if (t1 != NULL) { (*count)--; t = t1; } } SET_BIT(t->bits, SCRATCH_BIT); } return(t); } /* demod */ /************* * * struct term *left_most_one_step(t, contract_proc, demods, c, histp) * *************/ static struct term *left_most_one_step(struct term *t, struct term *(*contract_proc)(struct term *t, int *demods, struct context *c, int *demod_id_p), int *demods, struct context *c, struct ilist **histp) { struct term *t1; struct ilist *ip; struct rel *r; int demod_id; if (t->type == VARIABLE || TP_BIT(t->bits, SCRATCH_BIT)) return(NULL); else { t1 = (*contract_proc)(t, demods, c, &demod_id); if (t1 != NULL) { if (*histp != NULL) { ip = get_ilist(); ip->i = demod_id; (*histp)->next = ip; *histp = ip; } } else { if (Internal_flags[DOLLAR_PRESENT]) { t1 = dollar_contract(t); } } if (t1 != NULL) return(t1); else { r = t->farg; while (r != NULL) { t1 = left_most_one_step(r->argval, contract_proc, demods, c, histp); if (t1 != NULL) { r->argval = t1; return(t); } SET_BIT(r->argval->bits, SCRATCH_BIT); r = r->narg; } return(NULL); } } } /* left_most_one_step */ /************* * * struct term *demod_out_in(term, contract_proc, demods, count, subst, histp) * *************/ static struct term *demod_out_in(struct term *t, struct term *(*contract_proc)(struct term *t, int *demods, struct context *c, int *demod_id_p), int *demods, long int *count, struct context *c, struct ilist **histp) { struct term *t1; t1 = left_most_one_step(t, contract_proc, demods, c, histp); while (t1 != NULL) { (*count)--; if (*count <= 0) return(t1); else { t = t1; t1 = left_most_one_step(t, contract_proc, demods, c, histp); } } return(t); } /* demod_out_in */ /************* * * un_share_special(term) * * Given a term in which some of the subterms (not the term * itself) may be referenced more than once (fpa_id > 0), * transform it into a term in which all of the subterms * are referenced exactly once (a normal nonintegrated term) * by copying the appropriate subterms. * Also clear the SCRATCH bit in all subterms visited. * *************/ void un_share_special(struct term *t) { struct rel *r; CLEAR_BIT(t->bits, SCRATCH_BIT); if (t->type != COMPLEX) return; else { r = t->farg; while (r != NULL) { if (r->argval->fpa_id != 0) { r->argval->fpa_id--; r->argval = copy_term(r->argval); } else un_share_special(r->argval); r = r->narg; } } } /* un_share_special */ /************* * * convenient_demod(t) * *************/ struct term *convenient_demod(struct term *t) { struct term *t1; struct context *c; struct ilist *hist; long limit; limit = Parms[DEMOD_LIMIT].val; limit = (limit == -1 ? MAX_LONG_INT : limit); hist = NULL; /* so that history will not be kept */ c = get_context(); if (Flags[DEMOD_OUT_IN].val) { if (Flags[DEMOD_LINEAR].val) t1 = demod_out_in(t, contract_lin, (int *) Demodulators, &limit, c,&hist); else t1 = demod_out_in(t, contract_imd, (int *) Demod_imd, &limit, c, &hist); } else { if (Flags[DEMOD_LINEAR].val) t1 = demod(t, contract_lin, (int *) Demodulators, &limit, c, &hist); else t1 = demod(t, contract_imd, (int *) Demod_imd, &limit, c, &hist); } free_context(c); un_share_special(t1); return(t1); } /* convenient_demod */ /************* * * zap_term_special(term) -- Special term deletion. * * Deletion of nonintegrated term in which the term and * some of its subterms might be referenced more than once. * term->fpa_id is a count of the number of extra references. * If we get to a term with more than one reference, then * decrement the number of references; else recurse on the * subterms and free the node. * *************/ void zap_term_special(struct term *t) { struct rel *r1, *r2; if (t->occ.rel != NULL) { printf("WARNING, zap_term_special called with contained term: "); print_term(stdout, t); printf("\n"); } else if (t->fpa_id != 0) t->fpa_id--; else { if (t->type == COMPLEX) { /* complex term */ r1 = t->farg; while (r1 != NULL) { zap_term_special(r1->argval); r2 = r1; r1 = r1->narg; free_rel(r2); } } free_term(t); } } /* zap_term_special */ /************* * * struct term *apply_demod(t, context, mult_flag_ptr) * * Special purpose apply -- for demodulation. * * If t is a variable instantiated to some term t2, * then increment the reference count of t2, and return t2; * else create a new node and recurse on any subterms. * * mult_flag_ptr is a pointer to flag for incrementing multiplier * for demodulators that have a variable on the right that doesn't * occur on the left: If an uninstantiated variable is encountered, * then the flag is set; when finished applying to beta, if the * flag is set, then the multiplier is incremented. * (It may be the case that demods of this type are not allowed.) * *************/ struct term *apply_demod(struct term *t, struct context *c, int *pf) { struct term *t2; struct rel *r1, *r2, *r3; if (t->type == VARIABLE && c->terms[t->varnum] != NULL) { /* bound var */ t2 = c->terms[t->varnum]; t2->fpa_id++; /* count of extra references to a term */ return(t2); } if (t->type == VARIABLE) { /* unboud variable */ t2 = get_term(); t2->type = VARIABLE; t2->varnum = c->multiplier * MAX_VARS + t->varnum; *pf = 1; /* when finished applying to beta, increment multiplier */ return(t2); } else if (t->type == NAME) { /* name */ t2 = get_term(); t2->type = NAME; t2->sym_num = t->sym_num; return(t2); } else { /* complex term */ t2 = get_term(); t2->type = COMPLEX; t2->sym_num = t->sym_num; r3 = NULL; r1 = t->farg; while (r1 != NULL ) { r2 = get_rel(); if (r3 == NULL) t2->farg = r2; else r3->narg = r2; r2->argval = apply_demod(r1->argval, c, pf); r3 = r2; r1 = r1->narg; } return(t2); } } /* apply_demod */ /************* * * demod_cl(c) -- demodulate a clause * *************/ void demod_cl(struct clause *c) { struct literal *lit; struct term *atom; int linear, out_in, hist; long limit_save, limit; struct context *subst; struct ilist *ip_save, *ip_send, *ip_d; int *d; static int limit_warning_issued; linear = Flags[DEMOD_LINEAR].val; limit = Parms[DEMOD_LIMIT].val; out_in = Flags[DEMOD_OUT_IN].val; limit_save = limit = (limit == -1 ? MAX_LONG_INT : limit); hist = Flags[DEMOD_HISTORY].val; if (c->parents == NULL) ip_d = ip_save = get_ilist(); else { ip_save = c->parents; while (ip_save->next != NULL) ip_save = ip_save->next; ip_d = NULL; } /* ip_save saves position to insert "d" if any demodulation occurs */ ip_send = (hist ? ip_save : NULL); subst = get_context(); subst->multiplier = 1; if (linear) d = (int *) Demodulators; else d = (int *) Demod_imd; lit = c->first_lit; while (lit != NULL && limit > 0) { atom = lit->atom; atom->occ.lit = NULL; /* reset at end of loop */ if (out_in) { if (linear) atom = demod_out_in(atom, contract_lin, d, &limit, subst, &ip_send); else atom = demod_out_in(atom, contract_imd, d, &limit, subst, &ip_send); } else { if (linear) atom = demod(atom, contract_lin, d, &limit, subst, &ip_send); else atom = demod(atom, contract_imd, d, &limit, subst, &ip_send); } if (atom->type == VARIABLE) { abend("demod_cl, an atom has been rewritten to a variable ---\n" "perhaps you are using a symbol as both a function symbol\n" "and as a relation symbol."); } un_share_special(atom); if (atom->varnum == TERM) { /* if the atom itself was changed */ lit->atom = atom; mark_literal(lit); } atom->occ.lit = lit; lit = lit->next_lit; } if (subst->multiplier != 1) { /* new variables were introduced */ if (renumber_vars(c) == 0) { print_clause(stdout, c); abend("demod_cl, demodulation introduced too many variables."); } } if (limit <= 0) { Stats[DEMOD_LIMITS]++; if (!limit_warning_issued) { printf("WARNING, demod_limit (given clause %ld): ", Stats[CL_GIVEN]); print_clause(stdout, c); fprintf(stderr, "\n%cWARNING, demod_limit stopped the demodulation of a clause.\nThis warning will not be repeated.\n\n", Bell); limit_warning_issued = 1; } else printf("WARNING, demod_limit.\n"); } /* if some demodulation occured, insert DEMOD_RULE into parent list */ if (limit_save > limit) { if (ip_d != NULL) { c->parents = ip_d; } else { ip_d = get_ilist(); ip_d->next = ip_save->next; ip_save->next = ip_d; } ip_d->i = DEMOD_RULE; } else if (ip_d != NULL) free_ilist(ip_d); Stats[REWRITES] += (limit_save - limit); free_context(subst); } /* demod_cl */ /************* * * back_demod(d, c, input, lst) - back demodulate with d * * But don't back demodulate d or c * *************/ void back_demod(struct clause *d, struct clause *c, int input, struct list *lst) { struct term *atom; struct term_ptr *tp, *tp2; struct clause_ptr *cp, *cp2; struct ilist *ip0, *ip1; struct clause *c1, *c2; int ok; atom = ith_literal(d,1)->atom; if (Flags[INDEX_FOR_BACK_DEMOD].val) tp = all_instances_fpa(atom, Fpa_back_demod); else tp = all_instances(atom); cp = NULL; while (tp) { all_cont_cl(tp->term, &cp); tp2 = tp; tp = tp->next; free_term_ptr(tp2); } while (cp) { c1 = cp->c; ok = 0; if (c1 == d || c1 == c) ok = 0; /* don't back demodulate yourself */ else if (c1->container == Usable) { ok = 1; CLOCK_START(UN_INDEX_TIME); un_index_lits_all(c1); un_index_lits_clash(c1); CLOCK_STOP(UN_INDEX_TIME); } else if (c1->container == Sos) { ok = 1; CLOCK_START(UN_INDEX_TIME); un_index_lits_all(c1); CLOCK_STOP(UN_INDEX_TIME); } else if (c1->container == Demodulators) { if (ith_literal(c1,1)->atom->varnum == CONDITIONAL_DEMOD) ok = 0; else { if (Flags[DEMOD_LINEAR].val == 0) { CLOCK_START(UN_INDEX_TIME); imd_delete(c1, Demod_imd); CLOCK_STOP(UN_INDEX_TIME); } if (c1->parents != NULL && c1->parents->i == NEW_DEMOD_RULE) { /* just delete it. this works because list is decreasing; */ /* dynamic demodulator has id greater than parent. */ rem_from_list(c1); hide_clause(c1); ok = 0; } else { ith_literal(c1,1)->atom->varnum = POS_EQ; /* in case lex-dep */ ok = 1; } } } if (ok) { Stats[CL_BACK_DEMOD]++; if (Flags[PRINT_BACK_DEMOD].val || input) printf(" >> back demodulating %d with %d.\n", c1->id, d->id); rem_from_list(c1); c2 = cl_copy(c1); ip0 = get_ilist(); ip0->i = BACK_DEMOD_RULE; ip1 = get_ilist(); ip1->i = c1->id; c2->parents = ip0; ip0->next = ip1; hide_clause(c1); CLOCK_STOP(BACK_DEMOD_TIME); CLOCK_STOP(POST_PROC_TIME); pre_process(c2, 0,lst); CLOCK_START(POST_PROC_TIME); CLOCK_START(BACK_DEMOD_TIME); } cp2 = cp; cp = cp->next; free_clause_ptr(cp2); } } /* back_demod */ /************* * * int lit_t_f_reduce(c) -- evaluate evaluable literals * * delete any false literals, $F or -$T. * * return: 0 -- clause evaluated successfully. * 1 -- clause evaluated successfully to TRUE (clause/lits * not deallocated). * *************/ int lit_t_f_reduce(struct clause *c) { struct literal *lit, *prev_lit, *next_lit; int atom_true, atom_false; char *s; int changed = 0; int eval_to_true = 0; lit = c->first_lit; prev_lit = NULL; while (lit != NULL && !eval_to_true) { next_lit = lit->next_lit; if (lit->atom->varnum == EVALUABLE) { s = sn_to_str(lit->atom->sym_num); atom_true = str_ident(s, "$T"); atom_false = str_ident(s, "$F"); if (atom_true || atom_false) { changed = 1; if ((atom_true && lit->sign ) || (atom_false && lit->sign == 0 )) eval_to_true = 1; else if ((atom_false && lit->sign) || (atom_true && lit->sign == 0 )) { /* lit is false, so delete it */ if (prev_lit == NULL) { c->first_lit = next_lit; lit->atom->occ.lit = NULL; zap_term(lit->atom); free_literal(lit); lit = NULL; } else { prev_lit->next_lit = next_lit; lit = prev_lit; } } } } prev_lit = lit; lit = next_lit; } if (changed) { /* append "PROPOSITIONAL_RULE" to list of parents */ struct ilist *p1, *p2, *p3; for (p1 = NULL, p2 = c->parents; p2; p1 = p2, p2 = p2->next); p3 = get_ilist(); p3->i = PROPOSITIONAL_RULE; if (p1) p1->next = p3; else c->parents = p3; } return(eval_to_true); } /* lit_t_f_reduce */ /************* * * int check_input_demod(c) * * Check if it is a valid demodulator, possibly flipping and * making lex_dependent. * *************/ int check_input_demod(struct clause *c) { struct term *atom, *alpha, *beta; if (!unit_clause(c)) return(0); else if (num_literals_including_answers(c) != 1) return(0); else { /* exactly one literal, which is non-answer */ atom = ith_literal(c,1)->atom; if (atom->varnum == CONDITIONAL_DEMOD) { alpha = atom->farg->narg->argval->farg->argval; beta = atom->farg->narg->argval->farg->narg->argval; return(!term_ident(alpha, beta)); } else if (atom->varnum != POS_EQ) return(0); else { alpha = atom->farg->argval; beta = atom->farg->narg->argval; if (term_ident(alpha, beta)) return(0); else { /* it can be a demodulator */ if (!Flags[LRPO].val) { if (term_ident_x_vars(alpha, beta)) { printf("lex dependent demodulator: "); print_clause(stdout, c); atom->varnum = LEX_DEP_DEMOD; } } else { if (lrpo_greater(alpha, beta)) ; /* do nothing */ else if (lrpo_greater(beta, alpha)) { /* flip args */ printf("Flipping following input demodulator due to lrpo ordering: "); print_clause(stdout, c); atom->farg->argval = beta; atom->farg->narg->argval = alpha; } else { printf("LRPO dependent demodulator: "); print_clause(stdout, c); atom->varnum = LEX_DEP_DEMOD; } } #if 0 if (!var_subset(atom->farg->narg->argval,atom->farg->argval)) { printf("beta has a variable not in alpha: "); return(0); } else #endif return(1); } } } } /* check_input_demod */ /************* * * dynamic_demodulator(c) * * return 0: don't make it a demodulator * 1: regular demodulator * 2: lex- or lrpo- dependent demodulator * *************/ int dynamic_demodulator(struct clause *c) { struct literal *l; struct term *alpha, *beta; int wt_left, wt_right; l = ith_literal(c, 1); alpha = l->atom->farg->argval; beta = l->atom->farg->narg->argval; if (TP_BIT(l->atom->bits, ORIENTED_EQ_BIT)) { if (Flags[LRPO].val) return(1); else if (var_subset(beta, alpha)) { if (Flags[DYNAMIC_DEMOD_ALL].val) return(1); else { wt_left = weight(alpha, Weight_terms_index); wt_right = weight(beta, Weight_terms_index); if (wt_right <= Parms[DYNAMIC_DEMOD_RHS].val && wt_left - wt_right >= Parms[DYNAMIC_DEMOD_DEPTH].val) return(1); } } } if (!Flags[DYNAMIC_DEMOD_LEX_DEP].val) return(0); else if (Flags[LRPO].val) { if (var_subset(beta, alpha) && !term_ident(alpha, beta)) return(2); else return(0); } else { if (!Flags[DYNAMIC_DEMOD_ALL].val) return(0); else if (term_ident_x_vars(alpha, beta) && !term_ident(alpha, beta)) return(2); else return(0); } } /* dynamic_demodulator */ /************* * * new_demod(c, demod_flag) * * Make an equality unit into a demodulator. * It has already been checked (in order_equalities) if * alpha > beta. (Don't flip or back demodulate.) * * If demod_flag == 2, make it lex-dependent. * * If back_demod is set, set SCRATCH_BIT in the atom so that * post_process knows to back demodulate. * * Return the new demodulator. * *************/ struct clause *new_demod(struct clause *c, int demod_flag) { struct clause *d; struct ilist *ip0, *ip1; Stats[NEW_DEMODS]++; d = cl_copy(c); ip0 = get_ilist(); ip0->i = NEW_DEMOD_RULE; ip1 = get_ilist(); ip1->i = c->id; d->parents = ip0; ip0->next = ip1; cl_integrate(d); if (demod_flag == 2) ith_literal(d,1)->atom->varnum = LEX_DEP_DEMOD; if (Flags[BACK_DEMOD].val) { struct term *atom; atom = ith_literal(c,1)->atom; SET_BIT(atom->bits, SCRATCH_BIT); } if (Flags[DEMOD_LINEAR].val == 0) { if (Demod_imd == NULL) Demod_imd = get_imd_tree(); imd_insert(d, Demod_imd); } append_cl(Demodulators, d); return(d); } /* new_demod */ otter-3.3f/source/sed.prototypes0100644000076400007640000000001607264331220016422 0ustar mccunemccune/{/d s/)$/);/ otter-3.3f/source/foreign.c0100644000076400007640000002320707343604671015314 0ustar mccunemccune/* * foreign.c -- routines for interface to user-supplied evaluable functions * */ #include "header.h" /************* * * foo * *************/ long foo(long int l, double d, char *s) { printf("enter foo with args: %ld %f %s.\n", l, d, s); return(l+d); } /* foo */ /************* * * user_test_long * *************/ long user_test_long(long int l, double d, int b, char *s, struct term *t) { printf("enter user_test_long: %ld %f %d %s ", l, d, b, s); p_term(t); return(l+3); } /* user_test_long */ /************* * * user_test_double * *************/ double user_test_double(long int l, double d, int b, char *s, struct term *t) { printf("enter user_test_double: %ld %f %d %s ", l, d, b, s); p_term(t); return(d+3.0); } /* user_test_double */ /************* * * user_test_bool * *************/ int user_test_bool(long int l, double d, int b, char *s, struct term *t) { printf("enter user_test_bool: %ld %f %d %s ", l, d, b, s); p_term(t); return(!b); } /* user_test_bool */ /************* * * user_test_string * *************/ char *user_test_string(long int l, double d, int b, char *s, struct term *t) { printf("enter user_test_string: %ld %f %d %s ", l, d, b, s); p_term(t); return("\"Returned string\""); } /* user_test_string */ /************* * * user_test_term * *************/ struct term *user_test_term(long int l, double d, int b, char *s, struct term *t) { struct term *t1; printf("enter user_test_term: %ld %f %d %s ", l, d, b, s); p_term(t); t1 = get_term(); t1->type = NAME; t1->sym_num = str_to_sn("new_term", 0); return(t1); } /* user_test_term */ /************* * * declare_user_functions() * *************/ void declare_user_functions(void) { struct sym_ent *se; struct user_function *p; /* Here is an example of how to declare a function. START OF TEMPLATE (note that arity is specified twice) se = insert_sym("$FOO_BAR", 5); se->eval_code = FOO_BAR_FUNC; p = &(User_functions[FOO_BAR_FUNC]); p->arity = 5; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = BOOL_TYPE; p->arg_types[3] = STRING_TYPE; p->arg_types[4] = TERM_TYPE; p->result_type = LONG_TYPE; END OF TEMPLATE */ /********************************/ se = insert_sym("$FOO", 3); se->eval_code = FOO_FUNC; p = &(User_functions[FOO_FUNC]); p->arity = 3; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = STRING_TYPE; p->result_type = LONG_TYPE; /********************************/ se = insert_sym("$TEST_LONG", 5); se->eval_code = TEST_LONG_FUNC; p = &(User_functions[TEST_LONG_FUNC]); p->arity = 5; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = BOOL_TYPE; p->arg_types[3] = STRING_TYPE; p->arg_types[4] = TERM_TYPE; p->result_type = LONG_TYPE; /********************************/ se = insert_sym("$TEST_DOUBLE", 5); se->eval_code = TEST_DOUBLE_FUNC; p = &(User_functions[TEST_DOUBLE_FUNC]); p->arity = 5; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = BOOL_TYPE; p->arg_types[3] = STRING_TYPE; p->arg_types[4] = TERM_TYPE; p->result_type = DOUBLE_TYPE; /********************************/ se = insert_sym("$TEST_BOOL", 5); se->eval_code = TEST_BOOL_FUNC; p = &(User_functions[TEST_BOOL_FUNC]); p->arity = 5; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = BOOL_TYPE; p->arg_types[3] = STRING_TYPE; p->arg_types[4] = TERM_TYPE; p->result_type = BOOL_TYPE; /********************************/ se = insert_sym("$TEST_STRING", 5); se->eval_code = TEST_STRING_FUNC; p = &(User_functions[TEST_STRING_FUNC]); p->arity = 5; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = BOOL_TYPE; p->arg_types[3] = STRING_TYPE; p->arg_types[4] = TERM_TYPE; p->result_type = STRING_TYPE; /********************************/ se = insert_sym("$TEST_TERM", 5); se->eval_code = TEST_TERM_FUNC; p = &(User_functions[TEST_TERM_FUNC]); p->arity = 5; p->arg_types[0] = LONG_TYPE; p->arg_types[1] = DOUBLE_TYPE; p->arg_types[2] = BOOL_TYPE; p->arg_types[3] = STRING_TYPE; p->arg_types[4] = TERM_TYPE; p->result_type = TERM_TYPE; /********************************/ } /* declare_user_functions */ /************* * * int get_args_for_user_function * *************/ int get_args_for_user_function(struct term *t, int op_code, long int *long_args, double *double_args, int *bool_args, char **string_args, struct term **term_args) { int i; long l; double d; struct rel *r; struct term *ti; struct user_function *p; char *s; p = &(User_functions[op_code]); for (r = t->farg, i=0; r; r = r->narg, i++); if (i != p->arity) { abend("get_args, bad arity."); } for (r = t->farg, i=0; r; r = r->narg, i++) { ti = r->argval; switch (p->arg_types[i]) { case LONG_TYPE: if (ti->type != NAME) return(0); else if (!str_long(sn_to_str(ti->sym_num), &l)) return(0); else long_args[i] = l; break; case DOUBLE_TYPE: if (ti->type != NAME) return(0); else if (!str_double(sn_to_str(ti->sym_num), &d)) return(0); else double_args[i] = d; break; case BOOL_TYPE: if (ti->type != NAME) return(0); else { s = sn_to_str(ti->sym_num); if (str_ident(s,"$T")) bool_args[i] = 1; else if (str_ident(s,"$F")) bool_args[i] = 0; else return(0); } break; case STRING_TYPE: if (ti->type != NAME) return(0); else string_args[i] = sn_to_str(ti->sym_num); break; case TERM_TYPE: term_args[i] = ti; break; default: abend("get_args, bad arg type."); } } return(1); } /* get_args_for_user_function */ /************* * * long_to_term -- Build a constant (NAME) term corresp. to a C long. * *************/ struct term *long_to_term(long int i) { struct term *t; char s[MAX_NAME]; t = get_term(); t->type = NAME; long_str(i, s); t->sym_num = str_to_sn(s, 0); return(t); } /* long_to_term */ /************* * * double_to_term -- Build a constant (NAME) term corresp. to a C double. * *************/ struct term *double_to_term(double d) { struct term *t; char s[MAX_NAME]; t = get_term(); t->type = NAME; double_str(d, s); t->sym_num = str_to_sn(s, 0); return(t); } /* double_to_term */ /************* * * bool_to_term -- Build a constant (NAME) term corresp. to a C boolean. * *************/ struct term *bool_to_term(int i) { struct term *t; t = get_term(); t->type = NAME; t->sym_num = str_to_sn(i ? "$T" : "$F", 0); return(t); } /* bool_to_term */ /************* * * string_to_term -- Build a constant (NAME) term corresp. to a string. * *************/ struct term *string_to_term(char *s) { struct term *t; t = get_term(); t->type = NAME; t->sym_num = str_to_sn(s, 0); return(t); } /* string_to_term */ /************* * * evaluate_user_function * *************/ struct term *evaluate_user_function(struct term *t, int op_code) { long long_args[MAX_USER_ARGS]; double double_args[MAX_USER_ARGS]; int bool_args[MAX_USER_ARGS]; char *string_args[MAX_USER_ARGS]; struct term *term_args[MAX_USER_ARGS]; long l; double d; int b; char *s; struct term *t1; if (!get_args_for_user_function(t, op_code, long_args, double_args, bool_args, string_args, term_args)) return(NULL); /* arg types wrong, so do nothing */ else { switch (op_code) { /* Here is an example of how to call your function. This example takes one arg of each type. The call for a function taking two doubles and returning a double would be d = foo_bar(double_args[0],double_args[1]); The routines to translate the C result to an Otter term are long_to_term, double_to_term, bool_to_term, and string_to_term. START OF TEMPLATE case FOO_BAR_FUNC: l = foo_bar(long_args[0], double_args[1], bool_args[2], string_args[3], term_args[4]); return(long_to_term(l)); END OF TEMPLATE */ /******************************/ case FOO_FUNC: l = foo(long_args[0], double_args[1], string_args[2]); return(long_to_term(l)); /******************************/ case TEST_LONG_FUNC: l = user_test_long(long_args[0], double_args[1], bool_args[2], string_args[3], term_args[4]); return(long_to_term(l)); /******************************/ case TEST_DOUBLE_FUNC: d = user_test_double(long_args[0], double_args[1], bool_args[2], string_args[3], term_args[4]); return(double_to_term(d)); /******************************/ case TEST_BOOL_FUNC: b = user_test_bool(long_args[0], double_args[1], bool_args[2], string_args[3], term_args[4]); return(bool_to_term(b)); /******************************/ case TEST_STRING_FUNC: s = user_test_string(long_args[0], double_args[1], bool_args[2], string_args[3], term_args[4]); return(string_to_term(s)); /******************************/ case TEST_TERM_FUNC: t1 = user_test_term(long_args[0], double_args[1], bool_args[2], string_args[3], term_args[4]); return(t1); /******************************/ default: abend("evaluate_user_function, bad code."); } return(NULL); /* to quiet lint */ } } /* evaluate_user_function */ otter-3.3f/source/proto.h0100644000076400007640000007354010041254556015030 0ustar mccunemccune/* proto.h made Thursday, July 17, 10:19:37 AM 2003 (CDT) */ /* main.c */ void print_banner(int argc, char **argv); /* av.c */ int **tp_alloc(int n); struct term *get_term(void); void free_term(struct term *p); struct rel *get_rel(void); void free_rel(struct rel *p); struct sym_ent *get_sym_ent(void); void free_sym_ent(struct sym_ent *p); struct term_ptr *get_term_ptr(void); void free_term_ptr(struct term_ptr *p); struct formula_ptr_2 *get_formula_ptr_2(void); void free_formula_ptr_2(struct formula_ptr_2 *p); struct fpa_tree *get_fpa_tree(void); void free_fpa_tree(struct fpa_tree *p); struct fpa_head *get_fpa_head(void); void free_fpa_head(struct fpa_head *p); struct context *get_context(void); void free_context(struct context *p); struct trail *get_trail(void); void free_trail(struct trail *p); struct imd_tree *get_imd_tree(void); void free_imd_tree(struct imd_tree *p); struct imd_pos *get_imd_pos(void); void free_imd_pos(struct imd_pos *p); struct is_tree *get_is_tree(void); void free_is_tree(struct is_tree *p); struct is_pos *get_is_pos(void); void free_is_pos(struct is_pos *p); struct fsub_pos *get_fsub_pos(void); void free_fsub_pos(struct fsub_pos *p); struct literal *get_literal(void); void free_literal(struct literal *p); struct clause *get_clause(void); void free_clause(struct clause *p); struct list *get_list(void); void free_list(struct list *p); struct clash_nd *get_clash_nd(void); void free_clash_nd(struct clash_nd *p); struct clause_ptr *get_clause_ptr(void); void free_clause_ptr(struct clause_ptr *p); struct ci_ptr *get_ci_ptr(void); void free_ci_ptr(struct ci_ptr *p); struct ilist *get_ilist(void); void free_ilist(struct ilist *p); struct ans_lit_node *get_ans_lit_node(void); void free_ans_lit_node(struct ans_lit_node *p); struct formula_box *get_formula_box(void); void free_formula_box(struct formula_box *p); struct formula *get_formula(void); void free_formula(struct formula *p); struct formula_ptr *get_formula_ptr(void); void free_formula_ptr(struct formula_ptr *p); struct cl_attribute *get_cl_attribute(void); void free_cl_attribute(struct cl_attribute *p); struct link_node *get_link_node(void); void free_link_node(struct link_node *p); void free_imd_pos_list(struct imd_pos *p); void free_is_pos_list(struct is_pos *p); struct glist *get_glist(void); void free_glist(struct glist *p); struct g2list *get_g2list(void); void free_g2list(struct g2list *p); struct fnode *get_fnode(void); void free_fnode(struct fnode *p); void print_mem(FILE *fp); void print_mem_brief(FILE *fp); int total_mem(void); int total_mem_calls(void); void print_linked_ur_mem_stats(void); /* io.c */ int str_double(char *s, double *dp); void double_str(double d, char *s); int str_int(char *s, int *np); void int_str(int i, char *s); int str_long(char *s, long int *np); int bits_ulong(char *s, long unsigned int *np); void long_str(long int i, char *s); void ulong_bits(long unsigned int i, char *s); void cat_str(char *s1, char *s2, char *s3); int str_ident(char *s, char *t); void reverse(char *s); struct sym_ent *insert_sym(char *s, int arity); int str_to_sn(char *str, int arity); void print_syms(FILE *fp); void p_syms(void); char *sn_to_str(int sym_num); int sn_to_arity(int sym_num); struct sym_ent *sn_to_node(int sym_num); int sn_to_ec(int sym_num); struct sym_ent *sym_tab_member(char *str, int arity); int in_sym_tab(char *s); void free_sym_tab(void); int is_symbol(struct term *t, char *str, int arity); void mark_as_skolem(int sym_num); int is_skolem(int sym_num); int initial_str(char *s, char *t); int set_vars(struct term *t); int set_vars_term(struct term *t, char **varnames); int var_name(char *s); struct term_ptr *read_list(FILE *fp, int *ep, int integrate); void print_list(FILE *fp, struct term_ptr *p); void bird_print(FILE *fp, struct term *t); void write_term(FILE *fp, struct term *t, int n, int *prev); void display_term(FILE *fp, struct term *t); void print_term(FILE *fp, struct term *t); void p_term(struct term *t); void d_term(struct term *t); void print_term_nl(FILE *fp, struct term *t); int print_term_length(struct term *t); void pretty_print_term(FILE *fp, struct term *t, int indents); void print_variable(FILE *fp, struct term *t); void built_in_symbols(void); int declare_op(int prec, int type, char *str); void init_special_ops(void); int process_op_command(struct term *t); void skip_white(char *buf, int *p); int name_sym(char *s); void print_error(FILE *fp, char *buf, int pos); struct term *str_to_term(char *buf, int *p, int in_list); int read_buf(FILE *fp, char *buf); struct term *term_fixup(struct term *t); struct term *term_fixup_2(struct term *t); struct term *read_term(FILE *fp, int *rcp); void merge_sort(void **a, void **w, int start, int end, int (*comp_proc)(void *v1, void *v2)); int compare_for_auto_lex_order(void *d1, void *d2); void auto_lex_order(void); /* share.c */ struct term *integrate_term(struct term *t); void disintegrate_term(struct term *t); void set_up_pointers(struct term *t); void zap_term(struct term *t); void print_term_tab(FILE *fp); void p_term_tab(void); void test_terms(FILE *fp); struct term_ptr *all_instances(struct term *atom); struct term_ptr *all_instances_fpa(struct term *atom, struct fpa_index *fpa); void bd_kludge_insert(struct term *t); void bd_kludge_delete(struct term *t); /* fpa.c */ struct fpa_index *alloc_fpa_index(void); void term_fpa_rec(int insert, struct term *t, struct term *super_term, struct fpa_index *index, int *path, int j, int bound); void fpa_insert(struct term *t, int level, struct fpa_index *index); void fpa_delete(struct term *t, int level, struct fpa_index *index); struct fpa_tree *build_tree(struct term *t, int u_type, int bound, struct fpa_index *index); struct term *next_term(struct fpa_tree *n, int max); struct fpa_tree *build_for_all(struct fpa_index *index); void zap_prop_tree(struct fpa_tree *n); void print_fpa_tab(FILE *fp, struct fpa_index *index); void p_fpa_tab(struct fpa_index *index); void print_prop_tree(FILE *fp, struct fpa_tree *n, int level); void p_prop_tree(struct fpa_tree *n); void print_path(FILE *fp, int *path); void p_path(int *path); int new_sym_num(void); /* clocks.c */ void clock_init(void); long clock_val(int c); void clock_reset(int c); char *get_time(void); long system_time(void); long run_time(void); long wall_seconds(void); /* unify.c */ int occur_check(int vn, struct context *vc, struct term *t, struct context *c); int unify(struct term *t1, struct context *c1, struct term *t2, struct context *c2, struct trail **trp); int unify_no_occur_check(struct term *t1, struct context *c1, struct term *t2, struct context *c2, struct trail **trp); int match(struct term *t1, struct context *c1, struct term *t2, struct trail **trp); struct term *apply(struct term *t, struct context *c); int term_ident(struct term *t1, struct term *t2); void clear_subst_2(struct trail *t1, struct trail *t2); void clear_subst_1(struct trail *t1); void print_subst(FILE *fp, struct context *c); void p_subst(struct context *c); void print_trail(FILE *fp, struct trail *t); /* demod.c */ void un_share_special(struct term *t); struct term *convenient_demod(struct term *t); void zap_term_special(struct term *t); struct term *apply_demod(struct term *t, struct context *c, int *pf); void demod_cl(struct clause *c); void back_demod(struct clause *d, struct clause *c, int input, struct list *lst); int lit_t_f_reduce(struct clause *c); int check_input_demod(struct clause *c); int dynamic_demodulator(struct clause *c); struct clause *new_demod(struct clause *c, int demod_flag); /* weight.c */ struct term_ptr *read_wt_list(FILE *fp, int *ep); int noncomplexifying(struct context *c); int overbeek_match(struct term *t); int weight(struct term *t, struct is_tree *wt_index); int wt_match(struct term *t, struct term *template, int *wtp, struct is_tree *wt_index); void set_wt_list(struct term_ptr *wt_list, struct is_tree *wt_index, int *ep); void weight_index_delete(struct is_tree *wt_index); int lex_order(struct term *t1, struct term *t2); int lex_order_vars(struct term *t1, struct term *t2); int lex_check(struct term *t1, struct term *t2); int var_subset(struct term *t1, struct term *t2); void order_equalities(struct clause *c); int term_ident_x_vars(struct term *t1, struct term *t2); /* imd.c */ void imd_insert(struct clause *demod, struct imd_tree *imd); void imd_delete(struct clause *demod, struct imd_tree *root_imd); struct term *contract_imd(struct term *t_in, int *demods, struct context *subst, int *demod_id_p); void print_imd_tree(FILE *fp, struct imd_tree *imd, int level); void p_imd_tree(struct imd_tree *imd); /* is.c */ void is_insert(struct term *t, struct is_tree *root_is); void is_delete(struct term *t, struct is_tree *root_is); struct term_ptr *is_retrieve(struct term *t, struct context *subst, struct is_tree *is, struct is_pos **is_pos); struct term *fs_retrieve(struct term *t, struct context *subst, struct is_tree *is, struct fsub_pos **fs_pos); void canc_fs_pos(struct fsub_pos *pos, struct context *subst); void print_is_tree(FILE *fp, struct is_tree *is); void p_is_tree(struct is_tree *is); /* clause.c */ void reset_clause_counter(void); int next_cl_num(void); void assign_cl_id(struct clause *c); void hot_cl_integrate(struct clause *c); void cl_integrate(struct clause *c); void cl_del_int(struct clause *c); void cl_del_non(struct clause *c); void cl_int_chk(struct clause *c); struct term *clause_to_term(struct clause *c); struct clause *term_to_clause(struct term *t); struct clause *read_sequent_clause(FILE *fp, int *rcp); struct clause *read_clause(FILE *fp, int *rcp); struct list *read_cl_list(FILE *fp, int *ep); int set_vars_cl(struct clause *cl); void print_sequent_clause(FILE *fp, struct clause *c); void print_justification(FILE *fp, struct ilist *just); void print_clause_bare(FILE *fp, struct clause *cl); void print_clause(FILE *fp, struct clause *cl); void print_clause_without_just(FILE *fp, struct clause *cl); void p_clause(struct clause *cl); void print_cl_list(FILE *fp, struct list *lst); void cl_merge(struct clause *c); int tautology(struct clause *c); int prf_weight(struct clause *c); int proof_length(struct clause *c); int subsume(struct clause *c, struct clause *d); int map_rest(struct clause *c, struct clause *d, struct context *s, struct trail **trp); int anc_subsume(struct clause *c, struct clause *d); struct clause *for_sub_prop(struct clause *d); struct clause *forward_subsume(struct clause *d); struct clause_ptr *back_subsume(struct clause *c); struct clause_ptr *unit_conflict(struct clause *c); int propositional_clause(struct clause *c); int xx_resolvable(struct clause *c); int pos_clause(struct clause *c); int answer_lit(struct literal *lit); int pos_eq_lit(struct literal *lit); int neg_eq_lit(struct literal *lit); int eq_lit(struct literal *lit); int neg_clause(struct clause *c); int num_literals(struct clause *c); int num_answers(struct clause *c); int num_literals_including_answers(struct clause *c); int literal_number(struct literal *lit); int unit_clause(struct clause *c); int horn_clause(struct clause *c); int equality_clause(struct clause *c); int symmetry_clause(struct clause *c); struct literal *ith_literal(struct clause *c, int n); void append_cl(struct list *l, struct clause *c); void prepend_cl(struct list *l, struct clause *c); void insert_before_cl(struct clause *c, struct clause *c_new); void insert_after_cl(struct clause *c, struct clause *c_new); void rem_from_list(struct clause *c); void insert_clause(struct clause *c, struct clause_ptr **cpp); int max_literal_weight(struct clause *c, struct is_tree *wt_index); int weight_cl(struct clause *c, struct is_tree *wt_index); void hide_clause(struct clause *c); struct clause *proof_last_hidden_empty(void); void del_hidden_clauses(void); struct clause *cl_copy(struct clause *c); int clause_ident(struct clause *c1, struct clause *c2); void remove_var_syms(struct term *t); void cl_insert_tab(struct clause *c); void cl_delete_tab(struct clause *c); struct clause *cl_find(int id); int lit_compare(struct literal *l1, struct literal *l2); int ordered_sub_clause(struct clause *c1, struct clause *c2); int sub_clause(struct clause *c1, struct clause *c2); int sort_lits(struct clause *c); void all_cont_cl(struct term *t, struct clause_ptr **cpp); void zap_cl_list(struct list *lst); int is_eq(int sym_num); void mark_literal(struct literal *lit); int get_ancestors(struct clause *c, struct clause_ptr **cpp, struct ilist **ipp); struct ilist *clauses_to_ids(struct clause_ptr *p); void free_clause_ptr_list(struct clause_ptr *p); struct ilist *get_ancestors2(struct clause *c); struct ilist *just_to_supporters(struct ilist *ip); int renumber_vars_term(struct term *t); int renumber_vars(struct clause *c); int renum_vars_term(struct term *t, int *varnums); void clear_var_names(struct term *t); void cl_clear_vars(struct clause *c); int distinct_vars(struct clause *c); struct clause *find_first_cl(struct list *l); struct clause *find_last_cl(struct list *l); struct clause *find_random_cl(struct list *l); struct clause_ptr *get_clauses_of_wt_range(struct clause *c, int min, int max); int clause_ptr_list_size(struct clause_ptr *p); struct clause *nth_clause(struct clause_ptr *p, int n); void zap_clause_ptr_list(struct clause_ptr *p); struct clause *find_random_lightest_cl(struct list *l); struct clause *find_mid_lightest_cl(struct list *l); struct clause *find_lightest_cl(struct list *l); struct clause *find_lightest_geo_child(struct list *l); struct clause *find_interactive_cl(void); struct clause *find_given_clause(void); struct clause *extract_given_clause(void); int unit_del(struct clause *c); void back_unit_deletion(struct clause *c, int input); /* options.c */ void init_options(void); void print_options(FILE *fp); void p_options(void); void auto_change_flag(FILE *fp, int index, int val); void dependent_flags(FILE *fp, int index); void auto_change_parm(FILE *fp, int index, int val); void dependent_parms(FILE *fp, int index); int change_flag(FILE *fp, struct term *t, int set); int change_parm(FILE *fp, struct term *t); void check_options(void); /* resolve.c */ int maximal_lit(struct literal *l1); void hyper_res(struct clause *giv_cl); void neg_hyper_res(struct clause *giv_cl); void ur_res(struct clause *giv_cl); int one_unary_answer(struct clause *c); struct term *build_term(int sn, struct term *arg1, struct term *arg2, struct term *arg3); void combine_answers(struct clause *res, struct term *a1, struct context *s1, struct term *a2, struct context *s2); struct clause *build_bin_res(struct term *a1, struct context *s1, struct term *a2, struct context *s2); struct clause *apply_clause(struct clause *c, struct context *s); void bin_res(struct clause *giv_cl); struct clause *first_or_next_factor(struct clause *c, struct literal **l1p, struct literal **l2p); void all_factors(struct clause *c, struct list *lst); int factor_simplify(struct clause *c); /* index.c */ void index_lits_all(struct clause *c); void un_index_lits_all(struct clause *c); void index_lits_clash(struct clause *c); void un_index_lits_clash(struct clause *c); /* paramod.c */ void para_from(struct clause *giv_cl); void para_into(struct clause *giv_cl); /* formula.c */ void print_formula(FILE *fp, struct formula *f); void p_formula(struct formula *f); struct term *formula_to_term(struct formula *f); struct formula *term_to_formula(struct term *t); struct formula *read_formula(FILE *fp, int *rcp); struct formula_ptr *read_formula_list(FILE *fp, int *ep); void print_formula_list(FILE *fp, struct formula_ptr *p); struct formula *copy_formula(struct formula *f); void zap_formula(struct formula *f); struct formula *negate_formula(struct formula *f); struct formula *nnf(struct formula *f); struct formula *skolemize(struct formula *f); struct formula *anti_skolemize(struct formula *f); void subst_free_formula(struct term *var, struct formula *f, struct term *sk); void gen_sk_sym(struct term *t); int skolem_symbol(int sn); int contains_skolem_symbol(struct term *t); int new_var_name(void); int new_functor_name(int arity); void unique_all(struct formula *f); struct formula *zap_quant(struct formula *f); void flatten_top(struct formula *f); struct formula *cnf(struct formula *f); struct formula *dnf(struct formula *f); void rename_syms_formula(struct formula *f, struct formula *fr); void subst_sn_term(int old_sn, struct term *t, int new_sn, int type); void subst_sn_formula(int old_sn, struct formula *f, int new_sn, int type); int gen_subsume_prop(struct formula *c, struct formula *d); struct formula *subsume_conj(struct formula *c); struct formula *subsume_disj(struct formula *c); int formula_ident(struct formula *f, struct formula *g); void conflict_tautology(struct formula *f); void ts_and_fs(struct formula *f); struct list *clausify(struct formula *f); struct list *clausify_formula_list(struct formula_ptr *fp); struct formula *negation_inward(struct formula *f); struct formula *expand_imp(struct formula *f); struct formula *iff_to_conj(struct formula *f); struct formula *iff_to_disj(struct formula *f); struct formula *nnf_cnf(struct formula *f); struct formula *nnf_dnf(struct formula *f); struct formula *nnf_skolemize(struct formula *f); struct formula *clausify_formed(struct formula *f); void rms_conflict_tautology(struct formula *f); struct formula *rms_subsume_conj(struct formula *c); struct formula *rms_subsume_disj(struct formula *c); int free_occurrence(struct term *v, struct formula *f); struct formula *rms_distribute_quants(struct formula *f_quant); struct formula *rms_push_free(struct formula *f); struct formula *rms_quantifiers(struct formula *f); struct formula *rms(struct formula *f); struct formula *renumber_unique(struct formula *f, int *vnum_p); int gen_subsume_rec(struct formula *c, struct context *cs, struct formula *d, struct context *ds, struct trail **tr_p); int gen_subsume(struct formula *c, struct formula *d); int gen_conflict(struct formula *c, struct formula *d); int gen_tautology(struct formula *c, struct formula *d); struct formula *rms_cnf(struct formula *f); struct formula *rms_dnf(struct formula *f); struct formula *distribute_quantifier(struct formula *f); /* process.c */ void post_proc_all(struct clause *lst_pos, int input, struct list *lst); void infer_and_process(struct clause *giv_cl); int proc_gen(struct clause *c, int input); void pre_process(struct clause *c, int input, struct list *lst); /* misc.c */ void init(void); void abend(char *str); void read_a_file(FILE *in_fp, FILE *out_fp); void sos_argument(char *buf); void read_all_input(int argc, char **argv); void set_lex_vals(struct term *t); void set_lrpo_status(struct term *t, int val); void set_special_unary(struct term *t); void set_skolem(struct term *t); void free_all_mem(void); void output_stats(FILE *fp, int level); void print_stats(FILE *fp); void print_stats_brief(FILE *fp); void p_stats(void); void print_times(FILE *fp); void print_times_brief(FILE *fp); void p_times(void); void append_lists(struct list *l1, struct list *l2); struct term *copy_term(struct term *t); int biggest_var(struct term *t); int biggest_var_clause(struct clause *c); int ground_clause(struct clause *c); void zap_list(struct term_ptr *p); int occurs_in(struct term *t1, struct term *t2); int occurrences(struct term *s, struct term *t); int sn_occur(int sn, struct term *t); int is_atom(struct term *t); int ident_nested_skolems(struct clause *c); int ground(struct term *t); void cleanup(void); int check_stop(void); void report(void); void control_memory(void); void print_proof(FILE *fp, struct clause *c); struct clause *check_for_proof(struct clause *c); int proper_list(struct term *t); void move_clauses(int (*clause_proc)(struct clause *c), struct list *source, struct list *destination); void automatic_1_settings(void); int sos_has_pos_nonground(void); void automatic_2_settings(void); void log_for_x_show(FILE *fp); int same_structure(struct term *t1, struct term *t2); void zap_variable_names(struct term *t); int commuted_terms(struct term *t1, struct term *t2); int symbol_count(struct term *t); int commutativity_consequence(struct clause *c); /* lrpo.c */ int lrpo(struct term *t1, struct term *t2); int lrpo_greater(struct term *t1, struct term *t2); void order_equalities_lrpo(struct clause *c); /* linkur.c */ void linked_ur_res(struct clause *giv_cl); int process_linked_tags(struct clause *cp); /* linkhyp.c */ void linked_hyper_res(struct clause *giv_cl); /* foreign.c */ long foo(long int l, double d, char *s); long user_test_long(long int l, double d, int b, char *s, struct term *t); double user_test_double(long int l, double d, int b, char *s, struct term *t); int user_test_bool(long int l, double d, int b, char *s, struct term *t); char *user_test_string(long int l, double d, int b, char *s, struct term *t); struct term *user_test_term(long int l, double d, int b, char *s, struct term *t); void declare_user_functions(void); int get_args_for_user_function(struct term *t, int op_code, long int *long_args, double *double_args, int *bool_args, char **string_args, struct term **term_args); struct term *long_to_term(long int i); struct term *double_to_term(double d); struct term *bool_to_term(int i); struct term *string_to_term(char *s); struct term *evaluate_user_function(struct term *t, int op_code); /* geometry.c */ int geo_rewrite(struct clause *c); void geometry_rule_unif(struct clause *giv_cl); int child_of_geometry(struct clause *c); void gl_demod(struct clause *c, struct list *lst); /* hot.c */ void init_hot(void); int heat_is_on(void); void switch_to_hot_index(void); void switch_to_ordinary_index(void); void hot_index_clause(struct clause *c); void hot_dynamic(struct clause *c); void hot_mark_clash_cl(struct clause *c, int mark); void hot_inference(struct clause *new_cl); /* nonport.c */ void non_portable_init(int argc, char **argv); void sig_handler(int condition); char *username(void); char *hostname(void); void interact(void); void foreach_sos(void); FILE *init_log_for_x_show(void); int my_process_id(void); /* check.c */ struct gen_node *get_gen_node(void); struct proof_object *get_proof_object(void); struct proof_object_node *get_proof_object_node(void); int trivial_subst(struct context *c); struct proof_object_node *connect_new_node(struct proof_object *new_proof); void print_term_s(FILE *fp, struct term *t); void p_term_s(struct term *t); void print_clause_s(FILE *fp, struct clause *c); void p_clause_s(struct clause *c); void print_clause_s2(FILE *fp, struct clause *c); void p_clause_s2(struct clause *c); void print_proof_object_node(FILE *fp, struct proof_object_node *pn); void p_proof_object_node(struct proof_object_node *pn); void print_proof_object(FILE *fp, struct proof_object *po); void p_proof_object(struct proof_object *po); struct clause *cl_copy_delete_literal(struct clause *c, int n); int variant(struct term *t1, struct context *c1, struct term *t2, struct context *c2, struct trail **trp, int flip); struct ilist *match_clauses(struct clause *c1, struct clause *c2); struct clause *cl_append(struct clause *c1, struct clause *c2); struct clause *identity_resolve(struct clause *c1, int i1, struct clause *c2, int i2); void renumber_vars_subst(struct clause *c, struct term **terms); int finish_translating(struct clause *c, struct ilist *rest_of_history, struct proof_object_node *current, struct proof_object *new_proof); int ipx(struct ilist *ip, int n); struct proof_object_node *find_match2(struct clause *c, struct proof_object *obj, struct term **vars); int contains_answer_literal(struct clause *c); int contains_rule(struct clause *c, int rule); struct ilist *trans_2_pos(int id, struct ilist *pos); void type_2_trans(struct proof_object *po); int glist_subsume(struct clause *c, struct glist *g); void p_proof_object_as_hints(struct proof_object *po); struct literal *remove_answer_literals(struct literal *lit); void build_proof_object(struct clause *c); void init_proof_object_environment(void); /* hints.c */ void compile_hints(void); void print_hint_clause(FILE *fp, struct clause *c); void p_hint_clause(struct clause *c); void print_hints_cl_list(FILE *fp, struct list *lst); void p_hints_cl_list(struct list *lst); void adjust_weight_with_hints(struct clause *c); int hint_keep_test(struct clause *c); /* hints2.c */ struct clause *find_hint2(struct clause *c); void print_hint2_clause(FILE *fp, struct clause *c); void print_hints2_cl_list(FILE *fp, struct list *lst); void hint2_integrate(struct clause *h); void compile_hints2(void); void adjust_weight_with_hints2(struct clause *c); int hint2_keep_test(struct clause *c); void back_demod_hints(struct clause *d); void zap_hints2(void); /* attrib.c */ void init_attributes(void); int get_attribute_index(char *s); int attribute_type(int name); struct cl_attribute *get_attribute(struct clause *c, int name); void set_attribute(struct clause *c, int name, void *val_ptr); void delete_attributes(struct clause *c); struct cl_attribute *term_to_attributes(struct term *t); void print_attributes(FILE *fp, struct cl_attribute *a); /* case.c */ int splitting(void); int max_split_depth(void); int splitable_literal(struct clause *c, struct literal *l); int splitable_clause(struct clause *c); struct clause *compare_splitable_clauses(struct clause *c, struct clause *d); void print_case(FILE *fp); void p_case(void); void print_case_n(FILE *fp, int n); void p_case_n(int n); void p_assumption_depths(char assumptions[]); struct ilist *current_case(void); void add_subcase(int i); int case_depth(void); struct clause *find_clause_to_split(void); struct term *find_atom_to_split(void); int prover_forks(int n, int *ip, char assumptions[]); int split_clause(struct clause *giv_cl); int split_atom(void); void possible_split(void); void always_split(void); void possible_given_split(struct clause *c); void assumps_to_parent(struct clause *e); void exit_with_possible_model(void); /* lisp.c */ /* ivy.c */ int special_is_symbol(struct term *t, char *str, int arity); void trans_logic_symbols(struct term *t); struct proof_object *parse_initial_proof_object(FILE *fp); struct list *init_proof_object(FILE *fin, FILE *fout); struct proof_object *retrieve_initial_proof_object(void); /* pickdiff.c */ struct ilist *cldiff(struct clause *c, struct clause *d); void zap_ci_ptr_list(struct ci_ptr *p); struct clause *find_pickdiff_cl(struct list *sos, struct list *usable); /* overbeek.c */ void overbeek_insert(struct term *t); int overbeek_weight(struct term *t, int *ip); void print_overbeek_world(void); void check_overbeek_world(void); /* multijust.c */ struct glist *keep_only(struct glist *a, int i); struct glist *remove_supersets(struct glist *a, struct ilist *s); struct glist *remove_all_supersets(struct glist *a, struct glist *b); struct g2list *g2_remove_supersets(struct g2list *g2, struct ilist *p); int input_clause(int id); int first_just_input_only(struct g2list *p); int all_supporters_less_than(struct clause *c, struct ilist *supporters); int derived_from_itself(struct clause *c, struct ilist *supporters); int proof_not_longer_than(struct clause *c, struct ilist *p); void possibly_append_parents(struct clause *c, struct ilist *ip); int map_demod(struct ilist *p, int i); void set_jset_size(int n); int *get_jset(void); int *copy_jset(int *a); int jset_member(int *s, int n); void add_to_jset(int *s, int n); void remove_from_jset(int *s, int n); void print_set(int *s); void print_set_b_to_a(int *s); int subset_or_input(struct ilist *a, struct ilist *b); struct ilist *jset_to_ilist(int *s); int *ilist_to_jset(struct ilist *p); void multi_just_process(struct clause *c); int multi_justifications(); /* lists.c */ void free_ilist_list(struct ilist *p); struct ilist *ilist_tack_on(struct ilist *a, int i); struct ilist *iset_add(int i, struct ilist *p); struct ilist *iset_remove(int i, struct ilist *p); int ilist_member(int i, struct ilist *p); int iset_subset(struct ilist *a, struct ilist *b); struct ilist *iset_subtract(struct ilist *a, struct ilist *b); struct ilist *iset_sort(struct ilist *a); struct ilist *idempot_ip(struct ilist *a); struct ilist *reverse_ip(struct ilist *ip1, struct ilist *ip2); struct ilist *ilist_append(struct ilist *a, struct ilist *b); struct ilist *copy_ilist(struct ilist *p); int ilist_length(struct ilist *a); struct ilist *copy_ilist_segment(struct ilist *p, int n); void print_ilist(FILE *fp, struct ilist *ip); void p_ilist(struct ilist *ip); int glist_length(struct glist *a); struct glist *copy_glist(struct glist *p); struct glist *glist_append(struct glist *a, struct glist *b); struct glist *glist_prepend(void *p, struct glist *a); struct glist *glist_tack_on(struct glist *a, void *v); void free_glist_list(struct glist *p); int g2list_length(struct g2list *a); int member_is_subset(struct glist *a, struct ilist *s); struct glist *copy_glist_of_ilists(struct glist *a); void free_glist_of_ilists(struct glist *p); otter-3.3f/source/clocks.c0100644000076400007640000000610410103514452015117 0ustar mccunemccune/* * clocks.c -- This file has various timing routines. (Some of them * have been moved to macros.h.) * */ #include "header.h" /************* * * clock_init() - Initialize all clocks. * *************/ void clock_init(void) { int i; for (i=0; inext) { if (!set_vars(p2->term)) { fprintf(stdout, "ERROR, too many variables, max is %d: ", MAX_VARS); print_term_nl(stdout, p2->term); (*ep)++; } } Internal_flags[REALLY_CHECK_ARITY] = 0; return(p1); } /* read_wt_list */ /************* * * static struct is_tree *weight_retrieve(t, wt_index) * *************/ static struct is_tree *weight_retrieve(struct term *t, struct is_tree *wt_index) { struct is_tree *is; if (!wt_index) return(NULL); else { is = wt_index->u.kids; while (is && ((t->type != is->type) || (t->type != VARIABLE && (t->sym_num != is->lab)))) is = is->next; return(is); } } /* weight_retrieve */ /************* * * int noncomplexifying(c) -- True iff c is a noncomplexifying substitution * *************/ int noncomplexifying(struct context *c) { int i; for (i = 0; i < MAX_VARS; i++) { if (c->terms[i] && c->terms[i]->type == COMPLEX) return(0); } return(1); } /* noncomplexifying */ /************* * * int overbeek_match(t) -- True iff t is instance of one of the overbeek_terms. * *************/ int overbeek_match(struct term *t) { struct term *l, *member; struct context *c; struct trail *tr; c = get_context(); /* Assume Overbeek_terms is a proper list. */ for (l = Overbeek_terms; l->sym_num != Nil_sym_num; l = l->farg->narg->argval) { member = l->farg->argval; tr = NULL; if (match(member, c, t, &tr)) { if (noncomplexifying(c)) { clear_subst_1(tr); free_context(c); return(1); } else clear_subst_1(tr); } } free_context(c); return(0); } /* overbeek_match */ /************* * * int weight(term, wt_index) -- Return the weight a term. * *************/ int weight(struct term *t, struct is_tree *wt_index) { struct is_tree *is; struct term_ptr *p; struct rel *r; int wt, w1, max; if (overbeek_weight(t, &wt)) return wt; is = weight_retrieve(t, wt_index); if (is) p = is->u.terms; else p = NULL; wt = 0; while (p != NULL && wt_match(t, p->term->farg->argval, &wt, wt_index) == 0) { p = p->next; wt = 0; } if (p != NULL) /* we have a match */ return(wt + p->term->farg->narg->argval->fpa_id); else if (is_atom(t) && t->varnum == ANSWER) return(0); /* default weight of answer atom */ else if (t->type == VARIABLE || t->type == NAME) return(1); /* default weight of symbol */ else { /* compute default weight of term or atom */ /* if (flag is set) weight of t is (max or weights of args) + 1 else weight of t is (sum weights of subterms) + 1 */ if (is_atom(t)) max = Flags[ATOM_WT_MAX_ARGS].val; else max = Flags[TERM_WT_MAX_ARGS].val; wt = 0; r = t->farg; while (r != NULL) { if (is_atom(t) && Overbeek_terms && overbeek_match(r->argval)) w1 = 0; else w1 = weight(r->argval, wt_index); if (max) wt = (w1 > wt ? w1 : wt); else wt += w1; r = r->narg; } return(wt + 1); } } /* weight */ /************* * * wt_match_dots() * *************/ static int wt_match_dots(struct term *t, struct term *template, int *wtp, struct is_tree *wt_index) { if (wt_match(t, template, wtp, wt_index)) return(1); else { struct rel *r; for (r = t->farg; r; r = r->narg) { if (wt_match_dots(r->argval, template, wtp, wt_index)) return(1); } return(0); } } /* wt_match_dots */ /************* * * int weight_match(term, template, wtp, wt_index) * * Attempt to match a term with a weight template. If * successful, add the weight of the term to *wtp, and * return(1); else return(0). * *************/ int wt_match(struct term *t, struct term *template, int *wtp, struct is_tree *wt_index) { struct rel *r1,*r2; int go; if (template->type == COMPLEX && template->sym_num == Dots_sym_num && wt_match_dots(t, template->farg->argval, wtp, wt_index)) return(1); else if (t->type != template->type) return(0); else if (t->type == VARIABLE) return(1); else if (t->type == NAME) return(t->sym_num == template->sym_num); else { /* complex */ if (t->sym_num != template->sym_num) return(0); else { go = 1; r1 = t->farg; r2 = template->farg; while (go && r1 != NULL && r2 != NULL) { if (TP_BIT(r2->argval->bits, SCRATCH_BIT)) /* term is a multiplier */ *wtp += r2->argval->fpa_id * weight(r1->argval,wt_index); else go = wt_match(r1->argval, r2->argval, wtp, wt_index); r1 = r1->narg; r2 = r2->narg; } return(go && r1 == NULL && r2 == NULL); } } } /* wt_match */ /************* * * static void set_wt_term(term) * * Mark multipliers with SCRATCH_BIT, * and store the multipliers in fpa_id field. * * This week, multipliers look like this: $(100), $(-3) * *************/ static void set_wt_term(struct term *t) { struct rel *r; int n; if (t->type == COMPLEX) { if (is_symbol(t, "$", 1) && t->farg->argval->type == NAME && str_int(sn_to_str(t->farg->argval->sym_num), &n)) { /* this is a trick to mark a multiplier */ SET_BIT(t->bits, SCRATCH_BIT); t->fpa_id = n; } else { for (r = t->farg; r; r = r->narg) set_wt_term(r->argval); } } } /* set_wt_term */ /************* * * static int set_wt_template(template) * * Make sure that the template is OK, and mark the multipliers * and the adder. Return 1 for success and 0 for failure. * Example weight templates: weight(f($1,f($3,a)),5), * weight(x,-100), (all variables have weight -100), * weight(f(x,g(a,x)),30) (x matches any variable, and the * two occurrences of x don't have to match the same variable. * *************/ static int set_wt_template(struct term *t) { int n; /* first make sure that template is ok; if ok, str_int gets adder */ if (t->type != COMPLEX || str_ident(sn_to_str(t->sym_num), "weight") == 0 || t->farg == NULL || t->farg->narg == NULL || t->farg->narg->narg != NULL || t->farg->narg->argval->type != NAME || str_int(sn_to_str(t->farg->narg->argval->sym_num), &n) == 0) { return(0); } else { /* stash adder in fpa_id field */ t->farg->narg->argval->fpa_id = n; set_wt_term(t->farg->argval); return(1); } } /* set_wt_template */ /************* * * static void weight_insert(t, wt_index) * *************/ static void weight_insert(struct term *t, struct is_tree *wt_index) { struct is_tree *is; struct term_ptr *tp, *new_tp; struct term *t1; new_tp = get_term_ptr(); new_tp->term = t; is = weight_retrieve(t->farg->argval, wt_index); if (is) { /* Put new template at end of list. */ tp = is->u.terms; while (tp->next) tp = tp->next; tp->next = new_tp; } else { t1 = t->farg->argval; is = get_is_tree(); is->type = t1->type; if (t1->type == VARIABLE) is->lab = t1->varnum; else is->lab = t1->sym_num; is->u.terms = new_tp; is->next = wt_index->u.kids; wt_index->u.kids = is; } } /* weight_insert */ /************* * * set_wt_list(wt_list, wt_index, error_ptr) -- Set a list of weight termplates. * *************/ void set_wt_list(struct term_ptr *wt_list, struct is_tree *wt_index, int *ep) { struct term_ptr *p; *ep = 0; p = wt_list; while (p != NULL) { if (set_wt_template(p->term) == 0) { fprintf(stdout, "ERROR, weight template: "); print_term_nl(stdout, p->term); (*ep)++; } else weight_insert(p->term, wt_index); p = p->next; } } /* set_wt_list */ /************* * * void weight_index_delete(wt_index) * *************/ void weight_index_delete(struct is_tree *wt_index) { struct is_tree *is1, *is2; struct term_ptr *tp1, *tp2; if (wt_index) { is1 = wt_index->u.kids; while (is1) { tp1 = is1->u.terms; while (tp1) { /* Do not free template; it belongs to Weight_list. */ tp2 = tp1; tp1 = tp1->next; free_term_ptr(tp2); } is2 = is1; is1 = is1->next; free_is_tree(is2); } free_is_tree(wt_index); } } /* weight_index_delete */ /************* * * lex_compare_sym_nums(n1, n2) * * We must always have a total order on the symbols. * *************/ static int lex_compare_sym_nums(int n1, int n2) { int v1, v2; struct sym_ent *p1, *p2; if (n1 == n2) return(SAME_AS); else { p1 = sn_to_node(n1); p2 = sn_to_node(n2); v1 = p1->lex_val; v2 = p2->lex_val; if (v1 < v2) return(LESS_THAN); else if (v1 > v2) return(GREATER_THAN); else /* This occurs if a lex command omits symbols or if * new symbols are introduced on the fly. */ return(compare_for_auto_lex_order(p1, p2)); } } /* lex_compare_sym_nums */ /************* * * int lex_order(t1, t2) * * Return SAME_AS, GREATER_THAN, LESS_THAN, or NOT_COMPARABLE. * * A variable is comparable only to an identical variable * (nonground terms can still be compared: if a < b, f(a,x) < f(b,y).) * For pairs of nonvariables, use the lex_val field of the symbol_table node; * if identical, use the sym_num's of the terms. * *************/ int lex_order(struct term *t1, struct term *t2) { struct rel *r1, *r2; int i, t1_special, t2_special; /* The following handles special unary functions that are to be */ /* ignored during lex_check. For example, when using lex-dependent */ /* demodulation to sort AC expressions, you can make the canonical */ /* form be a + -a + b + -b + c + -c. */ if (Internal_flags[SPECIAL_UNARY_PRESENT]) { t1_special = (t1->type == COMPLEX && sn_to_node(t1->sym_num)->special_unary); t2_special = (t2->type == COMPLEX && sn_to_node(t2->sym_num)->special_unary); if (t1_special && !t2_special) { if (term_ident(t1->farg->argval, t2)) return(GREATER_THAN); else return(lex_order(t1->farg->argval, t2)); } else if (!t1_special && t2_special) { if (term_ident(t2->farg->argval, t1)) return(LESS_THAN); else return(lex_order(t1, t2->farg->argval)); } else if (t1_special && t2_special) { int argcomp = lex_order(t1->farg->argval, t2->farg->argval); if (argcomp != SAME_AS) return(argcomp); /* else fall through and treat as normal terms */ } } /* end of special_unary code */ if (t1->type == VARIABLE) if (t2->type == VARIABLE) return(t1->varnum == t2->varnum ? SAME_AS : NOT_COMPARABLE); else return(occurs_in(t1, t2) ? LESS_THAN : NOT_COMPARABLE); else if (t2->type == VARIABLE) return(occurs_in(t2, t1) ? GREATER_THAN : NOT_COMPARABLE); else if (t1->sym_num == t2->sym_num) { r1 = t1->farg; r2 = t2->farg; i = SAME_AS; while (r1 && (i = lex_order(r1->argval,r2->argval)) == SAME_AS) { r1 = r1->narg; r2 = r2->narg; } return(i); } else return(lex_compare_sym_nums(t1->sym_num, t2->sym_num)); } /* lex_order */ /************* * * int lex_order_vars(t1, t2) * * Similar to lex_order, except that variables are lowest, and are ordered * by number. * *************/ int lex_order_vars(struct term *t1, struct term *t2) { struct rel *r1, *r2; int i, t1_special, t2_special; /* The following handles special unary functions that are to be */ /* ignored during lex_check. For example, when using lex-dependent */ /* demodulation to sort AC expressions, you can make the canonical */ /* form be a + -a + b + -b + c + -c. */ if (Internal_flags[SPECIAL_UNARY_PRESENT]) { t1_special = (t1->type == COMPLEX && sn_to_node(t1->sym_num)->special_unary); t2_special = (t2->type == COMPLEX && sn_to_node(t2->sym_num)->special_unary); if (t1_special && !t2_special) { if (term_ident(t1->farg->argval, t2)) return(GREATER_THAN); else return(lex_order_vars(t1->farg->argval, t2)); } else if (!t1_special && t2_special) { if (term_ident(t2->farg->argval, t1)) return(LESS_THAN); else return(lex_order_vars(t1, t2->farg->argval)); } else if (t1_special && t2_special) { int argcomp = lex_order_vars(t1->farg->argval, t2->farg->argval); if (argcomp != SAME_AS) return(argcomp); /* else fall through and treat as normal terms */ } } /* end of special_unary code */ if (t1->type == VARIABLE) if (t2->type == VARIABLE) if (t1->varnum == t2->varnum) return(SAME_AS); else return(t1->varnum > t2->varnum ? GREATER_THAN : LESS_THAN); else return(LESS_THAN); else if (t2->type == VARIABLE) return(GREATER_THAN); else if (t1->sym_num == t2->sym_num) { r1 = t1->farg; r2 = t2->farg; i = SAME_AS; while (r1 && (i = lex_order_vars(r1->argval,r2->argval)) == SAME_AS) { r1 = r1->narg; r2 = r2->narg; } return(i); } else return(lex_compare_sym_nums(t1->sym_num, t2->sym_num)); } /* lex_order_vars */ /************* * * int wt_lex_order(t1, t2) * * Return SAME_AS, GREATER_THAN, LESS_THAN, or NOT_COMPARABLE. * *************/ static int wt_lex_order(struct term *t1, struct term *t2) { int i1, i2; i1 = weight(t1, Weight_terms_index); i2 = weight(t2, Weight_terms_index); if (i1 > i2) return(GREATER_THAN); else if (i1 < i2) return(LESS_THAN); else return(lex_order(t1, t2)); } /* wt_lex_order */ /************* * * int lex_check(t1, t2) * * Return SAME_AS, GREATER_THAN, LESS_THAN, or NOT_COMPARABLE. * * Consult a flag to see if variables should be considered. * *************/ int lex_check(struct term *t1, struct term *t2) { if (Flags[LEX_ORDER_VARS].val) return(lex_order_vars(t1, t2)); else return(lex_order(t1, t2)); } /* lex_check */ /************* * * get_var_multiset(t, a) * * Get (or continue getting) multiset of variables in t by * Filling in array a. * *************/ static void get_var_multiset(struct term *t, int *a) { struct rel *r; if (t->type == VARIABLE) a[t->varnum]++; else if (t->type == COMPLEX) { r = t->farg; while (r != NULL) { get_var_multiset(r->argval, a); r = r->narg; } } } /* get_var_multiset */ /************* * * int var_subset(t1, t2) * * True if vars(t1) is a subset of vars(t2) * *************/ int var_subset(struct term *t1, struct term *t2) { int t1_vars[MAX_VARS], t2_vars[MAX_VARS], i; for (i = 0; i < MAX_VARS; i++) t1_vars[i] = t2_vars[i] = 0; get_var_multiset(t1, t1_vars); get_var_multiset(t2, t2_vars); /* now make sure every variable in t1 is in t2 */ for (i = 0; i < MAX_VARS; i++) if (t2_vars[i] == 0 && t1_vars[i] != 0) return(0); return(1); } /* var_subset */ /************* * * int sym_occur(sym_num, t) * * True if sym_num is the symbol number of one of the constants * or functors in t. * *************/ static int sym_occur(int sym_num, struct term *t) { struct rel *r; int found; if (t->type == VARIABLE) return(0); else if (t->sym_num == sym_num) return(1); /* NAME or COMPLEX */ else if (t->type == NAME) return(0); else { /* complex with different sym_num */ r = t->farg; found = 0; while (r != NULL && found == 0) { found = sym_occur(sym_num, r->argval); r = r->narg; } return(found); } } /* sym_occur */ /************* * * sym_elim(alpha, beta) * * True if alpha is complex, all args of alpha are unique vars, functor * of alpha doesn't occur in beta, and subset(vars(beta),vars(alpha)) . * (If true, alpha = beta can be made into a symbol-eliminating * demodulator.) * *************/ static int sym_elim(struct term *alpha, struct term *beta) { struct rel *r; struct term *t1; int i, a[MAX_VARS], ok; if (alpha->type == VARIABLE) return(0); else { if (alpha->type == NAME) ok = 0; else { /* check for list of unique vars */ for (i = 0; i < MAX_VARS; i++) a[i] = 0; ok = 1; r = alpha->farg; while (r != NULL && ok) { t1 = r->argval; ok = (t1->type == VARIABLE && a[t1->varnum] == 0); a[t1->varnum] = 1; r = r->narg; } } if (ok == 0) return(0); else { /* check that functor of alpha doesn't occur in beta */ /* and that vars(beta) is a subset of vars(alpha) */ return(sym_occur(alpha->sym_num, beta) == 0 && var_subset(beta, alpha)); } } } /* sym_elim */ /************* * * order_equalities(c) * * For each equality literal (pos or neg), flip args if the right * side is heavier. After possible filp, if the left side is * heavier, set the ORIENTED_EQ_BIT in the atom. * If the atom is flipped, set SCRATCH_BIT. * *************/ void order_equalities(struct clause *c) { struct literal *l; struct rel *r1, *r2; struct term *alpha, *beta; int alpha_bigger, beta_bigger; for (l = c->first_lit; l; l = l->next_lit) { alpha_bigger = 0; beta_bigger = 0; if (eq_lit(l)) { r1 = l->atom->farg; r2 = r1->narg; alpha = r1->argval; beta = r2->argval; if (!term_ident(alpha, beta)) { if (Flags[SYMBOL_ELIM].val && sym_elim(alpha, beta)) alpha_bigger = 1; else if (Flags[SYMBOL_ELIM].val && sym_elim(beta, alpha)) beta_bigger = 1; else if (occurs_in(beta, alpha)) alpha_bigger = 1; else if (occurs_in(alpha, beta)) beta_bigger = 1; else { int rc; rc = wt_lex_order(alpha, beta); if (rc == GREATER_THAN) alpha_bigger = 1; else if (rc == LESS_THAN) beta_bigger = 1; } if (alpha_bigger || beta_bigger) { if (beta_bigger) { r1->argval = beta; r2->argval = alpha; SET_BIT(l->atom->bits, SCRATCH_BIT); } SET_BIT(l->atom->bits, ORIENTED_EQ_BIT); } } } } } /* order_equalities */ /************* * * int term_ident_x_vars(term1, term2) -- Compare two terms, ignoring variables * * If identical except for vars, return(1); else return(0). The bits * field is not checked. * *************/ int term_ident_x_vars(struct term *t1, struct term *t2) { struct rel *r1, *r2; if (t1->type != t2->type) return(0); else if (t1->type == COMPLEX) { if (t1->sym_num != t2->sym_num) return(0); else { r1 = t1->farg; r2 = t2->farg; while (r1 && term_ident_x_vars(r1->argval,r2->argval)) { r1 = r1->narg; r2 = r2->narg; } return(r1 == NULL); } } else if (t1->type == VARIABLE) return(1); else /* NAME */ return(t1->sym_num == t2->sym_num); } /* term_ident_x_vars */ otter-3.3f/source/fpa.c.diffs0100644000076400007640000000563310041245671015514 0ustar mccunemccune219,221c219 < tp1 = get_term_ptr(); < fp3->terms = tp1; < tp1->term = t; --- > fp3->terms = flist_insert(NULL, t); 235,256c233 < < tp1 = fp1->terms; < tp2 = NULL; < /* keep list sorted, decreasing addresses */ < while (tp1 != NULL && tp1->term->fpa_id > t->fpa_id) { < tp2 = tp1; < tp1 = tp1->next; < } < if (tp1 != NULL && tp1->term == t) < Stats[FPA_OVERLOADS]++; /* term already in list */ < else { < tp3 = get_term_ptr(); < tp3->term = t; < if (tp2 == NULL) { /* insert at beginning */ < tp3->next = fp1->terms; < fp1->terms = tp3; < } < else { /* insert after tp2 */ < tp3->next = tp1; < tp2->next = tp3; < } < } --- > fp1->terms = flist_insert(fp1->terms, t); 291,314c268,275 < tp1 = fp1->terms; < tp2 = NULL; < /* list is sorted, decreasing addresses */ < while (tp1 != NULL && tp1->term->fpa_id > t->fpa_id) { < tp2 = tp1; < tp1 = tp1->next; < } < if (tp1 == NULL || tp1->term != t) < Stats[FPA_UNDERLOADS]++; /* term not found in list */ < else { < if (tp2 == NULL) { /* delete from beginning */ < fp1->terms = tp1->next; < if (fp1->terms == NULL) { /* delete fpa_head also */ < if (fp2 == NULL) < index->table[hashval] = fp1->next; < else < fp2->next = fp1->next; < free_fpa_head(fp1); < /* don't worry about fp1->path; let it be lost forever */ < } < } < else /* delete */ < tp2->next = tp1->next; < free_term_ptr(tp1); --- > fp1->terms = flist_delete(fp1->terms, t); > if (fp1->terms == NULL) { /* delete fpa_head also */ > if (fp2 == NULL) > index->table[hashval] = fp1->next; > else > fp2->next = fp1->next; > free_fpa_head(fp1); > /* don't worry about fp1->path; let it be lost forever */ 438c399 < pp->terms = fp->terms; --- > pp->position = first_fpos(fp->terms); 632a594 > 634,637c596,601 < tp = n->terms; /* fpa lists: terms have decreasing addresses */ < while (tp != NULL && max != 0 && tp->term->fpa_id > max) < tp = tp->next; < if (tp == NULL) { --- > struct term *t = FTERM(n->position); > while (t != NULL && max != 0 && t->fpa_id > max) { > n->position = next_fpos(n->position); > t = FTERM(n->position); > } > if (t == NULL) { 642,643c606,607 < n->terms = tp->next; < return(tp->term); --- > n->position = next_fpos(n->position); > return(t); 745c709 < p2->terms = h->terms; --- > p2->position = first_fpos(h->terms); 791d754 < struct term_ptr *tp; 798a762,763 > struct fposition fpos; > struct term *t; 800,801c765,767 < tp = f->terms; < while (tp != NULL) { --- > fpos = first_fpos(f->terms); > t = FTERM(fpos); > while (t != NULL) { 803,804c769,771 < print_term(fp, tp->term); < tp = tp->next; --- > print_term(fp, t); > fpos = first_fpos(f->terms); > t = FTERM(fpos); 935a903 > otter-3.3f/source/header.h0100644000076400007640000002300710103510725015076 0ustar mccunemccune#ifndef TP_HEADER_H /* to make sure we don't include this more than once */ #define TP_HEADER_H /* * header.h -- This is the main "include" file for Otter. * All of the .c files include this file. * */ /************ BASIC INCLUDES ************/ #include #include #include /*********** INCLUDES FOR TIMES AND DATES ************/ #include #ifdef TP_RUSAGE /* getrusage() */ # include /* needed for SunOS */ # include #endif /*********** SIZES OF INTEGERS ***************/ #include /* for sizes of integers, etc. */ #define MAX_LONG_INT LONG_MAX /* a big integer that fits into "long" */ #define MAX_INT INT_MAX /* a big integer that fits into "int" */ #define MAX_UNSIGNED_SHORT USHRT_MAX /******** MISCELLANEOUS LIMITS *********/ #define MAX_NAME 256 /* max chars in any symbol (including '\0') */ #define MAX_BUF 100000 /* max chars in input string (including '\0') */ #define MAX_VARS 64 /* maximum # of distinct variables in clause */ #define VAR_TYPE unsigned short /* must be able to hold MAX_VARS * (max-multiplier+1) */ #define FPA_SIZE 3793 /* size of FPA hash tables */ #define MAX_FS_TERM_DEPTH 300 /* max depth of terms in IS-tree */ #define MAX_AL_TERM_DEPTH 500 /* max depth of alphas in IMD-tree */ /******** TYPES *********/ #define NAME 1 /* basic types of term */ #define VARIABLE 2 #define COMPLEX 3 /* types of non-VARIABLE term -- varnum field is used */ #define TERM 0 /* not an atom */ #define NORM_ATOM 1 /* normal atom */ #define POS_EQ 2 /* positive equality atom */ #define NEG_EQ 3 /* negative equality atom */ #define ANSWER 4 /* answer literal atom */ #define LEX_DEP_DEMOD 5 /* lex-dependent demodulator atom */ #define EVALUABLE 6 /* $ID, $LT, etc */ #define CONDITIONAL_DEMOD 7 /* conditional demodulator */ /* types of unification property tree */ #define UNIFY 1 #define INSTANCE 2 #define MORE_GEN 3 /* integer codes for membes of parent lists */ /* positive integers are clause IDs */ #define BINARY_RES_RULE -1 #define HYPER_RES_RULE -2 #define NEG_HYPER_RES_RULE -3 #define UR_RES_RULE -4 #define PARA_INTO_RULE -5 #define PARA_FROM_RULE -6 #define LINKED_UR_RES_RULE -7 #define GEO_RULE -8 #define FACTOR_RULE -9 #define NEW_DEMOD_RULE -10 #define BACK_DEMOD_RULE -11 #define DEMOD_RULE -12 #define UNIT_DEL_RULE -13 #define EVAL_RULE -14 #define GEO_ID_RULE -15 #define FACTOR_SIMP_RULE -16 #define COPY_RULE -17 #define FLIP_EQ_RULE -18 #define CLAUSIFY_RULE -19 #define BACK_UNIT_DEL_RULE -20 #define SPLIT_RULE -21 #define SPLIT_NEG_RULE -22 #define PROPOSITIONAL_RULE -23 #define LIST_RULE -1000 /* integer codes for evaluable functions and predicates */ /* When adding more, update built_in_symbols in io.c. */ /* User-defined (foreign) evaluable functions are 0--1000 */ #define MAX_USER_EVALUABLE 1000 #define SUM_SYM 1001 #define PROD_SYM 1002 #define DIFF_SYM 1003 #define DIV_SYM 1004 #define MOD_SYM 1005 #define EQ_SYM 1006 #define NE_SYM 1007 #define LT_SYM 1008 #define LE_SYM 1009 #define GT_SYM 1010 #define GE_SYM 1011 #define FSUM_SYM 1012 #define FPROD_SYM 1013 #define FDIFF_SYM 1014 #define FDIV_SYM 1015 #define FEQ_SYM 1016 #define FNE_SYM 1017 #define FLT_SYM 1018 #define FLE_SYM 1019 #define FGT_SYM 1020 #define FGE_SYM 1021 #define BIT_AND_SYM 1022 #define BIT_OR_SYM 1023 #define BIT_XOR_SYM 1024 #define BIT_NOT_SYM 1025 #define SHIFT_LEFT_SYM 1026 #define SHIFT_RIGHT_SYM 1027 #define INT_TO_BITS_SYM 1028 #define BITS_TO_INT_SYM 1029 #define T_SYM 1030 #define F_SYM 1031 #define AND_SYM 1032 #define OR_SYM 1033 #define TRUE_SYM 1034 #define NOT_SYM 1035 #define IF_SYM 1036 #define ID_SYM 1037 #define LNE_SYM 1038 #define LLT_SYM 1039 #define LLE_SYM 1040 #define LGT_SYM 1041 #define LGE_SYM 1042 #define OCCURS_SYM 1043 #define VOCCURS_SYM 1044 #define VFREE_SYM 1045 #define RENAME_SYM 1046 #define NEXT_CL_NUM_SYM 1047 #define UNIQUE_NUM_SYM 1048 #define ATOMIC_SYM 1049 #define INT_SYM 1050 #define BITS_SYM 1051 #define VAR_SYM 1052 #define GROUND_SYM 1053 #define OUT_SYM 1054 #define COMMON_EXPRESSION_SYM 1055 /* comparing symbols and terms */ #define LESS_THAN 1 #define GREATER_THAN 2 #define SAME_AS 3 #define NOT_COMPARABLE 4 #define NOT_GREATER_THAN 5 #define NOT_LESS_THAN 6 #define LRPO_MULTISET_STATUS 0 /* lex RPO multiset status */ #define LRPO_LR_STATUS 1 /* lex RPO left-right status */ /* (RL status removed for Otter 3.0 release.) */ /* Operator types */ #define XFX 1 #define XFY 2 #define YFX 3 #define FX 4 #define FY 5 #define XF 6 #define YF 7 /* linked-UR resolution inference rule. */ #define BOOLEAN char #define FALSE 0 #define TRUE 1 #define UNDEFINED -1 #define NOT_SPECIFIED 0 #define NUCLEUS 1 #define LINK 2 #define BOTH 3 #define SATELLITE 4 /* first-order formulas */ #define ATOM_FORM 1 #define NOT_FORM 2 #define AND_FORM 3 #define OR_FORM 4 #define IMP_FORM 5 #define IFF_FORM 6 #define QUANT_FORM 7 #define ALL_QUANT 1 #define EXISTS_QUANT 2 /* exit codes */ #define KEEP_SEARCHING 100 #define INPUT_ERROR_EXIT 101 #define ABEND_EXIT 102 #define PROOF_EXIT 103 #define SOS_EMPTY_EXIT 104 #define MAX_GIVEN_EXIT 105 #define MAX_SECONDS_EXIT 106 #define MAX_GEN_EXIT 107 #define MAX_KEPT_EXIT 108 #define MAX_MEM_EXIT 109 #define MALLOC_NULL_EXIT 110 #define INTERACTIVE_EXIT 111 #define SEGV_EXIT 112 #define USR1_EXIT 113 #define POSSIBLE_MODEL_EXIT 114 #define MAX_LEVELS_EXIT 115 /************* END OF ALL GLOBAL CONSTANT DEFINITIONS ****************/ #include "cos.h" /* flag, parameter, statistic, and clock names */ #include "foreign.h" /* user-defined evaluable functions */ #include "macros.h" /* preprocessor (#define) macros */ #include "fpa2.h" /* new fpa code */ #include "types.h" /* all of the type declarations */ #include "proto.h" /* function prototypes */ /*********** GLOBAL VARIABLES ***********/ #ifdef IN_MAIN # define CLASS /* empty string if included by main program */ #else # define CLASS extern /* extern if included by anything else */ #endif /* lists of clauses */ CLASS struct list *Usable; CLASS struct list *Sos; CLASS struct list *Demodulators; CLASS struct list *Passive; CLASS struct list *Hot; CLASS struct list *Hints; CLASS struct list *Hints2; CLASS struct list *Mace_constraints; /* FPA (indexing) lists for resolution inference rules */ CLASS struct fpa_index *Fpa_clash_pos_lits; CLASS struct fpa_index *Fpa_clash_neg_lits; /* FPA lists for unit conflict and back subsumption */ CLASS struct fpa_index *Fpa_pos_lits; CLASS struct fpa_index *Fpa_neg_lits; /* FPA lists for paramodulation inference rules */ CLASS struct fpa_index *Fpa_clash_terms; /* clashable terms */ CLASS struct fpa_index *Fpa_alphas; /* alphas (left and right) */ /* FPA list for back demodulation */ CLASS struct fpa_index *Fpa_back_demod; /* back demod candidates */ /* discrimination tree forward subsumption index */ CLASS struct is_tree *Is_pos_lits; /* positive literals */ CLASS struct is_tree *Is_neg_lits; /* negative literals */ /* discrimination tree index for demodulators */ CLASS struct imd_tree *Demod_imd; /* Lists of weight templates */ CLASS struct term_ptr *Weight_purge_gen; /* screen generated clauses */ CLASS struct term_ptr *Weight_pick_given; /* pick given clause */ CLASS struct term_ptr *Weight_terms; /* order terms */ /* Simple indexes (one level only) for weight templates */ CLASS struct is_tree *Weight_purge_gen_index; CLASS struct is_tree *Weight_pick_given_index; CLASS struct is_tree *Weight_terms_index; /* options (Flags and Parms) */ CLASS struct { /* Flags are boolean valued options */ char *name; int val; } Flags[MAX_FLAGS]; CLASS struct { /* Parms are integer valued options */ char *name; int val; int min, max; /* minimum and maximum permissible values */ } Parms[MAX_PARMS]; CLASS int Internal_flags[MAX_INTERNAL_FLAGS]; /* invisible to user */ /* statistics */ CLASS long Stats[MAX_STATS]; CLASS int Subsume_count[100]; /* clocks */ CLASS struct clock Clocks[MAX_CLOCKS]; /* Other built-in symbols */ CLASS int Cons_sym_num, Nil_sym_num, Ignore_sym_num, Chr_sym_num, Dots_sym_num; /* table of user functions */ CLASS struct user_function User_functions[MAX_USER_FUNCTIONS]; CLASS FILE *Null_output; /* Miscellaneous global variables */ CLASS char Float_format[MAX_NAME]; CLASS struct term *Overbeek_terms; /* Special weighting */ CLASS struct term *Split_atoms; /* Atoms to split */ CLASS char Bell; CLASS int Max_input_id; /* Maxumim ID of an input clause */ /* More special weighting */ CLASS struct term_ptr **Overbeek_world; #endif /* ! TP_HEADER_H */ otter-3.3f/source/av.c.diffs0100644000076400007640000000017010041245670015342 0ustar mccunemccune371c371 < p->terms = NULL; --- > p->position = (struct fposition) {NULL, 0}; 1403a1404 > fprint_flist_mem(fp, 0); otter-3.3f/source/macros.h0100644000076400007640000000467510103514256015147 0ustar mccunemccune/* * macros.h -- This file contains some #define preprocessor macros * */ /************* * * CPU_TIME(sec, usec) - It has been sec seconds + usec microseconds * since the start of this process. * *************/ #if defined(TP_ABSOLUTELY_NO_CLOCKS) #define CPU_TIME(sec, usec) {sec = usec = 0;} #else #ifdef TP_RUSAGE #define CPU_TIME(sec, usec) \ { \ struct rusage r; \ getrusage(RUSAGE_SELF, &r); \ sec = r.ru_utime.tv_sec; \ usec = r.ru_utime.tv_usec; \ } /* CPU_TIME */ #else #define CPU_TIME(sec, usec) {sec = usec = 0;} #endif #endif /************* * * CLOCK_START(clock_num) - Start or continue timing. * * If the clock is already running, a warning message is printed. * *************/ #if defined(TP_ABSOLUTELY_NO_CLOCKS) #define CLOCK_START(c) /* empty string */ #else #define CLOCK_START(c) \ { \ if (Flags[CLOCKS].val) { \ struct clock *cp; \ \ cp = &Clocks[c]; \ if (cp->curr_sec != -1) { \ fprintf(stderr, "WARNING, CLOCK_START: clock %d already on.\n", c); \ printf("WARNING, CLOCK_START: clock %d already on.\n", c); \ } \ else \ CPU_TIME(cp->curr_sec, cp->curr_usec) \ }\ } /* CLOCK_START */ #endif /************* * * CLOCK_STOP(clock_num) - Stop timing and add to accumulated total. * * If the clock not running, a warning message is printed. * *************/ #if defined(TP_ABSOLUTELY_NO_CLOCKS) #define CLOCK_STOP(c) /* empty string */ #else #define CLOCK_STOP(c) \ { \ if (Flags[CLOCKS].val) { \ long sec, usec; \ struct clock *cp; \ \ cp = &Clocks[c]; \ if (cp->curr_sec == -1) { \ fprintf(stderr, "WARNING, CLOCK_STOP: clock %d already off.\n", c); \ printf("WARNING, CLOCK_STOP: clock %d already off.\n", c); \ } \ else { \ CPU_TIME(sec, usec) \ cp->accum_sec += sec - cp->curr_sec; \ cp->accum_usec += usec - cp->curr_usec; \ cp->curr_sec = -1; \ cp->curr_usec = -1; \ } \ }\ } /* CLOCK_STOP */ #endif /************* * * SET_BIT, CLEAR_BIT, BIT. * *************/ /* SCRATCH_BIT is by several operations to temporarily mark terms. * When using it, make sure that no other operation is using it, and * make sure to clear it when done. */ #define SET_BIT(bits, flag) (bits = bits | flag) #define CLEAR_BIT(bits, flag) (bits = bits & ~flag) #define TP_BIT(bits, flag) (bits & flag) /* for terms: */ #define SCRATCH_BIT 01 #define ORIENTED_EQ_BIT 02 /* for clauses: */ #define SCRATCH_BIT 01 otter-3.3f/source/func0100644000076400007640000000011607562232127014363 0ustar mccunemccune/************* * * func * *************/ static func() { } /* func */ otter-3.3f/source/unify.c0100644000076400007640000002677207653773062015034 0ustar mccunemccune/* * unify.c -- unification and matching routines * */ #include "header.h" /* The following macros are used throughout this file. */ #define BIND(i, c1, t2, c2, trp) { struct trail *tr; \ c1->terms[i] = t2; c1->contexts[i] = c2; \ tr = get_trail(); tr->varnum = i; tr->context = c1; \ tr->next = *trp; *trp = tr; } #define DEREFERENCE(t, c) { int i; \ while (t->type == VARIABLE && c->terms[i = t->varnum]) \ { t = c->terms[i]; c = c->contexts[i]; } } /************* * * int occur_check(varnum, var_context, term, term_context) * * Return 0 iff variable occurs in term under substitution * (including var==term). * *************/ int occur_check(int vn, struct context *vc, struct term *t, struct context *c) { if (t->type == NAME) return 1; else if (t->type == COMPLEX) { struct rel *r = t->farg; while (r != NULL && occur_check(vn, vc, r->argval, c)) r = r->narg; return (r == NULL); } else { /* variable */ int tvn = t->varnum; if (tvn == vn && c == vc) return 0; /* fail occur_check here */ else if (c->terms[tvn] == NULL) return 1; /* uninstantiated variable */ else return occur_check(vn, vc, c->terms[tvn], c->contexts[tvn]); } } /* occur_check */ /************* * * int unify(t1, c1, t2, c2, trail_address) * * Attempt to unify t1 in context c1 with t2 in context c2. * If successful, return 1 and and a pointer to the trail (a record * of the substitutions). The trail is extended by adding new * entries to the front, and the front is returned. On entry, * *trail_address must be either NULL or the result of a previous * call to unify. If unification fails, the trail is unchanged. * A context is a substitution table along with a multiplier for * the variables. The multiplier need not be present for * unification, but it is needed for `apply'. * * An example of its use: * * c1 = get_context(); c1->multiplier = 0; * c2 = get_context(); c2->multiplier = 1; * tr = NULL; * if (unify(t1, c1, t2, c2, &tr)) { * print_subst(stdout, c1); * print_subst(stdout, c2); * print_trail(stdout, tr); * t3 = apply(t1, c1); * t4 = apply(t2, c2); * printf("apply substitution: "); * print_term(stdout, t3); printf(" "); * print_term(stdout, t4); printf("\n"); * clear_subst_1(tr); * zap_term(t3); * zap_term(t4); * } * else * printf("unify fails\n"); * free_context(c1); * free_context(c2); * *************/ int unify(struct term *t1, struct context *c1, struct term *t2, struct context *c2, struct trail **trp) { DEREFERENCE(t1, c1); DEREFERENCE(t2, c2); /* Now, neither t1 nor t2 is a bound variable. */ if (t1->type == VARIABLE) { int vn1 = t1->varnum; if (t2->type == VARIABLE) { /* both t1 and t2 are variables */ if (vn1 == t2->varnum && c1 == c2) return 1; /* identical */ else { BIND(vn1, c1, t2, c2, trp); return 1; } } else { /* t1 variable, t2 not variable */ if (occur_check(vn1, c1, t2, c2)) { BIND(vn1, c1, t2, c2, trp); return 1; } else return 0; /* failed occur_check */ } } else if (t2->type == VARIABLE) { /* t2 variable, t1 not variable */ int vn2 = t2->varnum; if (occur_check(vn2, c2, t1, c1)) { BIND(vn2, c2, t1, c1, trp); return 1; } else return 0; /* failed occur_check */ } else if (t1->sym_num != t2->sym_num) return 0; /* fail because of symbol clash */ else if (t1->type == NAME) return 1; else { /* both COMPLEX with same functor */ struct trail *tpos = *trp; /* save trail position in case of failure */ struct rel *r1 = t1->farg; struct rel *r2 = t2->farg; while (r1 && unify(r1->argval, c1, r2->argval, c2, trp)) { r1 = r1->narg; r2 = r2->narg; } if (r1 == NULL) return 1; else { /* restore trail and fail */ struct trail *tp = *trp; while (tp != tpos) { struct trail *t3 = tp; tp->context->terms[tp->varnum] = NULL; tp = tp->next; free_trail(t3); } *trp = tpos; return 0; } } } /* unify */ /************* * * int unify_no_occur_check(t1, c1, t2, c2, trp) * *************/ int unify_no_occur_check(struct term *t1, struct context *c1, struct term *t2, struct context *c2, struct trail **trp) { DEREFERENCE(t1, c1); DEREFERENCE(t2, c2); /* Now, neither t1 nor t2 is a bound variable. */ if (t1->type == VARIABLE) { int vn1 = t1->varnum; if (t2->type == VARIABLE && vn1 == t2->varnum && c1 == c2) return 1; /* identical */ else { /* occur check would be here */ BIND(vn1, c1, t2, c2, trp); return 1; } } else if (t2->type == VARIABLE) { int vn2 = t2->varnum; /* occur check would be here */ BIND(vn2, c2, t1, c1, trp); return 1; } else if (t1->sym_num != t2->sym_num) return 0; /* fail because of symbol clash */ else if (t1->type == NAME) return 1; else { /* both COMPLEX with same functor */ struct trail *tpos = *trp; /* save trail position in case of failure */ struct rel *r1 = t1->farg; struct rel *r2 = t2->farg; while (r1 && unify_no_occur_check(r1->argval, c1, r2->argval, c2, trp)) { r1 = r1->narg; r2 = r2->narg; } if (r1 == NULL) return 1; else { /* restore trp and fail */ struct trail *tp = *trp; while (tp != tpos) { struct trail *t3 = tp; tp->context->terms[tp->varnum] = NULL; tp = tp->next; free_trail(t3); } *trp = tpos; return 0; } } } /* unify_no_occur_check */ /************* * * int match(t1, c1, t2, trail_address) -- one-way unification. * * Match returns 1 if t2 is an instance of {t1 in context c1}. * This is not a very general version, but it is useful for * demodulation and subsumption. It assumes that the variables * of t1 and t2 are separate, that none of the variables in t2 * have been instantiated, and that none of those t2's variables * will be instantiatied. Hence, there is no context for t2, * no need to dereference more than one level, and no need for * an occur_check. * * The use of the trail is the same as in `unify'. * *************/ int match(struct term *t1, struct context *c1, struct term *t2, struct trail **trp) { if (t1->type == VARIABLE) { /* t1 variable */ int vn = t1->varnum; if (c1->terms[vn] == NULL) { BIND(vn, c1, t2, NULL, trp); return 1; } else return term_ident(c1->terms[vn], t2); } else if (t2->type == VARIABLE) /* t1 not variable, t2 variable, so fail */ return 0; else /* neither term is a variable */ if (t1->sym_num != t2->sym_num) return 0; /* fail because of symbol clash */ else { /* following handles both names and complex terms */ struct trail *tpos = *trp; /* save trail position in case of failure */ struct rel *r1 = t1->farg; struct rel *r2 = t2->farg; /* arities are same because sym_nums are the same */ while (r1 != NULL && match(r1->argval, c1, r2->argval, trp)) { r1 = r1->narg; r2 = r2->narg; } if (r1 == NULL) return 1; else { /* restore from trail and fail */ struct trail *tp = *trp; while (tp != tpos) { struct trail *t3 = tp; tp->context->terms[tp->varnum] = NULL; tp = tp->next; free_trail(t3); } *trp = tpos; return 0; } } } /* match */ /************* * * struct term *apply(term, context) -- Apply a substitution to a term. * * Apply always succeeds and returns a pointer to the * instantiated term. * *************/ struct term *apply(struct term *t, struct context *c) { /* dereference if variable */ /* A NULL context means that the subst was generated by match. */ /* If the context is NULL, then apply just copies the term. */ while (t->type == VARIABLE && c != NULL && c->terms[t->varnum] != NULL) { int vn = t->varnum; t = c->terms[vn]; c = c->contexts[vn]; } if (t->type == VARIABLE) { /* variable */ struct term *t2 = get_term(); t2->type = VARIABLE; if (c == NULL) t2->varnum = t->varnum; else t2->varnum = c->multiplier * MAX_VARS + t->varnum; return t2; } else if (t->type == NAME) { /* name */ struct term *t2 = get_term(); t2->type = NAME; t2->sym_num = t->sym_num; return t2; } else { /* complex term */ struct rel *r1, *r2, *r3; struct term *t2 = get_term(); t2->type = COMPLEX; t2->sym_num = t->sym_num; r3 = NULL; r1 = t->farg; while (r1 != NULL ) { r2 = get_rel(); if (r3 == NULL) t2->farg = r2; else r3->narg = r2; r2->argval = apply(r1->argval, c); r3 = r2; r1 = r1->narg; } return t2; } } /* apply */ /************* * * int term_ident(term1, term2) -- Compare two terms. * * If identical return 1; else return 0. The bits * field is not checked. * *************/ int term_ident(struct term *t1, struct term *t2) { if (t1->type != t2->type) return 0; else if (t1->type == COMPLEX) { if (t1->sym_num != t2->sym_num) return 0; else { struct rel *r1 = t1->farg; struct rel *r2 = t2->farg; while (r1 && term_ident(r1->argval,r2->argval)) { r1 = r1->narg; r2 = r2->narg; } return (r1 == NULL); } } else if (t1->type == VARIABLE) return (t1->varnum == t2->varnum); else /* NAME */ return (t1->sym_num == t2->sym_num); } /* term_ident */ /************* * * clear_subst_2(trail_1, trail_2) -- Clear part of a substitution. * * It is assumed that trail_2 (including NULL) is a subtrail * of trail_1. This routine clears entries starting at trail_1, * up to (but not including) trail_2. * *************/ void clear_subst_2(struct trail *t1, struct trail *t2) { if (t1 == NULL || t1 == t2) return; else { clear_subst_2(t1->next, t2); t1->context->terms[t1->varnum] = NULL; free_trail(t1); } } /* clear_subst_2 */ /************* * * clear_subst_1(trail_1) -- Clear a substitution. * * Clear all members of the trail. * *************/ void clear_subst_1(struct trail *t1) { if (t1 == NULL) return; else { clear_subst_1(t1->next); t1->context->terms[t1->varnum] = NULL; free_trail(t1); } } /* clear_subst_1 */ /************* * * print_subst(file_ptr, context) * *************/ void print_subst(FILE *fp, struct context *c) { int i; fprintf(fp, "Substitution in context %p, multiplier %d\n", (void *) c, c->multiplier); for (i=0; i< MAX_VARS; i++) if (c->terms[i] != NULL) { fprintf(fp, "v%d -> ", i); print_term(fp, c->terms[i]); fprintf(fp, " context %p", (void *) c->contexts[i]); fprintf(fp, " status %d\n", c->status[i]); } } /* print_subst */ /************* * * p_subst(context) * *************/ void p_subst(struct context *c) { print_subst(stdout, c); } /* p_subst */ /************* * * print_trail(file_ptr, context) * *************/ void print_trail(FILE *fp, struct trail *t) { struct trail *t2; fprintf(fp, "Trail:"); t2 = t; while (t2 != NULL) { fprintf(fp, " <%d,%p>", t2->varnum, (void *) t2->context); t2 = t2->next; } fprintf(fp, ".\n"); } /* print_trail */ otter-3.3f/source/index.c0100644000076400007640000002052107343604672014767 0ustar mccunemccune/* * index.c -- Routines for indexing and unindexing clauses. * */ #include "header.h" /************* * * index_mark_clash(r) -- recursive routine to mark and index * clashable terms (terms that can be used by paramodulation). * *************/ static void index_mark_clash(struct rel *r) { struct term *t; struct rel *r1; t = r->argval; if (t->type == VARIABLE && Flags[PARA_INTO_VARS].val == 0) return; else { r1 = t->occ.rel; while (r1 != NULL && r1->clashable == 0) r1 = r1->nocc; r->clashable = 1; if (r1 != NULL) return; /* becuase t is already clashable */ else { if (Flags[PARA_FROM].val) fpa_insert(t, Parms[FPA_TERMS].val, Fpa_clash_terms); if (t->type == COMPLEX) { if (Flags[PARA_SKIP_SKOLEM].val == 0 || is_skolem(t->sym_num) == 0) { r = t->farg; while (r != NULL) { index_mark_clash(r); if (Flags[PARA_ONES_RULE].val) r = NULL; else r = r->narg; } } } } } } /* index_mark_clash */ /************* * * un_index_mark_clash(r) * * See index_mark_clash. * *************/ static void un_index_mark_clash(struct rel *r) { struct term *t; struct rel *r1; t = r->argval; if (t->type == VARIABLE && Flags[PARA_INTO_VARS].val == 0) return; else { r->clashable = 0; r1 = t->occ.rel; while (r1 != NULL && r1->clashable == 0) r1 = r1->nocc; if (r1 != NULL) return; /* becuase t is clashable from another containing term */ else { if (Flags[PARA_FROM].val) fpa_delete(t, Parms[FPA_TERMS].val, Fpa_clash_terms); if (t->type == COMPLEX) { if (Flags[PARA_SKIP_SKOLEM].val == 0 || is_skolem(t->sym_num) == 0) { r = t->farg; while (r != NULL) { un_index_mark_clash(r); if (Flags[PARA_ONES_RULE].val) r = NULL; else r = r->narg; } } } } } } /* un_index_mark_clash */ /************* * * index_paramod(atom) -- index for paramodulation inference rules * * Index clashable terms for `from' paramodulation, and * index clashable args of equality for `into' paramodulation. * * Also mark clashable terms for the paramodulation routines. * *************/ static void index_paramod(struct term *atom) { struct rel *r; struct literal *lit; lit = atom->occ.lit; if (eq_lit(lit)&&term_ident(atom->farg->argval, atom->farg->narg->argval)) return; /* First index clashable `into' terms for `from' paramodulation. */ if (!Flags[PARA_INTO_UNITS_ONLY].val || unit_clause(lit->container)) { if (pos_eq_lit(lit) || neg_eq_lit(lit)) { if (Flags[PARA_INTO_LEFT].val) index_mark_clash(atom->farg); if (Flags[PARA_INTO_RIGHT].val) index_mark_clash(atom->farg->narg); } else { for (r = atom->farg; r; r = r->narg) index_mark_clash(r); } } /* Now index clashable `from' terms for `into' paramodulation. */ if (!Flags[PARA_FROM_UNITS_ONLY].val || unit_clause(lit->container)) { if (pos_eq_lit(lit) && Flags[PARA_INTO].val) { if (Flags[PARA_FROM_LEFT].val) { if (Flags[PARA_FROM_VARS].val || atom->farg->argval->type != VARIABLE) fpa_insert(atom->farg->argval, Parms[FPA_TERMS].val, Fpa_alphas); } if (Flags[PARA_FROM_RIGHT].val) { if (Flags[PARA_FROM_VARS].val || atom->farg->narg->argval->type != VARIABLE) fpa_insert(atom->farg->narg->argval, Parms[FPA_TERMS].val, Fpa_alphas); } } } } /* index_paramod */ /************* * * un_index_paramod(atom) * * See index_paramod. * *************/ static void un_index_paramod(struct term *atom) { struct rel *r; struct literal *lit; lit = atom->occ.lit; if (eq_lit(lit)&&term_ident(atom->farg->argval, atom->farg->narg->argval)) return; if (!Flags[PARA_INTO_UNITS_ONLY].val || unit_clause(lit->container)) { if (pos_eq_lit(lit) || neg_eq_lit(lit)) { if (Flags[PARA_INTO_LEFT].val) un_index_mark_clash(atom->farg); if (Flags[PARA_INTO_RIGHT].val) un_index_mark_clash(atom->farg->narg); } else { for (r = atom->farg; r; r = r->narg) un_index_mark_clash(r); } } if (!Flags[PARA_FROM_UNITS_ONLY].val || unit_clause(lit->container)) { if (pos_eq_lit(lit) && Flags[PARA_INTO].val) { if (Flags[PARA_FROM_LEFT].val) if (Flags[PARA_FROM_VARS].val || atom->farg->argval->type != VARIABLE) fpa_delete(atom->farg->argval, Parms[FPA_TERMS].val, Fpa_alphas); if (Flags[PARA_FROM_RIGHT].val) if (Flags[PARA_FROM_VARS].val || atom->farg->narg->argval->type != VARIABLE) fpa_delete(atom->farg->narg->argval, Parms[FPA_TERMS].val, Fpa_alphas); } } } /* un_index_paramod */ /************* * * index_lits_all(c) * * Index literals for forward subsumption, back subsumption, and * unit conflict. * Positive and negative literals go into different indexes. * The NO_FAPL, NO_FANL and FOR_SUB_FPA flags are checked to determine * what and how to index. * * NO_FAPL can be set if you are generating only positive clauses * and back subsumption is off. It surpresses indexing of positive * literals in the non-clashable index. (The index for subsumption * and unit conflict.) * Similarly for negative literals with NO_FANL. * *************/ void index_lits_all(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit != NULL) { if (lit->atom->varnum == ANSWER) ; /* skip answer literal */ else if (lit->sign) { if (Flags[NO_FAPL].val == 0) fpa_insert(lit->atom, Parms[FPA_LITERALS].val, Fpa_pos_lits); if ((Flags[FOR_SUB_FPA].val == 0 && Flags[FOR_SUB].val) || (Flags[UNIT_DELETION].val && num_literals(c) == 1)) is_insert(lit->atom, Is_pos_lits); } else { if (Flags[NO_FANL].val == 0) fpa_insert(lit->atom, Parms[FPA_LITERALS].val, Fpa_neg_lits); if ((Flags[FOR_SUB_FPA].val == 0 && Flags[FOR_SUB].val) || (Flags[UNIT_DELETION].val && num_literals(c) == 1)) is_insert(lit->atom, Is_neg_lits); } lit = lit->next_lit; } } /* index_lits_all */ /************* * * un_index_lits_all(c) * * See index_lits_all. * *************/ void un_index_lits_all(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit != NULL) { if (lit->atom->varnum == ANSWER) ; /* skip answer literal */ else if (lit->sign) { if (Flags[NO_FAPL].val == 0) fpa_delete(lit->atom, Parms[FPA_LITERALS].val, Fpa_pos_lits); if ((Flags[FOR_SUB_FPA].val == 0 && Flags[FOR_SUB].val) || (Flags[UNIT_DELETION].val && num_literals(c) == 1)) is_delete(lit->atom, Is_pos_lits); } else { if (Flags[NO_FANL].val == 0) fpa_delete(lit->atom, Parms[FPA_LITERALS].val, Fpa_neg_lits); if ((Flags[FOR_SUB_FPA].val == 0 && Flags[FOR_SUB].val) || (Flags[UNIT_DELETION].val && num_literals(c) == 1)) is_delete(lit->atom, Is_neg_lits); } lit = lit->next_lit; } } /* un_index_lits_all */ /************* * * index_lits_clash(c) * * Index literals for inference rules, and index terms for paramodulation if * any paramodulation inference rules are set. * *************/ void index_lits_clash(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit != NULL) { if (lit->atom->varnum == ANSWER || lit->atom->varnum == EVALUABLE) ; /* skip answer literals and evaluable literals */ else if (lit->sign) fpa_insert(lit->atom, Parms[FPA_LITERALS].val, Fpa_clash_pos_lits); else fpa_insert(lit->atom, Parms[FPA_LITERALS].val, Fpa_clash_neg_lits); if (Flags[PARA_FROM].val || Flags[PARA_INTO].val) index_paramod(lit->atom); lit = lit->next_lit; if (Flags[HYPER_SYMMETRY_KLUDGE].val) break; } } /* index_lits_clash */ /************* * * un_index_lits_clash(c) * * See index_lits_clash. * *************/ void un_index_lits_clash(struct clause *c) { struct literal *lit; lit = c->first_lit; while (lit != NULL) { if (lit->atom->varnum == ANSWER || lit->atom->varnum == EVALUABLE) ; /* skip answer literals and evaluable literals */ else if (lit->sign) fpa_delete(lit->atom, Parms[FPA_LITERALS].val, Fpa_clash_pos_lits); else fpa_delete(lit->atom, Parms[FPA_LITERALS].val, Fpa_clash_neg_lits); if (Flags[PARA_FROM].val || Flags[PARA_INTO].val) un_index_paramod(lit->atom); lit = lit->next_lit; if (Flags[HYPER_SYMMETRY_KLUDGE].val) break; } } /* un_index_lits_clash */ otter-3.3f/README.Win320100644000076400007640000000040507714463670013777 0ustar mccunemccuneThe Otter 3.3 / Mace 2.2 version for Microsoft Windows is packaged separately from the UNIX version. The place from which you obtained the UNIX version might also have the Microsoft Windows version. See the Otter Web page http://www.mcs.anl.gov/AR/otter/ otter-3.3f/util/0040755000076400007640000000000007714312621013164 5ustar mccunemccuneotter-3.3f/util/make-example-htmls0100755000076400007640000000440107705604257016612 0ustar mccunemccune#!/usr/bin/perl -w sub do_directory { $exdir = `pwd`; open(FH1, ">index.html") || die "cannot create file"; ########################################### print FH1 < $exdir

$exdir

END_OF_HEAD ########################################### if (-e "README") { print FH1 "
\n"; print FH1 `cat README`; print FH1 "
\n"; } foreach $i (`/bin/ls *.in`) { chop $i; if (-e "program") { $program = `cat program`; chop $program; } else { $program = "otter"; } if ($program eq "mace2") { $parms = `grep 'benchmark parameters' $i | sed 's/.*parameters//'`; chop $parms; } else { $parms = ""; } $i =~ s/\.in//; print FH1 "

$program $parms < $i.in > $i.out\n"; } ########################################### print FH1 <

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. END_OF_TAIL ########################################### } $base = `pwd`; chop $base; open(FH, ">index.html") || die "cannot create file"; ########################################### print FH < $base

$base

END_OF_HEAD ########################################### # if (-e "README") { # print FH "
\n"; # print FH `cat README`; # print FH "
\n"; # } print FH "
    \n"; foreach $i (`/bin/ls -d [[:lower:]]*`) { chop $i; if (-d $i) { print FH "
  • $i\n"; if (-e "$i/README") { # print FH "
    \n"; # print FH `cat $i/README`; # print FH "
    \n"; print FH ".\n"; print FH `cat $i/README`; } chdir $i; &do_directory; chdir $base; } } print FH "
\n"; ########################################### print FH <

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. END_OF_TAIL ########################################### otter-3.3f/README.make0100644000076400007640000000060310014507101013761 0ustar mccunemccuneIf you are on recent Linux or Macintosh operating system, Running "make all" from the main directory might be all that is necessary. If it succeeds, binaries for {otter,mace2,anldp} will appear in the directory bin/. The Otter source is in the directory source/; the Mace2 source is in the directory mace2/. See Makefiles in those directories for hints if you have trouble compiling. otter-3.3f/README.first0100644000076400007640000000110110103530466014176 0ustar mccunemccuneOtter 3.3 and Mace 2.2 QUICK INSTALL If you are using a recent Linux or Macintosh computer you'll probably be able to use the pre-compiled binaries. Try the commands % gunzip -c otter-3.3.tar.gz | tar xvf - % cd otter-3.3 % make install (if that fails, try ./make-install) This will try to determine what kind of computer you are using and copy the appropriate binaries to the bin/ subdirectory. It will then run a few simple tests to see if the binaries are okay for your machine. For more information, point your browser at index.html in this directory. otter-3.3f/Makefile0100644000076400007640000000173710103515551013645 0ustar mccunemccune# Top Makefile for Otter 3.3 / Mace 2.2 install: ./QuickInstall test-otter: bin/otter < examples/auto/steam.in | awk '/PROOF/,/end of proof/' @echo "If you see 'end of proof', the test was successful." @echo "Now try 'make test-mace2'." test-mace test-mace2: bin/mace2 -n6 -p < examples-mace2/basic/noncommutative_group.in | \ awk '/Model/,/end_of_model/' @echo "If you see a group table, the test was successful." realclean: cd source && $(MAKE) realclean cd mace2 && $(MAKE) realclean cd examples && $(MAKE) realclean cd examples-mace2 && $(MAKE) realclean /bin/rm -f bin/* /bin/rm -f *~ all: $(MAKE) realclean cd source && $(MAKE) CC=gcc all cd mace2 && $(MAKE) CC=gcc all # The following cleans up, then makes a .tar.gz file of the current # directory, leaving it in the parent directory. DIR = $(shell basename $(PWD)) dist: $(MAKE) realclean cd .. && tar cvf $(DIR).tar $(DIR) gzip -f ../$(DIR).tar ls -lt ../$(DIR).tar.gz otter-3.3f/documents/0040755000076400007640000000000007720505115014207 5ustar mccunemccuneotter-3.3f/documents/old_READMEs/0040755000076400007640000000000007714312620016165 5ustar mccunemccuneotter-3.3f/documents/old_READMEs/new_305.txt0100644000076400007640000000656306473054664020131 0ustar mccunemccune ------------------------- What's New in Otter 3.0.5 ------------------------- W. McCune February, 1998. Here are a few notes on changes since version 3.0.4. See the file New_304.txt for changes from 3.0.0 to 3.0.4. No major bugs have been discovered in 3.0.4, so there is probably no need to upgrade to 3.0.5 unless you need one of the new features. See the file "Changelog" in the main directory for bug fixes. There are two major new features in Otter 3.0.5. The first is a new autonomous mode, obtained with set(auto2). The old autonomous mode is still available with set(auto). The second is an experimental case splitting rule. See the file split.txt. As I write this, Otter 3.0.5 has not been compiled for Microsoft or Macintosh (I no longer try to manage those ports---any volunteers?). Check the Otter web page http://www.mcs.anl.gov/home/mccune/ar/otter/ for current information. Because there are only a few other new features and changes, I'll describe those first, then I'll describe the new autonomous mode. MISCELLANOUS NEW FEATURES 1. New flag set(tptp_eq). Ordinarily, a predicate symbol is recognized as equality for paramodulation and demodulation if it is "=", or if it starts with "EQ", "eq", or "Eq". If tptp_eq is set, a predicate symbol is equality iff it is "equal". This flag makes Otter compatible with TPTP, because TPTP's one and only equality predicate is "equal". In particular, TPTP has nonequality predicate symbols that start with "eq". 2. Two new parameters: warn_mem and warn_mem_max_weight. These are used together to reset the max_weight (to warn_mem_max_weight), when a specified amount of memory (warn_mem) has been used. For example, if you wish to reset the max_weight to 10 after 90 megabytes of memory has been used, include the following in your input file. assign(warn_mem, 90000). assign(warn_mem_max_weight, 10). 3. New heuristic flag set(discard_non_oriented_eq). This will, if order_eq is set, discard nonorientable positive equality units. 4. New heuristic flag set(discard_xx_resolvable). This causes nonunit clauses containing a literal that can be resolved with x=x to be deleted. 5. New flag set(back_unit_deletion) which causes all new units to be used for unit deletion with all existing clauses. This is analogous to back demodulation. (This can be an expensive operation.) CHANGES TO PROOF OBJECTS I changed the format of proof objects. (Proof objects are the very detailed proofs that you get with set(build_proof_object)). I added a new field to lines in proof objects. If the new field is not empty, it gives the ID number of the corresponding (equivalent) line in the ordinary Otter proof. Old form: ( ) New form: ( ) NEW AUTONOMOUS MODE The important changes in the new autonomous mode (auto2) are 1. Paramodulation is from and into units only. This is incomplete, but probably more useful in practice. 2. UR resolution is used (along with hyperresolution) for nonunit sets containing either non-Horn clauses or equality literals. The OLD autonomous mode is available with set(auto1) or set(auto). The NEW autonomous mode is available with set(auto2). (Think of set(auto) as a symbolic link to the "official" auto mode.) otter-3.3f/documents/old_READMEs/README.3060100644000076400007640000000074207272347031017357 0ustar mccunemccune -------------------- Otter, Version 3.0.6 -------------------- The only substantial change from 3.0.5 is that a new kind of proof object can be output: set(build_proof_object_2). This is used for the Ivy project (see http://www-unix.mcs.anl.gov/~mccune/acl2/). FTP Otter 3.0.6 from ftp://info.mcs.anl.gov/pub/Otter/otter-3.0.6.tar.Z W. McCune (otter@mcs.anl.gov) Argonne National Laboratory April, 2000 otter-3.3f/documents/old_READMEs/README.3020100644000076400007640000000265207272347030017354 0ustar mccunemccune Otter, Version 3.0.2 -------------------- Summary of changes from 3.0.0. See Changelog for details. 1. Several bugs related to answer literals have been fixed. 2. Forward subsumption on nonunits has been made a bit faster. 3. FormEd string parsing has been fixed. 4. Otter can output its input clauses in a form suitable for ANL-DP, a program that searches for small models. If the flag dp_transform is set, Otter will translate the input clauses then exit without searching for a proof. See the report anl-dp, which can be FTPed from info.mcs.anl.gov in pub/Otter/papers. ANL-DP will be distributed later. 5. Otter can output proofs in a very detailed form with set(build_proof_object). This produces a proof object (an s-expression) containing all the substitutions and positions for the inferences so that a very simple independent program can check the proofs (without having to know about unification or matching). E-mail mccune@mcs.anl.gov for more information. 6. Otter prints its ordinary proofs in a bit more detail than before. (As a result, Sec. 15, "Output and Exit Codes", of the manual is out of date.) FTP Otter 3.0.2 from info.mcs.anl.gov in pub/Otter/otter-3.0.2.tar.Z . See pub/Otter/README for information on DOS (3.0.1) and Mac (3.0.0) versions. W. McCune (otter@mcs.anl.gov) Argonne National Laboratory June 16, 1994 otter-3.3f/documents/old_READMEs/README.3040100644000076400007640000000107607272347030017355 0ustar mccunemccune -------------------- Otter, Version 3.0.4 -------------------- It has been about a year since the release of Otter 3.0.3. Since then, here have been many small bug fixes, a few changes, and many small enhancements. See document/New_304.txt for a summary of changes since 3.0.0, and see Changelog for complete details on bug fixes and new features, FTP Otter 3.0.4 from info.mcs.anl.gov in pub/Otter/otter-3.0.4.tar.Z . W. McCune (otter@mcs.anl.gov) Argonne National Laboratory August 16, 1995 otter-3.3f/documents/old_READMEs/new_304.txt0100644000076400007640000002033606014514350020102 0ustar mccunemccune ------------------------- What's New in Otter 3.0.4 ------------------------- W. McCune August, 1995. Here are a few notes on the Otter features that have been installed since version 3.0.0, that is, the ones that are not documented in "Otter 3.0 Reference Manual and Guide". See the file "Changelog" in the main directory for bug fixes. Special thanks to Bob Veroff, who developed many of these new features. Thanks also to Larry Wos, Ken Kunen, Ingo Dahn, and Yuan Yu for suggestions. 1. PROOFS Ordinary proofs have a bit more detail, and several new flags are available. Flag formula_history -- default clear. If this flag is set, quantified formulas (if any) that occur in proofs will be listed in the proofs with their own IDs, and clauses generated from the formulas will have justification [clausify, ]. Flag build_proof_object -- default clear. If set, this flag causes a very detailed "proof object" to be printed along with ordinary proofs. The purpose is so that in independent program can check the proof. We have such a program, written in the Boyer-Moore logic; e-mail mccune@mcs.anl.gov for details. Flag proof_weight -- default clear. The proof weight of a clause is the number of occurrences of its ancestors. (Proof length is the size of the set of ancestors.) If this flag is set, proof weight, instead of proof length, is used for ancestor subsumption. Also, the proof weight is printed along with proofs. WARNING: don't set this flag if a lot of demodulation is expected (e.g., dynamic_demod or knuth_bendix), because the proof weight can be too big to count in a reasonable amount of time. 2. PROCESSING INFERRED CLAUSES Parameter max_answers -- default -1. If n >= 0, then inferred clauses with more than n answer literals will not be retained. This does not apply to input clauses, even if the flag process_input is set. Flag gl_rewrite_before -- default clear. If this flag is set, (gL) simplification is attempted before ordinary demodulation. Flag gl_rewrite_after -- default clear. If this flag is set, (gL) simplification is attempted after ordinary demodulation. The preceding two flags replace flag geometric_rewrite, which acted like the new flag gl_rewrite_after. Parameters dynamic_demod_depth (default -1) dynamic_demod_rhs (default 1). This is an extension of the ad hoc ordering when deciding whether a new equality should be a demodulator. (It is not used if flag lrpo is set.) The equality is first oriented as described in the manual. Let it be alpha=beta. If wt(beta) <= dynamic_demod_rhs and if wt(alpha) - wt(beta) >= dynamic_demod_depth, then the equality can be a demodulator. With the default values for these parameters, Otter should behave as described in the manual. Parameter age_factor -- default 0. If not 0, then the value (number_of_clauses_given / age_factor) is added to the pick-given weight of clauses. Parameter distinct_vars_factor -- default 0. If not 0, then the value (number_of_distinct_variables * distinct_vars_factor) is added to the pick-given weight of clauses. Parameter debug_first -- default 0. This parameter is consulted if the flag very_verbose is set. Verbose output will begin when a clause is KEPT and given an ID of this value. Parameter debug_last -- default -1. This parameter is consulted if the flag very_verbose is set. Verbose output will end when a clause is KEPT and given an ID of this value. Parameter verbose_demod_skip -- default 0. This parameter is consulted during demodulation if the flag very_verbose is set. Verbose output will not occur during the first n rewrites. Special_unary processing has been improved. If you use this feature, check the code in lex_order() and lex_order_vars() to see how it works now. 3. HINTS The main purpose of the hints mechanism is to set or adjust the pick-given weight of clauses. A hint H can apply to a clause C in 3 ways: H subsumes C (forward subsume, fsub), C subsumes H (back subsume, bsub), and H is equivalent to C (equiv, which implies fsub and bsub). Two more ways, which apply to unit clauses only, may be added later: H and C unify H anc C have the same shape, like weighting works now Another purpose of hints is to retain clauses that would otherwise be discarded because the purge-gen weight is too high. The Flag KEEP_HINT_SUBSUMERS (default clear) says to skip the purge-gen test on generated clauses that subsume hints (i.e., bsub). The parameters are FSUB_HINT_WT FSUB_HINT_ADD_WT BSUB_HINT_WT BSUB_HINT_ADD_WT EQUIV_HINT_WT EQUIV_HINT_ADD_WT These can be overridden for individual hints with corresponding attributes (see the next section) on the hints, e.g., p0(a,x) # bsub_hint_wt(200) # fsub_hint_wt(100). If the parameters (attributes) are not set, they are not used; if you have a list of hints with no attributes, and if you don't set any hint parameters, the hints won't be used for anything. If more than one parameter (attribute) might apply, equiv is tested first, then fsub, then bsub. If you use both WT and ADD_WT variants then BOTH can apply, e.g., when the hint p # bsub_hint_wt(200) # bsub_hint_add_wt(20). applies to a clause, the clause gets pick-given weight 220. Parameter fsub_hint_add_wt -- default 0. Parameter bsub_hint_add_wt -- default 0. Parameter equiv_hint_add_wt -- default 0. Parameter fsub_hint_wt -- default MAX_INT. Parameter bsub_hint_wt -- default MAX_INT. Parameter equiv_hint_wt -- default MAX_INT. 4. CLAUSE ATTRIBUTES Attributes can now be attached to clauses. There are currently 7 types of attribute, all used by the hints mechanism. Six of these correspond to the 6 hints parameters, and the seventh is a label attribute. The 6 hint-parameter attributes are used to override the ordinary hints parameters for particular clauses (see the preceding section). If a hint has a label attribute, and if that hint causes the pick-given weight of a new clause to be adjusted, the label attribute is copied to the new clause. See the files examples/fringe/{luka5h,rob_ocd}.in for examples. Here are examples of label attributes on clauses: -p(x) | q(x) # label("This string is the label!"). a = b # label(this_is_a_constant_label). See the preceding section for examples of hint-parameter attributes. 5. MISCELLANY Flag dp_int_domain -- default set. This flag is consulted when Otter is used as a preprocessor for MACE, a program that searches for small finite models. If the flag is set, integers in clauses are interpreted as domain elements rather than as constants. This reduces the number of isomorphic models that are generated by MACE. (One can also, as in the previous version, use the passive list to make such assignments, but that way is less efficient.) Parameter new_symbol_lex_position -- default MAX_INT/2. New symbols can be created during the search, usually by $-evaluation. With this parameter, the user can specify where they will occur in the lex ordering. If there is a lex command, all new symbols will have a lex values between the n-th and (n+1)-th symbol in the lex command. The ordering among the new symbols is the default ordering. This also applies to input symbols not occurring in the lex command. Weighting has been extended to allow the user to specify terms that CONTAIN particular terms. This is done with a new unary function symbol $dots(_). If $dots(t) occurs in a weight template, it will match any term that contains a term that matches t. This is very useful for discarding "bad" clauses. Here is part of an output file that illustrates $dots. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% list(sos). 1 [] p(f(g(g(g(g(g(h(h(h(h(j(b)))))))))))). 2 [] p(F(g(g(h(g(H(g(h(g(g(g(B)))))))))))). 3 [] p(f3(g(h(a)),g(g(b)),h(h(c)))). end_of_list. weight_list(pick_given). weight(f($dots(j($(5)))),100). weight(F($dots(H($dots(B)))),1000). weight(f3($dots(a),$dots(b),$dots(c)),2000). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=106) 1 [] p(f(g(g(g(g(g(h(h(h(h(j(b)))))))))))). given clause #2: (wt=1001) 2 [] p(F(g(g(h(g(H(g(h(g(g(g(B)))))))))))). given clause #3: (wt=2001) 3 [] p(f3(g(h(a)),g(g(b)),h(h(c)))). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% otter-3.3f/documents/old_READMEs/README.3030100644000076400007640000000333507272347030017354 0ustar mccunemccune Otter, Version 3.0.3 -------------------- Summary of changes from 3.0.2. 1. Several bugs have been fixed (see Changelog). (One known bug has not fixed: Do not use lex-dependent demodulation with build_proof_object.) 2. Two new features: A new parameter, max_answers, allows the user to limit the number of answer literal in a clause. For example, assign(max_answers, 3). Weighting has been extended to allow the user to specify terms that _contain_ particular terms. This is done with a new unary function symbol $dots(_). If $dots(t) occurs in a weight template, it will match any term that contains a term that matches t. This is very useful for discarding "bad" clauses. Here is part of an output file that illustrates $dots. 3. An ASCII version of the manual is included. ************************************************************************ list(sos). 1 [] p(f(g(g(g(g(g(h(h(h(h(j(b)))))))))))). 2 [] p(F(g(g(h(g(H(g(h(g(g(g(B)))))))))))). 3 [] p(f3(g(h(a)),g(g(b)),h(h(c)))). end_of_list. weight_list(pick_given). weight(f($dots(j($(5)))),100). weight(F($dots(H($dots(B)))),1000). weight(f3($dots(a),$dots(b),$dots(c)),2000). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=106) 1 [] p(f(g(g(g(g(g(h(h(h(h(j(b)))))))))))). given clause #2: (wt=1001) 2 [] p(F(g(g(h(g(H(g(h(g(g(g(B)))))))))))). given clause #3: (wt=2001) 3 [] p(f3(g(h(a)),g(g(b)),h(h(c)))). ************************************************************************ FTP Otter 3.0.3 from info.mcs.anl.gov in pub/Otter/otter-3.0.3.tar.Z . W. McCune (otter@mcs.anl.gov) Argonne National Laboratory August 27, 1994 otter-3.3f/documents/old_READMEs/README.hints20100644000076400007640000000547607654035456020300 0ustar mccunemccuneThe Hints2 Mechanism W. McCune April 2003 The original hints code has been in Otter for a long time. Bob Veroff first put a version into his own copy of Otter, then we installed a similar version in the official Otter in 1995. See documents/new_304.txt for documentation on the original hints. The problem with that version of hints is that it does not use indexing to find hints that match a clause, so it can be very slow. I finally got around to installing indexed hints late in 2002. The new mechanism is called hints2. Hints2 is not as general as the original hints code. It is independent of the original hints (except that both cannot be used at the same time). To get the new mechanism use list(hints2). and to use the old code, use list(hints). For now, I'll call the original hints code hints1. Differences between hints1 and hints2. 1. Hints2 does bsub matching only. That is, a clause matches a hint iff it subsumes the hint. Hints1 also does fsub matching (a clause matches a hint if it is subsumed by the hint) and equiv matching (the clause is equivalent to the hint). The parameters bsub_hint_wt and bsub_hint_add_wt apply to hints2. bsub_hint_wt (default MAX_INT, meaning don't use it) is the pick-given weight given to a clause that subsumes a hint. bsub_hint_add_wt (default 0) is the amount added to the ordinary pick-given weight of a clause that subsumes a hint. This is usually negative, which gives preference to clauses that match hints. 2. Hints2 are back demodulated, but the undemodulated copy is also kept. 3. Hints2 has Veroff's "hint degradation option", which is enabled with set(degrade_hints2). If this option is enabled, the hint becomes less important (the bsub_add_wt is cut in half) each time it matches a clause. For this to make sense, the bsub_hint_add_wt should start out as a large negative number (usually -1000). Similarities of hints1 and hints2. 1. Both can have labels attributes attached to hints, and when a clause matches a labeled hint, the clause gets a copy of the label. 2. In both, the bsub_hint_wt and bsub_hint_add_wt can be given as attributes on hints as well as ordinary program parameters (with attributes overriding parameters). This allows some hints to be more or less important than others. The ordinary way to use hints2 is assign(bsub_hint_add_wt,-1000). set(keep_hint_subsumers). set(degrade_hints2). list(hints2). ... end_of_list. For example input files, see examples/fringe/*hints*.in References R. Veroff,``Using hints to increase the effectiveness of an automated reasoning program: Case studies'', \emph{J. Automated Reasoning} 16(3), 1996. R. Veroff, ``Solving open questions and other challenge problems using proof sketches'', \emph{J. Automated Reasoning}, 27(2), 2001. otter-3.3f/documents/old_READMEs/README.split0100644000076400007640000001646706472411144020213 0ustar mccunemccuneCASE SPLITTING IN OTTER William McCune, Dale Myers, Rusty Lusk, Mohammed Alumlla December 1997 This implementation uses the UNIX fork() command to make copies of the current state of the process for the cases. This avoids having to explicitly save the state and restore it for the next case. (That is, it was easy to implement.) When enabled, splitting occurs periodically during the search. The default is to split after every 5 given clauses. This can be changed to some other number of given clauses, say 10, with the command assign(split_given, 10). % default 5 Instead, one can split after a specified number of seconds, with a command such as assign(split_seconds, 10). % default infinity which asks Otter to attempt a split every (approximately) 10 seconds. (Jobs that use split_seconds are usually not repeatable.) A third method is to split when a nonunit ground clause is selected as the given clause. This option is specified with the command set(split_when_given). which causes splitting on the given clause if (1) it is ground, (2) it is within the split_depth bound (see below), and (3) it satisfies the split_pos and split_neg flags (see below). If you wish to limit the depth of splitting, use a command such as assign(split_depth, 3). % default 256 (which is also the maximum) which will not allow a case such as "Case [1.1.1.1]". There are two kinds of splitting: on ground clauses and on ground atoms. Clause splitting constructs one case for each literal, and atom splitting, say on p, constructs two cases: p is true; p is false (or, as Larry Wos says, splitting on a tautology). Sequence of Splitting Processes Say Otter decides to split the search into n cases. For each case, the fork() command creates a child process for the case, then the parent process waits for the child to exit. If any child fails to refute its case, the parent exits in failure (causing all ancestor processes to fail as well). If each child refutes its case, the parent exits with success. The Output File Various messages about the splitting events are sent to the output file. To get an overview of the search from an output file, say problem.out, one can use the following command. egrep "Splitting|Assumption|Refuted|skip|That" problem.out Splitting Clauses The following commands enables splitting on clauses after some number of given clauses have been used (see split_given), or after some number of seconds (see split_seconds). set(split_clause). % default clear The following command simply asks Otter to split on ground given clauses. set(split_when_given). % default clear (I suppose one could use both of the preceding commands at the same time---I haven't tried it.) If Otter finds a suitable (see flags below) nonunit ground clause for splitting, say "p | q | r", the assumptions for three cases are Case 1: p. Case 2: -p & q. Case 3: -p & -q & r. Eligible Clauses for Splitting Otter splits on ground nonunit clauses only. They can occur in Usable or in Sos. The following commands can be used to specify the type of clause to split. set(split_pos). % split on positive clauses only (default clear) set(split_neg). % split on negative clauses only (default clear) set(split_nonhorn). % split on nonhorn clauses only (default clear) If none of the preceding flags are set, all ground clauses are eligible. Selecting the Best Eligible Clause The default method for selecting the best eligible clause for splitting is simply to take the first, lowest weight (using the pick_given scale) clause from Usable+Sos. Instead, one can use The command set(split_min_max). % default clear which says to use the following method to compare two eligible clauses C and D. Prefer the clause with the lighter heaviest literal (pick_given scale); if the heaviest literals have the same weight, use the lighter clause; if the clauses have the same weight, use the first in Usable+Sos. Splitting Atoms The following commands enables splitting on atoms after some number of given clauses have been used (see split_given), or after some number of seconds (see split_seconds). set(split_atom). (For propositional problems with assign(split_given, 0), this will cause Otter to perform a (not very speedy) Davis-Putnam search.) To select an atom for splitting, we consider OCCURRENCES of atoms within clauses. Eligible Atoms Otter splits on atoms that occur in nonunit ground clauses. The command set(split_pos). % default clear says to split on atoms the occur only in positive clauses, set(split_neg). % default clear says to split on atoms the occur only in negative clauses, and set(split_nonhorn). % default clear says to split on atoms that occur positively in nonHorn clauses. Selecting the Best Eligible Atom Default method for comparing two eligible atom-occurrences: Prefer the atom that occurs in the lower weight clause. If the clauses have the same weight, prefer the atom with the lower weight. An optional method for selecting an atom considers the number of occurrences of the atom. The command set(split_popular). % default clear says to prefer the atom that occurs in the greatest number of clauses. All clauses in Usable+Sos containing the atom are counted. Another Way to Split Atoms If the user has an idea of how atom splitting should occur, he/she can give a sequence of atoms in the input file, and Otter will split accordingly. (As above, the TIME of splitting is determined as above with the split_given and split_seconds parameters.) For example, with the commands set(split_atom). split_atoms([P, a=b, R]). assign(split_given, 0). Otter will immediately (because of split_given) split the search into 8 cases (because there are 3 atoms), then do no more splitting. Problems With This Implementation Splitting is permanent. That is, if a case fails, the whole search fails (no backing up to try a different split). If Otter fails to find a proof for a particular case (e.g., the Sos empties or some limit is reached), the whole attempt fails. If the search strategy is complete, then an empty Sos indicates satisfiability, and the set of assumptions introduced by splitting give you a partial model; however, it is up to the user to figure this out. When splitting is enabled, max_seconds (for the initial process and all descendent processes) is checked against the wall clock (from the start of the initial process) instead of against the process clock. This is problematic if the computer is busy with other processes. Getting the Total Process Time The process clock ("user CPU" statistic) is initialized at the start of the process, and each process prints statistics once at the end of its life. Therefore, one can get the total process by summing all of the "user CPU" times in the output file. The command grep "user CPU" problem.out | awk '{sum += $4}END{print sum}' can be used to get the approximate total process time from an output file problem.out. Advice on Using Otter's Splitting (from McCune) At this time, we don't have much data. A general strategy for nonground problems is the following. set(split_when_given). set(split_pos). % Also try it without this command. assign(split_depth, 10). For ground (propositional) problems, try the following, which is essentially a Davis-Putnam procedure. set(split_atom). set(split_pos). assign(split_given, 0). otter-3.3f/documents/old_READMEs/README0100644000076400007640000000017607714274271017057 0ustar mccunemccuneMost of the information in these old README files has been included in the updated Otter manual (otter33.pdf and otter33.ps). otter-3.3f/documents/old_READMEs/README.3050100644000076400007640000000120307272347030017346 0ustar mccunemccune -------------------- Otter, Version 3.0.5 -------------------- It has been more than two years since the release of Otter 3.0.4. I haven't done a lot of work on Otter since then, but there have been a few small bug fixes, and a few new features. See document/New_305.txt for a summary and Changelog for more complete details. If you're happy with version 3.0.4, there shouldn't be any hurry to upgrade to 3.0.5. FTP Otter 3.0.5 from ftp://info.mcs.anl.gov/pub/Otter/otter-3.0.5.tar.Z . W. McCune (otter@mcs.anl.gov) Argonne National Laboratory February 18, 1998 otter-3.3f/documents/mace2.tex0100644000076400007640000006637007305750411015731 0ustar mccunemccune\documentclass[11pt]{article} \usepackage{amsmath} % The following line causes PostScript ``times'' fonts to be used for % everything (instead of Computer Modern). With these, no bitmapped % fonts are put into the PostScript, which makes PDF look much % better on the screen. To use ordinary LaTeX (computer modern) fonts, % just remove this line. \usepackage{times} \usepackage{moreverb} % for boxedverbatim (which shouldn't be used in lists) \setlength{\textwidth}{6.25in} \setlength{\textheight}{9in} \setlength{\hoffset}{-.55in} \setlength{\voffset}{-.7in} \setlength{\parskip}{.1in} \begin{document} \sloppy \pagenumbering{roman} \setcounter{page}{1} \thispagestyle{empty} \begin{center} \vspace*{-1in} Argonne National Laboratory \\ 9700 South Cass Avenue\\ Argonne, IL 60439 \vspace{.2in} \rule{1.5in}{.01in}\\ [1ex] ANL/MCS-TM-249 \\ \rule{1.5in}{.01in} \vspace{1in} {\Large\bf MACE 2.0 Reference Manual and Guide} \vspace{.2in} by \\ [3ex] {\Large\it William McCune}\\ %%%%%%%%%%%%%%%%%%%%% \thispagestyle{empty} \vspace{1.5in} Mathematics and Computer Science Division \bigskip Technical Memorandum No. 249 \vspace{1in} May 2001 \end{center} \vfill \noindent This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38. %%%%%%%%%%%%%%%%%%%%% %%% Local Variables: %%% mode: latex %%% TeX-master: "snadiopt" %%% End: \newpage \pagenumbering{roman} \setcounter{page}{2} \noindent Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is owned by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. \vspace{2in} \begin{center} {\bf DISCLAIMER} \end{center} \noindent This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor The University of Chicago, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately-owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of document authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, Argonne National Laboratory, or The University of Chicago. \newpage \pagestyle{plain} \tableofcontents \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagenumbering{arabic} \setcounter{page}{1} \title{MACE 2.0 Reference Manual and Guide} \author{\emph{William McCune}} % \author{{\em William McCune}\thanks % { % This work was supported by the Mathematical, Information, and % Computational Sciences Division subprogram of the Office of Advanced % Scientific Computing Research, U.S. Department of Energy, under % Contract W-31-109-Eng-38. % } \\ % Mathematics and Computer Science Division\\ % Argonne National Laboratory\\ % Argonne, Illinois, 60439, U.S.A.\\ % {\ttfamily http://www.mcs.anl.gov/\~{}mccune} % } % \date{} \maketitle \addcontentsline{toc}{section}{Abstract} \begin{abstract} MACE is a program that searches for finite models of first-order statements. The statement to be modeled is first translated to clauses, then to relational clauses; finally for the given domain size, the ground instances are constructed. A Davis-Putnam-Loveland-Logeman procedure decides the propositional problem, and any models found are translated to first-order models. MACE is a useful complement to the theorem prover Otter, with Otter searching for proofs and MACE looking for countermodels. \end{abstract} \section{Introduction} MACE (Models And CounterExamples) is a program that searches for small finite models of first-order statements. It is frequently used along with our first-order theorem prover Otter~\cite{otter3,otter-web}, with Otter searching for proofs and MACE looking for countermodels. The two programs accept almost the same language, so the same input file can usually be used for both programs. MACE has been used for many applications including quasigroup existence problems~\cite{dp-quasi}, ortholattice problems~\cite{ortholattice}, and lattice and Boolean algebra problems~\cite{wm-rp:monograph,monograph-web}. Other successful programs that look for finite models of first-order statements are SEM~\cite{sem} and FINDER~\cite{finder}. A related class of programs can produce finite models when the search for a refutation fails. Examples of these are SATCHMO~\cite{satchmo} and MGTP~\cite{mgtp}. At its core, MACE has a Davis-Putnam-Loveland-Logeman propositional decision procedure named ANLDP. ANLDP can be used directly to decide propositional (SAT) problems given in conjunctive normal form (see Section~\ref{anldp}). Section~\ref{history} gives differences between MACE 2.0 and previous versions. The MACE Web site is \texttt{http://www.mcs.anl.gov/AR/mace}. \section{A Little Motivation} Say you've just invented group theory by writing down the following three axioms, \begin{align*} e * x & = x\\ g(x) * x & = e\\ (x * y) * z & = x * (y * z) \end{align*} and you are wondering whether all groups are commutative. You prepare the following input file, named \texttt{group.in}. \begin{center} \begin{small} \begin{boxedverbatim} set(auto). list(usable). e * x = x. % left identity g(x) * x = e. % left inverse (x * y) * z = x * (y * z). % associativity a * b != b * a. % denial of commutativity end_of_list. \end{boxedverbatim} \end{small} \end{center} \noindent Now you give the input file to Otter to search for a proof (actually a refutation). % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} % otter < group.in > group.out \end{verbatim} \end{small} \noindent and to MACE to look for a countermodel (actually a model) of size 4, as follows. % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} % mace -n4 -p -c < group.in > group4.out \end{verbatim} \end{small} \noindent Both programs fail immediately. But looking at the Otter output makes you suspect that not all groups are commutative, so you go forward, looking for larger countermodels. The command % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} % mace -n6 -p -c < group.in > group6.out \end{verbatim} \end{small} \noindent succeeds, and the output file contains the following noncommutative group of order 6. % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} ======================= Model #1 at 1.13 seconds: e: 0 a: 1 b: 2 *: | 0 1 2 3 4 5 --+------------ 0 | 0 1 2 3 4 5 1 | 1 0 3 2 5 4 2 | 2 4 0 5 1 3 3 | 3 5 1 4 0 2 4 | 4 2 5 0 3 1 5 | 5 3 4 1 2 0 g: 0 1 2 3 4 5 --------------- 0 1 2 4 3 5 \end{verbatim} \end{small} \noindent Hmmm, very interesting: I wonder what happens if we add $x*x=e$ to our theory. \section{How to Tell MACE What to Do} Three kinds of input determine how MACE works. First, the clauses or formulas in the input file specify the theory for which you seek a model. Second, special commands in the input file put constraints on the models. Third, command-line options give general constraints on the search. \subsection{The Formulas} MACE reads the input (from stdin) and takes formulas and clauses from the lists \texttt{usable}, \texttt{sos}, \texttt{demodulators}, and \texttt{passive} as its basic theory.\footnote { One can argue that the hot list should also be considered as part of the basic theory, because Otter uses the hot list to make inferences. MACE ignores the hot list, however, because hot list clauses almost always occur also in usable or sos, and MACE suffers if it gets duplicate clauses. I suppose MACE could get around this by doing a subsumption check. } Like Otter, MACE immediately transforms any first-order formulas to clauses. MACE is a bit more restrictive than Otter in the language it accepts, and it interprets some symbols differently. See Section~\ref{language}. \subsection{Constraints in the Input} Constraints are specified in an optional list \texttt{mace\_constraints} in the input file.\footnote { Previous versions of MACE used the \texttt{passive} list for constraints. } (If you give Otter an input file containing a \texttt{mace\_constraints} list, Otter ignores it.) Two kinds of constraint are accepted: assignments for the models and properties of relations or functions. Here is an example list that shows all of the types of constraint. % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} list(mace_constraints). assign(e, 0). % constant symbol assign(g(2), 1). % function symbol assign(3*4, 2). % function symbol assign(P(1), T). % relation symbol assign(Q(0,3), F). % relation symbol property(same(_,_), equality). property(lt(_,_), order). property(g(_), bijection). property(_*_, quasigroup). end_of_list. \end{verbatim} \end{small} The assignments simply give function values or relation values for particular members of the domain.\footnote { Why not place assignments in with the clauses that specify the theory? This can be done, but such assignments might not make sense if the input is also being used for Otter. } Members of the domain are always named $0, 1, \ldots, n-1$, where $n$ is the domain size. The Boolean constants (relation values) are named \texttt{T} and \texttt{F}. Note that assigning values to constants can also be done with the \texttt{-c} command-line option (see the next subsection). The following properties of function and relation symbols can be specified in the \texttt{mace\_constraints} list. \begin{description} \item{\texttt{equality}}\\ This applies to binary relation symbols. It is necessary only if a nonstandard equality symbol is being used, because any binary relation recognized by Otter as an equality symbol is also recognized by MACE as an equality symbol. See Section~\ref{syntax}. \item{\texttt{order}}\\ This applies to binary relation symbols. It is necessary only if a nonstandard order symbol is being used. MACE (but not Otter) automatically recognizes binary $<$ as an order relation. The ``order'' is the obvious order on the members of the domain: $0<1<\ldots R(x) & S(x)). exists e ((all x (f(e,x) = x)) & (all x exists y (f(y,x) = e))). end_of_list. \end{verbatim} \end{small} \paragraph{Variables vs.~Constants in Clauses.} Clauses do not have explicit quantifiers, so we need a rule to distinguish variables from constants. The default rule is that symbols starting with \texttt{u} through \texttt{z} are variables. If the command \texttt{set(prolog\_style\_variables)} is in effect, symbols starting with upper-case letters are variables. \paragraph{Equality Symbols.} How do we recognize binary relations as equality relations? The default rule is that the symbol \texttt{=} and symbols matching the pattern [\texttt{Ee}][\texttt{Qq}].* are equality symbols. If the input contains the command \texttt{set(tptp\_eq)}, then \texttt{equal} is the one and only equality symbol. \paragraph{Infix Notation.} One can declare binary symbols to be infix and to have a precedence and associativity so that some parentheses can be omitted. Many symbols such as \texttt{=} and \texttt{*} have built-in declarations. \section{How MACE Works} The methods used by MACE are described in detail in~\cite{dp-quasi}. Here is a summary. For a given domain size, MACE transforms the (first-order) input into an equivalent propositional problem. This is possible because, for a fixed finite domain, the first-order problem is decidable. The propositional problem is then given to a DPLL (Davis-Putnam-Loveland-Logeman) procedure. If satisfiability is detected, the propositional model is transformed into a first-order model of the original problem. Consider the following input file. \begin{center} \begin{small} \begin{boxedverbatim} list(usable). even(a). -even(x) | even(s(s(x))). -even(s(a)). end_of_list. \end{boxedverbatim} \end{small} \end{center} MACE first flattens the clauses into a relational form. This step involves replacing each $n$-ary function with an $n+1$-ary relation. MACE's output for this example contains something like % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} Processing clause: -a(v0) | even(v0). Processing clause: -s(v0,v1) | -s(v1,v2) | -even(v0) | even(v2). Processing clause: -a(v0) | -s(v0,v1) | -even(v1). \end{verbatim} \end{small} If we ask for models of size 3, MACE generates propositional clauses corresponding to all instances of the transformed clauses over the set \{0,1,2\}. The output also contains the statements % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} Function s/2 well-defined and closed. Function a/1 well-defined and closed. \end{verbatim} \end{small} \noindent which indicate that MACE has generated propositional clauses asserting that the new $n+1$-ary relations are functions. The DPLL procedure finds a model of the set of propositional clauses, and the propositional model is transformed into the following first-order model. % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} a: 2 even: 0 1 2 s: 0 1 2 --------- --------- T F T 0 0 1 \end{verbatim} \end{small} \paragraph{Scalability.} Unfortunately, this method does not scale well as the domain increases or as the size of clauses increases. Consider a distributivity axiom, $x * (y + z) = (x + y) * (x + z)$. The transformation to relational form produces the following two clauses. % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} -+(v0,v1,v2) -+(v0,v3,v4) -*(v4,v2,v5) -+(v3,v1,v6) *(v0,v6,v5) -+(v0,v1,v2) -+(v0,v3,v4) *(v4,v2,v5) -+(v3,v1,v6) -*(v0,v6,v5) \end{verbatim} \end{small} \noindent For a domain of 6, each of these (7-variable) clauses produces $6^7=279,936$ propositional clauses. MACE can usually handle this many clauses, but it's hard to fight exponential behavior. The program SEM~\cite{sem} is usually better than MACE for large clauses or large domains. \section{Differences from Previous Versions} \label{history} Major changes from earlier versions of MACE are listed here. \begin{enumerate} \item Previous versions of MACE called Otter to parse the input and to produce an intermediate form that was given to a program named ANLDP. MACE 2.0 is self-contained, making it easier to install and run. \item Previous versions of MACE worked for a fixed domain size, and there was a separate script (mace-loop) to iterate through domain sizes and calling MACE. \item Previous versions of MACE used Otter's \texttt{passive} list for constraints (assignments and properties). MACE 2.0 uses the new list \texttt{mace\_constraints} for that purpose; clauses in \texttt{passive} are now taken as part of the theory. \item MACE 2.0 allows answer literals in the clauses. (Answer literals are removed by MACE before the search for models.) \item Previous versions of MACE could handle sorted logic (with disjoint domains). MACE 2.0 cannot. Most of the code for sorted logic is still in place, so it is possible that future versions will handle sorted logic. Sorted logic can sharply cut down the search time. Consider a domain of size 12 that can be partitioned into 8 and 4. A 2-variable relational clause, with one variable for each sort, produces 144 propositional clauses with unsorted logic and 32 clauses in the sorted case. Let us know if you need sorted logic. \item Previous versions of MACE had a checkpointing feature whereby the state of the search was periodically backed up to a file, and the search could be resumed from one of those states. MACE 2.0 does not have this feature. \end{enumerate} \section{Calling MACE From Other Programs} MACE returns an exit code when it terminates. This makes it convenient to call MACE from other programs. Here is a list of MACE's exit codes. (This list changes from time to time; the current list can be found in the source file \texttt{Mace.h}.) \begin{description} \item{\texttt{11 (ABEND\_EXIT)}} This usually indicates an error in the input (not all input errors are covered by \texttt{INPUT\_ERROR\_EXIT} below). Occasionally it is caused by a bug in MACE. When you get this exit code, look in the output for an error message. \item{\texttt{12 (UNSATISFIABLE\_EXIT)}} MACE completed its search and determined that no models exist within the given domain size(s) and other constraints. \emph{It does not mean that the input clauses are unsatisfiable.} \item{\texttt{13 (MAX\_SECONDS\_EXIT)}} MACE terminated because of the time limit given on command line (with \texttt{-t}). \item{\texttt{14 (MAX\_MEM\_EXIT)}} MACE terminated because of the memory limit given on the command line (with \texttt{-k}). \item{\texttt{15 (MAX\_MODELS\_EXIT)}} MACE terminated because it found the number of models requested on the command line (with \texttt{-m}). \item{\texttt{16 (ALL\_MODELS\_EXIT)}} MACE completed its search and found all models (at least one) within the given constraints. \item{\texttt{17 (SIGINT\_EXIT)}} MACE terminated because it received the interrupt signal. \item{\texttt{18 (SEGV\_EXIT)}} MACE crashed. \item{\texttt{19 (INPUT\_ERROR\_EXIT)}} Errors were found in the input. The output file should point to the error(s). \end{description} Say we have a list of equations containing a binary function symbol \texttt{f}, and we wish to remove the equations that have a noncommutative model of size $\leq 4$. If we put the equations in a file, with one equation on each line, for example, \begin{center} \begin{small} \begin{boxedverbatim} f(f(x,f(f(z,x),x)),f(z,f(y,x))) = z. f(f(f(x,f(z,x)),x),f(z,f(y,x))) = z. f(f(f(f(y,x),z),x),f(f(u,y),x)) = x. f(f(f(f(y,x),z),x),f(f(y,u),x)) = x. \end{boxedverbatim} \end{small} \end{center} we can write a simple program to loop through the equations, calling MACE for each and printing those that have no noncommutative models of size $\leq 4$. Here is an example Perl program that does the job. \begin{center} \begin{footnotesize} % # Build a file containing equation and denial of commutativity. % # Run MACE, discarding stdout and stderr, and capturing exit code. % # Print equation if it has no noncommutative models <= 4. \begin{boxedverbatim} #!/usr/local/bin/perl5 $mace = "/home/mccune/bin-linux/mace"; # MACE binary $unsatisfiable_exit = 12; # exit code of interest $input = "/tmp/mace$$"; # temporary input file while ($equation = ) { open(FH, ">$input") || die "Cannot open file $input"; print FH "list(usable). $equation f(0,1)!=f(1,0). end_of_list.\n"; close(FH); $rc = system("$mace -N4 < $input > /dev/null 2> /dev/null"); $rc = $rc / 256; # This gets the actual exit code. if ($rc == $unsatisfiable_exit) { print $equation; } } system("/bin/rm $input"); \end{boxedverbatim} \end{footnotesize} \end{center} If our data file is named \texttt{identities} and our Perl script is named \texttt{commute4\_filter}, then the command \begin{small} \begin{verbatim} % commute4_filter < identities > candidates \end{verbatim} \end{small} \noindent will remove two of the four equations within a few seconds. \section{The ANLDP Propositional Decision Procedure} \label{anldp} If you have a propositional (SAT) problem in conjunctive normal form, you can call MACE's DPLL procedure directly with the program ANLDP. ANLDP is included in the MACE distribution package. Input to ANLDP is a sequence of integers (no comments are allowed). The propositional variables are \texttt{1,2,3,\ldots}. Positive integers are positive literals, negative integers are negative literals, and 0 marks the ends of clauses. For example, here is an (unsatisfiable) input consisting of four 2-literal clauses. % Following blank line gets around LaTeX squeeze bug. \begin{small} \begin{verbatim} 1 2 0 1 -2 0 -1 2 0 -1 -2 0 \end{verbatim} \end{small} \noindent The command-line options of ANLDP are a subset of MACE's: \begin{clo} \item[-p] (Lower case.) This tells ANLDP to print models as they are found. \item[-m $n$] This tells ANLDP to stop after finding $n$ models. The default is 1. \item[-t $n$] This tells ANLDP to stop after about $n$ seconds. The default is unlimited. \item[-k $n$] This tells ANLDP to stop if it tries to allocate more than $n$ kilobytes of memory. The default is 48000 (about 48 megabytes). \item[-s] This tells ANLDP to perform unit subsumption as it searches. (Unit subsumption is always performed on the input.) When ANLDP gets a new unit (by splitting or by unit propagation), two operations are ordinarily performed: (1) unit resolution, to remove complementary literals from all clauses, and (2) unit subsumption, to mark as subsumed all clauses containing the unit as a literal. Because of our data structures, unit subsumption nearly always costs more time than it saves. But this option allows you to use unit subsumption if you wish. % \item[-h] % This tells ANLDP to print a summary of these command-line options. \end{clo} ANLDP is an implementation of the Davis-Putnam-Loveland-Logeman procedure. Efficient data structures and algorithms are used, but the procedure is otherwise standard. When the time comes to select the next propositional variable for splitting, ANLDP simply takes the first variable of the first shortest positive clause. Details of the implementation can be found in~\cite{dp-quasi}. \addcontentsline{toc}{section}{References} \bibliographystyle{plain} \bibliography{/home/mccune/papers/bib/master} \end{document} otter-3.3f/documents/mace2.ps0100644000076400007640000016432107305750521015550 0ustar mccunemccune%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: mace2.dvi %%Pages: 13 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %%+ Courier-Oblique %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips mace2 %DVIPSParameters: dpi=300 %DVIPSSource: TeX output 2001.06.01:1230 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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b(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f (.)g(.)g(.)g(.)g(.)h(.)95 b(30)602 3855 y(8.1.2)110 b(Orienting)25 b(Equalities)h(\(Ad)d(Hoc\))56 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f (.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(31)602 4028 y(8.1.3)110 b(Determining)25 b(Dynamic)f(Demodulators)i(\(Ad)d (Hoc\))52 b(.)45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(31)602 4201 y(8.1.4)110 b(Le)o(x-dependent)27 b(Demodulation)f(\(Ad)d (Hoc\))45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.) 95 b(31)393 4374 y(8.2)h(LRPO)57 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.) f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(32)602 4547 y(8.2.1)110 b(T)-6 b(erm)22 b(Ordering)j(\()r FE(L)t(R)t(P)t(O)r FK(\))61 b(.)45 b(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(32)602 4720 y(8.2.2)110 b(Orienting)25 b(Equalities)h(\()r FE(L)t(R)t(P)t(O)r FK(\))71 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(32)602 4893 y(8.2.3)110 b(Determining)25 b(Dynamic)f(Demodulators)i(\()r FE(L)t(R)t(P)t(O)r FK(\))67 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(33)602 5066 y(8.2.4)112 b FE(L)t(R)t(P)t(O)r FK(-dependent)29 b(Demodulation)d(\()r FE(L)t(R)t(P)t(O)r FK(\))64 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(33)393 5238 y(8.3)h(Knuth-Bendix)26 b(Completion)71 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.) g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(33)257 5502 y FF(9)c(Ev)o(aluable)24 b(Functions)f(and)f(Pr)n(edicates)j(\()p FD($SUM)p FF(,)c FD($LT)p FF(,)g FC(:)15 b(:)g(:)q FF(\))1022 b(35)393 5675 y FK(9.1)96 b(Using)24 b(More)g(Natural)g(Expressions)i (for)e(Ev)n(aluation)56 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.) g(.)g(.)g(.)h(.)95 b(38)1873 5946 y(i)n(v)p eop %%Page: 5 5 5 4 bop 393 388 a FK(9.2)96 b(Ev)n(aluation)26 b(Examples)65 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.) h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(39)257 652 y FF(10)46 b(W)-6 b(eighting)2676 b(40)393 825 y FK(10.1)51 b(W)-7 b(eighing)25 b(Clauses)g(and)f(Literals)68 b(.)45 b(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.) h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(40)393 998 y(10.2)51 b(W)-7 b(eighing)25 b(Atoms)e(and)h(T)-6 b(erms)90 b(.)46 b(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(41)393 1171 y(10.3)51 b(Containment)26 b(W)-7 b(eight)24 b(T)-6 b(emplates)31 b(.)45 b(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.) h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(41)257 1434 y FF(11)46 b(Answer)23 b(Literals)2451 b(42)257 1698 y(12)46 b(The)22 b(P)o(assi)o(v)o(e)j(List)2445 b(42)257 1962 y(13)46 b(Clause)24 b(Attrib)n(utes)2391 b(43)257 2226 y(14)46 b(The)22 b(Hints)h(Strategy)2338 b(43)393 2399 y FK(14.1)51 b(Hints)24 b(\(the)g(General)h(V)-10 b(ersion\))40 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(44)393 2572 y(14.2)51 b(Hints2)24 b(\(the)h(F)o(ast)d(V)-10 b(ersion\))65 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(45)393 2745 y(14.3)51 b(Label)24 b(Attrib)n(utes)i(on)d(Hints)49 b(.)c(.)g(.)h(.)f(.)g(.)g(.) g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)g(.)h(.)95 b(46)393 2917 y(14.4)51 b(Generating)26 b(Hints)e(from)f(Proofs)k(.)46 b(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.) g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(46)257 3181 y FF(15)46 b(Interaction)25 b(during)e(the)g(Sear)n(ch) 1921 b(46)257 3445 y(16)46 b(Output)22 b(and)g(Exit)h(Codes)2177 b(47)257 3709 y(17)46 b(Contr)n(olling)25 b(Memory)2270 b(49)257 3973 y(18)46 b(A)-5 b(utonomous)23 b(Mode)2338 b(50)257 4237 y(19)46 b(Fringe)23 b(F)n(eatur)n(es)2460 b(51)393 4409 y FK(19.1)51 b(Ancestor)25 b(Subsumption)77 b(.)45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.) f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(51)393 4582 y(19.2)51 b(The)23 b(Hot)g(List)32 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.) g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(51)393 4755 y(19.3)51 b(Sequent)25 b(Notation)g(for)f(Clauses)42 b(.)k(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(53)393 4928 y(19.4)51 b(Conditional)26 b(Demodulation)72 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.) 95 b(53)393 5101 y(19.5)51 b(Deb)n(ugging)26 b(Searches)f(and)f (Demodulation)76 b(.)46 b(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(54)393 5274 y(19.6)51 b(Special)25 b(Unary)f(Function)h(Demodulation)46 b(.)f(.)h(.)f(.)g(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(54)393 5447 y(19.7)51 b(The)23 b(In)l(visible)k(Ar)n(gument)38 b(.)45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.) f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(55)393 5620 y(19.8)51 b(Floating-Point)26 b(Operations)j(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(55)1884 5946 y(v)p eop %%Page: 6 6 6 5 bop 393 388 a FK(19.9)51 b(F)o(oreign)24 b(Ev)n(aluable)h (Functions)65 b(.)46 b(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(56)393 561 y(19.10)6 b(The)23 b(Inference)j(Rule)e FC(g)s(L)f FK(for)h(Cubic)g(Curv)o(es)38 b(.)46 b(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(56)393 734 y(19.11)6 b(Link)o(ed)25 b(UR-Resolution)77 b(.)45 b(.)g(.)g(.)h(.)f(.) g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)g(.)h(.)95 b(57)393 907 y(19.12)6 b(Splitting)48 b(.)e(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.) h(.)95 b(58)602 1080 y(19.12.1)20 b(Splitting)25 b(on)f(Ground)g (Clauses)60 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.) h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(59)602 1253 y(19.12.2)20 b(Splitting)25 b(on)f(Atoms)58 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f (.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(60)602 1425 y(19.12.3)20 b(More)k(on)f(Splitting)38 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.) g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(61)257 1689 y FF(20)46 b(Soundness)22 b(and)g(Completeness)1938 b(61)393 1862 y FK(20.1)51 b(Soundness)42 b(.)j(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.) g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)95 b(61)393 2035 y(20.2)51 b(Completeness)57 b(.)45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.) g(.)g(.)h(.)95 b(62)257 2299 y FF(21)46 b(Limits,)23 b(Abnormal)g(Ends,)e(and)i(Fixes)1740 b(62)257 2563 y(22)46 b(Obtaining)23 b(and)f(Installing)27 b FK(O)q FE(T)t(T)t(E)t(R)1833 b FF(63)257 2827 y(Refer)n(ences)2789 b(64)1871 5946 y FK(vi)p eop %%Page: 1 7 1 6 bop 1047 752 a FA(O)s FB(T)8 b(T)g(E)g(R)35 b FA(3.3)g(Reference)e (Manual)1571 1065 y Fz(W)-5 b(illiam)23 b(McCune)1752 1560 y Fy(Abstract)611 1753 y Fw(O)q Fx(T)t(T)t(E)t(R)33 b Fw(is)g(a)e(resolution-style)f(theorem-pro)o(ving)d(program)i(for)i (\002rst-order)f(logic)h(with)484 1853 y(equality)-5 b(.)33 b(O)q Fx(T)t(T)t(E)t(R)25 b Fw(includes)d(the)h(inference)e (rules)i(binary)e(resolution,)h(hyperresolution,)e(UR-)484 1952 y(resolution,)c(and)g(binary)g(paramodulation.)k(Some)d(of)f(its)i (other)e(abilities)i(and)e(features)g(are)h(con-)484 2052 y(v)o(ersion)g(from)g(\002rst-order)f(formulas)h(to)h(clauses,)g (forw)o(ard)e(and)i(back)f(subsumption,)f(f)o(actoring,)484 2152 y(weighting,)24 b(answer)g(literals,)h(term)f(ordering,)f(forw)o (ard)f(and)i(back)f(demodulation,)g(e)n(v)n(aluable)484 2251 y(functions)d(and)h(predicates,)g(Knuth-Bendix)f(completion,)g (and)h(the)h(hints)f(strate)o(gy)-5 b(.)30 b(O)q Fx(T)t(T)t(E)t(R)24 b Fw(is)484 2351 y(coded)19 b(in)h(ANSI)h(C,)g(is)g(free,)e(and)h(is)h (portable)e(to)h(man)o(y)f(dif)n(ferent)g(kinds)h(of)f(computer)-5 b(.)257 2703 y FJ(1)119 b(Intr)n(oduction)259 2970 y FK(O)q FE(T)t(T)t(E)t(R)65 b FK(\(Or)n(ganized)e(T)-6 b(echniques)64 b(for)d(Theorem-pro)o(ving)k(and)c(Ef)n(fecti)n(v)o(e)h (Research\))h(is)e(a)257 3083 y(resolution-style)51 b(theorem)c(pro)o (v)o(er)l(,)52 b(similar)47 b(in)f(scope)i(and)e(purpose)i(to)e(the)j FE(AU)t(R)t(A)e FK([24)q(])f(and)259 3196 y FE(L)t(M)t(A)t FK(/)t FE(I)t(T)t(P)36 b FK([15)q(])31 b(theorem)h(pro)o(v)o(ers,)h (which)e(are)g(also)h(associated)i(with)c(Ar)n(gonne.)55 b(O)q FE(T)t(T)t(E)t(R)34 b FK(applies)257 3309 y(to)27 b(statements)j(written)e(in)g(\002rst-order)h(logic)g(with)e(equality) -6 b(.)44 b(The)27 b(primary)h(design)i(considerations)257 3422 y(ha)n(v)o(e)25 b(been)h(performance,)h(portability)-6 b(,)28 b(and)e(e)o(xtensibility)-6 b(.)36 b(The)24 b(programming)j (language)g(ANSI)c(C)257 3535 y(is)g(used.)400 3708 y(O)q FE(T)t(T)t(E)t(R)32 b FK(features)f(the)d(inference)j(rules)f(binary)g (resolution,)i(hyperresolution,)i(UR-resolution,)257 3821 y(and)d(binary)h(paramodulation.)55 b(These)31 b(inference)i (rules)f(tak)o(e)g(a)e(small)h(set)g(of)g(clauses)h(and)g(infer)f(a)257 3934 y(clause;)k(if)30 b(the)h(inferred)i(clause)e(is)g(ne)n(w)-6 b(,)31 b(interesting,)k(and)c(useful,)i(it)d(is)g(stored)i(and)f(may)f (become)257 4047 y(a)n(v)n(ailable)c(for)d(subsequent)k(inferences.)32 b(Other)23 b(features)j(of)f(O)q FE(T)t(T)t(E)t(R)j FK(are)23 b(the)h(follo)n(wing.)393 4294 y Fv(\017)46 b FK(Statements)41 b(of)e(the)g(problem)i(may)e(be)g(input)i(either)f(with)f (\002rst-order)i(formulas)g(or)e(with)484 4407 y(clauses)24 b(\(a)e(clause)h(is)f(a)g(disjunction)j(with)d(implicit)h(uni)n(v)o (ersal)h(quanti\002ers)g(and)e(no)g(e)o(xistential)484 4520 y(quanti\002ers\).)31 b(If)23 b(\002rst-order)j(formulas)f(are)e (input,)k(O)q FE(T)t(T)t(E)t(R)g FK(translates)f(them)e(to)f(clauses.) 393 4708 y Fv(\017)46 b FK(F)o(orw)o(ard)32 b(demodulation)j(re)n (writes)e(and)f(simpli\002es)h(ne)n(wly)f(inferred)i(clauses)g(with)d (a)h(set)g(of)484 4821 y(equalities,)38 b(and)33 b(back)h(demodulation) i(uses)e(a)e(ne)n(wly)h(inferred)i(equality)g(\(which)f(has)f(been)484 4934 y(added)25 b(to)e(the)h(set)g(of)f(demodulators\))k(to)d(re)n (write)g(all)f(e)o(xisting)j(clauses.)393 5121 y Fv(\017)46 b FK(F)o(orw)o(ard)35 b(subsumption)j(deletes)f(an)e(inferred)i(clause) f(if)f(it)g(is)g(subsumed)i(by)e(an)o(y)g(e)o(xisting)484 5234 y(clause,)g(and)d(back)h(subsumption)i(deletes)e(all)f(clauses)h (that)g(are)f(subsumed)h(by)f(an)g(inferred)484 5347 y(clause.)393 5535 y Fv(\017)46 b FK(A)29 b(v)n(ariant)j(of)e(the)h (Knuth-Bendix)h(method)g(can)e(search)i(for)f(a)f(complete)h(set)g(of)f (reductions)484 5648 y(and)24 b(help)g(with)g(proof)g(searches.)1884 5946 y(1)p eop %%Page: 2 8 2 7 bop 393 388 a Fv(\017)46 b FK(W)-7 b(eight)24 b(functions)i(and)e (le)o(xical)h(ordering)h(decide)f(the)f(v)n(alue)g(of)f(clauses)j(and)e (terms.)393 570 y Fv(\017)46 b FK(Answer)24 b(literals)h(can)f(gi)n(v)o (e)f(information)j(about)f(the)f(proofs)h(that)f(are)g(found.)30 b(See)23 b(Sec.)f(11.)393 753 y Fv(\017)46 b FK(Ev)n(aluable)32 b(functions)h(and)f(predicates)h(b)n(uild)f(in)f(inte)o(ger)g (arithmetic,)j(Boolean)e(operations,)484 866 y(and)k(le)o(xical)g (comparisons)i(and)e(enable)g(users)g(to)f(\223program\224)i(aspects)g (of)e(deduction)j(pro-)484 979 y(cesses.)30 b(See)23 b(Sec.)g(9.)393 1161 y Fv(\017)46 b FK(Proofs)38 b(can)f(be)g (presented)j(in)d(a)f(v)o(ery)i(detailed)h(form,)h(called)e FG(pr)l(oof)g(objects)p FK(,)k(which)c(can)484 1274 y(be)d(used)g(by)g (other)h(programs,)i(for)d(e)o(xample,)j(to)c(check)i(or)f(to)f (translate)j(the)e(proofs.)64 b(See)484 1387 y(Sec.)23 b(20.1.)393 1570 y Fv(\017)46 b FK(The)26 b FG(hints)h(str)o(ate)l(gy)i FK(can)d(be)g(used)i(to)e(pro)o(vide)h(heuristic)i(guidance)g(to)d(the) g(search.)39 b(T)-7 b(o)25 b(apply)484 1683 y(this)d(feature,)i(the)e (user)g(gi)n(v)o(es)g(a)f(set)h(of)g FG(hint)g(clauses)p FK(,)i(and)e(clauses)h(similar)f(to)g(the)g(hint)g(clauses)484 1796 y(are)i(emphasized)i(during)f(the)f(search.)30 b(See)23 b(Sec.)f(14.)393 1978 y Fv(\017)48 b FK(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)42 b(input)f(is)f(compatible,)46 b(for)40 b(the)g(most)g(part,)k(with)c(a)f(complementary)k(program)484 2091 y(MA)l(CE)34 b(2.0)h([17)q(],)i(which)f(looks)h(for)e(\002nite)h (models)g(of)f(\002rst-order)i(statements.)66 b(Gi)n(v)o(en)35 b(a)484 2204 y(conjecture,)f(O)q FE(T)t(T)t(E)t(R)e FK(can)c(search)i (for)e(a)g(proof,)i(and)f(MA)l(CE)d(can)i(look)h(for)g(a)e(countere)o (xam-)484 2317 y(ple,)g(usually)i(from)d(the)h(same)g(input)g(\002le.) 38 b(MA)l(CE)24 b(2.0)j(is)f(included)j(in)e(the)f(standard)31 b(O)q FE(T)t(T)t(E)t(R)484 2430 y FK(3.3)23 b(distrib)n(ution)28 b(packages.)398 2665 y(Although)22 b(O)q FE(T)t(T)t(E)t(R)g FK(has)c(an)g(autonomous)j(mode,)e(most)f(w)o(ork)h(with)g(O)q FE(T)t(T)t(E)t(R)j FK(in)l(v)n(olv)o(es)f(interaction)257 2777 y(with)36 b(the)h(user)-5 b(.)69 b(After)37 b(encoding)i(a)d (problem)i(into)g(\002rst-order)g(logic)g(or)f(into)g(clauses,)k(the)c (user)257 2890 y(usually)30 b(chooses)g(inference)h(rules,)f(sets)f (options)h(to)e(control)i(the)f(processing)i(of)d(inferred)j(clauses,) 257 3003 y(and)22 b(decides)i(which)f(input)g(formulas)g(or)f(clauses)i (are)e(to)g(be)g(in)g(the)h(initial)g(set)f(of)g(support)i(and)f(which) 257 3116 y(\(if)f(an)o(y\))h(equalities)i(are)e(to)f(be)h (demodulators.)31 b(If)24 b(O)q FE(T)t(T)t(E)t(R)j FK(f)o(ails)c(to)f (\002nd)g(a)h(proof,)g(the)g(user)g(may)f(wish)257 3229 y(to)c(try)g(again)h(with)f(dif)n(ferent)i(initial)g(conditions.)30 b(In)18 b(the)g(autonomous)j(mode,)e(the)g(user)f(inputs)i(a)e(set)g (of)257 3342 y(clauses)23 b(and/or)h(formulas,)f(and)i(O)q FE(T)t(T)t(E)t(R)g FK(does)e(a)f(simple)g(syntactic)i(analysis)g(and)f (decides)h(inference)257 3455 y(rules)32 b(and)g(strate)o(gies.)53 b(The)31 b(autonomous)j(mode)d(is)g(frequently)j(useful)f(for)e(the)h (\002rst)e(attempt)i(at)f(a)257 3568 y(proof.)257 3875 y FI(1.1)99 b(What)27 b Ft(O)p Fu(T)t(T)t(E)t(R)k FI(Isn't)257 4109 y FK(Some)21 b(of)i(the)f(\002rst)g(applications)k(that)d(come)g (to)f(mind)g(when)h(one)g(hears)g(\223automated)i(theorem)e(pro)o(v-) 257 4222 y(ing\224)29 b(are)g(number)g(theory)-6 b(,)31 b(calculus,)h(and)c(plane)i(geometry)-6 b(,)31 b(because)g(these)e(are) g(some)f(of)h(the)f(\002rst)257 4335 y(areas)23 b(in)e(which)h(math)g (students)i(try)e(to)g(pro)o(v)o(e)g(theorems.)30 b(Unfortunately)-6 b(,)27 b(O)q FE(T)t(T)t(E)t(R)f FK(cannot)d(do)f(much)257 4448 y(in)32 b(these)h(areas:)47 b(interesting)35 b(number)e(theory)g (problems)h(usually)g(require)f(induction,)k(interesting)257 4560 y(calculus)c(and)e(analysis)h(problems)h(usually)f(require)g (higher)n(-order)j(functions,)f(and)d(the)g(\002rst-order)257 4673 y(axiomatizations)g(of)c(geometry)i(are)e(not)h(practical.)42 b(\(Nonetheless,)31 b(Art)c(Quaife)g(has)h(pro)o(v)o(ed)g(man)o(y)257 4786 y(interesting)34 b(theorems)e(in)f(number)h(theory)h(and)e (geometry)i(using)h(O)q FE(T)t(T)t(E)t(R)h FK([22)q(,)30 b(21)q(].\))51 b(F)o(or)31 b(practi-)257 4899 y(cal)f(theorem)i(pro)o (ving)g(in)e(inducti)n(v)o(e)i(theories,)i(see)d(the)g(w)o(ork)f(of)g (Bo)o(yer)l(,)j(Moore,)f(and)f(Kaufmann)257 5012 y([2)q(,)22 b(10)q(].)400 5185 y(O)q FE(T)t(T)t(E)t(R)33 b FK(is)d(also)g(not)g (tar)n(geted)i(to)n(w)o(ard)d(synthesizing)34 b(or)29 b(v)o(erifying)j(formal)e(hardw)o(are)h(or)e(soft-)257 5298 y(w)o(are)23 b(systems.)30 b(See)23 b([6)q(,)f(5)q(])h(for)g(w)o (ork)h(in)g(those)g(areas.)398 5471 y(Summaries)e(of)f(other)h (theorem-pro)o(ving)j(systems)e(can)f(be)f(found)i(in)e(proceedings)k (of)c(the)h(recent)257 5584 y(Conferences)k(on)e(Automated)g(Deduction) i(\(CADE\))c(and)i(in)f(co)o(v)o(erage)i(of)f(the)f(CADE)f(A)-10 b(TP)21 b(System)257 5697 y(Competition)k(\(CASC\).)1884 5946 y(2)p eop %%Page: 3 9 3 8 bop 257 388 a FI(1.2)99 b(History)-5 b(,)23 b(New)i(F)n(eatur)n (es,)h(and)f(Changes)257 622 y FK(There)h(ha)n(v)o(e)h(been)g(se)n(v)o (eral)g(pre)n(vious)h(releases)g(of)g(O)q FE(T)t(T)t(E)t(R)r FK(,)h(starting)f(with)e(v)o(ersion)h(0.9,)g(which)f(w)o(as)257 735 y(distrib)n(uted)g(at)c(the)i(9th)f(International)j(Conference)f (on)e(Automated)h(Deduction)h(\(CADE-9\))c(in)i(May)257 848 y(1988.)34 b(Man)o(y)25 b(ne)n(w)g(features)i(ha)n(v)o(e)e(been)h (added)h(since)f(then,)g(man)o(y)f(b)n(ugs)h(ha)n(v)o(e)g(been)f(\002x) o(ed,)g(and)h(\(of)257 961 y(course\))f(man)o(y)e(b)n(ugs)i(ha)n(v)o(e) f(been)h(introduced.)257 1270 y FI(1.3)99 b(Useful)25 b(Backgr)n(ound)257 1504 y FK(This)c(manual)h(does)g(not)g(contain)h (an)f(introduction)j(to)c(\002rst-order)i(logic)g(or)e(to)g(automated)j (deduction.)257 1617 y(W)-7 b(e)22 b(assume)h(that)h(the)f(reader)h (kno)n(ws)f(the)g(basic)h(terminology)i(including)f FG(term)e FK(\()p FG(variable)p FK(,)i FG(constant)p FK(,)257 1730 y FG(comple)n(x)38 b(term)p FK(\),)i FG(atom)p FK(,)g FG(liter)o(al)p FK(,)i FG(clause)p FK(,)f FG(pr)l(opositional)g (variable)p FK(,)i FG(function)c(symbol)p FK(,)i FG(pr)m(edicate)257 1843 y(symbol)p FK(,)30 b FG(Sk)o(olem)g(constant)p FK(,)h FG(Sk)o(olem)f(function)p FK(,)i FG(formula)p FK(,)e FG(conjunctive)i(normal)d(form)g FK(\()p FG(CNF)p FK(\),)e FG(r)m(es-)257 1956 y(olution)p FK(,)40 b FG(hyperr)m(esolution)p FK(,)j(and)36 b FG(par)o(amodulation)p FK(.)69 b(See)35 b([3)q(,)f(14)q(,)g(32)q(])h(for)h(an)g(introductions)k(and)257 2069 y(o)o(v)o(ervie)n(ws)30 b(of)g(automated)i(theorem)f(pro)o(ving,)i (see)d([23)q(,)f(1])h(for)g(collections)i(of)e(important)i(papers,)257 2182 y(see)25 b([30)q(])f(for)h(a)f(list)h(of)g(general)h(problems)g (in)f(the)g(\002eld,)f(and)h(see)g([33)q(,)f(8,)g(18)q(])g(for)h (introductions)k(and)257 2295 y(applications)e(that)d(focus)h(on)e(the) h(use)g(of)h(O)q FE(T)t(T)t(E)t(R)r FK(.)257 2647 y FJ(2)119 b(Outline)31 b(of)i Fr(O)r Fs(T)6 b(T)g(E)g(R)s FJ(')l(s)29 b(Infer)n(ence)i(Pr)n(ocess)257 2914 y FK(Once)21 b(O)q FE(T)t(T)t(E)t(R)i FK(gets)d(going)h(with)e(its)g(real)h(w)o (ork\227making)h(inferences)h(and)e(searching)i(for)d(proofs\227it)257 3027 y(operates)28 b(on)e(clauses)i(and)e(on)g(clauses)i(only)-6 b(.)36 b(If)26 b(the)g(user)h(inputs)g(nonclausal)i(\002rst-order)f (formulas,)259 3140 y(O)q FE(T)t(T)t(E)t(R)34 b FK(immediately)f (translates)g(them)e(to)f(clauses,)k(by)d(a)f(straightforw)o(ard)k (procedure)g(in)l(v)n(olving)257 3253 y(ne)o(gation)j(normal)g(form)e (con)l(v)o(ersion,)42 b(Sk)o(olemization,)f(quanti\002er)d(operations,) j(and)36 b(conjuncti)n(v)o(e)257 3366 y(normal)24 b(form)g(con)l(v)o (ersion.)398 3539 y(As)29 b(with)g(its)h(predecessors)35 b FE(AU)t(R)t(A)c FK(and)h FE(L)t(M)t(A)t FK(/)t FE(I)t(T)t(P)r FK(,)k(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)32 b(basic)e(inference)i (mechanism)f(is)257 3652 y(the)c FG(given-clause)j(algorithm)p FK(,)f(which)e(can)f(be)h(vie)n(wed)g(as)f(a)g(simple)i(implementation) h(of)e(the)f(set)h(of)257 3765 y(support)e(strate)o(gy)g([31)r(].)30 b(O)q FE(T)t(T)t(E)t(R)d FK(maintains)e(four)g(lists)f(of)f(clauses:) 257 4012 y FD(usable.)42 b FK(This)23 b(list)h(contains)i(clauses)f (that)f(are)g(a)n(v)n(ailable)i(to)d(mak)o(e)h(inferences.)257 4200 y FD(sos.)43 b FK(Clauses)32 b(in)e(list)g FD(sos)e FK(\(set)j(of)f(support\))j(are)d(not)h(a)n(v)n(ailable)h(to)e(mak)o(e) h(inferences;)36 b(the)o(y)31 b(are)484 4313 y(w)o(aiting)25 b(to)e(participate)k(in)c(the)h(search.)257 4501 y FD(passive.)42 b FK(These)26 b(clauses)i(do)e(not)h(directly)h(participate)h(in)d(the) g(search;)j(the)o(y)e(are)f(used)h(only)g(for)484 4614 y(forw)o(ard)e(subsumption)i(and)d(unit)h(con\003ict.)30 b(The)24 b(passi)n(v)o(e)h(list)f(is)f(\002x)o(ed)h(at)g(input)h(and)f (does)h(not)484 4726 y(change)g(during)g(the)f(search.)30 b(See)23 b(Sec.)g(12.)257 4914 y FD(demodulators.)39 b FK(These)c(are)g(equalities)i(that)d(are)h(used)g(as)f(rules)i(to)e (re)n(write)h(ne)n(wly)f(inferred)484 5027 y(clauses.)257 5275 y(The)25 b FG(main)h(loop)h FK(for)f(inferring)i(and)f(processing) h(clauses)g(and)e(searching)j(for)d(a)f(refutation)k(operates)257 5388 y(mainly)24 b(on)g(the)g(lists)g FD(usable)c FK(and)k FD(sos)p FK(:)456 5647 y Fq(While)49 b(\(sos)g(is)g(not)h(empty)f(and)g (no)g(refutation)f(has)h(been)h(found\))1884 5946 y FK(3)p eop %%Page: 4 10 4 9 bop 655 388 a Fq(1.)50 b(Let)f(given_clause)f(be)h(the)g(``best'')g (clause)f(in)i(sos;)655 488 y(2.)g(Move)f(given_clause)e(from)i(sos)h (to)f(usable;)655 587 y(3.)h(Infer)f(and)g(process)f(new)i(clauses)e (using)h(the)g(inference)954 687 y(rules)g(in)h(effect;)e(each)h(new)g (clause)g(must)g(have)g(the)954 786 y(given_clause)f(as)h(one)g(of)h (its)f(parents)g(and)g(members)954 886 y(of)h(usable)e(as)i(its)f (other)g(parents;)98 b(new)49 b(clauses)954 986 y(that)g(pass)g(the)h (retention)e(tests)h(are)g(appended)f(to)i(sos;)456 1085 y(End)f(of)h(while)f(loop.)398 1358 y FK(The)24 b(set)g(of)g(support)i (strate)o(gy)f(requires)h(the)f(user)f(to)g(partition)j(the)d(input)h (clauses)h(into)e(tw)o(o)g(sets:)257 1471 y(those)k(with)f(support)i (and)f(those)g(without.)40 b(F)o(or)26 b(each)i(inference,)i(at)d (least)h(one)g(of)f(the)g(parents)i(must)257 1584 y(ha)n(v)o(e)c (support.)35 b(Retained)26 b(inferences)i(recei)n(v)o(e)e(support.)35 b(In)25 b(other)h(w)o(ords,)f(no)g(inferences)j(are)d(made)257 1697 y(in)e(which)g(all)g(parents)i(are)e(nonsupported)28 b(input)c(clauses.)30 b(At)22 b(input)i(time,)h(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)26 b(list)d FD(sos)e FK(is)i(the)257 1810 y(set)30 b(of)f(supported)j(clauses,)h(and)d FD(usable)c FK(is)j(the)h(nonsupported)k(clauses.)48 b(\(Once)30 b(the)g(main)f(loop)257 1922 y(has)c(started,)g FD(usable)c FK(no)k(longer)g(corresponds)j(to)c(nonsupported)29 b(clauses,)d (because)g FD(sos)c FK(clauses)257 2035 y(ha)n(v)o(e)j(mo)o(v)o(ed)f (there.\))35 b(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)27 b(main)d(loop)h(implements)h(the)f(set)g(of)f(support)i(strate)o(gy)-6 b(,)27 b(because)f(no)257 2148 y(inferences)g(are)e(made)f(in)h(which)g (all)f(of)h(the)g(parents)h(are)f(from)f(the)h(initial)h FD(usable)20 b FK(list.)398 2321 y FG(The)31 b(following)j(par)o(a)o (gr)o(aph)h(tries)d(to)g(answer)h(the)f(fr)m(equently)j(ask)o(ed)e (question)h(\223At)d(a)g(certain)257 2434 y(point,)39 b FK(O)q FE(T)t(T)t(E)t(R)f FG(has)d(all)f(of)g(the)h(clauses)g (available)i(to)d(mak)o(e)g(the)h(infer)m(ence)h(I)d(want,)k(and)e(one) f(of)257 2547 y(the)e(potential)i(par)m(ents)g(is)e(selected)i(as)e (the)g(given)h(clause\227why)g(doesn')m(t)i(the)d(pr)l(o)o(gr)o(am)h (mak)o(e)f(the)257 2660 y(infer)m(ence?\224)400 2833 y FK(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)24 b(main)e(loop)h(eliminates)h (an)e(important)i(kind)f(of)f(redundanc)o(y)-6 b(.)31 b(Suppose)23 b(one)g(can)f(infer)257 2946 y(clause)i FC(C)k FK(from)23 b(clauses)i FC(A)d FK(and)h FC(B)5 b FK(,)22 b(and)h(suppose)i(both)e FC(A)g FK(and)g FC(B)j FK(are)d(in)g(list)g FD(sos)p FK(.)k(If)22 b FC(A)g FK(is)h(selected) 257 3059 y(as)28 b(the)h(gi)n(v)o(en)f(clause,)j(it)d(will)g(be)g(mo)o (v)o(ed)h(to)f FD(usable)d FK(and)j(inferences)j(will)d(be)h(made;)i(b) n(ut)e FC(A)e FG(will)257 3172 y(not)e FK(mate)g(with)f FC(B)29 b FK(to)c(infer)g FC(C)7 b FK(,)24 b(because)j FC(B)h FK(is)d(still)g(in)g FD(sos)p FK(.)31 b(W)-7 b(e)24 b(must)g(w)o(ait)h(until)h FC(B)i FK(has)e(also)f(been)257 3284 y(selected)30 b(as)e(gi)n(v)o(en)h(clause.)43 b(Otherwise,)30 b(we)d(w)o(ould)i(infer)g FC(C)34 b FK(twice.)42 b(\(The)28 b(redundanc)o(y)j(w)o(ould)e(be)257 3397 y(much)e(w)o(orse)h(with)f (inference)j(rules)e(such)g(as)f(hyperresolution)k(and)d(UR-resolution) i(with)d(which)g(a)257 3510 y(clause)f(can)g(ha)n(v)o(e)g(man)o(y)f (parents.\))36 b(In)25 b(general,)i(all)e(parents)i(that)f(participate) i(in)d(an)g(inference)j(must)257 3623 y(either)e(ha)n(v)o(e)g(been)g (in)f(the)h(initial)h FD(usable)21 b FK(list)26 b(or)f(ha)n(v)o(e)h (been)g(selected)h(as)e(gi)n(v)o(en)h(clauses.)36 b(\(This)25 b(is)257 3736 y(not)f(true)g(when)f(demodulators)k(are)d(considered)i (as)e(parents.\))257 3909 y(The)g(procedure)j(for)e(processing)j(a)c (ne)n(wly)h(inferred)i(clause)f FD(new_cl)21 b FK(follo)n(ws;)26 b(steps)g(mark)o(ed)f(with)257 4022 y FD(*)d FK(are)i(optional.)406 4281 y Fq(1.)100 b(Renumber)48 b(variables.)307 4381 y(*)h(2.)100 b(Output)48 b(new_cl.)406 4480 y(3.)100 b(Demodulate)47 b(new_cl)i(\(including)f($)i(evaluation\).)307 4580 y(*)f(4.)100 b(Orient)48 b(equalities.)307 4680 y(*)h(5.)100 b(Apply)48 b(unit)h(deletion.)406 4779 y(6.)100 b(Merge)48 b(identical)h(literals)f(\(leftmost)g(copy)h(is)g(kept\).) 307 4879 y(*)g(7.)100 b(Apply)48 b(factor-simplification.)307 4979 y(*)h(8.)100 b(Discard)48 b(new_cl)h(and)g(exit)g(if)g(too)h(many) f(literals)f(or)i(variables.)406 5078 y(9.)100 b(Discard)48 b(new_cl)h(and)g(exit)g(if)g(new_cl)g(is)h(a)f(tautology.)307 5178 y(*)g(10.)h(Discard)e(new_cl)h(and)g(exit)g(if)g(new_cl)g(is)h (too)f(`heavy'.)307 5277 y(*)g(11.)h(Sort)f(literals.)307 5377 y(*)g(12.)h(Discard)e(new_cl)h(and)g(exit)g(if)g(new_cl)g(is)h (subsumed)e(by)h(any)h(clause)805 5477 y(in)f(usable,)g(sos,)g(or)g (passive)g(\(forward)f(subsumption\).)406 5576 y(13.)i(Integrate)e (new_cl)g(and)i(append)e(it)i(to)f(sos.)307 5676 y(*)g(14.)h(Output)e (kept)h(clause.)1884 5946 y FK(4)p eop %%Page: 5 11 5 10 bop 406 388 a Fq(15.)50 b(If)f(new_cl)g(has)g(0)h(literals,)e(a)h (refutation)f(has)h(been)h(found.)406 488 y(16.)g(If)f(new_cl)g(has)g (1)h(literal,)e(then)h(search)g(usable,)f(sos,)h(and)855 587 y(passive)f(for)h(unit)g(conflict)g(\(refutation\))e(with)i (new_cl.)307 687 y(*)g(17.)h(Print)e(the)i(proof)f(if)g(a)h(refutation) e(has)h(been)g(found.)307 786 y(*)g(18.)h(Try)f(to)g(make)g(new_cl)g (into)g(a)h(demodulator.)406 886 y(-------------)307 986 y(*)f(19.)h(Back)f(demodulate)f(if)h(Step)g(18)g(made)h(new_cl)e (into)h(a)h(demodulator.)307 1085 y(*)f(20.)h(Discard)e(each)h(clause)g (in)g(usable)g(or)g(sos)h(that)f(is)g(subsumed)f(by)855 1185 y(new_cl)g(\(back)h(subsumption\).)307 1285 y(*)g(21.)h(Factor)e (new_cl)h(and)g(process)g(factors.)257 1543 y FK(Steps)24 b(19\22621)h(are)f(delayed)i(until)e(steps)h(1\22618)g(ha)n(v)o(e)f (been)h(applied)g(to)f(all)g(clauses)h(inferred)h(from)e(the)257 1656 y(acti)n(v)o(e)g(gi)n(v)o(en)g(clause.)257 2006 y FJ(3)119 b(Starting)33 b Fr(O)r Fs(T)6 b(T)g(E)g(R)257 2273 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(in)h(pure)g(pre\002x)257 4431 y(form.)28 b(The)c(follo)n(wing)h(input) f(\002le)f(can)h(be)g(used)g(to)f(test)h(the)g(preceding)i(e)o(xample.) 456 4690 y Fq(assign\(stats_level,)46 b(0\).)456 4790 y(set\(display_terms\).)456 4890 y(formula_list\(usable\).)456 4989 y(p|)k(-q&r->)e(-s|t.)348 b(\045)50 b(This)f(formula)f(has)h (minimum)g(whitespace.)456 5089 y(end_of_list.)257 5361 y FK(In)22 b(general,)i(whitespace)h(is)d(required)j(around)f FD(all)c FK(and)j FD(exists)c FK(and)k(to)g(the)f(left)h(of)g FD(-)p FK(;)f(otherwise,)257 5474 y(whitespace)j(around)h(the)d(logic)i (symbols)g(can)f(be)f(remo)o(v)o(ed.)30 b(See)23 b(Sec.)f(4.6)i(for)f (the)h(rules.)1884 5946 y(8)p eop %%Page: 9 15 9 14 bop 257 388 a FI(4.6)99 b(In\002x,)25 b(Pr)n(e\002x,)h(and)f(P)n (ost\002x)g(Expr)n(essions)257 622 y FK(Man)o(y)g(Prolog)h(systems)g (ha)n(v)o(e)g(a)f(feature)i(that)f(allo)n(ws)f(users)i(to)e(declare)i (that)f(particular)i(function)f(or)257 735 y(predicate)g(symbols)e(are) 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FK(does)c(not)g(treat)h(comma)e(as)h(an) g(operator;)i(in)e(particular)l(,)j FD(a,b,c)21 b FK(cannot)26 b(be)f(a)f(term,)484 2021 y(as)g(in)f FD(a,b,c)52 b(->)i(d,e,f)p FK(.)393 2208 y Fv(\017)48 b FK(O)q FE(T)t(T)t(E)t(R)31 b FK(treats)d(the)g(quanti\002ers)h FD(all)c FK(and)i FD(exists)d FK(as)j(special)h(cases,)h(because)g(the)o(y)f(don')n(t)484 2321 y(seem)c(to)f(\002t)g(neatly)i(into)f(the)g(standard)h(Prolog)f (mechanism.)393 2509 y Fv(\017)48 b FK(O)q FE(T)t(T)t(E)t(R)27 b FK(requires)f(whitespace)g(in)d(some)h(cases)g(where)g(the)g(Prolog)g (systems)h(do)e(not.)398 2757 y(Symbols)33 b(to)f(be)h(treated)h(in)f (this)g(special)h(w)o(ay)e(are)h(gi)n(v)o(en)g(a)f(type)i(and)f(a)f (precedence.)59 b(Either)259 2869 y(O)q FE(T)t(T)t(E)t(R)27 b FK(predeclares)g(the)d(symbol')-5 b(s)25 b(properties,)h(or)d(the)h (user)h(gi)n(v)o(es)h(O)q FE(T)t(T)t(E)t(R)h FK(a)c(command)i(of)e(one) h(of)257 2982 y(the)g(follo)n(wing)h(forms.)484 3217 y Fq(op\()p Fl(precedence)p Fq(,)47 b Fl(type)p Fq(,)i Fl(symbol)p Fq(\).)484 3316 y(op\()p Fl(precedence)p Fq(,)e Fl(type)p Fq(,)i Fl(list-of-symbols)p Fq(\).)257 3564 y FK(The)34 b FD(precedence)c FK(is)35 b(an)f(inte)o(ger)j FC(i)p FK(,)g Fp(0)46 b FC(<)g(i)h(<)f Fp(1000)p FK(,)39 b(and)c FD(type)d FK(is)j(one)g(of)g(the)g(follo)n(wing:)257 3677 y FD(xfx)p FK(,)26 b FD(xfy)p FK(,)g FD(yfx)f FK(\(in\002x\),)k FD(fx)p FK(,)d FD(fy)g FK(\(pre\002x\),)j FD(xf)p FK(,)d FD(yf)g FK(\(post\002x\).)41 b(See)27 b(T)-7 b(able)28 b(3)f(for)g(the)h(commands)257 3790 y(corresponding)g(to)23 b(the)h(predeclared)j(symbols.)1361 4054 y(T)-7 b(able)24 b(3:)k(Predeclared)e(Symbols)p 911 4085 1993 4 v 960 4155 a Fq(op\(800,)49 b(xfy,)g(#)h(\).)960 4255 y(op\(800,)f(xfx,)g (->\).)149 b(op\(700,)48 b(xfx,)h(@<\).)960 4354 y(op\(800,)g(xfx,)g (<->\).)99 b(op\(700,)48 b(xfx,)h(@>\).)960 4454 y(op\(790,)g(xfy,)g (|\).)199 b(op\(700,)48 b(xfx,)h(@<=\).)960 4554 y(op\(780,)g(xfy,)g (&\).)199 b(op\(700,)48 b(xfx,)h(@>=\).)960 4753 y(op\(700,)g(xfx,)g 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b(a)g(name)g(and)g(opening)i(parenthesis.)69 b(The)36 b(rule)g(to)g(use)h(is:)54 b FG(Insert)37 b(some)f(white)g(space)h(if) 257 1894 y(and)32 b(only)h(if)e(it)h(is)f FK(not)h FG(a)g(standar)m(d)i (application.)56 b FK(F)o(or)31 b(e)o(xample,)k(the)d(tw)o(o)f(pieces)i (of)f(white)g(space)257 2007 y(in)i FD(\(a+)53 b(\(b+c\)\)=)f(\(d+e\)) 31 b FK(are)j(required,)39 b(and)c(no)f(white)g(space)i(is)e(allo)n (wed)h(after)g FD(f)e FK(or)h FD(g)f FK(in)257 2120 y FD(f\(x,g\(x\)\))p FK(.)257 2429 y FI(4.8)99 b(Bugs)25 b(and)h(Other)f(Anomalies)f(in)h(the)h(Input)g(and)g(Output)g(of)f (Expr)n(essions)393 2640 y Fv(\017)46 b FK(The)26 b(symbol)i FD(|)d FK(is)i(either)g(Prolog-style)j(list)d(punctuation)j(or)c(part)i (of)e(a)g(special)j(name.)38 b(W)l(ith)484 2753 y(the)32 b(b)n(uilt-in)i(declaration)g(of)e FD(|)e FK(as)i(in\002x,)h(the)f (term)f FD([a|b])e FK(is)i(ambiguous,)k(with)d(possible)484 2866 y(interpretations)c FC(t)1065 2880 y Fk(1)1130 2866 y Fp(=)p FD($cons\(a,b\))18 b FK(and)25 b 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b(Sk)o(olem)484 1253 y(property)77 b(is)e(used)h(by)f(the)g (options)i FD(para_skip_skole)o(m)68 b FK(\(Sec.)74 b(6.1.4\))i(and)484 1366 y FD(delete_identica)o(l_)o(ne)o(ste)o(d_)o(sk)o(ol)o(em)16 b FK(\(Sec.)23 b(6.1.5\).)257 1554 y FD(lrpo)p 482 1554 28 4 v 31 w(multiset)p 953 1554 V 29 w(status\([...]\))p FF(.)39 b FK(This)k(command)g(speci\002es)h(multiset)h(status)f(for)f (the)484 1667 y(le)o(xicographic)27 b(recursi)n(v)o(e)f(path)e (ordering)i(\(\003ag)d FD(lrpo)p FK(\).)j(See)d(Sec.)g(8.2.)257 1976 y FI(5.6)99 b(Other)25 b(Commands)257 2210 y FK(The)k(command)i FD(op\()p FG(pr)m(ecedence)p FD(,)57 b FG(type)p FD(,)e FG(name\(s\))p FD(\))p FK(,)32 b(e)o(xample)f FD(op\(400,xfy,+\))p FK(,)25 b(declares)257 2323 y(one)38 b(or)g(more)g(symbols)h(to)f(ha)n (v)o(e)g(special)i(properties)h(with)c(respect)j(to)e(input)h(and)f (output.)74 b(See)257 2436 y(Sec.)23 b(4.6.)398 2609 y(The)88 b(command)h FD(make)p 1298 2609 V 31 w(evaluable\()p FG(symbol)p FD(,)51 b FG(e)o(valuable-symbol)p 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b(Def)o(ault)33 b(set.)55 b(If)32 b(this)h(\003ag)f(is)g(set,)i (paramodulation)j(is)32 b(allo)n(wed)h FG(into)g FK(left)257 4990 y(sides)27 b(of)g(positi)n(v)o(e)h(and)f(ne)o(gati)n(v)o(e)g (equalities.)41 b(\(Applies)27 b(to)g(both)g FD(para_into)22 b FK(and)27 b FD(para_from)257 5103 y FK(inference)f(rules.\))257 5276 y FD(para_into_righ)o(t)p FK(.)j(Def)o(ault)e(set.)35 b(If)26 b(this)g(\003ag)g(is)f(set,)i(paramodulation)i(is)d(allo)n(wed) h FG(into)f FK(right)257 5388 y(sides)h(of)g(positi)n(v)o(e)h(and)f(ne) o(gati)n(v)o(e)g(equalities.)41 b(\(Applies)27 b(to)g(both)g FD(para_into)22 b FK(and)27 b FD(para_from)257 5501 y FK(inference)f(rules.\))257 5674 y FD(para_from_vars)o FK(.)52 b(Def)o(ault)34 b(clear)-5 b(.)59 b(If)33 b(this)h(\003ag)f(is) g(set,)i(paramodulation)j FG(fr)l(om)33 b FK(v)n(ariables)i(is)1861 5946 y(17)p eop %%Page: 18 24 18 23 bop 257 388 a FK(allo)n(wed.)40 b FG(W)-8 b(arning:)37 b(Setting)28 b(this)g(option)g(may)f(pr)l(oduce)i(too)e(many)g(par)o 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b(this)h(\003ag)f(is)g(set,)h(paramodulation) j(is)c(allo)n(wed)257 1584 y(only)e(if)g(the)g FG(into)g FK(clause)h(is)e(a)g(unit.)33 b(\(Applies)26 b(to)f(both)g FD(para_into)20 b FK(and)25 b FD(para_from)20 b FK(inference)257 1697 y(rules.\))257 1870 y FD(para_skip_skol)o(em)p FK(.)31 b(Def)o(ault)d(clear)-5 b(.)39 b(If)27 b(this)g(\003ag)g(is)f(set,)i (paramodulation)i(is)d(ne)n(v)o(er)g(allo)n(wed)257 1983 y FG(into)21 b FK(subterms)h(of)e(Sk)o(olem)g(e)o(xpressions)j([16)r (].)k(\(Applies)21 b(to)g(both)g FD(para_into)15 b FK(and)21 b FD(para_from)257 2096 y FK(inference)26 b(rules.\))257 2269 y FD(para_ones_rule)o FK(.)39 b(Def)o(ault)30 b(clear)-5 b(.)46 b(If)28 b(this)i(\003ag)e(is)h(set,)h(paramodulation)j(obe)o(ys) d(the)f(1')-5 b(s)30 b(rule.)257 2382 y(\(The)22 b(1')-5 b(s)22 b(rule)h(is)e(a)h(special-purpose)27 b(strate)o(gy)d(for)e (problems)h(in)f(combinatory)j(logic;)f(its)e(usefulness)257 2495 y(has)32 b(not)g(been)g(demonstrated)i(else)n(where.\))55 b(\(Applies)33 b(to)e(both)h FD(para_into)27 b FK(and)32 b FD(para_from)257 2607 y FK(inference)26 b(rules.\))257 2780 y FD(para_all)p FK(.)35 b(Def)o(ault)28 b(clear)-5 b(.)41 b(If)27 b(this)h(\003ag)f(is)g(set,)h(all)f(occurrences)k(of)c (the)g FG(into)h FK(term)f(are)h(replaced)257 2893 y(with)37 b(the)g(replacement)j(term.)70 b(\(Applies)38 b(to)f(both)h FD(para_into)33 b FK(and)k FD(para_from)c FK(inference)257 3006 y(rules.\))257 3312 y FF(6.1.5)92 b(Flags)23 b(f)n(or)h(Handling)e (Generated)i(Clauses)257 3546 y FK(\(Section)h(6.1.6)e(describes)j (equality-related)i(\003ags)c(for)g(handling)h(generated)i(clauses.\)) 257 3719 y FD(detailed_histo)o(ry)p FK(.)44 b(Def)o(ault)32 b(set.)52 b(This)31 b(\003ag)g(af)n(fects)h(the)g(parent)g(lists)g(in)f (clauses)i(that)f(are)257 3832 y(deri)n(v)o(ed)d(by)e FD(binary_res)p FK(,)c FD(para_from)p FK(,)g(or)28 b FD(para_into)p FK(.)36 b(If)27 b(the)h(\003ag)f(is)g(set,)i(the)e (positions)257 3945 y(of)f(the)g(uni\002ed)h(literals)h(or)e(terms)g (are)g(gi)n(v)o(en)h(along)g(with)f(the)h(IDs)e(of)h(the)h(parents.)38 b(See)25 b(Sec.)h(16)g(for)257 4058 y(e)o(xamples.)257 4231 y FD(order_history)p FK(.)i(Def)o(ault)f(clear)-5 b(.)36 b(This)25 b(\003ag)g(af)n(fects)i(the)f(order)h(of)e(parent)i (lists)g(in)e(clauses)i(that)257 4344 y(are)k(deri)n(v)o(ed)h(by)f (hyperresolution,)36 b(ne)o(gati)n(v)o(e)c(hyperresolution,)37 b(or)30 b(UR-resolution.)53 b(If)31 b(the)g(\003ag)f(is)257 4457 y(set,)36 b(then)e(the)g(nucleus)i(is)d(listed)i(\002rst,)g(and)g (the)e(satellites)j(are)e(listed)h(in)f(the)g(order)g(in)g(which)g(the) 257 4570 y(corresponding)27 b(literals)d(appear)g(in)e(the)h(nucleus.) 30 b(If)22 b(the)h(\003ag)f(is)h(clear)g(\(or)g(if)f(the)h(clause)h(w)o (as)e(deri)n(v)o(ed)257 4683 y(by)h(some)h(other)h(inference)h(rule\),) e(the)f(gi)n(v)o(en)i(clause)f(is)g(listed)h(\002rst.)257 4855 y FD(unit_deletion)p FK(.)62 b(Def)o(ault)38 b(clear)-5 b(.)69 b(If)37 b(this)g(\003ag)f(is)h(set,)j(unit)e(deletion)h(is)d (applied)j(to)e(ne)n(wly)257 4968 y(generated)g(clauses.)63 b(Unit)34 b(deletion)j(remo)o(v)o(es)e(a)f(literal)i(from)e(a)g(ne)n (wly)h(generated)i(clause)f(if)e(the)257 5081 y(literal)c(is)g(the)f (ne)o(gation)i(of)e(an)h(instance)h(of)e(a)g(unit)h(clause)h(that)f (occurs)h(in)e FD(usable)d FK(or)j FD(sos)p FK(.)44 b(F)o(or)257 5194 y(e)o(xample,)23 b(the)g(second)h(literal)g(of)e FD(p\(a,x\))52 b(|)i(q\(a,x\))19 b FK(is)j(remo)o(v)o(ed)h(by)g(the)f (unit)h FD(-q\(u,v\))p FK(;)c(b)n(ut)257 5307 y(it)k(is)h(not)g(remo)o (v)o(ed)h(by)f(the)g(unit)g FD(-q\(u,b\))p FK(,)c(because)26 b(that)e(uni\002cation)i(causes)f(the)g(instantiation)i(of)257 5420 y FD(x)p FK(.)40 b(All)27 b(such)i(literals)g(are)f(remo)o(v)o(ed) h(from)e(the)h(ne)n(wly)g(generated)j(clause,)f(e)n(v)o(en)e(if)f(the)h (result)h(is)f(the)257 5533 y(empty)j(clause.)51 b(One)31 b(can)g(vie)n(w)f(unit)h(deletion)i(with)d(unit)i(clause)g FD(P)d FK(as)i(demodulation)j(applied)e(to)257 5646 y(literals)27 b(with)f(the)g(demodulator)i FD(P)54 b(=)g($T)p FK(.)24 b(\(Unit)i(deletion)i(is)d(not)i(useful)g(if)e(all)h(generated)i (clauses)1861 5946 y(18)p eop %%Page: 19 25 19 24 bop 257 388 a FK(are)24 b(units.\))257 561 y FD(back_unit_dele)o (tio)o(n)p FK(.)k(Def)o(ault)e(clear)-5 b(.)36 b(If)25 b(this)h(\003ag)f(is)g(set,)h(then)h(whene)n(v)o(er)f(a)f(unit)h (clause)h(is)257 674 y(deri)n(v)o(ed)c(and)g(k)o(ept,)g(it)f(is)g(used) h(to)g(apply)g(unit)g(deletion)i(to)d(all)g(e)o(xisting)i(clauses)g(in) e FD(usable)d FK(or)j FD(sos)p FK(.)257 847 y FD(delete_identic)o(al_)o (ne)o(st)o(ed)o(_s)o(kol)o(em)o FK(.)27 b(Def)o(ault)f(clear)-5 b(.)35 b(If)25 b(this)h(\003ag)f(is)g(set,)g(clauses)i(with)257 960 y(the)36 b(nested)i(Sk)o(olem)e(property)j(are)d(deleted.)69 b(A)35 b(clause)j(has)e(the)h(nested)g(Sk)o(olem)g(property)h(if)e(it) 257 1073 y(contains)22 b(a)e(a)g(Sk)o(olem)g(e)o(xpression)j(that)e (\(properly\))i(contains)g(an)d(occurrence)j(of)d(its)h(leading)h(Sk)o (olem)257 1185 y(symbol.)32 b(F)o(or)24 b(e)o(xample,)h(if)f FD(f)f FK(is)h(a)g(Sk)o(olem)h(function,)h(a)e(clause)i(containing)h(a) d(term)h FD(f\(f\(x\)\))20 b FK(or)k(a)257 1298 y(term)f FD(f\(g\(f\(x\)\)\))18 b FK(is)24 b(deleted.)257 1471 y FD(sort_literals)p FK(.)g(Def)o(ault)h(clear)-5 b(.)32 b(If)24 b(this)h(\003ag)f(is)g(set,)g(literals)i(of)f(ne)n(wly)f (generated)j(clauses)f(are)257 1584 y(sorted\227ne)o(gati)n(v)o(e)32 b(literals,)g(then)e(positi)n(v)o(e)h(literals,)h(then)e(answer)f (literals.)48 b(The)29 b(main)g(purpose)i(of)257 1697 y(this)25 b(\003ag)g(is)g(to)g(mak)o(e)g(clauses)i(more)e(readable.)36 b(In)25 b(some)g(cases,)h(this)g(\003ag)e(can)i(speed)g(up)f(subsump-) 257 1810 y(tion)f(on)g(non-unit)h(clauses.)257 1983 y FD(for_sub)p FK(.)37 b(Def)o(ault)29 b(set.)42 b(If)28 b(this)g(\003ag)f(is)h(set,)h(forw)o(ard)g(subsumption)i(is)c(applied)j (during)f(the)f(pro-)257 2096 y(cessing)d(of)f(ne)n(wly)f(generated)k (clauses.)j(\(Ne)n(w)23 b(clauses)i(are)f(deleted)h(if)e(subsumed)j(by) d(an)o(y)h(clause)h(in)257 2209 y FD(usable)20 b FK(or)j FD(sos)p FK(.\))257 2382 y FD(back_sub)p FK(.)47 b(Def)o(ault)32 b(set.)52 b(If)31 b(this)g(\003ag)g(is)g(set,)i(back)f(subsumption)i (is)d(applied)i(during)g(the)e(pro-)257 2495 y(cessing)25 b(of)f(ne)n(wly)g(k)o(ept)h(clauses.)31 b(\(Clauses)25 b(in)f FD(usable)c FK(or)k FD(sos)d FK(are)j(deleted)i(if)d(subsumed)j (by)e(the)257 2607 y(ne)n(wly)f(k)o(ept)i(clause.\))257 2780 y FD(factor)p FK(.)k(Def)o(ault)c(clear)-5 b(.)34 b(If)24 b(this)i(\003ag)e(is)h(set,)g(f)o(actoring)i(is)d(applied)j(in) e(tw)o(o)f(w)o(ays.)33 b(First,)25 b(f)o(actoring)257 2893 y(is)i(applied)i(as)e(a)g(simpli\002cation)j(rule)e(to)f(ne)n(wly) g(generated)j(clauses.)42 b(If)27 b(a)g(generated)j(clause)f FC(C)k FK(has)257 3006 y(f)o(actors)k(that)e(subsume)i FC(C)7 b FK(,)36 b(it)f(is)g(replaced)j(with)d(its)g(smallest)h (subsuming)i(f)o(actor)-5 b(.)65 b(Second,)38 b(it)d(is)257 3119 y(applied)30 b(as)e(an)g(inference)i(rule)f(to)f(ne)n(wly)g(k)o (ept)h(clauses.)44 b(Note)28 b(that)g(unlik)o(e)i(other)f(inference)h (rules,)257 3232 y(f)o(actoring)24 b(is)d(not)h(applied)i(to)d(the)h (gi)n(v)o(en)g(clause;)i(it)e(is)f(applied)i(to)f(a)f(ne)n(w)g(clause)i (as)f(soon)g(as)g(it)f(is)g(k)o(ept.)257 3345 y(All)26 b(f)o(actors)i(are)f(generated)i(in)e(an)f(iterati)n(v)o(e)i(manner)-5 b(.)39 b(F)o(actoring)28 b FG(is)e FK(attempted)j(on)d(answer)i (literals.)257 3458 y(If)d FD(factor)d FK(is)j(set,)h(a)f(clause)i (with)e FC(n)g FK(literals)i(will)e FG(not)h FK(cause)g(a)f(clause)i (with)f(fe)n(wer)f(than)h FC(n)e FK(literals)257 3571 y(to)f(be)h(deleted)h(by)f(subsumption.)257 3877 y FF(6.1.6)92 b(Demodulation)23 b(and)f(Ordering)h(Flags)257 4111 y FD(demod_history)p FK(.)29 b(Def)o(ault)e(set.)37 b(If)25 b(this)i(\003ag)e(is)h(set,)h(then)g(when)f(a)f(clause)j(is)e (demodulated,)j(the)257 4224 y(ID)22 b(numbers)j(of)f(the)g (demodulators)i(are)e(included)i(in)d(the)h(deri)n(v)n(ation)i(history) f(of)f(the)f(clause.)257 4397 y FD(order_eq)p FK(.)g(Def)o(ault)f (clear)-5 b(.)29 b(If)21 b(this)g(\003ag)g(is)g(set,)g(equalities)j (are)d(\003ipped)h(if)f(the)g(right)h(side)g(is)f(hea)n(vier)257 4510 y(than)j(the)g(left.)29 b(See)23 b(Secs.)29 b(8.1.2)23 b(and)h(8.2.2)g(for)f(the)h(meaning)h(of)e(\223hea)n(vier\224.)257 4683 y FD(eq_units_both_)o(way)o(s)p FK(.)54 b(Def)o(ault)36 b(clear)-5 b(.)62 b(If)34 b(this)h(\003ag)g(is)f(set,)j(unit)e (equality)i(clauses)f(\(both)257 4795 y(positi)n(v)o(e)28 b(and)g(ne)o(gati)n(v)o(e\))g(are)f(sometimes)h(stored)g(in)f(both)h (orientations;)k(the)27 b(action)i(tak)o(en)f(depends)257 4908 y(on)37 b(the)g(\003ag)g FD(order_eq)p FK(.)64 b(If)37 b FD(order_eq)32 b FK(is)37 b(clear)l(,)k(then)d(whene)n(v)o(er)g(a)e (unit,)41 b(say)c FC(\013)51 b Fp(=)f FC(\014)5 b FK(,)39 b(is)257 5021 y(processed,)28 b FC(\014)34 b Fp(=)29 b FC(\013)c FK(is)g(automatically)j(generated)g(and)e(processed.)37 b(If)25 b FD(order_eq)c FK(is)26 b(set,)g(then)g(the)257 5134 y(re)n(v)o(ersed)j(equality)h(is)e(generated)i(only)f(if)e(the)i (equality)h(cannot)f(be)f(oriented)i(\(see)e(Secs.)42 b(8.1.2)28 b(and)257 5247 y(8.2.2\).)257 5420 y FD(demod_linear)p FK(.)21 b(Def)o(ault)g(clear)-5 b(.)29 b(If)20 b(this)h(\003ag)e(is)h (set,)h(demodulation)j(inde)o(xing)e(is)e(disabled,)j(and)d(a)257 5533 y(linear)26 b(search)h(of)e FD(demodulators)20 b FK(are)25 b(used)h(when)g(re)n(writing)g(terms.)35 b(W)l(ith)26 b(inde)o(xing)h(disabled,)257 5646 y(if)f(more)h(than)h(one)f (demodulator)i(can)f(be)e(applied)j(to)e(re)n(write)g(a)f(term,)h(then) h(the)f(one)g(whose)h(clause)1861 5946 y(19)p eop %%Page: 20 26 20 25 bop 257 388 a FK(number)19 b(is)g(lo)n(west)f(is)h(applied;)j (this)d(\003ag)f(is)g(useful)i(when)f(demodulation)j(is)c(used)h(to)g (do)f(\223procedural\224)257 501 y(things.)42 b(W)l(ith)27 b(inde)o(xing)j(enabled)f(\(the)f(def)o(ault\),)i(demodulation)h(is)c (much)g(f)o(aster)l(,)j(b)n(ut)e(the)g(order)g(in)257 614 y(which)c FD(demodulators)17 b FK(is)23 b(applied)j(is)d(not)h (under)h(the)f(control)h(of)e(the)h(user)-5 b(.)257 787 y FD(demod_out_in)p FK(.)22 b(Def)o(ault)g(clear)-5 b(.)29 b(If)21 b(this)h(\003ag)f(is)g(set,)h(terms)g(are)g(demodulated)i (outside-in,)g(left)e(to)257 900 y(right.)30 b(In)24 b(other)h(w)o(ords,)f(the)g(program)h(attempts)g(to)f(re)n(write)g(a)g (term)f(before)j(re)n(writing)f(\(left)f(to)g(right\))257 1013 y(its)19 b(subterms.)29 b(The)18 b(algorithm)j(is)e(\223repeat)h Fv(f)p FK(re)n(write)g(the)f(leftmost)i(outermost)f(re)n(writable)h (term)p Fv(g)e FK(until)257 1125 y(no)k(more)g(re)n(writing)h(can)g(be) f(done)h(or)f(the)g(limit)g(is)g(reached\224.)31 b(\(The)23 b(ef)n(fect)h(is)f(lik)o(e)h(a)e(standard)k(reduc-)257 1238 y(tion)c(in)f(lambda)h(calculus)h(or)f(in)f(combinatory)j (logic.\))29 b(If)21 b(this)h(\003ag)f(is)g(clear)l(,)h(terms)g(are)f (demodulated)257 1351 y(inside-out)32 b(\(all)d(subterms)i(are)e(fully) h(demodulated)i(before)e(attempting)i(to)d(re)n(write)g(a)g(term\).)45 b(\(The)257 1464 y(e)n(v)n(aluable)32 b(conditional)i(term)c FD($IF\()p FG(condition)p FD(,)p FG(then-value)p FD(,)p FG(else-v)q(alu)q(e)p FD(\))35 b FK(is)c(an)f(e)o(xception)j(when)257 1577 y(inside-out)26 b(demodulation)h(is)c(in)h(ef)n(fect.)29 b(See)23 b(Sec.)g(9.\))257 1750 y FD(dynamic_demod)p FK(.)33 b(Def)o(ault)28 b(clear)-5 b(.)41 b(If)27 b(this)h(\003ag)f(is) g(set,)h FG(some)f FK(ne)n(wly)g(k)o(ept)i(equalities)g(are)f(made)257 1863 y(into)37 b(demodulators)j(\(Secs.)68 b(8.1.3)36 b(and)h(8.2.3\).)68 b(Setting)38 b(this)f(\003ag)f(automatically)j (sets)f(the)e(\003ag)257 1976 y FD(order_eq)p FK(.)257 2149 y FD(dynamic_demod_)o(all)o FK(.)50 b(Def)o(ault)33 b(clear)-5 b(.)58 b(If)32 b(this)i(\003ag)e(is)g(set,)37 b(O)q FE(T)t(T)t(E)t(R)g FK(attempts)d(to)f(mak)o(e)g FG(all)257 2262 y FK(ne)n(wly)21 b(k)o(ept)h(equalities)i(into)e (demodulators)j(\(Sec.)20 b(8.1.3\).)29 b(Setting)22 b(this)g(\003ag)e(automatically)25 b(sets)d(the)257 2375 y(\003ags)h FD(dynamic_demod)17 b FK(and)24 b FD(order_eq)p FK(.)257 2547 y FD(dynamic_demod_)o(lex)o(_d)o(ep)o FK(.)52 b(Def)o(ault)34 b(clear)-5 b(.)59 b(If)33 b(this)h(\003ag)e(is)i(set,)h (dynamic)g(demodulators)257 2660 y(may)23 b(be)h(le)o(x-dependent)j(or) e FE(L)t(R)t(P)t(O)r FK(-dependent.)34 b(See)23 b(Secs.)29 b(8.1.3)23 b(and)h(8.2.3.)257 2833 y FD(back_demod)p FK(.)97 b(Def)o(ault)49 b(clear)-5 b(.)103 b(If)48 b(this)g(\003ag)g (is)g(set,)54 b(back)49 b(demodulation)i(is)d(applied)i(to)257 2946 y FD(demodulators)p FK(,)28 b FD(usable)p FK(,)j(and)i FD(sos)d FK(whene)n(v)o(er)j(a)f(ne)n(w)g(demodulator)j(is)e(added.)56 b(Back)33 b(de-)257 3059 y(modulation)38 b(is)d(delayed)j(until)e(the)g (inference)i(rules)e(are)g(\002nished)h(generating)h(clauses)f(from)f (the)257 3172 y(current)28 b(gi)n(v)o(en)e(clause)i(\(delayed)g(until)f FD(post_process)p FK(\).)j(Setting)d(the)f FD(back_demod)21 b FK(\003ag)26 b(au-)257 3285 y(tomatically)g(sets)e(the)g(\003ags)f FD(order_eq)c FK(and)24 b FD(dynamic_demod)p FK(.)257 3458 y FD(anl_eq)p FK(.)99 b(Def)o(ault)49 b(clear)-5 b(.)103 b(If)48 b(this)h(\003ag)e(is)h(set,)54 b(a)48 b(standard)i(equational)h(strate)o(gy)f(will)e(be)257 3571 y(applied)57 b(to)f(the)f(search.)126 b(This)56 b(\003ag)f(is)g(really)i(a)e(meta\003ag;)72 b(its)56 b(only)g(ef)n(fect)g(is)g(to)f(alter)257 3684 y(other)28 b(\003ags)g(as)f(follo)n(ws:)38 b Fq(set\(para_from\))p Fw(,)22 b Fq(set\(para_into\))p Fw(,)h Fq(set\(para_from_left\))p Fw(,)257 3797 y Fq(clear\(para_from_right\))p Fw(,)45 b Fq(set\(para_into_left\))p Fw(,)h Fq(clear\(para_into_right\))p Fw(,)257 3909 y Fq(set\(para_from_vars\))p Fw(,)21 b Fq(set\(eq_units_both_ways\))p Fw(,)f Fq(set\(dynamic_demod_all\))p Fw(,)257 4022 y Fq(set\(back_demod\))p Fw(,)28 b Fq (set\(process_input\))p Fw(,)g(and)h Fq(set\(lrpo\))p FK(.)54 b(This)33 b(strate)o(gy)i(is)e(deri)n(v)o(ed)257 4135 y(mostly)24 b(from)f(equational)j(strate)o(gies)f(de)n(v)o(eloped) g(at)e(Ar)n(gonne)i(by)e(Larry)h(W)-7 b(os)22 b(and)i(Ross)f(Ov)o (erbeek.)257 4248 y(It)g(can)h(also)g(be)g(used)g(for)g(Knuth-Bendix)i (completion.)31 b(See)23 b(Sec.)f(8.3)i(for)g(more)f(details.)257 4421 y FD(knuth_bendix)p FK(.)82 b(Def)o(ault)45 b(clear)-5 b(.)89 b(Setting)44 b(this)g(\003ag)g(simply)g(causes)h(the)f (preceding)i(\003ag,)257 4534 y FD(anl_eq)p FK(,)20 b(to)j(be)h(set.) 257 4707 y FD(lrpo)p FK(.)29 b(Def)o(ault)d(clear)-5 b(.)32 b(If)25 b(this)g(\003ag)f(is)g(set,)h(then)h(the)e(le)o (xicographic)29 b(recursi)n(v)o(e)d(path)f(ordering)i(\(also)257 4820 y(called)g FE(R)t(P)t(O)g FK(with)d(status\))h(is)f(used)i(to)e (compare)h(terms.)31 b(If)24 b(this)h(\003ag)e(is)i(clear)l(,)g(weight) g(templates)h(and)257 4933 y(le)o(xicographic)h(order)e(are)e(used)i (\(Secs.)j(8.2)c(and)g(8.3\).)257 5106 y FD(lex_order_vars)o FK(.)31 b(Def)o(ault)d(clear)-5 b(.)38 b(This)26 b(\003ag)g(af)n(fects) i(le)o(x-dependent)i(demodulation)g(and)d(the)257 5219 y(e)n(v)n(aluable)e(functions)h(and)d(predicates)j(that)e(perform)g(le) o(xical)g(comparisons.)32 b(If)23 b(this)g(\003ag)g(is)g(set,)g(then) 257 5331 y(le)o(xical)35 b(ordering)g(is)f(a)f(total)h(order)h(on)e (terms;)39 b(v)n(ariables)d(are)d(lo)n(west)h(in)g(the)f(term)h(order)l (,)j(with)c FD(x)257 5444 y Fv(\036)c FD(y)g Fv(\036)g FD(z)g Fv(\036)g FD(u)g Fv(\036)h FD(v)f Fv(\036)g FD(w)g Fv(\036)g FD(v6)g Fv(\036)g FD(v7)f Fv(\036)h FD(v8)g Fv(\036)g(\001)15 b(\001)g(\001)h FK(.)49 b(If)30 b(this)g(\003ag)g(is) g(clear)l(,)j(then)e(a)f(v)n(ariable)i(is)257 5557 y(comparable)d(only) g(to)e(another)i(occurrence)h(of)e(the)f(same)h(v)n(ariable;)j(it)c(is) g(not)h(comparable)i(to)d(other)257 5670 y(v)n(ariables)34 b(or)f(to)f(non)l(v)n(ariables.)59 b(F)o(or)32 b(e)o(xample,)j FD($LLT\(f\(x\),f\(y\)\))25 b FK(e)n(v)n(aluates)34 b(to)f FD($T)d FK(if)j(and)1861 5946 y(20)p eop %%Page: 21 27 21 26 bop 257 388 a FK(only)31 b(if)g FD(lex_order_vars)23 b FK(is)31 b(set.)50 b FG(If)30 b FD(lrpo)e FG(is)j(set,)h FD(lex_order_vars)24 b FG(has)31 b(no)g(ef)n(fect)h(on)257 501 y(demodulation)27 b FK(\(Sec.)h(8.1.1\).)257 674 y FD(symbol_elim)p FK(.)91 b(Def)o(ault)48 b(clear)-5 b(.)98 b(If)46 b(this)h(\003ag)f(is)g(set,)52 b(then)c(ne)n(w)d (demodulators)50 b(are)d(ori-)257 787 y(ented,)k(if)44 b(possible,)52 b(so)45 b(that)g(function)i(symbols)f(\(e)o(xcluding)h (constants\))h(are)d(eliminated.)94 b(A)257 900 y(demodulator)47 b(can)f(eliminate)g(all)f(occurrences)j(of)d(a)g(function)i(symbol)f (if)e(the)i(ar)n(guments)h(on)257 1013 y(the)38 b(left)g(side)h(are)f (all)g(dif)n(ferent)i(v)n(ariables)g(and)e(if)f(the)i(function)h (symbol)e(of)g(the)g(left)h(side)f(does)257 1125 y(not)47 b(occur)g(in)f(the)h(right)g(side.)98 b(F)o(or)46 b(e)o(xample,)53 b(the)46 b(demodulators)k FD(g\(x\))j(=)h(f\(x,x\))43 b FK(and)257 1238 y FD(h\(x,y\))52 b(=)i(f\(x,f\(y,f\(g\(x\))o(,g)o (\(y\))o(\)\))o(\))12 b FK(eliminate)20 b(all)f(occurrences)j(of)c FD(g)g FK(and)h FD(h)p FK(,)f(respec-)257 1351 y(ti)n(v)o(ely)-6 b(.)257 1524 y FD(rewriter)p FK(.)84 b(Def)o(ault)44 b(clear)-5 b(.)89 b(If)43 b(this)h(\003ag)f(is)g(set,)49 b(then)44 b(the)f(clauses)i(in)f(the)f FD(sos)f FK(list)h(will)257 1637 y(simply)k(be)g(demodulated)i(by)e(the)g(demodulators,)56 b(the)47 b(run)g(will)f(terminate.)100 b(This)46 b(is)h(really)257 1750 y(just)39 b(a)g(meta\003ag,)k(which)d(automatically)i(causes)e (the)g(se)n(v)o(eral)g(other)g(options)h(parameters)g(to)e(be)257 1863 y(changed)h(as)d(follo)n(ws:)59 b FD(set\(demod_inf\))p FK(,)34 b FD(clear\(for_sub\))p FK(,)g FD(clear\(back_sub\))o FK(,)257 1976 y(and)24 b FD(assign\(max_lev)o(els)o(,)48 b(1\))p FK(.)257 2282 y FF(6.1.7)92 b(Input)22 b(Flags)257 2516 y FD(check_arity)p FK(.)h(Def)o(ault)i(set.)k(If)24 b(this)g(\003ag)f(is)h(set,)f(a)h(w)o(arning)h(is)e(gi)n(v)o(en)h(if)g (symbols)h(ha)n(v)o(e)f(v)n(ariable)257 2629 y(arities)30 b(\(dif)n(ferent)g(numbers)g(of)e(ar)n(guments)j(in)d(dif)n(ferent)j (places)e(in)g(the)f(input\).)45 b(F)o(or)28 b(e)o(xample,)i(the)257 2742 y(term)h FD(f\(a,a\(b\)\))c FK(w)o(ould)32 b(be)g(\003agged.)53 b(\(Constants)34 b(ha)n(v)o(e)e(arity)h(0.\))53 b(If)31 b(this)h(\003ag)f(is)h(clear)l(,)i(then)257 2855 y(v)n(ariable)g (arities)g(are)e(permitted;)39 b(in)33 b(the)f(preceding)k(term,)e(the) f(tw)o(o)f(occurrences)j(of)e FD(a)e FK(w)o(ould)i(be)257 2968 y(treated)25 b(as)e(dif)n(ferent)j(symbols.)257 3140 y FD(prolog_style_v)o(ari)o(ab)o(le)o(s)p FK(.)20 b(Def)o(ault)g(clear)-5 b(.)27 b(If)19 b(this)g(\003ag)f(is)g(set,)i(a) e(name)h(with)f(no)h(ar)n(guments)257 3253 y(in)k(a)g(clause)i(is)f(a)f (v)n(ariable)i(if)e(and)h(only)h(if)e(it)g(starts)i(with)e FD(A)f FK(through)k FD(Z)c FK(\(upper)j(case\))g(or)e(with)g FD(_)p FK(.)257 3426 y FD(echo_included_)o(fil)o(es)o FK(.)45 b(Def)o(ault)32 b(set.)52 b(If)31 b(this)h(\003ag)f(is)g(set,)i (input)f(\002les)f(included)j(with)d(the)257 3539 y FD(include\()p FG(\002lename)p FD(\))20 b FK(command)25 b(are)e(echoed)j(in)d(the)h (same)f(w)o(ay)h(as)f(ordinary)j(input.)257 3712 y FD(simplify_fol)p FK(.)k(Def)o(ault)d(set.)37 b(If)26 b(this)g(\003ag)g(is)g(set,)h(then) f(some)h(propositional)j(simpli\002cation)e(is)257 3825 y(attempted)j(when)e(con)l(v)o(erting)k(input)d(\002rst-order)h (formulas)g(into)f(clauses.)48 b(The)29 b(simpli\002cation)j(oc-)257 3938 y(curs)25 b(after)h(Sk)o(olemization,)h(during)g(the)e(CNF)e (translation.)36 b(If)24 b(simpli\002cation)k(detects)e(a)f (refutation,)257 4051 y(it)i(will)h(al)o(w)o(ays)g(produce)i(the)e (empty)g(clause)h FD($F)p FK(,)d(b)n(ut)k(O)q FE(T)t(T)t(E)t(R)h FK(will)d(not)g(recognize)i(the)e(proof)h(\(i.e.,)257 4164 y(gi)n(v)o(e)23 b(the)h(proof)h(message)g(and)f(stop\))g(unless)h (the)f(\003ag)f FD(process_input)17 b FK(is)23 b(set.)257 4337 y FD(process_input)p FK(.)65 b(Def)o(ault)39 b(clear)-5 b(.)73 b(If)37 b(this)i(\003ag)e(is)h(set,)k(input)d FD(usable)34 b FK(and)k FD(sos)e FK(clauses)257 4450 y(\(including)k(clauses)g(from)d(formula)i(input\))g(are)f(processed)i (as)e(if)f(the)o(y)h(had)g(been)h(generated)h(by)257 4563 y(an)c(inference)i(rule.)67 b(\(See)36 b(the)g(procedure)i(for)f (processing)i(ne)n(wly)d(inferred)i(clauses)f(in)f(Sec.)f(2.\))257 4675 y(The)h(e)o(xceptions)j(are)d(\(1\))g(the)h(follo)n(wing)h (clause-processing)j(options)e(are)d(not)h(applied)h(to)e(input)257 4788 y(clauses:)46 b FD(max_literals)p FK(,)26 b FD(max_weight)p FK(,)i FD(delete_identic)o(al)o(_ne)o(st)o(ed)o(_s)o(ko)o(lem)o FK(,)257 4901 y(and)j FD(max_distinct_v)o(ars)o FK(,)25 b(\(2\))31 b(clauses)h(input)g(on)e(list)h FD(usable)c FK(remain)32 b(there)f(if)f(retained,)257 5014 y(and)24 b(\(3\))g(some)f(output)i(appears)h(e)n(v)o(en)d(if)h(the)f(output)j (\003ags)d(\(Sec.)g(6.1.8\))h(are)g(clear)-5 b(.)257 5187 y FD(tptp_eq)p FK(.)54 b(Def)o(ault)35 b(clear)-5 b(.)59 b(If)33 b(this)h(\003ag)f(is)h(set,)i(then)e(\223)p FD(EQUAL)p FK(\224)d(is)i(the)h(one)g(and)g(only)g(symbol)257 5300 y(recognized)d(as)e(the)g(equality)h(relation)h(for)d(the)h (operations)j(that)d(b)n(uild)g(in)g(equality)i(\(demodulation)257 5413 y(and)24 b(paramodulation\).)1861 5946 y(21)p eop %%Page: 22 28 22 27 bop 257 388 a FF(6.1.8)92 b(Output)21 b(Flags)257 622 y FD(very_verbose)p FK(.)44 b(Def)o(ault)32 b(clear)-5 b(.)51 b(If)31 b(this)g(\003ag)f(is)h(set,)i(a)d(tremendous)j(amount)f (of)f(information)257 735 y(about)25 b(the)e(processing)k(of)c (generated)j(clauses)g(is)d(output.)257 908 y FD(print_kept)p FK(.)g(Def)o(ault)h(set.)29 b(If)23 b(this)g(\003ag)g(is)g(set,)g(ne)n (w)f(clauses)j(are)f(output)g(if)f(the)o(y)h(are)f(retained)i(\(if)257 1021 y(the)o(y)f(pass)g(all)g(retention)i(tests\).)257 1194 y FD(print_proofs)p FK(.)d(Def)o(ault)i(set.)30 b(If)24 b(this)g(\003ag)g(is)f(set,)h(all)g(proofs)i(that)e(are)g (found)h(are)f(printed)i(to)e(the)257 1307 y(output)h(\002le.)j(If)23 b(this)h(\003ag)f(is)h(clear)l(,)g(no)g(proofs)h(are)f(printed.)257 1480 y FD(build_proof_ob)o(jec)o(t_)o(1)p FK(.)44 b(Def)o(ault)32 b(clear)-5 b(.)51 b(If)31 b(this)g(\003ag)g(is)g(set,)h(then)g(whene)n (v)o(er)g(a)e(proof)i(is)257 1593 y(found,)21 b(a)e FG(type)h(1)f(pr)l (oof)h(object)j FK(is)c(printed)i(to)e(the)h(output)h(\002le.)27 b(Proof)19 b(objects)i(are)f(v)o(ery)g(detailed)h(proof)257 1706 y(and)31 b(were)g(introduced)j(for)d(tw)o(o)f(purposes:)47 b(so)31 b(that)g(proofs)h(can)g(be)f(check)o(ed)i(by)e(an)f (independent)257 1818 y(program,)j(and)e(so)f(that)i(proofs)f(can)g(be) g(translated)i(into)e(other)h(forms)e(by)h(other)h(programs.)51 b(Proof)257 1931 y(objects)35 b(are)e(written)h(in)f(a)g(Lisp-lik)o(e)h (notation.)60 b(\(T)-7 b(ype)33 b(2)g(proof)h(objects)h(are)f(usually)h (preferred.\))257 2044 y FG(W)-8 b(arning:)30 b(Construction)d(of)c(pr) l(oof)i(objects)g(is)e(fr)o(a)o(gile\227sometimes)k(it)c(simply)h (fails.)257 2217 y FD(build_proof_ob)o(jec)o(t_)o(2)p FK(.)44 b(Def)o(ault)32 b(clear)-5 b(.)51 b(If)31 b(this)g(\003ag)g(is) g(set,)h(then)g(whene)n(v)o(er)g(a)e(proof)i(is)257 2330 y(found,)23 b(a)e FG(type)h(2)f(pr)l(oof)i(object)h FK(is)e(printed)h (to)e(the)h(output)h(\002le.)28 b(T)-7 b(ype)21 b(2)g(proof)i(objects)g (are)f(used)g(in)g(the)257 2443 y(IVY)h(v)o(eri\002cation)j(project)h ([19)q(],)d(and)h(a)f(detailed)i(description)i(\(de\002nition)e(in)f(A) l(CL2\))e(can)i(be)g(found)257 2556 y(there.)k FG(W)-8 b(arning:)31 b(construction)c(of)c(pr)l(oof)i(objects)g(is)f(fr)o(a)o (gile\227sometimes)i(it)d(simply)h(fails.)257 2729 y FD(print_new_demo)o(d)p FK(.)d(Def)o(ault)h(set.)28 b(If)21 b(this)h(\003ag)e(is)h(set,)h(demodulators)i(that)e(are)f(adjoined)i (during)257 2842 y(the)k(search)i(\()p FD(dynamic_demod)p FK(\))20 b(are)28 b(printed.)41 b(Ne)n(w)25 b(demodulators)31 b(are)c(al)o(w)o(ays)h(printed)g(during)257 2955 y(input)c(processing.) 257 3128 y FD(print_back_dem)o(od)p FK(.)h(Def)o(ault)h(set.)33 b(If)24 b(this)h(\003ag)g(is)f(set,)h(clauses)i(are)e(printed)h(as)f (the)o(y)g(are)g(back)257 3240 y(demodulated.)31 b(Back-demodulated)d (clauses)d(are)f(al)o(w)o(ays)g(printed)h(during)h(input)e(processing.) 257 3413 y FD(print_back_sub)o FK(.)47 b(Def)o(ault)33 b(set.)54 b(If)32 b(this)g(\003ag)f(is)h(set,)i(clauses)g(are)e (printed)h(if)f(the)o(y)g(are)g(back)257 3526 y(subsumed.)e (Back-subsumed)d(clauses)e(are)f(al)o(w)o(ays)g(printed)h(during)h (input)e(processing.)257 3699 y FD(display_terms)p FK(.)44 b(Def)o(ault)32 b(clear)-5 b(.)51 b(If)31 b(this)g(\003ag)g(is)g(set,)h (all)f(clauses)i(and)e(terms)g(are)g(printed)i(in)257 3812 y(pure)24 b(pre\002x)g(form)f(\(Sec.)g(4.3\).)29 b(This)24 b(feature)h(can)f(be)f(useful)i(for)f(deb)n(ugging)i(the)e (input.)257 3985 y FD(pretty_print)p FK(.)33 b(Def)o(ault)27 b(clear)-5 b(.)40 b(If)27 b(this)h(\003ag)e(is)h(set,)h(clauses)g(are)f (output)i(in)e(an)g(indented)i(form)257 4098 y(that)34 b(is)f(sometimes)i(easier)g(to)e(read.)60 b(The)33 b(parameter)i FD(pretty_print_ind)o(en)o(t)26 b FK(\(def)o(ault)36 b(4\))257 4211 y(speci\002es)25 b(the)e(number)i(of)e(spaces)i(for)f (each)g(indent)h(le)n(v)o(el.)257 4384 y FD(bird_print)p FK(.)177 b(Def)o(ault)76 b(clear)-5 b(.)184 b(If)75 b(this)g(\003ag)f (is)h(set,)88 b(terms)75 b(constructed)j(with)257 4497 y(the)e(binary)h(function)i FD(a)74 b FK(are)i(output)i(in)e (combinatory)i(logic)f(notation)h(\(without)g(the)257 4610 y(function)73 b(symbol)g FD(a)p FK(,)82 b(and)71 b(left)h(associated)j(unless)d(otherwise)h(indicated\).)176 b(F)o(or)70 b(e)o(x-)257 4722 y(ample,)84 b(the)72 b(clause)i FD(a\(a\(a\(S,x\),y\),)o(z\))48 b(=)54 b(a\(a\(x,z\),a\(y,z\))o(\))65 b FK(is)72 b(output)h(as)257 4835 y FD(S)54 b(x)g(y)g(z)g(=)g(x)g(z)g (\(y)g(z\))p FK(.)27 b(T)-6 b(erms)23 b(cannot)i(be)e(input)i(in)e (combinatory)k(logic)d(notation.)257 5008 y FD(formula_histor)o(y)p FK(.)e(Def)o(ault)h(clear)-5 b(.)30 b(If)22 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(demodulation)i(still)e(w)o(orks,)h(b)n(ut)f(it)f(is)g(much)h(slo)n (wer)-5 b(.)257 1134 y FD(for_sub_fpa)p FK(.)21 b(Def)o(ault)f(clear)-5 b(.)28 b(If)18 b(this)h(\003ag)f(is)h(set,)i FE(F)t(P)m(A)h FK(inde)o(xing)f(is)d(used)i(for)f(forw)o(ard)g(subsump-)257 1247 y(tion.)30 b(If)24 b(this)g(\003ag)g(is)f(clear)l(,)i (discrimination)j(tree)c(inde)o(xing)i(is)e(used.)30 b(Setting)25 b(this)f(\003ag)g(can)g(decrease)257 1360 y(the)i(amount)h(of)f(memory)g(required)i(by)f(O)q FE(T)t(T)t(E)t(R)r FK(.)38 b(Discrimination)28 b(tree)f(inde)o(xing)h(can)e(require)h(a)f (lot)257 1473 y(of)d(memory)-6 b(,)24 b(b)n(ut)g(it)f(is)h(usually)h FG(muc)o(h)e FK(f)o(aster)i(than)h FE(F)t(P)m(A)h FK(inde)o(xing.)257 1646 y FD(no_fapl)p FK(.)e(Def)o(ault)f(clear)-5 b(.)30 b(If)23 b(this)h(\003ag)f(is)h(set,)f(positi)n(v)o(e)i(literals)h(are)d (not)h(inde)o(x)o(ed)h(for)f(unit)g(con\003ict)257 1758 y(or)36 b(back)g(subsumption.)69 b(This)35 b(option)j(should)f(be)f 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y(memory)-6 b(.)257 3028 y FF(6.1.10)92 b(Miscellaneous)25 b(Flags)257 3262 y FD(control_memory)o FK(.)34 b(Def)o(ault)28 b(clear)-5 b(.)41 b(If)27 b(this)g(\003ag)g(is)g(set,)h(then)g(the)g (automatic)h(memory-control)257 3375 y(feature)c(is)e(enabled)j(\(Sec.) d(17\).)257 3548 y FD(propositional)p FK(.)41 b(Def)o(ault)31 b(clear)-5 b(.)50 b(If)29 b(this)i(\003ag)f(is)f(set,)34 b(O)q FE(T)t(T)t(E)t(R)g FK(assumes)d(that)g(all)f(clauses)i(are)257 3661 y(propositional,)27 b(and)e(it)e(mak)o(es)h(some)g(optimizations.) 33 b FG(The)23 b(user)h(should)i(set)e(this)g(\003a)o(g)g(only)h(when)f (all)257 3774 y(clauses)h(ar)m(e)f(pr)l(opositional;)k(otherwise)f FK(O)q FE(T)t(T)t(E)t(R)g FG(may)c(mak)o(e)h(unsound)i(infer)m(ences)g (and/or)f(cr)o(ash.)257 3946 y FD(really_delete_)o(cla)o(us)o(es)o FK(.)32 b(Def)o(ault)27 b(clear)-5 b(.)39 b(If)26 b(this)i(\003ag)e(is) g(clear)l(,)j(clauses)f(that)f(are)g(deleted)257 4059 y(by)35 b(back)h(subsumption)i(or)c(back)i(demodulation)i(are)e(not)f (really)h(remo)o(v)o(ed)g(from)e(memory;)42 b(the)o(y)257 4172 y(are)31 b(retained)h(in)e(a)h(special)h(place)f(so)g(that)g(the)o (y)g(can)g(be)f(printed)i(if)f(the)o(y)g(occur)g(in)g(a)f(proof.)50 b(If)31 b(the)257 4285 y(job)25 b(in)l(v)n(olv)o(es)i(much)d(back)i (subsumption)h(or)d(back)i(demodulation)h(and)e(if)g(memory)f(conserv)n (ation)k(is)257 4398 y(important,)j(these)f(\223deleted\224)h(clauses)f (can)f(be)f(remo)o(v)o(ed)h(from)g(memory)f(by)h(setting)h(this)f (\003ag)f(\(and)257 4511 y(an)o(y)23 b(proof)i(containing)i(such)d(a)f (clause)i(will)e(not)h(be)g(printed)h(in)e(full\).)257 4684 y FD(atom_wt_max_ar)o(gs)p FK(.)50 b(Def)o(ault)34 b(clear)-5 b(.)59 b(If)33 b(this)g(\003ag)g(is)g(set,)j(the)d(def)o (ault)i(weight)f(of)f(an)g(atom)257 4797 y(\(the)27 b(weight)g(if)f(no) h(template)h(matches)f(the)g(atom\))g(is)f(1)g(plus)h(the)g(maximum)g (of)f(the)h(weights)g(of)g(the)257 4910 y(ar)n(guments.)j(If)19 b(this)i(\003ag)e(is)h(clear)l(,)i(the)e(def)o(ault)i(weight)e(of)g(an) g(atom)g(is)g(1)f(plus)i(the)f(sum)g(of)g(the)g(weights)257 5023 y(of)j(the)h(ar)n(guments.)257 5196 y FD(term_wt_max_ar)o(gs)p FK(.)61 b(Def)o(ault)37 b(clear)-5 b(.)69 b(If)37 b(this)g(\003ag)f(is) h(set,)j(the)d(def)o(ault)h(weight)f(of)g(a)f(term)257 5308 y(\(the)27 b(weight)g(if)f(no)h(template)h(matches)f(the)g(atom\)) g(is)f(1)g(plus)h(the)g(maximum)g(of)f(the)h(weights)g(of)g(the)257 5421 y(ar)n(guments.)k(If)23 b(this)h(\003ag)e(is)i(clear)l(,)g(the)f (def)o(ault)i(weight)f(of)g(a)e(term)i(is)f(1)g(plus)h(the)f(sum)g(of)g (the)h(weights)257 5534 y(of)f(the)h(ar)n(guments.)1861 5946 y(23)p eop %%Page: 24 30 24 29 bop 257 388 a FD(free_all_mem)p FK(.)32 b(Def)o(ault)27 b(clear)-5 b(.)40 b(If)26 b(this)h(\003ag)g(is)f(set,)h(then)h(at)e (the)h(end)h(of)e(the)h(search,)i(most)e(dy-)257 501 y(namically)f(allocated)h(memory)d(is)g(returned)j(to)d(the)h(memory)f (managers.)33 b(This)24 b(\003ag)g(is)g(used)h(mainly)257 614 y(for)33 b(deb)n(ugging,)39 b(in)33 b(particular)l(,)39 b(to)33 b(help)h(\002nd)f(memory)g(leaks.)59 b(Setting)35 b(this)e(\003ag)g(will)g FG(not)h FK(cause)259 727 y(O)q FE(T)t(T)t(E)t(R)27 b FK(to)d(use)g(less)g(memory)-6 b(.)257 900 y FD(sigint_interac)o(t)p FK(.)47 b(Def)o(ault)33 b(set.)54 b(If)31 b(this)i(\003ag)e(is)h(set,)h(then)g(when)h(O)q FE(T)t(T)t(E)t(R)i FK(recei)n(v)o(es)d(an)f(in-)257 1013 y(terrupt)g(signal)g(from)f(the)g(operating)i(system)e(\(usually)i (caused)f(by)f(the)g(user)g(pressing)i(control-C\),)259 1125 y(O)q FE(T)t(T)t(E)t(R)27 b FK(will)c(enter)i(a)e(primiti)n(v)o(e) h(interacti)n(v)o(e)i(mode,)e(which)g(is)f(described)j(in)d(Sec.)g(15.) 257 1435 y FI(6.2)99 b(P)o(arameters)257 1669 y FK(P)o(arameters)25 b(are)g(inte)o(ger)n(-v)n(alued)k(options.)34 b(In)25 b(the)g(descriptions)j(that)e(follo)n(w)-6 b(,)25 b Fv(1)f FK(is)g(a)h(lar)n(ge)h(inte)o(ger)l(,)257 1782 y(usually)32 b(the)e(size)g(of)g(the)g(lar)n(gest)i(ordinary)h(inte)o(ger)e(on)f (the)g(user')-5 b(s)31 b(computer)h(\(i.e.,)f(INT)p 3218 1782 28 4 v 32 w(MAX)d(in)257 1895 y(ANSI)22 b(C\).)257 2201 y FF(6.2.1)92 b(Monitoring)24 b(Pr)n(ogr)n(ess)257 2435 y FD(assign\(report,)o FC(n)p FD(\))p FK(.)38 b(Def)o(ault)30 b Fv(\000)p Fp(1)p FK(,)g(range)g([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)44 b(If)29 b FC(n)35 b(>)g Fp(0)p FK(,)30 b(then)g(statistics)h(are)e(output)257 2548 y(approximately)e (e)n(v)o(ery)d FC(n)g FE(C)t(P)t(U)i FK(seconds.)31 b(The)24 b(time)f(is)g(not)i(e)o(xact)f(because)h(statistics)h(will)e(be)f (output)257 2661 y(only)i(after)f(the)g(current)i(gi)n(v)o(en)e(clause) h(is)f(\002nished.)31 b(This)24 b(feature)h(can)f(be)g(used)h(in)f (conjunction)j(with)259 2774 y FE(U)t(N)t(I)t(X)e FK(programs)g(such)g (as)e FD(grep)e FK(and)j FD(awk)d FK(to)j(con)l(v)o(eniently)j(monitor) g(O)q FE(T)t(T)t(E)t(R)g FK(jobs.)257 3079 y FF(6.2.2)92 b(Placing)23 b(Limits)g(on)g(the)g(Sear)n(ch)257 3314 y FD(assign\(max_sec)o(ond)o(s,)o FC(n)p FD(\))o FK(.)55 b(Def)o(ault)36 b Fv(\000)p Fp(1)p FK(,)g(range)g([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)60 b(If)35 b FC(n)45 b Fv(6)p Fp(=)g Fv(\000)p Fp(1)p FK(,)36 b(the)f(search)h(is)257 3427 y(terminated)24 b(after)g(about)g FC(n)f FE(C)t(P)t(U)i FK(seconds.)30 b(The)23 b(time)f(is)h(not)g(e)o(xact)g(because)k(O)q FE(T)t(T)t(E)t(R)f FK(will)d(w)o(ait)f(until)257 3540 y(the)i(current)h(gi)n(v)o(en)f(clause)h(is)e(\002nished)i(before)g (stopping.)257 3712 y FD(assign\(max_gen)o(,)p FC(n)p FD(\))o FK(.)d(Def)o(ault)i Fv(\000)p Fp(1)p FK(,)e(range)i([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)k(If)23 b FC(n)h Fv(6)p Fp(=)h Fv(\000)p Fp(1)p FK(,)e(the)g(search)h(is)f(terminated) 257 3825 y(after)30 b(about)g FC(n)e FK(clauses)j(ha)n(v)o(e)f(been)h (generated.)48 b(The)29 b(number)h(is)f(not)h(e)o(xact)g(because)j(O)q FE(T)t(T)t(E)t(R)g FK(will)257 3938 y(w)o(ait)23 b(until)i(it)e(is)g 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FK(.)100 b(Def)o(ault)50 b Fv(\000)p Fp(1)p FK(,)56 b(range)50 b([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)107 b(If)49 b FC(n)73 b Fv(6)p Fp(=)g Fv(\000)p Fp(1)p FK(,)56 b(the)49 b(\003ag)257 4909 y FD(sos_queue)31 b FK(will)k(be)h(automatically)j (set,)g(causing)f(a)d(le)n(v)o(el)h(saturation)j(\(breadth-\002rst\))g (search.)257 5022 y(In)23 b(this)h(case)h(the)e(search)i(is)f (terminated)h(after)f FC(n)f FK(le)n(v)o(els)h(ha)n(v)o(e)g(been)g (processed.)257 5194 y FD(assign\(max_mem)o(,)p FC(n)p FD(\))o FK(.)32 b(Def)o(ault)c Fv(\000)p Fp(1)p FK(,)f(range)h([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)39 b(If)26 b FC(n)32 b Fv(6)p Fp(=)f Fv(\000)p Fp(1)p FK(,)e(O)q FE(T)t(T)t(E)t(R)i FK(will)26 b(terminate)257 5307 y(the)e(search)h(before)f(more)g(than)g FC(n)f FK(kilobytes)j(ha)n(v)o(e)e(been)g(dynamically)i(allocated)g(\() p FD(malloc)p FK(\).)1861 5946 y(24)p eop %%Page: 25 31 25 30 bop 257 388 a FF(6.2.3)92 b(Limits)23 b(on)g(Pr)n(operties)i(of)e (Generated)h(Clauses)257 622 y FD(assign\(max_lit)o(era)o(ls)o(,)p FC(n)o FD(\))p FK(.)g(Def)o(ault)i Fv(\000)p Fp(1)p FK(,)e(range)h([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)31 b(If)24 b FC(n)i Fv(6)p Fp(=)h Fv(\000)p Fp(1)p FK(,)d(ne)n(w)g(clauses)i(are)257 735 y(discarded)g(if)d(the)o(y)h(contain)h(more)f(than)g FC(n)f FK(literals.)257 908 y FD(assign\(max_wei)o(ght)o(,)p FC(n)o FD(\))p FK(.)106 b(Def)o(ault)53 b Fv(1)p FK(,)58 b(range)53 b([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)112 b(Ne)n(w)50 b(clauses)j(are)f(dis-)257 1021 y(carded)38 b(if)e(their)i(weight)f(is)g(more)g(than)g FC(n)p FK(.)67 b(The)36 b(weight)i(list)f FD(purge_gen)32 b FK(or)k(the)h(weight)h (list)257 1134 y FD(pick_and_purge)16 b FK(is)24 b(used)g(to)f(weigh)h (clauses)i(\(both)e(lists)g(may)g(not)g(be)f(present;)j(see)e(Sec.)e (10\).)257 1307 y FD(assign\(max_dis)o(tin)o(ct)o(_v)o(ar)o(s,)o FC(n)p FD(\))p FK(.)53 b(Def)o(ault)35 b Fv(\000)p Fp(1)p FK(,)h(range)g([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)60 b(If)34 b FC(n)44 b Fv(6)p Fp(=)h 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4594 y(deciding)j(whether)f(a)f(ne)n(w)g(equality)i(should)g(be)e(a)f (demodulator)-5 b(.)64 b(\(It)34 b(is)g(not)g(used)h(if)f(\003ag)g FD(lrpo)257 4707 y FK(is)e(set.\))58 b(The)32 b(equality)-6 b(,)37 b(say)c FC(\013)43 b Fp(=)g FC(\014)5 b FK(,)34 b(is)f(\002rst)f(oriented)j(as)e(described)i(in)e(Sec.)f(8.1.)57 b(If)32 b FC(w)r(t)p Fp(\()p FC(\014)5 b Fp(\))44 b Fv(\024)257 4820 y FD(dynamic_demod_)o(rhs)22 b FK(and)30 b(if)g FC(w)r(t)p Fp(\()p FC(\013)p Fp(\))c Fv(\000)e FC(w)r(t)p Fp(\()p FC(\014)5 b Fp(\))38 b Fv(\025)29 b FD(dynamic_demod_)o(dep)o (th)o FK(,)24 b(then)31 b(the)257 4933 y(equality)24 b(can)e(be)g(a)g(demodulator)-5 b(.)31 b(W)l(ith)22 b(the)h(def)o(ault) h(v)n(alues)f(for)f(these)h(parameters,)h(the)f(beha)n(vior)h(is)257 5046 y(as)f(described)j(in)e(Sec.)f(8.1)257 5219 y FD(assign\(new_sym)o (bol)o(_l)o(ex)o(_p)o(os)o(iti)o(on)o(,)p FC(n)o FD(\))p FK(.)e(Def)o(ault)g Fv(1)p FK(,)f(range)h([1)f(..)p Fv(1)p FK(].)27 b(Ne)n(w)19 b(symbols)257 5331 y(can)k(be)g(created)h(during)h (the)e(search,)h(usually)h(by)e($-e)n(v)n(aluation.)31 b(W)l(ith)24 b(this)f(parameter)l(,)i(the)e(user)h(can)257 5444 y(specify)37 b(where)f(the)o(y)h(will)e(occur)i(in)f(the)g(symbol) g(ordering.)68 b(If)35 b(there)i(is)f(a)f FD(lex)f FK(command,)39 b(all)257 5557 y(ne)n(w)26 b(symbols)i(will)e(ha)n(v)o(e)h(a)f(le)o (xical)i(v)n(alues)f(between)h(the)f FC(n)p FK(th)f(and)h Fp(\()p FC(n)22 b Fp(+)g(1\))p FK(th)27 b(symbol)h(in)e(the)h FD(lex)257 5670 y FK(command.)35 b(The)25 b(ordering)j(among)e(the)f (ne)n(w)g(symbols)i(is)e(the)h(def)o(ault)h(ordering.)37 b(This)25 b(also)h(applies)1861 5946 y(26)p eop %%Page: 27 33 27 32 bop 257 388 a FK(to)23 b(input)i(symbols)g(not)f(occurring)i(in)d (the)h FD(lex)d FK(command.)257 741 y FJ(7)119 b(Demodulation)257 1008 y FK(Basic)35 b(demodulation)j(is)d(straightforw)o(ard,)41 b(b)n(ut)36 b(there)g(are)f(man)o(y)g(v)n(ariations)i(and)f (enhancements)257 1121 y(whose)e(descriptions)k(are)d(scattered)h 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a Fw(Le)o(x)d Fq($)h Fw(e)n(v)n(aluation)p 1623 2522 V 1640 2522 V 771 w(le)o(x-order)p 2639 2522 V 2656 2522 V 710 w(le)o(x-order)p 3505 2522 V 307 2525 3201 4 v 257 2871 a FI(8.1)99 b(Ad)25 b(Hoc)g(Ordering)257 3106 y FF(8.1.1)92 b(T)-8 b(erm)22 b(Ordering)h(\(Ad)g(Hoc\))257 3340 y FK(T)-7 b(w)o(o)22 b(types)j(of)e(ad)h(hoc)g(term)f(ordering)j(are)e(used:)30 b(le)o(x-order)25 b(and)f(weight-le)o(x-order)-5 b(.)33 b(The)23 b(user)h(does)257 3453 y(not)33 b(ha)n(v)o(e)g(a)f(choice)i (between)g(these)g(tw)o(o;)j(the)c(one)g(that)g(is)f(applied)j(depends) f(on)f(the)g(conte)o(xt,)j(as)257 3566 y(described)26 b(in)d(the)h(follo)n(wing)h(subsections.)257 3811 y FG(le)n(x-or)m(der) -10 b(.)48 b FK(This)33 b(is)g(a)g(basic)h(le)o(xicographic)j(e)o (xtension)e(of)e(the)g(symbol)h(order)-5 b(.)59 b(T)-7 b(o)32 b(compare)i(tw)o(o)484 3924 y(terms,)22 b(one)g(reads)g(them)f (left)h(to)f(right,)h(stopping)i(at)d(the)h(\002rst)f(symbols)h(where)g (the)o(y)g(dif)n(fer;)h(the)484 4037 y(relationship)31 b(of)26 b(those)i(symbols)h(determines)g(the)e(term)g(order)-5 b(.)40 b(The)26 b(treatment)j(of)e(v)n(ariables)484 4150 y(depends)f(on)d(the)h(\003ag)f FD(lex_order_vars)p FK(:)484 4337 y FD(lex)p 654 4337 28 4 v 31 w(order)p 960 4337 V 31 w(vars)e FF(is)i(set.)46 b FK(V)-10 b(ariables)24 b(are)e(the)g(lo)n(west)g(in)f(the)h(symbol)h(ordering,)h(with)e FD(x)e Fv(\036)684 4450 y FD(y)26 b Fv(\036)h FD(z)f Fv(\036)h FD(u)f Fv(\036)h FD(v)f Fv(\036)h FD(w)f Fv(\036)h FD(v6)e Fv(\036)i FD(v7)f Fv(\036)g FD(v8)g Fv(\036)h(\001)15 b(\001)g(\001)h FK(.)40 b(Since)28 b(the)g(order)h(on)e(symbols)i(is) 684 4563 y(total)c(\(an)o(y)g(tw)o(o)f(symbols)h(are)g(comparable\),)h (the)f(le)o(xical)g(order)h(on)e(terms)g(is)h(total)g(\(an)o(y)684 4676 y(tw)o(o)g(terms)g(are)g(comparable\).)35 b(Note)25 b(that)g(applying)j(a)c(substitution)k(to)d(a)g(pair)g(of)g(terms)684 4789 y(may)e(change)j(their)e(relati)n(v)o(e)h(order)-5 b(.)484 4934 y FD(lex)p 654 4934 V 31 w(order)p 960 4934 V 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b(clear)-5 b(.)1861 5946 y(30)p eop %%Page: 31 37 31 36 bop 257 388 a FF(8.1.2)92 b(Orienting)23 b(Equalities)h(\(Ad)e (Hoc\))257 622 y FK(If)32 b(the)i(\003ag)e FD(order_eq)d FK(is)j(set)h(and)h FD(lrpo)c FK(is)j(clear)l(,)j(then)e(equality)h (literals)f(\(both)g(positi)n(v)o(e)h(and)257 735 y(ne)o(gati)n(v)o (e\))24 b(in)g(inferred)h(clauses)h(are)d(processed)j(as)e(follo)n(ws.) 370 983 y(1.)46 b(If)35 b(the)g FD(symbol_elim)29 b FK(\003ag)34 b(is)h(set)g(and)g(if)g(the)g(equality)i(is)e(a)f(symbol-eliminating)39 b(type)484 1096 y(\(Sec.)23 b(6.1.6\),)h(the)f(equality)j(is)d (oriented)j(in)e(the)f(appropriate)k(direction.)370 1283 y(2.)46 b(If)22 b(one)h(ar)n(gument)i(is)d(a)g(proper)i(subterm)g(of)f (the)f(other)i(ar)n(gument,)g(the)f(equality)i(is)d(oriented)j(so)484 1396 y(that)f(the)g(subterm)h(is)e(the)h(right-hand)i(ar)n(gument.)370 1584 y(3.)46 b(If)23 b(one)h(ar)n(gument)h(is)e(greater)i(in)e(the)h (weight-le)o(x-order)l(,)j(say)c FC(\015)31 b Fv(\037)25 b FC(\016)s 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y(demodulator)-5 b(.)370 4306 y(4.)46 b(If)19 b FD(dynamic_demod_l)o(ex)o(_d)o(ep)12 b FK(and)20 b FD(dynamic_demod_)o(al)o(l)12 b FK(are)20 b(both)g(set,)g(if)f FC(\013)g FK(and)484 4419 y FC(\014)27 b FK(are)c(identical-e)o (xcept-v)n(ari)q(abl)q(es)28 b(\(Sec.)22 b(8.1.4\),)h(and)g(if)g FC(v)s(ar)s(s)p Fp(\()p FC(\013)p Fp(\))j Fv(\023)f FC(v)s(ar)s(s)p Fp(\()p FC(\014)5 b Fp(\))p FK(,)22 b(the)h(equality)484 4532 y(becomes)i(a)e(le)o(x-dependent)k(demodulator)-5 b(.)257 4838 y FF(8.1.4)92 b(Lex-dependent)22 b(Demodulation)h(\(Ad)g (Hoc\))257 5072 y FK(T)-7 b(w)o(o)19 b(terms)i(are)f FG(identical-e)n(xcept-v)q(ar)q(iab)q(les)26 b FK(if)21 b(the)o(y)g(are)f(identical)j(after)e(replacing)i(all)e(occurrences)257 5185 y(of)36 b(v)n(ariables)j(with)d FD(x)p FK(.)67 b(An)36 b(input)h(or)g(dynamic)h(demodulator)h(is)d(le)o(x-dependent)41 b(only)c(if)f FC(\013)h FK(and)257 5298 y FC(\014)f FK(are)d (identical-e)o(xcept-v)n(aria)q(ble)q(s.)60 b(\(See)32 b(Sec.)f(8.1.3)i(for)f(determining)j(le)o(x-dependent)h(dynamic)257 5411 y(demodulators.\))31 b(A)19 b(le)o(x-dependent)24 b(demodulator)e(applies)g(to)e(a)g(term)g(only)h(if)e(the)i (replacement)h(term)257 5524 y(is)30 b(smaller)h(in)f(the)h(le)o (x-order)-5 b(.)50 b(In)31 b(particular)l(,)36 b(O)q FE(T)t(T)t(E)t(R)e FK(will)c(apply)h(a)f(le)o(x-dependent)k (demodulator)257 5637 y FC(\013)26 b Fp(=)f FC(\014)i FK(if)d(and)g(only)g(if)f FC(\013\033)29 b Fv(\037)c FC(\014)5 b(\033)26 b FK(in)e(the)g(le)o(x-order)l(,)h(where)f FC(\033)i FK(is)d(the)h(matching)h(substitution.)1861 5946 y(31)p eop %%Page: 32 38 32 37 bop 398 388 a FK(F)o(or)24 b(e)o(xample,)i(in)f(the)g(presence)i (of)e(the)g FD(lex)e FK(command)j(and)f(the)h(\(le)o(x-dependent\))j (demodula-)257 501 y(tors)456 760 y Fq(lex\([a,)49 b(b,)g(c,)g(d,)h (or\(_,_\)]\).)456 959 y(list\(demodulators\).)556 1059 y(or\(x,y\))e(=)i(or\(y,x\).)556 1159 y(or\(x,or\(y,z\)\))d(=)j (or\(y,or\(x,z\)\).)456 1258 y(end_of_list.)257 1531 y FK(the)27 b(term)g FD(or\(or\(d,b\),or\()o(a,)o(c\))o(\))20 b FK(will)26 b(be)h(demodulated)j(to)c FD(or\(a,or\(b,or\(c,d)o(\)\))o (\))257 1644 y FK(\(in)e(se)n(v)o(eral)g(steps\).)257 1953 y FI(8.2)99 b(LRPO)257 2187 y FF(8.2.1)92 b(T)-8 b(erm)22 b(Ordering)h(\()r FE(L)t(R)t(P)t(O)r FF(\))257 2421 y FK(The)g FG(le)n(xico)o(gr)o(aphic)29 b(r)m(ecur)o(sive)d(path)f (or)m(dering)h FK(\()r FE(L)t(R)t(P)t(O)r FK(,)f(or)h FE(R)t(P)t(O)h FK(with)c(status\))j([4)q(,)d(7,)g(9)q(])g(is)h(a)g (method)257 2534 y(for)h(comparing)h(terms.)33 b(The)24 b(important)i(theoretical)i(property)f(of)f FE(L)t(R)t(P)t(O)i FK(is)c(that)h(it)g(is)f(a)h FG(termination)257 2647 y(or)m(dering)p FK(.)30 b(That)22 b(is,)g(let)g FC(R)g FK(be)f(a)h(set)g(of)g(demodulators)j(in)d(which)g(in)g(each)h (demodulator)l(,)i(the)d(left)g(side)257 2760 y(is)30 b FE(L)t(R)t(P)t(O)r FK(-greater)j(than)d(the)f(right)g(side;)k(then)c (demodulation)j(\(applying)g(the)d(demodulators)j(left)d(to)257 2873 y(right\))c(is)e(guaranteed)j(to)e(terminate.)398 3046 y(T)-7 b(o)32 b(use)k FE(L)t(R)t(P)t(O)g FK(one)e(typically)i (uses)e(the)g FD(lex)d FK(command)j(\(Sec.)58 b(5.5\))33 b(to)h(assign)g(an)g(ordering)257 3159 y(on)27 b(constant)h(and)g (function)h(symbols.)39 b(If)26 b(the)h FD(lex)e FK(command)i(is)g(not) g(present,)k(O)q FE(T)t(T)t(E)t(R)f FK(assigns)f(an)257 3272 y(ordering)d(\(which)g(is)e(frequently)j(inef)n(fecti)n(v)o(e\).) 34 b(\()r(O)q FE(T)t(T)t(E)t(R)29 b FK(uses)c(a)f(total)h(ordering)i (on)d(symbols)i(that)f(is)257 3385 y(\002x)o(ed)k(at)h(input)h(time.)48 b(Other)30 b(implementations)j(of)f FE(L)t(R)t(P)t(O)h FK(use)e(partial)g(orderings)h(or)e(dynamically)257 3498 y(changing)c(orderings.\))398 3671 y(W)l(ith)d(respect)h(to)g FE(L)t(R)t(P)t(O)r FK(,)f(function)i(symbols)e(can)g(ha)n(v)o(e)g (either)h FG(left-to-right)h(status)f FK(\(the)f(def)o(ault\))257 3783 y(or)e FG(multiset)i(status)p FK(.)30 b(The)21 b(command)h FD(lrpo)p 1691 3783 28 4 v 31 w(multiset)p 2162 3783 V 29 w(status\()p FG(symbol)p 2832 3783 V 31 w(list)p FD(\))g FK(gi)n(v)o(es)g(symbols)257 3896 y(multiset)j(status.)400 4069 y(L)t FE(R)t(P)t(O)e FK(comparison)g(is)d(used)i(when)f(orienting) i(equality)g(literals,)f(deciding)h(whether)f(an)f(equality)257 4182 y(should)f(be)f(a)f(demodulator)j(or)d(an)j FE(L)t(R)t(P)t(O)r FK(-dependent)j(demodulator)l(,)e(and)d(deciding)i(whether)e(to)g (apply)257 4295 y(an)38 b FE(L)t(R)t(P)t(O)r FK(-dependent)j (demodulator)-5 b(.)71 b(L)t FE(R)t(P)t(O)38 b FK(comparison)g(is)e(ne) n(v)o(er)g(used)h(when)f(e)n(v)n(aluating)j(the)257 4408 y(functions/predicate)q(s)29 b(that)24 b(perform)g(le)o(xical)h (comparison)h(\()p FD($LLT)p FK(,)21 b FD($LGT)p FK(,)g(etc.\).)257 4714 y FF(8.2.2)92 b(Orienting)23 b(Equalities)h(\()r FE(L)t(R)t(P)t(O)r FF(\))257 4948 y FK(If)c(the)h(\003ag)g FD(order_eq)16 b FK(is)21 b(set)g(and)g(if)f(one)h(ar)n(gument)i(of)e (the)g(equality)i(literal)f(\(positi)n(v)o(e)g(or)f(ne)o(gati)n(v)o (e\))257 5061 y(is)f(greater)h(in)f(the)i FE(L)t(R)t(P)t(O)h FK(order)l(,)f(the)e(greater)i(ar)n(gument)g(is)e(placed)h(on)f(the)g (left)h(side.)28 b(This)20 b(rule)g(applies)257 5174 y(to)g(input)h(demodulators,)j(to)c(inferred)i(clauses,)g(and,)f(if)f (the)g(\003ag)g FD(process_input)13 b FK(is)20 b(set,)h(to)f(input)257 5287 y FD(usable)g FK(and)k FD(sos)d FK(clauses.)1861 5946 y(32)p eop %%Page: 33 39 33 38 bop 257 388 a FF(8.2.3)92 b(Determining)23 b(Dynamic)g (Demodulators)h(\()r FE(L)t(R)t(P)t(O)r FF(\))257 622 y FK(If)e(the)i(\003ag)e FD(dynamic_demod)16 b FK(is)23 b(set,)i(O)q FE(T)t(T)t(E)t(R)i FK(attempts)d(to)f(mak)o(e)g(all)g (equalities)i(into)f(demodula-)257 735 y(tors)i(\()p FD(dynamic_demod_al)o(l)19 b FK(is)26 b(ignored)h(when)f FD(lrpo)e FK(is)h(set\).)37 b(If)25 b FC(\013)30 b Fv(\037)g FC(\014)g FK(in)c(the)i FE(L)t(R)t(P)t(O)h FK(order)l(,)257 848 y(the)j(deri)n(v)o(ed)h(equality)i(becomes)e(a)f(demodulator)i(\()p FC(\013)e FK(is)g(not)j FE(L)t(R)t(P)t(O)r FK(-less-than)h FC(\014)5 b FK(,)33 b(because)h(orient-)257 961 y(ing)29 b(has)g(already)h(occurred\).)47 b(If)28 b FD(dynamic_demod_l)o(ex_)o (de)o(p)22 b FK(is)28 b(set,)i(if)e(neither)j(ar)n(gument)f(is)259 1074 y FE(L)t(R)t(P)t(O)r FK(-less-than)c(the)c(other)l(,)h(and)f(if)f (e)n(v)o(ery)h(v)n(ariable)i(that)e(occurs)h(in)f FC(\014)k FK(also)c(occurs)h(in)e FC(\013)p FK(,)h(the)g(deri)n(v)o(ed)257 1187 y(equality)j(becomes)g(an)h FE(L)t(R)t(P)t(O)r FK(-dependent)i (demodulator)-5 b(.)257 1493 y FF(8.2.4)94 b FE(L)t(R)t(P)t(O)r FF(-dependent)23 b(Demodulation)h(\()r FE(L)t(R)t(P)t(O)r FF(\))257 1727 y FK(An)j FE(L)t(R)t(P)t(O)r FK(-dependent)j (demodulator)f(is)c(allo)n(wed)i(to)e(re)n(write)i(a)e(term)g(if)h(and) g(only)h(if)e(its)h(application)257 1840 y(produces)g(an)f FE(L)t(R)t(P)t(O)r FK(-less-than)j(term.)257 2149 y FI(8.3)99 b(Knuth-Bendix)27 b(Completion)257 2383 y FK(The)i(Knuth-Bendix)j (completion)g(procedure)g([12)q(])d(attempts)i(to)e(transform)i(a)e (set)h FC(E)k FK(of)29 b(equalities)257 2496 y(into)d(a)g(terminating,) i(canonical)g(set)e(of)g(re)n(write)g(rules)h(\(demodulators\).)39 b(If)26 b(it)f(is)h(successful,)j(the)d(re-)257 2609 y(sulting)d(set)f(of)f(re)n(write)h(rules,)h(a)e FG(complete)i(set)e (of)h(r)m(eductions)p FK(,)i(is)d(a)g(decision)j(procedure)g(for)e (equality)257 2722 y(of)k(terms)h(in)f(the)h(theory)h FC(E)5 b FK(.)37 b(There)27 b(are)f(man)o(y)h(v)n(ariations)i(and)e (re\002nements)g(of)g(the)g(Knuth-Bendix)257 2835 y(procedure.)398 3008 y(Setting)21 b(either)g(of)e(the)h(\003ags)g FD(anl_eq)c FK(or)k FD(knuth_bendix)13 b FK(causes)24 b(O)q FE(T)t(T)t(E)t(R)f FK(to)d(automatically)257 3121 y(alter)27 b(a)f(set)h(of)f(options)j (so)d(that)h(its)g(search)h(will)e(beha)n(v)o(e)i(lik)o(e)f(a)f (Knuth-Bendix)j(completion)g(proce-)257 3234 y(dure.)i(If)26 b(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)26 b(search)g(stops)f(because)h (its)e FD(sos)e FK(list)i(is)g(empty)-6 b(,)25 b(and)f(if)g(certain)i (other)f(conditions)257 3347 y(are)e(met,)g(then)h(the)f(resulting)j (set)d(of)g(equalities)j(should)f(be)e(a)g(complete)i(set)e(of)g (reductions.)32 b(\()r(O)q FE(T)t(T)t(E)t(R)257 3460 y FK(w)o(as)26 b(not)h(designed)j(to)c(implement)i(a)e(completion)k (procedure,)g(and)d(it)f(has)h(not)h(been)f(optimized)i(for)257 3572 y(completion.\))257 3745 y FG(Conjectur)m(e)p FK(.)58 b(If)32 b(\(1\))h(the)f(set)h FC(E)k FK(of)c(equalities,)k(along)d (with)e FD(x=x)p FK(,)h(is)f(input)i(in)e(list)h FD(sos)p FK(,)g(\(2\))f(\003ag)257 3858 y FD(anl_eq)17 b FK(is)k(set,)h(\(3\))f (other)h(options)h(that)f(are)f(changed)i(from)e(the)h(def)o(aults)h (do)e(not)h(af)n(fect)g(the)f(search,)257 3971 y(\(4\))33 b(O)q FE(T)t(T)t(E)t(R)h FK(stops)e(with)f(\223sos)g(empty\224,)i(and)e (\(5\))g(other)h(than)f FD(x=x)p FK(,)f(the)h(\002nal)g FD(usable)c FK(list)k(is)g(the)257 4084 y(same)24 b(as)h(the)g(\002nal) f FD(demodulators)18 b FK(list,)25 b(then)g(the)g FD(demodulators)18 b FK(list)25 b(is)f(a)g(complete)i(set)f(of)257 4197 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Fk(2)1405 3657 y FK(;)c(if)g(the)h(result)g(is)g(neither)h FD($T)c FK(nor)j FD($F)p FK(,)d(demodulation)28 b(returns)e(to)484 3770 y(its)g(normal)g(beha)n(vior)-5 b(.)36 b(Note)26 b(that)g(if)f(the)g(condition)k(e)n(v)n(aluates)e(to)e(a)g(Boolean)i(v) n(alue,)f(demod-)484 3883 y(ulation)g(de)n(viates)f(from)f(its)g (inside-out)j(beha)n(vior)l(,)f(because)g(just)e(one)h(of)e FC(t)2883 3897 y Fk(1)2946 3883 y FK(and)h FC(t)3133 3897 y Fk(2)3195 3883 y FK(is)g(demod-)484 3996 y(ulated.)40 b(\(If)27 b(demodulation)k(were)26 b(al)o(w)o(ays)i(outside-in,)j FD($IF)24 b FK(w)o(ould)k(not)f(need)h(to)f(be)g(b)n(uilt)h(in)484 4109 y(because)g(it)e(could)i(be)e(ef)n(\002ciently)i(de\002ned)f(with) f(the)h(tw)o(o)f(demodulators)j FD(if\($T,x,y\)=x)484 4222 y FK(and)24 b FD(if\($F,x,y\)=y)p FK(.\))393 4410 y Fv(\017)46 b FC(ter)s(m)18 b Fv(\002)f FC(ter)s(m)25 b Fv(!)g FC(bool)f FK(\(le)o(xical\).)31 b(These)23 b(operations)j(are) d(analogous)j(to)d(the)g(six)g(operations)484 4522 y(in)31 b FC(int)25 b Fv(\002)g FC(int)38 b Fv(!)h FC(bool)32 b FK(e)o(xcept)g(that)f(the)g(comparisons)j(are)c(le)o(xical)i(instead) h(of)d(arithmetic.)484 4635 y(The)h(symbol)h FD($ID)d FK(tests)k(identity)g(of)e(terms.)53 b(The)30 b(le)o(xical)j (comparison)h(is)d(the)g(same)h(as)f(in)484 4748 y(le)o(x-dependent)c (demodulation;)f(in)d(particular)l(,)j(the)d(\003ag)g FD(lex_order_vars)15 b FK(\(Secs.)29 b(6.1.6)484 4861 y(and)24 b(8.1.1\))g(is)f(consulted)j(during)g(these)e(operations.)393 5049 y Fv(\017)46 b FC(ter)s(m)5 b Fv(\002)g FC(ter)s(m)23 b Fv(!)j FC(bool)20 b FK(\(other\).)29 b(The)19 b(term)g FD($OCCURS\()p FC(t)2392 5063 y Fk(1)2428 5049 y FD(,)p FC(t)2516 5063 y Fk(2)2555 5049 y FD(\))f FK(is)h(true)h(if)f FC(t)2974 5063 y Fk(1)3032 5049 y FK(is)g(a)g(subterm)h(of)484 5162 y FC(t)517 5176 y Fk(2)556 5162 y FK(,)25 b(including)j(the)e (case)g(when)f(the)o(y)h(are)f(the)h(same.)34 b(The)25 b(term)g FD($VOCCURS\()p FC(t)3089 5176 y Fk(1)3124 5162 y FD(,)p FC(t)3212 5176 y Fk(2)3251 5162 y FD(\))f FK(is)h(true)484 5275 y(if)20 b FC(t)592 5289 y Fk(1)650 5275 y FK(is)f(a)h(v)n(ariable) h(that)g(occurs)g(in)e FC(t)1632 5289 y Fk(2)1672 5275 y FK(.)26 b(The)20 b(term)f FD($VFREE\()p FC(t)2485 5289 y Fk(1)2521 5275 y FD(,)p FC(t)2609 5289 y Fk(2)2648 5275 y FD(\))g FK(is)g(true)i(if)e FC(t)3069 5289 y Fk(1)3127 5275 y FK(is)h(a)f(v)n(ariable)484 5388 y(that)30 b(does)g(not)g(occur) h(in)e FC(t)1352 5402 y Fk(2)1391 5388 y FK(.)46 b(The)29 b(term)g FD($RENAME\()p FC(t)2298 5402 y Fk(1)2334 5388 y FD(,)p FC(t)2422 5402 y Fk(2)2460 5388 y FD(\))g FK(is)g(true)h(if)f FC(t)2920 5402 y Fk(1)2988 5388 y FK(and)h FC(t)3181 5402 y Fk(2)3249 5388 y FK(ha)n(v)o(e)g(the)484 5500 y(same)24 b(structure;)i(that)e(is,)f(if)g(we)g(rename)h(all)g(v)n (ariables)h(to)f FC(x)p FK(,)e(the)i(terms)g(are)g(identical.)1861 5946 y(36)p eop %%Page: 37 43 37 42 bop 393 388 a Fv(\017)46 b FC(ter)s(m)d Fv(!)h FC(bool)r FK(.)58 b(A)33 b(term)g(is)h FD($ATOMIC)29 b FK(if)n(f)34 b(it)f(is)g(a)h(constant)h(\(including)i(inte)o(ger)e (and)f(bit)484 501 y(string\),)g(a)d(term)g(is)f(a)h FD($INT)d FK(if)n(f)j(it)g(is)f(an)h(inte)o(ger)l(,)k(a)30 b(term)h(is)g(a)f FD($BITS)e FK(if)n(f)j(it)g(is)f(a)h(string)h(of)484 614 y Fv(f)p FK(0,1)p Fv(g)p FK(,)24 b(a)g(term)f(is)h(a)f FD($VAR)f FK(if)n(f)h(it)h(is)f(a)h(\(unbound\))i(v)n(ariable,)g(and)e (a)f(term)h(is)g(a)f FD($GROUND)d FK(if)n(f)j(it)484 727 y(does)h(not)g(contain)i(an)o(y)d(v)n(ariables.)393 914 y Fv(\017)46 b(!)27 b FC(int)p FK(.)i(The)24 b(term)g FD($NEXT_CL_NUM)18 b FK(\(no)25 b(ar)n(guments\))h(e)n(v)n(aluates)h (to)d(the)g(ne)o(xt)h(inte)o(ger)g(that)484 1027 y(will)31 b(be)h(assigned)i(as)d(a)g(clause)i(identi\002er)g(\(this)g(is)e (useful)i(for)f(placing)h(the)f(ID)f(of)g(a)h(clause)484 1140 y(within)g(the)f(clause\).)54 b(A)30 b(sequence)k(of)d(calls)h(to) f FD($UNIQUE_NUM)26 b FK(\(no)32 b(ar)n(guments\))h(returns)484 1253 y Fp([1)p FC(;)15 b Fp(2)p FC(;)g Fp(3)p FC(;)g Fv(\001)g(\001)g(\001)k Fp(])p FK(.)398 1499 y(Ev)n(aluation)31 b(occurs)g(as)e(part)h(of)f(the)h(demodulation)i(process.)48 b(In)29 b(particular)l(,)34 b(if)29 b(demodulation)257 1612 y(comes)j(across)i(an)e(e)n(v)n(aluable)i(term,)g(say)f FD($SUM\(2,3\))p FK(,)c(it)j(tries)g(to)h(con)l(v)o(ert)h(the)e(ar)n (guments)i(into)257 1725 y(the)g(appropriate)i(type)e(\(inte)o(gers)i (for)e FD($SUM)p FK(\);)d(then)j(if)f(the)h(ar)n(guments)i(ha)n(v)o(e)e (the)g(correct)h(type,)h(it)257 1838 y(re)n(writes)h(the)g(term)g(to)f (the)h(result)h(of)f(the)g(operation,)42 b(in)37 b(this)g(case,)j(just) d(as)g(if)f(the)h(demodulator)257 1951 y FD($SUM\(2,3\)=5)26 b FK(had)32 b(been)h(present.)56 b(The)32 b(e)n(v)n(aluation)i (mechanisms,)i(along)d(with)f(ordinary)i(de-)257 2064 y(modulation,)e(form)d(a)g(reasonably)j(complete)e(\(although)i(not)d (particularly)j(speedy)f(or)e(con)l(v)o(enient\))257 2177 y(equational)d(programming)g(subsystem.)398 2349 y(Ev)n(aluation/demodulation)33 b(can)28 b(also)f(occur)l(,)j(in)d(a)f (v)o(ery)i(particular)i(w)o(ay)-6 b(,)27 b(during)i(hyperresolu-)257 2462 y(tion.)45 b(\(Recall)29 b(that)g(hyperresolution)k(tak)o(es)d(a)e (clause,)j(the)e FG(nucleus)p FK(,)j(with)c(some)h(ne)o(gati)n(v)o(e)h (literals,)257 2575 y(the)24 b(conditions,)k(and)c(resolv)o(es)i(each)g (ne)o(gati)n(v)o(e)f(literal)g(with)f(a)g(positi)n(v)o(e)i(clause,)g (producing)h(a)d(clause)257 2688 y(with)35 b(no)g(ne)o(gati)n(v)o(e)h (literals.\))65 b(Just)36 b(as)f(e)n(v)n(aluation)i(during)g (demodulation)h(can)e(be)f(thought)i(of)e(as)257 2801 y(re)n(writing)c(with)e(an)g(implicit)i(demodulator)l(,)j(e)n(v)n (aluation)e(during)f(hyperresolution)j(can)29 b(be)h(thought)257 2914 y(of)25 b(resolving)k(with)c(the)h(implicit)h(positi)n(v)o(e)g (unit)g(clause)g FD($T)d FK(\(meaning)j(\223true\224\).)37 b(The)25 b(mechanism)i(is)257 3027 y(this:)i(if)21 b(hyperresolution)26 b(encounters)f(a)d(ne)o(gati)n(v)o(e)g(literal)h(that)f(has)h(an)e(e)n (v)n(aluable)j(predicate)g(symbol,)257 3140 y(then)g(it)f(demodulates)j (the)d(atom)g(\(the)h(literal)g(without)h(the)e(sign\);)i(if)d(the)i (result)g(of)f(the)h(demodulation)257 3253 y(is)f FD($T)p FK(,)f(then)i(the)g(literal)h(is)e(considered)k(to)c(ha)n(v)o(e)h(been) h(resolv)o(ed.)398 3426 y(During)39 b(hyperresolution,)45 b(demodulation/e)n(v)n(aluat)q(ion)f(is)38 b(triggered)i(by)f(the)f (presence)i(of)e(an)257 3539 y(e)n(v)n(aluable)33 b(literal.)54 b(In)32 b(man)o(y)f(cases,)j(ho)n(we)n(v)o(er)l(,)g(the)e(user)g (de\002nes)g(a)g(Boolean)g(function)i(to)d(trigger)257 3651 y(the)c(mechanism.)39 b(Consider)28 b(the)f(follo)n(wing)i (de\002nition)f(of)f(list)g(membership,)i(written)e(as)g(demodu-)257 3764 y(lators:)456 4022 y Fq(member\(x,[]\))48 b(=)h($F.)456 4122 y(member\(x,[y|z]\))e(=)j($IF\($ID\(x,y\),)1602 4222 y($T,)1602 4321 y(member\(x,y\)\).)257 4592 y FK(Because)37 b(the)g(symbol)g FD(member)c FK(is)j(not)h(e)n(v)n(aluable,)k(the)c (demodulation/e)n(v)n(aluatio)q(n)42 b(mechanism)257 4705 y(will)32 b(not)h(be)g(acti)n(v)n(ated;)39 b(ho)n(we)n(v)o(er)l(,) d(the)d(unary)g(e)n(v)n(aluable)i(predicate)g FD($TRUE)30 b FK(can)j(be)g(used)g(in)g(the)257 4818 y(follo)n(wing)25 b(w)o(ay)e(to)h(trigger)h(demodulation/e)n(v)n(aluatio)q(n.)484 5051 y Fo(\000)p Fn(L)606 5063 y Fd(1)692 5051 y Fq(|)50 b Fo(\001)14 b(\001)g(\001)63 b Fq(|)50 b(-$TRUE\(member\()p Fi(element)p Fq(,)c Fi(list)p Fq(\)\))k(|)g Fo(\001)14 b(\001)g(\001)63 b Fq(|)50 b Fo(\000)p Fn(L)2840 5063 y Fc(n)2934 5051 y Fq(|)g Fn(M)9 b Fw(.)257 5298 y FK(Ev)n(aluable)35 b(functions)i(and)d(predicates)j(are)d(useful)i(to)e(implement)h(forw)o (ard-chaining)j(rule-based)257 5411 y(systems,)24 b(for)g(e)o(xample,)g (state-space)j(search)d(problems)i(\(Sec.)d(9.2\).)398 5584 y(Hyperresolution)h(operates)d(on)f(the)g(conditions)i(\(ne)o (gati)n(v)o(e)f(literals\))g(in)f(order)l(,)h(left)f(to)g(right.)28 b(\(The)257 5697 y(preceding)23 b(sentence)g(is)e(not)g(quite)h(true)f (because)i(the)e(\002rst)f(step)h(is)g(typically)i(resolution)h(of)c(a) h(positi)n(v)o(e)1861 5946 y(37)p eop %%Page: 38 44 38 43 bop 257 388 a FK(gi)n(v)o(en)22 b(clause)g(with)f(an)o(y)g(one)h (of)f(the)h(conditions,)i(b)n(ut)e(for)f(this)h(paragraph,)i(we)d(may)f (assume)i(that)g(it)f(is)257 501 y(true.\))29 b(If)23 b(a)g(literal)i(resolv)o(es)g(or)e(e)n(v)n(aluates,)i(the)f(ne)o(xt)f (literal)i(is)e(considered.)32 b(If)23 b(nothing)i(more)e(can)h(be)257 614 y(done)j(with)f(a)f(literal,)j(then)f(hyperresolution)j(backtracks) f(to)d(the)h(preceding)h(literal)g(in)e(search)h(of)f(an)257 727 y(alternati)n(v)o(e.)k(When)20 b(a)f(nucleus)j(contains)h(e)n(v)n (aluable)f(conditions,)h(the)d(order)h(of)f(the)h(conditions)i(is)d (im-)257 840 y(portant)27 b(both)g(for)e(ef)n(\002cienc)o(y)i(and)f (for)g(actually)h(deri)n(ving)h(hyperresolv)o(ents.)39 b(Ev)n(aluable)27 b(conditions)257 953 y(typically)k(ha)n(v)o(e)e(v)n (ariables)h(that)f(must)g(be)f(instantiated)k(when)d(none)n(v)n (aluable)j(literals)e(are)e(resolv)o(ed.)257 1065 y(If)e(an)h(e)n(v)n (aluable)h(literal)g(is)f(too)g(f)o(ar)g(to)f(the)h(left,)h(its)e(v)n (ariables)j(will)d(not)h(be)g(suf)n(\002ciently)i(instantiated)257 1178 y(when)f(hyperresolution)k(encounters)f(it,)e(e)n(v)n(aluation)h (will)e(f)o(ail,)h(and)g(possible)h(paths)f(to)f(hyperresol-)257 1291 y(v)o(ents)c(will)f(be)g(block)o(ed.)31 b(If)23 b(an)g(e)n(v)n(aluable)i(literal)f(is)g(too)f(f)o(ar)h(to)f(the)g (right,)h(then)g(hyperresolution)k(can)257 1404 y(e)o(xplore)d(man)o(y) e(paths)i(that)f(are)g(sure)g(to)f(f)o(ail.)257 1577 y FG(T)-8 b(ec)o(hnical)33 b(Note)f(and)h(Advice)o(.)54 b FK(The)32 b(e)n(v)n(aluable)i(symbols)g(are)e(an)g(add-on)i(feature)g (rather)f(than)g(an)257 1690 y(inte)o(gral)25 b(part)g(of)h(O)q FE(T)t(T)t(E)t(R)r FK(.)32 b(In)24 b(particular)l(,)i(the)f(objects)g (that)g(are)f(manipulated)j(\(inte)o(gers,)e(bit)g(strings,)257 1803 y(etc.\))37 b(in)26 b(most)g(cases)h(are)f(stored)i(by)g(O)q FE(T)t(T)t(E)t(R)i 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FK(-symbol)i(to)e(an)o(y)h(other)h(symbol)257 3821 y(of)g(the)h(same)g(arity)-6 b(.)29 b(The)23 b(form)h(of)f(the)h (command)g(is)484 4056 y Fq(make)p 689 4056 25 4 v 29 w(evaluable\()p Fl(any-symbol)p Fq(,)p Fl(evaluable-symbo)o(l)p Fq(\).)257 4303 y FK(The)e(symbols)j(in)e(the)g(command)h(are)f(gi)n(v) o(en)g(dummy)g(ar)n(guments)j(to)c(specify)j(the)e(arity)-6 b(.)30 b(The)22 b(follo)n(w-)257 4416 y(ing)27 b(list)h(contains)h (typical)g(e)o(xamples)g(for)e(inte)o(ger)i(arithmetic)g(\(assuming)g (the)e(symbols)i(on)e(the)h(left)257 4529 y(are)c(already)h(kno)n(wn)f (to)f(be)h(in\002x\).)484 4763 y Fq(make_evaluable\(_+_,)46 b($SUM\(_,_\)\).)484 4863 y(make_evaluable\(_-_,)g($DIFF\(_,_\)\).)484 4963 y(make_evaluable\(_>_,)g($GT\(_,_\)\).)484 5062 y(make_evaluable\(_>=_,)g($GE\(_,_\)\).)257 5370 y FG(W)-8 b(arning)55 b(1.)121 b FK(If)54 b(a)g(binary)i(symbol)f(that)g(is)g (recognized)i(by)e(paramodulation)j(or)c(demod-)257 5483 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y(gt_list\(z,[]\))e(=)h([].)356 4007 y(gt_list\(z,[x|y]\))e(=)j ($IF\($LGT\(x,z\),)1552 4107 y([x|gt_list\(z,y\)],)1552 4206 y(gt_list\(z,y\)\).)257 4512 y FF(A)35 b(State-Space)j(Sear)n(ch.) 92 b FK(Here)36 b(is)h(a)f(complete)k(O)q FE(T)t(T)t(E)t(R)h FK(input)d(\002le)e(for)h(a)g(simple)g(state-space)257 4625 y(search.)257 4884 y Fq(\045)49 b(We)h(have)f(a)h(3-gallon)e(jug)h (and)g(a)h(4-gallon)e(jug,)h(both)g(empty,)257 4984 y(\045)g(and)h(a)f (well.)g(Our)g(goal)h(is)f(to)g(have)g(exactly)g(2)h(gallons)e(in)i (the)257 5084 y(\045)f(4-gallon)g(jug.)99 b(We)49 b(can)g(fill)g(a)h (jug)f(from)g(the)h(well,)e(empty)h(a)257 5183 y(\045)g(jug)h(onto)f (the)g(ground,)g(and)g(carefully)f(pour)h(water)g(from)g(one)257 5283 y(\045)g(jug)h(into)f(the)g(other.)257 5382 y(\045)257 5482 y(\045)g(j\(m,)h(n\))f(is)g(the)h(state)f(in)g(which)g(the)g (3-gallon)f(jug)i(contains)257 5582 y(\045)f(m)h(gallons,)e(and)i(the)f (4-gallon)f(jug)h(contains)g(n)g(gallons.)1861 5946 y FK(39)p eop %%Page: 40 46 40 45 bop 257 388 a Fq(set\(hyper_res\).)257 587 y (make_evaluable\(_+_,)46 b($SUM\(_,_\)\).)257 687 y (make_evaluable\(_-_,)g($DIFF\(_,_\)\).)257 786 y (make_evaluable\(_<=_,)g($LE\(_,_\)\).)257 886 y(make_evaluable\(_>_,)g ($GT\(_,_\)\).)257 1085 y(list\(usable\).)257 1185 y(-j\(x,)j(y\))g(|)h (j\(3,)f(y\).)99 b(\045)50 b(fill)f(the)g(3-gallon)f(jug)257 1285 y(-j\(x,)h(y\))g(|)h(j\(0,)f(y\).)99 b(\045)50 b(empty)e(the)i (3-gallon)e(jug)257 1384 y(-j\(x,)h(y\))g(|)h(j\(x,)f(4\).)99 b(\045)50 b(fill)f(the)g(4-gallon)f(jug)257 1484 y(-j\(x,)h(y\))g(|)h (j\(x,)f(0\).)99 b(\045)50 b(empty)e(the)i(4-gallon)e(jug)257 1583 y(-j\(x,)h(y\))g(|)h(-\(x+y)f(<=)g(4\))h(|)f(j\(0,)g(y+x\).)248 b(\045)50 b(small)f(->)g(big;)g(it)h(fits)257 1683 y(-j\(x,)f(y\))g(|)h (-\(x+y)f(>)99 b(4\))50 b(|)f(j\(x-)g(\(4-y\),4\).)f(\045)i(small)f(->) g(big,)g(until)g(full)257 1783 y(-j\(x,)g(y\))g(|)h(-\(x+y)f(<=)g(3\))h (|)f(j\(x+y,)g(0\).)248 b(\045)50 b(big)f(->)h(small;)e(it)i(fits)257 1882 y(-j\(x,)f(y\))g(|)h(-\(x+y)f(>)99 b(3\))50 b(|)f(j\(3,y-)g (\(3-x\)\).)f(\045)i(big)f(->)h(small,)e(until)h(full)257 2082 y(-j\(x,)g(2\).)99 b(\045)49 b(goal)g(state)g(---)h(4-gallon)e (jug)h(containing)f(2)i(gallons)257 2181 y(end_of_list.)257 2380 y(list\(sos\).)257 2480 y(j\(0,)f(0\).)149 b(\045)49 b(initial)g(state)g(---)g(both)g(jugs)g(empty)257 2580 y(end_of_list.)257 2932 y FJ(10)119 b(W)-8 b(eighting)259 3199 y FK(O)q FE(T)t(T)t(E)t(R)25 b FK(recognizes)f(four)e(lists)g(of)f (weight)h(templates.)30 b(\(See)21 b(Sec.)f(5.4)i(for)f(input)i(of)e (weight)h(template)257 3312 y(lists.\))257 3579 y FD(weight)p 592 3579 28 4 v 30 w(list\(pick)p 1117 3579 V 28 w(given\).)43 b FK(This)24 b(list)h(is)f(used)h(for)f(selection)j(of)d(gi)n(v)o(en)h (clauses)h(from)f(list)484 3692 y FD(sos)p FK(.)i(When)c(the)h(weight)g (of)g(a)f(clause)i(is)e(printed,)i(it)f(is)f(the)h FD(pick_given)18 b FK(weight.)257 3878 y FD(weight)p 592 3878 V 30 w(list\(purge)p 1172 3878 V 28 w(gen\).)43 b FK(This)29 b(list)g(is)g(used)h(in)f (conjunction)j(with)d(the)g FD(max_weight)484 3991 y FK(parameter)c(to)f(discard)h(generated)h(clauses.)257 4177 y FD(weight)p 592 4177 V 30 w(list\(pick)p 1117 4177 V 28 w(and)p 1310 4177 V 32 w(purge\).)42 b FK(In)i(man)o(y)f (cases,)49 b(one)c(can)f(use)g(the)f(same)h(weight-)484 4290 y(ing)37 b(strate)o(gy)h(for)f(both)h(selecting)h(gi)n(v)o(en)e (clauses)h(and)f(pur)n(ging)i(generated)h(clauses.)69 b(The)484 4403 y FD(pick_and_purge)34 b FK(list)41 b(serv)o(es)h(the)f (purposes)j(of)d(both)g(the)h FD(pick_given)35 b FK(and)42 b(the)484 4516 y FD(purge_gen)f FK(lists.)94 b(If)46 b(the)f FD(pick_and_purge)38 b FK(list)46 b(is)f(present,)53 b(then)46 b(neither)h(the)484 4629 y FD(pick_given)18 b FK(nor)24 b(the)g FD(purge_gen)19 b FK(list)24 b(may)f(be)g(present.) 257 4815 y FD(weight)p 592 4815 V 30 w(list\(terms\).)40 b FK(This)24 b(list)h(is)f(for)h(calculating)j(the)c(weight)h(of)g (terms)f(when)h(using)h(the)484 4928 y(weight-le)o(x-order)31 b(\(Sec.)d(8.1.1\))g(to)f(compare)i(terms.)41 b(This)28 b(occurs)h(when)f(the)g(\003ag)f FD(lrpo)e FK(is)484 5041 y(clear)f(when)g(orienting)i(equality)g(literals)f(\(Secs.)k (8.1.2)23 b(and)h(8.1.3\).)257 5349 y FI(10.1)99 b(W)-6 b(eighing)24 b(Clauses)g(and)i(Literals)257 5584 y FK(The)20 b(weight)i(of)e(a)h(clause)h(is)f(al)o(w)o(ays)g(the)g(sum)g(of)g(the)g (weights)h(of)f(its)f(literals)j(\(e)o(xcluding)g(an)o(y)e(answer)257 5697 y(literals\).)32 b(The)23 b(weight)i(of)f(a)f(positi)n(v)o(e)i (literal)h(is)d(the)i(weight)f(of)g(its)g(atom.)30 b(The)23 b(weight)i(of)f(a)f(ne)o(gati)n(v)o(e)1861 5946 y(40)p eop %%Page: 41 47 41 46 bop 257 388 a FK(literal)25 b(is)e(the)h(weight)g(of)f(its)h (atom)g(plus)g(the)g(v)n(alue)g(of)g(the)f FD(neg_weight)c FK(parameter)25 b(\(Sec.)e(6.2.5\).)257 691 y FI(10.2)99 b(W)-6 b(eighing)24 b(Atoms)g(and)i(T)-9 b(erms)257 925 y FK(Atoms)27 b(and)h(terms)g(are)g(weighed)h(top-do)n(wn.)42 b(T)-7 b(o)27 b(weigh)h(a)f(gi)n(v)o(en)h(term,)j(O)q FE(T)t(T)t(E)t(R)g FK(searches)f(the)e(ap-)257 1038 y(propriate)c (weight)e(list)g(\(in)g(the)g(order)h(input\))g(for)f(the)g(\002rst)f (matching)i(template.)30 b(If)21 b(a)g(match)h(is)g(found,)257 1151 y(then)32 b(the)g(subterms)h(of)e(the)h(gi)n(v)o(en)g(term)f(that) h(match)g(the)g(inte)o(gers)h(in)e(the)h(template)g(are)g(weighed.)257 1264 y(The)27 b(weight)h(of)f(the)h(gi)n(v)o(en)f(term)h(is)f(the)g (sum)g(of)h(the)f(products)j(of)d(each)h(inte)o(ger)h(and)f(the)f (weight)h(of)257 1376 y(its)d(corresponding)k(subterm,)d(plus)g(the)f (second)h(ar)n(gument)h(of)e(the)g(weight)g(template.)34 b(F)o(or)24 b(e)o(xample,)257 1489 y(the)g(template)484 1704 y FD(weight\(f\(g\($\(2\))o(\),)o($\()o(-3\))o(\),)48 b(-50\).)257 1918 y FK(matches)24 b(the)g(gi)n(v)o(en)g(term)484 2132 y FD(f\(g\(h\(a\)\),f\(b,x)o(\)\))o(.)257 2346 y FK(Let)f FC(w)r(t)p Fp(\()p FC(t)p Fp(\))g FK(be)h(the)g(weight)g(of)f (term)h(or)f(atom)h FC(t)p FK(.)j(Then)484 2560 y FC(w)r(t)p Fp(\()p FD(f\(g\(h\(a\)\),f\(b,x\)\))-7 b Fp(\))26 b(=)f(2)r Fv(\003)r FC(w)r(t)p Fp(\()p FD(h\(a\))p Fp(\))r(+)r(\()p Fv(\000)p Fp(3\))r Fv(\003)r FC(w)r(t)p Fp(\()p FD(f\(b,x\))q Fp(\))r(+)r(\()p Fv(\000)p Fp(50\))p FK(.)257 2774 y(If)45 b(a)f(matching)j(weight)f(template)h(is)e(not)g(found,)52 b(then)46 b(the)f(weight)h(of)f(the)h(gi)n(v)o(en)f(term)g(is)g(1)257 2887 y(plus)33 b(the)f(sum)g(of)g(the)g(weights)i(of)e(the)g(subterms.) 56 b(\(See)32 b(the)g(\003ags)g FD(atom_wt_max_args)25 b FK(and)257 3000 y FD(term_wt_max_ar)o(gs)p FK(,)e(Sec.)28 b(6.1.10,)i(for)f(o)o(v)o(errides.\))47 b(Note)28 b(that)i(this)f (weighting)i(scheme)f(im-)257 3113 y(plies)j(that)f(if)g(no)g(weight)g (templates)i(are)e(present,)k(the)c(def)o(ault)h(weight)g(of)f(a)f (term)h(or)g(atom)g(is)g(the)257 3226 y(number)24 b(of)g(v)n(ariable,)h (constant,)g(function,)h(and)e(predicate)i(symbols)e(\(the)g(symbol)h (count\).)398 3399 y(V)-10 b(ariables)47 b(in)e(weight)h(templates)h (are)f(generic.)95 b(A)45 b(v)n(ariable)i(in)e(a)g(weight)h(template)g (will)257 3512 y(match)c(an)o(y)h(v)n(ariable,)48 b(and)43 b(only)g(a)f(v)n(ariable,)48 b(in)42 b(the)h(gi)n(v)o(en)g(term.)85 b(As)41 b(a)h(consequence,)50 b(it)42 b(is)257 3625 y(ne)n(v)o(er)j (necessary)i(to)e(use)g(dif)n(ferent)h(v)n(ariable)h(names)e(in)g(a)f (weight)h(template.)94 b(F)o(or)43 b(e)o(xample,)257 3738 y FD(weight\(f\(x,x\),)o(-7\))27 b FK(matches)35 b(the)g(term)g FD(f\(u,v\))p FK(,)e(and)i FD(weight\(x,32\))28 b FK(matches)36 b(all)257 3851 y(v)n(ariables.)398 4024 y FG(W)-8 b(arning)o(.)88 b FK(The)43 b(tw)o(o)f(occurrences)47 b(of)c(symbol)h FD(f)d FK(in)i(the)h(term)f FD(f\(f,x\))c FK(are)k(treated)i(by)259 4136 y(O)q FE(T)t(T)t(E)t(R)f FK(as)c(dif)n(ferent)j(symbols)e(because)i(the)o(y)e(ha)n(v)o(e)g(dif)n (ferent)h(arities.)81 b(The)40 b(weight)h(template)257 4249 y FD(weight\(f,)50 b(0\))22 b FK(applies)j(to)f(the)g(second)h (occurrence)h(b)n(ut)e(not)g(to)g(the)g(\002rst.)398 4422 y(The)d(def)o(ault)j(weight)e(of)g(an)g(answer)g(literal)h(is)f (0,)g(b)n(ut)g(templates)h(can)g(be)e(used)i(to)f(assign)h(weights)257 4535 y(to)g(answer)h(literals.)31 b(The)23 b(parameter)i FD(neg_weight)18 b FK(ne)n(v)o(er)24 b(applies)i(to)d(answer)h (literals.)398 4708 y(If)i(one)h(wishes)g(to)g(ha)n(v)o(e)g(a)f(weight) h(template)h(containing)i(a)c(Sk)o(olem)h(function)h(or)f(constant)h (that)257 4821 y(is)f(generated)j(by)g(O)q FE(T)t(T)t(E)t(R)r FK(,)g(one)d(must)h(\002rst)f(mak)o(e)h(a)f(short)h(trial)g(run)g(to)f (\002nd)g(out)h(ho)n(w)f(the)h(formulas)257 4934 y(are)21 b(Sk)o(olemized,)i(then)f(return)g(to)f(the)g(input)i(\002le)d(and)i (insert)g(the)f(weight)h(list)f(containing)k(the)c(Sk)o(olem)257 5047 y(symbol)j FG(after)h FK(the)f(formula)g(lists.)257 5349 y FI(10.3)99 b(Containment)26 b(W)-6 b(eight)24 b(T)-9 b(emplates)257 5584 y FK(T)j(erm)24 b(weighting)j(has)f(an)f (additional)k(feature)e(that)f(allo)n(ws)f(the)h(user)g(to)f(specify)j (terms)d(that)h FG(contain)257 5697 y FK(particular)35 b(terms.)58 b(This)33 b(is)g(done)g(with)g(a)g(unary)h(function)h (symbol)f FD($dots\()p FC(t)p FD(\))p FK(.)53 b(If)33 b FD($dots\()p FC(t)p FD(\))1861 5946 y FK(41)p eop %%Page: 42 48 42 47 bop 257 388 a FK(occurs)23 b(in)f(a)g(weight)g(template,)i(it)e (will)f(match)i(an)o(y)f(term)g(that)g(contains)i(a)e(term)g(that)g (matches)h(t.)28 b(This)257 501 y(is)23 b(v)o(ery)h(useful)g(for)g (discarding)i(\223bad\224)e(clauses.)31 b(Here)23 b(is)g(part)h(of)f (an)g(output)i(\002le)e(that)g(illustrates)j(this)257 614 y(feature.)356 873 y Fq(list\(sos\).)356 973 y(1)50 b([])g(p\(f\(g\(g\(g\(g\(g\(h\(h\(h\(h\(j\(b\)\)\)\)\)\)\)\))o (\)\)\)\).)356 1072 y(2)g([])g (p\(F\(g\(g\(h\(g\(H\(g\(h\(g\(g\(g\(B\)\)\)\)\)\)\)\))o(\)\)\)\).)356 1172 y(3)g([])g(p\(f3\(g\(h\(a\)\),g\(g\(b\)\),h\(h\(c\)\)\)\).)356 1272 y(end_of_list.)356 1471 y(weight_list\(pick_given\).)356 1570 y(weight\(f\($dots\(j\($\(5\)\)\)\),100\).)356 1670 y(weight\(F\($dots\(H\($dots\(B\)\)\)\),1000\).)356 1770 y(weight\(f3\($dots\(a\),$dots\(b\),$dots\(c\)\),)o(2000\))o(.)356 1869 y(end_of_list.)356 2069 y(=======)f(end)g(of)h(input)f(processing) e(=======)356 2168 y(===========)h(start)h(of)h(search)e(===========) 356 2367 y(given)h(#1:)h(\(wt=106\))e(1)i([])f (p\(f\(g\(g\(g\(g\(g\(h\(h\(h\(h\(j\(b\)\)\)\)\)\)\)\)\)\))o(\)\).)356 2467 y(given)g(#2:)h(\(wt=1001\))e(2)h([])h (p\(F\(g\(g\(h\(g\(H\(g\(h\(g\(g\(g\(B\)\)\)\)\)\)\)\)\))o(\)\)\).)356 2567 y(given)f(#3:)h(\(wt=2001\))e(3)h([])h (p\(f3\(g\(h\(a\)\),g\(g\(b\)\),h\(h\(c\)\)\)\).)257 2919 y FJ(11)119 b(Answer)31 b(Literals)257 3186 y FK(The)25 b(main)g(use)h(of)g(answer)g(literals)h(is)e(to)h(record,)h(during)g(a) e(search)i(for)e(a)h(refutation,)i(instantiations)257 3299 y(of)i(v)n(ariables)i(in)e(input)h(clauses.)51 b(F)o(or)29 b(e)o(xample,)j(if)e(the)g(theorem)i(under)f(consideration)j(states)d (that)257 3412 y(an)f(object)i(e)o(xists,)g(then)f(the)g(denial)h(of)e 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FE(T)t(T)t(E)t(R)g FG(does)e FK(attempt)f(to)g(f)o(actor)g (answer)h(literals.)257 4728 y FJ(12)119 b(The)30 b(P)o(assi)o(v)o(e)e (List)257 4995 y FK(Either)19 b(clauses)i(or)e(formulas)i(can)e(be)g (input)h(to)g(list)f FD(passive)p FK(.)k(After)c(input,)i(the)f(passi)n (v)o(e)g(list)f(is)g(\002x)o(ed)257 5108 y(for)j(the)f(rest)h(of)g(the) g(run.)28 b(Clauses)23 b(in)e(the)h(passi)n(v)o(e)h(list)e(are)h(used)h (for)e(e)o(xactly)i(tw)o(o)e(purposes:)31 b(forw)o(ard)257 5221 y(subsumption)24 b(and)d(unit)g(con\003ict.)29 b(If)21 b(forw)o(ard)g(subsumption)j(is)d(enabled,)i(a)d(ne)n(wly)h(generated)j (clause)257 5334 y(will)h(be)g(deleted)i(if)e(it)g(is)g(subsumed)i(by)f (an)o(y)f(clause)i(in)e FD(usable)p FK(,)d FD(sos)p FK(,)h(or)j FD(passive)p FK(,)21 b(and)26 b(ne)n(wly)257 5447 y(k)o(ept)35 b(unit)f(clauses)i(are)e(check)o(ed)i(for)e(unit)g(con\003ict)h (against)g(unit)g(clauses)h(in)d FD(usable)p FK(,)g FD(sos)p FK(,)h(or)257 5560 y FD(passive)p FK(.)1861 5946 y(42)p eop %%Page: 43 49 43 48 bop 398 388 a FK(The)24 b(passi)n(v)o(e)i(list)f(has)g(been)h (most)e(useful)j(for)d(monitoring)j(the)e(progress)i(of)e(a)f(search.) 34 b(Suppose)257 501 y(we)28 b(are)h(trying)h(to)f(pro)o(v)o(e)g(a)f (dif)n(\002cult)i(theorem,)h(we)d(ha)n(v)o(e)i(some)f(lemmas)f(in)h (mind,)h(and)f(we)f(w)o(ould)257 614 y(lik)o(e)g(to)g(kno)n(w)g (whether)j(O)q FE(T)t(T)t(E)t(R)h FK(has)c(pro)o(v)o(ed)h(the)f (lemmas.)42 b(Then)28 b(denials)i(of)e(the)g(lemmas)g(can)g(be)257 727 y(placed)k(in)f(the)h(passi)n(v)o(e)g(list,)h(and)g(O)q FE(T)t(T)t(E)t(R)i FK(will)c(report)h(proofs)h(if)e(it)f(pro)o(v)o(es)i (an)o(y)f(lemmas,)i(b)n(ut)f(the)257 840 y(denials)27 b(of)f(the)g(lemmas)g(will)f(not)h(interfere)i(with)e(the)g(search)h (for)f(the)g(main)g(theorem.)36 b(\(Recall)26 b(that)257 953 y(an)e(appropriate)j(v)n(alue)d(must)g(be)g(assigned)i(to)d FD(max_proofs)p FK(;)c(otherwise)28 b(O)q FE(T)t(T)t(E)t(R)f FK(will)d(stop)g(at)g(the)257 1065 y(\002rst)f(proof.\))257 1418 y FJ(13)119 b(Clause)30 b(Attrib)n(utes)257 1685 y FK(Attrib)n(utes)f(can)f(be)f(attached)j(to)d(clauses.)42 b(This)27 b(feature)i(w)o(as)e(introduced)k(at)c(the)h(same)f(time)g (as)h(the)257 1798 y(hints)g(strate)o(gy)h(\(Sec.)e(14\),)i(and)e(all)h (of)f(the)h(current)h(attrib)n(utes)h(are)e(speci\002cally)h(for)f(the) g(hints)g(strat-)257 1911 y(e)o(gy)-6 b(.)39 b(In)27 b(case)g(some)g(future)i(enhancements)h(of)f(O)q FE(T)t(T)t(E)t(R)i FK(will)26 b(use)h(attrib)n(utes,)k(the)c(general)i(attrib)n(ute)257 2024 y(mechanism)c(is)e(gi)n(v)o(en)h(here.)398 2197 y(Each)34 b(attrib)n(ute)j(is)e(identi\002ed)h(by)e(a)g(name,)j(and)e (each)g(attrib)n(ute)i(has)e(a)f(type.)63 b(\(Users)34 b(cannot)257 2310 y(introduce)d(ne)n(w)e(attrib)n(utes\227the)o(y)k (are)c(b)n(uilt)h(into)g(the)f(code)h(of)h(O)q FE(T)t(T)t(E)t(R)r FK(.\))48 b(The)28 b(attrib)n(ute)k(types)e(are)257 2423 y(inte)o(ger)l(,)25 b(string,)g(and)f(term.)30 b(Attrib)n(utes)c(are)e (attached)i(to)d(clauses)j(with)e(the)g(operator)i(\223)p FD(#)p FK(\224,)d(and)h(must)257 2535 y(appear)h(after)f(all)g (literals.)398 2708 y(F)o(or)g(e)o(xample,)i(if)f(attrib)n(ute)i FD(a1)d FK(has)h(type)h(inte)o(ger)l(,)h(attrib)n(ute)g FD(a2)c FK(has)j(type)g(string,)g(and)g(attrib)n(ute)257 2821 y FD(a3)c FK(has)i(type)g(term,)f(then)h(a)f(user)h(can)g(write)g (a)f(clause)i(with)e(attrib)n(utes)k(as)c(follo)n(ws.)356 3081 y Fq(f\(x,y\)!=f\(x,z\))48 b(|)h(y=z)h(#)f(a1\(23\))g(#)g (a2\("left)g(cancel"\))f(#)i(a3\(g\(b\)\).)257 3433 y FJ(14)119 b(The)30 b(Hints)g(Strategy)257 3700 y FK(The)18 b FG(hints)i(str)o(ate)l(gy)h FK(can)f(be)f(used)h(if)e(the)i(user)f (has)h(a)e(set)h(of)g(clauses)i(that)e(might)h(be)f(rele)n(v)n(ant)h (to)f(\002nding)257 3813 y(a)j(proof.)30 b(The)22 b(clauses,)j(called)f FG(hints)p FK(,)g(do)f(not)g(necessarily)j(hold)e(in)e(the)h(theory)i (being)f(e)o(xplored,)h(and)257 3926 y(the)o(y)h(are)h(not)f(used)h (for)f(making)h(inferences.)40 b(Hints)26 b(are)g(used)h(only)g(as)f(a) g(heuristic)i(for)f(guiding)h(the)257 4039 y(search,)d(in)f(particular) l(,)i(in)e(selecting)i(the)e(gi)n(v)o(en)h(clauses)g(and)g(in)e (deciding)j(whether)f(to)f(k)o(eep)h(deri)n(v)o(ed)257 4152 y(clauses.)398 4325 y(The)31 b(main)g(function)j(of)e(the)f(hints) i(strate)o(gy)g(is)e(to)h(adjust)g(the)g(pick-gi)n(v)o(en)i(weight)e (of)g(clauses.)257 4438 y(The)25 b(user)i(can)f(specify)-6 b(,)28 b(for)e(e)o(xample,)h(that)f(an)o(y)g(deri)n(v)o(ed)h(clause)h (that)e(matches)h(a)e(hint)i(should)g(ha)n(v)o(e)257 4551 y(its)g(pick-gi)n(v)o(en)j(weight)e(reduced)h(by)e(1000.)41 b(In)27 b(addition,)j(the)e(user)g(can)g(specify)-6 b(,)29 b(with)e(an)h(attrib)n(ute)257 4663 y(on)21 b(a)g(hint,)h(ho)n(w)f (that)h(hint)g(should)h(be)e(used)h(to)g(adjust)g(the)g(pick-gi)n(v)o (en)i(weight)d(of)h(clauses)h(that)f(match)257 4776 y(the)h(hint.)29 b(Clauses)c(can)e(match)g(hints)i(in)e(se)n(v)o(eral)h(w)o(ays)f(as)g (speci\002ed)h(by)g(\(ordinary\))h(parameters)h(and)257 4889 y(by)d(attrib)n(utes)k(on)c(hints.)398 5062 y(Because)33 b(of)f(the)h(distinction)i(between)e(the)f(pick-gi)n(v)o(en)j(and)d (pur)n(ge-gen)j(weights)f(of)e(clauses,)257 5175 y(and)37 b(because)h(the)e(hints)i(mechanism)f(af)n(fects)h(only)f(the)f (pick-gi)n(v)o(en)j(weight,)h(se)n(v)o(eral)d(additional)257 5288 y(\003ags)f(e)o(xist.)66 b(If)36 b(a)f(clause)j(matching)f(a)f (hint)g(is)g(deri)n(v)o(ed,)k(one)c(typically)i(w)o(ants)f(it)e(to)h (be)g(k)o(ept)h(so)257 5401 y(that)e(it)f(can)h(be)f(selected)i(as)f(a) e(gi)n(v)o(en)i(clause.)63 b(Ho)n(we)n(v)o(er)l(,)37 b(the)d(clause)i(may)e(be)g(discarded)j(by)e(the)257 5514 y FD(max_weight)22 b FK(parameter)-5 b(.)43 b(T)-7 b(o)27 b(address)j(this)e(problem,)i(the)e(\003ags)f FD(keep_hint_subsum)o(er)o(s)257 5627 y FK(and)36 b FD(keep_hint_equiv) o(ale)o(nt)o(s)29 b FK(say)36 b(that)h(the)f FD(max_weight)31 b FK(parameter)37 b(should)h(be)e(ig-)1861 5946 y(43)p eop %%Page: 44 50 44 49 bop 257 388 a FK(nored)33 b(for)f(all)g(clauses)h(that)g(match)f (hints)h(in)f(those)g(w)o(ays)g(\(details)i(are)e(in)g(the)g(follo)n (wing)h(subsec-)257 501 y(tions\).)398 674 y(The)20 b(hints)i(strate)o (gy)h(w)o(as)e(introduced)j(by)d(Bob)g(V)-10 b(erof)n(f,)21 b(who)g(implemented)h(it)f(in)g(a)g(pre)n(vious)i(v)o(er)n(-)257 787 y(sion)f(of)g(O)q FE(T)t(T)t(E)t(R)j FK(and)d(used)g(it)e(in)h(man) o(y)g(applications)k([27)q(,)20 b(28].)30 b(O)q FE(T)t(T)t(E)t(R)25 b FK(currently)e(has)e(tw)o(o)g(separate)257 900 y(hints)33 b(mechanisms,)j(named)d(\223hints\224)h(and)f(\223hints2\224,)k(both)c (deri)n(v)o(ed)g(from)g(V)-10 b(erof)n(f)5 b(')-5 b(s)33 b(methods)h(and)257 1013 y(ideas.)c(The)23 b(\002rst)g(is)g(more)h (general,)h(and)f(the)g(second)h(is)e(much)h(f)o(aster)-5 b(.)257 1321 y FI(14.1)99 b(Hints)24 b(\(the)i(General)f(V)-10 b(ersion\))257 1555 y FK(The)24 b(hint)h(clauses)h(are)e(gi)n(v)o(en)h (in)f(one)h(or)f(more)g(lists.)32 b(All)24 b(of)g(the)g(lists)h(must)g (be)f(named)h(\223hints\224)h(as)e(in)257 1668 y(the)g(follo)n(wing)h (e)o(xample.)456 1921 y Fq(list\(hints\).)456 2021 y(-p\(x\))49 b(|)h(q\(x\))f(|)g(r\(x\).)456 2121 y(end_of_list.)257 2387 y FK(A)22 b(clause)j FC(C)k FK(can)24 b(match)g(a)f(hint)h FC(H)30 b FK(in)23 b(three)i(w)o(ays.)370 2630 y(1.)46 b FC(C)29 b FK(subsumes)d FC(H)7 b FK(.)27 b(This)d(is)f(referred)i(to) f(as)f(\223bsub\224,)i(in)f(analogy)h(to)f(back)g(subsumption.)370 2816 y(2.)46 b FC(C)32 b FK(is)26 b(subsumed)i(by)f FC(H)7 b FK(.)36 b(This)26 b(is)g(referred)i(to)f(as)f(\223fsub\224,)i(in)e (analogy)j(to)d(forw)o(ard)h(subsump-)484 2929 y(tion.)370 3114 y(3.)46 b FC(C)29 b FK(is)24 b(equi)n(v)n(alent)i(to)d FC(H)7 b FK(.)257 3357 y(Six)23 b(parameters)i(and)f(tw)o(o)g(\003ags)f (determine)i(the)f(beha)n(vior)i(of)e(the)f(hints)i(mechanism.)257 3530 y FD(assign\(equiv_h)o(int)o(_w)o(t,)o FC(n)p FD(\))o FK(.)d(Def)o(ault)g Fv(1)p FK(,)e(range)j([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)j(If)21 b FC(n)k Fv(6)p Fp(=)20 b Fv(1)p FK(,)h(clauses)i(that)f(are)257 3643 y(equi)n(v)n(alent)k(to)d (a)g(hint)h(recei)n(v)o(e)h(a)e(pick-gi)n(v)o(en)j(weight)e(of)g FC(n)p FK(.)257 3816 y FD(assign\(equiv_h)o(int)o(_a)o(dd)o(_w)o(t,)o FC(n)p FD(\))p FK(.)70 b(Def)o(ault)40 b(0,)j(range)e([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)76 b(Clauses)41 b(that)f(are)257 3929 y(equi)n(v)n(alent)26 b(to)d(a)g(hint)h(ha)n(v)o(e)h FC(n)d FK(added)j(to)e(their)i(ordinary)g(pick-gi)n(v)o(en)h(weight.) 257 4102 y FD(assign\(fsub_hi)o(nt_)o(wt)o(,)p FC(n)o FD(\))p FK(.)i(Def)o(ault)f Fv(1)p FK(,)e(range)i([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)34 b(If)25 b FC(n)k Fv(6)p Fp(=)c Fv(1)p FK(,)g(clauses)j(that)e(are)257 4215 y(subsumed)f(by)f(a) f(hint)h(recei)n(v)o(e)h(a)e(pick-gi)n(v)o(en)j(weight)e(of)f FC(n)p FK(.)257 4388 y FD(assign\(fsub_hi)o(nt_)o(ad)o(d_)o(wt)o(,)p FC(n)o FD(\))p FK(.)36 b(Def)o(ault)29 b(0,)g(range)g([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)41 b(Clauses)29 b(that)g(are)f(sub-)257 4500 y(sumed)c(by)g(a)f(hint)h(ha)n(v)o(e)g FC(n)e FK(added)j(to)f (their)g(ordinary)i(pick-gi)n(v)o(en)g(weight.)257 4673 y FD(assign\(bsub_hi)o(nt_)o(wt)o(,)p FC(n)o FD(\))p FK(.)55 b(Def)o(ault)35 b Fv(1)p FK(,)i(range)e([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)61 b(If)34 b FC(n)45 b Fv(6)p Fp(=)34 b Fv(1)p FK(,)i(clauses)g(that)257 4786 y(subsume)25 b(a)e(hint)h(recei)n(v)o(e)h(a)e(pick-gi)n(v)o(en)j(weight)e(of)f FC(n)p FK(.)257 4959 y FD(assign\(bsub_hi)o(nt_)o(ad)o(d_)o(wt)o(,)p FC(n)o FD(\))p FK(.)30 b(Def)o(ault)d(0,)f(range)h([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)35 b(Clauses)27 b(that)g(subsume)257 5072 y(a)c(hint)h(ha)n(v)o(e)g FC(n)f FK(added)h(to)g(their)g(ordinary) i(pick-gi)n(v)o(en)g(weight.)398 5245 y(A)c(clause)j(can)e(match)h (more)f(than)h(one)g(hint,)g(and)f(a)g(clause)i(can)f(match)f(a)g(hint) h(in)f(more)h(than)g(one)257 5358 y(w)o(ay)-6 b(,)28 b(so)g(the)g(order)h(of)f(operations)j(is)c(rele)n(v)n(ant.)43 b(The)28 b(rules)g(are)g(as)g(follo)n(ws.)42 b(\(1\))28 b(The)g(\002rst)f(hint)i(\(as)257 5471 y(gi)n(v)o(en)e(in)f(the)g (input)i(\002le\))e(that)h(matches)g(the)g(clause)g(is)g(used.)37 b(\(2\))27 b(Equi)n(v)n(alence)h(is)e(tested)i(\002rst,)e(then)257 5584 y(fsub,)e(then)g(bsub)l(.)30 b(\(3\))23 b(W)l(ithin)h(match)g (type)g(\(e.g.,)f(bsub\),)h(both)g(types)h(of)e(weight)h(adjustment)h (can)f(be)257 5697 y(applied)h(\(e.g.,)e FD(bsub_hint_wt)17 b FK(and)24 b FD(bsub_hint_ad_wt)p FK(\).)1861 5946 y(44)p eop %%Page: 45 51 45 50 bop 398 388 a FK(The)36 b(hint-adjustment)41 b(parameters)e(can)e (be)g(o)o(v)o(erridden)i(by)e(attrib)n(utes)j(on)d(indi)n(vidual)i (hints.)257 501 y(\(This)25 b(feature)h(can)g(be)e(used,)i(for)f(e)o (xample,)h(if)f(some)g(hints)h(are)f(more)g(important)h(than)g (others.\))34 b(The)257 614 y(attrib)n(ute)h(names)f(for)g(hints)g (correspond)i(to)d(the)h(six)f(parameters)j(listed)e(abo)o(v)o(e.)59 b(F)o(or)32 b(e)o(xample,)k(if)257 727 y(the)c(parameter)h FD(bsub_hint_add_wt)24 b FK(is)32 b(set)g(to)f(-1000,)k(that)e(v)n (alue)f(can)h(be)e(o)o(v)o(erridden)j(for)e(a)257 840 y(particular)26 b(hint)e(by)g(gi)n(ving)h(it)e(an)g(attrib)n(ute)j(as)e (follo)n(ws.)456 1078 y Fq(f\(x,f\(x,f\(x,y\)\)\)=f\(x,y\))46 b(#)j(bsub_hint_add_wt\(-2000\).)398 1329 y FK(The)21 b(follo)n(wing)j(tw)o(o)d(\003ags)h(were)g(introduced)j(because)f(the)e (hints)h(mechanism)g(adjusts)h(the)e(pick-)257 1442 y(gi)n(v)o(en)i (weight)g(of)g(clauses)h(and)f(does)g(not)g(af)n(fect)g(the)g(pur)n (ge-gen)j(weight)d(of)g(clauses.)257 1615 y(Flag)h FD(keep_hint_subsu)o (me)o(rs)o FK(.)i(Def)o(ault)g(clear)-5 b(.)34 b(If)25 b(this)h(\003ag)f(is)g(set,)h(then)g(the)f FD(max_weight)257 1728 y FK(parameter)g(is)e(ignored)j(for)e(deri)n(v)o(ed)g(clauses)i (that)e(subsume)h(an)o(y)e(hints.)257 1901 y(Flag)57 b FD(keep_hint_equiv)o(ale)o(nt)o(s)p FK(.)124 b(Def)o(ault)58 b(clear)-5 b(.)132 b(If)58 b(this)g(\003ag)f(is)g(set,)66 b(then)59 b(the)257 2014 y FD(max_weight)18 b FK(parameter)25 b(is)f(ignored)h(for)f(deri)n(v)o(ed)g(clauses)i(that)e(are)g(equi)n(v) n(alent)h(to)f(an)o(y)g(hints.)257 2316 y FF(Practical)29 b(Advice.)91 b FK(If)28 b(one)g(has)g(a)f(set)h(of)f(clauses)j(that)e (one)g(wishes)g(to)g(use)g(as)f(hints,)j(say)e(from)f(a)257 2429 y(proof)d(of)g(a)f(related)i(theorem,)f(a)g(good)g(\002rst)f (attempt)i(is)e(to)h(use)f(the)h(follo)n(wing)h(settings.)475 2681 y FD(assign\(bsub_hin)o(t_)o(ad)o(d_)o(wt,)48 b(-1000\).)475 2794 y(set\(keep_hint_s)o(ub)o(su)o(me)o(rs\))o(.)257 3045 y FK(If)21 b(one)h(has)g(more)f(than)i(a)e(fe)n(w)f(hints,)j(and)f (one)g(wishes)g(to)g(use)g(only)g(the)g(preceding)i(settings,)g(then)e (we)257 3158 y(recommend)j(using)f(hints2)h(\(the)g(f)o(ast)f(v)o (ersion\).)257 3464 y FI(14.2)99 b(Hints2)24 b(\(the)i(F)n(ast)e(V)-10 b(ersion\))257 3698 y FK(The)32 b(general)j(hints)e(mechanism)h (described)i(in)d(the)g(preceding)i(paragraphs)h(can)d(be)g(v)o(ery)g (slo)n(w)f(if)257 3811 y(there)g(are)g(man)o(y)f(hints,)k(because)e (each)f(hint)g(clause)h(is)f(tested)h(until)f(a)f(match)h(is)f(found.) 54 b(The)31 b(f)o(ast)257 3924 y(hints)j(mechanism)h(uses)g(inde)o (xing)h(to)d(\002nd)g(hints.)61 b(T)-7 b(o)32 b(acti)n(v)n(ate)j(the)f (f)o(ast)g(hints)h(mechanism,)i(hint)257 4037 y(clauses)25 b(are)f(placed)h(in)e(one)h(or)g(more)f(lists)i(named)f(\223hints2\224) h(as)f(in)f(the)h(follo)n(wing)h(e)o(xample.)456 4275 y Fq(list\(hints2\).)456 4375 y(-p\(x\))49 b(|)h(q\(x\))f(|)g(r\(x\).) 456 4475 y(end_of_list.)257 4726 y FK(Only)25 b(one)g(type)h(of)f (matching)i(can)e(be)g(used)h(with)f(hints2\227a)h(clause)h(matches)f (a)f(hint)g(if)g(and)g(only)h(if)257 4839 y(it)d(subsumes)i(the)f (hint.)30 b(T)-7 b(w)o(o)22 b(parameters)j(and)f(tw)o(o)f(\003ags)h (apply)h(to)e(hints2.)257 5012 y FD(assign\(bsub_hi)o(nt_)o(wt)o(,)p FC(n)o FD(\))p FK(.)55 b(Def)o(ault)35 b Fv(1)p FK(,)i(range)e([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)61 b(If)34 b FC(n)45 b Fv(6)p Fp(=)34 b Fv(1)p FK(,)i(clauses)g(that)257 5125 y(subsume)25 b(a)e(hint)h(recei)n(v)o(e)h(a)e(pick-gi)n(v)o(en)j (weight)e(of)f FC(n)p FK(.)257 5298 y FD(assign\(bsub_hi)o(nt_)o(ad)o (d_)o(wt)o(,)p FC(n)o FD(\))p FK(.)30 b(Def)o(ault)d(0,)f(range)h([)p Fv(\0001)p FK(..)p Fv(1)p FK(].)35 b(Clauses)27 b(that)g(subsume)257 5411 y(a)c(hint)h(ha)n(v)o(e)g FC(n)f FK(added)h(to)g(their)g(ordinary) i(pick-gi)n(v)o(en)g(weight.)257 5584 y(Flag)f FD(keep_hint_subsu)o(me) o(rs)o FK(.)i(Def)o(ault)g(clear)-5 b(.)34 b(If)25 b(this)h(\003ag)f (is)g(set,)h(then)g(the)f FD(max_weight)257 5697 y FK(parameter)g(is)e (ignored)j(for)e(deri)n(v)o(ed)g(clauses)i(that)e(subsume)h(an)o(y)e (hints.)1861 5946 y(45)p eop %%Page: 46 52 46 51 bop 257 388 a FK(Flag)27 b FD(degrade_hints2)p FK(.)35 b(Def)o(ault)29 b(clear)-5 b(.)42 b(If)28 b(this)g(\003ag)g(is) f(set,)i(Bob)f(V)-10 b(erof)n(f)5 b(')-5 b(s)28 b(hint-de)o(gradation) 257 501 y(strate)o(gy)f(is)e(applied.)36 b(When)25 b(a)g(hint)h(is)f (\002rst)g(read,)h(its)g FD(bsub_hint_add_)o(wt)18 b FK(is)25 b(associated)j(with)257 614 y(it;)45 b(this)38 b(v)n(alue)g(can)h(come)e(from)h(the)g(parameter)h(or)f(from)g(an)f (attrib)n(ute.)74 b(The)37 b(hint-de)o(gradation)257 727 y(strate)o(gy)h(says)g(that)f(each)h(time)f(a)f(hint)h(is)g(used)h (to)f(adjust)h(the)f(weight)g(of)g(a)g(deri)n(v)o(ed)h(clause,)j(its) 257 840 y FD(bsub_hint_add_)o(wt)18 b FK(is)24 b(cut)h(in)g(half.)33 b(Assuming)26 b(that)g(it)e(initially)j(has)e(a)g(lar)n(ge)h(ne)o(gati) n(v)o(e)f(v)n(alue,)257 953 y(this)h(strate)o(gy)i(mak)o(es)f(a)e(hint) i(progressi)n(v)o(ely)i(less)e(important)h(as)d(it)h(matches)h(more)f (deri)n(v)o(ed)i(clauses.)257 1065 y(This)c(strate)o(gy)h(w)o(as)f (introduced)j(because)e(\(contrary)i(to)c(intuition\))k(man)o(y)d(dif)n (ferent)h(generalizations)257 1178 y(of)e(a)g(hint)i(can)e(be)h(deri)n (v)o(ed.)257 1488 y FI(14.3)99 b(Label)25 b(Attrib)n(utes)h(on)f(Hints) 257 1722 y FK(If)e(a)g(hint)h(clause)h(has)f(a)f(label)i(attrib)n(ute,) g(for)f(e)o(xample,)366 1969 y FD(f\(x,f\(x,f\(x,y\)\))o(\)=)o(f\()o (x,)o(y\))48 b(#)54 b(label\("hint)c(32)j(from)g(proof)f(12"\).)257 2217 y FK(and)22 b(if)f(such)i(a)e(hint)h(is)g(used)g(to)g(adjust)h (the)f(pick-gi)n(v)o(en)i(weight)e(of)g(a)f(clause)i FC(C)7 b FK(,)21 b(the)h(label)g(is)g(inherited)257 2330 y(by)i FC(C)7 b FK(.)29 b(This)24 b(feature,)h(which)f(is)g(useful)i (for)e(tracking)i(the)e(application)j(of)d(hints,)h(applies)h(to)e (both)h(the)257 2443 y(general)g(and)f(the)g(f)o(ast)g(hints)h (mechanisms.)257 2752 y FI(14.4)99 b(Generating)25 b(Hints)g(fr)n(om)g (Pr)n(oofs)257 2986 y FK(The)i(main)g(source)i(for)f(hints)h(is)e (proofs)i(of)e(related)i(theorems.)42 b(\(If)28 b(the)g(goal)g(is)f(to) h(shorten)h(a)e(proof,)257 3099 y(hints)d(often)h(come)f(from)f(proofs) i(of)e(the)h(same)g(theorem.\))257 3272 y(Flag)g FD(print_proof_as_h)o (in)o(ts)o FK(.)i(Def)o(ault)f(clear)-5 b(.)33 b(If)25 b(this)g(\003ag)f(is)h(set,)g(then)g(whene)n(v)o(er)h(a)e(proof)257 3385 y(is)h(found,)i(it)e(is)g(printed)i(as)f(a)e(hints)j(list)f(in)f (a)g(form)g(that)h(can)g(be)f(input)i(to)e(a)g(subsequent)30 b(O)q FE(T)t(T)t(E)t(R)g FK(job)l(.)257 3498 y(The)d(proof)h(that)g(is) f(printed)i(contains)g(more)e(detail)i(than)f(the)f(ordinary)j(proofs)e (printed)h(by)g(O)q FE(T)t(T)t(E)t(R)r FK(.)257 3611 y(In)i(particular)l(,)k(when)d(the)f(proof)h(contains)i(demodulation,)i (clauses)c(are)g(printed)g(for)g(each)g(re)n(write)257 3724 y(step)24 b(of)f(demodulation.)32 b(This)24 b(\003ag)f(is)g (independent)k(of)d(the)g(hints)g(mechanism.)257 4076 y FJ(15)119 b(Interaction)30 b(during)h(the)g(Sear)n(ch)259 4343 y FK(O)q FE(T)t(T)t(E)t(R)23 b FK(has)d(a)f(primiti)n(v)o(e)i (interacti)n(v)o(e)h(feature)f(that)f(allo)n(ws)g(the)f(user)i(to)e (interrupt)j(the)e(search,)h(modify)257 4456 y(the)26 b(options,)j(and)e(then)g(continue)i(the)d(search.)39 b(The)26 b(interrupt)i(is)f(triggered)h(in)f(tw)o(o)f(w)o(ays:)35 b(\(1\))26 b(with)259 4569 y(O)q FE(T)t(T)t(E)t(R)e FK(running)f(in)d (the)h(fore)o(ground,)i(the)e(user)g(types)h(the)f(\223interrupt\224)i (character)g(\(often)h FE(D)t(E)t(L)t(E)t(T)t(E)i FK(or)257 4682 y(control-C\),)20 b(or)f(\(2\))h(if)e(the)i(parameter)g FD(interrupt_given)12 b FK(is)19 b(set)g(to)g FC(n)p FK(,)f(the)i(search)g(is)f(interrupted)257 4795 y(after)k(e)n(v)o(ery)f FC(n)f FK(gi)n(v)o(en)i(clauses.)30 b(When)23 b(interrupted,)k(O)q FE(T)t(T)t(E)t(R)f FK(immediately)e(goes)f(into)g(a)e(simple)i(loop)257 4908 y(to)g(read)h(and)g(e)o(x)o(ecute)h(commands.)30 b(The)23 b(accepted)j(commands)e(are)g(listed)h(in)e(T)-7 b(able)24 b(8.)257 5081 y(The)f(follo)n(wing)i(notes)g(elaborate)g(on)f (the)g(interacti)n(v)o(e)i(feature.)393 5329 y Fv(\017)46 b FK(The)23 b(\003ag)f FD(interactive_giv)o(en)15 b FK(\(Sec.)23 b(6.1.1\))g(can)g(be)g(useful)h(with)f(the)g(interacti)n(v)o(e)j(fea-) 484 5441 y(ture.)35 b(F)o(or)25 b(e)o(xample,)h(if)f(one)h(thinks)h (the)f(search)h(is)e(going)i(to)e(f)o(ail,)h(one)g(can)g(interrupt)i (it,)d(print)484 5554 y(list)c FD(sos)p FK(,)e(set)i(the)g FD(interactive_gi)o(ve)o(n)14 b FK(\003ag,)20 b(then)i(continue,)h (selecting)g(gi)n(v)o(en)e(clauses)484 5667 y(interacti)n(v)o(ely)-6 b(.)1861 5946 y(46)p eop %%Page: 47 53 47 52 bop 1331 442 a FK(T)-7 b(able)23 b(8:)29 b(Interaction)e (Commands)p 499 455 2816 4 v 549 524 a Fq(help.)950 b Fw(Gi)n(v)o(e)20 b(simple)g(help.)549 624 y Fq(set\()p Fi(\003a)o(g-name)p Fq(\).)566 b Fw(Set)21 b(a)g(\003ag.)549 724 y Fq(clear\()p Fi(\003a)o(g-name)p Fq(\).)466 b Fw(Clear)21 b(a)g(\003ag.)549 823 y Fq(assign\()p Fi(par)o(am-name)p Fq(,)p Fi(value)p Fq(\).)93 b Fw(Assign)21 b(a)f(v)n(alue)g(to)g(a)h (parameter)-5 b(.)549 923 y Fq(stats.)900 b Fw(Send)20 b(statistics)i(to)e(std.)26 b(output)19 b(and)g(the)h(terminal.)549 1022 y Fq(usable.)850 b Fw(Print)21 b(list)g Fq(usable)e Fw(on)h(the)g(terminal.)549 1122 y Fq(sos.)1000 b Fw(Print)21 b(list)g Fq(sos)f Fw(on)g(the)g(terminal.)549 1222 y Fq(demodulators.)550 b Fw(Print)21 b(list)g Fq(demodulators)d Fw(on)i(the)g(terminal.)549 1321 y Fq(passive.)800 b Fw(Print)21 b(list)g Fq(passive)e Fw(on)h(the)g(terminal.)549 1421 y Fq(fork.)950 b Fw(F)o(ork)20 b(and)f(run)h(the)g(child)g (process;)2006 1521 y(resume)g(parent)f(when)h(child)f(\002nishes.)549 1620 y Fq(continue.)750 b Fw(Continue)20 b(the)g(search.)549 1720 y Fq(kill.)950 b Fw(Send)20 b(statistics)i(to)e(standard)f (output,)g(and)h(e)o(xit.)p 499 1753 V 393 2010 a Fv(\017)46 b FK(The)22 b FD(fork)d FK(command)k(creates)h(a)d(separate)k(cop)o(y) -6 b(,)23 b(called)g(a)f FG(c)o(hild)p FK(,)h(of)f(the)g(entire)j(O)q FE(T)t(T)t(E)t(R)h FK(pro-)484 2123 y(cess.)36 b(Immediately)27 b(after)g(the)f(fork,)g(the)g(child)h(is)f(running)h(\(w)o(aiting)g (for)f(more)g(commands\),)484 2236 y(and)e(the)g(original)i(process,)f (the)f FG(par)m(ent)p FK(,)g(is)g(w)o(aiting)g(for)g(the)g(child)h(to)e (\002nish.)29 b(When)24 b(the)g(child)484 2349 y(\002nishes,)33 b(the)f(parent)g(resumes)g(\(w)o(aiting)g(for)f(more)g(commands\).)51 b(Changes)33 b(that)e(the)g(child)484 2462 y(mak)o(es)24 b(to)f(the)g(clause)h(space,)g(options,)h(and)f(so)f(forth,)h(are)f (not)g(re\003ected)i(in)e(the)g(parent;)i(when)484 2575 y(the)30 b(parent)i(resumes,)g(it)e(is)g(in)g(e)o(xactly)h(the)g(same)f (state)h(as)f(when)g(the)g(fork)h(occurred.)50 b(\(The)484 2688 y(timing)23 b(statistics)j(are)c(not)i(handled)g(correctly)h(in)e (child)h(processes;)i(CPU)20 b(times)j(are)g(from)g(the)484 2801 y(start)g(of)f(the)h(current)g(process;)i(w)o(all-clock)f(time)e (is)g(correct;)j(other)e(timings)g(are)g(not)f(reliable.\))393 2988 y Fv(\017)46 b FK(The)21 b(interacti)n(v)o(e)j(routine)f(is)e(an)h (area)g(where)f(a)g(user)h(who)f(is)h(also)g(a)f(C)f(programmer)j(can)f (easily)484 3101 y(add)35 b(features.)65 b(F)o(or)34 b(e)o(xample,)k(most)d(of)g(the)g(ordinary)i(input)f(commands)g(could)g (be)f(made)484 3214 y(a)n(v)n(ailable)26 b(in)d(the)h(interacti)n(v)o (e)i(mode.)393 3402 y Fv(\017)46 b FK(This)102 b(kind)h(of)f (interaction)j(can)d(be)g(disabled)j(by)d(using)h(the)f(command)484 3515 y FD(clear\(sigint_in)o(te)o(ra)o(ct\))o FK(.)257 3762 y FG(W)-8 b(arning)o(.)29 b FK(Do)23 b(not)h(interacti)n(v)o(ely)i (change)g(an)o(y)d(option)i(that)f(af)n(fects)h(term)f(or)f(literal)i (inde)o(xing.)257 4115 y FJ(16)119 b(Output)31 b(and)f(Exit)g(Codes)259 4382 y FK(O)q FE(T)t(T)t(E)t(R)35 b FK(sends)e(most)f(of)g(its)g (output)h(to)f(\223standard)i(output\224,)h(which)d(is)g(usually)h (redirected)i(by)d(the)257 4495 y(user)f(to)f(a)g(\002le;)j(we)d(just)g (call)h(it)f(the)h(output)g(\002le.)49 b(The)30 b(\002rst)g(part)g(of)h (the)f(output)i(\002le)e(is)g(an)g(echo)h(of)257 4608 y(most)j(of)g(the)g(input)h(and)g(some)f(additional)j(information,)i (including)d(identi\002cation)h(numbers)f(for)257 4721 y(clauses)26 b(and)g(description)i(of)c(some)h(input)h(processing.)36 b(Comments)25 b(are)g(not)g(echoed)i(to)e(the)g(output.)257 4834 y(The)30 b(second)j(part)e(of)g(the)g(output)h(\002le)e (re\003ects)i(the)f(search.)51 b(V)-10 b(arious)32 b(print)g(\003ags)f (determine)h(what)257 4947 y(is)d(output.)46 b(Gi)n(v)o(en)29 b(clauses,)j(generated)g(clauses,)g(k)o(ept)d(clauses,)j(and)e(se)n(v)o (eral)g(messages)g(about)h(the)257 5059 y(processing)26 b(of)e(generated)h(and)f(k)o(ept)h(clauses)g(can)e(be)h(printed.)30 b(Both)24 b(statistics)h(from)f(the)f(parameter)257 5172 y FD(report)f FK(and)k(proofs)i(can)e(also)g(be)g(printed)i(during)f (the)f(search.)37 b(The)25 b(\002nal)h(part)g(of)g(the)g(output)i (\002le)257 5285 y(lists)c(counts)g(of)f(v)n(arious)i(e)n(v)o(ents)f (\(such)g(as)f(clauses)h(gi)n(v)o(en)g(and)g(clauses)g(k)o(ept\))g(and) g(times)f(for)g(v)n(arious)257 5398 y(operations.)398 5571 y(Whene)n(v)o(er)h(a)f(clause)i(is)e(printed,)i(it)e(is)h(printed) h(with)e(its)g(inte)o(ger)i(identi\002er)g(\(ID\))e(and)h(a)f (justi\002ca-)257 5684 y(tion)h(list,)g(which)g(is)f(enclosed)j(in)d (brack)o(ets.)31 b(Examples:)1861 5946 y(47)p eop %%Page: 48 54 48 53 bop 356 388 a Fq(4)100 b([])49 b(-j\(x,y\)|j\(x,0\).)356 488 y(13)h([hyper,11,8,eval,demod])45 b(j\(3,1\).)356 587 y(41)50 b([31,demod])e(p\([a,b,b,c,c,c,d,e,f]\).)356 687 y(14)i([new_demod,13])d(f\(y,f\(y,f\(y,x\)\)\)=x.)356 786 y(71)j([back_demod,58,demod,70,14,55,11,34)o(,11])43 b(e!=e.)356 886 y(12)50 b([demod,9])e (f\(a,f\(b,f\(g\(a\),g\(b\)\)\)\)!=e.)356 986 y(77)i ([binary,57.3,30.2])c(sm|mm|)j(-sl.)356 1085 y(33,32)g ([para_from,26.1.1,15.1.1.2,demod,21])43 b(g\(x\)=f\(x,x\).)356 1185 y(36)50 b([hyper,31,2,26,30,unit_del,19,18,20)o(,19])43 b(p\(k,g\(k\)\).)356 1285 y(4)100 b([factor_simp,factor_simp])506 1384 y(p\(x\)|p\($f1\(x\)\)|)47 b(-q\($f2\(y\)\)|)h(-q\(y\)|p\($c6\).) 356 1484 y(199)i([binary,198.1,191.1,factor_simp])44 b(q\($c14\).)257 1756 y FK(If)23 b(the)g(justi\002cation)j(list)e(is)f (empty)-6 b(,)24 b(the)f(clause)i(w)o(as)e(input.)30 b(Otherwise,)24 b(the)f FG(\002r)o(st)h FK(item)g(in)f(the)g (justi\002-)257 1869 y(cation)i(list)f(is)f(one)h(of)f(the)h(follo)n (wing.)257 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b(one)g(third)g(of)f(a)n(v)n(ailable)j (memory)257 5295 y(\()p FD(max_mem)16 b FK(parameter\))21 b(has)f(been)g(\002lled,)i(O)q FE(T)t(T)t(E)t(R)h FK(assigns)f(or)d (reassigns)j(a)d(maximum)g(weight.)28 b(The)257 5408 y(ne)n(w)e(maximum,)i(say)g FC(n)p FK(,)e(is)h(such)h(that)g(5\045)f (of)g(all)g(clauses)i(in)e FD(sos)e FK(ha)n(v)o(e)j(weight)g Fv(\024)j FC(n)p FK(.)39 b(From)26 b(then)257 5521 y(on,)21 b(at)g(e)n(v)o(ery)h(tenth)g(iteration)h(of)e(the)h(main)f(loop,)j(O)q FE(T)t(T)t(E)t(R)h FK(calculates)f(a)d(prospecti)n(v)o(e)j(ne)n(w)c (maximum)257 5634 y FC(n)312 5601 y Fj(0)362 5634 y FK(in)29 b(the)g(same)f(w)o(ay)-6 b(.)44 b(If)28 b FC(n)1168 5601 y Fj(0)1225 5634 y FC(<)34 b(n)p FK(,)29 b(then)g(the)g(maximum)f(is)g (reset)i(to)e FC(n)2597 5601 y Fj(0)2620 5634 y FK(.)43 b(The)28 b(v)n(alues)i Fp(1)p FC(=)p Fp(3)f FK(and)g(5\045)1861 5946 y(49)p eop %%Page: 50 56 50 55 bop 257 388 a FK(were)23 b(determined)j(by)e(trial)g(and)g(error) -5 b(.)29 b(Perhaps)c(these)f(v)n(alues)h(should)g(be)f(parameters.)257 694 y FF(Reducing)c FD(max)p 816 694 28 4 v 31 w(weight)e FF(on)j(the)g(Fly)-6 b(.)90 b FK(In)21 b(man)o(y)h(searches,)h(the)f (number)g(of)g(k)o(ept)g(clauses)h(gro)n(ws)257 807 y(much)29 b(f)o(aster)i(than)f(the)g(number)g(of)f(gi)n(v)o(en)h(clauses.)48 b(In)30 b(other)g(w)o(ords,)h(the)f(list)g FD(sos)d FK(is)i(v)o(ery)h (lar)n(ge,)257 920 y(and)24 b(most)h(of)f(those)h(clauses)h(ne)n(v)o (er)f(participate)i(in)d(the)g(search.)33 b(T)-7 b(o)23 b(sa)n(v)o(e)h(memory)-6 b(,)25 b(one)g(can)f(use)h(the)257 1033 y FD(max_weight)17 b FK(parameter)25 b(to)e(discard)h(man)o(y)f (of)g(the)g(clauses)i(that)e(will)g(\(probably\))j(ne)n(v)o(er)d (become)257 1145 y(gi)n(v)o(en)h(clauses.)398 1318 y(A)k(fe)n(w)h (searches)i(and)f(proofs)h(sho)n(w)f(a)f(phenomenon)j(we)c(call)i(the)g FG(comple)n(xity)i(hump)p FK(.)46 b(T)-7 b(o)29 b(get)257 1431 y(a)k(search)i(started,)i(one)d(must)g(use)g(comple)o(x)g (clauses;)41 b(then)34 b(one)g(can)g(continue)i(the)e(search)h(using) 257 1544 y(simpler)d(clauses.)55 b(That)32 b(is,)h(the)f(\002rst)f(fe)n (w)g(steps)i(in)e(the)h(proof)h(are)f(comple)o(x,)i(and)e(the)g (remaining)257 1657 y(steps)c(are)g(simpler)-5 b(.)41 b(If)28 b(one)g(needs)g(to)g(carefully)h(conserv)o(e)h(memory)d(when)h (a)f(comple)o(xity)i(hump)f(is)257 1770 y(present,)22 b(one)g(can)f(use)f(the)h(parameters)i FD(change_limit_af)o(te)o(r)14 b FK(and)21 b FD(new_max_weight)13 b FK(to)257 1883 y(change)25 b(the)f(v)n(alue)g(of)g FD(max_weight)18 b FK(after)24 b(a)f(speci\002ed)i(number)g(of)e(gi)n(v)o(en)h(clauses.)257 2056 y FD(assign\(change_)o(lim)o(it)o(_a)o(ft)o(er)o(,)p FC(n)p FD(\))o FK(.)64 b(Def)o(ault)38 b(0,)j(range)e([0..)p Fv(1)p FK(].)70 b(If)37 b FC(n)f FK(\(the)j(v)n(alue\))f(is)257 2169 y(not)g(0,)j(this)d(parameter)i(has)e(ef)n(fect.)73 b(After)38 b FC(n)f FK(gi)n(v)o(en)h(clauses)i(ha)n(v)o(e)e(been)h (used,)j(the)c(parameter)257 2282 y FD(max_weight)18 b FK(is)23 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b(search)i(strate)o (gy)g(that)259 3812 y(O)q FE(T)t(T)t(E)t(R)30 b FK(selects)f(for)e(a)f (particular)j(set)e(of)g(clauses)i(is)d(usually)j(refutation)g (complete)g(\(e)o(xcept)f(for)f(the)257 3925 y(\003ag)j FD(control_memory)p FK(\),)c(b)n(ut)32 b(the)f(user)g(should)i(not)e(e) o(xpect)i(it)d(to)h(be)g(especially)j(ef)n(fecti)n(v)o(e.)52 b(It)257 4037 y(will)22 b(\002nd)g(proofs)i(for)f(man)o(y)g(easy)g (theorems,)h(and)f(e)n(v)o(en)g(for)f(cases)i(in)f(which)g(it)f(f)o (ails)h(to)g(\002nd)f(a)g(proof,)257 4150 y(it)h(pro)o(vides)j(a)d (reasonable)j(starting)g(point.)398 4323 y(In)h(the)g(input)h(\002le,)f (the)g(command)h FD(set\(auto\))22 b FK(must)27 b(occur)h(before)g(an)o (y)f(input)h(clauses,)i(and)257 4436 y(all)j(input)h(clauses)g(must)f (be)g(in)f(list)i FD(usable)p FK(;)g(it)e(is)h(an)g(error)g(to)g(place) h(input)g(clauses)g(on)f(an)o(y)g(of)257 4549 y(the)h(other)g(lists)g (when)g(in)f(autonomous)k(mode.)60 b(O)q FE(T)t(T)t(E)t(R)38 b FK(will)33 b(mo)o(v)o(e)g(some)g(of)h(the)g(input)g(clauses)257 4662 y(to)f FD(sos)e FK(before)j(starting)h(the)e(search.)59 b(When)36 b(O)q FE(T)t(T)t(E)t(R)g FK(processes)g(the)d FD(set\(auto\))c FK(command,)257 4775 y(it)38 b(alters)h(some)g (options,)k(e)n(v)o(en)c(before)g(e)o(xamining)h(the)f(input)g (clauses.)75 b(If)38 b(the)g(user)h(wishes)g(to)257 4888 y(augment)e(the)e(autonomous)j(mode)e(by)g(including)i(some)d(ordinary) 40 b(O)q FE(T)t(T)t(E)t(R)f FK(commands)e(\(includ-)257 5001 y(ing)28 b(o)o(v)o(erriding)k(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)30 b(choices\),)g(the)e(commands)h(should)g(be)e(placed)j (after)e FD(set\(auto\))23 b FK(and)257 5114 y(before)i FD(list\(usable\))p FK(.)398 5287 y(After)k FD(list\(usable\))23 b FK(has)29 b(been)h(read,)j(O)q FE(T)t(T)t(E)t(R)f FK(e)o(xamines)f (the)e(input)h(clauses)h(for)e(se)n(v)o(eral)257 5400 y(syntactic)j(properties)h(and)d(decides)i(which)e(inference)i(rules)f (and)f(strate)o(gies)i(should)g(be)e(used,)i(and)257 5512 y(which)22 b(clauses)h(should)g(be)f(mo)o(v)o(ed)f(to)h FD(sos)p FK(.)k(The)21 b(user)h(cannot)h(o)o(v)o(erride)g(the)f (decisions)i(that)g(O)q FE(T)t(T)t(E)t(R)257 5625 y FK(mak)o(es)g(at)f (this)h(stage.)1861 5946 y(50)p eop %%Page: 51 57 51 56 bop 400 388 a FK(O)q FE(T)t(T)t(E)t(R)41 b FK(looks)e(for)f(the)f (follo)n(wing)i(syntactic)h(properties)g(of)e(the)f(set)h(of)f(input)i (clauses:)59 b(\(1\))257 501 y(whether)39 b(it)e(is)h(propositional,)45 b(\(2\))38 b(whether)h(it)f(is)g(Horn,)j(\(3\))d(whether)h(equality)h (is)e(present,)43 b(\(4\))257 614 y(whether)28 b(equality)i(axioms)f (are)e(present,)k(and)d(\(5\))f(the)h(maximum)g(number)g(of)g(literals) h(in)f(a)f(clause.)257 727 y(The)c(program)i(then)f(considers)i(six)e (basic)g(combinations)j(of)c(the)h(properties:)32 b(\(1\))24 b(propositional,)j(\(2\))257 840 y(equality)c(in)e(which)g(all)g (clauses)i(are)e(units,)h(and)g(\(3\2266\))g(the)f(four)h(combinations) i(of)d Fv(f)p FK(equality)-6 b(,)24 b(Horn)p Fv(g)p FK(.)257 953 y(T)-7 b(o)33 b(see)i(precisely)i(what)g(O)q FE(T)t(T)t(E)t(R)h FK(does)e(for)f(these)g(cases,)j(the)d(reader)h(can)f(set)g(up)g(and)g (run)g(some)257 1065 y(simple)24 b(e)o(xperiments.)398 1238 y(Please)h(be)f(a)o(w)o(are)g(that)h(the)f(autonomous)j(mode)d (re\003ects)h(indi)n(vidual)i(e)o(xperience)g(with)f(O)q FE(T)t(T)t(E)t(R)r FK(;)257 1351 y(other)36 b(users)h(w)o(ould)f (certainly)h(formulate)h(dif)n(ferent)f(metastrate)o(gies.)67 b(F)o(or)35 b(e)o(xample,)k(one)d(might)257 1464 y(prefer)c (UR-resolution)h(to)e(hyperresolution)36 b(or)30 b(in)h(addition)i(to)e (hyperresolution)36 b(in)31 b(rich)g(Horn)g(or)257 1577 y(nearly-Horn)36 b(theories,)j(and)c(one)f(might)h(prefer)g(to)g(add)f (fe)n(w)g(or)g(no)g(dynamic)i(demodulators)h(for)257 1690 y(equality)25 b(theories.)257 2043 y FJ(19)119 b(Fringe)30 b(F)m(eatur)n(es)257 2310 y FK(This)36 b(section)h(describes)i (features)e(that)g(are)f(ne)n(w)-6 b(,)38 b(not)f(well)e(tested,)40 b(and)d(not)f(well)g(documented.)259 2423 y(O)q FE(T)t(T)t(E)t(R)23 b FK(is)18 b(not)i(as)f(rob)n(ust)h(when)f(using)i(these)f(features,)h (especially)h(when)d(more)g(than)h(fringe)g(features)257 2535 y(is)j(being)i(used.)257 2845 y FI(19.1)99 b(Ancestor)25 b(Subsumption)259 3079 y FK(O)q FE(T)t(T)t(E)t(R)h FK(does)d(not)f (necessarily)j(prefer)e(short)g(or)f(simple)h(proofs\227it)h(simply)f (reports)h(the)e(proofs)h(that)257 3192 y(it)i(\002nds.)36 b(An)25 b(option)i FD(ancestor_subsum)o(e)19 b FK(e)o(xtends)27 b(the)f(concept)i(of)e(subsumption)i(to)e(include)257 3305 y(the)e(deri)n(v)n(ation)h(history)-6 b(,)25 b(so)f(that)g(if)f (tw)o(o)g(clause)i(occurrences)i(are)c(logically)j(identical,)g(the)d (one)h(with)257 3418 y(fe)n(wer)f(ancestors)j(is)e(preferred.)31 b(The)23 b(moti)n(v)n(ation)i(is)e(to)h(\002nd)f(short)h(proofs.)257 3591 y(Flag)36 b FD(ancestor_subsum)o(e)p FK(.)60 b(Def)o(ault)37 b(clear)-5 b(.)68 b(If)36 b(this)h(\003ag)f(is)g(set,)k(the)c(notion)i (of)e(subsump-)257 3703 y(tion)47 b(\(forw)o(ard)g(and)g(back\))g(is)f (replaced)i(with)e FG(ancestor)n(-subsumptio)q(n)p FK(.)102 b(Clause)47 b FC(C)k FK(ancestor)n(-)257 3816 y(subsumes)56 b(clause)g FC(D)h FK(if)n(f)d FC(C)61 b FK(properly)56 b(subsumes)h FC(D)f FK(or)f(if)f FC(C)61 b FK(and)55 b FC(D)h FK(are)f(v)n(ariants)i(and)257 3929 y FC(siz)t(e)p Fp(\()p FC(ancestor)s(set)p Fp(\()p FC(C)7 b Fp(\)\))26 b Fv(\024)f FC(siz)t(e)p Fp(\()p FC(ancestor)s(set)p Fp(\()p FC(D)s Fp(\)\))p FK(.)398 4102 y(When)36 b(setting)h FD(ancestor_subsu)o(me)o FK(,)32 b(we)i(strongly)k(recommend)f(not)e (clearing)j(the)d(\003ag)257 4215 y FD(back_subsume)p FK(,)20 b(because)28 b(doing)f(so)f(can)g(cause)h(man)o(y)f (occurrences)j(of)d(the)g(same)g(clause)h(to)f(be)257 4328 y(retained)f(and)f(used)h(as)e(gi)n(v)o(en)h(clauses.)257 4637 y FI(19.2)99 b(The)26 b(Hot)e(List)257 4871 y FK(The)c(hot)h(list) g(is)g(a)f(strate)o(gy)i(that)g(can)f(be)g(used)g(to)g(emphasize)h (particular)i(clauses.)29 b(It)21 b(w)o(as)f(in)l(v)o(ented)j(by)257 4984 y(Larry)i(W)-7 b(os)25 b(in)h(the)f(conte)o(xt)i(of)f (paramodulation,)j(and)d(it)f(has)h(been)g(e)o(xtended)h(to)f(most)f (of)j(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)257 5097 y(inference)38 b(rules.)67 b(T)-7 b(o)35 b(use)i(the)f(strate)o(gy)-6 b(,)41 b(the)36 b(user)h(simply)g(inputs)g(one)g(or)f(more)g(clauses)i (in)e(the)257 5210 y(special)e(list)g(named)f FD(hot)p FK(.)55 b(Whene)n(v)o(er)35 b(a)d(clause)i(is)f(generated)j(and)d(k)o (ept)h(by)h(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)36 b(ordinary)257 5323 y(mechanisms,)25 b(it)e(is)g(immediately)j(considered)g(for)e (inference)i(with)d(clauses)i(in)f(the)g(hot)g(list.)1861 5946 y(51)p eop %%Page: 52 58 52 57 bop 257 388 a FF(Which)18 b(Clauses)i(Should)e(Be)h(Hot?)92 b FK(Clauses)20 b(input)h(in)f(the)g(hot)g(list)g(are)g(usually)h (copies)h(of)d(clauses)257 501 y(that)30 b(occur)g(also)g(in)f FD(sos)e FK(or)i FD(usable)p FK(.)43 b(The)o(y)28 b(are)i(typically)h (clauses)g(that)f(the)g(user)g(belie)n(v)o(es)g(will)257 614 y(play)24 b(a)f(k)o(e)o(y)h(role)g(in)f(the)h(search)h(for)f(a)f (proof,)h(for)g(e)o(xample,)g(special)h(hypotheses.)257 920 y FF(Managing)j(Hot-List)h(Clauses.)91 b FK(Input)29 b(to)f(the)h(hot)f(list)g(is)g(the)h(same)f(as)g(input)h(to)f(other)h (lists)g(and)257 1033 y(can)24 b(be)f(in)h(either)g(clause)h(or)f (formula)g(form,)g(for)f(e)o(xample,)456 1292 y Fq(list\(hot\).)456 1391 y(f\(x,x\))49 b(=)g(x.)100 b(m\(m\(x\)\))48 b(=)i(x.)456 1491 y(end_of_list.)257 1764 y FK(The)24 b(\003ag)g FD(process_input)18 b FK(has)25 b(no)g(ef)n(fect)h(on)e(hot-list)j(clauses;)g(the)o(y)e (are)g(ne)n(v)o(er)g(altered)h(during)257 1877 y(input.)59 b(Hot-list)35 b(clauses)g(are)f(ne)n(v)o(er)g(deleted,)j(for)d(e)o (xample)g(by)f(back)i(subsumption)h(or)d(back)i(de-)257 1989 y(modulation.)40 b(Ev)o(en)26 b(if)g(a)g(hot-list)i(clause)g(is)e (identical)j(to)e(a)f(clause)h(in)g(another)h(list,)f(it)g(has)f(a)g (unique)257 2102 y(identifying)j(number)l(,)e(and)f(proofs)h(that)f (use)g(hot-list)h(clauses)h(generally)g(refer)e(to)g(tw)o(o)f(copies)i (\(with)257 2215 y(dif)n(ferent)e(ID)e(numbers\))i(of)e(those)i (clauses.)257 2521 y FF(Hot)e(Infer)n(ence)i(Rules.)91 b FK(The)23 b(inference)j(rules)f(that)f(are)g(applied)i(to)d(ne)n(wly) h(k)o(ept)h(clauses)g(and)f(hot-)257 2634 y(list)30 b(clauses)i(are)f (the)f(same)h(as)f(the)g(rules)i(in)e(ef)n(fect)h(for)f(ordinary)j (inference,)h(with)c(the)g(e)o(xceptions)257 2747 y FD(demod_inf)p FK(,)g FD(geometric_rule)p FK(,)f(and)k FD(linked_ur_res)p FK(,)c(which)34 b(are)f(ne)n(v)o(er)h(applied)h(to)257 2860 y(hot-list)25 b(clauses.)257 3166 y FF(A)n(pplying)d(Hot)h(Infer)n (ence.)93 b FK(When)23 b(hot)h(inference)i(is)d(applied,)j(the)d(ne)n (wly)h(k)o(ept)g(clause)h(is)e(treated)257 3279 y(as)28 b(the)g(gi)n(v)o(en)g(clause,)j(and)d(the)g(hot)h(list)f(is)g(treated)h (as)f(the)g(usable)i(list.)42 b(\(Note)28 b(that)h(the)f(ne)n(wly)g(k)o (ept)257 3392 y(clause)d(is)e(not)h(in)g(the)g(hot)g(list,)g(so)f(it)h (will)f(not)h(be)g(considered)j(for)c(inference)j(with)e(itself,)g(as)g (happens)257 3504 y(with)f(the)h(gi)n(v)o(en)h(clause)g(in)e(ordinary)j (inference.\))32 b(F)o(or)23 b(inference)j(rules)f(such)f(as)g (hyperresolution)k(or)257 3617 y(UR-resolution)j(that)f(can)g(use)f (more)g(than)h(tw)o(o)f(parents,)j FG(all)e FK(of)f(the)g(other)h (parents)h(must)e(be)h(in)f(the)257 3730 y(hot)21 b(list;)i(this)f (generally)h(means)f(that)f(the)h(nucleus)h(and)e(other)i(satellites)g (must)e(be)g(in)g(the)h(hot)f(list.)28 b(Hot)257 3843 y(inference)e(is)d(not)h(applied)h(to)f(clauses)h(that)f(are)g(\223k)o (ept\224)h(during)g(processing)i(of)c(the)h(input.)257 4149 y FF(Le)o(v)o(el)e(of)h(Hot)f(Infer)n(ence)h(\(P)o(arameter)h FD(heat)p FF(\).)89 b FK(T)-7 b(o)21 b(pre)n(v)o(ent)j(long)f (sequences)i(of)e(hot)f(inferences)257 4262 y(\(i.e.,)28 b(hot)g(inference)i(applied)g(to)e(a)f(clause)i(generated)i(by)c(hot)i (inference,)i(and)d(so)g(on\))g(we)f(consider)257 4375 y(the)j FG(heat)g(le)o(vel)h FK(of)f(hot)g(inference.)50 b(The)29 b(heat)i(le)n(v)o(el)f(of)f(an)h(ordinary)i(inference)h(is)c (0,)i(and)f(the)g(heat)257 4488 y(le)n(v)o(el)21 b(of)g(a)g(hotly)h (inferred)h(clause)g(is)e(one)h(more)f(than)h(the)f(heat)h(le)n(v)o(el) g(of)f(the)g(ne)n(w-clause)i(parent.)29 b(The)257 4601 y(parameter)21 b FD(heat)p FK(,)c(def)o(ault)j(1,)g(range)g([0..100],)h (is)e(the)g(maximum)g(heat)h(le)n(v)o(el)f(that)h(will)f(be)g (generated.)257 4714 y(When)24 b(a)f(clause)i(is)e(printed,)i(its)f (heat)g(le)n(v)o(el,)f(if)h(greater)h(than)f(0,)f(is)g(also)h(printed.) 257 5019 y FF(Dynamic)31 b(Hot)g(Clauses)h(\(P)o(arameter)h FD(dynamic)p 2006 5019 28 4 v 30 w(heat)p 2256 5019 V 30 w(weight)p FF(\).)89 b FK(Clauses)32 b(can)g(be)g(added)257 5132 y(to)f(the)h(hot)g(list)f(during)i(a)e(search.)54 b(If)31 b(the)h FD(pick_given)26 b FK(weight)32 b(of)f(a)g(k)o(ept)h (clause)h(is)e(less)h(than)257 5245 y(or)25 b(equal)i(to)e(the)h (parameter)h FD(dynamic_heat_w)o(ei)o(ght)o FK(,)19 b(def)o(ault)27 b Fv(\0001)p FK(,)d(range)j([)p Fv(\0001)p FK(..)p Fv(1)p FK(],)d(then)257 5358 y(the)g(clause)g(will)g(be)f(added)i(to)e(the)h (hot)g(list)g(and)g(used)g(for)g(subsequent)j(hot)d(inference.)31 b(Input)24 b(clauses)257 5471 y(that)34 b(are)f(\223k)o(ept\224)i (during)g(processing)h(of)d(the)h(input)g(are)f(ne)n(v)o(er)h(made)f (into)h(dynamic)h(hot)f(clauses.)257 5584 y(Dynamic)24 b(hot)g(clauses)h(can)f(be)f(added)i(to)f(an)f(empty)h(hot)g(list)g (\(i.e.,)f(no)h(input)g(hot)g(list\).)1861 5946 y(52)p eop %%Page: 53 59 53 58 bop 257 388 a FI(19.3)99 b(Sequent)27 b(Notation)e(f)n(or)f (Clauses)257 622 y FK(T)-7 b(w)o(o)22 b(\003ags)h(enable)i(the)f(use)g (of)g(sequent)h(notation)h(for)e(clauses.)257 795 y(Flag)j FD(input_sequent)p FK(.)32 b(Def)o(ault)c(clear)-5 b(.)40 b(If)26 b(this)i(\003ag)e(is)h(set,)h(clauses)h(in)d(the)i(input)g (\002le)e(must)h(be)257 908 y(in)c(sequent)j(notation.)257 1081 y(Flag)j FD(output_sequent)p FK(.)41 b(Def)o(ault)30 b(clear)-5 b(.)49 b(If)29 b(this)h(\003ag)g(is)f(set,)i(then)g(sequent) h(notation)g(is)d(used)257 1194 y(when)23 b(clauses)j(are)d(output.)257 1367 y(Syntax:)393 1610 y Fv(\017)46 b FK(All)23 b(sequent)i(clauses)h (ha)n(v)o(e)e(an)f(arro)n(w)-6 b(.)393 1787 y Fv(\017)46 b FK(The)35 b(ne)o(gati)n(v)o(e)g(literals)i(\(if)e(an)o(y\))g(are)g (written)h(on)f(the)g(left)h(side)f(of)g(the)h(arro)n(w)-6 b(,)37 b(are)e(written)484 1900 y(without)25 b(the)e(ne)o(gation)i (sign,)f(and)g(are)g(separated)i(by)e(commas.)393 2078 y Fv(\017)46 b FK(The)18 b(positi)n(v)o(e)i(literals)g(\(if)f(an)o(y\)) g(are)f(written)h(on)g(the)g(right)g(side)g(of)g(the)g(arro)n(w)f(and)h (are)g(separated)484 2191 y(by)24 b(commas.)257 2434 y(T)-7 b(able)23 b(10)h(lists)g(some)g(e)o(xamples.)1184 2688 y(T)-7 b(able)24 b(10:)29 b(Examples)24 b(of)g(Sequent)g(Clauses)p 962 2719 1891 4 v 1012 2798 a(Ordinary)g(Clause)p 2151 2832 4 113 v 594 w(Sequent)h(Clause)p 962 2836 1891 4 v 1012 2915 a FD(-p)53 b(|)h(-q)g(|)g(-r)g(|)g(s)g(|)g(t)p 2151 2948 4 113 v 99 w(p,q,r->s,t)1012 3027 y(p\(a,b,c\))p 2151 3061 V 750 w(->)g(p\(a,b,c\))1012 3140 y(a!=b)p 2151 3174 V 970 w(a=b)f(->)1012 3253 y($F)21 b FK(\(the)j(empty)g (clause\))p 2151 3287 V 390 w FD(->)p 962 3290 1891 4 v 398 3533 a FK(Note)f(that)h FD(p,q->r,s)c FK(is)j(ordinarily)j (thought)g(of)d(as)h(\()p FD(p)e FG(and)i FD(q)p FK(\))f FG(implies)h FK(\()p FD(r)f FG(or)g FD(s)p FK(\).)398 3706 y(Sequent)k(clauses)g(are)e(treated)i(as)f(\(parsed)h(as\))f(a)f (special)i(case)f(because)h(the)o(y)f(can')n(t)h(be)f(made)f(to)257 3819 y(\002t)d(within)k(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)26 b(ordinary)g(syntax.)257 4124 y FI(19.4)99 b(Conditional)24 b(Demodulation)257 4358 y FK(A)e(conditional)27 b(demodulator)f(has)e (the)g(form)484 4581 y FG(condition)i FD(->)54 b FG(equality-liter)o (al)p FK(.)257 4803 y(The)19 b(equality)i(is)f(applied)h(as)e(a)g (demodulator)j(if)e(and)g(only)g(if)f(the)h(instantiated)j FG(condition)f FK(e)n(v)n(aluates)f(to)257 4916 y FD($T)p FK(.)16 b(The)i(equality)i(of)e(a)g(conditional)k(demodulator)f(is)d (not)h(subjected)h(on)f(input)g(to)f(being)i(\003ipped)f(or)f(to)257 5029 y(being)i(\003agged)h(as)e(a)g(le)o(x-dependent)k(demodulator)l(,) g(and)d(conditional)j(demodulators)g(are)c(ne)n(v)o(er)h(back)257 5142 y(demodulated.)49 b(In)30 b(other)g(w)o(ays,)h(conditional)i (demodulators)f(beha)n(v)o(e)f(as)f(ordinary)h(demodulators.)257 5255 y(Examples)24 b(are)g(\()p FD(member)c FK(and)k FD(gcd)d FK(are)j(de\002ned)h(in)e(Sec.)g(9.\))456 5485 y Fq($ATOMIC\(x\))48 b(->)h(conjunctive_normal_form\(x\)=x.)456 5584 y(member\(gcd\(4,x\),y\))e(->)i(Equal\(f\(x,y\),)e(g\(y\)\).)456 5684 y($GT\($NEXT_CL_NUM,1000\))f(->)j(e\(x,x\))g(=)h(junk.)1861 5946 y FK(53)p eop %%Page: 54 60 54 59 bop 257 388 a FI(19.5)99 b(Deb)n(ugging)25 b(Sear)n(ches)i(and)e (Demodulation)257 622 y FK(The)32 b(\003ag)h FD(very_verbose)27 b FK(causes)34 b(too)g(much)f(output)h(to)f(be)g(used)h(with)f(lar)n (ge)h(searches.)59 b(The)257 735 y(follo)n(wing)25 b(parameters)g(can)f (turn)g(on)g(v)o(erbose)h(output)g(for)f(a)f(se)o(gment)h(of)g(the)g (search.)257 908 y FD(assign\(debug_f)o(irs)o(t,)o FC(n)p FD(\))o FK(.)43 b(Def)o(ault)31 b(0,)g(range)h([0)e(..)p Fv(1)p FK(].)48 b(This)30 b(parameter)i(is)e(consulted)j(if)257 1021 y(the)23 b(\003ag)f FD(very_verbose)17 b FK(is)22 b(set.)29 b(V)-10 b(erbose)24 b(output)g(will)f(be)o(gin)g(when)g(a)g (clause)h(is)f(k)o(ept)g(and)g(gi)n(v)o(en)257 1134 y(an)g (identi\002er)i(of)f(this)g(v)n(alue.)257 1307 y FD(assign\(debug_f)o (irs)o(t,)o FC(n)p FD(\))o FK(.)30 b(Def)o(ault)d(-1,)f(range)h([-1)g (..)p Fv(1)p FK(].)35 b(This)26 b(parameter)i(is)e(consulted)i(if)257 1420 y(the)f(\003ag)g FD(very_verbose)20 b FK(is)27 b(set.)40 b(V)-10 b(erbose)28 b(output)g(will)f(end)g(when)g(a)g(clause)h(is)f(k) o(ept)h(and)f(gi)n(v)o(en)257 1533 y(an)c(identi\002er)i(of)f(this)g(v) n(alue.)257 1706 y FD(assign\(verbose)o(_de)o(mo)o(d_)o(sk)o(ip)o(,)p FC(n)p FD(\))o FK(.)62 b(Def)o(ault)38 b(0,)i(range)e([0)f(..)p Fv(1)p FK(].)68 b(This)37 b(parameter)h(is)257 1818 y(consulted)27 b(during)f(demodulation)h(if)d(the)h(\003ag)f FD(very_verbose)18 b FK(is)24 b(set.)31 b(V)-10 b(erbose)26 b(output)g(will)e(not)257 1931 y(occur)g(during)i(the)d(\002rst)h FC(n)e FK(re)n(writes.)257 2233 y FI(19.6)99 b(Special)25 b(Unary)g(Function)h(Demodulation)257 2467 y FK(A)19 b(feature,)j(acti)n(v)n(ated)g(by)f(the)f FD(special_unary)14 b FK(command,)21 b(allo)n(ws)i(O)q FE(T)t(T)t(E)t(R)h FK(to)c(a)n(v)n(oid)i(one)f(of)f(the)257 2580 y(problems)34 b(caused)h(by)e(the)g(lack)h(of)f(associati)n(v)o (e-commutati)n(v)o(e)38 b(matching)c(during)h(demodulation.)257 2693 y(The)23 b(feature)i(is)e(useful)h(when)g(an)f(associati)n(v)o (e-commutati)n(v)o(e)28 b(function)e(and)e(an)f(in)l(v)o(erse)i(are)f (present,)257 2806 y(as)f(in)h(rings.)29 b(W)l(ithout)d(this)e (feature,)g(the)g(follo)n(wing)h FD(lex)d FK(command)i(and)g (demodulators)456 3019 y Fq(lex\([0,a,b,c,d,e,g\(_\),f\(_,_\)]\).)456 3218 y(list\(demodulators\).)456 3318 y(f\(x,y\))49 b(=)g(f\(y,x\).)456 3417 y(f\(x,f\(y,z\)\))f(=)h(f\(y,f\(x,z\)\).)456 3517 y(f\(x,g\(x\)\))f(=)i(0.)456 3616 y(f\(x,f\(g\(x\),y\)\))d(=)j (f\(0,y\).)456 3716 y(f\(0,x\))f(=)g(x.)456 3816 y(end_of_list.)257 4042 y FK(will)23 b(cause)i(the)e(e)o(xpression)456 4254 y Fq(f\(f\(f\(g\(b\),a\),c\),f\(b,g\(c\)\)\))257 4480 y FK(to)g(be)h(sorted)h(into)456 4693 y Fq (f\(a,f\(b,f\(c,f\(g\(b\),g\(c\)\)\)\)\).)257 4919 y FK(One)19 b(w)o(ould)h(lik)o(e)g FD(b)e FK(and)i FD(g\(b\))c FK(to)k(be)f(ne)o(xt)h(to)f(each)h(other)g(so)g(that)g(the)o(y)f(could) i(be)e(canceled)j(by)d(one)h(of)257 5032 y(the)k(in)l(v)o(erse)h (demodulators.)32 b(The)23 b(special-unary)k(feature)e(accomplishes)i (just)d(that.)29 b(The)23 b(command)456 5245 y Fq (special_unary\([g\(x\)]\))257 5471 y FK(causes)g FD(g)d FK(to)h(be)h(ignored)h(during)g(term)f(comparisons,)i(and)e(the)g(e)o (xpression)i(will)d(be)h(demodulated)i(to)257 5584 y FD(a)p FK(.)31 b(The)25 b FD(special_unary)18 b FK(command)26 b(has)f(no)g(ef)n(fect)g(if)g(the)g(\003ag)g FD(lrpo)d FK(is)j(set.)33 b FG(This)24 b(is)h(a)g(highly)257 5697 y(e)n(xperimental)h(featur)m(e)o(.)k(Its)24 b(behavior)i(has)e(not)g (been)g(well)f(analyzed.)1861 5946 y FK(54)p eop %%Page: 55 61 55 60 bop 257 388 a FI(19.7)99 b(The)26 b(In)l(visible)e(Ar)o(gument) 259 622 y FK(O)q FE(T)t(T)t(E)t(R)k FK(recognizes)g(a)c(b)n(uilt-in)j (unary)f(function)g(symbol)g FD($IGNORE\(_\))p FK(.)h(F)o(orw)o(ard)d (subsumption)257 735 y(treats)i(each)g(term)f(that)h(starts)g(with)f FD($IGNORE)c FK(as)k(the)g(constant)j FD($IGNORE)p FK(,)20 b(completely)28 b(ignoring)257 848 y(its)k(ar)n(gument.)56 b(F)o(or)32 b(e)o(xample,)i FD(p\(a,$IGNORE\(b\)\))25 b FK(subsumes)34 b FD(p\(a,$IGNORE\(c\))o(\))p FK(.)48 b(All)257 961 y(other)26 b(operations)i(\(in)e(particular)l(,)i (inference)g(rules,)e(demodulation,)j(and)d(back)g(subsumption\))i (treat)257 1074 y FD($IGNORE)19 b FK(as)24 b(an)f(ordinary)j(function)g (symbol.)398 1247 y(The)20 b(purpose)j(of)e FD($IGNORE)16 b FK(is)21 b(to)g(record)h(data)f(about)h(the)f(deri)n(v)n(ation)i(of)e (a)f(clause)i(without)g(ha)n(v-)257 1360 y(ing)27 b(that)g(data)g(pre)n (v)o(ent)h(the)f(forw)o(ard)h(subsumption)h(of)e(clauses)h(that)g(w)o (ould)f(be)g(subsumed)h(without)257 1473 y(that)h(data.)46 b(The)28 b FD($IGNORE)d FK(term)k(is)f(the)h(term)g(analog)h(of)f(the)g (answer)h(literal.)46 b(F)o(or)28 b(e)o(xample,)j(one)257 1586 y(can)c(use)g FD($IGNORE)c FK(terms)k(in)f(the)h(jugs)h(and)f(w)o (ater)g(puzzle)h(\(Sec.)e(9.2\))h(to)g(record)h(the)f(sequence)i(of)257 1698 y(pourings)d(that)e(leads)g(to)g(each)g(state.)257 2003 y FI(19.8)99 b(Floating-P)n(oint)24 b(Operations)257 2237 y FK(T)-7 b(able)28 b(11)g(lists)g(a)g(set)g(of)g (\003oating-point)j(e)n(v)n(aluable)f(functions)g(and)f(predicates)i (that)d(are)g(analogous)257 2350 y(to)h(the)g(inte)o(ger)i(arithmetic)g (operations)h(listed)e(in)f(Sec.)g(9.)45 b(The)o(y)29 b(operate)i(in)e(the)g(same)h(w)o(ay)f(as)g(the)257 2463 y(inte)o(ger)c(operations.)1250 2717 y(T)-7 b(able)23 b(11:)30 b(Floating-Point)c(Operations)p 601 2749 2613 4 v 599 2862 4 113 v 650 2828 a FC(f)10 b(l)r(oat)20 b Fv(\002)g FC(f)10 b(l)r(oat)24 b Fv(!)h FC(f)10 b(l)r(oat)p 1575 2862 V 99 w FD($FSUM)p FK(,)20 b FD($FPROD)p FK(,)g FD($FDIFF)p FK(,)g FD($FDIV)p 3211 2862 V 601 2865 2613 4 v 599 2978 4 113 v 650 2944 a FC(f)10 b(l)r(oat)20 b Fv(\002)g FC(f)10 b(l)r(oat)24 b Fv(!)h FC(bool)p 1575 2978 V 154 w FD($FEQ)p FK(,)c FD($FNE)p FK(,)f FD($FLT)p FK(,)h FD($FLE)p FK(,)f FD($FGT)p FK(,)h FD($FGE)p 3211 2978 V 601 2981 2613 4 v 398 3224 a FK(The)e(\003oating-point)k (constants,)f(ho)n(we)n(v)o(er)l(,)f(are)e(a)g(little)i(peculiar)l(,)h (both)e(in)g(the)f(w)o(ay)g(the)o(y)h(look)h(and)257 3337 y(in)29 b(the)h(w)o(ay)f(the)o(y)h(beha)n(v)o(e.)48 b(The)o(y)29 b(are)h(written)g(as)f(quoted)i(strings,)i(using)d(either) h(single)g(or)e(double)257 3450 y(quotes.)64 b(\(Otherwise,)39 b(the)o(y)c(w)o(ould)g(not)h(be)f(able)g(to)g(contain)i(decimal)f (points.\))64 b(Other)35 b(than)h(the)257 3563 y(quotation)26 b(marks,)e(the)f(form)h(of)f(the)h(\003oating-point)j(constants)f (accepted)g(by)f(O)q FE(T)t(T)t(E)t(R)i FK(is)d(e)o(xactly)h(the)257 3676 y(same)f(as)h(the)g(form)f(accepted)j(by)e(the)f(C)g(programming)i (language)h(\(actually)g(the)e(C)e(library)k(used)e(by)257 3789 y(the)e(compiler\).)30 b(Examples)24 b(are)f FD("1.2")p FK(,)d FD("10e6")p FK(,)f FD("-3.333E-5")p FK(.)k(A)f(\003oating-point) k(constant)257 3902 y(must)d(contain)j(either)e(a)g(decimal)g(point)h (or)e(an)h(e)o(xponent)h(character)h FD(e)c FK(or)i FD(E)p FK(.)398 4075 y(The)32 b(peculiar)j(beha)n(vior)h(comes)d(from)g(the)g (f)o(act)j(O)q FE(T)t(T)t(E)t(R)g FK(stores)f(the)e(\003oating)h(point) g(numbers)257 4188 y(as)25 b(character)j(strings)f(instead)g(of)f (directly)h(as)f(\003oating)g(point)h(numbers.)36 b(T)-7 b(o)24 b(apply)j(a)e(\003oating-point)257 4300 y(operation,)f(O)q FE(T)t(T)t(E)t(R)f FK(starts)d(with)f(the)g(operand)i(strings,)h (translates)f(them)e(to)g(true)h(\003oating-point)i(num-)257 4413 y(bers)30 b(\(the)h(C)e(data)h(type)h(\223double\224)i(is)c (used\),)k(performs)e(the)f(operation,)k(then)d(translates)i(the)d (result)257 4526 y(into)c(a)f(string)h(so)f(that)h(it)f(can)h(be)f(an)i (O)q FE(T)t(T)t(E)t(R)i FK(constant.)36 b(As)25 b(well)g(as)g(being)h (inef)n(\002cient,)h(this)f(scheme)257 4639 y(also)32 b(has)g(a)g(problem)h(with)e(precision,)36 b(because)e(a)d(\002x)o(ed)g (format)i(is)e(used)i(to)f(translate)h(the)f(results)257 4752 y(back)25 b(into)g(strings.)34 b(The)24 b(def)o(ault)i(format)f (is)g FD("\045.12f")p FK(,)20 b(and)25 b(it)g(can)g(be)f(changed)j (with)d(a)g(command)257 4865 y(such)g(as)484 5075 y Fq (float_format\("\04517.8f"\))257 5298 y FG(Caution.)66 b FK(O)q FE(T)t(T)t(E)t(R)39 b FK(does)d(not)f(check)h(that)g(the)f (string)h(in)f(the)g FD(float_format)29 b FK(command)36 b(is)e(a)257 5411 y(well-formed)25 b(format)f(speci\002cation.)31 b(This)24 b(is)f(the)h(user')-5 b(s)25 b(responsibility)-6 b(.)398 5584 y(T)f(o)31 b(fully)j(understand)i(ho)n(w)c(this)h(w)o (orks,)i(see)e(the)g(standard)h(C)e(language)j(reference)g([11)q(,)e (Ap-)257 5697 y(pendix)20 b(B];)e(in)g(particular)l(,)k(the)d(C)f (library)i(functions)h FD(sscanf)15 b FK(and)k FD(sprintf)14 b FK(are)19 b(used)g(to)g(translate)1861 5946 y(55)p eop %%Page: 56 62 56 61 bop 257 388 a FK(to)23 b(and)h(from)g(strings.)257 697 y FI(19.9)99 b(F)n(or)n(eign)24 b(Ev)o(aluable)i(Functions)259 931 y FK(O)q FE(T)t(T)t(E)t(R)32 b FK(pro)o(vides)e(a)e(general)i (mechanism)g(through)g(which)f(one)g(can)f(create)i(one')-5 b(s)29 b(o)n(wn)f(e)n(v)n(aluable)257 1044 y(functions)35 b(and)f(predicates.)59 b(The)33 b(user)g(\(1\))g(declares)i(the)e (function,)38 b(its)33 b(ar)n(gument)h(types,)j(and)c(its)257 1157 y(result)21 b(type,)h(\(2\))e(inserts)i(a)e(call)h(to)f(the)g (function)j(in)d(the)j(O)q FE(T)t(T)t(E)t(R)h FK(source)e(code,)f (\(3\))g(writes)f(a)g(C)f(routine)257 1270 y(to)k(implement)h(the)f (function,)i(and)e(\(4\))g(recompiles)k(O)q FE(T)t(T)t(E)t(R)r FK(.)k(The)22 b(user)i(must)f(ha)n(v)o(e)g(a)g(personal)i(cop)o(y)257 1383 y(of)20 b(the)g(source)i(code)f(to)f(use)g(this)h(feature.)29 b(See)20 b(the)g(source)i(code)e(\002le)g FD(foreign.h)15 b FK(for)20 b(step-by-step)257 1496 y(instructions,)27 b(e)o(xamples,)d(templates,)h(and)f(test)g(\002les.)257 1669 y FG(Important)51 b(note)o(.)107 b FK(Man)o(y)49 b(times)g(you)h(can)g(a)n(v)n(oid)h(ha)n(ving)g(to)f(do)f(all)g(of)h (this)g(by)f(just)h(writ-)257 1782 y(ing)e(your)h(function)i(with)d (demodulators)j(and)e(using)g(e)o(xisting)h(b)n(uilt-in)g(functions.) 106 b(F)o(or)47 b(e)o(x-)257 1895 y(ample,)i(if)43 b(you)h(need)g(the)g (maximum)g(of)f(tw)o(o)h(doubles,)50 b(you)44 b(can)g(just)g(use)g(the) g(demodulator)257 2008 y FD(float_max\(x,y\))k(=)54 b ($IF\($FGT\(x,y\),)48 b(x,)54 b(y\))p FK(.)257 2317 y FI(19.10)99 b(The)26 b(Infer)n(ence)h(Rule)e Fa(g)t(L)f FI(f)n(or)h(Cubic)g(Cur)o(v)o(es)257 2551 y FK(Based)d(on)h(w)o(ork)f (of)g(R.)f(P)o(admanabhan)j(and)e(others,)i(a)d(ne)n(w)h(inference)i (rule,)f FC(g)s(L)f FK(\(\223geometric)j(La)o(w\224,)257 2664 y(or)i(\223Local)g(to)g(global\224\),)j(w)o(as)d(added)h(to)h(O)q FE(T)t(T)t(E)t(R)r FK(.)41 b(The)27 b(rule)h(implements)g(a)f (local-to-global)k(gener)n(-)257 2777 y(alization)26 b(principle)f(that)f(has)g(a)f(geometric)i(interpretation)j(for)23 b(cubic)i(curv)o(es.)30 b(The)23 b(article)h([20)r(])f(and)257 2890 y(the)h(monograph)i([18)q(])e(contain)i(descriptions)h(of)d(the)g (rule,)g(some)g(details)i(about)f(its)f(implementation)257 3003 y(in)h(O)q FE(T)t(T)t(E)t(R)r FK(,)g(and)f(se)n(v)o(eral)h(ne)n(w) e(results)i(obtained)h(with)d(its)h(use.)398 3176 y(The)c(rule)g FC(g)s(L)g FK(applies)i(to)e(single)i(positi)n(v)o(e)f(unit)g (equalities,)i(and)e(it)f(is)g(implemented)i(in)e(tw)o(o)g(w)o(ays:)257 3289 y(as)29 b(an)h(inference)i(rule,)f(with)e(uni\002cation,)k(and)d (as)g(a)f(re)n(write)h(rule,)h(for)f(when)f(the)h(tar)n(get)h(terms)f (are)257 3401 y(already)25 b(identical.)398 3574 y(Flag)33 b FD(geometric_rule)p FK(.)51 b(Def)o(ault)35 b(clear)-5 b(.)59 b(When)34 b(this)g(\003ag)f(is)g(set,)j FC(g)s(L)d FK(is)g(applied)j(as)d(an)257 3687 y(inference)28 b(rule)f(\(along)g (with)f(an)o(y)g(other)i(inference)g(rules)f(that)g(are)f(set\))g(to)g (each)h(gi)n(v)o(en)g(clause.)37 b(The)257 3800 y(rule)24 b FC(g)s(L)f FK(applies)i(to)f(single)h(positi)n(v)o(e)g(unit)f (equalities.)398 3973 y(Flag)32 b FD(geometric_rewri)o(te)o(_b)o(ef)o (or)o(e)p FK(.)48 b(Def)o(ault)33 b(clear)-5 b(.)55 b(When)33 b(this)f(\003ag)g(is)g(set,)i FC(g)s(L)e FK(is)257 4086 y(applied)25 b(as)f(a)f(re)n(write)h(rule,)f(before)i(ordinary)h (demodulation,)h(to)c(each)h(generated)i(clause.)398 4259 y(Flag)36 b FD(geometric_rewr)o(it)o(e_a)o(ft)o(er)o FK(.)60 b(Def)o(ault)36 b(clear)-5 b(.)67 b(When)37 b(this)f(\003ag)g (is)f(set,)40 b FC(g)s(L)35 b FK(is)257 4372 y(applied)25 b(as)f(a)f(re)n(write)h(rule,)f(after)i(ordinary)g(demodulation,)i(to)c (each)i(generated)h(clause.)398 4545 y(Flag)32 b FD(gl_demod)p FK(.)49 b(Def)o(ault)32 b(clear)-5 b(.)55 b(When)32 b(this)g(\003ag)g (is)f(set,)j(ordinary)g(demodulation)h(is)d(not)257 4658 y(applied)d(to)e(an)o(y)g(deri)n(v)o(ed)i(clauses.)41 b(Instead,)30 b(after)e(a)e(clause)j(is)e(k)o(ept,)i(it)d(is)h(copied,) j(and)d(the)h(cop)o(y)g(is)257 4771 y(demodulated)e(and)e(processed.) 398 4943 y(Our)k(e)o(xperience)j(has)e(sho)n(wn)f(that)h(gi)n(v)o(en)g (tw)o(o)f(equalities)j(of)e(equal)g(weight,)h(one)f(the)g(result)g(of) 257 5056 y FC(g)s(L)h FK(and)g(the)g(other)h(not,)h(the)e FC(g)s(L)g FK(result)h(is)f(usually)i(more)e(interesting.)51 b(The)30 b(follo)n(wing)h(parameter)257 5169 y(can)24 b(gi)n(v)o(e)f(preference)k(to)c FC(g)s(L)g FK(results.)257 5342 y FD(assign\(geo_giv)o(en_)o(ra)o(ti)o(o,)o FC(n)p FD(\))o FK(.)40 b(Def)o(ault)30 b(1,)g(range)g([)p Fv(\000)p Fp(1)p FK(..)p Fv(1)p FK(].)46 b(When)29 b(this)h(parameter)h(is)257 5455 y(not)25 b Fv(\000)p Fp(1)p FK(,)g(it)f(af)n(fects)i(selection)i (of)d(the)g(gi)n(v)o(en)g(clause)i(in)e(a)f(w)o(ay)h(similar)g(to)g FD(pick_given_ratio)o FK(.)257 5568 y(If)38 b(the)g(ratio)h(is)e FC(n)p FK(,)j(then)f(for)f(each)h FC(n)e FK(gi)n(v)o(en)h(clauses)i (selected)g(in)e(the)g(normal)h(w)o(ay)f(by)g(weight,)257 5681 y(one)k(gi)n(v)o(en)h(clause)g(is)f(selected)i(because)g(it)d(is)h (the)h(lightest)g FC(g)s(L)f FK(result)h(a)n(v)n(ailable)i(in)c FD(sos)p FK(.)82 b(If)1861 5946 y(56)p eop %%Page: 57 63 57 62 bop 257 388 a FD(pick_given_rat)o(io)21 b FK(and)29 b FD(geo_given_rati)o(o)21 b FK(are)29 b(both)g(in)f(ef)n(fect,)i(then) f(clashes)h(are)f(re-)257 501 y(solv)o(ed)c(in)e(f)o(a)n(v)n(or)i(of)e FD(geo_given_ratio)p FK(.)257 810 y FI(19.11)99 b(Link)o(ed)26 b(UR-Resolution)259 1044 y FK(O)q FE(T)t(T)t(E)t(R)34 b FK(has)d(an)g(inference)i(rule,)g FD(linked_ur_res)p FK(,)25 b(that)31 b(is)g(an)f(application)k(of)d(the)g(link)o(ed)h(in-) 257 1157 y(ference)39 b(principle)h(to)d(UR-resolution.)72 b(Link)o(ed)38 b(inference)i(rules)e(can)g(tak)o(e)g(much)g(lar)n(ger)h (infer)n(-)257 1270 y(ence)27 b(steps)g(than)g(the)f(corresponding)k (nonlink)o(ed)f(rules,)f(thereby)g(a)n(v)n(oiding)g(the)f(retention)h (of)e(man)o(y)257 1383 y(clauses)33 b(that)f(correspond)j(to)d(lo)n (w-le)n(v)o(el)g(deduction)i(steps)f(which)f(can)g(interfere)i(with)d (the)h(o)o(v)o(erall)257 1496 y(proof)24 b(search)h(strate)o(gy)-6 b(.)398 1669 y(W)f(e)22 b(refer)h(the)g(reader)g(to)g([29)q(,)e(34)q(,) h(26)q(])g(for)g(background)k(on)d(link)o(ed)h(inference)h(rules,)e (and)g(we)f(fo-)257 1782 y(cus)i(here)g(on)g(specifying)i(the)e (constraints)j(on)d(link)o(ed)h(UR-resolution)h(for)g(O)q FE(T)t(T)t(E)t(R)r FK(.)31 b(The)23 b(constraints)257 1895 y(are)h(speci\002ed)g(by)g(six)g(\003ags,)f(tw)o(o)g(parameters,)j (and)e(annotations)i(on)e(input)h(clauses.)257 2201 y FF(Link)o(ed)d(UR)g(Flags)257 2373 y FK(Flag)27 b FD(linked_ur_res)p FK(.)35 b(Def)o(ault)29 b(clear)-5 b(.)42 b(If)28 b(this)g(\003ag)g(is) f(set,)i(link)o(ed)g(UR-resolution)i(is)c(applied)257 2486 y(to)c(all)h(gi)n(v)o(en)g(clauses.)257 2659 y(Flag)f FD(linked_ur_trace)p FK(.)f(Def)o(ault)j(clear)-5 b(.)31 b(If)23 b(this)i(\003ag)e(is)h(set,)g(detailed)h(information)i(about)e (the)257 2772 y(linking)g(process)h(is)d(sent)h(to)g(the)f(output)i (\002le.)257 2945 y(Flag)30 b FD(linked_sub_unit_)o(us)o(ab)o(le)o FK(.)44 b(Def)o(ault)32 b(clear)-5 b(.)51 b(If)30 b(this)i(\003ag)e(is) g(set,)j(intermediate)g(unit)257 3058 y(clauses)25 b(are)f(check)o(ed)h (for)f(subsumption)j(against)d(the)g FD(usable)c FK(list.)257 3231 y(Flag)h FD(linked_sub_unit)o(_s)o(os)p FK(.)g(Def)o(ault)h(clear) -5 b(.)29 b(If)21 b(this)i(\003ag)e(is)g(set,)h(intermediate)i(unit)e (clauses)257 3344 y(are)i(check)o(ed)h(for)f(subsumption)i(against)f (the)f FD(sos)d FK(list.)257 3517 y(Flag)34 b FD(linked_unit_de)o(l)p FK(.)53 b(Def)o(ault)35 b(clear)-5 b(.)60 b(If)34 b(this)g(\003ag)g(is) g(set,)i(unit)f(deletion)h(is)d(applied)j(to)257 3630 y(intermediate)26 b(clauses.)257 3803 y(Flag)d FD(linked_target_a)o(ll) o FK(.)f(Def)o(ault)j(clear)-5 b(.)29 b(If)24 b(this)g(\003ag)f(is)g (set,)h(an)o(y)f(literal)i(can)f(be)g(a)f(tar)n(get.)257 4108 y FF(Link)o(ed)f(UR)g(P)o(arameters)257 4281 y FD(assign\(max_ur_) o(dep)o(th)o(,)p FC(n)o FD(\))p FK(.)47 b(Def)o(ault)33 b(5,)h(range)f([0)f(..)53 b(100].)i(This)32 b(parameter)h(limits)g(the) 257 4394 y(depth)25 b(of)e(link)o(ed)i(UR-resolution.)31 b(Note)24 b(that)g(the)g(depth)g(of)g(ordinary)h(UR-resolution)h(is)e (0.)257 4567 y FD(assign\(max_ur_)o(ded)o(uc)o(ti)o(on)o(_s)o(ize)o(,)p FC(n)o FD(\))p FK(.)k(Def)o(ault)f(20,)f(range)h([0)e(..)34 b(100].)i(This)26 b(parame-)257 4680 y(ter)f(limits)h(the)g(size)g(of)f (link)o(ed)i(UR-resolution)h(inferences,)h(that)d(is,)f(the)h(number)g (of)g(corresponding)257 4793 y(binary)i(resolution)i(steps.)39 b(In)27 b(other)h(w)o(ords,)g(the)f(size)g(of)g(a)f(link)o(ed)i (inference)i(step)d(is)g(one)g(less)g(than)257 4906 y(the)d(number)g (of)g(clauses)h(that)f(participate.)257 5212 y FF(Link)o(ed)e(UR)g (Annotations)257 5385 y FK(Each)27 b(clause)i(that)f(participates)j(in) c(a)g(link)o(ed)i(UR-resolution)h(inference)g(is)e(classi\002ed)h(as)e (a)g FG(nucleus)257 5498 y FK(\(the)22 b(nonunit)i(clause)f(containing) i(the)d(tar)n(get)h(literal\),)g(a)e FG(link)j FK(\(nonunit)g(clauses)g (all)e(of)f(whose)h(literals)257 5611 y(are)i(resolv)o(ed\),)h(or)e(a)g FG(satellite)j FK(\(unit)f(clauses\).)1861 5946 y(57)p eop %%Page: 58 64 58 63 bop 398 388 a FK(Input)26 b(clauses)g(can)g(be)f(annotated)i (with)e(special)h(literals)h(specifying)g(the)f(role\(s\))g(the)o(y)f (can)g(play)257 501 y(in)e(link)o(ed)i(UR)d(inferences.)32 b(The)23 b(clause)i(annotations)i(are)c(as)h(follo)n(ws.)257 674 y FD($NUCLEUS\([)p FG(list-of-liter)o(al-number)o(s)p FD(]\))36 b FK(\227)f(the)h(clause)h(\(assumed)h(to)d(be)h(nonunit\))i (can)f(be)e(a)257 787 y(nucleus.)50 b(The)29 b(ar)n(gument)j(is)e(a)g (list)g(of)g(positi)n(v)o(e)h(inte)o(gers)h(identifying)h(the)d (literals)i(that)f(can)f(act)g(as)257 900 y(tar)n(gets.)257 1073 y FD($LINK\([]\))22 b FK(\227)j(the)i(clause)h(\(assumed)h(to)d (be)h(nonunit\))i(can)e(act)g(as)f(a)g(link.)39 b(The)26 b(ar)n(gument)j(must)257 1185 y(be)23 b(the)h(empty)g(list.)257 1358 y FD($BOTH\([)p FG(list-of-liter)o(al-number)o(s)p FD(]\))30 b FK(\227)e(the)h(clause)h(\(assumed)g(to)f(be)g(nonunit\))i (can)e(be)g(either)g(a)257 1471 y(nucleus)24 b(or)e(a)g(link,)h(and)g (when)f(it)g(is)g(used)h(as)f(a)g(nucleus,)i(the)f(admissible)h(tar)n (get)g(literals)g(are)e(gi)n(v)o(en)h(in)257 1584 y(the)h(list.)257 1757 y FD($SATELLITE\([]\))14 b FK(\227)21 b(the)h(clause)h(\(assumed)g 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FK(list)k(is)g (annotated,)i(and)e(\(3\))g(e)n(v)o(ery)g(clause)i(in)d(the)h FD(sos)e FK(list)i(is)f(a)h(unit)g(and)g(is)g FG(not)i FK(annotated.)257 3267 y(Link)o(ed)31 b(UR)f(seems)h(to)f(beha)n(v)o(e) j(correctly)g(under)f(these)g(constraints,)j(b)n(ut)c(se)n(v)o(eral)h (problems)g(ha)n(v)o(e)257 3380 y(been)24 b(noticed)i(with)d(other)h (initial)h(conditions.)257 3682 y FF(Ackno)o(wledgment.)90 b FK(The)37 b(link)o(ed)h(UR-resolution)h(rule)e(w)o(as)g(implemented)i (by)e(Nick)f(Karonis,)257 3795 y(with)23 b(collaboration)28 b(from)23 b(Bob)g(V)-10 b(erof)n(f)24 b(and)g(Larry)g(W)-7 b(os.)257 4100 y FI(19.12)99 b(Splitting)257 4335 y FK(T)-7 b(o)29 b(address)34 b(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)33 b(poor)e(performance)h(on)f(man)o(y)f(non-Horn)h(problems,)i(a)d (splitting)j(rule)d(w)o(as)257 4448 y(installed)d(in)f(O)q FE(T)t(T)t(E)t(R)i FK(\(in)d(No)o(v)o(ember)g(1997\).)33 b(By)23 b(\223splitting\224)28 b(we)c(mean)g(that)h(the)g(search)h(is)e (di)n(vided)257 4560 y(into)f(tw)o(o)f(or)h(more)g(independent)j (branches)f(such)e(that)g(if)g(each)g(of)g(the)g(branches)i(is)d (refuted,)i(then)g(the)257 4673 y(state)g(before)h(the)f(split)g(has)g (been)h(refuted.)30 b(Splitting)25 b(is)e(typically)j(recursi)n(v)o(e.) 400 4846 y(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)43 b(splitting)g (implementation)g(uses)f(the)h FE(U)t(N)t(I)t(X)f FK(fork\(\))g(system) f(call,)k(which)c(creates)257 4959 y(copies)28 b(of)f(the)g(state)h(of) f(the)j(O)q FE(T)t(T)t(E)t(R)g FK(process.)41 b(An)27 b(additional)i(hypothesis)h(is)d(asserted)i(on)e(the)g(\002rst)257 5072 y(branch,)g(and)g(the)f(\002rst)f(branch)i(continues)i(e)o(x)o (ecuting)e(while)f(the)g(second)i(branch)f(w)o(aits.)36 b(If)25 b(the)h(\002rst)257 5185 y(branch)36 b(is)f(refuted,)40 b(the)35 b(second)i(branch)f(starts)g(running)h(with)e(its)g (additional)j(hypothesis.)66 b(This)257 5298 y(method)24 b(a)n(v)n(oids)i(e)o(xplicit)f(backtracking.)398 5471 y(T)-7 b(w)o(o)17 b(splitting)k(methods)f(are)f(a)n(v)n(ailable:)30 b(splitting)21 b(on)d(ground)j(clauses,)g(and)e(splitting)i(on)e (ground)257 5584 y(atoms.)44 b(In)29 b(both)g(methods,)i(the)e (parameter)i FD(split_depth)23 b FK(can)29 b(be)f(used)i(to)f(limit)f (the)h(depth)h(of)257 5697 y(splitting.)h(F)o(or)22 b(e)o(xample,)j (with)e(the)h(command)1861 5946 y(58)p eop %%Page: 59 65 59 64 bop 456 388 a Fq(assign\(split_depth,)46 b(3\).)257 661 y FK(a)23 b(case)h(such)g(as)g([1.1.1.1])g(will)f(not)h(occur)-5 b(.)257 966 y FF(19.12.1)92 b(Splitting)24 b(on)e(Gr)n(ound)h(Clauses) 257 1201 y FK(Clause)j(splitting)i(can)f(be)e(triggered)k(in)c(tw)o(o)h (w)o(ays:)34 b(either)27 b(periodically)i(or)d(when)g(a)f(ground)j (clause)257 1314 y(is)e(selected)i(as)f(the)f(gi)n(v)o(en)h(clause.)39 b(In)26 b(both)h(methods,)h(the)f(clauses)h(on)e(which)h(splitting)i (occurs)f(can)257 1426 y(be)23 b(constrained)k(by)d(an)o(y)f(of)h(the)g (follo)n(wing)h(three)f(\003ags)g(\(all)g(clear)g(by)g(def)o(ault\).) 456 1686 y Fq(set\(split_pos\).)246 b(\045)50 b(split)f(on)g(positive)g (clauses)f(only)456 1785 y(set\(split_neg\).)246 b(\045)50 b(split)f(on)g(negative)g(clauses)f(only)456 1885 y (set\(split_nonhorn\).)e(\045)k(split)f(on)g(non-Horn)g(clauses)f(only) 257 2158 y FK(These)27 b(\003ags)f(determine)i(eligibility)-6 b(.)41 b(If)26 b(none)h(of)g(the)f(\003ags)h(is)f(set,)h(all)g(ground)h (nonunit)h(clauses)f(are)257 2270 y(eligible.)257 2576 y FF(Splitting)c(P)n(eriodically)j(on)d(Clauses.)92 b FK(T)-7 b(o)23 b(enable)j(the)f(periodic)i(splitting)g(method,)f(one)f (uses)h(the)257 2689 y(follo)n(wing)f(command.)456 2948 y Fq(set\(split_clause\).)257 3221 y FK(The)g(def)o(ault)i(period)g(is) e(e)n(v)o(ery)h(5)f(gi)n(v)o(en)h(clauses.)36 b(T)-7 b(o)24 b(change)j(the)f(period,)h(say)f(to)f(10)h(gi)n(v)o(en)g (clauses,)257 3334 y(use)e(the)g(follo)n(wing)h(command.)456 3593 y Fq(assign\(split_given,)46 b(10\).)257 3866 y FK(Instead)25 b(of)f(splitting)i(after)e(some)g(number)g(of)g(gi)n(v)o (en)g(clauses,)h(one)f(can)g(split)g(after)h(some)f(number)g(of)257 3979 y(seconds,)h(say)f(4,)f(with)g(the)h(follo)n(wing)h(command.)456 4238 y Fq(assign\(split_seconds,)46 b(4\).)257 4510 y FK(The)28 b(clause)i(on)e(which)h(to)g(split)g(can)g(be)g(selected)h (from)f(the)g(set)f(of)h(eligible)h(clauses)h(in)d(tw)o(o)g(w)o(ays.) 257 4623 y(The)23 b(def)o(ault)i(method)f(is)g(to)f(select)i(the)f (\002rst,)f(lightest)i(\(using)g(the)f(pick-gi)n(v)o(en)i(scale\))e (eligible)i(clause)257 4736 y(from)d(the)h(sequence)i FD(usable+sos)p FK(.)d(Instead,)i(one)f(can)g(use)g(the)g(command)456 4995 y Fq(set\(split_min_max\).)257 5268 y FK(which)i(says)g(to)g(use)g (the)g(follo)n(wing)h(method)f(to)g(compare)g(tw)o(o)g(eligible)h (clauses.)37 b(Prefer)26 b(the)g(clause)257 5381 y(with)e(the)h (lighter)h(hea)n(viest)g(literal)g(\(using)g(the)f(pick-gi)n(v)o(en)i (scale\);)f(if)e(the)h(hea)n(viest)i(literals)f(ha)n(v)o(e)f(the)257 5494 y(same)32 b(weight,)j(use)d(the)h(lighter)h(clause;)k(if)32 b(the)g(clauses)i(ha)n(v)o(e)f(the)f(same)g(weight,)j(use)e(the)f (\002rst)g(in)257 5607 y FD(usable+sos)p FK(.)1861 5946 y(59)p eop %%Page: 60 66 60 65 bop 257 388 a FF(Splitting)24 b(When)f(Gi)o(v)o(en.)91 b FK(T)-7 b(o)24 b(specify)i(that)f(clause)h(splitting)h(should)f(be)f (occur)h(whene)n(v)o(er)f(an)g(eli-)257 501 y(gible)f(clause)h(is)f (selected)h(as)f(the)f(gi)n(v)o(en)i(clause,)f(one)g(uses)g(the)g (follo)n(wing)h(command.)456 753 y Fq(set\(split_when_given\).)257 1057 y FF(The)g(Branches)i(f)n(or)g(Clause)f(Splitting)o(.)91 b FK(If)28 b(O)q FE(T)t(T)t(E)t(R)j FK(decides)d(to)f(split)h(on)e(a)h (clause,)h(say)f FD(P|Q|R)p FK(,)257 1170 y(the)d(assumptions)i(for)e (the)f(three)i(cases)f(are)456 1422 y Fq(Case)49 b(1:)h(P.)456 1521 y(Case)f(2:)h(-P)f(&)h(Q.)456 1621 y(Case)f(3:)h(-P)f(&)h(-Q)f(&)h (R.)257 1886 y FK(One)32 b(system)h(fork)g(occurs,)j(and)d(Case)g(1)f (e)o(x)o(ecutes.)57 b(If)32 b(it)g(succeeds,)37 b(a)32 b(second)i(fork)g(occurs,)i(and)257 1999 y(Case)29 b(2)g(e)o(x)o (ecutes.)47 b(If)29 b(that)h(succeeds,)j(Case)c(3)g(e)o(x)o(ecutes.)47 b(If)29 b(an)o(y)g(of)g(the)h(cases)g(f)o(ails)g(to)f(produce)i(a)257 2112 y(refutation,)26 b(the)e(f)o(ailure)h(is)e(propagated)j(to)e(the)f (top,)h(and)g(the)g(entire)h(search)g(f)o(ails.)257 2417 y FF(19.12.2)92 b(Splitting)24 b(on)e(Atoms)257 2651 y FK(T)-7 b(o)32 b(split)j(on)f(atoms,)k(O)q FE(T)t(T)t(E)t(R)f FK(periodically)g(selects)f(a)d(ground)i(atom,)h(say)e FD(P)p FK(,)e(and)i(considers)i(tw)o(o)257 2764 y(branches,)d(one)d (with)f(assertion)j FD(P)p FK(,)c(and)i(the)f(other)i(with)e FD(-P)p FK(.)f(The)h(follo)n(wing)i(command)f(speci\002es)257 2877 y(splitting)c(on)d(atoms.)456 3128 y Fq(set\(split_atom\).)257 3393 y FK(The)d(parameters)j FD(split_given)15 b FK(and)21 b FD(split_seconds)14 b FK(determine)22 b(\(just)f(as)g(for)g(clause)h (split-)257 3506 y(ting\))37 b(when)g(atom)g(splitting)i(occurs.)70 b(If)36 b(all)h(input)h(clauses)g(are)f(ground,)42 b(and)37 b(if)f(the)h(parameter)257 3619 y FD(split_given)31 b FK(is)36 b(assigned)j(0,)h(then)d(the)g(resulting)i(procedure)g(is)e (essentially)j(a)c(\(v)o(ery)h(slo)n(w\))257 3732 y(Da)n(vis-Putnam-Lo) o(v)o(eland-Logemann)29 b(SA)-10 b(T)21 b(procedure.)398 3905 y(An)g(atom)h(is)g(eligible)i(for)e(splitting)i(if)e(it)f(occurs)j (in)d(an)h(eligible)i(nonunit)g(ground)g(clause.)29 b(Clause)257 4018 y(eligibility)22 b(is)d(determined)i(just)f(as)f(in)g(the)g (clause)i(splitting)g(case,)f(that)g(is,)g(by)f(the)g(\003ags)g FD(split_pos)p FK(,)257 4131 y FD(split_neg)p FK(,)f(and)24 b FD(split_nonhorn)p FK(.)398 4304 y(All)e(clauses)j(in)e FD(usable+sos)18 b FK(are)23 b(considered)j(when)d(deciding)j(the)d (best)h(eligible)h(atom.)j(The)257 4417 y(def)o(ault)j(method)f(select) h(the)f(lightest)h(atom)f(in)f(the)h(lightest)i(clause)e(\(using)h(the) f(pick-gi)n(v)o(en)i(scale\).)257 4530 y(An)20 b(optional)k(method)e (for)g(selecting)i(an)d(atom)g(considers)j(the)e(number)g(of)g (occurrences)i(of)e(the)f(atom.)257 4642 y(The)i(command)456 4894 y Fq(set\(split_popular\).)257 5159 y FK(says)h(to)g(prefer)g(the) g(atom)g(that)g(occurs)h(in)e(the)h(greatest)h(number)g(of)e(clauses.) 398 5332 y(Instead)j(of)d(ha)n(ving)28 b(O)q FE(T)t(T)t(E)t(R)g FK(decide)d(the)f(atoms)h(on)f(which)g(to)g(split,)g(the)h(user)f(can)g (specify)i(them)257 5445 y(in)d(the)h(input)h(\002le)e(with)g(a)g (command)h(such)h(as)456 5697 y Fq(split_atoms\([P,)47 b(a=b,)i(R]\).)1861 5946 y FK(60)p eop %%Page: 61 67 61 66 bop 257 388 a FK(which)26 b(says)g(to)f(split,)h(in)g(order)l(,)h (on)e(those)i(atoms.)34 b(In)26 b(this)g(e)o(xample,)g(we)f(get)g (eight)i(cases,)f(and)g(then)257 501 y(no)c(more)h(splitting)h(occurs.) 30 b(The)22 b(time)g(at)h(which)g(the)f(splitting)j(occurs)f(is)e (determined,)j(as)d(abo)o(v)o(e,)h(by)257 614 y(the)h(parameters)h FD(split_given)18 b FK(and)24 b FD(split_seconds)p FK(.)257 916 y FF(19.12.3)92 b(Mor)n(e)25 b(on)d(Splitting)257 1150 y FK(If)k(O)q FE(T)t(T)t(E)t(R)i FK(f)o(ails)d(to)g(\002nd)f(a)f (proof)j(for)e(a)g(particular)j(case)e(\(e.g.,)f(the)h(list)g FD(sos)d FK(empties)j(or)g(some)f(limit)257 1263 y(is)h(reached\),)j (the)d(whole)h(attempt)h(f)o(ails.)35 b(If)25 b(the)h(search)g(strate)o (gy)h(is)f(complete,)h(then)f(an)f(empty)h FD(sos)257 1376 y FK(list)g(indicates)j(satis\002ability)-6 b(,)30 b(and)d(the)f(set)h(of)f(assumptions)j(introduced)g(by)e(splitting)h (gi)n(v)o(e)f(a)f(partial)257 1489 y(model.)j(It)23 b(is)h(up)f(to)h (the)g(user)l(,)g(ho)n(we)n(v)o(er)l(,)g(to)f(complete)i(the)f(model.) 398 1662 y(When)k(O)q FE(T)t(T)t(E)t(R)h FK(\002nds)d(a)f(refutation)j (by)e(splitting,)i(the)e(output)h(\002le)e(does)h(not)g(contain)i(an)d (o)o(v)o(erall)257 1775 y(proof.)30 b(A)22 b(proof)j(is)e(gi)n(v)o(en)h (for)g(each)g(leaf)g(in)g(the)f(tree,)h(and)g(those)h(proofs)g(contain) g(clauses)g(such)g(as)456 2013 y Fq(496)49 b([264,split.1.1.1.1])e (nop\(C,D\)!=nop\(A,A\).)257 2264 y FK(in)31 b(which)h(the)g (justi\002cation)i(indicates)g(that)f(a)e(split)h(occurred)i(on)e (clause)h(264,)h(and)e(this)g(clause)h(is)257 2377 y(the)23 b(assertion)j(for)e(case)g([1.1.1.1].)29 b(Other)24 b(information)i (about)e(splitting)i(is)d(gi)n(v)o(en)h(in)f(the)h(output)h(\002le,)257 2490 y(for)k(e)o(xample,)h(when)f(a)f(split)h(occurs,)i(the)e(case)g (numbers,)i(the)e(case)g(assertions,)k(and)c(when)f(fork)o(ed)257 2603 y(processed)e(be)o(gin)e(and)g(end.)398 2776 y(When)e(splitting)i (is)d(enabled,)i(the)f(parameter)h FD(max_seconds)16 b FK(\(for)22 b(the)g(initial)h(process)g(and)f(all)257 2889 y(descendant)g(processes\))h(is)c(check)o(ed)j(against)f(the)f(w)o (all)f(clock)i(\(from)e(the)h(start)h(of)e(the)h(initial)h(process\)) 257 3002 y(instead)26 b(of)e(against)i(the)f(process)h(clock.)32 b(This)24 b(is)h(problematic)h(if)e(the)h(computer)h(is)e(b)n(usy)i (with)e(other)257 3115 y(processes.)400 3288 y(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)36 b(splitting)g(rule)e(is)f(highly)j(e)o(xperimental,)i (and)c(we)f(do)g(not)h(ha)n(v)o(e)h(much)e(e)o(xperience)257 3400 y(with)23 b(it.)29 b(A)22 b(general)j(strate)o(gy)g(that)g(may)e (be)g(useful)i(for)f(non-Horn)h(problems)g(is)f(the)f(follo)n(wing.)456 3638 y Fq(set\(split_when_given\).)456 3738 y(set\(split_pos\).)595 b(\045)50 b(Also)f(try)g(it)g(without)g(this)g(command.)456 3838 y(assign\(split_depth,)d(10\).)257 4089 y FK(The)28 b(O)q FE(T)t(T)t(E)t(R)i FK(distrib)n(ution)g(packages)f(should)f (contain)g(a)e(directory)j(of)e(sample)g(input)g(\002les)g(that)g(use) 257 4202 y(the)d(splitting)h(rule.)257 4504 y FF(Ackno)o(wledgment)91 b FK(The)34 b(splitting)i(rule)f(w)o(as)g(de)n(v)o(eloped)h(in)f (collaboration)j(with)c(Dale)h(Myers,)257 4617 y(Rusty)24 b(Lusk,)f(and)h(Mohammed)g(Almulla.)257 4966 y FJ(20)119 b(Soundness)31 b(and)g(Completeness)257 5237 y FI(20.1)99 b(Soundness)259 5471 y FK(O)q FE(T)t(T)t(E)t(R)29 b FK(has)c(a)g(v)o (ery)g(good)h(record)g(with)f(respect)i(to)e(soundness,)j(b)n(ut)d (\(as)g(f)o(ar)h(as)f(we)f(kno)n(w\))h(no)g(parts)257 5584 y(of)33 b(it)h(\(the)g(C)e(code\))j(ha)n(v)o(e)f(been)g(formally)h (v)o(eri\002ed.)59 b(If)33 b(an)o(ything)j(depends)f(on)f(proofs)h (found)g(by)259 5697 y(O)q FE(T)t(T)t(E)t(R)r FK(,)25 b(the)f(proofs)h(should)g(be)e(carefully)j(check)o(ed,)g(by)d(hand)i (or)e(by)h(an)f(independent)k(program.)1861 5946 y(61)p eop %%Page: 62 68 62 67 bop 398 388 a FK(The)28 b(IVY)f(project)j([19)q(])e(contains)j(a) d(component)i(that)f(checks)h(the)f(proof)h(objects)g(\(Sec.)e(6.1.8\)) 257 501 y(produced)k(by)g(O)q FE(T)t(T)t(E)t(R)r FK(.)49 b(The)29 b(main)h(result)g(of)g(the)g(IVY)e(project)k(is)d(a)g(hybrid)i (system,)h(constructed)257 614 y(in)c(the)g(A)l(CL2)f(v)o (eri\002cation)j(en)l(vironment)i([10)q(],)c(that)h(tak)o(es)g(a)f (\002rst-order)i(conjecture,)i(translates)e(it)257 727 y(to)k(clauses,)k(sends)e(the)e(clauses)i(to)g(O)q FE(T)t(T)t(E)t(R)r FK(,)i(and)d(checks)h(an)o(y)e(proof)h(objects)h(that)f(are)f (returned.)257 840 y(A)l(CL2)g(has)i(been)g(used)g(to)f(pro)o(v)o(e)h (v)n(arious)h(soundness)h(properties)g(of)d(the)h(clause)h(translator)l (,)k(the)257 953 y(proof)24 b(check)o(er)l(,)i(and)e(their)g (composition)j(as)c(a)g(hybrid)i(system.)257 1262 y FI(20.2)99 b(Completeness)257 1496 y FK(If)21 b(the)g(clause)i(set)e(does)h(not)g (in)l(v)n(olv)o(e)h(equality)-6 b(,)24 b(or)d(if)g(it)g(in)l(v)n(olv)o (es)j(equality)f(and)f(includes)h(the)f(equality)257 1609 y(axioms,)28 b(then)f(man)o(y)g(of)f(the)h(common)h (refutation-complete)j(resolution)f(search)e(strate)o(gies)h(can)e(be) 257 1722 y(easily)35 b(achie)n(v)o(ed)h(with)g(O)q FE(T)t(T)t(E)t(R)r FK(.)63 b(F)o(or)33 b(e)o(xample,)k(hyperresolution)i(and)34 b(f)o(actoring,)40 b(with)34 b(positi)n(v)o(e)257 1835 y(clauses)24 b(in)e(the)g(list)h FD(sos)d FK(and)i(nonpositi)n(v)o(e)j (clauses)f(in)e(the)h(list)f FD(usable)p FK(,)d(is)j(complete.)30 b(If)21 b(the)i(input)257 1948 y(clause)h(set)g(is)f(Horn,)g(then)h(f)o (actoring)h(is)e(not)h(required.)31 b(The)22 b(def)o(ault)j(method)f (of)f(selecting)j(the)d(gi)n(v)o(en)257 2061 y(clause)g(\(tak)o(e)f (one)h(with)e(the)h(fe)n(west)g(symbols\))h(does)f(not)g(interfere)i (with)e(completeness,)i(and)e(neither)257 2173 y(forw)o(ard)j(nor)f (back)g(subsumption,)j(as)c(implemented)j(in)f(O)q FE(T)t(T)t(E)t(R)r FK(,)h(interferes)g(with)d(completeness)k(of)257 2286 y(the)d(basic)g(inference)i(rules.)398 2459 y(Completeness)i(issues)f (are)f(more)g(comple)o(x)g(when)g(paramodulation)k(is)25 b(the)h(inference)i(rule,)f(es-)257 2572 y(pecially)g(when)e(the)h(set) f(of)g(support)i(strate)o(gy)g(is)e(considered.)36 b(A)24 b(simple)i(and)f(complete)i(paramodu-)257 2685 y(lation)e(strate)o(gy)g (for)h(O)q FE(T)t(T)t(E)t(R)h FK(is)c(\(1\))h(paramodulate)j FG(fr)l(om)c FK(and)h FG(into)g FK(the)g(gi)n(v)o(en)g(clause,)h(\(2\)) e(paramod-)257 2798 y(ulate)37 b FG(fr)l(om)f FK(and)h FG(into)g FK(both)g(sides)g(of)f(equality)j(literals,)i(\(3\))36 b(paramodulate)j FG(fr)l(om)d FK(\(b)n(ut)h(not)g FG(into)p FK(\))257 2911 y(v)n(ariables,)28 b(and)d(\(4\))h(place)g(all)g(input)h (clauses)g(in)e(the)h(list)g FD(sos)p FK(.)32 b(The)25 b(equality)i FD(x=x)c FK(is)j(required,)h(b)n(ut)257 3024 y(the)d(functionally)j(re\003e)o(xi)n(v)o(e)d(axioms)g(are)g(not)g (required.)398 3197 y(Completeness)57 b(of)e(the)g(basic)h(inference)h (rules)e(is)g(important,)64 b(b)n(ut)55 b(incomplete)i(restric-)257 3310 y(tions)51 b(and)f(re\002nements)i(are)e(frequently)j(required)f (to)e(\002nd)g(proofs.)110 b(F)o(or)49 b(e)o(xample,)58 b(we)49 b(al-)257 3423 y(most)40 b(al)o(w)o(ays)i(use)f(the)g FD(max_weight)35 b FK(parameter;)51 b(strictly)43 b(speaking,)k(it)40 b(is)h(incomplete,)46 b(b)n(ut)257 3535 y(it)36 b(sa)n(v)o(es)h(a)f (lot)g(of)g(time)g(and)h(memory)-6 b(,)39 b(and)e(careful)h(use)e(of)g (it)g(does)h(not)g(pre)n(v)o(ent)i(O)q FE(T)t(T)t(E)t(R)h FK(from)257 3648 y(\002nding)48 b(proofs)h(in)e(practice.)102 b(F)o(or)46 b(paramodulation,)57 b(we)47 b(generally)i(use)f(the)g (\003ag)f FD(anl_eq)257 3761 y FK(with)f(additional)k (restrictions\227some)h(are)46 b(kno)n(wn)h(to)g(be)g(incomplete,)54 b(and)47 b(others)h(ha)n(v)o(e)g(not)257 3874 y(been)42 b(analyzed.)84 b(W)-7 b(e)40 b(sometimes)i(use)g(UR-resolution)i(on)d (non-Horn)i(sets,)j(which)41 b(is)g(incom-)257 3987 y(plete.)98 b(And)46 b(we)g(mak)o(e)g(e)o(xtensi)n(v)o(e)i(use)f(of)g(weighting)h (to)e(pur)n(ge)i(uninteresting)i(clauses)f(and)257 4100 y(the)44 b(options)h FD(delete_identica)o(l_)o(ne)o(st)o(ed_)o(sk)o(ol) o(em)o FK(,)d FD(max_distinct_v)o(ars)o FK(,)g(and)257 4213 y FD(max_literals)p FK(,)17 b(all)23 b(of)h(which)g(interfere)h (with)f(completeness.)257 4566 y FJ(21)119 b(Limits,)29 b(Abnormal)h(Ends,)g(and)h(Fixes)259 4833 y FK(O)q FE(T)t(T)t(E)t(R)j FK(has)d(se)n(v)o(eral)h(compile-time)g(limits.)50 b(If)30 b(a)h(limit)f(is)g(e)o(xceeded,)k(a)c(message)i(containing)i(the)257 4945 y(name)22 b(of)f(the)h(limit)g(will)f(appear)i(in)f(the)g(output)h (\002le)e(and/or)j(at)d(the)h(terminal.)29 b(T)-7 b(o)21 b(raise)i(the)f(limit,)f(\002nd)257 5058 y(the)k(appropriate)k (de\002nition)e(\()p FD(#define)p FK(\))21 b(in)k(a)g FD(.h)e FK(or)j FD(.c)d FK(\002le,)i(increase)i(the)e(limit,)h(and)f (recompile)259 5171 y(O)q FE(T)t(T)t(E)t(R)r FK(.)31 b(\(Of)23 b(course,)i(one)f(must)g(ha)n(v)o(e)g(one')-5 b(s)25 b(o)n(wn)e(cop)o(y)i(of)f(the)g(source)h(code)f(to)g(do)g (this.\))30 b(Some)23 b(of)257 5284 y(the)h(limits)g(are)f(as)h(follo)n (ws.)257 5457 y FD(MAX_NAME)d FK(\227)k(Maximum)h(number)h(of)f (characters)j(in)c(a)h(v)n(ariable,)i(constant,)g(function,)h(or)d (predi-)257 5570 y(cate)e(symbol.)1861 5946 y(62)p eop %%Page: 63 69 63 68 bop 257 388 a FD(MAX_BUF)29 b FK(\227)k(Maximum)h(number)g(of)g (characters)i(in)d(an)h(input)h(string)g(\(clause,)i(formula,)g(com-) 257 501 y(mand,)23 b(weight)h(template,)h(etc.\).)257 674 y FD(MAX_VARS)19 b FK(\227)k(Maximum)g(number)i(of)e(distinct)i(v)n (ariables)h(in)e(a)f(clause.)257 847 y FD(MAX_FS_TERM_DE)o(PTH)12 b FK(\227)18 b(Maximum)i(depth)h(of)e(terms)h(in)f(the)h(forw)o(ard)g (subsumption)j(discrim-)257 960 y(ination)i(tree.)257 1133 y FD(MAX_AL_TERM_DE)o(PTH)f FK(\227)32 b(Maximum)g(depth)h(of)g (left-hand)h(ar)n(guments)h(of)d(equalities)j(in)d(the)257 1245 y(demodulation)27 b(discrimination)g(tree.)257 1551 y FF(Conser)o(ving)d(Memory)-6 b(.)92 b FK(Se)n(v)o(eral)23 b(steps)i(can)f(be)f(tak)o(en)i(if)g(O)q FE(T)t(T)t(E)t(R)j FK(is)23 b(using)i(too)f(much)f(memory)-6 b(.)393 1799 y Fv(\017)46 b FK(Use)23 b FD(max_weight)c FK(to)k(discard)j(\(more\))e (generated)j(clauses.)k(This)23 b(is)h(a)f(v)o(ery)h(ef)n(fecti)n(v)o (e)h(w)o(ay)484 1912 y(to)f(sa)n(v)o(e)g(memory)f(\(and)i(time\).)393 2099 y Fv(\017)46 b FK(Set)23 b(the)h(\003ag)f FD(control_memory)16 b FK(\(Sec.)23 b(6.1.10\),)h(or)g(use)g(the)f(parameters)484 2212 y FD(change_limit_af)o(te)o(r)17 b FK(and)24 b FD(new_max_weight) 16 b FK(\(Sec.)23 b(17\).)393 2400 y Fv(\017)46 b FK(Decrease)29 b(\(do)n(wn)f(to)g(0\))f(the)h(v)n(alue)h(of)f(the)g FD(fpa_literals)21 b FK(and)28 b FD(fpa_terms)23 b FK(parame-)484 2513 y(ters.)393 2701 y Fv(\017)46 b FK(Set)23 b(the)h FD(for_sub_fpa)18 b FK(\003ag)23 b(to)g(switch)h(forw)o(ard)h (subsumption)h(inde)o(xing)g(from)e(discrimi-)484 2813 y(nation)h(tree)f(to)i FE(F)t(P)m(A)g FK(inde)o(xing.)393 3001 y Fv(\017)46 b FK(If)30 b(the)g(inference)j(rules)e(being)g(used)g (are)g(binary)g(resolution)i(or)d(paramodulation,)36 b(clear)31 b(the)484 3114 y(\003ag)23 b FD(detailed_histor)o(y)p FK(.)393 3302 y Fv(\017)46 b FK(If)51 b(a)g(lot)g(of)h(back)g (subsumption)i(or)d(back)h(demodulation)j(is)c(e)o(xpected,)59 b(set)52 b(the)f(\003ag)484 3415 y FD(really_delete_c)o(la)o(us)o(es)16 b FK(\(Sec.)23 b(6.1.10\).)393 3602 y Fv(\017)46 b FK(If)23 b(applicable,)j(set)e FD(no_fapl)c FK(or)j FD(no_fanl)d FK(\(Sec.)j(6.1.9\).)393 3790 y Fv(\017)46 b FK(If)23 b(back)i(demodulation)h(is)e(being)h(used,)f(clear)g(the)g(\003ag)f FD(index_for_back_)o(de)o(mo)o(d)p FK(.)393 3977 y Fv(\017)46 b FK(Run)20 b(an)j(O)q FE(T)t(T)t(E)t(R)i FK(job)c(until)g(memory)g (runs)g(out,)h(collect)g(interesting)h(lemmas)e(from)g(the)f(output)484 4090 y(\002le,)j(then)h(rerun)h(the)f(job)g(including)i(the)e(lemmas)g (as)f(input)i(clauses.)30 b(Repeat.)g(\(This)24 b(can)g(be)f(a)484 4203 y(good)i(strate)o(gy)g(e)n(v)o(en)f(when)f(memory)h(is)f(not)h(a)f (problem.\))257 4556 y FJ(22)119 b(Obtaining)31 b(and)g(Installing)i Fr(O)r Fs(T)6 b(T)g(E)g(R)259 4823 y FK(O)q FE(T)t(T)t(E)t(R)91 b FK(3)c(is)g(free,)104 b(and)87 b(there)i(are)e(no)h(restrictions)i (on)d(cop)o(ying)j(or)d(distrib)n(ut-)257 4936 y(ing)76 b(it.)187 b(The)75 b(main)i(means)f(of)g(distrib)n(ution)k(is)c(from)g (the)j(O)q FE(T)t(T)t(E)t(R)h FK(W)-7 b(eb)76 b(site)g(at)257 5049 y FD(http://www.mcs)o(.an)o(l.)o(go)o(v/)o(AR)o(/ot)o(te)o(r/)o FK(.)398 5222 y(Once)26 b(one)h(has)g(a)f(cop)o(y)h(of)f(the)j(O)q FE(T)t(T)t(E)t(R)h FK(3)c(distrib)n(ution)k(directory)-6 b(,)29 b(one)e(should)h(look)f(at)f(the)h(\002le)257 5335 y FD(README)c FK(for)k(instructions)j(on)c(installing)k(and)d (testing)j(O)q FE(T)t(T)t(E)t(R)r FK(.)40 b(On)28 b FE(U)t(N)t(I)t(X)r FK(-lik)o(e)g(systems,)i(O)q FE(T)t(T)t(E)t(R)257 5447 y FK(may)d(ha)n(v)o(e)h(to)g(be)g(compiled.)42 b(There)28 b(may)f(also)h(be)g(e)o(x)o(ecutable)i(v)o(ersions)f(for)f(Microsoft)h (W)l(indo)n(ws)257 5560 y(a)n(v)n(ailable)d(on)d(the)j(O)q FE(T)t(T)t(E)t(R)h FK(W)-7 b(eb)24 b(site.)1861 5946 y(63)p eop %%Page: 64 70 64 69 bop 257 388 a FJ(Ackno)o(wledgments)257 655 y FK(Much)28 b(of)h(my)e(w)o(ork)i(o)o(v)o(er)f(the)h(past)g(fe)n(w)e(years)i(has)g (been)g(in)f(collaboration)33 b(with)28 b(Larry)g(W)-7 b(os.)43 b(T)-7 b(o-)257 768 y(w)o(ard)22 b(our)i(goal)f(of)g(creating) h(programs)g(that)g(are)f(e)o(xpert)g(assistants)j(for)c (mathematicians,)k(logicians,)257 881 y(engineers,)c(and)e(other)h (scientists,)i(we)18 b(ha)n(v)o(e)i(w)o(ork)o(ed)h(together)h(on)d(man) o(y)h(applications)j(of)c(automated)257 994 y(deduction,)26 b(and)e(that)g(w)o(ork)g(has)f(led)h(to)g(man)o(y)f(of)j(O)q FE(T)t(T)t(E)t(R)r FK(')-5 b(s)26 b(current)f(features.)398 1167 y(The)32 b(basic)i(design)g(of)e(the)h(program,)j(including)f(the) d(data)i(structures)h(and)e(the)g(use)f(of)h(inde)o(x-)257 1280 y(ing,)26 b(descends)h(mostly)f(from)f(theorem)i(pro)o(v)o(ers)f (designed)i(and)d(implemented)i(by)f(Ross)f(Ov)o(erbeek.)257 1392 y(The)j(inde)o(xing)j(mechanisms,)h(which)d(are)g(in)g(lar)n(ge)h (part)g(responsible)i(for)d(the)g(performance)j(of)d(the)257 1505 y(program,)24 b(ha)n(v)o(e)g(bene\002ted)h(from)f(discussions)j (with)c(Ov)o(erbeek,)i(Mark)e(Stick)o(el,)h(and)g(Rusty)g(Lusk.)398 1678 y(F)o(or)k(man)o(y)h(years)i(Bob)e(V)-10 b(erof)n(f)29 b(has)h(maintained)h(his)f(o)n(wn)e(v)o(ersions)j(of)h(O)q FE(T)t(T)t(E)t(R)r FK(.)47 b(Man)o(y)30 b(of)f(his)257 1791 y(enhancements)e(ha)n(v)o(e)d(been)g(adopted)i(for)d(the)h(of)n (\002cial)g(v)o(ersions)i(of)f(O)q FE(T)t(T)t(E)t(R)r FK(.)398 1964 y(The)39 b(e)o(xpert)h(users)g(of)h(O)q FE(T)t(T)t(E)t(R)r FK(,)k(including)d(Larry)d(W)-7 b(os,)43 b(Bob)c(V)-10 b(erof)n(f,)43 b(John)d(Kalman,)j(K)n(en)257 2077 y(K)o(unen,)25 b(Art)e(Quaife,)i(Dale)g(Myers,)g(Johan)h(Belinf)o (ante,)g(Michael)g(Beeson,)f(Branden)h(Fitelson,)g(and)257 2190 y(Zac)d(Ernst,)g(ha)n(v)o(e)h(track)o(ed)i(do)n(wn)d(b)n(ugs)i (and)f(suggested)i(useful)f(enhancements.)257 2538 y FJ(Refer)n(ences)302 2778 y FK([1])47 b(W)-8 b(.)26 b(Bledsoe)k(and)e (D.)f(Lo)o(v)o(eland,)j(editors.)50 b FG(A)n(utomated)30 b(Theor)m(em)e(Pr)l(o)o(ving:)40 b(After)28 b(25)g(Y)-8 b(ear)o(s)p FK(,)454 2891 y(v)n(olume)24 b(29)g(of)f FG(Contempor)o(ary)j(Mathematics)p FK(.)35 b(AMS,)22 b(1984.)302 3070 y([2])47 b(R.)30 b(S.)g(Bo)o(yer)j(and)f(J)f(S.)f (Moore.)61 b FG(A)30 b(Computational)35 b(Lo)o(gic)d(Handbook)p FK(.)62 b(Academic)32 b(Press,)454 3183 y(Ne)n(w)22 b(Y)-10 b(ork,)23 b(1988.)302 3362 y([3])47 b(C.-L.)31 b(Chang)i(and)g(R.)e (C.-T)-7 b(.)31 b(Lee.)62 b FG(Symbolic)34 b(Lo)o(gic)g(and)f(Mec)o (hanical)h(Theor)m(em)f(Pr)l(o)o(ving)p FK(.)454 3475 y(Academic)24 b(Press,)f(Ne)n(w)f(Y)-10 b(ork,)24 b(1973.)302 3654 y([4])47 b(N.)22 b(Dersho)n(witz.)34 b(T)-6 b(ermination)25 b(of)e(re)n(writing.)35 b FG(J)n(.)22 b(Symbolic)j(Computation)p FK(,)h(3:69\226116,)g(1987.)302 3833 y([5])47 b(C.)25 b(A.)g(R.)g(Hoare)i(and)g(M.)f(J.)g(C.)f(Gordon,)j(editors.)45 b FG(Mec)o(hanized)29 b(Reasoning)g(and)e(Har)m(dwar)m(e)454 3946 y(Design)p FK(.)34 b(Prentice)24 b(Hall,)f(1992.)302 4125 y([6])47 b(J)29 b(S.)f(Moore,)j(editor.)54 b(Special)31 b(Issue)f(on)g(System)g(Veri\002cation.)54 b FG(J)n(.)28 b(A)n(utomated)j(Reasoning)p FK(,)454 4237 y(5\(4\),)24 b(1989.)302 4416 y([7])47 b(J.-P)-10 b(.)36 b(Jouannaud,)44 b(editor)-5 b(.)79 b FG(Re)o(writing)38 b(T)-8 b(ec)o(hniques)39 b(and)f(Applications,)43 b(Lectur)m(e)38 b(Notes)g(in)454 4529 y(Computer)24 b(Science)o(,)h(V)-10 b(ol.)23 b(202)p FK(,)h(Berlin,)f(1985.)i(Springer)n(-V)-10 b(erlag.)302 4708 y([8])47 b(J.)29 b(Kalman.)53 b FG(A)n(utomated)32 b(Reasoning)g(with)d(Otter)p FK(.)54 b(Rinton)31 b(Press,)g(Princeton,) i(Ne)n(w)28 b(Jerse)o(y)-6 b(,)454 4821 y(2001.)302 5000 y([9])47 b(D.)28 b(Kapur)i(and)g(H.)e(Zhang.)54 b(RRL:)28 b(Re)n(write)h(Rule)h(Laboratory)i(User')-5 b(s)30 b(Manual.)54 b(T)-6 b(echnical)454 5113 y(Report)24 b(89-03,)g(Department)h(of)f (Computer)g(Science,)g(Uni)n(v)o(ersity)h(of)f(Io)n(w)o(a,)f(1989.)257 5292 y([10])47 b(M.)21 b(Kaufmann,)j(P)-10 b(.)21 b(Manolios,)k(and)e (J)g(Moore.)33 b FG(Computer)n(-Aided)25 b(Reasoning:)31 b(An)22 b(Appr)l(oac)o(h)p FK(.)454 5405 y(Adv)n(ances)j(in)e(F)o (ormal)g(Methods.)i(Kluwer)e(Academic,)h(2000.)257 5584 y([11])47 b(B.)25 b(K)n(ernighan)j(and)f(D.)e(Ritchie.)44 b FG(The)27 b(C)e(Pr)l(o)o(gr)o(amming)j(Langua)o(g)o(e)p FK(.)45 b(Prentice)27 b(Hall,)g(second)454 5697 y(edition)e(edition,)g (1988.)1861 5946 y(64)p eop %%Page: 65 71 65 70 bop 257 388 a FK([12])47 b(D.)20 b(Knuth)i(and)g(P)-10 b(.)19 b(Bendix.)30 b(Simple)21 b(w)o(ord)h(problems)h(in)e(uni)n(v)o (ersal)j(algebras.)31 b(In)21 b(J.)g(Leech,)h(ed-)454 501 y(itor)l(,)j FG(Computational)i(Pr)l(oblems)e(in)f(Abstr)o(act)i (Alg)o(ebr)o(as)p FK(,)f(pages)h(263\226297.)g(Per)n(gamon)f(Press,)454 614 y(Oxford,)f(1970.)257 801 y([13])47 b(A.)22 b(G.)g(K)o(urosh.)34 b FG(The)23 b(Theory)h(of)f(Gr)l(oups)p FK(,)i(v)n(olume)f(1.)33 b(Chelsea,)24 b(Ne)n(w)e(Y)-10 b(ork,)24 b(1956.)257 989 y([14])47 b(D.)20 b(Lo)o(v)o(eland.)31 b FG(A)n(utomated)24 b(Theor)m(em)e(Pr)l(o)o(ving:)30 b(A)20 b(Lo)o(gical)k(Basis)p FK(.)30 b(North-Holland,)25 b(Amster)n(-)454 1102 y(dam,)e(1978.)257 1290 y([15])47 b(E.)34 b(Lusk)h(and)h(R.)e(Ov)o(erbeek.)72 b(The)35 b(Automated)h(Reasoning)i(System)d(ITP.)70 b(T)-6 b(ech.)34 b(Report)454 1402 y(ANL-84/27,)23 b(Ar)n(gonne)j(National)e (Laboratory)-6 b(,)26 b(Ar)n(gonne,)f(IL,)d(April)i(1984.)257 1590 y([16])47 b(W)-8 b(.)16 b(McCune.)23 b(Sk)o(olem)18 b(functions)j(and)e(equality)h(in)e(automated)i(deduction.)25 b(In)18 b FG(Pr)l(oceedings)j(of)454 1703 y(the)f(Eighth)h(National)h (Confer)m(ence)g(on)e(Arti\002cial)i(Intellig)o(ence)p FK(,)i(pages)d(246\226251,)i(Cambridge,)454 1816 y(MA,)f(1990.)i(MIT)e (Press.)257 2004 y([17])47 b(W)-8 b(.)32 b(McCune.)68 b(MA)l(CE)33 b(2.0)h(Reference)i(Manual)f(and)g(Guide.)68 b(T)-6 b(ech.)34 b(Memo)f(ANL/MCS-)454 2116 y(TM-249,)19 b(Mathematics)i(and)e(Computer)h(Science)g(Di)n(vision,)g(Ar)n(gonne)h (National)f(Laboratory)-6 b(,)454 2229 y(Ar)n(gonne,)25 b(IL,)d(June)i(2001.)257 2417 y([18])47 b(W)-8 b(.)31 b(McCune)j(and)g(R.)d(P)o(admanabhan.)66 b FG(A)n(utomated)35 b(Deduction)g(in)e(Equational)j(Lo)o(gic)d(and)454 2530 y(Cubic)i(Curves)p FK(,)j(v)n(olume)e(1095)g(of)e FG(Lectur)m(e)i (Notes)f(in)f(Computer)i(Science)g(\(AI)e(subseries\))p FK(.)454 2643 y(Springer)n(-V)-10 b(erlag,)26 b(Berlin,)e(1996.)257 2830 y([19])47 b(W)-8 b(.)24 b(McCune)j(and)f(O.)f(Shumsk)o(y)-6 b(.)42 b(IVY:)25 b(A)g(preprocessor)30 b(and)d(proof)g(check)o(er)h (for)e(\002rst-order)454 2943 y(logic.)38 b(In)25 b(M.)f(Kaufmann,)i(P) -10 b(.)23 b(Manolios,)k(and)e(J)f(Moore,)i(editors,)h FG(Computer)n(-Aided)g(Reason-)454 3056 y(ing:)i(A)m(CL2)23 b(Case)g(Studies)p FK(,)i(chapter)g(16.)f(Kluwer)f(Academic,)h(2000.) 257 3244 y([20])47 b(R.)27 b(P)o(admanabhan)k(and)f(W)-8 b(.)27 b(McCune.)51 b(Automated)31 b(reasoning)g(about)g(cubic)f(curv)o (es.)52 b FG(Com-)454 3357 y(puter)o(s)25 b(and)f(Mathematics)h(with)f (Applications)p FK(,)i(29\(2\):17\22626,)h(1995.)257 3544 y([21])47 b(A.)26 b(Quaife.)49 b(Automated)29 b(de)n(v)o(elopment) i(of)d(Tarski')-5 b(s)29 b(geometry)-6 b(.)50 b FG(J)n(.)27 b(A)n(utomated)i(Reasoning)p FK(,)454 3657 y(5\(1\):97\226118,)e(1989.) 257 3845 y([22])47 b(A.)31 b(Quaife.)62 b FG(A)n(utomated)33 b(De)o(velopment)h(of)e(Fundamental)j(Mathematical)f(Theories)p FK(.)63 b(PhD)454 3958 y(thesis,)24 b(Uni)n(v)o(ersity)h(of)f (California)h(at)e(Berk)o(ele)o(y)-6 b(,)25 b(1990.)257 4146 y([23])47 b(J.)26 b(Siekmann)i(and)f(G.)f(Wrightson,)k(editors.)46 b FG(A)n(utomation)29 b(of)d(Reasoning:)39 b(Classical)28 b(P)-7 b(aper)o(s)454 4258 y(on)23 b(Computational)k(Lo)o(gic)p FK(,)c(v)n(olume)i(1)e(and)h(2.)33 b(Springer)n(-V)-10 b(erlag,)26 b(Berlin,)e(1983.)257 4446 y([24])47 b(B.)32 b(Smith.)64 b(Reference)35 b(Manual)f(for)g(the)f(En)l(vironmental)k (Theorem)d(Pro)o(v)o(er:)48 b(An)33 b(Incarna-)454 4559 y(tion)26 b(of)f(A)-5 b(URA.)37 b(T)-6 b(ech.)24 b(Report)i(ANL-88-2,)g (Ar)n(gonne)h(National)f(Laboratory)-6 b(,)28 b(Ar)n(gonne,)f(IL,)454 4672 y(March)d(1988.)257 4860 y([25])47 b(G.)20 b(Sutclif)n(fe)j(and)f (C)e(Suttner)-5 b(.)30 b(The)22 b(TPTP)d(Problem)j(Library)g(for)g (Automated)h(Theorem)f(Pro)o(v-)454 4972 y(ing.)33 b FD(http://www.tptp.)o(or)o(g/)o FK(.)257 5160 y([26])47 b(R.)27 b(V)-10 b(erof)n(f.)49 b(An)28 b(Algorithm)i(for)e(the)h(Ef)n (\002cient)g(Implementation)i(of)e(Link)o(ed)g(UR-resolution.)454 5273 y(T)-6 b(ech.)19 b(Report)j(CD92-17,)f(Department)h(of)e(Computer) i(Science,)f(Uni)n(v)o(ersity)h(of)f(Ne)n(w)e(Me)o(xico,)454 5386 y(1992.)257 5574 y([27])47 b(R.)29 b(V)-10 b(erof)n(f.)55 b(Using)31 b(hints)g(to)f(increase)j(the)d(ef)n(fecti)n(v)o(eness)j(of) e(an)f(automated)i(reasoning)h(pro-)454 5686 y(gram:)c(Case)23 b(studies.)35 b FG(J)n(.)23 b(A)n(utomated)i(Reasoning)p FK(,)g(16\(3\):223\226239,)j(1996.)1861 5946 y(65)p eop %%Page: 66 72 66 71 bop 257 388 a FK([28])47 b(R.)20 b(V)-10 b(erof)n(f.)29 b(Solving)22 b(open)h(questions)h(and)e(other)h(challenge)h(problems)f (using)f(proof)h(sk)o(etches.)454 501 y FG(J)n(.)f(A)n(utomated)j (Reasoning)p FK(,)g(27\(2\):157\226174,)j(2001.)257 689 y([29])47 b(R.)31 b(V)-10 b(erof)n(f)32 b(and)h(L.)e(W)-7 b(os.)61 b(The)32 b(link)o(ed)h(inference)i(principle,)i(i:)46 b(The)32 b(formal)h(treatment.)63 b FG(J)n(.)454 801 y(A)n(utomated)25 b(Reasoning)p FK(,)g(8\(2\):213\226274,)i(1992.)257 989 y([30])47 b(L.)26 b(W)-7 b(os.)47 b FG(A)n(utomated)29 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53 85 d1 53 0 0 87 0 -2 cm BI /IM true/W 53/H 87/BPC 1/F/CCF/DP<> ID #Å8&ÁѧòpÊØD"ë`ˆƒA7àŸÞƒÓ^û×þÝõÿëÿúŽ—…­iH…&D¨ò03gPj„µ ‚­ Y !  \O °°µHŠ_þ¿õ×ÿõÿî»úþþÂÝv°ÚØhÿ\0Á'°Á/ á…ÈÀ¯ EI endstream endobj 131 0 obj <> stream 51 0 0 0 0 0 d1 endstream endobj 132 0 obj <> stream 34 0 0 0 0 0 d1 endstream endobj 133 0 obj <> stream 0 0 0 0 79 82 d1 79 0 0 82 0 0 cm BI /IM true/W 79/H 82/BPC 1/F/CCF/DP<> ID #ƒ&@Ý\<ЃínàÁûíðß~~ÿÛíÿ¿¿öøÿ¿÷ÿýÿÿÿÿÿÿÿÿ_ÿ_úÿÿÂ_ÿ…×ý/_ét¸^‚ëë¥Ð\¡Lƒü) ð¾A @ EI endstream endobj 134 0 obj <> stream 92 0 0 0 0 0 d1 endstream endobj 135 0 obj <> stream 0 0 0 30 56 84 d1 56 0 0 54 0 30 cm BI /IM true/W 56/H 54/BPC 1/F/CCF/DP<> ID )/ ÿOúÓþƒÈ‘ü-÷ÂÿI¿Öÿ§ý&ÿXзú ÿ§ý[þºÞŸÃ¯Ó…ºaù5ˆg5ÿð EI endstream endobj 136 0 obj <> stream 45 0 0 0 0 0 d1 endstream endobj 137 0 obj <> stream 0 0 0 0 80 85 d1 80 0 0 85 0 0 cm BI /IM true/W 80/H 85/BPC 1/F/CCF/DP<> ID & \“ÿ8" ¼Ð@Õ¨WÿaVÃ×ÿµ½öÂ_ë¾ð¿Ö݆¾Y?ï[ û×ö·…ÿÛKÿÃXzÿ[uþ}ëû_Þ×÷¯á¯áëöÒÿñÚþÂÿÚÿÃ_Ú€€ EI endstream endobj 138 0 obj <> stream 0 0 0 28 54 108 d1 54 0 0 80 0 28 cm BI /IM true/W 54/H 80/BPC 1/F/CCF/DP<> ID )ÃtðDB : < ô› ›­þ ÿOÿÿÿ†×û a¥°°õl— AŠú °² :„ äR”µ¯ýÿ>$8" „ˆyÀì Þž‚nÿH0ÿ§­ÿÿÿÿÿÿ÷­­ál/ÌÊi[ûi¨a„G¼px0ƒ2 j&²€€ EI endstream endobj 139 0 obj <> stream 0 0 0 0 78 82 d1 78 0 0 82 0 0 cm BI /IM true/W 78/H 82/BPC 1/F/CCF/DP<> ID #rQuÿYÀÂÍí|/[ ëþ¿ëÂÿýz!_ÿ¯ÒýøKëúúþÒÿõøKõÿé}ÿëô¿_þúþ¾¿…ô¿ý~ýú_Aúý/×ÿ„¾¿¯¯á}/ÿ_„¿_þ—ÐIÿƃ¤DƒäpP@€ÅX€ EI endstream endobj 140 0 obj <> stream 0 0 0 -1 26 82 d1 26 0 0 83 0 -1 cm BI /IM true/W 26/H 83/BPC 1/F/CCF/DP<> ID &¡•ù˜[_ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿë äÔÿÍ€€ EI endstream endobj 141 0 obj <> stream 0 0 0 0 64 82 d1 64 0 0 82 0 0 cm BI /IM true/W 64/H 82/BPC 1/F/CCF/DP<> ID #_þhDÑVÁûÿ‡áÿß¿ý÷ÿûÿÿÿü?ÃÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿpŸ‘ÃOÿ EI endstream endobj 142 0 obj <> stream 0 0 0 -1 57 84 d1 57 0 0 85 0 -1 cm BI /IM true/W 57/H 85/BPC 1/F/CCF/DP<> ID )y¤Pm˜{ „0ö‚oÂ|S·ý½?û÷ÿ÷÷ÿÿÿÿÿÿú_ÿ¯õõÿ[]„þ– /Y@» ^>\#ÿÿÿÿÿÿÿõ…òjæ‚@@ EI endstream endobj 143 0 obj <> stream 68 0 0 0 0 0 d1 endstream endobj 144 0 obj <> stream 0 0 0 30 56 106 d1 56 0 0 76 0 30 cm BI /IM true/W 56/H 76/BPC 1/F/CCF/DP<> ID >, pœ"<|ïM½¿‡Ãûïk†›ü}ßÛÿÂÓþŸôÿ þDŒ-á?ëÓÖôÿ­ÿOXzø[þÖôÿ­ÿO[þž°úp·L ÿ& ` æ¿þ  EI endstream endobj 145 0 obj <> stream 0 0 0 70 14 105 d1 14 0 0 35 0 70 cm BI /IM true/W 14/H 35/BPC 1/F/CCF/DP<> ID /ovïnø~÷ß¿ûóg„0¿×ú‡†  EI endstream endobj 146 0 obj <> stream 0 0 0 0 35 82 d1 35 0 0 82 0 0 cm BI /IM true/W 35/H 82/BPC 1/F/CCF/DP<> ID &¡§ù8bÕ¯ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ§Oɨiþ  EI endstream endobj 147 0 obj <> stream 42 0 0 0 0 0 d1 endstream endobj 148 0 obj <> stream 0 0 0 3 49 85 d1 49 0 0 82 0 3 cm BI /IM true/W 49/H 82/BPC 1/F/CCF/DP<> ID "Áðƒ„DðáaÐ n“zzMÐWá‡Õ÷¯«ý_ßúÿ_ÿúÿÿ÷_ÿ_[ýuß ÖŽÒö½´»Þ¸1 †B'¿¿û¿öùP] 0ÿÛíûø{oÇV Ž,‡¦ÅA¨aI0° EI endstream endobj 149 0 obj <> stream 0 0 0 3 49 85 d1 49 0 0 82 0 3 cm BI /IM true/W 49/H 82/BPC 1/F/CCF/DP<> ID "M@G„Eàè7ƒ¤Ý&ôøO[…½ÿé0ÿ[ÿÿ[Óÿÿÿëÿÿÿÿÿÿÿÿÿÿÿÿï_ÿÿûiÿýë÷…µ‡¯ì-†•ëkm-¬0@¬T0¤@H€ EI endstream endobj 150 0 obj <> stream 0 0 0 1 51 82 d1 51 0 0 81 0 1 cm BI /IM true/W 51/H 81/BPC 1/F/CCF/DP<> ID %Á£òÿÿÿÿÿ& §üšB!Ãûíÿ¿oßû†ÿßß¾ý¿÷á‡ïý¾þûûì?ðý¿íöÿ߆¿öÿØïýáýýýïü@ EI endstream endobj 151 0 obj <> stream 0 0 0 3 49 85 d1 49 0 0 82 0 3 cm BI /IM true/W 49/H 82/BPC 1/F/CCF/DP<> ID #ΡŸÊÄ"Öˆëp‚o è&éCý&ò*¿Aß÷öÿÿý¬0±ÿKýBúXZ¥J°JuøY !ÁÊ@–ï ;{Ýý¿æg ÿ ßûÿ¥ÿì(_É„î¡û +– Ć F€€ EI endstream endobj 152 0 obj <> stream 0 0 0 3 49 85 d1 49 0 0 82 0 3 cm BI /IM true/W 49/H 82/BPC 1/F/CCF/DP<> ID :“†:# 8[ F¡4ßz 7¶￾þí?»\Cûÿ»ÈÀœê ðÜŽ| ¼$Þ·¤ü&ÿÂLjÒÿt¿õ÷ÿÿëÿÿúÿ×ïÿJÿ…oá-÷Xa¥z¶•´CþÅA¨aH€ EI endstream endobj 153 0 obj <> stream 0 0 0 53 32 61 d1 32 0 0 8 0 53 cm BI /IM true/W 32/H 8/BPC 1/F/CCF/DP<> ID & Õÿø€ EI endstream endobj 154 0 obj <> stream 56 0 0 0 0 0 d1 endstream endobj 155 0 obj <> stream 0 0 0 3 49 85 d1 49 0 0 82 0 3 cm BI /IM true/W 49/H 82/BPC 1/F/CCF/DP<> ID #Ρ£Â„ 8[ F¡! è=&ôíÒ~Þú‡÷_ÿþí_׬5¸.Öõl,6—¶‚°a+Õ°” c† XP‚¬ pžAŒOA0é7î&ô  ›×áÿOýÿúßÜ/íaÂÛKÕ†•†–-ˆPaC D€€ EI endstream endobj 156 0 obj <> stream 0 0 0 0 78 85 d1 78 0 0 85 0 0 cm BI /IM true/W 78/H 85/BPC 1/F/CCF/DP<> ID "äh3ø pˆZ8,:jôôƒtƒp·Aza÷¤Ý~Ý/ýÿ zûÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿý?ô Șcò84’àcÿÀ@ EI endstream endobj 157 0 obj <> stream 0 0 0 70 13 82 d1 13 0 0 12 0 70 cm BI /IM true/W 13/H 12/BPC 1/F/CCF/DP<> ID 6pøOÿ x`  EI endstream endobj 158 0 obj <> stream 93 0 0 0 0 0 d1 endstream endobj 159 0 obj <> stream 28 0 0 0 0 0 d1 endstream endobj 160 0 obj <> stream 49 0 0 0 0 0 d1 endstream endobj 161 0 obj <> stream 0 0 0 30 13 82 d1 13 0 0 52 0 30 cm BI /IM true/W 13/H 52/BPC 1/F/CCF/DP<> ID 6pøOÿ x`£ÿÿÿÍœ Âá¯á‚€€ EI endstream endobj 162 0 obj <> stream 39 0 0 0 0 0 d1 endstream endobj 163 0 obj <> stream 0 0 0 -2 79 84 d1 79 0 0 86 0 -2 cm BI /IM true/W 79/H 86/BPC 1/F/CCF/DP<> ID "AŸÉ€i„E¨†4 !¢€ˆ¦ÂŠ0D¬- 0Ht™éj­Ip¥8º0Aëê†ä Á„ƒ}o¸H µ~LSx[õ§}$ëõÿ¤÷_þú_þ¿á~¡ÿÿÿÿÿÿÿÿÿÿÿý†¯õÿ÷ýÿÿ·ÖöµÿÛaW¶‰U¿ °Ã¤°á†•n(]°ÂKpb à ¶KlRý†–ÂÃÕ´´°am„ Ã+†  ÃB† ¡…"@ð EI endstream endobj 164 0 obj <> stream 54 0 0 0 0 0 d1 endstream endobj 165 0 obj <> stream 40 0 0 0 0 0 d1 endstream endobj 166 0 obj <> stream 26 0 0 0 0 0 d1 endstream endobj 167 0 obj <> stream 0 0 0 1 52 85 d1 52 0 0 84 0 1 cm BI /IM true/W 52/H 84/BPC 1/F/CCF/DP<> ID #~ƒÿÿÿÿßÿÿ‡ÿûûûýûø}ûûîøwÜ=÷»Ûö<_¾ß{oïÃï°ßîÞß¼?íÿ"”Á EI endstream endobj 168 0 obj <> stream 0 0 0 3 47 82 d1 47 0 0 79 0 3 cm BI /IM true/W 47/H 79/BPC 1/F/CCF/DP<> ID #†×øw½ÿ†L l7~ÛØ~øo·{·°ûÛ½¼=Øváì;{Ý»Ã~Þïoáû~ìÀº¦ÿÿ¯×_³l/ï[\>è-¥VVÂY{ Â†§  EI endstream endobj 169 0 obj <> stream 0 0 0 3 47 85 d1 47 0 0 82 0 3 cm BI /IM true/W 47/H 82/BPC 1/F/CCF/DP<> ID 5„ Ü0DZ:âZ‡H7§„›Óuð®“úú"{÷÷÷ÿþÖÖ?ÿ^¿_ÏÁw iÖÒÁ®ÒÍ_ ¼.…ÉÂÿÿÿÿÿù€Æ ðxx{ÞB†òA8 x€ EI endstream endobj 170 0 obj <> stream 55 0 0 0 0 0 d1 endstream endobj 171 0 obj <> stream 95 0 0 0 0 0 d1 endstream endobj 172 0 obj <> stream 0 0 0 3 39 82 d1 39 0 0 79 0 3 cm BI /IM true/W 39/H 79/BPC 1/F/CCF/DP<> ID .¿-Zÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ&¡|Éà_¼<<@ EI endstream endobj 173 0 obj <> stream 0 0 0 0 79 70 d1 79 0 0 70 0 0 cm BI /IM true/W 79/H 70/BPC 1/F/CCF/DP<> ID &¡”F—ÿù8„Lµ[_Þ¶¿‡­¯ïXaxXý¯ìŒºÚþ¶¿½a…ýámzÚþõµü=mzà ûÂÇíkøkû_Ø_ÚþÔ@ EI endstream endobj 174 0 obj <> stream 0 0 0 0 57 70 d1 57 0 0 70 0 0 cm BI /IM true/W 57/H 70/BPC 1/F/CCF/DP<> ID >G@ûC>–{,ào ü=>›ÿûÿ¿ÿÿÿÿÿþ¿×þºúÜ,[\%ŠÈ#‚á…ÌÃÿÿÿÿÿÿýdÔ4ÿ“„€€ EI endstream endobj 175 0 obj <> stream 0 0 0 25 38 70 d1 38 0 0 45 0 25 cm BI /IM true/W 38/H 45/BPC 1/F/CCF/DP<> ID &¦h ÀhÄ<Cx ú|+þ›úõ¯\(AŒè $á— «ªKÂ!–ˆ,$9:# ø^—ðþ× l0[àò@!÷ø€ EI endstream endobj 176 0 obj <> stream 0 0 0 6 36 70 d1 36 0 0 64 0 6 cm BI /IM true/W 36/H 64/BPC 1/F/CCF/DP<> ID 5…ÀŠpLz~ð”?ßÿÿÿÿ5ÿÿÿÿÿÿÿþMA¯ÿ6¾¨þþþÿÿÿþ  EI endstream endobj 177 0 obj <> stream 0 0 0 25 42 70 d1 42 0 0 45 0 25 cm BI /IM true/W 42/H 45/BPC 1/F/CCF/DP<> ID &¡™ÿóàŸÿÿÿÿÿÿÿþÿ!Ü}= ÿáéäÔ2»ä3¸…Úá©8€Èçð EI endstream endobj 178 0 obj <> stream 0 0 0 25 51 70 d1 51 0 0 45 0 25 cm BI /IM true/W 51/H 45/BPC 1/F/CCF/DP<> ID $$ À€ ª Q `àÏÉ/ý?ÿûÿ ÷ðøaø}Ñx1ÃΡ™ Ãg0I›ÿO ÿõõþ—\ AX«  x€ EI endstream endobj 179 0 obj <> stream 48 0 0 0 0 0 d1 endstream endobj 180 0 obj <> stream 0 0 0 25 43 70 d1 43 0 0 45 0 25 cm BI /IM true/W 43/H 45/BPC 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stream 0 0 0 -2 74 76 d1 74 0 0 78 0 -2 cm BI /IM true/W 74/H 78/BPC 1/F/CCF/DP<> ID "Ad3øAÁ´ tBTé7 xA7I‡^“~ô¯®ÿßøWWÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿýÓ„ rj F Êÿÿ EI endstream endobj 725 0 obj <> stream 0 0 0 -38 105 37 d1 105 0 0 75 0 -38 cm BI /IM true/W 105/H 75/BPC 1/F/CCF/DP<> ID #s£:G_Ãýóáò\,5µjîý÷·ßîƒþþýÈŽáýûÿöÃÿðû¿°û«þ·øoÞÝÿáûþïÿÞÝßaÿÿÛì({ð¾ûÛþû‡÷ïÿØaþðþúßzûý¿{wÿ‡áÿwÿï Ýöÿÿ[}ÓßþûØdq?ûâÃßþËö> startxref 195788 %%EOF otter-3.3f/documents/group.in0100644000076400007640000000040307300322621015656 0ustar mccunemccune set(auto). list(usable). e * x = x. % left identity g(x) * x = e. % left inverse (x * y) * z = x * (y * z). % associativity a * b != b * a. % denial of commutativity end_of_list. otter-3.3f/documents/anldp.tex0100644000076400007640000010474207277004246016042 0ustar mccunemccune\documentstyle[11pt]{article} % \renewcommand{\baselinestretch}{2} % \setlength{\textwidth}{6.25in} % \setlength{\textheight}{9in} \setlength{\hoffset}{-.5in} \setlength{\voffset}{-1in} \setlength{\parskip}{.1in} % \voffset=-.5in \hoffset=-.7in \parskip=.1in \textwidth=16cm \textheight=23.5cm \newcommand{\otter}{{\sc Otter}} % \pagestyle{empty} % \pagestyle{myheadings} \markright{DRAFT} \begin{document} \title{{\Large\bf A Davis-Putnam Program \\ and Its Application to Finite First-Order Model Search: Quasigroup Existence Problems}\thanks{This work was supported by the Office of Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38.}} \author{{\it William McCune} \\ \\ Mathematics and Computer Science Division \\ Argonne National Laboratory \\ Argonne, Illinois 60439-4844, U.S.A. \\ e-mail: mccune@mcs.anl.gov \\ phone: 708-252-3065} \date{September 1994} \maketitle % \thispagestyle{empty} \begin{abstract} This document describes the implementation and use of a Davis-Putnam procedure for the propositional satisfiability problem. It also describes code that takes statements in first-order logic with equality and a domain size $n$ then searches for models of size $n$. The first-order model-searching code transforms the statements into set of propositional clauses such that the first-order statements have a model of size $n$ if and only if the propositional clauses are satisfiable. The propositional set is then given to the Davis-Putnam code; any propositional models that are found can be translated to models of the first-order statements. The first-order model-searching program accepts statements only in a flattened relational clause form without function symbols. Additional code was written to take input statements in the language of \otter\ 3.0 and produce the flattened relational form. The program was successfully applied to several open questions on the existence of orthogonal quasigroups. \end{abstract} \section{The Davis-Putnam Procedure} The Davis-Putnam procedure is widely regarded as the best method for deciding the satisfiability of a set of propositional clauses. I'll assume that the reader is familiar with it. I list here some features of our implementation. \begin{enumerate} \item There are no checks for pure literals. Experience has shown that such checks are usually more expensive than they are worth. \item Deletion of subsumed clauses is optional. Again, experience has shown that it is too expensive. \item The variable selected for splitting is the always first literal of the first, shortest positive clause. \end{enumerate} \subsection{Implementation} The data structures for clauses and for propositional variables and the algorithms are similar to the ones Mark Stickel uses in LDPP \cite{dp-trie}. Variables are integers $\geq 1$. Associated with the set of variables is an array, indexed by the variables, of variable structures. Each variable structure contains the following fields. \begin{itemize} \item {\verb:value:.} The current value (true, false, or unassigned) of the variable. \item {\verb:enqueued_value:.} A field to speed the bottleneck operation of unit propagation (see below). \item {\verb:pos_occ:.} A list of pointers to clauses that contain the variable in a positive literal. \item {\verb:neg_occ:.} A list of pointers to clauses that contain the variable in a negative literal. \end{itemize} Each clause contains the following fields. \begin{itemize} \item {\verb:pos:.} A list of variables representing positive literals. \item {\verb:neg:.} A list of variables representing negative literals. \item {\verb:active_pos:.} The number of positive literals that have not been resolved away. \item {\verb:active_neg:.} The number of negative literals that have not been resolved away. \item {\verb:subsumer:.} A field set to the responsible variable if the clause has been inactivated by subsumption. \end{itemize} \paragraph{Assignment.} When a variable is assigned a value, say true, by splitting or during unit propagation, unit resolution is performed by traversing the \verb:neg_occ: list of the variable: for each clause that has not been subsumed, the \verb:active_neg: field is simply decremented by 1. If \verb:active_pos+active_neg: becomes 0, the empty clause has been found and backtracking occurs. If \verb:active_pos+active_neg: becomes 1, the new unit clause is queued for unit propagation. In addition, if subsumption is enabled, (back) subsumption is performed by traversing the \verb:pos_occ: list of the variable: for each clause that is not already subsumed, the \verb:subsumer: field is set to the variable. Variables must be unassigned during backtracking, and the process is essentially the reverse of assignment. \paragraph{Unit Propagation.} A split causes an assignment. The unit propagation queue is then processed (causing further assignments and possibly more units to be queued) until empty or the empty clause is found. Each split typically causes many assignments, so unit propagation must be done efficiently. To avoid duplicates in the queue, and to detect the empty clause during the enqueue operation rather than during assignment, we set the field \verb:enqueued_value: of the variable when the corresponding literal is enqueued. That way we can quickly tell whether a literal or its complement is already in the queue. \paragraph{Unit Preprocessing.} If the set of input clauses contains any units, unit propagation is applied. During assignment, back subumption is always applied, because assignments made during this phase are never undone. \paragraph{Selecting Variables for Splitting.} The variable selected for splitting is the first literal in the first, shortest nonsubsumed positive clause. After the unit preprocessing, pointers to all of the non-Horn clauses (i.e., clauses with two or more positive literals) are collected into a list. In order to select a variable for splitting, the list is simply traversed. Subsumed clauses must be ignored; if subsumption is enabled, the subsumer field is checked; otherwise the clause is scanned for a literal with value true. (If all clauses in the list are subsumed, a model has been found.) \subsection{Pigeonhole Problems} The pigeonhole problems are a set of artificial propositional problems that are used to test the efficiency of propositional theorem provers. See the sample input files that come with ANL-DP for examples. Table \ref{pigeon} lists the performance of ANL-DP on several instances of the pigeonhole problems. The jobs were run on a SPARC 2. \begin{table}[htbp] \centering \caption{ANL-DP on the Pigeonhole Problems} \label{pigeon} \begin{tabular}{lrr} & Branches & Seconds \\ \hline 7 pigeons, 6 holes & 719 & .15 \\ 8 pigeons, 7 holes & 5039 & 1.14 \\ 9 pigeons, 8 holes & 40319 & 9.16 \\ 10 pigeons, 9 holes & 362879 & 88.43 \\ 11 pigeons, 10 holes & 3628799 & 916.62 \\ \hline \end{tabular} \end{table} \subsection{Using ANL-DP} \label{use-prop} Propositional input to ANL-DP is a sequence of clauses. (See Sec. \ref{use-fo} for input to the first-order model-searching program.) Literals are nonzero integers (negative integers represent negative literals), and each clause is terminated with 0. (Hence, the entire input is just a sequence of integers.) The input is taken from \verb:stdin: (the standard input). ANL-DP accepts the following command-line options. \begin{description} \item {\verb:-s:.} Perform subsumption. (Subsumption is always performed during unit preprocessing.) \item {\verb:-p:.} Print models as they are found. \item {\verb:-m: $n$.} Stop when the $n$-th model is found. \item {\verb:-t: $n$.} Stop after $n$ seconds. \item {\verb:-k: $n$.} Allocate at most $n$ kbytes for storage of clauses. \item {\verb:-x: $n$.} Quasigroup experiment $n$. See Section \ref{qg}. \item {\verb:-B: {\it file}.} Backup assignments to a file. \item {\verb:-b: $n$.} Backup assignments every $n$ seconds. \item {\verb:-R: {\it file}.} Restore assignments from a file. The file typically contains just the last line of a backup file. Other input, in particular the clauses, must be given exactly as in the original search. \item {\verb:-n: $n$.} This option is used for first-order model searches. The parameter $n$ specifies the domain size, and its presence tells the program to read first-order flattened relational input clauses instead of propositional clauses. \end{description} \section{The First-Order Model-Searching Program} The first practical program for searching for small models of first-order statements was FINDER \cite{finder3}. Another model-searching program is MGTP \cite{qg-slaney-fujita-stickel}, which uses a somewhat different approach. The third class of programs, including LDPP \cite{dp-trie}, SATO \cite{dp-trie}, and the one described here, are based on Davis-Putnam procedures. None of these programs is clearly better than the others, and each has answered open questions about quasigroups (see Sec. \ref{qg}). The Davis-Putnam approach is quite elegant, because the computational engine---the Davis-Putnam code---is in no way tailored to first-order model searching. First-order clauses and a domain size $n$ are input; then ground instances (over the domain) of the first-order clauses are generated and given to the Davis-Putnam code. Any propositional models that are found can be easily translated to first-order models (e.g., an $n\times n$ table for a binary function). The steps, which are summarized in Figure \ref{trans}, are as follows. \begin{figure}[h] \begin{picture}(400,80)(-35,0) \thicklines \put(0,60){FO formula} \put(100,60){FO clauses} \put(200,60){FO flat clauses} \put(300,60){Prop. clauses} \put(300,0){Prop. models} \put(100,0){FO models} \put(65,63){\vector(1,0){30}} \put(70,68){(1)} \put(160,63){\vector(1,0){35}} \put(168,68){(2)} \put(275,63){\vector(1,0){20}} \put(275,68){(3)} \put(330,55){\vector(0,-1){40}} \put(333,35){(4)} \put(295,3){\vector(-1,0){135}} \put(230,8){(5)} \thinlines % \put(125,55){\vector(0,-1){40}} \put(125,17){\dashbox(0,38)} \put(125,18){\vector(0,-1){3}} \end{picture} \caption{Searching for First-Order Models} \label{trans} \end{figure} \begin{enumerate} \item[(1)] Take an arbitrary first-order formula (possibly involving equality), and produce a set of clauses. \otter 's clausification code is sufficient for this. \item[(2)] Take a set of first-order clauses, and produce a set of flattened, relational clauses that contain no constants or function symbols---all arguments of the literals are variables. The steps are as follows: \begin{enumerate} \item[a.] For each $n$-ary function symbol (including constants), an $n+1$-ary predice symbol is introduced. For the examples, function symbols are lower-case letters, and new predicate symbols are the corresponding upper-case letters. \item[b.] To flatten the clauses, the following kind of equality transformation is applied to nonvariable terms (excepting arguments of positive equalities): $P[t]$ is rewritten to $t\neq x \; |\; P[x]$. \item[c.] A clause containing a positive equality $\alpha=\beta$, where both arguments are nonvariable, is made into two clauses: $L\;|\;\alpha=\beta$ becomes $L\;|\;\alpha\neq x\;|\;\beta=x$ and $L\;|\;\beta\neq x\;|\;\alpha=x$. \item[d.] Each functional literal, say $f(x,y)=z$, is rewritten into its relational form, say $F(x,y,z)$. (The resulting clauses may contain ordinary equality literals as well.) \end{enumerate} For example, the equality $f(g(x),x)=e$ produces the two clauses \begin{verse} $\neg G(x,y) \;|\;\neg E(z) \;|\;F(y,x,z)$ \\ $\neg G(x,y) \;|\;E(z) \;|\;\neg F(y,x,z)$ \end{verse} \item[(3)] Take a set of flattened relational clauses and a domain size, and generate a set of propositional clauses. For each relational clause, the set of instances over the domain is constructed. (With domain size $n$, a clause with $m$ variables produces $n^m$ instances.) Each atom is encoded into a unique integer that becomes the propositional variable. Also, we must assert that the $(n+1)$-ary predicates introduced above represent total functions, so for each, we assert two sets of propositional clauses. For example, for ternary relation $F$, we must say that the last argument is a function of the others, \begin{verse} $\neg F(x,y,z_1) \;|\; \neg F(x,y,z_2)$, for $z_1 < z_2$ (well-defined) \end{verse} and that the function is total and its value always lies in the domain (elements of the domain are named $0, 1, \cdots, n-1$): \begin{verse} $F(x,y,0) \;|\; F(x,y,1) \;|\; \cdots \;|\; F(x,y,n-1)$ (closed and total). \end{verse} If the flattened relational clauses contain any equality literals, the $n^2$ units for the equality relation are asserted. Nothing special needs to be done for ordinary predicate symbols. \item[(4)] The Davis-Putnam procedure searches for models of the propositional clauses. \item[(5)] For each propositional model, we generate the corresponding first-order model. The clauses given in (3) above ensure that from the propositional model, we can build a function for each function symbol (including constants). \end{enumerate} \subsection{Additional Constraints} For various reasons, the most important being to reduce the number of isomorphic models that are found, the user can specify part of the model by supplying ground clauses over the domain. For example, if a noncommutative group is being sought, with constants $a$ and $b$ as noncommuting elements, the user can assign 0 to the identity, 1 to $a$, and 2 to $b$. In this case, nothing is lost by making them distinct. Symbols can be given the following properties. \begin{description} \item{\verb:quasigroup:.} This can be applied to ternary relations that represent binary functions. The multiplication table of a quasigroup has one of each element in each row and each column. \item{\verb:bijection:.} This can be applied to binary relations that represent unary functions. \item{\verb:equality:.} This can be applied to binary relations. It is just equality of domain elements. \item{\verb:order:.} This can be applied to binary relations. This is just the less-than relation on the domain elements. \item{\verb:holey:.} This can be applied to ternary relations that represent binary functions. See Sec. \ref{holey}. \item{\verb:hole:.} This can be applied to binary relations. See Sec. \ref{holey}. \end{description} \subsection{Using the Program to Search for First-Order Models} \label{use-fo} The first-order searcher is part of ANL-DP, and it is invoked as described in Sec. \ref{use-prop}. The command-line option ``\verb:-n: $n$'' specifies the domain size and indicates that the input will be given as first-order flat clauses. Here is an example input specifying a noncommutative group. \begin{verbatim} function F 3 quasigroup function E 1 ----- function G 2 bijection function A 1 ----- function B 1 ----- end_of_symbols -E v0 F v0 v1 v1 . -E v0 -G v1 v2 F v2 v1 v0 . E v0 -G v1 v2 -F v2 v1 v0 . -F v0 v1 v2 -F v3 v2 v4 -F v3 v0 v5 F v5 v1 v4 . -F v0 v1 v2 F v3 v2 v4 -F v3 v0 v5 -F v5 v1 v4 . -F v0 v1 v2 -B v0 -A v1 -F v1 v0 v2 . end_of_clauses E 0 A 1 B 2 end_of_assignments \end{verbatim} \begin{description} \item{Symbol Declarations.} In the first section of the input, each symbol is declared with four strings: type (\verb:function: or \verb:relation:), symbol, arity ($n$+1 for functions), and properties (\verb:equality:, \verb:order:, \verb:quasigroup:, \verb:bijection:, or \verb:-----:). \item{Clauses.} Flat relational clauses appear in the second section. Variables can be any strings. {\em Whitespace is required before the periods that terminates clauses.} \item{Assignments.} Ground units (without periods) can appear in the third section. \end{description} \subsection{Using \otter\ to Generate the Flat Clauses} \otter\ 3.0.2 \cite{otter3} and later versions can take ordinary formulas or clauses and produce the flat relational clauses for input to ANL-DP. Here is an \otter\ input file for a noncommutative group that will produce something like the file in Sec. \ref{use-fo}. \begin{verbatim} set(dp_transform). list(usable). f(e,x) = x. f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). f(a,b) != f(b,a). end_of_list. list(passive). properties(f(_,_), quasigroup). properties(g(_), bijection). assign(e, 0). assign(a, 1). assign(b, 2). end_of_list. \end{verbatim} The command \verb:set(dp_transform): tells \otter\ to generate input for an ANL-DP search and then exit. The output of \otter\ contains extraneous text, so it must be passed though a filter before ANL-DP can receive it. See the example files and scripts in the distribution directories. \subsection{The Order Relation} \label{order} The ordered semigroup example in the FINDER 3.0 manual \cite[Sec. 4.1.5]{finder3} motivated me to have ANL-DP recognize the less-than relation on domain elements. The input (in \otter\ form) for the ordered semigroup problems is as follows. \begin{verbatim} set(dp_transform). list(usable). f(f(x,y),z) = f(x,f(y,z)). -(f(x,y) < f(x,z)) | y < z. -(f(y,x) < f(z,x)) | y < z. end_of_list. \end{verbatim} (\otter\ recognizes \verb:<: as the order relation and gives it the property ``order'' in its output.) Table \ref{order-tab} compares the results of FINDER and ANL-DP, both run on SPARC 2 computers, on the ordered semigroup problems. FINDER's search algorithm was developed with this type of problem in mind; ANL-DP simply adds the $n^2$ unit clauses for the less-than relation. I believe this distinction explains most of the disparity of the times. \begin{table}[htb] \centering \caption{Ordered Semigroup Problems -- FINDER vs. ANL-DP} \label{order-tab} \begin{tabular}{crrr} Order & Models & FINDER & ANL-DP \\ \hline 3 & 44 & 0.1 & 0.1 \\ 4 & 386 & 0.6 & 2.6 \\ 5 & 3852 & 9.2 & 58.0 \\ \end{tabular} \end{table} \subsection{Application to Quasigroup Problems} \label{qg} In the multiplication table of an order-$n$ quasigroup, each row and each column are a permutation of the $n$ elements. For these problems, we are interested only in idempotent (i.e., $xx=x$) models. Additional constraints are given for the seven problems listed in Table \ref{qg-tab}. (Notes: (1) For QG1 and QG2, the disjunction to the right of the implication is ordinarily a conjunction; the forms are equivalent for quasigroups, and models are found more easily with disjunction. (2) The second and third equalities for QG5 and the second equality for QG7 are dependent.) See \cite{qg-survey} and \cite{qg-slaney-fujita-stickel} for details on the quasigroup problems. \begin{table}[htb] \centering \caption{The Quasigroup Problems} \label{qg-tab} \begin{tabular}{ll} Name & Constraints \\ \hline QG1 & $xy=u \;\wedge\; zw=u \;\wedge\; vy=x \;\wedge\; vw= z \rightarrow x=z \;\vee\; y=w$ \\ QG2 & $xy=u \;\wedge\; zw=u \;\wedge\; vx=y \;\wedge\; vz= w \rightarrow x=z \;\vee\; y=w$ \\ QG3 & $(xy)(yx)=x$ \\ QG4 & $(xy)(yx)=y$ \\ QG5 & $((xy)x)x=y \;\wedge\; x((yx)x)=y \;\wedge\; (x(yx))x=y$ \\ QG6 & $(xy)y = x(xy)$ \\ QG7 & $((xy)x)y=x \;\wedge\; ((xy)y)(xy)=x$ \\ \hline \end{tabular} \end{table} We also used the following cycle constraint on the last column to eliminate some isomorphic models \cite{qg-slaney-fujita-stickel}: \begin{verse} $\neg f(x,n,z)$, for $z < x-1$. \end{verse} The constraint requires that cycles in the last column be made up of contiguous elements. This constraint is specified to ANL-DP with the command-line option ``\verb:-x1:''; {\em the quasigroup operation must be \verb:f: (lower-case) for this to work}. Table \ref{qg-tab-compare} gives summaries of the performance of ANL-DP (C, list structure), SATO-2 (C, trie structure), and LDPP$'$ (Lisp, list structure) on some cases of the quasigroup problems. The SATO and LDPP figures are taken from \cite{dp-trie}. All runs were made on a SPARC 2 or similar computer. All programs used the cycle constraint and similar selection functions for splitting. I believe that differences in the number of branches are due mostly to the order of clauses and literals. Search time is given in seconds. \begin{table}[htb] \centering \caption{Quasigroup Problems -- Comparison} \label{qg-tab-compare} \begin{tabular}{rc|rr|rr|rr} & & \multicolumn{2}{c}{ANL-DP} & \multicolumn{2}{c}{SATO-2}& \multicolumn{2}{c}{LDPP$'$} \\ Problem & Models & Branches & Search & Branches & Search & Branches & Search \\ \hline QG1.7 & 8 & 388 & 2.05 & 376 & 1 & 389 & 26\\ .8 & 16 & 100731 & 852.81 & 102610 & 379 & 101129 & 3463\\ \hline QG2.7 & 14 & 361 & 2.23 & 340 & 1 & 205 & 8\\ .8 & 2 & 77158 & 810.75 & 80245 & 341 & 33835 & 1358\\ \hline QG3.8 & 18 & 1017 & 2.82 & 1072 & 3 & 573 & 5\\ .9 & - & 39461 & 155.12 & 48545 & 157 & 24763 & 208\\ \hline QG4.8 & - & 891 & 2.40 & 925 & 2 & 602 & 4\\ .9 & 178 & 52939 & 209.76 & 52826 & 168 & 27479 & 228\\ \hline QG5.9 & - & 14 & .22 & 19 & .2 & 15 & .4\\ .10 & - & 37 & .52 & 62 & .5 & 38 & .9\\ .11 & 5 & 112 & 2.16 & 111 & 2 & 125 & 5\\ .12 & - & 369 & 6.61 & 369 & 7 & 369 & 15\\ .13 & - & 9588 & 242.54 & 10764 & 224 & 12686 & 639\\ \hline QG6.9 & 4 & 17 & .25 & 24 & .2 & 18 & .4\\ .10 & - & 58 & .54 & 150 & .7 & 59 & .8\\ .11 & - & 537 & 5.36 & 519 & 6 & 539 & 11\\ .12 & - & 7306 & 95.41 & 5728 & 92 & 7288 & 177\\ \hline QG7.9 & 4 & 7 & .19 & 7 & .2 & 8 & .3\\ .10 & - & 39 & .38 & 54 & .4 & 40 & .7\\ .11 & - & 291 & 2.98 & 254 & 3 & 294 & 6\\ .12 & - & 1578 & 17.87 & 1281 & 22 & 1592 & 38\\ .13 & 64 & 33946 & 493.67 & 27988 & 592 & 34726 & 1050\\ \hline \end{tabular} \end{table} \newpage Table \ref{qg-tab-stats} lists some additional statistics for ANL-DP on the quasigroup problems. ``Generated'' and ``Searched'' are the number of propositional clauses generated and the number remaining after subsumption and the initial unit propagation. ``Create'' is the time (in seconds) used to construct the propositional clauses. \begin{table}[htb] \centering \caption{Quasigroup Problems -- ANL-DP Full Statistics} \label{qg-tab-stats} \begin{tabular}{rrrrrrrr} Problem & Models & Branches & Generated & Searched & Memory & Create & Search \\ \hline QG1.7 & 8 & 388 & 120954 & 8952 & 886 K & 4.79 & 2.05 \\ .8 & 16 & 100731 & 267805 & 28877 & 2061 K & 10.85 & 852.81 \\ \hline QG2.7 & 14 & 361 & 120954 & 9830 & 886 K & 4.72 & 2.23 \\ .8 & 2 & 77158 & 267805 & 30902 & 2061 K & 10.88 & 810.75 \\ \hline QG3.8 & 18 & 1017 & 9757 & 3830 & 303 K & 0.26 & 2.82 \\ .9 & - & 39461 & 15670 & 6966 & 601 K & 0.39 & 155.12 \\ \hline QG4.8 & - & 891 & 9757 & 3830 & 303 K & 0.25 & 2.40 \\ .9 & 178 & 52939 & 15670 & 6966 & 601 K & 0.37 & 209.76 \\ \hline QG5.9 & - & 14 & 28792 & 9694 & 894 K & 0.85 & 0.22 \\ .10 & - & 37 & 43946 & 17274 & 1193 K & 1.39 & 0.52 \\ .11 & 5 & 112 & 64428 & 28488 & 1786 K & 2.05 & 2.16 \\ .12 & - & 369 & 91363 & 44302 & 2674 K & 2.93 & 6.61 \\ .13 & - & 9588 & 125984 & 65790 & 3562 K & 4.02 & 242.54 \\ \hline QG6.9 & 4 & 17 & 22231 & 7653 & 601 K & 0.66 & 0.25 \\ .10 & - & 58 & 33946 & 13579 & 900 K & 1.02 & 0.54 \\ .11 & - & 537 & 49787 & 22332 & 1493 K & 1.54 & 5.36 \\ .12 & - & 7306 & 70627 & 34662 & 2088 K & 2.24 & 95.41 \\ \hline QG7.9 & 4 & 7 & 22231 & 5838 & 601 K & 0.61 & 0.19 \\ .10 & - & 39 & 33946 & 11038 & 900 K & 1.04 & 0.38 \\ .11 & - & 291 & 49787 & 18944 & 1493 K & 1.48 & 2.98 \\ .12 & - & 1578 & 70627 & 30309 & 2088 K & 2.14 & 17.87 \\ .13 & 64 & 33946 & 97423 & 45967 & 2683 K & 3.14 & 493.67 \\ \hline \end{tabular} \end{table} \subsubsection{Cyclically Generated Quasigroups} The command-line option \verb:-x2: constrains models of quasigroup \verb:f: to have the property $f(x+1,y+1)=f(x,y)+1$, where addition is (mod $n$); that is, all the diagonals count up (mod {\em domain-size}). The command-line option \verb:-x:$i$, where $11\leq i \leq 19$, constrains models of quasigroup \verb:f: in the following way. Consider the square of size $x=i-10$ in the lower right corner and the remaining square of size $m=n-x$ in the upper left corner. The diagonals of the upper left square count up (mod $m$), except for diagonals that consist of the same element in $m,\cdots,n-1$. Also, the first $m$ elements of the last $x$ rows and columns count up (mod $m$). For example (see \cite[Example 8.1]{qg-survey} with the input (note that the only upper left corner is idempotent) {\small \begin{verbatim} set(dp_transform). list(usable). % (3,1,2)-COLS f(x,y)!=u | f(z,w)!=u | f(v,x)!=y | f(v,z)!= w | x=z | y=w. end_of_list. list(passive). properties(f(_,_), quasigroup). assign(f(0,0),0). end_of_list. \end{verbatim}} \noindent and the options ``\verb:-n 10 -x13 -p:'', we get {\small \begin{verbatim} Model #1 at 333.47 seconds (SPARC 10): f | 0 1 2 3 4 5 6 7 8 9 --------------------------- 0 | 0 4 1 7 9 2 8 3 6 5 1 | 8 1 5 2 7 9 3 4 0 6 2 | 4 8 2 6 3 7 9 5 1 0 3 | 9 5 8 3 0 4 7 6 2 1 4 | 7 9 6 8 4 1 5 0 3 2 5 | 6 7 9 0 8 5 2 1 4 3 6 | 3 0 7 9 1 8 6 2 5 4 | 7 | 1 2 3 4 5 6 0 7 8 9 8 | 2 3 4 5 6 0 1 8 9 7 9 | 5 6 0 1 2 3 4 9 7 8 \end{verbatim}} \noindent The \verb:-x:$i$ option can also be used when searching for quasigroups with holes. \subsubsection{Quasigroups with Holes} \label{holey} We simply list an example. The input (compare with above input) {\small \begin{verbatim} set(dp_transform). list(usable). same_hole(x,x) | f(x,x) = x. % (3,1,2)-COLS f(x,y)!=u | f(z,w)!=u | f(v,x)!=y | f(v,z)!= w | x=z | y=w. end_of_list. list(passive). properties(f(_,_), quasigroup_holey). properties(same_hole(_,_), hole). % The program makes same_hole symmetric and transitive. assign(same_hole(7,8), T). assign(same_hole(8,9), T). end_of_list. \end{verbatim}} \noindent with the command-line options ``\verb:-n10 -x13 -p:'' produces the following: \newpage {\small \begin{verbatim} Model #1 at 50.07 seconds (SPARC 2): f | 0 1 2 3 4 5 6 7 8 9 -------------------------- 0 | 0 6 7 5 8 9 3 1 2 4 1 | 4 1 0 7 6 8 9 2 3 5 2 | 9 5 2 1 7 0 8 3 4 6 3 | 8 9 6 3 2 7 1 4 5 0 4 | 2 8 9 0 4 3 7 5 6 1 5 | 7 3 8 9 1 5 4 6 0 2 6 | 5 7 4 8 9 2 6 0 1 3 7 | 3 4 5 6 0 1 2 - - - 8 | 6 0 1 2 3 4 5 - - - 9 | 1 2 3 4 5 6 0 - - - \end{verbatim}} \subsubsection{Open Quasigroup Questions Answered} \paragraph{Orthogonal Mendelsohn Triple Systems (OMTS).} Corollary 5.2 of \cite{somts} states \begin{quote} The necessary condition for the existence of a pair of OMTS($v$), that is, $v\equiv$ 0 or 1 (mod 3), is also sufficient except for $v$=3,6 and possibly excepting $v\in \{9,10,12,18\}$. \end{quote} See \cite{somts} for definitions. The input {\small \begin{verbatim} set(dp_transform). list(usable). f(x,x) = x. h(x,x) = x. f(x,f(y,x))=y. h(x,h(y,x))=y. f(x,y)!=u | f(z,w)!=u | h(x,y)!=v | h(z,w)!=v | x=z | y=w. end_of_list. list(passive). properties(f(_,_), quasigroup). properties(h(_,_), quasigroup). end_of_list. \end{verbatim}} \noindent with the options ``\verb:-n9 -x1 -p:'' produces the following quasigroups, which correspond to a pair of orthogonal Mendelsohn triple systems of order 9. {\small \begin{verbatim} Model #1 at 54.58 seconds (SPARC 2): f | 0 1 2 3 4 5 6 7 8 h | 0 1 2 3 4 5 6 7 8 ------------------------ ------------------------ 0 | 0 8 5 2 7 4 3 6 1 0 | 0 2 6 4 3 1 8 5 7 1 | 8 1 7 6 3 2 5 4 0 1 | 5 1 0 8 2 3 7 6 4 2 | 3 5 2 8 6 0 4 1 7 2 | 1 4 2 6 7 8 0 3 5 3 | 6 4 0 3 8 7 1 5 2 3 | 4 5 7 3 0 6 2 8 1 4 | 5 7 6 1 4 8 2 0 3 4 | 3 8 1 0 4 7 5 2 6 5 | 2 6 1 7 0 5 8 3 4 5 | 7 0 8 1 6 5 3 4 2 6 | 7 3 4 0 2 1 6 8 5 6 | 2 7 3 5 8 4 6 1 0 7 | 4 2 8 5 1 3 0 7 6 7 | 8 6 4 2 5 0 1 7 3 8 | 1 0 3 4 5 6 7 2 8 8 | 6 3 5 7 1 2 4 0 8 \end{verbatim}} \noindent An analogous search for OMTS(10) ran for several days without finding a model. \paragraph{QG3($2^8$).} A quasigroup of type $h^n$ has order $h*n$ and $n$ holes of size $h$. Frank Bennett posed \cite{bennett-email} the question of the existence of QG3($2^8$). (Mark Stickel had already answered positively the question of the existence of QG3($2^6$) \cite{bennett-email}.) The ANL-DP input {\small \begin{verbatim} relation = 2 equality relation same_hole 2 hole function f 3 quasigroup_holey end_of_symbols f v0 v0 v0 same_hole v0 v0 . -f v0 v1 v2 -f v1 v0 v3 f v3 v2 v1 . -f v0 v1 v2 -f v0 v2 v1 = v0 v1 . -f v0 v1 v2 -f v2 v1 v0 = v0 v1 . end_of_clauses same_hole 0 7 same_hole 1 8 same_hole 2 9 same_hole 3 10 same_hole 4 11 same_hole 5 12 same_hole 6 13 same_hole 14 15 end_of_assignments \end{verbatim}} \noindent with the options ``\verb:-n16 -p:'' produces the following holey quasigroup. {\small \begin{verbatim} Model #1 at 76086.21 seconds (i468 DX2/66): f | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ------------------------------------------------------ 0 | - 2 3 12 1 4 5 - 10 11 14 15 13 8 6 9 1 | 3 - 6 5 15 0 14 12 - 4 11 7 10 2 9 13 2 | 11 15 - 0 10 14 12 13 7 - 5 6 3 4 1 8 3 | 2 13 1 - 9 7 4 15 11 12 - 0 14 5 8 6 4 | 5 10 7 1 - 6 9 8 14 3 15 - 2 0 13 12 5 | 13 4 11 14 0 - 8 6 15 7 9 10 - 1 2 3 6 | 4 0 15 9 14 11 - 3 12 5 2 8 7 - 10 1 7 | - 6 8 13 2 9 15 - 5 14 4 12 1 11 3 10 8 | 14 - 4 6 3 2 10 9 - 0 13 5 15 7 12 11 9 | 15 3 - 11 6 8 7 1 13 - 12 14 0 10 4 5 10 | 6 5 14 - 7 15 11 2 9 1 - 13 8 12 0 4 11 | 8 12 10 2 - 1 3 14 6 13 7 - 9 15 5 0 12 | 10 9 0 8 13 - 1 11 4 15 6 3 - 14 7 2 13 | 9 14 12 15 5 3 - 10 2 8 0 1 4 - 11 7 14 | 1 7 13 4 12 10 0 5 3 6 8 2 11 9 - - 15 | 12 11 5 7 8 13 2 4 0 10 1 9 6 3 - - \end{verbatim}} \noindent (In case the reader is wondering why the holes are irregular in the lower right corner, the reason is that preliminary runs on QG3($2^6$) ran faster with a similar hole configuration than with a regular configuration.) \paragraph{QG7(17,5).} Frank Bennett posed \cite{bennett-email} the question of whether the the quasigroup identity (QG7a) $x(yx) = (yx)y$ implies either $(xy)x = x(yx)$ or $xy(yx) = y$. He suggested looking at models of order 17 with a hole of size 5, if they exist, as possible counterexamples. The identity (QG7b) $((xy)x)y = x$, which is conjugate-equivalent \cite{qg-survey} to (QG7a), is much easier to work with, so we put ANL-DP to work with the input {\small \begin{verbatim} relation same_hole 2 hole function f 3 quasigroup_holey end_of_symbols f v0 v0 v0 same_hole v0 v0 . -f v0 v1 v2 -f v2 v0 v3 f v3 v1 v0 . end_of_clauses same_hole 12 13 same_hole 13 14 same_hole 14 15 same_hole 15 16 end_of_assignments \end{verbatim}} \noindent and the options ``\verb:-n17 -x1 -p:'', which produced the following {\small \begin{verbatim} Model #1 at 172914.77 seconds (SPARC 2): f | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 --------------------------------------------------------- 0 | 0 2 1 16 13 11 12 8 5 15 14 7 4 6 9 10 3 1 | 16 1 3 2 10 13 9 12 15 4 6 14 5 7 8 11 0 2 | 3 16 2 0 15 9 14 10 12 7 5 13 11 8 4 6 1 3 | 1 0 16 3 8 15 11 14 6 12 13 4 10 9 5 7 2 4 | 8 13 10 15 4 6 5 16 2 14 0 12 9 3 11 1 7 5 | 13 9 15 11 16 5 7 6 14 3 12 1 8 2 10 0 4 6 | 11 12 9 14 7 16 6 4 13 0 15 2 3 10 1 8 5 7 | 12 10 14 8 5 4 16 7 1 13 3 15 2 11 0 9 6 8 | 15 6 5 12 14 1 2 13 8 10 9 16 0 4 7 3 11 9 | 7 15 12 4 0 14 13 3 16 9 11 10 1 5 6 2 8 10 | 5 14 13 6 12 3 0 15 11 16 10 8 7 1 2 4 9 11 | 14 4 7 13 2 12 15 1 9 8 16 11 6 0 3 5 10 12 | 10 11 4 5 3 2 8 9 7 6 1 0 - - - - - 13 | 9 8 6 7 11 10 3 2 0 1 4 5 - - - - - 14 | 4 5 8 9 1 0 10 11 3 2 7 6 - - - - - 15 | 6 7 11 10 9 8 1 0 4 5 2 3 - - - - - 16 | 2 3 0 1 6 7 4 5 10 11 8 9 - - - - - \end{verbatim}} \noindent The conjugate-equivalent quasigroup corresponding to (QG7a) was then generated and found to falsify the two identities in question, giving a counterexample to the problem. % \section{Conclusion} \nocite{qg-ijcai} \bibliographystyle{plain} % \bibliography{bib} \begin{thebibliography}{1} \bibitem{bennett-email} F.~E. Bennett. \newblock Correspondence by electronic mail, 1994. \bibitem{qg-survey} F.~E. Bennett and L.~Zhu. \newblock Conjugate-orthogonal Latin squares and related structures. \newblock In J.~H. Dinitz and D.~R. Stinson, editors, {\em Contemporary Design Theory: A Collection of Surveys}, pages 41--96. John Wiley \& Sons, 1992. \bibitem{somts} F.~E. Bennett and L.~Zhu. \newblock Self-orthogonal {M}endelsohn triple systems. \newblock Preprint, 1994. \bibitem{qg-ijcai} M.~Fujita, J.~Slaney, and F.~E. Bennett. \newblock Automatic generation of some results in finite algebra. \newblock In {\em International Joint Conference on Artificial Intelligence}, 1993. \bibitem{otter3} W.~McCune. \newblock {\sc Otter} 3.0 {R}eference {M}anual and {G}uide. \newblock Tech. Report ANL-94/6, Argonne National Laboratory, Argonne, Ill., 1994. \bibitem{finder3} J.~Slaney. \newblock FINDER version 3.0 notes and guide. \newblock Tech. report, Centre for Information Science Research, Australian National University, 1993. \bibitem{qg-slaney-fujita-stickel} J.~Slaney, M.~Fujita, and M.~Stickel. \newblock Automated reasoning and exhaustive search: Quasigroup existence problems. \newblock {\em Computers and Mathematics with Applications}, 1994. \newblock To appear. \bibitem{dp-trie} H.~Zhang and M.~Stickel. \newblock Implementing the {D}avis-{P}utnam algorithm by tries. \newblock Preprint, 1994. \end{thebibliography} \end{document} otter-3.3f/documents/README0100644000076400007640000000043207676327662015106 0ustar mccunemccuneOtter 3.3 Reference Manual otter33.tex otter33.ps otter33.pdf MACE 2.0 Reference Manual and Guide mace2.tex mace2.ps mace2.pdf A Davis-Putnam Program and Its Application to Finite First-Order Model Search: Quasigroup Existence Problems 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1475 3235 4 5 v 1475 3235 V 1475 2924 V 1475 2924 V 1475 2941 4 9 v 1475 2957 V 1475 2974 V 1475 2991 V 1475 3007 V 1475 3024 V 1475 3040 V 1475 3057 V 1475 3074 V 1475 3090 V 1475 3107 V 1475 3123 V 1475 3140 V 1475 3157 V 1475 3173 V 1475 3190 V 1475 3206 V 1475 3223 V 1475 2941 V 1475 2957 V 1475 2974 V 1475 2991 V 1475 3007 V 1475 3024 V 1475 3040 V 1475 3057 V 1475 3074 V 1475 3090 V 1475 3107 V 1475 3123 V 1475 3140 V 1475 3157 V 1475 3173 V 1475 3190 V 1475 3206 V 1475 3223 V 1475 3252 4 25 v 1477 3252 a Fg(?)1179 3573 y Fq(Figure)f(1:)41 b(Searc)m(hing)30 b(for)g(First-Order)f(Mo)s(dels)214 3885 y(\(1\))47 b(T)-8 b(ak)m(e)37 b(an)e(arbitrary)g(\014rst-order)g (form)m(ula)g(\(p)s(ossibly)e(in)m(v)m(olving)h(equalit)m(y\),)j(and)f (pro)s(duce)e(a)i(set)h(of)376 3998 y(clauses.)j Ff(Otter)p Fq('s)29 b(clausi\014cation)g(co)s(de)i(is)e(su\016cien)m(t)h(for)g (this.)214 4185 y(\(2\))47 b(T)-8 b(ak)m(e)40 b(a)g(set)h(of)e (\014rst-order)g(clauses,)j(and)d(pro)s(duce)f(a)i(set)g(of)g 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b Fm(6)p Fq(=)g Fj(x)g Fm(j)g Fj(P)13 b Fq([)p Fj(x)p Fq(].)464 5343 y(c.)47 b(A)25 b(clause)g(con)m(taining)f(a)h(p)s (ositiv)m(e)f(equalit)m(y)h Fj(\013)h Fq(=)f Fj(\014)5 b Fq(,)26 b(where)f(b)s(oth)f(argumen)m(ts)h(are)h(non)m(v)-5 b(ariable,)576 5455 y(is)26 b(made)i(in)m(to)f(t)m(w)m(o)i(clauses:)39 b Fj(L)25 b Fm(j)h Fj(\013)g Fq(=)f Fj(\014)32 b Fq(b)s(ecomes)c Fj(L)d Fm(j)h Fj(\013)g Fm(6)p Fq(=)f Fj(x)g Fm(j)g Fj(\014)31 b Fq(=)25 b Fj(x)i Fq(and)g Fj(L)e Fm(j)h Fj(\014)k Fm(6)p Fq(=)25 b Fj(x)g Fm(j)h Fj(\013)g Fq(=)f Fj(x)p Fq(.)2015 5732 y(4)p eop %%Page: 5 5 5 4 bop 454 23 a Fq(d.)46 b(Eac)m(h)e(functional)e(literal,)j(sa)m(y)f Fj(f)10 b Fq(\()p Fj(x;)15 b(y)s Fq(\))48 b(=)e Fj(z)t Fq(,)i(is)42 b(rewritten)h(in)m(to)g(its)g(relational)g(form,)j(sa)m(y) 576 136 y Fj(F)13 b Fq(\()p Fj(x;)i(y)s(;)g(z)t Fq(\).)42 b(\(The)30 b(resulting)f(clauses)h(ma)m(y)h(con)m(tain)f(ordinary)f (equalit)m(y)h(literals)f(as)h(w)m(ell.\))376 313 y(F)-8 b(or)31 b(example,)f(the)h(equalit)m(y)f Fj(f)10 b Fq(\()p Fj(g)s Fq(\()p Fj(x)p Fq(\))p Fj(;)15 b(x)p Fq(\))26 b(=)f Fj(e)31 b Fq(pro)s(duces)e(the)i(t)m(w)m(o)g(clauses)576 490 y Fm(:)p Fj(G)p Fq(\()p Fj(x;)15 b(y)s Fq(\))26 b Fm(j)f(:)p Fj(E)5 b Fq(\()p Fj(z)t Fq(\))27 b Fm(j)e Fj(F)13 b Fq(\()p Fj(y)s(;)i(x;)g(z)t Fq(\))576 603 y Fm(:)p Fj(G)p Fq(\()p Fj(x;)g(y)s Fq(\))26 b Fm(j)f Fj(E)5 b Fq(\()p Fj(z)t Fq(\))27 b Fm(j)e(:)p Fj(F)13 b Fq(\()p Fj(y)s(;)i(x;)g(z)t Fq(\))214 781 y(\(3\))47 b(T)-8 b(ak)m(e)33 b(a)g(set)f(of)h(\015attened)f(relational)f(clauses)h(and)g(a)g(domain) f(size,)i(and)e(generate)j(a)e(set)h(of)f(prop)s(o-)376 894 y(sitional)j(clauses.)59 b(F)-8 b(or)38 b(eac)m(h)g(relational)e (clause,)i(the)f(set)g(of)g(instances)g(o)m(v)m(er)h(the)f(domain)e(is) h(con-)376 1007 y(structed.)50 b(\(With)34 b(domain)f(size)g Fj(n)p Fq(,)i(a)f(clause)g(with)e Fj(m)i Fq(v)-5 b(ariables)32 b(pro)s(duces)g Fj(n)3161 974 y Fe(m)3261 1007 y Fq(instances.\))51 b(Eac)m(h)376 1120 y(atom)34 b(is)e(enco)s(ded)i(in)m(to)f(a)h(unique)d (in)m(teger)j(that)g(b)s(ecomes)g(the)g(prop)s(ositional)c(v)-5 b(ariable.)49 b(Also,)34 b(w)m(e)376 1232 y(m)m(ust)29 b(assert)i(that)f(the)g(\()p Fj(n)19 b Fq(+)g(1\)-ary)31 b(predicates)f(in)m(tro)s(duced)e(ab)s(o)m(v)m(e)j(represen)m(t)f (total)h(functions,)e(so)376 1345 y(for)i(eac)m(h,)i(w)m(e)e(assert)h (t)m(w)m(o)h(sets)e(of)h(prop)s(ositional)c(clauses.)43 b(F)-8 b(or)32 b(example,)g(for)f(ternary)g(relation)g Fj(F)13 b Fq(,)376 1458 y(w)m(e)30 b(m)m(ust)h(sa)m(y)g(that)g(the)f (last)h(argumen)m(t)f(is)g(a)h(function)e(of)h(the)h(others,)576 1636 y Fm(:)p Fj(F)13 b Fq(\()p Fj(x;)i(y)s(;)g(z)965 1650 y Fd(1)1005 1636 y Fq(\))26 b Fm(j)f(:)p Fj(F)13 b Fq(\()p Fj(x;)i(y)s(;)g(z)1505 1650 y Fd(2)1545 1636 y Fq(\),)31 b(for)f Fj(z)1817 1650 y Fd(1)1882 1636 y Fj(<)25 b(z)2020 1650 y Fd(2)2090 1636 y Fq(\(w)m(ell-de\014ned\))376 1813 y(and)39 b(that)h(the)g(function)e(is)h(total)h(and)f(its)g(v)-5 b(alue)39 b(alw)m(a)m(ys)h(lies)f(in)f(the)i(domain)e(\(elemen)m(ts)j (of)f(the)376 1926 y(domain)29 b(are)i(named)f(0)p Fj(;)15 b Fq(1)p Fj(;)g Fm(\001)g(\001)g(\001)i Fj(;)e(n)21 b Fm(\000)f Fq(1\):)576 2104 y Fj(F)13 b Fq(\()p Fj(x;)i(y)s(;)g Fq(0\))27 b Fm(j)e Fj(F)13 b Fq(\()p Fj(x;)i(y)s(;)g Fq(1\))27 b Fm(j)41 b(\001)15 b(\001)g(\001)41 b(j)26 b Fj(F)13 b Fq(\()p Fj(x;)i(y)s(;)g(n)21 b Fm(\000)f Fq(1\))31 b(\(closed)f(and)g(total\).)376 2281 y(If)25 b(the)h(\015attened)g(relational)e(clauses)i(con)m(tain)g(an)m(y)g (equalit)m(y)f(literals,)g(the)h Fj(n)3038 2248 y Fd(2)3103 2281 y Fq(units)e(for)h(the)h(equalit)m(y)376 2394 y(relation)j(are)i (asserted.)41 b(Nothing)30 b(sp)s(ecial)f(needs)h(to)h(b)s(e)f(done)g (for)g(ordinary)f(predicate)h(sym)m(b)s(ols.)214 2571 y(\(4\))47 b(The)29 b(Da)m(vis-Putnam)i(pro)s(cedure)e(searc)m(hes)i (for)g(mo)s(dels)e(of)h(the)h(prop)s(ositional)d(clauses.)214 2749 y(\(5\))47 b(F)-8 b(or)22 b(eac)m(h)h(prop)s(ositional)18 b(mo)s(del,)23 b(w)m(e)f(generate)h(the)e(corresp)s(onding)f (\014rst-order)h(mo)s(del.)36 b(The)21 b(clauses)376 2862 y(giv)m(en)32 b(in)g(\(3\))h(ab)s(o)m(v)m(e)h(ensure)e(that)h (from)g(the)f(prop)s(ositional)f(mo)s(del,)h(w)m(e)h(can)g(build)d(a)j (function)e(for)376 2975 y(eac)m(h)g(function)e(sym)m(b)s(ol)g (\(including)f(constan)m(ts\).)148 3273 y Fn(2.1)113 b(Additional)35 b(Constrain)m(ts)148 3505 y Fq(F)-8 b(or)45 b(v)-5 b(arious)43 b(reasons,)48 b(the)c(most)g(imp)s(ortan)m(t)f(b)s (eing)g(to)i(reduce)e(the)h(n)m(um)m(b)s(er)f(of)h(isomorphic)e(mo)s (dels)148 3618 y(that)e(are)f(found,)g(the)g(user)f(can)h(sp)s(ecify)e (part)i(of)f(the)h(mo)s(del)f(b)m(y)g(supplying)e(ground)h(clauses)i(o) m(v)m(er)h(the)148 3731 y(domain.)57 b(F)-8 b(or)37 b(example,)h(if)d (a)i(noncomm)m(utativ)m(e)g(group)f(is)f(b)s(eing)g(sough)m(t,)j(with)d (constan)m(ts)j Fj(a)e Fq(and)f Fj(b)i Fq(as)148 3844 y(noncomm)m(uting)32 b(elemen)m(ts,)i(the)e(user)g(can)h(assign)f(0)g (to)i(the)e(iden)m(tit)m(y)-8 b(,)33 b(1)g(to)g Fj(a)p Fq(,)h(and)d(2)i(to)g Fj(b)p Fq(.)47 b(In)32 b(this)f(case,)148 3957 y(nothing)f(is)f(lost)h(b)m(y)h(making)e(them)i(distinct.)289 4130 y(Sym)m(b)s(ols)e(can)i(b)s(e)e(giv)m(en)i(the)f(follo)m(wing)f (prop)s(erties.)194 4352 y Fl(quasigroup)p Fq(.)59 b(This)36 b(can)i(b)s(e)f(applied)e(to)j(ternary)g(relations)e(that)i(represen)m (t)g(binary)e(functions.)60 b(The)376 4465 y(m)m(ultiplication)23 b(table)k(of)g(a)g(quasigroup)f(has)g(one)i(of)f(eac)m(h)h(elemen)m(t)f (in)e(eac)m(h)j(ro)m(w)f(and)g(eac)m(h)h(column.)194 4642 y Fl(bijection)p Fq(.)38 b(This)29 b(can)h(b)s(e)g(applied)e(to)j (binary)e(relations)g(that)i(represen)m(t)g(unary)e(functions.)194 4820 y Fl(equality)p Fq(.)38 b(This)29 b(can)h(b)s(e)g(applied)e(to)k (binary)c(relations.)40 b(It)30 b(is)g(just)g(equalit)m(y)g(of)g (domain)f(elemen)m(ts.)194 4997 y Fl(order)p Fq(.)72 b(This)40 b(can)i(b)s(e)f(applied)e(to)j(binary)e(relations.)73 b(This)40 b(is)g(just)h(the)h(less-than)f(relation)f(on)i(the)376 5110 y(domain)29 b(elemen)m(ts.)194 5287 y Fl(holey)p Fq(.)37 b(This)24 b(can)h(b)s(e)g(applied)e(to)j(ternary)f(relations)g (that)h(represen)m(t)f(binary)e(functions.)38 b(See)25 b(Sec.)40 b(2.5.2.)194 5465 y Fl(hole)p Fq(.)f(This)29 b(can)i(b)s(e)e(applied)f(to)k(binary)c(relations.)40 b(See)31 b(Sec.)41 b(2.5.2.)2015 5732 y(5)p eop %%Page: 6 6 6 5 bop 148 23 a Fn(2.2)113 b(Using)37 b(the)g(Program)g(to)g(Searc)m (h)h(for)f(First-Order)g(Mo)s(dels)148 254 y Fq(The)i(\014rst-order)f (searc)m(her)i(is)e(part)h(of)g(ANL-DP)-8 b(,)41 b(and)d(it)h(is)f(in)m (v)m(ok)m(ed)i(as)f(describ)s(ed)e(in)h(Sec.)67 b(1.3.)h(The)148 367 y(command-line)26 b(option)g(\\)p Fl(-n)h Fj(n)p Fq(")g(sp)s(eci\014es)f(the)h(domain)f(size)h(and)g(indicates)f(that)h (the)h(input)d(will)f(b)s(e)j(giv)m(en)148 480 y(as)k(\014rst-order)e (\015at)i(clauses.)40 b(Here)31 b(is)f(an)g(example)g(input)f(sp)s (ecifying)f(a)i(noncomm)m(utativ)m(e)i(group.)530 728 y Fl(function)46 b(F)h(3)h(quasigroup)530 841 y(function)e(E)h(1)h (-----)530 954 y(function)e(G)h(2)h(bijection)530 1066 y(function)e(A)h(1)h(-----)530 1179 y(function)e(B)h(1)h(-----)530 1292 y(end_of_symbols)530 1518 y(-E)f(v0)143 b(F)47 b(v0)h(v1)f(v1)g(.) 530 1631 y(-E)g(v0)143 b(-G)47 b(v1)g(v2)143 b(F)47 b(v2)h(v1)f(v0)g(.) 530 1744 y(E)h(v0)142 b(-G)47 b(v1)h(v2)142 b(-F)47 b(v2)h(v1)f(v0)g(.) 530 1857 y(-F)g(v0)g(v1)h(v2)142 b(-F)47 b(v3)h(v2)f(v4)142 b(-F)48 b(v3)f(v0)g(v5)143 b(F)47 b(v5)g(v1)g(v4)h(.)530 1970 y(-F)f(v0)g(v1)h(v2)142 b(F)48 b(v3)f(v2)g(v4)143 b(-F)47 b(v3)g(v0)g(v5)143 b(-F)47 b(v5)g(v1)g(v4)h(.)530 2083 y(-F)f(v0)g(v1)h(v2)142 b(-B)47 b(v0)143 b(-A)47 b(v1)143 b(-F)47 b(v1)g(v0)g(v2)h(.)530 2196 y(end_of_clauses)530 2421 y(E)g(0)530 2534 y(A)g(1)530 2647 y(B)g(2)530 2760 y(end_of_assignments)194 3033 y Fq(Sym)m(b)s(ol)42 b(Declarations.)83 b(In)44 b(the)h(\014rst)e(section)i(of)f(the)h(input,)h(eac)m(h)f(sym)m (b)s(ol)e(is)h(declared)f(with)h(four)376 3146 y(strings:)g(t)m(yp)s(e) 33 b(\()p Fl(function)e Fq(or)h Fl(relation)p Fq(\),)g(sym)m(b)s(ol,)h (arit)m(y)f(\()p Fj(n)p Fq(+1)h(for)g(functions\),)f(and)g(prop)s (erties)376 3258 y(\()p Fl(equality)p Fq(,)c Fl(order)p Fq(,)i Fl(quasigroup)p Fq(,)d Fl(bijection)p Fq(,)h(or)j Fl(-----)p Fq(\).)194 3446 y(Clauses.)61 b(Flat)38 b(relational)f (clauses)g(app)s(ear)g(in)f(the)i(second)g(section.)63 b(V)-8 b(ariables)37 b(can)h(b)s(e)f(an)m(y)h(strings.)376 3559 y Fi(Whitesp)-5 b(ac)g(e)34 b(is)e(r)-5 b(e)g(quir)g(e)g(d)34 b(b)-5 b(efor)g(e)34 b(the)f(p)-5 b(erio)g(ds)35 b(that)f(terminates)f (clauses.)194 3747 y Fq(Assignmen)m(ts.)40 b(Ground)29 b(units)g(\(without)h(p)s(erio)s(ds\))e(can)j(app)s(ear)e(in)g(the)i (third)d(section.)148 4050 y Fn(2.3)113 b(Using)37 b Fc(Otter)g Fn(to)g(Generate)h(the)f(Flat)g(Clauses)148 4282 y Ff(Otter)c Fq(3.0.2)j([5)q(])e(and)g(later)g(v)m(ersions)f(can)i (tak)m(e)g(ordinary)e(form)m(ulas)g(or)h(clauses)g(and)f(pro)s(duce)g (the)i(\015at)148 4395 y(relational)23 b(clauses)h(for)f(input)f(to)j (ANL-DP)-8 b(.)25 b(Here)f(is)f(an)h Ff(Otter)f Fq(input)f(\014le)h (for)g(a)h(noncomm)m(utativ)m(e)h(group)148 4508 y(that)31 b(will)d(pro)s(duce)h(something)h(lik)m(e)g(the)g(\014le)g(in)f(Sec.)41 b(2.2.)530 4755 y Fl(set\(dp_transform\).)530 4981 y(list\(usable\).) 530 5094 y(f\(e,x\))46 b(=)i(x.)530 5207 y(f\(g\(x\),x\))d(=)j(e.)530 5320 y(f\(f\(x,y\),z\))d(=)i(f\(x,f\(y,z\)\).)530 5433 y(f\(a,b\))f(!=)h(f\(b,a\).)2015 5732 y Fq(6)p eop %%Page: 7 7 7 6 bop 530 23 a Fl(end_of_list.)530 248 y(list\(passive\).)530 361 y(properties\(f\(_,_\),)43 b(quasigroup\).)530 474 y(properties\(g\(_\),)g(bijection\).)530 587 y(assign\(e,)i(0\).)530 700 y(assign\(a,)g(1\).)530 813 y(assign\(b,)g(2\).)530 926 y(end_of_list.)148 1173 y Fq(The)33 b(command)g Fl (set\(dp_transform\))28 b Fq(tells)33 b Ff(Otter)f Fq(to)i(generate)g (input)e(for)h(an)g(ANL-DP)h(searc)m(h)f(and)148 1286 y(then)d(exit.)289 1459 y(The)h(output)g(of)h Ff(Otter)e Fq(con)m(tains)i(extraneous)g(text,)h(so)e(it)g(m)m(ust)h(b)s(e)f (passed)g(though)g(a)h(\014lter)e(b)s(efore)148 1572 y(ANL-DP)h(can)g(receiv)m(e)g(it.)41 b(See)30 b(the)h(example)f (\014les)f(and)h(scripts)f(in)g(the)i(distribution)26 b(directories.)148 1875 y Fn(2.4)113 b(The)37 b(Order)h(Relation)148 2107 y Fq(The)25 b(ordered)f(semigroup)g(example)h(in)f(the)h(FINDER)g (3.0)i(man)m(ual)d([6)q(,)i(Sec.)39 b(4.1.5])27 b(motiv)-5 b(ated)26 b(me)f(to)h(ha)m(v)m(e)148 2220 y(ANL-DP)33 b(recognize)g(the)f(less-than)f(relation)h(on)f(domain)g(elemen)m(ts.) 46 b(The)32 b(input)e(\(in)h Ff(Otter)f Fq(form\))i(for)148 2333 y(the)f(ordered)f(semigroup)f(problems)f(is)i(as)g(follo)m(ws.)339 2580 y Fl(set\(dp_transform\).)339 2693 y(list\(usable\).)339 2805 y(f\(f\(x,y\),z\))45 b(=)i(f\(x,f\(y,z\)\).)339 2918 y(-\(f\(x,y\))f(<)h(f\(x,z\)\))f(|)h(y)h(<)f(z.)339 3031 y(-\(f\(y,x\))f(<)h(f\(z,x\)\))f(|)h(y)h(<)f(z.)339 3144 y(end_of_list.)148 3391 y Fq(\()p Ff(Otter)41 b Fq(recognizes)h Fl(<)f 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Modern). With these, no bitmapped % fonts are put into the PostScript, which makes PDF look much % better on the screen. To use ordinary LaTeX (computer modern) fonts, % just remove this line. \usepackage{times} \usepackage{moreverb} % for boxedverbatim (which shouldn't be used in lists) % \setlength{\textwidth}{6.25in} % \setlength{\textheight}{9in} % \setlength{\hoffset}{-.55in} % \setlength{\voffset}{-.7in} % \setlength{\parskip}{.1in} \setlength{\textwidth}{5.5in} \setlength{\textheight}{9in} \setlength{\hoffset}{-.25in} \setlength{\voffset}{-1in} \setlength{\parskip}{.1in} \begin{document} \sloppy \pagenumbering{roman} \setcounter{page}{1} \thispagestyle{empty} \begin{center} % \vspace*{-1in} Argonne National Laboratory \\ 9700 South Cass Avenue\\ Argonne, IL 60439 \vspace{.2in} \rule{1.5in}{.01in}\\ [1ex] ANL/MCS-TM-263 \\ \rule{1.5in}{.01in} \vspace{1in} {\Large\bf O{\large\bf TTER} 3.3 Reference Manual} \vspace{.2in} by \\ [3ex] {\Large\it William McCune}\\ %%%%%%%%%%%%%%%%%%%%% \thispagestyle{empty} \vspace{1.5in} Mathematics and Computer Science Division \bigskip Technical Memorandum No. 263 \vspace{1in} August 2003 \end{center} \vfill \noindent \emph{ This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-ENG-38.} %%%%%%%%%%%%%%%%%%%%% %%% Local Variables: %%% mode: latex %%% TeX-master: "snadiopt" %%% End: \newpage \pagenumbering{roman} \setcounter{page}{2} \noindent Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is owned by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. \vspace{2in} \begin{center} {\bf DISCLAIMER} \end{center} \noindent This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor The University of Chicago, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately-owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of document authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, Argonne National Laboratory, or The University of Chicago. \newpage \pagestyle{plain} \tableofcontents \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\otter}{{\sc Otter}} \newcommand{\maxint}{$\infty$} \newcommand{\unix}{{\sc unix}} \pagenumbering{arabic} \setcounter{page}{1} \title{\otter\ 3.3 Reference Manual} \author{\emph{William McCune}} \date{} \maketitle \addcontentsline{toc}{section}{Abstract} \begin{abstract} \otter\ is a resolution-style theorem-proving program for first-order logic with equality. \otter\ includes the inference rules binary resolution, hyperresolution, UR-resolution, and binary paramodulation. Some of its other abilities and features are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, evaluable functions and predicates, Knuth-Bendix completion, and the hints strategy. \otter\ is coded in ANSI C, is free, and is portable to many different kinds of computer. \end{abstract} \section{Introduction} \otter\ (Organized Techniques for Theorem-proving and Effective Research) is a resolution-style theorem prover, similar in scope and purpose to the {\sc aura} \cite{AURA} and {\sc lma/itp} \cite{ITP} theorem provers, which are also associated with Argonne. \otter\ applies to statements written in first-order logic with equality. The primary design considerations have been performance, portability, and extensibility. The programming language ANSI C is used. \otter\ features the inference rules binary resolution, hyperresolution, UR-resolution, and binary paramodulation. These inference rules take a small set of clauses and infer a clause; if the inferred clause is new, interesting, and useful, it is stored and may become available for subsequent inferences. Other features of \otter\ are the following. \begin{itemize} \item Statements of the problem may be input either with first-order formulas or with clauses (a clause is a disjunction with implicit universal quantifiers and no existential quantifiers). If first-order formulas are input, \otter\ translates them to clauses. \item Forward demodulation rewrites and simplifies newly inferred clauses with a set of equalities, and back demodulation uses a newly inferred equality (which has been added to the set of demodulators) to rewrite all existing clauses. \item Forward subsumption deletes an inferred clause if it is subsumed by any existing clause, and back subsumption deletes all clauses that are subsumed by an inferred clause. \item A variant of the Knuth-Bendix method can search for a complete set of reductions and help with proof searches. \item Weight functions and lexical ordering decide the value of clauses and terms. \item Answer literals can give information about the proofs that are found. See Sec.~\ref{answer}. \item Evaluable functions and predicates build in integer arithmetic, Boolean operations, and lexical comparisons and enable users to ``program'' aspects of deduction processes. See Sec.~\ref{eval}. \item Proofs can be presented in a very detailed form, called \emph{proof objects}, which can be used by other programs, for example, to check or to translate the proofs. See Sec.~\ref{ivy}. \item The \emph{hints strategy} can be used to provide heuristic guidance to the search. To apply this feature, the user gives a set of \emph{hint clauses}, and clauses similar to the hint clauses are emphasized during the search. See Sec.~\ref{hints}. \item \otter's input is compatible, for the most part, with a complementary program MACE 2.0 \cite{mace2}, which looks for finite models of first-order statements. Given a conjecture, \otter\ can search for a proof, and MACE can look for a counterexample, usually from the same input file. MACE 2.0 is included in the standard \otter\ 3.3 distribution packages. \end{itemize} Although \otter\ has an autonomous mode, most work with \otter\ involves interaction with the user. After encoding a problem into first-order logic or into clauses, the user usually chooses inference rules, sets options to control the processing of inferred clauses, and decides which input formulas or clauses are to be in the initial set of support and which (if any) equalities are to be demodulators. If \otter\ fails to find a proof, the user may wish to try again with different initial conditions. In the autonomous mode, the user inputs a set of clauses and/or formulas, and \otter\ does a simple syntactic analysis and decides inference rules and strategies. The autonomous mode is frequently useful for the first attempt at a proof. \subsection{What \otter\ Isn't} Some of the first applications that come to mind when one hears ``automated theorem proving'' are number theory, calculus, and plane geometry, because these are some of the first areas in which math students try to prove theorems. Unfortunately, \otter\ cannot do much in these areas: interesting number theory problems usually require induction, interesting calculus and analysis problems usually require higher-order functions, and the first-order axiomatizations of geometry are not practical. (Nonetheless, Art Quaife has proved many interesting theorems in number theory and geometry using \otter\ \cite{quaife-thesis,quaife-geo}.) For practical theorem proving in inductive theories, see the work of Boyer, Moore, and Kaufmann \cite{boyer-moore-2,acl2-approach}. \otter\ is also not targeted toward synthesizing or verifying formal hardware or software systems. See \cite{bm-verify,hw-verify} for work in those areas. Summaries of other theorem-proving systems can be found in proceedings of the recent Conferences on Automated Deduction (CADE) and in coverage of the CADE ATP System Competition (CASC). \subsection{History, New Features, and Changes} There have been several previous releases of \otter, starting with version 0.9, which was distributed at the 9th International Conference on Automated Deduction (CADE-9) in May 1988. Many new features have been added since then, many bugs have been fixed, and (of course) many bugs have been introduced. \subsection{Useful Background} This manual does not contain an introduction to first-order logic or to automated deduction. We assume that the reader knows the basic terminology including {\it term} ({\it variable}, {\it constant}, {\it complex term}), {\it atom}, {\it literal}, {\it clause}, {\it propositional variable}, {\it function symbol}, {\it predicate symbol}, {\it Skolem constant}, {\it Skolem function}, {\it formula}, {\it conjunctive normal form} ({\it CNF}), {\it resolution}, {\it hyperresolution}, and {\it paramodulation}. See \cite{chang-lee,loveland,JAR-overview} for an introductions and overviews of automated theorem proving, see \cite{siekmann-wrightson,after-25-years} for collections of important papers, see \cite{book2} for a list of general problems in the field, and see \cite{fascinating,kalman-otter,wm-rp:monograph} for introductions and applications that focus on the use of \otter. \section{Outline of \otter's Inference Process} \label{outline} Once \otter\ gets going with its real work---making inferences and searching for proofs---it operates on clauses and on clauses only. If the user inputs nonclausal first-order formulas, \otter\ immediately translates them to clauses, by a straightforward procedure involving negation normal form conversion, Skolemization, quantifier operations, and conjunctive normal form conversion. As with its predecessors {\sc aura} and {\sc lma/itp}, \otter's basic inference mechanism is the {\em given-clause algorithm}, which can be viewed as a simple implementation of the set of support strategy \cite{book1a}. \otter\ maintains four lists of clauses: \begin{description} \item[{\tt usable.}] This list contains clauses that are available to make inferences. \item[{\tt sos.}] Clauses in list \verb:sos: (set of support) are not available to make inferences; they are waiting to participate in the search. \item[{\tt passive.}] These clauses do not directly participate in the search; they are used only for forward subsumption and unit conflict. The passive list is fixed at input and does not change during the search. See Sec.~\ref{passive}. \item[{\tt demodulators.}] These are equalities that are used as rules to rewrite newly inferred clauses. \end{description} \noindent The {\em main loop} for inferring and processing clauses and searching for a refutation operates mainly on the lists \verb:usable: and \verb:sos:: {\small \begin{verbatim} While (sos is not empty and no refutation has been found) 1. Let given_clause be the ``best'' clause in sos; 2. Move given_clause from sos to usable; 3. Infer and process new clauses using the inference rules in effect; each new clause must have the given_clause as one of its parents and members of usable as its other parents; new clauses that pass the retention tests are appended to sos; End of while loop. \end{verbatim} } The set of support strategy requires the user to partition the input clauses into two sets: those with support and those without. For each inference, at least one of the parents must have support. Retained inferences receive support. In other words, no inferences are made in which all parents are nonsupported input clauses. At input time, \otter's list \verb:sos: is the set of supported clauses, and \verb:usable: is the nonsupported clauses. (Once the main loop has started, \verb:usable: no longer corresponds to nonsupported clauses, because \verb:sos: clauses have moved there.) \otter's main loop implements the set of support strategy, because no inferences are made in which all of the parents are from the initial \verb:usable: list. {\em The following paragraph tries to answer the frequently asked question ``At a certain point, \otter\ has all of the clauses available to make the inference I want, and one of the potential parents is selected as the given clause---why doesn't the program make the inference?''} \otter's main loop eliminates an important kind of redundancy. Suppose one can infer clause $C$ from clauses $A$ and $B$, and suppose both $A$ and $B$ are in list \verb:sos:. If $A$ is selected as the given clause, it will be moved to \verb:usable: and inferences will be made; but $A$ {\em will not} mate with $B$ to infer $C$, because $B$ is still in \verb:sos:. We must wait until $B$ has also been selected as given clause. Otherwise, we would infer $C$ twice. (The redundancy would be much worse with inference rules such as hyperresolution and UR-resolution with which a clause can have many parents.) In general, all parents that participate in an inference must either have been in the initial \verb:usable: list or have been selected as given clauses. (This is not true when demodulators are considered as parents.) \noindent The procedure for processing a newly inferred clause \verb:new_cl: follows; steps marked with \verb:*: are optional. {\small \begin{verbatim} 1. Renumber variables. * 2. Output new_cl. 3. Demodulate new_cl (including $ evaluation). * 4. Orient equalities. * 5. Apply unit deletion. 6. Merge identical literals (leftmost copy is kept). * 7. Apply factor-simplification. * 8. Discard new_cl and exit if too many literals or variables. 9. Discard new_cl and exit if new_cl is a tautology. * 10. Discard new_cl and exit if new_cl is too `heavy'. * 11. Sort literals. * 12. Discard new_cl and exit if new_cl is subsumed by any clause in usable, sos, or passive (forward subsumption). 13. Integrate new_cl and append it to sos. * 14. Output kept clause. 15. If new_cl has 0 literals, a refutation has been found. 16. If new_cl has 1 literal, then search usable, sos, and passive for unit conflict (refutation) with new_cl. * 17. Print the proof if a refutation has been found. * 18. Try to make new_cl into a demodulator. ------------- * 19. Back demodulate if Step 18 made new_cl into a demodulator. * 20. Discard each clause in usable or sos that is subsumed by new_cl (back subsumption). * 21. Factor new_cl and process factors. \end{verbatim} } %$ \noindent Steps 19--21 are delayed until steps 1--18 have been applied to all clauses inferred from the active given clause. \section{Starting \otter} Although \otter\ has a primitive interactive feature (Sec.~\ref{interact}), it is essentially a noninteractive program. On {\sc unix}-like systems it reads from the standard input and writes to the standard output: \begin{verse} \tt otter < \it input-file \tt > \it output-file \end{verse} No command-line options are accepted; all options are given in the input file. \section{Syntax} \otter\ recognizes two basic types of statement: clauses and formulas. Clauses are simple disjunctions whose variables are implicitly universally quantified. \otter's searches for proofs operate on clauses. Formulas are first-order statements without free variables---all variables are explicitly quantified. When formulas are input, \otter\ immediately translates them to clauses. \subsection{Comments} Comments can be placed in the input file by using the symbol \verb:%:. All characters from the first \verb:%: on a line to the end of the line are ignored. Comments can occur within terms. Comments are not echoed to the output file. \subsection{Names for Variables, Constants, Functions, and Predicates} \label{names} Three kinds of character string, collectively referred to as {\em names}, can be used for variables, constants, function symbols, and predicate symbols: \begin{itemize} \item An {\em ordinary name} is a string of alphanumerics, \verb:$:, and \verb:_:. %$ \item A {\em special name} is a string of characters in the set \verb|*+-/\^<>=`~:?@&!;#| (and sometimes \verb:|:). \item A {\em quoted name} is any string enclosed in two quotation marks of the same type, either \verb:": or \verb:':. We have no trick for including a quotation mark of the same type in a quoted name. \end{itemize} (The reason for separating ordinary and special names has to do with infix, prefix, and postfix operators; see Sec.~\ref{ops}.) For completeness, we list here the meanings of the remaining printable characters. \begin{itemize} \item \verb:.: (period) --- terminates input expressions. \item \verb:%: --- starts a comment (which ends with the end of the line). \item \verb:,()[]{}: (and sometimes \verb:|:) --- are punctuation and grouping symbols. \end{itemize} \paragraph{Variables.} Determining whether a simple term is a constant or a variable depends on the context of the term. If it occurs in a clause, the symbol determines the type: the default rule is that a simple term is a variable if it starts with \verb:u:, \verb:v:, \verb:w:, \verb:x:, \verb:y:, or \verb:z:. If the flag \verb:prolog_style_variables: is set, a simple term is a variable if and only if it starts with an upper-case letter or with \verb:_:. (Therefore, variables in clauses must be ordinary names.) In a formula, a simple term is a variable if and only if it is bound by a quantifier. \paragraph{Reserved and Built-in Names.} Names that start with \verb:$: %$ are reserved for special purposes, including evaluable functions and predicates (Sec.~\ref{eval}), answer literals and terms (Sec.~\ref{answer}), and some internal system names. The name \verb:=: and any name that starts with \verb:eq:, \verb:EQ:, or \verb:Eq:, when used as a binary predicate symbol, is recognized as an equality predicate by the demodulation and paramodulation processes. And some names, when they occur in clauses or formulas, are recognized as logic symbols. \paragraph{Overloaded Symbols.} The user can use a name for more than one purpose, for example as a constant and as a 5-ary predicate symbol. When the flag \verb:check_arity: is set (the default), the user is warned about such uses. Some built-in names are also overloaded; for example, \verb:|: is used both for disjunction and as Prolog-style list punctuation, and although the symbol \verb:-: is built in as logical negation, it can be used for both unary and binary minus as well. \subsection{Terms and Atoms} \label{syntax-terms} Recall that, when interpreted, terms are evaluated as objects in some domain, and atoms are evaluated as truth values. Constants and variables are terms. An $n$-ary function symbol applied to $n$ terms is also a term. An $n$-ary predicate symbol applied to $n$ terms is an atom. A nullary predicate symbol (also referred to as a propositional variable) is also an atom. The pure way of writing complex terms and atoms is with {\em standard application}: the function or predicate symbol, opening parenthesis, arguments separated by commas, then closing parenthesis, for example, \verb:f(a,b,c): and \verb:=(f(x,e),x):. If all subterms of a term are written with standard application, the term is in {\em pure prefix form}. Whitespace (spaces, tabs, newlines, and comments) can appear in standard application terms anywhere {\em except} between a function or predicate symbol and its opening parenthesis. If the flag \verb:display_terms: is set, \otter\ will output terms in pure prefix form. \paragraph{Infix Equality.} Some binary symbols can be written in infix form; the most important is \verb:=:. In addition, a negated equality, \verb:-(a=b): can be abbreviated \verb:a!=b:. \paragraph{List Notation.} Prolog-style list notation can be used to write terms that usually represent lists. Table \ref{list-tab} gives some example terms in list notation and the corresponding pure prefix form. \begin{table}[htbp] \centering \small \caption{List Notation} \label{list-tab} \begin{tabular}{ll} \hline \verb:[]: & \verb:$nil: \\ \verb:[x|y]: & \verb:$cons(x,y): \\ \verb:[x,y]: & \verb:$cons(x,$cons(y,$nil)): \\ \verb:[a,b,c,d]: & \verb:$cons(a,$cons(b,$cons(c,$cons(d,$nil)))): \\ \verb:[a,b,c|x]: & \verb:$cons(a,$cons(b,$cons(c,x))): \\ \hline \end{tabular} \end{table} %$ Of course, lists can contain complex terms, including other lists. \subsection{Literals and Clauses} A literal is either an atom or the negation of an atom. A clause is a disjunction of literals. The built-in symbols for negation and disjunction are \verb:-: and \verb:|:, respectively. Although clauses can be written in pure prefix form, with \verb:-: as a unary symbol and \verb:|: as a binary symbol, they are rarely written that way. Instead, they are almost always written in infix form, without parentheses. For example, the following is a clause in both forms. \begin{tabbing} mm\=mmmmmmmmmmmmm\=\kill \>Pure prefix: \> \verb:|(-(a),|(=(b1,b2),-(=(c1,c2)))):\\ \>Infix (abbreviated): \> \verb:-a | b1=b2 | c1!=c2: \end{tabbing} \otter\ accepts both forms. (Clauses are parsed by the general term-parsing mechanism presented in Sec.~\ref{ops}). \subsection{Formulas} Table \ref{ops-tab} lists the built-in logic symbols for constructing formulas. \begin{table}[ht] \centering \caption{Logic Symbols} \label{ops-tab} \begin{tabular}{ll} \hline negation & \verb:-: \\ disjunction & \verb:|: \\ conjunction & \verb:&: \\ implication & \verb:->: \\ equivalence & \verb:<->: \\ existential quantification & \verb:exists: \\ universal quantification & \verb:all: \\ \hline \end{tabular} \end{table} \paragraph{Formulas in Pure Prefix Form.} Although the practice is rarely done, formulas can be written in pure prefix form. Quantification is the only tricky part: there is a special variable-arity symbol, \verb:$Quantified:, for quantified formulas. For example, $\forall x y \exists z (P(x,y,z) | Q(x,z))$ is represented by {\small \begin{verbatim} $Quantified(all,x,y,exists,z,|(P(x,y,z),Q(x,z))). \end{verbatim} } \paragraph{Abbreviated Formulas.} Formulas are usually abbreviated in a natural way. The associativity and precedence rules for abbreviating formulas and the mechanism for parsing formulas are presented in Sec.~\ref{ops}. Here are some examples. {\small \begin{tabbing} m\=mmmmmmmmmmmmmmmmmmmm\=\kill \> Standard Usage \> \otter\ syntax (abbreviated) \\ \> $\forall x P(x)$ \> \verb:all x P(x): \\ \> $\forall x y \exists z (P(x,y,z)\;\vee\; Q(x,z))$ \> \verb:all x y exists z (P(x,y,z) | Q(x,z)): \\ \> $\forall x (P(x)\wedge Q(x)\wedge R(x)\;\rightarrow\;S(x))$ \> \verb:all x (P(x) & Q(x) & R(x) -> S(x)): \end{tabbing} } Note that if a formula has a string of identical quantifiers, all but the first can be dropped. For example, \verb:all x all y all z p(x,y,z): can be shortened to \verb:all x y z p(x,y,z):. In expressions involving the associative operations \verb:&: and \verb:|:, extra parentheses can be dropped. Moreover, a default precedence on the logic symbols allows us to drop more parentheses: \verb:<->: has the same precedence as \verb:->:, and the rest in decreasing order are \verb:->:, \verb:|:, \verb:&:, \verb:-:. Greater precedence means closer to the root of the term (i.e., larger scope). For example, the following three strings represent the same formula. {\small \begin{verbatim} p | -q & r -> -s | t. (p | (-(q) & r)) -> (-(s) | t). ->(|(p,&(-(q),r)),|(-(s),t)). \end{verbatim} } \noindent When in doubt about how a particular string will be parsed, one can simply add additional parentheses and/or test the string by having \otter\ read it and then display it in pure prefix form. The following input file can be used to test the preceding example. {\small \begin{verbatim} assign(stats_level, 0). set(display_terms). formula_list(usable). p| -q&r-> -s|t. % This formula has minimum whitespace. end_of_list. \end{verbatim} } \noindent In general, whitespace is required around \verb:all: and \verb:exists: and to the left of \verb:-:; otherwise, whitespace around the logic symbols can be removed. See Sec.~\ref{ops} for the rules. \subsection{Infix, Prefix, and Postfix Expressions} \label{ops} Many Prolog systems have a feature that allows users to declare that particular function or predicate symbols are infix, prefix, or postfix and to specify a precedence and associativity so that parentheses can sometimes be dropped. \otter\ has a similar feature. In fact, the clause and formula parsing routines use the feature. Users who use only the predeclared logic operators for clauses and formulas and the predeclared infix equality \verb:=: can skip the rest of this section. Prolog users who are familiar with the declaration mechanism should note the following differences between the ordinary Prolog mechanism and \otter's. \begin{itemize} \item The predeclared operators are different. See Table \ref{predeclared-ops}. \item \otter\ does not treat comma as an operator; in particular, \verb:a,b,c: cannot be a term, as in \verb:a,b,c -> d,e,f:. \item \otter\ treats the quantifiers \verb:all: and \verb:exists: as special cases, because they don't seem to fit neatly into the standard Prolog mechanism. \item \otter\ requires whitespace in some cases where the Prolog systems do not. \end{itemize} Symbols to be treated in this special way are given a type and a precedence. Either \otter\ predeclares the symbol's properties, or the user gives \otter\ a command of one of the following forms. \begin{verse} \small {\tt op(\em precedence\tt , \em type\tt , \em symbol\tt ).} \\ {\tt op(\em precedence\tt , \em type\tt , \em list-of-symbols\tt ).} \end{verse} The \verb:precedence: is an integer $i$, $0).: & \verb:op(700, xfx, @<).: \\ \verb:op(800, xfx, <->).: & \verb:op(700, xfx, @>).: \\ \verb:op(790, xfy, |).: & \verb:op(700, xfx, @<=).: \\ \verb:op(780, xfy, &).: & \verb:op(700, xfx, @>=).: \\ \\ \verb:op(700, xfx, =).: & \verb:op(500, xfy, +).: \\ \verb:op(700, xfx, !=).: & \verb:op(500, xfx, -).: \\ \\ \verb:op(700, xfx, <).: & \verb:op(500, fx, +).: \\ \verb:op(700, xfx, >).: & \verb:op(500, fx, -).: \\ \verb:op(700, xfx, <=).: \\ \verb:op(700, xfx, >=).: & \verb:op(400, xfy, *).: \\ \verb:op(700, xfx, ==).: & \verb:op(400, xfx, /).: \\ \verb:op(700, xfx, =/=).: & \verb:op(300, xfx, mod).: \\ \hline \end{tabular} \end{table} Given an expression that looks like it might be associated in a number of ways, the relative precedence of the operators determines, in part, how it is associated. A symbol with higher precedence is more dominant (closer to the root of the term), and one with lower precedence binds more tightly. For example, the symbols \verb:->:, \verb:|:, \verb:&:, and \verb:-: have decreasing precedence; therefore the expression \verb:p & - q | r -> s: is understood as \verb:((p & (-q)) | r) -> s:. In each of the types, \verb:f: represents the symbol, and \verb:x: and \verb:y:, which represent the expressions to which the symbol applies, specify how terms are associated. Given an expression involving symbols of the {\em same} precedence, the types of the symbol determines, in part, the association. See Table \ref{op-types}. \begin{table}[htbp] \centering \caption{Symbol Types} \label{op-types} \begin{tabular}{lll} \hline \verb:xfx: & infix (binary) & don't associate \\ \verb:xfy: & infix (binary) & associate right \\ \verb:yfx: & infix (binary) & associate left \\ \verb:fx: & prefix (unary) & don't associate \\ \verb:fy: & prefix (unary) & associate \\ \verb:xf: & postfix (unary) & don't associate \\ \verb:yx: & postfix (unary) & associate \\ \hline \end{tabular} \end{table} The following are examples of associativity: \begin{itemize} \item If \verb:+: has type \verb:xfy:, then \verb:a+b+c+d: is understood as \verb:a+(b+(c+d)):. \item If \verb:->: has type \verb:xfx:, then \verb:a->b->c: is not well formed. \item If \verb:-: has type \verb:fy:, then \verb:- - -p: is understood as \verb:-(-(-(p))):. (The spaces are necessary; otherwise, \verb:---: will be parsed as single name.) \item If \verb:-: has type \verb:fx:, then \verb:- - -p: is not well formed. \end{itemize} \noindent {\it Caution:} The associativity specifications in the infix symbol declarations say nothing about the logical associativity of the operation, for example, whether \verb:(a+b)+c: is the same object as as \verb:a+(b+c):. The specifications are only about parsing ambiguous expressions. In most cases, when an operator is \verb:xfy: or \verb:yfx:, it is also logically associative, but the logical associativity is handled separately; it is built-in in the case of the logic symbols \verb:|: and \verb:&: in \otter\ clauses and formulas, and it must be axiomatized in other cases. \paragraph{Details of the Symbol Declarations.} (This paragraph can be skipped by most users.) The precedence of symbols extends to the precedence of expressions in the following way. The precedence of an atomic, parenthesized, or standard application expression is 0. Respective examples are \verb:p:, \verb:(x+y):, and \verb:p(a+b,c,d):. The precedence of a (well-formed) nonparenthesized nonatomic expression is the same as the precedence of the root symbol. For example, \verb:a&b: has the precedence of \verb:&:, and \verb:a&b|c: has the precedence of the greater symbol. In the type specifications, \verb:x: represents an expression of lower precedence than the symbol, and \verb:y: represents an expression with precedence less than or equal to the symbol. Consider \verb:a+b+c:, where \verb:+: has type \verb:xfy:; if association is to the left, then the second occurrence of \verb:+: does {\em not} fit the type, because \verb:a+b:, which corresponds to \verb:x:, does not have a lower precedence than \verb:+:; if association is to the right, then all is well. If we extend the example, under the declarations \verb:op(700, xfx, =): and \verb:op(500, xfy, +):, the expression \verb:a+b+c=d+e: must be understood as \verb:(a+ (b+c))= (d+e):. \subsection{Whitespace in Expressions} The reason for separating ordinary names from special names (Sec. \ref{names}) is so that some whitespace (spaces, tabs, newline, and comments) can be removed. We can write \verb:a+b+c: (instead of having to write \verb:a + b + c:), because ``\verb:a+b+c:'' cannot be a name, that is, it must be parsed into five names. \noindent{\em Caution.} There is a deficiency in \otter's parser having to do with whitespace between a name and opening parenthesis. The rule to use is: {\em Insert some white space if and only if it is {\em not} a standard application.} For example, the two pieces of white space in \verb:(a+ (b+c))= (d+e): are required, and no white space is allowed after \verb:f: or \verb:g: in \verb:f(x,g(x)):. \subsection{Bugs and Other Anomalies in the Input and Output of Expressions} \begin{itemize} \item The symbol \verb:|: is either Prolog-style list punctuation or part of a special name. With the built-in declaration of \verb:|: as infix, the term \verb:[a|b]: is ambiguous, with possible interpretations $t_1=$\verb:$cons(a,b): and $t_2=$\verb:$cons(|(a,b),$nil):. %$ \otter\ recognizes it as the first. The term $t_2$ can be written \verb:[(a|b)]:. The bug is that $t_2$ will be output without the parentheses. This is the only case we know in which \otter\ cannot correctly read a term it has written. \item A term consisting of a unary \verb:+: or \verb:-: applied to a nonnegative integer is always translated to a constant. \item Parsing large terms without parentheses, say \verb:a1+a2+a3+...+a1000:, can be very slow if the operator is left associative (\verb:yfx:). If one intends to parse such terms, one should make the operator right associative (\verb:xyf:). \item Quoted strings cannot contain a quotation mark of the same type. \item The flag \verb:check_arity: sometimes issues warnings when it should not. \item Braces (\verb:{}:) can be used to group input expressions, but \otter\ always uses ordinary parentheses on output. \end{itemize} \subsection{Examples of Operator Declarations} \paragraph{Group Theory.} Suppose we like to see group theory expressions in the form $(ab^{-1}c^{-1-1})^{-1}$, in which right association is assumed. We can approximate this for \otter\ with \verb:(a*b^ *c^ ^)^:. (We have to make the group operator explicit; \verb:-1: is not a legal \otter\ name; the whitespace shown is required.) The declarations \verb:op(400, xfy, *): and \verb:op(350, yf, ^): suffice. Other examples of expressions (with minimum whitespace) using these declarations are \verb:(x*y)*z=x*y*z: and \verb:(y*x)^ =x^ *y^:. \paragraph{\otter\ Options.} Options are normally input (Sec.~\ref{input-options}) as in the following examples. \begin{verse} \small \verb:set(prolog_style_variables):. \\ \verb:clear(print_kept):. \\ \verb:assign(max_given, 300):. \end{verse} If, however, we make the declarations (the precedences are irrelevant in this case) \begin{verse} \small \verb:op(100, fx, set).: \\ \verb:op(100, fx, clear).: \\ \verb:op(100, xfx, assign).: \\ \end{verse} then we may write \begin{verse} \small \verb:set prolog_style_variables:. \\ \verb:clear print_kept:. \\ \verb:max_given assign 300:. \end{verse} \section{Commands and the Input File} \label{commands} Input to \otter\ consists of a small set of commands, some of which indicate that a list of objects (clauses, formulas, or weight templates) follows the command. All lists of objects are terminated with \verb:end_of_list:. The commands are given in Table \ref{command-tab}. There are a few other commands for fringe features (Sec.~\ref{fringe}). \begin{table}[ht] \centering \small \caption{Commands} \label{command-tab} \begin{tabular}{ll} \hline {\tt include({\it file\_name}).} & \verb:% read input from another file: \\ {\tt op({\it precedence}, {\it type}, {\it name(s)}).} & \verb:% declare operator(s): \\ {\tt make\_evaluable({\it sym}, {\it eval-sym}).} & \verb:% make a symbol evaluable: \\ {\tt set({\it flag\_name}).} & \verb:% set a flag: \\ {\tt clear({\it flag\_name}).} & \verb:% clear a flag: \\ {\tt assign({\it parameter\_name},{\it integer}).} & \verb:% assign to a parameter: \\ {\tt list({\it list\_name}).} & \verb:% read a list of clauses: \\ {\tt formula\_list({\it list\_name}).} & \verb:% read a list formulas: \\ {\tt weight\_list({\it weight\_list\_name}).} & \verb:% read weight templates: \\ {\tt lex({\it symbol\_list}).} & \verb:% assign an ordering on symbols: \\ {\tt skolem({\it symbol\_list}).} & \verb:% identify skolem functions: \\ {\tt lrpo\_multiset\_status({\it symbol\_list}).} & \verb:% status for LRPO: \\ \hline \end{tabular} \end{table} \noindent \subsection{Input of Options} \label{input-options} \otter\ recognizes two kinds of option: flags and parameters. Flags are Boolean-valued options; they are changed with the \verb:set: and the \verb:clear: commands, which take the name of the flag as the argument. Parameters are integer-valued options; they are changed with the \verb:assign: command, which takes the name of the parameter as the first argument and an integer as the second. Examples are {\small \begin{verbatim} set(binary_res). % enable binary resolution clear(back_sub). % do not use back subsumption assign(max_seconds, 300). % stop after about 300 CPU seconds \end{verbatim} } \noindent The options are described and their default values are given in Sec.~\ref{options}. \subsection{Input of Lists of Clauses} A list of clauses is specified with one of the following and is terminated with \verb:end_of_list:. Each clause is terminated with a period. {\small \begin{verbatim} list(usable). list(sos). list(demodulators). list(passive). \end{verbatim} } \noindent Example: {\small \begin{verbatim} list(usable). x = x. % reflexivity f(e,x) = x. % left identity f(g(x),x) = e. % left inverse f(f(x,y),z) = f(x,f(y,z)). % associativity f(z,x) != f(z,y) | x = y. % left cancellation f(x,z) != f(y,z) | x = y. % right cancellation end_of_list. \end{verbatim} } \noindent If the input contains more than one clause list of the same type, the lists will simply be concatenated. \subsection{Input of Lists of Formulas} A list of formulas is specified with one of the following and is terminated with \verb:end_of_list:. Each formula is terminated with a period. (Note that demodulators cannot be input as formulas.) {\small \begin{verbatim} formula_list(usable). formula_list(sos). formula_list(passive). \end{verbatim} } \noindent Example (analogous to above): {\small \begin{verbatim} formula_list(usable). all a (a = a). % reflexivity all a (f(e,a) = a). % left identity all a (f(g(a),a) = e). % left inverse all a b c (f(f(a,b),c) = f(a,f(b,c))). % associativity all a b c (f(c,a) = f(c,b) -> a = b). % left cancellation all a b c (f(a,c) = f(b,c) -> a = b). % right cancellation end_of_list. \end{verbatim} } \noindent If the input contains more than one formula list of the same type, the lists will simply be concatenated. \subsection{Input of Lists of Weight Templates} \label{input-weight} A list of weight templates is specified with one of the following and is terminated with \verb:end_of_list:. Each weight template is terminated with a period. {\small \begin{verbatim} weight_list(pick_given). % to select given clauses weight_list(purge_gen). % to discard generated clauses weight_list(pick_and_purge). % to both pick and purge weight_list(terms). % to order terms \end{verbatim} } \noindent Example: {\small \begin{verbatim} weight_list(pick_and_purge). weight(a, 0). % weight of constant a is 0 weight(g($(2)), -50). % twice weight of arg -50 weight(P($(1),$(1)), 100). % sum of weights of args +100 weight(x, 5). % all variables have weight 5 weight(f(g($(3)),$(4)), -300). % see Sec. ``Weighting'' end_of_list. \end{verbatim} } %$ \noindent See Sec.~\ref{weighting} for the syntax and use of weight templates. \subsection{The Commands {\tt lex}, {\tt skolem}, and {\tt lrpo\_multiset\_status}} \label{symbol-commands} Each of the commands \verb:lex:, \verb:skolem:, and \verb:lrpo_multiset_status: takes a list of terms as an argument. The \verb:lex: command specifies an ordering on symbols, and the others give properties to symbols. An example is {\small \begin{verbatim} lex( [a, b, f(_,_), d, g(_), c] ). \end{verbatim} } \noindent The arguments of \verb:f: and \verb:g: serve as place-holders only; they identify \verb:f: and \verb:g: as function or predicate symbols and specify the arity. \begin{description} \item[{\tt lex([...])}.] The \verb:lex: command specifies an ordering (smallest-first) on function and constant symbols. Lexical ordering on terms is used in four contexts: orienting equality literals (Secs. \ref{orient} and \ref{orient-lrpo}), deciding whether an equality will be used as a demodulator (Secs. \ref{dynamic} and \ref{dynamic-lrpo}), deciding whether to apply a lex-dependent demodulator (Secs. \ref{lex-dep} and \ref{lex-dep-lrpo}), and evaluating functions/predicates that perform lexical comparisons (Sec.~\ref{eval}). If a \verb:lex: command is not present, then \otter\ uses a default ordering (Sec.~\ref{ordering}). \item[{\tt skolem([...])}.] The \verb:skolem: command identifies constant and function symbols as Skolem symbols. (If the user inputs quantified formulas and \otter\ Skolemizes, this command is not necessary.) The Skolem property is used by the options \verb:para_skip_skolem: (Sec.~\ref{para-flags}) and \verb:delete_identical_nested_skolem: (Sec.~\ref{gen-flags}). \item[{\tt lrpo\_multiset\_status([...])}.] This command specifies multiset status for the lexicographic recursive path ordering (flag \verb:lrpo:). See Sec.~\ref{lrpo}. \end{description} \subsection{Other Commands} The command {\tt op({\it precedence}, {\it type}, {\it name(s)})}, example \verb:op(400,xfy,+):, declares one or more symbols to have special properties with respect to input and output. See Sec.~\ref{ops}. \begin{sloppypar} The command {\tt make\_evaluable({\it symbol}, {\it evaluable-symbol})}, for example \verb:make_evaluable(_+_, $SUM(_,_):, copies evaluation properties from an evaluable symbol to another symbol, so that one can write \verb:x+3: instead of \verb:$SUM(x,3):. See Sec.~\ref{make-eval}. \end{sloppypar} The command {\tt include({\it file\_name})} causes input to be read from another input file. When the included file has been read, \otter\ resumes reading commands after the \verb:include: command. The file name must be recognized as an \otter\ name, so if it contains characters such as period, slash, or hyphen, it must be enclosed in (single or double) quotes. Included files can include still other files. {\em A list of objects (clauses, formulas, or weight templates) cannot be split among different input files.} One can, however, read clauses into a list from more than one file, as in the following example. \begin{center} \begin{tabular}{l|l|l} standard input & file f1.in & file f2.in \\ \hline \verb:include("f1.in").: & \verb:list(usable).: & \verb:list(usable).: \\ \verb:include("f2.in").: & \verb:p(a).: & \verb:p(b).: \\ & \verb:end_of_list.: & \verb:end_of_list.: \end{tabular} \end{center} \section{Options} \label{options} Flags are Boolean-valued options, and parameters are integer-valued options. When the user changes an option, \otter\ sometimes automatically changes other options. The user is informed in the output file when such a change occurs. Several additional flags and parameters are described in Sec.~\ref{fringe}. \subsection{Flags} Flags are changed with the \verb:set: and \verb:clear: commands, for example, {\small \begin{verbatim} set(sos_queue). clear(print_given). \end{verbatim} } \subsubsection{Main Loop Flags} \label{loop-flags} A given clause is taken from \verb:sos: at the beginning of each iteration of the main loop. The default is to take the lightest clause with respect to either \verb:weight_list(pick_given): or \verb:weight_list(pick_and_purge):. If neither weight list is present, the weight of a clause is its number of symbols. \noindent \verb:sos_queue:. Default clear. If this flag is set, the first clause in \verb:sos: is selected as the given clause (the set of support list operates as a queue). This causes a breadth-first search, also called level saturation. Some information about search levels is printed (see Sec.~\ref{output}) if this flag is set. \noindent \verb:sos_stack:. Default clear. If this flag is set, the last clause in \verb:sos: becomes the given clause (the set of support list operates as a stack). This causes a depth-first search (which rarely is useful with \otter). \noindent \verb:input_sos_first:. Default clear. If this flag is set, the input clauses in \verb:sos: are given a very low \verb:pick_given: weight so that they are the first clauses selected as given clauses. \noindent \verb:interactive_given:. Default clear. If this flag is set, then when it's time to select a new given clause, the user is prompted for a choice. This flag has priority over all other flags that govern selection of the given clause. \noindent \verb:print_given:. Default set. If this flag is set, clauses are output when they become given clauses. \noindent \verb:print_lists_at_end:. Default clear. If this flag is set, then \verb:usable:, \verb:sos:, and \verb:demodulators: are printed at the end of the search. \subsubsection{Inference Rules} \label{inf-flags} \verb:binary_res:. Default clear. If this flag is set, the inference rule binary resolution (along with any other inference rules that are set) is used to generate new clauses. Setting this flag causes the flags \verb:factor: and \verb:unit_deletion: to be automatically set. \noindent \verb:hyper_res:. Default clear. If this flag is set, the inference rule (positive) hyperresolution (along with any other inference rules that are set) is used to generate new clauses. \noindent \verb:neg_hyper_res:. Default clear. If this flag is set, the inference rule negative hyperresolution (along with any other inference rules that are set) is used to generate new clauses. \noindent \verb:ur_res:. Default clear. If this flag is set, the inference rule UR-resolution (unit-resulting resolution) (along with any other inference rules that are set) is used to generate new clauses. \noindent \verb:para_into:. Default clear. If this flag is set, the inference rule ``paramodulation {\it into} the given clause'' (along with any other inference rules that are set) is used to generate new clauses. When using paramodulation, one should include the appropriate clause for reflexivity of equality, for example, \verb:x=x:. \noindent \verb:para_from:. Default clear. If this flag is set, the inference rule ``paramodulation {\it from} the given clause'' (along with any other inference rules that are set) is used to generate new clauses. When using paramodulation, one should include the appropriate clause for reflexivity of equality, for example, \verb:x=x:. \noindent \verb:demod_inf:. Default clear. If this flag is set, demodulation is applied, as if it were an inference rule, to the given clause. This is useful when term rewriting is the main objective. When this flag is set, the given clause is copied, then processed just like any newly generated clause. \subsubsection{Resolution Restriction Flags} \label{res-flags} \noindent \verb:order_hyper:. Default set. If this flag is set, then the inference rules \verb:hyper_res: and \verb:neg_hyper_res: are constrained by an ordering strategy. A literal in a satellite is allowed to resolve only if it is maximal in the satellite. (A literal is maximal in a clause if and only if there is no larger literal.) The ordering uses only the lexical value (as in the \verb:lex: command or the default, Sec.~\ref{symbol-commands}) of the predicate symbol. (This flag is irrelevant for positive hyperresolution with a Horn set.) \noindent \verb:unit_res:. Default clear. This flag is a restriction on binary resolution. If it is set, then all binary resolution inferences must be unit resolutions; that is, one of the parents must be a unit clause. Setting this flag causes to the flag \verb:binary_res: to be set as well. \noindent \verb:ur_last:. Default clear. This flag is a restriction on unit-resulting resolution. If it is set, then the UR-resolvent must come from the last literal of the nonunit parent (the nucleus). This is related to the \emph{target strategy} in linked UR-resolution. \subsubsection{Paramodulation Restriction Flags} \label{para-flags} \verb:para_from_left:. Default set. If this flag is set, paramodulation is allowed {\it from} the left sides of equality literals. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_from_right:. Default set. If this flag is set, paramodulation is allowed {\it from} the right sides of equality literals. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_into_left:. Default set. If this flag is set, paramodulation is allowed {\it into} left sides of positive and negative equalities. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_into_right:. Default set. If this flag is set, paramodulation is allowed {\it into} right sides of positive and negative equalities. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_from_vars:. Default clear. If this flag is set, paramodulation {\it from} variables is allowed. {\em Warning: Setting this option may produce too many paramodulants.} (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_into_vars:. Default clear. If this flag is set, paramodulation {\it into} variables is allowed. {\em Warning: Setting this option may produce too many paramodulants.} (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_from_units_only:. Default clear. If this flag is set, paramodulation is allowed only if the {\it from} clause is a unit (equality). (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_into_units_only:. Default clear. If this flag is set, paramodulation is allowed only if the {\it into} clause is a unit. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_skip_skolem:. Default clear. If this flag is set, paramodulation is never allowed {\it into} subterms of Skolem expressions \cite{skolem-aaai}. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_ones_rule:. Default clear. If this flag is set, paramodulation obeys the 1's rule. (The 1's rule is a special-purpose strategy for problems in combinatory logic; its usefulness has not been demonstrated elsewhere.) (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \noindent \verb:para_all:. Default clear. If this flag is set, all occurrences of the {\it into} term are replaced with the replacement term. (Applies to both \verb:para_into: and \verb:para_from: inference rules.) \subsubsection{Flags for Handling Generated Clauses} \label{gen-flags} (Section~\ref{eq-flags} describes equality-related flags for handling generated clauses.) \noindent \verb:detailed_history:. Default set. This flag affects the parent lists in clauses that are derived by \verb:binary_res:, \verb:para_from:, or \verb:para_into:. If the flag is set, the positions of the unified literals or terms are given along with the IDs of the parents. See Sec.~\ref{output} for examples. \noindent \verb:order_history:. Default clear. This flag affects the order of parent lists in clauses that are derived by hyperresolution, negative hyperresolution, or UR-resolution. If the flag is set, then the nucleus is listed first, and the satellites are listed in the order in which the corresponding literals appear in the nucleus. If the flag is clear (or if the clause was derived by some other inference rule), the given clause is listed first. \noindent \verb:unit_deletion:. Default clear. If this flag is set, unit deletion is applied to newly generated clauses. Unit deletion removes a literal from a newly generated clause if the literal is the negation of an instance of a unit clause that occurs in \verb:usable: or \verb:sos:. For example, the second literal of \verb:p(a,x) | q(a,x): is removed by the unit \verb:-q(u,v):; but it is not removed by the unit \verb:-q(u,b):, because that unification causes the instantiation of \verb:x:. All such literals are removed from the newly generated clause, even if the result is the empty clause. One can view unit deletion with unit clause \verb:P: as demodulation applied to literals with the demodulator \verb:P = $T:. %$ (Unit deletion is not useful if all generated clauses are units.) \noindent \verb:back_unit_deletion:. Default clear. If this flag is set, then whenever a unit clause is derived and kept, it is used to apply unit deletion to all existing clauses in \verb:usable: or \verb:sos:. \noindent \verb:delete_identical_nested_skolem:. Default clear. If this flag is set, clauses with the nested Skolem property are deleted. A clause has the nested Skolem property if it contains a a Skolem expression that (properly) contains an occurrence of its leading Skolem symbol. For example, if \verb:f: is a Skolem function, a clause containing a term \verb:f(f(x)): or a term \verb:f(g(f(x))): is deleted. \noindent \verb:sort_literals:. Default clear. If this flag is set, literals of newly generated clauses are sorted---negative literals, then positive literals, then answer literals. The main purpose of this flag is to make clauses more readable. In some cases, this flag can speed up subsumption on non-unit clauses. \noindent \verb:for_sub:. Default set. If this flag is set, forward subsumption is applied during the processing of newly generated clauses. (New clauses are deleted if subsumed by any clause in \verb:usable: or \verb:sos:.) \noindent \verb:back_sub:. Default set. If this flag is set, back subsumption is applied during the processing of newly kept clauses. (Clauses in \verb:usable: or \verb:sos: are deleted if subsumed by the newly kept clause.) \noindent \verb:factor:. Default clear. If this flag is set, factoring is applied in two ways. First, factoring is applied as a simplification rule to newly generated clauses. If a generated clause $C$ has factors that subsume $C$, it is replaced with its smallest subsuming factor. Second, it is applied as an inference rule to newly kept clauses. Note that unlike other inference rules, factoring is not applied to the given clause; it is applied to a new clause as soon as it is kept. All factors are generated in an iterative manner. Factoring {\em is} attempted on answer literals. If \verb:factor: is set, a clause with $n$ literals will {\em not} cause a clause with fewer than $n$ literals to be deleted by subsumption. \subsubsection{Demodulation and Ordering Flags} \label{eq-flags} \verb:demod_history:. Default set. If this flag is set, then when a clause is demodulated, the ID numbers of the demodulators are included in the derivation history of the clause. \noindent \verb:order_eq:. Default clear. If this flag is set, equalities are flipped if the right side is heavier than the left. See Secs. \ref{orient} and \ref{orient-lrpo} for the meaning of ``heavier''. \noindent \verb:eq_units_both_ways:. Default clear. If this flag is set, unit equality clauses (both positive and negative) are sometimes stored in both orientations; the action taken depends on the flag \verb:order_eq:. If \verb:order_eq: is clear, then whenever a unit, say $\alpha=\beta$, is processed, $\beta=\alpha$ is automatically generated and processed. If \verb:order_eq: is set, then the reversed equality is generated only if the equality cannot be oriented (see Secs. \ref{orient} and \ref{orient-lrpo}). \noindent \verb:demod_linear:. Default clear. If this flag is set, demodulation indexing is disabled, and a linear search of \verb:demodulators: are used when rewriting terms. With indexing disabled, if more than one demodulator can be applied to rewrite a term, then the one whose clause number is lowest is applied; this flag is useful when demodulation is used to do ``procedural'' things. With indexing enabled (the default), demodulation is much faster, but the order in which \verb:demodulators: is applied is not under the control of the user. \noindent \verb:demod_out_in:. Default clear. If this flag is set, terms are demodulated outside-in, left to right. In other words, the program attempts to rewrite a term before rewriting (left to right) its subterms. The algorithm is ``repeat \{rewrite the leftmost outermost rewritable term\} until no more rewriting can be done or the limit is reached''. (The effect is like a standard reduction in lambda calculus or in combinatory logic.) If this flag is clear, terms are demodulated inside-out (all subterms are fully demodulated before attempting to rewrite a term). (The evaluable conditional term {\tt \$IF({\it condition},{\it then-value},{\it else-value})} is an exception when inside-out demodulation is in effect. See Sec.~\ref{eval}.) \noindent \verb:dynamic_demod:. Default clear. If this flag is set, {\it some} newly kept equalities are made into demodulators (Secs. \ref{dynamic} and \ref{dynamic-lrpo}). Setting this flag automatically sets the flag \verb:order_eq:. \noindent \verb:dynamic_demod_all:. Default clear. If this flag is set, \otter\ attempts to make {\it all} newly kept equalities into demodulators (Sec.~\ref{dynamic}). Setting this flag automatically sets the flags \verb:dynamic_demod: and \verb:order_eq:. \noindent \verb:dynamic_demod_lex_dep:. Default clear. If this flag is set, dynamic demodulators may be lex-dependent or {\sc lrpo}-dependent. See Secs. \ref{dynamic} and \ref{dynamic-lrpo}. \noindent \verb:back_demod:. Default clear. If this flag is set, back demodulation is applied to \verb:demodulators:, \verb:usable:, and \verb:sos: whenever a new demodulator is added. Back demodulation is delayed until the inference rules are finished generating clauses from the current given clause (delayed until \verb:post_process:). Setting the \verb:back_demod: flag automatically sets the flags \verb:order_eq: and \verb:dynamic_demod:. \noindent \verb:anl_eq:. Default clear. If this flag is set, a standard equational strategy will be applied to the search. This flag is really a metaflag; its only effect is to alter other flags as follows: {\small \verb:set(para_from):, \verb:set(para_into):, \verb:set(para_from_left):, \verb:clear(para_from_right):, \verb:set(para_into_left):, \verb:clear(para_into_right):, \verb:set(para_from_vars):, \verb:set(eq_units_both_ways):, \verb:set(dynamic_demod_all):, \verb:set(back_demod):, \verb:set(process_input):, and \verb:set(lrpo):}. This strategy is derived mostly from equational strategies developed at Argonne by Larry Wos and Ross Overbeek. It can also be used for Knuth-Bendix completion. See Sec.~\ref{kb} for more details. \noindent \verb:knuth_bendix:. Default clear. Setting this flag simply causes the preceding flag, \verb:anl_eq:, to be set. \noindent \verb:lrpo:. Default clear. If this flag is set, then the lexicographic recursive path ordering (also called {\sc rpo} with status) is used to compare terms. If this flag is clear, weight templates and lexicographic order are used (Secs. \ref{lrpo} and \ref{kb}). \noindent \verb:lex_order_vars:. Default clear. This flag affects lex-dependent demodulation and the evaluable functions and predicates that perform lexical comparisons. If this flag is set, then lexical ordering is a total order on terms; variables are lowest in the term order, with \verb:x: $\prec$ \verb:y: $\prec$ \verb:z: $\prec$ \verb:u: $\prec$ \verb:v: $\prec$ \verb:w: $\prec$ \verb:v6: $\prec$ \verb:v7: $\prec$ \verb:v8: $\prec$ $\cdots$. If this flag is clear, then a variable is comparable only to another occurrence of the same variable; it is not comparable to other variables or to nonvariables. For example, \verb:$LLT(f(x),f(y)): evaluates to \verb:$T: if and only if \verb:lex_order_vars: is set. {\it If \verb:lrpo: is set, \verb:lex_order_vars: has no effect on demodulation} (Sec. \ref{lex-order}). \noindent \verb:symbol_elim:. Default clear. If this flag is set, then new demodulators are oriented, if possible, so that function symbols (excluding constants) are eliminated. A demodulator can eliminate all occurrences of a function symbol if the arguments on the left side are all different variables and if the function symbol of the left side does not occur in the right side. For example, the demodulators \verb:g(x) = f(x,x): and \verb:h(x,y) = f(x,f(y,f(g(x),g(y)))): eliminate all occurrences of \verb:g: and \verb:h:, respectively. \noindent \verb:rewriter:. Default clear. If this flag is set, then the clauses in the \verb:sos: list will simply be demodulated by the demodulators, the run will terminate. This is really just a metaflag, which automatically causes the several other options parameters to be changed as follows: \verb:set(demod_inf):, \verb:clear(for_sub):, \verb:clear(back_sub):, and \verb:assign(max_levels, 1):. \subsubsection{Input Flags} \verb:check_arity:. Default set. If this flag is set, a warning is given if symbols have variable arities (different numbers of arguments in different places in the input). For example, the term \verb:f(a,a(b)): would be flagged. (Constants have arity 0.) If this flag is clear, then variable arities are permitted; in the preceding term, the two occurrences of \verb:a: would be treated as different symbols. \noindent \verb:prolog_style_variables:. Default clear. If this flag is set, a name with no arguments in a clause is a variable if and only if it starts with \verb:A: through \verb:Z: (upper case) or with \verb:_:. \noindent \verb:echo_included_files:. Default set. If this flag is set, input files included with the {\tt include(\it filename\tt )} command are echoed in the same way as ordinary input. \noindent \verb:simplify_fol:. Default set. If this flag is set, then some propositional simplification is attempted when converting input first-order formulas into clauses. The simplification occurs after Skolemization, during the CNF translation. If simplification detects a refutation, it will always produce the empty clause \verb:$F:, %$ but \otter\ will not recognize the proof (i.e., give the proof message and stop) unless the flag \verb:process_input: is set. \noindent \verb:process_input:. Default clear. If this flag is set, input \verb:usable: and \verb:sos: clauses (including clauses from formula input) are processed as if they had been generated by an inference rule. (See the procedure for processing newly inferred clauses in Sec.~\ref{outline}.) The exceptions are (1) the following clause-processing options are not applied to input clauses: \verb:max_literals:, \verb:max_weight:, \verb:delete_identical_nested_skolem:, and \verb:max_distinct_vars:, (2) clauses input on list {\tt usable} remain there if retained, and (3) some output appears even if the output flags (Sec.~\ref{output-flags}) are clear. \noindent \verb:tptp_eq:. Default clear. If this flag is set, then ``\verb:EQUAL:'' is the one and only symbol recognized as the equality relation for the operations that build in equality (demodulation and paramodulation). \subsubsection{Output Flags} \label{output-flags} \noindent \verb:very_verbose:. Default clear. If this flag is set, a tremendous amount of information about the processing of generated clauses is output. \noindent \verb:print_kept:. Default set. If this flag is set, new clauses are output if they are retained (if they pass all retention tests). \noindent \verb:print_proofs:. Default set. If this flag is set, all proofs that are found are printed to the output file. If this flag is clear, no proofs are printed. \noindent \verb:build_proof_object_1:. Default clear. If this flag is set, then whenever a proof is found, a \emph{type 1 proof object} is printed to the output file. Proof objects are very detailed proof and were introduced for two purposes: so that proofs can be checked by an independent program, and so that proofs can be translated into other forms by other programs. Proof objects are written in a Lisp-like notation. (Type 2 proof objects are usually preferred.) \emph{Warning: Construction of proof objects is fragile---sometimes it simply fails.} \noindent \verb:build_proof_object_2:. Default clear. If this flag is set, then whenever a proof is found, a \emph{type 2 proof object} is printed to the output file. Type 2 proof objects are used in the IVY verification project \cite{ivy}, and a detailed description (definition in ACL2) can be found there. \emph{Warning: construction of proof objects is fragile---sometimes it simply fails.} \noindent \verb:print_new_demod:. Default set. If this flag is set, demodulators that are adjoined during the search (\verb:dynamic_demod:) are printed. New demodulators are always printed during input processing. \noindent \verb:print_back_demod:. Default set. If this flag is set, clauses are printed as they are back demodulated. Back-demodulated clauses are always printed during input processing. \noindent \verb:print_back_sub:. Default set. If this flag is set, clauses are printed if they are back subsumed. Back-subsumed clauses are always printed during input processing. \noindent \verb:display_terms:. Default clear. If this flag is set, all clauses and terms are printed in pure prefix form (Sec.~\ref{syntax-terms}). This feature can be useful for debugging the input. \noindent \verb:pretty_print:. Default clear. If this flag is set, clauses are output in an indented form that is sometimes easier to read. The parameter \verb:pretty_print_indent: (default 4) specifies the number of spaces for each indent level. \noindent \verb:bird_print:. Default clear. If this flag is set, terms constructed with the binary function \verb:a: are output in combinatory logic notation (without the function symbol \verb:a:, and left associated unless otherwise indicated). For example, the clause \verb:a(a(a(S,x),y),z) = a(a(x,z),a(y,z)): is output as \verb:S x y z = x z (y z):. Terms cannot be input in combinatory logic notation. \noindent \verb:formula_history:. Default clear. If this flag is set, and if quantified formulas are given as input, then the formulas will occur in proofs, and the clauses derived from the formulas will refer to the formulas with the justification \verb:clausify:. \subsubsection{Indexing Flags} \label{index-flags} \verb:index_for_back_demod:. Default set. If this flag is set, all nonvariable terms in all clauses are indexed so that the appropriate ones can be quickly retrieved when applying a dynamic demodulator to the clause space (back demodulation). This type of indexing can use a lot of memory. If the flag is clear, back demodulation still works, but it is much slower. \noindent \verb:for_sub_fpa:. Default clear. If this flag is set, {\sc fpa} indexing is used for forward subsumption. If this flag is clear, discrimination tree indexing is used. Setting this flag can decrease the amount of memory required by \otter. Discrimination tree indexing can require a lot of memory, but it is usually {\em much} faster than {\sc fpa} indexing. \noindent \verb:no_fapl:. Default clear. If this flag is set, positive literals are not indexed for unit conflict or back subsumption. This option should be used only when no negative units will be generated (as with hyperresolution), back subsumption is disabled, and discrimination tree indexing is being used for forward subsumption. This option can save a little time and memory. \noindent \verb:no_fanl:. Default clear. If this flag is set, negative literals are not indexed for unit conflict or back subsumption. This option should be used only when no positive units will be generated (as with negative hyperresolution), back subsumption is disabled, and discrimination tree indexing is being used for forward subsumption. This option can save a little time and memory. \subsubsection{Miscellaneous Flags} \label{misc-flags} \verb:control_memory:. Default clear. If this flag is set, then the automatic memory-control feature is enabled (Sec.~\ref{mem-control}). \noindent \verb:propositional:. Default clear. If this flag is set, \otter\ assumes that all clauses are propositional, and it makes some optimizations. {\em The user should set this flag only when all clauses are propositional; otherwise \otter\ may make unsound inferences and/or crash.} \noindent \verb:really_delete_clauses:. Default clear. If this flag is clear, clauses that are deleted by back subsumption or back demodulation are not really removed from memory; they are retained in a special place so that they can be printed if they occur in a proof. If the job involves much back subsumption or back demodulation and if memory conservation is important, these ``deleted'' clauses can be removed from memory by setting this flag (and any proof containing such a clause will not be printed in full). \noindent \verb:atom_wt_max_args:. Default clear. If this flag is set, the default weight of an atom (the weight if no template matches the atom) is 1 plus the maximum of the weights of the arguments. If this flag is clear, the default weight of an atom is 1 plus the sum of the weights of the arguments. \noindent \verb:term_wt_max_args:. Default clear. If this flag is set, the default weight of a term (the weight if no template matches the atom) is 1 plus the maximum of the weights of the arguments. If this flag is clear, the default weight of a term is 1 plus the sum of the weights of the arguments. \noindent \verb:free_all_mem:. Default clear. If this flag is set, then at the end of the search, most dynamically allocated memory is returned to the memory managers. This flag is used mainly for debugging, in particular, to help find memory leaks. Setting this flag will {\em not} cause \otter\ to use less memory. \noindent \verb:sigint_interact:. Default set. If this flag is set, then when \otter\ receives an interrupt signal from the operating system (usually caused by the user pressing control-C), \otter\ will enter a primitive interactive mode, which is described in Sec.~\ref{interact}. \subsection{Parameters} Parameters are integer-valued options. In the descriptions that follow, \maxint\ is a large integer, usually the size of the largest ordinary integer on the user's computer (i.e., INT\_MAX in ANSI C). \subsubsection{Monitoring Progress} \verb:assign(report,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n>0$, then statistics are output approximately every $n$ {\sc cpu} seconds. The time is not exact because statistics will be output only after the current given clause is finished. This feature can be used in conjunction with {\sc unix} programs such as \verb:grep: and \verb:awk: to conveniently monitor \otter\ jobs. \subsubsection{Placing Limits on the Search} \verb:assign(max_seconds,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, the search is terminated after about $n$ {\sc cpu} seconds. The time is not exact because \otter\ will wait until the current given clause is finished before stopping. \noindent \verb:assign(max_gen,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, the search is terminated after about $n$ clauses have been generated. The number is not exact because \otter\ will wait until it is finished with the current given clause before stopping. \noindent \verb:assign(max_kept,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, the search is terminated after about $n$ clauses have been kept. The number is not exact because \otter\ will wait until it is finished with the current given clause before stopping. \noindent \verb:assign(max_given,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, the search is terminated after $n$ given clauses have been used. \noindent \verb:assign(max_levels,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, the flag \verb:sos_queue: will be automatically set, causing a level saturation (breadth-first) search. In this case the search is terminated after $n$ levels have been processed. \noindent \verb:assign(max_mem,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, \otter\ will terminate the search before more than $n$ kilobytes have been dynamically allocated (\verb:malloc:). \subsubsection{Limits on Properties of Generated Clauses} \verb:assign(max_literals,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, new clauses are discarded if they contain more than $n$ literals. \noindent \verb:assign(max_weight,:$n$\verb:):. Default \maxint, range [$-$\maxint ..\maxint ]. New clauses are discarded if their weight is more than $n$. The weight list \verb:purge_gen: or the weight list \verb:pick_and_purge: is used to weigh clauses (both lists may not be present; see Sec.~\ref{weighting}). \noindent \verb:assign(max_distinct_vars,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, new clauses are discarded if they contain more than $n$ distinct variables. \noindent \verb:assign(max_answers,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n\neq -1$, new clauses are discarded if they contain more than $n$ answer literals. \subsubsection{Indexing Parameters} \verb:assign(fpa_literals,:$n$\verb:):. Default 8, range [0..100]. $n$ is the {\sc fpa} indexing depth for literals. ({\sc fpa} literal indexing is used for resolution inference rules, back subsumption, and unit conflict. It is also used for forward subsumption if the flag \verb:for_sub_fpa: is set.) If $n=0$, indexing is by predicate symbol only; if $n=1$, indexing looks at the predicate symbol and the leading symbols of the arguments of the literal, and so on. Greater indexing depth requires more memory, but it can be faster. Changing this parameter will not change the clauses that are generated or kept. \noindent \verb:assign(fpa_terms,:$n$\verb:):. Default 8, range [0..100]. $n$ is the {\sc fpa} indexing depth for terms. ({\sc fpa} term indexing is used for paramodulation inference rules and back demodulation.) If $n=0$, indexing is by symbol only; if $n=1$, indexing looks at the symbol and the leading symbols of the arguments of the term; and so on. Greater indexing depth requires more memory, but it can be faster. Changing this parameter will not change the clauses that are generated or kept. \subsubsection{Miscellaneous Parameters} \label{misc-parms} \verb:assign(pick_given_ratio,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. This parameter causes some given clauses to be selected by weight and others in a breadth-first manner (by age). If $n \neq -1$, $n$ given clauses are are selected by (smallest \verb:pick_given:) weight, then the first clause in \verb:sos: is selected as given clause, then $n$ given clauses are selected by weight, and so forth. This method allows heavy clauses to enter into the search while focusing mainly on light clauses. It combines breadth-first search and best-first search (default selection by weight). If $n$ is $-1$, then the clause with smallest \verb:pick_given: weight is always selected. \noindent \verb:assign(age_factor,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. If $n\neq$0, then the pick-given weight of clauses is adjusted as follows. If $g$ is the number of clauses that have been given \emph{at the time the clause is kept}, and $n$ is the age factor, then $g / n$ (with integer division) is added to the pick-given weight of the clause. \noindent \verb:assign(distinct_vars_factor,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. If $n\neq$0, then the pick-given weight of clauses is adjusted as follows. If $v$ is the number of variable in the clause, and $n$ is the age factor, then $v / n$ (with integer division) is added to the pick-given weight of the clause. \noindent \verb:assign(interrupt_given,:$n$\verb:):. Default $-1$, range [$-1$..\maxint ]. If $n>0$, then after $n$ given clauses have been used, \otter\ goes into its interactive mode (Sec.~\ref{interact}). \noindent \verb:assign(demod_limit,:$n$\verb:):. Default 1000, range [$-1$..\maxint ]. If $n\neq -1$, $n$ is the maximum number of rewrites that will be applied when demodulating a clause. The count includes \verb:$: %$ symbol evaluation. If $n$ is $-1$, there is no limit. A warning message is printed if \otter\ attempts to exceed the limit. \noindent \verb:assign(max_proofs,:$n$\verb:):. Default 1, range [$-1$..\maxint ]. If $n = 1$, \otter\ will stop if it finds a proof. If $n > 1$, then \otter\ will not stop when it has found the first proof; instead, it will try to keep searching until it has found $n$ proofs. (Some of the proofs may in fact be identical.) (Because forward subsumption occurs before unit conflict, a clause representing a truly different proof may be discarded by forward subsumption before unit conflict detects the proof.) If $n = -1$, \otter\ will find as many proofs as it can (within other constraints). \noindent \verb:assign(min_bit_width,:$n$\verb:):. Default {\em bits-per-long}, range [0..{\em bits-per-long}]. When the evaluable bit operations (Sec.~\ref{eval}) produce a new bit string, leading zeros are suppressed under the constraint that $n$ is the minimum string length. (The value \emph{bits-per-long} is the number of bits in the C data type long integer.) \noindent \verb:assign(neg_weight,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. The value $n$ is the additional weight (positive or negative) that is given to negated literals. Weight templates cannot be used for this purpose because the negation sign on a literal cannot occur in weight templates. (Atoms, not literals, are weighed with weight templates; see Sec.~\ref{weighting}.) \noindent \verb:assign(pretty_print_indent,:$n$\verb:):. Default 4, range [0..16]. See flag \verb:pretty_print:, Sec.~\ref{output-flags}. \noindent \verb:assign(stats_level,:$n$\verb:):. Default 2, range [0..4]. This indicates the level of detail of statistics printed in reports and at the end of the search. If $n = 0$, no statistics are output; if $n = 1$, a few important search and time statistics are output; if $n = 2$, all search and time statistics are output; if $n = 3$, search, time, and memory statistics are output; and if $n = 4$, search, time, and memory statistics and option values are output. This parameter does not affect the speed of \otter, because all statistics are always kept. \noindent \verb:assign(dynamic_demod_depth,:$n$\verb:):. Default -1, range [$-$1 ..\maxint ].\\ \verb:assign(dynamic_demod_rhs,:$n$\verb:):. Default 1, range [$-$\maxint ..\maxint ].\\ These two parameters work together, allowing an extension of the ad hoc ordering when deciding whether a new equality should be a demodulator. (It is not used if flag \verb:lrpo: is set.) The equality, say $\alpha=\beta$, is first oriented as described in Sec.~\ref{ad-hoc}. If $wt(\beta)\leq$ \verb:dynamic_demod_rhs: and if $wt(\alpha) - wt(\beta) \geq$ \verb:dynamic_demod_depth:, then the equality can be a demodulator. With the default values for these parameters, the behavior is as described in Sec.~\ref{ad-hoc} \noindent \verb:assign(new_symbol_lex_position,:$n$\verb:):. Default \maxint, range [1 ..\maxint ]. New symbols can be created during the search, usually by \$-evaluation. %$ With this parameter, the user can specify where they will occur in the symbol ordering. If there is a \verb:lex: command, all new symbols will have a lexical values between the $n$th and $(n+1)$th symbol in the \verb:lex: command. The ordering among the new symbols is the default ordering. This also applies to input symbols not occurring in the \verb:lex: command. \section{Demodulation} Basic demodulation is straightforward, but there are many variations and enhancements whose descriptions are scattered throughout this manual. This section (which is mostly redundant) lists some overall comments on demodulation and points the reader to the appropriate sections on variations and enhancements. \paragraph{The Equality Symbol.} The binary symbol \verb:=: (which can be used as an infix symbol) and any name that starts with \verb:eq:, \verb:EQ:, or \verb:Eq:, when used as a binary predicate symbol, is recognized as an equality predicate by demodulation. \emph{An exception:} if the flag \verb:tptp_eq: is set, then \verb:EQUAL: is the one and only equality symbol; this flag was introduced for compatibility with the TPTP problem library \cite{tptp-web}. \paragraph{When and How It Is Applied.} Demodulation is applied, using equalities in the list \verb:demodulators:, to every clause that is generated by an inference rule. Also, when the flag \verb:demod_inf: (Sec.~\ref{inf-flags}) is set, demodulation is, in effect, treated as an inference rule. \paragraph{Demodulation of Atomic Formulas.} Atomic formulas (literals with any negation sign removed) can be demodulated. Useful examples are {\small \begin{verbatim} (x*y = x*z) = (y = z). % one form of cancellation D(x,y) = D(y,x). % lex-dependent atom demodulator P(junk) = $T. % trick to get rid of a literal \end{verbatim} } %$ \noindent The appropriate clause simplification occurs if the right side of an atom demodulator is one of the Boolean constants \verb:$T: or \verb:$F:. Negated literals cannot be demodulated, but the atom of a negative literal can be demodulated. \paragraph{Inside-out or Outside-in.} The user has the option of having terms rewritten inside-out or outside-in. (See the description of the flag \verb:demod_out_in: in Sec.~\ref{eq-flags}.) Although the choice makes little difference for many applications, we nearly always recommend inside-out. Outside-in can be much faster in cases where the left side of the demodulator has a variable not in the right side. \paragraph{Order of Demodulators.} By default, demodulation uses an indexing mechanism to find demodulators that can rewrite a given term; if more than one demodulator can apply, the user has no control over which one is used. To order the set of demodulators for application, the user can set the flag \verb:demod_linear: (Sec.~\ref{eq-flags}). \paragraph{Dynamic Demodulation and Back Demodulation.} Positive equality units derived during the search can be made into demodulators (Secs. \ref{eq-flags}, \ref{dynamic}, and \ref{dynamic-lrpo}). Demodulators adjoined during the search can be used to rewrite previously derived clauses (Sec.~\ref{eq-flags}). \paragraph{Termination.} With the default ad hoc ordering, demodulation is not guaranteed to terminate by itself. Therefore, a parameter (\verb:demod_limit:) specifies the maximum number of rewrite steps that will be applied to a clause. With the lexicographic recursive path ordering (flag \verb:lrpo:), demodulation will always terminate by itself. (Even with \verb:lrpo:, the parameter \verb:demod_limit: has effect because demodulation sequences can have an unreasonable number of steps.) \paragraph{Introduction of New Variables.} A demodulator introduces new variables if it has variables on the right side that do not occur on the left. The {\sc lrpo} flag does not allow demodulators to introduce new variables. The default ordering allows variable introductions only for input demodulators. \paragraph{Lex- and {\sc lrpo}-dependent Demodulation.} Ordinary demodulators are used unconditionally; they usually simplify or canonicalize regardless of the context in which they are applied. But some equalities that are not normally thought of as rewrite rules can be used as such and are applied only if the application produces a ``better'' term. These are called lex- or {\sc lrpo}-dependent demodulators (depending on whether the flag \verb:lrpo: is set). For example, commutativity of an operation, say $x+y=y+x$, can be used to rewrite $b+a$ to $a+b$ if $a+b\prec b+a$. See Secs. \ref{eq-flags}, \ref{lex-dep}, and \ref{lex-dep-lrpo}. Do not confuse this type of demodulation with conditional demodulation. \paragraph{Demodulation of Evaluable Terms.} \otter\ has many built-in function and predicate symbols for doing arithmetic, logic operations, bit operations, and other operations. The evaluation of terms containing these built-in symbols is done as a part of demodulation (Sec.~\ref{eval}). \paragraph{Conditional Demodulation.} Demodulators can be written with conditions as \begin{verse} {\em condition} \verb:->: $\alpha=\beta$. \end{verse} The demodulator is applied only if the condition, instantiated with the matching substitution, demodulates to \verb:$T: (meaning {\em true}). %$ This is a ``fringe feature'', and it has not been heavily used (Sec.~\ref{cond-demod}). \paragraph{Demodulation as Equational Programming.} \otter's demodulation, especially with the evaluable symbols, can be used as a general-purpose (although not particularly efficient or convenient) equational programming system (Sec.~\ref{eval}). We have not seen many cases where this is useful in the context of a traditional refutation search, but it has proved to be very useful for various symbolic programming tasks, particularly with hyperresolution. \paragraph{Demodulation to Delete Clauses.} Demodulation can be used as a trick to overcome one of the deficiencies of the weighting mechanism (Sec.~\ref{weighting}) to discard undesired clauses. Weighting does not implement a true match (one-way unification) operation. If the user wishes to discard every clause that contains an instance of a particular term, say \verb:f(x,x):, a demodulator, say \verb:f(x,x) = junk:, can be input along with a weight template that gives \verb:junk: a \verb:purge_gen: weight higher than \verb:max_weight:. (When using this and similar tricks, the user must make sure that the clauses containing \verb:junk: are really discarded by weighting or another means; on occasion we have found proofs that are incorrect because they depend on \verb:junk:.) \section{Ordering and Dynamic Demodulation} \label{ordering} \begin{sloppypar} This section contains a more complete explanation of the options \verb:lex_order_vars:, \verb:order_eq:, \verb:symbol_elim:, \verb:dynamic_demod:, \verb:dynamic_demod_all:, \verb:lrpo:, and \verb:dynamic_demod_lex_dep:. It gives all the rules---built in and optional---for orienting equality literals and deciding which equalities will be dynamic demodulators. \otter\ uses two kinds of term ordering. \begin{description} \item[{\it ad hoc ordering.}] This is a collection of ordering methods that we have accumulated through many years of experimentation. The methods do not have a substantial theoretical foundation, but they are useful in many cases. This is the default ordering; it is presented in Sec.~\ref{ad-hoc}. \item[{\sc lrpo}.] This is the {\em lexicographic recursive path ordering} (also called {\sc rpo} with status). It has nice theoretical properties and is easier to use than the ad hoc ordering, but it is more computationally expensive. The {\sc lrpo} ordering is enabled with the flag \verb:lrpo:; it is described in Sec.~\ref{lrpo}. \end{description} \end{sloppypar} Both kinds of term ordering use an ordering on constant and function symbols. The \verb:lex: command (Sec.~\ref{symbol-commands}) is used to assign an ordering on symbols. For example, the command {\small \begin{verbatim} lex( [a, b, c, d, or(_,_)] ). \end{verbatim} } \noindent specifies {\tt a $\prec$ b $\prec$ c $\prec$ d $\prec$ or} ({\tt or} is a binary symbol). If a \verb:lex: command is given, all constant and function symbols in terms that will be compared must be included. If a \verb:lex: command is not given, \otter\ uses the following default ordering. \begin{verse} {\tt [\em constants\tt , \em high-arity\tt, $\cdots$, \em binary\tt , \em unary\tt]} \end{verse} Within arity, the lexicographic {\sc ascii} ordering (i.e., the C library routine \verb:strcomp():) is used. The methods for orienting equalities and for determining dynamic and lex-dependent demodulators apply to all inferred clauses; if the flag \verb:process_input: is set, they also apply to input \verb:usable: and \verb:sos: clauses. In this section, $\alpha$ and $\beta$ always refer to the left and right arguments, respectively, of the equality literal under consideration; $wt(\gamma)$ refers to the weight of $\gamma$ using \verb:weight_list_terms:; $vars(\gamma)$ is the set of variables in $\gamma$. The symbols $\succ$ and $\prec$ are used for several orderings; the one referred to should be clear from the context. Table \ref{order-tab} is a quick reference guide to the ordering mechanisms presented in Secs. \ref{ad-hoc} and \ref{lrpo}. {\small \begin{table}[htbp] \centering \small \caption{Quick Reference to Ordering} \label{order-tab} \begin{tabular}{|l|l||l||l|} \hline \multicolumn{2}{|c||}{Situation} & \multicolumn{1}{c||}{Ad Hoc} & \multicolumn{1}{c|}{LRPO} \\ \hline\hline Input demods & flip? & no & if $\alpha\prec\beta$ \\ \cline{2-4} & lex-dependent? & if ident-x-vars & if neither is greater \\ \hline \multicolumn{2}{|l||}{Orienting eqs ({\tt order\_eq} set)} & \parbox{1.5in}{flip if sym-elim,\\ occurs-in, or wt-lex-ord} & flip if $\alpha\prec\beta$ \\ \hline & \verb:d_d_all: clear & \parbox{1.5in}{if oriented, var-subset,\\ and $wt(\beta) \leq 1$} & if $\alpha\succ\beta$ \\ \cline{2-4} Dynamic demod? & \verb:d_d_all: set & \parbox{1.5in}{if oriented and var-subset} & if $\alpha\succ\beta$ \\ \cline{2-4} & lex-dependent? & \parbox{1.5in}{if ident-x-vars and \\ {\tt dynamic\_demod\_all} set} & \parbox{1.25in}{if neither is greater,\\and var-subset} \\ \hline \multicolumn{2}{|l||}{Apply lex-dependent demod?} & lex-order($\alpha\sigma,\beta\sigma$) & $\alpha\sigma\succ\beta\sigma$ \\ \hline \multicolumn{2}{|l||}{Lex {\tt \$} evaluation}& lex-order & lex-order \\ \hline \end{tabular} \end{table} } \subsection{Ad Hoc Ordering} \label{ad-hoc} \subsubsection{Term Ordering (Ad Hoc)} \label{lex-order} Two types of ad hoc term ordering are used: lex-order and weight-lex-order. The user does not have a choice between these two; the one that is applied depends on the context, as described in the following subsections. \begin{description} \item[{\it lex-order.}] This is a basic lexicographic extension of the symbol order. To compare two terms, one reads them left to right, stopping at the first symbols where they differ; the relationship of those symbols determines the term order. The treatment of variables depends on the flag \verb:lex_order_vars:: \begin{description} \item[{\tt lex\_order\_vars} is set.] Variables are the lowest in the symbol ordering, with \verb:x: $\prec$ \verb:y: $\prec$ \verb:z: $\prec$ \verb:u: $\prec$ \verb:v: $\prec$ \verb:w: $\prec$ \verb:v6: $\prec$ \verb:v7: $\prec$ \verb:v8: $\prec$ $\cdots$. Since the order on symbols is total (any two symbols are comparable), the lexical order on terms is total (any two terms are comparable). Note that applying a substitution to a pair of terms may change their relative order. \item[{\tt lex\_order\_vars} is clear (the default).] A variable is comparable only to itself and to a term that contains the variable. The order on terms is partial. Note that if $t_1 \prec t_2$, and if $\sigma$ is any substitution, then $t_1\sigma \prec t_2\sigma$. \end{description} \begin{sloppypar} \item[{\it weight-lex-order.}] In comparing two terms, they are first weighed with \verb:weight_list_terms:. If one term is heavier, it is greater in the order. If the terms have equal weight, they are compared with respect to the lex-order as if \verb:lex_order_vars: is clear. \end{sloppypar} \end{description} \subsubsection{Orienting Equalities (Ad Hoc)} \label{orient} If the flag \verb:order_eq: is set and \verb:lrpo: is clear, then equality literals (both positive and negative) in inferred clauses are processed as follows. \begin{enumerate} \item If the \verb:symbol_elim: flag is set and if the equality is a symbol-eliminating type (Sec.~\ref{eq-flags}), the equality is oriented in the appropriate direction. \item If one argument is a proper subterm of the other argument, the equality is oriented so that the subterm is the right-hand argument. \item If one argument is greater in the weight-lex-order, say $\gamma\succ\delta$, the equality is oriented with $\gamma$ as the left side. \end{enumerate} The preceding steps do not apply to equalities input on the list \verb:demodulators:. \subsubsection{Determining Dynamic Demodulators (Ad Hoc)} \label{dynamic} A dynamic demodulator is a demodulator that is inferred rather than input. If either of the flags \verb:dynamic_demod: or \verb:dynamic_demod_all: is set, the flag \verb:order_eq: will also be set, and \otter\ will attempt to make some or all inferred positive equality units into demodulators. If the flag \verb:process_input: is set, the procedure applies to input \verb:usable: and \verb:sos: equalities. The procedure assumes that equalities have already been oriented. \begin{enumerate} \item If the flag \verb:symbol_elim: is set and if $\alpha=\beta$ is symbol-eliminating, the equality becomes a demodulator. \item If $\beta$ is a proper subterm of $\alpha$, the equality becomes a demodulator. \item If $\alpha\succ\beta$ in the weight-lex-order, and if $vars(\alpha) \supseteq vars(\beta)$, \begin{itemize} \item[(a)] if \verb:dynamic_demod_all: is set, the equality becomes a demodulator; \item[(b)] if \verb:dynamic_demod_all: is clear and if $wt(\beta) \leq 1$, the equality becomes a demodulator. \end{itemize} \item If \verb:dynamic_demod_lex_dep: and \verb:dynamic_demod_all: are both set, if $\alpha$ and $\beta$ are identical-except-variables (Sec.~\ref{lex-dep}), and if $vars(\alpha) \supseteq vars(\beta)$, the equality becomes a lex-dependent demodulator. \end{enumerate} \subsubsection{Lex-dependent Demodulation (Ad Hoc)} \label{lex-dep} Two terms are {\it identical-except-variables} if they are identical after replacing all occurrences of variables with \verb:x:. An input or dynamic demodulator is lex-dependent only if $\alpha$ and $\beta$ are identical-except-variables. (See Sec.~\ref{dynamic} for determining lex-dependent dynamic demodulators.) A lex-dependent demodulator applies to a term only if the replacement term is smaller in the lex-order. In particular, \otter\ will apply a lex-dependent demodulator $\alpha=\beta$ if and only if $\alpha\sigma\succ\beta\sigma$ in the lex-order, where $\sigma$ is the matching substitution. For example, in the presence of the \verb:lex: command and the (lex-dependent) demodulators {\small \begin{verbatim} lex([a, b, c, d, or(_,_)]). list(demodulators). or(x,y) = or(y,x). or(x,or(y,z)) = or(y,or(x,z)). end_of_list. \end{verbatim} } \noindent the term \verb:or(or(d,b),or(a,c)): will be demodulated to \verb:or(a,or(b,or(c,d))): (in several steps). \subsection{LRPO} \label{lrpo} \subsubsection{Term Ordering ({\sc lrpo})} The {\em lexicographic recursive path ordering} ({\sc lrpo}, or {\sc rpo} with status) \cite{termination,rta-85,rrl} is a method for comparing terms. The important theoretical property of {\sc lrpo} is that it is a {\em termination ordering}. That is, let $R$ be a set of demodulators in which in each demodulator, the left side is {\sc lrpo}-greater than the right side; then demodulation (applying the demodulators left to right) is guaranteed to terminate. To use {\sc lrpo} one typically uses the \verb:lex: command (Sec. \ref{symbol-commands}) to assign an ordering on constant and function symbols. If the \verb:lex: command is not present, \otter\ assigns an ordering (which is frequently ineffective). (\otter\ uses a total ordering on symbols that is fixed at input time. Other implementations of {\sc lrpo} use partial orderings or dynamically changing orderings.) With respect to {\sc lrpo}, function symbols can have either {\em left-to-right status} (the default) or {\em multiset status}. The command {\tt lrpo\_multiset\_status({\it symbol\_list})} gives symbols multiset status. {\sc Lrpo} comparison is used when orienting equality literals, deciding whether an equality should be a demodulator or an {\sc lrpo}-dependent demodulator, and deciding whether to apply an {\sc lrpo}-dependent demodulator. {\sc Lrpo} comparison is never used when evaluating the functions/predicates that perform lexical comparison (\verb:$LLT:, \verb:$LGT:, etc.). \subsubsection{Orienting Equalities ({\sc lrpo})} \label{orient-lrpo} If the flag \verb:order_eq: is set and if one argument of the equality literal (positive or negative) is greater in the {\sc lrpo} order, the greater argument is placed on the left side. This rule applies to input demodulators, to inferred clauses, and, if the flag \verb:process_input: is set, to input \verb:usable: and \verb:sos: clauses. \subsubsection{Determining Dynamic Demodulators ({\sc lrpo})} \label{dynamic-lrpo} If the flag \verb:dynamic_demod: is set, \otter\ attempts to make all equalities into demodulators (\verb:dynamic_demod_all: is ignored when \verb:lrpo: is set). If $\alpha\succ\beta$ in the {\sc lrpo} order, the derived equality becomes a demodulator ($\alpha$ is not {\sc lrpo}-less-than $\beta$, because orienting has already occurred). If \verb:dynamic_demod_lex_dep: is set, if neither argument is {\sc lrpo}-less-than the other, and if every variable that occurs in $\beta$ also occurs in $\alpha$, the derived equality becomes an {\sc lrpo}-dependent demodulator. \subsubsection{{\sc lrpo}-dependent Demodulation ({\sc lrpo})} \label{lex-dep-lrpo} An {\sc lrpo}-dependent demodulator is allowed to rewrite a term if and only if its application produces an {\sc lrpo}-less-than term. \subsection{Knuth-Bendix Completion} \label{kb} The Knuth-Bendix completion procedure \cite{knuth-bendix} attempts to transform a set $E$ of equalities into a terminating, canonical set of rewrite rules (demodulators). If it is successful, the resulting set of rewrite rules, a {\em complete set of reductions}, is a decision procedure for equality of terms in the theory $E$. There are many variations and refinements of the Knuth-Bendix procedure. Setting either of the flags \verb:anl_eq: or \verb:knuth_bendix: causes \otter\ to automatically alter a set of options so that its search will behave like a Knuth-Bendix completion procedure. If \otter's search stops because its \verb:sos: list is empty, and if certain other conditions are met, then the resulting set of equalities should be a complete set of reductions. (\otter\ was not designed to implement a completion procedure, and it has not been optimized for completion.) \noindent {\em Conjecture}. If (1) the set $E$ of equalities, along with \verb:x=x:, is input in list \verb:sos:, (2) flag \verb:anl_eq: is set, (3) other options that are changed from the defaults do not affect the search, (4) \otter\ stops with ``sos empty'', and (5) other than \verb:x=x:, the final \verb:usable: list is the same as the final \verb:demodulators: list, then the \verb:demodulators: list is a complete set of reductions for $E$. Here is an input file that causes \otter\ to search for and quickly find a complete set of reductions for free groups. Note that the predeclared (right associative) infix operator \verb:*: is used. {\small \begin{verbatim} set(anl_eq). set(print_lists_at_end). lex([e, _*_, g(_)]). list(sos). x = x. e*x = x. % left identity g(x)*x = e. % left inverse (x*y)*z = x*y*z. % associativity end_of_list. \end{verbatim} } \noindent The critical issue in most applications of the Knuth-Bendix completion procedure is the choice of ordering scheme and/or the specific ordering on symbols. Note, in this case, that if the \verb:lex: command is absent, the default symbol ordering suffices because it is essentially the same as the one specified. The \verb:anl_eq: flag is also very useful when trying to prove equational theorems. When using \verb:anl_eq: to search for proofs, we are not bound by the conditions listed in the above claim; in fact, we usually apply additional strategies such as limiting the size of retained equalities, being more selective about making equalities into demodulators, and disabling {\sc lrpo} ordering. With the following input file, \otter\ uses the \verb:anl_eq: option to prove the difficult half of a group theory theorem of Levi: {\it The commutator operation is associative if and only if the commutator of any two elements lies in the center of the group.} (A textbook proof can be found in \cite{kurosh}.) Note that, contrary to common practice, the symbol order does not cause the definition of the commutator operation \verb:h(_,_): to be used as a rewrite rule to eliminate commutator expressions in \verb:h:. Note also that weight templates are used to eliminate clauses containing terms with particular structures; this decision is purely heuristic, derived from experimentation and intuition. \otter\ finds a proof in about a minute and uses about 6 megabytes of memory. {\small \begin{verbatim} set(anl_eq). lex([a,b,c,e,h(_,_),f(_,_),g(_)]). assign(max_weight, 20). assign(pick_given_ratio, 5). clear(print_kept). clear(print_new_demod). clear(print_back_demod). list(usable). x = x. f(e,x) = x. % group theory f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). end_of_list. list(sos). f(g(x),f(g(y),f(x,y))) = h(x,y). % definition of commutator h(h(x,y),z) = h(x,h(y,z)). % commutator is associative % Denial: there are two elements whose commutator % is not in the center. f(h(a,b),c) != f(c,h(a,b)). end_of_list. weight_list(purge_gen). weight(h($(0),f($(0),h($(0),$(0)))), 100). weight(h(f($(0),h($(0),$(0))),$(0)), 100). weight(h($(0),f(h($(0),$(0)),$(0))), 100). weight(h(f(h($(0),$(0)),$(0)),$(0)), 100). weight(h($(0),h($(0),h($(0),$(0)))), 100). weight(h($(0),f($(0),f($(0),$(0)))), 100). weight(h(f($(0),f($(0),$(0))),$(0)), 100). end_of_list. \end{verbatim} } \section{Evaluable Functions and Predicates ({\tt \$SUM}, {\tt \$LT}, $\ldots$)} \label{eval} \otter\ can be used in a ``programmed'' mode that is quite different from normal refutational theorem proving. When using the programmed mode, one generally has in mind a particular method for solving a problem; and when writing clauses for the programmed mode, one generally knows exactly how they will be used by \otter. The programmed mode frequently involves a set of evaluable function and predicate symbols known as the \verb:$:-symbols (because each starts with \verb:$:). Examples are \verb:$SUM: and \verb:$LT: for integer arithmetic and \verb:$AND: for Boolean operations. %$ The evaluable symbols operate on five types of \otter\ term: integer constants, floating-point constants, bit-string constants, the Boolean constants \verb:$T: and \verb:$F:, and arbitrary terms. The symbols that evaluate to type Boolean can occur either as function symbols or as predicate symbols. The integer, bit, and floating-point operations behave the same as the underlying C operations applied to the data types ``long int'', ``unsigned long int'', and ``double'', respectively. Table \ref{eval-tab} lists the evaluable functions and predicates by type. \begin{table}[ht] \centering \caption{Evaluable Functions and Predicates} \label{eval-tab} \begin{tabular}{|l|l|} \hline $int \times int \rightarrow int$ & \verb:$SUM:, \verb:$PROD:, \verb:$DIFF:, \verb:$DIV:, \verb:$MOD: \\ \hline $int \times int \rightarrow bool$ & \verb:$EQ:, \verb:$NE:, \verb:$LT:, \verb:$LE:, \verb:$GT:, \verb:$GE: \\ \hline \hline $float \times float \rightarrow float$ & \verb:$FSUM:, \verb:$FPROD:, \verb:$FDIFF:, \verb:$FDIV: \\ \hline $float \times float \rightarrow bool$ & \verb:$FEQ:, \verb:$FNE:, \verb:$FLT:, \verb:$FLE:, \verb:$FGT:, \verb:$FGE: \\ \hline \hline $bits \times bits \rightarrow bits$ & \verb:$BIT_AND:, \verb:$BIT_OR:, \verb:$BIT_XOR: \\ \hline $bits \times int \rightarrow bits$ & \verb:$SHIFT_LEFT:, \verb:$SHIFT_RIGHT: \\ \hline $bits \rightarrow bits$ & \verb:$BIT_NOT: \\ \hline $int \rightarrow bits$ & \verb:$INT_TO_BITS: \\ \hline $bits \rightarrow int$ & \verb:$BITS_TO_INT: \\ \hline \hline $\rightarrow bool$ & \verb:$T:, \verb:$F: \\ \hline $bool \times bool \rightarrow bool$ & \verb:$AND:, \verb:$OR: \\ \hline $bool \rightarrow bool$ & \verb:$TRUE:, \verb:$NOT: \\ \hline $bool \times term \times term \rightarrow term$ & \verb:$IF: \\ \hline \hline $term \times term \rightarrow bool$ (lexical) & \verb:$ID:, \verb:$LNE:, \verb:$LLT:, \verb:$LLE:, \verb:$LGT:, \verb:$LGE: \\ \hline $term \times term \rightarrow bool$ (other) & \verb:$OCCURS:, \verb:$VOCCURS:, \verb:$VFREE:, \verb:$RENAME: \\ \hline $term \rightarrow bool$ & \verb:$ATOMIC:, \verb:$INT:, \verb:$BITS:, \verb:$VAR:, \verb:$GROUND: \\ \hline \hline $\rightarrow int$ & \verb:$NEXT_CL_NUM:, \verb:$UNIQUE_NUM: \\ \hline \end{tabular} \end{table} Additional notes on the operations (unless otherwise stated, the term in question evaluates if all arguments demodulate/evaluate to the appropriate type): \begin{itemize} \item $int \times int \rightarrow int$. The symbol \verb:$SUM: is addition, \verb:$PROD: is multiplication, \verb:$DIFF: is subtraction, \verb:$DIV: is integer division, and \verb:$MOD: is remainder. \item $float \times float \rightarrow float$. These operations are analogous to the integer operations except that there is no floating-point remainder operation. The syntax of floating-point numbers is described in Sec.~\ref{float} \item $int \times int \rightarrow bool$. These are the ordinary relational operations on integers. The symbol \verb:$EQ: is $=$, \verb:$NE: is $\neq$, \verb:$LT: is $<$, \verb:$LE: is $\leq$, \verb:$GT: is $>$, and \verb:$GE: is $\geq$. \item $bits \times int \rightarrow bits$. The shift operations \verb:$SHIFT_LEFT: and \verb:$SHIFT_RIGHT: shift the first argument by the number of places given by the second argument. \item $bits \times bits\rightarrow bits$. The symbols \verb:$BIT_AND:, \verb:$BIT_OR:, and \verb:$BIT_XOR: are the bitwise conjunction, disjunction, and exclusive-or operations. \item $bits \rightarrow bits$. The symbol \verb:$BIT_NOT: is the one's complement operation on bit strings. \item $int \rightarrow bits$. The symbol \verb:$INTS_TO_BITS: translates a decimal integer to a bit string. \item $bits \rightarrow int$. The symbol \verb:$BITS_TO_INT: translates a bit string to the corresponding decimal integer. \item $\rightarrow bool$. The symbols \verb:$T: and \verb:$F: represent {\em true} and {\em false}. When they appear as literals or atomic formulas in clauses, the clauses are simplified as appropriate. % \item % $bool \times bool \rightarrow bool$. \item $bool \rightarrow bool$. The symbol \verb:$TRUE: is essentially a ``no operation'' on Boolean constants. It is used to trick hyperresolution into evaluating literals (see below). \item $bool \times term \times term \rightarrow term$. The \verb:$IF: function is the {\it if-then-else} operator. When inside-out (the default) demodulation encounters a term {\tt \$IF({\it condition}, $t_1$, $t_2$)}, demodulation takes a path different from its normal inside-out behavior. The term {\it condition} is demodulated (evaluated); if the result is \verb:$T:, the value of the \verb:$IF: term is the result of demodulating $t_1$; if the result is \verb:$F:, the value of the \verb:$IF: term is the result of demodulating $t_2$; if the result is neither \verb:$T: nor \verb:$F:, demodulation returns to its normal behavior. Note that if the condition evaluates to a Boolean value, demodulation deviates from its inside-out behavior, because just one of $t_1$ and $t_2$ is demodulated. (If demodulation were always outside-in, \verb:$IF: would not need to be built in because it could be efficiently defined with the two demodulators \verb:if($T,x,y)=x: and \verb:if($F,x,y)=y:.) \item $term \times term \rightarrow bool$ (lexical). These operations are analogous to the six operations in $int \times int \rightarrow bool$ except that the comparisons are lexical instead of arithmetic. The symbol \verb:$ID: tests identity of terms. The lexical comparison is the same as in lex-dependent demodulation; in particular, the flag \verb:lex_order_vars: (Secs. \ref{eq-flags} and \ref{lex-order}) is consulted during these operations. \item $term \times term \rightarrow bool$ (other). The term \texttt{\$OCCURS($t_1$,$t_2$)} is true if $t_1$ is a subterm of $t_2$, including the case when they are the same. The term \texttt{\$VOCCURS($t_1$,$t_2$)} is true if $t_1$ is a variable that occurs in $t_2$. The term \texttt{\$VFREE($t_1$,$t_2$)} is true if $t_1$ is a variable that does not occur in $t_2$. The term \texttt{\$RENAME($t_1$,$t_2$)} is true if $t_1$ and $t_2$ have the same structure; that is, if we rename all variables to $x$, the terms are identical. \item $term \rightarrow bool$. A term is \verb:$ATOMIC: iff it is a constant (including integer and bit string), a term is a \verb:$INT: iff it is an integer, a term is a \verb:$BITS: iff it is a string of \{0,1\}, a term is a \verb:$VAR: iff it is a (unbound) variable, and a term is a \verb:$GROUND: iff it does not contain any variables. \item $ \rightarrow int$. The term \verb:$NEXT_CL_NUM: (no arguments) evaluates to the next integer that will be assigned as a clause identifier (this is useful for placing the ID of a clause within the clause). A sequence of calls to \verb:$UNIQUE_NUM: (no arguments) returns $[1,2,3,\cdots]$. \end{itemize} Evaluation occurs as part of the demodulation process. In particular, if demodulation comes across an evaluable term, say \verb:$SUM(2,3):, it tries to convert the arguments into the appropriate type (integers for \verb:$SUM:); then if the arguments have the correct type, it rewrites the term to the result of the operation, in this case, just as if the demodulator \verb:$SUM(2,3)=5: had been present. The evaluation mechanisms, along with ordinary demodulation, form a reasonably complete (although not particularly speedy or convenient) equational programming subsystem. Evaluation/demodulation can also occur, in a very particular way, during hyperresolution. (Recall that hyperresolution takes a clause, the {\em nucleus}, with some negative literals, the conditions, and resolves each negative literal with a positive clause, producing a clause with no negative literals.) Just as evaluation during demodulation can be thought of as rewriting with an implicit demodulator, evaluation during hyperresolution can be thought of resolving with the implicit positive unit clause \verb:$T: %$ (meaning ``true''). The mechanism is this: if hyperresolution encounters a negative literal that has an evaluable predicate symbol, then it demodulates the atom (the literal without the sign); if the result of the demodulation is \verb:$T:, %$ then the literal is considered to have been resolved. During hyperresolution, demodulation/evaluation is triggered by the presence of an evaluable literal. In many cases, however, the user defines a Boolean function to trigger the mechanism. Consider the following definition of list membership, written as demodulators: {\small \begin{verbatim} member(x,[]) = $F. member(x,[y|z]) = $IF($ID(x,y), $T, member(x,y)). \end{verbatim} } \noindent Because the symbol \verb:member: is not evaluable, the demodulation/evaluation mechanism will not be activated; however, the unary evaluable predicate \verb:$TRUE: %$ can be used in the following way to trigger demodulation/evaluation. \begin{verse} \small {\tt $-L_1$ | $\cdots$ | -\$TRUE(member({\it element}, {\it list})) | $\cdots$ | $-L_n$ | $M$}. \end{verse} Evaluable functions and predicates are useful to implement forward-chaining rule-based systems, for example, state-space search problems (Sec.~\ref{eval-examples}). Hyperresolution operates on the conditions (negative literals) in order, left to right. (The preceding sentence is not quite true because the first step is typically resolution of a positive given clause with any one of the conditions, but for this paragraph, we may assume that it is true.) If a literal resolves or evaluates, the next literal is considered. If nothing more can be done with a literal, then hyperresolution backtracks to the preceding literal in search of an alternative. When a nucleus contains evaluable conditions, the order of the conditions is important both for efficiency and for actually deriving hyperresolvents. Evaluable conditions typically have variables that must be instantiated when nonevaluable literals are resolved. If an evaluable literal is too far to the left, its variables will not be sufficiently instantiated when hyperresolution encounters it, evaluation will fail, and possible paths to hyperresolvents will be blocked. If an evaluable literal is too far to the right, then hyperresolution can explore many paths that are sure to fail. \noindent {\em Technical Note and Advice.} The evaluable symbols are an add-on feature rather than an integral part of \otter. In particular, the objects that are manipulated (integers, bit strings, etc.) in most cases are stored by \otter\ as character strings rather than as the appropriate data type. To evaluate a term, say \verb:$SUM(2,3):, %$ \otter\ must find the strings \verb:"2": and \verb:"3": in a hash table, translate them to integers, add them, translate the result to the string \verb:"5":, then look up \verb:"5":, and possibly insert it into the hash table. This procedure is obviously much slower than it needs to be. If a problem requires a hundred million evaluations, the user should consider using something else, including writing a special-purpose C program. \noindent {\em Warning 1.} The evaluable symbols should not be thought of as theories ``built in'' to \otter. As theories, they are very incomplete, and \otter\ uses them only in very constrained ways. \noindent {\em Warning 2.} Ordinary resolution inference rules (e.g., \verb:binary_res:, \verb:hyper_res:, \verb:ur_res:) never apply to evaluable literals. \subsection{Using More Natural Expressions for Evaluation} \label{make-eval} Writing complex evaluable expressions with \verb:$:-symbols can be quite tedious. Therefore, a feature was added that allows more natural expressions. The command \verb:make_evaluable: copies the evaluation properties from a \verb:$:-symbol to any other symbol of the same arity. The form of the command is \begin{verse} \small {\tt make\_evaluable(\em any-symbol\tt ,\em evaluable-symbol\tt ).} \end{verse} The symbols in the command are given dummy arguments to specify the arity. The following list contains typical examples for integer arithmetic (assuming the symbols on the left are already known to be infix). \begin{verse} \small \verb:make_evaluable(_+_, $SUM(_,_)).:\\ \verb:make_evaluable(_-_, $DIFF(_,_)).:\\ \verb:make_evaluable(_>_, $GT(_,_)).:\\ \verb:make_evaluable(_>=_, $GE(_,_)).: \end{verse} \noindent \noindent {\em Warning 1.} If a binary symbol that is recognized by paramodulation or demodulation as an equality symbol is given evaluation properties, it will no longer be recognized by paramodulation or demodulation. For example, if the command \verb:make_evaluable(_=_, $EQ(_,_)): %$ is issued, paramodulation and demodulation will not recognize \verb:a=b: as an equality. The convention is to use \verb:==: for evaluation. \noindent {\em Warning 2.} This is not an ``alias'' mechanism; the symbols remain distinct for unification, matching, and identity testing. \subsection{Evaluation Examples} \label{eval-examples} \paragraph{Equational Programming.} The evaluable functions and predicates enable the use of equalities with demodulation as a general-purpose equational programming language. Here are some examples. {\small \begin{verbatim} gcd(x,y) = % greatest common divisor for nonnegative integers $IF($EQ(x,0), y, $IF($EQ(y,0), x, $IF($LT(x,y), gcd(x,$DIFF(y,x)), gcd(y,$DIFF(x,y))))). factorial(x) = % factorial for nonnegative integers $IF($EQ(x,0), 1, $PROD(x,factorial($DIFF(x,1)))). quick_sort([]) = []. % naive quicksort quick_sort([x|y]) = append(quick_sort(le_list(x,y)), [x|quick_sort(gt_list(x,y))]). le_list(z,[]) = []. le_list(z,[x|y]) = $IF($LLE(x,z), [x|le_list(z,y)], le_list(z,y)). gt_list(z,[]) = []. gt_list(z,[x|y]) = $IF($LGT(x,z), [x|gt_list(z,y)], gt_list(z,y)). \end{verbatim} } \paragraph{A State-Space Search.} Here is a complete \otter\ input file for a simple state-space search. {\small \begin{verbatim} % We have a 3-gallon jug and a 4-gallon jug, both empty, % and a well. Our goal is to have exactly 2 gallons in the % 4-gallon jug. We can fill a jug from the well, empty a % jug onto the ground, and carefully pour water from one % jug into the other. % % j(m, n) is the state in which the 3-gallon jug contains % m gallons, and the 4-gallon jug contains n gallons. set(hyper_res). make_evaluable(_+_, $SUM(_,_)). make_evaluable(_-_, $DIFF(_,_)). make_evaluable(_<=_, $LE(_,_)). make_evaluable(_>_, $GT(_,_)). list(usable). -j(x, y) | j(3, y). % fill the 3-gallon jug -j(x, y) | j(0, y). % empty the 3-gallon jug -j(x, y) | j(x, 4). % fill the 4-gallon jug -j(x, y) | j(x, 0). % empty the 4-gallon jug -j(x, y) | -(x+y <= 4) | j(0, y+x). % small -> big; it fits -j(x, y) | -(x+y > 4) | j(x- (4-y),4). % small -> big, until full -j(x, y) | -(x+y <= 3) | j(x+y, 0). % big -> small; it fits -j(x, y) | -(x+y > 3) | j(3,y- (3-x)). % big -> small, until full -j(x, 2). % goal state --- 4-gallon jug containing 2 gallons end_of_list. list(sos). j(0, 0). % initial state --- both jugs empty end_of_list. \end{verbatim} } \section{Weighting} \label{weighting} \otter\ recognizes four lists of weight templates. (See Sec.~\ref{input-weight} for input of weight template lists.) \begin{description} \item[{\tt weight\_list(pick\_given).}] This list is used for selection of given clauses from list \verb:sos:. When the weight of a clause is printed, it is the \verb:pick_given: weight. \item[{\tt weight\_list(purge\_gen).}] This list is used in conjunction with the \verb:max_weight: parameter to discard generated clauses. \item[{\tt weight\_list(pick\_and\_purge).}] In many cases, one can use the same weighting strategy for both selecting given clauses and purging generated clauses. The \verb:pick_and_purge: list serves the purposes of both the \verb:pick_given: and the \verb:purge_gen: lists. If the \verb:pick_and_purge: list is present, then neither the \verb:pick_given: nor the \verb:purge_gen: list may be present. \item[{\tt weight\_list(terms).}] This list is for calculating the weight of terms when using the weight-lex-order (Sec.~\ref{lex-order}) to compare terms. This occurs when the flag \verb:lrpo: is clear when orienting equality literals (Secs. \ref{orient} and \ref{dynamic}). \end{description} \subsection{Weighing Clauses and Literals} The weight of a clause is always the sum of the weights of its literals (excluding any answer literals). The weight of a positive literal is the weight of its atom. The weight of a negative literal is the weight of its atom plus the value of the \verb:neg_weight: parameter (Sec.~\ref{misc-parms}). \subsection{Weighing Atoms and Terms} Atoms and terms are weighed top-down. To weigh a given term, \otter\ searches the appropriate weight list (in the order input) for the first matching template. If a match is found, then the subterms of the given term that match the integers in the template are weighed. The weight of the given term is the sum of the products of each integer and the weight of its corresponding subterm, plus the second argument of the weight template. For example, the template \begin{verse} \verb:weight(f(g($(2)),$(-3)), -50).: \end{verse} matches the given term \begin{verse} \verb:f(g(h(a)),f(b,x)).: \end{verse} Let $wt(t)$ be the weight of term or atom $t$. Then \begin{verse} $wt(\mbox{\tt f(g(h(a)),f(b,x))}) = 2*wt(\mbox{\tt h(a)}) + (-3)*wt(\mbox{\tt f(b,x)}) + (-50)$. \end{verse} If a matching weight template is not found, then the weight of the given term is 1 plus the sum of the weights of the subterms. (See the flags \verb:atom_wt_max_args: and \verb:term_wt_max_args:, Sec.~\ref{misc-flags}, for overrides.) Note that this weighting scheme implies that if no weight templates are present, the default weight of a term or atom is the number of variable, constant, function, and predicate symbols (the symbol count). Variables in weight templates are generic. A variable in a weight template will match any variable, and only a variable, in the given term. As a consequence, it is never necessary to use different variable names in a weight template. For example, \verb:weight(f(x,x),-7): matches the term \verb:f(u,v):, and \verb:weight(x,32): matches all variables. {\em Warning.} The two occurrences of symbol \verb:f: in the term \verb:f(f,x): are treated by \otter\ as different symbols because they have different arities. The weight template \verb:weight(f, 0): applies to the second occurrence but not to the first. The default weight of an answer literal is 0, but templates can be used to assign weights to answer literals. The parameter \verb:neg_weight: never applies to answer literals. If one wishes to have a weight template containing a Skolem function or constant that is generated by \otter, one must first make a short trial run to find out how the formulas are Skolemized, then return to the input file and insert the weight list containing the Skolem symbol {\it after} the formula lists. \subsection{Containment Weight Templates} Term weighting has an additional feature that allows the user to specify terms that \emph{contain} particular terms. This is done with a unary function symbol \verb:$dots(:$t$\verb:):. If \verb:$dots(:$t$\verb:): occurs in a weight template, it will match any term that contains a term that matches t. This is very useful for discarding ``bad'' clauses. Here is part of an output file that illustrates this feature. {\small \begin{verbatim} list(sos). 1 [] p(f(g(g(g(g(g(h(h(h(h(j(b)))))))))))). 2 [] p(F(g(g(h(g(H(g(h(g(g(g(B)))))))))))). 3 [] p(f3(g(h(a)),g(g(b)),h(h(c)))). end_of_list. weight_list(pick_given). weight(f($dots(j($(5)))),100). weight(F($dots(H($dots(B)))),1000). weight(f3($dots(a),$dots(b),$dots(c)),2000). end_of_list. ======= end of input processing ======= =========== start of search =========== given #1: (wt=106) 1 [] p(f(g(g(g(g(g(h(h(h(h(j(b)))))))))))). given #2: (wt=1001) 2 [] p(F(g(g(h(g(H(g(h(g(g(g(B)))))))))))). given #3: (wt=2001) 3 [] p(f3(g(h(a)),g(g(b)),h(h(c)))). \end{verbatim} } %$ \section{Answer Literals} \label{answer} The main use of answer literals is to record, during a search for a refutation, instantiations of variables in input clauses. For example, if the theorem under consideration states that an object exists, then the denial of the theorem contains a variable, and an answer literal containing the variable can be appended to the denial. If a refutation is found, then the empty clause has an answer literal that contains the object whose existence has just been proved. Any literal whose predicate symbol starts with \verb:$ans:, \verb:$Ans:, or \verb:$ANS: is an answer literal. Most %$ routines---including the ones that count literals and decide whether a clause is positive or negative---ignore any answer literals. The inference rules insert, into the children, the appropriate instances of any answer literals in the parents. If factoring is enabled, \otter\ {\it does} attempt to factor answer literals. \section{The Passive List} \label{passive} Either clauses or formulas can be input to list \verb:passive:. After input, the passive list is fixed for the rest of the run. Clauses in the passive list are used for exactly two purposes: forward subsumption and unit conflict. If forward subsumption is enabled, a newly generated clause will be deleted if it is subsumed by any clause in \verb:usable:, \verb:sos:, or \verb:passive:, and newly kept unit clauses are checked for unit conflict against unit clauses in \verb:usable:, \verb:sos:, or \verb:passive:. The passive list has been most useful for monitoring the progress of a search. Suppose we are trying to prove a difficult theorem, we have some lemmas in mind, and we would like to know whether \otter\ has proved the lemmas. Then denials of the lemmas can be placed in the passive list, and \otter\ will report proofs if it proves any lemmas, but the denials of the lemmas will not interfere with the search for the main theorem. (Recall that an appropriate value must be assigned to \verb:max_proofs:; otherwise \otter\ will stop at the first proof.) \section{Clause Attributes} \label{attributes} Attributes can be attached to clauses. This feature was introduced at the same time as the hints strategy (Sec.~\ref{hints}), and all of the current attributes are specifically for the hints strategy. In case some future enhancements of \otter\ will use attributes, the general attribute mechanism is given here. Each attribute is identified by a name, and each attribute has a type. (Users cannot introduce new attributes---they are built into the code of \otter.) The attribute types are integer, string, and term. Attributes are attached to clauses with the operator ``\verb:#:'', and must appear after all literals. For example, if attribute \verb:a1: has type integer, attribute \verb:a2: has type string, and attribute \verb:a3: has type term, then a user can write a clause with attributes as follows. {\small \begin{verbatim} f(x,y)!=f(x,z) | y=z # a1(23) # a2("left cancel") # a3(g(b)). \end{verbatim} } \section{The Hints Strategy} \label{hints} The \emph{hints strategy} can be used if the user has a set of clauses that might be relevant to finding a proof. The clauses, called \emph{hints}, do not necessarily hold in the theory being explored, and they are not used for making inferences. Hints are used only as a heuristic for guiding the search, in particular, in selecting the given clauses and in deciding whether to keep derived clauses. The main function of the hints strategy is to adjust the pick-given weight of clauses. The user can specify, for example, that any derived clause that matches a hint should have its pick-given weight reduced by 1000. In addition, the user can specify, with an attribute on a hint, how that hint should be used to adjust the pick-given weight of clauses that match the hint. Clauses can match hints in several ways as specified by (ordinary) parameters and by attributes on hints. Because of the distinction between the pick-given and purge-gen weights of clauses, and because the hints mechanism affects only the pick-given weight, several additional flags exist. If a clause matching a hint is derived, one typically wants it to be kept so that it can be selected as a given clause. However, the clause may be discarded by the \verb:max_weight: parameter. To address this problem, the flags \verb:keep_hint_subsumers: and \verb:keep_hint_equivalents: say that the \verb:max_weight: parameter should be ignored for all clauses that match hints in those ways (details are in the following subsections). The hints strategy was introduced by Bob Veroff, who implemented it in a previous version of \otter\ and used it in many applications \cite{veroff:hints,veroff:sketches}. \otter\ currently has two separate hints mechanisms, named ``hints'' and ``hints2'', both derived from Veroff's methods and ideas. The first is more general, and the second is much faster. \subsection{Hints (the General Version)} The hint clauses are given in one or more lists. All of the lists must be named ``hints'' as in the following example. {\small \begin{verbatim} list(hints). -p(x) | q(x) | r(x). end_of_list. \end{verbatim} } \noindent A clause $C$ can match a hint $H$ in three ways. \begin{enumerate} \item $C$ subsumes $H$. This is referred to as ``bsub'', in analogy to back subsumption. \item $C$ is subsumed by $H$. This is referred to as ``fsub'', in analogy to forward subsumption. \item $C$ is equivalent to $H$. \end{enumerate} Six parameters and two flags determine the behavior of the hints mechanism. \noindent \verb:assign(equiv_hint_wt,:$n$\verb:):. Default \maxint, range [$-$\maxint ..\maxint ]. If $n \neq$ \maxint, clauses that are equivalent to a hint receive a pick-given weight of $n$. \noindent \verb:assign(equiv_hint_add_wt,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. Clauses that are equivalent to a hint have $n$ added to their ordinary pick-given weight. \noindent \verb:assign(fsub_hint_wt,:$n$\verb:):. Default \maxint, range [$-$\maxint ..\maxint ]. If $n \neq$ \maxint, clauses that are subsumed by a hint receive a pick-given weight of $n$. \noindent \verb:assign(fsub_hint_add_wt,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. Clauses that are subsumed by a hint have $n$ added to their ordinary pick-given weight. \noindent \verb:assign(bsub_hint_wt,:$n$\verb:):. Default \maxint, range [$-$\maxint ..\maxint ]. If $n \neq$ \maxint, clauses that subsume a hint receive a pick-given weight of $n$. \noindent \verb:assign(bsub_hint_add_wt,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. Clauses that subsume a hint have $n$ added to their ordinary pick-given weight. A clause can match more than one hint, and a clause can match a hint in more than one way, so the order of operations is relevant. The rules are as follows. (1) The first hint (as given in the input file) that matches the clause is used. (2) Equivalence is tested first, then fsub, then bsub. (3) Within match type (e.g., bsub), both types of weight adjustment can be applied (e.g., \verb:bsub_hint_wt: and \verb:bsub_hint_ad_wt:). The hint-adjustment parameters can be overridden by attributes on individual hints. (This feature can be used, for example, if some hints are more important than others.) The attribute names for hints correspond to the six parameters listed above. For example, if the parameter \verb:bsub_hint_add_wt: is set to -1000, that value can be overridden for a particular hint by giving it an attribute as follows. {\small \begin{verbatim} f(x,f(x,f(x,y)))=f(x,y) # bsub_hint_add_wt(-2000). \end{verbatim} } The following two flags were introduced because the hints mechanism adjusts the pick-given weight of clauses and does not affect the purge-gen weight of clauses. \noindent Flag \verb:keep_hint_subsumers:. Default clear. If this flag is set, then the \verb:max_weight: parameter is ignored for derived clauses that subsume any hints. \noindent Flag \verb:keep_hint_equivalents:. Default clear. If this flag is set, then the \verb:max_weight: parameter is ignored for derived clauses that are equivalent to any hints. \paragraph{Practical Advice.} If one has a set of clauses that one wishes to use as hints, say from a proof of a related theorem, a good first attempt is to use the following settings. \begin{verbatim} assign(bsub_hint_add_wt, -1000). set(keep_hint_subsumers). \end{verbatim} If one has more than a few hints, and one wishes to use only the preceding settings, then we recommend using hints2 (the fast version). \subsection{Hints2 (the Fast Version)} The general hints mechanism described in the preceding paragraphs can be very slow if there are many hints, because each hint clause is tested until a match is found. The fast hints mechanism uses indexing to find hints. To activate the fast hints mechanism, hint clauses are placed in one or more lists named ``hints2'' as in the following example. {\small \begin{verbatim} list(hints2). -p(x) | q(x) | r(x). end_of_list. \end{verbatim} } \noindent Only one type of matching can be used with hints2---a clause matches a hint if and only if it subsumes the hint. Two parameters and two flags apply to hints2. \noindent \verb:assign(bsub_hint_wt,:$n$\verb:):. Default \maxint, range [$-$\maxint ..\maxint ]. If $n \neq$ \maxint, clauses that subsume a hint receive a pick-given weight of $n$. \noindent \verb:assign(bsub_hint_add_wt,:$n$\verb:):. Default 0, range [$-$\maxint ..\maxint ]. Clauses that subsume a hint have $n$ added to their ordinary pick-given weight. \noindent Flag \verb:keep_hint_subsumers:. Default clear. If this flag is set, then the \verb:max_weight: parameter is ignored for derived clauses that subsume any hints. \noindent Flag \verb:degrade_hints2:. Default clear. If this flag is set, Bob Veroff's hint-degradation strategy is applied. When a hint is first read, its \verb:bsub_hint_add_wt: is associated with it; this value can come from the parameter or from an attribute. The hint-degradation strategy says that each time a hint is used to adjust the weight of a derived clause, its \verb:bsub_hint_add_wt: is cut in half. Assuming that it initially has a large negative value, this strategy makes a hint progressively less important as it matches more derived clauses. This strategy was introduced because (contrary to intuition) many different generalizations of a hint can be derived. \subsection{Label Attributes on Hints} If a hint clause has a label attribute, for example, \begin{verbatim} f(x,f(x,f(x,y)))=f(x,y) # label("hint 32 from proof 12"). \end{verbatim} and if such a hint is used to adjust the pick-given weight of a clause $C$, the label is inherited by $C$. This feature, which is useful for tracking the application of hints, applies to both the general and the fast hints mechanisms. \subsection{Generating Hints from Proofs} The main source for hints is proofs of related theorems. (If the goal is to shorten a proof, hints often come from proofs of the same theorem.) \noindent Flag \verb:print_proof_as_hints:. Default clear. If this flag is set, then whenever a proof is found, it is printed as a hints list in a form that can be input to a subsequent \otter\ job. The proof that is printed contains more detail than the ordinary proofs printed by \otter. In particular, when the proof contains demodulation, clauses are printed for each rewrite step of demodulation. This flag is independent of the hints mechanism. \section{Interaction during the Search} \label{interact} \otter\ has a primitive interactive feature that allows the user to interrupt the search, modify the options, and then continue the search. The interrupt is triggered in two ways: (1) with \otter\ running in the foreground, the user types the ``interrupt'' character (often {\sc delete} or control-C), or (2) if the parameter \verb:interrupt_given: is set to $n$, the search is interrupted after every $n$ given clauses. When interrupted, \otter\ immediately goes into a simple loop to read and execute commands. The accepted commands are listed in Table \ref{interact-tab}. \begin{table}[htbf] \centering \small \caption{Interaction Commands} \label{interact-tab} \begin{tabular}{ll} \hline {\tt help.} & Give simple help. \\ {\tt set({\it flag-name}).} & Set a flag. \\ {\tt clear({\it flag-name}).} & Clear a flag.\\ {\tt assign({\it param-name},{\it value}).} & Assign a value to a parameter. \\ {\tt stats.} & Send statistics to std. output and the terminal. \\ {\tt usable.} & Print list \verb:usable: on the terminal. \\ {\tt sos.} & Print list \verb:sos: on the terminal. \\ {\tt demodulators.} & Print list \verb:demodulators: on the terminal. \\ {\tt passive.} & Print list \verb:passive: on the terminal. \\ {\tt fork.} & Fork and run the child process; \\ & \hspace{1cm} resume parent when child finishes. \\ {\tt continue.} & Continue the search. \\ {\tt kill.} & Send statistics to standard output, and exit. \\ \hline \end{tabular} \end{table} \noindent The following notes elaborate on the interactive feature. \begin{itemize} \item The flag \verb:interactive_given: (Sec.~\ref{loop-flags}) can be useful with the interactive feature. For example, if one thinks the search is going to fail, one can interrupt it, print list \verb:sos:, set the \verb:interactive_given: flag, then continue, selecting given clauses interactively. \item The \verb:fork: command creates a separate copy, called a {\em child}, of the entire \otter\ process. Immediately after the fork, the child is running (waiting for more commands), and the original process, the {\em parent}, is waiting for the child to finish. When the child finishes, the parent resumes (waiting for more commands). Changes that the child makes to the clause space, options, and so forth, are not reflected in the parent; when the parent resumes, it is in exactly the same state as when the fork occurred. (The timing statistics are not handled correctly in child processes; CPU times are from the start of the current process; wall-clock time is correct; other timings are not reliable.) \item The interactive routine is an area where a user who is also a C programmer can easily add features. For example, most of the ordinary input commands could be made available in the interactive mode. \item This kind of interaction can be disabled by using the command \verb:clear(sigint_interact):. \end{itemize} {\em Warning.} Do not interactively change any option that affects term or literal indexing. \section{Output and Exit Codes} \label{output} \otter\ sends most of its output to ``standard output'', which is usually redirected by the user to a file; we just call it the output file. The first part of the output file is an echo of most of the input and some additional information, including identification numbers for clauses and description of some input processing. Comments are not echoed to the output. The second part of the output file reflects the search. Various print flags determine what is output. Given clauses, generated clauses, kept clauses, and several messages about the processing of generated and kept clauses can be printed. Both statistics from the parameter \verb:report: and proofs can also be printed during the search. The final part of the output file lists counts of various events (such as clauses given and clauses kept) and times for various operations. Whenever a clause is printed, it is printed with its integer identifier (ID) and a justification list, which is enclosed in brackets. Examples: {\small \begin{verbatim} 4 [] -j(x,y)|j(x,0). 13 [hyper,11,8,eval,demod] j(3,1). 41 [31,demod] p([a,b,b,c,c,c,d,e,f]). 14 [new_demod,13] f(y,f(y,f(y,x)))=x. 71 [back_demod,58,demod,70,14,55,11,34,11] e!=e. 12 [demod,9] f(a,f(b,f(g(a),g(b))))!=e. 77 [binary,57.3,30.2] sm|mm| -sl. 33,32 [para_from,26.1.1,15.1.1.2,demod,21] g(x)=f(x,x). 36 [hyper,31,2,26,30,unit_del,19,18,20,19] p(k,g(k)). 4 [factor_simp,factor_simp] p(x)|p($f1(x))| -q($f2(y))| -q(y)|p($c6). 199 [binary,198.1,191.1,factor_simp] q($c14). \end{verbatim} } \noindent If the justification list is empty, the clause was input. Otherwise, the {\em first} item in the justification list is one of the following. \begin{description} \item[An inference rule.] The clause was generated by an inference rule. The IDs of the parents are listed after the inference rule with the given clause ID listed first (unless \verb:order_history is set):. \item[A clause identifier.] The clause was generated by the \verb:demod_inf: rule. \item[{\tt new\_demod}.] The clause is a dynamically generated demodulator; it is a copy of the clause whose ID is listed after \verb:new_demod:. \item[{\tt back\_demod}.] The clause was generated by back demodulating the clause whose ID is listed after \verb:back_demod:. \item[{\tt demod}.] The clause was generated by back demodulating an input clause. \item[{\tt factor\_simp}.] The clause was generated by factor-simplifying an input clause. For example, \verb:p(x)|p(a): factor-simplifies to \verb:p(a):. \end{description} The sublist $[\mbox{\tt demod}, id_1, id_2, \ldots]$ indicates demodulation with $id_1, id_2, \ldots$. The sublist $[\mbox{\tt unit\_del}, id_1, id_2, \ldots]$ indicates unit deletion with $id_1, id_2, \ldots$. The symbols \verb:eval: indicates that a literal was ``resolved'' by evaluation (Sec.~\ref{eval}) during hyperresolution. The sublist $[\mbox{\tt factor\_simp}, \mbox{\tt factor\_simp}, \ldots]$ indicates a sequence of factor-simplification steps (Sec.~\ref{gen-flags}). In proofs, some clauses are printed with two (consecutive) IDs. In such a case, the clause is a dynamically generated demodulator, and the two IDs refer to different copies of the same clause: the first ID refers to its use for inference rules, and the second to its use as a demodulator. If the flag \verb:detailed_history: is set, then for the inference rules \verb:binary_res:, \verb:para_from:, and \verb:para_into:, the positions of the unified literals or terms are listed along with the parent IDs. For example, \verb:[binary,57.3,30.2]: means that the third literal of clause 57 was resolved with the second literal of clause 30. For paramodulation, the ``from'' parent is listed as $ID.i.j$, where $i$ is the literal number of the equality literal, and $j$ (either 1 or 2) is the number of the unified equality argument; the ``into'' parent is listed as $ID.i.j_1.\cdots.j_n$, where $i$ is the literal number of the ``into'' term, and $j_1.\cdots.j_n$ is the {\em position vector} of the ``into'' term; for example, \verb:400.3.1.2: refers to the second argument of the first argument of third literal of clause 400. If the flag \verb:para_all: is set, then the paramodulation positions are not listed. When the flag \verb:sos_queue: is set, the search is breadth first (level saturation), and \otter\ sends a message to the output file when given clauses start on a new level. (Input clauses have level 0, and generated clauses have level one greater than the maximum of the levels of the parents. Since clauses are given in the order in which they are retained, the level of given clauses never decreases.) \paragraph{Exit Codes.} When \otter\ stops running, it sends an exit code to the operating system, giving the reason for termination. The codes are useful when another program or system calls \otter. Table \ref{exit-tab} lists the exit codes. Note that we do not follow the \unix\ convention of returning zero for normal and nonzero for abnormal termination. \begin{table}[htbp] \centering \caption{Exit Codes} \label{exit-tab} \begin{tabular}{cl} \hline 101 & Input error(s) \\ 102 & Abnormal end (compile-time limit or \otter\ bug) \\ 103 & Proof(s) found (stopped by \verb:max_proofs):\\ 104 & \verb:sos: list empty \\ 105 & \verb:max_given: parameter exceeded \\ 106 & \verb:max_seconds: parameter exceeded \\ 107 & \verb:max_gen: parameter exceeded \\ 108 & \verb:max_kept: parameter exceeded \\ 109 & \verb:max_mem: parameter exceeded \\ 110 & Operating system out of memory \\ 111 & Interactive exit \\ 112 & Memory error (probable \otter\ bug) \\ 113 & A USR1 signal was received \\ 114 & The splitting rule terminated with a possible model \\ 115 & \verb:max_levels: parameter exceeded \\ \hline \end{tabular} \end{table} \section{Controlling Memory} \label{mem-control} In many \otter\ searches, the \verb:sos: list accumulates many clauses that never enter the search, possibly wasting a lot of memory. The normal way to conserve memory is to put a maximum on the weight of kept clauses. It can be difficult, however, to find an appropriate maximum. \otter\ has a feature, enabled by the command \verb:set(control_memory):, that attempts to automatically adjust the maximum. The memory-control feature operates as follows. When one third of available memory (\verb:max_mem: parameter) has been filled, \otter\ assigns or reassigns a maximum weight. The new maximum, say $n$, is such that 5\% of all clauses in \verb:sos: have weight $\leq n$. From then on, at every tenth iteration of the main loop, \otter\ calculates a prospective new maximum $n'$ in the same way. If $n' < n$, then the maximum is reset to $n'$. The values $1/3$ and 5\% were determined by trial and error. Perhaps these values should be parameters. \paragraph{Reducing {\tt max\_weight} on the Fly.} In many searches, the number of kept clauses grows much faster than the number of given clauses. In other words, the list \verb:sos: is very large, and most of those clauses never participate in the search. To save memory, one can use the \verb:max_weight: parameter to discard many of the clauses that will (probably) never become given clauses. A few searches and proofs show a phenomenon we call the {\it complexity hump}. To get a search started, one must use complex clauses; then one can continue the search using simpler clauses. That is, the first few steps in the proof are complex, and the remaining steps are simpler. If one needs to carefully conserve memory when a complexity hump is present, one can use the parameters \verb:change_limit_after: and \verb:new_max_weight: to change the value of \verb:max_weight: after a specified number of given clauses. \noindent \verb:assign(change_limit_after,:$n$\verb:):. Default 0, range [0..\maxint ]. If $n$ (the value) is not 0, this parameter has effect. After $n$ given clauses have been used, the parameter \verb:max_weight: is automatically reset to the value of the parameter \verb:new_max_weight:. \noindent \verb:assign(new_max_weight,:$n$\verb:):. Default \maxint , range [$-$\maxint ..\maxint ]. See the description of the preceding parameter. Note that the memory-control feature (Sec.~\ref{mem-control}) can also address the complexity hump phenomenon. \section{Autonomous Mode} \label{auto} If the flag \verb:auto: is set, \otter\ will scan the input clauses for some simple syntactic properties and decide on inference rules and a search strategy. We think of the autonomous mode as providing a built-in metastrategy for selecting search strategies. The search strategy that \otter\ selects for a particular set of clauses is usually refutation complete (except for the flag \verb:control_memory:), but the user should not expect it to be especially effective. It will find proofs for many easy theorems, and even for cases in which it fails to find a proof, it provides a reasonable starting point. In the input file, the command \verb:set(auto): must occur before any input clauses, and all input clauses must be in list \verb:usable:; it is an error to place input clauses on any of the other lists when in autonomous mode. \otter\ will move some of the input clauses to \verb:sos: before starting the search. When \otter\ processes the \verb:set(auto): command, it alters some options, even before examining the input clauses. If the user wishes to augment the autonomous mode by including some ordinary \otter\ commands (including overriding \otter's choices), the commands should be placed after \verb:set(auto): and before \verb:list(usable):. After \verb:list(usable): has been read, \otter\ examines the input clauses for several syntactic properties and decides which inference rules and strategies should be used, and which clauses should be moved to \verb:sos:. The user cannot override the decisions that \otter\ makes at this stage. \otter\ looks for the following syntactic properties of the set of input clauses: (1) whether it is propositional, (2) whether it is Horn, (3) whether equality is present, (4) whether equality axioms are present, and (5) the maximum number of literals in a clause. The program then considers six basic combinations of the properties: (1) propositional, (2) equality in which all clauses are units, and (3--6) the four combinations of \{equality, Horn\}. To see precisely what \otter\ does for these cases, the reader can set up and run some simple experiments. Please be aware that the autonomous mode reflects individual experience with \otter; other users would certainly formulate different metastrategies. For example, one might prefer UR-resolution to hyperresolution or in addition to hyperresolution in rich Horn or nearly-Horn theories, and one might prefer to add few or no dynamic demodulators for equality theories. \section{Fringe Features} \label{fringe} This section describes features that are new, not well tested, and not well documented. \otter\ is not as robust when using these features, especially when more than fringe features is being used. \subsection{Ancestor Subsumption} \otter\ does not necessarily prefer short or simple proofs---it simply reports the proofs that it finds. An option \verb:ancestor_subsume: extends the concept of subsumption to include the derivation history, so that if two clause occurrences are logically identical, the one with fewer ancestors is preferred. The motivation is to find short proofs. \noindent Flag \verb:ancestor_subsume:. Default clear. If this flag is set, the notion of subsumption (forward and back) is replaced with {\it ancestor-subsumption}. Clause $C$ ancestor-subsumes clause $D$ iff $C$ properly subsumes $D$ or if $C$ and $D$ are variants and $size(ancestorset(C)) \leq size(ancestorset(D))$. When setting \verb:ancestor_subsume:, we strongly recommend not clearing the flag \verb:back_subsume:, because doing so can cause many occurrences of the same clause to be retained and used as given clauses. \subsection{The Hot List} \label{hot} The hot list is a strategy that can be used to emphasize particular clauses. It was invented by Larry Wos in the context of paramodulation, and it has been extended to most of \otter's inference rules. To use the strategy, the user simply inputs one or more clauses in the special list named \verb:hot:. Whenever a clause is generated and kept by \otter's ordinary mechanisms, it is immediately considered for inference with clauses in the hot list. \paragraph{Which Clauses Should Be Hot?} Clauses input in the hot list are usually copies of clauses that occur also in \verb:sos: or \verb:usable:. They are typically clauses that the user believes will play a key role in the search for a proof, for example, special hypotheses. \paragraph{Managing Hot-List Clauses.} Input to the hot list is the same as input to other lists and can be in either clause or formula form, for example, {\small \begin{verbatim} list(hot). f(x,x) = x. m(m(x)) = x. end_of_list. \end{verbatim} } \noindent The flag \verb:process_input: has no effect on hot-list clauses; they are never altered during input. Hot-list clauses are never deleted, for example by back subsumption or back demodulation. Even if a hot-list clause is identical to a clause in another list, it has a unique identifying number, and proofs that use hot-list clauses generally refer to two copies (with different ID numbers) of those clauses. \paragraph{Hot Inference Rules.} The inference rules that are applied to newly kept clauses and hot-list clauses are the same as the rules in effect for ordinary inference, with the exceptions \verb:demod_inf:, \verb:geometric_rule:, and \verb:linked_ur_res:, which are never applied to hot-list clauses. \paragraph{Applying Hot Inference.} When hot inference is applied, the newly kept clause is treated as the given clause, and the hot list is treated as the usable list. (Note that the newly kept clause is not in the hot list, so it will not be considered for inference with itself, as happens with the given clause in ordinary inference.) For inference rules such as hyperresolution or UR-resolution that can use more than two parents, {\em all} of the other parents must be in the hot list; this generally means that the nucleus and other satellites must be in the hot list. Hot inference is not applied to clauses that are ``kept'' during processing of the input. \paragraph{Level of Hot Inference (Parameter {\tt heat}).} To prevent long sequences of hot inferences (i.e., hot inference applied to a clause generated by hot inference, and so on) we consider the {\em heat level} of hot inference. The heat level of an ordinary inference is 0, and the heat level of a hotly inferred clause is one more than the heat level of the new-clause parent. The parameter \verb:heat:, default 1, range [0..100], is the maximum heat level that will be generated. When a clause is printed, its heat level, if greater than 0, is also printed. \paragraph{Dynamic Hot Clauses (Parameter {\tt dynamic\_heat\_weight}).} Clauses can be added to the hot list during a search. If the \verb:pick_given: weight of a kept clause is less than or equal to the parameter \verb:dynamic_heat_weight:, default $-$\maxint , range [$-$\maxint ..\maxint], then the clause will be added to the hot list and used for subsequent hot inference. Input clauses that are ``kept'' during processing of the input are never made into dynamic hot clauses. Dynamic hot clauses can be added to an empty hot list (i.e., no input hot list). \subsection{Sequent Notation for Clauses} \label{sequent} Two flags enable the use of sequent notation for clauses. \noindent Flag \verb:input_sequent:. Default clear. If this flag is set, clauses in the input file must be in sequent notation. \noindent Flag \verb:output_sequent:. Default clear. If this flag is set, then sequent notation is used when clauses are output. \noindent Syntax: \begin{itemize} \item All sequent clauses have an arrow. \item The negative literals (if any) are written on the left side of the arrow, are written without the negation sign, and are separated by commas. \item The positive literals (if any) are written on the right side of the arrow and are separated by commas. \end{itemize} \noindent Table \ref{sequent-tab} lists some examples. \begin{table}[ht] \centering \caption{Examples of Sequent Clauses} \label{sequent-tab} \begin{tabular}{l|l} \hline Ordinary Clause & Sequent Clause \\ \hline \verb:-p | -q | -r | s | t: & \verb:p,q,r->s,t: \\ \verb:p(a,b,c): & \verb:-> p(a,b,c): \\ \verb:a!=b: & \verb:a=b ->: \\ \verb:$F: (the empty clause) & \verb:->: \\ \hline \end{tabular} \end{table} %$ Note that \verb:p,q->r,s: is ordinarily thought of as (\verb:p: {\em and} \verb:q:) {\em implies} (\verb:r: {\em or} \verb:s:). Sequent clauses are treated as (parsed as) a special case because they can't be made to fit within \otter's ordinary syntax. \subsection{Conditional Demodulation} \label{cond-demod} A conditional demodulator has the form \begin{verse} {\it condition \tt -> \it equality-literal}. \end{verse} The equality is applied as a demodulator if and only if the instantiated {\it condition} evaluates to \verb:$T:. %$ The equality of a conditional demodulator is not subjected on input to being flipped or to being flagged as a lex-dependent demodulator, and conditional demodulators are never back demodulated. In other ways, conditional demodulators behave as ordinary demodulators. Examples are (\verb:member: and \verb:gcd: are defined in Sec.~\ref{eval}.) {\small \begin{verbatim} $ATOMIC(x) -> conjunctive_normal_form(x)=x. member(gcd(4,x),y) -> Equal(f(x,y), g(y)). $GT($NEXT_CL_NUM,1000) -> e(x,x) = junk. \end{verbatim} } %$ \subsection{Debugging Searches and Demodulation} The flag \verb:very_verbose: causes too much output to be used with large searches. The following parameters can turn on verbose output for a segment of the search. \noindent \verb:assign(debug_first,:$n$\verb:):. Default 0, range [0 ..\maxint ]. This parameter is consulted if the flag \verb:very_verbose: is set. Verbose output will begin when a clause is kept and given an identifier of this value. \noindent \verb:assign(debug_first,:$n$\verb:):. Default -1, range [-1 ..\maxint ]. This parameter is consulted if the flag \verb:very_verbose: is set. Verbose output will end when a clause is kept and given an identifier of this value. \noindent \verb:assign(verbose_demod_skip,:$n$\verb:):. Default 0, range [0 ..\maxint ]. This parameter is consulted during demodulation if the flag \verb:very_verbose: is set. Verbose output will not occur during the first $n$ rewrites. \subsection{Special Unary Function Demodulation} A feature, activated by the \verb:special_unary: command, allows \otter\ to avoid one of the problems caused by the lack of associative-commutative matching during demodulation. The feature is useful when an associative-commutative function and an inverse are present, as in rings. Without this feature, the following \verb:lex: command and demodulators {\small \begin{verbatim} lex([0,a,b,c,d,e,g(_),f(_,_)]). list(demodulators). f(x,y) = f(y,x). f(x,f(y,z)) = f(y,f(x,z)). f(x,g(x)) = 0. f(x,f(g(x),y)) = f(0,y). f(0,x) = x. end_of_list. \end{verbatim} } \noindent will cause the expression {\small \begin{verbatim} f(f(f(g(b),a),c),f(b,g(c))) \end{verbatim} } \noindent to be sorted into {\small \begin{verbatim} f(a,f(b,f(c,f(g(b),g(c))))). \end{verbatim} } \noindent One would like \verb:b: and \verb:g(b): to be next to each other so that they could be canceled by one of the inverse demodulators. The special-unary feature accomplishes just that. The command {\small \begin{verbatim} special_unary([g(x)]) \end{verbatim} } \noindent causes \verb:g: to be ignored during term comparisons, and the expression will be demodulated to \verb:a:. The \verb:special_unary: command has no effect if the flag \verb:lrpo: is set. {\it This is a highly experimental feature. Its behavior has not been well analyzed.} \subsection{The Invisible Argument} \otter\ recognizes a built-in unary function symbol \verb:$IGNORE(_):. %$ Forward subsumption treats each term that starts with \verb:$IGNORE: as the constant \verb:$IGNORE:, completely ignoring its argument. For example, \verb:p(a,$IGNORE(b)): subsumes \verb:p(a,$IGNORE(c)):. All other operations (in particular, inference rules, demodulation, and back subsumption) treat \verb:$IGNORE: as an ordinary function symbol. The purpose of \verb:$IGNORE: is to record data about the derivation of a clause without having that data prevent the forward subsumption of clauses that would be subsumed without that data. The \verb:$IGNORE: term is the term analog of the answer literal. For example, one can use \verb:$IGNORE: terms in the jugs and water puzzle (Sec.~\ref{eval-examples}) to record the sequence of pourings that leads to each state. \subsection{Floating-Point Operations} \label{float} Table \ref{float-tab} lists a set of floating-point evaluable functions and predicates that are analogous to the integer arithmetic operations listed in Sec.~\ref{eval}. They operate in the same way as the integer operations. \begin{table}[ht] \centering \caption{Floating-Point Operations} \label{float-tab} \begin{tabular}{|l|l|} \hline $float \times float \rightarrow float$ & \verb:$FSUM:, \verb:$FPROD:, \verb:$FDIFF:, \verb:$FDIV: \\ \hline $float \times float \rightarrow bool$ & \verb:$FEQ:, \verb:$FNE:, \verb:$FLT:, \verb:$FLE:, \verb:$FGT:, \verb:$FGE: \\ \hline \end{tabular} \end{table} The floating-point constants, however, are a little peculiar, both in the way they look and in the way they behave. They are written as quoted strings, using either single or double quotes. (Otherwise, they would not be able to contain decimal points.) Other than the quotation marks, the form of the floating-point constants accepted by \otter\ is exactly the same as the form accepted by the C programming language (actually the C library used by the compiler). Examples are \verb:"1.2":, \verb:"10e6":, \verb:"-3.333E-5":. A floating-point constant must contain either a decimal point or an exponent character \verb:e: or \verb:E:. The peculiar behavior comes from the fact \otter\ stores the floating point numbers as character strings instead of directly as floating point numbers. To apply a floating-point operation, \otter\ starts with the operand strings, translates them to true floating-point numbers (the C data type ``double'' is used), performs the operation, then translates the result into a string so that it can be an \otter\ constant. As well as being inefficient, this scheme also has a problem with precision, because a fixed format is used to translate the results back into strings. The default format is \verb:"%.12f":, and it can be changed with a command such as \begin{verse} \small \verb:float_format("%17.8f"): \end{verse} {\em Caution.} \otter\ does not check that the string in the \verb:float_format: command is a well-formed format specification. This is the user's responsibility. To fully understand how this works, see the standard C language reference \cite[Appendix B]{c-2ed}; in particular, the C library functions \verb:sscanf: and \verb:sprintf: are used to translate to and from strings. \subsection{Foreign Evaluable Functions} \label{foreign} \otter\ provides a general mechanism through which one can create one's own evaluable functions and predicates. The user (1) declares the function, its argument types, and its result type, (2) inserts a call to the function in the \otter\ source code, (3) writes a C routine to implement the function, and (4) recompiles \otter. The user must have a personal copy of the source code to use this feature. See the source code file \verb:foreign.h: for step-by-step instructions, examples, templates, and test files. \noindent {\em Important note.} Many times you can avoid having to do all of this by just writing your function with demodulators and using existing built-in functions. For example, if you need the maximum of two doubles, you can just use the demodulator \verb:float_max(x,y) = $IF($FGT(x,y), x, y):. \subsection{The Inference Rule $gL$ for Cubic Curves} \label{gl} Based on work of R.~Padmanabhan and others, a new inference rule, $gL$ (``geometric Law'', or ``Local to global''), was added to \otter. The rule implements a local-to-global generalization principle that has a geometric interpretation for cubic curves. The article \cite{gl} and the monograph \cite{wm-rp:monograph} contain descriptions of the rule, some details about its implementation in \otter, and several new results obtained with its use. The rule $gL$ applies to single positive unit equalities, and it is implemented in two ways: as an inference rule, with unification, and as a rewrite rule, for when the target terms are already identical. Flag \noindent \verb:geometric_rule:. Default clear. When this flag is set, $gL$ is applied as an inference rule (along with any other inference rules that are set) to each given clause. The rule $gL$ applies to single positive unit equalities. Flag \noindent \verb:geometric_rewrite_before:. Default clear. When this flag is set, $gL$ is applied as a rewrite rule, before ordinary demodulation, to each generated clause. Flag \noindent \verb:geometric_rewrite_after:. Default clear. When this flag is set, $gL$ is applied as a rewrite rule, after ordinary demodulation, to each generated clause. Flag \noindent \verb:gl_demod:. Default clear. When this flag is set, ordinary demodulation is not applied to any derived clauses. Instead, after a clause is kept, it is copied, and the copy is demodulated and processed. Our experience has shown that given two equalities of equal weight, one the result of $gL$ and the other not, the $gL$ result is usually more interesting. The following parameter can give preference to $gL$ results. \noindent \verb:assign(geo_given_ratio,:$n$\verb:):. Default 1, range [$-1$..\maxint ]. When this parameter is not $-1$, it affects selection of the given clause in a way similar to \verb:pick_given_ratio:. If the ratio is $n$, then for each $n$ given clauses selected in the normal way by weight, one given clause is selected because it is the lightest $gL$ result available in \verb:sos:. If \verb:pick_given_ratio: and \verb:geo_given_ratio: are both in effect, then clashes are resolved in favor of \verb:geo_given_ratio:. \subsection{Linked UR-Resolution} \otter\ has an inference rule, \verb:linked_ur_res:, that is an application of the linked inference principle to UR-resolution. Linked inference rules can take much larger inference steps than the corresponding nonlinked rules, thereby avoiding the retention of many clauses that correspond to low-level deduction steps which can interfere with the overall proof search strategy. We refer the reader to \cite{link-I,link-II,link-implement} for background on linked inference rules, and we focus here on specifying the constraints on linked UR-resolution for \otter. The constraints are specified by six flags, two parameters, and annotations on input clauses. \paragraph{Linked UR Flags} \strut \noindent Flag \verb:linked_ur_res:. Default clear. If this flag is set, linked UR-resolution is applied to all given clauses. \noindent Flag \verb:linked_ur_trace:. Default clear. If this flag is set, detailed information about the linking process is sent to the output file. \noindent Flag \verb:linked_sub_unit_usable:. Default clear. If this flag is set, intermediate unit clauses are checked for subsumption against the \verb:usable: list. \noindent Flag \verb:linked_sub_unit_sos:. Default clear. If this flag is set, intermediate unit clauses are checked for subsumption against the \verb:sos: list. \noindent Flag \verb:linked_unit_del:. Default clear. If this flag is set, unit deletion is applied to intermediate clauses. \noindent Flag \verb:linked_target_all:. Default clear. If this flag is set, any literal can be a target. \paragraph{Linked UR Parameters} \strut \noindent \verb:assign(max_ur_depth,:$n$\verb:):. Default 5, range [0 .. 100]. This parameter limits the depth of linked UR-resolution. Note that the depth of ordinary UR-resolution is 0. \noindent \verb:assign(max_ur_deduction_size,:$n$\verb:):. Default 20, range [0 .. 100]. This parameter limits the size of linked UR-resolution inferences, that is, the number of corresponding binary resolution steps. In other words, the size of a linked inference step is one less than the number of clauses that participate. \paragraph{Linked UR Annotations} \strut \noindent Each clause that participates in a linked UR-resolution inference is classified as a \emph{nucleus} (the nonunit clause containing the target literal), a \emph{link} (nonunit clauses all of whose literals are resolved), or a \emph{satellite} (unit clauses). Input clauses can be annotated with special literals specifying the role(s) they can play in linked UR inferences. The clause annotations are as follows. \noindent \verb:$NUCLEUS([:\emph{list-of-literal-numbers}\verb:]): --- %$ the clause (assumed to be nonunit) can be a nucleus. The argument is a list of positive integers identifying the literals that can act as targets. \noindent \verb:$LINK([]): --- %$ the clause (assumed to be nonunit) can act as a link. The argument must be the empty list. \noindent \verb:$BOTH([:\emph{list-of-literal-numbers}\verb:]): --- %$ the clause (assumed to be nonunit) can be either a nucleus or a link, and when it is used as a nucleus, the admissible target literals are given in the list. \noindent \verb:$SATELLITE([]): --- %$ the clause (assumed to be unit) can act as a satellite. The argument must be the empty list. For example, the annotation on the following four-literal clause says that it can act as a nucleus with the fourth literal as the target. {\small \begin{verbatim} $NUCLEUS([4]) | -go | -P31 | -Q31 | R3_LD1_DS5. \end{verbatim} } %$ \noindent Input clauses on the \verb:usable: list must be annotated to participate in linked UR. Units on the list \verb:sos: are assumed to be satellites and need not be annotated. Most experiments with linked UR-resolution have been done under the following constraints. (1) Linked UR is the only inference rule being used, (2) every input clause in the \verb:usable: list is annotated, and (3) every clause in the \verb:sos: list is a unit and is \emph{not} annotated. Linked UR seems to behave correctly under these constraints, but several problems have been noticed with other initial conditions. \paragraph{Acknowledgment.} The linked UR-resolution rule was implemented by Nick Karonis, with collaboration from Bob Veroff and Larry Wos. \subsection{Splitting} To address \otter's poor performance on many non-Horn problems, a splitting rule was installed in \otter\ (in November 1997). By ``splitting'' we mean that the search is divided into two or more independent branches such that if each of the branches is refuted, then the state before the split has been refuted. Splitting is typically recursive. \otter's splitting implementation uses the \unix\ fork() system call, which creates copies of the state of the \otter\ process. An additional hypothesis is asserted on the first branch, and the first branch continues executing while the second branch waits. If the first branch is refuted, the second branch starts running with its additional hypothesis. This method avoids explicit backtracking. Two splitting methods are available: splitting on ground clauses, and splitting on ground atoms. In both methods, the parameter \verb:split_depth: can be used to limit the depth of splitting. For example, with the command {\small \begin{verbatim} assign(split_depth, 3). \end{verbatim} } \noindent a case such as [1.1.1.1] will not occur. \subsubsection{Splitting on Ground Clauses} Clause splitting can be triggered in two ways: either periodically or when a ground clause is selected as the given clause. In both methods, the clauses on which splitting occurs can be constrained by any of the following three flags (all clear by default). {\small \begin{verbatim} set(split_pos). % split on positive clauses only set(split_neg). % split on negative clauses only set(split_nonhorn). % split on non-Horn clauses only \end{verbatim} } \noindent These flags determine eligibility. If none of the flags is set, all ground nonunit clauses are eligible. \paragraph{Splitting Periodically on Clauses.} To enable the periodic splitting method, one uses the following command. {\small \begin{verbatim} set(split_clause). \end{verbatim} } \noindent The default period is every 5 given clauses. To change the period, say to 10 given clauses, use the following command. {\small \begin{verbatim} assign(split_given, 10). \end{verbatim} } \noindent Instead of splitting after some number of given clauses, one can split after some number of seconds, say 4, with the following command. {\small \begin{verbatim} assign(split_seconds, 4). \end{verbatim} } \noindent The clause on which to split can be selected from the set of eligible clauses in two ways. The default method is to select the first, lightest (using the pick-given scale) eligible clause from the sequence \verb:usable+sos:. Instead, one can use the command {\small \begin{verbatim} set(split_min_max). \end{verbatim} } \noindent which says to use the following method to compare two eligible clauses. Prefer the clause with the lighter heaviest literal (using the pick-given scale); if the heaviest literals have the same weight, use the lighter clause; if the clauses have the same weight, use the first in \verb:usable+sos:. \paragraph{Splitting When Given.} To specify that clause splitting should be occur whenever an eligible clause is selected as the given clause, one uses the following command. {\small \begin{verbatim} set(split_when_given). \end{verbatim} } \paragraph{The Branches for Clause Splitting.} If \otter\ decides to split on a clause, say \verb:P|Q|R:, the assumptions for the three cases are {\small \begin{verbatim} Case 1: P. Case 2: -P & Q. Case 3: -P & -Q & R. \end{verbatim} } \noindent One system fork occurs, and Case 1 executes. If it succeeds, a second fork occurs, and Case 2 executes. If that succeeds, Case 3 executes. If any of the cases fails to produce a refutation, the failure is propagated to the top, and the entire search fails. \subsubsection{Splitting on Atoms} To split on atoms, \otter\ periodically selects a ground atom, say \verb:P:, and considers two branches, one with assertion \verb:P:, and the other with \verb:-P:. The following command specifies splitting on atoms. {\small \begin{verbatim} set(split_atom). \end{verbatim} } \noindent The parameters \verb:split_given: and \verb:split_seconds: determine (just as for clause splitting) when atom splitting occurs. If all input clauses are ground, and if the parameter \verb:split_given: is assigned 0, then the resulting procedure is essentially a (very slow) Davis-Putnam-Loveland-Logemann SAT procedure. An atom is eligible for splitting if it occurs in an eligible nonunit ground clause. Clause eligibility is determined just as in the clause splitting case, that is, by the flags \verb:split_pos:, \verb:split_neg:, and \verb:split_nonhorn:. All clauses in \verb:usable+sos: are considered when deciding the best eligible atom. The default method select the lightest atom in the lightest clause (using the pick-given scale). An optional method for selecting an atom considers the number of occurrences of the atom. The command {\small \begin{verbatim} set(split_popular). \end{verbatim} } \noindent says to prefer the atom that occurs in the greatest number of clauses. Instead of having \otter\ decide the atoms on which to split, the user can specify them in the input file with a command such as {\small \begin{verbatim} split_atoms([P, a=b, R]). \end{verbatim} } \noindent which says to split, in order, on those atoms. In this example, we get eight cases, and then no more splitting occurs. The time at which the splitting occurs is determined, as above, by the parameters \verb:split_given: and \verb:split_seconds:. \subsubsection{More on Splitting} If \otter\ fails to find a proof for a particular case (e.g., the list \verb:sos: empties or some limit is reached), the whole attempt fails. If the search strategy is complete, then an empty \verb:sos: list indicates satisfiability, and the set of assumptions introduced by splitting give a partial model. It is up to the user, however, to complete the model. When \otter\ finds a refutation by splitting, the output file does not contain an overall proof. A proof is given for each leaf in the tree, and those proofs contain clauses such as {\small \begin{verbatim} 496 [264,split.1.1.1.1] nop(C,D)!=nop(A,A). \end{verbatim} } \noindent in which the justification indicates that a split occurred on clause 264, and this clause is the assertion for case [1.1.1.1]. Other information about splitting is given in the output file, for example, when a split occurs, the case numbers, the case assertions, and when forked processed begin and end. When splitting is enabled, the parameter \verb:max_seconds: (for the initial process and all descendant processes) is checked against the wall clock (from the start of the initial process) instead of against the process clock. This is problematic if the computer is busy with other processes. \otter's splitting rule is highly experimental, and we do not have much experience with it. A general strategy that may be useful for non-Horn problems is the following. {\small \begin{verbatim} set(split_when_given). set(split_pos). % Also try it without this command. assign(split_depth, 10). \end{verbatim} } \noindent The \otter\ distribution packages should contain a directory of sample input files that use the splitting rule. \paragraph{Acknowledgment} The splitting rule was developed in collaboration with Dale Myers, Rusty Lusk, and Mohammed Almulla. % end of fringe features \section{Soundness and Completeness} \subsection{Soundness} \label{ivy} \otter\ has a very good record with respect to soundness, but (as far as we know) no parts of it (the C code) have been formally verified. If anything depends on proofs found by \otter, the proofs should be carefully checked, by hand or by an independent program. The IVY project \cite{ivy} contains a component that checks the proof objects (Sec.~\ref{output-flags}) produced by \otter. The main result of the IVY project is a hybrid system, constructed in the ACL2 verification environment \cite{acl2-approach}, that takes a first-order conjecture, translates it to clauses, sends the clauses to \otter, and checks any proof objects that are returned. ACL2 has been used to prove various soundness properties of the clause translator, the proof checker, and their composition as a hybrid system. \subsection{Completeness} If the clause set does not involve equality, or if it involves equality and includes the equality axioms, then many of the common refutation-complete resolution search strategies can be easily achieved with \otter. For example, hyperresolution and factoring, with positive clauses in the list \verb:sos: and nonpositive clauses in the list \verb:usable:, is complete. If the input clause set is Horn, then factoring is not required. The default method of selecting the given clause (take one with the fewest symbols) does not interfere with completeness, and neither forward nor back subsumption, as implemented in \otter, interferes with completeness of the basic inference rules. Completeness issues are more complex when paramodulation is the inference rule, especially when the set of support strategy is considered. A simple and complete paramodulation strategy for \otter\ is (1) paramodulate {\em from} and {\em into} the given clause, (2) paramodulate {\em from} and {\em into} both sides of equality literals, (3) paramodulate {\em from} (but not {\em into}) variables, and (4) place all input clauses in the list \verb:sos:. The equality \verb:x=x: is required, but the functionally reflexive axioms are not required. Completeness of the basic inference rules is important, but incomplete restrictions and refinements are frequently required to find proofs. For example, we almost always use the \verb:max_weight: parameter; strictly speaking, it is incomplete, but it saves a lot of time and memory, and careful use of it does not prevent \otter\ from finding proofs in practice. For paramodulation, we generally use the flag \verb:anl_eq: with additional restrictions---some are known to be incomplete, and others have not been analyzed. We sometimes use UR-resolution on non-Horn sets, which is incomplete. And we make extensive use of weighting to purge uninteresting clauses and the options \verb:delete_identical_nested_skolem:, \verb:max_distinct_vars:, and \verb:max_literals:, all of which interfere with completeness. \section{Limits, Abnormal Ends, and Fixes} \otter\ has several compile-time limits. If a limit is exceeded, a message containing the name of the limit will appear in the output file and/or at the terminal. To raise the limit, find the appropriate definition (\verb:#define:) in a \verb:.h: or \verb:.c: file, increase the limit, and recompile \otter. (Of course, one must have one's own copy of the source code to do this.) Some of the limits are as follows. \noindent \verb:MAX_NAME: --- Maximum number of characters in a variable, constant, function, or predicate symbol. \noindent \verb:MAX_BUF: --- Maximum number of characters in an input string (clause, formula, command, weight template, etc.). \noindent \verb:MAX_VARS: --- Maximum number of distinct variables in a clause. \noindent \verb:MAX_FS_TERM_DEPTH: --- Maximum depth of terms in the forward subsumption discrimination tree. \noindent \verb:MAX_AL_TERM_DEPTH: --- Maximum depth of left-hand arguments of equalities in the demodulation discrimination tree. \paragraph{Conserving Memory.} Several steps can be taken if \otter\ is using too much memory. \begin{itemize} \item Use \verb:max_weight: to discard (more) generated clauses. This is a very effective way to save memory (and time). \item Set the flag \verb:control_memory: (Sec.~\ref{misc-flags}), or use the parameters \\ \verb:change_limit_after: and \verb:new_max_weight: (Sec.~\ref{mem-control}). \item Decrease (down to 0) the value of the \verb:fpa_literals: and \verb:fpa_terms: parameters. \item Set the \verb:for_sub_fpa: flag to switch forward subsumption indexing from discrimination tree to {\sc fpa} indexing. \item If the inference rules being used are binary resolution or paramodulation, clear the flag \verb:detailed_history:. \item If a lot of back subsumption or back demodulation is expected, set the flag \verb:really_delete_clauses: (Sec.~\ref{misc-flags}). \item If applicable, set \verb:no_fapl: or \verb:no_fanl: (Sec.~\ref{index-flags}). \item If back demodulation is being used, clear the flag \verb:index_for_back_demod:. \item Run an \otter\ job until memory runs out, collect interesting lemmas from the output file, then rerun the job including the lemmas as input clauses. Repeat. (This can be a good strategy even when memory is not a problem.) \end{itemize} \section{Obtaining and Installing \otter} \otter\ 3 is free, and there are no restrictions on copying or distributing it. The main means of distribution is from the \otter\ Web site at \verb|http://www.mcs.anl.gov/AR/otter/|. Once one has a copy of the \otter\ 3 distribution directory, one should look at the file \verb:README: for instructions on installing and testing \otter. On \unix-like systems, \otter\ may have to be compiled. There may also be executable versions for Microsoft Windows available on the \otter\ Web site. \section*{Acknowledgments} Much of my work over the past few years has been in collaboration with Larry Wos. Toward our goal of creating programs that are expert assistants for mathematicians, logicians, engineers, and other scientists, we have worked together on many applications of automated deduction, and that work has led to many of \otter's current features. The basic design of the program, including the data structures and the use of indexing, descends mostly from theorem provers designed and implemented by Ross Overbeek. The indexing mechanisms, which are in large part responsible for the performance of the program, have benefited from discussions with Overbeek, Mark Stickel, and Rusty Lusk. For many years Bob Veroff has maintained his own versions of \otter. Many of his enhancements have been adopted for the official versions of \otter. 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(The "make" command is part of the "developer's tools", which contains compilers, etc.) In January 2004 I updated the installation procedure, including a few scripts to replace the "make" commands. See README in this directory. otter-3.3f/bin-Darwin/0040755000076400007640000000000010103524060014165 5ustar mccunemccuneotter-3.3f/bin-Darwin/otter0100755000076400007640000117267410103775704015304 0ustar mccunemccuneþíúÎ ˆ…8__PAGEZEROÐ__TEXT``__text__TEXT$tÀ t€__picsymbol_stub__TEXTä€Ô€€$__symbol_stub__TEXTä€Ô€€__picsymbolstub1__TEXTä€ Ô€€ __cstring__TEXTê … Ú __literal8__TEXToÀ8_ÀÐ__DATApÀ`__data__DATAp0`__la_symbol_ptr__DATAp0Ä`01__nl_symbol_ptr__DATApôä`ôb__dyld__DATAqØaØ__bss__DATAqô{__common__DATAí708__LINKEDIT0p…¼ /usr/lib/dyld 4@·BõG/usr/lib/libSystem.B.dylibpá­ÐGì PããÈ«6«d›ªŒ6°($t|: x8!ÿüT!48”!ÿÀ€z8š;cW{:|¤ÚH à|¦¿ÿð”!ÿ BŸè¦||x|#x|¾+xH±<_“‚KD<_“¢KH<_“ÂKL<_€BL@‚/ŒA¾ }‰¦N€!<_€BL<‚/ŒA¾ }‰¦N€!H¿¡<_‚KX€ /€A¾ }‰¦N€!Hõ<_‚KT€ /€A¾ }‰¦N€!<8cÅè8@He€a@/ƒA¾H¿%8<_€BL8=}"Kx/‰Ažd9@9`ˆ |t/€Až0|X®|t/€/@¾}K9k}"Kx| X®|t/€@žÿØ/ŠAž 8 H€<_KPÆóx€/€Až„/€@žÿøƒãx¤ëxÅóx8ÆHÕH¾Q|¦“áÿü”!ÿ BŸè¦<8cÄt8@Hy@}‰¦N€!€h8!`|¦ƒáÿüN€ =`kqØ,‹A†N€ 8 N8€`„êì8`8D8`;8Dà=€€ qØ| ¦=€aŒN€ =`kqÜ}i¦N€ |¦¿¡ÿô”!ÿ |> 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|¦¿Áÿø”!ÿ°BŸè¦|~x=?9)œ€I8BIˆ|t/€A¾ €c H¡ÃóxH™€X8!P|¦»ÁÿøN€ |¦¿Áÿø”!ÿ°|~xˆ|t/€@¾€cKÿÿÙ€~KÿÿÑÃóxKÿÿe€X8!P|¦»ÁÿøN€ |¦“áÿü”!ÿ°BŸè¦ˆ|t/€Až€c <Ÿ8„‘TKÿþMH €cKÿÿÁ€X8!P|¦ƒáÿüN€ |¦¿ÿð”!ÿ°BŸè¦||x|#xˆ|t/€Až€d „ãxH áH´|ƒ#xKÿÿe/ƒAž\8`(„ãxH¾ëx€/€A¾|ƒãx€žKÿÿ€^€/€A¾8` „ãxHIƒÞ€/€@žÿÌH@8`(„ãxH)ƒãx€KÿÿE<8c‘8€8 †ãxH%ƒãx€Kÿÿ!8`)„ãxHí€X8!P|¦»ÿðN€ |¦¿¡ÿô”!ÿ°BŸè¦|dx?¿ƒ½‘”8}XKÿþÕ8` H8}XH=€X8!P|¦»¡ÿôN€ 8/ƒ Až,/ƒ Až$/ƒ Až/ƒ Až/ƒ Až /ƒ @¾8|xN€ 8cÿØ c8`|cN€ |¦¿Aÿè”!ÿ BŸè¦|zx;€HCÓxH É|}x/ƒÿÿAž|ctKÿÿq/ƒ@žÿà/ÿÿAž¬?;{ €HP»á®/œc;œ@¾48|á®<€cð8c°<Ÿ8„\<¿8¥ €H¡8`HÙCÓxH Q|}x/ÿÿAž(¾tÃóxKÿþõ/ƒ@žÃóxKÿÿ%/ƒAžÿŒ/)Až/œAž/(@¾£ëxDÓxH }<_8B €8|ᮣëx€h8!`|¦»AÿèN€ |¦¿Áÿø”!ÿ°BŸè¦;Àˆ|t/€A¾ €c <Ÿ8„Ž4Kÿû)/ƒAž;ÀÃóx€X8!P|¦»ÁÿøN€ |¦¿Áÿø”!ÿ°BŸè¦;Àˆ|t/€A¾ €c <Ÿ8„ ÜKÿúÉ/ƒAž;ÀÃóx€X8!P|¦»ÁÿøN€ |¦¿¡ÿô”!ÿ°BŸè¦|~x; ˆ|t/€@žÈ€~Kÿÿm/ƒAž €^ˆ|t/€@žd€bKÿþé/ƒAžT/AžL€^€bKÿÿ-/ƒ@ž8€^€€^€bKÿúÙ€~KÿúÑ€~KÿúÉÃóxKÿúÁH,<8cœ8€8 <߀Æ8Æ°H¡8`H¹ÝóxƒÞˆ|t/€Ažÿ@€X8!P|¦»¡ÿôN€ |¦¿aÿì”!ÿ BŸè¦||xKÿüý|~x<8c ˜<Ÿ8„”Kÿùe/ƒ@¾,KÿùÅ|}x8˜<8c ˜Kÿùi} £ëxHŒ8`/ž)Až€8`/ž(@žtKÿù…|{x|~xƒãxKÿÿq|cyA‚,; ›¾~Kÿù]~|~xƒãxKÿÿI|cy@‚ÿàƒãxHA<8cŒlKÿøí~ 8˜cÛxKÿþcÛx€h8!`|¦»aÿìN€ ˆc|ctN€ €cN€ €cN€ €C€bN€ €C€B€bN€ |¦¿Áÿø”!ÿ°|~xKÿÿµ8/ƒ@¾ÃóxKÿÿµKÿÿÕ8|x€X8!P|¦»ÁÿøN€ |¦BŸ}h¦=k|¦…‹‹¨}‰¦N€ |¦BŸ}h¦=k|¦…‹‹Œ}‰¦N€ |¦BŸ}h¦=k|¦…‹‹p}‰¦N€ |¦BŸ}h¦=k|¦…‹‹T}‰¦N€ |¦BŸ}h¦=k|¦…‹‹8}‰¦N€ |¦BŸ}h¦=k|¦…‹‹}‰¦N€ |¦BŸ}h¦=k|¦…‹‹}‰¦N€ |¦BŸ}h¦=k|¦…‹Šä}‰¦N€ |¦BŸ}h¦=k|¦…‹ŠÈ}‰¦N€ |¦BŸ}h¦=k|¦…‹Š¬}‰¦N€ |¦BŸ}h¦=k|¦…‹Š}‰¦N€ |¦BŸ}h¦=k|¦…‹Št}‰¦N€ |¦BŸ}h¦=k|¦…‹ŠX}‰¦N€ |¦BŸ}h¦=k|¦…‹Š<}‰¦N€ |¦BŸ}h¦=k|¦…‹Š }‰¦N€ |¦BŸ}h¦=k|¦…‹Š}‰¦N€ |¦BŸ}h¦=k|¦…‹‰è}‰¦N€ |¦BŸ}h¦=k|¦…‹‰Ì}‰¦N€ |¦BŸ}h¦=k|¦…‹‰°}‰¦N€ |¦BŸ}h¦=k|¦…‹‰”}‰¦N€ |¦BŸ}h¦=k|¦…‹‰x}‰¦N€ |¦BŸ}h¦=k|¦…‹‰\}‰¦N€ |¦BŸ}h¦=k|¦…‹‰@}‰¦N€ |¦BŸ}h¦=k|¦…‹‰$}‰¦N€ |¦BŸ}h¦=k|¦…‹‰}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆì}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆÐ}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆ´}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆ˜}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆ|}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆ`}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆD}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆ(}‰¦N€ |¦BŸ}h¦=k|¦…‹ˆ }‰¦N€ |¦BŸ}h¦=k|¦…‹‡ð}‰¦N€ |¦BŸ}h¦=k|¦…‹‡Ô}‰¦N€ |¦BŸ}h¦=k|¦…‹‡¸}‰¦N€ |¦BŸ}h¦=k|¦…‹‡œ}‰¦N€ |¦BŸ}h¦=k|¦…‹‡€}‰¦N€ |¦BŸ}h¦=k|¦…‹‡d}‰¦N€ |¦BŸ}h¦=k|¦…‹‡H}‰¦N€ |¦BŸ}h¦=k|¦…‹‡,}‰¦N€ |¦BŸ}h¦=k|¦…‹‡}‰¦N€ |¦BŸ}h¦=k|¦…‹†ô}‰¦N€ |¦BŸ}h¦=k|¦…‹†Ø}‰¦N€ |¦BŸ}h¦=k|¦…‹†¼}‰¦N€ |¦BŸ}h¦=k|¦…‹† }‰¦N€ |¦BŸ}h¦=k|¦…‹†„}‰¦N€ |¦BŸ}h¦=k|¦…‹†h}‰¦N€ __dyld_mod_term_funcs__dyld_make_delayed_module_initializer_callsThe kernel support for the dynamic linker is not present to run this program. %d input errors were found.%c %d input errors were found. =========== start of search =========== Starting on level %d, last kept clause of level %d is %d. %cStarting on level %d, last kept clause of level %d is %d. given clause #%ld: (wt=%d) %c%ld clauses have been given. reducing weight limit to %d. %cSearch stopped because sos empty. Search stopped because sos empty.max_givenmax_genmax_keptmax_secondsmax_levels??? %cSearch stopped by %s option. Search stopped by %s option. ----- Otter %s, %s ----- 3.3fAugust 2004The process was started by %s on %s, %sThe command was " %s%s". The process ID is %d. Atom: sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d .%d%s%d.%d]Refuted case The Assumption for case was not used;: s:therefore we skip case%s Process %d finished %s I tried to split, but I could not find a suitable clause. Splitting on clause Case splitting (fork) failed. Returning to search. That finishes the proof of the theorem.%c That finishes the proof of the theorem. Case (process %d): Assumption: case failure I tried to split, but I could not find a suitable atom. Splitting on atom always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch . Here are the clauses in Usable and SoS. It seems that no moreinferences or splitting can be done. If the search strategy iscomplete, these clauses should lead to a model of the input. list(usable). list(sos). ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause.cl_del_int, bad clause.checking clause, address:%p literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p -|$F# ERROR, clause contains variable literal: end_of_list ERROR, text after term: ERROR, input clause contains too many variables: ERROR, input clause contains Skolem symbol: ERROR, arrow not found in sequent: ERROR, input literal contains Skolem symbol: , -> .%dbinaryhyperneg_hyperurpara_intopara_fromfactorfactor_simpnew_demodback_demoddemodunit_dellinked_urevalgL-idgLcopyflipclausifyback_unit_delsplitsplit_negpropositional%d%d (heat=%d) [] | (list nil) end_of_list. forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.equalEQEqeq=$ANS$Ans$ans->WARNING, clause %d not found, proof is incomplete. find_random_cl, sos bad./dev/ttyrwinteraction failure: cannot find tty.interaction failure: cannot find tty. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %s%c Not an integer: "%s", try again. Turning off interactive_given mode. Turning off interactive_given mode. %c Clause %d not found. %c Clause %d not in sos. Ok, clause %d will be given. WARNING, CLOCK_START: clock %d already on. WARNING, CLOCK_STOP: clock %d already off. unit_del, too many variables introduced./dev/null%.12f %c********** ABNORMAL END ********** ********** %s ********** ABNORMAL END ********** includeERROR, bad argument to include: ERROR, cannot open file %s. ------- start included file %s------- ------- end included file %s------- setclearassignlistERROR, bad argument to list: usableaxiomsNOTICE: Please change 'axioms' to 'usable'. sosdemodulatorspassivehothintshints2mace_constraintsforeachName of axioms list is now 'usable'. ERROR, unknown list: formula_list -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, unknown formula_list: weight_listERROR, bad argument to Weight_list: purge_gen----> ERROR, already have purge weight list. pick_given----> ERROR, already have pick weight list. pick_and_purge----> ERROR, already have pick weight list or purge weight list. terms----> ERROR, already have term weight list. ERROR, unknown Weight_list: lexERROR, argument of lex term is not a list: lrpo_multiset_statusERROR, argument of lrpo_status term is not a list: lrpo_lr_status ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. skolemERROR, argument of skolem term is not a list: overbeek_termsERROR, argument of overbeek_terms is not a list: split_atomsERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: special_unaryERROR, argument of special_unary term is not a list: opfloat_formatERROR, float_format term must have one argument. make_evaluableERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: initial_proof_objectoverbeek_worldoverbeek_world: term errorsoverbeek_world: too many variablesERROR, command not found: ERROR, characters after term: ERROR, clause contains too many variables: list(sos). -f ERROR, input file %s not found. %% Reading file %s. -sERROR, missing sos (-s) argument. %% Reading sos clause from the command line. ERROR, bad demodulator: list(hints) and list(hints2) are incompatible. ------------> process usable: ------------> process sos: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. %2d:%-4d %2d:%-4d All others: %d. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld (hot clauses kept)%7ld ----------- times (seconds) ----------- user CPU time %10.2f (%ld hr, %ld min, %ld sec) system CPU time %10.2f wall-clock time %7ld (%ld hr, %ld min, %ld sec) input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f ============ end of search ============ list(demodulators). ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. sos_size=%d %c--- refuted case %c-- HEY %s, WE HAVE A PROOF!! -- %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d. ---------------- PROOF ---------------- %d, ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> $nil$consPassive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will beordered hyperresolution with the propositionaloptimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; thestrategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists willbe printed at the end of the search. This is a non-Horn set without equality. The strategy willbe ordered hyper_res, unit deletion, and factoring, withsatellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy willbe hyperresolution, with satellites in sos and nucleiin usable. This ia a non-Horn set with equality. The strategy will beKnuth-Bendix, ordered hyper_res, factoring, and unitdeletion, with positive clauses in sos and nonpositiveclauses in usable. There is a clause for symmetry of equality, so it is This is a Horn set with equality. The strategy will beKnuth-Bendix and hyper_res, with positive clauses insos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it isassumed that equality is fully axiomatized; therefore,paramodulation is disabled. Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty);therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set thepropositional flag and use ordered hyperresolution.Setting pick_given_ratio to 2, because all clauses are units.Setting hyper_res, because there are nonunits.Setting ur_res, because this is a nonunit set containingeither equality literals or non-Horn clauses.Clearing order_hyper, because all clauses are Horn.Setting factor and unit_deletion, because there are non-Horn clauses.Equality is present, so we set the knuth_bendix flag.As an incomplete heuristic, we paramodulate with units only.There is a clause for symmetry of equality, so it isgiven %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. %s%c The job finished %s Otter killed by SIGUSR1 signal. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. %cSearch stopped by SIGINT. Search stopped by SIGINT. Commands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Malformed term. helpfork%c Fork failed. Fork failed. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- statskill killed level %d search during interaction. killed level %d search during interaction. ok. continue ok.optionssymbols command not understood. Command not understood. ok. > --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- . %s Job %d %Fork failedXlog_%d>>>> Starting back demodulation with %d. %d back subsumes %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. after demodulation: keeping clause because it matches a hint. deleted because weight=%d. Subsumed by %d. Following clause subsumed by %d during input processing: ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) %cSearch stopped by max_proofs option. Search stopped by max_proofs option.CLAUSE %d %d -1 -2 build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there) ========== Jhash ==========%d: [%d] resolved: === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not found[] IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof =====Level %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ======================== end multijust ============build_tree_local, var and not more general. fpa index %p bucket %d and or *] new_sym_num: too many symbols requested.tp_alloc, request too big: %d Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (free_all_mem cleared). (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. ------------- memory usage ------------ %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu $Quantified$Hyps$Concs%c WARNING, multiple arity: %s/%d, %s/%d. $Connect$NUCLEUS$BOTH$LINK$SATELLITE$FSUB$BSUB$EQUIV%c WARNING, unrecognized $ symbol: %s. %d %s/%d, lex_val=%d mark_as_skolem, no symbol for %d.is_skolem, no symbol for %d.(nil)a ([]%s%s%s( %c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$T$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE<->&!=<><=>====/=@<@>@<=@>=+/mod'op command must have arity 3. ERROR: first argument of op command must be 1..999.xfxinfixxfyinfix_rightyfxinfix_leftfxprefixxfpostfixfyprefix_assocyfpostfix_assoc ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: third argument of op command must be a name or a list. ERROR: list in op command must be all names. ERROR, name too big, max is %d; ERROR, quoted name has no end; ***HERE*** adjusted term: ERROR, functor has no arguments: ERROR, comma or ) expected: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, unrecognized error in term: ERROR, term too big: allexists ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.ERROR, too many variables, max is %d: weightERROR, weight template: Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>integrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: bucket %d: bucket %d: containing terms: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: ur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).build_term, bad arity.ifis_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p geo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH.TRUEFALSE ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: ERROR, skolem gets: $c$fk WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.introduce_var, bad formula.renumber_unique, too many vars.renumber_unique, bad formula.bsub_hint_wtfsub_hint_wtequiv_hint_wtbsub_hint_add_wtfsub_hint_add_wtequiv_hint_add_wtlabelattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer: # %s(truefalse%fcldiff, bad PICK_DIFF %cWARNING, hint will not be used, because no weights have been set for it: %d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d] (hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bdNEW HINT: binary_reshyper_resneg_hyper_resur_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subback_subfree_all_memno_faplno_fanlprint_keptdemod_historyunit_deletionsort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_alldelete_identical_nested_skolempara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdiscard_commutativity_consequencesdegrade_hints2clocksfpa_literalsfpa_termsdemod_limitmax_weightneg_weightmax_memmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_max --------------- options --------------- set(clear(%s). assign(%s, %d). dependent: %s(%s). dependent: assign(%s, %d). ERROR: must have one simple argument. flag name not found. lex_rpo ERROR, flag `lex_rpo' has been changed to `lrpo'. print_level ERROR, flag `print_level' no longer exists. new_functions ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. WARNING: flag already set. flag already clear. must have two simple arguments. parameter name not found. reduce_weight_limit ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. integer must be in range [%d,%d]. already has that value. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatibleinsert_into_gen_tab, key already thereundefinedinputeq-axiominstantiateresolveparamodunknownv%d(%s(not (or (%d %d ( . v%d)(v%d . )) %d %d) print_proof_object_node, bad rule (%d) NIL) new_literal_index, bad mapmatch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewrites ABOUT TO ABEND!old demod: new demod: clause: translate_demod_unit: cannot rewritefinish_translating, bad rulefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: NULL postrans_2_pos: proof node not foundtrans_2_pos: clause not foundtrans_2_pos: empty clauselist(%s). %% Hints from process %d, %send_of_list.build_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is given ;; BEGINNING OF PROOF OBJECT;; END OF PROOF OBJECTERROR, dollar_contract, bad op_code: %d. integer divide by 0.float divide by 0.ERROR, dollar_contract, bad op_type: %d. demod term: --> result: demod<%d> WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. WARNING, demod_limit. >> back demodulating %d with %d. lex dependent demodulator: Flipping following input demodulator due to lrpo ordering: LRPO dependent demodulator: enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s "Returned string"enter user_test_term: %ld %f %d %s new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.evaluate_user_function, bad code. HOT NEW CLAUSE!: WARNING, instance of x=x cannot be inserted into demod_imd index: imd_delete, can't find alpha.imd_delete, can't find atom.contract_imd, increase MAX_AL_TERM_DEPTH.%p start of index-match-demodulate treev%d %s demod=NOTORparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)INPUTEQ-AXIOMparse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object overbeek_insert, bad termoverbeek_insert, bad weight in termThere is no Overbeek World to print! start of Overbeek_world %d: end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check!check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: constructing nodes for remaining lits:ERROR: constructing children told target here with already target setERROR ... non UNIT clause looks UNITcouldn't get context from clause couldn't get link_nodecouldn't get context nodeERROR: constructing children told target here and target not found hereFPA indexing not supported for linked res subsumable unitFPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c followsUD UD exiting linked_unit_del, not subsumedattempted to back up from a node with a child********entering Linked UR***********ERROR: unable to initialize linked UR inference tree********tree before BIG loop open lit %d nres %d attempting to find clash for term in clause first time = %c res_count = %d clashed against term: in clause ERROR: moved forward to %p first = FALSE did not attempt to resolve ... appears in ancestryERROR: found non_target back_up < 0ERROR: left_sibling chain to NULL***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d resolvent = -- FAIL --***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable()ERROR: forward failed, has first_child that's NOT tarERROR: forward failed with target child (has sibs)ERROR: couldn't get context for dummy nodeERROR: couldn't get link node for dummyERROR: couldn't get context for given nodecouldn't get given link_nodechecking is_in_ancestry on lit at %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: **<< -----start node at %p------ parent = %p prev_sibling = %p next_sibling = %p first_child = %p current_clause >> (NIL) <<first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d goal to resolve ... from literal from clause subst = %p subst->multiplier = %d tr = %p unif_position = %p -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tarNUC failed depth check TRASHEDNUC in on only tar TRASHEDlinked hyper not implemented yet.%c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. apply_substitute, term not COMPLEX.apply_substitute: term too deep.WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! 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|¦BŸ}h¦=k|¦…‹¨0}‰¦N€ |¦BŸ}h¦=k|¦…‹¨}‰¦N€ |¦BŸ}h¦=k|¦…‹§ø}‰¦N€ |¦BŸ}h¦=k|¦…‹§Ü}‰¦N€ |¦BŸ}h¦=k|¦…‹§À}‰¦N€ |¦BŸ}h¦=k|¦…‹§¤}‰¦N€ |¦BŸ}h¦=k|¦…‹§ˆ}‰¦N€ |¦BŸ}h¦=k|¦…‹§l}‰¦N€ |¦BŸ}h¦=k|¦…‹§P}‰¦N€ |¦BŸ}h¦=k|¦…‹§4}‰¦N€ |¦BŸ}h¦=k|¦…‹§}‰¦N€ |¦BŸ}h¦=k|¦…‹¦ü}‰¦N€ |¦BŸ}h¦=k|¦…‹¦à}‰¦N€ |¦BŸ}h¦=k|¦…‹¦Ä}‰¦N€ |¦BŸ}h¦=k|¦…‹¦¨}‰¦N€ |¦BŸ}h¦=k|¦…‹¦Œ}‰¦N€ |¦BŸ}h¦=k|¦…‹¦p}‰¦N€ |¦BŸ}h¦=k|¦…‹¦T}‰¦N€ |¦BŸ}h¦=k|¦…‹¦8}‰¦N€ |¦BŸ}h¦=k|¦…‹¦}‰¦N€ |¦BŸ}h¦=k|¦…‹¦}‰¦N€ |¦BŸ}h¦=k|¦…‹¥ä}‰¦N€ |¦BŸ}h¦=k|¦…‹¥È}‰¦N€ |¦BŸ}h¦=k|¦…‹¥¬}‰¦N€ |¦BŸ}h¦=k|¦…‹¥}‰¦N€ |¦BŸ}h¦=k|¦…‹¥t}‰¦N€ |¦BŸ}h¦=k|¦…‹¥X}‰¦N€ |¦BŸ}h¦=k|¦…‹¥<}‰¦N€ |¦BŸ}h¦=k|¦…‹¥ }‰¦N€ |¦BŸ}h¦=k|¦…‹¥}‰¦N€ |¦BŸ}h¦=k|¦…‹¤è}‰¦N€ |¦BŸ}h¦=k|¦…‹¤Ì}‰¦N€ |¦BŸ}h¦=k|¦…‹¤°}‰¦N€ |¦BŸ}h¦=k|¦…‹¤”}‰¦N€ |¦BŸ}h¦=k|¦…‹¤x}‰¦N€ |¦BŸ}h¦=k|¦…‹¤\}‰¦N€ |¦BŸ}h¦=k|¦…‹¤@}‰¦N€ |¦BŸ}h¦=k|¦…‹¤$}‰¦N€ |¦BŸ}h¦=k|¦…‹¤}‰¦N€ __dyld_mod_term_funcs__dyld_make_delayed_module_initializer_callsThe kernel support for the dynamic linker is not present to run this program. ----- MACE %s, %s ----- 2.2fAugust 2004The process was started by %s on %s, %sThe command was " %s%s".MACE %s -- Search for finite models. Input clauses are taken from standard input. Command-line options: -n n : Search for model of size n (default %d). -N n : Iterate up to size n (default: don't iterate). -c : Assume constants are distinct (up to domain size). -z n : Apply isomorphism constraints to first n constants (default %d). Overridden by -c. -p : Print models in human format as they are found. -P : Print models in portable format as they are found. -I : Print models in IVY format as they are found. -m n : Stop when the n-th model is found (default %d). -t n : Stop after about n seconds. -k n : Dynamically allocate at most n Kbytes (default %d). -s : Perform unit subsumption. (Always done on input.) -C : Split on clauses instead of on atoms. -r : Record and print the order of assignments. -x : Quasigroup constraint. -y : Iso experiment (implies -C and -z0). -v n : Try to part flattened clauses with n or more variables (default %d). -h : Print this message. Examples of constraints given in input: list(mace_constraints). assign(a, 3). assign(f(2,3), 1). assign(P(0), F). assign(P(1), T). property(r(_,_), equality). property(lt(_,_), order). property(f(_,_), quasigroup). property(g(_), bijection). end_of_list. distinct_constantssubsumeprint_modelsprint_models_portableprint_models_ivyqg_constraintiso_xclause_splitiso_constantsrecord_assignmentsmax_modelsmax_secondsmax_memDomain size must be > 0. Domain size must be <= %d. Maximum domain size must be > 0. Maximum domain size must be <= %d. part_varsspPIhcxyCrm:t:k:n:N:d:z:v: +----------------------------------------------------------+ | SEGMENTATION FAULT!! This is probably caused by a bug | | in MACE. Please send copy of the input file to | | otter@mcs.anl.gov, let us know what version of MACE you | | are using, and send any other info that might be useful. | +----------------------------------------------------------+ %s%cMACE_sig_handler, cannot handle signal %d. WARNING, MACE_CLOCK_STOP: clock %d not running. WARNING, MACE_CLOCK_STOP: clock %d not running. list(flattened_and_parted_clauses). --- Starting search for models of size %d --- in MACE_tp_alloc, request too big.in MACE_tp_alloc, operating system cannot supply any more memory. --------------- options --------------- set(clear(%s). assign(%s, %d). setclear dependent: %s(%s). dependent: assign(%s, %d). ERROR: flag `%s' not found. WARNING: flag `%s' already set. flag `%s' already clear. ERROR: parameter `%s' not found. ERROR: assign(%s, %d), integer must be in range [%d,%d]. WARNING: assign(%s, %d), already has that value. Called MACE_check_options. ------------- memory usage ------------ Memory dynamically allocated (MACE_tp_alloc): %d. ----- statistics for domain size %d ---- Input: Clauses input %7ld Literal occurrences input %7ld Greatest atom %7ld Unit preprocess: Preprocess unit assignments %7ld Clauses after subsumption %7ld Literal occ. after subsump. %7ld Selectable clauses %7ld Decide: Splits %7ld Unit assignments %7ld Failed paths %7ld Memory: Memory malloced %7ld K Memory MACE_tp_alloced %7d K Time (seconds): Generate ground clauses %10.2f DPLL %10.2f ======================================= Total times for run (seconds): user CPU time %10.2f (%ld hr, %ld min, %ld sec) system CPU time %10.2f wall-clock time %7ld Abnormal end.Exit by max_seconds parameter.Exit by max_mem parameter.Exit by max_models parameter.The search is complete.Killed by SIGINT signal.Killed by SIGSEGV signal.Input error.Exit with unknown code. Input error. See the output file. The set is satisfiable (%d model(s) found).No models were found. %s %s  %s %s The job finished %s ********** ABNORMAL END ********** ********** %s answer literals not allowed in MACE inputevaluable literals not allowed in MACE inputequal=dp_trans, too many variables%% WARNING: possible error in check_transformed_clause: %% original: %% transformed: unit_enqueue: queue too small( -%d %d ) active_neg=%d, active_pos=%d, subsumer=%d ), active=%d Atom=%d, value=%d, pos_occ=%x, neg_occ=.%dPropositional input must be all integers; if you have first-order input, the domain size must be given (-n). Selectable clauses:HERE it is!!atom_value, atom out of rangeatom_value, bad value Initial assigments: Order of assigments for the following model:: Model #%d: %dend_of_modelstth The %d%s model has been found. assign: atom already assignedunassign: atom not assigned After all unit preprocessing, %ld atoms are still unassigned; %ld clauses remain; %ld of those are non-Horn (selectable); %ld K allocated; cpu time so far for this domain size: %.2f sec. declare_symbol_sorted, too many symbols%sdeclare_symbol_sorted: sort not found- %s%s %s%s(%s%s%sv%d) ,*** Unsatisfiability detected ***add_unit: element out of domainadd_unit: sign must be 1 or -1well_defined, bad arityclosed, bad arityprocess_variables, variable too big.process_variables, badly sorted clausefadd_clauses_for_qg_constraint, symbol f not foundAdding basic QG constraints on last column of f. The bad element is %d. number_variables, element out of range Maximum number of variables is %d. number_variables, too many variablestrans_relational_clause: too many first_order clausestrans_relational_clause: bad DP argtrans_relational_clause: bad DP arg (right)trans_relational_clause: bad eq argBad name=%s trans_relational_clause, bad functorRemoving answer literals from clause %d. WARNING, CLOCK_START: clock %d already on. list(clauses).WARNING, CLOCK_STOP: clock %d already off. MACE_collect_symbols, multiple arityarity too greatuniv<Applying isomorphism constraints to constants: %sdp_trans, wrong arity in mace_constraints list.dp_trans, symbol in mace_constraints list not foundpropertyequalityorderquasigroupbijectioncommutativedp_trans, mace_constrationts property not understoodassigndp_trans, mace_constraints command not understoodBad name=%s, dp_trans, bad functordp_trans, bad integer (RHS) in assignmentTFdp_trans, bad truth value in assignmentdp_trans, bad integer (LHS) in assignmentAdding unit assigning %s%sCannot make constant %s distinct, domain is too small. Adding unit assigning %s %d (distinct_constants). order relation must have args of same typeequality relation must have args of same typefunction %s bijection. function %s quasigroup. %d clauses were generated; %d of those survived the first stage of unit preprocessing; there are %d atoms. %s: %d %2d--%3d--- %s : --- - - | --+%5d |? %s: %s %2s ======================= Model #%d at %.2f seconds: Dimension %d table for %s not printed $Connectend_of_model function(%s, [%d]) function(%s(_), [, ]) function(%s(_,_), [ %d, %d, %d ])%d, 10 predicate(%s, [%s]) predicate(%s(_), [ predicate(%s(_,_), [ %s, %s, %s ]) predicate(%s(_,_,_), [ %s, predicate(%s(_,_,_,_), [ interpretation( %d, [ , Dimension %d table for %s not printed ]). ((%s . 0) . ((nil . %d))) ((%s . 1) . ( ((%d) . %d) )) ((%s . 2) . ( ((%d %d) . %d) ((%s . 3) . ( ((%d %d %d) . %d) tnil ((%s . 0) . ((nil . %s))) ((%d) . %s) ((%d %d) . %s) ((%d %d %d) . %s) ((%s . 4) . ( ((%d %d %d %d) . %s) ;; BEGINNING OF IVY MODEL (0 . ((. %d) . ( ( print_model_ivy, max relation arity is 4 ) . ( print_model_ivy, max function arity is 3 ) ) ) ;; END OF IVY MODEL v%d SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. The job finished %s Otter killed by SIGUSR1 signal. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. ??? %cSearch stopped by SIGINT. Search stopped by SIGINT. /dev/ttyrwCommands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. interaction failure: cannot find tty.interaction failure: cannot find tty. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Malformed term. helpfork%c Fork failed. Fork failed. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- statskill killed level %d search during interaction. killed level %d search during interaction. ok. continue ok.sosusabledemodulatorspassiveoptionssymbols command not understood. Command not understood. ok. > --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- end_of_list. %s Job %d %Fork failedXlog_%d/dev/null%.12f %c********** ABNORMAL END ********** ********** ABNORMAL END ********** includeERROR, bad argument to include: ERROR, cannot open file %s. ------- start included file %s------- ------- end included file %s------- listERROR, bad argument to list: axiomsNOTICE: Please change 'axioms' to 'usable'. hothintshints2mace_constraintsforeachName of axioms list is now 'usable'. ERROR, unknown list: formula_list -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, unknown formula_list: weight_listERROR, bad argument to Weight_list: purge_gen----> ERROR, already have purge weight list. pick_given----> ERROR, already have pick weight list. pick_and_purge----> ERROR, already have pick weight list or purge weight list. terms----> ERROR, already have term weight list. ERROR, unknown Weight_list: lexERROR, argument of lex term is not a list: lrpo_multiset_statusERROR, argument of lrpo_status term is not a list: lrpo_lr_status ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. skolemERROR, argument of skolem term is not a list: overbeek_termsERROR, argument of overbeek_terms is not a list: split_atomsERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: special_unaryERROR, argument of special_unary term is not a list: opfloat_formatERROR, float_format term must have one argument. make_evaluableERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: initial_proof_objectoverbeek_worldoverbeek_world: term errorsoverbeek_world: too many variablesend_of_list. ERROR, command not found: ERROR, characters after term: ERROR, clause contains too many variables: ERROR, input clause contains Skolem symbol: . list(sos). -f ERROR, input file %s not found. %% Reading file %s. -sERROR, missing sos (-s) argument. %% Reading sos clause from the command line. ERROR, bad demodulator: list(hints) and list(hints2) are incompatible. ------------> process usable: ------------> process sos: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. %2d:%-4d %2d:%-4d All others: %d. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld (hot clauses kept)%7ld ----------- times (seconds) ----------- user CPU time %10.2f (%ld hr, %ld min, %ld sec) system CPU time %10.2f wall-clock time %7ld (%ld hr, %ld min, %ld sec) input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f ============ end of search ============ list(usable). list(sos). list(demodulators). That finishes the proof of the theorem. Process %d finished %s ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. sos_size=%d %c--- refuted case %c-- HEY %s, WE HAVE A PROOF!! -- %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d. ---------------- PROOF ---------------- %d, ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> $nil$consPassive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will beordered hyperresolution with the propositionaloptimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; thestrategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists willbe printed at the end of the search. This is a non-Horn set without equality. The strategy willbe ordered hyper_res, unit deletion, and factoring, withsatellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy willbe hyperresolution, with satellites in sos and nucleiin usable. This ia a non-Horn set with equality. The strategy will beKnuth-Bendix, ordered hyper_res, factoring, and unitdeletion, with positive clauses in sos and nonpositiveclauses in usable. There is a clause for symmetry of equality, so it is This is a Horn set with equality. The strategy will beKnuth-Bendix and hyper_res, with positive clauses insos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it isassumed that equality is fully axiomatized; therefore,paramodulation is disabled. Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty);therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set thepropositional flag and use ordered hyperresolution.Setting pick_given_ratio to 2, because all clauses are units.Setting hyper_res, because there are nonunits.Setting ur_res, because this is a nonunit set containingeither equality literals or non-Horn clauses.Clearing order_hyper, because all clauses are Horn.Setting factor and unit_deletion, because there are non-Horn clauses.Equality is present, so we set the knuth_bendix flag.As an incomplete heuristic, we paramodulate with units only.There is a clause for symmetry of equality, so it isgiven %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause.cl_del_int, bad clause.checking clause, address:%p literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p |$F# ERROR, clause contains variable literal: ERROR, text after term: ERROR, input clause contains too many variables: ERROR, arrow not found in sequent: ERROR, input literal contains Skolem symbol: -> .%dbinaryhyperneg_hyperurpara_intopara_fromfactorfactor_simpnew_demodback_demoddemodunit_dellinked_urevalgL-idgLcopyflipclausifyback_unit_delsplitsplit_negpropositional(heat=%d) [] | (list nil) forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.EQEqeq$ANS$Ans$ans->WARNING, clause %d not found, proof is incomplete. find_random_cl, sos bad. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %c Not an integer: "%s", try again. Turning off interactive_given mode. Turning off interactive_given mode. %c Clause %d not found. %c Clause %d not in sos. Ok, clause %d will be given. unit_del, too many variables introduced.tp_alloc, request too big: %d Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (free_all_mem cleared). (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu $Quantified$Hyps$Concs%c WARNING, multiple arity: %s/%d, %s/%d. $NUCLEUS$BOTH$LINK$SATELLITE$FSUB$BSUB$EQUIV%c WARNING, unrecognized $ symbol: %s. %d %s/%d, lex_val=%d mark_as_skolem, no symbol for %d.is_skolem, no symbol for %d.(nil)a ([]( %c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$T$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE<->&!=><=>====/=@<@>@<=@>=+*/mod'op command must have arity 3. ERROR: first argument of op command must be 1..999.xfxinfixxfyinfix_rightyfxinfix_leftfxprefixxfpostfixfyprefix_assocyfpostfix_assoc ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: third argument of op command must be a name or a list. ERROR: list in op command must be all names. ERROR, name too big, max is %d; ERROR, quoted name has no end; ***HERE*** adjusted term: ERROR, functor has no arguments: ERROR, comma or ) expected: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, unrecognized error in term: ERROR, term too big: allexists ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>CLAUSE %d -1 -2 build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there ========== Jhash ==========%d: [%d] resolved: === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not found[] IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof =====Level %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ======================== end multijust ============%d%sbinary_reshyper_resneg_hyper_resur_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subback_subfree_all_memno_faplno_fanlprint_keptdemod_historyunit_deletionsort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_alldelete_identical_nested_skolempara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdiscard_commutativity_consequencesdegrade_hints2clocksfpa_literalsfpa_termsdemod_limitmax_weightmax_givenmax_levelsneg_weightmax_keptmax_genmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastfsub_hint_add_wtbsub_hint_add_wtequiv_hint_add_wtfsub_hint_wtbsub_hint_wtequiv_hint_wtverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_maxERROR: must have one simple argument. flag name not found. lex_rpo ERROR, flag `lex_rpo' has been changed to `lrpo'. print_level ERROR, flag `print_level' no longer exists. new_functions ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. flag already set. flag already clear. must have two simple arguments. parameter name not found. reduce_weight_limit ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatibleintegrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: bucket %d: bucket %d: containing terms: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: %cWARNING, hint will not be used, because no weights have been set for it: %d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d] (hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bdNEW HINT: build_tree_local, var and not more general. fpa index %p bucket %d and or ] new_sym_num: too many symbols requested.insert_into_gen_tab, key already thereundefinedinputeq-axiominstantiateresolveparamodunknown(%s(not false(or true(%d %d ( . v%d)(v%d . )) %d %d) print_proof_object_node, bad rule (%d) NIL) new_literal_index, bad mapmatch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewrites ABOUT TO ABEND!old demod: new demod: clause: translate_demod_unit: cannot rewritefinish_translating, bad rulefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: NULL postrans_2_pos: proof node not foundtrans_2_pos: clause not foundtrans_2_pos: empty clauselist(%s). %% Hints from process %d, %send_of_list.build_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is given ;; BEGINNING OF PROOF OBJECT;; END OF PROOF OBJECTERROR, dollar_contract, bad op_code: %d. integer divide by 0.float divide by 0.ERROR, dollar_contract, bad op_type: %d. demod term: --> result: demod<%d> WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. WARNING, demod_limit. >> back demodulating %d with %d. lex dependent demodulator: Flipping following input demodulator due to lrpo ordering: LRPO dependent demodulator: TRUEFALSE ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: ERROR, skolem gets: $c$fk WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.introduce_var, bad formula.renumber_unique, too many vars.renumber_unique, bad formula.Atom: sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d %d.%d]Refuted case The Assumption for case was not used;s:therefore we skip case%s I tried to split, but I could not find a suitable clause. Splitting on clause Case splitting (fork) failed. Returning to search.%c That finishes the proof of the theorem. Case (process %d): Assumption: case failure I tried to split, but I could not find a suitable atom. Splitting on atom always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch Here are the clauses in Usable and SoS. It seems that no moreinferences or splitting can be done. If the search strategy iscomplete, these clauses should lead to a model of the input.enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s "Returned string"enter user_test_term: %ld %f %d %s new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.evaluate_user_function, bad code. HOT NEW CLAUSE!: WARNING, instance of x=x cannot be inserted into demod_imd index: imd_delete, can't find alpha.imd_delete, can't find atom.contract_imd, increase MAX_AL_TERM_DEPTH.%p start of index-match-demodulate treev%d %s demod=labelattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer: # %s(%fNOTORparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)INPUTEQ-AXIOMparse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object overbeek_insert, bad termoverbeek_insert, bad weight in termThere is no Overbeek World to print! start of Overbeek_world %d: end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check!check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: >>>> Starting back demodulation with %d. %d back subsumes %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. after demodulation: keeping clause because it matches a hint. deleted because weight=%d. Subsumed by %d. Following clause subsumed by %d during input processing: ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) %cSearch stopped by max_proofs option. Search stopped by max_proofs option.constructing nodes for remaining lits:ERROR: constructing children told target here with already target setERROR ... non UNIT clause looks UNITcouldn't get context from clause couldn't get link_nodecouldn't get context nodeERROR: constructing children told target here and target not found hereFPA indexing not supported for linked res subsumable unitFPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c followsUD UD exiting linked_unit_del, not subsumedattempted to back up from a node with a child********entering Linked UR***********ERROR: unable to initialize linked UR inference tree********tree before BIG loop open lit %d nres %d attempting to find clash for term in clause first time = %c res_count = %d clashed against term: in clause ERROR: moved forward to %p first = FALSE did not attempt to resolve ... appears in ancestryERROR: found non_target back_up < 0ERROR: left_sibling chain to NULL***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d resolvent = -- FAIL --***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable()ERROR: forward failed, has first_child that's NOT tarERROR: forward failed with target child (has sibs)ERROR: couldn't get context for dummy nodeERROR: couldn't get link node for dummyERROR: couldn't get context for given nodecouldn't get given link_nodechecking is_in_ancestry on lit at %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: **<< -----start node at %p------ parent = %p prev_sibling = %p next_sibling = %p first_child = %p current_clause >> (NIL) <<first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d goal to resolve ... from literal from clause subst = %p subst->multiplier = %d tr = %p unif_position = %p -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tarNUC failed depth check TRASHEDNUC in on only tar TRASHEDERROR, too many variables, max is %d: weightERROR, weight template: ur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).build_term, bad arity.ifis_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p geo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH.cldiff, bad PICK_DIFF%c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! 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|¦BŸ}h¦=k|¦…‹¢}‰¦N€ |¦BŸ}h¦=k|¦…‹¡ø}‰¦N€ |¦BŸ}h¦=k|¦…‹¡Ü}‰¦N€ |¦BŸ}h¦=k|¦…‹¡À}‰¦N€ |¦BŸ}h¦=k|¦…‹¡¤}‰¦N€ |¦BŸ}h¦=k|¦…‹¡ˆ}‰¦N€ |¦BŸ}h¦=k|¦…‹¡l}‰¦N€ |¦BŸ}h¦=k|¦…‹¡P}‰¦N€ |¦BŸ}h¦=k|¦…‹¡4}‰¦N€ |¦BŸ}h¦=k|¦…‹¡}‰¦N€ |¦BŸ}h¦=k|¦…‹ ü}‰¦N€ |¦BŸ}h¦=k|¦…‹ à}‰¦N€ |¦BŸ}h¦=k|¦…‹ Ä}‰¦N€ |¦BŸ}h¦=k|¦…‹ ¨}‰¦N€ |¦BŸ}h¦=k|¦…‹ Œ}‰¦N€ |¦BŸ}h¦=k|¦…‹ p}‰¦N€ |¦BŸ}h¦=k|¦…‹ T}‰¦N€ |¦BŸ}h¦=k|¦…‹ 8}‰¦N€ |¦BŸ}h¦=k|¦…‹ }‰¦N€ |¦BŸ}h¦=k|¦…‹ }‰¦N€ |¦BŸ}h¦=k|¦…‹Ÿä}‰¦N€ |¦BŸ}h¦=k|¦…‹ŸÈ}‰¦N€ |¦BŸ}h¦=k|¦…‹Ÿ¬}‰¦N€ |¦BŸ}h¦=k|¦…‹Ÿ}‰¦N€ |¦BŸ}h¦=k|¦…‹Ÿt}‰¦N€ __dyld_mod_term_funcs__dyld_make_delayed_module_initializer_callsThe kernel support for the dynamic linker is not present to run this program. ----- ANLDP %s, %s ----- 2.2August 2003The process was started by %s on %s, %sThe command was " %s%s". ANLDP %s -- Search for finite models. Input clauses are taken from standard input. command-line options: -p | Print all models as they are found. -m n | Stop when the n-th model is found. -t n | Stop after n seconds. -k n | Tp_allocate at most n K bytes. -s | Perform unit subsumption. (Always done on input.) -h | Print this message.subsumeprint_modelsmax_modelsmax_secondsmax_memspPIhcm:t:k:n:d:x: +----------------------------------------------------------+ | SEGMENTATION FAULT!! This is probably caused by a bug | | in MACE. Please send copy of the input file to | | otter@mcs.anl.gov, let us know what version of MACE you | | are using, and send any other info that might be useful. | +----------------------------------------------------------+ %sMACE_sig_handler, cannot handle signal %d. WARNING, MACE_CLOCK_STOP: clock %d not running. WARNING, MACE_CLOCK_STOP: clock %d not running. in MACE_tp_alloc, request too big.in MACE_tp_alloc, operating system cannot supply any more memory.print_models_portableprint_models_ivydistinct_constantsqg_constraintrecord_assignmentsclause_splitiso_xiso_constantspart_vars --------------- options --------------- set(clear(%s). assign(%s, %d). setclear dependent: %s(%s). dependent: assign(%s, %d). ERROR: flag `%s' not found. WARNING: flag `%s' already set. flag `%s' already clear. ERROR: parameter `%s' not found. ERROR: assign(%s, %d), integer must be in range [%d,%d]. WARNING: assign(%s, %d), already has that value. Called MACE_check_options. ------------- memory usage ------------ Memory dynamically allocated (MACE_tp_alloc): %d. ----- statistics for domain size %d ---- Input: Clauses input %7ld Literal occurrences input %7ld Greatest atom %7ld Unit preprocess: Preprocess unit assignments %7ld Clauses after subsumption %7ld Literal occ. after subsump. %7ld Selectable clauses %7ld Decide: Splits %7ld Unit assignments %7ld Failed paths %7ld Memory: Memory malloced %7ld K Memory MACE_tp_alloced %7d K Time (seconds): Generate ground clauses %10.2f DPLL %10.2f ======================================= Total times for run (seconds): user CPU time %10.2f (%ld hr, %ld min, %ld sec) system CPU time %10.2f wall-clock time %7ld Abnormal end.Exit by max_seconds parameter.Exit by max_mem parameter.Exit by max_models parameter.The search is complete.Killed by SIGINT signal.Killed by SIGSEGV signal.Input error.Exit with unknown code. Input error. See the output file. The set is satisfiable (%d model(s) found).No models were found. %s %s  %s %s The job finished %s ********** ABNORMAL END ********** ********** %s answer literals not allowed in MACE inputevaluable literals not allowed in MACE inputequal=dp_trans, too many variables%% WARNING: possible error in check_transformed_clause: %% original: %% transformed: unit_enqueue: queue too small( -%d %d ) active_neg=%d, active_pos=%d, subsumer=%d ), active=%d Atom=%d, value=%d, pos_occ=%x, neg_occ=.%dPropositional input must be all integers; if you have first-order input, the domain size must be given (-n). Selectable clauses:HERE it is!!atom_value, atom out of rangeatom_value, bad value Initial assigments: Order of assigments for the following model:: Model #%d: %dend_of_modelstth The %d%s model has been found. assign: atom already assignedunassign: atom not assigned After all unit preprocessing, %ld atoms are still unassigned; %ld clauses remain; %ld of those are non-Horn (selectable); %ld K allocated; cpu time so far for this domain size: %.2f sec. declare_symbol_sorted, too many symbols%sdeclare_symbol_sorted: sort not found- %s%s %s%s(%s%s%sv%d) ,*** Unsatisfiability detected ***add_unit: element out of domainadd_unit: sign must be 1 or -1well_defined, bad arityclosed, bad arityprocess_variables, variable too big.process_variables, badly sorted clausefadd_clauses_for_qg_constraint, symbol f not foundAdding basic QG constraints on last column of f. The bad element is %d. number_variables, element out of range Maximum number of variables is %d. number_variables, too many variablestrans_relational_clause: too many first_order clausestrans_relational_clause: bad DP argtrans_relational_clause: bad DP arg (right)trans_relational_clause: bad eq argBad name=%s trans_relational_clause, bad functorRemoving answer literals from clause %d. WARNING, CLOCK_START: clock %d already on. list(clauses).WARNING, CLOCK_STOP: clock %d already off. MACE_collect_symbols, multiple arityarity too greatuniv<Applying isomorphism constraints to constants: %sdp_trans, wrong arity in mace_constraints list.dp_trans, symbol in mace_constraints list not foundpropertyequalityorderquasigroupbijectioncommutativedp_trans, mace_constrationts property not understoodassigndp_trans, mace_constraints command not understoodBad name=%s, dp_trans, bad functordp_trans, bad integer (RHS) in assignmentTFdp_trans, bad truth value in assignmentdp_trans, bad integer (LHS) in assignmentAdding unit assigning %s%sCannot make constant %s distinct, domain is too small. Adding unit assigning %s %d (distinct_constants). order relation must have args of same typeequality relation must have args of same typefunction %s bijection. function %s quasigroup. %d clauses were generated; %d of those survived the first stage of unit preprocessing; there are %d atoms. %s: %d %2d--%3d--- %s : --- - - | --+%5d |? %s: %s %2s ======================= Model #%d at %.2f seconds: Dimension %d table for %s not printed $Connectend_of_model function(%s, [%d]) function(%s(_), [, ]) function(%s(_,_), [ %d, %d, %d ])%d, 10 predicate(%s, [%s]) predicate(%s(_), [ predicate(%s(_,_), [ %s, %s, %s ]) predicate(%s(_,_,_), [ %s, predicate(%s(_,_,_,_), [ interpretation( %d, [ , Dimension %d table for %s not printed ]). ((%s . 0) . ((nil . %d))) ((%s . 1) . ( ((%d) . %d) )) ((%s . 2) . ( ((%d %d) . %d) ((%s . 3) . ( ((%d %d %d) . %d) tnil ((%s . 0) . ((nil . %s))) ((%d) . %s) ((%d %d) . %s) ((%d %d %d) . %s) ((%s . 4) . ( ((%d %d %d %d) . %s) ;; BEGINNING OF IVY MODEL (0 . ((. %d) . ( ( print_model_ivy, max relation arity is 4 ) . ( print_model_ivy, max function arity is 3 ) ) ) ;; END OF IVY MODEL v%d SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. %s%c The job finished %s Otter killed by SIGUSR1 signal. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. ??? %cSearch stopped by SIGINT. Search stopped by SIGINT. /dev/ttyrwCommands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. interaction failure: cannot find tty.interaction failure: cannot find tty. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Malformed term. helpfork%c Fork failed. Fork failed. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- statskill killed level %d search during interaction. killed level %d search during interaction. ok. continue ok.sosusabledemodulatorspassiveoptionssymbols command not understood. Command not understood. ok. > --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- end_of_list. %s Job %d %Fork failedXlog_%d/dev/null%.12f %c********** ABNORMAL END ********** ********** ABNORMAL END ********** includeERROR, bad argument to include: ERROR, cannot open file %s. ------- start included file %s------- ------- end included file %s------- listERROR, bad argument to list: axiomsNOTICE: Please change 'axioms' to 'usable'. hothintshints2mace_constraintsforeachName of axioms list is now 'usable'. ERROR, unknown list: formula_list -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, unknown formula_list: weight_listERROR, bad argument to Weight_list: purge_gen----> ERROR, already have purge weight list. pick_given----> ERROR, already have pick weight list. pick_and_purge----> ERROR, already have pick weight list or purge weight list. terms----> ERROR, already have term weight list. ERROR, unknown Weight_list: lexERROR, argument of lex term is not a list: lrpo_multiset_statusERROR, argument of lrpo_status term is not a list: lrpo_lr_status ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. skolemERROR, argument of skolem term is not a list: overbeek_termsERROR, argument of overbeek_terms is not a list: split_atomsERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: special_unaryERROR, argument of special_unary term is not a list: opfloat_formatERROR, float_format term must have one argument. make_evaluableERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: initial_proof_objectoverbeek_worldoverbeek_world: term errorsoverbeek_world: too many variablesend_of_list. ERROR, command not found: ERROR, characters after term: ERROR, clause contains too many variables: ERROR, input clause contains Skolem symbol: . list(sos). -f ERROR, input file %s not found. %% Reading file %s. -sERROR, missing sos (-s) argument. %% Reading sos clause from the command line. ERROR, bad demodulator: list(hints) and list(hints2) are incompatible. ------------> process usable: ------------> process sos: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. %2d:%-4d %2d:%-4d All others: %d. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld (hot clauses kept)%7ld ----------- times (seconds) ----------- user CPU time %10.2f (%ld hr, %ld min, %ld sec) system CPU time %10.2f wall-clock time %7ld (%ld hr, %ld min, %ld sec) input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f ============ end of search ============ list(usable). list(sos). list(demodulators). That finishes the proof of the theorem. Process %d finished %s ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. sos_size=%d %c--- refuted case %c-- HEY %s, WE HAVE A PROOF!! -- %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d. ---------------- PROOF ---------------- %d, ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> $nil$consPassive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will beordered hyperresolution with the propositionaloptimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; thestrategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists willbe printed at the end of the search. This is a non-Horn set without equality. The strategy willbe ordered hyper_res, unit deletion, and factoring, withsatellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy willbe hyperresolution, with satellites in sos and nucleiin usable. This ia a non-Horn set with equality. The strategy will beKnuth-Bendix, ordered hyper_res, factoring, and unitdeletion, with positive clauses in sos and nonpositiveclauses in usable. There is a clause for symmetry of equality, so it is This is a Horn set with equality. The strategy will beKnuth-Bendix and hyper_res, with positive clauses insos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it isassumed that equality is fully axiomatized; therefore,paramodulation is disabled. Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty);therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set thepropositional flag and use ordered hyperresolution.Setting pick_given_ratio to 2, because all clauses are units.Setting hyper_res, because there are nonunits.Setting ur_res, because this is a nonunit set containingeither equality literals or non-Horn clauses.Clearing order_hyper, because all clauses are Horn.Setting factor and unit_deletion, because there are non-Horn clauses.Equality is present, so we set the knuth_bendix flag.As an incomplete heuristic, we paramodulate with units only.There is a clause for symmetry of equality, so it isgiven %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause.cl_del_int, bad clause.checking clause, address:%p literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p |$F# ERROR, clause contains variable literal: ERROR, text after term: ERROR, input clause contains too many variables: ERROR, arrow not found in sequent: ERROR, input literal contains Skolem symbol: -> .%dbinaryhyperneg_hyperurpara_intopara_fromfactorfactor_simpnew_demodback_demoddemodunit_dellinked_urevalgL-idgLcopyflipclausifyback_unit_delsplitsplit_negpropositional(heat=%d) [] | (list nil) forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.EQEqeq$ANS$Ans$ans->WARNING, clause %d not found, proof is incomplete. find_random_cl, sos bad. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %c Not an integer: "%s", try again. Turning off interactive_given mode. Turning off interactive_given mode. %c Clause %d not found. %c Clause %d not in sos. Ok, clause %d will be given. unit_del, too many variables introduced.tp_alloc, request too big: %d Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (free_all_mem cleared). (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu $Quantified$Hyps$Concs%c WARNING, multiple arity: %s/%d, %s/%d. $NUCLEUS$BOTH$LINK$SATELLITE$FSUB$BSUB$EQUIV%c WARNING, unrecognized $ symbol: %s. %d %s/%d, lex_val=%d mark_as_skolem, no symbol for %d.is_skolem, no symbol for %d.(nil)a ([]( %c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$T$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE<->&!=><=>====/=@<@>@<=@>=+*/mod'op command must have arity 3. ERROR: first argument of op command must be 1..999.xfxinfixxfyinfix_rightyfxinfix_leftfxprefixxfpostfixfyprefix_assocyfpostfix_assoc ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: third argument of op command must be a name or a list. ERROR: list in op command must be all names. ERROR, name too big, max is %d; ERROR, quoted name has no end; ***HERE*** adjusted term: ERROR, functor has no arguments: ERROR, comma or ) expected: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, unrecognized error in term: ERROR, term too big: allexists ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>CLAUSE %d -1 -2 build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there ========== Jhash ==========%d: [%d] resolved: === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not found[] IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof =====Level %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ======================== end multijust ============%d%sbinary_reshyper_resneg_hyper_resur_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subback_subfree_all_memno_faplno_fanlprint_keptdemod_historyunit_deletionsort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_alldelete_identical_nested_skolempara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdiscard_commutativity_consequencesdegrade_hints2clocksfpa_literalsfpa_termsdemod_limitmax_weightmax_givenmax_levelsneg_weightmax_keptmax_genmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastfsub_hint_add_wtbsub_hint_add_wtequiv_hint_add_wtfsub_hint_wtbsub_hint_wtequiv_hint_wtverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_maxERROR: must have one simple argument. flag name not found. lex_rpo ERROR, flag `lex_rpo' has been changed to `lrpo'. print_level ERROR, flag `print_level' no longer exists. new_functions ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. flag already set. flag already clear. must have two simple arguments. parameter name not found. reduce_weight_limit ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatibleintegrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: bucket %d: bucket %d: containing terms: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: %cWARNING, hint will not be used, because no weights have been set for it: %d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d] (hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bdNEW HINT: build_tree_local, var and not more general. fpa index %p bucket %d and or ] new_sym_num: too many symbols requested.insert_into_gen_tab, key already thereundefinedinputeq-axiominstantiateresolveparamodunknown(%s(not false(or true(%d %d ( . v%d)(v%d . )) %d %d) print_proof_object_node, bad rule (%d) NIL) new_literal_index, bad mapmatch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewrites ABOUT TO ABEND!old demod: new demod: clause: translate_demod_unit: cannot rewritefinish_translating, bad rulefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: NULL postrans_2_pos: proof node not foundtrans_2_pos: clause not foundtrans_2_pos: empty clauselist(%s). %% Hints from process %d, %send_of_list.build_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is given ;; BEGINNING OF PROOF OBJECT;; END OF PROOF OBJECTERROR, dollar_contract, bad op_code: %d. integer divide by 0.float divide by 0.ERROR, dollar_contract, bad op_type: %d. demod term: --> result: demod<%d> WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. WARNING, demod_limit. >> back demodulating %d with %d. lex dependent demodulator: Flipping following input demodulator due to lrpo ordering: LRPO dependent demodulator: TRUEFALSE ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: ERROR, skolem gets: $c$fk WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.introduce_var, bad formula.renumber_unique, too many vars.renumber_unique, bad formula.Atom: sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d %d.%d]Refuted case The Assumption for case was not used;s:therefore we skip case%s I tried to split, but I could not find a suitable clause. Splitting on clause Case splitting (fork) failed. Returning to search.%c That finishes the proof of the theorem. Case (process %d): Assumption: case failure I tried to split, but I could not find a suitable atom. Splitting on atom always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch Here are the clauses in Usable and SoS. It seems that no moreinferences or splitting can be done. If the search strategy iscomplete, these clauses should lead to a model of the input.enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s "Returned string"enter user_test_term: %ld %f %d %s new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.evaluate_user_function, bad code. HOT NEW CLAUSE!: WARNING, instance of x=x cannot be inserted into demod_imd index: imd_delete, can't find alpha.imd_delete, can't find atom.contract_imd, increase MAX_AL_TERM_DEPTH.%p start of index-match-demodulate treev%d %s demod=labelattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer: # %s(%fNOTORparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)INPUTEQ-AXIOMparse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object overbeek_insert, bad termoverbeek_insert, bad weight in termThere is no Overbeek World to print! start of Overbeek_world %d: end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check!check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: >>>> Starting back demodulation with %d. %d back subsumes %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. after demodulation: keeping clause because it matches a hint. deleted because weight=%d. Subsumed by %d. Following clause subsumed by %d during input processing: ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) %cSearch stopped by max_proofs option. Search stopped by max_proofs option.constructing nodes for remaining lits:ERROR: constructing children told target here with already target setERROR ... non UNIT clause looks UNITcouldn't get context from clause couldn't get link_nodecouldn't get context nodeERROR: constructing children told target here and target not found hereFPA indexing not supported for linked res subsumable unitFPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c followsUD UD exiting linked_unit_del, not subsumedattempted to back up from a node with a child********entering Linked UR***********ERROR: unable to initialize linked UR inference tree********tree before BIG loop open lit %d nres %d attempting to find clash for term in clause first time = %c res_count = %d clashed against term: in clause ERROR: moved forward to %p first = FALSE did not attempt to resolve ... appears in ancestryERROR: found non_target back_up < 0ERROR: left_sibling chain to NULL***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d resolvent = -- FAIL --***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable()ERROR: forward failed, has first_child that's NOT tarERROR: forward failed with target child (has sibs)ERROR: couldn't get context for dummy nodeERROR: couldn't get link node for dummyERROR: couldn't get context for given nodecouldn't get given link_nodechecking is_in_ancestry on lit at %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: **<< -----start node at %p------ parent = %p prev_sibling = %p next_sibling = %p first_child = %p current_clause >> (NIL) <<first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d goal to resolve ... from literal from clause subst = %p subst->multiplier = %d tr = %p unif_position = %p -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tarNUC failed depth check TRASHEDNUC in on only tar TRASHEDERROR, too many variables, max is %d: weightERROR, weight template: ur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).build_term, bad arity.ifis_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p geo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH.cldiff, bad PICK_DIFF%c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! 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0ustar mccunemccune#!/bin/csh bin/mace2 -n6 -p < examples-mace2/basic/noncommutative_group.in | \ awk '/Model/,/end_of_model/' echo "If you see a group table, the test was successful." otter-3.3f/Legal0100644000076400007640000000226007714273233013160 0ustar mccunemccuneOtter and MACE Legal Page November 21, 2001. This information refers to the Otter and MACE automated deduction software, created at Argonne National Laboratory. Copyrights The University of Chicago has declined to assert its copyrights in this software. It may be used by the public without restriction and is available here by download. License This material resulted from work developed under a U.S. Government contract and is subject to the following license: the Government is granted for itself and the public a paid-up, nonexclusive, irrevocable worldwide license in this material to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly. Disclaimer NEITHER THE UNITED STATES GOVERNMENT NOR ANY AGENCY THEREOF, NOR ANY OF THEIR EMPLOYEES OR OFFICERS, MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LEGAL LIABILITY OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR USEFULNESS OF ANY INFORMATION, APPARATUS, PRODUCT, OR PROCESS DISCLOSED, OR REPRESENTS THAT ITS USE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS. These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory otter-3.3f/bin-Linux/0040755000076400007640000000000010103520103014032 5ustar mccunemccuneotter-3.3f/bin-Linux/otter0100775000076400007640000100500110103775523015133 0ustar mccunemccuneELF¤‹4(v4 (44€4€àà€€kkkûû˜t´0k0û0ûÈÈ((( Qåtd/lib/ld-linux.so.2GNU%/)-,$' *.! 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‹Cÿpè\üÿÿƒÄÿsèQüÿÿƒÄÿ3èGüÿÿ‰$è?üÿÿƒÄë ÿ5ÄüjjhêèE*ýÿÇ$èé)ýÿ‰ß‹[€{„Wÿÿÿeô[^_ÉÃU‰åWVSƒì‹uVèÆýÿÿ‰Ãƒìh²ihàwè\ûÿÿƒÄ „Àuè¤ûÿÿ‰ÃÆ@ƒì hàwè[ûÿÿ‰C ‰Øës¸ƒû)ti¸ƒû(u_èqûÿÿ‰Ç‰Ãƒì VèŽÿÿÿƒÄ…Àt ÆC‰èRûÿÿ‰C‰Ãƒì VènÿÿÿƒÄ…Àuàƒì Vè)ýÿÇ$¼|èòúÿÿ‰C ÆC‰<$èwþÿÿ‰øeô[^_ÉÃU‰å‹E¾@ÉÃU‰å‹E‹ÉÃU‰å‹E‹@ÉÃU‰å‹E‹@‹ÉÃU‰å‹E‹@‹@‹ÉÃU‰åSƒì‹]Sè²ÿÿÿƒÄº…Àuƒì Sè³ÿÿÿ‰$èÓÿÿÿƒÄ‰ÂB‰Ð‹]üÉÃU‰åWVSƒì ‹]…Ûuè(ÿÿ‰Ã‹E ‰ƒ<ǃ@é¡»@…´‹“<‹M ‹A;B} ƒìQéÆ‹u ;³<uƒìVhPêé¸+ƒ@‹ƒ‹M ‹A;B~ƒìQjèjÿÿÿ‰˜DëNèt'ÿÿ‰Æ¿Èº¹È‹“‰ŽÇ“BA9ú|퉾@¸)ø‰ƒ@‰žDƒìÿu Vèÿÿÿ‰Ã雃»Dt6‹“D¸+‚@‹‚‹u ‹F;BƒìVÿ³DèÖþÿÿ‰ƒDë\‹»@¸‰Á)ùùJ‹‹‹u ‹F‰Æ;B}Aù1‹‹;p|ïù!‹E ;‹uƒìPh„êÿ5Äüè’%ýÿƒÄë=¸)ø9Áu ‹u ‰t‹üë ¸‰Â)ú9Ê} ‹“‰D“üB9Ê|ô‹E ‰D‹üG‰ƒ@‰Øeô[^_ÉÃU‰åWVSƒì ‹]ƒ»Dtg‹“D‹ƒ@‚@=N‰Ö¹;‹@}&‹º@º)¸)È‹ƒ‰–A;‹@|à‹ƒ@†@ƒì Sè&ÿÿ‰ðë‰Øeô[^_ÉÃU‰åWVSƒì ‹u‹} …öu ƒìWh¸êëo‹–<‹G;B}ƒìWÿ¶DèÅÿÿÿ‰†Dé«‹†@‰Eð¸‰Á+Mðù‹Ž‹G‰Ã;B}Aù‹Ž;X|ï;<ŽtƒìWhèêÿ5Äüè($ýÿëW‰Ê¸+Eð9Á~¸‰Á+Mð‹D–ü‰–J9ÊôÇ–‹EðH‰†@…Àu‹žDƒì Vè#%ÿÿ‰Þë ƒì Vè‹þÿÿ‰ÆƒÄ‰ðeô[^_ÉÃU‰åVS‹u‹] …ÛuÇÇF빉Ê+“@‰‰V‰ð[^ÉÂU‰åWVSƒì ‹}‹M ‹]sþ‰È‰òëUèƒìÿ±DRè“ÿÿÿ‹Eè‹U쉉W‰øeô[^_ÉÂU‰åWVSƒì è[æ•èš"ýÿ“ ÿÿÿ‹ ÿÿÿ)Ê1öÁú9Ös‰×ÿ”³ ÿÿÿF9þrôƒÄ [^_ÉÃU‰åVSè[Ãb•‹ ÿÿÿƒ ÿÿÿ)ÁÁù…Éqÿu è:[^ÉÉöÿ”³ ÿÿÿ‰òN…ÒuòëåU‰åSR¡ûƒøÿ»ût ƒëÿЋƒøÿuôX[ÉÃU‰åSè[Ãû”RèÞ$ýÿ‹]üÉà %d input errors were found.%c =========== start of search =========== Starting on level %d, last kept clause of level %d is %d. %cStarting on level %d, last kept clause of level %d is %d. %c%ld clauses have been given. reducing weight limit to %d. %cSearch stopped because sos empty. Search stopped because sos empty. %cSearch stopped by %s option. Search stopped by %s option. The process was started by %s on %s, %s%d input errors were found. given clause #%ld: (wt=%d) max_givenmax_genmax_keptmax_secondsmax_levels???August 20043.3f----- Otter %s, %s ----- The command was "". The process ID is %d. ˜­Ÿ¦»»»»»»´ ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause. literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p ERROR, clause contains variable literal: ERROR, input clause contains too many variables: ERROR, input clause contains Skolem symbol: ERROR, arrow not found in sequent: ERROR, input literal contains Skolem symbol: forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.WARNING, clause %d not found, proof is incomplete. interaction failure: cannot find tty.interaction failure: cannot find tty. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %c Not an integer: "%s", try again. Turning off interactive_given mode. Turning off interactive_given mode. Ok, clause %d will be given. WARNING, CLOCK_START: clock %d already on. WARNING, CLOCK_STOP: clock %d already off. unit_del, too many variables introduced.cl_del_int, bad clause.checking clause, address:%p |$F#end_of_list ERROR, text after term: , .%dbinaryneg_hyperpara_intopara_fromfactor_simplinked_urevalgL-idgLcopyflipclausifyback_unit_delsplitsplit_negpropositional(heat=%d) [] | (list nil) end_of_list. equalEq$ANS$Ans$ansfind_random_cl, sos bad./dev/tty%c Clause %d not found. %c Clause %d not in sos. ¼¥«¥š¥‰¥x¥g¥V¥Ƥ4¥#¥¥ð¤â¤Ô¤¸¤E¥¥ª¤œ¤Ž¤€¤j¤\¤ur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).$Tbuild_term, bad arity.ifFALSE&<->exists$QuantifiedERROR, skolem gets: $c$fintroduce_var, bad formula.renumber_unique, bad formula.¹ÝÆÆÆƶ R 5 í í ² X Ò ¶ R ‰   ¨ Z Ë  ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.renumber_unique, too many vars.>>>> Starting back demodulation with %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. keeping clause because it matches a hint. Following clause subsumed by %d during input processing: %cSearch stopped by max_proofs option. Search stopped by max_proofs option.%d back subsumes %d. after demodulation: deleted because weight=%d. Subsumed by %d. ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) Process %d finished %s/dev/null********** %s includeERROR, cannot open file %s. setclearassignaxiomsdemodulatorspassivehotmace_constraintsforeachERROR, unknown list: formula_listERROR, bad argument to list: ERROR, unknown formula_list: weight_listpurge_genpick_givenpick_and_purgeERROR, unknown Weight_list: lexlrpo_multiset_statuslrpo_lr_statusoverbeek_termssplit_atomsspecial_unaryopfloat_formatmake_evaluableinitial_proof_objectoverbeek_worldoverbeek_world: term errorsERROR, command not found: list(sos). -f %% Reading file %s. -sERROR, bad demodulator: ------------> process sos:%2d:%-4d %2d:%-4d All others: %d. (hot clauses kept)%7ld user CPU time %10.2f system CPU time %10.2f wall-clock time %7ld input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f list(usable). list(sos). list(demodulators).sos_size=%d %c--- refuted case %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d.%d,$nil$consclauses in usable. paramodulation is disabled. given %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f %c********** ABNORMAL END ********** ********** ABNORMAL END ********** ERROR, bad argument to include: ------- start included file %s------- ------- end included file %s------- NOTICE: Please change 'axioms' to 'usable'. Name of axioms list is now 'usable'. -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, bad argument to Weight_list: ----> ERROR, already have purge weight list. ----> ERROR, already have pick weight list. ----> ERROR, already have pick weight list or purge weight list. ----> ERROR, already have term weight list. ERROR, argument of lex term is not a list: ERROR, argument of lrpo_status term is not a list: ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. ERROR, argument of skolem term is not a list: ERROR, argument of overbeek_terms is not a list: ERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: ERROR, argument of special_unary term is not a list: ERROR, float_format term must have one argument. ERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: overbeek_world: too many variables ERROR, characters after term: ERROR, clause contains too many variables: ERROR, input file %s not found. ERROR, missing sos (-s) argument. %% Reading sos clause from the command line. list(hints) and list(hints2) are incompatible. ------------> process usable: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld ----------- times (seconds) ----------- (%ld hr, %ld min, %ld sec) (%ld hr, %ld min, %ld sec) ============ end of search ============ That finishes the proof of the theorem. ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. %c-- HEY %s, WE HAVE A PROOF!! -- ---------------- PROOF ---------------- ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> Passive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will beordered hyperresolution with the propositionaloptimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; thestrategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists willbe printed at the end of the search. This is a non-Horn set without equality. The strategy willbe ordered hyper_res, unit deletion, and factoring, withsatellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy willbe hyperresolution, with satellites in sos and nuclei This ia a non-Horn set with equality. The strategy will beKnuth-Bendix, ordered hyper_res, factoring, and unitdeletion, with positive clauses in sos and nonpositive There is a clause for symmetry of equality, so it is This is a Horn set with equality. The strategy will beKnuth-Bendix and hyper_res, with positive clauses insos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it isassumed that equality is fully axiomatized; therefore,Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty);therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set thepropositional flag and use ordered hyperresolution.Setting pick_given_ratio to 2, because all clauses are units.Setting hyper_res, because there are nonunits.Setting ur_res, because this is a nonunit set containingeither equality literals or non-Horn clauses.Clearing order_hyper, because all clauses are Horn.Setting factor and unit_deletion, because there are non-Horn clauses.Equality is present, so we set the knuth_bendix flag.As an incomplete heuristic, we paramodulate with units only.There is a clause for symmetry of equality, so it iszD@@%c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. constructing nodes for remaining lits:ERROR: constructing children told target here with already target setERROR ... non UNIT clause looks UNITERROR: constructing children told target here and target not found hereFPA indexing not supported for linked res subsumable unitFPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c followsUD exiting linked_unit_del, not subsumedattempted to back up from a node with a childERROR: unable to initialize linked UR inference tree********tree before BIG loop open lit %d nres %d attempting to find clash for term first time = %c res_count = %d ERROR: moved forward to %p first = FALSE ERROR: found non_target back_up < 0ERROR: left_sibling chain to NULL***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d ***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable()ERROR: forward failed, has first_child that's NOT tarERROR: forward failed with target child (has sibs)ERROR: couldn't get context for dummy nodeERROR: couldn't get link node for dummyERROR: couldn't get context for given nodechecking is_in_ancestry on lit parent = %p prev_sibling = %p next_sibling = %p first_child = %p first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d subst = %p subst->multiplier = %d tr = %p unif_position = %p ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tarNUC failed depth check TRASHEDcouldn't get context from clause couldn't get link_nodecouldn't get context nodeUD ********entering Linked UR*********** in clause clashed against term: in clause did not attempt to resolve ... appears in ancestryresolvent = []-- FAIL --couldn't get given link_nodeat %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: << -----start node at %p------ current_clause >> (NIL) <<goal to resolve ... from literal -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d $NUCLEUS$LINK$BOTH$SATELLITENUC in on only tar TRASHEDÄÈÎÈØÈâÈìÈlinked hyper not implemented yet.enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s enter user_test_term: %ld %f %d %s evaluate_user_function, bad code.@@"Returned string"new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.§Ø•×Ö×Ø}ØŸØ;ÛÚ6ÚmÚ¦ÚÚÚÛgeo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH. HOT NEW CLAUSE!: SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. Otter killed by SIGUSR1 signal. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. %cSearch stopped by SIGINT. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Commands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- killed level %d search during interaction. killed level %d search during interaction. --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- %s%c The job finished %s Search stopped by SIGINT. Malformed term. helpfork%c Fork failed. Fork failed.statskill ok. continue ok.optionssymbols command not understood. Command not understood. ok. > %. %s Job %d Fork failedXlog_%dinsert_into_gen_tab, key already thereprint_proof_object_node, bad rulematch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewritestranslate_demod_unit: cannot rewritefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: proof node not foundlist(%s). %% Hints from process %d, %sbuild_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is givenunknownundefinedeq-axiominstantiateresolveparamodv%d(%s(not false(or true(%d %d ( . v%d)(v%d . )) %d %d) (%d) NIL( new_literal_index, bad map ABOUT TO ABEND!old demod: new demod: clause: finish_translating, bad ruletrans_2_pos: NULL postrans_2_pos: clause not foundtrans_2_pos: empty clauseend_of_list. ;; BEGINNING OF PROOF OBJECT;; END OF PROOF OBJECTñ¤ñ«ñ²ñ¹ñÀñÇñÎñ×õ»ô»ôÊô“õ]õ]õ¦õnàà´ààààà´@˜àদŠà|n %cWARNING, hint will not be used, because no weights have been set for it: Œ&„&”&¤&œ&¬&%d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d(hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). bdNEW HINT: %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bsub_hint_wtfsub_hint_wtequiv_hint_wtbsub_hint_add_wtfsub_hint_add_wtequiv_hint_add_wtlabel # %s(%fattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer: è6è6è6è6è6è6ï6q7q7x7ˆ77n8ª8³8Å8×8t99š9­9»9Atom: %d%s%d]Refuted case The Assumption for case was not used;therefore we skip case%s Splitting on clause Case (process %d): Assumption: case failure Splitting on atom sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d I tried to split, but I could not find a suitable clause.Case splitting (fork) failed. Returning to search.%c That finishes the proof of the theorem. I tried to split, but I could not find a suitable atom. always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch Here are the clauses in Usable and SoS. It seems that no moreinferences or splitting can be done. If the search strategy iscomplete, these clauses should lead to a model of the input.INPUTEQ-AXIOMparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)parse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object cldiff, bad PICK_DIFFoverbeek_insert, bad term start of Overbeek_world overbeek_insert, bad weight in termThere is no Overbeek World to print! end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check!check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: CLAUSE %d -1 -2 ========== Jhash ==========[%d] resolved: IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof =====build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not foundLevel %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ======================== end multijust ============tp_alloc, request too big: %d (free_all_mem cleared). Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. ------------- memory usage ------------ %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu $tDP?$Hyps$Concs$Connect$FSUB$BSUB$EQUIV%d %s/%d, lex_val=%d is_skolem, no symbol for %d.(nil)%s%s%s%c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE!==/=@<@>@<=@>=+/'op command must have arity 3.xfxinfixxfyinfix_rightyfxinfix_leftprefixxfpostfixprefix_assocyfpostfix_assoc ***HERE*** adjusted term: ERROR, comma or ) expected: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, term too big: %c WARNING, multiple arity: %s/%d, %s/%d. %c WARNING, unrecognized $ symbol: %s. mark_as_skolem, no symbol for %d. ERROR: first argument of op command must be 1..999. ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: third argument of op command must be a name or a list. ERROR: list in op command must be all names. ERROR, name too big, max is %d; ERROR, quoted name has no end; ERROR, functor has no arguments: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, unrecognized error in term: ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.integrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: bucket %d: bucket %d: containing terms: build_tree_local, var and not more general.new_sym_num: too many symbols requested. fpa index %p bucket %d and or ] Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>integer divide by 0.float divide by 0. demod term: --> result: demod<%d> WARNING, demod_limit.lex dependent demodulator: LRPO dependent demodulator: ERROR, dollar_contract, bad op_code: %d. ERROR, dollar_contract, bad op_type: %d. WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. >> back demodulating %d with %d. Flipping following input demodulator due to lrpo ordering: ÷ò÷ò÷ò÷ò÷òóóóóóó@ó@ó@ó@óGóGóGóGóGóGóNóNóNó9óUóUó\ócó´ÿ´ÿóóóóóóóóóóójójójójó$óqó+ó+ó+ó+ó+ó2ó¦ÿ–ó¼ôÃõ¨ö_÷Ò÷\øvøù1ù€ùÞúüÜüˆýþ|þtÿ\ômôôô¤ôNõ_õsõ‡õ›õ¯õý÷ø øø2ø7ø“ø™øÎøùùpûûªû¸ûÆûÝûERROR, too many variables, max is %d: ERROR, weight template: WARNING, instance of x=x cannot be inserted into demod_imd index: contract_imd, increase MAX_AL_TERM_DEPTH.start of index-match-demodulate treeimd_delete, can't find alpha.imd_delete, can't find atom.v%d %s demod=is_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p binary_resneg_hyper_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subfree_all_memno_faplno_fanlprint_keptdemod_historysort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_allpara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdegrade_hints2clocksfpa_literalsfpa_termsdemod_limitneg_weightmax_memmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_maxset(clear(%s). assign(%s, %d). dependent: %s(%s). ERROR: flag name not found. lex_rpoprint_levelnew_functionsWARNING: flag already set. flag already clear. parameter name not found. reduce_weight_limit already has that value. delete_identical_nested_skolemdiscard_commutativity_consequences --------------- options --------------- dependent: assign(%s, %d). must have one simple argument. ERROR, flag `lex_rpo' has been changed to `lrpo'. ERROR, flag `print_level' no longer exists. ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. must have two simple arguments. ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. integer must be in range [%d,%d]. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatibleÜF™H™H™H™H™H™H™HñF™H™H™H™H™H™H™H™H™H™H™HG™H™H™H=H™H™H™H™H™H™H™H™H™H™HÓFÊF™HÊF)FF™H™H™HUH™H™H™H™H™H™HúF™H™HIHHH™H™H™H™H™H™H™H™H™H™H™H G™H™H™H™H™H™HIH™H™H™H™H™HH#G{G™H™H™H™H'H'H'Happly_substitute, term not COMPLEX.apply_substitute: term too deep.dot_trans, bad dot notation fill_word, word too big: |%s| WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! WARNING: flist_delete, item %d not found (2)! ÿÿÿÿÿÿÿÿ$ üˆ øfH… ‚ { üû@¼‡œ‡ þÿÿol‡ÿÿÿoðÿÿo ‡0û*‰:‰J‰Z‰j‰z‰Š‰š‰ª‰º‰ʉÚ‰ê‰ú‰ ŠŠ*Š:ŠJŠZŠjŠzŠŠŠšŠªŠºŠÊŠÚŠêŠúŠ ‹‹*‹:‹J‹Z‹j‹z‹Š‹š‹(ûGCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7)GCC: (GNU) 3.3.3 20040412 (Red Hat Linux 3.3.3-7).symtab.strtab.shstrtab.interp.note.ABI-tag.hash.dynsym.dynstr.gnu.version.gnu.version_r.rel.dyn.rel.plt.init.text.fini.rodata.eh_frame.ctors.dtors.jcr.dynamic.got.got.plt.data.bss.comment#(( 1HHX7  ‚ ð?…{Gÿÿÿo ‡ ^Tþÿÿol‡l0c œ‡œ l ¼‡¼@ uüˆüp‰ {¤‹¤ TÛøføæ‡gçÿƒëk™ûk $û$k§,û,k¬0û0kȵøûøkºüûük¬Ã¨ü¨l ÉÀüÀlв ÎÀl‘Qu׈z`Mâ èÇB(H ‚… ‡l‡œ‡¼‡ üˆ ‰ ¤‹ øf gëû$û,û0ûøûüû¨üÀüÈ‹ ñÿû*$û8,ûE°üIÌüUì‹ k(Œ ñÿw û„(û‘ëŸ,û«Ôf ÁñÿÈñÿÑñÿÚ$8êЗ³ ûʘ @8d(8%àüD;0îÇ BñÿL(Ôî X×ë ^ñÿf$ú³ w×ú³ ‹Šûo ™ùüo ªñÿ´ ù Éà m Ý0 ç äwd ô°8¬8 ¤8¨8%¥ ,ÿN ?MD U0` cÚ‡ n/Ï Ï‹ Z^ ¸¦ ¬^ j ¸,(ì Æ+i Õ+-s èž-• ö 3Ÿ ñÿ ì4~ «>( 'ñÿ.‰–“ @´8N¸8cr›Û qñÿx¼8ˆè¬± —™­ £¬­» ¬g®> ¼¥®» Î`¯˜ Üñÿ倱  þŽÈO ÞÍ" mÓ 7Œ´ Gµ< WÙ¶Á `ñÇ lªÅq |«Ì> ˜Î ©Å ¼jò ÄÇÖ Ó˜Á‹ æÄ£ ýÀ› #ÂF &iÂm 4Ö” DÍÄ S¿Ä[ iãÑñ zÝÉÎ ‘éÌ1 £ÏÐ »Î ÓÔÒ6 ã Óc ññÿûñÿñÿXÛ  #bÛG 7Ýf HxÝã Z[Þç kñÿqÐ8‰Ô8¡Ü8¶Ø8ÆÀ8ÙÄ8ìÌ8üÈ8šáŽ (⎠'ñÿ1à8@8 9EñÿMrï' Z™ïŒ n%ðC „hðI Ž±ð+ ›,9©†ñO ±àöC Ã#÷« Þ¾ø íªû¯ þáüŸ €þ  ,u :h Oj[ g(9|Åp ‘- Ù ¦© ¿¯Y Ï9Q ÜŠx íE ûG] ¤B  æª  é * $98 ñÿ@ &$ X ñÿa 09q 0,6 … f,1 ˜ —,( ¢ ¿,  ² .h ¾ ƒ.« × G2[ í ¢2` ú 3 ñÿ ñÿ Ä:` . < @ ,<N O z<§ ` 89o ñÿu <9Š MM › ÝMv ® zPV ¾ ñÿÉ S3 Ó ?S* Ü iS@ ä ©SS í üSG õ CTe ¨Ts  U‰  $V|  ¤U€ *W[ 3 ñÿ> ´XK I ñÿU 0\d m ¬]C y R^x ˆ d`† Ÿ ê`< ¾ &a Ò H9Ù îa  í @9ó X9ý øb  D9 P9 L9 T9" \9+ f^ 5 `9> df I d9O }f< U ¹fQ j l9r g-  h9‡ 7gc œ šg4 © ×hn µ Ei1 ¿ vi Ç i Ï ¬iY Û jf î äjH õ Œ9ú ˆ9 „9 €9 |9 ,nm 0 ™nW ; ‹oB N Íos W t9\ @qÈ e p9l x9u ñÿ} ñÿ‚ ”9Ž ˜9˜ :¥ :¯ œ9º :Æ :Ñ $:Ú  9ä ,:ï (:ù 0:¤98:#4:1<:?¨9ND:^@:mH:€¬9”P:©L:½T:Ë°9Ú\:êX:ù`:´9h:&d:59=l:J¸9Xt:gp:ux:€¼9Œ€:™|:¥„:³À9ÂŒ:Òˆ:á:îÄ9ü˜: ”:œ:&È94¤:C :Q¨:]Ì9j°:x¬:…´:“Ð9¢¼:²¸:ÁÀ:ÎÔ9ÜÈ:ëÄ:ùÌ:Ø9Ô: Ð:-Ø:7Ü9Bà:NÜ:Yä:gà9vì:†è:•ð:¥ä9¶ø:Èô:Ùü:åè9ò;; ;ì9$;1 ;= ;Oô9b(;v$;‰,;šø9¬4;¿0;Ñ8;Þü9ì@;û<; D;:,L;?H;QP;c:vX;ŠT;;¬ð9¼;Í;Ý\;è:ôd;`; h; :&p;4l;At;L:X|;ex;qñÿv ;È~ ¥z Ž€;”»ß ¤ù»5 ­†¼| ¼½ ǽ3 Ø’½× áÀ} ó}Ád ÿáÃò ÓĦ yÆ| 'ñÿ/ÒU 9mÒz F€<D;OÄwYñÿ_ÚÜ3 m Ý5 wBÝN Ý ‹«ÝD •ïÝ® ¤Þ ³ÈwÀÌwÍaà{ ÛÜà/ é á¿ úÐw ñÿñÿÜï´ 'ñ^ ;îñˆ FÔwSvòM  cÃÿ_ s": y\¹ ŒV ™Øw°ñÿ¹öO Éj] ×Ê~ ãHœ óä{ ,U ÒW #VB 4Z >pÇ GñÿMÌ K ]é"ç jñÿoà*e ~r,÷ Šñÿ”ñÿžüP' ¯#Rs ¾–SÄ ÛZT èvVì øÂXr ñÿ¤\ Â\6 &ø\- 0Dx5%]2 @HxF·^0 Qç^ Wú^ì aàwdf`8 kV`Ì uñÿ|>d† ˆcv3 “ø¯ò ˜˜Î’ ¥·x; º×y ÆÏe7 × %À ä%ûT îwÍ' ©Üi `x`"õa  ¯à- 8ÀšK;„" YVå e=Ä wàš(†r¡À ”¢OØ ¨²vE »›Á²¡ Îkjy Þ$å2 ðb/ û–[ Âe8 Q²  ›- v 8º_ ILžA Sé7H fLP$ rlà }UšF1 ªø…! ¼•{! 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esetprint_proof_objectrms_subsume_conjis_insertprint_memp_clause_sget_listrms_cnfwall_secondsDemod_imdunit_delis_skolemcompile_hintssplit_atomnext_fposis_symbolsymmetry_clauseconvenient_demodwrite_termcl_del_intindex_lits_clashnnf_dnffpa_deletefree_fpa_treeattribute_typesos_argumentget_is_treeproc_gensubsume_conjrun_timeFpa_neg_litsfs_retrievecl_int_chkoccur_checkprint_symssubst_free_formulaprf_weightprint_term_nllex_order_varsclause_to_termlinked_ur_restime@@GLIBC_2.0get_relhorn_clausesystem_timefinish_translatingfree_fsub_pos_startcontains_skolem_symbolrms_quantifierssub_clauseis_deletematch_clausescompare_for_auto_lex_orderget_fnodeevaluate_user_functionall_factorsget_is_posread_sequent_clausefree_formula_boxcl_copy_delete_literalprint_bannerprint_trailsubsumeWeight_pick_given_indexforeach_sosmark_as_skolemrms_distribute_quantsis_eqp_proof_object_as_hintsbits_ulongfputs@@GLIBC_2.0get_ci_ptrfree_clauseilist_to_jsetterm_to_clauseorder_equalitiesdeclare_user_functionsget_termilist_appendinsert_clauseDemodulatorscase_depthinitial_strsn_to_nodesplitable_clausehot_inferencein_sym_tabOverbeek_termsprint_case_nFpa_alphasdouble_to_termglist_prependsame_structurelrpo_greateroutput_statsget_formula_ptriset_addp_optionsfree_sym_entnew_functor_nameget_imd_posgen_subsumebuild_termzap_prop_treepossible_given_splitprint_errorfree_link_nodeinitcdrfind_lightest_geo_childclock_valcl_mergepretty_print_termprint_term_sfree_is_posfree_is_pos_listcl_insert_tabimd_insertindex_lits_allprint_hints2_cl_listlong_to_termget_ilistneg_clauseget_attribute_indexautomatic_2_settings__fini_array_startprepend_clgen_tautologyfputc@@GLIBC_2.0__libc_csu_initnullpp_statsprint_overbeek_worldfind_match2From_parentnth_clausep_symsfind_first_clstr_to_termis_retrieve__bss_starthot_index_clauseprint_formula_listzap_clause_ptr_listmaincleanupget_clauseassign_cl_idparse_initial_proof_objectrms_dnfWeight_pick_givensn_to_arityone_unary_answerstr_doublerms_subsume_disjfind_clause_to_splitpos_eq_litpossible_splithot_dynamiccl_find__libc_start_main@@GLIBC_2.0print_listfree_term_ptrg2list_length__init_array_endSosadd_to_jsetrmslog_for_x_showmax_literal_weightall_supporters_less_thanget_trailmap_restpara_fromfree_imd_treeget_link_nodeIgnore_sym_numprint_set_b_to_aintegrate_termun_share_specialp_case_nrenumber_uniquepost_proc_allterm_fixupread_a_filedel_hidden_clausesfor_sub_propget_proof_objectfirst_or_next_factoranc_subsumetotal_memanswer_litprint_hints_cl_listprint_variablep_proof_objectmove_clausesmax_split_depthdata_startasctime@@GLIBC_2.0nnfrms_push_freeSubsume_countnext_cl_numprintf@@GLIBC_2.0propositional_clauseSplit_atomsfind_lightest_clfind_random_clzap_termgetuid@@GLIBC_2.0_finiprint_sequent_clauseconnect_new_nodeautomatic_1_settingsp_is_treegl_demodstr_to_snilist_memberIs_neg_litsconflict_tautologyprint_formulap_termfclose@@GLIBC_2.1iset_subsetget_attributefree_all_membuild_bin_resset_wt_listts_and_fsunit_conflictcopy_jsetatomsym_tab_memberrem_from_listfprint_btreeget_jsetproper_listclausifyget_ans_lit_nodeback_subsumeWeight_purge_gen_indexp_clauseoverbeek_insertuser_test_bool__preinit_array_endauto_change_flagoccurrencesground_clauseprover_forksset_lrpo_statuslinked_hyper_resOverbeek_worldget_sym_entgethostname@@GLIBC_2.0get_ancestorsskolemizechange_flaginfer_and_processget_fpa_headsymbol_countis_atomstring_to_terminit_optionsstr_longread_all_inputp_assumption_depthsbd_kludge_deletezap_formulafind_random_lightest_clback_unit_deletioninit_special_opsnnf_cnfinit_proof_object_environmentrenum_vars_termreportget_g2listprint_attributesp_timesprocess_op_commandprint_prop_treefind_atom_to_splitflist_deleteexit@@GLIBC_2.0check_overbeek_worldfoobuilt_in_symbolsp_ilistzap_term_specialfree_formulap_casep_btreecalloc@@GLIBC_2.0init_log_for_x_showprint_casebd_kludge_insertiset_sortjset_to_ilistdynamic_demodulatorget_fpa_treeappend_lists_edata_GLOBAL_OFFSET_TABLE_free@@GLIBC_2.0_endmatchget_gen_nodednfParmsp_substilist_lengthget_imd_treep_prop_treefree_clause_ptr_listremove_var_symsapply_demodunify_no_occur_checkMace_constraintsg2_remove_supersetsskolem_symbolfree_cl_attributeFpa_clash_pos_litsprint_timeskeep_onlyith_literalp_clause_s2p_pathstdin@@GLIBC_2.0occurs_intotal_mem_callsidentity_resolvefree_literalfree_ilistget_glistprint_ilistimd_deleteread_bufclausify_formedmy_process_idget_formula_boxfpa_insertwt_matchinit_attributesnegate_formulaforward_subsumesn_to_ecprint_termvariantname_symfopen@@GLIBC_2.1ordered_sub_clauseiff_to_disjtrue_listpcombine_answers__init_array_startcl_del_nonuser_test_doublehide_clausestr_intFlagsilist_tack_onhyper_resapplyget_literal_IO_stdin_usedget_cl_attributeformula_to_termcommutativity_consequenceprint_stats_briefget_args_for_user_functionlong_strrename_syms_formulaget_fsub_posprint_term_lengthd_termcl_integratesubst_sn_termglist_lengthzap_btreeget_formula_ptr_2glist_tack_ondependent_parmsset_skolemread_formula_listalloc_fpa_indexdistinct_varssprintf@@GLIBC_2.0ident_nested_skolemslit_t_f_reduceHints2fwrite@@GLIBC_2.0biggest_va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ÆC‰4$è„þÿÿ‰ðë¸eô[^_]ÃvU‰å‹E¾@]ÃU‰å‹E‹]ÉöU‰å‹E‹@]ÃU‰å‹E‹@‹]ÃvU‰å‹E‹@‹@‹]ÃU‰åSƒì‹]Sè¬ÿÿÿƒÄ…Àuƒì Sè´ÿÿÿ‰$èØÿÿÿƒÄ@ë‰ö¸‹]üÉÉöU‰åSƒì¡Ù»Ùƒøÿtv¼'ƒëÿЋƒøÿuôX[]ÃU‰åƒì‰ì]öU‰åSRè[â×vèwŠüÿ‹]üÉÃAugust 20042.2f----- MACE %s, %s ----- The command was "". spPIhcxyCrm:t:k:n:N:d:z:v:distinct_constantsprint_modelsprint_models_portableprint_models_ivyqg_constraintiso_xclause_splitiso_constantsrecord_assignmentsmax_modelsmax_secondsmax_memDomain size must be > 0. Domain size must be <= %d. part_vars%s%cThe process was started by %s on %s, %sMACE %s -- Search for finite models. Input clauses are taken from standard input. Command-line options: -n n : Search for model of size n (default %d). -N n : Iterate up to size n (default: don't iterate). -c : Assume constants are distinct (up to domain size). -z n : Apply isomorphism constraints to first n constants (default %d). Overridden by -c. -p : Print models in human format as they are found. -P : Print models in portable format as they are found. -I : Print models in IVY format as they are found. -m n : Stop when the n-th model is found (default %d). -t n : Stop after about n seconds. -k n : Dynamically allocate at most n Kbytes (default %d). -s : Perform unit subsumption. (Always done on input.) -C : Split on clauses instead of on atoms. -r : Record and print the order of assignments. -x : Quasigroup constraint. -y : Iso experiment (implies -C and -z0). -v n : Try to part flattened clauses with n or more variables (default %d). -h : Print this message. Examples of constraints given in input: list(mace_constraints). assign(a, 3). assign(f(2,3), 1). assign(P(0), F). assign(P(1), T). property(r(_,_), equality). property(lt(_,_), order). property(f(_,_), quasigroup). property(g(_), bijection). end_of_list. Maximum domain size must be > 0. Maximum domain size must be <= %d. +----------------------------------------------------------+ | SEGMENTATION FAULT!! This is probably caused by a bug | | in MACE. Please send copy of the input file to | | otter@mcs.anl.gov, let us know what version of MACE you | | are using, and send any other info that might be useful. | +----------------------------------------------------------+ MACE_sig_handler, cannot handle signal %d. WARNING, MACE_CLOCK_STOP: clock %d not running. WARNING, MACE_CLOCK_STOP: clock %d not running. list(flattened_and_parted_clauses). --- Starting search for models of size %d --- ÀÀÀÀXŽÀÀÀÀÀŽÀÀÀÀ(ÀøÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÌÀÀÀÀÀÀÀÄŽÀ„ŽäŽÀìÀdŽÜ¤ŽÀÀŽŽtin MACE_tp_alloc, request too big.in MACE_tp_alloc, operating system cannot supply any more memory.г@set(clear(%s). assign(%s, %d). setclear dependent: %s(%s). ERROR: flag `%s' not found. WARNING: flag `%s' already set. flag `%s' already clear. ERROR: assign(%s, %d),WARNING: assign(%s, %d), already has that value. Called MACE_check_options. --------------- options --------------- dependent: assign(%s, %d). ERROR: parameter `%s' not found. integer must be in range [%d,%d]. ------------- memory usage ------------ Memory dynamically allocated (MACE_tp_alloc): %d. ----- statistics for domain size %d ---- Clauses input %7ld Literal occurrences input %7ld Greatest atom %7ld Preprocess unit assignments %7ld Clauses after subsumption %7ld Literal occ. after subsump. %7ld Selectable clauses %7ld Splits %7ld Unit assignments %7ld Failed paths %7ld Memory malloced %7ld K Memory MACE_tp_alloced %7d K Generate ground clauses %10.2f DPLL %10.2f ======================================= Total times for run (seconds): user CPU time %10.2f system CPU time %10.2f wall-clock time %7ld Input: Unit preprocess: Decide: Memory: Time (seconds): (%ld hr, %ld min, %ld sec) @@Abnormal end.The search is complete.Exit by max_mem parameter.Exit by max_models parameter.Killed by SIGINT signal.Killed by SIGSEGV signal.Input error.Exit with unknown code.No models were found. %s %s ********** %s Exit by max_seconds parameter. Input error. See the output file. The set is satisfiable (%d model(s) found). ********** ABNORMAL END ********** ˜ ¸   ¨ ° ¸ À È Рanswer literals not allowed in MACE inputevaluable literals not allowed in MACE input%% WARNING: possible error in check_transformed_clause: equaldp_trans, too many variables%% original: %% transformed: unit_enqueue: queue too small( -%d ), active=%d Atom=%d, value=%d, pos_occ=%x, neg_occ= Selectable clauses: HERE it is!!atom_value, atom out of rangeatom_value, bad value Initial assigments: Model #%d:end_of_model assign: atom already assignedunassign: atom not assigned) active_neg=%d, active_pos=%d, subsumer=%d insert_dp_clause, increase ATOM_INT_MAX and recompile.Propositional input must be all integers; if you have first-order input, the domain size must be given (-n). Order of assigments for the following model: The %d%s model has been found. After all unit preprocessing, %ld atoms are still unassigned; %ld clauses remain; %ld of those are non-Horn (selectable); %ld K allocated; cpu time so far for this domain size: %.2f sec. declare_symbol_sorted, too many symbolsdeclare_symbol_sorted: sort not found*** Unsatisfiability detected *** add_unit: element out of domainadd_unit: sign must be 1 or -1process_variables, variable too big.process_variables, badly sorted clauseadd_clauses_for_qg_constraint, symbol f not foundAdding basic QG constraints on last column of f. number_variables, element out of range Maximum number of variables is %d. number_variables, too many variablestrans_relational_clause: too many first_order clausestrans_relational_clause: bad DP argtrans_relational_clause: bad DP arg (right)trans_relational_clause: bad eq argtrans_relational_clause, bad functorRemoving answer literals from clause %d. WARNING, CLOCK_START: clock %d already on. WARNING, CLOCK_STOP: clock %d already off. MACE_collect_symbols, multiple arityApplying isomorphism constraints to constants:dp_trans, wrong arity in mace_constraints list.dp_trans, symbol in mace_constraints list not founddp_trans, mace_constrationts property not understooddp_trans, mace_constraints command not understooddp_trans, bad integer (RHS) in assignmentdp_trans, bad truth value in assignmentdp_trans, bad integer (LHS) in assignmentCannot make constant %s distinct, domain is too small. Adding unit assigning %s %d (distinct_constants). order relation must have args of same typeequality relation must have args of same type %d clauses were generated; %d of those survived the first stage of unit preprocessing; there are %d atoms. %s%s%s%s%swell_defined, bad arityclosed, bad arity The bad element is %d. Bad name=%s list(clauses). arity too greatunivpropertyequalityorderquasigroupbijectioncommutativeassignBad name=%s, dp_trans, bad functorAdding unit assigning %s%sfunction %s bijection. function %s quasigroup. @ÈHÈLÈXÈlÈÈ×Ü×ì× Ø8Ø %s: %d %2d%3d %s : --- - | --+%5d | %s: %s %2s$Connect function(%s, [%d]) function(%s(_), [ function(%s(_,_), [ %d, %d, %d ])%d, 0 predicate(%s, [%s]) predicate(%s(_), [%s, %s, %s ])%s, interpretation( %d, [ ]). ((%s . 0) . ((nil . %d))) ((%s . 1) . ( ((%d) . %d) )) ((%s . 2) . ( ((%s . 3) . ( ((%s . 0) . ((nil . %s))) ((%d) . %s) ((%s . 4) . ( ;; BEGINNING OF IVY MODEL (0 . ((. %d) . ( ( ) . ( ) ) ) ;; END OF IVY MODEL ======================= Model #%d at %.2f seconds: Dimension %d table for %s not printed predicate(%s(_,_), [ predicate(%s(_,_,_), [ predicate(%s(_,_,_,_), [ Dimension %d table for %s not printed ((%d %d) . %d) ((%d %d %d) . %d) ((%d %d) . %s) ((%d %d %d) . %s) ((%d %d %d %d) . %s) print_model_ivy, max relation arity is 4print_model_ivy, max function arity is 3@þLþXþdþpþ” ¬¸Ä v%dtp_alloc, request too big: %d (free_all_mem cleared). Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu €„Ž@P?$Quantified$Hyps$Concs$ANS$Ans$ans$NUCLEUS$BOTH$LINK$SATELLITE$FSUB$BSUB$EQUIV%d %s/%d, lex_val=%d is_skolem, no symbol for %d.end_of_listend_of_list. (nil)$nil$cons[]%c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$T$F$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE#<->&!====/=@<@>@<=@>=/'xfxinfixxfyinfix_rightyfxinfix_leftprefixxfpostfixprefix_assocyfpostfix_assoc ***HERE*** adjusted term: ERROR, comma or ) expected: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, term too big: exists ERROR, text after term: %c WARNING, multiple arity: %s/%d, %s/%d. %c WARNING, unrecognized $ symbol: %s. mark_as_skolem, no symbol for %d.op command must have arity 3. ERROR: first argument of op command must be 1..999. ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: list in op command must be all names. ERROR: third argument of op command must be a name or a list. ERROR, name too big, max is %d; ERROR, quoted name has no end; ERROR, functor has no arguments: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, unrecognized error in term: ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.integrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: bucket %d: bucket %d: containing terms: build_tree_local, var and not more general.new_sym_num: too many symbols requested. fpa index %p bucket %d and or Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>ERROR, too many variables, max is %d: ERROR, weight template: ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause. literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p ERROR, clause contains variable literal: ERROR, arrow not found in sequent: ERROR, input clause contains too many variables: ERROR, input clause contains Skolem symbol: ERROR, input literal contains Skolem symbol: forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.WARNING, clause %d not found, proof is incomplete. interaction failure: cannot find tty. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %c Not an integer: "%s", try again. Turning off interactive_given mode. Ok, clause %d will be given. unit_del, too many variables introduced.cl_del_int, bad clause.checking clause, address:%p .%dbinaryneg_hyperpara_intopara_fromfactor_simplinked_urevalgL-idgLcopyflipclausifyback_unit_delsplit_negpropositional(heat=%d) [] | (list nil) Eqfind_random_cl, sos bad./dev/tty%c Clause %d not found. %c Clause %d not in sos. „®x®l®`®T®H®<®¸­$®®ø­è­Ø­È­¨­0®®˜­ˆ­x­h­X­H­ur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).build_term, bad arity.ifFALSEERROR, skolem gets: $c$fintroduce_var, bad formula.renumber_unique, bad formula.dxxxxÌÆÐРL¸Æhää€8¨ ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.renumber_unique, too many vars.>>>> Starting back demodulation with %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. keeping clause because it matches a hint. Following clause subsumed by %d during input processing: %cSearch stopped by max_proofs option. Search stopped by max_proofs option. %d back subsumes %d. after demodulation: deleted because weight=%d. Subsumed by %d. ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) Process %d finished %s/dev/null%.12fincludeERROR, cannot open file %s. ERROR, bad argument to list: axiomsdemodulatorspassivehotmace_constraintsforeachERROR, unknown list: formula_listERROR, unknown formula_list: weight_listpurge_genpick_givenpick_and_purgeERROR, unknown Weight_list: lexlrpo_multiset_statuslrpo_lr_statusoverbeek_termssplit_atomsspecial_unaryopfloat_formatmake_evaluableinitial_proof_objectoverbeek_worldoverbeek_world: term errorsERROR, command not found: list(sos). -f %% Reading file %s. -sERROR, bad demodulator: ------------> process sos: %2d:%-4d %2d:%-4d All others: %d. (hot clauses kept)%7ld user CPU time %10.2f system CPU time %10.2f wall-clock time %7ld input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f list(usable). list(demodulators). sos_size=%d %c--- refuted case %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d.%d,clauses in usable. paramodulation is disabled. given %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f %c********** ABNORMAL END ********** ********** ABNORMAL END ********** ERROR, bad argument to include: ------- start included file %s------- ------- end included file %s------- NOTICE: Please change 'axioms' to 'usable'. Name of axioms list is now 'usable'. -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, bad argument to Weight_list: ----> ERROR, already have purge weight list. ----> ERROR, already have pick weight list. ----> ERROR, already have pick weight list or purge weight list. ----> ERROR, already have term weight list. ERROR, argument of lex term is not a list: ERROR, argument of lrpo_status term is not a list: ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. ERROR, argument of skolem term is not a list: ERROR, argument of overbeek_terms is not a list: ERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: ERROR, argument of special_unary term is not a list: ERROR, float_format term must have one argument. ERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: overbeek_world: too many variables ERROR, characters after term: ERROR, clause contains too many variables: ERROR, input file %s not found. ERROR, missing sos (-s) argument. %% Reading sos clause from the command line. list(hints) and list(hints2) are incompatible. ------------> process usable: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld ----------- times (seconds) ----------- (%ld hr, %ld min, %ld sec) (%ld hr, %ld min, %ld sec) ============ end of search ============ That finishes the proof of the theorem. ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. %c-- HEY %s, WE HAVE A PROOF!! -- ---------------- PROOF ---------------- ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> Passive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will be ordered hyperresolution with the propositional optimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists will be printed at the end of the search. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, with positive clauses in sos and nonpositive There is a clause for symmetry of equality, so it is assumed that equality is fully axiomatized; therefore, This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it is Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty); therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set the propositional flag and use ordered hyperresolution. Setting pick_given_ratio to 2, because all clauses are units. Setting hyper_res, because there are nonunits. Setting ur_res, because this is a nonunit set containing either equality literals or non-Horn clauses. Clearing order_hyper, because all clauses are Horn. Setting factor and unit_deletion, because there are non-Horn clauses. Equality is present, so we set the knuth_bendix flag. As an incomplete heuristic, we paramodulate with units only. There is a clause for symmetry of equality, so it is %c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. constructing nodes for remaining lits: ERROR: constructing children told target here with already target set ERROR ... non UNIT clause looks UNIT ERROR: constructing children told target here and target not found here FPA indexing not supported for linked res subsumable unitUD entering linked_unit_del, passed term follows FPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c follows UD exiting linked_unit_del, not subsumed attempted to back up from a node with a child ERROR: unable to initialize linked UR inference tree ********tree before BIG loop open lit %d nres %d attempting to find clash for term first time = %c res_count = %d ERROR: moved forward to %p first = FALSE ERROR: found non_target back_up < 0 ERROR: left_sibling chain to NULL ***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d ***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable() ERROR: forward failed, has first_child that's NOT tar ERROR: forward failed with target child (has sibs) ERROR: couldn't get context for dummy node ERROR: couldn't get link node for dummy ERROR: couldn't get context for given node checking is_in_ancestry on lit parent = %p prev_sibling = %p next_sibling = %p first_child = %p first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d subst = %p subst->multiplier = %d tr = %p unif_position = %p ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tar NUC failed depth check TRASHED couldn't get link_node couldn't get context from clause couldn't get context node UD ********entering Linked UR *********** in clause clashed against term: in clause did not attempt to resolve ... appears in ancestry resolvent = [] -- FAIL -- couldn't get given link_node at %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: **<< -----start node at %p------ current_clause >> (NIL) << goal to resolve ... from literal -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d NUC in on only tar TRASHED dÖpÖ|ÖˆÖ”Ölinked hyper not implemented yet. enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s enter user_test_term: %ld %f %d %s evaluate_user_function, bad code.@"Returned string"new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.ˆåÌåæ|æœæ$èLè„èÀèôè(égeo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH. HOT NEW CLAUSE!: SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. %cSearch stopped by SIGINT. Commands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- killed level %d search during interaction. killed level %d search during interaction. --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- The job finished %s??? Search stopped by SIGINT. Malformed term. helpfork%c Fork failed. statskill ok. continue ok.optionssymbols command not understood. Command not understood. ok. > %. %s Job %d Fork failedXlog_%dinsert_into_gen_tab, key already thereprint_proof_object_node, bad rulematch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewritestranslate_demod_unit: cannot rewritefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: proof node not foundlist(%s). %% Hints from process %d, %sbuild_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is given ;; BEGINNING OF PROOF OBJECT undefinedeq-axiominstantiateresolveparamodunknown(%s(not false(or true(%d %d ( . v%d)(v%d . )) %d %d) (%d) NILnew_literal_index, bad map ABOUT TO ABEND! old demod: new demod: clause: finish_translating, bad ruletrans_2_pos: NULL postrans_2_pos: clause not foundtrans_2_pos: empty clause;; END OF PROOF OBJECT ¬´¼ÄÌÔÜä   0ØØHÔ/X0X0(0X0X0X0X0X0(0¤/0X0X000ø/X0è/Ô/ %cWARNING, hint will not be used, because no weights have been set for it: ,7$747D7<7L7%d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d(hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). bdNEW HINT: %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bsub_hint_wtfsub_hint_wtequiv_hint_wtbsub_hint_add_wtfsub_hint_add_wtequiv_hint_add_wtlabel # %s(%fattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer: ÌGÌGÌGÌGÌGÌGÔG\H\HhHxH€H`I¨I´IÄIØItJˆJ¬JÀJÔJAtom: %d%s%d]Refuted case The Assumption for case was not used; s:therefore we skip case%s Splitting on clause Case (process %d): Assumption: case failure Splitting on atom sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d I tried to split, but I could not find a suitable clause. Case splitting (fork) failed. Returning to search. %c That finishes the proof of the theorem. I tried to split, but I could not find a suitable atom. always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch Here are the clauses in Usable and SoS. It seems that no more inferences or splitting can be done. If the search strategy is complete, these clauses should lead to a model of the input. INPUTEQ-AXIOMparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)parse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object cldiff, bad PICK_DIFFoverbeek_insert, bad term start of Overbeek_world overbeek_insert, bad weight in termThere is no Overbeek World to print! end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check! check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: CLAUSE %d -1 -2 ========== Jhash ========== [%d] resolved: IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof ===== build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not foundLevel %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ============ ============ end multijust ============ WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! WARNING: flist_delete, item %d not found (2)! integer divide by 0.float divide by 0. demod term: --> result: demod<%d> WARNING, demod_limit. lex dependent demodulator: LRPO dependent demodulator: ERROR, dollar_contract, bad op_code: %d. ERROR, dollar_contract, bad op_type: %d. WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. >> back demodulating %d with %d. Flipping following input demodulator due to lrpo ordering: Ü“Ü“Ü“Ü“Ü“è“è“è“è“è“è“<”<”<”<”D”D”D”D”D”D”L”L”L”4”T”T”\”d”J£J£ô“ô“”” ”””””””l”l”l”l””t”$”$”$”$”$”,”¤”ð•X—<˜ü˜x™TšpšT›h›ì›dŸ ¡€¡ô¡£h•x•Œ•œ•°•€–¤–È–ì–—4—¬™Ä™Ü™ô™š,š”š°šèš ›<›ô$žTž„ž´žØž WARNING, instance of x=x cannot be inserted into demod_imd index: contract_imd, increase MAX_AL_TERM_DEPTH.start of index-match-demodulate treeimd_delete, can't find alpha.imd_delete, can't find atom.v%d %s demod=is_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p binary_resneg_hyper_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subfree_all_memno_faplno_fanlprint_keptdemod_historysort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_allpara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdegrade_hints2clocksfpa_literalsfpa_termsdemod_limitmax_givenmax_levelsneg_weightmax_keptmax_genmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_maxERROR: flag name not found. lex_rpoprint_levelnew_functions flag already set. flag already clear. parameter name not found. reduce_weight_limitdelete_identical_nested_skolemdiscard_commutativity_consequences must have one simple argument. ERROR, flag `lex_rpo' has been changed to `lrpo'. ERROR, flag `print_level' no longer exists. ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. must have two simple arguments. ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatible ÝìßìßìßìßìßìßìßÀÝìßìßìßìßìßìßìßìßìßìßìßèÝìßìßì߈ßìßìßìßìßìßìßìßìßìßìߌÝxÝìßdÝÀܬÜìßìßìߨßìßìßìßìßìßìßÔÝìßìß`ß@ß@ßìßìßìßìßìßìßìßìßìßìßìßüÝìßìßìßìßìßìߘßìßìßìßìßìß,ßÞ¤Þìßìßìßìßpßpßpßapply_substitute, term not COMPLEX.apply_substitute: term too deep.dot_trans, bad dot notation fill_word, word too big: |%s| (Ù ‰ €(p…€‚ § ,Ù@Ї¨‡(þÿÿox‡ÿÿÿoðÿÿo‡ÿÿÿÿÿÿÿÿTØ>‰N‰^‰n‰~‰Ž‰ž‰®‰¾‰ΉÞ‰î‰þ‰ŠŠ.Š>ŠNŠ^ŠnŠ~ŠŽŠžŠ®Š¾ŠΊÞŠîŠþŠ‹‹.‹>‹N‹^‹n‹~‹Ž‹ž‹®‹¢ƒdä‹dä‹9<H€r€Œ€»€ó€0€€Ò€ý€,€V€€™€´€Õ€€1€V€€€©‚¢¢ ‚cV$‚ï[L‚b‚y‚¢¢¢‚ØƀǢڀ ñ€!€"€#3€%K€&a€1x€2€3§€4À€5Ø€6ñ€8 €9"€;B€=X€>n€?„€@š€A±€BÉ€C߀Dö€E €F$€G;€HT€Ii€NÏ€Qç€R€S€T9€UU€Vm€X…€[Ÿ€^·€eÍ€hç€l €q €r5 €uP €vm €yˆ €z¥ €}½ €€Ö €ƒñ €„ €‡& €Š@ ‚Ë”t ‚Fœ €¢Ò € €#V €Y €4u €< €Cú €F €S© €Zç €^€Ù€lù€tM€yn€ö€†4€Œ¢¢‚ L€b€8¢w‚Š‚b‚¢œ‚¢É€K¢¢L€€#Ô‚ç‚5ÁLÂwŠ‚Âœ¢Âø€×€€H8€Kg€L˜€UË€Z€^?€aw€b¯€\€€û€r€­¢¢–€5 €7!€89€9S€:¢m dä‹init.c/usr/src/build/87998-i386/BUILD/glibc-2.2.5/csu/gcc2_compiled.int:t(0,1)=r(0,1);-2147483648;2147483647;char:t(0,2)=r(0,2);0;127;long int:t(0,3)=r(0,3);-2147483648;2147483647;unsigned int:t(0,4)=r(0,4);0000000000000;0037777777777;long unsigned int:t(0,5)=r(0,5);0000000000000;0037777777777;long long int:t(0,6)=@s64;r(0,6);01000000000000000000000;0777777777777777777777;long long unsigned int:t(0,7)=@s64;r(0,7);0000000000000;01777777777777777777777;short int:t(0,8)=@s16;r(0,8);-32768;32767;short unsigned int:t(0,9)=@s16;r(0,9);0;65535;signed char:t(0,10)=@s8;r(0,10);-128;127;unsigned char:t(0,11)=@s8;r(0,11);0;255;float:t(0,12)=r(0,1);4;0;double:t(0,13)=r(0,1);8;0;long double:t(0,14)=r(0,1);12;0;complex int:t(0,15)=s8real:(0,1),0,32;imag:(0,1),32,32;;complex float:t(0,16)=r(0,16);8;0;complex double:t(0,17)=r(0,17);16;0;complex long double:t(0,18)=r(0,18);24;0;__builtin_va_list:t(0,19)=*(0,20)=(0,20)../include/libc-symbols.h/usr/src/build/87998-i386/BUILD/glibc-2.2.5/build-i386-linux/config.h../sysdeps/gnu/_G_config.h../sysdeps/unix/sysv/linux/bits/types.h../include/features.h../include/sys/cdefs.h../misc/sys/cdefs.h/usr/lib/gcc-lib/i386-redhat-linux/2.96/include/stddef.hsize_t:t(8,1)=(0,4)__u_char:t(4,1)=(0,11)__u_short:t(4,2)=(0,9)__u_int:t(4,3)=(0,4)__u_long:t(4,4)=(0,5)__u_quad_t:t(4,5)=(0,7)__quad_t:t(4,6)=(0,6)__int8_t:t(4,7)=(0,10)__uint8_t:t(4,8)=(0,11)__int16_t:t(4,9)=(0,8)__uint16_t:t(4,10)=(0,9)__int32_t:t(4,11)=(0,1)__uint32_t:t(4,12)=(0,4)__int64_t:t(4,13)=(0,6)__uint64_t:t(4,14)=(0,7)__qaddr_t:t(4,15)=(4,16)=*(4,6)__dev_t:t(4,17)=(4,5)__uid_t:t(4,18)=(4,3)__gid_t:t(4,19)=(4,3)__ino_t:t(4,20)=(4,4)__mode_t:t(4,21)=(4,3)__nlink_t:t(4,22)=(4,3)__off_t:t(4,23)=(0,3)__loff_t:t(4,24)=(4,6)__pid_t:t(4,25)=(0,1)__ssize_t:t(4,26)=(0,1)__rlim_t:t(4,27)=(4,4)__rlim64_t:t(4,28)=(4,5)__id_t:t(4,29)=(4,3)__fsid_t:t(4,30)=(4,31)=s8__val:(4,32)=ar(4,33)=r(4,33);0000000000000;0037777777777;;0;1;(0,1),0,64;;__daddr_t:t(4,34)=(0,1)__caddr_t:t(4,35)=(4,36)=*(0,2)__time_t:t(4,37)=(0,3)__useconds_t:t(4,38)=(0,4)__suseconds_t:t(4,39)=(0,3)__swblk_t:t(4,40)=(0,3)__clock_t:t(4,41)=(0,3)__clockid_t:t(4,42)=(0,1)__timer_t:t(4,43)=(0,1)__key_t:t(4,44)=(0,1)__ipc_pid_t:t(4,45)=(0,9)__blksize_t:t(4,46)=(0,3)__blkcnt_t:t(4,47)=(0,3)__blkcnt64_t:t(4,48)=(4,6)__fsblkcnt_t:t(4,49)=(4,4)__fsblkcnt64_t:t(4,50)=(4,5)__fsfilcnt_t:t(4,51)=(4,4)__fsfilcnt64_t:t(4,52)=(4,5)__ino64_t:t(4,53)=(4,5)__off64_t:t(4,54)=(4,24)__t_scalar_t:t(4,55)=(0,3)__t_uscalar_t:t(4,56)=(0,5)__intptr_t:t(4,57)=(0,1)__socklen_t:t(4,58)=(0,4)../linuxthreads/sysdeps/pthread/bits/pthreadtypes.h../sysdeps/unix/sysv/linux/bits/sched.h__sched_param:T(10,1)=s4__sched_priority:(0,1),0,32;;_pthread_fastlock:T(9,1)=s8__status:(0,3),0,32;__spinlock:(0,1),32,32;;_pthread_descr:t(9,2)=(9,3)=*(9,4)=xs_pthread_descr_struct:__pthread_attr_s:T(9,5)=s36__detachstate:(0,1),0,32;__schedpolicy:(0,1),32,32;__schedparam:(10,1),64,32;__inheritsched:(0,1),96,32;__scope:(0,1),128,32;__guardsize:(8,1),160,32;__stackaddr_set:(0,1),192,32;__stackaddr:(0,19),224,32;__stacksize:(8,1),256,32;;pthread_attr_t:t(9,6)=(9,5)pthread_cond_t:t(9,7)=(9,8)=s12__c_lock:(9,1),0,64;__c_waiting:(9,2),64,32;;pthread_condattr_t:t(9,9)=(9,10)=s4__dummy:(0,1),0,32;;pthread_key_t:t(9,11)=(0,4)pthread_mutex_t:t(9,12)=(9,13)=s24__m_reserved:(0,1),0,32;__m_count:(0,1),32,32;__m_owner:(9,2),64,32;__m_kind:(0,1),96,32;__m_lock:(9,1),128,64;;pthread_mutexattr_t:t(9,14)=(9,15)=s4__mutexkind:(0,1),0,32;;pthread_once_t:t(9,16)=(0,1)_pthread_rwlock_t:T(9,17)=s32__rw_lock:(9,1),0,64;__rw_readers:(0,1),64,32;__rw_writer:(9,2),96,32;__rw_read_waiting:(9,2),128,32;__rw_write_waiting:(9,2),160,32;__rw_kind:(0,1),192,32;__rw_pshared:(0,1),224,32;;pthread_rwlock_t:t(9,18)=(9,17)pthread_rwlockattr_t:t(9,19)=(9,20)=s8__lockkind:(0,1),0,32;__pshared:(0,1),32,32;;pthread_spinlock_t:t(9,21)=(0,1)pthread_barrier_t:t(9,22)=(9,23)=s20__ba_lock:(9,1),0,64;__ba_required:(0,1),64,32;__ba_present:(0,1),96,32;__ba_waiting:(9,2),128,32;;pthread_barrierattr_t:t(9,24)=(9,25)=s4__pshared:(0,1),0,32;;pthread_t:t(9,26)=(0,5)wchar_t:t(11,1)=(0,3)wint_t:t(11,2)=(0,4)../include/wchar.h../wcsmbs/wchar.h../sysdeps/unix/sysv/linux/i386/bits/wchar.h__mbstate_t:t(13,1)=(13,2)=s8__count:(0,1),0,32;__value:(13,3)=u4__wch:(11,2),0,32;__wchb:(13,4)=ar(4,33);0;3;(0,2),0,32;;,32,32;;_G_fpos_t:t(3,1)=(3,2)=s12__pos:(4,23),0,32;__state:(13,1),32,64;;_G_fpos64_t:t(3,3)=(3,4)=s16__pos:(4,54),0,64;__state:(13,1),64,64;;../include/gconv.h../iconv/gconv.h :T(17,1)=e__GCONV_OK:0,__GCONV_NOCONV:1,__GCONV_NODB:2,__GCONV_NOMEM:3,__GCONV_EMPTY_INPUT:4,__GCONV_FULL_OUTPUT:5,__GCONV_ILLEGAL_INPUT:6,__GCONV_INCOMPLETE_INPUT:7,__GCONV_ILLEGAL_DESCRIPTOR:8,__GCONV_INTERNAL_ERROR:9,; :T(17,2)=e__GCONV_IS_LAST:1,__GCONV_IGNORE_ERRORS:2,;__gconv_fct:t(17,3)=(17,4)=*(17,5)=f(0,1)__gconv_init_fct:t(17,6)=(17,7)=*(17,8)=f(0,1)__gconv_end_fct:t(17,9)=(17,10)=*(17,11)=f(0,20)__gconv_trans_fct:t(17,12)=(17,13)=*(17,14)=f(0,1)__gconv_trans_context_fct:t(17,15)=(17,16)=*(17,17)=f(0,1)__gconv_trans_query_fct:t(17,18)=(17,19)=*(17,20)=f(0,1)__gconv_trans_init_fct:t(17,21)=(17,22)=*(17,23)=f(0,1)__gconv_trans_end_fct:t(17,24)=(17,25)=*(17,26)=f(0,20)__gconv_trans_data:T(17,27)=s20__trans_fct:(17,12),0,32;__trans_context_fct:(17,15),32,32;__trans_end_fct:(17,24),64,32;__data:(0,19),96,32;__next:(17,28)=*(17,27),128,32;;__gconv_step:T(17,29)=s56__shlib_handle:(17,30)=*(17,31)=xs__gconv_loaded_object:,0,32;__modname:(17,32)=*(0,2),32,32;__counter:(0,1),64,32;__from_name:(4,36),96,32;__to_name:(4,36),128,32;__fct:(17,3),160,32;__init_fct:(17,6),192,32;__end_fct:(17,9),224,32;__min_needed_from:(0,1),256,32;__max_needed_from:(0,1),288,32;__min_needed_to:(0,1),320,32;__max_needed_to:(0,1),352,32;__stateful:(0,1),384,32;__data:(0,19),416,32;;__gconv_step_data:T(17,33)=s36__outbuf:(17,34)=*(0,11),0,32;__outbufend:(17,34),32,32;__flags:(0,1),64,32;__invocation_counter:(0,1),96,32;__internal_use:(0,1),128,32;__statep:(17,35)=*(13,1),160,32;__state:(13,1),192,64;__trans:(17,28),256,32;;__gconv_info:T(17,36)=s8__nsteps:(8,1),0,32;__steps:(17,37)=*(17,29),32,32;__data:(17,38)=ar(4,33);0;-1;(17,33),64,0;;__gconv_t:t(17,39)=(17,40)=*(17,36)_G_iconv_t:t(3,5)=(3,6)=u44__cd:(17,36),0,64;__combined:(3,7)=s44__cd:(17,36),0,64;__data:(17,33),64,288;;,0,352;;_G_int16_t:t(3,8)=(0,8)_G_int32_t:t(3,9)=(0,1)_G_uint16_t:t(3,10)=(0,9)_G_uint32_t:t(3,11)=(0,4)_IO_stdin_used:G(0,1)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)GCC: (GNU) 2.96 20000731 (Red Hat Linux 7.3 2.96-110)01.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.0101.01.symtab.strtab.shstrtab.interp.note.ABI-tag.hash.dynsym.dynstr.gnu.version.gnu.version_r.rel.dyn.rel.plt.init.text.fini.rodata.data.eh_frame.dynamic.ctors.dtors.got.bss.stab.stabstr.comment.noteô€ô# 1((X7 €‚€ð?p…p§Gÿÿÿo‡^Tþÿÿox‡x0c ¨‡¨(l ЇÐ@ u‰ p(‰( {À‹À Àu€€‡  _Æ ØHP•PØPHŸTØTHȨÙI¯$Ù$I¶,Ù,I°»àÙàI–é ÀàI¤ Æ„QƒÏkc Øjv$ŽzÞôð^¼ äÞƒNô€(€‚p…‡x‡¨‡Ї ‰ (‰ À‹ €  ØPØTØÙ$Ù,ÙàÙñÿñÿä‹ "ä‹ 2ñÿŒ =ØA$ÙO Ø[Œ qPØ„pŒ ðÙ˜€Œ ¤°Œ ¯Ø½Ù2ñÿ@ Ë@ á Ù¤p ¯PØî(ÙûPØñÿ€ ñÿÀŒ ØØ'ÀŒ£ 9d5 GœV aô r„! y¨Ö ‰ñÿÜ“ ‘ñÿ”” ™””& £Úª¼”9 ¶ÚÁÚÍ Ú×Úäñÿ`– ëñÿœ óñÿx  ñÿ ¢ \£@ œ£X )ô¤X 7L¥p @¼¥1 Fñÿœ§ K ØXœ§7 dHÚrÔ§ ,Ú…¬¨ •@Ú¦DÚ¶Ȩ! 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gelrpo.cwarning_given.0sym_precedencelrpo_statuslrpo_lexnum_occurrencesset_multiset_difflrpo_multisetlinkur.cconstruct_children_nodeslinked_print_clauseposs_nuc_linkwrite_target_distancessubsumable_unitlinked_unit_delbackwardkeep_clauseinitialize_treelinked_print_link_node_treepass_parms_checkgenerate_resolventforwardis_in_ancestrybuild_ur_resolventforward_from_resolved_treebuild_parental_chaincheck_down_treecheck_up_treefirst_unifiablenext_unifiablefree_linked_node_treeterm_ident_substlinked_print_link_nodemore_targets_hereprocess_this_resolutionpass_target_depth_checkwrite_down_treewrite_up_treelinkhyp.cforeign.cgeometry.cis_geometry_symbolgeo_rewrite_recursegeo_replace_unifgeo_generate_unifgeo_recurse_unifhot.cOrdinary_clash_pos_litsOrdinary_clash_neg_litsOrdinary_clash_termsOrdinary_alphasHot_clash_pos_litsHot_clash_neg_litsHot_clash_termsHot_alphashot_mark_clashhot_unmark_clashnonport.chost.0fork_level.1check.cinit_gen_tabinsert_into_gen_tabretrieve_from_gen_tabp_gen_tabcheck_eq_litNew_proof_tabpo_rulenew_literal_indexcopy_subst_to_proof_objectmatch_literalsidentity_paramodtranslate_unit_deletiontranslate_factor_simpfirst_rewritefirst_rewrite_clausetranslate_demod_nonunitNew_proof_old_id_tabtranslate_demod_unittranslate_resolutionorder_new_lits_for_hypertranslate_hypertranslate_urtranslate_factorpara_positiontranslate_paramodvarmapmatch2translate_stepOld_proof_tabhints.cprocess_hint_attributeshints2.cFpa_hints2_litsfirst_nonanswer_litnext_nonanswer_litzap_ilistcopy_hint2_dataindex_hint2process_hint2_attributesall_containing_hints2xx_tautologyhint2_subsumedattrib.ccase.ccompare_literal_datainit_literal_datap_literal_dataget_literal_datanext_attempt.0ivy.cInitial_proof_objectbnode_to_naturalbnode_to_ottertermbnode_to_clausepickdiff.ccopy_relszap_relsremove1add_vecsle_vecsdiff_listsdiffmin_diffdiff2diff2_listsget_ci_of_wt_rangeoverbeek.chash_term2multijust.cremove_those_containingg2_supersetappend_parentsprint_multi_supportersjust_lists_to_supporters_listsbuild_support_listsAlistscollapse_new_demod2AsizeDemod_mapmulti_mapBsizeA_to_BBlistsB_to_ASet_sizej_compareComparesjhash_initJhashjhashjhash_member_recurseCrashesjhash_memberLookupsjhash_insert_recursejhash_insertprint_jhashget_jnodeb_inputa_inputprint_jnodeprint_jnode_b_to_ajproofKeptSubsumedPrunedGeneratedExpandedj_subsumed_recursej_subsumediset_jset_disjointj_expandJendj_searchJstartJcurrentlists.cfpa2.cconsolidatedemod.ccontract_lindollar_out_non_listdollar_outunique_num.0dollar_contractreplace_specialdemodleft_most_one_stepdemod_out_inlimit_warning_issued.1imd.cinsert_imd_treeend_term_imdis.cinsert_is_treeend_term_isoptions.cindex.cindex_mark_clashun_index_mark_clashindex_paramodun_index_paramodparamod.capply_substitutebuild_bin_parainsert_detailed_para_historypara_from_uppara_from_alphapara_into_termslisp.cstr_identnew_str_copyget_bnodeGetsfree_bnodeFreeswhite_charparenfill_wordWorddotpdot_transMACE_Parmscopy_ilistlrpoterm_fixup_2copy_glist_of_ilistsmaximal_litremove_from_jsetcontract_imdcl_appendfind_given_clausegeo_rewriteMACE_FlagsUser_functionscarswitch_to_ordinary_indexFpa_clash_neg_litsfree_clash_ndsig_handlerprint_times_briefNext_baseInternal_flagsset_vars_termtrans_logic_symbolscopy_ilist_segmentHintsread_cl_listsubset_or_inputnon_portable_initfind_hint2sn_occurgen_sk_symfirst_fposWeight_terms_indexreverse_ipinsert_before_clsn_to_strterm_to_attributesMACE_total_mempre_processheat_is_on__strtod_internal@@GLIBC_2.0hint2_keep_testfree_ans_lit_nodefree_termcl_copyfind_pickdiff_clp_hint_clausecl_delete_tablex_ordernew_var_nameinteractunifyget_term_ptrMax_input_idgen_subsume_propFpa_clash_termsMACE_Clockslit_compareprint_pathcontains_ruleunit_clausefree_trailexit_with_messagefree_is_treeCurrent_casefree_imd_pos_listp_fpa_tabMACE_clock_resettest_termsChr_sym_numbiggest_var_clausevar_nametype_2_transnnf_skolemizefree_glist_of_ilistsdeclare_opusernameuser_test_stringreverseprint_model_ivyset_up_pointersFloat_formatungetc@@GLIBC_2.0pos_clauseprint_substproof_last_hidden_emptygetpid@@GLIBC_2.0_DYNAMICauto_change_parmcheck_input_demodHotipxweight_index_deleteinit_hotMACE_p_optionsspecial_is_symbolfirst_just_input_onlynum_literals_including_answersdelete_attributesuser_test_termUsableprint_imd_treecheck_for_proofflatten_topjust_to_supporterspossibly_append_parents__register_frame_info@@GLIBC_2.0input_clauseget_contextall_cont_clprint_proof_object_nodewrite@@GLIBC_2.0Is_pos_litslocaltime@@GLIBC_2.0gen_subsume_recinsert_after_clcheck_stopreset_clause_counternoncomplexifyingstrcmp@@GLIBC_2.0proof_not_longer_thanall_instancesbool_to_termdecode_and_p_clauseMACE_pp_clauseiset_subtractprint_hint_clauseget_timeWeight_termsterm_fpa_recset_jset_sizeSymbolsexpand_implex_check_fp_hwremove_answer_literalsStatskludgey_e_subsumeread_listMACE_change_parmglist_subsumefree_glistassumps_to_parentfprintf@@GLIBC_2.0fork@@GLIBC_2.0tmpfile@@GLIBC_2.1more_setupiso_prunesignal@@GLIBC_2.0print_setfflush@@GLIBC_2.0set_varsmap_demodprint_clause_baresubsume_disjnext_termprint_proofget_clause_ptrderived_from_itselfmerge_sortcontrol_memoryoverbeek_weightmulti_justificationsjset_membernum_answersterm_identterm_to_formulamember_is_subsetclear_subst_1check_optionsbuild_for_allDomain_sizeprint_fpa_tabgetrusage@@GLIBC_2.0print_statsget_clauses_of_wt_rangefind_interactive_clp_term_shot_cl_integrateflist_insertget_formulaadd_args_to_setread_termset_special_unaryFpa_back_demodnew_sym_numNil_sym_numadjust_weight_with_hintshint2_integratedistribute_quantifierzap_quantpara_intoxx_resolvablesos_has_pos_nongroundMACE_dependent_flagslengthrenumber_vars_substfree_fnodeswitch_to_hot_indexulong_bitsprint_clauseliteral_numberbuild_proof_objectdisplay_termcldiffprint_hint2_clausecommuted_termsdemod_clweight_clskip_whitereinit_dpgetpwuid@@GLIBC_2.0Fpa_pos_litsread_formulaprint_cl_listBellzap_listhostnamecanc_fs_posiff_to_conjgen_conflictclear_var_namesMACE_init_optionsfree_formula_ptrmark_literalMACE_p_clausehot_mark_clash_clfree_contextback_demod_hintsretrieve_initial_proof_objectdisintegrate_termfind_mid_lightest_clp_term_tabgeometry_rule_unifrewind@@GLIBC_2.0unique_allNull_outputinit_clocksp_formularms_conflict_tautologyWeight_purge_genprint_justificationclause_identcaddrfree_fpa_headfree_sym_tabset_lex_valsprint_clause_s2process_negative_equalitiesun_index_lits_clashneg_eq_litp_imd_treesplitable_literalclause_ptr_list_sizeMACE_dependent_parmsclear_subst_2formula_identcat_strprint_clause_sreinit_generatecurrent_casesubsumedadd_subcaseur_resmulti_just_processremove_all_supersetsremove_supersetsproof_length_initset_vars_clprint_model_portablep_unitMACE_tp_allocdp_transabendfree_g2listreinit_memtp_allocauto_lex_ordercontains_answer_literalmalloc@@GLIBC_2.0zap_ci_ptr_listanti_skolemizebuild_treeiset_removeprint_mem_briefint_termsplittingtrivial_substfscanf@@GLIBC_2.0free_ilist_listcopy_formulagetppid@@GLIBC_2.0read_clauseneg_hyper_respipe@@GLIBC_2.0cnfAttributesun_index_lits_allsplit_clauseterm_ident_x_varsTo_childrenchange_parmprint_clause_without_justdomain_elementfree_clause_ptrFirst_orderapply_clauseget_proof_object_nodeclausify_formula_list__deregister_frame_info@@GLIBC_2.0print_linked_ur_mem_statsfree_reldecode_intDots_sym_numparse_lispeq_litcl_clear_varsdependent_flagsnegation_inwardback_demodalways_splitTo_parentfree_imd_posglist_appendread_wt_listall_instances_fpap_proof_object_nodebird_printFrom_childrenclock_initdouble_strinsert_symstdout@@GLIBC_2.0append_clstderr@@GLIBC_2.0order_equalities_lrpozap_hints2subst_sn_formulabin_resMACE_abendfactor_simplifycompare_splitable_clauseshint_keep_testclock_resetprint_proof_objectrms_subsume_conjis_insertprint_memp_clause_sget_listrms_cnfwall_secondsDemod_imdunit_delis_skolemflatten_clausescompile_hintssplit_atomnext_fposis_symbolsymmetry_clauseconvenient_demodcl_del_intwrite_termindex_lits_clashnnf_dnffpa_deletefree_fpa_treeattribute_typesos_argumentget_is_treeproc_gensubsume_conjrun_timeFpa_neg_litsfs_retrievecl_int_chkoccur_checkprint_symssubst_free_formulaprf_weightprint_term_nllex_order_varsclause_to_termlinked_ur_restime@@GLIBC_2.0get_relhorn_clausesystem_timefinish_translatingfree_fsub_pos_startcontains_skolem_symbolrms_quantifierssub_clausegetopt@@GLIBC_2.0is_deleteMACE_output_statsmatch_clausesinsert_dp_clausecompare_for_auto_lex_orderget_fnodeevaluate_user_functionall_factorsget_is_posread_sequent_clausefree_formula_boxatom_valuecl_copy_delete_literalprint_trailsubsumeWeight_pick_given_indexforeach_sosmark_as_skolemMACE_print_statsMACE_print_optionsrms_distribute_quantsis_eqp_proof_object_as_hintsbits_ulongget_ci_ptrInit_wall_secondsfree_clauseilist_to_jsetterm_to_clauseorder_equalitiesdeclare_user_functionsget_termilist_appendinsert_clauseDemodulatorscase_depthinitial_strsn_to_nodesplitable_clausehot_inferenceinit_dpin_sym_tabOverbeek_termsprint_case_nFpa_alphasdouble_to_termglist_prependsame_structurelrpo_greater__strtol_internal@@GLIBC_2.0auto_MACE_change_parmoutput_statsget_formula_ptriset_addp_optionsfree_sym_entnew_functor_nameget_imd_posgen_subsumebuild_termzap_prop_treepossible_given_splitprint_errorfree_link_nodeinitcdrfind_lightest_geo_childclock_valcl_mergeMACE_clock_valpretty_print_termprint_term_sfree_is_posfree_is_pos_listcl_insert_tabimd_insertindex_lits_allprint_hints2_cl_listlong_to_termneg_clauseget_ilistget_attribute_indexautomatic_2_settingsprepend_clprint_modelgen_tautologyMACE_change_flagnullpp_statsprint_overbeek_worldfind_match2From_parentnth_clausep_symsfind_first_clstr_to_termis_retrieve__bss_starthot_index_clauseprint_formula_listzap_clause_ptr_listmaincleanupget_clauseassign_cl_idparse_initial_proof_objectrms_dnfWeight_pick_givensn_to_arityone_unary_answerrms_subsume_disjstr_doublefind_clause_to_splitpos_eq_litMACE_Statspossible_splithot_dynamiccl_find__libc_start_main@@GLIBC_2.0print_listfree_term_ptrg2list_lengthSosadd_to_jsetrmslog_for_x_showmax_literal_weightall_supporters_less_thanget_trailmap_restpara_fromfree_imd_treeget_link_nodeIgnore_sym_numprint_set_b_to_aintegrate_termun_share_specialp_case_nrenumber_uniquepost_proc_allterm_fixupread_a_filedel_hidden_clausesfor_sub_propget_proof_objectfirst_or_next_factoranc_subsumetotal_memanswer_litprint_hints_cl_listMACE_print_memprint_variablep_proof_objectmove_clausesmax_split_depthdata_startasctime@@GLIBC_2.0read_all_mace_inputnnfrms_push_freeSubsume_countnext_cl_numprintf@@GLIBC_2.0propositional_clauseSplit_atomsfind_lightest_clfind_random_clzap_termcheck_for_bad_thingsgetuid@@GLIBC_2.0_finiprint_sequent_clausememcpy@@GLIBC_2.0connect_new_nodeautomatic_1_settingsp_is_treegl_demodstr_to_snilist_memberIs_neg_litsconflict_tautologyprint_formulap_termfclose@@GLIBC_2.1auto_MACE_change_flagiset_subsetread_all_clausesget_attributefree_all_membuild_bin_resset_wt_listts_and_fsunit_conflictcopy_jsetatomsym_tab_memberrem_from_listfprint_btreeGreatest_atomproper_listget_jsetclausifyget_ans_lit_nodeback_subsumeWeight_purge_gen_indexp_clauseModelsoverbeek_insertuser_test_boolauto_change_flagoccurrencesground_clauseprover_forksset_lrpo_statuslinked_hyper_resMACE_pp_clause_activeOverbeek_worldget_sym_entgethostname@@GLIBC_2.0get_ancestorsskolemizechange_flaginfer_and_processget_fpa_headsymbol_countis_atomstring_to_terminit_optionsstr_longread_all_inputp_assumption_depthsbd_kludge_deletezap_formulafind_random_lightest_clback_unit_deletioninit_special_opsnnf_cnfinit_proof_object_environmentrenum_vars_termreportget_g2listprint_attributesp_timesprocess_op_commandprint_prop_treefind_atom_to_splitflist_deleteexit@@GLIBC_2.0check_overbeek_worldfoobuilt_in_symbolsMACE_check_optionsp_ilistzap_term_specialfree_formulap_caseMACE_p_statsp_btreecalloc@@GLIBC_2.0init_log_for_x_showprint_casebd_kludge_insertiset_sortjset_to_ilistdynamic_demodulatorget_fpa_treeappend_lists_edata_GLOBAL_OFFSET_TABLE_free@@GLIBC_2.0variable_optimize_endmatchget_gen_nodednfParmsp_substilist_lengthget_imd_treep_prop_treefree_clause_ptr_listremove_var_symsapply_demodunify_no_occur_checkMace_constraintsg2_remove_supersetsskolem_symbolfree_cl_attributeFpa_clash_pos_litsprint_timeskeep_onlyith_literalp_memp_clause_s2p_pathstdin@@GLIBC_2.0occurs_intotal_mem_callsidentity_resolvefree_literalfree_ilistget_glistprint_ilistimd_deleteread_bufclausify_formeddp_provermy_process_idget_formula_boxfpa_insertwt_matchinit_attributesnegate_formulaforward_subsumesn_to_ecprint_termvariantname_symfopen@@GLIBC_2.1Sortsordered_sub_clauseiff_to_disjtrue_listpcombine_answerscl_del_nonoptarg@@GLIBC_2.0user_test_doublehide_clausestr_intFlagsilist_tack_onhyper_resapplyget_literal_IO_stdin_usedget_cl_attributeformula_to_termcommutativity_consequenceprint_stats_briefget_args_for_user_functionlong_strrename_syms_formulaget_fsub_posprint_term_lengthd_termcl_integratesubst_sn_termglist_lengthzap_btreep_atomget_formula_ptr_2Num_sortsNum_symbolsglist_tack_ondependent_parmsset_skolemread_formula_listdistinct_varsalloc_fpa_indexsprintf@@GLIBC_2.0exit_if_over_time_limitident_nested_skolemslit_t_f_reduceHints2biggest_varuser_test_longprint_is_treeadjust_weight_with_hints2init_proof_objectPassive__data_startget_clash_ndcopy_termexit_with_possible_modelset_attributeget_ancestors2zap_variable_namesequality_clause_IO_getc@@GLIBC_2.0free_listflatten_clausefunction_valuefree_glist_listprocess_linked_tagscadrCons_sym_numtautologyrand@@GLIBC_2.0overbeek_matchclauses_to_idsint_strrenumber_vars_termnew_demodp_hints_cl_listsort_litsweightinit_statszap_cl_listfree_ci_ptrvar_subsetextract_given_clauseread@@GLIBC_2.0child_of_geometryfree_formula_ptr_2find_last_clcheck_transformed_clausegroundClocksprint_optionsnum_literalsMACE_print_timesidempot_ipfree_occurrencewait@@GLIBC_2.0copy_glisttrans_2_pos__gmon_start__print_term_tabcompile_hints2strcpy@@GLIBC_2.0renumber_varsotter-3.3f/bin-Linux/anldp0100755000076400007640000122257210103520051015070 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Sè´ÿÿÿ‰$èØÿÿÿƒÄ@ë‰ö¸‹]üÉÉöU‰åSƒì¡”Ñ»”уøÿtv¼'ƒëÿЋƒøÿuôX[]ÃU‰åƒì‰ì]öU‰åSRè[ÃÓvèwüÿ‹]üÉÃAugust 20032.2----- ANLDP %s, %s ----- The command was "". command-line options: spPIhcm:t:k:n:d:x:print_modelsmax_modelsmax_secondsmax_mem%sThe process was started by %s on %s, %s ANLDP %s -- Search for finite models. Input clauses are taken from standard input. -p | Print all models as they are found. -m n | Stop when the n-th model is found. -t n | Stop after n seconds. -k n | Tp_allocate at most n K bytes. -s | Perform unit subsumption. (Always done on input.) -h | Print this message. +----------------------------------------------------------+ | SEGMENTATION FAULT!! This is probably caused by a bug | | in MACE. Please send copy of the input file to | | otter@mcs.anl.gov, let us know what version of MACE you | | are using, and send any other info that might be useful. | +----------------------------------------------------------+ MACE_sig_handler, cannot handle signal %d. WARNING, MACE_CLOCK_STOP: clock %d not running. WARNING, MACE_CLOCK_STOP: clock %d not running. ¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨Ž¨ŽxŽ¨Ž@Ž¨Ž¨Ž$Ž¨Ž¨ŽŽ\Žin MACE_tp_alloc, request too big.in MACE_tp_alloc, operating system cannot supply any more memory.г@print_models_portableprint_models_ivydistinct_constantsqg_constraintrecord_assignmentsclause_splitiso_xiso_constantspart_varsset(clear(%s). assign(%s, %d). setclear dependent: %s(%s). ERROR: flag `%s' not found. WARNING: flag `%s' already set. flag `%s' already clear. ERROR: assign(%s, %d),WARNING: assign(%s, %d), already has that value. Called MACE_check_options. --------------- options --------------- dependent: assign(%s, %d). ERROR: parameter `%s' not found. integer must be in range [%d,%d]. ------------- memory usage ------------ Memory dynamically allocated (MACE_tp_alloc): %d. ----- statistics for domain size %d ---- Clauses input %7ld Literal occurrences input %7ld Greatest atom %7ld Preprocess unit assignments %7ld Clauses after subsumption %7ld Literal occ. after subsump. %7ld Selectable clauses %7ld Splits %7ld Unit assignments %7ld Failed paths %7ld Memory malloced %7ld K Memory MACE_tp_alloced %7d K Generate ground clauses %10.2f DPLL %10.2f ======================================= Total times for run (seconds): user CPU time %10.2f system CPU time %10.2f wall-clock time %7ld Input: Unit preprocess: Decide: Memory: Time (seconds): (%ld hr, %ld min, %ld sec) @@Abnormal end.The search is complete.Exit by max_mem parameter.Exit by max_models parameter.Killed by SIGINT signal.Killed by SIGSEGV signal.Input error.Exit with unknown code.No models were found. %s %s ********** %s Exit by max_seconds parameter. Input error. See the output file. The set is satisfiable (%d model(s) found). ********** ABNORMAL END ********** ”´œ¤¬´¼ÄÌanswer literals not allowed in MACE inputevaluable literals not allowed in MACE input%% WARNING: possible error in check_transformed_clause: equaldp_trans, too many variables%% original: %% transformed: unit_enqueue: queue too small( -%d ), active=%d Atom=%d, value=%d, pos_occ=%x, neg_occ= Selectable clauses: HERE it is!!atom_value, atom out of rangeatom_value, bad value Initial assigments: Model #%d:end_of_model assign: atom already assignedunassign: atom not assigned) active_neg=%d, active_pos=%d, subsumer=%d insert_dp_clause, increase ATOM_INT_MAX and recompile.Propositional input must be all integers; if you have first-order input, the domain size must be given (-n). Order of assigments for the following model: The %d%s model has been found. After all unit preprocessing, %ld atoms are still unassigned; %ld clauses remain; %ld of those are non-Horn (selectable); %ld K allocated; cpu time so far for this domain size: %.2f sec. declare_symbol_sorted, too many symbolsdeclare_symbol_sorted: sort not found*** Unsatisfiability detected *** add_unit: element out of domainadd_unit: sign must be 1 or -1process_variables, variable too big.process_variables, badly sorted clauseadd_clauses_for_qg_constraint, symbol f not foundAdding basic QG constraints on last column of f. number_variables, element out of range Maximum number of variables is %d. number_variables, too many variablestrans_relational_clause: too many first_order clausestrans_relational_clause: bad DP argtrans_relational_clause: bad DP arg (right)trans_relational_clause: bad eq argtrans_relational_clause, bad functorRemoving answer literals from clause %d. WARNING, CLOCK_START: clock %d already on. WARNING, CLOCK_STOP: clock %d already off. MACE_collect_symbols, multiple arityApplying isomorphism constraints to constants:dp_trans, wrong arity in mace_constraints list.dp_trans, symbol in mace_constraints list not founddp_trans, mace_constrationts property not understooddp_trans, mace_constraints command not understooddp_trans, bad integer (RHS) in assignmentdp_trans, bad truth value in assignmentdp_trans, bad integer (LHS) in assignmentCannot make constant %s distinct, domain is too small. Adding unit assigning %s %d (distinct_constants). order relation must have args of same typeequality relation must have args of same type %d clauses were generated; %d of those survived the first stage of unit preprocessing; there are %d atoms. %s%s%s%s%swell_defined, bad arityclosed, bad arity The bad element is %d. Bad name=%s list(clauses). arity too greatunivpropertyequalityorderquasigroupbijectioncommutativeassignBad name=%s, dp_trans, bad functorAdding unit assigning %s%sfunction %s bijection. function %s quasigroup. <ÅDÅHÅTÅhÅÄÔØÔèÔÕ4Õ %s: %d %2d%3d %s : --- - | --+%5d | %s: %s %2s$Connect function(%s, [%d]) function(%s(_), [ function(%s(_,_), [ %d, %d, %d ])%d, 0 predicate(%s, [%s]) predicate(%s(_), [%s, %s, %s ])%s, interpretation( %d, [ ]). ((%s . 0) . ((nil . %d))) ((%s . 1) . ( ((%d) . %d) )) ((%s . 2) . ( ((%s . 3) . ( ((%s . 0) . ((nil . %s))) ((%d) . %s) ((%s . 4) . ( ;; BEGINNING OF IVY MODEL (0 . ((. %d) . ( ( ) . ( ) ) ) ;; END OF IVY MODEL ======================= Model #%d at %.2f seconds: Dimension %d table for %s not printed predicate(%s(_,_), [ predicate(%s(_,_,_), [ predicate(%s(_,_,_,_), [ Dimension %d table for %s not printed ((%d %d) . %d) ((%d %d %d) . %d) ((%d %d) . %s) ((%d %d %d) . %s) ((%d %d %d %d) . %s) print_model_ivy, max relation arity is 4print_model_ivy, max function arity is 3<ûHûTû`ûlûœ¨´À v%dtp_alloc, request too big: %d (free_all_mem cleared). Search stopped in tp_alloc by max_mem option. %cSearch stopped in tp_alloc by max_mem option. (print_lists_at_end cleared). ABEND, malloc returns NULL (out of memory). %cABEND, malloc returns NULL (out of memory). ERROR, context %x, var %d not null. %d mallocs of %d bytes each, %.1f K. type (bytes each) gets frees in use avail bytes sym_ent (%4d) %11lu%11lu%11lu%11lu%9.1f K term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr_2 (%4d)%11lu%11lu%11lu%11lu%9.1f K fpa_head (%4d) %11lu%11lu%11lu%11lu%9.1f K fnode (%4d) %11lu%11lu%11lu%11lu%9.1f K fpa_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context (%4d) %11lu%11lu%11lu%11lu%9.1f K trail (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K imd_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K is_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K fsub_pos (%4d) %11lu%11lu%11lu%11lu%9.1f K literal (%4d) %11lu%11lu%11lu%11lu%9.1f K clause (%4d) %11lu%11lu%11lu%11lu%9.1f K list (%4d) %11lu%11lu%11lu%11lu%9.1f K clash_nd (%4d) %11lu%11lu%11lu%11lu%9.1f K clause_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K ilist (%4d) %11lu%11lu%11lu%11lu%9.1f K ci_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K link_node (%4d) %11lu%11lu%11lu%11lu%9.1f K ans_lit_node(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_box(%4d) %11lu%11lu%11lu%11lu%9.1f K formula(%4d) %11lu%11lu%11lu%11lu%9.1f K formula_ptr(%4d) %11lu%11lu%11lu%11lu%9.1f K cl_attribute(%4d) %11lu%11lu%11lu%11lu%9.1f K glist (%4d) %11lu%11lu%11lu%11lu%9.1f K g2list (%4d) %11lu%11lu%11lu%11lu%9.1f K type (bytes each) gets frees in use avail bytes term (%4d) %11lu%11lu%11lu%11lu%9.1f K rel (%4d) %11lu%11lu%11lu%11lu%9.1f K term_ptr (%4d) %11lu%11lu%11lu%11lu%9.1f K is_tree (%4d) %11lu%11lu%11lu%11lu%9.1f K context gets=%lu frees=%lu inuse=%lu trail gets=%lu frees=%lu inuse=%lu fpa_tree gets=%lu frees=%lu inuse=%lu term gets=%lu frees=%lu inuse=%lu link_node gets=%lu frees=%lu inuse=%lu €„Ž@P?$Quantified$Hyps$Concs$ANS$Ans$ans$NUCLEUS$BOTH$LINK$SATELLITE$FSUB$BSUB$EQUIV%d %s/%d, lex_val=%d is_skolem, no symbol for %d.end_of_listend_of_list. (nil)$nil$cons[]%c%d$IGNORE$CHR$dots$$SUM$PROD$DIFF$DIV$MOD$EQ$NE$LT$LE$GT$GE$AND$OR$NOT$TRUE$T$F$ID$LNE$LLT$LLE$LGT$LGE$BIT_AND$BIT_OR$BIT_XOR$BIT_NOT$SHIFT_LEFT$SHIFT_RIGHT$INT_TO_BITS$BITS_TO_INT$IF$NEXT_CL_NUM$ATOMIC$INT$BITS$VAR$GROUND$OUT$FSUM$FPROD$FDIFF$FDIV$FEQ$FNE$FLT$FLE$FGT$FGE$COMMON_EXPRESSION$RENAME$UNIQUE_NUM$OCCURS$VOCCURS$VFREE#<->&!====/=@<@>@<=@>=/'xfxinfixxfyinfix_rightyfxinfix_leftprefixxfpostfixprefix_assocyfpostfix_assoc ***HERE*** adjusted term: ERROR, comma or ) expected: ERROR, name expected: ERROR, ')' expected: ERROR, '}' expected: ERROR, term too big: exists ERROR, text after term: %c WARNING, multiple arity: %s/%d, %s/%d. %c WARNING, unrecognized $ symbol: %s. mark_as_skolem, no symbol for %d.op command must have arity 3. ERROR: first argument of op command must be 1..999. ERROR: second argument of op command must be xfx, xfy, yfx, xf, yf, fx, or fy. ERROR: list in op command must be all names. ERROR: third argument of op command must be a name or a list. ERROR, name too big, max is %d; ERROR, quoted name has no end; ERROR, functor has no arguments: ERROR, ']' expected in list: ERROR, ], |, or comma expected in list: ERROR, unrecognized error in term: ERROR in quantifier prefix starting here: ERROR, the %d terms/operators in the following sequence are OK, but they could not be combined into a single term with special operators. The context of the bad sequence is: ERROR, characters after last period: %s read_buf, quoted string has no end:%sread_buf, input string has more than %d characters, increase MAX_BUFread_buf, input string (which contains quote mark) has more than %d characters, increase MAX_BUFcompare_for_auto_lex_order, strings the same: %s.integrate_term, already integrated.WARNING, disintegrate_term, contained term. WARNING, disintegrate_term, contained term: disintegrate_term, cannot find term.disintegrate_term, bad containment.WARNING, zap_term, contained term. WARNING, zap_term, contained term: WARNING, bd_kludge_delete, term not found. WARNING, bd_kludge_delete, term not found: bucket %d: bucket %d: containing terms: build_tree_local, var and not more general.new_sym_num: too many symbols requested. fpa index %p bucket %d and or Substitution in context %p, multiplier %d v%d -> context %p status %d Trail: <%d,%p>ERROR, too many variables, max is %d: ERROR, weight template: ***** Turn Debugging Mode ON ***** ***** Turn Debugging Mode OFF ***** WARNING, cl_integrate gets clause with ID: cl_del_int, bad equality clause. literal, address:%p sign:%d type:%d; atom: cont_cl:%p, atom container:%p ERROR, clause contains variable literal: ERROR, arrow not found in sequent: ERROR, input clause contains too many variables: ERROR, input clause contains Skolem symbol: ERROR, input literal contains Skolem symbol: forward_subsume, MAX_LITS too small.back_subsume, MAX_LITS too small. NOTE: back_subsume called with empty clause. cl_insert_tab, clause already there.cl_delete_tab, clause not found.ordered_sub_clause: not total.WARNING, clause %d not found, proof is incomplete. interaction failure: cannot find tty. Enter clause number of next given clause, or 0 to terminate interactive_given mode, or -1 to print list sos. ? %c Not an integer: "%s", try again. Turning off interactive_given mode. Ok, clause %d will be given. unit_del, too many variables introduced.cl_del_int, bad clause.checking clause, address:%p .%dbinaryneg_hyperpara_intopara_fromfactor_simplinked_urevalgL-idgLcopyflipclausifyback_unit_delsplit_negpropositional(heat=%d) [] | (list nil) Eqfind_random_cl, sos bad./dev/tty%c Clause %d not found. %c Clause %d not in sos. €«t«h«\«P«D«8«´ª ««ôªäªÔªĪ¤ª,««”ª„ªtªdªTªDªur_res: too many clash nodes (nuc).ur_res: too many clash nodes (sat).build_term, bad arity.ifFALSEERROR, skolem gets: $c$fintroduce_var, bad formula.renumber_unique, bad formula.`ŒttttÈ  Ì Ì œ H ´  d à à | 4 ¤  ERROR, input formula contains Skolem symbol: ERROR, skolem gets negated non-atom: WARNING, the following formula has constant '%s', whose name may be misinterpreted by the user as a variable. disj_to_clause, too many variables in clause, max is %d.rms_push_free has extra quantifier.renumber_unique, too many vars.>>>> Starting back demodulation with %d. >>>> Starting back unit deletion with %d. Memory warning: resetting max_weight to %d. keeping clause because it matches a hint. Following clause subsumed by %d during input processing: %cSearch stopped by max_proofs option. Search stopped by max_proofs option. %d back subsumes %d. after demodulation: deleted because weight=%d. Subsumed by %d. ** KEPT (pick-wt=%d): ---> New Demodulator: (lex-dependent) Process %d finished %s/dev/null%.12fincludeERROR, cannot open file %s. ERROR, bad argument to list: axiomsdemodulatorspassivehotmace_constraintsforeachERROR, unknown list: formula_listERROR, unknown formula_list: weight_listpurge_genpick_givenpick_and_purgeERROR, unknown Weight_list: lexlrpo_multiset_statuslrpo_lr_statusoverbeek_termssplit_atomsspecial_unaryopfloat_formatmake_evaluableinitial_proof_objectoverbeek_worldoverbeek_world: term errorsERROR, command not found: list(sos). -f %% Reading file %s. -sERROR, bad demodulator: ------------> process sos: %2d:%-4d %2d:%-4d All others: %d. (hot clauses kept)%7ld user CPU time %10.2f system CPU time %10.2f wall-clock time %7ld input time %10.2f clausify time %10.2f process input %10.2f pick given time %10.2f binary_res time %10.2f hyper_res time %10.2f neg_hyper_res time%9.2f ur_res time %10.2f para_into time %10.2f para_from time %10.2f linked_ur time %10.2f back unit del time%9.2f pre_process time %10.2f renumber time %10.2f demod time %10.2f order equalities%9.2f unit deleletion%10.2f factor simplify%10.2f weigh cl time %10.2f hints keep time%10.2f sort lits time %10.2f forward subsume%10.2f delete cl time %10.2f keep cl time %10.2f hints time %10.2f print_cl time %10.2f conflict time %10.2f new demod time %10.2f post_process time%10.2f back demod time%10.2f back subsume %10.2f factor time %10.2f hot list time %10.2f unindex time %10.2f neg_hyper time %10.2f UR_res time %10.2f for_sub time %10.2f back_sub time %10.2f conflict time %10.2f demod time %10.2f list(usable). list(demodulators). sos_size=%d %c--- refuted case %c-------- PROOF -------- Length of proof is %d. Level of proof is %d. Case Weight of proof is %d.%d,clauses in usable. paramodulation is disabled. given %ld generated %ld kept %ld usable %ld sos %ld demods %ld passive %ld hot %ld kbytes %ld wall-time %.2f user-time %.2f sys-time %.2f %c********** ABNORMAL END ********** ********** ABNORMAL END ********** ERROR, bad argument to include: ------- start included file %s------- ------- end included file %s------- NOTICE: Please change 'axioms' to 'usable'. Name of axioms list is now 'usable'. -------> usable clausifies to: list(usable). -------> sos clausifies to: list(sos). -------> passive clausifies to: list(passive). -------> hot list clausifies to: list(hot). ERROR, bad argument to Weight_list: ----> ERROR, already have purge weight list. ----> ERROR, already have pick weight list. ----> ERROR, already have pick weight list or purge weight list. ----> ERROR, already have term weight list. ERROR, argument of lex term is not a list: ERROR, argument of lrpo_status term is not a list: ERROR, the command lrpo_lr_status no longer exists. Symbols have lr status by default. The command lrpo_multiset_status gives symbols multiset status. ERROR, argument of skolem term is not a list: ERROR, argument of overbeek_terms is not a list: ERROR, argument of split_atoms is not a list: ERROR, split_atoms must be gound: ERROR, argument of special_unary term is not a list: ERROR, float_format term must have one argument. ERROR, make_evaluable term must have two arguments: ERROR, second arg is not evaluable: ERROR, args have different arities: overbeek_world: too many variables ERROR, characters after term: ERROR, clause contains too many variables: ERROR, input file %s not found. ERROR, missing sos (-s) argument. %% Reading sos clause from the command line. list(hints) and list(hints2) are incompatible. ------------> process usable: ======= end of input processing ======= Forward subsumption counts, subsumer:number_subsumed. ------- statistics (process %d) ------- -------------- statistics ------------- clauses given %7ld clauses generated %7ld (hot clauses generated)%7ld binary_res generated %7ld hyper_res generated %7ld neg_hyper_res generated%7ld para_from generated %7ld para_into generated %7ld factors generated %7ld gL rule generated %7ld demod_inf generated %7ld ur_res generated %7ld linked_ur_res generated%7ld back unit del. gen. %7ld demod & eval rewrites %7ld clauses wt,lit,sk delete %7ld tautologies deleted %7ld clauses forward subsumed %7ld cl not subsumed due to ancestor_subsume %7ld (subsumed by sos) %7ld unit deletions %7ld factor simplifications %7ld clauses kept %7ld (hot clauses kept) %7ld new demodulators %7ld empty clauses %7ld clauses back demodulated %7ld clauses back subsumed %7ld usable size %7ld sos size %7ld demodulators size %7ld passive size %7ld hot size %7ld Kbytes malloced %7ld linked UR depth hits %7ld linked UR deduct hits %7ld cl deletes, too many vars %7ld fpa argument overloads %7ld fpa argument underloads %7ld demodulations stopped by limit %7ld ----------- times (seconds) ----------- (%ld hr, %ld min, %ld sec) (%ld hr, %ld min, %ld sec) ============ end of search ============ That finishes the proof of the theorem. ----- report at %9.2f seconds ----- %s%cA report (%.2f seconds) has been sent to the output file. %c Resetting weight limit to %d. Resetting weight limit to %d. %c-- HEY %s, WE HAVE A PROOF!! -- ---------------- PROOF ---------------- ------------ end of proof ------------- -----> EMPTY CLAUSE at %6.2f sec ----> ----> UNIT CONFLICT at %6.2f sec ----> Passive list not accepted in auto1 mode.Demodulators list not accepted in auto1 mode.Weight lists not accepted in auto1 mode.WARNING: Sos list not accepted in auto1 mode: sos clauses are being moved to usable list. SCAN INPUT: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. The clause set is propositional; the strategy will be ordered hyperresolution with the propositional optimizations, with satellites in sos and nuclei in usable. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. There is no negative clause, so all clause lists will be printed at the end of the search. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, with positive clauses in sos and nonpositive There is a clause for symmetry of equality, so it is assumed that equality is fully axiomatized; therefore, This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. There is a clause for symmetry of equality is, so it is Passive list not accepted in auto2 mode.Demodulators list not accepted in auto2 mode.Weight lists not accepted in auto2 mode.Sos has positive nonground clause; therefore it is not changed. Every positive clause in sos is ground (or sos is empty); therefore we move all positive usable clauses to sos. Properties of input clauses: prop=%d, horn=%d, equality=%d, symmetry=%d, max_lits=%d. All clauses are propositional; therefore we set the propositional flag and use ordered hyperresolution. Setting pick_given_ratio to 2, because all clauses are units. Setting hyper_res, because there are nonunits. Setting ur_res, because this is a nonunit set containing either equality literals or non-Horn clauses. Clearing order_hyper, because all clauses are Horn. Setting factor and unit_deletion, because there are non-Horn clauses. Equality is present, so we set the knuth_bendix flag. As an incomplete heuristic, we paramodulate with units only. There is a clause for symmetry of equality, so it is %c WARNING: at least one symbol, %s, is not lexically comparable. If you use a lex command, you should include all symbols that will be compared. This warning will not be given again. constructing nodes for remaining lits: ERROR: constructing children told target here with already target set ERROR ... non UNIT clause looks UNIT ERROR: constructing children told target here and target not found here FPA indexing not supported for linked res subsumable unitUD entering linked_unit_del, passed term follows FPA indexing not supported for linked res linked_unit_delUD exiting linked_unit_del, subsuming clause c follows UD exiting linked_unit_del, not subsumed attempted to back up from a node with a child ERROR: unable to initialize linked UR inference tree ********tree before BIG loop open lit %d nres %d attempting to find clash for term first time = %c res_count = %d ERROR: moved forward to %p first = FALSE ERROR: found non_target back_up < 0 ERROR: left_sibling chain to NULL ***RESOLVED AWAY TREE curr_node at %p target at %p open lit %d nres %d ***tree end BIG loop curr_node %p tar %p open lit %d ********tree leaving linked UR open lit %d nres %d ** HIT maximum linked UR depth %d times ** HIT maximum linked UR deduction size %d times unable to renumber vas in fist_unifiable() ERROR: forward failed, has first_child that's NOT tar ERROR: forward failed with target child (has sibs) ERROR: couldn't get context for dummy node ERROR: couldn't get link node for dummy ERROR: couldn't get context for given node checking is_in_ancestry on lit parent = %p prev_sibling = %p next_sibling = %p first_child = %p first = %c unit_deleted = %c near_poss_nuc = %d farthest_sat = %d target_dist = %d back_up = %d subst = %p subst->multiplier = %d tr = %p unif_position = %p ERROR, argument of link tag is not a list: ERROR, list member has bad literal number: %s brought NUC is TRASHED .. already have tar NUC failed depth check TRASHED couldn't get link_node couldn't get context from clause couldn't get context node UD ********entering Linked UR *********** in clause clashed against term: in clause did not attempt to resolve ... appears in ancestry resolvent = [] -- FAIL -- couldn't get given link_node at %p >>NOT_SPECIFIED: NUCLEUS: LINK: BOTH: SATELLITE: ** UNKNOWN **: **<< -----start node at %p------ current_clause >> (NIL) << goal to resolve ... from literal -----end node at %p------ max ur depth hit # %d max ur ded size hit # %d NUC in on only tar TRASHED `ÓlÓxÓ„ÓÓlinked hyper not implemented yet. enter foo with args: %ld %f %s. enter user_test_long: %ld %f %d %s enter user_test_double: %ld %f %d %s enter user_test_bool: %ld %f %d %s enter user_test_string: %ld %f %d %s enter user_test_term: %ld %f %d %s evaluate_user_function, bad code.@"Returned string"new_term$FOO$TEST_LONG$TEST_DOUBLE$TEST_BOOL$TEST_STRING$TEST_TERMget_args, bad arity.get_args, bad arg type.„âÈâ ãxã˜ã åHå€å¼åðå$ægeo_rewrite_recurse, too many variables.geo_recurse, MAX_DEPTH. HOT NEW CLAUSE!: SEGMENTATION FAULT!! This is probably caused by a bug in Otter. Please send copy of the input file to otter@mcs.anl.gov, let us know what version of Otter you are using, and send any other info that might be useful. Otter killed by SIGUSR1 signal. sig_handler, cannot handle signal %d. %cSearch stopped by SIGINT. Commands are help, kill, continue, set(_), clear(_), assign(_,_), usable, sos, demodulators, passive, stats, fork, and options. All commands end with a period. --- Begin interaction (level %d) --- Type `help.' for the list of commands. > Received end-of-file character. Level %d process started and running (waiting for commands); level %d process will resume when %d finishes. Level %d process started and running. --- Continue interaction at level %d --- killed level %d search during interaction. killed level %d search during interaction. --- End interaction, continue search at level %d --- --- End interaction, continue search at level %d --- %s%c The job finished %s??? Search stopped by SIGINT. Malformed term. helpfork%c Fork failed. statskill ok. continue ok.optionssymbols command not understood. Command not understood. ok. > %. %s Job %d Fork failedXlog_%dinsert_into_gen_tab, key already thereprint_proof_object_node, bad rulematch_clauses, different numbers of literalsmatch_clauses, literals don't matchtranslate_unit_deletion, unit deletion not foundtranslate_factor_simp, factor not foundtranslate_factor_simp, literals don't unifytranslate_factor_simp: merge failedtranslate_demod_nonunit, wrong number of rewritestranslate_demod_unit: cannot rewritefinish_translating, merge not found. finish_translating, literal flippedfinish_translating, subsumption failuretranslate_resolution, can't find first listtranslate_resolution, can't find second listtranslate_resolution: signs wrong. translate_resolution: unify fails on the preceding. translate_hyper: unify fails on the preceding. translate_ur: sat_map for box=%d, orig= translate_ur: unify fails on the preceding. translate_factor, literals don't unifytranslate_paramod, can't find first listtranslate_paramod, can't find second listtranslate_paramod: unify fails on the preceding. translate_step, clauses don't matchtranslate_step: rule %d not handled. trans_2_pos: proof node not foundlist(%s). %% Hints from process %d, %sbuild_proof_object: flag order_history must be setbuild_proof_object: flag detailed_history must be setbuild_proof_object: proof objects cannot contain answer literalsbuild_proof_object: neg_hyper_res not allowedbuild_proof_object: gL rule not allowedbuild_proof_object: gL-id not allowedbuild_proof_object: linked_ur_res not allowedbuild_proof_object: eval rule not allowedbuild_proof_object: clausify rule not allowedbuild_proof_object, at most one proof object can be built when an initial proof object is given ;; BEGINNING OF PROOF OBJECT undefinedeq-axiominstantiateresolveparamodunknown(%s(not false(or true(%d %d ( . v%d)(v%d . )) %d %d) (%d) NILnew_literal_index, bad map ABOUT TO ABEND! old demod: new demod: clause: finish_translating, bad ruletrans_2_pos: NULL postrans_2_pos: clause not foundtrans_2_pos: empty clause;; END OF PROOF OBJECT ¨ý°ý¸ýÀýÈýÐýØýàý,ÔÔDÐ,T-T-$-T-T-T-T-T-$- ,-T-T---ô,T-ä,Ð, %cWARNING, hint will not be used, because no weights have been set for it: (4 404@484H4%d [ fsub_wt=%d bsub_wt=%d equiv_wt=%d(hints list nil) bsub_wt=%d, bsub_add_wt=%d(hints2 list nil) list(hints2). bdNEW HINT: %cWARNING, hint cannot be used, because no weights have been set for it: +++ bsub adjust, cl %d, new wt %d back_demod_hints: clause not in Hints2. >> BACK DEMODULATING HINT %d WITH %d. bsub_hint_wtfsub_hint_wtequiv_hint_wtbsub_hint_add_wtfsub_hint_add_wtequiv_hint_add_wtlabel # %s(%fattribute_type: unknown attribute nameattributes must have arity 1: attribute value should be integer: ÈDÈDÈDÈDÈDÈDÐDXEXEdEtE|E\F¤F°FÀFÔFpG„G¨G¼GÐGAtom: %d%s%d]Refuted case The Assumption for case was not used; s:therefore we skip case%s Splitting on clause Case (process %d): Assumption: case failure Splitting on atom sign=%d, equality=%d, atom_wt=%d, cl_id=%d, cl_wt=%d, cl_type=%d, variables=%d, pos=%d, neg=%d, pos_binary=%d, neg_binary=%d I tried to split, but I could not find a suitable clause. Case splitting (fork) failed. Returning to search. %c That finishes the proof of the theorem. I tried to split, but I could not find a suitable atom. always_split: returning because no splitting is possible at this time. Possible model detected on branch %cPossible model detected on branch Here are the clauses in Usable and SoS. It seems that no more inferences or splitting can be done. If the search strategy is complete, these clauses should lead to a model of the input. INPUTEQ-AXIOMparse_proof_object: parse_listp returns NULLparse_proof_object: parse_listp nonlistparse_proof_object: step length < 3parse_proof_object: bad justification (1)parse_proof_object: bad justification (2)parse_proof_object: NULL clauseerror parsing initial proof object cldiff, bad PICK_DIFFoverbeek_insert, bad term start of Overbeek_world overbeek_insert, bad weight in termThere is no Overbeek World to print! end of Overbeek_world, terms=%d, overflow=%d, max_overflow=%d. There is no Overbeek World to check! check_overbeek_world, wrong weight: %d %d check_overbeek_world, term not found: CLAUSE %d -1 -2 ========== Jhash ========== [%d] resolved: IDs in original proof: IDs in short proof: original - short: short - original: ==== end jproof ===== build_support_lists: clause not found removing %d and changing references to %d jhash_inset_recurse: already there === JPROOF === Expanded %d, Generated %d, Pruned %d, Subsumed %d, Kept %d. jproof: derived clause not foundjproof: justification not found ==== SHORT_PROOF ===== Length %d (starting length %d) jproof: input clause not foundLevel %d, last kept clause of level %d is %d. Level %d, last kept clause of level %d is %d, %.2f seconds. expanded %d, generated %d, pruned %d, subsumed %d, kept %d, user time %.2f, lookups/second %d Looking through the multi justifications for a short proof. Looking through the multi justifications for a short proof. ============ MULTIJUST ============ ============ end multijust ============ WARNING: flist_insert, item %d already here (1)! WARNING: flist_insert, item %d already here (2)! WARNING: flist_delete, item %d not found (1)! WARNING: flist_delete, item %d not found (2)! integer divide by 0.float divide by 0. demod term: --> result: demod<%d> WARNING, demod_limit. lex dependent demodulator: LRPO dependent demodulator: ERROR, dollar_contract, bad op_code: %d. ERROR, dollar_contract, bad op_type: %d. WARNING, zap_term_special called with contained term: demod_cl, an atom has been rewritten to a variable --- perhaps you are using a symbol as both a function symbol and as a relation symbol.demod_cl, demodulation introduced too many variables.WARNING, demod_limit (given clause %ld): %cWARNING, demod_limit stopped the demodulation of a clause. This warning will not be repeated. >> back demodulating %d with %d. Flipping following input demodulator due to lrpo ordering: ØØØØØääääää8‘8‘8‘8‘@‘@‘@‘@‘@‘@‘H‘H‘H‘0‘P‘P‘X‘`‘F F ððüü‘‘‘‘‘‘‘h‘h‘h‘h‘‘p‘ ‘ ‘ ‘ ‘ ‘(‘ ‘ì’T”8•ø•t–P—l—P˜d˜è˜`šœü|žðž d’t’ˆ’˜’¬’|“ “Ä“è“ ”0”¨–À–Ø–ð–—(——¬—ä—˜8˜ðš ›P›€›°›Ô› WARNING, instance of x=x cannot be inserted into demod_imd index: contract_imd, increase MAX_AL_TERM_DEPTH.start of index-match-demodulate treeimd_delete, can't find alpha.imd_delete, can't find atom.v%d %s demod=is_delete, can't find end.is_delete, can't find term.is_retrieve, increase MAX_FS_TERM_DEPTH.don't know how to print is tree %p binary_resneg_hyper_respara_from_leftpara_from_rightpara_from_varspara_into_varspara_into_leftpara_into_rightpara_ones_rulepara_alldemod_infdemod_linearvery_verbosefor_sub_fpafor_subfree_all_memno_faplno_fanlprint_keptdemod_historysort_literalsprint_givenprint_back_subcheck_aritysos_queueatom_wt_max_argsterm_wt_max_argsprint_lists_at_endorder_eqdynamic_demodprint_new_demodprint_back_demoddemod_out_inprocess_inputsimplify_folanl_eqknuth_bendixrewriterprint_proofssymbol_elimlex_order_varsdynamic_demod_allpara_from_units_onlypara_into_units_onlyreally_delete_clauseslrpoprolog_style_variablessos_stackdynamic_demod_lex_depprog_synthesisancestor_subsumeinput_sos_firstlinked_ur_reslinked_ur_tracepara_skip_skolemindex_for_back_demodlinked_sub_unit_usablelinked_sub_unit_soslinked_unit_dellinked_target_alllinked_hyper_rescontrol_memoryorder_historydisplay_termsgeometric_rulegeometric_rewrite_beforegeometric_rewrite_afterpretty_printinput_sequentoutput_sequentecho_included_filesinteractive_givendetailed_historyorder_hyperautoauto1auto2eq_units_both_waysbird_printbuild_proof_objectbuild_proof_object_1build_proof_object_2log_for_x_showformula_historykeep_hint_subsumerskeep_hint_equivalentsproof_weighthyper_symmetry_kludgegl_demoddiscard_non_orientable_eqdiscard_xx_resolvabletptp_eqbellback_unit_deletionsplit_clausesplit_possplit_nonhornsplit_min_maxsplit_atomsplit_popularsplit_when_givenunit_ressigint_interactur_lastliterals_weigh_onepick_diff_simpick_random_lightestpick_last_lightestpick_mid_lightestfor_sub_equivalents_onlymulti_justmulti_just_lessmulti_just_shorterprint_proof_as_hintsdegrade_hints2clocksfpa_literalsfpa_termsdemod_limitmax_givenmax_levelsneg_weightmax_keptmax_genmax_literalsreportmax_proofsstats_levelmax_ur_depthmax_ur_deduction_sizemax_distinct_varspick_given_ratiochange_limit_afternew_max_weightgeo_given_ratiopretty_print_indentmin_bit_widthinterrupt_givenheatdynamic_heat_weightmax_answersdebug_firstdebug_lastverbose_demod_skipdynamic_demod_depthdynamic_demod_rhsage_factordistinct_vars_factornew_symbol_lex_positionwarn_memwarn_mem_max_weightsplit_secondssplit_givensplit_depthpick_diffpick_diff_rangemulti_just_maxERROR: flag name not found. lex_rpoprint_levelnew_functions flag already set. flag already clear. parameter name not found. reduce_weight_limitdelete_identical_nested_skolemdiscard_commutativity_consequences must have one simple argument. ERROR, flag `lex_rpo' has been changed to `lrpo'. ERROR, flag `print_level' no longer exists. ERROR, flag `new_functions' no longer exists. ERROR, flag `bird_print' no longer exists. must have two simple arguments. ERROR, parameter `reduce_weight_limit' has been changed to the pair `change_limit_after' and `new_max_weight'. second argument must be integer. WARNING: no inference rules are set. WARNING: PARA_FROM is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_INTO is set, but PARA_FROM_LEFT and PARA_FROM_RIGHT are both clear. WARNING: PARA_FROM, PARA_INTO rules are clear, but PARA_ONES_RULE is set. WARNING: NO_FAPL is set, but HYPER_RES is clear. WARNING: NO_FAPL and FOR_SUB_FPA are both set. WARNING: NO_FAPL and BACK_SUB are both set. WARNING: ANL_EQ is set and LRPO is clear. WARNING: demod_limit=0; set it to -1 for no limit. WARNING: max_literals=0; set it to -1 for no limit. WARNING: max_proofs=0; set it to -1 for no limit. WARNING: INTERACTIVE_GIVEN has highest precedence for picking given clause. WARNING: SOS_STACK has priority over PICK_GIVEN_RATIO. WARNING: SOS_QUEUE has priority over PICK_GIVEN_RATIO. WARNING, SOS_QUEUE has priority over SOS_STACK. WARNING, INPUT_SOS_FIRST ignored, because SOS_STACK is set. WARNING, detailed paramod history is ignored when para_all is set. WARNING, with splitting, max_seconds is checked against the wall clock. WARNING, keep_hint_subsumers is ignored when keep_hint_equivalents is set. ancestor_subsume and multi_just are incompatibleœÚèÜèÜèÜèÜèÜèÜèܼÚèÜèÜèÜèÜèÜèÜèÜèÜèÜèÜèÜäÚèÜèÜèÜ„ÜèÜèÜèÜèÜèÜèÜèÜèÜèÜè܈ÚtÚèÜ`Ú¼Ù¨ÙèÜèÜèܤÜèÜèÜèÜèÜèÜèÜÐÚèÜèÜ\Ü<Ü<ÜèÜèÜèÜèÜèÜèÜèÜèÜèÜèÜèÜøÚèÜèÜèÜèÜèÜèÜ”ÜèÜèÜèÜèÜèÜ(ÜÛ ÛèÜèÜèÜèÜlÜlÜlÜapply_substitute, term not COMPLEX.apply_substitute: term too deep.dot_trans, bad dot notation fill_word, word too big: |%s|  Ñ ‰ €þ(p…€‚ § ¤Ñ@Ї¨‡(þÿÿox‡ÿÿÿoðÿÿo‡ÿÿÿÿÿÿÿÿÌÐ>‰N‰^‰n‰~‰Ž‰ž‰®‰¾‰ΉÞ‰î‰þ‰ŠŠ.Š>ŠNŠ^ŠnŠ~ŠŽŠžŠ®Š¾ŠΊÞŠîŠþŠ‹‹.‹>‹N‹^‹n‹~‹Ž‹ž‹®‹¢ƒdä‹dä‹9<H€r€Œ€»€ó€0€€Ò€ý€,€V€€™€´€Õ€€1€V€€€©‚¢¢ ‚cV$‚ï[L‚b‚y‚¢¢¢‚ØƀǢڀ ñ€!€"€#3€%K€&a€1x€2€3§€4À€5Ø€6ñ€8 €9"€;B€=X€>n€?„€@š€A±€BÉ€C߀Dö€E €F$€G;€HT€Ii€NÏ€Qç€R€S€T9€UU€Vm€X…€[Ÿ€^·€eÍ€hç€l €q €r5 €uP €vm €yˆ €z¥ €}½ €€Ö €ƒñ €„ €‡& €Š@ ‚Ë”t ‚Fœ €¢Ò € €#V €Y €4u €< €Cú €F €S© €Zç €^€Ù€lù€tM€yn€ö€†4€Œ¢¢‚ L€b€8¢w‚Š‚b‚¢œ‚¢É€K¢¢L€€#Ô‚ç‚5ÁLÂwŠ‚Âœ¢Âø€×€€H8€Kg€L˜€UË€Z€^?€aw€b¯€\€€û€r€­¢¢–€5 €7!€89€9S€:¢m dä‹init.c/usr/src/build/87998-i386/BUILD/glibc-2.2.5/csu/gcc2_compiled.int:t(0,1)=r(0,1);-2147483648;2147483647;char:t(0,2)=r(0,2);0;127;long int:t(0,3)=r(0,3);-2147483648;2147483647;unsigned int:t(0,4)=r(0,4);0000000000000;0037777777777;long unsigned int:t(0,5)=r(0,5);0000000000000;0037777777777;long long int:t(0,6)=@s64;r(0,6);01000000000000000000000;0777777777777777777777;long long unsigned int:t(0,7)=@s64;r(0,7);0000000000000;01777777777777777777777;short int:t(0,8)=@s16;r(0,8);-32768;32767;short unsigned int:t(0,9)=@s16;r(0,9);0;65535;signed char:t(0,10)=@s8;r(0,10);-128;127;unsigned char:t(0,11)=@s8;r(0,11);0;255;float:t(0,12)=r(0,1);4;0;double:t(0,13)=r(0,1);8;0;long double:t(0,14)=r(0,1);12;0;complex int:t(0,15)=s8real:(0,1),0,32;imag:(0,1),32,32;;complex float:t(0,16)=r(0,16);8;0;complex double:t(0,17)=r(0,17);16;0;complex long double:t(0,18)=r(0,18);24;0;__builtin_va_list:t(0,19)=*(0,20)=(0,20)../include/libc-symbols.h/usr/src/build/87998-i386/BUILD/glibc-2.2.5/build-i386-linux/config.h../sysdeps/gnu/_G_config.h../sysdeps/unix/sysv/linux/bits/types.h../include/features.h../include/sys/cdefs.h../misc/sys/cdefs.h/usr/lib/gcc-lib/i386-redhat-linux/2.96/include/stddef.hsize_t:t(8,1)=(0,4)__u_char:t(4,1)=(0,11)__u_short:t(4,2)=(0,9)__u_int:t(4,3)=(0,4)__u_long:t(4,4)=(0,5)__u_quad_t:t(4,5)=(0,7)__quad_t:t(4,6)=(0,6)__int8_t:t(4,7)=(0,10)__uint8_t:t(4,8)=(0,11)__int16_t:t(4,9)=(0,8)__uint16_t:t(4,10)=(0,9)__int32_t:t(4,11)=(0,1)__uint32_t:t(4,12)=(0,4)__int64_t:t(4,13)=(0,6)__uint64_t:t(4,14)=(0,7)__qaddr_t:t(4,15)=(4,16)=*(4,6)__dev_t:t(4,17)=(4,5)__uid_t:t(4,18)=(4,3)__gid_t:t(4,19)=(4,3)__ino_t:t(4,20)=(4,4)__mode_t:t(4,21)=(4,3)__nlink_t:t(4,22)=(4,3)__off_t:t(4,23)=(0,3)__loff_t:t(4,24)=(4,6)__pid_t:t(4,25)=(0,1)__ssize_t:t(4,26)=(0,1)__rlim_t:t(4,27)=(4,4)__rlim64_t:t(4,28)=(4,5)__id_t:t(4,29)=(4,3)__fsid_t:t(4,30)=(4,31)=s8__val:(4,32)=ar(4,33)=r(4,33);0000000000000;0037777777777;;0;1;(0,1),0,64;;__daddr_t:t(4,34)=(0,1)__caddr_t:t(4,35)=(4,36)=*(0,2)__time_t:t(4,37)=(0,3)__useconds_t:t(4,38)=(0,4)__suseconds_t:t(4,39)=(0,3)__swblk_t:t(4,40)=(0,3)__clock_t:t(4,41)=(0,3)__clockid_t:t(4,42)=(0,1)__timer_t:t(4,43)=(0,1)__key_t:t(4,44)=(0,1)__ipc_pid_t:t(4,45)=(0,9)__blksize_t:t(4,46)=(0,3)__blkcnt_t:t(4,47)=(0,3)__blkcnt64_t:t(4,48)=(4,6)__fsblkcnt_t:t(4,49)=(4,4)__fsblkcnt64_t:t(4,50)=(4,5)__fsfilcnt_t:t(4,51)=(4,4)__fsfilcnt64_t:t(4,52)=(4,5)__ino64_t:t(4,53)=(4,5)__off64_t:t(4,54)=(4,24)__t_scalar_t:t(4,55)=(0,3)__t_uscalar_t:t(4,56)=(0,5)__intptr_t:t(4,57)=(0,1)__socklen_t:t(4,58)=(0,4)../linuxthreads/sysdeps/pthread/bits/pthreadtypes.h../sysdeps/unix/sysv/linux/bits/sched.h__sched_param:T(10,1)=s4__sched_priority:(0,1),0,32;;_pthread_fastlock:T(9,1)=s8__status:(0,3),0,32;__spinlock:(0,1),32,32;;_pthread_descr:t(9,2)=(9,3)=*(9,4)=xs_pthread_descr_struct:__pthread_attr_s:T(9,5)=s36__detachstate:(0,1),0,32;__schedpolicy:(0,1),32,32;__schedparam:(10,1),64,32;__inheritsched:(0,1),96,32;__scope:(0,1),128,32;__guardsize:(8,1),160,32;__stackaddr_set:(0,1),192,32;__stackaddr:(0,19),224,32;__stacksize:(8,1),256,32;;pthread_attr_t:t(9,6)=(9,5)pthread_cond_t:t(9,7)=(9,8)=s12__c_lock:(9,1),0,64;__c_waiting:(9,2),64,32;;pthread_condattr_t:t(9,9)=(9,10)=s4__dummy:(0,1),0,32;;pthread_key_t:t(9,11)=(0,4)pthread_mutex_t:t(9,12)=(9,13)=s24__m_reserved:(0,1),0,32;__m_count:(0,1),32,32;__m_owner:(9,2),64,32;__m_kind:(0,1),96,32;__m_lock:(9,1),128,64;;pthread_mutexattr_t:t(9,14)=(9,15)=s4__mutexkind:(0,1),0,32;;pthread_once_t:t(9,16)=(0,1)_pthread_rwlock_t:T(9,17)=s32__rw_lock:(9,1),0,64;__rw_readers:(0,1),64,32;__rw_writer:(9,2),96,32;__rw_read_waiting:(9,2),128,32;__rw_write_waiting:(9,2),160,32;__rw_kind:(0,1),192,32;__rw_pshared:(0,1),224,32;;pthread_rwlock_t:t(9,18)=(9,17)pthread_rwlockattr_t:t(9,19)=(9,20)=s8__lockkind:(0,1),0,32;__pshared:(0,1),32,32;;pthread_spinlock_t:t(9,21)=(0,1)pthread_barrier_t:t(9,22)=(9,23)=s20__ba_lock:(9,1),0,64;__ba_required:(0,1),64,32;__ba_present:(0,1),96,32;__ba_waiting:(9,2),128,32;;pthread_barrierattr_t:t(9,24)=(9,25)=s4__pshared:(0,1),0,32;;pthread_t:t(9,26)=(0,5)wchar_t:t(11,1)=(0,3)wint_t:t(11,2)=(0,4)../include/wchar.h../wcsmbs/wchar.h../sysdeps/unix/sysv/linux/i386/bits/wchar.h__mbstate_t:t(13,1)=(13,2)=s8__count:(0,1),0,32;__value:(13,3)=u4__wch:(11,2),0,32;__wchb:(13,4)=ar(4,33);0;3;(0,2),0,32;;,32,32;;_G_fpos_t:t(3,1)=(3,2)=s12__pos:(4,23),0,32;__state:(13,1),32,64;;_G_fpos64_t:t(3,3)=(3,4)=s16__pos:(4,54),0,64;__state:(13,1),64,64;;../include/gconv.h../iconv/gconv.h :T(17,1)=e__GCONV_OK:0,__GCONV_NOCONV:1,__GCONV_NODB:2,__GCONV_NOMEM:3,__GCONV_EMPTY_INPUT:4,__GCONV_FULL_OUTPUT:5,__GCONV_ILLEGAL_INPUT:6,__GCONV_INCOMPLETE_INPUT:7,__GCONV_ILLEGAL_DESCRIPTOR:8,__GCONV_INTERNAL_ERROR:9,; :T(17,2)=e__GCONV_IS_LAST:1,__GCONV_IGNORE_ERRORS:2,;__gconv_fct:t(17,3)=(17,4)=*(17,5)=f(0,1)__gconv_init_fct:t(17,6)=(17,7)=*(17,8)=f(0,1)__gconv_end_fct:t(17,9)=(17,10)=*(17,11)=f(0,20)__gconv_trans_fct:t(17,12)=(17,13)=*(17,14)=f(0,1)__gconv_trans_context_fct:t(17,15)=(17,16)=*(17,17)=f(0,1)__gconv_trans_query_fct:t(17,18)=(17,19)=*(17,20)=f(0,1)__gconv_trans_init_fct:t(17,21)=(17,22)=*(17,23)=f(0,1)__gconv_trans_end_fct:t(17,24)=(17,25)=*(17,26)=f(0,20)__gconv_trans_data:T(17,27)=s20__trans_fct:(17,12),0,32;__trans_context_fct:(17,15),32,32;__trans_end_fct:(17,24),64,32;__data:(0,19),96,32;__next:(17,28)=*(17,27),128,32;;__gconv_step:T(17,29)=s56__shlib_handle:(17,30)=*(17,31)=xs__gconv_loaded_object:,0,32;__modname:(17,32)=*(0,2),32,32;__counter:(0,1),64,32;__from_name:(4,36),96,32;__to_name:(4,36),128,32;__fct:(17,3),160,32;__init_fct:(17,6),192,32;__end_fct:(17,9),224,32;__min_needed_from:(0,1),256,32;__max_needed_from:(0,1),288,32;__min_needed_to:(0,1),320,32;__max_needed_to:(0,1),352,32;__stateful:(0,1),384,32;__data:(0,19),416,32;;__gconv_step_data:T(17,33)=s36__outbuf:(17,34)=*(0,11),0,32;__outbufend:(17,34),32,32;__flags:(0,1),64,32;__invocation_counter:(0,1),96,32;__internal_use:(0,1),128,32;__statep:(17,35)=*(13,1),160,32;__state:(13,1),192,64;__trans:(17,28),256,32;;__gconv_info:T(17,36)=s8__nsteps:(8,1),0,32;__steps:(17,37)=*(17,29),32,32;__data:(17,38)=ar(4,33);0;-1;(17,33),64,0;;__gconv_t:t(17,39)=(17,40)=*(17,36)_G_iconv_t:t(3,5)=(3,6)=u44__cd:(17,36),0,64;__combined:(3,7)=s44__cd:(17,36),0,64;__data:(17,33),64,288;;,0,352;;_G_int16_t:t(3,8)=(0,8)_G_int32_t:t(3,9)=(0,1)_G_uint16_t:t(3,10)=(0,9)_G_uint32_t:t(3,11)=(0,4)_IO_stdin_used:G(0,1)GCC: 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rtcontrol_memoryoverbeek_weightmulti_justificationsjset_membernum_answersterm_identterm_to_formulamember_is_subsetclear_subst_1check_optionsbuild_for_allDomain_sizeprint_fpa_tabgetrusage@@GLIBC_2.0print_statsget_clauses_of_wt_rangefind_interactive_clp_term_shot_cl_integrateflist_insertget_formulaadd_args_to_setread_termset_special_unaryFpa_back_demodnew_sym_numNil_sym_numadjust_weight_with_hintshint2_integratedistribute_quantifierzap_quantpara_intoxx_resolvablesos_has_pos_nongroundMACE_dependent_flagslengthrenumber_vars_substfree_fnodeswitch_to_hot_indexulong_bitsprint_clauseliteral_numberbuild_proof_objectdisplay_termcldiffprint_hint2_clausecommuted_termsdemod_clweight_clskip_whitereinit_dpgetpwuid@@GLIBC_2.0Fpa_pos_litsread_formulaprint_cl_listBellzap_listhostnamecanc_fs_posiff_to_conjgen_conflictclear_var_namesMACE_init_optionsfree_formula_ptrmark_literalMACE_p_clausehot_mark_clash_clfree_contextback_demod_hintsretrieve_initial_proof_objectdisintegrate_termfind_mid_lightest_clp_term_tabgeometry_rule_unifrewind@@GLIBC_2.0unique_allNull_outputinit_clocksp_formularms_conflict_tautologyWeight_purge_genprint_justificationclause_identcaddrfree_fpa_headfree_sym_tabset_lex_valsprint_clause_s2process_negative_equalitiesun_index_lits_clashneg_eq_litp_imd_treesplitable_literalclause_ptr_list_sizeMACE_dependent_parmsclear_subst_2formula_identcat_strprint_clause_sreinit_generatecurrent_casesubsumedadd_subcaseur_resmulti_just_processremove_all_supersetsremove_supersetsproof_length_initset_vars_clprint_model_portablep_unitMACE_tp_allocdp_transabendfree_g2listreinit_memtp_allocauto_lex_ordercontains_answer_literalmalloc@@GLIBC_2.0zap_ci_ptr_listanti_skolemizebuild_treeiset_removeprint_mem_briefint_termsplittingtrivial_substfscanf@@GLIBC_2.0free_ilist_listcopy_formulagetppid@@GLIBC_2.0read_clauseneg_hyper_respipe@@GLIBC_2.0cnfAttributesun_index_lits_allsplit_clauseterm_ident_x_varsTo_childrenchange_parmprint_clause_without_justdomain_elementfree_clause_ptrFirst_orderapply_clauseget_proof_object_nodeclausify_formula_list__deregister_frame_info@@GLIBC_2.0print_linked_ur_mem_statsfree_reldecode_intDots_sym_numparse_lispeq_litcl_clear_varsdependent_flagsnegation_inwardback_demodalways_splitTo_parentfree_imd_posglist_appendread_wt_listall_instances_fpap_proof_object_nodebird_printFrom_childrenclock_initdouble_strinsert_symstdout@@GLIBC_2.0append_clstderr@@GLIBC_2.0order_equalities_lrpozap_hints2subst_sn_formulabin_resMACE_abendfactor_simplifycompare_splitable_clauseshint_keep_testclock_resetprint_proof_objectrms_subsume_conjis_insertprint_memp_clause_sget_listrms_cnfwall_secondsDemod_imdunit_delis_skolemflatten_clausescompile_hintssplit_atomnext_fposis_symbolsymmetry_clauseconvenient_demodcl_del_intwrite_termindex_lits_clashnnf_dnffpa_deletefree_fpa_treeattribute_typesos_argumentget_is_treeproc_gensubsume_conjrun_timeFpa_neg_litsfs_retrievecl_int_chkoccur_checkprint_symssubst_free_formulaprf_weightprint_term_nllex_order_varsclause_to_termlinked_ur_restime@@GLIBC_2.0get_relhorn_clausesystem_timefinish_translatingfree_fsub_pos_startcontains_skolem_symbolrms_quantifierssub_clausegetopt@@GLIBC_2.0is_deleteMACE_output_statsmatch_clausesinsert_dp_clausecompare_for_auto_lex_orderget_fnodeevaluate_user_functionall_factorsget_is_posread_sequent_clausefree_formula_boxatom_valuecl_copy_delete_literalprint_trailsubsumeWeight_pick_given_indexforeach_sosmark_as_skolemMACE_print_statsMACE_print_optionsrms_distribute_quantsis_eqp_proof_object_as_hintsbits_ulongget_ci_ptrInit_wall_secondsfree_clauseilist_to_jsetterm_to_clauseorder_equalitiesdeclare_user_functionsget_termilist_appendinsert_clauseDemodulatorscase_depthinitial_strsn_to_nodesplitable_clausehot_inferenceinit_dpin_sym_tabOverbeek_termsprint_case_nFpa_alphasdouble_to_termglist_prependsame_structurelrpo_greater__strtol_internal@@GLIBC_2.0auto_MACE_change_parmoutput_statsget_formula_ptriset_addp_optionsfree_sym_entnew_functor_nameget_imd_posgen_subsumebuild_termzap_prop_treepossible_given_splitprint_errorfree_link_nodeinitcdrfind_lightest_geo_childclock_valcl_mergeMACE_clock_valpretty_print_termprint_term_sfree_is_posfree_is_pos_listcl_insert_tabimd_insertindex_lits_allprint_hints2_cl_listlong_to_termneg_clauseget_ilistget_attribute_indexautomatic_2_settingsprepend_clprint_modelgen_tautologyMACE_change_flagnullpp_statsprint_overbeek_worldfind_match2From_parentnth_clausep_symsfind_first_clstr_to_termis_retrieve__bss_starthot_index_clauseprint_formula_listzap_clause_ptr_listmaincleanupget_clauseassign_cl_idparse_initial_proof_objectrms_dnfWeight_pick_givensn_to_arityone_unary_answerrms_subsume_disjstr_doublefind_clause_to_splitpos_eq_litMACE_Statspossible_splithot_dynamiccl_find__libc_start_main@@GLIBC_2.0print_listfree_term_ptrg2list_lengthSosadd_to_jsetrmslog_for_x_showmax_literal_weightall_supporters_less_thanget_trailmap_restpara_fromfree_imd_treeget_link_nodeIgnore_sym_numprint_set_b_to_aintegrate_termun_share_specialp_case_nrenumber_uniquepost_proc_allterm_fixupread_a_filedel_hidden_clausesfor_sub_propget_proof_objectfirst_or_next_factoranc_subsumetotal_memanswer_litprint_hints_cl_listMACE_print_memprint_variablep_proof_objectmove_clausesmax_split_depthdata_startasctime@@GLIBC_2.0read_all_mace_inputnnfrms_push_freeSubsume_countnext_cl_numprintf@@GLIBC_2.0propositional_clauseSplit_atomsfind_lightest_clfind_random_clzap_termcheck_for_bad_thingsgetuid@@GLIBC_2.0_finiprint_sequent_clausememcpy@@GLIBC_2.0connect_new_nodeautomatic_1_settingsp_is_treegl_demodstr_to_snilist_memberIs_neg_litsconflict_tautologyprint_formulap_termfclose@@GLIBC_2.1auto_MACE_change_flagiset_subsetread_all_clausesget_attributefree_all_membuild_bin_resset_wt_listts_and_fsunit_conflictcopy_jsetatomsym_tab_memberrem_from_listfprint_btreeGreatest_atomproper_listget_jsetclausifyget_ans_lit_nodeback_subsumeWeight_purge_gen_indexp_clauseModelsoverbeek_insertuser_test_boolauto_change_flagoccurrencesground_clauseprover_forksset_lrpo_statuslinked_hyper_resMACE_pp_clause_activeOverbeek_worldget_sym_entgethostname@@GLIBC_2.0get_ancestorsskolemizechange_flaginfer_and_processget_fpa_headsymbol_countis_atomstring_to_terminit_optionsstr_longread_all_inputp_assumption_depthsbd_kludge_deletezap_formulafind_random_lightest_clback_unit_deletioninit_special_opsnnf_cnfinit_proof_object_environmentrenum_vars_termreportget_g2listprint_attributesp_timesprocess_op_commandprint_prop_treefind_atom_to_splitflist_deleteexit@@GLIBC_2.0check_overbeek_worldfoobuilt_in_symbolsMACE_check_optionsp_ilistzap_term_specialfree_formulap_caseMACE_p_statsp_btreecalloc@@GLIBC_2.0init_log_for_x_showprint_casebd_kludge_insertiset_sortjset_to_ilistdynamic_demodulatorget_fpa_treeappend_lists_edata_GLOBAL_OFFSET_TABLE_free@@GLIBC_2.0variable_optimize_endmatchget_gen_nodednfParmsp_substilist_lengthget_imd_treep_prop_treefree_clause_ptr_listremove_var_symsapply_demodunify_no_occur_checkMace_constraintsg2_remove_supersetsskolem_symbolfree_cl_attributeFpa_clash_pos_litsprint_timeskeep_onlyith_literalp_memp_clause_s2p_pathstdin@@GLIBC_2.0occurs_intotal_mem_callsidentity_resolvefree_literalfree_ilistget_glistprint_ilistimd_deleteread_bufclausify_formeddp_provermy_process_idget_formula_boxfpa_insertwt_matchinit_attributesnegate_formulaforward_subsumesn_to_ecprint_termvariantname_symfopen@@GLIBC_2.1Sortsordered_sub_clauseiff_to_disjtrue_listpcombine_answerscl_del_nonoptarg@@GLIBC_2.0user_test_doublehide_clausestr_intFlagsilist_tack_onhyper_resapplyget_literal_IO_stdin_usedget_cl_attributeformula_to_termcommutativity_consequenceprint_stats_briefget_args_for_user_functionlong_strrename_syms_formulaget_fsub_posprint_term_lengthd_termcl_integratesubst_sn_termglist_lengthzap_btreep_atomget_formula_ptr_2Num_sortsNum_symbolsglist_tack_ondependent_parmsset_skolemread_formula_listdistinct_varsalloc_fpa_indexsprintf@@GLIBC_2.0exit_if_over_time_limitident_nested_skolemslit_t_f_reduceHints2biggest_varuser_test_longprint_is_treeadjust_weight_with_hints2init_proof_objectPassive__data_startget_clash_ndcopy_termexit_with_possible_modelset_attributeget_ancestors2zap_variable_namesequality_clause_IO_getc@@GLIBC_2.0free_listflatten_clausefunction_valuefree_glist_listprocess_linked_tagscadrCons_sym_numtautologyrand@@GLIBC_2.0overbeek_matchclauses_to_idsint_strrenumber_vars_termnew_demodp_hints_cl_listsort_litsweightinit_statszap_cl_listfree_ci_ptrvar_subsetextract_given_clauseread@@GLIBC_2.0child_of_geometryfree_formula_ptr_2find_last_clcheck_transformed_clausegroundClocksprint_optionsnum_literalsMACE_print_timesidempot_ipfree_occurrencewait@@GLIBC_2.0copy_glisttrans_2_pos__gmon_start__print_term_tabcompile_hints2strcpy@@GLIBC_2.0renumber_varsotter-3.3f/make-test-otter0100755000076400007640000000025510000602666015152 0ustar mccunemccune#!/bin/csh bin/otter < examples/auto/steam.in | awk '/PROOF/,/end of proof/' echo "If you see 'end of proof', the test was successful." echo "Now try './make-test-mace2'." otter-3.3f/Changelog0100644000076400007640000012040310103530555014010 0ustar mccunemccuneIn this file I'll try to record the differences in the various patchlevels of Otter 3.0. The most recent entries are at the end. Mace2 changes are not listed here. -------------------------------------------------------- Otter 2.99 released November 25, 1993. -------------------------------------------------------- Many small changes. Otter 3.0.0 released January 24, 1994. -------------------------------------------------------- Check for errors when reading clause id from terminal, flag interactive_given, routine find_interactive_clause(). FormEd only: parsing strings read interactively, routine str_2_formula(). Problem with dynamic demodulators that have answer literal before equality. (Answer lits are not propagated during demodulation, so I can't see any use for answer lits on input demodulators, but they can occur in dynamic demodulators.) Changed contract_lin(), insert_imd(), delete_imd(), new_demod(), back_demod(), post_process(), so that they use ith_literal(), which skips answer lits. Also changed check_input_demod() to allow answer lits on input demodulators. Otter 3.0.1 - DOS version released Feb 22, 1994. -------------------------------------------------------- Optimized forward subsumption for nonunit clauses: require that found literal be first literal. Routine forward subsume() in file clause.c. Mar. 21, 1994. Bug in unit deletion when answer literals with fresh variables introduced. Factor_simp crashes because variables not renumbered. Fix: in unit_del(), renumber variables if ANY answer literals introduced. Result is otter301b. March 31, 1994. Added code to translate otter input for Davis-Putnam model searcher: set(dp_transform). Result is otter301dp. Apr. 13, 1994. Slight change to Davis-Putnam translator so that it outputs variable names with "v" instead of plain integers. May 23, 1994. Kunen convinced me to make answer literals sound. In particular, if they occur on demodulators, then they should be inherited by rewritten clauses. Since inheriting during demodulation would slow it down, would take a lot of time to code, and would be of questionable value, I'll simply not let demodulators have answer literals. Fix: check_input_demod(), pre_process(); new routine num_literals_including_answers(). NOTE: Subsumption still ignores answer literals, and factoring still attempts to factor answer literals. Result is otter301c. June 8, 1994. In procgen() (process generated clauses) moved cl_merge() after factor_simplify() to make construction of proof objects easier. June 8, 1994. When input clauses are changed in procgen() (due to flag process_input), e.g., by demod, unit_del, or factor_simp, the original input clause is now assigned an ID and appears in proofs. The new inference rule "copy" indicates this. Changed header.h, pre_process(), and print_clause(). Motivation: to make proofs easier to read and to ease proof object construction. June 8, 1994. When equality literals are flipped, add an entry to the justification list. Changed order_equalities(), order_equalities_lrpo(), post_process(), header.h, proc_gen(), print_clause(), maybe others??. Motivation: to make proofs easier to read and to ease proof object construction. June 9--16, 1994. Various changes related to construction of proof objects. Otter 3.0.2 - UNIX version released June 17, 1994 -------------------------------------------------------- July 14, 1994. Bug in FPA indexing, because abs(2^31) returns 2^31, a negative number! Change one line in hash_path(), file fpa.c. Result is otter302a. July 14, 1994. Bug (feature?) about symbol order of dynamically-introduced symbols. (Arose with sort_literals, $SUM, without lex([...]) command. Change lex_compare_sym_nums() so that if either has no lex value, then call compare_for_auto_lex_order() to compare. Note that this may change behavior, because before the fix, if one symbol has lex_val and the other does not, then the one with lex_val is smaller. Result is otter302b. August 5, 1994. Bug with dynamic hot list. When making hot inference with a clause C, if new clause was added to hot list, then when return to making hot inferences with C, the ordinary index would be used instead of the hot index. Result: lose a few hot inferences, get a lot of bogus (but sound) hot inferences. Also, one other small bug: heat_level was not copied to new hot list clauses. Bugs fixed. Result is otter302c. ----------------------------------------------------------- August 23, 1994. Added new flag `log_for_x_show' which causes some statistics to be periodically logged to a special file so that the user can have a real-time X display of some properties of the search. August 24, 1994. Added two new statistics: PASSIVE_SIZE and HOT_SIZE. August 25, 1994. Added $dots for weight templates. Added parameter MAX_ANSWERS. ----------------------------------------------------------- Otter 3.0.3 released August 26, 1994. ----------------------------------------------------------- Sept. 21, 1994. (Veroff,Kunen) Bug getting ancestors with [...,flip,1,...], because the 1 does not refer to a clause. Change the flip position to a list (like all other positions). Now get [...,flip.1,...], (note period). Changed post_process(), proc_gen(), and finish_translating(). Oct 24, 1995. Deleted GEOMETRIC_REWRITE (which occurred after demod), and added GEOMETRIC_REWRITE_BEFORE and GEOMETRIC_REWRITE_AFTER (demod). Jan 4, 1995. Overbeek requested an extension to weighting. This includes the new command "overbeek_terms([])." When an argument of an atom is being weighed, if it is an instance of a term in overbeek_terms, then it gets weight 0. Jan 12, 1995. Overbeek requested a change (see preceding) so that we check for a noncomplexifying instance. The result is otter303b. Jan 22, 1995. Veroff found a bug about reordering equalities in nonunits. Equalities that should not be flipped are sometimes flipped. Changed order_equalities() in weight.c. The result is otter303c. Feb 21, 1995. Yuan Yu pointed out that max_answers doesn't work. Fix is s/MAX_LITERALS/MAX_ANSWERS/ in process.c (line 411 in 3.0.3, line 415 in current). Looks like it wasn't tested when first installed. The result is otter303d. Feb 21, 1995. log_for_x_show() in misc.c had new_style procedure declaration (so it wouldn't work with cc). Fixed. March 7, 1995. Bug in ancestor_subsume (wos). If, during a given clause, you keep more than one occurrence, back subsumption (because it didn't check anc_subsume()), deletes all but the first. The fix is to have back_subsume() check anc_subsume() (file clause.c). Fixed. The result is otter303e. March 31, 1995. Enhancement suggested by Ingo Dahn: quantified formulas can now appear in proofs, just like clauses do. The skolemized input clauses can have the quantified formula as parent, e.g., [clausify,4]. One gets this feature by setting the new flag formula_history. The result is otter303f. April 7, 1995. Updated build_proof_object so that it can build proof objects with lex-dependent demodulation. April 9, 1995. Installed primitive "hints" mechanism. (It will be changed when the real hints mech. is installed.) April 11, 1995. Some cleanup and bug fixes from Art Quaife (email #27, 9/6/94). Two bugs: getppid() call in init_log_for_x_show() (misc.c) undefined for nonNUIX systems. Move to nonport.c and call only if TP_NAMES is defined. variant() in check.c forgot to tpos=*trp. In av.c, discarded routines term_ptr_get_size() and is_tree_get_size(), because obsolete. Fixed "unreachable break"s in several places. Unit deletion doesn't work if forward subsumption is disabled. Fixed by changing index_lits_all() and un_index_lits_all(). If the two symbols given to the make_evaluable command have different arities, CRASH! Fixed by including check in read_a_file(). Passive list units used for unit deletion. The manual says that the passive list is used only for subsumption and unit conflict. Fixed unit_del() in file clause.c April 12, 1995. Removed all ROO code and references (#ifdefs). April 12-13, 1995. Install some of Veroff's features: (1) Debugging: DEBUG_FIRST DEBUG_LAST VERBOSE_DEMOD_SKIP (2) Hints: FSUB_HINT_ADD_WT BSUB_HINT_ADD_WT EQUIV_HINT_ADD_WT KEEP_HINT_SUBSUMERS (3) Evaluable symbols: $UNIQUE_NUM, $RENAME(_,_); April 21, 1995. Add flag PROOF_WEIGHT. If set, (1) the "weight" of a proof is printed along with its level and length, and (2) ancestor subsumption uses "weight" instead of the proof length. The weight of a proof is the number of leaves in the proof tree, that is, the number of OCCURRENCES of input clauses in the proof tree. The result is otter303g. April 25, 1995. Bug (wos). If more than 32767 symbols, CRASH!, because term->sym_num was short, and no check in new_sym_num(). Fix: make sym_num unsigned short (so we can have 65535 symbols), and put check in new_sym_num(), so it will abend instead of crash. April 25, 1995. Secret flag, hyper_symmetry_kludge. The result if otter303h. May 18, 1995. Bug (kunen). Unit deletion with a unit containing answer literals. This can cause an infinite loop, incorrect answers, or a crash. The problem is a leftover context pointer in a substitution. Otter was designed for this to be ok, but I forgot that when updating unit_del to handle answers. The solution is to set the context pointer to NULL when binding variables in is_retrieve(). I changed imd_retrieve() analogously. May 18, 1995. Bug (Ohlbach). set(auto), set(free_all_mem) -> CRASH! when printing statistics at the end of the run. Because free_all_mem deletes lists, then stats (level 1) tries to look at lists. Fixed by including more checks in print_*_brief() in misc.c. otter303i ------------ June 5, 1995. DP preprocessing - delete some subsumed clauses. June 16, 1995. DP preprocessing - change form of output; output ordinary clauses as well as relational clauses, and all clauses get IDs (in preparations for Olga's MACE enhancements). otter303j ------------ June 20--23, 1995. Veroff visit. We made a great many changes. Here is a summary. 1. New parameters to decide dynamic demodulators when lrpo is clear: dynamic_demod_depth (default -1) dynamic_demod_rhs (default 1) Here is the new code. /* equality alpha=beta */ else if (var_subset(beta, alpha)) { if (Flags[DYNAMIC_DEMOD_ALL].val) return(1); /* make it a demodulator */ else { wt_left = weight(alpha, Weight_terms_index); wt_right = weight(beta, Weight_terms_index); if (wt_right <= Parms[DYNAMIC_DEMOD_RHS].val && wt_left - wt_right >= Parms[DYNAMIC_DEMOD_DEPTH].val) return(1); /* make it a demodulator */ } } If these parameters are not used, Otter should behave as before. 2. New parameters to adjust the pick_given weight of clauses. age_factor (default 0) distinct_vars_factor (default 0) Here is the new code. /* c is a newly kept clause that already has its ordinary pick-weight. */ if (Parms[AGE_FACTOR].val != 0) c->pick_weight = c->pick_weight + (Stats[CL_GIVEN] / Parms[AGE_FACTOR].val); if (Parms[DISTINCT_VARS_FACTOR].val != 0) c->pick_weight = c->pick_weight + (distinct_vars(c) * Parms[DISTINCT_VARS_FACTOR].val); 3. Special_unary processing has been improved. If you use this feature, check the code in lex_order() and lex_order_vars() to see how it works now. 4. The hints mechanism has been overhauled. From hints.c: The main purpose of the hints mechanism is to set or adjust the pick-given weight of clauses. A hint H can apply to a clause C in 3 ways: H subsumes C (forward subsume, fsub), C subsumes H (back subsume, bsub), and H is equivalent to C (equiv, which implies fsub and bsub). 2 more ways, which apply to unit clauses only, to be added later: H and C unify H anc C have the same shape (identical-except-variables) Another purpose of hints is to retain clauses that would otherwise be discarded because the purge-gen weight is too high. The Flag KEEP_HINT_SUBSUMERS (default clear) says to skip the purge-gen test on generated clauses that subsume hints (i.e., bsub). The Parms are FSUB_HINT_WT FSUB_HINT_ADD_WT BSUB_HINT_WT BSUB_HINT_ADD_WT EQUIV_HINT_WT EQUIV_HINT_ADD_WT These can be overridden for individual hints with corresponding attributes on the hints, e.g., p0(a,x) # bsub_hint_wt(200) # fsub_hint_wt(100). If the Parms (attributes) are not set, they are not used; if you have a list of hints with no attributes, and you don't set any hint parms, the hints won't be used for anything. If more than Parm (attribute) might apply, equiv is tested first, then fsub, then bsub. If you use both WT and ADD_WT, then BOTH can apply, e.g., when the hint p # bsub_hint_wt(200) # bsub_hint_add_wt(20). applies to a clause, the clause gets pick-given weight 220. The hint attributes and parameters are compiled into a special structure that is attached to the hint clause with the parents pointer. This causes several problems. (1) Compiled hints must be printed with print_hint_clause() instead of print_clause(), and (2) the Parms in effect at the start of the search are compiled in; if the user changes hint parms during the search, this will have no effect. 5. A new attribute mechanism has been installed. This allows users to attach supported attributes to clauses, and allows Otter programmers to easily add new attributes. Each attribute has a type in [boolean, integer, double, string, otter-term]. W.r.t. I/O, attributes look just like positive literals with one argument. The name of the attribute is the "predicate symbol", and the value is the argument. Attributes are appended to clauses with the "#" operator. For example, the following clause has two literals and two attributes (integer and string). p | q # bsub_hint_wt(-10) # label("This is a label"). We think the Boolean and integer types will be useful to have flags and parameters apply only to particular clauses. The first set of attributes are for the hints mechanism. bsub_hint_wt fsub_hint_wt equiv_hint_wt bsub_hint_add_wt fsub_hint_add_wt equiv_hint_add_wt These have type integer, and correspond to the ordinary hint parameters of the same names, and can be used to override the ordinary parameters for particular hint clauses. Another implemented attribute is label, whose type is string. The way it works is that if the pick-given weight of a clause is changed by a hint with a label attribute, the clause gets a copy of the label attribute. ------------ July 6, 1995. DP preprocessing - fix g(0)=1 bug, introduce flag dp_int_domain to say that integers are domain elements, and make several small changes. ------------ otter303k - July 7, 1995. ------------ July 14, 1995. Improve demodulation in proof object construction. July 26, 1995. Prevent paramodulation from t=t in para_from rule. July 27, 1995. Install Slaney's Scott fragments, all with #ifdef SCOTT. otter303l - Aug 4, 1995. August 9, 1995. A few minor corrections to the manual. (The manual does not document any of the new features.) August 10, 1995. Change dp_transform so that Sos and Demodulators are used as well as Usable. This is so that ordinary Otter input files (except for passive list) can be used for MACE input. August 16, 1995. A few small things suggested by Mark Stickel for the Macintosh version. --------------- Otter 3.0.4 released -- August 16, 1995. --------------- Sept 24, 1995 -- 3 minor corrections in the examples directory. wos/manyval.sparc2 is missing the statistics, wos/README is missing, and examples/README refers to a 486 instead of a Sparc2. I'll just silently rerelease 3.0.4, because Otter hasn't changed. --------------- Otter 3.0.4 rereleased -- Sept. 24, 1995. --------------- Nov 16, 1995. Minor bug (incompleteness) in build_proof_object that sometimes causes abend with lex-dependent demodulators. Fixed. Result is otter304a. Feb 12, 1996. Very minor bug: auto output message in misc.c corrected. Feb 28, 1996. Added flag "discard_non_oriented_eq", which will, if order_eq is set, discard nonorientable positive equality units. Result is otter304b. May 6, 1996. Bug in forward subsumption when doing ancestor subsumption with nonunits. I believe the only bad effect of the bug is that subsumption can be incomplete, that is, a subsumed clause will be kept. This is not a major bug, because (a) almost no one uses ancestor subsumption (b) when it is used, it is almost always with units, (c) when the problem occurs, an error message goes to stdout, (d) ancestor subsumption is highly experimental and not well understood anyway. To fix, move clear_subst_1(tr) call in forward_subsume(). Result is otter304c. April 2, 1997. New flag "discard_xx_resolvable", which causes nonunit clauses containing a literal that can be resolved with x=x to be deleted. (For new-foundations project.) Result is otter304d. April 12, 1997. Change the format of proof objects. I added a new field to lines in proof objects. If the new field is not empty, it gives the ID number of the corresponding (equivalent) line in the ordinary Otter proof. Before: ( ) After: ( ) ---------------- June 1997. Several changes to prepare for CASC-14 (CADE-14 contest). 1. New flag set(tptp_eq). Ordinarily, a predicate symbol is recognized as equality for paramodulation and demodulation if it is "=", or if it starts with "EQ", "eq", or "Eq". If tptp_eq is set, a predicate symbol is equality iff it is "equal". This is because TPTP has nonequality predicate symbols that start with "eq". 2. A new automatic mode. I wish to be able to introduce new auto modes and keep all of the old auto modes. But if the user has to choose between auto modes, the program is not really automatic. Therefore, I'll have flags "auto1", "auto2", ..., for the auto modes, and also have a flag "auto" (like a symbolic link) which which specifies the default auto mode. Two new flags: auto1 and auto2. auto1 specifies the old auto mode, and auto2 the new one. The default will be auto2. (So if you you wish your old auto input files to work the same way with the new otter, you should use set(auto1). See README.305 for a description of the new auto mode. The result of these changes is called otter305-beta, the version used for CASC-14 (July 16, 1997). August 21, 1997. Two new parameters: warn_mem and warn_mem_max_weight. These are used together to reset the max_weight (to warn_mem_max_weight), when a specified amount of memory (warn_mem) has been used. For example, if you wish to reset the max_weight to 10 after 90 megabytes of memory has been used, include the following in your input file. assign(warn_mem, 90000). assign(warn_mem_max_weight, 10). September 12, 1997. Bug reported by Dale Myers. If the search is stopped before the first given clause is used (for example max_given=0) the would-be first given clause is lost. Ordinarily this doesn't matter, because the search is over. But if you have set(print_lists_at_end), that clause will not appear in the output. Easy fix in file main.c. September 16, 1997. I moved the extra source code for the FormEd program into a subdirectory called formed, which has its own makefile for FormEd. Sept?--Nov?, 1997. Otter now catches the SIGUSR1 signal; when it happens, statistics are sent to the output file, and Otter exits with code 113. The reason for this is so that if you have a long-term Otter jobs that is no longer attached to a login shell (i.e., you started Otter in the background, then logged out, then logged in again), you can kill Otter and get statistics. To kill Otter and get statistics at the end of the output, run "kill -USR1 ". This probably works only under UNIX. ----------- November 1997. Dale Myers (Univ. of HI Math Dept) visited for three weeks, and we installed a splitting rule. Mohammed Almulla (Univ. of Kuwait) was also visiting, and he contributed to the effort. See split.txt in the documentation directory. Splitting uses the UNIX fork() system call, so I doubt it will work as is for Macintosh or Microsoft. The splitting rule required the introduction of a new flag set(back_unit_deletion), which causes any new unit to be used to remove literals from existing clauses. Analogous to back demodulation. This flag should also be useful when not splitting. Also, to make more sense of output files when splitting is used, I changed some of the messages that go to the output file---for example, the first few lines and the last few lines of the output. Also, a new flag BELL (default set). If you clear it, Otter won't ring the bell when important things (like a proof) happen. Requested by Dale Myers. ------------- Feb 19, 1998. Preparing for the release of 3.0.5. I had been planning to make the new auto mode (auto2) the default, but I have changed my mind---the old auto mode (auto1) will be the default. (set(auto) gives the default auto mode.) The reasons: (1) auto1 is closer to being complete, and (2) users will be annoyed if their old auto files don't work with 3.0.5. --------------- Otter 3.0.5 released -- February 19, 1998. --------------- March 4, 1998. Added new flag "unit_res", default clear. If set, then for each binary resolution inference, one of the parents must be a unit clause. Requested by Jim Boyle. Note that you still have to set binary_res. The result of this change is otter305b. April 1, 1998 (no fooling). Bug in example input file examples/split/zebra2.in. Two clauses missing: ivory!=5, green!=1. Fixed. June 17, 1998. Changed memory counters (term_gets, etc.) from long to unsigned long. ---------------------------- 1999 June 7, 1999. Type 2 proof objects (binary OR clauses), and several other changes for the Otter-Ivy interface. July 30, 1999. Version 306-beta included in Ivy package for ACL2 submission. We intend to release 306 as the version in IVY-1.0. Sept 8, 1999. When sorting literals of input clauses, add "propositional" to the justification (so that type 2 proof objects can be constructed). Sept 15, 1999. Bug in case splitting (reported by Oswaldo Teran.) If clear(print_proofs), Otter will hang after finding the first refutation. The process that finds the refutation is supposed to send the split assumptions used to its parent; but that info was sent in the print_proof routine!. If clear(print_proofs), the info doesn't get sent, and the parent waits forever trying to read it. FIX: Send the info just before exit in pre_process(). Files changed: process.c, misc.c, case.c, proto.h. FIXED. Interim release: otter-3.0.6-beta2, for anyone who needs the case split fix. Sept 15, 1999. ftp://info.mcs.anl.gov/pub/Otter/otter-3.0.6-beta2.tar.gz Nov 24, 1999. Added flag "ur_last". This is a restriction on UR resolution: the target literal must be the last literal of the nucleus. Nov 24, 1999. Changed splitting to allow split_atom with split_when_given option. This is a little kludgey, but it makes sense if you wish to exhaust the non-splitting inferences before splitting on atoms. (To do this, the pick_given weighting strategy should pick splittable clauses last. Even though we're not splitting on clauses, we use the selection of a splittable clause to trigger split_atom.) -------------------------- 2000 Feb 21, 2000. Bug when building more than one type 2 proof objects when there is an initial proof object (as when called by Ivy). There isn't an easy fix (see build_proof_object for notes), so we'll just abend in that case. Feb 23, 2000 -- Send IVY-v1 to Texas. (Along with MACE-1.3.4 and current otter). March 14, 2000 -- minor bug in back_unit_deletion. If using back_unit_deletion and there are clauses in passive, you might get some messages like "ERROR, context 0, var 0 not null." Nothing bad will happen when this occurs. Fixed. April 14, 2000 -- silently release Otter-3.0.6. April 15, 2000 -- otter306 goes into Ivy-v2 package for ACL2 book. April 17, 2000 -- Bug from Bob Veroff. FACTOR_RULE builds parent list incorrectly: [factor,186,1,2]. Fix: factored literals should be a list: [factor,186.1.2]. 1 and 2 were being interpreted as clause numbers. This usually didn't cause cause a crash, because 1 and 2 are usually valid clause numbers. However, it did incorrectly put clauses 1 and 2 into the proof. The bug surfaced, because clause 1 was a hint. The fix required changes all_factors() in resolve.c and to translate_factor() in check.c. We had a similar bug involving FLIP_RULE (see Sept. 21, 1994 entry above). April 18, 2000 -- New evaluable functions of type (term x term -> bool). $OCCURS(x,y) -- term x occurs in term y. $VOCCURS(x,y) -- variable x occurs in term y. $VFREE(x,y) -- variable x does not occur in term y. May 1, 2000 -- Installed several new options for picking the given clause: PICK_DIFF_SIM, PICK_RANDOM_LIGHTEST, PICK_LAST_LIGHTEST, PICK_MID_LIGHTEST, These were for some one-time experiments, and I have not documented them. May 11, 2000 -- auto1 mode doesn't accept Sos clauses. I changed it so that does. If there are any Sos clauses, they are immediately moved to Usable and a warning message is printed. (Recall that auto2 mode accepts Sos clasues.) May 12, 2000 -- Remove references to SCOTT, PRUNE, TURBO_C, TP_DYNIX. These are all conditional compilation for old stuff that I think is irrelevant now. May 15, 2000 -- Change to new-style functions (types go in the argument list rather than after), update the prototype extraction script, and get closer to ANSI conformance. On linux, it compiles cleanly (well, almost) with "gcc -ansi -pedantic -Wall". On solaris, it compiles cleanly with "cc -Xc", which checks for strict ANSI conformance. Also, I made a LOT of little changes, including re-indenting all of the source, so diffs with previous versions will be useless. Version 3.1-b0 July 30, 2000 -- added flag sos_arg (default clear). If set, then Otter expects to find a clause as a command-line argument; the clause is appended to the sos list. August 1, 2000 -- SOUNDNESS BUG! (from Dale Myers) If you use set(really_delete_clauses) with case splitting, You will probably get unsound proofs or refutations of consistent theories. The reason: when splitting, there is a check to see if assumptions are used. If not, subsequent cases are skipped. If really_delete_clasues is set, the check can say that an assumption was not used (because it can't be found), and required cases are skipped. The (not very satisfying) fix. If really_delete_clasues is set, The redundancy check is not performed. ------------------------------------------------------------------ Feb 19, 2001 -- added flag FOR_SUB_EQUIVALENTS_ONLY, which restricts forward subsumption to equivalence. That is, a clause is deleted by forward subsumption iff it is equivalent to an existing clause. There is no need for an analogous flag for back subsumption: just turn off back subsumption when using this new flag. This interplay with ancestor subsumption has not been analyzed: use them together at your own risk! -------------------------------------------------------- Feb 20, 2001 -- added new command overbeek_world, for some weighting experiments Overbeek, Swartz and I are doing. See new source file overbeek.c for documentation. Let it be otter-3.1b1 (bin-linux/otter31b1). April 4, 2001 -- Looked at renumbering of variables in proc_gen() and added a few comments. Checked how renumbering occurs during various kinds of processing. Changed geo_rewrite_recurse() to abend if too many variables; changed forward_subsume() so that vars are not renumberd for ancestor subsumption. April 5, 2001 -- Installed new flag KEEP_HINT_EQUIVALENTS. See process() and hint_keep_test(). This was suggested by Veroff and Fitelson. April 6--9, 2001 -- Kal Hodgson installed SCOTT ifdefs. He has an enhanced version of Otter, called SCOTT, that uses semantics to guide searches. If SCOTT is not defined when Otter is compiled, you get ordinary Otter. The rest of the SCOTT stuff is not included in Otter 3.1. If you're interested, contact Kal at kahlil@discus.anu.edu.au. April 13, 2001 -- Changed the scripts that run the test problems. See examples/README. May, first half, 2001 -- I decided to make MACE a self-contained program. (Previously, MACE would call Otter to parse the input and create an intermediate form, then send that to ANLDP.) MACE is now in a subdirectory of the Otter source. After that was done, I removed the Otter code that created the intermediate form (flag dp_transform, file dp_util.c). May 11, 2001 -- release Otter 3.2-beta (and MACE 2.0-beta) August 13, 2001 -- release Otter 3.2 and MACE 2.0 for Unix. --------------------------------- August-Sept, 2001 -- added experimental feature to try to find shorter proofs. Multiple justifications are kept for each clause, and when a proof is found, look through the multi-justifications for the shortest proof. So far, it's practical only for proofs that are short to begin with. See file multijust.c. October 26, 2001 -- added list(foreach). This is intended to be a high-performance version of otter-loop. Read the ordinary input; Then foreach clause in list(foreach), fork a child process, add the clause to sos, then search; parent waits for child to finish. October 30, 2001 -- added flag set(print_proof_as_hints). After an ordinary proof is printed, a corresponding list of hints is printed. It contains all of the clauses in the proof and the intermediate demodulants. Also, each equality unit (pos or neg) is printed in both orientations. (Some extra clauses are printed as well.) otter-3.2b ---------------------------------- December 13, 2001. Minor bug from Pavel Podgoretsky. symmetry_clause() in clause.c has precedence problem: else if (!l1->atom->farg->argval->type = VARIABLE) Fixed. otter-3.2c. ---------------------------------- May 1, 2002. Bug from Jean-Luc Delatre. Conditional outside-in demodulation. In contract_imd, add call to un_share_special(t2) right after apply_demod(). Same fix to contract_lin. Also make un_share_special non-static. This pointed out a feature (bug?) in conditional demodulation. Conditions were always rewritten inside-out. Fixed by updating convenient_demod(). The fix has not been well tested. otter-3.2d. ---------------------------------- Date unknown. Install flag discard_commutativity_consequences (default clear). If set, positive unit equalities (a=b) be discarded if a and b are commuted variants of each other (assuming that all binary operations are commutative). otter-3.2e ---------------------------------- November 5-7, 2002. Install new hints code (hints2.c). This is in addition to the old hints code. To get the new code, use list(hints2) instead of list(hints). The new code indexes hints. The new code allows bsub checks only. fsub and equiv are not available. If back demodulation is set, hints are back demodulated, but the back demodulated hints are retained. If order_eq is set, backward equalities in hints are flipped. Change print_proof_as_hints so that it if order_eq is set, all equalities are ordered. Also, a (forward) subsumption check is done of the proof hints. otter-3.2f. Allow OPS-style operator declarations: infix instead of xfx, etc. ---------------------------------- December 11, 2002. Bug in hints2 (Wos) when hints2 list is empty (index doesn't get allocated). Fixed. Bug (jsruokom@cc.hut.fi) in demodulation when an absorption demoulator applies to an atom (resulting in a variable atom). Fix: abend in this case. The only way I can see this occurring is when a symbol is used as both a function and relation symbol, which is bad style (and shouln't be allowed anyway). otter-3.2g. ---------------------------------- January 2, 2003. Install Bob Veroff's hint degradation strategy. in hints2.c. To use it, there's a new flag, set(degrade_hints2). otter-3.2h. ---------------------------------- February 6, 2003. Michael Beeson suggested that changing the size of the FPA hash tables from 500 to 3793 will improve performance. Done. In the same sprit I changed the size of the Term hash table (share.c) from 2000 to 3793. otter-3.2i. ---------------------------------- April 30, 2003. Michael Beeson sent (on Feb 27) a list of warning messages he got when he compiled Otter on a Windows PC. These weren't serious. Most of these have been addressed. Bob Veroff reported a bug in the hints2 code: if a hint is an empty clause (these can sneak in when hints are derived from proofs), a segfault occurs. Fixed. Changed mace/anldp.c so that it compiles (it got messed up when we added the iso_prune feature to mace in the summer of 2001. ---------------------------------- June 2003. Updating the Otter3 manual. The new version will be an MCS Tech. Memo. named "Otter 3.3 Reference Manual". Many new flags and parameters are documented, and there are new sections on Hints, Splitting, and Linked UR. ---------------------------------- June 23, 2003. Changed the name of the knuth_bendix flag to anl_eq. The reasons: (1) Although it can be essentially KB, it was derived mostly from equational methods developed at Argonne (by Wos and Overbeek). (2) It was designed for proving theorems, not completion. (3) It applies to any theory with equality, not just equational theories. The flag knuth_bendix still works, as an alias to anl_eq. ---------------------------------- July 16, 2003. Added max_levels parameter (for use with sos_queue). Added meta-option rewriter (to demodulate a list of clauses). ---------------------------------- July 17--18, 2003. Reorganized the disribution directories. ---------------------------------- July 22. Discovered bug introduced in otter32f when installing hints2. input_sos_first ignored if process_input. Fixed. ---------------------------------- September 8, 2003 -- release Otter 3.3 / Mace 2.2 http://www.mcs.anl.gov/AR/otter/dist33/otter-3.3.tar.gz ---------------------------------- Jan 12, 2004 -- I realized that the MacOS X installation doesn't work if the developer tools (compilers, make) aren't installed (even though binaries are included). So I changed the installation procedure and replaced the unix package with http://www.mcs.anl.gov/AR/otter/dist33/otter-3.3b.tar.gz ---------------------------------- December 23, 2003 -- memory allocation problem if there are a GREAT number of constants in the input (Rick Stevens, bio app). Fix: in av.c, change TP_ALLOC_SIZE from 32700 to 1000000. ---------------------------------- February 9, 2004 -- Hints2 incomplete for nonunits (Geoff Sutcliffe). Fix: minor change in hints2.c (index all literals of hints2). This changes output (trivially) in one of the example problems, fringe/olsax_hints.out, so I replaed the output for that example. ---------------------------------- February 9, 2004 -- max_levels limit didn't work correctly in some cases. Fixed. otter-3.3x2.tar.gz released to Geoff Sutcliffe. ---------------------------------- Feb 3--6, 2004 --- I went to ABQ to visit Bob Veroff, and the following changes were prompted by work during that visit. ---------------------------------- February 10, 2004 -- It has been known for a long time that build_proof_object sometimes fails to translate demodulation steps, causing an ABNORMAL END. I have made another attempt to fix it. (The algorithm and code are so messy that I'll never be confident that build_proof_object works well.) However, as far as I know, it has never produced a bad proof object--- when it does fail, it always seems to trigger an ABNORMAL END. Anyway, this attempt: Stop calling order_equalities* and simply use the justification to flip equalities. This might fix the unit case, but I think there are still problems with nonunits. otter-3.3x3.tar.gz released to Bob Veroff ---------------------------------- Feb 10, 2004. Change quote characters. Previously, ' and " could be used for string symbols, e.g., p("Hi there!", 'good bye...'). Now, single quotes are in the set of characters that are used for "special names" [3.3 manual, p. 6]. Also, the default type and precedence [3.3 manual, p. 9] for ' is op(300, XF, '). The whole purpose of this change is so that we can use ' as a postfix operation (without any declaration), e.g., (x * y)' = y' * x'. Also, this change makes the language a bit more compatible with Mace4 and future provers. ---------------------------------- Feb 10, 2004. Change command-line argument processing. Previously, the only command-line argument that was accepted was a clause to be appended to sos (if set(sos_arg). was in the input), e.g., otter 'f(x,x)=x.' < in > out Now, that is accomplished with (and flag sos_arg has been eliminated) otter -s 'f(x,x)=x.' < in > out Also, we can now give input filenames as arguments instead of using the standard input. All arguments after -f are understood as input files, e.g., otter -f f1 f2 f3 f4 > out If -s and -f are used together, -s must be first, so the acceptable ways to call otter now are otter < in > out otter -f f1 f2 f3 > out otter -s 'f(x,x)=x.' < in > out otter -s 'f(x,x)=x.' -f f1 f2 f3 > out ---------------------------------- Feb 17, 2004. Mark Stickel pointed out that the detailed timing can really slow down an Otter job on the Mac. (Similar to Solaris.) It can cause a substantial penalty, even in Linux, so we're changing the default configuration so that it's disabled. If you need detailed timing, use (in the source directory) 'make otter'. ---------------------------------- April 19, 2004. Install improved FPA indexing. Insertions and queries should be about the same performance; deletions should be much faster ("unindex time" in statistics). Function should be unchanged (queries return same terms in same order). Memory usage a bit higher for small problems, a bit lower for big problems. For that reason, if max_mem, control_mem, or auto are used, the updated otter may give a different search. otter-3.3d ---------------------------------- August 2, 2004. Install new flag set(clocks). Default clear. This turns on detailed timing for various operations during the search. Previously this always occurred (unless the code was compliled with TP_NO_CLOCKS). As hardware gets faster, the percentage of CPU time used to obtain detailed timings has been increasing, so it is now disabled by default and can be enabled by setting this flag in the input file. Because clocks are off by default, I have removed the TP_NO_CLOCKS #ifdefs. otter-3.3f otter-3.3f/mace2/0040755000076400007640000000000010103775525013200 5ustar mccunemccuneotter-3.3f/mace2/clock.c0100644000076400007640000000167407714207010014435 0ustar mccunemccune#include #include #include "Clock.h" struct MACE_clock MACE_Clocks[MACE_MAX_CLOCKS]; /************* * * init_clocks() - Initialize all clocks. * *************/ void init_clocks(void) { int i; for (i = 0; i < MACE_MAX_CLOCKS; i++) MACE_clock_reset(i); } /* init_clocks */ /************* * * long MACE_clock_val(clock_num) - Returns accumulated time in milliseconds. * * Clock need not be stopped. * *************/ long MACE_clock_val(int c) { long msec, i, j; i = MACE_Clocks[c].accum_msec; if (MACE_Clocks[c].level == 0) return(i); else { MACE_CPU_TIME(msec) j = msec - MACE_Clocks[c].curr_msec; return(i+j); } } /* MACE_clock_val */ /************* * * MACE_clock_reset(clock_num) - MACE_Clocks must be reset before being used. * *************/ void MACE_clock_reset(int c) { MACE_Clocks[c].accum_msec = 0; MACE_Clocks[c].level = 0; } /* MACE_clock_reset */ otter-3.3f/mace2/TAGS0100644000076400007640000013710607714212257013670 0ustar mccunemccune anldp.c,631 #define VERSION 16,320 #define VDATE 17,342 #define MACE_ABEND_EXIT 32,641 #define UNSATISFIABLE_EXIT 33,676 #define MACE_MAX_SECONDS_EXIT 34,711 #define MACE_MAX_MEM_EXIT 35,746 #define MAX_MODELS_EXIT 36,781 #define ALL_MODELS_EXIT 37,816 #define MACE_SIGINT_EXIT 38,851 #define MACE_SEGV_EXIT 39,886 #define MACE_INPUT_ERROR_EXIT 40,921 int First_order;52,1147 int Domain_size 53,1190 int Init_wall_seconds;54,1236 int Models 55,1282 static void MACE_print_banner(68,1577 static void usage_message(89,2034 static int process_command_line_args(112,2731 static void MACE_sig_handler(163,3667 int main(198,4600 avail.c,329 #define TP_ALLOC_SIZE 3,59 static char *Alloc_block;5,133 static char *Alloc_pos;6,209 static int Malloc_calls;8,272 static int Free_calls;9,330 static Gen_ptr_ptr Chunks;13,467 static void add_chunk(21,575 static void free_chunks(35,790 void reinit_mem(51,1092 void *MACE_tp_alloc(67,1391 int MACE_total_mem(107,2476 clock.c,120 struct MACE_clock MACE_Clocks[5,59 void init_clocks(13,192 long MACE_clock_val(28,469 void MACE_clock_reset(48,833 dp.c,1855 #define SUBSUMED(SUBSUMED13,177 int Greatest_atom;21,421 static int Subsume;25,516 static int Check_time;26,593 static int Num_clauses;28,668 static Clause_ptr Clauses;29,692 static Atom_ptr Atoms;30,719 static int Num_selectable_clauses;31,797 static Clause_ptr *Selectable_clauses;32,832 static int *Unit_queue;34,898 static int Unit_queue_size;35,964 static int Unit_queue_first,36,1042 static int Unit_queue_first, Unit_queue_last;36,1042 static Gen_ptr_ptr Gen_ptr_avail;38,1089 static Clause_ptr Prev_dp;39,1166 static int Next_message 40,1234 static int Num_assignments;44,1363 static int *Assignments;45,1391 static int *Split_positions;46,1457 static Gen_ptr_ptr get_gen_ptr(54,1573 static void free_gen_ptr(74,1916 void init_dp(86,2082 void exit_if_over_time_limit(99,2242 int subsumed(114,2542 static void init_unit_queue(132,2868 static int unit_enqueue(148,3209 static int unit_dequeue(228,5126 void MACE_p_clause(253,5549 void MACE_pp_clause(272,5933 void MACE_pp_clause_active(290,6266 void p_atom(313,6694 void insert_dp_clause(336,7195 static int read_one_clause(400,8764 int read_all_clauses(429,9274 int more_setup(452,9829 static void select_init(548,12292 static int select_atom(610,14098 static Clause_ptr select_clause(645,14807 int atom_value(676,15493 static void print_initial_assignments(696,15921 static void print_assignments(712,16206 static void model(738,16743 static int assign(811,18675 static void unassign(888,20217 static void dp(943,21307 #define ISO_PRUNE 1037,23221 #define SPECIFIED 1038,23243 #define UNSPECIFIED 1039,23265 int function_value(1047,23348 int iso_prune(1062,23566 void add_args_to_set(1101,24365 static void clause_split(1126,24829 static void delete_pointers_to_subsumed_clauses(1237,27752 int dp_prover(1272,28709 void reinit_dp(1356,31086 flatten.c,466 int kludgey_e_subsume(13,239 void check_for_bad_things(45,942 int int_term(64,1411 int domain_element(78,1634 static struct term *build_binary_term(89,1775 static struct term *replace_term(109,2173 void process_negative_equalities(132,2652 static struct term *yankable_term(180,3724 static struct term *yankable(207,4289 static int eq_sn(233,4819 void flatten_clause(253,5184 struct list *flatten_clauses(282,5797 void check_transformed_clause(307,6385 generate.c,2028 #define PRINT_CLAUSES 16,398 #define MAX_MLITERALS 23,550 #define MAX_CLAUSES 24,595 struct rel_lit rel_lit28,690 struct rel_clause rel_clause35,964 struct sort Sorts[47,1240 int Num_sorts;48,1270 struct symbol Symbols[50,1286 int Next_base 51,1322 int Num_symbols;52,1341 static int Clauses_generated;54,1359 static int Clauses_inserted;55,1389 static struct rel_clause Clauses[57,1419 static int Num_rel_clauses;58,1466 static int *Units;60,1495 static int Unsatisfiable 61,1514 static int sort_index(69,1640 static int declare_symbol_sorted(84,1872 static int str_to_id(127,2792 int decode_int(146,3226 void p_unit(191,4129 void decode_and_p_clause(211,4491 static void p_relational_clause(232,4908 static void sort_clause(264,5596 static int unit_subsumed(284,5961 static int MACE_tautology(302,6286 static int merge_lits(317,6544 static int unit_delete(342,7082 static void add_clause(368,7628 static void add_2clause(400,8255 static void add_unit(415,8476 static void well_defined_0(453,9621 static void well_defined_1(470,9930 static void well_defined_2(489,10299 static void well_defined_3(510,10726 static void closed_0(533,11262 static void closed_1(550,11528 static void closed_2(570,11877 static void closed_3(592,12300 static void well_defined(616,12796 static void closed(633,13135 static void one_one(650,13433 static void onto(670,13771 static void left_cancel(691,14116 static void right_cancel(714,14537 static void left_onto(737,14957 static void right_onto(760,15385 static int process_variables(787,16010 static void generate_prop_clauses(834,17146 static void add_clauses_for_qg_constraint(933,20157 static int number_variables(969,20946 static int trans_relational_clause(1015,22051 void read_all_mace_input(1108,24625 static void remove_ans_literals(1140,25228 static void MACE_collect_symbols(1169,25848 static void iso_constants_recurse(1220,27096 static void iso_constants(1264,28104 int dp_trans(1308,29381 void reinit_generate(1632,38063 mace2.c,448 #define VERSION 14,263 #define VDATE 15,285 static int Domain_min 21,373 static int Domain_max 22,431 int Models 24,495 int First_order 25,555 int Domain_size;26,601 int Init_wall_seconds;27,650 static void MACE_print_banner(36,780 static void usage_message(57,1218 static int process_command_line_args(111,3072 static void MACE_sig_handler(214,5295 static void reinit(249,6234 static void try_domain_size(268,6559 int main(295,7088 miscellany.c,56 void exit_with_message(11,158 void MACE_abend(55,1503 opts.c,329 struct flag MACE_Flags[3,19 struct parm MACE_Parms[4,60 void MACE_init_options(12,166 void MACE_print_options(101,1969 void MACE_p_options(141,2859 void auto_MACE_change_flag(152,3011 void MACE_dependent_flags(173,3587 void MACE_dependent_parms(219,4557 int MACE_change_parm(272,5703 void MACE_check_options(313,6774 part.c,709 #define MAX_LITS 3,20 static int num_pos_lits(11,100 static struct literal *copy_literal(27,356 static void append_literal(41,605 static void append_subterm(59,944 static void p_vars(80,1280 static void intersect_vars(95,1489 static void union_vars(111,1712 static int cardinality(127,1928 static int diff_cardinality(143,2146 static void which_vars_term(159,2390 static void which_vars(177,2699 static void which_vars_part(192,2993 static int gen_connector_symnum(211,3362 static struct literal *connector(232,3742 static void score_the_part(263,4305 static void parts(316,5741 static void try_to_part(339,6070 static struct list *var_opt(422,8037 struct list *variable_optimize(446,8485 print.c,1256 static int function_value_0(23,515 static int function_value_1(39,789 static int function_value_2(55,1073 static int function_value_3(71,1367 static void print_table_f0(87,1669 static void print_table_f1(98,1871 static void print_table_f2(132,2479 static void print_table_r0(178,3281 static void print_table_r1(198,3642 static void print_table_r2(231,4309 void print_model(278,5466 static void print_table_f0_portable(321,6569 static void print_table_f1_portable(332,6813 static void print_table_f2_portable(353,7229 static void print_table_f3_portable(382,7824 static void print_table_r0_portable(415,8509 static void print_table_r1_portable(435,8914 static void print_table_r2_portable(467,9530 static void print_table_r3_portable(503,10288 static void print_table_r4_portable(543,11107 void print_model_portable(597,12549 static void print_table_f0_ivy(655,13984 static void print_table_f1_ivy(666,14215 static void print_table_f2_ivy(684,14596 static void print_table_f3_ivy(705,15053 static void print_table_r0_ivy(729,15579 static void print_table_r1_ivy(749,15975 static void print_table_r2_ivy(775,16527 static void print_table_r3_ivy(804,17167 static void print_table_r4_ivy(836,17843 void print_model_ivy(880,18967 stats.c,280 long MACE_Stats[3,20 struct MACE_clock MACE_Clocks[4,54 int Internal_flags[5,103 void init_stats(16,306 void MACE_print_mem(33,569 void p_mem(47,826 void MACE_print_stats(58,954 void MACE_p_stats(89,2557 void MACE_print_times(100,2701 void MACE_output_stats(130,3647 ../source/attrib.c,300 } Attributes[11,104 void init_attributes(19,196 int get_attribute_index(57,1205 int attribute_type(76,1540 struct cl_attribute *get_attribute(102,2223 void set_attribute(116,2479 void delete_attributes(151,3083 struct cl_attribute *term_to_attributes(173,3482 void print_attributes(238,4915 ../source/av.c,8940 #define TP_ALLOC_SIZE 10,131 #define ALLOC_ARG_T 11,159 static char *Alloc_block;13,189 static char *Alloc_pos;14,264 static struct term *term_avail;18,387 static struct rel *rel_avail;19,419 static struct sym_ent *sym_ent_avail;20,449 static struct term_ptr *term_ptr_avail;21,487 static struct formula_ptr_2 *formula_ptr_2_avail;22,527 static struct fpa_tree *fpa_tree_avail;23,577 static struct fpa_head *fpa_head_avail;24,617 static struct context *context_avail;25,657 static struct trail *trail_avail;26,695 static struct imd_tree *imd_tree_avail;27,729 static struct imd_pos *imd_pos_avail;28,769 static struct is_tree *is_tree_avail;29,807 static struct is_pos *is_pos_avail;30,845 static struct fsub_pos *fsub_pos_avail;31,881 static struct literal *literal_avail;32,921 static struct clause *clause_avail;33,959 static struct list *list_avail;34,995 static struct clash_nd *clash_nd_avail;35,1027 static struct clause_ptr *clause_ptr_avail;36,1067 static struct ci_ptr *ci_ptr_avail;37,1111 static struct ilist *ilist_avail;38,1147 static struct link_node *link_node_avail;40,1182 static struct ans_lit_node *ans_lit_node_avail;41,1224 static struct formula_box *formula_box_avail;42,1272 static struct formula *formula_avail;43,1318 static struct formula_ptr *formula_ptr_avail;44,1356 static struct cl_attribute *cl_attribute_avail;45,1402 static struct glist *glist_avail;46,1450 static struct g2list *g2list_avail;47,1484 static int Malloc_calls;49,1521 static unsigned long term_gets,53,1655 static unsigned long term_gets, term_frees,53,1655 static unsigned long term_gets, term_frees, term_avails;53,1655 static unsigned long rel_gets,54,1712 static unsigned long rel_gets, rel_frees,54,1712 static unsigned long rel_gets, rel_frees, rel_avails;54,1712 static unsigned long sym_ent_gets,55,1766 static unsigned long sym_ent_gets, sym_ent_frees,55,1766 static unsigned long sym_ent_gets, sym_ent_frees, sym_ent_avails;55,1766 static unsigned long term_ptr_gets,56,1832 static unsigned long term_ptr_gets, term_ptr_frees,56,1832 static unsigned long term_ptr_gets, term_ptr_frees, term_ptr_avails;56,1832 static unsigned long formula_ptr_2_gets,57,1901 static unsigned long formula_ptr_2_gets, formula_ptr_2_frees,57,1901 static unsigned long formula_ptr_2_gets, formula_ptr_2_frees, formula_ptr_2_avails;57,1901 static unsigned long fpa_tree_gets,58,1985 static unsigned long fpa_tree_gets, fpa_tree_frees,58,1985 static unsigned long fpa_tree_gets, fpa_tree_frees, fpa_tree_avails;58,1985 static unsigned long fpa_head_gets,59,2054 static unsigned long fpa_head_gets, fpa_head_frees,59,2054 static unsigned long fpa_head_gets, fpa_head_frees, fpa_head_avails;59,2054 static unsigned long context_gets,60,2123 static unsigned long context_gets, context_frees,60,2123 static unsigned long context_gets, context_frees, context_avails;60,2123 static unsigned long trail_gets,61,2189 static unsigned long trail_gets, trail_frees,61,2189 static unsigned long trail_gets, trail_frees, trail_avails;61,2189 static unsigned long imd_tree_gets,62,2249 static unsigned long imd_tree_gets, imd_tree_frees,62,2249 static unsigned long imd_tree_gets, imd_tree_frees, imd_tree_avails;62,2249 static unsigned long imd_pos_gets,63,2318 static unsigned long imd_pos_gets, imd_pos_frees,63,2318 static unsigned long imd_pos_gets, imd_pos_frees, imd_pos_avails;63,2318 static unsigned long is_tree_gets,64,2384 static unsigned long is_tree_gets, is_tree_frees,64,2384 static unsigned long is_tree_gets, is_tree_frees, is_tree_avails;64,2384 static unsigned long is_pos_gets,65,2450 static unsigned long is_pos_gets, is_pos_frees,65,2450 static unsigned long is_pos_gets, is_pos_frees, is_pos_avails;65,2450 static unsigned long fsub_pos_gets,66,2513 static unsigned long fsub_pos_gets, fsub_pos_frees,66,2513 static unsigned long fsub_pos_gets, fsub_pos_frees, fsub_pos_avails;66,2513 static unsigned long literal_gets,67,2582 static unsigned long literal_gets, literal_frees,67,2582 static unsigned long literal_gets, literal_frees, literal_avails;67,2582 static unsigned long clause_gets,68,2648 static unsigned long clause_gets, clause_frees,68,2648 static unsigned long clause_gets, clause_frees, clause_avails;68,2648 static unsigned long list_gets,69,2711 static unsigned long list_gets, list_frees,69,2711 static unsigned long list_gets, list_frees, list_avails;69,2711 static unsigned long clash_nd_gets,70,2768 static unsigned long clash_nd_gets, clash_nd_frees,70,2768 static unsigned long clash_nd_gets, clash_nd_frees, clash_nd_avails;70,2768 static unsigned long clause_ptr_gets,71,2837 static unsigned long clause_ptr_gets, clause_ptr_frees,71,2837 static unsigned long clause_ptr_gets, clause_ptr_frees, clause_ptr_avails;71,2837 static unsigned long ci_ptr_gets,72,2912 static unsigned long ci_ptr_gets, ci_ptr_frees,72,2912 static unsigned long ci_ptr_gets, ci_ptr_frees, ci_ptr_avails;72,2912 static unsigned long ilist_gets,73,2975 static unsigned long ilist_gets, ilist_frees,73,2975 static unsigned long ilist_gets, ilist_frees, ilist_avails;73,2975 static unsigned long link_node_gets,75,3036 static unsigned long link_node_gets, link_node_frees,75,3036 static unsigned long link_node_gets, link_node_frees, link_node_avails;75,3036 static unsigned long ans_lit_node_gets,76,3108 static unsigned long ans_lit_node_gets, ans_lit_node_frees,76,3108 static unsigned long ans_lit_node_gets, ans_lit_node_frees, ans_lit_node_avails;76,3108 static unsigned long formula_box_gets,77,3189 static unsigned long formula_box_gets, formula_box_frees,77,3189 static unsigned long formula_box_gets, formula_box_frees, formula_box_avails;77,3189 static unsigned long formula_gets,78,3267 static unsigned long formula_gets, formula_frees,78,3267 static unsigned long formula_gets, formula_frees, formula_avails;78,3267 static unsigned long formula_ptr_gets,79,3333 static unsigned long formula_ptr_gets, formula_ptr_frees,79,3333 static unsigned long formula_ptr_gets, formula_ptr_frees, formula_ptr_avails;79,3333 static unsigned long cl_attribute_gets,80,3411 static unsigned long cl_attribute_gets, cl_attribute_frees,80,3411 static unsigned long cl_attribute_gets, cl_attribute_frees, cl_attribute_avails;80,3411 static unsigned long glist_gets,81,3492 static unsigned long glist_gets, glist_frees,81,3492 static unsigned long glist_gets, glist_frees, glist_avails;81,3492 static unsigned long g2list_gets,82,3552 static unsigned long g2list_gets, g2list_frees,82,3552 static unsigned long g2list_gets, g2list_frees, g2list_avails;82,3552 int **tp_alloc(92,3744 struct term *get_term(153,5555 void free_term(180,6003 struct rel *get_rel(194,6212 void free_rel(221,6635 struct sym_ent *get_sym_ent(235,6830 void free_sym_ent(266,7394 struct term_ptr *get_term_ptr(280,7619 void free_term_ptr(303,8033 struct formula_ptr_2 *get_formula_ptr_2(317,8275 void free_formula_ptr_2(345,8840 struct fpa_tree *get_fpa_tree(359,9107 void free_fpa_tree(386,9606 struct fpa_head *get_fpa_head(400,9838 void free_fpa_head(424,10271 struct context *get_context(438,10497 void free_context(468,11075 struct trail *get_trail(493,11549 void free_trail(515,11906 struct imd_tree *get_imd_tree(529,12117 void free_imd_tree(555,12579 struct imd_pos *get_imd_pos(569,12809 void free_imd_pos(591,13192 struct is_tree *get_is_tree(605,13415 void free_is_tree(630,13847 struct is_pos *get_is_pos(644,14068 void free_is_pos(666,14438 struct fsub_pos *get_fsub_pos(680,14656 void free_fsub_pos(701,15055 struct literal *get_literal(715,15306 void free_literal(740,15753 struct clause *get_clause(754,15978 void free_clause(788,16592 struct list *get_list(802,16805 void free_list(826,17215 struct clash_nd *get_clash_nd(840,17441 void free_clash_nd(864,17875 struct clause_ptr *get_clause_ptr(878,18111 void free_clause_ptr(901,18548 struct ci_ptr *get_ci_ptr(915,18790 void free_ci_ptr(939,19190 struct ilist *get_ilist(953,19402 void free_ilist(976,19771 struct ans_lit_node *get_ans_lit_node(990,19990 void free_ans_lit_node(1016,20482 struct formula_box *get_formula_box(1030,20748 void free_formula_box(1058,21363 struct formula *get_formula(1072,21614 void free_formula(1098,22083 struct formula_ptr *get_formula_ptr(1112,22314 void free_formula_ptr(1136,22770 struct cl_attribute *get_cl_attribute(1150,23031 void free_cl_attribute(1174,23501 struct link_node *get_link_node(1188,23763 void free_link_node(1229,24660 void free_imd_pos_list(1243,24935 void free_is_pos_list(1267,25361 struct glist *get_glist(1291,25746 void free_glist(1314,26118 struct g2list *get_g2list(1328,26325 void free_g2list(1352,26727 void print_mem(1366,26925 void print_mem_brief(1412,34958 int total_mem(1432,36372 int total_mem_calls(1443,36534 void print_linked_ur_mem_stats(1454,36697 ../source/case.c,1320 #define MAX_SPLIT_DEPTH 14,192 #define POS_CLAUSE 16,258 #define NEG_CLAUSE 17,279 #define MIX_CLAUSE 18,300 #define FORK_FAIL 20,322 #define PARENT 21,343 #define CHILD 22,364 #define CHILD_FAIL 23,385 struct ilist *Current_case 27,476 struct literal_data literal_data36,805 int To_parent,58,1407 int To_parent, From_parent;58,1407 int To_children,59,1481 int To_children, From_children;59,1481 int splitting(67,1637 int max_split_depth(80,1886 int splitable_literal(93,2124 static struct literal_data compare_literal_data(118,2722 int splitable_clause(150,3440 struct clause *compare_splitable_clauses(176,4006 static void init_literal_data(214,5005 static void p_literal_data(225,5216 static void get_literal_data(244,5844 void print_case(306,7396 void p_case(321,7663 void print_case_n(332,7822 void p_case_n(348,8081 void p_assumption_depths(359,8215 struct ilist *current_case(378,8607 void add_subcase(389,8785 int case_depth(409,9135 struct clause *find_clause_to_split(422,9356 struct term *find_atom_to_split(452,10045 int prover_forks(522,12388 int split_clause(648,15559 int split_atom(778,19123 void possible_split(874,21783 void always_split(920,22766 void possible_given_split(949,23338 void assumps_to_parent(998,24566 void exit_with_possible_model(1040,25662 ../source/check.c,2529 #define GEN_TAB_SIZE 16,281 struct gen_node gen_node18,307 struct gen_tab gen_tab24,375 static struct gen_tab *Old_proof_tab;30,456 static struct gen_tab *New_proof_old_id_tab;31,494 static struct gen_tab *New_proof_tab;32,539 struct gen_node *get_gen_node(40,636 struct proof_object *get_proof_object(55,889 struct proof_object_node *get_proof_object_node(71,1196 static struct gen_tab *init_gen_tab(97,1745 static int insert_into_gen_tab(115,2102 static void * retrieve_from_gen_tab(150,2734 static void p_gen_tab(164,3014 static int check_eq_lit(182,3325 int trivial_subst(198,3666 struct proof_object_node *connect_new_node(225,4159 static char *po_rule(254,4778 void print_term_s(277,5333 void p_term_s(303,5818 void print_clause_s(316,6024 void p_clause_s(340,6469 void print_clause_s2(353,6684 void p_clause_s2(391,7436 void print_proof_object_node(402,7598 void p_proof_object_node(472,9141 void print_proof_object(483,9335 void p_proof_object(499,9643 static int new_literal_index(512,9890 static void copy_subst_to_proof_object(528,10186 struct clause *cl_copy_delete_literal(570,11016 int variant(606,11960 static int match_literals(649,12693 struct ilist *match_clauses(713,14310 struct clause *cl_append(769,15389 struct clause *identity_resolve(796,15881 static struct clause *identity_paramod(816,16228 void renumber_vars_subst(861,17288 static int translate_unit_deletion(896,17924 static int translate_factor_simp(974,20052 static struct ilist *first_rewrite(1048,22026 static struct ilist *first_rewrite_clause(1111,23466 static int translate_demod_nonunit(1144,24445 static int translate_demod_unit(1244,27438 int finish_translating(1336,30117 static int translate_resolution(1523,35758 static struct ilist *order_new_lits_for_hyper(1671,40348 static int translate_hyper(1716,41236 int ipx(1830,44676 static int translate_ur(1847,44896 static int translate_factor(2016,49226 static struct term *para_position(2083,50938 static int translate_paramod(2106,51351 static void varmap(2251,55688 static BOOLEAN match2(2265,56008 struct proof_object_node *find_match2(2299,56820 static int translate_step(2322,57415 int contains_answer_literal(2428,60563 int contains_rule(2443,60835 struct ilist *trans_2_pos(2460,61085 void type_2_trans(2505,62053 int glist_subsume(2529,62618 void p_proof_object_as_hints(2545,62887 struct literal *remove_answer_literals(2584,63763 void build_proof_object(2610,64357 void init_proof_object_environment(2710,68061 ../source/clause.c,3761 #define CLAUSE_TAB_SIZE 8,109 static struct clause_ptr *Clause_tab[11,184 static int Clause_id_count;14,264 static struct clause *Hidden_clauses;17,348 #define MAX_LITS 20,442 static char Map_array[21,463 void reset_clause_counter(29,563 int next_cl_num(42,783 void assign_cl_id(55,996 void hot_cl_integrate(88,2059 void cl_integrate(114,2688 void cl_del_int(178,4175 void cl_del_non(270,6091 void cl_int_chk(300,6682 static struct term *literals_to_term(323,7312 struct term *clause_to_term(357,8018 static struct literal *term_to_literals(377,8359 struct clause *term_to_clause(407,8989 struct clause *read_sequent_clause(456,10063 struct clause *read_clause(657,14269 struct list *read_cl_list(710,15369 int set_vars_cl(756,16300 void print_sequent_clause(782,16753 void print_justification(814,17331 void print_clause_bare(880,19538 void print_clause(895,19827 void print_clause_without_just(991,21758 void p_clause(1066,23259 void print_cl_list(1077,23408 void cl_merge(1100,23812 int tautology(1130,24367 int prf_weight(1157,24865 int proof_length(1191,25678 int subsume(1215,26213 int map_rest(1237,26605 int anc_subsume(1296,28043 struct clause *for_sub_prop(1317,28449 struct clause *forward_subsume(1341,28884 struct clause_ptr *back_subsume(1482,32598 struct clause_ptr *unit_conflict(1553,34344 int propositional_clause(1617,35837 int xx_resolvable(1638,36217 int pos_clause(1669,36855 int answer_lit(1688,37226 int pos_eq_lit(1699,37430 int neg_eq_lit(1710,37634 int eq_lit(1721,37839 int neg_clause(1734,38059 int num_literals(1753,38450 int num_answers(1774,38792 int num_literals_including_answers(1795,39114 int literal_number(1812,39472 int unit_clause(1833,39816 int horn_clause(1848,40062 int equality_clause(1867,40408 int symmetry_clause(1885,40741 struct literal *ith_literal(1920,41560 void append_cl(1945,41914 void prepend_cl(1973,42374 void insert_before_cl(1999,42836 void insert_after_cl(2031,43390 void rem_from_list(2063,43931 void insert_clause(2098,44597 int max_literal_weight(2126,45083 int weight_cl(2149,45591 void hide_clause(2180,46273 struct clause *proof_last_hidden_empty(2192,46454 void del_hidden_clauses(2217,46976 struct clause *cl_copy(2236,47290 int clause_ident(2271,47952 void remove_var_syms(2294,48470 void cl_insert_tab(2311,48764 void cl_delete_tab(2348,49435 struct clause *cl_find(2383,50075 int lit_compare(2411,50550 int ordered_sub_clause(2452,51675 int sub_clause(2497,52759 int sort_lits(2524,53250 void all_cont_cl(2564,54069 void zap_cl_list(2592,54590 int is_eq(2611,54841 void mark_literal(2635,55330 int get_ancestors(2684,56670 struct ilist *clauses_to_ids(2765,58519 void free_clause_ptr_list(2783,58823 struct ilist *get_ancestors2(2799,59109 struct ilist *just_to_supporters(2820,59522 int renumber_vars_term(2867,60696 int renumber_vars(2888,61112 int renum_vars_term(2915,61557 void clear_var_names(2957,62290 void cl_clear_vars(2975,62566 static void distinct_vars_rec(2989,62822 int distinct_vars(3018,63443 struct clause *find_first_cl(3039,63803 struct clause *find_last_cl(3057,64057 struct clause *find_random_cl(3075,64309 struct clause_ptr *get_clauses_of_wt_range(3102,64761 int clause_ptr_list_size(3123,65248 struct clause *nth_clause(3137,65493 void zap_clause_ptr_list(3155,65810 struct clause *find_random_lightest_cl(3169,66056 struct clause *find_mid_lightest_cl(3192,66557 struct clause *find_lightest_cl(3221,67284 struct clause *find_lightest_geo_child(3251,67984 struct clause *find_interactive_cl(3274,68418 struct clause *find_given_clause(3334,69866 struct clause *extract_given_clause(3384,71045 int unit_del(3413,71735 void back_unit_deletion(3524,74186 ../source/clocks.c,177 void clock_init(15,218 long clock_val(60,1037 void clock_reset(81,1477 char *get_time(93,1739 long system_time(110,2032 long run_time(139,2550 long wall_seconds(170,3021 ../source/demod.c,673 static struct term *contract_lin(18,350 static void dollar_out_non_list(94,1959 static void dollar_out(110,2287 static struct term *dollar_contract(159,4086 static struct term *replace_special(556,16479 static struct term *demod(593,17616 static struct term *left_most_one_step(692,20357 static struct term *demod_out_in(749,21553 void un_share_special(787,22560 struct term *convenient_demod(814,23003 void zap_term_special(861,24263 struct term *apply_demod(905,25496 void demod_cl(957,26656 void back_demod(1065,29636 int lit_t_f_reduce(1165,32155 int check_input_demod(1229,33653 int dynamic_demodulator(1300,35398 struct clause *new_demod(1364,36893 ../source/foreign.c,446 long foo(14,155 long user_test_long(28,343 double user_test_double(45,616 int user_test_bool(62,885 char *user_test_string(79,1152 struct term *user_test_term(96,1460 void declare_user_functions(116,1849 int get_args_for_user_function(211,4633 struct term *long_to_term(289,6201 struct term *double_to_term(307,6517 struct term *bool_to_term(325,6836 struct term *string_to_term(341,7121 struct term *evaluate_user_function(357,7351 ../source/formula.c,3021 static int Sk_func_num,11,201 static int Sk_func_num, Sk_const_num;11,201 void print_formula(19,374 void p_formula(87,1809 static struct term *formula_args_to_term(101,2094 struct term *formula_to_term(142,3123 struct formula *term_to_formula(207,4583 struct formula *read_formula(278,6318 struct formula_ptr *read_formula_list(323,7236 void print_formula_list(378,8349 struct formula *copy_formula(396,8720 void zap_formula(433,9494 struct formula *negate_formula(460,9977 struct formula *nnf(495,10754 static void rename_free_formula(603,13339 static struct formula *skolem(631,13962 struct formula *skolemize(722,16180 struct formula *anti_skolemize(742,16544 static void subst_free_term(755,16839 void subst_free_formula(784,17385 void gen_sk_sym(811,17981 int skolem_symbol(849,18677 int contains_skolem_symbol(868,19009 int new_var_name(897,19623 int new_functor_name(926,20173 static void uq_all(949,20570 void unique_all(996,21594 static void mark_free_var_term(1022,22112 static void mark_free_var_formula(1057,22820 struct formula *zap_quant(1084,23547 static void flatten_top_2(1125,24302 void flatten_top(1160,25069 static struct formula *distribute(1183,25530 struct formula *cnf(1264,27078 struct formula *dnf(1307,27910 static void rename_syms_term(1320,28147 void rename_syms_formula(1359,29156 void subst_sn_term(1378,29524 void subst_sn_formula(1405,30065 int gen_subsume_prop(1430,30665 struct formula *subsume_conj(1470,31932 struct formula *subsume_disj(1536,33411 int formula_ident(1599,34728 void conflict_tautology(1634,35671 void ts_and_fs(1676,36657 static int set_vars_term_2(1730,37624 static int set_vars_cl_2(1775,38545 static struct clause *disj_to_clause(1799,38954 static struct list *cnf_to_list(1864,40647 struct list *clausify(1896,41284 struct list *clausify_formula_list(1920,41707 struct formula *negation_inward(1972,42835 struct formula *expand_imp(2017,43811 struct formula *iff_to_conj(2036,44153 struct formula *iff_to_disj(2076,44852 struct formula *nnf_cnf(2109,45476 struct formula *nnf_dnf(2120,45633 struct formula *nnf_skolemize(2131,45796 struct formula *clausify_formed(2142,45979 void rms_conflict_tautology(2164,46459 struct formula *rms_subsume_conj(2219,47554 struct formula *rms_subsume_disj(2285,49035 int free_occurrence(2348,50339 struct formula *rms_distribute_quants(2389,51153 static void separate_free(2428,51980 struct formula *rms_push_free(2492,53263 struct formula *rms_quantifiers(2538,54279 static struct formula *rms_distribute(2614,55990 struct formula *rms(2691,57481 static void introduce_var_term(2739,58440 static void introduce_var(2772,59078 struct formula *renumber_unique(2808,59835 int gen_subsume_rec(2859,61026 int gen_subsume(2904,62504 int gen_conflict(2941,63251 int gen_tautology(2979,64090 struct formula *rms_cnf(3012,64752 struct formula *rms_dnf(3023,64909 static struct formula *push_free(3039,65305 struct formula *distribute_quantifier(3088,66470 ../source/fpa.c,919 #define AND 48,1654 #define OR 49,1668 #define LEAF 50,1681 #define MAX_PATH 54,1801 struct fpa_index *alloc_fpa_index(62,1884 static void path_mark_end(83,2261 static int hash_path(112,2855 static int path_comp(130,3100 static int path_size(153,3440 static int *path_copy(171,3650 static void insert_fpa_tab(196,4090 static void delete_fpa_tab(269,5767 void term_fpa_rec(327,7154 void fpa_insert(377,8244 void fpa_delete(404,8886 static struct fpa_tree *get_leaf_node(422,9253 static int all_args_vars(449,9843 static struct fpa_tree *build_tree_local(504,11443 struct fpa_tree *build_tree(598,13534 struct term *next_term(625,14358 struct fpa_tree *build_for_all(732,16809 void zap_prop_tree(771,17605 void print_fpa_tab(786,17889 void p_fpa_tab(818,18478 void print_prop_tree(832,18777 void p_prop_tree(859,19261 void print_path(870,19451 void p_path(904,20075 int new_sym_num(921,20389 ../source/geometry.c,348 #define MAX_DEPTH 31,1181 static int is_geometry_symbol(39,1298 static int geo_rewrite_recurse(56,1619 int geo_rewrite(123,3347 static struct term *geo_replace_unif(146,3820 static void geo_generate_unif(173,4302 static void geo_recurse_unif(215,5354 void geometry_rule_unif(260,6528 int child_of_geometry(282,6975 void gl_demod(303,7289 ../source/hints2.c,771 struct hint2_data hint2_data17,402 static struct fpa_index *Fpa_hints2_lits 22,460 #define KEEP_BACK_DEMODULATED_HINTS 26,537 static struct literal *first_nonanswer_lit(34,646 static void zap_ilist(52,956 static struct hint2_data *copy_hint2_data(66,1141 void print_hint2_clause(82,1486 void print_hints2_cl_list(113,2080 void hint2_integrate(140,2614 static void index_hint2(161,3093 static void process_hint2_attributes(184,3741 void compile_hints2(220,4691 static struct clause *find_hint2(239,5073 void adjust_weight_with_hints2(278,6039 int hint2_keep_test(323,7371 static void all_containing_hints2(345,7893 static int xx_tautology(375,8514 static struct clause *hint2_subsumed(403,9125 void back_demod_hints(436,9935 void zap_hints2(536,12205 ../source/hints.c,307 struct hint_data hint_data65,2095 static void process_hint_attributes(79,2366 void compile_hints(132,3955 void print_hint_clause(147,4228 void p_hint_clause(182,4928 void print_hints_cl_list(193,5088 void p_hints_cl_list(216,5463 void adjust_weight_with_hints(234,5872 int hint_keep_test(305,7377 ../source/hot.c,733 static struct fpa_index *Hot_clash_pos_lits;23,696 static struct fpa_index *Hot_clash_neg_lits;24,741 static struct fpa_index *Hot_alphas;25,786 static struct fpa_index *Hot_clash_terms;26,823 static struct fpa_index *Ordinary_clash_pos_lits;30,905 static struct fpa_index *Ordinary_clash_neg_lits;31,955 static struct fpa_index *Ordinary_alphas;32,1005 static struct fpa_index *Ordinary_clash_terms;33,1047 void init_hot(41,1187 int heat_is_on(66,1873 void switch_to_hot_index(78,2060 void switch_to_ordinary_index(92,2354 void hot_index_clause(108,2721 void hot_dynamic(127,3051 static void hot_mark_clash(154,3530 static void hot_unmark_clash(195,4305 void hot_mark_clash_cl(240,5348 void hot_inference(280,6124 ../source/imd.c,240 static struct imd_tree *insert_imd_tree(16,242 void imd_insert(95,2022 static struct imd_tree *end_term_imd(147,3611 void imd_delete(208,5012 struct term *contract_imd(294,7012 void print_imd_tree(460,11267 void p_imd_tree(499,12050 ../source/index.c,283 static void index_mark_clash(15,262 static void un_index_mark_clash(58,1126 static void index_paramod(105,2227 static void un_index_paramod(158,3583 void index_lits_all(215,5299 void un_index_lits_all(249,6186 void index_lits_clash(284,7182 void un_index_lits_clash(312,7900 ../source/io.c,2308 #define SYM_TAB_SIZE 18,343 #define MAX_COMPLEX 19,369 struct sequence_member sequence_member23,509 static struct sym_ent *Sym_tab[31,642 int str_double(41,855 void double_str(67,1307 int str_int(92,1722 void int_str(121,2184 int str_long(153,2681 int bits_ulong(187,3252 void long_str(206,3573 void ulong_bits(236,3992 void cat_str(258,4492 int str_ident(277,4796 void reverse(291,5006 struct sym_ent *insert_sym(312,5402 int str_to_sn(339,6051 void print_syms(423,8169 void p_syms(443,8503 char *sn_to_str(454,8675 int sn_to_arity(473,9024 struct sym_ent *sn_to_node(494,9392 int sn_to_ec(512,9738 struct sym_ent *sym_tab_member(534,10145 int in_sym_tab(561,10609 void free_sym_tab(583,10956 int is_symbol(607,11354 void mark_as_skolem(622,11642 int is_skolem(643,11958 int initial_str(665,12335 int set_vars(686,12830 int set_vars_term(703,13089 int var_name(746,13987 struct term_ptr *read_list(766,14470 void print_list(820,15534 void bird_print(836,15792 #define OPEN_PAREN 927,18720 #define OTHER_PUNC 928,18742 #define NAME_SYM 929,18764 #define SYM_SYM 930,18786 static int next_token_type(941,18991 void write_term(1006,20514 void display_term(1204,25107 void print_term(1238,25818 void p_term(1257,26167 void d_term(1270,26379 void print_term_nl(1283,26602 int print_term_length(1296,26788 void pretty_print_term(1327,27305 void print_variable(1372,28166 void built_in_symbols(1404,28870 int declare_op(1489,32587 void init_special_ops(1534,33345 int process_op_command(1579,34349 static void fill_in_op_data(1646,36170 static int is_white(1683,36968 void skip_white(1702,37357 static int is_symbol_char(1723,37716 static int is_alpha_numeric(1756,38180 int name_sym(1771,38423 static void get_name(1789,38717 void print_error(1844,39812 static struct term *seq_to_quant_term(1903,41084 static struct term *seq_to_term(1970,42672 static struct term *str_to_args(2131,46293 static struct term *str_to_list(2187,47437 static int str_to_sequence(2272,49646 struct term *str_to_term(2380,52319 int read_buf(2437,53886 struct term *term_fixup(2528,55870 struct term *term_fixup_2(2574,56807 struct term *read_term(2606,57542 void merge_sort(2652,58297 int compare_for_auto_lex_order(2695,59139 void auto_lex_order(2736,59993 ../source/is.c,298 static struct is_tree *insert_is_tree(15,220 void is_insert(95,2078 static struct is_tree *end_term_is(122,2848 void is_delete(181,4174 struct term_ptr *is_retrieve(270,6410 struct term *fs_retrieve(393,9646 void canc_fs_pos(441,10658 void print_is_tree(463,11019 void p_is_tree(475,11225 ../source/ivy.c,413 static struct proof_object *Initial_proof_object 10,114 static int bnode_to_natural(14,249 static struct term *bnode_to_otterterm(29,535 int special_is_symbol(82,1828 void trans_logic_symbols(90,2082 static struct clause *bnode_to_clause(113,2727 struct proof_object *parse_initial_proof_object(135,3236 struct list *init_proof_object(175,4553 struct proof_object *retrieve_initial_proof_object(198,5273 ../source/linkhyp.c,30 void linked_hyper_res(14,141 ../source/linkur.c,1421 static void construct_children_nodes(125,4477 static struct clause *subsumable_unit(285,8717 static struct clause *linked_unit_del(425,14029 static struct link_node *backward(557,18387 void linked_ur_res(702,22141 static struct ilist *build_parental_chain(1096,34176 static struct clause *build_ur_resolvent(1145,35385 static BOOLEAN check_down_tree(1206,36938 static BOOLEAN check_up_tree(1259,38136 static struct term *first_unifiable(1314,39534 static struct link_node *forward(1354,40665 static struct link_node *forward_from_resolved_tree(1484,44080 static void free_linked_node_tree(1558,46012 static struct term *generate_resolvent(1588,46913 static struct link_node *initialize_tree(1630,48026 static BOOLEAN is_in_ancestry(1711,50240 static BOOLEAN keep_clause(1776,51984 static void linked_print_clause(1852,53724 static void linked_print_link_node(1908,54874 static void linked_print_link_node_tree(1985,57052 static BOOLEAN more_targets_here(2010,57691 static struct term *next_unifiable(2042,58463 static BOOLEAN poss_nuc_link(2132,60642 static BOOLEAN pass_parms_check(2164,61420 static BOOLEAN pass_target_depth_check(2247,63593 int process_linked_tags(2265,64002 static BOOLEAN process_this_resolution(2432,68907 static int term_ident_subst(2533,71032 static void write_down_tree(2596,72633 static void write_up_tree(2627,73462 static void write_target_distances(2665,74627 ../source/lisp.c,714 #define MAX_WORD 3,19 static char Word[4,40 static int Gets,5,68 static int Gets, Frees;5,68 static char *new_str_copy(22,524 static Bnode get_bnode(31,746 static void free_bnode(44,1027 /**/ void zap_btree(54,1215 /**/ BOOLEAN true_listp(65,1428 /**/ void fprint_btree(75,1653 /**/ void p_btree(100,2202 static BOOLEAN white_char(109,2387 static BOOLEAN paren(119,2668 static int fill_word(127,2836 /**/ BOOLEAN nullp(154,3405 static BOOLEAN dotp(159,3500 static void dot_trans 166,3671 /**/ Bnode parse_lisp(194,4261 /**/ int atom(229,5019 /**/ Bnode car(234,5152 /**/ Bnode cdr(239,5283 /**/ Bnode cadr(244,5414 /**/ Bnode caddr(249,5552 /**/ int length(254,5697 /**/ int main(263,5876 ../source/lists.c,864 void free_ilist_list(16,222 struct ilist *ilist_tack_on(30,419 struct ilist *iset_add(49,705 struct ilist *iset_remove(76,1140 int ilist_member(102,1519 int iset_subset(118,1753 struct ilist *iset_subtract(132,1987 struct ilist *iset_sort(148,2293 struct ilist *idempot_ip(166,2565 struct ilist *reverse_ip(187,2904 struct ilist *ilist_append(204,3217 struct ilist *copy_ilist(222,3513 int ilist_length(240,3784 struct ilist *copy_ilist_segment(254,4011 void print_ilist(272,4333 void p_ilist(288,4606 int glist_length(302,4833 struct glist *copy_glist(316,5063 struct glist *glist_append(334,5365 struct glist *glist_prepend(350,5641 struct glist *glist_tack_on(364,5852 void free_glist_list(383,6147 int g2list_length(399,6420 int member_is_subset(415,6699 struct glist *copy_glist_of_ilists(431,6975 void free_glist_of_ilists(449,7296 ../source/lrpo.c,298 static int sym_precedence(16,257 static int lrpo_status(51,1151 static int lrpo_lex(68,1539 static int num_occurrences(109,2537 static struct term *set_multiset_diff(136,3136 static int lrpo_multiset(184,4416 int lrpo(222,5220 int lrpo_greater(267,6403 void order_equalities_lrpo(294,6923 ../source/main.c,133 #define OTTER_VERSION 14,265 #define VERSION_DATE 15,293 #define IN_MAIN 17,330 /**/ int main(20,427 void print_banner(162,4523 ../source/misc.c,1462 void init(14,152 void abend(51,992 void read_a_file(71,1364 void sos_argument(702,19592 void read_all_input(770,21001 void set_lex_vals(924,24691 void set_lrpo_status(949,25218 void set_special_unary(970,25693 void set_skolem(992,26300 void free_all_mem(1009,26614 void output_stats(1099,28528 void print_stats(1140,29326 void print_stats_brief(1226,33317 void p_stats(1251,34212 void print_times(1262,34334 void print_times_brief(1336,38143 void p_times(1387,40243 void append_lists(1398,40417 struct term *copy_term(1448,41547 int biggest_var(1482,42152 int biggest_var_clause(1510,42608 int ground_clause(1529,42932 void zap_list(1540,43139 int occurs_in(1560,43447 int occurrences(1585,43861 int sn_occur(1610,44296 int is_atom(1640,44885 static int id_nested_skolems(1653,45134 int ident_nested_skolems(1692,45834 int ground(1712,46172 void cleanup(1735,46519 int check_stop(1776,47777 void report(1813,48677 void control_memory(1838,49259 static void proof_message(1905,50806 void print_proof(1937,51505 struct clause *check_for_proof(2000,53060 int proper_list(2061,54525 void move_clauses(2081,54947 void automatic_1_settings(2109,55523 int sos_has_pos_nonground(2230,60437 void automatic_2_settings(2255,61002 void log_for_x_show(2377,65107 int same_structure(2402,65969 void zap_variable_names(2432,66512 int commuted_terms(2449,66830 int symbol_count(2484,67743 int commutativity_consequence(2503,68092 ../source/multijust.c,2590 static int Asize;24,704 static int Bsize;25,722 static struct glist **Alists;26,740 static struct glist **Blists;27,770 static int *A_to_B;28,800 static int *B_to_A;29,820 static struct ilist *Demod_map;31,841 static struct glist *remove_those_containing(39,990 struct glist *keep_only(61,1421 struct glist *remove_supersets(81,1724 struct glist *remove_all_supersets(103,2140 static int g2_superset(130,2716 struct g2list *g2_remove_supersets(149,3084 static void append_parents(173,3549 int input_clause(205,4270 int first_just_input_only(222,4518 int all_supporters_less_than(238,4809 int derived_from_itself(254,5126 int proof_not_longer_than(265,5337 void possibly_append_parents(292,6126 static void print_multi_supporters(332,7269 static struct glist *just_lists_to_supporters_lists(352,7708 static void build_support_lists(370,8067 int map_demod(400,8917 static void collapse_new_demod2(421,9366 static void multi_map(460,10216 #define INT_BIT 542,12168 static int Set_size;543,12187 static unsigned Compares;544,12235 void set_jset_size(552,12321 int *get_jset(563,12463 int *copy_jset(574,12599 int jset_member(589,12794 void add_to_jset(602,12976 void remove_from_jset(615,13164 static int j_compare(630,13397 #define JHASH_SIZE 653,13851 static struct glist **Jhash;655,13898 static unsigned int Lookups;656,13927 static unsigned int Crashes;657,13956 static void jhash_init(665,14042 static int jhash(676,14199 static int jhash_member_recurse(691,14421 static int jhash_member(714,14821 static struct glist *jhash_insert_recurse(727,15021 static void jhash_insert(761,15701 void print_set(773,15882 void print_set_b_to_a(793,16188 static void print_jhash(813,16511 struct jnode jnode838,17006 static struct jnode *Jstart;847,17283 static struct jnode *Jend;848,17312 static struct jnode *Jcurrent;849,17339 static int Expanded;851,17371 static int Generated;852,17392 static int Pruned;853,17414 static int Subsumed;854,17433 static int Kept;855,17454 static struct jnode *get_jnode(863,17527 static int b_input(880,17822 static int a_input(891,17949 static void print_jnode(902,18088 static void print_jnode_b_to_a(918,18380 int subset_or_input(934,18726 static void jproof(954,19148 static int j_subsumed_recurse(1069,22312 static int j_subsumed(1109,23145 struct ilist *jset_to_ilist(1142,23746 int *ilist_to_jset(1162,24075 static int iset_jset_disjoint(1176,24296 static int j_expand(1192,24564 static int j_search(1264,26157 void multi_just_process(1315,27525 int multi_justifications(1364,28577 ../source/nonport.c,220 void non_portable_init(30,499 void sig_handler(49,779 char *username(92,1891 char *hostname(113,2275 void interact(134,2602 void foreach_sos(308,7616 FILE *init_log_for_x_show(364,8720 int my_process_id(381,8990 ../source/options.c,264 void init_options(14,149 void print_options(669,18918 void p_options(706,19663 void auto_change_flag(717,19793 void dependent_flags(740,20351 void dependent_parms(892,24865 int change_flag(913,25301 int change_parm(981,27143 void check_options(1058,29213 ../source/overbeek.c,205 #define OVERBEEK_WORLD_SIZE 64,1563 static unsigned hash_term2(74,1746 void overbeek_insert(98,2253 int overbeek_weight(130,3070 void print_overbeek_world(160,3720 void check_overbeek_world(197,4482 ../source/paramod.c,304 static struct term *apply_substitute(17,337 static struct clause *build_bin_para(76,1757 static void insert_detailed_para_history(154,3988 static void para_from_up(203,5164 static void para_from_alpha(264,6866 void para_from(307,7991 static void para_into_terms(342,8861 void para_into(416,10940 ../source/pickdiff.c,520 static struct rel *copy_rels(9,132 static void zap_rels(27,466 static struct rel *remove1(42,705 static struct ilist *add_vecs(64,1101 static int le_vecs(86,1523 static struct ilist *diff_lists(108,1943 static struct ilist *diff(134,2536 static struct ilist *min_diff(167,3336 static struct ilist *diff2_lists(200,3982 static struct ilist *diff2(229,4661 struct ilist *cldiff(258,5343 static struct ci_ptr *get_ci_of_wt_range(282,5911 void zap_ci_ptr_list(305,6428 struct clause *find_pickdiff_cl(322,6676 ../source/process.c,183 static void post_process(20,530 void post_proc_all(143,3758 static int given_clause_ok(185,4709 void infer_and_process(206,5134 int proc_gen(337,8736 void pre_process(584,14893 ../source/resolve.c,491 static struct clause *build_hyper(17,332 int maximal_lit(176,3908 static void clash(225,5721 void hyper_res(394,9698 void neg_hyper_res(596,14970 void ur_res(800,20339 int one_unary_answer(1047,26551 struct term *build_term(1068,27064 void combine_answers(1103,27658 struct clause *build_bin_res(1165,29243 struct clause *apply_clause(1252,31330 void bin_res(1282,31977 struct clause *first_or_next_factor(1345,33565 void all_factors(1419,35235 int factor_simplify(1460,36321 ../source/share.c,533 #define TERM_TAB_SIZE 8,93 static struct term_ptr *Term_tab[12,155 static struct term_ptr *Bd_kludge;17,356 static int hash_term(30,668 static int term_compare(62,1492 struct term *integrate_term(103,2521 void disintegrate_term(181,4209 void set_up_pointers(251,5725 void zap_term(272,6121 void print_term_tab(302,6702 void p_term_tab(327,7094 void test_terms(341,7335 struct term_ptr *all_instances(375,8033 struct term_ptr *all_instances_fpa(431,9283 void bd_kludge_insert(492,10734 void bd_kludge_delete(516,11120 ../source/unify.c,358 #define BIND(BIND10,142 #define DEREFERENCE(DEREFERENCE15,337 int occur_check(28,681 int unify(92,2810 int unify_no_occur_check(172,4568 int match(248,6632 struct term *apply(301,8040 int term_ident(360,9402 void clear_subst_2(394,10240 void clear_subst_1(414,10610 void print_subst(431,10883 void p_subst(453,11360 void print_trail(464,11513 ../source/weight.c,742 struct term_ptr *read_wt_list(17,291 static struct is_tree *weight_retrieve(43,858 int noncomplexifying(65,1328 int overbeek_match(81,1650 int weight(112,2278 static int wt_match_dots(176,3653 int wt_match(203,4264 static void set_wt_term(252,5472 static int set_wt_template(287,6371 static void weight_insert(312,7038 void set_wt_list(352,7850 void weight_index_delete(379,8330 static int lex_compare_sym_nums(411,8935 int lex_order(450,9880 int lex_order_vars(517,11860 static int wt_lex_order(587,13822 int lex_check(613,14325 static void get_var_multiset(631,14667 int var_subset(655,15080 static int sym_occur(685,15668 static int sym_elim(719,16451 void order_equalities(764,17537 int term_ident_x_vars(819,18828 otter-3.3f/mace2/b2.in0100644000076400007640000000041310070414043014012 0ustar mccunemccuneset(prolog_style_variables). set(tptp_eq). set(auto). clear(print_given). list(usable). equal(A,A). -equal(d,A)| -equal(b,B)|equal(a,B)|equal(c,A). -equal(d,A)| -equal(c,B)|equal(a,B)|equal(b,A). -equal(d,A)| -equal(a,A). -equal(c,A)| -equal(b,A). end_of_list. otter-3.3f/mace2/print.c0100644000076400007640000005006107714207010014470 0ustar mccunemccune#include "Mace2.h" extern struct sort Sorts[MAX_SORTS]; extern int Num_sorts; extern struct symbol Symbols[MAX_SYMBOLS]; extern int Next_base; extern int Num_symbols; /* function_value_n() -- these routines find the value of functions at * given points. It is assumed that we have a model including the * well-defined and closed properties. The DP code knows the * model, so we call atom_value. This is used mostly for printing * models. */ /************* * * function_value_0() * *************/ static int function_value_0(struct symbol *s) { int b, k; int n0 = s->args[0].n; b = ATOM1(s, 0); for (k = 0; k < n0 && atom_value(b+k) != 1; k++); return(k == n0 ? -1 : k); } /* function_value_0 */ /************* * * function_value_1() * *************/ static int function_value_1(struct symbol *s, int i) { int b, k; int n1 = s->args[1].n; b = ATOM2(s, i, 0); for (k = 0; k < n1 && atom_value(b+k) != 1; k++); return(k == n1 ? -1 : k); } /* function_value_1 */ /************* * * function_value_2() * *************/ static int function_value_2(struct symbol *s, int i, int j) { int b, k; int n2 = s->args[2].n; b = ATOM3(s, i, j, 0); for (k = 0; k < n2 && atom_value(b+k) != 1; k++); return(k == n2 ? -1 : k); } /* function_value_2 */ /************* * * function_value_3() * *************/ static int function_value_3(struct symbol *s, int i, int j, int a) { int b, k; int n3 = s->args[3].n; b = ATOM4(s, i, j, a, 0); for (k = 0; k < n3 && atom_value(b+k) != 1; k++); return(k == n3 ? -1 : k); } /* function_value_3 */ /************* * * print_table_f0() * *************/ static void print_table_f0(FILE *fp, struct symbol *s) { fprintf(fp, "\n %s: %d\n", s->name, function_value_0(s)); } /* print_table_f0 */ /************* * * print_table_f1() * *************/ static void print_table_f1(FILE *fp, struct symbol *s) { int i; char *s1, *s2; int n0 = s->args[0].n; if (n0 <= 10) { s1 = "%2d"; s2 = "--"; } else { s1 = "%3d"; s2 = "---"; } fprintf(fp, "\n %s :\n", s->name); fprintf(fp, " "); for (i = 0; i < n0; i++) fprintf(fp, s1, i); fprintf(fp, "\n ---"); for (i = 0; i < n0; i++) fprintf(fp, s2); fprintf(fp, "\n "); for (i = 0; i < n0; i++) fprintf(fp, s1, function_value_1(s, i)); fprintf(fp, "\n"); } /* print_table_f1 */ /************* * * print_table_f2() * *************/ static void print_table_f2(FILE *fp, struct symbol *s) { int i, j, v; char *s1, *s2, *s3; int n0 = s->args[0].n; int n1 = s->args[1].n; if (n1 <= 10) { s1 = "%2d"; s2 = "--"; s3 = " -"; } else { s1 = "%3d"; s2 = "---"; s3 = " -"; } fprintf(fp, "\n %s :\n", s->name); fprintf(fp, " |"); for (i = 0; i < n1; i++) fprintf(fp, s1, i); fprintf(fp, "\n --+"); for (i = 0; i < n1; i++) fprintf(fp, s2); fprintf(fp, "\n"); for (i = 0; i < n0; i++) { fprintf(fp, "%5d |", i); for (j = 0; j < n1; j++) { v = function_value_2(s, i, j); if (v < 0) fprintf(fp, s3); else fprintf(fp, s1, v); } fprintf(fp, "\n"); } } /* print_table_f2 */ /************* * * print_table_r0() * *************/ static void print_table_r0(FILE *fp, struct symbol *s) { int v; char *s1; v = atom_value(ATOM0(s)); switch(v) { case 0: s1 = "F"; break; case 1: s1 = "T"; break; case 2: s1 = "F"; break; default: s1 = "?"; break; } fprintf(fp, "\n %s: %s\n", s->name, s1); } /* print_table_r0 */ /************* * * print_table_r1() * *************/ static void print_table_r1(FILE *fp, struct symbol *s) { int i, v; char *s1; int n0=s->args[0].n; fprintf(fp, "\n %s :\n", s->name); fprintf(fp, " "); for (i = 0; i < n0; i++) fprintf(fp, "%2d", i); fprintf(fp, "\n ---"); for (i = 0; i < n0; i++) fprintf(fp, "--"); fprintf(fp, "\n "); for (i = 0; i < n0; i++) { v = atom_value(ATOM1(s, i)); switch(v) { case 0: s1 = "F"; break; case 1: s1 = "T"; break; case 2: s1 = "F"; break; default: s1 = "?"; break; } fprintf(fp, "%2s", s1); } fprintf(fp, "\n"); } /* print_table_r1 */ /************* * * print_table_r2() * *************/ static void print_table_r2(FILE *fp, struct symbol *s) { int i, j, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; fprintf(fp, "\n %s :\n", s->name); fprintf(fp, " |"); for (i = 0; i < n1; i++) fprintf(fp, "%2d", i); fprintf(fp, "\n --+"); for (i = 0; i < n1; i++) fprintf(fp, "--"); fprintf(fp, "\n"); for (i = 0; i < n0; i++) { fprintf(fp, "%5d |", i); for (j = 0; j < n1; j++) { v = atom_value(ATOM2(s, i, j)); switch(v) { case 0: s1 = "F"; break; case 1: s1 = "T"; break; case 2: s1 = "F"; break; default: s1 = "?"; break; } fprintf(fp, "%2s", s1); } fprintf(fp, "\n"); } } /* print_table_r2 */ /************* * * print_model() * * Print the current model as a first-order model. The DP code * knows about the propositional model, so we call atom_value() * to get the information to print the first-order model. * * Assume unassigned atoms are true, because dp determines that * we have a model when all remaining clauses are positive. * * Don't print equality, order, or $Connect relations. * *************/ void print_model(FILE *fp) { int i; struct symbol *s; static int count; #if 1 fprintf(fp, "\n======================= Model #%d at %.2f seconds:\n", ++count, run_time() / 1000.); #endif for (i = 0; i < Num_symbols; i++) { s = Symbols + i; if (s->type == FUNCTION) { switch (s->arity) { case 1: print_table_f0(fp, s); break; case 2: print_table_f1(fp, s); break; case 3: print_table_f2(fp, s); break; default: fprintf(fp, "Dimension %d table for %s not printed\n", s->arity-1, s->name); } } else if (!TP_BIT(s->properties, MACE_ORDER_BIT) && !TP_BIT(s->properties, MACE_EQ_BIT) && !initial_str("$Connect", s->name)) { switch (s->arity) { case 0: print_table_r0(fp, s); break; case 1: print_table_r1(fp, s); break; case 2: print_table_r2(fp, s); break; default: fprintf(fp, "Dimension %d table for %s not printed\n", s->arity, s->name); } } } fprintf(fp, "end_of_model\n"); } /* print_model */ /************* * * print_table_f0_portable() * *************/ static void print_table_f0_portable(FILE *fp, struct symbol *s) { fprintf(fp, "\n function(%s, [%d])",s->name,function_value_0(s)); } /* print_table_f0_portable */ /************* * * print_table_f1_portable() * *************/ static void print_table_f1_portable(FILE *fp, struct symbol *s) { int i; int n0 = s->args[0].n; fprintf(fp, "\n function(%s(_), [", s->name); for (i = 0; i < n0; i++) { fprintf(fp, "%d", function_value_1(s, i)); if (i < n0-1) fprintf(fp, ", "); else fprintf(fp, "])"); } } /* print_table_f1_portable */ /************* * * print_table_f2_portable() * *************/ static void print_table_f2_portable(FILE *fp, struct symbol *s) { int i, j, v; int n0 = s->args[0].n; int n1 = s->args[1].n; fprintf(fp, "\n function(%s(_,_), [\n", s->name); for (i = 0; i < n0; i++) { fprintf(fp, " "); /* print row */ for (j = 0; j < n1; j++) { v = function_value_2(s, i, j); if (j < n1-1) fprintf(fp, "%d, ", v); else if (i < n0-1) fprintf(fp, "%d,\n", v); else fprintf(fp, "%d ])", v); } } } /* print_table_f2_portable */ /************* * * print_table_f3_portable() * *************/ static void print_table_f3_portable(FILE *fp, struct symbol *s) { int i, j, k, v; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; fprintf(fp, "\n function(%s(_,_), [\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { fprintf(fp, " "); for (k = 0; k < n2; k++) { v = function_value_3(s, i, j, k); if (k < n2-1) fprintf(fp, "%d, ", v); else if (j < n1-1) fprintf(fp, "%d,\n", v); else if (i < n0-1) fprintf(fp, "%d,\n\n", v); else fprintf(fp, "%d ])", v); } } } } /* print_table_f3_portable */ /************* * * print_table_r0_portable() * *************/ static void print_table_r0_portable(FILE *fp, struct symbol *s) { int v; char *s1; v = atom_value(ATOM0(s)); switch(v) { case 0: s1 = "0"; break; case 1: s1 = "1"; break; case 2: s1 = "0"; break; default: s1 = "?"; break; } fprintf(fp, "\n predicate(%s, [%s])",s->name, s1); } /* print_table_r0_portable */ /************* * * print_table_r1_portable() * *************/ static void print_table_r1_portable(FILE *fp, struct symbol *s) { int i, v; char *s1; int n0=s->args[0].n; fprintf(fp, "\n predicate(%s(_), [", s->name); for (i = 0; i < n0; i++) { v = atom_value(ATOM1(s, i)); switch(v) { case 0: s1 = "0"; break; case 1: s1 = "1"; break; case 2: s1 = "0"; break; default: s1 = "?"; break; } fprintf(fp, "%s", s1); if (i < n0-1) fprintf(fp, ", "); else fprintf(fp, "])"); } for (i = 0; i < n0; i++) { } } /* print_table_r1_portable */ /************* * * print_table_r2_portable() * *************/ static void print_table_r2_portable(FILE *fp, struct symbol *s) { int i, j, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; fprintf(fp, "\n predicate(%s(_,_), [\n", s->name); for (i = 0; i < n0; i++) { fprintf(fp, " "); /* print row */ for (j = 0; j < n1; j++) { v = atom_value(ATOM2(s, i, j)); switch(v) { case 0: s1 = "0"; break; case 1: s1 = "1"; break; case 2: s1 = "0"; break; default: s1 = "?"; break; } if (j < n1-1) fprintf(fp, "%s, ", s1); else if (i < n0-1) fprintf(fp, "%s,\n", s1); else fprintf(fp, "%s ])", s1); } } } /* print_table_r2_portable */ /************* * * print_table_r3_portable() * *************/ static void print_table_r3_portable(FILE *fp, struct symbol *s) { int i, j, k, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; int n2=s->args[2].n; fprintf(fp, "\n predicate(%s(_,_,_), [\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { fprintf(fp, " "); for (k = 0; k < n2; k++) { v = atom_value(ATOM3(s, i, j, k)); switch(v) { case 0: s1 = "0"; break; case 1: s1 = "1"; break; case 2: s1 = "0"; break; default: s1 = "?"; break; } if (k < n2-1) fprintf(fp, "%s, ", s1); else if (j < n1-1) fprintf(fp, "%s,\n", s1); else if (i < n0-1) fprintf(fp, "%s,\n\n", s1); else fprintf(fp, "%s ])", s1); } } } } /* print_table_r3_portable */ /************* * * print_table_r4_portable() * *************/ static void print_table_r4_portable(FILE *fp, struct symbol *s) { int i, j, k, l, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; int n2=s->args[2].n; int n3=s->args[3].n; fprintf(fp, "\n predicate(%s(_,_,_,_), [\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { for (k = 0; k < n2; k++) { fprintf(fp, " "); for (l = 0; l < n3; l++) { v = atom_value(ATOM4(s, i, j, k, l)); switch(v) { case 0: s1 = "0"; break; case 1: s1 = "1"; break; case 2: s1 = "0"; break; default: s1 = "?"; break; } if (l < n3-1) fprintf(fp, "%s, ", s1); /* in i */ else if (k < n2-1) fprintf(fp, "%s,\n", s1); /* end of i; in j */ else if (j < n1-1) fprintf(fp, "%s,\n\n", s1); /* end of i,j; in k */ else if (i < n0-1) fprintf(fp, "%s,\n\n", s1); /* end of i,j,k; in l */ else fprintf(fp, "%s ])", s1); /* end of i,j,k,l */ } } } } } /* print_table_r4_portable */ /************* * * print_model_portable() * * Print the current model as a first-order model. The DP code * knows about the propositional model, so we call atom_value() * to get the information to print the first-order model. * * Assume unassigned atoms are true, because dp determines that * we have a model when all remaining clauses are positive. * * Don't print equality or $Connect relations. * *************/ void print_model_portable(FILE *fp) { int i, domain_size, syms_printed; struct symbol *s; static int count; domain_size = Sorts[0].n; fprintf(fp, "\n======================= Model #%d at %.2f seconds:\n", ++count, run_time() / 1000.); fprintf(fp, "interpretation( %d, [\n", domain_size); syms_printed = 0; for (i = 0; i < Num_symbols; i++) { s = Symbols + i; if (!TP_BIT(s->properties, MACE_EQ_BIT) && !initial_str("$Connect", s->name)) { if (syms_printed > 0) fprintf(fp, ",\n"); if (s->type == FUNCTION) { switch (s->arity) { case 1: print_table_f0_portable(fp, s); break; case 2: print_table_f1_portable(fp, s); break; case 3: print_table_f2_portable(fp, s); break; case 4: print_table_f3_portable(fp, s); break; default: fprintf(fp, "Dimension %d table for %s not printed", s->arity-1, s->name); } } else { switch (s->arity) { case 0: print_table_r0_portable(fp, s); break; case 1: print_table_r1_portable(fp, s); break; case 2: print_table_r2_portable(fp, s); break; case 3: print_table_r3_portable(fp, s); break; case 4: print_table_r4_portable(fp, s); break; default: fprintf(fp, "Dimension %d table for %s not printed\n", s->arity, s->name); } } syms_printed++; } } fprintf(fp, "\n]).\n"); fprintf(fp, "end_of_model\n"); } /* print_model_portable */ /************* * * print_table_f0_ivy() * *************/ static void print_table_f0_ivy(FILE *fp, struct symbol *s) { fprintf(fp, " ((%s . 0) . ((nil . %d)))\n",s->name,function_value_0(s)); } /* print_table_f0_ivy */ /************* * * print_table_f1_ivy() * *************/ static void print_table_f1_ivy(FILE *fp, struct symbol *s) { int i; int n0 = s->args[0].n; fprintf(fp, " ((%s . 1) . (\n", s->name); for (i = 0; i < n0; i++) { fprintf(fp, " ((%d) . %d)\n", i, function_value_1(s, i)); } fprintf(fp, " ))\n"); } /* print_table_f1_ivy */ /************* * * print_table_f2_ivy() * *************/ static void print_table_f2_ivy(FILE *fp, struct symbol *s) { int i, j; int n0 = s->args[0].n; int n1 = s->args[1].n; fprintf(fp, " ((%s . 2) . (\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { fprintf(fp, " ((%d %d) . %d)\n", i, j, function_value_2(s, i, j)); } } fprintf(fp, " ))\n"); } /* print_table_f2_ivy */ /************* * * print_table_f3_ivy() * *************/ static void print_table_f3_ivy(FILE *fp, struct symbol *s) { int i, j, k; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; fprintf(fp, " ((%s . 3) . (\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { for (k = 0; k < n2; k++) { fprintf(fp, " ((%d %d %d) . %d)\n",i,j,k,function_value_3(s, i, j, k)); } } } fprintf(fp, " ))\n"); } /* print_table_f3_ivy */ /************* * * print_table_r0_ivy() * *************/ static void print_table_r0_ivy(FILE *fp, struct symbol *s) { int v; char *s1; v = atom_value(ATOM0(s)); switch(v) { case 0: s1 = "nil"; break; case 1: s1 = "t"; break; case 2: s1 = "nil"; break; default: s1 = "?"; break; } fprintf(fp, " ((%s . 0) . ((nil . %s)))\n", s->name, s1); } /* print_table_r0_ivy */ /************* * * print_table_r1_ivy() * *************/ static void print_table_r1_ivy(FILE *fp, struct symbol *s) { int i, v; char *s1; int n0=s->args[0].n; fprintf(fp, " ((%s . 1) . (\n", s->name); for (i = 0; i < n0; i++) { v = atom_value(ATOM1(s, i)); switch(v) { case 0: s1 = "nil"; break; case 1: s1 = "t"; break; case 2: s1 = "nil"; break; default: s1 = "nil"; break; } fprintf(fp, " ((%d) . %s)\n", i, s1); } fprintf(fp, " ))\n"); } /* print_table_r1_ivy */ /************* * * print_table_r2_ivy() * *************/ static void print_table_r2_ivy(FILE *fp, struct symbol *s) { int i, j, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; fprintf(fp, " ((%s . 2) . (\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { v = atom_value(ATOM2(s, i, j)); switch(v) { case 0: s1 = "nil"; break; case 1: s1 = "t"; break; case 2: s1 = "nil"; break; default: s1 = "nil"; break; } fprintf(fp, " ((%d %d) . %s)\n", i, j, s1); } } fprintf(fp, " ))\n"); } /* print_table_r2_ivy */ /************* * * print_table_r3_ivy() * *************/ static void print_table_r3_ivy(FILE *fp, struct symbol *s) { int i, j, k, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; int n2=s->args[2].n; fprintf(fp, " ((%s . 3) . (\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { for (k = 0; k < n2; k++) { v = atom_value(ATOM3(s, i, j, k)); switch(v) { case 0: s1 = "nil"; break; case 1: s1 = "t"; break; case 2: s1 = "nil"; break; default: s1 = "nil"; break; } fprintf(fp, " ((%d %d %d) . %s)\n", i, j, k, s1); } } } fprintf(fp, " ))\n"); } /* print_table_r3_ivy */ /************* * * print_table_r4_ivy() * *************/ static void print_table_r4_ivy(FILE *fp, struct symbol *s) { int i, j, k, l, v; char *s1; int n0=s->args[0].n; int n1=s->args[1].n; int n2=s->args[2].n; int n3=s->args[3].n; fprintf(fp, " ((%s . 4) . (\n", s->name); for (i = 0; i < n0; i++) { for (j = 0; j < n1; j++) { for (k = 0; k < n2; k++) { for (l = 0; l < n3; l++) { v = atom_value(ATOM4(s, i, j, k, l)); switch(v) { case 0: s1 = "nil"; break; case 1: s1 = "t"; break; case 2: s1 = "nil"; break; default: s1 = "nil"; break; } fprintf(fp, " ((%d %d %d %d) . %s)\n", i, j, k, l, s1); } } } } fprintf(fp, " ))\n"); } /* print_table_r4_ivy */ /************* * * print_model_ivy() * * Print the current model as a first-order model. The DP code * knows about the propositional model, so we call atom_value() * to get the information to print the first-order model. * * Assume unassigned atoms are true, because dp determines that * we have a model when all remaining clauses are positive. * * Don't print equality relation "=". * *************/ void print_model_ivy(FILE *fp) { int i, domain_size; struct symbol *s; static int count; domain_size = Sorts[0].n; fprintf(fp, "\n======================= Model #%d at %.2f seconds:\n", ++count, run_time() / 1000.); fprintf(fp, "\n;; BEGINNING OF IVY MODEL\n"); if (domain_size == 1) fprintf(fp, "(0 .\n"); else { int i; fprintf(fp, "(("); for (i = 0; i < domain_size-1; i++) fprintf(fp, "%d ", i); fprintf(fp, ". %d) .\n (\n (\n", domain_size-1); } for (i = 0; i < Num_symbols; i++) { s = Symbols + i; if (s->type == RELATION) { if (!(TP_BIT(s->properties, MACE_EQ_BIT) && str_ident(s->name, "=")) && !initial_str("$Connect", s->name)) { switch (s->arity) { case 0: print_table_r0_ivy(fp, s); break; case 1: print_table_r1_ivy(fp, s); break; case 2: print_table_r2_ivy(fp, s); break; case 3: print_table_r3_ivy(fp, s); break; case 4: print_table_r4_ivy(fp, s); break; default: MACE_abend("print_model_ivy, max relation arity is 4"); } } } } fprintf(fp, " )\n .\n (\n"); for (i = 0; i < Num_symbols; i++) { s = Symbols + i; if (s->type == FUNCTION) { switch (s->arity) { case 1: print_table_f0_ivy(fp, s); break; case 2: print_table_f1_ivy(fp, s); break; case 3: print_table_f2_ivy(fp, s); break; case 4: print_table_f3_ivy(fp, s); break; default: MACE_abend("print_model_ivy, max function arity is 3"); } } } fprintf(fp, " )\n )\n)\n"); fprintf(fp, ";; END OF IVY MODEL\n"); } /* print_model_ivy */ otter-3.3f/mace2/Generate.h0100644000076400007640000000423207723141750015102 0ustar mccunemccune#ifndef TP_GENERATE_H #define TP_GENERATE_H #define FUNCTION 0 #define RELATION 1 #define MACE_EQ_BIT 1 #define MACE_ORDER_BIT 2 #define MACE_QUASIGROUP_BIT 4 #define MACE_BIJECTION_BIT 8 #define MACE_COMMUTATIVE_BIT 16 #define MAX_MNAME 32 /* string length of functors */ #define MAX_ARITY 4 /* See generate_prop_clauses(), ATOM, etc. */ #define MAX_MVARS 12 /* If changed, change generate_prop_clauses(). */ #define MAX_SYMBOLS 500 /* number of functors */ #define MAX_SORTS 10 /* number of sorts */ struct sort { char name[MAX_MNAME]; /* name of sort */ int n; /* size of sort */ }; struct symbol { int base; /* prop. atom numbers start here */ int end; /* prop. atom numbers end here */ int arity; /* of symbol */ struct { int sort; /* index of sort */ int n; /* size of sort */ int mult; /* for constructing prop. variables */ } args[MAX_ARITY]; char name[MAX_MNAME]; /* for printing */ int type; /* FUNCTION or RELATION */ int properties; /* special properties of symbol */ int assigned_value; /* for distinct constants option */ }; /* The following macros take sequences of integers and give unique integers * that are the propositional variables. The input, for example b,i,j, * represents application of symbol with "base" b to elements of the * domain. */ #define ATOM0(s) (s->base) #define ATOM1(s,i) (i + s->base) #define ATOM2(s,i,j) ((i)*s->args[0].mult + j + s->base) #define ATOM3(s,i,j,k) ((i)*s->args[0].mult + (j)*s->args[1].mult + k + s->base) #define ATOM4(s,i,j,k,l) ((i)*s->args[0].mult + (j)*s->args[1].mult + (k)*s->args[2].mult + l + s->base) /* function prototypes from generate.c */ void read_all_mace_input(int argc, char **argv); int dp_trans(int domain_size, int distinct_constants, int qg_constraint); void decode_and_p_clause(int c[], int n); void reinit_generate(void); int decode_int(int atom, char **func, int *arity, int *args); void p_unit(int u); #endif /* ! TP_GENERATE_H */ otter-3.3f/mace2/Makefile0100644000076400007640000000126710011766727014645 0ustar mccunemccuneDFLAGS = -DTP_NAMES -DTP_SIGNAL -DTP_RUSAGE CC = gcc CFLAGS = -O $(DFLAGS) # CFLAGS = -g $(DFLAGS) # Checks for gcc: # CFLAGS = -ansi -pedantic -Wall OBJECTS = clock.o avail.o opts.o stats.o miscellany.o flatten.o\ dp.o generate.o print.o part.o all: mace2 anldp install clean mace2: mace2.o $(OBJECTS) $(CC) $(CFLAGS) mace2.o $(OBJECTS) ../source/libotter.a -o mace2 anldp: anldp.o $(OBJECTS) $(CC) $(CFLAGS) anldp.o $(OBJECTS) ../source/libotter.a -o anldp mace2.o anldp.o $(OBJECTS): Mace2.h Clock.h Avail.h Opts.h Stats.h\ Miscellany.h Dp.h Generate.h Flatten.h Part.h install: /bin/mv mace2 anldp ../bin clean: /bin/rm -f *.o realclean: /bin/rm -f *.o mace2 anldp *~ otter-3.3f/mace2/opts.c0100644000076400007640000001535007714207010014323 0ustar mccunemccune#include "Opts.h" struct flag MACE_Flags[MACE_MAX_FLAGS]; struct parm MACE_Parms[MACE_MAX_PARMS]; /************* * * MACE_init_options() * *************/ void MACE_init_options(void) { int i; struct flag *f; struct parm *p; for (i = 0; i < MACE_MAX_FLAGS; i++) MACE_Flags[i].name = ""; for (i = 0; i < MACE_MAX_PARMS; i++) MACE_Parms[i].name = ""; /* MACE_Flags are Boolean-valued options */ f = &(MACE_Flags[PRINT_MODELS]); f->name = "print_models"; f->val = 0; f = &(MACE_Flags[PRINT_MODELS_PORTABLE]); f->name = "print_models_portable"; f->val = 0; f = &(MACE_Flags[PRINT_MODELS_IVY]); f->name = "print_models_ivy"; f->val = 0; f = &(MACE_Flags[SUBSUME]); f->name = "subsume"; f->val = 0; f = &(MACE_Flags[DISTINCT_CONSTANTS]); f->name = "distinct_constants"; f->val = 0; f = &(MACE_Flags[QG_CONSTRAINT]); f->name = "qg_constraint"; f->val = 0; f = &(MACE_Flags[RECORD_ASSIGNMENTS]); f->name = "record_assignments"; f->val = 0; f = &(MACE_Flags[CLAUSE_SPLIT]); f->name = "clause_split"; f->val = 0; f = &(MACE_Flags[ISO_X]); f->name = "iso_x"; f->val = 0; /* MACE_Parms are integer-valued options */ p = &(MACE_Parms[MACE_MAX_MEM]); p->name = "max_mem"; p->min = 0; p->max = INT_MAX; p->val = 96000; p = &(MACE_Parms[MAX_TP_SECONDS]); p->name = "max_seconds"; p->min = 0; p->max = INT_MAX; p->val = INT_MAX; p = &(MACE_Parms[MAX_MODELS]); p->name = "max_models"; p->min = 1; p->max = INT_MAX; p->val = 1; p = &(MACE_Parms[ISO_CONSTANTS]); p->name = "iso_constants"; p->min = 0; p->max = INT_MAX; p->val = 5; p = &(MACE_Parms[PART_VARS]); p->name = "part_vars"; p->min = 0; p->max = INT_MAX; p->val = 1; } /* MACE_init_options */ /************* * * MACE_print_options(fp) * *************/ void MACE_print_options(FILE *fp) { int i, j; fprintf(fp, "\n--------------- options ---------------\n"); j = 0; for (i = 0; i < MACE_MAX_FLAGS; i++) /* print set flags */ if (MACE_Flags[i].name[0] != '\0') { fprintf(fp, "%s", MACE_Flags[i].val ? "set(" : "clear("); fflush(stdout); fprintf(fp, "%s). ", MACE_Flags[i].name); fflush(stdout); j++; if (j % 3 == 0) fprintf(fp, "\n"); fflush(stdout); } fprintf(fp, "\n\n"); j = 0; for (i = 0; i < MACE_MAX_PARMS; i++) /* print parms */ if (MACE_Parms[i].name[0] != '\0') { fprintf(fp, "assign("); fprintf(fp, "%s, %d). ", MACE_Parms[i].name, MACE_Parms[i].val); j++; if (j % 3 == 0) fprintf(fp, "\n"); } fprintf(fp, "\n"); } /* MACE_print_options */ /************* * * MACE_p_options() * *************/ void MACE_p_options(void) { MACE_print_options(stdout); } /* MACE_p_options */ /************* * * auto_MACE_change_flag() * *************/ void auto_MACE_change_flag(FILE *fp, int index, int val) { if (MACE_Flags[index].val != val) { fprintf(fp, " dependent: %s(%s).\n", val ? "set" : "clear", MACE_Flags[index].name); MACE_Flags[index].val = val; MACE_dependent_flags(fp, index); } } /* auto_MACE_change_flag */ /************* * * void MACE_dependent_flags(FILE *fp, int index) * * Flag[index] has just been changed. Change any flags or parms that * depend on it. Write actions to *fp. * * Mutually recursive with auto_MACE_change_flag and auto_MACE_change_parm. * *************/ void MACE_dependent_flags(FILE *fp, int index) { /* This part handles flags that have just been set. */ if (MACE_Flags[index].val) { switch (index) { } } /* This part handles flags that have just been cleared. */ if (MACE_Flags[index].val) { switch (index) { } } } /* MACE_dependent_flags */ /************* * * auto_MACE_change_parm() * *************/ void auto_MACE_change_parm(FILE *fp, int index, int val) { if (MACE_Parms[index].val != val) { fprintf(fp, " dependent: assign(%s, %d).\n", MACE_Parms[index].name, val); MACE_Parms[index].val = val; MACE_dependent_parms(fp, index); } } /* auto_MACE_change_parm */ /************* * * void MACE_dependent_parms(FILE *fp, int index) * * MACE_Parms[index] has just been changed. Change any flags or parms that * depend on it. Write actions to *fp. * * Mutually recursive with auto_MACE_change_flag and auto_MACE_change_parm. * *************/ void MACE_dependent_parms(FILE *fp, int index) { switch (index) { } } /* MACE_dependent_parms */ /************* * * int MACE_change_flag(fp, flag_name, set) * * If success, return index of flag, if fail, return -1. * Warning and error messages go to file fp. * *************/ int MACE_change_flag(FILE *fp, char *flag_name, int set) { int index, found; found = 0; index = 0; while (index < MACE_MAX_FLAGS && !found) if (strcmp(flag_name, MACE_Flags[index].name) == 0) found = 1; else index++; if (!found) { fprintf(fp, "ERROR: flag `%s' not found.\n", flag_name); return(-1); } else if (MACE_Flags[index].val == set) { fprintf(fp, "WARNING: "); if (set) fprintf(fp, " flag `%s' already set.\n", flag_name); else fprintf(fp, " flag `%s' already clear.\n", flag_name); return(index); } else { MACE_Flags[index].val = set; return(index); } } /* MACE_change_flag */ /************* * * int MACE_change_parm(fp, parm_name, val) * * If success, return index of parm, if fail, return -1. * Warning and error messages go to file fp. * *************/ int MACE_change_parm(FILE *fp, char *parm_name, int val) { int index, found; found = 0; index = 0; while (index < MACE_MAX_PARMS && !found) if (strcmp(parm_name, MACE_Parms[index].name) == 0) found = 1; else index++; if (!found) { fprintf(fp, "ERROR: parameter `%s' not found.\n", parm_name); return(-1); } else if (val < MACE_Parms[index].min || val > MACE_Parms[index].max) { fprintf(fp, "ERROR: assign(%s, %d),", parm_name, val); fprintf(fp, " integer must be in range [%d,%d].\n", MACE_Parms[index].min, MACE_Parms[index].max); return(-1); } else if (val == MACE_Parms[index].val) { fprintf(fp, "WARNING: assign(%s, %d),", parm_name, val); fprintf(fp, " already has that value.\n"); return(index); } else { MACE_Parms[index].val = val; return(index); } } /* MACE_change_parm */ /************* * * MACE_check_options(fp) -- check for inconsistent or odd settings * * If a bad combination of settings is found, either a warning * message is printed, or an ABEND occurs. * *************/ void MACE_check_options(FILE *fp) { fprintf(fp, "Called MACE_check_options.\n"); } /* MACE_check_options */ otter-3.3f/mace2/anldp.c0100644000076400007640000001232207714246130014436 0ustar mccunemccune/* ANLDP 2.0 * * Copyright (C) 2001 by Argonne National Laboratory * * William McCune * Mathematics and Computer Science Division * Argonne National Laboratory * Argonne, IL 60439 * U.S.A. * * E-mail: mccune@mcs.anl.gov * Web: http://www.mcs.anl.gov/~mccune * http://www.mcs.anl.gov/AR/mace */ #define VERSION "2.2" #define VDATE "August 2003" #include #include #include #include /* for getopt */ #ifdef TP_NAMES /* for calls to getpwuid() and gethostname() */ # include # include # include #endif /******** Types of exit ********/ #define MACE_ABEND_EXIT 11 #define UNSATISFIABLE_EXIT 12 #define MACE_MAX_SECONDS_EXIT 13 #define MACE_MAX_MEM_EXIT 14 #define MAX_MODELS_EXIT 15 #define ALL_MODELS_EXIT 16 #define MACE_SIGINT_EXIT 17 #define MACE_SEGV_EXIT 18 #define MACE_INPUT_ERROR_EXIT 19 /************* END OF ALL GLOBAL CONSTANT DEFINITIONS ****************/ #include "Opts.h" #include "Stats.h" #include "Avail.h" #include "Clock.h" #include "Miscellany.h" #include "Dp.h" int First_order; /* used by dp.c */ int Domain_size = 0; /* used by stats.c */ int Init_wall_seconds; /* used by stats.c */ int Models = 0; /* used with dp.c, miscellany.c */ /* I didn't want ANLDP to depend on any of the otter code in the * parent directory, so I copied the few routines that it needs * and put them here. */ /************* * * void MACE_print_banner(argc, argv) * *************/ static void MACE_print_banner(int argc, char **argv) { int i; printf("----- ANLDP %s, %s -----\n", VERSION, VDATE); printf("The process was started by %s on %s,\n%s", username(), hostname(), get_time()); printf("The command was \""); for(i = 0; i < argc; i++) printf("%s%s", argv[i], (i < argc-1 ? " " : "")); printf("\".\n"); } /* MACE_print_banner */ /************* * * usage_message() * *************/ static void usage_message(void) { printf("\nANLDP %s -- Search for finite models.\n\n", VERSION); printf("\nInput clauses are taken from standard input.\n"); printf("\ncommand-line options:\n"); printf(" -p | Print all models as they are found.\n"); printf(" -m n | Stop when the n-th model is found.\n"); printf(" -t n | Stop after n seconds.\n"); printf(" -k n | Tp_allocate at most n K bytes.\n"); printf(" -s | Perform unit subsumption. (Always done on input.)\n"); printf(" -h | Print this message.\n"); printf("\n"); } /* usage_message */ /************* * * process_command_line_args() * *************/ static int process_command_line_args(int argc, char **argv) { extern char *optarg; int c, n; int error = 0; while ((c = getopt(argc, argv, "spPIhcm:t:k:n:d:x:")) != EOF) { switch (c) { case 's': MACE_change_flag(stderr, "subsume", 1); break; case 'p': MACE_change_flag(stderr, "print_models", 1); break; case 'm': n = atoi(optarg); if (MACE_change_parm(stderr, "max_models", n) == -1) error++; break; case 't': n = atoi(optarg); if (MACE_change_parm(stderr, "max_seconds", n) == -1) error++; break; case 'k': n = atoi(optarg); if (MACE_change_parm(stderr, "max_mem", n) == -1) error++; break; case 'h': case '?': default: error = 1; break; } } return(error == 0); } /* process_command_line_args */ /************* * * MACE_sig_handler() * *************/ #ifdef TP_SIGNAL #include static void MACE_sig_handler(int condition) { if (condition == SIGSEGV) { char message[] = "\n" "+----------------------------------------------------------+\n" "| SEGMENTATION FAULT!! This is probably caused by a bug |\n" "| in MACE. Please send copy of the input file to |\n" "| otter@mcs.anl.gov, let us know what version of MACE you |\n" "| are using, and send any other info that might be useful. |\n" "+----------------------------------------------------------+\n\n"; fprintf(stderr, "%s\007", message); exit_with_message(MACE_SEGV_EXIT, 1); } else if (condition == SIGINT) { exit_with_message(MACE_SIGINT_EXIT, 1); } else { char s[100]; sprintf(s, "MACE_sig_handler, cannot handle signal %d.\n", condition); MACE_abend(s); } } /* MACE_sig_handler */ #endif /* TP_SIGNAL */ /************* * * main * *************/ int main(int argc, char **argv) { int rc; #ifdef TP_SIGNAL signal(SIGINT, MACE_sig_handler); signal(SIGSEGV, MACE_sig_handler); #endif MACE_print_banner(argc, argv); init_dp(); /* This is MACE's initialization. */ Init_wall_seconds = wall_seconds(); rc = process_command_line_args(argc, argv); if (!rc) { usage_message(); exit(0); } init(); /* This is Otter's initialization. */ /*************************************************************************/ rc = read_all_clauses(stdin); rc = more_setup(); MACE_CLOCK_START(DECIDE_TIME); rc = dp_prover(); MACE_CLOCK_STOP(DECIDE_TIME); exit_with_message(rc, 1); exit(99); /* This is to shut up the compiler. */ } /* main */ otter-3.3f/mace2/Clock.h0100644000076400007640000000503707316150130014375 0ustar mccunemccune#ifndef TP_CLOCKS_H #define TP_CLOCKS_H #include #ifdef TP_RUSAGE /* getrusage() */ # include /* needed for SunOS */ # include #endif /************* * * MACE_Clocks. To install a new clock, append a new name and * index to this list, then insert the code to output it in the * routine `MACE_print_times'. Example of use: MACE_CLOCK_START(INPUT_TIME), * MACE_CLOCK_STOP(INPUT_TIME), micro_sec = MACE_clock_val(INPUT_TIME);. * *************/ #define MACE_MAX_CLOCKS 40 #define GENERATE_TIME 0 #define DECIDE_TIME 1 struct MACE_clock { /* for timing, see cos.h, macros.h, and clocks.c */ unsigned long accum_msec; /* accumulated time */ unsigned long curr_msec; /* time since clock has been turned on */ int level; /* STARTs - STOPs */ }; extern struct MACE_clock MACE_Clocks[MACE_MAX_CLOCKS]; /************* * * MACE_CPU_TIME(msec) - It has been sec milliseconds (UNIX user time) * since the start of this process. * *************/ #ifdef TP_RUSAGE #define MACE_CPU_TIME(msec) \ { \ struct rusage r; \ getrusage(RUSAGE_SELF, &r); \ msec = r.ru_utime.tv_sec * 1000 + r.ru_utime.tv_usec / 1000; \ } /* MACE_CPU_TIME */ #else #define MACE_CPU_TIME(msec) {msec = 0;} #endif /************* * * MACE_CLOCK_START(clock_num) - Start or continue timing. * *************/ #ifdef NO_CLOCK #define MACE_CLOCK_START(c) /* empty string */ #else #define MACE_CLOCK_START(c) \ { \ struct MACE_clock *cp; \ cp = &MACE_Clocks[c]; \ cp->level++; \ if (cp->level == 1) \ MACE_CPU_TIME(cp->curr_msec) \ } /* MACE_CLOCK_START */ #endif /************* * * MACE_CLOCK_STOP(clock_num) - Stop timing and add to accumulated total. * * If the clock not running, a warning message is printed. * *************/ #ifdef NO_CLOCK #define MACE_CLOCK_STOP(c) /* empty string */ #else #define MACE_CLOCK_STOP(c) \ { \ long msec; \ struct MACE_clock *cp; \ cp = &MACE_Clocks[c]; \ cp->level--; \ if (cp->level < 0) { \ fprintf(stderr, "\007WARNING, MACE_CLOCK_STOP: clock %d not running.\n", c); \ printf("WARNING, MACE_CLOCK_STOP: clock %d not running.\n", c); \ cp->level = 0; \ } \ else if (cp->level == 0) { \ MACE_CPU_TIME(msec) \ cp->accum_msec += msec - cp->curr_msec; \ } \ } /* MACE_CLOCK_STOP */ #endif /* function prototypes from clocks.c */ void init_clocks(void); long MACE_clock_val(int c); void MACE_clock_reset(int c); #endif /* ! TP_CLOCKS_H */ otter-3.3f/mace2/flatten.c0100644000076400007640000001523407714207010014774 0ustar mccunemccune#include "Mace2.h" /************* * * kludgey_e_subsume(c, d) * * Does c subsume d (mod equality flipping)? This works by * inserting flips into (a copy of) d then doing an ordinary * subsumption check. * *************/ int kludgey_e_subsume(struct clause *c, struct clause *d) { struct clause *d1; struct literal *l1, *l2; struct term *t; int rc; d1 = cl_copy(d); for (l1 = d1->first_lit; l1; l1 = l1->next_lit) { if (is_eq(l1->atom->sym_num)) { l2 = get_literal(); l2->next_lit = d1->first_lit; d1->first_lit = l2; l2->sign = l1->sign; l2->atom = copy_term(l1->atom); t = l2->atom->farg->argval; l2->atom->farg->argval = l2->atom->farg->narg->argval; l2->atom->farg->narg->argval = t; } } rc = subsume(c, d1); cl_del_non(d1); return(rc); } /* kludgey_e_subsume */ /************* * * check_for_bad_things() * *************/ void check_for_bad_things(struct clause *c) { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) { if (answer_lit(lit)) abend("answer literals not allowed in MACE input"); if (lit->atom->varnum == EVALUABLE) abend("evaluable literals not allowed in MACE input"); } } /* check_for_bad_things */ /************* * * int_term(t) * * Is t a constant with a symbol representing a positive integer? * *************/ int int_term(struct term *t) { int i; return(t->type == NAME && str_int(sn_to_str(t->sym_num),&i) && i>=0); } /* int_term */ /************* * * domain_element(t) * * Is t a domain element? * *************/ int domain_element(struct term *t) { return(int_term(t)); } /* int_term */ /************* * * build_binary_term * *************/ static struct term *build_binary_term(int sn, struct term *t1, struct term *t2) { struct term *t; struct rel *r1, *r2; t = get_term(); t->type = COMPLEX; t->sym_num = sn; r1 = get_rel(); r1->argval = t1; r2 = get_rel(); r2->argval = t2; t->farg = r1; r1->narg = r2; return(t); } /* build_binary_term */ /************* * * replace_term() * *************/ static struct term *replace_term(struct term *t, struct term *ct, struct term *vt) { if (term_ident(t, ct)) return(copy_term(vt)); else { struct rel *r; for (r = t->farg; r; r= r->narg) r->argval = replace_term(r->argval, ct, vt); return(t); } } /* replace_term */ /************* * * process_negative_equalities() * * Simplify literals x!=t, where x does not occur in t, by, * in effect, rewolving with x=x. * *************/ void process_negative_equalities(struct clause *c) { struct literal *curr, *prev, *l; struct term *t1, *t2, *v, *t; t = NULL; /* to quiet -Wall */ curr = c->first_lit; prev = NULL; while (curr) { if (is_eq(curr->atom->sym_num) && !curr->sign) { t1 = curr->atom->farg->argval; t2 = curr->atom->farg->narg->argval; v = NULL; if (t1->type == VARIABLE && !occurs_in(t1, t2)) { v = t1; t = t2; } else if (t2->type == VARIABLE && !occurs_in(t2, t1)) { v = t2; t = t1; } if (v) { if (prev) prev->next_lit = curr->next_lit; else c->first_lit = curr->next_lit; for (l = c->first_lit; l; l = l->next_lit) l->atom = replace_term(l->atom, v, t); } else prev = curr; } else prev = curr; curr = curr->next_lit; } } /* process_negative_equalities */ /****************************************************************************/ /****************************************************************************/ /************* * * yankable_term() * *************/ static struct term *yankable_term(struct term *t, int check) { if (check && t->type != VARIABLE && !domain_element(t)) return t; else { struct rel *r; struct term *t1; for (r = t->farg; r; r = r->narg) { t1 = yankable_term(r->argval, 1); if (t1 != NULL) return t1; } return NULL; } } /* yankable_term */ /************* * * yankable() * * Given a clause, return the first yankable term. * * A term is yankable if it is not a variable, domain element, * or the left side of an equality. * *************/ static struct term *yankable(struct clause *c) { struct literal *lit; struct term *t = NULL; for (lit = c->first_lit; lit; lit = lit->next_lit) { struct term *a = lit->atom; if (!is_eq(a->sym_num)) t = yankable_term(a, 0); else { t = yankable_term(a->farg->argval, 0); if (t == NULL) t = yankable_term(a->farg->narg->argval, 1); } if (t != NULL) return t; } return NULL; } /* yankable */ /************* * * eq_sn() -- return a sym_num for equality * *************/ static int eq_sn() { if (Flags[TPTP_EQ].val) return str_to_sn("equal", 2); else return str_to_sn("=", 2); } /* eq_sn */ /************* * * flatten_clause() * * Apply this kind of transformation * * p(a) ========> a != x | p(x) * * to all terms except domain_elements and left sides of equalities (+ or -) * *************/ void flatten_clause(struct clause *d) { struct term *t, *t1, *t2; struct literal *lit; int vnum = MAX_VARS; t = yankable(d); while (t) { lit = get_literal(); lit->next_lit = d->first_lit; d->first_lit = lit; lit->sign = 0; t1 = copy_term(t); t2 = get_term(); t2->type = VARIABLE; t2->varnum = ++vnum; lit->atom = build_binary_term(eq_sn(), t1, t2); for (lit = lit->next_lit; lit; lit = lit->next_lit) lit->atom = replace_term(lit->atom, t, t2); t = yankable(d); } } /* flatten_clause */ /************* * * flatten_clauses() * *************/ struct list *flatten_clauses(struct list *l) { struct clause *c; struct list *nl = get_list(); for (c = l->first_cl; c; c = c->next_cl) { struct clause *d = cl_copy(c); d->id = c->id; /* This is questionable. */ check_for_bad_things(d); flatten_clause(d); if (renumber_vars(d) == 0) MACE_abend("dp_trans, too many variables"); append_cl(nl, d); } return nl; } /* flatten_clauses */ /************* * * check_transformed_clause() * * This checks that the transformed clause is equality-equivalent * to the original. * *************/ void check_transformed_clause(struct clause *c, struct clause *orig) { struct clause *d = cl_copy(c); process_negative_equalities(d); if (!kludgey_e_subsume(d, orig) || !kludgey_e_subsume(orig, d)) { printf("%% WARNING: possible error in check_transformed_clause:\n"); printf("%% original: "); p_clause(orig); printf("%% transformed: "); p_clause(d); } } /* check_transformed_clause */ otter-3.3f/mace2/Dp.h0100644000076400007640000000554407714006341013716 0ustar mccunemccune#ifndef TP_DP_H #define TP_DP_H #define UNSATISFIABLE 0 #define SATISFIABLE 1 #define NOT_DETERMINED 2 #define ATOM_FALSE 0 #define ATOM_TRUE 1 #define ATOM_NOT_ASSIGNED 2 /* Memory conservation is important, so the following integer types are * defined to be just as big as required. All can safely be unsigned. * * ATOM_INT: To store integers representing atoms. (The greatest number * of atoms I have seen is 37026 in qg7.33). * LIT_INT: To store the number of pos or neg literals in a clause. * For large problems, this is usually limited by the domain size. */ /* August 2003. When I installed the "parting" code, this allowed the number of atoms to go way up, so I changed the data type to int. */ #if 0 /* This is faster and uses less memory. */ # define ATOM_INT unsigned short # define ATOM_INT_MAX USHRT_MAX #else # define ATOM_INT int # define ATOM_INT_MAX INT_MAX #endif #define LIT_INT unsigned char #define LIT_INT_MAX UCHAR_MAX struct MACE_clause { LIT_INT num_pos; /* number of positive literals */ LIT_INT num_neg; /* number of negative literals */ LIT_INT active_pos; /* number of active (unassigned) positive literals */ LIT_INT active_neg; /* number of active (unassigned) negative literals */ /* The following two are dynamically allocated arrays of ATOM_INT. */ ATOM_INT *pos; /* array of positive literals */ ATOM_INT *neg; /* array of negative literals (stored positively) */ struct MACE_clause *next; ATOM_INT subsumer; /* 0 if not subsumed; else index of subsuming atom */ }; typedef struct MACE_clause *Clause_ptr; struct atom { int value; /* ATOM_TRUE, ATOM_FALSE, ATOM_NOT_ASSIGNED */ int enqueued_value; /* ATOM_TRUE, ATOM_FALSE, ATOM_NOT_ASSIGNED */ int num_pos_occ; /* number of positive occurrences */ int num_neg_occ; /* number of negative occurrences */ /* The following two are dynamically allocated arrays of ptrs to clauses. */ Clause_ptr *pos_occ; /* array of pos occurrences (pointers to clauses) */ Clause_ptr *neg_occ; /* array of neg occurrences (pointers to clauses) */ }; typedef struct atom *Atom_ptr; struct gen_ptr { /* for constructing lists of pointers or of integers */ struct gen_ptr *next; union { void *v; int i; } u; }; typedef struct gen_ptr *Gen_ptr_ptr; /* function prototypes from dp.c */ void init_dp(); void exit_if_over_time_limit(); int subsumed(Clause_ptr c); void MACE_p_clause(Clause_ptr c); void MACE_pp_clause(Clause_ptr c); void p_atom(int i); void insert_dp_clause(int c[], int n); int read_all_clauses(FILE *fp); int more_setup(); int atom_value(int atom); void save_if_appropriate(void); void restore_assignments(void); int dp_prover(); void reinit_dp(void); #endif /* ! TP_DP_H */ otter-3.3f/mace2/Flatten.h0100644000076400007640000000072307713534472014754 0ustar mccunemccune#ifndef TP_FLATTEN_H #define TP_FLATTEN_H int kludgey_e_subsume(struct clause *c, struct clause *d); void check_for_bad_things(struct clause *c); int int_term(struct term *t); int domain_element(struct term *t); void process_negative_equalities(struct clause *c); void flatten_clause(struct clause *d); struct list *flatten_clauses(struct list *l); void check_transformed_clause(struct clause *c, struct clause *orig); #endif /* ! TP_FLATTEN_H */ otter-3.3f/mace2/part.c0100644000076400007640000002117107714207010014302 0ustar mccunemccune#include "Mace2.h" #define MAX_LITS 100 /************* * * num_pos_lits() * *************/ static int num_pos_lits(struct clause *c) { struct literal *lit; int n = 0; for (lit = c->first_lit; lit; lit = lit->next_lit) if (lit->sign) n++; return n; } /* num_pos_lits */ /************* * * copy_literal() * *************/ static struct literal *copy_literal(struct literal *l1) { struct literal *l2 = get_literal(); l2->sign = l1->sign; l2->atom = copy_term(l1->atom); return l2; } /* copy_literal */ /************* * * append_literal() * *************/ static void append_literal(struct clause *c, struct literal *lit) { if (c->first_lit == NULL) c->first_lit = lit; else { struct literal *l2 = c->first_lit; while (l2->next_lit != NULL) l2 = l2->next_lit; l2->next_lit = lit; } } /* append_literal */ /************* * * append_subterm() * *************/ static void append_subterm(struct term *t, struct term *s) { struct rel *r = get_rel(); r->argval = s; if (t->farg == NULL) t->farg = r; else { struct rel *r2 = t->farg; while (r2->narg != NULL) r2 = r2->narg; r2->narg = r; } } /* append_subterm */ /************* * * p_vars() * *************/ static void p_vars(int *vars, int n) { int i; for (i = 0; i < n; i++) if (vars[i]) printf(" v%d", i); printf("\n"); } /* p_vars */ /************* * * intersect_vars() * *************/ static void intersect_vars(int *v1, int *v2, int n, int *c) { int i; for (i = 0; i < n; i++) c[i] = v1[i] && v2[i]; } /* intersect_vars */ /************* * * union_vars() * *************/ static void union_vars(int *v1, int *v2, int n, int *c) { int i; for (i = 0; i < n; i++) c[i] = v1[i] || v2[i]; } /* union_vars */ /************* * * cardinality() * *************/ static int cardinality(int *a, int n) { int card = 0; int i; for (i = 0; i < n; i++) if (a[i]) card++; return card; } /* cardinality */ /************* * * diff_cardinality() * *************/ static int diff_cardinality(int *a, int *b, int n) { int diff = 0; int i; for (i = 0; i < n; i++) if (a[i] && !b[i]) diff++; return diff; } /* diff_cardinality */ /************* * * which_vars_term() * *************/ static void which_vars_term(int *vars, struct term *t) { if (t->type == VARIABLE) vars[t->varnum] = 1; else { struct rel *r; for (r = t->farg; r; r = r->narg) { which_vars_term(vars, r->argval); } } } /* which_vars_term */ /************* * * which_vars() * *************/ static void which_vars(int *vars, struct clause *c) { struct literal *lit; for (lit = c->first_lit; lit; lit = lit->next_lit) which_vars_term(vars, lit->atom); } /* which_vars */ /************* * * which_vars_part() * * which_vars_part(vars_1, c, p, n, 0); * *************/ static void which_vars_part(int *vars, struct clause *c, int *part, int to_check) { struct literal *lit; int i; for (lit = c->first_lit, i = 0; lit; lit = lit->next_lit, i++) { if (part[i] == to_check) which_vars_term(vars, lit->atom); } } /* which_vars_part */ /************* * * gen_connector_symnum() * *************/ static int gen_connector_symnum(int arity) { static int Count; char s1[MAX_NAME], s2[MAX_NAME]; int symnum; int_str(++Count, s1); cat_str("$Connect", s1, s2); /* str_to_sn knows it's ok to use a symbol starting with $Connect */ symnum = str_to_sn(s2, arity); return symnum; } /* gen_connector_symnum */ /************* * * connector() * *************/ static struct literal *connector(int *vars, int n) { struct literal *lit; struct term *t = get_term(); int i; int arity = 0; for (i = 0; i < n; i++) { if (vars[i]) { struct term *var = get_term(); var->type = VARIABLE; var->varnum = i; append_subterm(t, var); arity++; } } t->sym_num = gen_connector_symnum(arity); t->type = (arity == 0 ? NAME : COMPLEX); lit = get_literal(); lit->sign = 1; lit->atom = t; return lit; } /* connector */ /************* * * score_the_part() * *************/ static void score_the_part(int *p, int n, struct clause *c, int *bp, int *bs) { int vars_1[MAX_VARS], vars_2[MAX_VARS]; int vars_union[MAX_VARS], vars_intersection[MAX_VARS]; int nvars = biggest_var_clause(c) + 1; int i, card_intersection; for (i = 0; i < MAX_VARS; i++) vars_1[i] = vars_2[i] = 0; which_vars_part(vars_1, c, p, 0); which_vars_part(vars_2, c, p, 1); union_vars(vars_1, vars_2, nvars, vars_union); intersect_vars(vars_1, vars_2, nvars, vars_intersection); card_intersection = cardinality(vars_intersection, nvars); if (card_intersection <= MAX_ARITY) { int c1 = cardinality(vars_1, nvars); int c2 = cardinality(vars_2, nvars); int diff1 = diff_cardinality(vars_union, vars_1, nvars); int diff2 = diff_cardinality(vars_union, vars_2, nvars); if (diff1 > 0 && diff2 > 0) { /* Each has a variable not in the other, so we calculate a score. Primary sort: fewest variables (in the clause with more variables). Secondary sort: smallest intersection. */ int score = (MAX(c1,c2) * 100) + card_intersection; if (score < *bs) { *bs = score; for (i = 0; i < n; i++) bp[i] = p[i]; } } } } /* score_the_part */ /************* * * parts() * * This goes through the 2^n ways to (binary) partition the clause. * It scores each partition, remembering the best score and partition. * *************/ static void parts(int i, int *p, int n, struct clause *c, int *bp, int *bs) { if (i == n) score_the_part(p, n, c, bp, bs); else { p[i] = 0; parts(i+1, p, n, c, bp, bs); p[i] = 1; parts(i+1, p, n, c, bp, bs); } } /* parts */ /************* * * try_to_part() * *************/ static void try_to_part(struct clause *c, struct clause **p1, struct clause **p2, int part_vars) { int nvars = biggest_var_clause(c) + 1; /* assume variables normalized */ *p1 = *p2 = NULL; if (nvars >= part_vars) { int p[MAX_LITS]; int bp[MAX_LITS]; /* best partition */ int bs = INT_MAX; /* best score */ int n = num_literals(c); int i; for (i = 0; i < n; i++) bp[i] = p[i] = 0; parts(0, p, n, c, bp, &bs); if (bs != INT_MAX) { /* We shall part the clause! */ struct clause *n1 = get_clause(); struct clause *n2 = get_clause(); n1->id = c->id; /* This is questionalble. */ n2->id = c->id; /* This is questionalble. */ for (i = 0; i < n; i++) { struct literal *lit = copy_literal(ith_literal(c, i+1)); if (bp[i] == 0) append_literal(n1, lit); else append_literal(n2, lit); } { struct literal *lit1; struct literal *lit2; int vars_1[MAX_VARS], vars_2[MAX_VARS], c_vars[MAX_VARS]; for (i = 0; i < MAX_VARS; i++) vars_1[i] = vars_2[i] = c_vars[i] = 0; which_vars(vars_1, n1); which_vars(vars_2, n2); intersect_vars(vars_1, vars_2, nvars, c_vars); lit1 = connector(c_vars, nvars); lit2 = copy_literal(lit1); /* It's very important to keep the number of non-Horn clauses small, because we have to scan them when selecting variables. In general it seems important to minimize the number positive literals in each clause. */ if (num_pos_lits(n1) < num_pos_lits(n2)) { lit1->sign = 1; lit2->sign = 0; } else { lit1->sign = 0; lit2->sign = 1; } append_literal(n1, lit1); append_literal(n2, lit2); #if 0 printf("\nParting clause: "); p_clause(c); printf("Part1: "); p_clause(n1); printf("Part2: "); p_clause(n2); #endif renumber_vars(n1); renumber_vars(n2); } *p1 = n1; *p2 = n2; } } } /* try_to_part */ /************* * * var_opt() * *************/ static struct list *var_opt(struct clause *c, int part_vars) { struct clause *p1, *p2; try_to_part(c, &p1, &p2, part_vars); if (p1 == NULL) { struct list *l = get_list(); append_cl(l, c); return l; } else { struct list *l1 = var_opt(p1, part_vars); struct list *l2 = var_opt(p2, part_vars); append_lists(l1, l2); return l1; } } /* var_opt */ /************* * * variable_optimize() * *************/ struct list *variable_optimize(struct list *l, int part_vars) { struct list *nl = get_list(); struct clause *c; for (c = l->first_cl; c; c = c->next_cl) { struct list *ol; struct clause *d = cl_copy(c); d->id = c->id; ol = var_opt(d, part_vars); append_lists(nl, ol); } return nl; } /* variable_optimize */ otter-3.3f/mace2/Changelog0100644000076400007640000001337210070421365015006 0ustar mccunemccuneAugust 16, 1995. mace 1.2.0 released April 1996. New print option -P, for printing in "portable format", which is for reading into another program (eqp semantic para). Result is mace-1.2.0a Sept 26, 1996. 1. New option -c, for distinct constants (up to n). This should work correctly with domain elemnts in clauses and special unit assignments, but NOT with -z. 2. time limit is checked during generation of prop. clauses (after processing of each FO clause). 3. For printing models, "-" changed to "T" in relations. Result is mace-1.3 July 2, 1997 (in preparation for CASC-14). 1. bug: crash if arity too great. fixed. 2. It used to abend if propositional unsatisfiability was detected in add_clause (e.g., conflicting units). Now, call exit(UNSATISFIABLE_EXIT) in that case. Result is mace-1.3.1 Nov 4, 1997. Changed MAX_CLAUSES from 100 to 500 (so we could do Dale Myers' zebra problem). Dec 1, 1997. Changed tp_alloc_size from 300,000 to 1,000,000 (for M. Spinks prob). result it mace-1.3.2. Dec 7, 1998. 1. Bug from Branden Fitelson: When printing relations, the nondetermined atoms (atom_value() = 2) should be "F", because the propositional engine selects positive clauses, and no more positive clauses (the termination condition), means that the unassigned atoms should be "F". The error was introduced in mace-1.3 above, item 3. 2. Increase default max-mem from 16MB to 48 MB. result is mace-1.3.3. June, 1999. New command-line option -I to print models in Ivy format. February, 2000. Release mace-1.3.4 May 16, 2000. Bug. I wasn't checking for symbol table overflow. Fixed. Also, I increased the symbol table size from 50 to 100, so it could handle the set problems in TPTP. (Well, it still can't handle the set problems in TPTP, because there is a clause with 13 variables. (Max is 12, and that limit is wired in.) May 16, 2000. Lots of cleaning up, and some reorganization of the code. ------ 2001------ 2001------ 2001------ 2001------ 2001------ 2001 May, first half, 2001. MAJOR overhaul of MACE, to make it self-contained. Now, Otter code (to parse input) is loaded along with MACE. This involved lots of soruce code reorganization. And there were more than a few changes to the functionality. A 9-page "MACE 2.0 User Manual and Guide" was written. May 11, 2001. Release MACE 2.0-beta as part of Otter-3.2-beta. May 14, 2001. Added -N option: ability to iterate through domain sizes. This eliminates the need for a separate maceloop program. This involved substantial reorganization of the MACE code. Updated manual. May 29, 2001. Bug (reported by Johan Bos) printing with -P. Comma after last printed symbol if equality relation is last. Fixed print_models_portable(). May 29, 2001. Changed Ivy (-I) printing to print equality relations other than "=", because "=" is the only equality built-in to Ivy. June 8, 2001. Added constraints (when -c is not used) to reduce number of isomorphic models w.r.t. constants. I believe it is complete, and it seems to work as well as -c for some examples. See iso_constants() in generate.c. mace-2-beta-4. June 11, 2001. Bug if more than 2^16 - 1 (65535) atoms. Fixed the code that does the check. It now abends. mace-2-beta-5. This is the deadline for CASC-2001 installation, so it got this version. June 12, 2001. The new iso constraints (June 8) are exponential in the number of constants. Added a new command-line switch: -z n says to apply the constraints to the first n constants. mace-2-beta-6. June 14, 2001. Bug in iso constraints. Fixed. Also, separated "theory elements" (domain elements in clause list) from "constraint elements" (domain elements in mace_constraints list). An element can be both theory and constraint (or neither). Iso constraints ignores constraint elements when asserting clauses. Also, changed -c so that it ignores constraint elements. mace-2-beta-8. July 2, 2001. Added option -C to split on clauses. Added option -r to print order of assignments for each model. mace-2-beta-11. August 13, 2001. Release Otter 3.2 and MACE 2.0 for Unix. June 2003. Reorganize directories in preparation for the Otter 3.3/Mace 2.2 release. August 4-6, 2003. At the model-building workshop at CADE-19, I heard a talk on mace2-style model searching by Koen Claessen and Niklas Sorensson. There was good evidence that dividing flattened clauses to reduce the number of variables pays off well. I've known about this method for several years, but I never got around to trying it myself, mostly because I've been focusing on mace4 (the equational method). Anyway, I tried it, and it works well enough to include as default in mace2. The new code is in part.c, and a command-line switch -vn (default n=1) says to apply the method to clauses with n or more variables. This changes the searches in most of the test problems, so the "official" output files were rebuilt. This new feature can be disabled with, for example, -v1000. August 12, 2003. Bug introduced in Aug 4--6 mods: answer literals not removed. Fixed. Second minor bug: if set(process_input), clasues don't get IDs. Fixed. August 27, 2003. Increased MAX_SYMBOLS in Generate.c from 100 to 500. ------------------------------------ August 27, 2003. Freeze for Otter 3.3 / Mace 2.2 release. February 9, 2004. Mace2 crashes if the input contains a hints2 list. Fix: minor change to read_all_mace_input. May 26, 2004. Send to Sutcliffe for CASC testing. mace 2.2E June 29, 2004. Sutcliffe finds soundness bug!! The mace2-for-casc script gives parameter -N100, but there's a limit of 50 in the code, and out-of-range was not checked. Fixed. (Limit was also changed to 100.) Mace 2.2E2 sent to Sutcliffe. otter-3.3f/mace2/.#TODO0120777000076400007640000000000010103770047022602 2mccune@theorem.mcs.anl.gov.14972:1059674717ustar mccunemccuneotter-3.3f/mace2/Part.h0100644000076400007640000000017707714011356014260 0ustar mccunemccune#ifndef TP_PART_H #define TP_PART_H struct list *variable_optimize(struct list *l, int part_vars); #endif /* ! TP_PART_H */ otter-3.3f/mace2/README.220100644000076400007640000000061507714266175014313 0ustar mccunemccuneMace 2.2 NEW FEATURE An optimization has been added. See the "August 4-6, 2003" entry in the Changelog file. COMPILING The code is linked with the the library ../source/libotter.a, which is created when Otter is compiled, so you have to compile Otter first. Compiling Mace2 from the parent directory (make all) puts the binaries in ../bin/. If you 'make mace2' here, the binary stays here. otter-3.3f/mace2/stats.c0100644000076400007640000000726207714207010014477 0ustar mccunemccune#include "Mace2.h" long MACE_Stats[MACE_MAX_STATS]; struct MACE_clock MACE_Clocks[MACE_MAX_CLOCKS]; int Internal_flags[MAX_INTERNAL_FLAGS]; extern int Domain_size; /* owned by mace.c */ extern int Init_wall_seconds; /* owned by mace.c */ /************* * * init_stats() * *************/ void init_stats() { int i; init_clocks(); for (i = 0; i < MAX_INTERNAL_FLAGS; i++) Internal_flags[i] = 0; for (i = 0; i < MACE_MAX_STATS; i++) MACE_Stats[i] = 0; } /* init_stats */ /************* * * MACE_print_mem() * *************/ void MACE_print_mem(FILE *fp) { fprintf(fp, "\n------------- memory usage ------------\n"); fprintf(fp, "Memory dynamically allocated (MACE_tp_alloc): %d.\n", MACE_total_mem()); } /* print_mem */ /************* * * p_mem * *************/ void p_mem(void) { MACE_print_mem(stdout); } /* p_mem */ /************* * * MACE_print_stats(fp) * *************/ void MACE_print_stats(FILE *fp) { fprintf(fp, "\n----- statistics for domain size %d ----\n", Domain_size); fprintf(fp, "Input:\n"); fprintf(fp, " Clauses input %7ld\n", MACE_Stats[INPUT_CLAUSES]); fprintf(fp, " Literal occurrences input %7ld\n", MACE_Stats[LIT_OCC_INPUT]); fprintf(fp, " Greatest atom %7ld\n", MACE_Stats[GREATEST_ATOM]); fprintf(fp, "Unit preprocess:\n"); fprintf(fp, " Preprocess unit assignments %7ld\n", MACE_Stats[PREPROCESS_UNIT_ASSIGNS]); fprintf(fp, " Clauses after subsumption %7ld\n", MACE_Stats[CLAUSES_AFTER_SUB]); fprintf(fp, " Literal occ. after subsump. %7ld\n", MACE_Stats[LIT_OCC_AFTER_SUB]); fprintf(fp, " Selectable clauses %7ld\n", MACE_Stats[SELECTABLE_CLAUSES]); fprintf(fp, "Decide:\n"); fprintf(fp, " Splits %7ld\n", MACE_Stats[SPLITS]); fprintf(fp, " Unit assignments %7ld\n", MACE_Stats[UNIT_ASSIGNS]); fprintf(fp, " Failed paths %7ld\n", MACE_Stats[FAILED_PATHS]); fprintf(fp, "Memory:\n"); fprintf(fp, " Memory malloced %7ld K\n", MACE_Stats[MEM_MALLOCED] / 1024); fprintf(fp, " Memory MACE_tp_alloced %7d K\n", MACE_total_mem()); fprintf(fp, "Time (seconds):\n"); fprintf(fp, " Generate ground clauses %10.2f\n", MACE_clock_val(GENERATE_TIME) / 1000.); fprintf(fp, " DPLL %10.2f\n", MACE_clock_val(DECIDE_TIME) / 1000.); } /* MACE_print_stats */ /************* * * MACE_p_stats() * *************/ void MACE_p_stats(void) { MACE_print_stats(stdout); } /* MACE_p_stats */ /************* * * MACE_print_times(fp) * *************/ void MACE_print_times(FILE *fp) { long t, min, hr; fprintf(fp, "\n=======================================\n"); fprintf(fp, "Total times for run (seconds):\n"); t = run_time(); fprintf(fp, " user CPU time %10.2f ", t / 1000.); t = t / 1000; hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); t = system_time(); fprintf(fp, " system CPU time %10.2f ", t/ 1000.); t = t / 1000; hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); t = wall_seconds() - Init_wall_seconds; fprintf(fp, " wall-clock time %7ld ", t); hr = t / 3600; t = t % 3600; min = t / 60; t = t % 60; fprintf(fp, " (%ld hr, %ld min, %ld sec)\n", hr, min, t); } /* MACE_print_times */ /************* * * MACE_output_stats * *************/ void MACE_output_stats(FILE *fp) { MACE_print_stats(fp); MACE_print_times(fp); } /* MACE_output_stats */ otter-3.3f/mace2/Mace.h0100644000076400007640000000142407705547717014232 0ustar mccunemccune#ifndef TP_MACE_HEADER_H #define TP_MACE_HEADER_H /************ BASIC INCLUDES ************/ #define IN_MAIN /* so that global vars in ../header.h will not be external */ #include "../source/header.h" /* Otter header */ #include "Opts.h" #include "Stats.h" #include "Avail.h" #include "Clock.h" #include "Miscellany.h" #include "Flatten.h" #include "Print.h" #include "Dp.h" #include "Generate.h" /******** Types of exit ********/ #define MACE_ABEND_EXIT 11 #define UNSATISFIABLE_EXIT 12 #define MACE_MAX_SECONDS_EXIT 13 #define MACE_MAX_MEM_EXIT 14 #define MAX_MODELS_EXIT 15 #define ALL_MODELS_EXIT 16 #define MACE_SIGINT_EXIT 17 #define MACE_SEGV_EXIT 18 #define MACE_INPUT_ERROR_EXIT 19 #endif /* ! TP_MACE_HEADER_H */ otter-3.3f/mace2/Miscellany.h0100644000076400007640000000026607300311476015446 0ustar mccunemccune#ifndef TP_MISC_H #define TP_MISC_H /* function prototypes from misc.c */ void exit_with_message(int exit_code, int stats); void MACE_abend(char *str); #endif /* ! TP_MISC_H */ otter-3.3f/mace2/b2.out0100644000076400007640000032117010070415442014225 0ustar mccunemccune----- MACE 2.2E, May 2004 ----- The process was started by mccune on gyro.thornwood, Tue Jun 29 20:45:05 2004 The command was "./mace2 -N100". set(prolog_style_variables). set(tptp_eq). set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). clear(print_given). list(usable). 0 [] equal(A,A). 0 [] -equal(d,A)| -equal(b,B)|equal(a,B)|equal(c,A). 0 [] -equal(d,A)| -equal(c,B)|equal(a,B)|equal(b,A). 0 [] -equal(d,A)| -equal(a,A). 0 [] -equal(c,A)| -equal(b,A). end_of_list. list(clauses). 1 [] equal(A,A). 2 [] -equal(d,A)| -equal(b,B)|equal(a,B)|equal(c,A). 3 [] -equal(d,A)| -equal(c,B)|equal(a,B)|equal(b,A). 4 [] -equal(d,A)| -equal(a,A). 5 [] -equal(c,A)| -equal(b,A). end_of_list. list(flattened_and_parted_clauses). 1 [] equal(A,A). 2 [] -equal(d,A)|equal(c,A)| -$Connect1. 2 [] -equal(b,A)|equal(a,A)|$Connect1. 3 [] -equal(d,A)|equal(b,A)| -$Connect2. 3 [] -equal(c,A)|equal(a,A)|$Connect2. 4 [] -equal(d,A)| -equal(a,A). 5 [] -equal(c,A)| -equal(b,A). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: d c b a. 27 clauses were generated; 19 of those survived the first stage of unit preprocessing; there are 14 atoms. After all unit preprocessing, 6 atoms are still unassigned; 10 clauses remain; 2 of those are non-Horn (selectable); 4882 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 19 Literal occurrences input 30 Greatest atom 14 Unit preprocess: Preprocess unit assignments 8 Clauses after subsumption 10 Literal occ. after subsump. 20 Selectable clauses 2 Decide: Splits 1 Unit assignments 4 Failed paths 2 Memory: Memory malloced 0 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: d c b a. 50 clauses were generated; 39 of those survived the first stage of unit preprocessing; there are 23 atoms. After all unit preprocessing, 10 atoms are still unassigned; 24 clauses remain; 10 of those are non-Horn (selectable); 4882 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 39 Literal occurrences input 74 Greatest atom 23 Unit preprocess: Preprocess unit assignments 13 Clauses after subsumption 24 Literal occ. after subsump. 57 Selectable clauses 10 Decide: Splits 1 Unit assignments 9 Failed paths 2 Memory: Memory malloced 0 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: d c b a. 80 clauses were generated; 63 of those survived the first stage of unit preprocessing; there are 34 atoms. After all unit preprocessing, 13 atoms are still unassigned; 39 clauses remain; 16 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 63 Literal occurrences input 130 Greatest atom 34 Unit preprocess: Preprocess unit assignments 21 Clauses after subsumption 39 Literal occ. after subsump. 103 Selectable clauses 16 Decide: Splits 1 Unit assignments 11 Failed paths 2 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: d c b a. 113 clauses were generated; 89 of those survived the first stage of unit preprocessing; there are 47 atoms. After all unit preprocessing, 16 atoms are still unassigned; 54 clauses remain; 19 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 5 ---- Input: Clauses input 89 Literal occurrences input 181 Greatest atom 47 Unit preprocess: Preprocess unit assignments 31 Clauses after subsumption 54 Literal occ. after subsump. 142 Selectable clauses 19 Decide: Splits 1 Unit assignments 13 Failed paths 2 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: d c b a. 151 clauses were generated; 119 of those survived the first stage of unit preprocessing; there are 62 atoms. After all unit preprocessing, 19 atoms are still unassigned; 71 clauses remain; 21 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 6 ---- Input: Clauses input 119 Literal occurrences input 234 Greatest atom 62 Unit preprocess: Preprocess unit assignments 43 Clauses after subsumption 71 Literal occ. after subsump. 181 Selectable clauses 21 Decide: Splits 1 Unit assignments 15 Failed paths 2 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 7 --- Applying isomorphism constraints to constants: d c b a. 195 clauses were generated; 154 of those survived the first stage of unit preprocessing; there are 79 atoms. After all unit preprocessing, 22 atoms are still unassigned; 91 clauses remain; 23 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 7 ---- Input: Clauses input 154 Literal occurrences input 295 Greatest atom 79 Unit preprocess: Preprocess unit assignments 57 Clauses after subsumption 91 Literal occ. after subsump. 226 Selectable clauses 23 Decide: Splits 1 Unit assignments 17 Failed paths 2 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 8 --- Applying isomorphism constraints to constants: d c b a. 245 clauses were generated; 194 of those survived the first stage of unit preprocessing; there are 98 atoms. After all unit preprocessing, 25 atoms are still unassigned; 114 clauses remain; 25 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 8 ---- Input: Clauses input 194 Literal occurrences input 364 Greatest atom 98 Unit preprocess: Preprocess unit assignments 73 Clauses after subsumption 114 Literal occ. after subsump. 277 Selectable clauses 25 Decide: Splits 1 Unit assignments 19 Failed paths 2 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 9 --- Applying isomorphism constraints to constants: d c b a. 301 clauses were generated; 239 of those survived the first stage of unit preprocessing; there are 119 atoms. After all unit preprocessing, 28 atoms are still unassigned; 140 clauses remain; 27 of those are non-Horn (selectable); 4885 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 9 ---- Input: Clauses input 239 Literal occurrences input 441 Greatest atom 119 Unit preprocess: Preprocess unit assignments 91 Clauses after subsumption 140 Literal occ. after subsump. 334 Selectable clauses 27 Decide: Splits 1 Unit assignments 21 Failed paths 2 Memory: Memory malloced 3 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 10 --- Applying isomorphism constraints to constants: d c b a. 363 clauses were generated; 289 of those survived the first stage of unit preprocessing; there are 142 atoms. After all unit preprocessing, 31 atoms are still unassigned; 169 clauses remain; 29 of those are non-Horn (selectable); 4886 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 10 ---- Input: Clauses input 289 Literal occurrences input 526 Greatest atom 142 Unit preprocess: Preprocess unit assignments 111 Clauses after subsumption 169 Literal occ. after subsump. 397 Selectable clauses 29 Decide: Splits 1 Unit assignments 23 Failed paths 2 Memory: Memory malloced 4 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 11 --- Applying isomorphism constraints to constants: d c b a. 431 clauses were generated; 344 of those survived the first stage of unit preprocessing; there are 167 atoms. After all unit preprocessing, 34 atoms are still unassigned; 201 clauses remain; 31 of those are non-Horn (selectable); 4886 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 11 ---- Input: Clauses input 344 Literal occurrences input 619 Greatest atom 167 Unit preprocess: Preprocess unit assignments 133 Clauses after subsumption 201 Literal occ. after subsump. 466 Selectable clauses 31 Decide: Splits 1 Unit assignments 25 Failed paths 2 Memory: Memory malloced 4 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 12 --- Applying isomorphism constraints to constants: d c b a. 505 clauses were generated; 404 of those survived the first stage of unit preprocessing; there are 194 atoms. After all unit preprocessing, 37 atoms are still unassigned; 236 clauses remain; 33 of those are non-Horn (selectable); 4887 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 12 ---- Input: Clauses input 404 Literal occurrences input 720 Greatest atom 194 Unit preprocess: Preprocess unit assignments 157 Clauses after subsumption 236 Literal occ. after subsump. 541 Selectable clauses 33 Decide: Splits 1 Unit assignments 27 Failed paths 2 Memory: Memory malloced 5 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 13 --- Applying isomorphism constraints to constants: d c b a. 585 clauses were generated; 469 of those survived the first stage of unit preprocessing; there are 223 atoms. After all unit preprocessing, 40 atoms are still unassigned; 274 clauses remain; 35 of those are non-Horn (selectable); 4888 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 13 ---- Input: Clauses input 469 Literal occurrences input 829 Greatest atom 223 Unit preprocess: Preprocess unit assignments 183 Clauses after subsumption 274 Literal occ. after subsump. 622 Selectable clauses 35 Decide: Splits 1 Unit assignments 29 Failed paths 2 Memory: Memory malloced 6 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 14 --- Applying isomorphism constraints to constants: d c b a. 671 clauses were generated; 539 of those survived the first stage of unit preprocessing; there are 254 atoms. After all unit preprocessing, 43 atoms are still unassigned; 315 clauses remain; 37 of those are non-Horn (selectable); 4889 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 14 ---- Input: Clauses input 539 Literal occurrences input 946 Greatest atom 254 Unit preprocess: Preprocess unit assignments 211 Clauses after subsumption 315 Literal occ. after subsump. 709 Selectable clauses 37 Decide: Splits 1 Unit assignments 31 Failed paths 2 Memory: Memory malloced 7 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 15 --- Applying isomorphism constraints to constants: d c b a. 763 clauses were generated; 614 of those survived the first stage of unit preprocessing; there are 287 atoms. After all unit preprocessing, 46 atoms are still unassigned; 359 clauses remain; 39 of those are non-Horn (selectable); 4890 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 15 ---- Input: Clauses input 614 Literal occurrences input 1071 Greatest atom 287 Unit preprocess: Preprocess unit assignments 241 Clauses after subsumption 359 Literal occ. after subsump. 802 Selectable clauses 39 Decide: Splits 1 Unit assignments 33 Failed paths 2 Memory: Memory malloced 8 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 16 --- Applying isomorphism constraints to constants: d c b a. 861 clauses were generated; 694 of those survived the first stage of unit preprocessing; there are 322 atoms. After all unit preprocessing, 49 atoms are still unassigned; 406 clauses remain; 41 of those are non-Horn (selectable); 4891 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 16 ---- Input: Clauses input 694 Literal occurrences input 1204 Greatest atom 322 Unit preprocess: Preprocess unit assignments 273 Clauses after subsumption 406 Literal occ. after subsump. 901 Selectable clauses 41 Decide: Splits 1 Unit assignments 35 Failed paths 2 Memory: Memory malloced 9 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 17 --- Applying isomorphism constraints to constants: d c b a. 965 clauses were generated; 779 of those survived the first stage of unit preprocessing; there are 359 atoms. After all unit preprocessing, 52 atoms are still unassigned; 456 clauses remain; 43 of those are non-Horn (selectable); 4892 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 17 ---- Input: Clauses input 779 Literal occurrences input 1345 Greatest atom 359 Unit preprocess: Preprocess unit assignments 307 Clauses after subsumption 456 Literal occ. after subsump. 1006 Selectable clauses 43 Decide: Splits 1 Unit assignments 37 Failed paths 2 Memory: Memory malloced 10 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 18 --- Applying isomorphism constraints to constants: d c b a. 1075 clauses were generated; 869 of those survived the first stage of unit preprocessing; there are 398 atoms. After all unit preprocessing, 55 atoms are still unassigned; 509 clauses remain; 45 of those are non-Horn (selectable); 4893 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 18 ---- Input: Clauses input 869 Literal occurrences input 1494 Greatest atom 398 Unit preprocess: Preprocess unit assignments 343 Clauses after subsumption 509 Literal occ. after subsump. 1117 Selectable clauses 45 Decide: Splits 1 Unit assignments 39 Failed paths 2 Memory: Memory malloced 11 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 19 --- Applying isomorphism constraints to constants: d c b a. 1191 clauses were generated; 964 of those survived the first stage of unit preprocessing; there are 439 atoms. After all unit preprocessing, 58 atoms are still unassigned; 565 clauses remain; 47 of those are non-Horn (selectable); 4894 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 19 ---- Input: Clauses input 964 Literal occurrences input 1651 Greatest atom 439 Unit preprocess: Preprocess unit assignments 381 Clauses after subsumption 565 Literal occ. after subsump. 1234 Selectable clauses 47 Decide: Splits 1 Unit assignments 41 Failed paths 2 Memory: Memory malloced 12 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 20 --- Applying isomorphism constraints to constants: d c b a. 1313 clauses were generated; 1064 of those survived the first stage of unit preprocessing; there are 482 atoms. After all unit preprocessing, 61 atoms are still unassigned; 624 clauses remain; 49 of those are non-Horn (selectable); 4895 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 20 ---- Input: Clauses input 1064 Literal occurrences input 1816 Greatest atom 482 Unit preprocess: Preprocess unit assignments 421 Clauses after subsumption 624 Literal occ. after subsump. 1357 Selectable clauses 49 Decide: Splits 1 Unit assignments 43 Failed paths 2 Memory: Memory malloced 13 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 21 --- Applying isomorphism constraints to constants: d c b a. 1441 clauses were generated; 1169 of those survived the first stage of unit preprocessing; there are 527 atoms. After all unit preprocessing, 64 atoms are still unassigned; 686 clauses remain; 51 of those are non-Horn (selectable); 4897 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 21 ---- Input: Clauses input 1169 Literal occurrences input 1989 Greatest atom 527 Unit preprocess: Preprocess unit assignments 463 Clauses after subsumption 686 Literal occ. after subsump. 1486 Selectable clauses 51 Decide: Splits 1 Unit assignments 45 Failed paths 2 Memory: Memory malloced 15 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 22 --- Applying isomorphism constraints to constants: d c b a. 1575 clauses were generated; 1279 of those survived the first stage of unit preprocessing; there are 574 atoms. After all unit preprocessing, 67 atoms are still unassigned; 751 clauses remain; 53 of those are non-Horn (selectable); 4898 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 22 ---- Input: Clauses input 1279 Literal occurrences input 2170 Greatest atom 574 Unit preprocess: Preprocess unit assignments 507 Clauses after subsumption 751 Literal occ. after subsump. 1621 Selectable clauses 53 Decide: Splits 1 Unit assignments 47 Failed paths 2 Memory: Memory malloced 16 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 23 --- Applying isomorphism constraints to constants: d c b a. 1715 clauses were generated; 1394 of those survived the first stage of unit preprocessing; there are 623 atoms. After all unit preprocessing, 70 atoms are still unassigned; 819 clauses remain; 55 of those are non-Horn (selectable); 4899 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 23 ---- Input: Clauses input 1394 Literal occurrences input 2359 Greatest atom 623 Unit preprocess: Preprocess unit assignments 553 Clauses after subsumption 819 Literal occ. after subsump. 1762 Selectable clauses 55 Decide: Splits 1 Unit assignments 49 Failed paths 2 Memory: Memory malloced 17 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 24 --- Applying isomorphism constraints to constants: d c b a. 1861 clauses were generated; 1514 of those survived the first stage of unit preprocessing; there are 674 atoms. After all unit preprocessing, 73 atoms are still unassigned; 890 clauses remain; 57 of those are non-Horn (selectable); 4901 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 24 ---- Input: Clauses input 1514 Literal occurrences input 2556 Greatest atom 674 Unit preprocess: Preprocess unit assignments 601 Clauses after subsumption 890 Literal occ. after subsump. 1909 Selectable clauses 57 Decide: Splits 1 Unit assignments 51 Failed paths 2 Memory: Memory malloced 19 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 25 --- Applying isomorphism constraints to constants: d c b a. 2013 clauses were generated; 1639 of those survived the first stage of unit preprocessing; there are 727 atoms. After all unit preprocessing, 76 atoms are still unassigned; 964 clauses remain; 59 of those are non-Horn (selectable); 4902 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 25 ---- Input: Clauses input 1639 Literal occurrences input 2761 Greatest atom 727 Unit preprocess: Preprocess unit assignments 651 Clauses after subsumption 964 Literal occ. after subsump. 2062 Selectable clauses 59 Decide: Splits 1 Unit assignments 53 Failed paths 2 Memory: Memory malloced 20 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 26 --- Applying isomorphism constraints to constants: d c b a. 2171 clauses were generated; 1769 of those survived the first stage of unit preprocessing; there are 782 atoms. After all unit preprocessing, 79 atoms are still unassigned; 1041 clauses remain; 61 of those are non-Horn (selectable); 4904 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 26 ---- Input: Clauses input 1769 Literal occurrences input 2974 Greatest atom 782 Unit preprocess: Preprocess unit assignments 703 Clauses after subsumption 1041 Literal occ. after subsump. 2221 Selectable clauses 61 Decide: Splits 1 Unit assignments 55 Failed paths 2 Memory: Memory malloced 22 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 27 --- Applying isomorphism constraints to constants: d c b a. 2335 clauses were generated; 1904 of those survived the first stage of unit preprocessing; there are 839 atoms. After all unit preprocessing, 82 atoms are still unassigned; 1121 clauses remain; 63 of those are non-Horn (selectable); 4906 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 27 ---- Input: Clauses input 1904 Literal occurrences input 3195 Greatest atom 839 Unit preprocess: Preprocess unit assignments 757 Clauses after subsumption 1121 Literal occ. after subsump. 2386 Selectable clauses 63 Decide: Splits 1 Unit assignments 57 Failed paths 2 Memory: Memory malloced 24 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 28 --- Applying isomorphism constraints to constants: d c b a. 2505 clauses were generated; 2044 of those survived the first stage of unit preprocessing; there are 898 atoms. After all unit preprocessing, 85 atoms are still unassigned; 1204 clauses remain; 65 of those are non-Horn (selectable); 4907 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 28 ---- Input: Clauses input 2044 Literal occurrences input 3424 Greatest atom 898 Unit preprocess: Preprocess unit assignments 813 Clauses after subsumption 1204 Literal occ. after subsump. 2557 Selectable clauses 65 Decide: Splits 1 Unit assignments 59 Failed paths 2 Memory: Memory malloced 25 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 29 --- Applying isomorphism constraints to constants: d c b a. 2681 clauses were generated; 2189 of those survived the first stage of unit preprocessing; there are 959 atoms. After all unit preprocessing, 88 atoms are still unassigned; 1290 clauses remain; 67 of those are non-Horn (selectable); 4909 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 29 ---- Input: Clauses input 2189 Literal occurrences input 3661 Greatest atom 959 Unit preprocess: Preprocess unit assignments 871 Clauses after subsumption 1290 Literal occ. after subsump. 2734 Selectable clauses 67 Decide: Splits 1 Unit assignments 61 Failed paths 2 Memory: Memory malloced 27 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 30 --- Applying isomorphism constraints to constants: d c b a. 2863 clauses were generated; 2339 of those survived the first stage of unit preprocessing; there are 1022 atoms. After all unit preprocessing, 91 atoms are still unassigned; 1379 clauses remain; 69 of those are non-Horn (selectable); 4911 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 30 ---- Input: Clauses input 2339 Literal occurrences input 3906 Greatest atom 1022 Unit preprocess: Preprocess unit assignments 931 Clauses after subsumption 1379 Literal occ. after subsump. 2917 Selectable clauses 69 Decide: Splits 1 Unit assignments 63 Failed paths 2 Memory: Memory malloced 29 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 31 --- Applying isomorphism constraints to constants: d c b a. 3051 clauses were generated; 2494 of those survived the first stage of unit preprocessing; there are 1087 atoms. After all unit preprocessing, 94 atoms are still unassigned; 1471 clauses remain; 71 of those are non-Horn (selectable); 4913 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 31 ---- Input: Clauses input 2494 Literal occurrences input 4159 Greatest atom 1087 Unit preprocess: Preprocess unit assignments 993 Clauses after subsumption 1471 Literal occ. after subsump. 3106 Selectable clauses 71 Decide: Splits 1 Unit assignments 65 Failed paths 2 Memory: Memory malloced 31 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 32 --- Applying isomorphism constraints to constants: d c b a. 3245 clauses were generated; 2654 of those survived the first stage of unit preprocessing; there are 1154 atoms. After all unit preprocessing, 97 atoms are still unassigned; 1566 clauses remain; 73 of those are non-Horn (selectable); 4914 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 32 ---- Input: Clauses input 2654 Literal occurrences input 4420 Greatest atom 1154 Unit preprocess: Preprocess unit assignments 1057 Clauses after subsumption 1566 Literal occ. after subsump. 3301 Selectable clauses 73 Decide: Splits 1 Unit assignments 67 Failed paths 2 Memory: Memory malloced 32 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 33 --- Applying isomorphism constraints to constants: d c b a. 3445 clauses were generated; 2819 of those survived the first stage of unit preprocessing; there are 1223 atoms. After all unit preprocessing, 100 atoms are still unassigned; 1664 clauses remain; 75 of those are non-Horn (selectable); 4916 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 33 ---- Input: Clauses input 2819 Literal occurrences input 4689 Greatest atom 1223 Unit preprocess: Preprocess unit assignments 1123 Clauses after subsumption 1664 Literal occ. after subsump. 3502 Selectable clauses 75 Decide: Splits 1 Unit assignments 69 Failed paths 2 Memory: Memory malloced 34 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 34 --- Applying isomorphism constraints to constants: d c b a. 3651 clauses were generated; 2989 of those survived the first stage of unit preprocessing; there are 1294 atoms. After all unit preprocessing, 103 atoms are still unassigned; 1765 clauses remain; 77 of those are non-Horn (selectable); 4918 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 34 ---- Input: Clauses input 2989 Literal occurrences input 4966 Greatest atom 1294 Unit preprocess: Preprocess unit assignments 1191 Clauses after subsumption 1765 Literal occ. after subsump. 3709 Selectable clauses 77 Decide: Splits 1 Unit assignments 71 Failed paths 2 Memory: Memory malloced 36 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 35 --- Applying isomorphism constraints to constants: d c b a. 3863 clauses were generated; 3164 of those survived the first stage of unit preprocessing; there are 1367 atoms. After all unit preprocessing, 106 atoms are still unassigned; 1869 clauses remain; 79 of those are non-Horn (selectable); 4921 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 35 ---- Input: Clauses input 3164 Literal occurrences input 5251 Greatest atom 1367 Unit preprocess: Preprocess unit assignments 1261 Clauses after subsumption 1869 Literal occ. after subsump. 3922 Selectable clauses 79 Decide: Splits 1 Unit assignments 73 Failed paths 2 Memory: Memory malloced 39 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 36 --- Applying isomorphism constraints to constants: d c b a. 4081 clauses were generated; 3344 of those survived the first stage of unit preprocessing; there are 1442 atoms. After all unit preprocessing, 109 atoms are still unassigned; 1976 clauses remain; 81 of those are non-Horn (selectable); 4923 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 36 ---- Input: Clauses input 3344 Literal occurrences input 5544 Greatest atom 1442 Unit preprocess: Preprocess unit assignments 1333 Clauses after subsumption 1976 Literal occ. after subsump. 4141 Selectable clauses 81 Decide: Splits 1 Unit assignments 75 Failed paths 2 Memory: Memory malloced 41 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 37 --- Applying isomorphism constraints to constants: d c b a. 4305 clauses were generated; 3529 of those survived the first stage of unit preprocessing; there are 1519 atoms. After all unit preprocessing, 112 atoms are still unassigned; 2086 clauses remain; 83 of those are non-Horn (selectable); 4925 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 37 ---- Input: Clauses input 3529 Literal occurrences input 5845 Greatest atom 1519 Unit preprocess: Preprocess unit assignments 1407 Clauses after subsumption 2086 Literal occ. after subsump. 4366 Selectable clauses 83 Decide: Splits 1 Unit assignments 77 Failed paths 2 Memory: Memory malloced 43 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 38 --- Applying isomorphism constraints to constants: d c b a. 4535 clauses were generated; 3719 of those survived the first stage of unit preprocessing; there are 1598 atoms. After all unit preprocessing, 115 atoms are still unassigned; 2199 clauses remain; 85 of those are non-Horn (selectable); 4927 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 38 ---- Input: Clauses input 3719 Literal occurrences input 6154 Greatest atom 1598 Unit preprocess: Preprocess unit assignments 1483 Clauses after subsumption 2199 Literal occ. after subsump. 4597 Selectable clauses 85 Decide: Splits 1 Unit assignments 79 Failed paths 2 Memory: Memory malloced 45 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 39 --- Applying isomorphism constraints to constants: d c b a. 4771 clauses were generated; 3914 of those survived the first stage of unit preprocessing; there are 1679 atoms. After all unit preprocessing, 118 atoms are still unassigned; 2315 clauses remain; 87 of those are non-Horn (selectable); 4929 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 39 ---- Input: Clauses input 3914 Literal occurrences input 6471 Greatest atom 1679 Unit preprocess: Preprocess unit assignments 1561 Clauses after subsumption 2315 Literal occ. after subsump. 4834 Selectable clauses 87 Decide: Splits 1 Unit assignments 81 Failed paths 2 Memory: Memory malloced 47 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 40 --- Applying isomorphism constraints to constants: d c b a. 5013 clauses were generated; 4114 of those survived the first stage of unit preprocessing; there are 1762 atoms. After all unit preprocessing, 121 atoms are still unassigned; 2434 clauses remain; 89 of those are non-Horn (selectable); 4932 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 40 ---- Input: Clauses input 4114 Literal occurrences input 6796 Greatest atom 1762 Unit preprocess: Preprocess unit assignments 1641 Clauses after subsumption 2434 Literal occ. after subsump. 5077 Selectable clauses 89 Decide: Splits 1 Unit assignments 83 Failed paths 2 Memory: Memory malloced 50 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 41 --- Applying isomorphism constraints to constants: d c b a. 5261 clauses were generated; 4319 of those survived the first stage of unit preprocessing; there are 1847 atoms. After all unit preprocessing, 124 atoms are still unassigned; 2556 clauses remain; 91 of those are non-Horn (selectable); 4934 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 41 ---- Input: Clauses input 4319 Literal occurrences input 7129 Greatest atom 1847 Unit preprocess: Preprocess unit assignments 1723 Clauses after subsumption 2556 Literal occ. after subsump. 5326 Selectable clauses 91 Decide: Splits 1 Unit assignments 85 Failed paths 2 Memory: Memory malloced 52 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 42 --- Applying isomorphism constraints to constants: d c b a. 5515 clauses were generated; 4529 of those survived the first stage of unit preprocessing; there are 1934 atoms. After all unit preprocessing, 127 atoms are still unassigned; 2681 clauses remain; 93 of those are non-Horn (selectable); 4937 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 42 ---- Input: Clauses input 4529 Literal occurrences input 7470 Greatest atom 1934 Unit preprocess: Preprocess unit assignments 1807 Clauses after subsumption 2681 Literal occ. after subsump. 5581 Selectable clauses 93 Decide: Splits 1 Unit assignments 87 Failed paths 2 Memory: Memory malloced 55 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 43 --- Applying isomorphism constraints to constants: d c b a. 5775 clauses were generated; 4744 of those survived the first stage of unit preprocessing; there are 2023 atoms. After all unit preprocessing, 130 atoms are still unassigned; 2809 clauses remain; 95 of those are non-Horn (selectable); 4939 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 43 ---- Input: Clauses input 4744 Literal occurrences input 7819 Greatest atom 2023 Unit preprocess: Preprocess unit assignments 1893 Clauses after subsumption 2809 Literal occ. after subsump. 5842 Selectable clauses 95 Decide: Splits 1 Unit assignments 89 Failed paths 2 Memory: Memory malloced 57 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 44 --- Applying isomorphism constraints to constants: d c b a. 6041 clauses were generated; 4964 of those survived the first stage of unit preprocessing; there are 2114 atoms. After all unit preprocessing, 133 atoms are still unassigned; 2940 clauses remain; 97 of those are non-Horn (selectable); 4942 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 44 ---- Input: Clauses input 4964 Literal occurrences input 8176 Greatest atom 2114 Unit preprocess: Preprocess unit assignments 1981 Clauses after subsumption 2940 Literal occ. after subsump. 6109 Selectable clauses 97 Decide: Splits 1 Unit assignments 91 Failed paths 2 Memory: Memory malloced 60 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 45 --- Applying isomorphism constraints to constants: d c b a. 6313 clauses were generated; 5189 of those survived the first stage of unit preprocessing; there are 2207 atoms. After all unit preprocessing, 136 atoms are still unassigned; 3074 clauses remain; 99 of those are non-Horn (selectable); 4944 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 45 ---- Input: Clauses input 5189 Literal occurrences input 8541 Greatest atom 2207 Unit preprocess: Preprocess unit assignments 2071 Clauses after subsumption 3074 Literal occ. after subsump. 6382 Selectable clauses 99 Decide: Splits 1 Unit assignments 93 Failed paths 2 Memory: Memory malloced 62 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 46 --- Applying isomorphism constraints to constants: d c b a. 6591 clauses were generated; 5419 of those survived the first stage of unit preprocessing; there are 2302 atoms. After all unit preprocessing, 139 atoms are still unassigned; 3211 clauses remain; 101 of those are non-Horn (selectable); 4947 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 46 ---- Input: Clauses input 5419 Literal occurrences input 8914 Greatest atom 2302 Unit preprocess: Preprocess unit assignments 2163 Clauses after subsumption 3211 Literal occ. after subsump. 6661 Selectable clauses 101 Decide: Splits 1 Unit assignments 95 Failed paths 2 Memory: Memory malloced 65 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 47 --- Applying isomorphism constraints to constants: d c b a. 6875 clauses were generated; 5654 of those survived the first stage of unit preprocessing; there are 2399 atoms. After all unit preprocessing, 142 atoms are still unassigned; 3351 clauses remain; 103 of those are non-Horn (selectable); 4950 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 47 ---- Input: Clauses input 5654 Literal occurrences input 9295 Greatest atom 2399 Unit preprocess: Preprocess unit assignments 2257 Clauses after subsumption 3351 Literal occ. after subsump. 6946 Selectable clauses 103 Decide: Splits 1 Unit assignments 97 Failed paths 2 Memory: Memory malloced 68 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 48 --- Applying isomorphism constraints to constants: d c b a. 7165 clauses were generated; 5894 of those survived the first stage of unit preprocessing; there are 2498 atoms. After all unit preprocessing, 145 atoms are still unassigned; 3494 clauses remain; 105 of those are non-Horn (selectable); 4953 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 48 ---- Input: Clauses input 5894 Literal occurrences input 9684 Greatest atom 2498 Unit preprocess: Preprocess unit assignments 2353 Clauses after subsumption 3494 Literal occ. after subsump. 7237 Selectable clauses 105 Decide: Splits 1 Unit assignments 99 Failed paths 2 Memory: Memory malloced 71 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 49 --- Applying isomorphism constraints to constants: d c b a. 7461 clauses were generated; 6139 of those survived the first stage of unit preprocessing; there are 2599 atoms. After all unit preprocessing, 148 atoms are still unassigned; 3640 clauses remain; 107 of those are non-Horn (selectable); 4956 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 49 ---- Input: Clauses input 6139 Literal occurrences input 10081 Greatest atom 2599 Unit preprocess: Preprocess unit assignments 2451 Clauses after subsumption 3640 Literal occ. after subsump. 7534 Selectable clauses 107 Decide: Splits 1 Unit assignments 101 Failed paths 2 Memory: Memory malloced 74 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 50 --- Applying isomorphism constraints to constants: d c b a. 7763 clauses were generated; 6389 of those survived the first stage of unit preprocessing; there are 2702 atoms. After all unit preprocessing, 151 atoms are still unassigned; 3789 clauses remain; 109 of those are non-Horn (selectable); 4958 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 50 ---- Input: Clauses input 6389 Literal occurrences input 10486 Greatest atom 2702 Unit preprocess: Preprocess unit assignments 2551 Clauses after subsumption 3789 Literal occ. after subsump. 7837 Selectable clauses 109 Decide: Splits 1 Unit assignments 103 Failed paths 2 Memory: Memory malloced 76 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 51 --- Applying isomorphism constraints to constants: d c b a. 8071 clauses were generated; 6644 of those survived the first stage of unit preprocessing; there are 2807 atoms. After all unit preprocessing, 154 atoms are still unassigned; 3941 clauses remain; 111 of those are non-Horn (selectable); 4961 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 51 ---- Input: Clauses input 6644 Literal occurrences input 10899 Greatest atom 2807 Unit preprocess: Preprocess unit assignments 2653 Clauses after subsumption 3941 Literal occ. after subsump. 8146 Selectable clauses 111 Decide: Splits 1 Unit assignments 105 Failed paths 2 Memory: Memory malloced 79 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 52 --- Applying isomorphism constraints to constants: d c b a. 8385 clauses were generated; 6904 of those survived the first stage of unit preprocessing; there are 2914 atoms. After all unit preprocessing, 157 atoms are still unassigned; 4096 clauses remain; 113 of those are non-Horn (selectable); 4964 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 52 ---- Input: Clauses input 6904 Literal occurrences input 11320 Greatest atom 2914 Unit preprocess: Preprocess unit assignments 2757 Clauses after subsumption 4096 Literal occ. after subsump. 8461 Selectable clauses 113 Decide: Splits 1 Unit assignments 107 Failed paths 2 Memory: Memory malloced 82 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 53 --- Applying isomorphism constraints to constants: d c b a. 8705 clauses were generated; 7169 of those survived the first stage of unit preprocessing; there are 3023 atoms. After all unit preprocessing, 160 atoms are still unassigned; 4254 clauses remain; 115 of those are non-Horn (selectable); 4968 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 53 ---- Input: Clauses input 7169 Literal occurrences input 11749 Greatest atom 3023 Unit preprocess: Preprocess unit assignments 2863 Clauses after subsumption 4254 Literal occ. after subsump. 8782 Selectable clauses 115 Decide: Splits 1 Unit assignments 109 Failed paths 2 Memory: Memory malloced 86 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 54 --- Applying isomorphism constraints to constants: d c b a. 9031 clauses were generated; 7439 of those survived the first stage of unit preprocessing; there are 3134 atoms. After all unit preprocessing, 163 atoms are still unassigned; 4415 clauses remain; 117 of those are non-Horn (selectable); 4971 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 54 ---- Input: Clauses input 7439 Literal occurrences input 12186 Greatest atom 3134 Unit preprocess: Preprocess unit assignments 2971 Clauses after subsumption 4415 Literal occ. after subsump. 9109 Selectable clauses 117 Decide: Splits 1 Unit assignments 111 Failed paths 2 Memory: Memory malloced 89 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 55 --- Applying isomorphism constraints to constants: d c b a. 9363 clauses were generated; 7714 of those survived the first stage of unit preprocessing; there are 3247 atoms. After all unit preprocessing, 166 atoms are still unassigned; 4579 clauses remain; 119 of those are non-Horn (selectable); 4974 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 55 ---- Input: Clauses input 7714 Literal occurrences input 12631 Greatest atom 3247 Unit preprocess: Preprocess unit assignments 3081 Clauses after subsumption 4579 Literal occ. after subsump. 9442 Selectable clauses 119 Decide: Splits 1 Unit assignments 113 Failed paths 2 Memory: Memory malloced 92 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 56 --- Applying isomorphism constraints to constants: d c b a. 9701 clauses were generated; 7994 of those survived the first stage of unit preprocessing; there are 3362 atoms. After all unit preprocessing, 169 atoms are still unassigned; 4746 clauses remain; 121 of those are non-Horn (selectable); 4977 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 56 ---- Input: Clauses input 7994 Literal occurrences input 13084 Greatest atom 3362 Unit preprocess: Preprocess unit assignments 3193 Clauses after subsumption 4746 Literal occ. after subsump. 9781 Selectable clauses 121 Decide: Splits 1 Unit assignments 115 Failed paths 2 Memory: Memory malloced 95 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 57 --- Applying isomorphism constraints to constants: d c b a. 10045 clauses were generated; 8279 of those survived the first stage of unit preprocessing; there are 3479 atoms. After all unit preprocessing, 172 atoms are still unassigned; 4916 clauses remain; 123 of those are non-Horn (selectable); 4981 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 57 ---- Input: Clauses input 8279 Literal occurrences input 13545 Greatest atom 3479 Unit preprocess: Preprocess unit assignments 3307 Clauses after subsumption 4916 Literal occ. after subsump. 10126 Selectable clauses 123 Decide: Splits 1 Unit assignments 117 Failed paths 2 Memory: Memory malloced 99 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 58 --- Applying isomorphism constraints to constants: d c b a. 10395 clauses were generated; 8569 of those survived the first stage of unit preprocessing; there are 3598 atoms. After all unit preprocessing, 175 atoms are still unassigned; 5089 clauses remain; 125 of those are non-Horn (selectable); 4984 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 58 ---- Input: Clauses input 8569 Literal occurrences input 14014 Greatest atom 3598 Unit preprocess: Preprocess unit assignments 3423 Clauses after subsumption 5089 Literal occ. after subsump. 10477 Selectable clauses 125 Decide: Splits 1 Unit assignments 119 Failed paths 2 Memory: Memory malloced 102 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 59 --- Applying isomorphism constraints to constants: d c b a. 10751 clauses were generated; 8864 of those survived the first stage of unit preprocessing; there are 3719 atoms. After all unit preprocessing, 178 atoms are still unassigned; 5265 clauses remain; 127 of those are non-Horn (selectable); 4987 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 59 ---- Input: Clauses input 8864 Literal occurrences input 14491 Greatest atom 3719 Unit preprocess: Preprocess unit assignments 3541 Clauses after subsumption 5265 Literal occ. after subsump. 10834 Selectable clauses 127 Decide: Splits 1 Unit assignments 121 Failed paths 2 Memory: Memory malloced 105 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 60 --- Applying isomorphism constraints to constants: d c b a. 11113 clauses were generated; 9164 of those survived the first stage of unit preprocessing; there are 3842 atoms. After all unit preprocessing, 181 atoms are still unassigned; 5444 clauses remain; 129 of those are non-Horn (selectable); 4991 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 60 ---- Input: Clauses input 9164 Literal occurrences input 14976 Greatest atom 3842 Unit preprocess: Preprocess unit assignments 3661 Clauses after subsumption 5444 Literal occ. after subsump. 11197 Selectable clauses 129 Decide: Splits 1 Unit assignments 123 Failed paths 2 Memory: Memory malloced 109 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 61 --- Applying isomorphism constraints to constants: d c b a. 11481 clauses were generated; 9469 of those survived the first stage of unit preprocessing; there are 3967 atoms. After all unit preprocessing, 184 atoms are still unassigned; 5626 clauses remain; 131 of those are non-Horn (selectable); 4994 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 61 ---- Input: Clauses input 9469 Literal occurrences input 15469 Greatest atom 3967 Unit preprocess: Preprocess unit assignments 3783 Clauses after subsumption 5626 Literal occ. after subsump. 11566 Selectable clauses 131 Decide: Splits 1 Unit assignments 125 Failed paths 2 Memory: Memory malloced 112 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 62 --- Applying isomorphism constraints to constants: d c b a. 11855 clauses were generated; 9779 of those survived the first stage of unit preprocessing; there are 4094 atoms. After all unit preprocessing, 187 atoms are still unassigned; 5811 clauses remain; 133 of those are non-Horn (selectable); 4998 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 62 ---- Input: Clauses input 9779 Literal occurrences input 15970 Greatest atom 4094 Unit preprocess: Preprocess unit assignments 3907 Clauses after subsumption 5811 Literal occ. after subsump. 11941 Selectable clauses 133 Decide: Splits 1 Unit assignments 127 Failed paths 2 Memory: Memory malloced 116 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 63 --- Applying isomorphism constraints to constants: d c b a. 12235 clauses were generated; 10094 of those survived the first stage of unit preprocessing; there are 4223 atoms. After all unit preprocessing, 190 atoms are still unassigned; 5999 clauses remain; 135 of those are non-Horn (selectable); 5002 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 63 ---- Input: Clauses input 10094 Literal occurrences input 16479 Greatest atom 4223 Unit preprocess: Preprocess unit assignments 4033 Clauses after subsumption 5999 Literal occ. after subsump. 12322 Selectable clauses 135 Decide: Splits 1 Unit assignments 129 Failed paths 2 Memory: Memory malloced 120 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 64 --- Applying isomorphism constraints to constants: d c b a. 12621 clauses were generated; 10414 of those survived the first stage of unit preprocessing; there are 4354 atoms. After all unit preprocessing, 193 atoms are still unassigned; 6190 clauses remain; 137 of those are non-Horn (selectable); 5005 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 64 ---- Input: Clauses input 10414 Literal occurrences input 16996 Greatest atom 4354 Unit preprocess: Preprocess unit assignments 4161 Clauses after subsumption 6190 Literal occ. after subsump. 12709 Selectable clauses 137 Decide: Splits 1 Unit assignments 131 Failed paths 2 Memory: Memory malloced 123 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 65 --- Applying isomorphism constraints to constants: d c b a. 13013 clauses were generated; 10739 of those survived the first stage of unit preprocessing; there are 4487 atoms. After all unit preprocessing, 196 atoms are still unassigned; 6384 clauses remain; 139 of those are non-Horn (selectable); 5009 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 65 ---- Input: Clauses input 10739 Literal occurrences input 17521 Greatest atom 4487 Unit preprocess: Preprocess unit assignments 4291 Clauses after subsumption 6384 Literal occ. after subsump. 13102 Selectable clauses 139 Decide: Splits 1 Unit assignments 133 Failed paths 2 Memory: Memory malloced 127 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 66 --- Applying isomorphism constraints to constants: d c b a. 13411 clauses were generated; 11069 of those survived the first stage of unit preprocessing; there are 4622 atoms. After all unit preprocessing, 199 atoms are still unassigned; 6581 clauses remain; 141 of those are non-Horn (selectable); 5013 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 66 ---- Input: Clauses input 11069 Literal occurrences input 18054 Greatest atom 4622 Unit preprocess: Preprocess unit assignments 4423 Clauses after subsumption 6581 Literal occ. after subsump. 13501 Selectable clauses 141 Decide: Splits 1 Unit assignments 135 Failed paths 2 Memory: Memory malloced 131 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 67 --- Applying isomorphism constraints to constants: d c b a. 13815 clauses were generated; 11404 of those survived the first stage of unit preprocessing; there are 4759 atoms. After all unit preprocessing, 202 atoms are still unassigned; 6781 clauses remain; 143 of those are non-Horn (selectable); 5017 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 67 ---- Input: Clauses input 11404 Literal occurrences input 18595 Greatest atom 4759 Unit preprocess: Preprocess unit assignments 4557 Clauses after subsumption 6781 Literal occ. after subsump. 13906 Selectable clauses 143 Decide: Splits 1 Unit assignments 137 Failed paths 2 Memory: Memory malloced 135 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 68 --- Applying isomorphism constraints to constants: d c b a. 14225 clauses were generated; 11744 of those survived the first stage of unit preprocessing; there are 4898 atoms. After all unit preprocessing, 205 atoms are still unassigned; 6984 clauses remain; 145 of those are non-Horn (selectable); 5021 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 68 ---- Input: Clauses input 11744 Literal occurrences input 19144 Greatest atom 4898 Unit preprocess: Preprocess unit assignments 4693 Clauses after subsumption 6984 Literal occ. after subsump. 14317 Selectable clauses 145 Decide: Splits 1 Unit assignments 139 Failed paths 2 Memory: Memory malloced 139 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 69 --- Applying isomorphism constraints to constants: d c b a. 14641 clauses were generated; 12089 of those survived the first stage of unit preprocessing; there are 5039 atoms. After all unit preprocessing, 208 atoms are still unassigned; 7190 clauses remain; 147 of those are non-Horn (selectable); 5025 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 69 ---- Input: Clauses input 12089 Literal occurrences input 19701 Greatest atom 5039 Unit preprocess: Preprocess unit assignments 4831 Clauses after subsumption 7190 Literal occ. after subsump. 14734 Selectable clauses 147 Decide: Splits 1 Unit assignments 141 Failed paths 2 Memory: Memory malloced 143 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 70 --- Applying isomorphism constraints to constants: d c b a. 15063 clauses were generated; 12439 of those survived the first stage of unit preprocessing; there are 5182 atoms. After all unit preprocessing, 211 atoms are still unassigned; 7399 clauses remain; 149 of those are non-Horn (selectable); 5029 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 70 ---- Input: Clauses input 12439 Literal occurrences input 20266 Greatest atom 5182 Unit preprocess: Preprocess unit assignments 4971 Clauses after subsumption 7399 Literal occ. after subsump. 15157 Selectable clauses 149 Decide: Splits 1 Unit assignments 143 Failed paths 2 Memory: Memory malloced 147 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 71 --- Applying isomorphism constraints to constants: d c b a. 15491 clauses were generated; 12794 of those survived the first stage of unit preprocessing; there are 5327 atoms. After all unit preprocessing, 214 atoms are still unassigned; 7611 clauses remain; 151 of those are non-Horn (selectable); 5033 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 71 ---- Input: Clauses input 12794 Literal occurrences input 20839 Greatest atom 5327 Unit preprocess: Preprocess unit assignments 5113 Clauses after subsumption 7611 Literal occ. after subsump. 15586 Selectable clauses 151 Decide: Splits 1 Unit assignments 145 Failed paths 2 Memory: Memory malloced 151 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 72 --- Applying isomorphism constraints to constants: d c b a. 15925 clauses were generated; 13154 of those survived the first stage of unit preprocessing; there are 5474 atoms. After all unit preprocessing, 217 atoms are still unassigned; 7826 clauses remain; 153 of those are non-Horn (selectable); 5037 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 72 ---- Input: Clauses input 13154 Literal occurrences input 21420 Greatest atom 5474 Unit preprocess: Preprocess unit assignments 5257 Clauses after subsumption 7826 Literal occ. after subsump. 16021 Selectable clauses 153 Decide: Splits 1 Unit assignments 147 Failed paths 2 Memory: Memory malloced 155 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 73 --- Applying isomorphism constraints to constants: d c b a. 16365 clauses were generated; 13519 of those survived the first stage of unit preprocessing; there are 5623 atoms. After all unit preprocessing, 220 atoms are still unassigned; 8044 clauses remain; 155 of those are non-Horn (selectable); 5041 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 73 ---- Input: Clauses input 13519 Literal occurrences input 22009 Greatest atom 5623 Unit preprocess: Preprocess unit assignments 5403 Clauses after subsumption 8044 Literal occ. after subsump. 16462 Selectable clauses 155 Decide: Splits 1 Unit assignments 149 Failed paths 2 Memory: Memory malloced 159 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 74 --- Applying isomorphism constraints to constants: d c b a. 16811 clauses were generated; 13889 of those survived the first stage of unit preprocessing; there are 5774 atoms. After all unit preprocessing, 223 atoms are still unassigned; 8265 clauses remain; 157 of those are non-Horn (selectable); 5046 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 74 ---- Input: Clauses input 13889 Literal occurrences input 22606 Greatest atom 5774 Unit preprocess: Preprocess unit assignments 5551 Clauses after subsumption 8265 Literal occ. after subsump. 16909 Selectable clauses 157 Decide: Splits 1 Unit assignments 151 Failed paths 2 Memory: Memory malloced 164 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 75 --- Applying isomorphism constraints to constants: d c b a. 17263 clauses were generated; 14264 of those survived the first stage of unit preprocessing; there are 5927 atoms. After all unit preprocessing, 226 atoms are still unassigned; 8489 clauses remain; 159 of those are non-Horn (selectable); 5050 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 75 ---- Input: Clauses input 14264 Literal occurrences input 23211 Greatest atom 5927 Unit preprocess: Preprocess unit assignments 5701 Clauses after subsumption 8489 Literal occ. after subsump. 17362 Selectable clauses 159 Decide: Splits 1 Unit assignments 153 Failed paths 2 Memory: Memory malloced 168 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 76 --- Applying isomorphism constraints to constants: d c b a. 17721 clauses were generated; 14644 of those survived the first stage of unit preprocessing; there are 6082 atoms. After all unit preprocessing, 229 atoms are still unassigned; 8716 clauses remain; 161 of those are non-Horn (selectable); 5054 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 76 ---- Input: Clauses input 14644 Literal occurrences input 23824 Greatest atom 6082 Unit preprocess: Preprocess unit assignments 5853 Clauses after subsumption 8716 Literal occ. after subsump. 17821 Selectable clauses 161 Decide: Splits 1 Unit assignments 155 Failed paths 2 Memory: Memory malloced 172 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 77 --- Applying isomorphism constraints to constants: d c b a. 18185 clauses were generated; 15029 of those survived the first stage of unit preprocessing; there are 6239 atoms. After all unit preprocessing, 232 atoms are still unassigned; 8946 clauses remain; 163 of those are non-Horn (selectable); 5059 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 77 ---- Input: Clauses input 15029 Literal occurrences input 24445 Greatest atom 6239 Unit preprocess: Preprocess unit assignments 6007 Clauses after subsumption 8946 Literal occ. after subsump. 18286 Selectable clauses 163 Decide: Splits 1 Unit assignments 157 Failed paths 2 Memory: Memory malloced 177 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 78 --- Applying isomorphism constraints to constants: d c b a. 18655 clauses were generated; 15419 of those survived the first stage of unit preprocessing; there are 6398 atoms. After all unit preprocessing, 235 atoms are still unassigned; 9179 clauses remain; 165 of those are non-Horn (selectable); 5063 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 78 ---- Input: Clauses input 15419 Literal occurrences input 25074 Greatest atom 6398 Unit preprocess: Preprocess unit assignments 6163 Clauses after subsumption 9179 Literal occ. after subsump. 18757 Selectable clauses 165 Decide: Splits 1 Unit assignments 159 Failed paths 2 Memory: Memory malloced 181 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 79 --- Applying isomorphism constraints to constants: d c b a. 19131 clauses were generated; 15814 of those survived the first stage of unit preprocessing; there are 6559 atoms. After all unit preprocessing, 238 atoms are still unassigned; 9415 clauses remain; 167 of those are non-Horn (selectable); 5068 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 79 ---- Input: Clauses input 15814 Literal occurrences input 25711 Greatest atom 6559 Unit preprocess: Preprocess unit assignments 6321 Clauses after subsumption 9415 Literal occ. after subsump. 19234 Selectable clauses 167 Decide: Splits 1 Unit assignments 161 Failed paths 2 Memory: Memory malloced 186 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 80 --- Applying isomorphism constraints to constants: d c b a. 19613 clauses were generated; 16214 of those survived the first stage of unit preprocessing; there are 6722 atoms. After all unit preprocessing, 241 atoms are still unassigned; 9654 clauses remain; 169 of those are non-Horn (selectable); 5073 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 80 ---- Input: Clauses input 16214 Literal occurrences input 26356 Greatest atom 6722 Unit preprocess: Preprocess unit assignments 6481 Clauses after subsumption 9654 Literal occ. after subsump. 19717 Selectable clauses 169 Decide: Splits 1 Unit assignments 163 Failed paths 2 Memory: Memory malloced 191 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 81 --- Applying isomorphism constraints to constants: d c b a. 20101 clauses were generated; 16619 of those survived the first stage of unit preprocessing; there are 6887 atoms. After all unit preprocessing, 244 atoms are still unassigned; 9896 clauses remain; 171 of those are non-Horn (selectable); 5077 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 81 ---- Input: Clauses input 16619 Literal occurrences input 27009 Greatest atom 6887 Unit preprocess: Preprocess unit assignments 6643 Clauses after subsumption 9896 Literal occ. after subsump. 20206 Selectable clauses 171 Decide: Splits 1 Unit assignments 165 Failed paths 2 Memory: Memory malloced 195 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 82 --- Applying isomorphism constraints to constants: d c b a. 20595 clauses were generated; 17029 of those survived the first stage of unit preprocessing; there are 7054 atoms. After all unit preprocessing, 247 atoms are still unassigned; 10141 clauses remain; 173 of those are non-Horn (selectable); 5082 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 82 ---- Input: Clauses input 17029 Literal occurrences input 27670 Greatest atom 7054 Unit preprocess: Preprocess unit assignments 6807 Clauses after subsumption 10141 Literal occ. after subsump. 20701 Selectable clauses 173 Decide: Splits 1 Unit assignments 167 Failed paths 2 Memory: Memory malloced 200 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 83 --- Applying isomorphism constraints to constants: d c b a. 21095 clauses were generated; 17444 of those survived the first stage of unit preprocessing; there are 7223 atoms. After all unit preprocessing, 250 atoms are still unassigned; 10389 clauses remain; 175 of those are non-Horn (selectable); 5087 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 83 ---- Input: Clauses input 17444 Literal occurrences input 28339 Greatest atom 7223 Unit preprocess: Preprocess unit assignments 6973 Clauses after subsumption 10389 Literal occ. after subsump. 21202 Selectable clauses 175 Decide: Splits 1 Unit assignments 169 Failed paths 2 Memory: Memory malloced 205 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 84 --- Applying isomorphism constraints to constants: d c b a. 21601 clauses were generated; 17864 of those survived the first stage of unit preprocessing; there are 7394 atoms. After all unit preprocessing, 253 atoms are still unassigned; 10640 clauses remain; 177 of those are non-Horn (selectable); 5092 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 84 ---- Input: Clauses input 17864 Literal occurrences input 29016 Greatest atom 7394 Unit preprocess: Preprocess unit assignments 7141 Clauses after subsumption 10640 Literal occ. after subsump. 21709 Selectable clauses 177 Decide: Splits 1 Unit assignments 171 Failed paths 2 Memory: Memory malloced 210 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 85 --- Applying isomorphism constraints to constants: d c b a. 22113 clauses were generated; 18289 of those survived the first stage of unit preprocessing; there are 7567 atoms. After all unit preprocessing, 256 atoms are still unassigned; 10894 clauses remain; 179 of those are non-Horn (selectable); 5097 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 85 ---- Input: Clauses input 18289 Literal occurrences input 29701 Greatest atom 7567 Unit preprocess: Preprocess unit assignments 7311 Clauses after subsumption 10894 Literal occ. after subsump. 22222 Selectable clauses 179 Decide: Splits 1 Unit assignments 173 Failed paths 2 Memory: Memory malloced 215 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 86 --- Applying isomorphism constraints to constants: d c b a. 22631 clauses were generated; 18719 of those survived the first stage of unit preprocessing; there are 7742 atoms. After all unit preprocessing, 259 atoms are still unassigned; 11151 clauses remain; 181 of those are non-Horn (selectable); 5101 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 86 ---- Input: Clauses input 18719 Literal occurrences input 30394 Greatest atom 7742 Unit preprocess: Preprocess unit assignments 7483 Clauses after subsumption 11151 Literal occ. after subsump. 22741 Selectable clauses 181 Decide: Splits 1 Unit assignments 175 Failed paths 2 Memory: Memory malloced 219 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 87 --- Applying isomorphism constraints to constants: d c b a. 23155 clauses were generated; 19154 of those survived the first stage of unit preprocessing; there are 7919 atoms. After all unit preprocessing, 262 atoms are still unassigned; 11411 clauses remain; 183 of those are non-Horn (selectable); 5107 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 87 ---- Input: Clauses input 19154 Literal occurrences input 31095 Greatest atom 7919 Unit preprocess: Preprocess unit assignments 7657 Clauses after subsumption 11411 Literal occ. after subsump. 23266 Selectable clauses 183 Decide: Splits 1 Unit assignments 177 Failed paths 2 Memory: Memory malloced 225 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 88 --- Applying isomorphism constraints to constants: d c b a. 23685 clauses were generated; 19594 of those survived the first stage of unit preprocessing; there are 8098 atoms. After all unit preprocessing, 265 atoms are still unassigned; 11674 clauses remain; 185 of those are non-Horn (selectable); 5112 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 88 ---- Input: Clauses input 19594 Literal occurrences input 31804 Greatest atom 8098 Unit preprocess: Preprocess unit assignments 7833 Clauses after subsumption 11674 Literal occ. after subsump. 23797 Selectable clauses 185 Decide: Splits 1 Unit assignments 179 Failed paths 2 Memory: Memory malloced 230 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 89 --- Applying isomorphism constraints to constants: d c b a. 24221 clauses were generated; 20039 of those survived the first stage of unit preprocessing; there are 8279 atoms. After all unit preprocessing, 268 atoms are still unassigned; 11940 clauses remain; 187 of those are non-Horn (selectable); 5117 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 89 ---- Input: Clauses input 20039 Literal occurrences input 32521 Greatest atom 8279 Unit preprocess: Preprocess unit assignments 8011 Clauses after subsumption 11940 Literal occ. after subsump. 24334 Selectable clauses 187 Decide: Splits 1 Unit assignments 181 Failed paths 2 Memory: Memory malloced 235 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 90 --- Applying isomorphism constraints to constants: d c b a. 24763 clauses were generated; 20489 of those survived the first stage of unit preprocessing; there are 8462 atoms. After all unit preprocessing, 271 atoms are still unassigned; 12209 clauses remain; 189 of those are non-Horn (selectable); 5122 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 90 ---- Input: Clauses input 20489 Literal occurrences input 33246 Greatest atom 8462 Unit preprocess: Preprocess unit assignments 8191 Clauses after subsumption 12209 Literal occ. after subsump. 24877 Selectable clauses 189 Decide: Splits 1 Unit assignments 183 Failed paths 2 Memory: Memory malloced 240 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 91 --- Applying isomorphism constraints to constants: d c b a. 25311 clauses were generated; 20944 of those survived the first stage of unit preprocessing; there are 8647 atoms. After all unit preprocessing, 274 atoms are still unassigned; 12481 clauses remain; 191 of those are non-Horn (selectable); 5127 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 91 ---- Input: Clauses input 20944 Literal occurrences input 33979 Greatest atom 8647 Unit preprocess: Preprocess unit assignments 8373 Clauses after subsumption 12481 Literal occ. after subsump. 25426 Selectable clauses 191 Decide: Splits 1 Unit assignments 185 Failed paths 2 Memory: Memory malloced 245 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 92 --- Applying isomorphism constraints to constants: d c b a. 25865 clauses were generated; 21404 of those survived the first stage of unit preprocessing; there are 8834 atoms. After all unit preprocessing, 277 atoms are still unassigned; 12756 clauses remain; 193 of those are non-Horn (selectable); 5132 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 92 ---- Input: Clauses input 21404 Literal occurrences input 34720 Greatest atom 8834 Unit preprocess: Preprocess unit assignments 8557 Clauses after subsumption 12756 Literal occ. after subsump. 25981 Selectable clauses 193 Decide: Splits 1 Unit assignments 187 Failed paths 2 Memory: Memory malloced 250 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 93 --- Applying isomorphism constraints to constants: d c b a. 26425 clauses were generated; 21869 of those survived the first stage of unit preprocessing; there are 9023 atoms. After all unit preprocessing, 280 atoms are still unassigned; 13034 clauses remain; 195 of those are non-Horn (selectable); 5138 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 93 ---- Input: Clauses input 21869 Literal occurrences input 35469 Greatest atom 9023 Unit preprocess: Preprocess unit assignments 8743 Clauses after subsumption 13034 Literal occ. after subsump. 26542 Selectable clauses 195 Decide: Splits 1 Unit assignments 189 Failed paths 2 Memory: Memory malloced 256 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 94 --- Applying isomorphism constraints to constants: d c b a. 26991 clauses were generated; 22339 of those survived the first stage of unit preprocessing; there are 9214 atoms. After all unit preprocessing, 283 atoms are still unassigned; 13315 clauses remain; 197 of those are non-Horn (selectable); 5143 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 94 ---- Input: Clauses input 22339 Literal occurrences input 36226 Greatest atom 9214 Unit preprocess: Preprocess unit assignments 8931 Clauses after subsumption 13315 Literal occ. after subsump. 27109 Selectable clauses 197 Decide: Splits 1 Unit assignments 191 Failed paths 2 Memory: Memory malloced 261 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 95 --- Applying isomorphism constraints to constants: d c b a. 27563 clauses were generated; 22814 of those survived the first stage of unit preprocessing; there are 9407 atoms. After all unit preprocessing, 286 atoms are still unassigned; 13599 clauses remain; 199 of those are non-Horn (selectable); 5149 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 95 ---- Input: Clauses input 22814 Literal occurrences input 36991 Greatest atom 9407 Unit preprocess: Preprocess unit assignments 9121 Clauses after subsumption 13599 Literal occ. after subsump. 27682 Selectable clauses 199 Decide: Splits 1 Unit assignments 193 Failed paths 2 Memory: Memory malloced 267 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 96 --- Applying isomorphism constraints to constants: d c b a. 28141 clauses were generated; 23294 of those survived the first stage of unit preprocessing; there are 9602 atoms. After all unit preprocessing, 289 atoms are still unassigned; 13886 clauses remain; 201 of those are non-Horn (selectable); 5154 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 96 ---- Input: Clauses input 23294 Literal occurrences input 37764 Greatest atom 9602 Unit preprocess: Preprocess unit assignments 9313 Clauses after subsumption 13886 Literal occ. after subsump. 28261 Selectable clauses 201 Decide: Splits 1 Unit assignments 195 Failed paths 2 Memory: Memory malloced 272 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 97 --- Applying isomorphism constraints to constants: d c b a. 28725 clauses were generated; 23779 of those survived the first stage of unit preprocessing; there are 9799 atoms. After all unit preprocessing, 292 atoms are still unassigned; 14176 clauses remain; 203 of those are non-Horn (selectable); 5160 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 97 ---- Input: Clauses input 23779 Literal occurrences input 38545 Greatest atom 9799 Unit preprocess: Preprocess unit assignments 9507 Clauses after subsumption 14176 Literal occ. after subsump. 28846 Selectable clauses 203 Decide: Splits 1 Unit assignments 197 Failed paths 2 Memory: Memory malloced 278 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 98 --- Applying isomorphism constraints to constants: d c b a. 29315 clauses were generated; 24269 of those survived the first stage of unit preprocessing; there are 9998 atoms. After all unit preprocessing, 295 atoms are still unassigned; 14469 clauses remain; 205 of those are non-Horn (selectable); 5165 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 98 ---- Input: Clauses input 24269 Literal occurrences input 39334 Greatest atom 9998 Unit preprocess: Preprocess unit assignments 9703 Clauses after subsumption 14469 Literal occ. after subsump. 29437 Selectable clauses 205 Decide: Splits 1 Unit assignments 199 Failed paths 2 Memory: Memory malloced 283 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 99 --- Applying isomorphism constraints to constants: d c b a. 29911 clauses were generated; 24764 of those survived the first stage of unit preprocessing; there are 10199 atoms. After all unit preprocessing, 298 atoms are still unassigned; 14765 clauses remain; 207 of those are non-Horn (selectable); 5171 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 99 ---- Input: Clauses input 24764 Literal occurrences input 40131 Greatest atom 10199 Unit preprocess: Preprocess unit assignments 9901 Clauses after subsumption 14765 Literal occ. after subsump. 30034 Selectable clauses 207 Decide: Splits 1 Unit assignments 201 Failed paths 2 Memory: Memory malloced 289 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 100 --- Applying isomorphism constraints to constants: d c b a. 30513 clauses were generated; 25264 of those survived the first stage of unit preprocessing; there are 10402 atoms. After all unit preprocessing, 301 atoms are still unassigned; 15064 clauses remain; 209 of those are non-Horn (selectable); 5177 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 100 ---- Input: Clauses input 25264 Literal occurrences input 40936 Greatest atom 10402 Unit preprocess: Preprocess unit assignments 10101 Clauses after subsumption 15064 Literal occ. after subsump. 30637 Selectable clauses 209 Decide: Splits 1 Unit assignments 203 Failed paths 2 Memory: Memory malloced 295 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.45 (0 hr, 0 min, 0 sec) system CPU time 0.11 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) The search is complete. No models were found. The job finished Tue Jun 29 20:45:06 2004 otter-3.3f/mace2/Avail.h0100644000076400007640000000027507300011042014364 0ustar mccunemccune#ifndef TP_AVAIL_H #define TP_AVAIL_H /* function prototypes from avail.c */ void reinit_mem(void); void *MACE_tp_alloc(size_t n); int MACE_total_mem(void); #endif /* ! TP_AVAIL_H */ otter-3.3f/mace2/generate.c0100644000076400007640000011330210070420065015120 0ustar mccunemccune#include "Mace2.h" /* This file has all of the code for the first-order interface to * propositional model searching. */ /* TO DO: (This list is very OLD!!) * 1. When add units from assignments, also add neg units?? * 2. Move unit preprocessing to DP code?? * 3. Enumerated sorts. * 4. Allow assigned or enumerated constants in clauses. * 5. Otter input for sorted logic. */ #if 0 #define PRINT_CLAUSES /* print ground clauses that are sent to DP */ #endif /* Limits * WARNING: you can't simply change MAX_VARS or MAX_ARITY. */ #define MAX_MLITERALS MAX_DOMAIN /* per clause */ #define MAX_CLAUSES 1000 /* first-order clauses */ /******** Type declarations *********/ struct rel_lit { /* first_order literal */ int sign; /* 1 or -1 */ int functor; /* index into Symbols */ int a[MAX_ARITY]; /* args: vars are +, domain elements are -(e+100). */ char ai[MAX_ARITY][MAX_MNAME]; /* array of args in string form */ }; struct rel_clause { /* first_order clause */ int id; int num_lits; struct rel_lit lits[MAX_MLITERALS]; }; /***************************************************************/ /******* Global variables ***************/ extern int Greatest_atom; /* owned by dp.c */ struct sort Sorts[MAX_SORTS]; int Num_sorts; struct symbol Symbols[MAX_SYMBOLS]; int Next_base = 1; int Num_symbols; static int Clauses_generated; static int Clauses_inserted; static struct rel_clause Clauses[MAX_CLAUSES]; static int Num_rel_clauses; static int *Units; static int Unsatisfiable = 0; /* This flags an unsatisfiable set */ /************* * * sort_index() * *************/ static int sort_index(char *s) { int i; for (i = 0; i < Num_sorts; i++) if (str_ident(s, Sorts[i].name)) return(i); return(-1); } /* sort_index */ /************* * * declare_symbol_sorted() * *************/ static int declare_symbol_sorted(char *name, int arity, char at[][MAX_MNAME]) { int i, j, m; struct symbol *s; if (Num_symbols == MAX_SYMBOLS) MACE_abend("declare_symbol_sorted, too many symbols"); s = Symbols + Num_symbols; Num_symbols++; strcpy(s->name, name); s->arity = arity; s->base = Next_base; s->assigned_value = -1; for (i = 0; i < arity; i++) { j = sort_index(at[i]); if (j == -1) { printf("%s", at[i]); MACE_abend("declare_symbol_sorted: sort not found"); } s->args[i].sort = j; s->args[i].n = Sorts[j].n; } for (i = arity-1, m = 1; i >= 0; i--) { s->args[i].mult = m; m = m * s->args[i].n; } s->end = (s->base + m) - 1; Next_base += m; return(Num_symbols-1); } /* declare_symbol_sorted */ /************* * * str_to_id() * * Given the string form of a functor, return the ID (or -1 if not found). * *************/ static int str_to_id(char *name) { int i; for (i = 0; i < Num_symbols; i++) if (str_ident(name, Symbols[i].name)) return(i); return(-1); } /* str_to_id */ /************* * * decode_int() * * Given a propositional variable (an integer), find the atom that * it represents. This is the inverse of the ATOM macros. * This is used mostly for printing ground clauses in a readable way. * *************/ int decode_int(int atom, char **func, int *arity, int *args) { int i, c; struct symbol *s; if (atom >= Next_base || atom < 1) return(-1); for (i = 0; i < Num_symbols; i++) if (atom < Symbols[i].base) break; i--; s = Symbols+i; c = atom - s->base; *func = s->name; *arity = s->arity; switch (*arity) { case 1: args[0] = c; break; case 2: args[1] = c % s->args[1].n; c = c / s->args[1].n; args[0] = c; break; case 3: args[2] = c % s->args[2].n; c = c / s->args[2].n; args[1] = c % s->args[1].n; c = c / s->args[1].n; args[0] = c; break; case 4: args[3] = c % s->args[3].n; c = c / s->args[3].n; args[2] = c % s->args[2].n; c = c / s->args[2].n; args[1] = c % s->args[1].n; c = c / s->args[1].n; args[0] = c; break; } return(1); } /* decode_int */ /************* * * p_unit(u) * *************/ void p_unit(int u) { char *name, *sign; int arity, args[MAX_ARITY], j; sign = (u < 0 ? "-" : ""); decode_int(abs(u), &name, &arity, args); printf(" %s%s", sign, name); for (j=0; jnum_lits; i++) { int v, sign; sign = c->lits[i].sign; arity = Symbols[c->lits[i].functor].arity; printf("%s%s%s", sign==1?"":"-", Symbols[c->lits[i].functor].name, arity>0?"(":""); for (j = 0; j < arity; j++) { v = c->lits[i].a[j]; if (v >= 0) printf("v%d", v); /* variable */ else printf("%d", -(v+100)); /* element */ printf("%s", j == arity-1 ? ") " : ","); } } printf("\n"); fflush(stdout); } /* p_relational_clause */ /************* * * sort_clause() -- propositional clause, by atom. * *************/ static void sort_clause(int c[], int n) { int i, j, temp; for (i = 0; i < n-1; i++) for (j = i+1; j < n; j++) if (abs(c[j]) < abs(c[i])) { temp = c[i]; c[i] = c[j]; c[j] = temp; } } /* sort_clause */ /************* * * unit_subsumed() * * Is a given propositional clause subsumed by anything in the Units array? * *************/ static int unit_subsumed(int c[], int n) { int i, a, sign; for (i = 0; i < n; i++) { a = abs(c[i]); sign = (c[i] < 0) ? -1 : 1; if (Units[a] == sign) return(1); } return(0); } /* unit_subsumed */ /************* * * MACE_tautology() -- propositional; assume sorted by atom. * *************/ static int MACE_tautology(int c[], int n) { int i; for (i = 0; i < n-1; i++) if (c[i] == -c[i+1]) return(1); return(0); } /* MACE_tautology */ /************* * * merge_lits() -- propositional; assume sorted by atom. * *************/ static int merge_lits(int c[], int n) { int i, j, m; m = n; for (i = 0; i < m-1; i++) if (c[i] == c[i+1]) { for (j = i+1; j < m-1; j++) c[j] = c[j+1]; m--; i--; } return(m); } /* merge_lits */ /************* * * unit_delete() * * Given a propositional clause, do unit resolution with Units array. * This kind of clause is an array of ground literals. When a literal * is removed, literals to the right are shifted left. * Return the number of remaining literals. * *************/ static int unit_delete(int c[], int n) { int i, j, l, a, v, m; m = n; for (i = 0; i < m; i++) { l = c[i]; a = abs(l); v = Units[a]; if ((v == -1 && l > 0) || (v == 1 && l < 0)) { for (j = i; j < m-1; j++) c[j] = c[j+1]; m--; i--; } } return(m); } /* unit_delete */ /************* * * add_clause() * * Given a propositional clause, do some preprocessing, and if it * passes the tests, send it to insert_dp_clause(), which is part * of the interface to the DP procedure. * *************/ static void add_clause(int c[], int n) { Clauses_generated++; #ifdef PRINT_CLAUSES decode_and_p_clause(c,n); #endif n = unit_delete(c, n); if (n == 0) { printf("*** Unsatisfiability detected ***\n"); Unsatisfiable = 1; } else { sort_clause(c, n); if (!unit_subsumed(c, n) && !MACE_tautology(c, n)) { n = merge_lits(c, n); if (n == 1) Units[abs(c[0])] = c[0] < 0 ? -1 : 1; insert_dp_clause(c, n); Clauses_inserted++; } } } /* add_clause */ /************* * * add_2clause() * * Given 2 literals, make a 2-clause and send it to add_clause. * *************/ static void add_2clause(int a, int b) { int c[2]; c[0] = a; c[1] = b; add_clause(c, 2); } /* add_2clause */ /************* * * add_unit() * * Build a literal and send it to add_clause. * *************/ static void add_unit(int sign, struct symbol *s, int a0, int a1, int a2, int a3) { int c[1]; if (a0 >= s->args[0].n || a1 >= s->args[1].n || a2 >= s->args[2].n || a3 >= s->args[3].n) MACE_abend("add_unit: element out of domain"); if (abs(sign) != 1) MACE_abend("add_unit: sign must be 1 or -1"); #if 0 printf("add_unit: %s%s %d %d %d %d.\n", sign==1?"":"-", Symbols[functor].name, a0, a1, a2, a3); #endif switch(s->arity) { case 0: c[0] = sign * ATOM0(s); break; case 1: c[0] = sign * ATOM1(s, a0); break; case 2: c[0] = sign * ATOM2(s, a0, a1); break; case 3: c[0] = sign * ATOM3(s, a0, a1, a2); break; case 4: c[0] = sign * ATOM4(s, a0, a1, a2, a3); break; } add_clause(c, 1); } /* add_unit */ /* * The following set of routines assert various properties of functions. * Recall that an n-ary function is handled as an (n+1)-ary relation, * so we have to say that the function is well-defined and closed. * Similar routines can be used to assert that functions are 1-1, onto, * cancellative, etc. */ /************* * * well_defined_0() - constant cannot have 2 values. * *************/ static void well_defined_0(struct symbol *s) { int y, z; int n0 = s->args[0].n; /* -By | -Bz, for y < z */ for (y = 0; y < n0; y++) for (z = y+1; z < n0; z++) add_2clause( - ATOM1(s,y), - ATOM1(s,z)); } /* well_defined_0 */ /************* * * well_defined_1() * *************/ static void well_defined_1(struct symbol *s) { int x, y, z; int n0 = s->args[0].n; int n1 = s->args[1].n; /* -Bxy | -Bxz, for y < z */ for (x = 0; x < n0; x++) for (y = 0; y < n1; y++) for (z = y+1; z < n1; z++) add_2clause( - ATOM2(s,x,y), - ATOM2(s,x,z)); } /* well_defined_1 */ /************* * * well_defined_2() * *************/ static void well_defined_2(struct symbol *s) { int u, x, y, z; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; /* -Buxy | -Buxz, for y < z */ for (u = 0; u < n0; u++) for (x = 0; x < n1; x++) for (y = 0; y < n2; y++) for (z = y+1; z < n2; z++) add_2clause( - ATOM3(s,u,x,y), - ATOM3(s,u,x,z)); } /* well_defined_2 */ /************* * * well_defined_3() * *************/ static void well_defined_3(struct symbol *s) { int v, u, x, y, z; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; int n3 = s->args[3].n; /* -Bvuxy | -Bvuxz, for y < z */ for (v = 0; v < n0; v++) for (u = 0; u < n1; u++) for (x = 0; x < n2; x++) for (y = 0; y < n3; y++) for (z = y+1; z < n3; z++) add_2clause( - ATOM4(s,v,u,x,y), - ATOM4(s,v,u,x,z)); } /* well_defined_3 */ /************* * * closed_0() - value of constant is one of the domain elements. * *************/ static void closed_0(struct symbol *s) { int x, c[MAX_MLITERALS]; int n0 = s->args[0].n; /* B0 | B1 | .. | Bn-1 */ for (x = 0; x < n0; x++) c[x] = ATOM1(s,x); add_clause(c, n0); } /* closed_0 */ /************* * * closed_1() * *************/ static void closed_1(struct symbol *s) { int x, y, c[MAX_MLITERALS]; int n0 = s->args[0].n; int n1 = s->args[1].n; /* Bx0 | Bx1 | .. | Bxn-1, 0<=x<=n-1 */ for (x = 0; x < n0; x++) { for (y = 0; y < n1; y++) c[y] = ATOM2(s,x,y); add_clause(c, n1); } } /* closed_1 */ /************* * * closed_2() * *************/ static void closed_2(struct symbol *s) { int x, y, z, c[MAX_MLITERALS]; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; /* Bxy0 | Bxy1 | .. | Bxyn-1, 0<=x<=n-1, 0<=y<=n-1 */ for (x = 0; x < n0; x++) for (y = 0; y < n1; y++) { for (z = 0; z < n2; z++) c[z] = ATOM3(s,x,y,z); add_clause(c, n2); } } /* closed_2 */ /************* * * closed_3() * *************/ static void closed_3(struct symbol *s) { int x, y, z, u, c[MAX_MLITERALS]; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; int n3 = s->args[3].n; /* Bxyz0 | Bxyz1 | .. | Bxyzn-1, 0<=x<=n-1, 0<=y<=n-1, 0<=z<=n-1 */ for (x = 0; x < n0; x++) for (y = 0; y < n1; y++) for (z = 0; z < n2; z++) { for (u = 0; u < n3; u++) c[u] = ATOM4(s,x,y,z,u); add_clause(c, n3); } } /* closed_3 */ /************* * * well_defined() * *************/ static void well_defined(struct symbol *s) { switch(s->arity) { case 1: well_defined_0(s); break; case 2: well_defined_1(s); break; case 3: well_defined_2(s); break; case 4: well_defined_3(s); break; default: MACE_abend("well_defined, bad arity"); } } /* well_defined */ /************* * * closed() * *************/ static void closed(struct symbol *s) { switch(s->arity) { case 1: closed_0(s); break; case 2: closed_1(s); break; case 3: closed_2(s); break; case 4: closed_3(s); break; default: MACE_abend("closed, bad arity"); } } /* closed */ /************* * * one_one() * *************/ static void one_one(struct symbol *s) { int x, y, z; int n0 = s->args[0].n; int n1 = s->args[1].n; /* -Bxy | -Bzy, x < z */ for (y = 0; y < n1; y++) for (x = 0; x < n0; x++) for (z = x+1; z < n0; z++) add_2clause( - ATOM2(s,x,y), - ATOM2(s,z,y)); } /* one_one */ /************* * * onto() * *************/ static void onto(struct symbol *s) { int x, y, c[MAX_MLITERALS]; int n0 = s->args[0].n; int n1 = s->args[1].n; /* B0x | B1x | .. | Bn-1x, 0<=x<=n-1 */ for (x = 0; x < n1; x++) { for (y = 0; y < n0; y++) c[y] = ATOM2(s,y,x); add_clause(c, n1); } } /* onto */ /************* * * left_cancel() * *************/ static void left_cancel(struct symbol *s) { int u, x, y, z; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; /* -Buyx | -Buzx, for y < z */ for (u = 0; u < n0; u++) for (x = 0; x < n2; x++) for (y = 0; y < n1; y++) for (z = y+1; z < n1; z++) add_2clause( - ATOM3(s,u,y,x), - ATOM3(s,u,z,x)); } /* left_cancel */ /************* * * right_cancel() * *************/ static void right_cancel(struct symbol *s) { int u, x, y, z; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; /* -Byux | -Bzux, for y < z */ for (u = 0; u < n1; u++) for (x = 0; x < n2; x++) for (y = 0; y < n0; y++) for (z = y+1; z < n0; z++) add_2clause( - ATOM3(s,y,u,x), - ATOM3(s,z,u,x)); } /* right_cancel */ /************* * * left_onto() * *************/ static void left_onto(struct symbol *s) { int x, y, z, c[MAX_MLITERALS]; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; /* Bx0y | Bx1y | .. | Bxn-1y, 0<=x<=n-1, 0<=y<=n-1 */ for (x = 0; x < n0; x++) for (y = 0; y < n2; y++) { for (z = 0; z < n1; z++) c[z] = ATOM3(s,x,z,y); add_clause(c, n1); } } /* left_onto */ /************* * * right_onto() * *************/ static void right_onto(struct symbol *s) { int x, y, z, c[MAX_MLITERALS]; int n0 = s->args[0].n; int n1 = s->args[1].n; int n2 = s->args[2].n; /* B0xy | B1xy | .. | Bn-1xy, 0<=x<=n-1, 0<=y<=n-1 */ for (x = 0; x < n1; x++) for (y = 0; y < n2; y++) { for (z = 0; z < n0; z++) c[z] = ATOM3(s,z,x,y); add_clause(c, n0); } } /* right_onto */ /************* * * process_variables() * * Check that all occurrences of each variable are in a position of the * same sort, collect the domain sizes of the variables into an array, * and return the biggest variable. * *************/ static int process_variables(struct rel_lit *lits, int num_lits, int domains[]) { int i, j, biggest_var, v; struct symbol *s; for (i = 0; i < MAX_MVARS; i++) domains[i] = -1; biggest_var = -1; for (i = 0; i < num_lits; i++) { s = Symbols + lits[i].functor; for (j = 0; j < s->arity; j++) { v = lits[i].a[j]; if (v >= 0) { if (v > biggest_var) { if (v >= MAX_MVARS) MACE_abend("process_variables, variable too big."); biggest_var = v; } if (domains[v] == -1) domains[v] = s->args[j].sort; else if (domains[v] != s->args[j].sort) MACE_abend("process_variables, badly sorted clause"); } } } /* Now replace sort indexes with sort sizes. */ for (i = 0; i <= biggest_var; i++) domains[i] = Sorts[domains[i]].n; return(biggest_var); } /* process_variables */ /************* * * generate_prop_clauses() * * Given a flattened general clause, generate the corresponding * ground clauses over the domain and send them to add_clause. * * Note that limits on the arity and on the number of variables * are wired into the code. * *************/ static void generate_prop_clauses(struct rel_clause *c) { int v0, v0_lim, v1, v1_lim, v2, v2_lim, v3, v3_lim, v4, v4_lim, v5, v5_lim; int v6, v6_lim, v7, v7_lim, v8, v8_lim, v9, v9_lim, v10, v10_lim, v11, v11_lim; int biggest_var, val[MAX_MVARS], i, sign, domains[MAX_MVARS]; int a0, a1, a2, a3; int prop_clause[MAX_MLITERALS]; struct symbol *s; struct rel_lit *lits = c->lits; int num_lits = c->num_lits; a0 = a1 = a2 = a3 = 0; biggest_var = process_variables(lits, num_lits, domains); #ifdef PRINT_CLAUSES printf(" biggest_var=%d: ", biggest_var); p_relational_clause(c); #endif /* Now domains[] has the domain sizes for all the variables. * Fill in the remaining slots with 1 so that the nested loops * below work correctly. */ for (i = biggest_var+1; i < MAX_MVARS; i++) domains[i] = 1; v0_lim = domains[0]; v1_lim = domains[1]; v2_lim = domains[2]; v3_lim = domains[3]; v4_lim = domains[4]; v5_lim = domains[5]; v6_lim = domains[6]; v7_lim = domains[7]; v8_lim = domains[8]; v9_lim = domains[9]; v10_lim = domains[10]; v11_lim = domains[11]; /* Check the time limit somewhere in here. It can be expensive, especially on solaris, so do do it too often. */ for (v0 = 0; v0 < v0_lim; v0++) { val[0] = v0; for (v1 = 0; v1 < v1_lim; v1++) { val[1] = v1; for (v2 = 0; v2 < v2_lim; v2++) { val[2] = v2; exit_if_over_time_limit(); for (v3 = 0; v3 < v3_lim; v3++) { val[3] = v3; for (v4 = 0; v4 < v4_lim; v4++) { val[4] = v4; for (v5 = 0; v5 < v5_lim; v5++) { val[5] = v5; for (v6 = 0; v6 < v6_lim; v6++) { val[6] = v6; for (v7 = 0; v7 < v7_lim; v7++) { val[7] = v7; for (v8 = 0; v8 < v8_lim; v8++) { val[8] = v8; for (v9 = 0; v9 < v9_lim; v9++) { val[9] = v9; for (v10 = 0; v10 < v10_lim; v10++) { val[10] = v10; for (v11 = 0; v11 < v11_lim; v11++) { val[11] = v11; for (i = 0; i < num_lits; i++) { s = Symbols + lits[i].functor; switch (s->arity) { /* note no breaks */ case 4: a3 = lits[i].a[3]; a3 = (a3 < 0 ? -(a3+100) : val[a3]); case 3: a2 = lits[i].a[2]; a2 = (a2 < 0 ? -(a2+100) : val[a2]); case 2: a1 = lits[i].a[1]; a1 = (a1 < 0 ? -(a1+100) : val[a1]); case 1: a0 = lits[i].a[0]; a0 = (a0 < 0 ? -(a0+100) : val[a0]); } #if 0 if (num_lits > 2 && a0 < a1 && TP_BIT(s->properties, MACE_COMMUTATIVE_BIT)) { int tmp = a0; a0 = a1; a1 = tmp; } #endif sign = lits[i].sign; switch (s->arity) { case 0: prop_clause[i] = sign * ATOM0(s); break; case 1: prop_clause[i] = sign * ATOM1(s,a0); break; case 2: prop_clause[i] = sign * ATOM2(s,a0,a1); break; case 3: prop_clause[i] = sign * ATOM3(s,a0,a1,a2); break; case 4: prop_clause[i] = sign * ATOM4(s,a0,a1,a2,a3); break; } } /* decode_and_p_clause(prop_clause, num_lits); */ add_clause(prop_clause, num_lits); }}}}}}}}}}}} } /* generate_prop_clauses */ /************* * * add_clauses_for_qg_constraint() * *************/ static void add_clauses_for_qg_constraint(void) { int i, k, id, n; struct symbol *s; n = Sorts[0].n; /* quasigroup constraint: x*n != z, when z < x-1. */ id = str_to_id("f"); if (id == -1) abend("add_clauses_for_qg_constraint, symbol f not found"); s = Symbols+id; printf("Adding basic QG constraints on last column of f.\n"); for (i = 0; i < n; i++) { for (k = 0; k < i-1; k++) { add_unit(-1, s, i, n-1, k, -1); } } } /* add_clauses_for_qg_constraint */ /************* * * number_variables() * * Given a first-order (flat) clause with string arguments * (vars and domain elements), assign vars positive ints, * and domain elements negative ints. * * Return the maximum domain element seen (-1 if none). * *************/ static int number_variables(struct rel_clause *c) { char *vnames[MAX_MVARS], *s; int i, j, k, arity, el; int max_element = -1; for (i = 0; i < MAX_MVARS; i++) vnames[i] = NULL; for (i = 0; i < c->num_lits; i++) { arity = Symbols[c->lits[i].functor].arity; for (j = 0; j < arity; j++) { s = c->lits[i].ai[j]; if (str_int(s, &el)) { /* Domain element */ if (el < 0 || el >= Symbols[c->lits[i].functor].args[j].n) { printf("\nThe bad element is %d.\n", el); MACE_abend("number_variables, element out of range"); } c->lits[i].a[j] = -(el+100); if (el > max_element) max_element = el; } else { /* Variable */ for (k = 0; k < MAX_MVARS && vnames[k] && !str_ident(s,vnames[k]); k++); if (k == MAX_MVARS) { printf("\nMaximum number of variables is %d.\n", MAX_MVARS); MACE_abend("number_variables, too many variables"); } else { c->lits[i].a[j] = k; if (vnames[k] == NULL) vnames[k] = s; } } } } return(max_element); } /* number_variables */ /************* * * trans_relational_clause() * *************/ static int trans_relational_clause(struct clause *cin) { struct literal *lit; struct rel_clause *c; struct rel_lit *l; int i, j, arity, fid; char *functor; struct symbol *s = NULL; int max_element; /* printf("translating: "); p_clause(cin); */ if (Num_rel_clauses == MAX_CLAUSES) MACE_abend("trans_relational_clause: too many first_order clauses"); c = Clauses + Num_rel_clauses; Num_rel_clauses++; j = 0; /* literal number */ for (lit = cin->first_lit; lit; lit = lit->next_lit) { struct term *a = lit->atom; struct rel *r; l = c->lits + j; l->sign = (lit->sign ? 1 : -1); if (is_eq(a->sym_num) && a->farg->argval->type != VARIABLE && !domain_element(a->farg->argval)) { /* f(t1,...,tn) = t4 */ functor = sn_to_str(a->farg->argval->sym_num); i = 0; /* Do the args of the function symbol. */ for (r = a->farg->argval->farg; r; r = r->narg) { if (r->argval->type == VARIABLE) sprintf(l->ai[i], "v%d", r->argval->varnum); else if (r->argval->type == NAME) sprintf(l->ai[i], "%s", sn_to_str(r->argval->sym_num)); else MACE_abend("trans_relational_clause: bad DP arg"); i++; } /* Do the right-hand arg. */ if (a->farg->narg->argval->type == VARIABLE) sprintf(l->ai[i], "v%d", a->farg->narg->argval->varnum); else if (a->farg->narg->argval->type == NAME) sprintf(l->ai[i], "%s", sn_to_str(a->farg->narg->argval->sym_num)); else MACE_abend("trans_relational_clause: bad DP arg (right)"); } else { /* t1 = t2 or p(t1,...,tn) */ functor = sn_to_str(a->sym_num); i = 0; for (r = a->farg; r; r = r->narg) { if (r->argval->type == VARIABLE) sprintf(l->ai[i], "v%d", r->argval->varnum); else if (domain_element(r->argval)) sprintf(l->ai[i], "%s", sn_to_str(r->argval->sym_num)); else MACE_abend("trans_relational_clause: bad eq arg"); i++; } } fid = str_to_id(functor); if (fid == -1) { printf("Bad name=%s\n", functor); MACE_abend("trans_relational_clause, bad functor"); } s = Symbols + fid; arity = s->arity; l->functor = fid; j++; /* move to next literal */ } c->num_lits = j; max_element = number_variables(c); #ifdef PRINT_CLAUSES p_relational_clause(c); #endif return(max_element); } /* trans_relational_clause */ /************* * * remove_ans_literals() * *************/ static void remove_ans_literals(struct list *lst) { struct clause *c; for (c = Usable->first_cl; c; c = c->next_cl) { if (num_answers(c) > 0) { struct literal *lit, *prev; printf("Removing answer literals from clause %d.\n", c->id); for (lit=c->first_lit, prev=NULL; lit; prev=lit, lit=lit->next_lit) { if (answer_lit(lit)) { if (prev == NULL) c->first_lit = lit->next_lit; else prev->next_lit = lit->next_lit; /* don't bother to deallocate lit */ } } } } } /* remove_ans_literals */ /************* * * read_all_mace_input() * * This is like Otter's read_all_input(), except that it * doesn't do the processining (in particular process_input) * after read_a_file(). * *************/ void read_all_mace_input(int argc, char **argv) { Usable = get_list(); Sos = get_list(); Demodulators = get_list(); Passive = get_list(); Hot = get_list(); Hints = get_list(); Hints2 = get_list(); Mace_constraints = get_list(); CLOCK_START(INPUT_TIME); read_a_file(stdin, stdout); /* Otter's routine */ /* Move Sos, Demodulators, and Passive into Usable */ append_lists(Usable,Sos); append_lists(Usable,Demodulators); append_lists(Usable,Passive); if (Flags[PROCESS_INPUT].val) { /* Integrate clauses so that they get IDs. */ struct clause *c; for (c = Usable->first_cl; c; c = c->next_cl) cl_integrate(c); printf("\nlist(clauses).\n"); print_cl_list(stdout, Usable); } remove_ans_literals(Usable); CLOCK_STOP(INPUT_TIME); fflush(stdout); } /* read_all_mace_input */ /************* * * MACE_collect_symbols() * *************/ static void MACE_collect_symbols(struct term *t, int type) { if (t->type == VARIABLE || domain_element(t)) return; else { char *name = sn_to_str(t->sym_num); int arity = sn_to_arity(t->sym_num) + (type == FUNCTION ? 1 : 0); int id = str_to_id(name); struct rel *r; if (id != -1) { /* We have already collected the symbol. */ struct symbol *s = Symbols + id; if (s->arity != arity) abend("MACE_collect_symbols, multiple arity"); } else { /* New symbol. */ int j; char arg_types[MAX_ARITY][MAX_MNAME]; struct symbol *s; if (arity > MAX_ARITY) MACE_abend("arity too great"); for (j = 0; j < arity; j++) strcpy(arg_types[j], "univ"); id = declare_symbol_sorted(name, arity, arg_types); s = Symbols + id; s->type = type; /* FUNCTION or RELATION */ if (type == RELATION) { if (is_eq(t->sym_num)) SET_BIT(s->properties, MACE_EQ_BIT); else if (t->sym_num == str_to_sn("<", 2)) SET_BIT(s->properties, MACE_ORDER_BIT); } } for (r = t->farg; r; r = r->narg) MACE_collect_symbols(r->argval, FUNCTION); } } /* MACE_collect_symbols */ /************* * * iso_constants_recurse() * *************/ static void iso_constants_recurse(struct symbol **c, /* constants */ int clause[], /* for building clauses */ int lits, /* current # of lits */ int tempclause[], int max_element, /* max on current path */ int domain_size) /* For 3 constants, e a b: * e0 * -e0 a0 a1 * -e0 -a0 b0 b1 * -e0 -a1 b0 b1 b2 */ { if (*c == NULL) return; else if (max_element + 2 >= domain_size) return; else { int i, j, n; n = lits; for (i = 0; i <= max_element+1; i++) clause[n++] = ATOM1((*c), i); #if 0 printf(">>>> "); decode_and_p_clause(clause,n); #endif for (j = 0; j < n; j++) tempclause[j] = clause[j]; add_clause(tempclause, n); for (i = 0; i <= max_element+1; i++) { clause[lits] = - ATOM1((*c), i); iso_constants_recurse(c+1,clause,lits+1,tempclause, MAX(max_element,i), domain_size); } } } /* iso_constants_recurse */ /************* * * iso_constants() * *************/ static void iso_constants(int domain_size, int max_element) { int id; int num_constants = 0; struct symbol *s, *constants[MAX_SYMBOLS]; int clause[MAX_SYMBOLS]; int tempclause[MAX_SYMBOLS]; /* because add_clause changes the clause! */ for (id = 0; id < Num_symbols; id++) { s = Symbols + id; if (s->type == FUNCTION && s->arity == 1 && s->assigned_value == -1) { constants[num_constants++] = s; } } num_constants = MIN(num_constants, MACE_Parms[ISO_CONSTANTS].val); constants[num_constants] = NULL; if (num_constants > 0) { int i, n; printf("Applying isomorphism constraints to constants:"); fflush(stdout); for (i = 0; i < num_constants; i++) { printf(" %s", constants[i]->name); } printf(".\n"); fflush(stdout); n = MACE_Stats[INPUT_CLAUSES]; iso_constants_recurse(constants, clause, 0, tempclause, max_element, domain_size); } } /* iso_constants */ /************* * * dp_trans() * * This is copied from Otter's dp_transform(), then modified. * Instead of writing symbols, transformed clauses, and assignments to * a file, it puts that data directly into the MACE data structures. * * If unsatisfiability is detected, return 0; else return 1. * *************/ int dp_trans(int domain_size, int distinct_constants, int qg_constraint) { struct clause *c, *d; struct term *a; struct rel *r; struct literal *lit; int i, k; int max_theory_element = -1; /* in ordinary clauses */ int max_constrained_element = -1; /* in mace_constraints */ int id; strcpy(Sorts[0].name, "univ"); Sorts[0].n = domain_size; Num_sorts = 1; Parms[STATS_LEVEL].val = 0; /* Go through all of the clauses, collecting names/arities of all the symbols (function, relation, constant). */ for (c = Usable->first_cl; c; c = c->next_cl) { for (lit = c->first_lit; lit; lit = lit->next_lit) { MACE_collect_symbols(lit->atom, RELATION); } } /* Get additional constraints from the Mace_constraints list. */ for (c = Mace_constraints->first_cl; c; c = c->next_cl) { int id; struct symbol *s; a = c->first_lit->atom; if (sn_to_arity(a->sym_num) != 2) MACE_abend("dp_trans, wrong arity in mace_constraints list."); id = str_to_id(sn_to_str(a->farg->argval->sym_num)); if (id == -1) MACE_abend("dp_trans, symbol in mace_constraints list not found"); s = Symbols + id; if (is_symbol(a, "property", 2)) { char *prop = sn_to_str(a->farg->narg->argval->sym_num); if (str_ident(prop, "equality")) SET_BIT(s->properties, MACE_EQ_BIT); else if (str_ident(prop, "order")) SET_BIT(s->properties, MACE_ORDER_BIT); else if (str_ident(prop, "quasigroup")) SET_BIT(s->properties, MACE_QUASIGROUP_BIT); else if (str_ident(prop, "bijection")) SET_BIT(s->properties, MACE_BIJECTION_BIT); else if (str_ident(prop, "commutative")) SET_BIT(s->properties, MACE_COMMUTATIVE_BIT); else MACE_abend("dp_trans, mace_constrationts property not understood"); } else if (!is_symbol(a, "assign", 2)) /* handle assigns below */ MACE_abend("dp_trans, mace_constraints command not understood"); } #if 0 /* Print data for each symbol. */ for (i = 0; i < Num_symbols; i++) { struct symbol *s = Symbols + i; printf("Symbol %2d, %s, %6s/%d, ", i, (s->type == FUNCTION ? "function" : "relation"), s->name, s->arity); printf("atoms %4d --%4d, %10d.\n", s->base, s->end, s->properties); } #endif /* Now we know how many atoms there are (determined by symbols/arities and domain-size). So let's set up the Units array, which is used for storing assignments to atoms. */ Greatest_atom = Next_base-1; i = Greatest_atom + 1; Units = malloc(i * sizeof(int)); MACE_Stats[MEM_MALLOCED] += i; for (i = 1; i <= Greatest_atom; i++) Units[i] = 0; /*****************************************************************/ /* Go through the clauses, making them into relational clauses, and storing the flat clauses on a stack (Clauses). */ for (c = Usable->first_cl; c; c = c->next_cl) { i = trans_relational_clause(c); if (i > max_theory_element) max_theory_element = i; } /* process Mace_constraints */ for (c = Mace_constraints->first_cl; c; c = c->next_cl) { a = c->first_lit->atom; if (is_symbol(a, "assign", 2)) { int arity; /* includes extra arg for functions */ struct symbol *s; int sign; /* -1 for negative, +1 for positive */ int relation; int arg[MAX_ARITY]; char *str, *functor; int func_val; int id; functor = sn_to_str(a->farg->argval->sym_num); id = str_to_id(functor); if (id == -1) { printf("Bad name=%s, \n", functor); MACE_abend("dp_trans, bad functor"); } s = Symbols + id; arity = s->arity; for (i = 0; i < MAX_ARITY; i++) arg[i] = -1; relation = (s->type == RELATION); if (!relation) { if (!str_int(sn_to_str(a->farg->narg->argval->sym_num), &func_val)) abend("dp_trans, bad integer (RHS) in assignment"); arg[arity-1] = func_val; sign = 1; } else { str = sn_to_str(a->farg->narg->argval->sym_num); if (!str_ident(str, "T") && !str_ident(str, "F")) abend("dp_trans, bad truth value in assignment"); sign = str_ident(str, "F") ? -1 : 1; } i = 0; for (r = a->farg->argval->farg; r; r = r->narg) { if (!str_int(sn_to_str(r->argval->sym_num), &k)) abend("dp_trans, bad integer (LHS) in assignment"); arg[i++] = k; } printf("Adding unit assigning %s%s", sign == -1 ? "-" : "", functor); for (i = 0; i < s->arity; i++) printf(" %d", arg[i]); printf("\n"); add_unit(sign, s, arg[0], arg[1], arg[2], arg[3]); if (Unsatisfiable) return 0; if (!relation && s->arity == 1) { s->assigned_value = arg[0]; if (arg[0] > max_constrained_element) max_constrained_element = arg[0]; } } } /* printf("\n%% =======END OF DP INPUT=======.\n"); */ if (!distinct_constants) { iso_constants(domain_size, max_theory_element); } else { struct symbol *s; int n = max_theory_element; for (id = 0; id < Num_symbols; id++) { s = Symbols + id; if (s->type == FUNCTION && s->arity == 1 && s->assigned_value == -1) { n++; if (n >= domain_size) printf("Cannot make constant %s distinct, domain is too small.\n", s->name); else { printf("Adding unit assigning %s %d (distinct_constants).\n", s->name, n); add_unit(1, s, n, -1, -1, -1); if (Unsatisfiable) return 0; } } } } /* distinct_constants */ /* Unit assignments for order, equality relations, if present. */ for (id = 0; id < Num_symbols; id++) { struct symbol *s = NULL; s = Symbols + id; if (s->type == RELATION && s->arity == 2) { if (TP_BIT(s->properties, MACE_ORDER_BIT)) { int n, j; if (s->args[0].sort != s->args[1].sort) MACE_abend("order relation must have args of same type"); n = s->args[0].n; #if 0 printf("Adding units for order relation %s.\n", s->name); #endif for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { if (i < j) add_unit(1, s, i, j, -1, -1); else add_unit(-1, s, i, j, -1, -1); } } } else if (TP_BIT(s->properties, MACE_EQ_BIT)) { int n, j; if (s->args[0].sort != s->args[1].sort) MACE_abend("equality relation must have args of same type"); n = s->args[0].n; #if 0 printf("Adding units for equality relation %s.\n", s->name); #endif for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { if (i == j) add_unit(1, s, i, j, -1, -1); else add_unit(-1, s, i, j, -1, -1); } } } } if (Unsatisfiable) return 0; } /* */ if (qg_constraint) add_clauses_for_qg_constraint(); if (Unsatisfiable) return 0; /* When processing generated clauses, forward unit subsumption and * forward unit deletion are applied, but the backward operations are not. * So to save memory, it's best to carefully order the generation of * clauses. Because of unit-deletion, it's not clear which way is best. */ for (i = 0; i < Num_rel_clauses; i++) { struct rel_clause *c = Clauses + i; if (c->num_lits <= 2) { #if 0 printf("Instantiating clause: "); p_relational_clause(c); #endif generate_prop_clauses(c); exit_if_over_time_limit(); if (Unsatisfiable) return 0; } } /* Well-defined, closed, quasigroup, bijection. */ for (i = 0; i < Num_symbols; i++) { struct symbol *s = Symbols + i; if (s->type == FUNCTION) { #if 0 printf("Function %s well-defined and closed.\n", s->name); #endif well_defined(s); closed(s); if (s->arity == 2 && TP_BIT(s->properties, MACE_BIJECTION_BIT)) { printf("function %s bijection.\n", s->name); one_one(s); onto(s); } else if (s->arity == 3 && TP_BIT(s->properties, MACE_QUASIGROUP_BIT)) { printf("function %s quasigroup.\n", s->name); left_cancel(s); right_cancel(s); left_onto(s); right_onto(s); } } if (Unsatisfiable) return 0; } for (i = 0; i < Num_rel_clauses; i++) { struct rel_clause *c = Clauses + i; if (c->num_lits > 2) { #if 0 printf("Instantiating clause: "); p_relational_clause(c); #endif generate_prop_clauses(c); exit_if_over_time_limit(); if (Unsatisfiable) return 0; } } printf("\n%d clauses were generated; %d of those survived the first stage\n" "of unit preprocessing; there are %d atoms.\n", Clauses_generated, Clauses_inserted, Greatest_atom); fflush(stdout); return 1; /* Unsatisfiability not detected */ } /* dp_trans */ /************* * * reinit_generate * * Free memory and reinitialize global variables in this file. * *************/ void reinit_generate(void) { free(Units); Num_sorts = 0; Next_base = 1; Num_symbols = 0; Clauses_generated = 0; Clauses_inserted = 0; Num_rel_clauses = 0; Units = NULL; Unsatisfiable = 0; } /* reinit_generate */ otter-3.3f/mace2/Stats.h0100644000076400007640000000224507300053730014437 0ustar mccunemccune#ifndef TP_STATS_H #define TP_STATS_H /************* * * Statistics. To install a new statistic, append a new name and * index to this list, then insert the code to output it in the * routine `MACE_print_stats'. * Example access: MACE_Stats[INPUT_ERRORS]++; * *************/ #define MACE_MAX_STATS 40 /* increase if necessary */ #define FAILED_PATHS 3 #define UNIT_ASSIGNS 4 #define SPLITS 5 #define PREPROCESS_UNIT_ASSIGNS 6 #define CLAUSES_AFTER_SUB 7 #define INPUT_CLAUSES 8 #define GREATEST_ATOM 9 #define LIT_OCC_INPUT 10 #define LIT_OCC_AFTER_SUB 11 #define MEM_MALLOCED 12 #define SELECTABLE_CLAUSES 13 /* end of MACE_Stats */ #define MAX_INTERNAL_FLAGS 10 extern long MACE_Stats[MACE_MAX_STATS]; extern int Internal_flags[MAX_INTERNAL_FLAGS]; /* function prototypes from stats.c */ void init_stats(); void MACE_print_mem(FILE *fp); void p_mem(void); void MACE_print_stats(FILE *fp); void MACE_p_stats(void); void MACE_print_times(FILE *fp); void MACE_p_times(void); void MACE_output_stats(FILE *fp); #endif /* ! TP_STATS_H */ otter-3.3f/mace2/avail.c0100644000076400007640000000505107714207010014427 0ustar mccunemccune#include "Mace2.h" /* for MACE_Parms[], MACE_abend(). */ #define TP_ALLOC_SIZE 5000000 /* Size of blocks allocated by malloc */ static char *Alloc_block; /* location returned by most recent malloc */ static char *Alloc_pos; /* current position in block */ static int Malloc_calls; /* number of calls to malloc */ static int Free_calls; /* number of calls to free */ /* Maintain a list of pointers to the malloced chunks so they can be freed. */ static Gen_ptr_ptr Chunks; /************* * * add_chunk -- to the front of Chunks * *************/ static void add_chunk(char *p) { Gen_ptr_ptr new = malloc(sizeof(struct gen_ptr)); new->u.v = p; new->next = Chunks; Chunks = new; } /* add_chunk */ /************* * * free_chunks * *************/ static void free_chunks(Gen_ptr_ptr p) { if (p != NULL) { free_chunks(p->next); /* free the tail */ free(p->u.v); /* free the chunk */ Free_calls++; free(p); /* free this node */ } } /* free_chunks */ /************* * * reinit_mem * *************/ void reinit_mem(void) { free_chunks(Chunks); /* free previously malloced memory */ Chunks = NULL; Alloc_block = NULL; Alloc_pos = NULL; } /* reinit_mem */ /************* * * void *MACE_tp_alloc(n) * * Allocate n contiguous bytes, aligned on pointer boundry. * *************/ void *MACE_tp_alloc(size_t n) { char *return_block; int scale; /* if n is not a multiple of sizeof(void *), then round up so that it is */ scale = sizeof(void *); if (n % scale != 0) n = n + (scale - (n % scale)); if (!Alloc_block || Alloc_block + TP_ALLOC_SIZE - Alloc_pos < n) { /* try to malloc a new block */ if (n > TP_ALLOC_SIZE) MACE_abend("in MACE_tp_alloc, request too big."); else if (MACE_Parms[MACE_MAX_MEM].val != -1 && ((Malloc_calls - Free_calls)+1)*(TP_ALLOC_SIZE/1024.0) > MACE_Parms[MACE_MAX_MEM].val) { exit_with_message(MACE_MAX_MEM_EXIT, 1); } else { Alloc_pos = Alloc_block = (char *) malloc((size_t) TP_ALLOC_SIZE); if (!Alloc_pos) MACE_abend("in MACE_tp_alloc, operating system cannot supply any more memory."); Malloc_calls++; add_chunk(Alloc_block); } } return_block = Alloc_pos; Alloc_pos += n; return(return_block); } /* MACE_tp_alloc */ /************* * * int MACE_total_mem() -- How many K are currently allocated? * *************/ int MACE_total_mem(void) { return( (int) ((Malloc_calls-Free_calls) * (TP_ALLOC_SIZE / 1024.))); } /* MACE_total_mem */ otter-3.3f/mace2/proto.h0100644000076400007640000000025507276052547014524 0ustar mccunemccune/* proto.h made Tuesday, May 08, 03:21:59 PM 2001 (CDT) */ /* print.c */ void print_model(FILE *fp); void print_model_portable(FILE *fp); void print_model_ivy(FILE *fp); otter-3.3f/mace2/dp.c0100644000076400007640000007562307714207010013752 0ustar mccunemccune#include "Mace2.h" /* #define WORK1 */ /* This file has code for the basic Davis-Putnam propositional decision * procedure. */ /* #define TRACE */ /****** Macros ******/ #define SUBSUMED(c) (Subsume ? c->subsumer : subsumed(c)) /****** Shared Variables ******/ extern int First_order; /* owned by mace.c */ extern int Models; /* owned by mace.c */ extern int Domain_size; /* owned by mace.c */ int Greatest_atom; /* used by generate.c */ /****** Global Static Variables ******/ static int Subsume; /* whether or not to mark subsumed clauses */ static int Check_time; /* whether or not there is a time limit */ static int Num_clauses; static Clause_ptr Clauses; static Atom_ptr Atoms; /* malloced when we know how many there are */ static int Num_selectable_clauses; static Clause_ptr *Selectable_clauses; /* for select_atom() */ static int *Unit_queue; /* queue for unit propagation */ static int Unit_queue_size; /* Actually, one less than this will fit. */ static int Unit_queue_first, Unit_queue_last; static Gen_ptr_ptr Gen_ptr_avail; /* list of available gen_ptr nodes */ static Clause_ptr Prev_dp; /* previously DP-inserted clause */ static int Next_message = 1; /* for printing models */ /* This set is for printing assignments (RECORD_ASSIGNMENTS) only */ static int Num_assignments; static int *Assignments; /* for RECORD_ASSIGNMENTS flag */ static int *Split_positions; /************* * * get_gen_ptr() -- allocate a gen_ptr node. * *************/ static Gen_ptr_ptr get_gen_ptr(void) { Gen_ptr_ptr p; if (!Gen_ptr_avail) p = MACE_tp_alloc(sizeof(struct gen_ptr)); else { p = Gen_ptr_avail; Gen_ptr_avail = Gen_ptr_avail->next; } p->next = NULL; return(p); } /* get_gen_ptr */ /************* * * free_gen_ptr() -- free a gen_ptr node. * *************/ static void free_gen_ptr(Gen_ptr_ptr p) { p->next = Gen_ptr_avail; Gen_ptr_avail = p; } /* free_gen_ptr */ /************* * * init_dp() * *************/ void init_dp() { MACE_init_options(); init_stats(); init_clocks(); } /* init_dp */ /************* * * exit_if_over_time_limit() * *************/ void exit_if_over_time_limit() { int sec = run_time() / 1000; if (sec > MACE_Parms[MAX_TP_SECONDS].val) exit_with_message(MACE_MAX_SECONDS_EXIT, 1); } /* exit_if_over_time_limit */ /************* * * subsumed() * * Check if any of the literals is assigned TRUE. * *************/ int subsumed(Clause_ptr c) { int i; for (i = 0; i < c->num_pos; i++) if (Atoms[c->pos[i]].value == ATOM_TRUE) return(1); for (i = 0; i < c->num_neg; i++) if (Atoms[c->neg[i]].value == ATOM_FALSE) return(1); return(0); } /* subsumed */ /************* * * init_unit_queue() * *************/ static void init_unit_queue(void) { Unit_queue_first = 0; Unit_queue_last = -1; } /* init_unit_queue */ /************* * * unit_enqueue(c) * * It is assumed that there is exactly 1 active literal. The clause * may be subsumed. The queue is not allowed to have duplicate or * complementary literals. * *************/ static int unit_enqueue(Clause_ptr c) { ATOM_INT *ip; int lit, ev, i; /* First find the unit (*ip gets atom, lit gets literal). * If subsumption is disabled, then a clause may have "true" * literals that are included in the "active" count; in this * case, c's "active" literal is already true, so it is not * enqueued. */ if (c->active_pos == 1) { for (ip=c->pos, i = 0; i < c->num_pos && Atoms[*ip].value != ATOM_NOT_ASSIGNED; ip++, i++); if (i == c->num_pos) { /* Subsumption must be off, and c is really subsumed. */ #ifdef TRACE2 printf(" ENQUEUE: subsumed: "); MACE_p_clause(c); #endif return(NOT_DETERMINED); } else lit = *ip; } else { for (ip=c->neg, i = 0; i < c->num_neg && Atoms[*ip].value != ATOM_NOT_ASSIGNED; ip++, i++); if (i == c->num_neg) { /* Subsumption must be off, and c is really subsumed. */ #ifdef TRACE2 printf(" ENQUEUE: subsumed: "); MACE_p_clause(c); #endif return(NOT_DETERMINED); } else lit = -(*ip); } ev = Atoms[*ip].enqueued_value; if (ev == NOT_DETERMINED) { Atoms[*ip].enqueued_value = lit > 0 ? ATOM_TRUE : ATOM_FALSE; Unit_queue_last++; if (Unit_queue_last == Unit_queue_size) MACE_abend("unit_enqueue: queue too small"); Unit_queue[Unit_queue_last] = lit; #ifdef WORK0 printf(" ENQUEUE: "); p_unit(lit); printf(" (%d) ", lit); MACE_pp_clause(c); #endif return(NOT_DETERMINED); } else if ((ev == ATOM_TRUE && lit < 0) || (ev == ATOM_FALSE && lit > 0)) { #ifdef TRACE printf(" ENQUEUE: %d unsat.\n", lit); #endif return(UNSATISFIABLE); } else { #ifdef TRACE2 printf(" ENQUEUE: %d already in queue.\n", lit); #endif return(NOT_DETERMINED); } } /* unit_enqueue */ /************* * * unit_dequeue() * * Also reset the enqueued_value field of the atom. * *************/ static int unit_dequeue(void) { int lit; if (Unit_queue_last < Unit_queue_first) return(0); else { lit = Unit_queue[Unit_queue_first]; Unit_queue_first++; Atoms[abs(lit)].enqueued_value = NOT_DETERMINED; #ifdef TRACE printf(" dequeue: "); p_unit(lit); printf(" (%d).\n", lit); #endif return(lit); } } /* unit_dequeue */ /************* * * MACE_p_clause() * *************/ void MACE_p_clause(Clause_ptr c) { int j; printf("( "); for (j = 0; j < c->num_neg; j++) printf("-%d ", c->neg[j]); for (j = 0; j < c->num_pos; j++) printf("%d ", c->pos[j]); printf(") active_neg=%d, active_pos=%d, subsumer=%d\n", c->active_neg, c->active_pos, c->subsumer); } /* MACE_p_clause */ /************* * * MACE_pp_clause() * *************/ void MACE_pp_clause(Clause_ptr c) { int j; printf("("); for (j = 0; j < c->num_neg; j++) p_unit(-(c->neg[j])); for (j = 0; j < c->num_pos; j++) p_unit(c->pos[j]); printf("), active=%d\n", c->active_pos+c->active_neg); } /* MACE_pp_clause */ /************* * * MACE_pp_clause_active() * *************/ void MACE_pp_clause_active(Clause_ptr c) { int j; for (j = 0; j < c->num_neg; j++) { int atom = c->neg[j]; if (Atoms[atom].value == ATOM_NOT_ASSIGNED) p_unit(-atom); } for (j = 0; j < c->num_pos; j++) { int atom = c->pos[j]; if (Atoms[atom].value == ATOM_NOT_ASSIGNED) p_unit(atom); } printf("\n"); } /* MACE_pp_clause_active */ /************* * * p_atom() * *************/ void p_atom(int i) { int j; Atom_ptr a = Atoms + i; printf("Atom=%d, value=%d, pos_occ=", i, a->value); for (j = 0; j < a->num_pos_occ; j++) printf("%x,", (unsigned) a->pos_occ[j]); printf(" neg_occ="); for (j = 0; j < a->num_neg_occ; j++) printf("%x,", (unsigned) a->neg_occ[j]); printf(".\n"); } /* p_atom */ /************* * * insert_dp_clause() * * Take a propositional clause (array of integers) and insert it into * the set of DP clauses. * *************/ void insert_dp_clause(int c[], int n) { Clause_ptr d; int i, np, nn; /* Find out how many pos and neg literals, so that arrays can be allocated. */ np = nn = 0; for (i = 0; i < n; i++) { if (abs(c[i]) > ATOM_INT_MAX) MACE_abend("insert_dp_clause, increase ATOM_INT_MAX and recompile."); if (abs(c[i]) > Greatest_atom) Greatest_atom = abs(c[i]); if (c[i] > 0) np++; else nn++; } /* Allocate the clause and the literal arrays. */ d = MACE_tp_alloc(sizeof(struct MACE_clause)); d->next = NULL; d->subsumer = 0; d->num_pos = np; d->active_pos = np; d->num_neg = nn; d->active_neg = nn; if (Prev_dp) Prev_dp->next = d; else Clauses = d; Prev_dp = d; d->pos = MACE_tp_alloc(np * sizeof(ATOM_INT)); /* ok if np==0 */ d->neg = MACE_tp_alloc(nn * sizeof(ATOM_INT)); /* ok if nn==0 */ /* Fill in the literal arrays (neg literals are stored positively). */ np = nn = 0; for (i = 0; i < n; i++) { if (c[i] > 0) d->pos[np++] = c[i]; else d->neg[nn++] = -c[i]; } Num_clauses++; MACE_Stats[INPUT_CLAUSES] = Num_clauses; MACE_Stats[GREATEST_ATOM] = Greatest_atom; #ifdef WORK1 MACE_pp_clause(d); #endif } /* insert_dp_clause */ /************* * * read_one_clause(fp) * * Read a propositional clause (sequence of nonzero integers, * terminated with 0) from a file, and insert it into the DP clause set. * (This is not used for first-order problems.) * * Return EOF at EOF, 0 if error, 1 if clase read successfully. * *************/ static int read_one_clause(FILE *fp) { int c[LIT_INT_MAX], num_lits, lit, rc; num_lits = 0; do { rc = fscanf(fp, "%d", &lit); if (rc == EOF) return(EOF); else if (rc == 0) return(0); else if (lit != 0) c[num_lits++] = lit; } while (lit != 0); insert_dp_clause(c, num_lits); return(1); } /* read_one_clause */ /************* * * read_all_clauses(fp) * * (This is not used for first-order problems.) * Abend if an error is found. * *************/ int read_all_clauses(FILE *fp) { int rc = 1; while (rc == 1) rc = read_one_clause(fp); if (rc == 0) MACE_abend("Propositional input must be all integers; if you have\nfirst-order input, the domain size must be given (-n)."); return(Num_clauses); } /* read_all_clauses */ /************* * * more_setup() * * Assume all clauses have been inserted into the DP set. This routine * sets up the unit propagation queue, and the atom array (which is * used for accessing clauses that contain a given atom). * *************/ int more_setup() { int i, j; Clause_ptr c; Atom_ptr a; #if 0 for (c = Clauses; c; c = c->next) MACE_p_clause(c); #endif /* Allocate queue for unit propagation (Unit_queue is a global variable). */ Unit_queue_size = Greatest_atom + 1; i = Unit_queue_size * sizeof(int); Unit_queue = malloc((size_t) i); MACE_Stats[MEM_MALLOCED] += i; init_unit_queue(); /* Now set up the atom array (indexed with 1--Greatest_atom). * Each atom struct has lists of positive occurrences and * negative occurrences. To save space, the lists are stored * as arrays; but we don't know how big the arrays should be * until we process the clauses. So we make two passes through * the clauses. */ i = (Greatest_atom+1) * sizeof(struct atom); Atoms = malloc((size_t) i); MACE_Stats[MEM_MALLOCED] += i; for (i = 0, a = Atoms; i <= Greatest_atom; i++, a++) { a->value = ATOM_NOT_ASSIGNED; a->enqueued_value = ATOM_NOT_ASSIGNED; a->num_pos_occ = 0; a->pos_occ = NULL; a->num_neg_occ = 0; a->neg_occ = NULL; } /* For each literal of each clause, increment occurrence count * in atom structure. (Pass 1 through the clauses.) */ for (c = Clauses; c; c = c->next) { for (j = 0; j < c->num_pos; j++) { a = Atoms + c->pos[j]; a->num_pos_occ++; } for (j = 0; j < c->num_neg; j++) { a = Atoms + c->neg[j]; a->num_neg_occ++; } } /* For each atom, allocate occurrence arrays, and reset occurrence * counts to 0. */ for (i = 0, a = Atoms; i <= Greatest_atom; i++, a++) { MACE_Stats[LIT_OCC_INPUT] += a->num_pos_occ; a->pos_occ = MACE_tp_alloc(a->num_pos_occ * sizeof(Clause_ptr)); a->num_pos_occ = 0; MACE_Stats[LIT_OCC_INPUT] += a->num_neg_occ; a->neg_occ = MACE_tp_alloc(a->num_neg_occ * sizeof(Clause_ptr)); a->num_neg_occ = 0; } exit_if_over_time_limit(); /* For each literal of each clause, add clause to occurrence * array of atom. (Pass 2 through the clauses.) */ for (c = Clauses; c; c = c->next) { for (j = 0; j < c->num_pos; j++) { a = Atoms + c->pos[j]; a->pos_occ[a->num_pos_occ++] = c; } for (j = 0; j < c->num_neg; j++) { a = Atoms + c->neg[j]; a->neg_occ[a->num_neg_occ++] = c; } } return(Num_clauses); } /* more_setup */ /************* * * select_init() * * Initialize the mechanism for selecting atoms for splitting; * *************/ static void select_init(void) { Clause_ptr c; int j; struct glist *selectable = NULL; struct glist *p; /* We will select literals from (smallest) positive clauses for splitting. * To avoid scanning all clauses, we build an array of pointers * to all of the nonsubsumed clauses with 2 or more positive literals. * (Horn clauses will be handled by unit propagation.) * * We'll first collect them into a list, then allocate an array * of the right size, then copy them into the array. */ for (c = Clauses, Num_selectable_clauses = 0; c; c = c->next) { /* Recall that even if subsumption is disabled, it is done * during preprocessing, which has just occurred. */ if (!c->subsumer && c->num_pos >= 2) { Num_selectable_clauses++; selectable = glist_prepend(c, selectable); } } /* Now we have the selectable clauses in reverse order. */ MACE_Stats[SELECTABLE_CLAUSES] = Num_selectable_clauses; /* Set up array of selectable clauses for select_atom(). */ j = Num_selectable_clauses * sizeof(Clause_ptr *); Selectable_clauses = malloc((size_t) j); MACE_Stats[MEM_MALLOCED] += j; /* Copy the list of pointers into the array and free the list. */ for (j = Num_selectable_clauses-1, p = selectable; j >= 0 && p != NULL; j--, p = p->next) { Selectable_clauses[j] = p->v; } free_glist_list(selectable); if (MACE_Flags[RECORD_ASSIGNMENTS].val) { printf("\nSelectable clauses:\n"); for (j = 0; j < Num_selectable_clauses; j++) MACE_pp_clause(Selectable_clauses[j]); } } /* select_init */ /************* * * select_atom() * * Go through the array of selectable clauses, and select the first active * literal in the first shortest nonsubsumed clause. * *************/ static int select_atom(void) { ATOM_INT *ip; int min, atom, i; Clause_ptr c; min = LIT_INT_MAX; atom = 0; #if 1 for (i = 0; i < Num_selectable_clauses; i++) #else for (i = Num_selectable_clauses-1; i >= 0; i--) #endif { c = Selectable_clauses[i]; if (c->active_neg == 0 && c->active_pos < min && !SUBSUMED(c)) { min = c->active_pos; for (ip = c->pos; Atoms[*ip].value != ATOM_NOT_ASSIGNED; ip++); atom = *ip; if (atom == 0) MACE_abend("HERE it is!!"); } } return(atom); } /* select_atom */ /************* * * select_clause() * * Go through the array of selectable clauses, and select the first * shortest nonsubsumed clause. * *************/ static Clause_ptr select_clause(void) { int min, i; Clause_ptr c, min_clause; min = LIT_INT_MAX; min_clause = 0; #if 1 for (i = 0; i < Num_selectable_clauses; i++) /* forward */ #else for (i = Num_selectable_clauses-1; i >= 0; i--) /* backward */ #endif { c = Selectable_clauses[i]; if (c->active_neg == 0 && c->active_pos < min && !SUBSUMED(c)) { min_clause = c; min = c->active_pos; } } return(min_clause); } /* select_clause */ /************* * * atom_value() * * Return the value of an atom. This can be called from outside code, * (i.e., first-order model printer) so the defined symbols are not used. * *************/ int atom_value(int atom) { int rc = -1; if (atom < 1 || atom > Greatest_atom) MACE_abend("atom_value, atom out of range"); switch(Atoms[atom].value) { case ATOM_FALSE: rc = 0; break; case ATOM_TRUE: rc = 1; break; case ATOM_NOT_ASSIGNED: rc = 2; break; default: MACE_abend("atom_value, bad value"); } return(rc); } /* atom_value */ /************* * * print_initial_assignments() * *************/ static void print_initial_assignments(void) { int i; printf("\nInitial assigments: "); for (i = 0; i < Num_assignments; i++) { p_unit(Assignments[i]); } printf("\n"); } /* print_initial_assignments */ /************* * * print_assignments(depth) * *************/ static void print_assignments(int depth) { int i, k, stop; printf("\nOrder of assigments for the following model:\n"); for (i = 0; i < depth; i++) { k = Split_positions[i]; p_unit(Assignments[k]); printf(": "); stop = (i < depth-1 ? Split_positions[i+1] : Num_assignments); for (k = k+1; k < stop; k++) { p_unit(Assignments[k]); } printf("\n\n"); } } /* print_assignments */ /************* * * model(depth) * * this routine is called when a model has been found. * *************/ static void model(int depth) { int i; if (MACE_Flags[RECORD_ASSIGNMENTS].val) print_assignments(depth); Models++; if (MACE_Flags[PRINT_MODELS].val) { if (!First_order) { printf("\nModel #%d:", Models); for (i = 1; i <= Greatest_atom; i++) if (Atoms[i].value == ATOM_TRUE) printf(" %d", i); printf("\n"); printf("end_of_model\n"); } else print_model(stdout); /* print first_order model */ } if (MACE_Flags[PRINT_MODELS_PORTABLE].val) { if (!First_order) { printf("\nModel #%d:", Models); for (i = 1; i <= Greatest_atom; i++) if (Atoms[i].value == ATOM_TRUE) printf(" %d", i); printf("\n"); printf("end_of_model\n"); } else print_model_portable(stdout); /* print first_order model */ } if (MACE_Flags[PRINT_MODELS_IVY].val) { if (!First_order) { printf("\nModel #%d:", Models); for (i = 1; i <= Greatest_atom; i++) if (Atoms[i].value == ATOM_TRUE) printf(" %d", i); printf("\n"); printf("end_of_model\n"); } else print_model_ivy(stdout); /* print first_order model */ } if (!MACE_Flags[PRINT_MODELS_PORTABLE].val && !MACE_Flags[PRINT_MODELS].val) { if (Models == Next_message) { printf("\nThe %d%s model has been found.\n", Models, Next_message == 1 ? "st" : "th"); Next_message *= 10; } } fflush(stdout); if (Models >= MACE_Parms[MAX_MODELS].val) exit_with_message(MAX_MODELS_EXIT, 1); } /* model */ /************* * * assign(lit) - make a literal true * * 1. Make the assignment in the atom array. * 2. (optional) Mark nonsubsumed clauses that contain it as subsumed by it. * 3. Unit resolution on clauses that are not marked as subsumed. * If a unit is found, enqueue it for unit propagation. * 4. If empty clause is found, return UNSATISFIABLE else NOT_DETERMINED. * *************/ static int assign(int lit) { Atom_ptr a; Clause_ptr c; int atom, value, i, rc, n, np, nn; #ifdef WORK0 p_unit(lit); printf("\n"); #endif value = (lit > 0 ? ATOM_TRUE : ATOM_FALSE); atom = abs(lit); rc = NOT_DETERMINED; a = Atoms + atom; np = a->num_pos_occ; nn = a->num_neg_occ; if (a->value != ATOM_NOT_ASSIGNED) MACE_abend("assign: atom already assigned"); else a->value = value; if (MACE_Flags[RECORD_ASSIGNMENTS].val) Assignments[Num_assignments++] = lit; if (value == ATOM_TRUE) { /* Assign true to atom */ if (Subsume) for (i = 0; i < np; i++) { c = a->pos_occ[i]; if (!c->subsumer) c->subsumer = atom; } for (i = 0; i < nn; i++) { c = a->neg_occ[i]; if (!c->subsumer) { c->active_neg--; n = c->active_pos + c->active_neg; if (n == 0) rc = UNSATISFIABLE; else if (n == 1 && unit_enqueue(c) == UNSATISFIABLE) rc = UNSATISFIABLE; } } } else { /* Assign false to atom */ if (Subsume) for (i = 0; i < nn; i++) { c = a->neg_occ[i]; if (!c->subsumer) c->subsumer = atom; } for (i = 0; i < np; i++) { c = a->pos_occ[i]; if (!c->subsumer) { c->active_pos--; n = c->active_neg + c->active_pos; if (n == 0) rc = UNSATISFIABLE; else if (n == 1 && unit_enqueue(c) == UNSATISFIABLE) rc = UNSATISFIABLE; } } } if (rc == UNSATISFIABLE) MACE_Stats[FAILED_PATHS]++; return(rc); } /* assign */ /************* * * unassign(lit) -- undo an assignment * *************/ static void unassign(int lit) { Atom_ptr a; Clause_ptr c; int i, atom, np, nn; atom = abs(lit); a = Atoms + atom; if (a->value == ATOM_NOT_ASSIGNED) MACE_abend("unassign: atom not assigned"); if (MACE_Flags[RECORD_ASSIGNMENTS].val) Num_assignments--; np = a->num_pos_occ; nn = a->num_neg_occ; if (a->value == ATOM_TRUE) { /* Unassign true. */ if (Subsume) for (i = 0; i < np; i++) { c = a->pos_occ[i]; if (c->subsumer == atom) c->subsumer = 0; } for (i = 0; i < nn; i++) { c = a->neg_occ[i]; if (!c->subsumer) c->active_neg++; } } else { /* Unassign false. */ if (Subsume) for (i = 0; i < nn; i++) { c = a->neg_occ[i]; if (c->subsumer == atom) c->subsumer = 0; } for (i = 0; i < np; i++) { c = a->pos_occ[i]; if (!c->subsumer) c->active_pos++; } } a->value = ATOM_NOT_ASSIGNED; } /* unassign */ /************* * * dp(depth) -- the kernel of the Davis-Putnam procedure * * depth: current recursion level---for debugging only. * *************/ static void dp(int depth) { int lit, unit, rc, j; Gen_ptr_ptr unit_assignments, p1; if (Check_time) exit_if_over_time_limit(); lit = select_atom(); if (lit == 0) { model(depth); /* Nothing to select, so we have a model. */ return; } MACE_Stats[SPLITS]++; for (j = 0; j < 2; j++) { init_unit_queue(); if (MACE_Flags[RECORD_ASSIGNMENTS].val) Split_positions[depth] = Num_assignments; #ifdef TRACE { int i; for (i = 0; i < depth; i++) printf(" "); p_unit(lit); printf(" %3d\n", lit); } #endif rc = assign(lit); /* Unit propagation */ unit_assignments = NULL; while (rc == NOT_DETERMINED && (unit = unit_dequeue()) != 0) { MACE_Stats[UNIT_ASSIGNS]++; #ifdef TRACE { int i; for (i = 0; i < depth; i++) printf(" "); p_unit(unit); printf(" %3d*\n", unit); } #endif rc = assign(unit); /* Save the assignment so that it can be undone. */ p1 = get_gen_ptr(); p1->u.i = unit; p1->next = unit_assignments; unit_assignments = p1; } if (rc == NOT_DETERMINED) dp(depth+1); else /* rc == UNSATISFIABLE, so empty queue to reset any enqueued_values */ while ((unit = unit_dequeue()) != 0); /* Undo unit propagation assignments */ while (unit_assignments) { #ifdef TRACE { int i; for (i = 0; i < depth; i++) printf(" "); p_unit(unit_assignments->u.i); printf(" [%3d]*\n", unit_assignments->u.i); } #endif unassign(unit_assignments->u.i); p1 = unit_assignments; unit_assignments = unit_assignments->next; free_gen_ptr(p1); } #ifdef TRACE { int i; for (i = 0; i < depth; i++) printf(" "); p_unit(lit); printf(" [%3d]\n", lit); } #endif unassign(lit); if (j == 0) lit = -lit; } } /* dp */ /* ISO_X experiment */ /* #define ISO_PRINT */ #define ISO_PRUNE 0 #define SPECIFIED 1 #define UNSPECIFIED 2 /************* * * function_value() * *************/ int function_value(int atom) { char *func; int arity; int args[4]; decode_int(atom, &func, &arity, args); return args[arity-1]; } /* function_value */ /************* * * iso_prune() * *************/ int iso_prune(int atom, int iso_set[], int iso_flag, int depth) { if (!MACE_Flags[ISO_X].val) return SPECIFIED; else { int fval = function_value(atom); int rc; if (jset_member(iso_set, fval)) rc = SPECIFIED; else if (iso_flag) rc = ISO_PRUNE; else { add_to_jset(iso_set, fval); rc = UNSPECIFIED; } #ifdef ISO_PRINT { int i; for (i = 0; i < depth; i++) printf(" "); printf("atom, depth %d:", depth); p_unit(atom); switch (rc) { case SPECIFIED: printf(" specified\n"); break; case UNSPECIFIED: printf(" unspecified\n"); break; case ISO_PRUNE: printf(" pruned\n"); break; } } #endif return rc; } } /* iso_prune */ /************* * * add_args_to_set() * *************/ void add_args_to_set(Clause_ptr c, int *iso_set) { int atom = c->pos[0]; char *func; int arity; int args[4]; int function_value; int i; decode_int(atom, &func, &arity, args); for (i = 0; i < (arity-1); i++) add_to_jset(iso_set, args[i]); } /* add_args_to_set */ /************* * * clause_split(depth) -- the kernel of the clause-splitting procedure * * depth: current recursion level---for debugging only. * *************/ static void clause_split(int depth, int *iso_set) { int unit, rc, j; Gen_ptr_ptr unit_assignments, p1; Clause_ptr c; int iso_flag = 0; /* Have we done a non specified element yet? */ int *iso_seta; if (Check_time) exit_if_over_time_limit(); c = select_clause(); #ifdef WORK0 if (c) { printf("Splitting clause" ); MACE_pp_clause_active(c); } #endif if (c == NULL) { model(depth); /* Nothing to select, so we have a model. */ return; } if (MACE_Flags[ISO_X].val) { iso_seta = copy_jset(iso_set); add_args_to_set(c, iso_seta); /* assume it is a closure clause */ #ifdef ISO_PRINT printf("\nIncoming set, depth %d: ", depth); print_set(iso_set); printf("Splitting clause" ); MACE_pp_clause_active(c); printf("Updated set: "); print_set(iso_seta); printf("\n"); #endif } MACE_Stats[SPLITS]++; /* We cannot assume that c is positive. */ for (j = 0; j < c->num_pos+c->num_neg; j++) { int sign = (j < c->num_pos); int atom = (j < c->num_pos ? c->pos[j] : c->neg[j - c->num_pos]); int lit = (sign ? atom : -atom); if (Atoms[atom].value == ATOM_NOT_ASSIGNED) { /* process active literals only */ int iso = iso_prune(atom, iso_seta, iso_flag, depth); if (iso == ISO_PRUNE) { /* do nothing */ } else { if (MACE_Flags[RECORD_ASSIGNMENTS].val) Split_positions[depth] = Num_assignments; init_unit_queue(); rc = assign(lit); /* Unit propagation */ unit_assignments = NULL; while (rc == NOT_DETERMINED && (unit = unit_dequeue()) != 0) { MACE_Stats[UNIT_ASSIGNS]++; rc = assign(unit); /* Save the assignment so that it can be undone. */ p1 = get_gen_ptr(); p1->u.i = unit; p1->next = unit_assignments; unit_assignments = p1; } if (rc == NOT_DETERMINED) clause_split(depth+1, iso_seta); else /* rc == UNSATISFIABLE, so empty queue to reset any enqueued_values */ while ((unit = unit_dequeue()) != 0); /* Undo unit propagation assignments */ while (unit_assignments) { unassign(unit_assignments->u.i); p1 = unit_assignments; unit_assignments = unit_assignments->next; free_gen_ptr(p1); } unassign(lit); if (iso == UNSPECIFIED) { remove_from_jset(iso_seta, function_value(atom)); iso_flag = 1; } } /* not pruned */ } /* active literals only */ } /* for each literal */ if (MACE_Flags[ISO_X].val) free(iso_seta); } /* clause_split */ /************* * * delete_pointers_to_subsumed_clauses() * * This routine is called after the initial unit propagation (before * any splitting). It goes through the occurrence lists in the * atom array and deletes references to subsumed clauses. The reason * for this is simply to speed traversals during assign() and unassign(). * * This is intended for use only after the initial unit propagation, * because this operation is not undoable. * *************/ static void delete_pointers_to_subsumed_clauses(void) { int i, j, k; Atom_ptr a; /* The set of occurrences, say positive, of an atom, is kept as * an array of pointers to clauses. Pointers to subsumed clauses * are removed, and the the others are shifted left the apropriate * amount. Same for negative occurrences. */ for (i = 1; i <= Greatest_atom; i++) { a = Atoms + i; for (j = 0, k = 0; j < a->num_pos_occ; j++) if (a->pos_occ[j]->subsumer == 0) a->pos_occ[k++] = a->pos_occ[j]; a->num_pos_occ = k; MACE_Stats[LIT_OCC_AFTER_SUB] += k; for (j = 0, k = 0; j < a->num_neg_occ; j++) if (a->neg_occ[j]->subsumer == 0) a->neg_occ[k++] = a->neg_occ[j]; a->num_neg_occ = k; MACE_Stats[LIT_OCC_AFTER_SUB] += k; } } /* delete_pointers_to_subsumed_clauses */ /************* * * dp_prover() * * This is the top (nonrecursive) routine of the Davis-Putnam procedure. * *************/ int dp_prover() { int rc, unit, n; Clause_ptr c; Check_time = (MACE_Parms[MAX_TP_SECONDS].val < INT_MAX); if (MACE_Flags[RECORD_ASSIGNMENTS].val) { Assignments = malloc((size_t) Greatest_atom * sizeof(int)); Split_positions = malloc((size_t) Greatest_atom * sizeof(int)); Num_assignments = 0; } /* Initial unit propagation and subsumption. */ Subsume = 1; /* Always mark subsumed clauses while preprocessing. */ for (c=Clauses, rc=NOT_DETERMINED; c && rc == NOT_DETERMINED; c = c->next) if (c->num_pos + c->num_neg == 1) { rc = unit_enqueue(c); } while (rc == NOT_DETERMINED && (unit = unit_dequeue()) != 0) { MACE_Stats[PREPROCESS_UNIT_ASSIGNS]++; rc = assign(unit); /* This can enqueue more units */ } if (MACE_Stats[PREPROCESS_UNIT_ASSIGNS] > 0) delete_pointers_to_subsumed_clauses(); else MACE_Stats[LIT_OCC_AFTER_SUB] = MACE_Stats[LIT_OCC_INPUT]; for (c = Clauses, n=0; c; c = c->next) if (c->subsumer) n++; MACE_Stats[CLAUSES_AFTER_SUB] = MACE_Stats[INPUT_CLAUSES] - n; Subsume = MACE_Flags[SUBSUME].val; /* Done with initial unit propagation and subsumption. */ select_init(); /* Initialize the selection mechanism for splitting. */ if (MACE_Flags[RECORD_ASSIGNMENTS].val) print_initial_assignments(); printf("\nAfter all unit preprocessing, %ld atoms are still unassigned;\n" "%ld clauses remain; %ld of those are non-Horn (selectable);\n" "%ld K allocated; cpu time so far for this domain size: %.2f sec.\n", Greatest_atom - MACE_Stats[PREPROCESS_UNIT_ASSIGNS], MACE_Stats[CLAUSES_AFTER_SUB], MACE_Stats[SELECTABLE_CLAUSES], MACE_Stats[MEM_MALLOCED]/1024 + MACE_total_mem(), (MACE_clock_val(DECIDE_TIME) + MACE_clock_val(GENERATE_TIME)) / 1000.); fflush(stdout); if (rc == NOT_DETERMINED) { if (MACE_Flags[CLAUSE_SPLIT].val) { int *iso_set; if (MACE_Flags[ISO_X].val) { set_jset_size(Domain_size); iso_set = get_jset(); } clause_split(0, iso_set); /* recursive clause-splitting routine */ } else dp(0); /* recursive Davis-Putnam routine */ } if (Models == 0) return(UNSATISFIABLE_EXIT); else return(ALL_MODELS_EXIT); } /* dp_prover */ /************* * * reinit_dp * * Free memory and reinitialize global variables in this file. * *************/ void reinit_dp(void) { free(Unit_queue); free(Atoms); free(Selectable_clauses); if (MACE_Flags[RECORD_ASSIGNMENTS].val) { free(Assignments); free(Split_positions); Num_assignments = 0; } Greatest_atom = 0; Subsume = 0; Check_time = 0; Num_clauses = 0; Clauses = NULL; Atoms = NULL; Num_selectable_clauses = 0; Selectable_clauses = NULL; Unit_queue = NULL; Unit_queue_size = 0; Unit_queue_first = 0; Unit_queue_last = 0; Prev_dp = NULL; Gen_ptr_avail = NULL; Next_message = 1; } /* reinit_dp */ otter-3.3f/mace2/Mace2.h0100644000076400007640000000163510070417712014274 0ustar mccunemccune#ifndef TP_MACE_HEADER_H #define TP_MACE_HEADER_H /************ BASIC INCLUDES ************/ #define IN_MAIN /* so that global vars in ../header.h will not be external */ #include "../source/header.h" /* Otter header */ #include "Opts.h" #include "Stats.h" #include "Avail.h" #include "Clock.h" #include "Miscellany.h" #include "Flatten.h" #include "Part.h" #include "Print.h" #include "Dp.h" #include "Generate.h" #define MAX(a,b) ((a) > (b) ? (a) : (b)) #define MIN(a,b) ((a) < (b) ? (a) : (b)) /******** Types of exit ********/ #define MACE_ABEND_EXIT 11 #define UNSATISFIABLE_EXIT 12 #define MACE_MAX_SECONDS_EXIT 13 #define MACE_MAX_MEM_EXIT 14 #define MAX_MODELS_EXIT 15 #define ALL_MODELS_EXIT 16 #define MACE_SIGINT_EXIT 17 #define MACE_SEGV_EXIT 18 #define MACE_INPUT_ERROR_EXIT 19 #define MAX_DOMAIN 100 #endif /* ! TP_MACE_HEADER_H */ otter-3.3f/mace2/mace2.c0100644000076400007640000002111210103517344014316 0ustar mccunemccune/* MACE 2.1 * * William McCune * Mathematics and Computer Science Division * Argonne National Laboratory * Argonne, IL 60439 * U.S.A. * * E-mail: mccune@mcs.anl.gov * Web: http://www.mcs.anl.gov/~mccune * http://www.mcs.anl.gov/AR/mace */ #define VERSION "2.2f" #define VDATE "August 2004" #include "Mace2.h" #include /* for getopt */ static int Domain_min = 2; /* default starting size */ static int Domain_max = 0; /* default will be Domain_min */ int Models = 0; /* shared with dp.c, miscellany.c */ int First_order = 1; /* shared with dp.c */ int Domain_size; /* shared with stats.c */ int Init_wall_seconds; /* shared with stats.c */ /************* * * void MACE_print_banner(argc, argv) * *************/ static void MACE_print_banner(int argc, char **argv) { int i; printf("----- MACE %s, %s -----\n", VERSION, VDATE); printf("The process was started by %s on %s,\n%s", username(), hostname(), get_time()); printf("The command was \""); for(i = 0; i < argc; i++) printf("%s%s", argv[i], (i < argc-1 ? " " : "")); printf("\".\n"); } /* MACE_print_banner */ /************* * * usage_message() * *************/ static void usage_message(void) { printf("MACE %s -- Search for finite models.\n" "\n" "Input clauses are taken from standard input.\n" "\n" "Command-line options:\n" "\n" " -n n : Search for model of size n (default %d).\n" " -N n : Iterate up to size n (default: don't iterate).\n" " -c : Assume constants are distinct (up to domain size).\n" " -z n : Apply isomorphism constraints to first n constants\n" " (default %d). Overridden by -c.\n" " -p : Print models in human format as they are found.\n" " -P : Print models in portable format as they are found.\n" " -I : Print models in IVY format as they are found.\n" " -m n : Stop when the n-th model is found (default %d).\n" " -t n : Stop after about n seconds.\n" " -k n : Dynamically allocate at most n Kbytes (default %d).\n" " -s : Perform unit subsumption. (Always done on input.)\n" " -C : Split on clauses instead of on atoms.\n" " -r : Record and print the order of assignments.\n" " -x : Quasigroup constraint.\n" " -y : Iso experiment (implies -C and -z0).\n" " -v n : Try to part flattened clauses with n or more variables (default %d).\n" " -h : Print this message.\n" "\n" "Examples of constraints given in input:\n" " list(mace_constraints).\n" " assign(a, 3).\n" " assign(f(2,3), 1).\n" " assign(P(0), F).\n" " assign(P(1), T).\n" " property(r(_,_), equality).\n" " property(lt(_,_), order).\n" " property(f(_,_), quasigroup).\n" " property(g(_), bijection).\n" " end_of_list.\n" , VERSION, Domain_min, MACE_Parms[ISO_CONSTANTS].val, MACE_Parms[MAX_MODELS].val, MACE_Parms[MACE_MAX_MEM].val, MACE_Parms[PART_VARS].val ); } /* usage_message */ /************* * * process_command_line_args() * *************/ static int process_command_line_args(int argc, char **argv) { extern char *optarg; int c, n; int error = 0; while ((c = getopt(argc, argv, "spPIhcxyCrm:t:k:n:N:d:z:v:")) != EOF) { switch (c) { case 'c': MACE_change_flag(stderr, "distinct_constants", 1); break; case 's': MACE_change_flag(stderr, "subsume", 1); break; case 'p': MACE_change_flag(stderr, "print_models", 1); break; case 'P': MACE_change_flag(stderr, "print_models_portable", 1); break; case 'I': MACE_change_flag(stderr, "print_models_ivy", 1); break; case 'x': MACE_change_flag(stderr, "qg_constraint", 1); break; case 'y': MACE_change_flag(stderr, "iso_x", 1); MACE_change_flag(stderr, "clause_split", 1); if (MACE_change_parm(stderr, "iso_constants", 0) == -1) error++; break; case 'C': MACE_change_flag(stderr, "clause_split", 1); break; case 'r': MACE_change_flag(stderr, "record_assignments", 1); break; case 'm': n = atoi(optarg); if (MACE_change_parm(stderr, "max_models", n) == -1) error++; break; case 't': n = atoi(optarg); if (MACE_change_parm(stderr, "max_seconds", n) == -1) error++; break; case 'k': n = atoi(optarg); if (MACE_change_parm(stderr, "max_mem", n) == -1) error++; break; case 'n': n = atoi(optarg); if (n < 1) { fprintf(stderr, "Domain size must be > 0.\n"); error++; } else if (n > MAX_DOMAIN) { fprintf(stderr, "Domain size must be <= %d.\n", MAX_DOMAIN); error++; } else Domain_min = n; break; case 'N': n = atoi(optarg); if (n < 1) { fprintf(stderr, "Maximum domain size must be > 0.\n"); error++; } else if (n > MAX_DOMAIN) { fprintf(stderr, "Maximum domain size must be <= %d.\n", MAX_DOMAIN); error++; } else Domain_max = n; break; case 'z': n = atoi(optarg); if (MACE_change_parm(stderr, "iso_constants", n) == -1) error++; break; case 'v': n = atoi(optarg); if (MACE_change_parm(stderr, "part_vars", n) == -1) error++; break; case 'h': case '?': default: error = 1; break; } } return(error == 0); } /* process_command_line_args */ /************* * * MACE_sig_handler() * *************/ #ifdef TP_SIGNAL #include static void MACE_sig_handler(int condition) { if (condition == SIGSEGV) { char message[] = "\n" "+----------------------------------------------------------+\n" "| SEGMENTATION FAULT!! This is probably caused by a bug |\n" "| in MACE. Please send copy of the input file to |\n" "| otter@mcs.anl.gov, let us know what version of MACE you |\n" "| are using, and send any other info that might be useful. |\n" "+----------------------------------------------------------+\n\n"; fprintf(stderr, "%s%c", message, Bell); exit_with_message(MACE_SEGV_EXIT, 1); } else if (condition == SIGINT) { exit_with_message(MACE_SIGINT_EXIT, 1); } else { char s[100]; sprintf(s, "MACE_sig_handler, cannot handle signal %d.\n", condition); MACE_abend(s); } } /* MACE_sig_handler */ #endif /* TP_SIGNAL */ /************* * * reinit * *************/ static void reinit(void) { reinit_mem(); reinit_dp(); reinit_generate(); /* Don't call init_dp here, because we don't want to reinitialize the options, because we're not going to read them again. */ init_clocks(); init_stats(); } /* reinit */ /************* * * try_domain_size * *************/ static void try_domain_size(void) { int rc; /* we can ignore the return codes */ MACE_CLOCK_START(GENERATE_TIME); rc = dp_trans(Domain_size, MACE_Flags[DISTINCT_CONSTANTS].val, MACE_Flags[QG_CONSTRAINT].val); if (!rc) return; /* Unsatisfiability detected by dp_trans */ else { rc = more_setup(); MACE_CLOCK_STOP(GENERATE_TIME); MACE_CLOCK_START(DECIDE_TIME); rc = dp_prover(); MACE_CLOCK_STOP(DECIDE_TIME); } } /* try_domain_size */ /************* * * main * *************/ int main(int argc, char **argv) { int rc, errors; struct list *usable_raw, *usable_flattened, *usable_parted; #ifdef TP_SIGNAL signal(SIGINT, MACE_sig_handler); signal(SIGSEGV, MACE_sig_handler); #endif MACE_print_banner(argc, argv); init_dp(); /* This is MACE's initialization. */ Init_wall_seconds = wall_seconds(); rc = process_command_line_args(argc, argv); if (!rc) { usage_message(); exit(MACE_INPUT_ERROR_EXIT); } init(); /* This is Otter's initialization. */ read_all_mace_input(argc, argv); errors = Stats[INPUT_ERRORS]; if (errors != 0) exit_with_message(MACE_INPUT_ERROR_EXIT, 1); usable_raw = Usable; usable_flattened=flatten_clauses(usable_raw); usable_parted=variable_optimize(usable_flattened,MACE_Parms[PART_VARS].val); printf("\nlist(flattened_and_parted_clauses).\n"); print_cl_list(stdout, usable_parted); Usable = usable_parted; if (Domain_max == 0) /* if it hasn't been set, make it Domain_min */ Domain_max = Domain_min; for (Domain_size = Domain_min; Domain_size <= Domain_max; Domain_size++) { printf("\n--- Starting search for models of size %d ---\n\n", Domain_size); try_domain_size(); MACE_print_stats(stdout); reinit(); } if (Models == 0) exit_with_message(UNSATISFIABLE_EXIT, 0); else exit_with_message(ALL_MODELS_EXIT, 0); exit(99); /* This won't be called. This is to shut up the compiler. */ } /* main */ otter-3.3f/mace2/Opts.h0100644000076400007640000000462207713765465014316 0ustar mccunemccune#ifndef TP_OPTIONS_H #define TP_OPTIONS_H /* This file does not depend on header.h */ #include #include /* for INT_MAX */ #include /* for strcmp() */ /************* * * MACE_Flags are boolean valued options. To install a new flag, append * a new name and index to the end of this list, then insert code to * initialize it in the routine `MACE_init_options'. * Example access: if (MACE_Flags[PARA_FROM_LEFT].val) { ... } * See routine `MACE_init_options' for defaults. * *************/ #define MACE_MAX_FLAGS 100 /* increase if necessary */ #define PRINT_MODELS 0 #define SUBSUME 1 #define PRINT_MODELS_PORTABLE 2 #define DISTINCT_CONSTANTS 3 #define PRINT_MODELS_IVY 4 #define QG_CONSTRAINT 5 #define RECORD_ASSIGNMENTS 6 #define CLAUSE_SPLIT 7 #define ISO_X 8 /* end of MACE_Flags */ /************* * * MACE_Parms are integer valued options. To install a new parm, append * a new name and index to this list, then insert code to * initialize it in the routine `MACE_init_options'. * Example access: if (MACE_Parms[FPA_LITERALS].val == 4) { ... } * See routine `MACE_init_options' for defaults. * *************/ #define MACE_MAX_PARMS 30 /* increase if necessary */ #define MACE_MAX_MEM 0 /* stop search after this many K bytes allocated */ #define MAX_TP_SECONDS 1 #define MAX_MODELS 2 #define ISO_CONSTANTS 3 #define PART_VARS 4 /* end of MACE_Parms */ struct flag { /* MACE_Flags are boolean valued options */ char *name; int val; }; struct parm { /* MACE_Parms are integer valued options */ char *name; int val; int min, max; /* minimum and maximum permissible values */ }; extern struct flag MACE_Flags[MACE_MAX_FLAGS]; extern struct parm MACE_Parms[MACE_MAX_PARMS]; /* function prototypes from options.c */ void MACE_init_options(void); void MACE_print_options(FILE *fp); void MACE_p_options(void); void auto_MACE_change_flag(FILE *fp, int index, int val); void MACE_dependent_flags(FILE *fp, int index); void auto_MACE_change_parm(FILE *fp, int index, int val); void MACE_dependent_parms(FILE *fp, int index); int MACE_change_flag(FILE *fp, char *flag_name, int set); int MACE_change_parm(FILE *fp, char *parm_name, int val); void MACE_check_options(FILE *fp); #endif /* ! TP_OPTIONS_H */ otter-3.3f/mace2/Print.h0100644000076400007640000000026307276052635014452 0ustar mccunemccune#ifndef TP_PRINT_H #define TP_PRINT_H /* print.c */ void print_model(FILE *fp); void print_model_portable(FILE *fp); void print_model_ivy(FILE *fp); #endif /* ! TP_PRINT_H */ otter-3.3f/mace2/miscellany.c0100644000076400007640000000345507714207010015501 0ustar mccunemccune#include "Mace2.h" /* for ABEND_EXIT */ extern int Models; /* owned by mace.c */ /************* * * exit_with_message(exit_code) * *************/ void exit_with_message(int exit_code, int stats) { char *m1, m2[100]; switch (exit_code) { case MACE_ABEND_EXIT: m1 = "Abnormal end."; break; case UNSATISFIABLE_EXIT: m1 = "The search is complete."; break; case MACE_MAX_SECONDS_EXIT: m1 = "Exit by max_seconds parameter."; break; case MACE_MAX_MEM_EXIT: m1 = "Exit by max_mem parameter."; break; case MAX_MODELS_EXIT: m1 = "Exit by max_models parameter."; break; case ALL_MODELS_EXIT: m1 = "The search is complete."; break; case MACE_SIGINT_EXIT: m1 = "Killed by SIGINT signal."; break; case MACE_SEGV_EXIT: m1 = "Killed by SIGSEGV signal."; break; case MACE_INPUT_ERROR_EXIT: m1 = "Input error."; break; default: m1 = "Exit with unknown code."; break; } if (exit_code == MACE_INPUT_ERROR_EXIT) fprintf(stderr, "\nInput error. See the output file.\n\n\007"); if (Models > 0) sprintf(m2, "The set is satisfiable (%d model(s) found).", Models); else sprintf(m2, "No models were found."); if (stats) MACE_print_stats(stdout); MACE_print_times(stdout); printf("\n%s %s\n\n", m1, m2); fprintf(stderr, "\007\n%s %s\n\n", m1, m2); printf("The job finished %s", get_time()); exit(exit_code); } /* exit_with_message */ /************* * * MACE_abend * *************/ void MACE_abend(char *str) { fprintf(stderr, "\007"); fprintf(stderr, "\n\n********** ABNORMAL END **********\n"); fprintf(stderr, "********** %s\n", str); fprintf(stdout, "\n\n********** ABNORMAL END **********\n"); fprintf(stdout, "********** %s\n", str); exit_with_message(MACE_ABEND_EXIT, 1); } /* MACE_abend */ otter-3.3f/bin/0040755000076400007640000000000010103776005012753 5ustar mccunemccuneotter-3.3f/QuickInstall0100755000076400007640000000320510103516546014533 0ustar mccunemccune#!/bin/csh # This script tries to determine what operating system is in use, # then it copies pre-compiled binaries to the ./bin directory. # Then it does quick tests to see if the binaries seem to be ok. set OS=`uname -s` if (-e bin-$OS) then /bin/rm -f bin/* echo "" echo "Copying bin-$OS/* to bin/" /bin/cp -p bin-$OS/* bin/ echo "" echo "Testing bin/otter ..." bin/otter < /dev/null >& /dev/null if ($status != 104) goto fail echo "Otter seems to be ok." echo "" echo "Testing bin/mace2 ..." bin/mace2 < /dev/null >& /dev/null if ($status != 15) goto fail echo "Mace2 seems to be ok." if ($1 == 'no_make') then echo "" echo "*********************************************************" echo "* The initial tests on the binaries succeeded. *" echo "* Now try './make-test-otter' and './make-test-mace2'. *" echo "*********************************************************" echo "" else echo "" echo "******************************************************" echo "* The initial tests on the binaries succeeded. *" echo "* Now try 'make test-otter' and 'make test-mace2'. *" echo "******************************************************" echo "" endif exit 0 endif fail: echo "" echo "***************************************************************" echo "* It looks like you cannot use the pre-compiled binaries. *" echo "* Try compiling Otter and Mace2 with the command 'make all' *" echo "* If that fails, see the files README and README.make. *" echo "***************************************************************" echo "" exit 1 otter-3.3f/README.Ivy0100644000076400007640000000157007720504470013637 0ustar mccunemccuneIvy is a system that checks Otter proofs and MACE models. Ivy is coded in ACL2 and many soundness metatheorems have been proved about the various programs in Ivy. See http://www.mcs.anl.gov/~mccune/acl2/ivy Ivy-2 is the current version. Otter-3.0.6 and MACE-1.3.4 come bundled with Ivy-2. If you wish to have Ivy-2 call Otter-3.3 and MACE-2. instead, you can do so by updating 2 Ivy files (after configuring Ivy): ivy-v2/ivy-sources/util/otter-mace.lisp Change the line (defvar mace-parms "6 60 -m1 -I -c") to (defvar mace-parms "-N6 -t60 -I") ivy-v2/ivy-sources/util/ivy Change the lines that begin set otter_binary= set mace_binary= so that they refer to the Otter-3.3 and MACE-2.1 binaries, for example, set otter_binary=/homes/mccune/bin-linux/otter33 set mace_binary=/homes/mccune/bin-linux/mace21 otter-3.3f/index.html0100644000076400007640000000311610103530622014167 0ustar mccunemccune Otter 3.3 / Mace 2.2 Package

Otter 3.3 Theorem Prover

Mace 2.2 Finite Model Searcher

This page is part of the Otter 3.3 / Mace 2.2 distribution package. For further information, see

The Official Web Pages

Documentation

Examples

The Distribution Package

Fetch the packages from the Otter Web page.

The basic Otter 3.3 / Mace 2.2 package is for UNIX-like operating systems. Here is some information on installation.

William McCune
Mathematics and Computer Science Division
Argonne National Laboratory otter-3.3f/README0100644000076400007640000000427510103530444013063 0ustar mccunemccune ------------------ Otter, Version 3.3 Search for Proofs ------------------ ------------------ Mace, Version 2.2 Search for Countermodels ------------------ (Also see index.html in this directory.) ---------------- OTTER HIGHLIGHTS ---------------- Over the years we've added many experimental features to Otter, but the basic functions haven't changed much in the past ten years. The Otter package now includes Mace 2 (as a separate program). ---------------- Mace2 HIGHLIGHTS ---------------- Mace2 is now in independent program. It no longer calls Otter to parse the input. It still accepts the same inputs as Otter. Performance is sometimes better than in previous versions (see mace2/README.22). ---------------- DOCUMENTS ---------------- The documents directory contains a (newly updated) Otter 3.3 manual and a Mace 2.0 manual. See documents/README. ---------------- FETCHING ---------------- Download Otter 3.3 and Mace 2.2 from the Otter Web page: http://www.mcs.anl.gov/AR/otter/ ---------------- INSTALLING AND TESTING (for unix-like systems) ---------------- Unpack the package with a command something like % gunzip -c otter-3.3.tar.gz | tar xvf - Then % cd otter-3.3 If you are on a recent linux or Macintosh system, try % make install (this just copies pre-compiled binaries to ./bin/) % make test-otter % make test-mace2 Macintosh users: If you see "make: Command not found.", it means you don't have the developer's tools (compliers, etc.) installed. The good news is that you don't need them. Instead, run the commands "./make-install", "./make-test-otter", and "./make-test-mace2". If test-otter gives a proof and test-mace2 gives a model, everything is probably okay. The binaries should be in the directory bin/. If something goes wrong, try % make all THEN % make test-otter % make test-mace2 If any of that fails, see README.make. To run the Otter test suite, "cd examples; ./Run_all". To run the Mace2 test suite, "cd examples-mace; ./Run_all". The Otter web page is http://www.mcs.anl.gov/AR/otter/ W. McCune (otter@mcs.anl.gov) Argonne National Laboratory August, 2003 (updated August 2004) otter-3.3f/examples-mace2/0040755000076400007640000000000010103524403014777 5ustar mccunemccuneotter-3.3f/examples-mace2/Run_mace0100755000076400007640000000354107705612033016471 0ustar mccunemccune#!/bin/csh # # Run a set of MACE jobs and compare the # results to previous results. # # If $2 is given, it is assumed to be the MACE use. # If $3 is given, it is the filename extension for new output files. # If $4 is given, it is the filename extension for old output files. # if ($#argv == 0) then echo "usage: Run_mace directory [mace | mace new | mace new old]" exit 1 endif if ($#argv >= 2) then set MACE=$2 else set MACE=../../bin/mace2 endif if ($#argv >= 3) then set NEW_OUT=$3 else set NEW_OUT=out$$ endif if ($#argv >= 4) then set BASE_OUT=$4 else set BASE_OUT=out endif if ($1 == propositional || $1 == sorted) then echo "This script is for unsorted first-order problems only." exit 1 endif cd $1 set errors=0 foreach i (*.in) echo "Running $1/$i ..." set parms=`grep "benchmark parameters" $i | sed 's/.*ters//'` $MACE $parms < $i >& $i:r.$NEW_OUT if (-e $i:r.$BASE_OUT) then set unit_old=`grep "Unit assign" $i:r.$BASE_OUT | awk '{print $3}' | tail -1` set unit_new=`grep "Unit assign" $i:r.$NEW_OUT | awk '{print $3}' | tail -1` if ($unit_new != $unit_old) then echo "There is a problem: $NEW_OUT assigned $unit_new, $BASE_OUT assigned $unit_old" set errors=1 else echo "Okay, it seems to have run correctly." endif else echo "Okay, but there's no file for comparison." set errors=1 endif end echo "" if (! $errors) then set time_old=`cat *.$BASE_OUT | grep "CPU time" | awk '{sum += $4} END {print sum}'` set time_new=`cat *.$NEW_OUT | grep "CPU time"| awk '{sum += $4} END {print sum}'` set speedup=`awk "END {print $time_old / $time_new}" /dev/null` echo "time_new=$time_new, time_old=$time_old." echo "The $NEW_OUT times are about $speedup times as fast as the $BASE_OUT times." endif echo "The output files have been left in $1/*.$NEW_OUT." echo "" cd .. otter-3.3f/examples-mace2/Makefile0100644000076400007640000000012207706065011016441 0ustar mccunemccuneall: ./Run_all clean realclean: /bin/rm -f */*.out[0-9]* *~ */*~ Run_all.out.* otter-3.3f/examples-mace2/basic/0040755000076400007640000000000010103524403016060 5ustar mccunemccuneotter-3.3f/examples-mace2/basic/temp0100644000076400007640000000755107714014220016762 0ustar mccunemccune----- MACE 2.2, August 2003 ----- The process was started by mccune on theorem.mcs.anl.gov, Tue Aug 5 15:50:24 2003 The command was "../../mace2/mace2 -n4 -v1 -I". list(usable). 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(y,z),e(z,x)))). 3 [] -P(e(a,a)). 4 [] -P(x)| -(x usable clausifies to: list(usable). 1 [] a(a(W,x),y)=a(a(x,y),y). 2 [] a(a(a(S,x),y),z)=a(a(x,z),a(y,z)). 3 [] a($c1,y)!=y. end_of_list. list(flattened_and_parted_clauses). 1 [] a(x,y)!=z|a(z,y)!=u|$Connect2(x,y,u). 1 [] a(x,y)=z| -$Connect1(u,x)| -$Connect2(u,y,z). 1 [] W!=x|a(x,y)!=z|$Connect1(y,z). 2 [] a(x,y)!=z|a(u,z)!=v|$Connect5(x,y,u,v). 2 [] a(x,y)!=z|$Connect4(u,y,x,v)| -$Connect5(u,y,z,v). 2 [] a(x,y)=z| -$Connect3(u,v,x)| -$Connect4(u,y,v,z). 2 [] S!=x|a(x,y)!=z|$Connect6(y,z). 2 [] a(x,y)!=z|$Connect3(y,u,z)| -$Connect6(u,x). 3 [] $c1!=x|a(x,y)!=y. end_of_list. --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: W S $c1. 1095 clauses were generated; 1075 of those survived the first stage of unit preprocessing; there are 279 atoms. After all unit preprocessing, 267 atoms are still unassigned; 1063 clauses remain; 13 of those are non-Horn (selectable); 4889 K allocated; cpu time so far for this domain size: 0.00 sec. The 1st model has been found. The 10th model has been found.  The search is complete. The set is satisfiable (20 model(s) found). ----- statistics for domain size 3 ---- Input: Clauses input 1075 Literal occurrences input 3131 Greatest atom 279 Unit preprocess: Preprocess unit assignments 12 Clauses after subsumption 1063 Literal occ. after subsump. 3119 Selectable clauses 13 Decide: Splits 111 Unit assignments 6537 Failed paths 92 Memory: Memory malloced 7 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (20 model(s) found). The job finished Mon Aug 2 15:44:30 2004 otter-3.3f/examples-mace2/basic/cd.in0100644000076400007640000000133507313414026017005 0ustar mccunemccune% benchmark parameters -n4 % The formulas below are theorems of the equivalential calculus. % We can show that neither is a single axiom, because e(x,x) does not % follow. list(usable). -P(e(x,y)) | -P(x) | P(y). % condensed detachment % P(e(e(x,y),e(e(y,z),e(x,z)))). % easier P(e(e(x,y),e(e(y,z),e(z,x)))). % a bit harder -P(e(a,a)). % The following can speed up finding models for CD problems. % It says that the all values for which P is false come before % any of the values for which P is true. % But it can be incomplete if you use -c or if you DON'T use % -z 0. In this case it works, because a gets assigned 0, % and there is a model in which P(a) is false. -P(x) | -(x < y) | P(y). end_of_list. otter-3.3f/examples-mace2/basic/tough-nut.out0100664000076400007640000000662210103523660020554 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:30 2004 The command was "../../bin/mace2 -n8". formula_list(usable). all x y (G5(x,y)<->x=0&y=0|x=7&y=7). end_of_list. -------> usable clausifies to: list(usable). 1 [] -G5(x,y)|x=0|x=7. 2 [] -G5(x,y)|x=0|y=7. 3 [] -G5(x,y)|y=0|x=7. 4 [] -G5(x,y)|y=0|y=7. 5 [] G5(x,y)|x!=0|y!=0. 6 [] G5(x,y)|x!=7|y!=7. end_of_list. list(usable). 7 [] -G3(0,y). 8 [] -G4(x,0). 9 [] -G1(7,y). 10 [] -G2(x,7). 11 [] S(0,1). 12 [] S(1,2). 13 [] S(2,3). 14 [] S(3,4). 15 [] S(4,5). 16 [] S(5,6). 17 [] S(6,7). 18 [] -S(x,y)|L(x,y). 19 [] -L(x,y)| -L(y,z)|L(x,z). 20 [] -L(x,y)| -L(y,z)| -S(x,z). 21 [] -L(x,y)|x!=y. 22 [] G1(x,y)|G2(x,y)|G3(x,y)|G4(x,y)|G5(x,y). 23 [] -G1(x,y)| -G2(x,y). 24 [] -G1(x,y)| -G3(x,y). 25 [] -G1(x,y)| -G4(x,y). 26 [] -G1(x,y)| -G5(x,y). 27 [] -G2(x,y)| -G3(x,y). 28 [] -G2(x,y)| -G4(x,y). 29 [] -G2(x,y)| -G5(x,y). 30 [] -G3(x,y)| -G4(x,y). 31 [] -G3(x,y)| -G5(x,y). 32 [] -G4(x,y)| -G5(x,y). 33 [] -S(x1,x2)| -G1(x1,y)|G3(x2,y). 34 [] -S(x1,x2)|G1(x1,y)| -G3(x2,y). 35 [] -S(y1,y2)| -G2(x,y1)|G4(x,y2). 36 [] -S(y1,y2)|G2(x,y1)| -G4(x,y2). end_of_list. list(flattened_and_parted_clauses). 1 [] -G5(x,y)|x=0|x=7. 2 [] -G5(x,y)|x=0|y=7. 3 [] -G5(x,y)|y=0|x=7. 4 [] -G5(x,y)|y=0|y=7. 5 [] G5(x,y)|x!=0|y!=0. 6 [] G5(x,y)|x!=7|y!=7. 7 [] -G3(0,x). 8 [] -G4(x,0). 9 [] -G1(7,x). 10 [] -G2(x,7). 11 [] S(0,1). 12 [] S(1,2). 13 [] S(2,3). 14 [] S(3,4). 15 [] S(4,5). 16 [] S(5,6). 17 [] S(6,7). 18 [] -S(x,y)|L(x,y). 19 [] -L(x,y)| -L(y,z)|L(x,z). 20 [] -L(x,y)| -L(y,z)| -S(x,z). 21 [] -L(x,y)|x!=y. 22 [] G1(x,y)|G2(x,y)|G3(x,y)|G4(x,y)|G5(x,y). 23 [] -G1(x,y)| -G2(x,y). 24 [] -G1(x,y)| -G3(x,y). 25 [] -G1(x,y)| -G4(x,y). 26 [] -G1(x,y)| -G5(x,y). 27 [] -G2(x,y)| -G3(x,y). 28 [] -G2(x,y)| -G4(x,y). 29 [] -G2(x,y)| -G5(x,y). 30 [] -G3(x,y)| -G4(x,y). 31 [] -G3(x,y)| -G5(x,y). 32 [] -G4(x,y)| -G5(x,y). 33 [] -S(x,y)| -G1(x,z)|G3(y,z). 34 [] -S(x,y)|G1(x,z)| -G3(y,z). 35 [] -S(x,y)| -G2(z,x)|G4(z,y). 36 [] -S(x,y)|G2(z,x)| -G4(z,y). end_of_list. --- Starting search for models of size 8 --- 4391 clauses were generated; 2042 of those survived the first stage of unit preprocessing; there are 512 atoms. After all unit preprocessing, 216 atoms are still unassigned; 560 clauses remain; 62 of those are non-Horn (selectable); 4896 K allocated; cpu time so far for this domain size: 0.01 sec.  The search is complete. No models were found. ----- statistics for domain size 8 ---- Input: Clauses input 2042 Literal occurrences input 4600 Greatest atom 512 Unit preprocess: Preprocess unit assignments 296 Clauses after subsumption 560 Literal occ. after subsump. 1216 Selectable clauses 62 Decide: Splits 145269 Unit assignments 5540344 Failed paths 145270 Memory: Memory malloced 14 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 1.52 ======================================= Total times for run (seconds): user CPU time 1.53 (0 hr, 0 min, 1 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:44:32 2004 otter-3.3f/examples-mace2/basic/cl_ql.in0100644000076400007640000000065407312420057017514 0ustar mccunemccune% benchmark parameters -n4 -m50 % A Problem in combinatory logic. % Show that no fixed point combinator Q, where Qx=x(Qx), % can be derived from combinators L and Q, where % Lxy = x(yy), % Qxyz = y(xz). list(usable). a(a(L,x),y) = a(x,a(y,y)). a(a(a(Q,x),y),z) = a(y,a(x,z)). end_of_list. formula_list(usable). % There does not exist a fixed-point combinator. -(exists Q all x (a(Q,x) = a(x,a(Q,x)))). end_of_list. otter-3.3f/examples-mace2/basic/tba.in0100644000076400007640000000054607313412122017163 0ustar mccunemccune% benchmark parameters -n3 -m10000 % Independence of a Ternary Boolean Algebra axiom. list(usable). % The following 5 equations are a basis for Ternary Boolean Algebra. f(f(v,w,x),y,f(v,w,z)) = f(v,w,f(x,y,z)). % f(y,x,x) = x. % We're showing that this axiom is independent. f(x,x,y) = x. f(g(y),y,x) = x. f(x,y,g(y)) = x. f(a,b,b) != b. end_of_list. otter-3.3f/examples-mace2/basic/noncommutative_group.in0100644000076400007640000000021007312421152022667 0ustar mccunemccune% benchmark parameters -n6 -m1000 list(usable). f(e,x) = x. f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). f(a,b) != f(b,a). end_of_list. otter-3.3f/examples-mace2/basic/cd.out0100664000076400007640000000415310103523656017212 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:30 2004 The command was "../../bin/mace2 -n4". list(usable). 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(y,z),e(z,x)))). 3 [] -P(e(a,a)). 4 [] -P(x)| -(x y < z). % first order axiom all x y z (y*x < z*x -> y < z). % second order axiom end_of_list. otter-3.3f/examples-mace2/basic/index.html0100644000076400007640000000236607714267463020111 0ustar mccunemccune /home/mccune/otter-3.3/examples-mace2/basic

/home/mccune/otter-3.3/examples-mace2/basic

Examples for a fixed domain size.

mace2 -n4 < cd.in > cd.out

mace2 -n4 -m50 < cl_ql.in > cl_ql.out

mace2 -n3 -m100000 < cl_sw.in > cl_sw.out

mace2 -n6 -m1000 < noncommutative_group.in > noncommutative_group.out

mace2 -n4 -m1000 < ordered_semi.in > ordered_semi.out

mace2 -n4 -m100 < ring.in > ring.out

mace2 -n3 -m10000 < tba.in > tba.out

mace2 -n8 < tough-nut.in > tough-nut.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/basic/README0100644000076400007640000000004207313720753016750 0ustar mccunemccuneExamples for a fixed domain size. otter-3.3f/examples-mace2/basic/tough-nut.in0100644000076400007640000000624107313412367020360 0ustar mccunemccune% benchmark parameters -n8 % % This is the mutilated checkerboard problem from John McCarthy's % 1964 Stanford AI memo "A Tough Nut for Proof Procedures". % % Of all the proofs I know about, this one comes closest to answersing % the exact challenge put forth in the memo; that is, showing % automatically that a set of first-order statements representing the % 8x8 problem is unsatisfiable. % % (Of course, the real AI interest is in discovering the coloring % argument, so most people focus on the 2n x 2n problem.) % % Running MACE with -n8 does not directly show that the % set is unsatisfiable; it just shows there are no models of size 8; % but that's all we're really interested in. In other words, it % would be fair to include % x = 0 | x = 1 | x = 2 | x = 3 | x = 4 | x = 5 | x = 6 | x = 7 % in McCarthy's set; then the MACE result would clearly be correct. % % (Stickel and Uribe have done the problem with a propositional % prover, but I believe they encoded it by hand into propositional % logic, obtaining a smaller propositional set than MACE uses.) % % If the board is % % (7,0) ... (7,7) % . . % . . % . . % (0,0) ... (0,7) % % G1(x,y) means that (x,y) and the space above are covered by a domino. % G2(x,y) means that (x,y) and the space to the right are covered by a domino. % G3(x,y) means that (x,y) and the space below are covered by a domino. % G4(x,y) means that (x,y) and the space to the left are covered by a domino. % G5(x,y) means that (x,y) is not allowed to be covered. % % S(x,y) is the successor relation for 0 ... 7. % L(x,y) is the less-than relation for 0 ... 7. % % The numbers in comments are McCarthy's axiom numbers. % formula_list(usable). % (formulas with explicit quantification) % List the squares that are not allowed to be covered. all x all y (G5(x,y) <-> (x=0 & y=0) | (x=7 & y=7)). % 11, 12 % Some test cases that are satisfiable: % % all x all y (G5(x,y) <-> (x=1 & y=1) | (x=1 & y=2) | % (x=2 & y=2) | (x=3 & y=2) ). % % all x all y (G5(x,y) <-> (x=0 & y=1) | (x=7 & y=7)). % % all x all y -G5(x,y). % complete board -- 12988816 models end_of_list. list(usable). % clauses (symbols [u-z]+ are variables). % Dominoes don't stick out. -G3(0,y). % 15 -G4(x,0). -G1(7,y). -G2(x,7). S(0,1). S(1,2). S(2,3). S(3,4). S(4,5). S(5,6). S(6,7). % 1 % To change the board size, update the preceding few clauses. % The rest of the clauses don't depend on the size of the board. -S(x,y) | L(x,y). % 2 -L(x,y) | -L(y,z) | L(x,z). % 3a -L(x,y) | -L(y,z) | -S(x,z). % 3b -L(x,y) | x != y. % 4 % = is built in, se we don't include McCarthy's axiom 5. % Every square must satify a Gi. G1(x,y) | G2(x,y) | G3(x,y) | G4(x,y) | G5(x,y). % 6 % Every square satifies at most one Gi. -G1(x,y) | -G2(x,y). % 7 -G1(x,y) | -G3(x,y). -G1(x,y) | -G4(x,y). -G1(x,y) | -G5(x,y). -G2(x,y) | -G3(x,y). % 8 -G2(x,y) | -G4(x,y). -G2(x,y) | -G5(x,y). -G3(x,y) | -G4(x,y). % 9 -G3(x,y) | -G5(x,y). -G4(x,y) | -G5(x,y). % 10 % Relationships between Gi's. -S(x1,x2) | -G1(x1,y) | G3(x2,y). % 13 -S(x1,x2) | G1(x1,y) | -G3(x2,y). -S(y1,y2) | -G2(x,y1) | G4(x,y2). % 14 -S(y1,y2) | G2(x,y1) | -G4(x,y2). end_of_list. otter-3.3f/examples-mace2/basic/cl_ql.out0100664000076400007640000000463010103523656017716 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:30 2004 The command was "../../bin/mace2 -n4 -m50". list(usable). 1 [] a(a(L,x),y)=a(x,a(y,y)). 2 [] a(a(a(Q,x),y),z)=a(y,a(x,z)). end_of_list. formula_list(usable). -(exists Q all x (a(Q,x)=a(x,a(Q,x)))). end_of_list. -------> usable clausifies to: list(usable). 3 [] a(x1,$f1(x1))!=a($f1(x1),a(x1,$f1(x1))). end_of_list. list(flattened_and_parted_clauses). 1 [] a(x,x)!=y|a(z,y)!=u|$Connect2(x,z,u). 1 [] a(x,y)=z| -$Connect1(u,x)| -$Connect2(y,u,z). 1 [] L!=x|a(x,y)!=z|$Connect1(y,z). 2 [] a(x,y)!=z|a(u,z)!=v|$Connect4(x,y,u,v). 2 [] a(x,y)=z| -$Connect3(u,v,x)| -$Connect4(u,y,v,z). 2 [] Q!=x|a(x,y)!=z|$Connect5(y,z). 2 [] a(x,y)!=z|$Connect3(u,y,z)| -$Connect5(u,x). 3 [] a(x,y)!=z|$f1(x)!=y| -$Connect6(y,z). 3 [] a(x,y)!=z|y!=z|$Connect6(x,y). end_of_list. --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: L Q. 3244 clauses were generated; 3144 of those survived the first stage of unit preprocessing; there are 536 atoms. After all unit preprocessing, 516 atoms are still unassigned; 3124 clauses remain; 22 of those are non-Horn (selectable); 4897 K allocated; cpu time so far for this domain size: 0.00 sec. The 1st model has been found. The 10th model has been found.  Exit by max_models parameter. The set is satisfiable (50 model(s) found). ----- statistics for domain size 4 ---- Input: Clauses input 3144 Literal occurrences input 9234 Greatest atom 536 Unit preprocess: Preprocess unit assignments 20 Clauses after subsumption 3124 Literal occ. after subsump. 9214 Selectable clauses 22 Decide: Splits 122 Unit assignments 9673 Failed paths 65 Memory: Memory malloced 15 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (50 model(s) found). The job finished Mon Aug 2 15:44:30 2004 otter-3.3f/examples-mace2/basic/ring.in0100644000076400007640000000115007313411373017353 0ustar mccunemccune% benchmark parameters -n4 -m100 % Generate some rings (not necessarily with unit). op(450, xfx, +). % sum op(400, xfx, *). % product op(350, fy, ~). % minus list(usable). 0+x=x. x+0=x. ~x+x=0. x+ ~x=0. (x+y)+z=x+ (y+z). x+y=y+x. % Product is associative: (x*y)*z=x* (y*z). % Left and right distributivity: x* (y+z)=x*y+x*z. (y+z)*x=y*x+z*x. % Here are alternate forms of distributivity which include % auxiliary 3-place functions. These use much less memory % than the ordinary forms of distributivity. % x* (y+z) = h(x,y,z). h(x,y,z) = x*y+x*z. % (y+z)*x = f(x,y,z). f(x,y,z) = y*x+z*x. end_of_list. otter-3.3f/examples-mace2/basic/cl_sw.in0100644000076400007640000000101307312420562017520 0ustar mccunemccune% benchmark parameters -n3 -m100000 % A Problem in combinatory logic. % Given combinators W and s, where % Wxy = xyy, % Sxyz = xz(yz), % show that the (weak) fixed point property does not hold, % that is, that there is a combinator f without a fixed point. % F combinator f has a fixed point if for all y, fy=y. formula_list(usable). all x y (a(a(W,x),y) = a(a(x,y),y)). all x y z (a(a(a(S,x),y),z) = a(a(x,z),a(y,z))). % There exsists an element without a fixed point: -(all f exists y (a(f,y)=y)). end_of_list. otter-3.3f/examples-mace2/basic/program0100644000076400007640000000000607705577561017476 0ustar mccunemccunemace2 otter-3.3f/examples-mace2/basic/ring.out0100664000076400007640000000462710103523656017571 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:30 2004 The command was "../../bin/mace2 -n4 -m100". op(450,xfx,+). op(400,xfx,*). op(350,fy,~). list(usable). 1 [] 0+x=x. 2 [] x+0=x. 3 [] ~x+x=0. 4 [] x+ ~x=0. 5 [] (x+y)+z=x+ (y+z). 6 [] x+y=y+x. 7 [] (x*y)*z=x* (y*z). 8 [] x* (y+z)=x*y+x*z. 9 [] (y+z)*x=y*x+z*x. end_of_list. list(flattened_and_parted_clauses). 1 [] 0+x=x. 2 [] x+0=x. 3 [] ~x!=y|y+x=0. 4 [] ~x!=y|x+y=0. 5 [] x+y!=z|u+z!=v|$Connect1(x,y,u,v). 5 [] x+y!=z|z+u=v| -$Connect1(y,u,x,v). 6 [] x+y!=z|y+x=z. 7 [] x*y!=z|u*z!=v|$Connect2(x,y,u,v). 7 [] x*y!=z|z*u=v| -$Connect2(y,u,x,v). 8 [] x*y!=z|u+z!=v|$Connect4(x,y,u,v). 8 [] x*y!=z|$Connect3(x,u,y,v)| -$Connect4(x,u,z,v). 8 [] x+y!=z|u*z=v| -$Connect3(u,y,x,v). 9 [] x*y!=z|u+z!=v|$Connect6(x,y,u,v). 9 [] x*y!=z|$Connect5(u,y,x,v)| -$Connect6(u,y,z,v). 9 [] x+y!=z|z*u=v| -$Connect5(y,u,x,v). end_of_list. --- Starting search for models of size 4 --- 10612 clauses were generated; 8234 of those survived the first stage of unit preprocessing; there are 1696 atoms. After all unit preprocessing, 1605 atoms are still unassigned; 8096 clauses remain; 28 of those are non-Horn (selectable); 4930 K allocated; cpu time so far for this domain size: 0.01 sec. The 1st model has been found. The 10th model has been found.  The search is complete. The set is satisfiable (40 model(s) found). ----- statistics for domain size 4 ---- Input: Clauses input 8234 Literal occurrences input 23440 Greatest atom 1696 Unit preprocess: Preprocess unit assignments 91 Clauses after subsumption 8096 Literal occ. after subsump. 23246 Selectable clauses 28 Decide: Splits 110 Unit assignments 26183 Failed paths 71 Memory: Memory malloced 48 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.01 ======================================= Total times for run (seconds): user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (40 model(s) found). The job finished Mon Aug 2 15:44:30 2004 otter-3.3f/examples-mace2/basic/noncommutative_group.out0100664000076400007640000000402610103523656023107 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:30 2004 The command was "../../bin/mace2 -n6 -m1000". list(usable). 1 [] f(e,x)=x. 2 [] f(g(x),x)=e. 3 [] f(f(x,y),z)=f(x,f(y,z)). 4 [] f(a,b)!=f(b,a). end_of_list. list(flattened_and_parted_clauses). 1 [] e!=x|f(x,y)=y. 2 [] e!=x|g(y)!=z|f(z,y)=x. 3 [] f(x,y)!=z|f(u,z)!=v|$Connect1(x,y,u,v). 3 [] f(x,y)!=z|f(z,u)=v| -$Connect1(y,u,x,v). 4 [] f(x,y)!=z|b!=x|a!=y|f(y,x)!=z. end_of_list. --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: e b a. 16780 clauses were generated; 13181 of those survived the first stage of unit preprocessing; there are 1602 atoms. After all unit preprocessing, 1483 atoms are still unassigned; 12987 clauses remain; 41 of those are non-Horn (selectable); 4927 K allocated; cpu time so far for this domain size: 0.01 sec. The 1st model has been found. The 10th model has been found.  The search is complete. The set is satisfiable (18 model(s) found). ----- statistics for domain size 6 ---- Input: Clauses input 13181 Literal occurrences input 37418 Greatest atom 1602 Unit preprocess: Preprocess unit assignments 119 Clauses after subsumption 12987 Literal occ. after subsump. 37149 Selectable clauses 41 Decide: Splits 413 Unit assignments 110216 Failed paths 396 Memory: Memory malloced 45 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.09 ======================================= Total times for run (seconds): user CPU time 0.10 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (18 model(s) found). The job finished Mon Aug 2 15:44:30 2004 otter-3.3f/examples-mace2/basic/ordered_semi.out0100664000076400007640000000430410103523656021263 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:30 2004 The command was "../../bin/mace2 -n4 -m1000". op(400,xfx,*). formula_list(usable). all x y z ((x*y)*z=x* (y*z)). all x y z (x*yyy usable clausifies to: list(usable). 1 [] (x*y)*z=x* (y*z). 2 [] -(x*y Complete. % Theorem formulation : Linearized. % English : % Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin % Source : [TPTP] % Names : % Status : satisfiable % Rating : 0.67 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 1.00 v2.0.0 % Syntax : Number of clauses : 19 ( 0 non-Horn; 19 unit; 1 RR) % Number of literals : 19 ( 19 equality) % Maximal clause size : 1 ( 1 average) % Number of predicates : 1 ( 0 propositional; 2-2 arity) % Number of functors : 9 ( 4 constant; 0-3 arity) % Number of variables : 37 ( 2 singleton) % Maximal term depth : 4 ( 2 average) % Comments : % : tptp2X -f otter:hypothesis:[set(tptp_eq),set(auto),clear(print_given)] -t rm_equality:stfp RNG025-8.p %-------------------------------------------------------------------------- set(prolog_style_variables). set(tptp_eq). set(auto). clear(print_given). list(usable). % reflexivity, axiom. equal(X, X). % commutativity_for_addition, axiom. equal(add(X, Y), add(Y, X)). % associativity_for_addition, axiom. equal(add(X, add(Y, Z)), add(add(X, Y), Z)). % left_additive_identity, axiom. equal(add(additive_identity, X), X). % right_additive_identity, axiom. equal(add(X, additive_identity), X). % left_multiplicative_zero, axiom. equal(multiply(additive_identity, X), additive_identity). % right_multiplicative_zero, axiom. equal(multiply(X, additive_identity), additive_identity). % left_additive_inverse, axiom. equal(add(additive_inverse(X), X), additive_identity). % right_additive_inverse, axiom. equal(add(X, additive_inverse(X)), additive_identity). % distribute1, axiom. equal(multiply(X, add(Y, Z)), add(multiply(X, Y), multiply(X, Z))). % distribute2, axiom. equal(multiply(add(X, Y), Z), add(multiply(X, Z), multiply(Y, Z))). % additive_inverse_additive_inverse, axiom. equal(additive_inverse(additive_inverse(X)), X). % right_alternative, axiom. equal(multiply(multiply(X, Y), Y), multiply(X, multiply(Y, Y))). % left_alternative, axiom. equal(multiply(multiply(X, X), Y), multiply(X, multiply(X, Y))). % linearised_associator1, axiom. equal(associator(X, Y, add(U, V)), add(associator(X, Y, U), associator(X, Y, V))). % linearised_associator2, axiom. equal(associator(X, add(U, V), Y), add(associator(X, U, Y), associator(X, V, Y))). % linearised_associator3, axiom. equal(associator(add(U, V), X, Y), add(associator(U, X, Y), associator(V, X, Y))). % commutator, axiom. equal(commutator(X, Y), add(multiply(Y, X), additive_inverse(multiply(X, Y)))). end_of_list. list(sos). % prove_flexible_law, conjecture. -equal(add(associator(a, b, c), associator(a, c, b)), additive_identity). end_of_list. %-------------------------------------------------------------------------- otter-3.3f/examples-mace2/iterate/noncommutive_ring1.out0100664000076400007640000002271110103523663023021 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:33 2004 The command was "../../bin/mace2 -N8 -p". op(450,xfx,+). op(400,xfx,*). op(350,fy,~). list(usable). 1 [] 0+x=x. 2 [] x+0=x. 3 [] ~x+x=0. 4 [] x+ ~x=0. 5 [] (x+y)+z=x+ (y+z). 6 [] x+y=y+x. 7 [] (x*y)*z=x* (y*z). 8 [] x* (y+z)=x*y+x*z. 9 [] (y+z)*x=y*x+z*x. 10 [] ~ ~x=x. 11 [] ~0=0. 12 [] 0*x=0. 13 [] x*0=0. 14 [] 1*x=x. 15 [] x*1=x. 16 [] a*b!=b*a. end_of_list. list(flattened_and_parted_clauses). 1 [] 0+x=x. 2 [] x+0=x. 3 [] ~x!=y|y+x=0. 4 [] ~x!=y|x+y=0. 5 [] x+y!=z|u+z!=v|$Connect1(x,y,u,v). 5 [] x+y!=z|z+u=v| -$Connect1(y,u,x,v). 6 [] x+y!=z|y+x=z. 7 [] x*y!=z|u*z!=v|$Connect2(x,y,u,v). 7 [] x*y!=z|z*u=v| -$Connect2(y,u,x,v). 8 [] x*y!=z|u+z!=v|$Connect4(x,y,u,v). 8 [] x*y!=z|$Connect3(x,u,y,v)| -$Connect4(x,u,z,v). 8 [] x+y!=z|u*z=v| -$Connect3(u,y,x,v). 9 [] x*y!=z|u+z!=v|$Connect6(x,y,u,v). 9 [] x*y!=z|$Connect5(u,y,x,v)| -$Connect6(u,y,z,v). 9 [] x+y!=z|z*u=v| -$Connect5(y,u,x,v). 10 [] ~x!=y| ~y=x. 11 [] ~0=0. 12 [] 0*x=0. 13 [] x*0=0. 14 [] 1*x=x. 15 [] x*1=x. 16 [] x*y!=z|b!=x|a!=y|y*x!=z. end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: b a. 389 clauses were generated; 153 of those survived the first stage of unit preprocessing; there are 124 atoms. After all unit preprocessing, 8 atoms are still unassigned; 8 clauses remain; 2 of those are non-Horn (selectable); 4885 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 153 Literal occurrences input 224 Greatest atom 124 Unit preprocess: Preprocess unit assignments 116 Clauses after subsumption 8 Literal occ. after subsump. 16 Selectable clauses 2 Decide: Splits 1 Unit assignments 4 Failed paths 2 Memory: Memory malloced 3 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: b a. 2631 clauses were generated; 986 of those survived the first stage of unit preprocessing; there are 564 atoms. After all unit preprocessing, 258 atoms are still unassigned; 618 clauses remain; 9 of those are non-Horn (selectable); 4898 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 986 Literal occurrences input 1910 Greatest atom 564 Unit preprocess: Preprocess unit assignments 306 Clauses after subsumption 618 Literal occ. after subsump. 1422 Selectable clauses 9 Decide: Splits 3 Unit assignments 299 Failed paths 4 Memory: Memory malloced 16 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: b a. 10726 clauses were generated; 4514 of those survived the first stage of unit preprocessing; there are 1704 atoms. After all unit preprocessing, 1059 atoms are still unassigned; 3667 clauses remain; 21 of those are non-Horn (selectable); 4930 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 4514 Literal occurrences input 10351 Greatest atom 1704 Unit preprocess: Preprocess unit assignments 645 Clauses after subsumption 3667 Literal occ. after subsump. 9125 Selectable clauses 21 Decide: Splits 8 Unit assignments 2162 Failed paths 9 Memory: Memory malloced 48 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: b a. 32262 clauses were generated; 15341 of those survived the first stage of unit preprocessing; there are 4060 atoms. After all unit preprocessing, 2936 atoms are still unassigned; 13733 clauses remain; 35 of those are non-Horn (selectable); 4997 K allocated; cpu time so far for this domain size: 0.02 sec. ----- statistics for domain size 5 ---- Input: Clauses input 15341 Literal occurrences input 38264 Greatest atom 4060 Unit preprocess: Preprocess unit assignments 1124 Clauses after subsumption 13733 Literal occ. after subsump. 35768 Selectable clauses 35 Decide: Splits 16 Unit assignments 9299 Failed paths 17 Memory: Memory malloced 115 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.01 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: b a. 79657 clauses were generated; 41893 of those survived the first stage of unit preprocessing; there are 8292 atoms. After all unit preprocessing, 6537 atoms are still unassigned; 39178 clauses remain; 52 of those are non-Horn (selectable); 5117 K allocated; cpu time so far for this domain size: 0.04 sec. ----- statistics for domain size 6 ---- Input: Clauses input 41893 Literal occurrences input 109472 Greatest atom 8292 Unit preprocess: Preprocess unit assignments 1755 Clauses after subsumption 39178 Literal occ. after subsump. 105022 Selectable clauses 52 Decide: Splits 53 Unit assignments 61215 Failed paths 54 Memory: Memory malloced 235 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.04 DPLL 0.11 --- Starting search for models of size 7 --- Applying isomorphism constraints to constants: b a. 171353 clauses were generated; 97612 of those survived the first stage of unit preprocessing; there are 15204 atoms. After all unit preprocessing, 12654 atoms are still unassigned; 93380 clauses remain; 73 of those are non-Horn (selectable); 5312 K allocated; cpu time so far for this domain size: 0.09 sec. ----- statistics for domain size 7 ---- Input: Clauses input 97612 Literal occurrences input 262490 Greatest atom 15204 Unit preprocess: Preprocess unit assignments 2550 Clauses after subsumption 93380 Literal occ. after subsump. 255250 Selectable clauses 73 Decide: Splits 270 Unit assignments 805684 Failed paths 271 Memory: Memory malloced 430 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.07 DPLL 2.15 --- Starting search for models of size 8 --- Applying isomorphism constraints to constants: b a. 333015 clauses were generated; 202155 of those survived the first stage of unit preprocessing; there are 25744 atoms. After all unit preprocessing, 22223 atoms are still unassigned; 195932 clauses remain; 98 of those are non-Horn (selectable); 10494 K allocated; cpu time so far for this domain size: 0.18 sec. ======================= Model #1 at 2.70 seconds: + : | 0 1 2 3 4 5 6 7 --+---------------- 0 | 0 1 2 3 4 5 6 7 1 | 1 0 4 5 2 3 7 6 2 | 2 4 0 6 1 7 3 5 3 | 3 5 6 0 7 1 2 4 4 | 4 2 1 7 0 6 5 3 5 | 5 3 7 1 6 0 4 2 6 | 6 7 3 2 5 4 0 1 7 | 7 6 5 4 3 2 1 0 ~ : 0 1 2 3 4 5 6 7 ------------------- 0 1 2 3 4 5 6 7 * : | 0 1 2 3 4 5 6 7 --+---------------- 0 | 0 0 0 0 0 0 0 0 1 | 0 1 2 3 4 5 6 7 2 | 0 2 0 0 2 2 0 2 3 | 0 3 2 3 6 0 6 2 4 | 0 4 2 3 1 7 6 5 5 | 0 5 0 0 5 5 0 5 6 | 0 6 2 3 3 2 6 0 7 | 0 7 0 0 7 7 0 7 b: 2 a: 3 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 8 ---- Input: Clauses input 202155 Literal occurrences input 554116 Greatest atom 25744 Unit preprocess: Preprocess unit assignments 3521 Clauses after subsumption 195932 Literal occ. after subsump. 543098 Selectable clauses 98 Decide: Splits 58 Unit assignments 54394 Failed paths 51 Memory: Memory malloced 729 K Memory MACE_tp_alloced 9765 K Time (seconds): Generate ground clauses 0.14 DPLL 0.15 ======================================= Total times for run (seconds): user CPU time 2.70 (0 hr, 0 min, 2 sec) system CPU time 0.07 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:35 2004 otter-3.3f/examples-mace2/iterate/noncommutive_ring1.in0100644000076400007640000000200707714213454022622 0ustar mccunemccune% benchmark parameters -N8 -p % Find a noncommutative ring. To make it more difficult, assume % the ring has a unit. op(450, xfx, +). % sum op(400, xfx, *). % product op(350, fy, ~). % minus list(usable). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % RING AXIOMS % <+,~,0> is an Abelian group: 0+x=x. x+0=x. ~x+x=0. x+ ~x=0. (x+y)+z=x+ (y+z). x+y=y+x. % Product is associative: (x*y)*z=x* (y*z). % Left and right distributivity: x* (y+z)=x*y+x*z. (y+z)*x=y*x+z*x. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Ring lemmas ~ ~x=x. ~0=0. 0*x=0. x*0=0. % Assume the ring has a unit. 1*x=x. x*1=x. % There are 2 noncommuting elements. a*b!=b*a. % Using constants a and b as the noncommuting elements allows % the possibility that they can be 0 or 1. % Since 0 and 1 commute with everything, we could fix the % noncommuting elements by using 2*3!=3*2 instead. % In general it's a good idea to do this, but it doesn't make % much difference in this case. % % 2*3!=3*2. end_of_list. otter-3.3f/examples-mace2/iterate/CAT019-5.in0100644000076400007640000000530607313415477020013 0ustar mccunemccune% benchmark parameters -n2 -N6 -p %-------------------------------------------------------------------------- % File : CAT019-5 : TPTP v2.3.0. Released v1.0.0. % Domain : Category Theory % Problem : Axiom of Indiscernibles % Version : [Sco79] axioms : Reduced & Augmented > Complete. % English : [all z (x=z <-> y=z)] -> x=y. % Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L % Source : [ANL] % Names : p15.ver3.no1.in [ANL] % Status : satisfiable % Rating : 0.67 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 1.00 v2.0.0 % Syntax : Number of clauses : 16 ( 0 non-Horn; 6 unit; 12 RR) % Number of literals : 30 ( 13 equality) % Maximal clause size : 3 ( 1 average) % Number of predicates : 3 ( 0 propositional; 1-2 arity) % Number of functors : 6 ( 3 constant; 0-2 arity) % Number of variables : 22 ( 2 singleton) % Maximal term depth : 3 ( 1 average) % Comments : Axioms simplified by Art Quaife. % : Assumes something exists. % : tptp2X -f otter:hypothesis:[set(tptp_eq),set(auto),clear(print_given)] -t rm_equality:stfp CAT019-5.p %-------------------------------------------------------------------------- set(prolog_style_variables). set(tptp_eq). set(auto). clear(print_given). list(usable). % reflexivity, axiom. equal(X, X). % equivalence_implies_existence1, axiom. -equivalent(X, Y) | there_exists(X). % equivalence_implies_existence2, axiom. -equivalent(X, Y) | equal(X, Y). % existence_and_equality_implies_equivalence1, axiom. -there_exists(X) | -equal(X, Y) | equivalent(X, Y). % domain_has_elements, axiom. -there_exists(domain(X)) | there_exists(X). % codomain_has_elements, axiom. -there_exists(codomain(X)) | there_exists(X). % composition_implies_domain, axiom. -there_exists(compose(X, Y)) | there_exists(domain(X)). % domain_codomain_composition1, axiom. -there_exists(compose(X, Y)) | equal(domain(X), codomain(Y)). % domain_codomain_composition2, axiom. -there_exists(domain(X)) | -equal(domain(X), codomain(Y)) | there_exists(compose(X, Y)). % associativity_of_compose, axiom. equal(compose(X, compose(Y, Z)), compose(compose(X, Y), Z)). % compose_domain, axiom. equal(compose(X, domain(X)), X). % compose_codomain, axiom. equal(compose(codomain(X), X), X). end_of_list. list(sos). % assume_c_exists, hypothesis. there_exists(c). % equality_of_a_and_b1, hypothesis. -there_exists(Z) | -equal(a, Z) | equal(b, Z). % equality_of_a_and_b2, hypothesis. -there_exists(Z) | equal(a, Z) | -equal(b, Z). % prove_a_equals_b, conjecture. -equal(a, b). end_of_list. %-------------------------------------------------------------------------- otter-3.3f/examples-mace2/iterate/cd.in0100644000076400007640000000130007313414233017351 0ustar mccunemccune% benchmark parameters -n2 -N6 -p % The formulas below are theorems of the equivalential calculus. % We can show that neither is a single axiom, because e(x,x) does not % follow. list(usable). -P(e(x,y)) | -P(x) | P(y). % P(e(e(x,y),e(e(y,z),e(x,z)))). % easier P(e(e(x,y),e(e(y,z),e(z,x)))). % harder -P(e(a,a)). % The following can speed up finding models for CD problems. % It says that the all values for which P is false come before % any of the values for which P is true. % But it can be incomplete if you use -c or if you DON'T use % -z 0. In this case it works, because a gets assigned 0, % and there is a model in which P(a) is false. % -P(x) | -(x < y) | P(y). end_of_list. otter-3.3f/examples-mace2/iterate/noncommutative_group.in0100644000076400007640000000021007313413664023255 0ustar mccunemccune% benchmark parameters -n2 -N6 -p list(usable). f(e,x) = x. f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). f(a,b) != f(b,a). end_of_list. otter-3.3f/examples-mace2/iterate/cd.out0100664000076400007640000001047210103523660017562 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:32 2004 The command was "../../bin/mace2 -n2 -N6 -p". list(usable). 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(y,z),e(z,x)))). 3 [] -P(e(a,a)). end_of_list. list(flattened_and_parted_clauses). 1 [] e(x,y)!=z| -P(z)| -P(x)|P(y). 2 [] e(x,y)!=z|e(u,x)!=v|$Connect2(y,z,u,v). 2 [] e(x,y)!=z|$Connect1(u,v,z)| -$Connect2(u,y,v,x). 2 [] e(x,y)!=z| -$Connect1(x,y,u)|$Connect3(z,u). 2 [] e(x,y)!=z|P(z)| -$Connect3(x,y). 3 [] a!=x|e(x,x)!=y| -P(y). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: a. 115 clauses were generated; 106 of those survived the first stage of unit preprocessing; there are 44 atoms. After all unit preprocessing, 38 atoms are still unassigned; 100 clauses remain; 4 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 106 Literal occurrences input 292 Greatest atom 44 Unit preprocess: Preprocess unit assignments 6 Clauses after subsumption 100 Literal occ. after subsump. 286 Selectable clauses 4 Decide: Splits 3 Unit assignments 46 Failed paths 4 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: a. 680 clauses were generated; 657 of those survived the first stage of unit preprocessing; there are 159 atoms. After all unit preprocessing, 147 atoms are still unassigned; 645 clauses remain; 9 of those are non-Horn (selectable); 4886 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 657 Literal occurrences input 1914 Greatest atom 159 Unit preprocess: Preprocess unit assignments 12 Clauses after subsumption 645 Literal occ. after subsump. 1902 Selectable clauses 9 Decide: Splits 91 Unit assignments 1982 Failed paths 92 Memory: Memory malloced 4 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: a. 2584 clauses were generated; 2540 of those survived the first stage of unit preprocessing; there are 424 atoms. After all unit preprocessing, 404 atoms are still unassigned; 2520 clauses remain; 16 of those are non-Horn (selectable); 4894 K allocated; cpu time so far for this domain size: 0.00 sec. ======================= Model #1 at 0.02 seconds: e : | 0 1 2 3 --+-------- 0 | 1 2 0 3 1 | 0 3 1 2 2 | 3 0 2 1 3 | 2 1 3 0 P : 0 1 2 3 ----------- F F T F a: 0 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 4 ---- Input: Clauses input 2540 Literal occurrences input 7504 Greatest atom 424 Unit preprocess: Preprocess unit assignments 20 Clauses after subsumption 2520 Literal occ. after subsump. 7484 Selectable clauses 16 Decide: Splits 1156 Unit assignments 37799 Failed paths 1151 Memory: Memory malloced 12 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.02 ======================================= Total times for run (seconds): user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:32 2004 otter-3.3f/examples-mace2/iterate/PUZ001-3.out0100664000076400007640000001257110103523663020240 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:35 2004 The command was "../../bin/mace2 -n2 -N6 -p". set(prolog_style_variables). set(tptp_eq). set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). clear(print_given). list(usable). 0 [] lives(agatha). 0 [] lives(butler). 0 [] lives(charles). 0 [] -killed(X,Y)| -richer(X,Y). 0 [] -hates(agatha,X)| -hates(charles,X). 0 [] -hates(X,agatha)| -hates(X,butler)| -hates(X,charles). 0 [] hates(agatha,agatha). 0 [] hates(agatha,charles). 0 [] -killed(X,Y)|hates(X,Y). 0 [] -hates(agatha,X)|hates(butler,X). 0 [] -lives(X)|richer(X,agatha)|hates(butler,X). end_of_list. list(sos). 0 [] killed(agatha,agatha)|killed(butler,agatha)|killed(charles,agatha). end_of_list. list(clauses). 1 [] lives(agatha). 2 [] lives(butler). 3 [] lives(charles). 4 [] -killed(X,Y)| -richer(X,Y). 5 [] -hates(agatha,X)| -hates(charles,X). 6 [] -hates(X,agatha)| -hates(X,butler)| -hates(X,charles). 7 [] hates(agatha,agatha). 8 [] hates(agatha,charles). 9 [] -killed(X,Y)|hates(X,Y). 10 [] -hates(agatha,X)|hates(butler,X). 11 [] -lives(X)|richer(X,agatha)|hates(butler,X). 12 [] killed(agatha,agatha)|killed(butler,agatha)|killed(charles,agatha). end_of_list. list(flattened_and_parted_clauses). 1 [] -equal(agatha,A)|lives(A). 2 [] -equal(butler,A)|lives(A). 3 [] -equal(charles,A)|lives(A). 4 [] -killed(A,B)| -richer(A,B). 5 [] -equal(charles,A)| -hates(A,B)| -$Connect1(B). 5 [] -equal(agatha,A)| -hates(A,B)|$Connect1(B). 6 [] -equal(charles,A)| -hates(B,A)| -$Connect2(B)| -$Connect3(B). 6 [] -equal(butler,A)| -hates(B,A)|$Connect3(B). 6 [] -equal(agatha,A)| -hates(B,A)|$Connect2(B). 7 [] -equal(agatha,A)|hates(A,A). 8 [] -equal(charles,A)| -equal(agatha,B)|hates(B,A). 9 [] -killed(A,B)|hates(A,B). 10 [] -equal(butler,A)|hates(A,B)| -$Connect4(B). 10 [] -equal(agatha,A)| -hates(A,B)|$Connect4(B). 11 [] -equal(butler,A)| -lives(B)|hates(A,B)| -$Connect5(B). 11 [] -equal(agatha,A)|richer(B,A)|$Connect5(B). 12 [] -equal(charles,A)| -equal(agatha,B)|killed(B,B)|killed(A,B)| -$Connect6(B). 12 [] -equal(butler,A)|killed(A,B)|$Connect6(B). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: agatha butler charles. 75 clauses were generated; 56 of those survived the first stage of unit preprocessing; there are 36 atoms. After all unit preprocessing, 16 atoms are still unassigned; 14 clauses remain; 6 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 56 Literal occurrences input 129 Greatest atom 36 Unit preprocess: Preprocess unit assignments 20 Clauses after subsumption 14 Literal occ. after subsump. 35 Selectable clauses 6 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: agatha butler charles. 162 clauses were generated; 118 of those survived the first stage of unit preprocessing; there are 66 atoms. After all unit preprocessing, 48 atoms are still unassigned; 88 clauses remain; 18 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ======================= Model #1 at 0.00 seconds: agatha: 0 lives : 0 1 2 --------- T T T butler: 1 charles: 2 killed : | 0 1 2 --+------ 0 | T F F 1 | F F T 2 | F F F richer : | 0 1 2 --+------ 0 | F F F 1 | T F F 2 | T F F hates : | 0 1 2 --+------ 0 | T F T 1 | T F T 2 | F F F end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 3 ---- Input: Clauses input 118 Literal occurrences input 291 Greatest atom 66 Unit preprocess: Preprocess unit assignments 18 Clauses after subsumption 88 Literal occ. after subsump. 240 Selectable clauses 18 Decide: Splits 3 Unit assignments 36 Failed paths 1 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:35 2004 otter-3.3f/examples-mace2/iterate/BOO032-1.in0100644000076400007640000000473107313415464020007 0ustar mccunemccune% benchmark parameters -n2 -N6 -p %-------------------------------------------------------------------------- % File : BOO032-1 : TPTP v2.3.0. Released v2.2.0. % Domain : Boolean Algebra % Problem : Independence of a system of Boolean algebra % Version : [MP96] (equality) axioms : Especial. % English : This is part of a proof that a self-dual 3-basis for Boolean % algebra is independent. % Refs : [McC98] McCune (1998), Email to G. Sutcliffe % : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq % Source : [McC98] % Names : DUAL-BA-9 [MP96] % Status : satisfiable % Rating : 1.00 v2.2.1 % Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 1 RR) % Number of literals : 14 ( 14 equality) % Maximal clause size : 1 ( 1 average) % Number of predicates : 1 ( 0 propositional; 2-2 arity) % Number of functors : 4 ( 1 constant; 0-2 arity) % Number of variables : 29 ( 10 singleton) % Maximal term depth : 4 ( 2 average) % Comments : The smallest model has 5 elements. % : tptp2X -f otter:hypothesis:[set(tptp_eq),set(auto),clear(print_given)] -t rm_equality:stfp BOO032-1.p %-------------------------------------------------------------------------- set(prolog_style_variables). set(tptp_eq). set(auto). clear(print_given). list(usable). % reflexivity, axiom. equal(X, X). % l1, axiom. equal(add(X, multiply(Y, multiply(X, Z))), X). % l3, axiom. equal(add(add(multiply(X, Y), multiply(Y, Z)), Y), Y). % property3, axiom. equal(multiply(add(X, inverse(X)), Y), Y). % l2, axiom. equal(multiply(X, add(Y, add(X, Z))), X). % l4, axiom. equal(multiply(multiply(add(X, Y), add(Y, Z)), Y), Y). % property3_dual, axiom. equal(add(multiply(X, inverse(X)), Y), Y). % majority1, axiom. equal(add(multiply(add(X, Y), X), multiply(X, Y)), X). % majority2, axiom. equal(add(multiply(add(X, X), Y), multiply(X, X)), X). % majority3, axiom. equal(add(multiply(add(X, Y), Y), multiply(X, Y)), Y). % majority1_dual, axiom. equal(multiply(add(multiply(X, Y), X), add(X, Y)), X). % majority2_dual, axiom. equal(multiply(add(multiply(X, X), Y), add(X, X)), X). % majority3_dual, axiom. equal(multiply(add(multiply(X, Y), Y), add(X, Y)), Y). end_of_list. list(sos). % prove_inverse_involution, conjecture. -equal(inverse(inverse(a)), a). end_of_list. %-------------------------------------------------------------------------- otter-3.3f/examples-mace2/iterate/index.html0100644000076400007640000000305707714267463020463 0ustar mccunemccune /home/mccune/otter-3.3/examples-mace2/iterate

/home/mccune/otter-3.3/examples-mace2/iterate

Examples that iterate through domain sizes.

mace2 -n2 -N6 -p < BOO032-1.in > BOO032-1.out

mace2 -n2 -N6 -p < CAT019-5.in > CAT019-5.out

mace2 -n2 -N6 -p < cd.in > cd.out

mace2 -N10 -p < kauer.in > kauer.out

mace2 -n2 -N6 -p < LAT025-1.in > LAT025-1.out

mace2 -n2 -N6 -p < LCL136-1.in > LCL136-1.out

mace2 -n2 -N6 -p < noncommutative_group.in > noncommutative_group.out

mace2 -N8 -p < noncommutive_ring1.in > noncommutive_ring1.out

mace2 -n2 -N6 -p < PUZ001-3.in > PUZ001-3.out

mace2 -n2 -N6 -p < RNG025-8.in > RNG025-8.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/iterate/README0100644000076400007640000000005407313721020017313 0ustar mccunemccuneExamples that iterate through domain sizes. otter-3.3f/examples-mace2/iterate/BOO032-1.out0100664000076400007640000002147310103523660020201 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:32 2004 The command was "../../bin/mace2 -n2 -N6 -p". set(prolog_style_variables). set(tptp_eq). set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). clear(print_given). list(usable). 0 [] equal(X,X). 0 [] equal(add(X,multiply(Y,multiply(X,Z))),X). 0 [] equal(add(add(multiply(X,Y),multiply(Y,Z)),Y),Y). 0 [] equal(multiply(add(X,inverse(X)),Y),Y). 0 [] equal(multiply(X,add(Y,add(X,Z))),X). 0 [] equal(multiply(multiply(add(X,Y),add(Y,Z)),Y),Y). 0 [] equal(add(multiply(X,inverse(X)),Y),Y). 0 [] equal(add(multiply(add(X,Y),X),multiply(X,Y)),X). 0 [] equal(add(multiply(add(X,X),Y),multiply(X,X)),X). 0 [] equal(add(multiply(add(X,Y),Y),multiply(X,Y)),Y). 0 [] equal(multiply(add(multiply(X,Y),X),add(X,Y)),X). 0 [] equal(multiply(add(multiply(X,X),Y),add(X,X)),X). 0 [] equal(multiply(add(multiply(X,Y),Y),add(X,Y)),Y). end_of_list. list(sos). 0 [] -equal(inverse(inverse(a)),a). end_of_list. list(clauses). 1 [] equal(X,X). 2 [] equal(add(X,multiply(Y,multiply(X,Z))),X). 3 [] equal(add(add(multiply(X,Y),multiply(Y,Z)),Y),Y). 4 [] equal(multiply(add(X,inverse(X)),Y),Y). 5 [] equal(multiply(X,add(Y,add(X,Z))),X). 6 [] equal(multiply(multiply(add(X,Y),add(Y,Z)),Y),Y). 7 [] equal(add(multiply(X,inverse(X)),Y),Y). 8 [] equal(add(multiply(add(X,Y),X),multiply(X,Y)),X). 9 [] equal(add(multiply(add(X,X),Y),multiply(X,X)),X). 10 [] equal(add(multiply(add(X,Y),Y),multiply(X,Y)),Y). 11 [] equal(multiply(add(multiply(X,Y),X),add(X,Y)),X). 12 [] equal(multiply(add(multiply(X,X),Y),add(X,X)),X). 13 [] equal(multiply(add(multiply(X,Y),Y),add(X,Y)),Y). 14 [] -equal(inverse(inverse(a)),a). end_of_list. list(flattened_and_parted_clauses). 1 [] equal(A,A). 2 [] -equal(multiply(A,B),C)|$Connect2(A,C). 2 [] equal(add(A,B),A)| -$Connect1(C,B)| -$Connect2(A,C). 2 [] -equal(multiply(A,B),C)|$Connect1(B,C). 3 [] -equal(multiply(A,B),C)|$Connect4(A,C). 3 [] -equal(add(A,B),C)|equal(add(C,D),D)| -$Connect3(D,A)| -$Connect4(D,B). 3 [] -equal(multiply(A,B),C)|$Connect3(B,C). 4 [] -equal(inverse(A),B)| -equal(add(A,B),C)|$Connect5(C). 4 [] equal(multiply(A,B),B)| -$Connect5(A). 5 [] -equal(add(A,B),C)|$Connect7(A,C). 5 [] equal(multiply(A,B),A)| -$Connect6(C,B)| -$Connect7(A,C). 5 [] -equal(add(A,B),C)|$Connect6(B,C). 6 [] -equal(add(A,B),C)|$Connect9(A,C). 6 [] -equal(multiply(A,B),C)|equal(multiply(C,D),D)| -$Connect8(D,A)| -$Connect9(D,B). 6 [] -equal(add(A,B),C)|$Connect8(B,C). 7 [] -equal(inverse(A),B)| -equal(multiply(A,B),C)|$Connect10(C). 7 [] equal(add(A,B),B)| -$Connect10(A). 8 [] -equal(multiply(A,B),C)| -equal(add(A,B),D)|$Connect11(A,C,D). 8 [] -equal(multiply(A,B),C)|equal(add(C,D),B)| -$Connect11(B,D,A). 9 [] -equal(multiply(A,A),B)|equal(add(C,B),A)| -$Connect13(A,C). 9 [] -equal(add(A,A),B)| -$Connect12(B,C)|$Connect13(A,C). 9 [] -equal(multiply(A,B),C)|$Connect12(A,C). 10 [] -equal(multiply(A,B),C)| -equal(add(A,B),D)|$Connect14(B,C,D). 10 [] -equal(multiply(A,B),C)|equal(add(C,D),B)| -$Connect14(B,D,A). 11 [] -equal(add(A,B),C)| -equal(multiply(A,B),D)|$Connect15(A,C,D). 11 [] -equal(add(A,B),C)|equal(multiply(C,D),B)| -$Connect15(B,D,A). 12 [] -equal(add(A,A),B)|equal(multiply(C,B),A)| -$Connect17(A,C). 12 [] -equal(multiply(A,A),B)| -$Connect16(B,C)|$Connect17(A,C). 12 [] -equal(add(A,B),C)|$Connect16(A,C). 13 [] -equal(add(A,B),C)| -equal(multiply(A,B),D)|$Connect18(B,C,D). 13 [] -equal(add(A,B),C)|equal(multiply(C,D),B)| -$Connect18(B,D,A). 14 [] -equal(a,A)| -equal(inverse(A),B)| -equal(inverse(B),A). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: a. 345 clauses were generated; 336 of those survived the first stage of unit preprocessing; there are 110 atoms. After all unit preprocessing, 100 atoms are still unassigned; 316 clauses remain; 8 of those are non-Horn (selectable); 4885 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 336 Literal occurrences input 913 Greatest atom 110 Unit preprocess: Preprocess unit assignments 10 Clauses after subsumption 316 Literal occ. after subsump. 872 Selectable clauses 8 Decide: Splits 2 Unit assignments 116 Failed paths 3 Memory: Memory malloced 3 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: a. 1424 clauses were generated; 1407 of those survived the first stage of unit preprocessing; there are 297 atoms. After all unit preprocessing, 284 atoms are still unassigned; 1386 clauses remain; 21 of those are non-Horn (selectable); 4890 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 1407 Literal occurrences input 3998 Greatest atom 297 Unit preprocess: Preprocess unit assignments 13 Clauses after subsumption 1386 Literal occ. after subsump. 3963 Selectable clauses 21 Decide: Splits 20 Unit assignments 1019 Failed paths 21 Memory: Memory malloced 8 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: a. 4040 clauses were generated; 4012 of those survived the first stage of unit preprocessing; there are 620 atoms. After all unit preprocessing, 599 atoms are still unassigned; 3980 clauses remain; 36 of those are non-Horn (selectable); 4899 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 4 ---- Input: Clauses input 4012 Literal occurrences input 11643 Greatest atom 620 Unit preprocess: Preprocess unit assignments 21 Clauses after subsumption 3980 Literal occ. after subsump. 11592 Selectable clauses 36 Decide: Splits 91 Unit assignments 6322 Failed paths 92 Memory: Memory malloced 17 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: a. 9222 clauses were generated; 9180 of those survived the first stage of unit preprocessing; there are 1115 atoms. After all unit preprocessing, 1084 atoms are still unassigned; 9135 clauses remain; 55 of those are non-Horn (selectable); 4913 K allocated; cpu time so far for this domain size: 0.01 sec. ======================= Model #1 at 0.02 seconds: multiply : | 0 1 2 3 4 --+---------- 0 | 0 3 3 3 0 1 | 3 1 3 3 1 2 | 3 3 2 3 2 3 | 3 3 3 3 3 4 | 0 1 2 3 4 add : | 0 1 2 3 4 --+---------- 0 | 0 4 4 0 4 1 | 4 1 4 1 4 2 | 4 4 2 2 4 3 | 0 1 2 3 4 4 | 4 4 4 4 4 inverse : 0 1 2 3 4 ------------- 1 2 0 4 3 a: 0 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 5 ---- Input: Clauses input 9180 Literal occurrences input 26974 Greatest atom 1115 Unit preprocess: Preprocess unit assignments 31 Clauses after subsumption 9135 Literal occ. after subsump. 26905 Selectable clauses 55 Decide: Splits 25 Unit assignments 2349 Failed paths 20 Memory: Memory malloced 31 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:32 2004 otter-3.3f/examples-mace2/iterate/kauer.out0100664000076400007640000001671010103523660020304 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:32 2004 The command was "../../bin/mace2 -N10 -p". op(700,xfx,<<). formula_list(usable). all x exists y (x< -(y< (exists z (x< usable clausifies to: list(usable). 1 [] x<<$f1(x). 2 [] -(x< -(y< (exists z (x< % Date: Fri, 08 Jan 1999 15:27:29 +0100 % To: mccune@mcs.anl.gov % % Dear Prof. McCune, % % I found the following problem: the following 3 axioms for a relation < % are given: % 1. all x exists y: x < y % 2. all x y: x < y => not y < x % 3. all x y: x < y => exists z: x < z and z < y % % One has to find a finite model. It is surprising and not obvious, that a % finite model exists, and it is not at all to find easily (at least for % me, may be for you). Since I sometimes work with OTTER, I remembered % MACE and tried to formulate and solve this problem with MACE, but % unfortunately was able to do it. % Is it possible to formulate and solve this problem with MACE and how? % % This problem was posed as an exercise in a very small german % mathematical magazin by Dr. Waldmann, a former colleague of mine, who % works now at another university. We both agree that the smallest model % has seven elements. % % Sincerely yours % % Stefan Kauer otter-3.3f/examples-mace2/iterate/LAT025-1.out0100664000076400007640000001757510103523660020214 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:32 2004 The command was "../../bin/mace2 -n2 -N6 -p". set(prolog_style_variables). set(tptp_eq). set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). clear(print_given). list(usable). 0 [] equal(X,X). 0 [] equal(meet(X,X),X). 0 [] equal(join(X,X),X). 0 [] equal(meet(X,join(X,Y)),X). 0 [] equal(join(X,meet(X,Y)),X). 0 [] equal(meet(X,Y),meet(Y,X)). 0 [] equal(join(X,Y),join(Y,X)). 0 [] equal(join(X,meet(Y,meet(X,Z))),X). 0 [] equal(meet(X,join(Y,join(X,Z))),X). 0 [] equal(meet2(X,X),X). 0 [] equal(meet2(X,join(X,Y)),X). 0 [] equal(join(X,meet2(X,Y)),X). 0 [] equal(meet2(X,Y),meet2(Y,X)). 0 [] equal(join(X,meet2(Y,meet2(X,Z))),X). 0 [] equal(meet2(X,join(Y,join(X,Z))),X). end_of_list. list(sos). 0 [] -equal(meet(a,b),meet2(a,b)). end_of_list. list(clauses). 1 [] equal(X,X). 2 [] equal(meet(X,X),X). 3 [] equal(join(X,X),X). 4 [] equal(meet(X,join(X,Y)),X). 5 [] equal(join(X,meet(X,Y)),X). 6 [] equal(meet(X,Y),meet(Y,X)). 7 [] equal(join(X,Y),join(Y,X)). 8 [] equal(join(X,meet(Y,meet(X,Z))),X). 9 [] equal(meet(X,join(Y,join(X,Z))),X). 10 [] equal(meet2(X,X),X). 11 [] equal(meet2(X,join(X,Y)),X). 12 [] equal(join(X,meet2(X,Y)),X). 13 [] equal(meet2(X,Y),meet2(Y,X)). 14 [] equal(join(X,meet2(Y,meet2(X,Z))),X). 15 [] equal(meet2(X,join(Y,join(X,Z))),X). 16 [] -equal(meet(a,b),meet2(a,b)). end_of_list. list(flattened_and_parted_clauses). 1 [] equal(A,A). 2 [] equal(meet(A,A),A). 3 [] equal(join(A,A),A). 4 [] -equal(join(A,B),C)|equal(meet(A,C),A). 5 [] -equal(meet(A,B),C)|equal(join(A,C),A). 6 [] -equal(meet(A,B),C)|equal(meet(B,A),C). 7 [] -equal(join(A,B),C)|equal(join(B,A),C). 8 [] -equal(meet(A,B),C)|$Connect2(A,C). 8 [] equal(join(A,B),A)| -$Connect1(C,B)| -$Connect2(A,C). 8 [] -equal(meet(A,B),C)|$Connect1(B,C). 9 [] -equal(join(A,B),C)|$Connect4(A,C). 9 [] equal(meet(A,B),A)| -$Connect3(C,B)| -$Connect4(A,C). 9 [] -equal(join(A,B),C)|$Connect3(B,C). 10 [] equal(meet2(A,A),A). 11 [] -equal(join(A,B),C)|equal(meet2(A,C),A). 12 [] -equal(meet2(A,B),C)|equal(join(A,C),A). 13 [] -equal(meet2(A,B),C)|equal(meet2(B,A),C). 14 [] -equal(meet2(A,B),C)|$Connect6(A,C). 14 [] equal(join(A,B),A)| -$Connect5(C,B)| -$Connect6(A,C). 14 [] -equal(meet2(A,B),C)|$Connect5(B,C). 15 [] -equal(join(A,B),C)|$Connect8(A,C). 15 [] equal(meet2(A,B),A)| -$Connect7(C,B)| -$Connect8(A,C). 15 [] -equal(join(A,B),C)|$Connect7(B,C). 16 [] -equal(meet2(A,B),C)| -equal(b,B)| -equal(a,A)| -equal(meet(A,B),C). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: b a. 201 clauses were generated; 135 of those survived the first stage of unit preprocessing; there are 64 atoms. After all unit preprocessing, 28 atoms are still unassigned; 66 clauses remain; 6 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 135 Literal occurrences input 237 Greatest atom 64 Unit preprocess: Preprocess unit assignments 36 Clauses after subsumption 66 Literal occ. after subsump. 134 Selectable clauses 6 Decide: Splits 1 Unit assignments 18 Failed paths 2 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: b a. 679 clauses were generated; 516 of those survived the first stage of unit preprocessing; there are 168 atoms. After all unit preprocessing, 102 atoms are still unassigned; 345 clauses remain; 18 of those are non-Horn (selectable); 4886 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 516 Literal occurrences input 1017 Greatest atom 168 Unit preprocess: Preprocess unit assignments 66 Clauses after subsumption 345 Literal occ. after subsump. 735 Selectable clauses 18 Decide: Splits 2 Unit assignments 53 Failed paths 3 Memory: Memory malloced 4 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: b a. 1664 clauses were generated; 1345 of those survived the first stage of unit preprocessing; there are 344 atoms. After all unit preprocessing, 240 atoms are still unassigned; 1024 clauses remain; 36 of those are non-Horn (selectable); 4891 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 1345 Literal occurrences input 2771 Greatest atom 344 Unit preprocess: Preprocess unit assignments 104 Clauses after subsumption 1024 Literal occ. after subsump. 2220 Selectable clauses 36 Decide: Splits 3 Unit assignments 262 Failed paths 4 Memory: Memory malloced 9 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: b a. 3394 clauses were generated; 2848 of those survived the first stage of unit preprocessing; there are 610 atoms. After all unit preprocessing, 460 atoms are still unassigned; 2325 clauses remain; 60 of those are non-Horn (selectable); 4899 K allocated; cpu time so far for this domain size: 0.00 sec. ======================= Model #1 at 0.01 seconds: meet : | 0 1 2 3 4 --+---------- 0 | 0 2 2 0 4 1 | 2 1 2 1 4 2 | 2 2 2 2 2 3 | 0 1 2 3 4 4 | 4 4 2 4 4 join : | 0 1 2 3 4 --+---------- 0 | 0 3 0 3 0 1 | 3 1 1 3 1 2 | 0 1 2 3 4 3 | 3 3 3 3 3 4 | 0 1 4 3 4 meet2 : | 0 1 2 3 4 --+---------- 0 | 0 4 2 0 4 1 | 4 1 2 1 4 2 | 2 2 2 2 2 3 | 0 1 2 3 4 4 | 4 4 2 4 4 b: 0 a: 1 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 5 ---- Input: Clauses input 2848 Literal occurrences input 5993 Greatest atom 610 Unit preprocess: Preprocess unit assignments 150 Clauses after subsumption 2325 Literal occ. after subsump. 5075 Selectable clauses 60 Decide: Splits 5 Unit assignments 476 Failed paths 2 Memory: Memory malloced 17 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:32 2004 otter-3.3f/examples-mace2/iterate/RNG025-8.out0100664000076400007640000002000310103523663020210 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:35 2004 The command was "../../bin/mace2 -n2 -N6 -p". set(prolog_style_variables). set(tptp_eq). set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). clear(print_given). list(usable). 0 [] equal(X,X). 0 [] equal(add(X,Y),add(Y,X)). 0 [] equal(add(X,add(Y,Z)),add(add(X,Y),Z)). 0 [] equal(add(additive_identity,X),X). 0 [] equal(add(X,additive_identity),X). 0 [] equal(multiply(additive_identity,X),additive_identity). 0 [] equal(multiply(X,additive_identity),additive_identity). 0 [] equal(add(additive_inverse(X),X),additive_identity). 0 [] equal(add(X,additive_inverse(X)),additive_identity). 0 [] equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))). 0 [] equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))). 0 [] equal(additive_inverse(additive_inverse(X)),X). 0 [] equal(multiply(multiply(X,Y),Y),multiply(X,multiply(Y,Y))). 0 [] equal(multiply(multiply(X,X),Y),multiply(X,multiply(X,Y))). 0 [] equal(associator(X,Y,add(U,V)),add(associator(X,Y,U),associator(X,Y,V))). 0 [] equal(associator(X,add(U,V),Y),add(associator(X,U,Y),associator(X,V,Y))). 0 [] equal(associator(add(U,V),X,Y),add(associator(U,X,Y),associator(V,X,Y))). 0 [] equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))). end_of_list. list(sos). 0 [] -equal(add(associator(a,b,c),associator(a,c,b)),additive_identity). end_of_list. list(clauses). 1 [] equal(X,X). 2 [] equal(add(X,Y),add(Y,X)). 3 [] equal(add(X,add(Y,Z)),add(add(X,Y),Z)). 4 [] equal(add(additive_identity,X),X). 5 [] equal(add(X,additive_identity),X). 6 [] equal(multiply(additive_identity,X),additive_identity). 7 [] equal(multiply(X,additive_identity),additive_identity). 8 [] equal(add(additive_inverse(X),X),additive_identity). 9 [] equal(add(X,additive_inverse(X)),additive_identity). 10 [] equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))). 11 [] equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))). 12 [] equal(additive_inverse(additive_inverse(X)),X). 13 [] equal(multiply(multiply(X,Y),Y),multiply(X,multiply(Y,Y))). 14 [] equal(multiply(multiply(X,X),Y),multiply(X,multiply(X,Y))). 15 [] equal(associator(X,Y,add(U,V)),add(associator(X,Y,U),associator(X,Y,V))). 16 [] equal(associator(X,add(U,V),Y),add(associator(X,U,Y),associator(X,V,Y))). 17 [] equal(associator(add(U,V),X,Y),add(associator(U,X,Y),associator(V,X,Y))). 18 [] equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))). 19 [] -equal(add(associator(a,b,c),associator(a,c,b)),additive_identity). end_of_list. list(flattened_and_parted_clauses). 1 [] equal(A,A). 2 [] -equal(add(A,B),C)|equal(add(B,A),C). 3 [] -equal(add(A,B),C)| -equal(add(C,D),E)|$Connect1(A,B,D,E). 3 [] -equal(add(A,B),C)|equal(add(D,C),E)| -$Connect1(D,A,B,E). 4 [] -equal(additive_identity,A)|equal(add(A,B),B). 5 [] -equal(additive_identity,A)|equal(add(B,A),B). 6 [] -equal(additive_identity,A)|equal(multiply(A,B),A). 7 [] -equal(additive_identity,A)|equal(multiply(B,A),A). 8 [] -equal(additive_identity,A)| -equal(additive_inverse(B),C)|equal(add(C,B),A). 9 [] -equal(additive_identity,A)| -equal(additive_inverse(B),C)|equal(add(B,C),A). 10 [] -equal(multiply(A,B),C)| -equal(add(D,C),E)|$Connect3(A,B,D,E). 10 [] -equal(multiply(A,B),C)|$Connect2(A,D,B,E)| -$Connect3(A,D,C,E). 10 [] -equal(add(A,B),C)|equal(multiply(D,C),E)| -$Connect2(D,B,A,E). 11 [] -equal(multiply(A,B),C)| -equal(add(D,C),E)|$Connect5(A,B,D,E). 11 [] -equal(multiply(A,B),C)|$Connect4(D,B,A,E)| -$Connect5(D,B,C,E). 11 [] -equal(add(A,B),C)|equal(multiply(C,D),E)| -$Connect4(B,D,A,E). 12 [] -equal(additive_inverse(A),B)|equal(additive_inverse(B),A). 13 [] -equal(multiply(A,A),B)| -equal(multiply(C,B),D)|$Connect6(A,C,D). 13 [] -equal(multiply(A,B),C)|equal(multiply(C,B),D)| -$Connect6(B,A,D). 14 [] -equal(multiply(A,B),C)| -equal(multiply(A,C),D)|$Connect7(A,B,D). 14 [] -equal(multiply(A,A),B)|equal(multiply(B,C),D)| -$Connect7(A,C,D). 15 [] -equal(associator(A,B,C),D)| -equal(associator(A,B,E),F)| -equal(add(F,D),G)| -equal(add(E,C),H)|equal(associator(A,B,H),G). 16 [] -equal(associator(A,B,C),D)| -equal(associator(A,E,C),F)| -equal(add(F,D),G)| -equal(add(E,B),H)|equal(associator(A,H,C),G). 17 [] -equal(associator(A,B,C),D)| -equal(associator(E,B,C),F)| -equal(add(F,D),G)| -equal(add(E,A),H)|equal(associator(H,B,C),G). 18 [] -equal(multiply(A,B),C)| -equal(additive_inverse(C),D)|$Connect8(A,B,D). 18 [] -equal(multiply(A,B),C)| -equal(add(C,D),E)|equal(commutator(B,A),E)| -$Connect8(B,A,D). 19 [] -equal(additive_identity,A)| -equal(add(B,C),A)| -$Connect9(C,B). 19 [] -equal(associator(A,B,C),D)| -equal(c,B)| -equal(b,C)| -equal(a,A)| -equal(associator(A,C,B),E)|$Connect9(D,E). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: additive_identity c b a. 1279 clauses were generated; 393 of those survived the first stage of unit preprocessing; there are 164 atoms. After all unit preprocessing, 60 atoms are still unassigned; 220 clauses remain; 13 of those are non-Horn (selectable); 4886 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 393 Literal occurrences input 1068 Greatest atom 164 Unit preprocess: Preprocess unit assignments 104 Clauses after subsumption 220 Literal occ. after subsump. 731 Selectable clauses 13 Decide: Splits 29 Unit assignments 116 Failed paths 30 Memory: Memory malloced 4 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: additive_identity c b a. 22931 clauses were generated; 7164 of those survived the first stage of unit preprocessing; there are 687 atoms. After all unit preprocessing, 464 atoms are still unassigned; 6842 clauses remain; 47 of those are non-Horn (selectable); 4901 K allocated; cpu time so far for this domain size: 0.01 sec. ======================= Model #1 at 0.02 seconds: add : | 0 1 2 --+------ 0 | 0 1 2 1 | 1 2 0 2 | 2 0 1 additive_identity: 0 multiply : | 0 1 2 --+------ 0 | 0 0 0 1 | 0 0 0 2 | 0 0 0 additive_inverse : 0 1 2 --------- 0 2 1 Dimension 3 table for associator not printed commutator : | 0 1 2 --+------ 0 | 0 0 0 1 | 0 0 0 2 | 0 0 0 c: 1 b: 1 a: 1 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 3 ---- Input: Clauses input 7164 Literal occurrences input 28293 Greatest atom 687 Unit preprocess: Preprocess unit assignments 223 Clauses after subsumption 6842 Literal occ. after subsump. 27799 Selectable clauses 47 Decide: Splits 89 Unit assignments 1843 Failed paths 78 Memory: Memory malloced 19 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:35 2004 otter-3.3f/examples-mace2/iterate/noncommutative_group.out0100664000076400007640000001464110103523661023463 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:33 2004 The command was "../../bin/mace2 -n2 -N6 -p". list(usable). 1 [] f(e,x)=x. 2 [] f(g(x),x)=e. 3 [] f(f(x,y),z)=f(x,f(y,z)). 4 [] f(a,b)!=f(b,a). end_of_list. list(flattened_and_parted_clauses). 1 [] e!=x|f(x,y)=y. 2 [] e!=x|g(y)!=z|f(z,y)=x. 3 [] f(x,y)!=z|f(u,z)!=v|$Connect1(x,y,u,v). 3 [] f(x,y)!=z|f(z,u)=v| -$Connect1(y,u,x,v). 4 [] f(x,y)!=z|b!=x|a!=y|f(y,x)!=z. end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: e b a. 107 clauses were generated; 66 of those survived the first stage of unit preprocessing; there are 38 atoms. After all unit preprocessing, 4 atoms are still unassigned; 8 clauses remain; 2 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 66 Literal occurrences input 133 Greatest atom 38 Unit preprocess: Preprocess unit assignments 34 Clauses after subsumption 8 Literal occ. after subsump. 19 Selectable clauses 2 Decide: Splits 1 Unit assignments 4 Failed paths 2 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: e b a. 621 clauses were generated; 408 of those survived the first stage of unit preprocessing; there are 135 atoms. After all unit preprocessing, 103 atoms are still unassigned; 365 clauses remain; 13 of those are non-Horn (selectable); 4885 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 408 Literal occurrences input 1022 Greatest atom 135 Unit preprocess: Preprocess unit assignments 32 Clauses after subsumption 365 Literal occ. after subsump. 968 Selectable clauses 13 Decide: Splits 5 Unit assignments 245 Failed paths 6 Memory: Memory malloced 3 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: e b a. 2373 clauses were generated; 1683 of those survived the first stage of unit preprocessing; there are 364 atoms. After all unit preprocessing, 309 atoms are still unassigned; 1603 clauses remain; 21 of those are non-Horn (selectable); 4892 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 1683 Literal occurrences input 4544 Greatest atom 364 Unit preprocess: Preprocess unit assignments 55 Clauses after subsumption 1603 Literal occ. after subsump. 4439 Selectable clauses 21 Decide: Splits 29 Unit assignments 1520 Failed paths 30 Memory: Memory malloced 10 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: e b a. 6917 clauses were generated; 5203 of those survived the first stage of unit preprocessing; there are 815 atoms. After all unit preprocessing, 731 atoms are still unassigned; 5073 clauses remain; 30 of those are non-Horn (selectable); 4905 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 5 ---- Input: Clauses input 5203 Literal occurrences input 14514 Greatest atom 815 Unit preprocess: Preprocess unit assignments 84 Clauses after subsumption 5073 Literal occ. after subsump. 14338 Selectable clauses 30 Decide: Splits 87 Unit assignments 11552 Failed paths 88 Memory: Memory malloced 23 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.01 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: e b a. 16780 clauses were generated; 13181 of those survived the first stage of unit preprocessing; there are 1602 atoms. After all unit preprocessing, 1483 atoms are still unassigned; 12987 clauses remain; 41 of those are non-Horn (selectable); 4927 K allocated; cpu time so far for this domain size: 0.01 sec. ======================= Model #1 at 0.06 seconds: e: 0 f : | 0 1 2 3 4 5 --+------------ 0 | 0 1 2 3 4 5 1 | 1 0 3 2 5 4 2 | 2 4 0 5 1 3 3 | 3 5 1 4 0 2 4 | 4 2 5 0 3 1 5 | 5 3 4 1 2 0 g : 0 1 2 3 4 5 --------------- 0 1 2 4 3 5 b: 1 a: 2 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 6 ---- Input: Clauses input 13181 Literal occurrences input 37418 Greatest atom 1602 Unit preprocess: Preprocess unit assignments 119 Clauses after subsumption 12987 Literal occ. after subsump. 37149 Selectable clauses 41 Decide: Splits 212 Unit assignments 50629 Failed paths 208 Memory: Memory malloced 45 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.04 ======================================= Total times for run (seconds): user CPU time 0.06 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:33 2004 otter-3.3f/examples-mace2/propositional/0040755000076400007640000000000010103524322017701 5ustar mccunemccuneotter-3.3f/examples-mace2/propositional/p8.out0100664000076400007640000000257010103523757020777 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 72 atoms are still unassigned; 297 clauses remain; 9 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 297 Literal occurrences input 648 Greatest atom 72 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 297 Literal occ. after subsump. 648 Selectable clauses 9 Decide: Splits 40319 Unit assignments 435837 Failed paths 40320 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.12 ======================================= Total times for run (seconds): user CPU time 0.12 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. 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-14 0 -3 -13 0 -2 -12 0 -1 -11 0 otter-3.3f/examples-mace2/propositional/p7.out0100664000076400007640000000257010103523757020776 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 56 atoms are still unassigned; 204 clauses remain; 8 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 204 Literal occurrences input 448 Greatest atom 56 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 204 Literal occ. after subsump. 448 Selectable clauses 8 Decide: Splits 5039 Unit assignments 50142 Failed paths 5040 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.01 ======================================= Total times for run (seconds): user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/propositional/f3.out0100664000076400007640000000256510103523757020764 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 3 atoms are still unassigned; 8 clauses remain; 4 of those are non-Horn (selectable); 4882 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 8 Literal occurrences input 24 Greatest atom 3 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 8 Literal occ. after subsump. 24 Selectable clauses 4 Decide: Splits 3 Unit assignments 0 Failed paths 4 Memory: Memory malloced 0 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/propositional/p9.out0100664000076400007640000000257110103523761020774 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 90 atoms are still unassigned; 415 clauses remain; 10 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 415 Literal occurrences input 900 Greatest atom 90 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 415 Literal occ. after subsump. 900 Selectable clauses 10 Decide: Splits 362879 Unit assignments 4234375 Failed paths 362880 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 1.16 ======================================= Total times for run (seconds): user CPU time 1.16 (0 hr, 0 min, 1 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:37 2004 otter-3.3f/examples-mace2/propositional/p6.in0100644000076400007640000000267607272354756020617 0ustar mccunemccune 37 38 39 40 41 42 0 31 32 33 34 35 36 0 25 26 27 28 29 30 0 19 20 21 22 23 24 0 13 14 15 16 17 18 0 7 8 9 10 11 12 0 1 2 3 4 5 6 0 -36 -42 0 -30 -42 0 -24 -42 0 -18 -42 0 -12 -42 0 -6 -42 0 -35 -41 0 -29 -41 0 -23 -41 0 -17 -41 0 -11 -41 0 -5 -41 0 -34 -40 0 -28 -40 0 -22 -40 0 -16 -40 0 -10 -40 0 -4 -40 0 -33 -39 0 -27 -39 0 -21 -39 0 -15 -39 0 -9 -39 0 -3 -39 0 -32 -38 0 -26 -38 0 -20 -38 0 -14 -38 0 -8 -38 0 -2 -38 0 -31 -37 0 -25 -37 0 -19 -37 0 -13 -37 0 -7 -37 0 -1 -37 0 -30 -36 0 -24 -36 0 -18 -36 0 -12 -36 0 -6 -36 0 -29 -35 0 -23 -35 0 -17 -35 0 -11 -35 0 -5 -35 0 -28 -34 0 -22 -34 0 -16 -34 0 -10 -34 0 -4 -34 0 -27 -33 0 -21 -33 0 -15 -33 0 -9 -33 0 -3 -33 0 -26 -32 0 -20 -32 0 -14 -32 0 -8 -32 0 -2 -32 0 -25 -31 0 -19 -31 0 -13 -31 0 -7 -31 0 -1 -31 0 -24 -30 0 -18 -30 0 -12 -30 0 -6 -30 0 -23 -29 0 -17 -29 0 -11 -29 0 -5 -29 0 -22 -28 0 -16 -28 0 -10 -28 0 -4 -28 0 -21 -27 0 -15 -27 0 -9 -27 0 -3 -27 0 -20 -26 0 -14 -26 0 -8 -26 0 -2 -26 0 -19 -25 0 -13 -25 0 -7 -25 0 -1 -25 0 -18 -24 0 -12 -24 0 -6 -24 0 -17 -23 0 -11 -23 0 -5 -23 0 -16 -22 0 -10 -22 0 -4 -22 0 -15 -21 0 -9 -21 0 -3 -21 0 -14 -20 0 -8 -20 0 -2 -20 0 -13 -19 0 -7 -19 0 -1 -19 0 -12 -18 0 -6 -18 0 -11 -17 0 -5 -17 0 -10 -16 0 -4 -16 0 -9 -15 0 -3 -15 0 -8 -14 0 -2 -14 0 -7 -13 0 -1 -13 0 -6 -12 0 -5 -11 0 -4 -10 0 -3 -9 0 -2 -8 0 -1 -7 0 otter-3.3f/examples-mace2/propositional/p6.out0100664000076400007640000000257010103523757020775 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 42 atoms are still unassigned; 133 clauses remain; 7 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 133 Literal occurrences input 294 Greatest atom 42 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 133 Literal occ. after subsump. 294 Selectable clauses 7 Decide: Splits 719 Unit assignments 6538 Failed paths 720 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/propositional/README.more0100644000076400007640000000017507313721043021532 0ustar mccunemccunep5.in -- p11.in: Pigeonhole problems. q10.in 10-Queens. f[234].in complete set on 2,3,4 variables. otter-3.3f/examples-mace2/propositional/p9.in0100644000076400007640000001107107272354756020607 0ustar mccunemccune 82 83 84 85 86 87 88 89 90 0 73 74 75 76 77 78 79 80 81 0 64 65 66 67 68 69 70 71 72 0 55 56 57 58 59 60 61 62 63 0 46 47 48 49 50 51 52 53 54 0 37 38 39 40 41 42 43 44 45 0 28 29 30 31 32 33 34 35 36 0 19 20 21 22 23 24 25 26 27 0 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 0 -81 -90 0 -72 -90 0 -63 -90 0 -54 -90 0 -45 -90 0 -36 -90 0 -27 -90 0 -18 -90 0 -9 -90 0 -80 -89 0 -71 -89 0 -62 -89 0 -53 -89 0 -44 -89 0 -35 -89 0 -26 -89 0 -17 -89 0 -8 -89 0 -79 -88 0 -70 -88 0 -61 -88 0 -52 -88 0 -43 -88 0 -34 -88 0 -25 -88 0 -16 -88 0 -7 -88 0 -78 -87 0 -69 -87 0 -60 -87 0 -51 -87 0 -42 -87 0 -33 -87 0 -24 -87 0 -15 -87 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After all unit preprocessing, 4 atoms are still unassigned; 16 clauses remain; 11 of those are non-Horn (selectable); 4882 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 16 Literal occurrences input 64 Greatest atom 4 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 16 Literal occ. after subsump. 64 Selectable clauses 11 Decide: Splits 7 Unit assignments 0 Failed paths 8 Memory: Memory malloced 0 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/propositional/f2.in0100644000076400007640000000003407272354756020563 0ustar mccunemccune1 2 0 1 -2 0 -1 2 0 -1 -2 0 otter-3.3f/examples-mace2/propositional/f2.out0100664000076400007640000000256510103523757020763 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 2 atoms are still unassigned; 4 clauses remain; 1 of those are non-Horn (selectable); 4882 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 4 Literal occurrences input 8 Greatest atom 2 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 4 Literal occ. after subsump. 8 Selectable clauses 1 Decide: Splits 1 Unit assignments 0 Failed paths 2 Memory: Memory malloced 0 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/propositional/p5.out0100664000076400007640000000256710103523757021002 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:35 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 30 atoms are still unassigned; 81 clauses remain; 6 of those are non-Horn (selectable); 4882 K allocated; cpu time so far for this domain size: 0.00 sec.  The search is complete. No models were found. ----- statistics for domain size 0 ---- Input: Clauses input 81 Literal occurrences input 180 Greatest atom 30 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 81 Literal occ. after subsump. 180 Selectable clauses 6 Decide: Splits 119 Unit assignments 981 Failed paths 120 Memory: Memory malloced 0 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/propositional/index.html0100644000076400007640000000213507714267463021724 0ustar mccunemccune /home/mccune/otter-3.3/examples-mace2/propositional

/home/mccune/otter-3.3/examples-mace2/propositional

Propositional examples for anldp.

anldp < f2.in > f2.out

anldp < f3.in > f3.out

anldp < f4.in > f4.out

anldp < p5.in > p5.out

anldp < p6.in > p6.out

anldp < p7.in > p7.out

anldp < p8.in > p8.out

anldp < p9.in > p9.out

anldp < q10.in > q10.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/propositional/README0100644000076400007640000000004207313721064020565 0ustar mccunemccunePropositional examples for anldp. otter-3.3f/examples-mace2/propositional/q10.out0100664000076400007640000000301110103523761021033 0ustar mccunemccune----- ANLDP 2.2, August 2003 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:37 2004 The command was "../../bin/anldp -m1000". After all unit preprocessing, 100 atoms are still unassigned; 1480 clauses remain; 10 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. The 1st model has been found. The 10th model has been found. The 100th model has been found.  The search is complete. The set is satisfiable (724 model(s) found). ----- statistics for domain size 0 ---- Input: Clauses input 1480 Literal occurrences input 3040 Greatest atom 100 Unit preprocess: Preprocess unit assignments 0 Clauses after subsumption 1480 Literal occ. after subsump. 3040 Selectable clauses 10 Decide: Splits 5715 Unit assignments 85716 Failed paths 4992 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.04 ======================================= Total times for run (seconds): user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (724 model(s) found). 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-4 -14 0 -8 -13 0 -3 -13 0 -7 -12 0 -2 -12 0 -6 -11 0 -1 -11 0 -5 -10 0 -4 -9 0 -3 -8 0 -2 -7 0 -1 -6 0 otter-3.3f/examples-mace2/propositional/f4.in0100644000076400007640000000030007272354756020561 0ustar mccunemccune1 2 3 4 0 1 2 3 -4 0 1 2 -3 4 0 1 2 -3 -4 0 1 -2 3 4 0 1 -2 3 -4 0 1 -2 -3 4 0 1 -2 -3 -4 0 -1 2 3 4 0 -1 2 3 -4 0 -1 2 -3 4 0 -1 2 -3 -4 0 -1 -2 3 4 0 -1 -2 3 -4 0 -1 -2 -3 4 0 -1 -2 -3 -4 0 otter-3.3f/examples-mace2/propositional/program0100644000076400007640000000000607705577601021312 0ustar mccunemccuneanldp otter-3.3f/examples-mace2/propositional/f3.in0100644000076400007640000000011407272354756020563 0ustar mccunemccune1 2 3 0 1 2 -3 0 1 -2 3 0 1 -2 -3 0 -1 2 3 0 -1 2 -3 0 -1 -2 3 0 -1 -2 -3 0 otter-3.3f/examples-mace2/propositional/p7.in0100644000076400007640000000434407272354756020612 0ustar mccunemccune 50 51 52 53 54 55 56 0 43 44 45 46 47 48 49 0 36 37 38 39 40 41 42 0 29 30 31 32 33 34 35 0 22 23 24 25 26 27 28 0 15 16 17 18 19 20 21 0 8 9 10 11 12 13 14 0 1 2 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mccunemccuneotter-3.3f/examples-mace2/lattice/lt-ol.out0100664000076400007640000001660010103523665020217 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -N6 -p". include("finite-lattice"). ------- start included file finite-lattice------- op(400,xfx,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] (x^y)^z=x^ (y^z). 3 [] x v y=y v x. 4 [] (x v y) v z=x v (y v z). 5 [] x^ (x v y)=x. 6 [] x v (x^y)=x. 7 [] x^x=x. 8 [] x v x=x. 9 [] 1 v x=1. 10 [] x v 1=1. 11 [] 1^x=x. 12 [] x^1=x. 13 [] 0^x=0. 14 [] x^0=0. 15 [] 0 v x=x. 16 [] x v 0=x. end_of_list. ------- end included file finite-lattice------- list(usable). 17 [] c(x) v x=1. 18 [] c(x)^x=0. 19 [] c(c(x))=x. 20 [] c(A^B)!=c(A) v c(B). end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x^y!=z|u^z!=v|$Connect1(x,y,u,v). 2 [] x^y!=z|z^u=v| -$Connect1(y,u,x,v). 3 [] x v y!=z|y v x=z. 4 [] x v y!=z|u v z!=v|$Connect2(x,y,u,v). 4 [] x v y!=z|z v u=v| -$Connect2(y,u,x,v). 5 [] x v y!=z|x^z=x. 6 [] x^y!=z|x v z=x. 7 [] x^x=x. 8 [] x v x=x. 9 [] 1 v x=1. 10 [] x v 1=1. 11 [] 1^x=x. 12 [] x^1=x. 13 [] 0^x=0. 14 [] x^0=0. 15 [] 0 v x=x. 16 [] x v 0=x. 17 [] c(x)!=y|y v x=1. 18 [] c(x)!=y|y^x=0. 19 [] c(x)!=y|c(y)=x. 20 [] c(x)!=y|z v y!=u|B!=x| -$Connect4(x,z,u). 20 [] c(x)!=y|A!=x| -$Connect3(z,x,u)|$Connect4(z,y,u). 20 [] x^y!=z|c(z)!=u|$Connect3(y,x,u). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: B A. 268 clauses were generated; 120 of those survived the first stage of unit preprocessing; there are 76 atoms. After all unit preprocessing, 16 atoms are still unassigned; 16 clauses remain; 2 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 120 Literal occurrences input 228 Greatest atom 76 Unit preprocess: Preprocess unit assignments 60 Clauses after subsumption 16 Literal occ. after subsump. 52 Selectable clauses 2 Decide: Splits 1 Unit assignments 8 Failed paths 2 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: B A. 1481 clauses were generated; 490 of those survived the first stage of unit preprocessing; there are 294 atoms. After all unit preprocessing, 65 atoms are still unassigned; 100 clauses remain; 5 of those are non-Horn (selectable); 4890 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 490 Literal occurrences input 949 Greatest atom 294 Unit preprocess: Preprocess unit assignments 229 Clauses after subsumption 100 Literal occ. after subsump. 310 Selectable clauses 5 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 8 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: B A. 5493 clauses were generated; 1691 of those survived the first stage of unit preprocessing; there are 808 atoms. After all unit preprocessing, 120 atoms are still unassigned; 97 clauses remain; 5 of those are non-Horn (selectable); 4904 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 1691 Literal occurrences input 3599 Greatest atom 808 Unit preprocess: Preprocess unit assignments 688 Clauses after subsumption 97 Literal occ. after subsump. 349 Selectable clauses 5 Decide: Splits 2 Unit assignments 26 Failed paths 3 Memory: Memory malloced 22 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: B A. 15656 clauses were generated; 5083 of those survived the first stage of unit preprocessing; there are 1810 atoms. After all unit preprocessing, 748 atoms are still unassigned; 2306 clauses remain; 21 of those are non-Horn (selectable); 4933 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 5083 Literal occurrences input 11737 Greatest atom 1810 Unit preprocess: Preprocess unit assignments 1062 Clauses after subsumption 2306 Literal occ. after subsump. 5861 Selectable clauses 21 Decide: Splits 1 Unit assignments 83 Failed paths 2 Memory: Memory malloced 51 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: B A. 37344 clauses were generated; 13328 of those survived the first stage of unit preprocessing; there are 3540 atoms. After all unit preprocessing, 1788 atoms are still unassigned; 7924 clauses remain; 34 of those are non-Horn (selectable); 4982 K allocated; cpu time so far for this domain size: 0.02 sec. ======================= Model #1 at 0.03 seconds: ^ : | 0 1 2 3 4 5 --+------------ 0 | 0 0 0 0 0 0 1 | 0 1 2 3 4 5 2 | 0 2 2 0 0 0 3 | 0 3 0 3 0 0 4 | 0 4 0 0 4 5 5 | 0 5 0 0 5 5 v : | 0 1 2 3 4 5 --+------------ 0 | 0 1 2 3 4 5 1 | 1 1 1 1 1 1 2 | 2 1 2 1 1 1 3 | 3 1 1 3 1 1 4 | 4 1 1 1 4 4 5 | 5 1 1 1 4 5 c : 0 1 2 3 4 5 --------------- 1 0 4 5 2 3 B: 2 A: 3 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 6 ---- Input: Clauses input 13328 Literal occurrences input 32612 Greatest atom 3540 Unit preprocess: Preprocess unit assignments 1752 Clauses after subsumption 7924 Literal occ. after subsump. 20668 Selectable clauses 34 Decide: Splits 10 Unit assignments 1589 Failed paths 5 Memory: Memory malloced 100 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.02 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/lattice/ml-mol.out0100664000076400007640000003013110103523667020362 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -N10 -p". include("finite-lattice"). ------- start included file finite-lattice------- op(400,xfx,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] (x^y)^z=x^ (y^z). 3 [] x v y=y v x. 4 [] (x v y) v z=x v (y v z). 5 [] x^ (x v y)=x. 6 [] x v (x^y)=x. 7 [] x^x=x. 8 [] x v x=x. 9 [] 1 v x=1. 10 [] x v 1=1. 11 [] 1^x=x. 12 [] x^1=x. 13 [] 0^x=0. 14 [] x^0=0. 15 [] 0 v x=x. 16 [] x v 0=x. end_of_list. ------- end included file finite-lattice------- list(usable). 17 [] c(x) v x=1. 18 [] c(x)^x=0. 19 [] c(c(x))=x. 20 [] x v (y^ (x v z))= (x v y)^ (x v z). 21 [] c(A^B)!=c(A) v c(B). end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x^y!=z|u^z!=v|$Connect1(x,y,u,v). 2 [] x^y!=z|z^u=v| -$Connect1(y,u,x,v). 3 [] x v y!=z|y v x=z. 4 [] x v y!=z|u v z!=v|$Connect2(x,y,u,v). 4 [] x v y!=z|z v u=v| -$Connect2(y,u,x,v). 5 [] x v y!=z|x^z=x. 6 [] x^y!=z|x v z=x. 7 [] x^x=x. 8 [] x v x=x. 9 [] 1 v x=1. 10 [] x v 1=1. 11 [] 1^x=x. 12 [] x^1=x. 13 [] 0^x=0. 14 [] x^0=0. 15 [] 0 v x=x. 16 [] x v 0=x. 17 [] c(x)!=y|y v x=1. 18 [] c(x)!=y|y^x=0. 19 [] c(x)!=y|c(y)=x. 20 [] x v y!=z|z^u!=v| -$Connect3(x,u)|$Connect4(x,y,u,v). 20 [] x^y!=z|u v z=v| -$Connect4(u,x,y,v). 20 [] x v y!=z|$Connect3(x,z). 21 [] c(x)!=y|z v y!=u|B!=x| -$Connect6(x,z,u). 21 [] c(x)!=y|A!=x| -$Connect5(z,x,u)|$Connect6(z,y,u). 21 [] x^y!=z|c(z)!=u|$Connect5(y,x,u). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: B A. 340 clauses were generated; 142 of those survived the first stage of unit preprocessing; there are 96 atoms. After all unit preprocessing, 18 atoms are still unassigned; 16 clauses remain; 2 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 142 Literal occurrences input 255 Greatest atom 96 Unit preprocess: Preprocess unit assignments 78 Clauses after subsumption 16 Literal occ. after subsump. 52 Selectable clauses 2 Decide: Splits 1 Unit assignments 8 Failed paths 2 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: B A. 1994 clauses were generated; 590 of those survived the first stage of unit preprocessing; there are 384 atoms. After all unit preprocessing, 77 atoms are still unassigned; 109 clauses remain; 5 of those are non-Horn (selectable); 4892 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 590 Literal occurrences input 1071 Greatest atom 384 Unit preprocess: Preprocess unit assignments 307 Clauses after subsumption 109 Literal occ. after subsump. 328 Selectable clauses 5 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 10 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: B A. 7605 clauses were generated; 2128 of those survived the first stage of unit preprocessing; there are 1080 atoms. After all unit preprocessing, 148 atoms are still unassigned; 97 clauses remain; 5 of those are non-Horn (selectable); 4912 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 4 ---- Input: Clauses input 2128 Literal occurrences input 4354 Greatest atom 1080 Unit preprocess: Preprocess unit assignments 932 Clauses after subsumption 97 Literal occ. after subsump. 349 Selectable clauses 5 Decide: Splits 2 Unit assignments 26 Failed paths 3 Memory: Memory malloced 30 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: B A. 22031 clauses were generated; 6668 of those survived the first stage of unit preprocessing; there are 2460 atoms. After all unit preprocessing, 1011 atoms are still unassigned; 3188 clauses remain; 21 of those are non-Horn (selectable); 4951 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 6668 Literal occurrences input 15151 Greatest atom 2460 Unit preprocess: Preprocess unit assignments 1449 Clauses after subsumption 3188 Literal occ. after subsump. 8117 Selectable clauses 21 Decide: Splits 1 Unit assignments 107 Failed paths 2 Memory: Memory malloced 69 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: B A. 53112 clauses were generated; 18024 of those survived the first stage of unit preprocessing; there are 4872 atoms. After all unit preprocessing, 2466 atoms are still unassigned; 11152 clauses remain; 34 of those are non-Horn (selectable); 5020 K allocated; cpu time so far for this domain size: 0.03 sec. ----- statistics for domain size 6 ---- Input: Clauses input 18024 Literal occurrences input 44095 Greatest atom 4872 Unit preprocess: Preprocess unit assignments 2406 Clauses after subsumption 11152 Literal occ. after subsump. 29440 Selectable clauses 34 Decide: Splits 10 Unit assignments 4915 Failed paths 11 Memory: Memory malloced 138 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.03 DPLL 0.01 --- Starting search for models of size 7 --- Applying isomorphism constraints to constants: B A. 112384 clauses were generated; 42626 of those survived the first stage of unit preprocessing; there are 8736 atoms. After all unit preprocessing, 5063 atoms are still unassigned; 30235 clauses remain; 51 of those are non-Horn (selectable); 5129 K allocated; cpu time so far for this domain size: 0.05 sec. ----- statistics for domain size 7 ---- Input: Clauses input 42626 Literal occurrences input 109671 Greatest atom 8736 Unit preprocess: Preprocess unit assignments 3673 Clauses after subsumption 30235 Literal occ. after subsump. 82163 Selectable clauses 51 Decide: Splits 20 Unit assignments 2568 Failed paths 21 Memory: Memory malloced 247 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.05 DPLL 0.01 --- Starting search for models of size 8 --- Applying isomorphism constraints to constants: B A. 215798 clauses were generated; 90239 of those survived the first stage of unit preprocessing; there are 14544 atoms. After all unit preprocessing, 9258 atoms are still unassigned; 69392 clauses remain; 72 of those are non-Horn (selectable); 5294 K allocated; cpu time so far for this domain size: 0.11 sec. ----- statistics for domain size 8 ---- Input: Clauses input 90239 Literal occurrences input 240487 Greatest atom 14544 Unit preprocess: Preprocess unit assignments 5286 Clauses after subsumption 69392 Literal occ. after subsump. 192782 Selectable clauses 72 Decide: Splits 133 Unit assignments 241256 Failed paths 134 Memory: Memory malloced 412 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.09 DPLL 0.56 --- Starting search for models of size 9 --- Applying isomorphism constraints to constants: B A. 384441 clauses were generated; 174684 of those survived the first stage of unit preprocessing; there are 22860 atoms. After all unit preprocessing, 15579 atoms are still unassigned; 141490 clauses remain; 97 of those are non-Horn (selectable); 10412 K allocated; cpu time so far for this domain size: 0.19 sec. ----- statistics for domain size 9 ---- Input: Clauses input 174684 Literal occurrences input 477559 Greatest atom 22860 Unit preprocess: Preprocess unit assignments 7281 Clauses after subsumption 141490 Literal occ. after subsump. 399817 Selectable clauses 97 Decide: Splits 60 Unit assignments 28320 Failed paths 61 Memory: Memory malloced 647 K Memory MACE_tp_alloced 9765 K Time (seconds): Generate ground clauses 0.16 DPLL 0.12 --- Starting search for models of size 10 --- Applying isomorphism constraints to constants: B A. 645256 clauses were generated; 314558 of those survived the first stage of unit preprocessing; there are 34320 atoms. After all unit preprocessing, 24626 atoms are still unassigned; 264028 clauses remain; 126 of those are non-Horn (selectable); 15620 K allocated; cpu time so far for this domain size: 0.33 sec. ======================= Model #1 at 1.42 seconds: ^ : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 0 0 0 0 0 0 0 0 0 1 | 0 1 2 3 4 5 6 7 8 9 2 | 0 2 2 0 0 0 0 2 0 2 3 | 0 3 0 3 6 0 6 8 8 6 4 | 0 4 0 6 4 5 6 5 0 6 5 | 0 5 0 0 5 5 0 5 0 0 6 | 0 6 0 6 6 0 6 0 0 6 7 | 0 7 2 8 5 5 0 7 8 2 8 | 0 8 0 8 0 0 0 8 8 0 9 | 0 9 2 6 6 0 6 2 0 9 v : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 1 2 3 4 5 6 7 8 9 1 | 1 1 1 1 1 1 1 1 1 1 2 | 2 1 2 1 1 7 9 7 7 9 3 | 3 1 1 3 1 1 3 1 3 1 4 | 4 1 1 1 4 4 4 1 1 1 5 | 5 1 7 1 4 5 4 7 7 1 6 | 6 1 9 3 4 4 6 1 3 9 7 | 7 1 7 1 1 7 1 7 7 1 8 | 8 1 7 3 1 7 3 7 8 1 9 | 9 1 9 1 1 1 9 1 1 9 c : 0 1 2 3 4 5 6 7 8 9 ----------------------- 1 0 4 5 2 3 7 6 9 8 B: 2 A: 3 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 10 ---- Input: Clauses input 314558 Literal occurrences input 876591 Greatest atom 34320 Unit preprocess: Preprocess unit assignments 9694 Clauses after subsumption 264028 Literal occ. after subsump. 756092 Selectable clauses 126 Decide: Splits 33 Unit assignments 25391 Failed paths 25 Memory: Memory malloced 972 K Memory MACE_tp_alloced 14648 K Time (seconds): Generate ground clauses 0.27 DPLL 0.11 ======================================= Total times for run (seconds): user CPU time 1.42 (0 hr, 0 min, 1 sec) system CPU time 0.12 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:39 2004 otter-3.3f/examples-mace2/lattice/ol-e4.out0100664000076400007640000003217410103523750020107 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:59 2004 The command was "../../bin/mace2 -N10 -p". include("ortholattice"). ------- start included file ortholattice------- op(400,infix,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] x v y=y v x. 3 [] (x v y) v z=x v (y v z). 4 [] c(c(x))=x. 5 [] x v (x^y)=x. 6 [] x^y=c(c(x) v c(y)). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x) v x=1. 10 [] c(x)^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. end_of_list. ------- end included file ortholattice------- list(usable). 19 [] c(A)=d2. 20 [] B v d2=d3. 21 [] B^d2=d4. 22 [] c(d3)=d5. 23 [] d2^c(B)=d8. 24 [] d3^A=d9. 25 [] d8 v d4=d10. 26 [] d10 v d9=d11. 27 [] d11^d2=d12. 28 [] d11 v d2=d13. 29 [] c(d11)^d2=d14. 30 [] d13^A=d16. 31 [] d14 v d12=d17. 32 [] d17 v d16=d18. 33 [] d5^d18=d19. 34 [] c(d18)^d5=d20. 35 [] d18 v d5=d21. 36 [] d21^d3=d22. 37 [] d19 v d22=d23. 38 [] d23 v d20!=1. end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x v y!=z|y v x=z. 3 [] x v y!=z|u v z!=v|$Connect1(x,y,u,v). 3 [] x v y!=z|z v u=v| -$Connect1(y,u,x,v). 4 [] c(x)!=y|c(y)=x. 5 [] x^y!=z|x v z=x. 6 [] c(x)!=y|z v y!=u|$Connect3(x,z,u). 6 [] c(x)!=y|$Connect2(z,x,u)| -$Connect3(z,y,u). 6 [] c(x)!=y|z^u=y| -$Connect2(u,z,x). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x)!=y|y v x=1. 10 [] c(x)!=y|y^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. 19 [] d2!=x|A!=y|c(y)=x. 20 [] d3!=x|d2!=y|B!=z|z v y=x. 21 [] d4!=x|d2!=y|B!=z|z^y=x. 22 [] d5!=x|d3!=y|c(y)=x. 23 [] d8!=x|d2!=y|y^z=x| -$Connect4(z). 23 [] B!=x|c(x)!=y|$Connect4(y). 24 [] d9!=x|A!=y|d3!=z|z^y=x. 25 [] d10!=x|d4!=y|d8!=z|z v y=x. 26 [] d11!=x|d9!=y|d10!=z|z v y=x. 27 [] d12!=x|d2!=y|d11!=z|z^y=x. 28 [] d13!=x|d2!=y|d11!=z|z v y=x. 29 [] d14!=x|d2!=y|z^y=x| -$Connect5(z). 29 [] d11!=x|c(x)!=y|$Connect5(y). 30 [] d16!=x|A!=y|d13!=z|z^y=x. 31 [] d17!=x|d12!=y|d14!=z|z v y=x. 32 [] d18!=x|d16!=y|d17!=z|z v y=x. 33 [] d19!=x|d18!=y|d5!=z|z^y=x. 34 [] d20!=x|d5!=y|z^y=x| -$Connect6(z). 34 [] d18!=x|c(x)!=y|$Connect6(y). 35 [] d21!=x|d5!=y|d18!=z|z v y=x. 36 [] d22!=x|d3!=y|d21!=z|z^y=x. 37 [] d23!=x|d22!=y|d19!=z|z v y=x. 38 [] d20!=x|d23!=y|y v x!=1. end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 394 clauses were generated; 229 of those survived the first stage of unit preprocessing; there are 104 atoms. After all unit preprocessing, 48 atoms are still unassigned; 123 clauses remain; 21 of those are non-Horn (selectable); 4885 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 229 Literal occurrences input 526 Greatest atom 104 Unit preprocess: Preprocess unit assignments 56 Clauses after subsumption 123 Literal occ. after subsump. 324 Selectable clauses 21 Decide: Splits 4 Unit assignments 161 Failed paths 5 Memory: Memory malloced 3 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 1557 clauses were generated; 849 of those survived the first stage of unit preprocessing; there are 279 atoms. After all unit preprocessing, 131 atoms are still unassigned; 527 clauses remain; 24 of those are non-Horn (selectable); 4890 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 849 Literal occurrences input 2010 Greatest atom 279 Unit preprocess: Preprocess unit assignments 148 Clauses after subsumption 527 Literal occ. after subsump. 1462 Selectable clauses 24 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 8 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 4726 clauses were generated; 2461 of those survived the first stage of unit preprocessing; there are 640 atoms. After all unit preprocessing, 96 atoms are still unassigned; 1039 clauses remain; 52 of those are non-Horn (selectable); 4900 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 2461 Literal occurrences input 6197 Greatest atom 640 Unit preprocess: Preprocess unit assignments 544 Clauses after subsumption 1039 Literal occ. after subsump. 3205 Selectable clauses 52 Decide: Splits 13 Unit assignments 788 Failed paths 14 Memory: Memory malloced 18 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 11882 clauses were generated; 6038 of those survived the first stage of unit preprocessing; there are 1295 atoms. After all unit preprocessing, 609 atoms are still unassigned; 3940 clauses remain; 157 of those are non-Horn (selectable); 4919 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 6038 Literal occurrences input 15943 Greatest atom 1295 Unit preprocess: Preprocess unit assignments 686 Clauses after subsumption 3940 Literal occ. after subsump. 11646 Selectable clauses 157 Decide: Splits 1 Unit assignments 104 Failed paths 2 Memory: Memory malloced 37 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 25950 clauses were generated; 13137 of those survived the first stage of unit preprocessing; there are 2376 atoms. After all unit preprocessing, 1288 atoms are still unassigned; 9483 clauses remain; 235 of those are non-Horn (selectable); 4950 K allocated; cpu time so far for this domain size: 0.02 sec. ----- statistics for domain size 6 ---- Input: Clauses input 13137 Literal occurrences input 35131 Greatest atom 2376 Unit preprocess: Preprocess unit assignments 1088 Clauses after subsumption 9483 Literal occ. after subsump. 27413 Selectable clauses 235 Decide: Splits 50 Unit assignments 10507 Failed paths 51 Memory: Memory malloced 68 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.01 --- Starting search for models of size 7 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 51210 clauses were generated; 26310 of those survived the first stage of unit preprocessing; there are 4039 atoms. After all unit preprocessing, 2433 atoms are still unassigned; 20484 clauses remain; 267 of those are non-Horn (selectable); 4997 K allocated; cpu time so far for this domain size: 0.03 sec. ----- statistics for domain size 7 ---- Input: Clauses input 26310 Literal occurrences input 70608 Greatest atom 4039 Unit preprocess: Preprocess unit assignments 1606 Clauses after subsumption 20484 Literal occ. after subsump. 57991 Selectable clauses 267 Decide: Splits 15 Unit assignments 5597 Failed paths 16 Memory: Memory malloced 115 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.03 DPLL 0.01 --- Starting search for models of size 8 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 93539 clauses were generated; 49346 of those survived the first stage of unit preprocessing; there are 6464 atoms. After all unit preprocessing, 4212 atoms are still unassigned; 40630 clauses remain; 289 of those are non-Horn (selectable); 5066 K allocated; cpu time so far for this domain size: 0.06 sec. ----- statistics for domain size 8 ---- Input: Clauses input 49346 Literal occurrences input 133203 Greatest atom 6464 Unit preprocess: Preprocess unit assignments 2252 Clauses after subsumption 40630 Literal occ. after subsump. 113939 Selectable clauses 289 Decide: Splits 127 Unit assignments 111635 Failed paths 128 Memory: Memory malloced 184 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.05 DPLL 0.19 --- Starting search for models of size 9 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 160567 clauses were generated; 87427 of those survived the first stage of unit preprocessing; there are 9855 atoms. After all unit preprocessing, 6817 atoms are still unassigned; 75001 clauses remain; 314 of those are non-Horn (selectable); 5162 K allocated; cpu time so far for this domain size: 0.10 sec. ----- statistics for domain size 9 ---- Input: Clauses input 87427 Literal occurrences input 237689 Greatest atom 9855 Unit preprocess: Preprocess unit assignments 3038 Clauses after subsumption 75001 Literal occ. after subsump. 209760 Selectable clauses 314 Decide: Splits 25 Unit assignments 14454 Failed paths 26 Memory: Memory malloced 280 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.08 DPLL 0.05 --- Starting search for models of size 10 --- Applying isomorphism constraints to constants: d2 A d3 B d4. 261928 clauses were generated; 147379 of those survived the first stage of unit preprocessing; there are 14440 atoms. After all unit preprocessing, 10464 atoms are still unassigned; 130321 clauses remain; 343 of those are non-Horn (selectable); 10175 K allocated; cpu time so far for this domain size: 0.16 sec. ======================= Model #1 at 28.75 seconds: ^ : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 0 0 0 0 0 0 0 0 0 1 | 0 1 2 3 4 5 6 7 8 9 2 | 0 2 2 0 2 0 0 9 0 9 3 | 0 3 0 3 0 0 6 6 3 0 4 | 0 4 2 0 4 5 0 9 5 9 5 | 0 5 0 0 5 5 0 0 5 0 6 | 0 6 0 6 0 0 6 6 6 0 7 | 0 7 9 6 9 0 6 7 6 9 8 | 0 8 0 3 5 5 6 6 8 0 9 | 0 9 9 0 9 0 0 9 0 9 v : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 1 2 3 4 5 6 7 8 9 1 | 1 1 1 1 1 1 1 1 1 1 2 | 2 1 2 1 4 4 1 1 1 2 3 | 3 1 1 3 1 8 3 1 8 1 4 | 4 1 4 1 4 4 1 1 1 4 5 | 5 1 4 8 4 5 8 1 8 4 6 | 6 1 1 3 1 8 6 7 8 7 7 | 7 1 1 1 1 1 7 7 1 7 8 | 8 1 1 8 1 8 8 1 8 1 9 | 9 1 2 1 4 4 7 7 1 9 c : 0 1 2 3 4 5 6 7 8 9 ----------------------- 1 0 3 2 6 7 4 5 9 8 d2: 2 A: 3 d3: 4 B: 5 d4: 0 d5: 6 d8: 9 d9: 0 d10: 9 d11: 9 d12: 9 d13: 2 d14: 0 d16: 0 d17: 9 d18: 9 d19: 0 d20: 6 d21: 7 d22: 9 d23: 9 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 10 ---- Input: Clauses input 147379 Literal occurrences input 403547 Greatest atom 14440 Unit preprocess: Preprocess unit assignments 3976 Clauses after subsumption 130321 Literal occ. after subsump. 364665 Selectable clauses 343 Decide: Splits 5405 Unit assignments 10802444 Failed paths 5399 Memory: Memory malloced 410 K Memory MACE_tp_alloced 9765 K Time (seconds): Generate ground clauses 0.14 DPLL 28.17 ======================================= Total times for run (seconds): user CPU time 28.75 (0 hr, 0 min, 28 sec) system CPU time 0.17 (0 hr, 0 min, 0 sec) wall-clock time 29 (0 hr, 0 min, 29 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:45:28 2004 otter-3.3f/examples-mace2/lattice/oml-mol.in0100644000076400007640000000073207714222266020347 0ustar mccunemccune% benchmark parameters -n5 -N10 -p % % Find an orthomodular lattice that is not a modular ortholattice. % include("ortholattice"). list(usable). % Orthomodular law (OML) x v (c(x) ^ (x v y)) = x v y. % Denial of Modularity: % If we assume A, B, and C are distinct, and if % none of them is 0 or 1, we can use domain elements % 2,3,4 instead. This speeds up the search. % A v (B ^ (A v C)) != (A v B) ^ (A v C). 2 v (4 ^ (2 v 3)) != (2 v 4) ^ (2 v 3). end_of_list. otter-3.3f/examples-mace2/lattice/ol-oml.in0100644000076400007640000000031007714221576020165 0ustar mccunemccune% benchmark parameters -N6 -p % % Find an ortholattice that is not orthomodular. % include("ortholattice"). list(usable). % Denial of orthomodularity: A v (c(A) ^ (A v B)) != A v B. end_of_list. otter-3.3f/examples-mace2/lattice/oml-mol.out0100664000076400007640000002112110103523757020540 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:28 2004 The command was "../../bin/mace2 -n5 -N10 -p". include("ortholattice"). ------- start included file ortholattice------- op(400,infix,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] x v y=y v x. 3 [] (x v y) v z=x v (y v z). 4 [] c(c(x))=x. 5 [] x v (x^y)=x. 6 [] x^y=c(c(x) v c(y)). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x) v x=1. 10 [] c(x)^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. end_of_list. ------- end included file ortholattice------- list(usable). 19 [] x v (c(x)^ (x v y))=x v y. 20 [] 2 v (4^ (2 v 3))!= (2 v 4)^ (2 v 3). end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x v y!=z|y v x=z. 3 [] x v y!=z|u v z!=v|$Connect1(x,y,u,v). 3 [] x v y!=z|z v u=v| -$Connect1(y,u,x,v). 4 [] c(x)!=y|c(y)=x. 5 [] x^y!=z|x v z=x. 6 [] c(x)!=y|z v y!=u|$Connect3(x,z,u). 6 [] c(x)!=y|$Connect2(z,x,u)| -$Connect3(z,y,u). 6 [] c(x)!=y|z^u=y| -$Connect2(u,z,x). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x)!=y|y v x=1. 10 [] c(x)!=y|y^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. 19 [] x v y!=z|$Connect4(x,z). 19 [] c(x)!=y|y^z!=u|x v u=z| -$Connect4(x,z). 20 [] 2 v 4!=x|x^y!=z|2 v 3!=y| -$Connect5(y,z). 20 [] 4^x!=y|2 v y!=z|$Connect5(x,z). end_of_list. --- Starting search for models of size 5 --- 10255 clauses were generated; 4055 of those survived the first stage of unit preprocessing; there are 1225 atoms. After all unit preprocessing, 522 atoms are still unassigned; 1850 clauses remain; 15 of those are non-Horn (selectable); 4916 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 4055 Literal occurrences input 9006 Greatest atom 1225 Unit preprocess: Preprocess unit assignments 703 Clauses after subsumption 1850 Literal occ. after subsump. 4519 Selectable clauses 15 Decide: Splits 1 Unit assignments 106 Failed paths 2 Memory: Memory malloced 34 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- 23484 clauses were generated; 9835 of those survived the first stage of unit preprocessing; there are 2304 atoms. After all unit preprocessing, 1195 atoms are still unassigned; 5960 clauses remain; 28 of those are non-Horn (selectable); 4947 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 6 ---- Input: Clauses input 9835 Literal occurrences input 23223 Greatest atom 2304 Unit preprocess: Preprocess unit assignments 1109 Clauses after subsumption 5960 Literal occ. after subsump. 15030 Selectable clauses 28 Decide: Splits 6 Unit assignments 3111 Failed paths 7 Memory: Memory malloced 65 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 7 --- 47852 clauses were generated; 21393 of those survived the first stage of unit preprocessing; there are 3969 atoms. After all unit preprocessing, 2338 atoms are still unassigned; 15173 clauses remain; 45 of those are non-Horn (selectable); 4994 K allocated; cpu time so far for this domain size: 0.03 sec. ----- statistics for domain size 7 ---- Input: Clauses input 21393 Literal occurrences input 52792 Greatest atom 3969 Unit preprocess: Preprocess unit assignments 1631 Clauses after subsumption 15173 Literal occ. after subsump. 39247 Selectable clauses 45 Decide: Splits 7 Unit assignments 2542 Failed paths 8 Memory: Memory malloced 112 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.02 DPLL 0.01 --- Starting search for models of size 8 --- 89272 clauses were generated; 42512 of those survived the first stage of unit preprocessing; there are 6400 atoms. After all unit preprocessing, 4119 atoms are still unassigned; 33158 clauses remain; 66 of those are non-Horn (selectable); 5063 K allocated; cpu time so far for this domain size: 0.05 sec. ----- statistics for domain size 8 ---- Input: Clauses input 42512 Literal occurrences input 108327 Greatest atom 6400 Unit preprocess: Preprocess unit assignments 2281 Clauses after subsumption 33158 Literal occ. after subsump. 87478 Selectable clauses 66 Decide: Splits 128 Unit assignments 124526 Failed paths 129 Memory: Memory malloced 181 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.04 DPLL 0.20 --- Starting search for models of size 9 --- 155457 clauses were generated; 78415 of those survived the first stage of unit preprocessing; there are 9801 atoms. After all unit preprocessing, 6730 atoms are still unassigned; 65024 clauses remain; 91 of those are non-Horn (selectable); 5159 K allocated; cpu time so far for this domain size: 0.08 sec. ----- statistics for domain size 9 ---- Input: Clauses input 78415 Literal occurrences input 204642 Greatest atom 9801 Unit preprocess: Preprocess unit assignments 3071 Clauses after subsumption 65024 Literal occ. after subsump. 174231 Selectable clauses 91 Decide: Splits 47 Unit assignments 26268 Failed paths 48 Memory: Memory malloced 277 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.06 DPLL 0.07 --- Starting search for models of size 10 --- 256160 clauses were generated; 136005 of those survived the first stage of unit preprocessing; there are 14400 atoms. After all unit preprocessing, 10387 atoms are still unassigned; 117560 clauses remain; 120 of those are non-Horn (selectable); 10173 K allocated; cpu time so far for this domain size: 0.13 sec. ======================= Model #1 at 6.32 seconds: ^ : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 0 0 0 0 0 0 0 0 0 1 | 0 1 2 3 4 5 6 7 8 9 2 | 0 2 2 0 0 0 2 0 0 2 3 | 0 3 0 3 0 3 0 0 0 3 4 | 0 4 0 0 4 0 0 0 0 0 5 | 0 5 0 3 0 5 8 0 8 3 6 | 0 6 2 0 0 8 6 0 8 2 7 | 0 7 0 0 0 0 0 7 0 0 8 | 0 8 0 0 0 8 8 0 8 0 9 | 0 9 2 3 0 3 2 0 0 9 v : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 1 2 3 4 5 6 7 8 9 1 | 1 1 1 1 1 1 1 1 1 1 2 | 2 1 2 9 1 1 6 1 6 9 3 | 3 1 9 3 1 5 1 1 5 9 4 | 4 1 1 1 4 1 1 1 1 1 5 | 5 1 1 5 1 5 1 1 5 1 6 | 6 1 6 1 1 1 6 1 6 1 7 | 7 1 1 1 1 1 1 7 1 1 8 | 8 1 6 5 1 5 6 1 8 1 9 | 9 1 9 9 1 1 1 1 1 9 c : 0 1 2 3 4 5 6 7 8 9 ----------------------- 1 0 5 6 7 2 3 4 9 8 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 10 ---- Input: Clauses input 136005 Literal occurrences input 361471 Greatest atom 14400 Unit preprocess: Preprocess unit assignments 4013 Clauses after subsumption 117560 Literal occ. after subsump. 318934 Selectable clauses 120 Decide: Splits 1430 Unit assignments 1915319 Failed paths 1420 Memory: Memory malloced 408 K Memory MACE_tp_alloced 9765 K Time (seconds): Generate ground clauses 0.10 DPLL 5.79 ======================================= Total times for run (seconds): user CPU time 6.32 (0 hr, 0 min, 6 sec) system CPU time 0.09 (0 hr, 0 min, 0 sec) wall-clock time 7 (0 hr, 0 min, 7 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:45:35 2004 otter-3.3f/examples-mace2/lattice/lt-ml.out0100664000076400007640000001420610103523665020215 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -N5 -p". include("finite-lattice"). ------- start included file finite-lattice------- op(400,xfx,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] (x^y)^z=x^ (y^z). 3 [] x v y=y v x. 4 [] (x v y) v z=x v (y v z). 5 [] x^ (x v y)=x. 6 [] x v (x^y)=x. 7 [] x^x=x. 8 [] x v x=x. 9 [] 1 v x=1. 10 [] x v 1=1. 11 [] 1^x=x. 12 [] x^1=x. 13 [] 0^x=0. 14 [] x^0=0. 15 [] 0 v x=x. 16 [] x v 0=x. end_of_list. ------- end included file finite-lattice------- list(usable). 17 [] A v (B^ (A v C))!= (A v B)^ (A v C). end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x^y!=z|u^z!=v|$Connect1(x,y,u,v). 2 [] x^y!=z|z^u=v| -$Connect1(y,u,x,v). 3 [] x v y!=z|y v x=z. 4 [] x v y!=z|u v z!=v|$Connect2(x,y,u,v). 4 [] x v y!=z|z v u=v| -$Connect2(y,u,x,v). 5 [] x v y!=z|x^z=x. 6 [] x^y!=z|x v z=x. 7 [] x^x=x. 8 [] x v x=x. 9 [] 1 v x=1. 10 [] x v 1=1. 11 [] 1^x=x. 12 [] x^1=x. 13 [] 0^x=0. 14 [] x^0=0. 15 [] 0 v x=x. 16 [] x v 0=x. 17 [] x v y!=z|z^u!=v|B!=y|A!=x| -$Connect3(x,u)| -$Connect4(x,y,u,v). 17 [] x^y!=z|u v z!=v|$Connect4(u,x,y,v). 17 [] C!=x|y v x!=z|$Connect3(y,z). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: B A C. 278 clauses were generated; 102 of those survived the first stage of unit preprocessing; there are 78 atoms. After all unit preprocessing, 18 atoms are still unassigned; 18 clauses remain; 3 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 102 Literal occurrences input 160 Greatest atom 78 Unit preprocess: Preprocess unit assignments 60 Clauses after subsumption 18 Literal occ. after subsump. 52 Selectable clauses 3 Decide: Splits 3 Unit assignments 16 Failed paths 4 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: B A C. 1716 clauses were generated; 396 of those survived the first stage of unit preprocessing; there are 324 atoms. After all unit preprocessing, 72 atoms are still unassigned; 48 clauses remain; 3 of those are non-Horn (selectable); 4891 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 396 Literal occurrences input 597 Greatest atom 324 Unit preprocess: Preprocess unit assignments 252 Clauses after subsumption 48 Literal occ. after subsump. 153 Selectable clauses 3 Decide: Splits 8 Unit assignments 52 Failed paths 9 Memory: Memory malloced 9 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: B A C. 6772 clauses were generated; 1470 of those survived the first stage of unit preprocessing; there are 940 atoms. After all unit preprocessing, 346 atoms are still unassigned; 514 clauses remain; 14 of those are non-Horn (selectable); 4908 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 4 ---- Input: Clauses input 1470 Literal occurrences input 2793 Greatest atom 940 Unit preprocess: Preprocess unit assignments 594 Clauses after subsumption 514 Literal occ. after subsump. 1387 Selectable clauses 14 Decide: Splits 17 Unit assignments 577 Failed paths 18 Memory: Memory malloced 26 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: B A C. 20046 clauses were generated; 4852 of those survived the first stage of unit preprocessing; there are 2190 atoms. After all unit preprocessing, 1080 atoms are still unassigned; 2686 clauses remain; 28 of those are non-Horn (selectable); 4944 K allocated; cpu time so far for this domain size: 0.01 sec. ======================= Model #1 at 0.01 seconds: ^ : | 0 1 2 3 4 --+---------- 0 | 0 0 0 0 0 1 | 0 1 2 3 4 2 | 0 2 2 0 0 3 | 0 3 0 3 3 4 | 0 4 0 3 4 v : | 0 1 2 3 4 --+---------- 0 | 0 1 2 3 4 1 | 1 1 1 1 1 2 | 2 1 2 1 1 3 | 3 1 1 3 4 4 | 4 1 1 4 4 B: 2 A: 3 C: 4 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 5 ---- Input: Clauses input 4852 Literal occurrences input 11119 Greatest atom 2190 Unit preprocess: Preprocess unit assignments 1110 Clauses after subsumption 2686 Literal occ. after subsump. 7447 Selectable clauses 28 Decide: Splits 17 Unit assignments 1045 Failed paths 15 Memory: Memory malloced 62 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/lattice/lt-ol.in0100644000076400007640000000042407714221231020007 0ustar mccunemccune% benchmark parameters -N6 -p % % Find an invertable lattice that is not an ortholattice. % include("finite-lattice"). list(usable). % Complement and Invertability c(x) v x = 1. c(x) ^ x = 0. c(c(x)) = x. % Denial of compatibility c(A ^ B) != c(A) v c(B). end_of_list. otter-3.3f/examples-mace2/lattice/finite-lattice0100644000076400007640000000143407714220753021266 0ustar mccunemccuneop(400, xfx, [^,v]). % infix operators list(usable). % Lattice Theory (LT) % Six axioms for a lattice. x ^ y = y ^ x. % comm of meet (x ^ y) ^ z = x ^ (y ^ z). % assoc of meet x v y = y v x. % comm of join (x v y) v z = x v (y v z). % assoc of join x ^ (x v y) = x. % absorption 1 x v (x ^ y) = x. % absorption 2 % Idempotence lemmas (follow from lattice axioms) x ^ x = x. x v x = x. % Lattices don't necessarily have 0 or 1, but every FINITE lattice does, % and MACE deals only with finite structures, so we can include the following. % (Some of these are dependent.) % Zero and One 1 v x = 1. x v 1 = 1. 1 ^ x = x. x ^ 1 = x. 0 ^ x = 0. x ^ 0 = 0. 0 v x = x. x v 0 = x. end_of_list. % end of finite lattice axioms otter-3.3f/examples-mace2/lattice/ortholattice0100644000076400007640000000103407714216200021052 0ustar mccunemccuneop(400, infix, [^,v]). % infix operators list(usable). % Axioms for an ortholattice. x ^ y = y ^ x. % dependent on other axioms % (x ^ y) ^ z = x ^ (y ^ z). % dependent on other axioms x v y = y v x. (x v y) v z = x v (y v z). c(c(x)) = x. % x v (y v c(y)) = y v c(y). % follows from lemmas below x v (x ^ y) = x. x ^ y = c(c(x) v c(y)). % Ortholattice lemmas. x ^ x = x. x v x = x. c(x) v x = 1. c(x) ^ x = 0. 1 v x = 1. x v 1 = 1. 1 ^ x = x. x ^ 1 = x. 0 ^ x = 0. x ^ 0 = 0. 0 v x = x. x v 0 = x. end_of_list. otter-3.3f/examples-mace2/lattice/lattice-axioms0100644000076400007640000000334507317133143021306 0ustar mccunemccune % Six axioms for lattice theory (LT). x ^ y = y ^ x. % comm of meet (x ^ y) ^ z = x ^ (y ^ z). % assoc of meet x v y = y v x. % comm of join (x v y) v z = x v (y v z). % assoc of join x ^ (x v y) = x. % absorption 1 x v (x ^ y) = x. % absorption 2 % Idempotence lemmas (follow from lattice axioms) x ^ x = x. x v x = x. % Lattices don't necessarily have 0 or 1, but every FINITE lattice % does, and MACE deals only with finite structures, so we can include % the following. (Some of these are dependent.) % Zero and One 1 v x = 1. x v 1 = 1. 1 ^ x = x. x ^ 1 = x. 0 ^ x = 0. x ^ 0 = 0. 0 v x = x. x v 0 = x. % Modularity (M) (pick one; they are equivalent in lattice theory) x v (y ^ (x v z)) = (x v y) ^ (x v z). % equational % x ^ y != x | x v (z ^ y) = (x v z) ^ y. % implicational % (LT) + (M) gives us modular lattice theory (ML). % ======================================================================== % Ortholattices (OL) % Include 0, 1 (if we don't already have them because of finiteness) % and complements. % Invertability (INVERT) c(x) v x = 1. c(x) ^ x = 0. c(c(x)) = x. % Compatibility (COMPAT) c(x ^ y) = c(x) v c(y). % Alternate versions of compatibility % x ^ y = c(c(x) v c(y)). % x ^ y != x | c(x) ^ c(y) = c(y). % (x <= y) -> (c(y) <= c(x)) Ortholattice lemmas useful for MACE: c(0) = 1. c(1) = 0. % (LT) + (INVERT) + (COMPAT) gives us ortholattice theory (OL) % ===================================================================== % Orthomodular lattices (OML) (note different from modular OL). x v (c(x) ^ (x v y)) = x v y. (OM) % Implicational form of OM % x ^ y != x | x v (c(x) ^ y) = y. % (OL) + (OM) = (OML). end_of_list. otter-3.3f/examples-mace2/lattice/ol-e1.out0100664000076400007640000003114610103523713020101 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:39 2004 The command was "../../bin/mace2 -N10 -p". include("ortholattice"). ------- start included file ortholattice------- op(400,infix,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] x v y=y v x. 3 [] (x v y) v z=x v (y v z). 4 [] c(c(x))=x. 5 [] x v (x^y)=x. 6 [] x^y=c(c(x) v c(y)). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x) v x=1. 10 [] c(x)^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. end_of_list. ------- end included file ortholattice------- list(usable). 19 [] A^c(B)=D1. 20 [] A v c(B)=D2. 21 [] A v B=D3. 22 [] c(A)=D4. 23 [] D2^D3=D5. 24 [] D4^c(D5)=D6. 25 [] D4^D5=D7. 26 [] D7 v D6=D8. 27 [] c(D1 v D4) v (D1 v D8)!=1. end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x v y!=z|y v x=z. 3 [] x v y!=z|u v z!=v|$Connect1(x,y,u,v). 3 [] x v y!=z|z v u=v| -$Connect1(y,u,x,v). 4 [] c(x)!=y|c(y)=x. 5 [] x^y!=z|x v z=x. 6 [] c(x)!=y|z v y!=u|$Connect3(x,z,u). 6 [] c(x)!=y|$Connect2(z,x,u)| -$Connect3(z,y,u). 6 [] c(x)!=y|z^u=y| -$Connect2(u,z,x). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x)!=y|y v x=1. 10 [] c(x)!=y|y^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. 19 [] D1!=x|A!=y|y^z=x| -$Connect4(z). 19 [] B!=x|c(x)!=y|$Connect4(y). 20 [] D2!=x|A!=y|y v z=x| -$Connect5(z). 20 [] B!=x|c(x)!=y|$Connect5(y). 21 [] D3!=x|B!=y|A!=z|z v y=x. 22 [] D4!=x|A!=y|c(y)=x. 23 [] D5!=x|D3!=y|D2!=z|z^y=x. 24 [] D6!=x|D4!=y|y^z=x| -$Connect6(z). 24 [] D5!=x|c(x)!=y|$Connect6(y). 25 [] D7!=x|D5!=y|D4!=z|z^y=x. 26 [] D8!=x|D6!=y|D7!=z|z v y=x. 27 [] D8!=x|y v x!=z|D1!=y| -$Connect8(y,z). 27 [] x v y!=1| -$Connect7(z,x)|$Connect8(z,y). 27 [] D4!=x|y v x!=z|$Connect9(y,z). 27 [] c(x)!=y|$Connect7(z,y)| -$Connect9(z,x). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 316 clauses were generated; 182 of those survived the first stage of unit preprocessing; there are 94 atoms. After all unit preprocessing, 38 atoms are still unassigned; 74 clauses remain; 10 of those are non-Horn (selectable); 4884 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 182 Literal occurrences input 400 Greatest atom 94 Unit preprocess: Preprocess unit assignments 56 Clauses after subsumption 74 Literal occ. after subsump. 192 Selectable clauses 10 Decide: Splits 4 Unit assignments 89 Failed paths 5 Memory: Memory malloced 2 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 1333 clauses were generated; 671 of those survived the first stage of unit preprocessing; there are 273 atoms. After all unit preprocessing, 125 atoms are still unassigned; 337 clauses remain; 13 of those are non-Horn (selectable); 4889 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 671 Literal occurrences input 1490 Greatest atom 273 Unit preprocess: Preprocess unit assignments 148 Clauses after subsumption 337 Literal occ. after subsump. 906 Selectable clauses 13 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 7 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 4233 clauses were generated; 2003 of those survived the first stage of unit preprocessing; there are 644 atoms. After all unit preprocessing, 100 atoms are still unassigned; 545 clauses remain; 41 of those are non-Horn (selectable); 4900 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 2003 Literal occurrences input 4771 Greatest atom 644 Unit preprocess: Preprocess unit assignments 544 Clauses after subsumption 545 Literal occ. after subsump. 1685 Selectable clauses 41 Decide: Splits 13 Unit assignments 471 Failed paths 14 Memory: Memory malloced 18 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 10961 clauses were generated; 5115 of those survived the first stage of unit preprocessing; there are 1315 atoms. After all unit preprocessing, 629 atoms are still unassigned; 2934 clauses remain; 146 of those are non-Horn (selectable); 4919 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 5115 Literal occurrences input 12937 Greatest atom 1315 Unit preprocess: Preprocess unit assignments 686 Clauses after subsumption 2934 Literal occ. after subsump. 8391 Selectable clauses 146 Decide: Splits 1 Unit assignments 104 Failed paths 2 Memory: Memory malloced 37 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 24406 clauses were generated; 11528 of those survived the first stage of unit preprocessing; there are 2418 atoms. After all unit preprocessing, 1330 atoms are still unassigned; 7744 clauses remain; 224 of those are non-Horn (selectable); 4951 K allocated; cpu time so far for this domain size: 0.02 sec. ----- statistics for domain size 6 ---- Input: Clauses input 11528 Literal occurrences input 29709 Greatest atom 2418 Unit preprocess: Preprocess unit assignments 1088 Clauses after subsumption 7744 Literal occ. after subsump. 21601 Selectable clauses 224 Decide: Splits 88 Unit assignments 18346 Failed paths 89 Memory: Memory malloced 69 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.01 --- Starting search for models of size 7 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 48812 clauses were generated; 23758 of those survived the first stage of unit preprocessing; there are 4109 atoms. After all unit preprocessing, 2503 atoms are still unassigned; 17745 clauses remain; 256 of those are non-Horn (selectable); 4999 K allocated; cpu time so far for this domain size: 0.03 sec. ----- statistics for domain size 7 ---- Input: Clauses input 23758 Literal occurrences input 61772 Greatest atom 4109 Unit preprocess: Preprocess unit assignments 1606 Clauses after subsumption 17745 Literal occ. after subsump. 48594 Selectable clauses 256 Decide: Splits 82 Unit assignments 16938 Failed paths 83 Memory: Memory malloced 117 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.02 DPLL 0.02 --- Starting search for models of size 8 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 90020 clauses were generated; 45558 of those survived the first stage of unit preprocessing; there are 6568 atoms. After all unit preprocessing, 4316 atoms are still unassigned; 36588 clauses remain; 278 of those are non-Horn (selectable); 5069 K allocated; cpu time so far for this domain size: 0.06 sec. ----- statistics for domain size 8 ---- Input: Clauses input 45558 Literal occurrences input 119793 Greatest atom 6568 Unit preprocess: Preprocess unit assignments 2252 Clauses after subsumption 36588 Literal occ. after subsump. 99767 Selectable clauses 278 Decide: Splits 301 Unit assignments 181517 Failed paths 302 Memory: Memory malloced 187 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.05 DPLL 0.29 --- Starting search for models of size 9 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 155624 clauses were generated; 82074 of those survived the first stage of unit preprocessing; there are 9999 atoms. After all unit preprocessing, 6961 atoms are still unassigned; 69317 clauses remain; 303 of those are non-Horn (selectable); 5166 K allocated; cpu time so far for this domain size: 0.09 sec. ----- statistics for domain size 9 ---- Input: Clauses input 82074 Literal occurrences input 218383 Greatest atom 9999 Unit preprocess: Preprocess unit assignments 3038 Clauses after subsumption 69317 Literal occ. after subsump. 189461 Selectable clauses 303 Decide: Splits 681 Unit assignments 370798 Failed paths 682 Memory: Memory malloced 284 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.07 DPLL 0.82 --- Starting search for models of size 10 --- Applying isomorphism constraints to constants: D1 A B D2 D3. 255222 clauses were generated; 140096 of those survived the first stage of unit preprocessing; there are 14630 atoms. After all unit preprocessing, 10654 atoms are still unassigned; 122620 clauses remain; 332 of those are non-Horn (selectable); 10180 K allocated; cpu time so far for this domain size: 0.14 sec. ======================= Model #1 at 19.49 seconds: ^ : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 0 0 0 0 0 0 0 0 0 1 | 0 1 2 3 4 5 6 7 8 9 2 | 0 2 2 2 0 2 0 2 0 0 3 | 0 3 2 3 0 3 0 2 0 0 4 | 0 4 0 0 4 4 0 0 4 0 5 | 0 5 2 3 4 5 0 2 4 0 6 | 0 6 0 0 0 0 6 9 6 9 7 | 0 7 2 2 0 2 9 7 9 9 8 | 0 8 0 0 4 4 6 9 8 9 9 | 0 9 0 0 0 0 9 9 9 9 v : | 0 1 2 3 4 5 6 7 8 9 --+-------------------- 0 | 0 1 2 3 4 5 6 7 8 9 1 | 1 1 1 1 1 1 1 1 1 1 2 | 2 1 2 3 5 5 1 7 1 7 3 | 3 1 3 3 5 5 1 1 1 1 4 | 4 1 5 5 4 5 8 1 8 8 5 | 5 1 5 5 5 5 1 1 1 1 6 | 6 1 1 1 8 1 6 1 8 6 7 | 7 1 7 1 1 1 1 7 1 7 8 | 8 1 1 1 8 1 8 1 8 8 9 | 9 1 7 1 8 1 6 7 8 9 c : 0 1 2 3 4 5 6 7 8 9 ----------------------- 1 0 8 6 7 9 3 4 2 5 D1: 2 A: 3 B: 4 D2: 1 D3: 5 D4: 6 D5: 5 D6: 9 D7: 0 D8: 9 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 10 ---- Input: Clauses input 140096 Literal occurrences input 376861 Greatest atom 14630 Unit preprocess: Preprocess unit assignments 3976 Clauses after subsumption 122620 Literal occ. after subsump. 336725 Selectable clauses 332 Decide: Splits 3802 Unit assignments 6934451 Failed paths 3798 Memory: Memory malloced 415 K Memory MACE_tp_alloced 9765 K Time (seconds): Generate ground clauses 0.11 DPLL 18.07 ======================================= Total times for run (seconds): user CPU time 19.49 (0 hr, 0 min, 19 sec) system CPU time 0.13 (0 hr, 0 min, 0 sec) wall-clock time 20 (0 hr, 0 min, 20 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:59 2004 otter-3.3f/examples-mace2/lattice/ol-oml.out0100664000076400007640000001652310103523750020366 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:45:28 2004 The command was "../../bin/mace2 -N6 -p". include("ortholattice"). ------- start included file ortholattice------- op(400,infix,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] x v y=y v x. 3 [] (x v y) v z=x v (y v z). 4 [] c(c(x))=x. 5 [] x v (x^y)=x. 6 [] x^y=c(c(x) v c(y)). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x) v x=1. 10 [] c(x)^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. end_of_list. ------- end included file ortholattice------- list(usable). 19 [] A v (c(A)^ (A v B))!=A v B. end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x v y!=z|y v x=z. 3 [] x v y!=z|u v z!=v|$Connect1(x,y,u,v). 3 [] x v y!=z|z v u=v| -$Connect1(y,u,x,v). 4 [] c(x)!=y|c(y)=x. 5 [] x^y!=z|x v z=x. 6 [] c(x)!=y|z v y!=u|$Connect3(x,z,u). 6 [] c(x)!=y|$Connect2(z,x,u)| -$Connect3(z,y,u). 6 [] c(x)!=y|z^u=y| -$Connect2(u,z,x). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x)!=y|y v x=1. 10 [] c(x)!=y|y^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. 19 [] B!=x|y v x!=z|A!=y| -$Connect4(y,z). 19 [] c(x)!=y|y^z!=u|x v u!=z|$Connect4(x,z). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: B A. 220 clauses were generated; 109 of those survived the first stage of unit preprocessing; there are 64 atoms. After all unit preprocessing, 5 atoms are still unassigned; 8 clauses remain; 2 of those are non-Horn (selectable); 4883 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 109 Literal occurrences input 202 Greatest atom 64 Unit preprocess: Preprocess unit assignments 59 Clauses after subsumption 8 Literal occ. after subsump. 20 Selectable clauses 2 Decide: Splits 1 Unit assignments 4 Failed paths 2 Memory: Memory malloced 1 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: B A. 1076 clauses were generated; 439 of those survived the first stage of unit preprocessing; there are 222 atoms. After all unit preprocessing, 74 atoms are still unassigned; 124 clauses remain; 5 of those are non-Horn (selectable); 4888 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 439 Literal occurrences input 829 Greatest atom 222 Unit preprocess: Preprocess unit assignments 148 Clauses after subsumption 124 Literal occ. after subsump. 307 Selectable clauses 5 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 6 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: B A. 3701 clauses were generated; 1420 of those survived the first stage of unit preprocessing; there are 568 atoms. After all unit preprocessing, 15 atoms are still unassigned; 33 clauses remain; 5 of those are non-Horn (selectable); 4898 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 1420 Literal occurrences input 2935 Greatest atom 568 Unit preprocess: Preprocess unit assignments 553 Clauses after subsumption 33 Literal occ. after subsump. 93 Selectable clauses 5 Decide: Splits 2 Unit assignments 14 Failed paths 3 Memory: Memory malloced 16 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: B A. 10031 clauses were generated; 3920 of those survived the first stage of unit preprocessing; there are 1210 atoms. After all unit preprocessing, 518 atoms are still unassigned; 1824 clauses remain; 21 of those are non-Horn (selectable); 4916 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 3920 Literal occurrences input 8765 Greatest atom 1210 Unit preprocess: Preprocess unit assignments 692 Clauses after subsumption 1824 Literal occ. after subsump. 4491 Selectable clauses 21 Decide: Splits 1 Unit assignments 106 Failed paths 2 Memory: Memory malloced 34 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: B A. 23088 clauses were generated; 9533 of those survived the first stage of unit preprocessing; there are 2280 atoms. After all unit preprocessing, 1185 atoms are still unassigned; 5852 clauses remain; 34 of those are non-Horn (selectable); 4946 K allocated; cpu time so far for this domain size: 0.01 sec. ======================= Model #1 at 0.03 seconds: ^ : | 0 1 2 3 4 5 --+------------ 0 | 0 0 0 0 0 0 1 | 0 1 2 3 4 5 2 | 0 2 2 3 0 0 3 | 0 3 3 3 0 0 4 | 0 4 0 0 4 4 5 | 0 5 0 0 4 5 v : | 0 1 2 3 4 5 --+------------ 0 | 0 1 2 3 4 5 1 | 1 1 1 1 1 1 2 | 2 1 2 2 1 1 3 | 3 1 2 3 1 1 4 | 4 1 1 1 4 5 5 | 5 1 1 1 5 5 c : 0 1 2 3 4 5 --------------- 1 0 4 5 2 3 B: 2 A: 3 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 6 ---- Input: Clauses input 9533 Literal occurrences input 22622 Greatest atom 2280 Unit preprocess: Preprocess unit assignments 1095 Clauses after subsumption 5852 Literal occ. after subsump. 14824 Selectable clauses 34 Decide: Splits 11 Unit assignments 1201 Failed paths 10 Memory: Memory malloced 64 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 ======================================= Total times for run (seconds): user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:45:28 2004 otter-3.3f/examples-mace2/lattice/ml-mol.in0100644000076400007640000000055307714222515020166 0ustar mccunemccune% benchmark parameters -N10 -p % % Find an invertable modular lattice that is a modular ortholattice. % include("finite-lattice"). list(usable). % Complement and Invertability c(x) v x = 1. c(x) ^ x = 0. c(c(x)) = x. % Equational form of modularity: x v (y ^ (x v z)) = (x v y) ^ (x v z). % Denial of compatibility c(A ^ B) != c(A) v c(B). end_of_list. otter-3.3f/examples-mace2/lattice/index.html0100644000076400007640000000232607714267463020451 0ustar mccunemccune /home/mccune/otter-3.3/examples-mace2/lattice

/home/mccune/otter-3.3/examples-mace2/lattice

Examples on the relationships between various varieties of lattice.

mace2 -N5 -p < lt-ml.in > lt-ml.out

mace2 -N6 -p < lt-ol.in > lt-ol.out

mace2 -N10 -p < ml-mol.in > ml-mol.out

mace2 -N6 -p < mol-ba.in > mol-ba.out

mace2 -N10 -p < ol-e1.in > ol-e1.out

mace2 -N10 -p < ol-e4.in > ol-e4.out

mace2 -N6 -p < ol-oml.in > ol-oml.out

mace2 -n5 -N10 -p < oml-mol.in > oml-mol.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/lattice/README0100644000076400007640000000010407714223124017306 0ustar mccunemccuneExamples on the relationships between various varieties of lattice. otter-3.3f/examples-mace2/lattice/mol-ba.out0100664000076400007640000001714010103523667020341 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:39 2004 The command was "../../bin/mace2 -N6 -p". include("ortholattice"). ------- start included file ortholattice------- op(400,infix,[^,v]). list(usable). 1 [] x^y=y^x. 2 [] x v y=y v x. 3 [] (x v y) v z=x v (y v z). 4 [] c(c(x))=x. 5 [] x v (x^y)=x. 6 [] x^y=c(c(x) v c(y)). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x) v x=1. 10 [] c(x)^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. end_of_list. ------- end included file ortholattice------- list(usable). 19 [] x v (y^ (x v z))= (x v y)^ (x v z). 20 [] A^ (B v C)!= (A^B) v (A^C). end_of_list. list(flattened_and_parted_clauses). 1 [] x^y!=z|y^x=z. 2 [] x v y!=z|y v x=z. 3 [] x v y!=z|u v z!=v|$Connect1(x,y,u,v). 3 [] x v y!=z|z v u=v| -$Connect1(y,u,x,v). 4 [] c(x)!=y|c(y)=x. 5 [] x^y!=z|x v z=x. 6 [] c(x)!=y|z v y!=u|$Connect3(x,z,u). 6 [] c(x)!=y|$Connect2(z,x,u)| -$Connect3(z,y,u). 6 [] c(x)!=y|z^u=y| -$Connect2(u,z,x). 7 [] x^x=x. 8 [] x v x=x. 9 [] c(x)!=y|y v x=1. 10 [] c(x)!=y|y^x=0. 11 [] 1 v x=1. 12 [] x v 1=1. 13 [] 1^x=x. 14 [] x^1=x. 15 [] 0^x=0. 16 [] x^0=0. 17 [] 0 v x=x. 18 [] x v 0=x. 19 [] x v y!=z|z^u!=v| -$Connect4(x,u)|$Connect5(x,y,u,v). 19 [] x^y!=z|u v z=v| -$Connect5(u,x,y,v). 19 [] x v y!=z|$Connect4(x,z). 20 [] x^y!=z|u v z!=v|C!=y|A!=x| -$Connect7(x,y,u,v). 20 [] x^y!=z|B!=y| -$Connect6(x,u,y,v)|$Connect7(x,u,z,v). 20 [] x v y!=z|u^z!=v|$Connect6(u,y,x,v). end_of_list. --- Starting search for models of size 2 --- Applying isomorphism constraints to constants: C A B. 366 clauses were generated; 156 of those survived the first stage of unit preprocessing; there are 114 atoms. After all unit preprocessing, 32 atoms are still unassigned; 30 clauses remain; 3 of those are non-Horn (selectable); 4885 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 2 ---- Input: Clauses input 156 Literal occurrences input 291 Greatest atom 114 Unit preprocess: Preprocess unit assignments 82 Clauses after subsumption 30 Literal occ. after subsump. 84 Selectable clauses 3 Decide: Splits 3 Unit assignments 18 Failed paths 4 Memory: Memory malloced 3 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 3 --- Applying isomorphism constraints to constants: C A B. 2214 clauses were generated; 656 of those survived the first stage of unit preprocessing; there are 468 atoms. After all unit preprocessing, 215 atoms are still unassigned; 228 clauses remain; 6 of those are non-Horn (selectable); 4895 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 3 ---- Input: Clauses input 656 Literal occurrences input 1258 Greatest atom 468 Unit preprocess: Preprocess unit assignments 253 Clauses after subsumption 228 Literal occ. after subsump. 615 Selectable clauses 6 Decide: Splits 0 Unit assignments 0 Failed paths 1 Memory: Memory malloced 13 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 4 --- Applying isomorphism constraints to constants: C A B. 8576 clauses were generated; 2397 of those survived the first stage of unit preprocessing; there are 1340 atoms. After all unit preprocessing, 488 atoms are still unassigned; 348 clauses remain; 10 of those are non-Horn (selectable); 4920 K allocated; cpu time so far for this domain size: 0.00 sec. ----- statistics for domain size 4 ---- Input: Clauses input 2397 Literal occurrences input 5382 Greatest atom 1340 Unit preprocess: Preprocess unit assignments 852 Clauses after subsumption 348 Literal occ. after subsump. 1085 Selectable clauses 10 Decide: Splits 9 Unit assignments 94 Failed paths 10 Memory: Memory malloced 38 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.00 --- Starting search for models of size 5 --- Applying isomorphism constraints to constants: C A B. 25051 clauses were generated; 7522 of those survived the first stage of unit preprocessing; there are 3090 atoms. After all unit preprocessing, 1916 atoms are still unassigned; 4117 clauses remain; 31 of those are non-Horn (selectable); 4969 K allocated; cpu time so far for this domain size: 0.01 sec. ----- statistics for domain size 5 ---- Input: Clauses input 7522 Literal occurrences input 19164 Greatest atom 3090 Unit preprocess: Preprocess unit assignments 1174 Clauses after subsumption 4117 Literal occ. after subsump. 12045 Selectable clauses 31 Decide: Splits 1 Unit assignments 135 Failed paths 2 Memory: Memory malloced 87 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.00 --- Starting search for models of size 6 --- Applying isomorphism constraints to constants: C A B. 60698 clauses were generated; 20314 of those survived the first stage of unit preprocessing; there are 6174 atoms. After all unit preprocessing, 4276 atoms are still unassigned; 13462 clauses remain; 45 of those are non-Horn (selectable); 5057 K allocated; cpu time so far for this domain size: 0.03 sec. ======================= Model #1 at 0.06 seconds: ^ : | 0 1 2 3 4 5 --+------------ 0 | 0 0 0 0 0 0 1 | 0 1 2 3 4 5 2 | 0 2 2 0 0 0 3 | 0 3 0 3 0 0 4 | 0 4 0 0 4 0 5 | 0 5 0 0 0 5 v : | 0 1 2 3 4 5 --+------------ 0 | 0 1 2 3 4 5 1 | 1 1 1 1 1 1 2 | 2 1 2 1 1 1 3 | 3 1 1 3 1 1 4 | 4 1 1 1 4 1 5 | 5 1 1 1 1 5 c : 0 1 2 3 4 5 --------------- 1 0 3 2 5 4 C: 2 A: 3 B: 4 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 6 ---- Input: Clauses input 20314 Literal occurrences input 56300 Greatest atom 6174 Unit preprocess: Preprocess unit assignments 1898 Clauses after subsumption 13462 Literal occ. after subsump. 40753 Selectable clauses 45 Decide: Splits 18 Unit assignments 6193 Failed paths 16 Memory: Memory malloced 175 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.03 DPLL 0.01 ======================================= Total times for run (seconds): user CPU time 0.06 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:39 2004 otter-3.3f/examples-mace2/lattice/ol-e1.in0100644000076400007640000000220707714216602017704 0ustar mccunemccune% benchmark parameters -N10 -p % % There is a model of size 10; it takes 275 seconds on a PIII933. % % We have an equation that holds for orthomodular lattices, % and we show that it does not hold for ortholattices by % finding an ortholattice in which the equation does not hold. % % The problem is from Norm Megill, September 1997. % % The equation is (E1) from % % @article{ ortholattice, % author = "W. McCune", % title = "Automatic Proofs and Counterexamples for some % Ortholattice Identities", % journal = "Information Processing Letters", % year = 1998, % volume = 65, % pages = "285--291"} % % See http://www-unix.mcs.anl.gov/~mccune/papers/ortholattice/ include("ortholattice"). list(usable). % The original denial: % % c((A ^ c(B)) v c(A)) v ((A ^ c(B)) v ((c(A) ^ ((A v c(B)) ^ % (A v B))) v (c(A) ^ c((A v c(B)) ^ (A v B))))) != A v c(A). % An equivalent denial that names subterms: (This is necessary, because % MACE cannot handle big equations.) A ^ c(B) = D1. A v c(B) = D2. A v B = D3. c(A) = D4. D2 ^ D3 = D5. D4 ^ c(D5) = D6. D4 ^ D5 = D7. D7 v D6 = D8. c(D1 v D4) v (D1 v D8) != 1. end_of_list. otter-3.3f/examples-mace2/lattice/mol-ba.in0100644000076400007640000000041407714221510020126 0ustar mccunemccune% benchmark parameters -N6 -p % % Find a modular ortholattice that is not a Boolean algebra. % include("ortholattice"). list(usable). % Modularity x v (y ^ (x v z)) = (x v y) ^ (x v z). % Denial of distributivity: A ^ (B v C) != (A ^ B) v (A ^ C). end_of_list. otter-3.3f/examples-mace2/lattice/program0100644000076400007640000000000607705577561020042 0ustar mccunemccunemace2 otter-3.3f/examples-mace2/lattice/ol-e4.in0100644000076400007640000000260207714217154017711 0ustar mccunemccune% benchmark parameters -N10 -p include("ortholattice"). list(usable). % This is the denial in which ground terms are "named". c(A) = d2. B v d2 = d3. B ^ d2 = d4. c(d3) = d5. d2 ^ c(B) = d8. d3 ^ A = d9. d8 v d4 = d10. d10 v d9 = d11. d11 ^ d2 = d12. d11 v d2 = d13. c(d11) ^ d2 = d14. d13 ^ A = d16. d14 v d12 = d17. d17 v d16 = d18. d5 ^ d18 = d19. c(d18) ^ d5 = d20. d18 v d5 = d21. d21 ^ d3 = d22. d19 v d22 = d23. d23 v d20 != 1. end_of_list. % list(usable). % Original denial. % ( ( c( c(A) v B ) ^ ( ( ( c(A) ^ ( ( ( c(A) ^ B % ) v ( c(A) ^ c(B) ) ) v ( A ^ ( c(A) v B ) ) ) ) v ( c(A) % ^ c( ( ( c(A) ^ B ) v ( c(A) ^ c(B) ) ) v ( A ^ ( c(A) v % B ) ) ) ) ) v ( A ^ ( c(A) v ( ( ( c(A) ^ B ) v ( c(A) ^ % c(B) ) ) v ( A ^ ( c(A) v B ) ) ) ) ) ) ) v ( c( c(A) v B % ) ^ c( ( ( c(A) ^ ( ( ( c(A) ^ B ) v ( c(A) ^ c(B) ) ) v % ( A ^ ( c(A) v B ) ) ) ) v ( c(A) ^ c( ( ( c(A) ^ B ) v % ( c(A) ^ c(B) ) ) v ( A ^ ( c(A) v B ) ) ) ) ) v ( A ^ ( % c(A) v ( ( ( c(A) ^ B ) v ( c(A) ^ c(B) ) ) v ( A ^ ( c(A) % v B ) ) ) ) ) ) ) ) v ( ( c(A) v B ) ^ ( c( c(A) v B ) % v ( ( ( c(A) ^ ( ( ( c(A) ^ B ) v ( c(A) ^ c(B) ) ) v ( A % ^ ( c(A) v B ) ) ) ) v ( c(A) ^ c( ( ( c(A) ^ B ) v ( c(A) % ^ c(B) ) ) v ( A ^ ( c(A) v B ) ) ) ) ) v ( A ^ ( c(A) % v ( ( ( c(A) ^ B ) v ( c(A) ^ c(B) ) ) v ( A ^ ( c(A) v B % ) ) ) ) ) ) ) ) != 1. % end_of_list. otter-3.3f/examples-mace2/lattice/lt-ml.in0100644000076400007640000000036207714220445020014 0ustar mccunemccune% benchmark parameters -N5 -p % % Find a nonmodular lattice. % The smallest ones are pentagon (-n5) and benzine (-n6). include("finite-lattice"). list(usable). % Denial of modularity: A v (B ^ (A v C)) != (A v B) ^ (A v C). end_of_list. otter-3.3f/examples-mace2/index.html0100644000076400007640000000146007714267464017023 0ustar mccunemccune /home/mccune/otter-3.3/examples-mace2

/home/mccune/otter-3.3/examples-mace2

  • basic . Examples for a fixed domain size.
  • iterate . Examples that iterate through domain sizes.
  • lattice . Examples on the relationships between various varieties of lattice.
  • propositional . Propositional examples for anldp.
  • quasigroup . Quasigroup problems from Frank Bennett.

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/README0100644000076400007640000000015007654045167015676 0ustar mccunemccuneOn a UNIX system, you should be able to run all of the tests with the following command. % ./Run_all otter-3.3f/examples-mace2/quasigroup/0040755000076400007640000000000010103524322017176 5ustar mccunemccuneotter-3.3f/examples-mace2/quasigroup/qg7bl.in0100644000076400007640000000027707276025537020572 0ustar mccunemccune% benchmark parameters -n11 -x -m1000 list(usable). f(x,x) = x. f(f(f(x,y),x),y)=x. f(f(f(x,y),y),f(x,y))=x. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg6.in0100644000076400007640000000025507276025537020247 0ustar mccunemccune% benchmark parameters -n11 -x -m1000 list(usable). f(x,x) = x. f(f(x,y),y) = f(x,f(x,y)). end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg4.out0100664000076400007640000000353310103523665020436 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -n8 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(f(x,y),f(y,x))=y. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(y,x)!=u|f(u,z)=x. end_of_list. --- Starting search for models of size 8 --- Adding basic QG constraints on last column of f. function f quasigroup. 9757 clauses were generated; 5744 of those survived the first stage of unit preprocessing; there are 576 atoms. After all unit preprocessing, 298 atoms are still unassigned; 3830 clauses remain; 162 of those are non-Horn (selectable); 4898 K allocated; cpu time so far for this domain size: 0.01 sec.  The search is complete. No models were found. ----- statistics for domain size 8 ---- Input: Clauses input 5744 Literal occurrences input 13401 Greatest atom 576 Unit preprocess: Preprocess unit assignments 278 Clauses after subsumption 3830 Literal occ. after subsump. 9632 Selectable clauses 162 Decide: Splits 891 Unit assignments 55768 Failed paths 892 Memory: Memory malloced 16 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.03 ======================================= Total times for run (seconds): user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/quasigroup/qg1d.out0100664000076400007640000000400610103523665020573 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:36 2004 The command was "../../bin/mace2 -n7 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(x,y)!=u|f(z,w)!=u|f(v,y)!=x|f(v,w)!=z|x=z|y=w. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(u,v)!=z|x=u|y=v| -$Connect1(x,y,u,v). 2 [] f(x,y)!=z|f(x,u)!=v|$Connect1(z,y,v,u). end_of_list. --- Starting search for models of size 7 --- Adding basic QG constraints on last column of f. function f quasigroup. 36919 clauses were generated; 12677 of those survived the first stage of unit preprocessing; there are 2793 atoms. After all unit preprocessing, 2542 atoms are still unassigned; 8906 clauses remain; 114 of those are non-Horn (selectable); 4961 K allocated; cpu time so far for this domain size: 0.01 sec. The 1st model has been found.  The search is complete. The set is satisfiable (8 model(s) found). ----- statistics for domain size 7 ---- Input: Clauses input 12677 Literal occurrences input 34943 Greatest atom 2793 Unit preprocess: Preprocess unit assignments 251 Clauses after subsumption 8906 Literal occ. after subsump. 25196 Selectable clauses 114 Decide: Splits 388 Unit assignments 48988 Failed paths 381 Memory: Memory malloced 79 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.04 ======================================= Total times for run (seconds): user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) The search is complete. The set is satisfiable (8 model(s) found). The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/quasigroup/omts9.in0100644000076400007640000000137507301003134020603 0ustar mccunemccune% benchmark parameters -n9 -p -x % % Orthogonal Mendelsohn Triple System (OMTS) of order 9. % % See the following, available in the MACE package. % % @techreport{ dp-quasi, % author = "W. McCune", % title = "A {D}avis-{P}utnam Program and its Application to % Finite First-Order Model Search: Quasigroup Existence Problems", % institution = "Argonne National Laboratory", % year = 1994, % type = "Tech. Report", % number = "ANL/MCS-TM-194", % address = "Argonne, IL", % month = "May"} list(usable). f(x,x) = x. h(x,x) = x. f(x,f(y,x))=y. h(x,h(y,x))=y. f(x,y)!=u | f(z,w)!=u | h(x,y)!=v | h(z,w)!=v | x=z | y=w. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). property(h(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg3.in0100644000076400007640000000024707276025537020245 0ustar mccunemccune% benchmark parameters -n8 -x -m1000 list(usable). f(x,x) = x. f(f(x,y),f(y,x)) = x. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg5l.out0100664000076400007640000000404310103523665020610 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -n11 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(f(f(x,y),x),x)=y. 3 [] f(x,f(f(y,x),x))=y. 4 [] f(f(x,f(y,x)),x)=y. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(z,x)!=u|f(u,x)=y. 3 [] f(x,y)!=z|f(z,y)!=u|f(y,u)=x. 4 [] f(x,y)!=z|f(y,z)!=u|f(u,y)=x. end_of_list. --- Starting search for models of size 11 --- Adding basic QG constraints on last column of f. function f quasigroup. 64428 clauses were generated; 40098 of those survived the first stage of unit preprocessing; there are 1452 atoms. After all unit preprocessing, 824 atoms are still unassigned; 28488 clauses remain; 312 of those are non-Horn (selectable); 4924 K allocated; cpu time so far for this domain size: 0.04 sec. The 1st model has been found.  The search is complete. The set is satisfiable (5 model(s) found). ----- statistics for domain size 11 ---- Input: Clauses input 40098 Literal occurrences input 103170 Greatest atom 1452 Unit preprocess: Preprocess unit assignments 628 Clauses after subsumption 28488 Literal occ. after subsump. 76077 Selectable clauses 312 Decide: Splits 112 Unit assignments 18310 Failed paths 108 Memory: Memory malloced 42 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.03 DPLL 0.07 ======================================= Total times for run (seconds): user CPU time 0.10 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (5 model(s) found). The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/quasigroup/qg3.out0100664000076400007640000000370610103523665020437 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -n8 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(f(x,y),f(y,x))=x. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(y,x)!=u|f(u,z)=y. end_of_list. --- Starting search for models of size 8 --- Adding basic QG constraints on last column of f. function f quasigroup. 9757 clauses were generated; 5744 of those survived the first stage of unit preprocessing; there are 576 atoms. After all unit preprocessing, 298 atoms are still unassigned; 3830 clauses remain; 162 of those are non-Horn (selectable); 4898 K allocated; cpu time so far for this domain size: 0.00 sec. The 1st model has been found. The 10th model has been found.  The search is complete. The set is satisfiable (18 model(s) found). ----- statistics for domain size 8 ---- Input: Clauses input 5744 Literal occurrences input 13396 Greatest atom 576 Unit preprocess: Preprocess unit assignments 278 Clauses after subsumption 3830 Literal occ. after subsump. 9623 Selectable clauses 162 Decide: Splits 1017 Unit assignments 60656 Failed paths 1000 Memory: Memory malloced 16 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.00 DPLL 0.04 ======================================= Total times for run (seconds): user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (18 model(s) found). The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/quasigroup/omts9.out0100664000076400007640000000545210103523664021017 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:36 2004 The command was "../../bin/mace2 -n9 -p -x". list(usable). 1 [] f(x,x)=x. 2 [] h(x,x)=x. 3 [] f(x,f(y,x))=y. 4 [] h(x,h(y,x))=y. 5 [] f(x,y)!=u|f(z,w)!=u|h(x,y)!=v|h(z,w)!=v|x=z|y=w. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). 0 [] property(h(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] h(x,x)=x. 3 [] f(x,y)!=z|f(y,z)=x. 4 [] h(x,y)!=z|h(y,z)=x. 5 [] f(x,y)!=z|f(u,v)!=z|x=u|y=v| -$Connect1(x,y,u,v). 5 [] h(x,y)!=z|h(u,v)!=z|$Connect1(x,y,u,v). end_of_list. --- Starting search for models of size 9 --- Adding basic QG constraints on last column of f. function f quasigroup. function h quasigroup. 137665 clauses were generated; 60281 of those survived the first stage of unit preprocessing; there are 8100 atoms. After all unit preprocessing, 7402 atoms are still unassigned; 49564 clauses remain; 414 of those are non-Horn (selectable); 5113 K allocated; cpu time so far for this domain size: 0.06 sec. ======================= Model #1 at 0.76 seconds: f : | 0 1 2 3 4 5 6 7 8 --+------------------ 0 | 0 8 5 2 7 4 3 6 1 1 | 8 1 7 6 3 2 5 4 0 2 | 3 5 2 8 6 0 4 1 7 3 | 6 4 0 3 8 7 1 5 2 4 | 5 7 6 1 4 8 2 0 3 5 | 2 6 1 7 0 5 8 3 4 6 | 7 3 4 0 2 1 6 8 5 7 | 4 2 8 5 1 3 0 7 6 8 | 1 0 3 4 5 6 7 2 8 h : | 0 1 2 3 4 5 6 7 8 --+------------------ 0 | 0 2 6 4 3 1 8 5 7 1 | 5 1 0 8 2 3 7 6 4 2 | 1 4 2 6 7 8 0 3 5 3 | 4 5 7 3 0 6 2 8 1 4 | 3 8 1 0 4 7 5 2 6 5 | 7 0 8 1 6 5 3 4 2 6 | 2 7 3 5 8 4 6 1 0 7 | 8 6 4 2 5 0 1 7 3 8 | 6 3 5 7 1 2 4 0 8 end_of_model  Exit by max_models parameter. The set is satisfiable (1 model(s) found). ----- statistics for domain size 9 ---- Input: Clauses input 60281 Literal occurrences input 165950 Greatest atom 8100 Unit preprocess: Preprocess unit assignments 698 Clauses after subsumption 49564 Literal occ. after subsump. 140030 Selectable clauses 414 Decide: Splits 2350 Unit assignments 366412 Failed paths 2339 Memory: Memory malloced 231 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.05 DPLL 0.71 ======================================= Total times for run (seconds): user CPU time 0.76 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Exit by max_models parameter. The set is satisfiable (1 model(s) found). The job finished Mon Aug 2 15:44:36 2004 otter-3.3f/examples-mace2/quasigroup/qg1d.in0100644000076400007640000000051707276025537020407 0ustar mccunemccune% benchmark parameters -n7 -x -m1000 list(usable). f(x,x) = x. % (3,2,1)-COLS % f(x,y)!=u | f(z,w)!=u | f(v,y)!=x | f(v,w)!= z | x=z. % f(x,y)!=u | f(z,w)!=u | f(v,y)!=x | f(v,w)!= z | y=w. f(x,y)!=u | f(z,w)!=u | f(v,y)!=x | f(v,w)!= z | x=z | y=w. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg7bl.out0100664000076400007640000000364310103523665020761 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -n11 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(f(f(x,y),x),y)=x. 3 [] f(f(f(x,y),y),f(x,y))=x. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(z,x)!=u|f(u,y)=x. 3 [] f(x,y)!=z|f(z,y)!=u|f(u,z)=x. end_of_list. --- Starting search for models of size 11 --- Adding basic QG constraints on last column of f. function f quasigroup. 49787 clauses were generated; 31819 of those survived the first stage of unit preprocessing; there are 1452 atoms. After all unit preprocessing, 755 atoms are still unassigned; 18944 clauses remain; 300 of those are non-Horn (selectable); 4924 K allocated; cpu time so far for this domain size: 0.03 sec.  The search is complete. No models were found. ----- statistics for domain size 11 ---- Input: Clauses input 31819 Literal occurrences input 79461 Greatest atom 1452 Unit preprocess: Preprocess unit assignments 697 Clauses after subsumption 18944 Literal occ. after subsump. 49569 Selectable clauses 300 Decide: Splits 291 Unit assignments 41021 Failed paths 292 Memory: Memory malloced 42 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.03 DPLL 0.07 ======================================= Total times for run (seconds): user CPU time 0.10 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/quasigroup/index.html0100644000076400007640000000226707714267464021230 0ustar mccunemccune /home/mccune/otter-3.3/examples-mace2/quasigroup

/home/mccune/otter-3.3/examples-mace2/quasigroup

Quasigroup problems from Frank Bennett.

mace2 -n9 -p -x < omts9.in > omts9.out

mace2 -n7 -x -m1000 < qg1d.in > qg1d.out

mace2 -n7 -x -m1000 < qg2d.in > qg2d.out

mace2 -n8 -x -m1000 < qg3.in > qg3.out

mace2 -n8 -x -m1000 < qg4.in > qg4.out

mace2 -n11 -x -m1000 < qg5l.in > qg5l.out

mace2 -n11 -x -m1000 < qg6.in > qg6.out

mace2 -n11 -x -m1000 < qg7bl.in > qg7bl.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/quasigroup/qg6.out0100664000076400007640000000354710103523665020445 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -n11 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(f(x,y),y)=f(x,f(x,y)). end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(x,u)!=y|f(y,u)=z. end_of_list. --- Starting search for models of size 11 --- Adding basic QG constraints on last column of f. function f quasigroup. 35146 clauses were generated; 23686 of those survived the first stage of unit preprocessing; there are 1452 atoms. After all unit preprocessing, 871 atoms are still unassigned; 17055 clauses remain; 318 of those are non-Horn (selectable); 4924 K allocated; cpu time so far for this domain size: 0.02 sec.  The search is complete. No models were found. ----- statistics for domain size 11 ---- Input: Clauses input 23686 Literal occurrences input 56374 Greatest atom 1452 Unit preprocess: Preprocess unit assignments 581 Clauses after subsumption 17055 Literal occ. after subsump. 42605 Selectable clauses 318 Decide: Splits 665 Unit assignments 84100 Failed paths 666 Memory: Memory malloced 42 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.01 DPLL 0.08 ======================================= Total times for run (seconds): user CPU time 0.09 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. No models were found. The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/quasigroup/README0100644000076400007640000000005007313721114020055 0ustar mccunemccuneQuasigroup problems from Frank Bennett. otter-3.3f/examples-mace2/quasigroup/qg5l.in0100644000076400007640000000032407276025537020417 0ustar mccunemccune% benchmark parameters -n11 -x -m1000 list(usable). f(x,x) = x. f(f(f(x,y),x),x) = y. f(x,f(f(y,x),x)) = y. f(f(x,f(y,x)),x) = y. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/program0100644000076400007640000000000607705577561020614 0ustar mccunemccunemace2 otter-3.3f/examples-mace2/quasigroup/qg4.in0100644000076400007640000000024707276025537020246 0ustar mccunemccune% benchmark parameters -n8 -x -m1000 list(usable). f(x,x) = x. f(f(x,y),f(y,x)) = y. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg2d.in0100644000076400007640000000051707714247064020406 0ustar mccunemccune% benchmark parameters -n7 -x -m1000 list(usable). f(x,x) = x. % (3,1,2)-COLS % f(x,y)!=u | f(z,w)!=u | f(v,x)!=y | f(v,z)!= w | x=z. % f(x,y)!=u | f(z,w)!=u | f(v,x)!=y | f(v,z)!= w | y=w. f(x,y)!=u | f(z,w)!=u | f(v,x)!=y | f(v,z)!= w | x=z | y=w. end_of_list. list(mace_constraints). property(f(_,_), quasigroup). end_of_list. otter-3.3f/examples-mace2/quasigroup/qg2d.out0100664000076400007640000000405010103523665020573 0ustar mccunemccune----- MACE 2.2f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:44:37 2004 The command was "../../bin/mace2 -n7 -x -m1000". list(usable). 1 [] f(x,x)=x. 2 [] f(x,y)!=u|f(z,w)!=u|f(v,x)!=y|f(v,z)!=w|x=z|y=w. end_of_list. list(mace_constraints). 0 [] property(f(_,_),quasigroup). end_of_list. list(flattened_and_parted_clauses). 1 [] f(x,x)=x. 2 [] f(x,y)!=z|f(u,v)!=z|x=u|y=v| -$Connect1(x,y,u,v). 2 [] f(x,y)!=z|f(x,u)!=v|$Connect1(y,z,u,v). end_of_list. --- Starting search for models of size 7 --- Adding basic QG constraints on last column of f. function f quasigroup. 36919 clauses were generated; 12677 of those survived the first stage of unit preprocessing; there are 2793 atoms. After all unit preprocessing, 2563 atoms are still unassigned; 9787 clauses remain; 120 of those are non-Horn (selectable); 4961 K allocated; cpu time so far for this domain size: 0.02 sec. The 1st model has been found. The 10th model has been found.  The search is complete. The set is satisfiable (14 model(s) found). ----- statistics for domain size 7 ---- Input: Clauses input 12677 Literal occurrences input 34943 Greatest atom 2793 Unit preprocess: Preprocess unit assignments 230 Clauses after subsumption 9787 Literal occ. after subsump. 27718 Selectable clauses 120 Decide: Splits 361 Unit assignments 49450 Failed paths 348 Memory: Memory malloced 79 K Memory MACE_tp_alloced 4882 K Time (seconds): Generate ground clauses 0.02 DPLL 0.04 ======================================= Total times for run (seconds): user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) The search is complete. The set is satisfiable (14 model(s) found). The job finished Mon Aug 2 15:44:37 2004 otter-3.3f/examples-mace2/Run_all0100755000076400007640000000132207714323642016334 0ustar mccunemccune#!/bin/csh if (-e Run_all.out) /bin/mv Run_all.out Run_all.out.$$ echo "Sending output to Run_all.out." echo "This should take about a minute on a 2 GHz P4." echo "Run_mace basic ..." ./Run_mace basic > Run_all.out echo "Run_mace iterate ..." ./Run_mace iterate >> Run_all.out echo "Run_mace quasigroup ..." ./Run_mace quasigroup >> Run_all.out echo "Run_mace lattice ..." ./Run_mace lattice >> Run_all.out echo "Run_anldp propositional ..." ./Run_anldp propositional >> Run_all.out echo "Done. The output files are in */*.out[0-9]*" echo "" grep "times as fast as" Run_all.out echo "" awk '/Running/ {p = $2} /There is a problem/ {print "Error running " p}' Run_all.out echo "" otter-3.3f/examples-mace2/Run_all.out0100664000076400007640000000725410103523761017141 0ustar mccunemccuneRunning basic/cd.in ... Okay, it seems to have run correctly. Running basic/cl_ql.in ... Okay, it seems to have run correctly. Running basic/cl_sw.in ... Okay, it seems to have run correctly. Running basic/noncommutative_group.in ... Okay, it seems to have run correctly. Running basic/ordered_semi.in ... Okay, it seems to have run correctly. Running basic/ring.in ... Okay, it seems to have run correctly. Running basic/tba.in ... Okay, it seems to have run correctly. Running basic/tough-nut.in ... Okay, it seems to have run correctly. time_new=1.75, time_old=1.7. The out9272 times are about 0.971429 times as fast as the out times. The output files have been left in basic/*.out9272. Running iterate/BOO032-1.in ... Okay, it seems to have run correctly. Running iterate/CAT019-5.in ... Okay, it seems to have run correctly. Running iterate/cd.in ... Okay, it seems to have run correctly. Running iterate/kauer.in ... Okay, it seems to have run correctly. Running iterate/LAT025-1.in ... Okay, it seems to have run correctly. Running iterate/LCL136-1.in ... Okay, it seems to have run correctly. Running iterate/noncommutative_group.in ... Okay, it seems to have run correctly. Running iterate/noncommutive_ring1.in ... Okay, it seems to have run correctly. Running iterate/PUZ001-3.in ... Okay, it seems to have run correctly. Running iterate/RNG025-8.in ... Okay, it seems to have run correctly. time_new=2.94, time_old=2.76. The out9368 times are about 0.938776 times as fast as the out times. The output files have been left in iterate/*.out9368. Running quasigroup/omts9.in ... Okay, it seems to have run correctly. Running quasigroup/qg1d.in ... Okay, it seems to have run correctly. Running quasigroup/qg2d.in ... Okay, it seems to have run correctly. Running quasigroup/qg3.in ... Okay, it seems to have run correctly. Running quasigroup/qg4.in ... Okay, it seems to have run correctly. Running quasigroup/qg5l.in ... Okay, it seems to have run correctly. Running quasigroup/qg6.in ... Okay, it seems to have run correctly. Running quasigroup/qg7bl.in ... Okay, it seems to have run correctly. time_new=1.25, time_old=1.22. The out9482 times are about 0.976 times as fast as the out times. The output files have been left in quasigroup/*.out9482. Running lattice/lt-ml.in ... Okay, it seems to have run correctly. Running lattice/lt-ol.in ... Okay, it seems to have run correctly. Running lattice/ml-mol.in ... Okay, it seems to have run correctly. Running lattice/mol-ba.in ... Okay, it seems to have run correctly. Running lattice/ol-e1.in ... Okay, it seems to have run correctly. Running lattice/ol-e4.in ... Okay, it seems to have run correctly. Running lattice/ol-oml.in ... Okay, it seems to have run correctly. Running lattice/oml-mol.in ... Okay, it seems to have run correctly. time_new=56.65, time_old=54.92. The out9578 times are about 0.969462 times as fast as the out times. The output files have been left in lattice/*.out9578. Running propositional/f2.in ... Okay, it seems to have run correctly. Running propositional/f3.in ... Okay, it seems to have run correctly. Running propositional/f4.in ... Okay, it seems to have run correctly. Running propositional/p5.in ... Okay, it seems to have run correctly. Running propositional/p6.in ... Okay, it seems to have run correctly. Running propositional/p7.in ... Okay, it seems to have run correctly. Running propositional/p8.in ... Okay, it seems to have run correctly. Running propositional/p9.in ... Okay, it seems to have run correctly. Running propositional/q10.in ... Okay, it seems to have run correctly. time_new=1.33, time_old=1.32. The out9678 times are about 0.992481 times as fast as the out times. The output files have been left in propositional/*.out9678. otter-3.3f/examples-mace2/Run_anldp0100755000076400007640000000331307706065736016674 0ustar mccunemccune#!/bin/csh # # Run some anldp jobs and compare the # results to existing outputs. # # If $2 is given, it is assumed to be the anldp use. # If $3 is given, it is the filename extension for output files. # If $4 is given, it is the filename extension for old output files. # if ($#argv == 0) then echo "usage: Run_anldp directory [anldp | anldp new | anldp new old]" exit 1 endif set DIR=$1 if ($#argv >= 2) then set ANLDP=$2 else set ANLDP=../../bin/anldp endif if ($#argv >= 3) then set NEW_OUT=$3 else set NEW_OUT=out$$ endif if ($#argv >= 4) then set OLD_OUT=$4 else set OLD_OUT=out endif cd $DIR set errors=0 foreach i (*.in) echo "Running $DIR/$i ..." $ANLDP -m1000 < $i >& $i:r.$NEW_OUT if (-e $i:r.$OLD_OUT) then set unit_old=`grep "Unit assign" $i:r.$OLD_OUT | awk '{print $3}' | tail -1` set unit_new=`grep "Unit assign" $i:r.$NEW_OUT | awk '{print $3}' | tail -1` if ($unit_new != $unit_old) then echo "There is a problem: $NEW_OUT assigned $unit_new, $OLD_OUT assigned $unit_old" set errors=1 else echo "Okay, it seems to have run correctly." endif else echo "Okay, but there's no file for comparison." set errors=1 endif end echo "" if (! $errors) then set time_old=`cat *.$OLD_OUT | grep "CPU time"| awk '{sum += $4} END {print sum}'` set time_new=`cat *.$NEW_OUT | grep "CPU time"| awk '{sum += $4} END {print sum}'` set speedup=`awk "END {print $time_old / $time_new}" /dev/null` echo "time_new=$time_new, time_old=$time_old." echo "The $NEW_OUT times are about $speedup times as fast as the $OLD_OUT times." endif echo "The output files have been left in $DIR/*.$NEW_OUT." echo "" cd .. otter-3.3f/examples-mace2/Perl-examples/0040755000076400007640000000000007714312621017530 5ustar mccunemccuneotter-3.3f/examples-mace2/Perl-examples/Sheffer-mgi-without-mirrors0100644000076400007640000003105207303025231024771 0ustar mccunemccunef(f(x,x),f(x,y)) = x. f(f(x,x),f(y,x)) = x. f(f(y,f(y,y)),f(x,x)) = x. f(f(f(y,y),y),f(x,x)) = x. f(f(x,f(y,z)),f(x,z)) = x. f(f(x,f(y,z)),f(z,x)) = x. f(f(x,f(y,z)),f(x,y)) = x. f(f(x,f(y,z)),f(y,x)) = x. f(f(f(y,z),x),f(x,z)) = x. f(f(f(y,z),x),f(z,x)) = x. f(f(f(y,z),x),f(x,y)) = x. f(f(f(y,z),x),f(y,x)) = x. f(f(x,f(y,f(y,y))),f(x,z)) = x. f(f(x,f(f(y,y),y)),f(x,z)) = x. f(f(x,f(y,f(y,y))),f(z,x)) = x. f(f(x,f(f(y,y),y)),f(z,x)) = x. f(f(f(y,f(y,y)),x),f(x,z)) = x. f(f(f(f(y,y),y),x),f(x,z)) = x. f(f(f(y,f(y,y)),x),f(z,x)) = x. f(f(f(f(y,y),y),x),f(z,x)) = x. f(f(x,f(f(x,y),y)),f(x,z)) = x. f(f(x,f(f(x,y),y)),f(z,x)) = x. f(f(f(f(x,y),z),z),f(x,x)) = x. f(f(x,f(y,f(x,y))),f(x,z)) = x. f(f(x,f(f(y,x),y)),f(x,z)) = x. f(f(x,f(y,f(x,y))),f(z,x)) = x. f(f(x,f(f(y,x),y)),f(z,x)) = x. f(f(x,f(y,f(y,x))),f(x,z)) = x. f(f(f(f(x,y),y),x),f(x,z)) = x. f(f(x,f(y,f(y,x))),f(z,x)) = x. f(f(f(f(x,y),y),x),f(z,x)) = x. f(f(f(f(y,x),z),z),f(x,x)) = x. f(f(y,f(f(x,z),y)),f(x,x)) = x. f(f(f(y,f(x,z)),y),f(x,x)) = x. f(f(f(y,f(x,y)),x),f(x,z)) = x. f(f(f(f(y,x),y),x),f(x,z)) = x. f(f(f(y,f(x,y)),x),f(z,x)) = x. f(f(f(f(y,x),y),x),f(z,x)) = x. f(f(y,f(f(z,x),y)),f(x,x)) = x. f(f(f(y,f(z,x)),y),f(x,x)) = x. f(f(f(y,f(y,x)),x),f(x,z)) = x. f(f(f(y,f(y,x)),x),f(z,x)) = x. f(f(y,f(y,f(x,z))),f(x,x)) = x. f(f(y,f(y,f(z,x))),f(x,x)) = x. f(f(x,f(f(x,x),y)),f(x,z)) = x. f(f(x,f(f(x,x),y)),f(z,x)) = x. f(f(f(f(x,x),y),x),f(x,z)) = x. f(f(f(f(x,x),y),x),f(z,x)) = x. f(f(x,f(y,f(x,x))),f(x,z)) = x. f(f(x,f(y,f(x,x))),f(z,x)) = x. f(f(f(y,f(x,x)),x),f(x,z)) = x. f(f(f(y,f(x,x)),x),f(z,x)) = x. f(f(x,f(y,f(y,y))),f(z,f(z,z))) = x. f(f(x,f(f(y,y),y)),f(z,f(z,z))) = x. f(f(x,f(y,f(y,y))),f(f(z,z),z)) = x. f(f(x,f(f(y,y),y)),f(f(z,z),z)) = x. f(f(f(y,f(y,y)),x),f(z,f(z,z))) = x. f(f(f(f(y,y),y),x),f(z,f(z,z))) = x. f(f(f(y,f(y,y)),x),f(f(z,z),z)) = x. f(f(f(f(y,y),y),x),f(f(z,z),z)) = x. f(f(f(f(x,y),y),y),f(x,f(z,y))) = x. f(f(f(f(x,y),y),y),f(x,f(y,z))) = x. f(f(f(f(x,y),y),y),f(f(z,y),x)) = x. f(f(f(f(x,y),y),y),f(f(y,z),x)) = x. f(f(y,f(f(x,y),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,y)),y),f(x,f(z,y))) = x. f(f(f(f(y,x),y),y),f(x,f(z,y))) = x. f(f(y,f(f(x,y),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,y)),y),f(x,f(y,z))) = x. f(f(f(f(y,x),y),y),f(x,f(y,z))) = x. f(f(y,f(f(x,y),y)),f(f(z,y),x)) = x. f(f(f(y,f(x,y)),y),f(f(z,y),x)) = x. f(f(f(f(y,x),y),y),f(f(z,y),x)) = x. f(f(y,f(f(x,y),y)),f(f(y,z),x)) = x. f(f(f(y,f(x,y)),y),f(f(y,z),x)) = x. f(f(f(f(y,x),y),y),f(f(y,z),x)) = x. f(f(y,f(y,f(x,y))),f(x,f(z,y))) = x. f(f(y,f(f(y,x),y)),f(x,f(z,y))) = x. f(f(f(y,f(y,x)),y),f(x,f(z,y))) = x. f(f(y,f(y,f(x,y))),f(x,f(y,z))) = x. f(f(y,f(f(y,x),y)),f(x,f(y,z))) = x. f(f(f(y,f(y,x)),y),f(x,f(y,z))) = x. f(f(y,f(y,f(x,y))),f(f(z,y),x)) = x. f(f(y,f(f(y,x),y)),f(f(z,y),x)) = x. f(f(f(y,f(y,x)),y),f(f(z,y),x)) = x. f(f(y,f(y,f(x,y))),f(f(y,z),x)) = x. f(f(y,f(f(y,x),y)),f(f(y,z),x)) = x. f(f(f(y,f(y,x)),y),f(f(y,z),x)) = x. f(f(y,f(y,f(y,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(y,x))),f(x,f(y,z))) = x. f(f(y,f(y,f(y,x))),f(f(z,y),x)) = x. f(f(y,f(y,f(y,x))),f(f(y,z),x)) = x. f(f(x,f(f(x,y),y)),f(z,f(z,z))) = x. f(f(x,f(f(x,y),y)),f(f(z,z),z)) = x. f(f(x,f(y,f(x,y))),f(z,f(z,z))) = x. f(f(x,f(f(y,x),y)),f(z,f(z,z))) = x. f(f(x,f(y,f(x,y))),f(f(z,z),z)) = x. f(f(x,f(f(y,x),y)),f(f(z,z),z)) = x. f(f(x,f(y,f(y,x))),f(z,f(z,z))) = x. f(f(f(f(x,y),y),x),f(z,f(z,z))) = x. f(f(x,f(y,f(y,x))),f(f(z,z),z)) = x. f(f(f(f(x,y),y),x),f(f(z,z),z)) = x. f(f(f(f(x,y),z),z),f(x,f(y,z))) = x. f(f(f(f(x,y),z),z),f(x,f(z,y))) = x. f(f(f(f(x,y),z),z),f(f(y,z),x)) = x. f(f(f(f(x,y),z),z),f(f(z,y),x)) = x. f(f(f(y,f(x,y)),x),f(z,f(z,z))) = x. f(f(f(f(y,x),y),x),f(z,f(z,z))) = x. f(f(f(y,f(x,y)),x),f(f(z,z),z)) = x. f(f(f(f(y,x),y),x),f(f(z,z),z)) = x. f(f(f(f(y,x),z),z),f(x,f(y,z))) = x. f(f(f(f(y,x),z),z),f(x,f(z,y))) = x. f(f(f(f(y,x),z),z),f(f(y,z),x)) = x. f(f(f(f(y,x),z),z),f(f(z,y),x)) = x. f(f(f(y,f(y,x)),x),f(z,f(z,z))) = x. f(f(f(y,f(y,x)),x),f(f(z,z),z)) = x. f(f(y,f(f(x,z),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,z)),y),f(x,f(z,y))) = x. f(f(y,f(f(x,z),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,z)),y),f(x,f(y,z))) = x. f(f(y,f(f(x,z),y)),f(f(z,y),x)) = x. f(f(f(y,f(x,z)),y),f(f(z,y),x)) = x. f(f(y,f(f(x,z),y)),f(f(y,z),x)) = x. f(f(f(y,f(x,z)),y),f(f(y,z),x)) = x. f(f(y,f(f(z,x),y)),f(x,f(z,y))) = x. f(f(f(y,f(z,x)),y),f(x,f(z,y))) = x. f(f(y,f(f(z,x),y)),f(x,f(y,z))) = x. f(f(f(y,f(z,x)),y),f(x,f(y,z))) = x. f(f(y,f(f(z,x),y)),f(f(z,y),x)) = x. f(f(f(y,f(z,x)),y),f(f(z,y),x)) = x. f(f(y,f(f(z,x),y)),f(f(y,z),x)) = x. f(f(f(y,f(z,x)),y),f(f(y,z),x)) = x. f(f(y,f(y,f(x,z))),f(x,f(z,y))) = x. f(f(y,f(y,f(x,z))),f(x,f(y,z))) = x. f(f(y,f(y,f(x,z))),f(f(z,y),x)) = x. f(f(y,f(y,f(x,z))),f(f(y,z),x)) = x. f(f(y,f(y,f(z,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(z,x))),f(x,f(y,z))) = x. f(f(y,f(y,f(z,x))),f(f(z,y),x)) = x. f(f(y,f(y,f(z,x))),f(f(y,z),x)) = x. f(f(x,f(f(x,x),y)),f(z,f(z,z))) = x. f(f(x,f(f(x,x),y)),f(f(z,z),z)) = x. f(f(f(f(x,x),y),x),f(z,f(z,z))) = x. f(f(f(f(x,x),y),x),f(f(z,z),z)) = x. f(f(f(f(x,x),y),y),f(x,f(z,y))) = x. f(f(f(f(x,x),y),y),f(x,f(y,z))) = x. f(f(f(f(x,x),y),y),f(f(z,y),x)) = x. f(f(f(f(x,x),y),y),f(f(y,z),x)) = x. f(f(x,f(y,f(x,x))),f(z,f(z,z))) = x. f(f(x,f(y,f(x,x))),f(f(z,z),z)) = x. f(f(f(y,f(x,x)),x),f(z,f(z,z))) = x. f(f(f(y,f(x,x)),x),f(f(z,z),z)) = x. f(f(y,f(f(x,x),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,x)),y),f(x,f(z,y))) = x. f(f(y,f(f(x,x),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,x)),y),f(x,f(y,z))) = x. f(f(y,f(f(x,x),y)),f(f(z,y),x)) = x. f(f(f(y,f(x,x)),y),f(f(z,y),x)) = x. f(f(y,f(f(x,x),y)),f(f(y,z),x)) = x. f(f(f(y,f(x,x)),y),f(f(y,z),x)) = x. f(f(y,f(y,f(x,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(x,x))),f(x,f(y,z))) = x. f(f(y,f(y,f(x,x))),f(f(z,y),x)) = x. f(f(y,f(y,f(x,x))),f(f(y,z),x)) = x. f(f(x,f(y,f(z,z))),f(x,f(u,z))) = x. f(f(x,f(y,f(z,z))),f(x,f(z,u))) = x. f(f(x,f(y,f(z,z))),f(f(u,z),x)) = x. f(f(x,f(y,f(z,z))),f(f(z,u),x)) = x. f(f(x,f(f(y,y),z)),f(x,f(u,y))) = x. f(f(x,f(f(y,y),z)),f(x,f(y,u))) = x. f(f(x,f(f(y,y),z)),f(f(u,y),x)) = x. f(f(x,f(f(y,y),z)),f(f(y,u),x)) = x. f(f(f(y,f(z,z)),x),f(x,f(u,z))) = x. f(f(f(y,f(z,z)),x),f(x,f(z,u))) = x. f(f(f(y,f(z,z)),x),f(f(u,z),x)) = x. f(f(f(y,f(z,z)),x),f(f(z,u),x)) = x. f(f(f(f(y,y),z),x),f(x,f(u,y))) = x. f(f(f(f(y,y),z),x),f(x,f(y,u))) = x. f(f(f(f(y,y),z),x),f(f(u,y),x)) = x. f(f(f(f(y,y),z),x),f(f(y,u),x)) = x. f(f(x,f(y,f(z,u))),f(x,f(u,z))) = x. f(f(x,f(y,f(z,u))),f(f(u,z),x)) = x. f(f(x,f(y,f(y,z))),f(x,f(u,z))) = x. f(f(x,f(y,f(y,z))),f(x,f(z,u))) = x. f(f(x,f(y,f(y,z))),f(f(u,z),x)) = x. f(f(x,f(y,f(y,z))),f(f(z,u),x)) = x. f(f(x,f(f(y,z),u)),f(x,f(z,y))) = x. f(f(x,f(f(y,z),u)),f(f(z,y),x)) = x. f(f(x,f(y,f(z,y))),f(x,f(u,z))) = x. f(f(x,f(f(y,z),y)),f(x,f(u,z))) = x. f(f(x,f(y,f(z,y))),f(x,f(z,u))) = x. f(f(x,f(f(y,z),y)),f(x,f(z,u))) = x. f(f(x,f(y,f(z,y))),f(f(u,z),x)) = x. f(f(x,f(f(y,z),y)),f(f(u,z),x)) = x. f(f(x,f(y,f(z,y))),f(f(z,u),x)) = x. f(f(x,f(f(y,z),y)),f(f(z,u),x)) = x. f(f(x,f(f(y,z),z)),f(x,f(u,y))) = x. f(f(x,f(f(y,z),z)),f(x,f(y,u))) = x. f(f(x,f(f(y,z),z)),f(f(u,y),x)) = x. f(f(x,f(f(y,z),z)),f(f(y,u),x)) = x. f(f(f(y,f(z,u)),x),f(x,f(u,z))) = x. f(f(f(y,f(z,u)),x),f(f(u,z),x)) = x. f(f(f(y,f(y,z)),x),f(x,f(u,z))) = x. f(f(f(y,f(y,z)),x),f(x,f(z,u))) = x. f(f(f(y,f(y,z)),x),f(f(u,z),x)) = x. f(f(f(y,f(y,z)),x),f(f(z,u),x)) = x. f(f(f(f(y,z),u),x),f(x,f(z,y))) = x. f(f(f(f(y,z),u),x),f(f(z,y),x)) = x. f(f(f(y,f(z,y)),x),f(x,f(u,z))) = x. f(f(f(f(y,z),y),x),f(x,f(u,z))) = x. f(f(f(y,f(z,y)),x),f(x,f(z,u))) = x. f(f(f(f(y,z),y),x),f(x,f(z,u))) = x. f(f(f(y,f(z,y)),x),f(f(u,z),x)) = x. f(f(f(f(y,z),y),x),f(f(u,z),x)) = x. f(f(f(y,f(z,y)),x),f(f(z,u),x)) = x. f(f(f(f(y,z),y),x),f(f(z,u),x)) = x. f(f(f(f(y,z),z),x),f(x,f(u,y))) = x. f(f(f(f(y,z),z),x),f(x,f(y,u))) = x. f(f(f(f(y,z),z),x),f(f(u,y),x)) = x. f(f(f(f(y,z),z),x),f(f(y,u),x)) = x. f(f(x,f(f(x,y),z)),f(x,f(u,y))) = x. f(f(x,f(f(x,y),z)),f(x,f(y,u))) = x. f(f(x,f(f(x,y),z)),f(f(u,y),x)) = x. f(f(x,f(f(x,y),z)),f(f(y,u),x)) = x. f(f(x,f(y,f(x,z))),f(x,f(u,z))) = x. f(f(x,f(y,f(x,z))),f(x,f(z,u))) = x. f(f(x,f(y,f(x,z))),f(f(u,z),x)) = x. f(f(x,f(y,f(x,z))),f(f(z,u),x)) = x. f(f(x,f(y,f(z,x))),f(x,f(u,z))) = x. f(f(x,f(y,f(z,x))),f(x,f(z,u))) = x. f(f(x,f(y,f(z,x))),f(f(u,z),x)) = x. f(f(x,f(y,f(z,x))),f(f(z,u),x)) = x. f(f(x,f(f(y,x),z)),f(x,f(u,y))) = x. f(f(x,f(f(y,x),z)),f(x,f(y,u))) = x. f(f(x,f(f(y,x),z)),f(f(u,y),x)) = x. f(f(x,f(f(y,x),z)),f(f(y,u),x)) = x. f(f(f(f(x,y),z),x),f(x,f(u,y))) = x. f(f(f(f(x,y),z),x),f(x,f(y,u))) = x. f(f(f(f(x,y),z),x),f(f(u,y),x)) = x. f(f(f(f(x,y),z),x),f(f(y,u),x)) = x. f(f(f(y,f(x,z)),x),f(x,f(u,z))) = x. f(f(f(y,f(x,z)),x),f(x,f(z,u))) = x. f(f(f(y,f(x,z)),x),f(f(u,z),x)) = x. f(f(f(y,f(x,z)),x),f(f(z,u),x)) = x. f(f(f(y,f(z,x)),x),f(x,f(u,z))) = x. f(f(f(y,f(z,x)),x),f(x,f(z,u))) = x. f(f(f(y,f(z,x)),x),f(f(u,z),x)) = x. f(f(f(y,f(z,x)),x),f(f(z,u),x)) = x. f(f(f(f(y,x),z),x),f(x,f(u,y))) = x. f(f(f(f(y,x),z),x),f(x,f(y,u))) = x. f(f(f(f(y,x),z),x),f(f(u,y),x)) = x. f(f(f(f(y,x),z),x),f(f(y,u),x)) = x. f(f(f(f(y,f(z,z)),z),z),f(x,x)) = x. f(f(y,f(f(z,f(y,y)),y)),f(x,x)) = x. f(f(f(y,f(z,f(y,y))),y),f(x,x)) = x. f(f(y,f(y,f(z,f(y,y)))),f(x,x)) = x. f(f(f(f(f(y,y),z),y),y),f(x,x)) = x. f(f(y,f(f(f(y,y),z),y)),f(x,x)) = x. f(f(f(y,f(f(y,y),z)),y),f(x,x)) = x. f(f(y,f(y,f(f(y,y),z))),f(x,x)) = x. f(f(y,f(y,f(z,f(z,z)))),f(x,x)) = x. f(f(y,f(y,f(f(z,z),z))),f(x,x)) = x. f(f(f(f(y,f(y,z)),z),z),f(x,x)) = x. f(f(f(f(y,f(z,y)),z),z),f(x,x)) = x. f(f(f(f(f(y,z),y),z),z),f(x,x)) = x. f(f(y,f(f(z,f(z,z)),y)),f(x,x)) = x. f(f(y,f(f(f(z,z),z),y)),f(x,x)) = x. f(f(f(y,f(z,f(z,z))),y),f(x,x)) = x. f(f(f(y,f(f(z,z),z)),y),f(x,x)) = x. f(f(y,f(f(z,f(z,y)),y)),f(x,x)) = x. f(f(f(y,f(z,f(z,y))),y),f(x,x)) = x. f(f(f(f(f(y,z),z),y),y),f(x,x)) = x. f(f(y,f(f(z,f(y,z)),y)),f(x,x)) = x. f(f(y,f(f(f(z,y),z),y)),f(x,x)) = x. f(f(f(y,f(z,f(y,z))),y),f(x,x)) = x. f(f(f(y,f(f(z,y),z)),y),f(x,x)) = x. f(f(y,f(y,f(z,f(z,y)))),f(x,x)) = x. f(f(y,f(f(f(y,z),z),y)),f(x,x)) = x. f(f(f(y,f(f(y,z),z)),y),f(x,x)) = x. f(f(y,f(y,f(z,f(y,z)))),f(x,x)) = x. f(f(y,f(y,f(f(z,y),z))),f(x,x)) = x. f(f(y,f(y,f(f(y,z),z))),f(x,x)) = x. f(f(f(f(y,f(y,y)),z),z),f(x,x)) = x. f(f(f(f(f(y,y),y),z),z),f(x,x)) = x. f(f(x,f(f(f(y,z),u),u)),f(x,z)) = x. f(f(x,f(f(f(y,z),u),u)),f(z,x)) = x. f(f(x,f(y,f(f(z,u),y))),f(x,u)) = x. f(f(x,f(f(y,f(z,u)),y)),f(x,u)) = x. f(f(x,f(y,f(f(z,u),y))),f(u,x)) = x. f(f(x,f(f(y,f(z,u)),y)),f(u,x)) = x. f(f(x,f(f(f(y,z),u),u)),f(x,y)) = x. f(f(x,f(f(f(y,z),u),u)),f(y,x)) = x. f(f(x,f(y,f(y,f(z,u)))),f(x,u)) = x. f(f(x,f(y,f(y,f(z,u)))),f(u,x)) = x. f(f(x,f(y,f(y,f(z,u)))),f(x,z)) = x. f(f(x,f(y,f(y,f(z,u)))),f(z,x)) = x. f(f(x,f(y,f(f(z,u),y))),f(x,z)) = x. f(f(x,f(f(y,f(z,u)),y)),f(x,z)) = x. f(f(x,f(y,f(f(z,u),y))),f(z,x)) = x. f(f(x,f(f(y,f(z,u)),y)),f(z,x)) = x. f(f(f(f(f(y,z),u),u),x),f(x,z)) = x. f(f(f(f(f(y,z),u),u),x),f(z,x)) = x. f(f(f(y,f(f(z,u),y)),x),f(x,u)) = x. f(f(f(f(y,f(z,u)),y),x),f(x,u)) = x. f(f(f(y,f(f(z,u),y)),x),f(u,x)) = x. f(f(f(f(y,f(z,u)),y),x),f(u,x)) = x. f(f(f(f(f(y,z),u),u),x),f(x,y)) = x. f(f(f(f(f(y,z),u),u),x),f(y,x)) = x. f(f(f(y,f(y,f(z,u))),x),f(x,u)) = x. f(f(f(y,f(y,f(z,u))),x),f(u,x)) = x. f(f(f(y,f(y,f(z,u))),x),f(x,z)) = x. f(f(f(y,f(y,f(z,u))),x),f(z,x)) = x. f(f(f(y,f(f(z,u),y)),x),f(x,z)) = x. f(f(f(f(y,f(z,u)),y),x),f(x,z)) = x. f(f(f(y,f(f(z,u),y)),x),f(z,x)) = x. f(f(f(f(y,f(z,u)),y),x),f(z,x)) = x. f(f(x,f(f(x,f(y,z)),u)),f(x,z)) = x. f(f(x,f(f(x,f(y,z)),u)),f(z,x)) = x. f(f(x,f(f(x,f(y,z)),u)),f(x,y)) = x. f(f(x,f(f(x,f(y,z)),u)),f(y,x)) = x. f(f(x,f(y,f(x,f(z,u)))),f(x,u)) = x. f(f(x,f(y,f(x,f(z,u)))),f(u,x)) = x. f(f(x,f(y,f(x,f(z,u)))),f(x,z)) = x. f(f(x,f(y,f(x,f(z,u)))),f(z,x)) = x. f(f(x,f(y,f(f(z,u),x))),f(x,u)) = x. f(f(x,f(y,f(f(z,u),x))),f(u,x)) = x. f(f(x,f(f(f(y,z),x),u)),f(x,z)) = x. f(f(x,f(f(f(y,z),x),u)),f(z,x)) = x. f(f(x,f(y,f(f(z,u),x))),f(x,z)) = x. f(f(f(f(x,f(y,z)),u),x),f(x,z)) = x. f(f(x,f(y,f(f(z,u),x))),f(z,x)) = x. f(f(f(f(x,f(y,z)),u),x),f(z,x)) = x. f(f(x,f(f(f(y,z),x),u)),f(x,y)) = x. f(f(x,f(f(f(y,z),x),u)),f(y,x)) = x. f(f(f(f(x,f(y,z)),u),x),f(x,y)) = x. f(f(f(f(x,f(y,z)),u),x),f(y,x)) = x. f(f(f(y,f(x,f(z,u))),x),f(x,u)) = x. f(f(f(y,f(x,f(z,u))),x),f(u,x)) = x. f(f(f(y,f(x,f(z,u))),x),f(x,z)) = x. f(f(f(y,f(x,f(z,u))),x),f(z,x)) = x. f(f(f(y,f(f(z,u),x)),x),f(x,u)) = x. f(f(f(y,f(f(z,u),x)),x),f(u,x)) = x. f(f(f(f(f(y,z),x),u),x),f(x,z)) = x. f(f(f(f(f(y,z),x),u),x),f(z,x)) = x. f(f(f(y,f(f(z,u),x)),x),f(x,z)) = x. f(f(f(y,f(f(z,u),x)),x),f(z,x)) = x. f(f(f(f(f(y,z),x),u),x),f(x,y)) = x. f(f(f(f(f(y,z),x),u),x),f(y,x)) = x. f(f(f(f(x,y),f(x,z)),u),f(x,x)) = x. f(f(f(f(x,y),f(z,x)),u),f(x,x)) = x. f(f(f(f(y,x),f(x,z)),u),f(x,x)) = x. f(f(y,f(f(x,z),f(x,u))),f(x,x)) = x. f(f(f(f(y,x),f(z,x)),u),f(x,x)) = x. f(f(y,f(f(x,z),f(u,x))),f(x,x)) = x. f(f(y,f(f(z,x),f(x,u))),f(x,x)) = x. f(f(y,f(f(z,x),f(u,x))),f(x,x)) = x. otter-3.3f/examples-mace2/Perl-examples/commute4_filter0100755000076400007640000000102707714247536022571 0ustar mccunemccune#!/usr/bin/perl -w $mace2 = "../../bin/mace2"; if (! -x $mace2) { die "binary $mace2 not found"; } $unsatisfiable_exit = 12; $input = "/tmp/mace2$$"; while ($equation = ) { open(FH, ">$input") || die "Cannot open file $input"; print FH "list(usable). $equation f(0,1)!=f(1,0). end_of_list.\n"; close(FH); $rc = system("$mace2 -N4 < $input > /dev/null 2> /dev/null"); $rc = $rc / 256; # This gets the actual exit code. if ($rc == $unsatisfiable_exit) { print $equation; } } system("/bin/rm $input"); otter-3.3f/examples-mace2/Perl-examples/index.html0100644000076400007640000000204507705552212021525 0ustar mccunemccune /sandbox/mccune/otter-3.3/mace2_examples/Perl-examples

/sandbox/mccune/otter-3.3/mace2_examples/Perl-examples

This directory contains an example of a Perl program that calls MACE. File Sheffer-mgi-without-mirrors contains Boolean algebra identities alpha=x in terms of the Sheffer stroke. Every such, identity of length <= 15, or its mirror image, is subsumed by a member of that file. The Perl program commute4_filter goes through a file of equations (one equation per line) and calls MACE for each, looking for a noncommutative model of size <= 4. If none exist, the equation is printed. The command commute4_filter < Sheffer-mgi-without-mirrors > candidates should produce 25 candidates. NOTE: You might have to edit commute4_filter to point it at the mace binary.

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples-mace2/Perl-examples/README0100644000076400007640000000123607714247505020417 0ustar mccunemccuneThis directory contains an example of a Perl program that calls MACE. File Sheffer-mgi-without-mirrors contains Boolean algebra identities alpha=x in terms of the Sheffer stroke. Every such, identity of length <= 15, or its mirror image, is subsumed by a member of that file. The Perl program commute4_filter goes through a file of equations (one equation per line) and calls MACE for each, looking for a noncommutative model of size <= 4. If none exist, the equation is printed. The command commute4_filter < Sheffer-mgi-without-mirrors > candidates should produce 25 candidates. NOTE: You might have to edit commute4_filter to point it at the mace2 binary. otter-3.3f/examples-mace2/Perl-examples/candidates0100644000076400007640000000163507303025516021552 0ustar mccunemccunef(f(y,f(f(x,y),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,y)),y),f(x,f(z,y))) = x. f(f(f(f(y,x),y),y),f(x,f(z,y))) = x. f(f(y,f(f(x,y),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,y)),y),f(x,f(y,z))) = x. f(f(f(f(y,x),y),y),f(x,f(y,z))) = x. f(f(y,f(y,f(x,y))),f(x,f(z,y))) = x. f(f(f(y,f(y,x)),y),f(x,f(z,y))) = x. f(f(y,f(y,f(x,y))),f(x,f(y,z))) = x. f(f(f(y,f(y,x)),y),f(x,f(y,z))) = x. f(f(y,f(y,f(y,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(y,x))),f(x,f(y,z))) = x. f(f(f(f(y,x),z),z),f(x,f(y,z))) = x. f(f(f(f(y,x),z),z),f(x,f(z,y))) = x. f(f(y,f(f(x,z),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,z)),y),f(x,f(z,y))) = x. f(f(f(y,f(x,z)),y),f(x,f(y,z))) = x. f(f(f(y,f(z,x)),y),f(x,f(z,y))) = x. f(f(f(y,f(z,x)),y),f(x,f(y,z))) = x. f(f(y,f(y,f(x,z))),f(x,f(z,y))) = x. f(f(y,f(y,f(z,x))),f(x,f(y,z))) = x. f(f(f(y,f(x,x)),y),f(x,f(z,y))) = x. f(f(f(y,f(x,x)),y),f(x,f(y,z))) = x. f(f(y,f(y,f(x,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(x,x))),f(x,f(y,z))) = x. otter-3.3f/examples/0040755000076400007640000000000010103530360014011 5ustar mccunemccuneotter-3.3f/examples/summary0100755000076400007640000000062507264412062015450 0ustar mccunemccune# if ($#argv != 2) then echo "need 2 args: directory extension" exit 1 endif foreach i ($1/*.out) echo "doing $i" if ( $1 == split ) then awk '/Otter/,/end of input/ {print} /clauses generated/ {print} /Process.*finished/ {print}' $i > $i:r.$2 else awk '/Otter/,/end of input/ {print} /statistics/,/Process.*finished/ {print}' $i > $i:r.$2 endif /bin/rm $i end otter-3.3f/examples/Run_group0100755000076400007640000000340607705611774015746 0ustar mccunemccune#!/bin/csh # # Run a set of otter jobs ($1/*.in) and compare the # results existing outputs. # # If $2 is given, it is assumed to be the Otter binary to use. # # If $3 is given, it is the filename extension for output files. # set base=out if ($#argv == 0) then echo "usage: Run_all directory [otter] [extension]" exit 1 endif if ($#argv >= 2) then set OTTER=$2 else set OTTER=../../bin/otter endif if ($#argv >= 3) then set OUT=$3 else set OUT=out$$ endif cd $1 set errors=0 foreach i (*.in) echo "Running $1/$i ..." $OTTER < $i >& $i:r.$OUT if (-e $i:r.$base) then set genold=`grep "clauses generated" $i:r.$base | awk '{gen+=$3} END {print gen}'` set gennew=`grep "clauses generated" $i:r.$OUT | awk '{gen+=$3} END {print gen}'` if ($gennew != $genold) then echo "There is a problem: your computer generated $gennew, $OUT generated $genold" set errors=1 else echo "Okay, it seems to have run correctly." endif else echo "Okay, but there's no file for comparison." set errors=1 endif end echo "" if (! $errors && $1 != split) then set timeold=`grep "CPU time" *.$base | awk '{sum += $4} END {print sum}'` set timenew=`grep "CPU time" *.$OUT | awk '{sum += $4} END {print sum}'` set speedup=`awk "END {print $timeold / $timenew}" /dev/null` echo "timenew=$timenew, timeold=$timeold." echo "The new ($OUT) times are about $speedup times as fast as the old ($base) times." set too_slow=`awk "END {if ($speedup < .1) print 1}" /dev/null` if ($too_slow) then echo "If this seems way too slow, edit source/Makefile," echo "including -DTP_NO_CLOCKS on the DFLAGS line," echo "then make clean; make otter." endif endif echo "The output files have been left in $1/*.$OUT." echo "" cd .. otter-3.3f/examples/auto/0040755000076400007640000000000010103530360014761 5ustar mccunemccuneotter-3.3f/examples/auto/robbins.out0100664000076400007640000001227010103522154017153 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8293. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] x+y=y+x. 0 [] (x+y)+z=x+y+z. 0 [] n(n(x+y)+n(x+n(y)))=x. 0 [] x+C=C. 0 [] n(A+n(B))+n(n(A)+n(B))!=B. end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=14): 1 [] n(A+n(B))+n(n(A)+n(B))!=B. ------------> process sos: ** KEPT (pick-wt=3): 2 [] x=x. ** KEPT (pick-wt=7): 3 [] x+y=y+x. ** KEPT (pick-wt=11): 4 [] (x+y)+z=x+y+z. ---> New Demodulator: 5 [new_demod,4] (x+y)+z=x+y+z. ** KEPT (pick-wt=13): 6 [] n(n(x+y)+n(x+n(y)))=x. ---> New Demodulator: 7 [new_demod,6] n(n(x+y)+n(x+n(y)))=x. ** KEPT (pick-wt=5): 8 [] x+C=C. ---> New Demodulator: 9 [new_demod,8] x+C=C. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x=x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x+y=y+x. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 2 [] x=x. given clause #2: (wt=5) 8 [] x+C=C. given clause #3: (wt=7) 3 [] x+y=y+x. given clause #4: (wt=5) 10 [para_into,3.1.1,8.1.1,flip.1] C+x=C. given clause #5: (wt=11) 4 [] (x+y)+z=x+y+z. given clause #6: (wt=13) 6 [] n(n(x+y)+n(x+n(y)))=x. given clause #7: (wt=8) 18 [para_into,6.1.1.1.1.1,10.1.1,demod,11] n(n(C)+n(C))=C. given clause #8: (wt=11) 15 [para_into,4.1.1.1,3.1.1,demod,5] x+y+z=y+x+z. given clause #9: (wt=11) 16 [para_into,4.1.1,3.1.1] x+y+z=y+z+x. given clause #10: (wt=11) 17 [copy,16,flip.1] x+y+z=z+x+y. given clause #11: (wt=14) 12 [para_from,3.1.1,1.1.1] n(n(A)+n(B))+n(A+n(B))!=B. given clause #12: (wt=11) 20 [para_into,6.1.1.1.1.1,8.1.1] n(n(C)+n(x+n(C)))=x. given clause #13: (wt=11) 40 [para_into,15.1.1,3.1.1,demod,5] x+y+z=x+z+y. given clause #14: (wt=11) 46 [para_into,16.1.1.2,3.1.1] x+y+z=z+y+x. given clause #15: (wt=11) 62 [para_into,20.1.1.1.2.1,3.1.1] n(n(C)+n(n(C)+x))=x. given clause #16: (wt=14) 13 [para_from,3.1.1,1.1.1.2.1] n(A+n(B))+n(n(B)+n(A))!=B. given clause #17: (wt=11) 64 [para_into,20.1.1.1,3.1.1] n(n(x+n(C))+n(C))=x. given clause #18: (wt=5) 107 [back_demod,89,demod,106,102] n(n(x))=x. -------- PROOF -------- ----> UNIT CONFLICT at 0.01 sec ----> 122 [binary,121.1,2.1] $F. Length of proof is 17. Level of proof is 8. ---------------- PROOF ---------------- 1 [] n(A+n(B))+n(n(A)+n(B))!=B. 2 [] x=x. 3 [] x+y=y+x. 4 [] (x+y)+z=x+y+z. 6 [] n(n(x+y)+n(x+n(y)))=x. 9,8 [] x+C=C. 11,10 [para_into,3.1.1,8.1.1,flip.1] C+x=C. 13 [para_from,3.1.1,1.1.1.2.1] n(A+n(B))+n(n(B)+n(A))!=B. 18 [para_into,6.1.1.1.1.1,10.1.1,demod,11] n(n(C)+n(C))=C. 20 [para_into,6.1.1.1.1.1,8.1.1] n(n(C)+n(x+n(C)))=x. 36 [para_from,18.1.1,6.1.1.1.2.1.2,demod,9] n(n(x+n(C)+n(C))+n(C))=x. 62 [para_into,20.1.1.1.2.1,3.1.1] n(n(C)+n(n(C)+x))=x. 64 [para_into,20.1.1.1,3.1.1] n(n(x+n(C))+n(C))=x. 88 [para_into,62.1.1.1.2,20.1.1] n(n(C)+x)=n(x+n(C)). 89 [para_into,62.1.1.1,3.1.1] n(n(n(C)+x)+n(C))=x. 91 [copy,88,flip.1] n(x+n(C))=n(n(C)+x). 98 [para_into,13.1.1.1.1,3.1.1] n(n(B)+A)+n(n(B)+n(A))!=B. 100,99 [para_into,64.1.1.1.1.1,4.1.1] n(n(x+y+n(C))+n(C))=x+y. 102,101 [back_demod,36,demod,100] x+n(C)=x. 106,105 [back_demod,91,demod,102,flip.1] n(n(C)+x)=n(x). 108,107 [back_demod,89,demod,106,102] n(n(x))=x. 120,119 [para_into,107.1.1.1,6.1.1,flip.1] n(x+y)+n(x+n(y))=n(x). 121 [back_demod,98,demod,120,108] B!=B. 122 [binary,121.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 18 clauses generated 213 clauses kept 81 clauses forward subsumed 191 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8293 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/pigeon.in0100644000076400007640000000152605515013240016577 0ustar mccunemccune% % Pigeon hole problem -- 5 pigeons into 4 holes. % set(auto) . list(usable) . % Every pigeon flies into a hole. p00 | p01 | p02 | p03 . p04 | p05 | p06 | p07 . p08 | p09 | p10 | p11 . p12 | p13 | p14 | p15 . p16 | p17 | p18 | p19 . % Each hole holds at most one piegeon. -p00 | -p04 . -p00 | -p08 . -p00 | -p12 . -p00 | -p16 . -p04 | -p08 . -p04 | -p12 . -p04 | -p16 . -p08 | -p12 . -p08 | -p16 . -p12 | -p16 . -p01 | -p05 . -p01 | -p09 . -p01 | -p13 . -p01 | -p17 . -p05 | -p09 . -p05 | -p13 . -p05 | -p17 . -p09 | -p13 . -p09 | -p17 . -p13 | -p17 . -p02 | -p06 . -p02 | -p10 . -p02 | -p14 . -p02 | -p18 . -p06 | -p10 . -p06 | -p14 . -p06 | -p18 . -p10 | -p14 . -p10 | -p18 . -p14 | -p18 . -p03 | -p07 . -p03 | -p11 . -p03 | -p15 . -p03 | -p19 . -p07 | -p11 . -p07 | -p15 . -p07 | -p19 . -p11 | -p15 . -p11 | -p19 . -p15 | -p19 . end_of_list . otter-3.3f/examples/auto/salt.in0100644000076400007640000000232405470212344016264 0ustar mccunemccune% Propositional version of the Salt and Mustard puzzle from Lewis Carroll set(auto). list(usable). sl | -mb | -sb | -sm | -ml | sc | mc | sd | md | mm. -sm | mb | ml. -sm | mb | sl. -sm | sb | ml. -sm | sb | sl. -ml | -mc | -mm. -ml | -mc | -sm. -ml | -sc | -mm. -ml | -sc | -sm. -md | -ml | -mm. -md | -ml | -sm. -md | -sl | -mm. -md | -sl | -sm. -sd | -mb | mc. -sd | -mb | sc. -sd | -sb | mc. -sd | -sb | sc. -mc | md | ml. -mc | md | sl. -mc | sd | ml. -mc | sd | sl. -mb | -md | mm. -mb | -md | sm. -mb | -sd | mm. -mb | -sd | sm. sd | -md | mm. -sd | md | mm. sc | -mc | mm. -sc | mc | mm. -sl | -ml | sm. -sb | -mb | sm. sd | -md | sl. -sd | md | sl. sb | -mb | sl. -sb | mb | sl. -sc | -mc | sd. -sl | -ml | mc. -sd | -md | mc. sb | -mb | sc. -sb | mb | sc. -sm | -mm | mb. sl | -ml | sb. -sl | ml | sb. sc | -mc | sb. -sc | mc | sb. -sc | -mb | -sb | -mm. -sc | -mb | -sb | -sm. -sc | sb | mb | -mm. -sc | sb | mb | -sm. -mm | -mc | -sc | -md | -sd. -mm | sc | mc | sd | md. -sl | -mb | -sb | -md | -sd. -sl | -mb | -sb | sd | md. -sl | sb | mb | -md | -sd. -sb | -mc | -sc | -ml | -sl. -sb | -mc | -sc | sl | ml. sm | mm | ml. sc | mc | ml. sm | mm | md. sl | ml | md. sb | mb | sd. sm | mm | sc. sd | md | mb. end_of_list. otter-3.3f/examples/auto/x2_quant.out0100664000076400007640000001034010103522154017252 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8328. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). formula_list(usable). all x (x=x). all x y z (f(f(x,y),z)=f(x,f(y,z))). exists e ((all x (f(e,x)=x))& (all x exists y (f(y,x)=e))& (all x (f(x,x)=e))). -(all x y (f(x,y)=f(y,x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] x=x. 0 [] f(f(x,y),z)=f(x,f(y,z)). 0 [] f($c1,x)=x. 0 [] f($f1(x1),x1)=$c1. 0 [] f(x2,x2)=$c1. 0 [] f($c3,$c2)!=f($c2,$c3). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=7): 1 [] f($c3,$c2)!=f($c2,$c3). ------------> process sos: ** KEPT (pick-wt=3): 2 [] x=x. ** KEPT (pick-wt=11): 3 [] f(f(x,y),z)=f(x,f(y,z)). ---> New Demodulator: 4 [new_demod,3] f(f(x,y),z)=f(x,f(y,z)). ** KEPT (pick-wt=5): 5 [] f($c1,x)=x. ---> New Demodulator: 6 [new_demod,5] f($c1,x)=x. ** KEPT (pick-wt=6): 7 [] f($f1(x),x)=$c1. ---> New Demodulator: 8 [new_demod,7] f($f1(x),x)=$c1. ** KEPT (pick-wt=5): 9 [] f(x,x)=$c1. ---> New Demodulator: 10 [new_demod,9] f(x,x)=$c1. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x=x. >>>> Starting back demodulation with 4. >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 2 [] x=x. given clause #2: (wt=5) 5 [] f($c1,x)=x. given clause #3: (wt=5) 9 [] f(x,x)=$c1. given clause #4: (wt=6) 7 [] f($f1(x),x)=$c1. given clause #5: (wt=11) 3 [] f(f(x,y),z)=f(x,f(y,z)). given clause #6: (wt=7) 11 [para_into,3.1.1.1,9.1.1,demod,6,flip.1] f(x,f(x,y))=y. given clause #7: (wt=4) 19 [para_into,11.1.1.2,7.1.1,demod,18] $f1(x)=x. given clause #8: (wt=5) 17 [para_into,11.1.1.2,9.1.1] f(x,$c1)=x. given clause #9: (wt=9) 15 [para_into,3.1.1,9.1.1,flip.1] f(x,f(y,f(x,y)))=$c1. given clause #10: (wt=7) 25 [para_from,15.1.1,11.1.1.2,demod,18,flip.1] f(x,f(y,x))=y. -------- PROOF -------- ----> UNIT CONFLICT at 0.00 sec ----> 30 [binary,29.1,1.1] $F. Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] f($c3,$c2)!=f($c2,$c3). 3 [] f(f(x,y),z)=f(x,f(y,z)). 6,5 [] f($c1,x)=x. 9 [] f(x,x)=$c1. 11 [para_into,3.1.1.1,9.1.1,demod,6,flip.1] f(x,f(x,y))=y. 15 [para_into,3.1.1,9.1.1,flip.1] f(x,f(y,f(x,y)))=$c1. 18,17 [para_into,11.1.1.2,9.1.1] f(x,$c1)=x. 25 [para_from,15.1.1,11.1.1.2,demod,18,flip.1] f(x,f(y,x))=y. 29 [para_from,25.1.1,11.1.1.2] f(x,y)=f(y,x). 30 [binary,29.1,1.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 10 clauses generated 77 clauses kept 16 clauses forward subsumed 72 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8328 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/lifsch.in0100644000076400007640000000061105470212343016565 0ustar mccunemccune% % A problem from Vladimir Lifschitz % % This problem was suggested as a challenge to resolution programs. % It is easily solved by Maslov's inverse method. % set(auto). formula_list(usable). -(exists x exists x1 all y exists z exists z1 ( ( -p(y,y) | p(x,x) | -s(z,x) ) & ( s(x,y) | -s(y,z) | q(z1,z1) ) & ( q(x1,y) | -q(y,z1) | s(x1,x1) ) )). end_of_list. otter-3.3f/examples/auto/mv25.out0100664000076400007640000002010710103522153016303 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8278. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] -P(i(x,y))| -P(x)|P(y). 0 [] P(i(x,i(y,x))). 0 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 0 [] P(i(i(i(x,y),y),i(i(y,x),x))). 0 [] P(i(i(n(x),n(y)),i(y,x))). 0 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). end_of_list. SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -P(i(x,y))| -P(x)|P(y). ** KEPT (pick-wt=12): 2 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). ------------> process sos: ** KEPT (pick-wt=6): 3 [] P(i(x,i(y,x))). ** KEPT (pick-wt=12): 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). ** KEPT (pick-wt=12): 5 [] P(i(i(i(x,y),y),i(i(y,x),x))). ** KEPT (pick-wt=10): 6 [] P(i(i(n(x),n(y)),i(y,x))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=6) 3 [] P(i(x,i(y,x))). given clause #2: (wt=8) 7 [hyper,3,1,3] P(i(x,i(y,i(z,y)))). given clause #3: (wt=10) 6 [] P(i(i(n(x),n(y)),i(y,x))). given clause #4: (wt=10) 8 [hyper,7,1,3] P(i(x,i(y,i(z,i(u,z))))). given clause #5: (wt=12) 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). given clause #6: (wt=12) 5 [] P(i(i(i(x,y),y),i(i(y,x),x))). given clause #7: (wt=10) 16 [hyper,4,1,3] P(i(i(i(x,y),z),i(y,z))). given clause #8: (wt=7) 23 [hyper,16,1,6] P(i(n(x),i(x,y))). given clause #9: (wt=8) 24 [hyper,16,1,5] P(i(x,i(i(x,y),y))). given clause #10: (wt=8) 26 [hyper,16,1,3] P(i(x,i(y,i(z,x)))). given clause #11: (wt=12) 9 [hyper,6,1,3] P(i(x,i(i(n(y),n(z)),i(z,y)))). given clause #12: (wt=9) 28 [hyper,23,1,3] P(i(x,i(n(y),i(y,z)))). given clause #13: (wt=10) 20 [hyper,5,1,7] P(i(i(i(x,i(y,x)),z),z)). given clause #14: (wt=4) 59 [hyper,20,1,16] P(i(x,x)). given clause #15: (wt=6) 64 [hyper,59,1,3] P(i(x,i(y,y))). given clause #16: (wt=12) 10 [hyper,8,1,3] P(i(x,i(y,i(z,i(u,i(v,u)))))). given clause #17: (wt=8) 62 [hyper,59,1,26] P(i(x,i(y,i(z,z)))). given clause #18: (wt=8) 63 [hyper,59,1,24] P(i(i(i(x,x),y),y)). given clause #19: (wt=10) 25 [hyper,16,1,4] P(i(x,i(i(x,y),i(z,y)))). given clause #20: (wt=10) 30 [hyper,24,1,16] P(i(x,i(i(i(y,x),z),z))). given clause #21: (wt=16) 11 [hyper,4,1,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #22: (wt=10) 32 [hyper,24,1,3] P(i(x,i(y,i(i(y,z),z)))). given clause #23: (wt=10) 41 [hyper,26,1,16] P(i(x,i(y,i(z,i(u,x))))). given clause #24: (wt=10) 43 [hyper,26,1,3] P(i(x,i(y,i(z,i(u,y))))). given clause #25: (wt=10) 65 [hyper,64,1,26] P(i(x,i(y,i(z,i(u,u))))). given clause #26: (wt=14) 12 [hyper,4,1,3] P(i(x,i(i(y,z),i(i(z,u),i(y,u))))). given clause #27: (wt=10) 66 [hyper,64,1,24] P(i(i(i(x,i(y,y)),z),z)). given clause #28: (wt=10) 67 [hyper,64,1,4] P(i(i(i(x,x),y),i(z,y))). given clause #29: (wt=10) 77 [hyper,63,1,3] P(i(x,i(i(i(y,y),z),z))). given clause #30: (wt=10) 126 [hyper,11,1,20] P(i(i(x,y),i(x,i(z,y)))). given clause #31: (wt=14) 13 [hyper,4,1,8] P(i(i(i(x,i(y,i(z,y))),u),i(v,u))). given clause #32: (wt=9) 193 [hyper,126,1,23] P(i(n(x),i(y,i(x,z)))). given clause #33: (wt=10) 192 [hyper,126,1,24] P(i(x,i(y,i(i(x,z),z)))). given clause #34: (wt=11) 27 [hyper,23,1,4] P(i(i(i(x,y),z),i(n(x),z))). given clause #35: (wt=7) 269 [hyper,27,1,63] P(i(n(i(x,x)),y)). given clause #36: (wt=12) 14 [hyper,4,1,7] P(i(i(i(x,i(y,x)),z),i(u,z))). given clause #37: (wt=8) 278 [hyper,27,1,6] P(i(n(n(x)),i(y,x))). given clause #38: (wt=9) 268 [hyper,27,1,66] P(i(n(i(x,i(y,y))),z)). given clause #39: (wt=9) 274 [hyper,27,1,20] P(i(n(i(x,i(y,x))),z)). given clause #40: (wt=9) 275 [hyper,27,1,16] P(i(n(i(x,y)),i(y,z))). given clause #41: (wt=14) 15 [hyper,4,1,6] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). given clause #42: (wt=9) 287 [hyper,269,1,3] P(i(x,i(n(i(y,y)),z))). given clause #43: (wt=10) 259 [hyper,27,1,27] P(i(n(i(x,y)),i(n(x),z))). given clause #44: (wt=10) 298 [hyper,278,1,126] P(i(n(n(x)),i(y,i(z,x)))). given clause #45: (wt=10) 305 [hyper,278,1,3] P(i(x,i(n(n(y)),i(z,y)))). given clause #46: (wt=16) 17 [hyper,5,1,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). given clause #47: (wt=10) 348 [hyper,15,1,63] P(i(i(n(x),n(i(y,y))),x)). given clause #48: (wt=6) 418 [hyper,348,1,27] P(i(n(n(x)),x)). given clause #49: (wt=6) 426 [hyper,418,1,348] P(n(n(i(x,x)))). given clause #50: (wt=6) 433 [hyper,418,1,6] P(i(x,n(n(x)))). given clause #51: (wt=14) 18 [hyper,5,1,3] P(i(x,i(i(i(y,z),z),i(i(z,y),y)))). given clause #52: (wt=8) 435 [hyper,418,1,3] P(i(x,i(n(n(y)),y))). given clause #53: (wt=8) 442 [hyper,426,1,3] P(i(x,n(n(i(y,y))))). given clause #54: (wt=8) 443 [hyper,433,1,433] P(n(n(i(x,n(n(x)))))). given clause #55: (wt=8) 445 [hyper,433,1,126] P(i(x,i(y,n(n(x))))). given clause #56: (wt=12) 19 [hyper,5,1,8] P(i(i(i(x,i(y,i(z,y))),u),u)). given clause #57: (wt=8) 446 [hyper,433,1,66] P(n(n(i(x,i(y,y))))). given clause #58: (wt=8) 453 [hyper,433,1,20] P(n(n(i(x,i(y,x))))). given clause #59: (wt=8) 455 [hyper,433,1,16] P(i(x,n(n(i(y,x))))). given clause #60: (wt=8) 461 [hyper,433,1,3] P(i(x,i(y,n(n(y))))). given clause #61: (wt=14) 21 [hyper,16,1,4] P(i(i(i(x,y),z),i(i(i(u,x),y),z))). given clause #62: (wt=8) 462 [hyper,433,1,426] P(n(n(n(n(i(x,x)))))). given clause #63: (wt=8) 463 [hyper,433,1,418] P(n(n(i(n(n(x)),x)))). given clause #64: (wt=8) 640 [hyper,455,1,6] P(i(n(i(x,n(y))),y)). given clause #65: (wt=9) 449 [hyper,433,1,27] P(i(n(x),n(n(i(x,y))))). given clause #66: (wt=12) 22 [hyper,16,1,3] P(i(x,i(i(i(y,z),u),i(z,u)))). given clause #67: (wt=7) 768 [hyper,449,1,6] P(i(n(i(x,y)),x)). given clause #68: (wt=7) 790 [hyper,768,1,6] P(i(x,i(n(x),y))). given clause #69: (wt=9) 471 [hyper,433,1,269] P(n(n(i(n(i(x,x)),y)))). given clause #70: (wt=9) 492 [hyper,433,1,23] P(n(n(i(n(x),i(x,y))))). given clause #71: (wt=12) 29 [hyper,24,1,24] P(i(i(i(x,i(i(x,y),y)),z),z)). given clause #72: (wt=9) 531 [hyper,443,1,23] P(i(n(i(x,n(n(x)))),y)). given clause #73: (wt=9) 735 [hyper,462,1,23] P(i(n(n(n(i(x,x)))),y)). given clause #74: (wt=9) 746 [hyper,463,1,23] P(i(n(i(n(n(x)),x)),y)). given clause #75: (wt=9) 782 [hyper,768,1,433] P(n(n(i(n(i(x,y)),x)))). given clause #76: (wt=12) 31 [hyper,24,1,4] P(i(i(i(i(x,y),y),z),i(x,z))). -------- PROOF -------- 978 [binary,977.1,2.1] $ANS(MV_25). ----> UNIT CONFLICT at 0.04 sec ----> 978 [binary,977.1,2.1] $ANS(MV_25). Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). 3 [] P(i(x,i(y,x))). 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 5 [] P(i(i(i(x,y),y),i(i(y,x),x))). 11 [hyper,4,1,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 16 [hyper,4,1,3] P(i(i(i(x,y),z),i(y,z))). 24 [hyper,16,1,5] P(i(x,i(i(x,y),y))). 31 [hyper,24,1,4] P(i(i(i(i(x,y),y),z),i(x,z))). 977 [hyper,31,1,11] P(i(i(x,y),i(i(z,x),i(z,y)))). 978 [binary,977.1,2.1] $ANS(MV_25). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 76 clauses generated 3375 clauses kept 977 clauses forward subsumed 2404 clauses back subsumed 7 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8278 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/steam.in0100644000076400007640000000431105515261704016434 0ustar mccunemccune% % Schubert's Steamroller % % Wolves, foxes, birds, caterpillars, and snails are animals, % and there are some of each of them. % % Also there are some grains, and grains are plants. % % Every animal either likes to eat all plants or all animals much % smaller than itself that like to eat some plants. % % Caterpillars and snails are much smaller than birds, which are much % smaller than foxes, which are in turn much smaller than wolves. % % Wolves do not like to eat foxes or grains, while birds like to eat % caterpillars but not snails. % % Caterpillars and snails like to eat some plants. % % Prove there is an animal that likes to eat a grain-eating animal. % set(auto). formula_list(usable). all x (Wolf(x) -> animal(x)). all x (Fox(x) -> animal(x)). all x (Bird(x) -> animal(x)). all x (Caterpillar(x) -> animal(x)). all x (Snail(x) -> animal(x)). all x (Grain(x) -> plant(x)). exists x Wolf(x). exists x Fox(x). exists x Bird(x). exists x Caterpillar(x). exists x Snail(x). exists x Grain(x). % All animals either eat all plants or eat all smaller animals that eat some plants. all x (animal(x) -> (all y (plant(y)->eats(x,y))) | (all z ( animal(z) & Smaller(z,x) & (exists u (plant(u)&eats(z,u))) -> eats(x,z)))). all x all y (Caterpillar(x) & Bird(y) -> Smaller(x,y)). all x all y (Snail(x) & Bird(y) -> Smaller(x,y)). all x all y (Bird(x) & Fox(y) -> Smaller(x,y)). all x all y (Fox(x) & Wolf(y) -> Smaller(x,y)). all x all y (Bird(x) & Caterpillar(y) -> eats(x,y)). all x (Caterpillar(x) -> (exists y (plant(y) & eats(x,y)))). all x (Snail(x) -> (exists y (plant(y) & eats(x,y)))). all x all y (Wolf(x) & Fox(y) -> -eats(x,y)). all x all y (Wolf(x) & Grain(y) -> -eats(x,y)). all x all y (Bird(x) & Snail(y) -> -eats(x,y)). % negation of "there is an animal that eats {an animal that eats all grains}". % Note the answer literal, which records the predator and the prey. -(exists x exists y ( -$answer(eats(x,y)) & animal(x) & animal(y) & eats(x,y) & (all z (Grain(z) -> eats(y,z))))). end_of_list. otter-3.3f/examples/auto/comm.in0100644000076400007640000000041605515260614016257 0ustar mccunemccune% The group theory commutator problem. % If xxx = e, then [[yz]z] = e, where [uv] = uv(u-1)(v-1). set(auto). list(usable). x = x. f(e,x) = x. f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). h(x,y) = f(x,f(y,f(g(x),g(y)))). f(x,f(x,x)) = e. h(h(a,b),b) != e. end_of_list. otter-3.3f/examples/auto/ring_x2.in0100644000076400007640000000053605515262550016700 0ustar mccunemccune% % Boolean (xx = x) rings are commutative. % set(auto). list(usable). x = x. % Ring axioms j(0,x) = x. j(g(x),x) = 0. j(j(x,y),z) = j(x,j(y,z)). j(x,y) = j(y,x). f(f(x,y),z) = f(x,f(y,z)). f(x,j(y,z)) = j(f(x,y),f(x,z)). f(j(y,z),x) = j(f(y,x),f(z,x)). f(x,x) = x. % Hypothesis f(a,b) != f(b,a). % Denial of conclusion end_of_list. otter-3.3f/examples/auto/tba_gg.in0100644000076400007640000000031705470212344016544 0ustar mccunemccune% Ternary boolean algebra: g(g(x) = x. set(auto). list(usable). x = x. f(f(v,w,x),y,f(v,w,z)) = f(v,w,f(x,y,z)). f(y,x,x) = x. f(x,x,y) = x. f(g(y),y,x) = x. f(x,y,g(y)) = x. g(g(a)) != a. end_of_list. otter-3.3f/examples/auto/x2_quant.in0100644000076400007640000000045505515262343017071 0ustar mccunemccune% % xx=e groups are commutative. % set(auto). formula_list(usable). all x (x = x). all x y z (f(f(x,y),z) = f(x,f(y,z))). exists e ( (all x (f(e,x) = x) ) & (all x exists y (f(y,x) = e) ) & (all x (f(x,x) = e)) ) . -(all x y (f(x,y) = f(y,x))). end_of_list. otter-3.3f/examples/auto/w_sk.in0100644000076400007640000000042405515262472016272 0ustar mccunemccune% % Combinatory Logic % Construct W in terms of S and K. Wxy = xyy. % set(auto). list(usable). x = x. a(a(a(S,x),y),z) = a(a(x,z),a(y,z)). a(a(K,x),y) = x. end_of_list. formula_list(usable). -(exists W all x all y (a(a(W,x),y) = a(a(x,y),y) & -$ans(W))). end_of_list. otter-3.3f/examples/auto/z11.out0100664000076400007640000002341010103522154016126 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8333. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] f(e,x)=x. 0 [] f(g(x),x)=e. 0 [] f(f(x,y),z)=f(x,f(y,z)). 0 [] f(a,b)=c. 0 [] f(b,c)=d. 0 [] f(c,d)=h. 0 [] f(d,h)=a. 0 [] f(h,a)=b. end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). There is no negative clause, so all clause lists will be printed at the end of the search. dependent: set(print_lists_at_end). ------------> process usable: ------------> process sos: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=5): 2 [] f(e,x)=x. ---> New Demodulator: 3 [new_demod,2] f(e,x)=x. ** KEPT (pick-wt=6): 4 [] f(g(x),x)=e. ---> New Demodulator: 5 [new_demod,4] f(g(x),x)=e. ** KEPT (pick-wt=11): 6 [] f(f(x,y),z)=f(x,f(y,z)). ---> New Demodulator: 7 [new_demod,6] f(f(x,y),z)=f(x,f(y,z)). ** KEPT (pick-wt=5): 8 [] f(a,b)=c. ---> New Demodulator: 9 [new_demod,8] f(a,b)=c. ** KEPT (pick-wt=5): 10 [] f(b,c)=d. ---> New Demodulator: 11 [new_demod,10] f(b,c)=d. ** KEPT (pick-wt=5): 12 [] f(c,d)=h. ---> New Demodulator: 13 [new_demod,12] f(c,d)=h. ** KEPT (pick-wt=5): 14 [] f(d,h)=a. ---> New Demodulator: 15 [new_demod,14] f(d,h)=a. ** KEPT (pick-wt=5): 16 [] f(h,a)=b. ---> New Demodulator: 17 [new_demod,16] f(h,a)=b. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back demodulation with 3. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 1 [] x=x. given clause #2: (wt=5) 2 [] f(e,x)=x. given clause #3: (wt=5) 8 [] f(a,b)=c. given clause #4: (wt=5) 10 [] f(b,c)=d. given clause #5: (wt=5) 12 [] f(c,d)=h. given clause #6: (wt=6) 4 [] f(g(x),x)=e. given clause #7: (wt=5) 14 [] f(d,h)=a. given clause #8: (wt=5) 16 [] f(h,a)=b. given clause #9: (wt=11) 6 [] f(f(x,y),z)=f(x,f(y,z)). given clause #10: (wt=7) 42 [back_demod,12,demod,27] f(a,f(b,d))=h. given clause #11: (wt=9) 26 [para_into,6.1.1.1,8.1.1] f(c,x)=f(a,f(b,x)). given clause #12: (wt=8) 28 [para_into,6.1.1.1,4.1.1,demod,3,flip.1] f(g(x),f(x,y))=y. given clause #13: (wt=5) 56 [para_into,28.1.1.2,4.1.1,demod,47] f(x,e)=x. given clause #14: (wt=4) 60 [para_into,56.1.1,4.1.1,flip.1] g(e)=e. given clause #15: (wt=6) 50 [para_into,28.1.1.2,10.1.1] f(g(b),d)=c. given clause #16: (wt=21) 30 [back_demod,20,demod,23,25,27,27,25,27] f(b,f(a,f(b,f(a,f(b,f(b,f(a,f(b,x))))))))=f(a,x). given clause #17: (wt=6) 52 [para_into,28.1.1.2,8.1.1] f(g(a),c)=b. given clause #18: (wt=8) 44 [para_into,28.1.1.2,42.1.1] f(g(a),h)=f(b,d). given clause #19: (wt=9) 38 [back_demod,14,demod,25,27] f(b,f(a,f(b,h)))=a. given clause #20: (wt=9) 46 [para_into,28.1.1.2,28.1.1] f(g(g(x)),y)=f(x,y). given clause #21: (wt=17) 32 [back_demod,18,demod,23,25,27,27] f(a,f(b,f(b,f(a,f(b,f(a,x))))))=f(b,x). given clause #22: (wt=5) 78 [para_into,46.1.1,56.1.1,demod,57] g(g(x))=x. given clause #23: (wt=6) 82 [para_into,46.1.1,4.1.1,flip.1] f(x,g(x))=e. given clause #24: (wt=8) 80 [para_into,46.1.1,28.1.1,flip.1] f(x,f(g(x),y))=y. given clause #25: (wt=8) 142 [para_into,82.1.1,26.1.1] f(a,f(b,g(c)))=e. given clause #26: (wt=11) 40 [back_demod,24,demod,27] f(d,x)=f(b,f(a,f(b,x))). given clause #27: (wt=7) 150 [para_from,142.1.1,28.1.1.2,demod,57,flip.1] f(b,g(c))=g(a). given clause #28: (wt=8) 158 [para_from,150.1.1,28.1.1.2,flip.1] g(c)=f(g(b),g(a)). given clause #29: (wt=8) 160 [para_from,158.1.1,78.1.1.1] g(f(g(b),g(a)))=c. given clause #30: (wt=10) 76 [para_from,38.1.1,28.1.1.2] f(g(b),a)=f(a,f(b,h)). given clause #31: (wt=12) 54 [para_into,28.1.1.2,6.1.1] f(g(f(x,y)),f(x,f(y,z)))=z. given clause #32: (wt=9) 174 [para_into,54.1.1.2.2,82.1.1,demod,57] f(g(f(x,y)),x)=g(y). given clause #33: (wt=5) 248 [back_demod,214,demod,245] f(a,h)=b. given clause #34: (wt=6) 252 [para_from,248.1.1,28.1.1.2] f(g(a),b)=h. given clause #35: (wt=7) 244 [back_demod,234,demod,239] f(a,f(a,a))=h. given clause #36: (wt=11) 188 [para_into,174.1.1.1.1,50.1.1,demod,159,7,flip.1] g(d)=f(g(b),f(g(a),g(b))). given clause #37: (wt=8) 246 [back_demod,232,demod,239] f(g(a),h)=f(a,a). given clause #38: (wt=9) 238 [back_demod,38,demod,211,211,223] f(a,f(a,f(a,d)))=a. given clause #39: (wt=7) 260 [para_from,238.1.1,28.1.1.2,demod,5,flip.1] f(a,f(a,d))=e. given clause #40: (wt=6) 262 [para_from,260.1.1,28.1.1.2,demod,57] g(a)=f(a,d). given clause #41: (wt=10) 198 [para_into,174.1.1.1.1,28.1.1,flip.1] g(f(x,y))=f(g(y),g(x)). given clause #42: (wt=6) 272 [back_demod,188,demod,263,7,237,267,57,245,249,9,225,243,261,57] g(d)=f(a,a). given clause #43: (wt=6) 274 [back_demod,158,demod,263,225,261,57,245,249,9] g(c)=f(a,c). given clause #44: (wt=8) 276 [para_into,198.1.1.1,248.1.1,demod,271,263,7,7,7,241,261,57,245,249,9] g(b)=f(a,f(a,c)). given clause #45: (wt=10) 270 [back_demod,200,demod,263,263,225,261,57,245,249,9,225,243,261,57,7,237,245,249,9,243,261,57,251] g(h)=f(a,f(a,f(a,c))). given clause #46: (wt=13) 210 [back_demod,136,demod,209,flip.1] f(b,x)=f(a,f(a,f(a,f(a,x)))). given clause #47: (wt=11) 216 [back_demod,132,demod,211,211,213] f(h,x)=f(a,f(a,f(a,x))). given clause #48: (wt=11) 242 [back_demod,10,demod,211] f(a,f(a,f(a,f(a,c))))=d. given clause #49: (wt=15) 240 [back_demod,26,demod,211] f(c,x)=f(a,f(a,f(a,f(a,f(a,x))))). given clause #50: (wt=23) 236 [back_demod,40,demod,211,211] f(d,x)=f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x))))))))). given clause #51: (wt=25) 212 [back_demod,208,demod,211] f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))))))=x. Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ list(usable). 1 [] x=x. 2 [] f(e,x)=x. 8 [] f(a,b)=c. 4 [] f(g(x),x)=e. 6 [] f(f(x,y),z)=f(x,f(y,z)). 28 [para_into,6.1.1.1,4.1.1,demod,3,flip.1] f(g(x),f(x,y))=y. 56 [para_into,28.1.1.2,4.1.1,demod,47] f(x,e)=x. 60 [para_into,56.1.1,4.1.1,flip.1] g(e)=e. 78 [para_into,46.1.1,56.1.1,demod,57] g(g(x))=x. 82 [para_into,46.1.1,4.1.1,flip.1] f(x,g(x))=e. 80 [para_into,46.1.1,28.1.1,flip.1] f(x,f(g(x),y))=y. 248 [back_demod,214,demod,245] f(a,h)=b. 244 [back_demod,234,demod,239] f(a,f(a,a))=h. 260 [para_from,238.1.1,28.1.1.2,demod,5,flip.1] f(a,f(a,d))=e. 262 [para_from,260.1.1,28.1.1.2,demod,57] g(a)=f(a,d). 198 [para_into,174.1.1.1.1,28.1.1,flip.1] g(f(x,y))=f(g(y),g(x)). 272 [back_demod,188,demod,263,7,237,267,57,245,249,9,225,243,261,57] g(d)=f(a,a). 274 [back_demod,158,demod,263,225,261,57,245,249,9] g(c)=f(a,c). 276 [para_into,198.1.1.1,248.1.1,demod,271,263,7,7,7,241,261,57,245,249,9] g(b)=f(a,f(a,c)). 270 [back_demod,200,demod,263,263,225,261,57,245,249,9,225,243,261,57,7,237,245,249,9,243,261,57,251] g(h)=f(a,f(a,f(a,c))). 210 [back_demod,136,demod,209,flip.1] f(b,x)=f(a,f(a,f(a,f(a,x)))). 216 [back_demod,132,demod,211,211,213] f(h,x)=f(a,f(a,f(a,x))). 242 [back_demod,10,demod,211] f(a,f(a,f(a,f(a,c))))=d. 240 [back_demod,26,demod,211] f(c,x)=f(a,f(a,f(a,f(a,f(a,x))))). 236 [back_demod,40,demod,211,211] f(d,x)=f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x))))))))). 212 [back_demod,208,demod,211] f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))))))=x. end_of_list. list(sos). end_of_list. list(demodulators). 3 [new_demod,2] f(e,x)=x. 5 [new_demod,4] f(g(x),x)=e. 7 [new_demod,6] f(f(x,y),z)=f(x,f(y,z)). 9 [new_demod,8] f(a,b)=c. 29 [new_demod,28] f(g(x),f(x,y))=y. 57 [new_demod,56] f(x,e)=x. 61 [new_demod,60] g(e)=e. 79 [new_demod,78] g(g(x))=x. 81 [new_demod,80] f(x,f(g(x),y))=y. 83 [new_demod,82] f(x,g(x))=e. 199 [new_demod,198] g(f(x,y))=f(g(y),g(x)). 211 [new_demod,210] f(b,x)=f(a,f(a,f(a,f(a,x)))). 213 [new_demod,212] f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))))))=x. 217 [new_demod,216] f(h,x)=f(a,f(a,f(a,x))). 237 [new_demod,236] f(d,x)=f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x))))))))). 241 [new_demod,240] f(c,x)=f(a,f(a,f(a,f(a,f(a,x))))). 243 [new_demod,242] f(a,f(a,f(a,f(a,c))))=d. 245 [new_demod,244] f(a,f(a,a))=h. 249 [new_demod,248] f(a,h)=b. 261 [new_demod,260] f(a,f(a,d))=e. 263 [new_demod,262] g(a)=f(a,d). 271 [new_demod,270] g(h)=f(a,f(a,f(a,c))). 273 [new_demod,272] g(d)=f(a,a). 275 [new_demod,274] g(c)=f(a,c). 277 [new_demod,276] g(b)=f(a,f(a,c)). end_of_list. -------------- statistics ------------- clauses given 51 clauses generated 427 clauses kept 139 clauses forward subsumed 411 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8333 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/pigeon.out0100664000076400007640000005315110103522153017000 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8283. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] p00|p01|p02|p03. 0 [] p04|p05|p06|p07. 0 [] p08|p09|p10|p11. 0 [] p12|p13|p14|p15. 0 [] p16|p17|p18|p19. 0 [] -p00| -p04. 0 [] -p00| -p08. 0 [] -p00| -p12. 0 [] -p00| -p16. 0 [] -p04| -p08. 0 [] -p04| -p12. 0 [] -p04| -p16. 0 [] -p08| -p12. 0 [] -p08| -p16. 0 [] -p12| -p16. 0 [] -p01| -p05. 0 [] -p01| -p09. 0 [] -p01| -p13. 0 [] -p01| -p17. 0 [] -p05| -p09. 0 [] -p05| -p13. 0 [] -p05| -p17. 0 [] -p09| -p13. 0 [] -p09| -p17. 0 [] -p13| -p17. 0 [] -p02| -p06. 0 [] -p02| -p10. 0 [] -p02| -p14. 0 [] -p02| -p18. 0 [] -p06| -p10. 0 [] -p06| -p14. 0 [] -p06| -p18. 0 [] -p10| -p14. 0 [] -p10| -p18. 0 [] -p14| -p18. 0 [] -p03| -p07. 0 [] -p03| -p11. 0 [] -p03| -p15. 0 [] -p03| -p19. 0 [] -p07| -p11. 0 [] -p07| -p15. 0 [] -p07| -p19. 0 [] -p11| -p15. 0 [] -p11| -p19. 0 [] -p15| -p19. end_of_list. SCAN INPUT: prop=1, horn=0, equality=0, symmetry=0, max_lits=4. The clause set is propositional; the strategy will be ordered hyperresolution with the propositional optimizations, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: set(propositional). dependent: set(sort_literals). ------------> process usable: ** KEPT (pick-wt=2): 1 [] -p00| -p04. ** KEPT (pick-wt=2): 2 [] -p00| -p08. ** KEPT (pick-wt=2): 3 [] -p00| -p12. ** KEPT (pick-wt=2): 4 [] -p00| -p16. ** KEPT (pick-wt=2): 5 [] -p04| -p08. ** KEPT (pick-wt=2): 6 [] -p04| -p12. ** KEPT (pick-wt=2): 7 [] -p04| -p16. ** KEPT (pick-wt=2): 8 [] -p08| -p12. ** KEPT (pick-wt=2): 9 [] -p08| -p16. ** KEPT (pick-wt=2): 10 [] -p12| -p16. ** KEPT (pick-wt=2): 11 [] -p01| -p05. ** KEPT (pick-wt=2): 12 [] -p01| -p09. ** KEPT (pick-wt=2): 13 [] -p01| -p13. ** KEPT (pick-wt=2): 14 [] -p01| -p17. ** KEPT (pick-wt=2): 15 [] -p05| -p09. ** KEPT (pick-wt=2): 16 [] -p05| -p13. ** KEPT (pick-wt=2): 17 [] -p05| -p17. ** KEPT (pick-wt=2): 18 [] -p09| -p13. ** KEPT (pick-wt=2): 19 [] -p09| -p17. ** KEPT (pick-wt=2): 20 [] -p13| -p17. ** KEPT (pick-wt=2): 21 [] -p02| -p06. ** KEPT (pick-wt=2): 22 [] -p02| -p10. ** KEPT (pick-wt=2): 23 [] -p02| -p14. ** KEPT (pick-wt=2): 24 [] -p02| -p18. ** KEPT (pick-wt=2): 25 [] -p06| -p10. ** KEPT (pick-wt=2): 26 [] -p06| -p14. ** KEPT (pick-wt=2): 27 [] -p06| -p18. ** KEPT (pick-wt=2): 28 [] -p10| -p14. ** KEPT (pick-wt=2): 29 [] -p10| -p18. ** KEPT (pick-wt=2): 30 [] -p14| -p18. ** KEPT (pick-wt=2): 31 [] -p03| -p07. ** KEPT (pick-wt=2): 32 [] -p03| -p11. ** KEPT (pick-wt=2): 33 [] -p03| -p15. ** KEPT (pick-wt=2): 34 [] -p03| -p19. ** KEPT (pick-wt=2): 35 [] -p07| -p11. ** KEPT (pick-wt=2): 36 [] -p07| -p15. ** KEPT (pick-wt=2): 37 [] -p07| -p19. ** KEPT (pick-wt=2): 38 [] -p11| -p15. ** KEPT (pick-wt=2): 39 [] -p11| -p19. ** KEPT (pick-wt=2): 40 [] -p15| -p19. ------------> process sos: ** KEPT (pick-wt=4): 41 [] p00|p01|p02|p03. ** KEPT (pick-wt=4): 42 [] p04|p05|p06|p07. ** KEPT (pick-wt=4): 43 [] p08|p09|p10|p11. ** KEPT (pick-wt=4): 44 [] p12|p13|p14|p15. ** KEPT (pick-wt=4): 45 [] p16|p17|p18|p19. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=4) 41 [] p00|p01|p02|p03. given clause #2: (wt=4) 42 [] p04|p05|p06|p07. given clause #3: (wt=4) 43 [] p08|p09|p10|p11. given clause #4: (wt=4) 44 [] p12|p13|p14|p15. given clause #5: (wt=4) 45 [] p16|p17|p18|p19. given clause #6: (wt=6) 46 [hyper,42,31,41] p00|p01|p02|p04|p05|p06. given clause #7: (wt=6) 47 [hyper,43,35,42] p04|p05|p06|p08|p09|p10. given clause #8: (wt=6) 48 [hyper,43,32,41] p00|p01|p02|p08|p09|p10. given clause #9: (wt=6) 49 [hyper,44,38,43] p08|p09|p10|p12|p13|p14. given clause #10: (wt=6) 50 [hyper,44,36,42] p04|p05|p06|p12|p13|p14. given clause #11: (wt=6) 51 [hyper,44,33,41] p00|p01|p02|p12|p13|p14. given clause #12: (wt=6) 52 [hyper,45,40,44] p12|p13|p14|p16|p17|p18. given clause #13: (wt=6) 53 [hyper,45,39,43] p08|p09|p10|p16|p17|p18. given clause #14: (wt=6) 54 [hyper,45,37,42] p04|p05|p06|p16|p17|p18. given clause #15: (wt=6) 55 [hyper,45,34,41] p00|p01|p02|p16|p17|p18. given clause #16: (wt=7) 56 [hyper,48,25,46] p00|p01|p02|p04|p05|p08|p09. given clause #17: (wt=7) 57 [hyper,50,28,47] p04|p05|p06|p08|p09|p12|p13. given clause #18: (wt=7) 58 [hyper,51,28,48] p00|p01|p02|p08|p09|p12|p13. given clause #19: (wt=7) 59 [hyper,51,26,46] p00|p01|p02|p04|p05|p12|p13. given clause #20: (wt=7) 60 [hyper,53,30,49] p08|p09|p10|p12|p13|p16|p17. given clause #21: (wt=7) 61 [hyper,54,30,50] p04|p05|p06|p12|p13|p16|p17. given clause #22: (wt=7) 62 [hyper,54,29,47] p04|p05|p06|p08|p09|p16|p17. given clause #23: (wt=7) 63 [hyper,55,30,51] p00|p01|p02|p12|p13|p16|p17. given clause #24: (wt=7) 64 [hyper,55,29,48] p00|p01|p02|p08|p09|p16|p17. given clause #25: (wt=7) 65 [hyper,55,27,46] p00|p01|p02|p04|p05|p16|p17. given clause #26: (wt=7) 66 [hyper,59,18,56] p00|p01|p02|p04|p05|p08|p12. given clause #27: (wt=7) 67 [hyper,62,20,57] p04|p05|p06|p08|p09|p12|p16. given clause #28: (wt=7) 68 [hyper,64,20,58] p00|p01|p02|p08|p09|p12|p16. given clause #29: (wt=7) 69 [hyper,65,20,59] p00|p01|p02|p04|p05|p12|p16. given clause #30: (wt=7) 70 [hyper,65,19,56] p00|p01|p02|p04|p05|p08|p16. given clause #31: (wt=6) 71 [hyper,70,10,66] p00|p01|p02|p04|p05|p08. given clause #32: (wt=6) 72 [hyper,71,9,69] p00|p01|p02|p04|p05|p12. given clause #33: (wt=5) 73 [hyper,72,8,71] p00|p01|p02|p04|p05. given clause #34: (wt=7) 74 [hyper,73,17,64] p00|p01|p02|p04|p08|p09|p16. given clause #35: (wt=7) 75 [hyper,73,17,63] p00|p01|p02|p04|p12|p13|p16. given clause #36: (wt=7) 76 [hyper,73,16,58] p00|p01|p02|p04|p08|p09|p12. given clause #37: (wt=6) 77 [hyper,76,10,74] p00|p01|p02|p04|p08|p09. given clause #38: (wt=5) 78 [hyper,77,15,73] p00|p01|p02|p04|p08. given clause #39: (wt=6) 79 [hyper,78,9,75] p00|p01|p02|p04|p12|p13. given clause #40: (wt=5) 80 [hyper,79,16,73] p00|p01|p02|p04|p12. given clause #41: (wt=4) 81 [hyper,80,8,78] p00|p01|p02|p04. given clause #42: (wt=6) 82 [hyper,81,7,68] p00|p01|p02|p08|p09|p12. given clause #43: (wt=5) 83 [hyper,82,6,81] p00|p01|p02|p08|p09. given clause #44: (wt=7) 84 [hyper,83,19,63] p00|p01|p02|p08|p12|p13|p16. given clause #45: (wt=6) 85 [hyper,84,7,81] p00|p01|p02|p08|p12|p13. given clause #46: (wt=5) 86 [hyper,85,18,83] p00|p01|p02|p08|p12. given clause #47: (wt=4) 87 [hyper,86,6,81] p00|p01|p02|p08. given clause #48: (wt=3) 88 [hyper,87,5,81] p00|p01|p02. given clause #49: (wt=7) 89 [hyper,88,24,54] p00|p01|p04|p05|p06|p16|p17. given clause #50: (wt=7) 90 [hyper,88,24,53] p00|p01|p08|p09|p10|p16|p17. given clause #51: (wt=7) 91 [hyper,88,24,52] p00|p01|p12|p13|p14|p16|p17. given clause #52: (wt=7) 92 [hyper,88,23,50] p00|p01|p04|p05|p06|p12|p13. given clause #53: (wt=7) 93 [hyper,88,23,49] p00|p01|p08|p09|p10|p12|p13. given clause #54: (wt=7) 94 [hyper,88,22,47] p00|p01|p04|p05|p06|p08|p09. given clause #55: (wt=7) 95 [hyper,92,20,89] p00|p01|p04|p05|p06|p12|p16. given clause #56: (wt=7) 96 [hyper,93,20,90] p00|p01|p08|p09|p10|p12|p16. given clause #57: (wt=7) 97 [hyper,94,19,89] p00|p01|p04|p05|p06|p08|p16. given clause #58: (wt=7) 98 [hyper,94,18,92] p00|p01|p04|p05|p06|p08|p12. given clause #59: (wt=6) 99 [hyper,98,10,97] p00|p01|p04|p05|p06|p08. given clause #60: (wt=6) 100 [hyper,99,9,95] p00|p01|p04|p05|p06|p12. given clause #61: (wt=5) 101 [hyper,100,8,99] p00|p01|p04|p05|p06. given clause #62: (wt=4) 102 [hyper,101,21,88] p00|p01|p04|p05. given clause #63: (wt=7) 103 [hyper,102,17,91] p00|p01|p04|p12|p13|p14|p16. given clause #64: (wt=7) 104 [hyper,102,17,90] p00|p01|p04|p08|p09|p10|p16. given clause #65: (wt=7) 105 [hyper,102,16,93] p00|p01|p04|p08|p09|p10|p12. given clause #66: (wt=6) 106 [hyper,105,10,104] p00|p01|p04|p08|p09|p10. given clause #67: (wt=5) 107 [hyper,106,22,88] p00|p01|p04|p08|p09. given clause #68: (wt=4) 108 [hyper,107,15,102] p00|p01|p04|p08. given clause #69: (wt=6) 109 [hyper,108,9,103] p00|p01|p04|p12|p13|p14. given clause #70: (wt=5) 110 [hyper,109,23,88] p00|p01|p04|p12|p13. given clause #71: (wt=4) 111 [hyper,110,16,102] p00|p01|p04|p12. given clause #72: (wt=3) 112 [hyper,111,8,108] p00|p01|p04. given clause #73: (wt=6) 113 [hyper,112,7,96] p00|p01|p08|p09|p10|p12. given clause #74: (wt=5) 114 [hyper,113,6,112] p00|p01|p08|p09|p10. given clause #75: (wt=4) 115 [hyper,114,22,88] p00|p01|p08|p09. given clause #76: (wt=7) 116 [hyper,115,19,91] p00|p01|p08|p12|p13|p14|p16. given clause #77: (wt=6) 117 [hyper,116,7,112] p00|p01|p08|p12|p13|p14. given clause #78: (wt=5) 118 [hyper,117,23,88] p00|p01|p08|p12|p13. given clause #79: (wt=4) 119 [hyper,118,18,115] p00|p01|p08|p12. given clause #80: (wt=3) 120 [hyper,119,6,112] p00|p01|p08. given clause #81: (wt=2) 121 [hyper,120,5,112] p00|p01. given clause #82: (wt=7) 122 [hyper,121,14,62] p00|p04|p05|p06|p08|p09|p16. given clause #83: (wt=7) 123 [hyper,121,14,61] p00|p04|p05|p06|p12|p13|p16. given clause #84: (wt=7) 124 [hyper,121,14,60] p00|p08|p09|p10|p12|p13|p16. given clause #85: (wt=7) 125 [hyper,121,13,57] p00|p04|p05|p06|p08|p09|p12. given clause #86: (wt=6) 126 [hyper,125,10,122] p00|p04|p05|p06|p08|p09. given clause #87: (wt=5) 127 [hyper,126,12,121] p00|p04|p05|p06|p08. given clause #88: (wt=6) 128 [hyper,127,9,123] p00|p04|p05|p06|p12|p13. given clause #89: (wt=5) 129 [hyper,128,13,121] p00|p04|p05|p06|p12. given clause #90: (wt=4) 130 [hyper,129,8,127] p00|p04|p05|p06. given clause #91: (wt=8) 131 [hyper,130,27,53] p00|p04|p05|p08|p09|p10|p16|p17. given clause #92: (wt=7) 134 [hyper,131,14,121] p00|p04|p05|p08|p09|p10|p16. given clause #93: (wt=8) 132 [hyper,130,27,52] p00|p04|p05|p12|p13|p14|p16|p17. given clause #94: (wt=7) 135 [hyper,132,14,121] p00|p04|p05|p12|p13|p14|p16. given clause #95: (wt=8) 133 [hyper,130,26,49] p00|p04|p05|p08|p09|p10|p12|p13. given clause #96: (wt=7) 136 [hyper,133,13,121] p00|p04|p05|p08|p09|p10|p12. given clause #97: (wt=6) 137 [hyper,136,10,134] p00|p04|p05|p08|p09|p10. given clause #98: (wt=5) 138 [hyper,137,25,130] p00|p04|p05|p08|p09. given clause #99: (wt=4) 139 [hyper,138,12,121] p00|p04|p05|p08. given clause #100: (wt=6) 140 [hyper,139,9,135] p00|p04|p05|p12|p13|p14. given clause #101: (wt=5) 141 [hyper,140,26,130] p00|p04|p05|p12|p13. given clause #102: (wt=4) 142 [hyper,141,13,121] p00|p04|p05|p12. given clause #103: (wt=3) 143 [hyper,142,8,139] p00|p04|p05. given clause #104: (wt=2) 144 [hyper,143,11,121] p00|p04. given clause #105: (wt=6) 145 [hyper,144,7,124] p00|p08|p09|p10|p12|p13. given clause #106: (wt=5) 146 [hyper,145,13,121] p00|p08|p09|p10|p12. given clause #107: (wt=4) 147 [hyper,146,6,144] p00|p08|p09|p10. given clause #108: (wt=8) 148 [hyper,147,29,52] p00|p08|p09|p12|p13|p14|p16|p17. given clause #109: (wt=7) 149 [hyper,148,14,121] p00|p08|p09|p12|p13|p14|p16. given clause #110: (wt=6) 150 [hyper,149,7,144] p00|p08|p09|p12|p13|p14. given clause #111: (wt=5) 151 [hyper,150,28,147] p00|p08|p09|p12|p13. given clause #112: (wt=4) 152 [hyper,151,13,121] p00|p08|p09|p12. given clause #113: (wt=3) 153 [hyper,152,6,144] p00|p08|p09. given clause #114: (wt=2) 154 [hyper,153,12,121] p00|p08. given clause #115: (wt=1) 155 [hyper,154,5,144] p00. given clause #116: (wt=6) 156 [hyper,155,4,67] p04|p05|p06|p08|p09|p12. given clause #117: (wt=5) 157 [hyper,156,3,155] p04|p05|p06|p08|p09. given clause #118: (wt=7) 158 [hyper,157,19,61] p04|p05|p06|p08|p12|p13|p16. given clause #119: (wt=6) 159 [hyper,158,4,155] p04|p05|p06|p08|p12|p13. given clause #120: (wt=5) 160 [hyper,159,18,157] p04|p05|p06|p08|p12. given clause #121: (wt=4) 161 [hyper,160,3,155] p04|p05|p06|p08. given clause #122: (wt=3) 162 [hyper,161,2,155] p04|p05|p06. given clause #123: (wt=7) 163 [hyper,162,27,53] p04|p05|p08|p09|p10|p16|p17. given clause #124: (wt=7) 164 [hyper,162,27,52] p04|p05|p12|p13|p14|p16|p17. given clause #125: (wt=7) 165 [hyper,162,26,49] p04|p05|p08|p09|p10|p12|p13. given clause #126: (wt=7) 166 [hyper,165,20,163] p04|p05|p08|p09|p10|p12|p16. given clause #127: (wt=6) 167 [hyper,166,4,155] p04|p05|p08|p09|p10|p12. given clause #128: (wt=5) 168 [hyper,167,3,155] p04|p05|p08|p09|p10. given clause #129: (wt=4) 169 [hyper,168,25,162] p04|p05|p08|p09. given clause #130: (wt=7) 170 [hyper,169,19,164] p04|p05|p08|p12|p13|p14|p16. given clause #131: (wt=6) 171 [hyper,170,4,155] p04|p05|p08|p12|p13|p14. given clause #132: (wt=5) 172 [hyper,171,26,162] p04|p05|p08|p12|p13. given clause #133: (wt=4) 173 [hyper,172,18,169] p04|p05|p08|p12. given clause #134: (wt=3) 174 [hyper,173,3,155] p04|p05|p08. given clause #135: (wt=2) 175 [hyper,174,2,155] p04|p05. given clause #136: (wt=7) 176 [hyper,175,17,60] p04|p08|p09|p10|p12|p13|p16. given clause #137: (wt=6) 177 [hyper,176,4,155] p04|p08|p09|p10|p12|p13. given clause #138: (wt=5) 178 [hyper,177,16,175] p04|p08|p09|p10|p12. given clause #139: (wt=4) 179 [hyper,178,3,155] p04|p08|p09|p10. given clause #140: (wt=8) 180 [hyper,179,29,52] p04|p08|p09|p12|p13|p14|p16|p17. given clause #141: (wt=7) 181 [hyper,180,17,175] p04|p08|p09|p12|p13|p14|p16. given clause #142: (wt=6) 182 [hyper,181,4,155] p04|p08|p09|p12|p13|p14. given clause #143: (wt=5) 183 [hyper,182,28,179] p04|p08|p09|p12|p13. given clause #144: (wt=4) 184 [hyper,183,16,175] p04|p08|p09|p12. given clause #145: (wt=3) 185 [hyper,184,3,155] p04|p08|p09. given clause #146: (wt=2) 186 [hyper,185,15,175] p04|p08. given clause #147: (wt=1) 187 [hyper,186,2,155] p04. -------- PROOF -------- -----> EMPTY CLAUSE at 0.01 sec ----> 188 [hyper,187,1,155] $F. Length of proof is 142. Level of proof is 99. ---------------- PROOF ---------------- 1 [] -p00| -p04. 2 [] -p00| -p08. 3 [] -p00| -p12. 4 [] -p00| -p16. 5 [] -p04| -p08. 6 [] -p04| -p12. 7 [] -p04| -p16. 8 [] -p08| -p12. 9 [] -p08| -p16. 10 [] -p12| -p16. 11 [] -p01| -p05. 12 [] -p01| -p09. 13 [] -p01| -p13. 14 [] -p01| -p17. 15 [] -p05| -p09. 16 [] -p05| -p13. 17 [] -p05| -p17. 18 [] -p09| -p13. 19 [] -p09| -p17. 20 [] -p13| -p17. 21 [] -p02| -p06. 22 [] -p02| -p10. 23 [] -p02| -p14. 24 [] -p02| -p18. 25 [] -p06| -p10. 26 [] -p06| -p14. 27 [] -p06| -p18. 28 [] -p10| -p14. 29 [] -p10| -p18. 30 [] -p14| -p18. 31 [] -p03| -p07. 32 [] -p03| -p11. 33 [] -p03| -p15. 34 [] -p03| -p19. 35 [] -p07| -p11. 36 [] -p07| -p15. 37 [] -p07| -p19. 38 [] -p11| -p15. 39 [] -p11| -p19. 40 [] -p15| -p19. 41 [] p00|p01|p02|p03. 42 [] p04|p05|p06|p07. 43 [] p08|p09|p10|p11. 44 [] p12|p13|p14|p15. 45 [] p16|p17|p18|p19. 46 [hyper,42,31,41] p00|p01|p02|p04|p05|p06. 47 [hyper,43,35,42] p04|p05|p06|p08|p09|p10. 48 [hyper,43,32,41] p00|p01|p02|p08|p09|p10. 49 [hyper,44,38,43] p08|p09|p10|p12|p13|p14. 50 [hyper,44,36,42] p04|p05|p06|p12|p13|p14. 51 [hyper,44,33,41] p00|p01|p02|p12|p13|p14. 52 [hyper,45,40,44] p12|p13|p14|p16|p17|p18. 53 [hyper,45,39,43] p08|p09|p10|p16|p17|p18. 54 [hyper,45,37,42] p04|p05|p06|p16|p17|p18. 55 [hyper,45,34,41] p00|p01|p02|p16|p17|p18. 56 [hyper,48,25,46] p00|p01|p02|p04|p05|p08|p09. 57 [hyper,50,28,47] p04|p05|p06|p08|p09|p12|p13. 58 [hyper,51,28,48] p00|p01|p02|p08|p09|p12|p13. 59 [hyper,51,26,46] p00|p01|p02|p04|p05|p12|p13. 60 [hyper,53,30,49] p08|p09|p10|p12|p13|p16|p17. 61 [hyper,54,30,50] p04|p05|p06|p12|p13|p16|p17. 62 [hyper,54,29,47] p04|p05|p06|p08|p09|p16|p17. 63 [hyper,55,30,51] p00|p01|p02|p12|p13|p16|p17. 64 [hyper,55,29,48] p00|p01|p02|p08|p09|p16|p17. 65 [hyper,55,27,46] p00|p01|p02|p04|p05|p16|p17. 66 [hyper,59,18,56] p00|p01|p02|p04|p05|p08|p12. 67 [hyper,62,20,57] p04|p05|p06|p08|p09|p12|p16. 68 [hyper,64,20,58] p00|p01|p02|p08|p09|p12|p16. 69 [hyper,65,20,59] p00|p01|p02|p04|p05|p12|p16. 70 [hyper,65,19,56] p00|p01|p02|p04|p05|p08|p16. 71 [hyper,70,10,66] p00|p01|p02|p04|p05|p08. 72 [hyper,71,9,69] p00|p01|p02|p04|p05|p12. 73 [hyper,72,8,71] p00|p01|p02|p04|p05. 74 [hyper,73,17,64] p00|p01|p02|p04|p08|p09|p16. 75 [hyper,73,17,63] p00|p01|p02|p04|p12|p13|p16. 76 [hyper,73,16,58] p00|p01|p02|p04|p08|p09|p12. 77 [hyper,76,10,74] p00|p01|p02|p04|p08|p09. 78 [hyper,77,15,73] p00|p01|p02|p04|p08. 79 [hyper,78,9,75] p00|p01|p02|p04|p12|p13. 80 [hyper,79,16,73] p00|p01|p02|p04|p12. 81 [hyper,80,8,78] p00|p01|p02|p04. 82 [hyper,81,7,68] p00|p01|p02|p08|p09|p12. 83 [hyper,82,6,81] p00|p01|p02|p08|p09. 84 [hyper,83,19,63] p00|p01|p02|p08|p12|p13|p16. 85 [hyper,84,7,81] p00|p01|p02|p08|p12|p13. 86 [hyper,85,18,83] p00|p01|p02|p08|p12. 87 [hyper,86,6,81] p00|p01|p02|p08. 88 [hyper,87,5,81] p00|p01|p02. 89 [hyper,88,24,54] p00|p01|p04|p05|p06|p16|p17. 90 [hyper,88,24,53] p00|p01|p08|p09|p10|p16|p17. 91 [hyper,88,24,52] p00|p01|p12|p13|p14|p16|p17. 92 [hyper,88,23,50] p00|p01|p04|p05|p06|p12|p13. 93 [hyper,88,23,49] p00|p01|p08|p09|p10|p12|p13. 94 [hyper,88,22,47] p00|p01|p04|p05|p06|p08|p09. 95 [hyper,92,20,89] p00|p01|p04|p05|p06|p12|p16. 96 [hyper,93,20,90] p00|p01|p08|p09|p10|p12|p16. 97 [hyper,94,19,89] p00|p01|p04|p05|p06|p08|p16. 98 [hyper,94,18,92] p00|p01|p04|p05|p06|p08|p12. 99 [hyper,98,10,97] p00|p01|p04|p05|p06|p08. 100 [hyper,99,9,95] p00|p01|p04|p05|p06|p12. 101 [hyper,100,8,99] p00|p01|p04|p05|p06. 102 [hyper,101,21,88] p00|p01|p04|p05. 103 [hyper,102,17,91] p00|p01|p04|p12|p13|p14|p16. 104 [hyper,102,17,90] p00|p01|p04|p08|p09|p10|p16. 105 [hyper,102,16,93] p00|p01|p04|p08|p09|p10|p12. 106 [hyper,105,10,104] p00|p01|p04|p08|p09|p10. 107 [hyper,106,22,88] p00|p01|p04|p08|p09. 108 [hyper,107,15,102] p00|p01|p04|p08. 109 [hyper,108,9,103] p00|p01|p04|p12|p13|p14. 110 [hyper,109,23,88] p00|p01|p04|p12|p13. 111 [hyper,110,16,102] p00|p01|p04|p12. 112 [hyper,111,8,108] p00|p01|p04. 113 [hyper,112,7,96] p00|p01|p08|p09|p10|p12. 114 [hyper,113,6,112] p00|p01|p08|p09|p10. 115 [hyper,114,22,88] p00|p01|p08|p09. 116 [hyper,115,19,91] p00|p01|p08|p12|p13|p14|p16. 117 [hyper,116,7,112] p00|p01|p08|p12|p13|p14. 118 [hyper,117,23,88] p00|p01|p08|p12|p13. 119 [hyper,118,18,115] p00|p01|p08|p12. 120 [hyper,119,6,112] p00|p01|p08. 121 [hyper,120,5,112] p00|p01. 122 [hyper,121,14,62] p00|p04|p05|p06|p08|p09|p16. 123 [hyper,121,14,61] p00|p04|p05|p06|p12|p13|p16. 124 [hyper,121,14,60] p00|p08|p09|p10|p12|p13|p16. 125 [hyper,121,13,57] p00|p04|p05|p06|p08|p09|p12. 126 [hyper,125,10,122] p00|p04|p05|p06|p08|p09. 127 [hyper,126,12,121] p00|p04|p05|p06|p08. 128 [hyper,127,9,123] p00|p04|p05|p06|p12|p13. 129 [hyper,128,13,121] p00|p04|p05|p06|p12. 130 [hyper,129,8,127] p00|p04|p05|p06. 131 [hyper,130,27,53] p00|p04|p05|p08|p09|p10|p16|p17. 132 [hyper,130,27,52] p00|p04|p05|p12|p13|p14|p16|p17. 133 [hyper,130,26,49] p00|p04|p05|p08|p09|p10|p12|p13. 134 [hyper,131,14,121] p00|p04|p05|p08|p09|p10|p16. 135 [hyper,132,14,121] p00|p04|p05|p12|p13|p14|p16. 136 [hyper,133,13,121] p00|p04|p05|p08|p09|p10|p12. 137 [hyper,136,10,134] p00|p04|p05|p08|p09|p10. 138 [hyper,137,25,130] p00|p04|p05|p08|p09. 139 [hyper,138,12,121] p00|p04|p05|p08. 140 [hyper,139,9,135] p00|p04|p05|p12|p13|p14. 141 [hyper,140,26,130] p00|p04|p05|p12|p13. 142 [hyper,141,13,121] p00|p04|p05|p12. 143 [hyper,142,8,139] p00|p04|p05. 144 [hyper,143,11,121] p00|p04. 145 [hyper,144,7,124] p00|p08|p09|p10|p12|p13. 146 [hyper,145,13,121] p00|p08|p09|p10|p12. 147 [hyper,146,6,144] p00|p08|p09|p10. 148 [hyper,147,29,52] p00|p08|p09|p12|p13|p14|p16|p17. 149 [hyper,148,14,121] p00|p08|p09|p12|p13|p14|p16. 150 [hyper,149,7,144] p00|p08|p09|p12|p13|p14. 151 [hyper,150,28,147] p00|p08|p09|p12|p13. 152 [hyper,151,13,121] p00|p08|p09|p12. 153 [hyper,152,6,144] p00|p08|p09. 154 [hyper,153,12,121] p00|p08. 155 [hyper,154,5,144] p00. 156 [hyper,155,4,67] p04|p05|p06|p08|p09|p12. 157 [hyper,156,3,155] p04|p05|p06|p08|p09. 158 [hyper,157,19,61] p04|p05|p06|p08|p12|p13|p16. 159 [hyper,158,4,155] p04|p05|p06|p08|p12|p13. 160 [hyper,159,18,157] p04|p05|p06|p08|p12. 161 [hyper,160,3,155] p04|p05|p06|p08. 162 [hyper,161,2,155] p04|p05|p06. 163 [hyper,162,27,53] p04|p05|p08|p09|p10|p16|p17. 164 [hyper,162,27,52] p04|p05|p12|p13|p14|p16|p17. 165 [hyper,162,26,49] p04|p05|p08|p09|p10|p12|p13. 166 [hyper,165,20,163] p04|p05|p08|p09|p10|p12|p16. 167 [hyper,166,4,155] p04|p05|p08|p09|p10|p12. 168 [hyper,167,3,155] p04|p05|p08|p09|p10. 169 [hyper,168,25,162] p04|p05|p08|p09. 170 [hyper,169,19,164] p04|p05|p08|p12|p13|p14|p16. 171 [hyper,170,4,155] p04|p05|p08|p12|p13|p14. 172 [hyper,171,26,162] p04|p05|p08|p12|p13. 173 [hyper,172,18,169] p04|p05|p08|p12. 174 [hyper,173,3,155] p04|p05|p08. 175 [hyper,174,2,155] p04|p05. 176 [hyper,175,17,60] p04|p08|p09|p10|p12|p13|p16. 177 [hyper,176,4,155] p04|p08|p09|p10|p12|p13. 178 [hyper,177,16,175] p04|p08|p09|p10|p12. 179 [hyper,178,3,155] p04|p08|p09|p10. 180 [hyper,179,29,52] p04|p08|p09|p12|p13|p14|p16|p17. 181 [hyper,180,17,175] p04|p08|p09|p12|p13|p14|p16. 182 [hyper,181,4,155] p04|p08|p09|p12|p13|p14. 183 [hyper,182,28,179] p04|p08|p09|p12|p13. 184 [hyper,183,16,175] p04|p08|p09|p12. 185 [hyper,184,3,155] p04|p08|p09. 186 [hyper,185,15,175] p04|p08. 187 [hyper,186,2,155] p04. 188 [hyper,187,1,155] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 147 clauses generated 410 clauses kept 187 clauses forward subsumed 267 clauses back subsumed 138 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8283 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/comm.out0100664000076400007640000001534010103522153016450 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8258. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] f(e,x)=x. 0 [] f(g(x),x)=e. 0 [] f(f(x,y),z)=f(x,f(y,z)). 0 [] h(x,y)=f(x,f(y,f(g(x),g(y)))). 0 [] f(x,f(x,x))=e. 0 [] h(h(a,b),b)!=e. end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=7): 1 [] h(h(a,b),b)!=e. ------------> process sos: ** KEPT (pick-wt=3): 2 [] x=x. ** KEPT (pick-wt=5): 3 [] f(e,x)=x. ---> New Demodulator: 4 [new_demod,3] f(e,x)=x. ** KEPT (pick-wt=6): 5 [] f(g(x),x)=e. ---> New Demodulator: 6 [new_demod,5] f(g(x),x)=e. ** KEPT (pick-wt=11): 7 [] f(f(x,y),z)=f(x,f(y,z)). ---> New Demodulator: 8 [new_demod,7] f(f(x,y),z)=f(x,f(y,z)). ** KEPT (pick-wt=13): 9 [] h(x,y)=f(x,f(y,f(g(x),g(y)))). ** KEPT (pick-wt=7): 10 [] f(x,f(x,x))=e. ---> New Demodulator: 11 [new_demod,10] f(x,f(x,x))=e. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x=x. >>>> Starting back demodulation with 4. >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. ** KEPT (pick-wt=13): 12 [copy,9,flip.1] f(x,f(y,f(g(x),g(y))))=h(x,y). >>>> Starting back demodulation with 11. Following clause subsumed by 9 during input processing: 0 [copy,12,flip.1] h(x,y)=f(x,f(y,f(g(x),g(y)))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 2 [] x=x. given clause #2: (wt=5) 3 [] f(e,x)=x. given clause #3: (wt=6) 5 [] f(g(x),x)=e. given clause #4: (wt=7) 10 [] f(x,f(x,x))=e. given clause #5: (wt=11) 7 [] f(f(x,y),z)=f(x,f(y,z)). given clause #6: (wt=13) 9 [] h(x,y)=f(x,f(y,f(g(x),g(y)))). given clause #7: (wt=8) 15 [para_into,7.1.1.1,5.1.1,demod,4,flip.1] f(g(x),f(x,y))=y. given clause #8: (wt=6) 29 [para_into,15.1.1.2,3.1.1] f(g(e),x)=x. given clause #9: (wt=7) 27 [para_into,15.1.1.2,5.1.1,demod,24] f(g(x),g(x))=x. given clause #10: (wt=5) 35 [back_demod,27,demod,34,34,8,11] f(x,e)=x. given clause #11: (wt=9) 13 [para_into,7.1.1.1,10.1.1,demod,4,8,flip.1] f(x,f(x,f(x,y)))=y. given clause #12: (wt=6) 33 [para_from,27.1.1,15.1.1.2,demod,22,flip.1] g(x)=f(x,x). given clause #13: (wt=13) 17 [para_into,7.1.1,10.1.1,demod,8,flip.1] f(x,f(y,f(x,f(y,f(x,y)))))=e. given clause #14: (wt=13) 46 [para_from,17.1.1,13.1.1.2.2,demod,36,flip.1] f(x,f(y,f(x,f(y,x))))=f(y,y). given clause #15: (wt=15) 41 [back_demod,12,demod,34,34,8,flip.1] h(x,y)=f(x,f(y,f(x,f(x,f(y,y))))). given clause #16: (wt=25) 43 [back_demod,40,demod,42,42,42,8,8,8,8,8,11,36,8,8,8,8,8,8,8,8,8,8,14,14] f(a,f(b,f(b,f(a,f(a,f(b,f(b,f(a,f(b,f(a,f(a,b)))))))))))!=e. given clause #17: (wt=15) 50 [para_from,46.1.1,13.1.1.2.2] f(x,f(x,f(y,y)))=f(y,f(x,f(y,x))). given clause #18: (wt=15) 53 [copy,50,flip.1] f(x,f(y,f(x,y)))=f(y,f(y,f(x,x))). given clause #19: (wt=17) 51 [para_from,46.1.1,7.1.1.1,demod,8,8,8,8,flip.1] f(x,f(y,f(x,f(y,f(x,z)))))=f(y,f(y,z)). given clause #20: (wt=17) 64 [para_from,53.1.1,13.1.1.2.2] f(x,f(x,f(y,f(y,f(x,x)))))=f(y,f(x,y)). given clause #21: (wt=21) 48 [para_into,46.1.1.2.2.2,7.1.1,demod,8,8] f(x,f(y,f(z,f(x,f(y,f(z,x))))))=f(y,f(z,f(y,z))). given clause #22: (wt=17) 65 [copy,64,flip.1] f(x,f(y,x))=f(y,f(y,f(x,f(x,f(y,y))))). given clause #23: (wt=19) 58 [para_from,50.1.1,7.1.1.1,demod,8,8,8,8,8] f(x,f(y,f(x,f(y,z))))=f(y,f(y,f(x,f(x,z)))). -------- PROOF -------- ----> UNIT CONFLICT at 0.01 sec ----> 159 [binary,158.1,2.1] $F. Length of proof is 19. Level of proof is 9. ---------------- PROOF ---------------- 1 [] h(h(a,b),b)!=e. 2 [] x=x. 4,3 [] f(e,x)=x. 5 [] f(g(x),x)=e. 8,7 [] f(f(x,y),z)=f(x,f(y,z)). 9 [] h(x,y)=f(x,f(y,f(g(x),g(y)))). 11,10 [] f(x,f(x,x))=e. 12 [copy,9,flip.1] f(x,f(y,f(g(x),g(y))))=h(x,y). 14,13 [para_into,7.1.1.1,10.1.1,demod,4,8,flip.1] f(x,f(x,f(x,y)))=y. 15 [para_into,7.1.1.1,5.1.1,demod,4,flip.1] f(g(x),f(x,y))=y. 17 [para_into,7.1.1,10.1.1,demod,8,flip.1] f(x,f(y,f(x,f(y,f(x,y)))))=e. 19 [para_from,9.1.1,1.1.1] f(h(a,b),f(b,f(g(h(a,b)),g(b))))!=e. 22,21 [para_into,15.1.1.2,15.1.1] f(g(g(x)),y)=f(x,y). 24,23 [para_into,15.1.1.2,10.1.1] f(g(x),e)=f(x,x). 27 [para_into,15.1.1.2,5.1.1,demod,24] f(g(x),g(x))=x. 34,33 [para_from,27.1.1,15.1.1.2,demod,22,flip.1] g(x)=f(x,x). 36,35 [back_demod,27,demod,34,34,8,11] f(x,e)=x. 40 [back_demod,19,demod,34,34,8] f(h(a,b),f(b,f(h(a,b),f(h(a,b),f(b,b)))))!=e. 42,41 [back_demod,12,demod,34,34,8,flip.1] h(x,y)=f(x,f(y,f(x,f(x,f(y,y))))). 43 [back_demod,40,demod,42,42,42,8,8,8,8,8,11,36,8,8,8,8,8,8,8,8,8,8,14,14] f(a,f(b,f(b,f(a,f(a,f(b,f(b,f(a,f(b,f(a,f(a,b)))))))))))!=e. 47,46 [para_from,17.1.1,13.1.1.2.2,demod,36,flip.1] f(x,f(y,f(x,f(y,x))))=f(y,y). 50 [para_from,46.1.1,13.1.1.2.2] f(x,f(x,f(y,y)))=f(y,f(x,f(y,x))). 51 [para_from,46.1.1,7.1.1.1,demod,8,8,8,8,flip.1] f(x,f(y,f(x,f(y,f(x,z)))))=f(y,f(y,z)). 58 [para_from,50.1.1,7.1.1.1,demod,8,8,8,8,8] f(x,f(y,f(x,f(y,z))))=f(y,f(y,f(x,f(x,z)))). 73,72 [para_into,51.1.1.2.2.2,7.1.1,demod,8,8,8] f(x,f(y,f(z,f(x,f(y,f(z,f(x,u)))))))=f(y,f(z,f(y,f(z,u)))). 158 [para_from,58.1.1,43.1.1.2.2.2.2.2.2,demod,73,14,47,11] e!=e. 159 [binary,158.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 23 clauses generated 419 clauses kept 118 clauses forward subsumed 399 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8258 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/salt.out0100664000076400007640000003455010103522154016465 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8298. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] sl| -mb| -sb| -sm| -ml|sc|mc|sd|md|mm. 0 [] -sm|mb|ml. 0 [] -sm|mb|sl. 0 [] -sm|sb|ml. 0 [] -sm|sb|sl. 0 [] -ml| -mc| -mm. 0 [] -ml| -mc| -sm. 0 [] -ml| -sc| -mm. 0 [] -ml| -sc| -sm. 0 [] -md| -ml| -mm. 0 [] -md| -ml| -sm. 0 [] -md| -sl| -mm. 0 [] -md| -sl| -sm. 0 [] -sd| -mb|mc. 0 [] -sd| -mb|sc. 0 [] -sd| -sb|mc. 0 [] -sd| -sb|sc. 0 [] -mc|md|ml. 0 [] -mc|md|sl. 0 [] -mc|sd|ml. 0 [] -mc|sd|sl. 0 [] -mb| -md|mm. 0 [] -mb| -md|sm. 0 [] -mb| -sd|mm. 0 [] -mb| -sd|sm. 0 [] sd| -md|mm. 0 [] -sd|md|mm. 0 [] sc| -mc|mm. 0 [] -sc|mc|mm. 0 [] -sl| -ml|sm. 0 [] -sb| -mb|sm. 0 [] sd| -md|sl. 0 [] -sd|md|sl. 0 [] sb| -mb|sl. 0 [] -sb|mb|sl. 0 [] -sc| -mc|sd. 0 [] -sl| -ml|mc. 0 [] -sd| -md|mc. 0 [] sb| -mb|sc. 0 [] -sb|mb|sc. 0 [] -sm| -mm|mb. 0 [] sl| -ml|sb. 0 [] -sl|ml|sb. 0 [] sc| -mc|sb. 0 [] -sc|mc|sb. 0 [] -sc| -mb| -sb| -mm. 0 [] -sc| -mb| -sb| -sm. 0 [] -sc|sb|mb| -mm. 0 [] -sc|sb|mb| -sm. 0 [] -mm| -mc| -sc| -md| -sd. 0 [] -mm|sc|mc|sd|md. 0 [] -sl| -mb| -sb| -md| -sd. 0 [] -sl| -mb| -sb|sd|md. 0 [] -sl|sb|mb| -md| -sd. 0 [] -sb| -mc| -sc| -ml| -sl. 0 [] -sb| -mc| -sc|sl|ml. 0 [] sm|mm|ml. 0 [] sc|mc|ml. 0 [] sm|mm|md. 0 [] sl|ml|md. 0 [] sb|mb|sd. 0 [] sm|mm|sc. 0 [] sd|md|mb. end_of_list. SCAN INPUT: prop=1, horn=0, equality=0, symmetry=0, max_lits=10. The clause set is propositional; the strategy will be ordered hyperresolution with the propositional optimizations, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: set(propositional). dependent: set(sort_literals). ------------> process usable: ** KEPT (pick-wt=10): 2 [copy,1,propositional] -mb| -sb| -sm| -ml|sl|sc|mc|sd|md|mm. ** KEPT (pick-wt=3): 3 [] -sm|mb|ml. ** KEPT (pick-wt=3): 5 [copy,4,propositional] -sm|sl|mb. ** KEPT (pick-wt=3): 6 [] -sm|sb|ml. ** KEPT (pick-wt=3): 8 [copy,7,propositional] -sm|sl|sb. ** KEPT (pick-wt=3): 9 [] -ml| -mc| -mm. ** KEPT (pick-wt=3): 11 [copy,10,propositional] -sm| -ml| -mc. ** KEPT (pick-wt=3): 12 [] -ml| -sc| -mm. ** KEPT (pick-wt=3): 14 [copy,13,propositional] -sm| -ml| -sc. ** KEPT (pick-wt=3): 16 [copy,15,propositional] -ml| -md| -mm. ** KEPT (pick-wt=3): 18 [copy,17,propositional] -sm| -ml| -md. ** KEPT (pick-wt=3): 20 [copy,19,propositional] -sl| -md| -mm. ** KEPT (pick-wt=3): 22 [copy,21,propositional] -sl| -sm| -md. ** KEPT (pick-wt=3): 24 [copy,23,propositional] -mb| -sd|mc. ** KEPT (pick-wt=3): 26 [copy,25,propositional] -mb| -sd|sc. ** KEPT (pick-wt=3): 28 [copy,27,propositional] -sb| -sd|mc. ** KEPT (pick-wt=3): 30 [copy,29,propositional] -sb| -sd|sc. ** KEPT (pick-wt=3): 32 [copy,31,propositional] -mc|ml|md. ** KEPT (pick-wt=3): 34 [copy,33,propositional] -mc|sl|md. ** KEPT (pick-wt=3): 36 [copy,35,propositional] -mc|ml|sd. ** KEPT (pick-wt=3): 38 [copy,37,propositional] -mc|sl|sd. ** KEPT (pick-wt=3): 39 [] -mb| -md|mm. ** KEPT (pick-wt=3): 40 [] -mb| -md|sm. ** KEPT (pick-wt=3): 41 [] -mb| -sd|mm. ** KEPT (pick-wt=3): 42 [] -mb| -sd|sm. ** KEPT (pick-wt=3): 44 [copy,43,propositional] -md|sd|mm. ** KEPT (pick-wt=3): 45 [] -sd|md|mm. ** KEPT (pick-wt=3): 47 [copy,46,propositional] -mc|sc|mm. ** KEPT (pick-wt=3): 48 [] -sc|mc|mm. ** KEPT (pick-wt=3): 49 [] -sl| -ml|sm. ** KEPT (pick-wt=3): 51 [copy,50,propositional] -mb| -sb|sm. ** KEPT (pick-wt=3): 53 [copy,52,propositional] -md|sl|sd. ** KEPT (pick-wt=3): 55 [copy,54,propositional] -sd|sl|md. ** KEPT (pick-wt=3): 57 [copy,56,propositional] -mb|sl|sb. ** KEPT (pick-wt=3): 59 [copy,58,propositional] -sb|sl|mb. ** KEPT (pick-wt=3): 60 [] -sc| -mc|sd. ** KEPT (pick-wt=3): 61 [] -sl| -ml|mc. ** KEPT (pick-wt=3): 62 [] -sd| -md|mc. ** KEPT (pick-wt=3): 64 [copy,63,propositional] -mb|sb|sc. ** KEPT (pick-wt=3): 65 [] -sb|mb|sc. ** KEPT (pick-wt=3): 66 [] -sm| -mm|mb. ** KEPT (pick-wt=3): 68 [copy,67,propositional] -ml|sl|sb. ** KEPT (pick-wt=3): 70 [copy,69,propositional] -sl|sb|ml. ** KEPT (pick-wt=3): 72 [copy,71,propositional] -mc|sb|sc. ** KEPT (pick-wt=3): 74 [copy,73,propositional] -sc|sb|mc. ** KEPT (pick-wt=4): 76 [copy,75,propositional] -mb| -sb| -sc| -mm. ** KEPT (pick-wt=4): 78 [copy,77,propositional] -mb| -sb| -sm| -sc. ** KEPT (pick-wt=4): 80 [copy,79,propositional] -sc| -mm|mb|sb. ** KEPT (pick-wt=4): 82 [copy,81,propositional] -sm| -sc|mb|sb. ** KEPT (pick-wt=5): 84 [copy,83,propositional] -sc| -mc| -sd| -md| -mm. ** KEPT (pick-wt=5): 85 [] -mm|sc|mc|sd|md. ** KEPT (pick-wt=5): 87 [copy,86,propositional] -sl| -mb| -sb| -sd| -md. ** KEPT (pick-wt=5): 88 [] -sl| -mb| -sb|sd|md. ** KEPT (pick-wt=5): 90 [copy,89,propositional] -sl| -sd| -md|mb|sb. ** KEPT (pick-wt=5): 92 [copy,91,propositional] -sl| -sb| -ml| -sc| -mc. ** KEPT (pick-wt=5): 94 [copy,93,propositional] -sb| -sc| -mc|sl|ml. ------------> process sos: ** KEPT (pick-wt=3): 96 [copy,95,propositional] sm|ml|mm. ** KEPT (pick-wt=3): 98 [copy,97,propositional] ml|sc|mc. ** KEPT (pick-wt=3): 100 [copy,99,propositional] sm|md|mm. ** KEPT (pick-wt=3): 101 [] sl|ml|md. ** KEPT (pick-wt=3): 103 [copy,102,propositional] mb|sb|sd. ** KEPT (pick-wt=3): 105 [copy,104,propositional] sm|sc|mm. ** KEPT (pick-wt=3): 107 [copy,106,propositional] mb|sd|md. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 96 [copy,95,propositional] sm|ml|mm. given clause #2: (wt=3) 98 [copy,97,propositional] ml|sc|mc. given clause #3: (wt=3) 100 [copy,99,propositional] sm|md|mm. given clause #4: (wt=3) 101 [] sl|ml|md. given clause #5: (wt=3) 103 [copy,102,propositional] mb|sb|sd. given clause #6: (wt=3) 105 [copy,104,propositional] sm|sc|mm. given clause #7: (wt=3) 107 [copy,106,propositional] mb|sd|md. given clause #8: (wt=3) 109 [hyper,96,6] sb|ml|mm. given clause #9: (wt=3) 111 [hyper,96,3] mb|ml|mm. given clause #10: (wt=3) 112 [hyper,98,74] sb|ml|mc. given clause #11: (wt=3) 113 [hyper,98,48] ml|mc|mm. given clause #12: (wt=3) 116 [hyper,101,70] sb|ml|md. given clause #13: (wt=3) 121 [hyper,107,55] sl|mb|md. given clause #14: (wt=3) 122 [hyper,107,45] mb|md|mm. given clause #15: (wt=4) 114 [hyper,100,8] sl|sb|md|mm. given clause #16: (wt=4) 119 [hyper,105,8] sl|sb|sc|mm. given clause #17: (wt=4) 120 [hyper,105,5] sl|mb|sc|mm. given clause #18: (wt=4) 123 [hyper,112,59] sl|mb|ml|mc. given clause #19: (wt=4) 124 [hyper,112,28,107] mb|ml|mc|md. given clause #20: (wt=3) 126 [hyper,124,61,121] mb|mc|md. given clause #21: (wt=4) 125 [hyper,116,65] mb|ml|sc|md. given clause #22: (wt=3) 128 [hyper,126,62,103] mb|sb|mc. given clause #23: (wt=3) 132 [hyper,126,20,123,113] mb|ml|mc. given clause #24: (wt=3) 133 [hyper,128,65] mb|sc|mc. given clause #25: (wt=3) 134 [hyper,128,59] sl|mb|mc. given clause #26: (wt=2) 136 [hyper,134,61,132] mb|mc. given clause #27: (wt=3) 137 [hyper,136,72] mb|sb|sc. given clause #28: (wt=3) 138 [hyper,136,47] mb|sc|mm. given clause #29: (wt=3) 139 [hyper,136,38] sl|mb|sd. given clause #30: (wt=3) 140 [hyper,136,36] mb|ml|sd. given clause #31: (wt=3) 141 [hyper,136,32] mb|ml|md. given clause #32: (wt=2) 146 [hyper,141,9,136,122] mb|md. given clause #33: (wt=3) 143 [hyper,137,80,111] mb|sb|ml. given clause #34: (wt=3) 144 [hyper,138,60,136] mb|sd|mm. given clause #35: (wt=3) 147 [hyper,143,65] mb|ml|sc. given clause #36: (wt=2) 149 [hyper,147,84,136,140,146,111] mb|ml. given clause #37: (wt=3) 150 [hyper,149,68] sl|mb|sb. given clause #38: (wt=2) 153 [hyper,150,90,103,146] mb|sb. given clause #39: (wt=2) 154 [hyper,153,65] mb|sc. given clause #40: (wt=2) 155 [hyper,153,59] sl|mb. given clause #41: (wt=1) 157 [hyper,155,92,153,149,154,136] mb. given clause #42: (wt=2) 160 [hyper,157,76,112,98,113] ml|mc. given clause #43: (wt=2) 161 [hyper,157,64] sb|sc. given clause #44: (wt=2) 162 [hyper,157,57] sl|sb. given clause #45: (wt=2) 164 [hyper,161,74] sb|mc. given clause #46: (wt=3) 158 [hyper,157,88,101,116] ml|sd|md. given clause #47: (wt=2) 165 [hyper,162,70] sb|ml. given clause #48: (wt=2) 166 [hyper,164,51,157] sm|mc. given clause #49: (wt=2) 170 [hyper,165,51,157] sm|ml. given clause #50: (wt=3) 168 [hyper,158,45] ml|md|mm. given clause #51: (wt=6) 167 [hyper,164,2,157,105,160] sl|sc|mc|sd|md|mm. given clause #52: (wt=3) 169 [hyper,158,26,157] ml|sc|md. given clause #53: (wt=2) 172 [hyper,169,78,157,165,170] ml|md. given clause #54: (wt=3) 173 [hyper,172,49,162] sb|sm|md. given clause #55: (wt=2) 175 [hyper,173,14,172,161] sb|md. given clause #56: (wt=5) 171 [hyper,167,88,157,164] sc|mc|sd|md|mm. given clause #57: (wt=2) 176 [hyper,175,51,157] sm|md. given clause #58: (wt=4) 178 [hyper,171,45] sc|mc|md|mm. given clause #59: (wt=3) 179 [hyper,178,78,157,175,176] mc|md|mm. given clause #60: (wt=4) 180 [hyper,179,85] sc|mc|sd|md. given clause #61: (wt=3) 182 [hyper,180,30,175] sc|mc|md. given clause #62: (wt=2) 183 [hyper,182,78,157,175,176] mc|md. given clause #63: (wt=1) 187 [hyper,183,18,166,160] mc. given clause #64: (wt=1) 193 [hyper,187,11,176,172] md. given clause #65: (wt=1) 195 [hyper,193,40,157] sm. given clause #66: (wt=2) 190 [hyper,187,38] sl|sd. given clause #67: (wt=1) 196 [hyper,193,39,157] mm. given clause #68: (wt=1) 197 [hyper,195,22,162,193] sb. given clause #69: (wt=1) 198 [hyper,190,22,195,193] sd. given clause #70: (wt=1) 199 [hyper,198,30,197] sc. -------- PROOF -------- -----> EMPTY CLAUSE at 0.01 sec ----> 201 [hyper,199,84,187,198,193,196] $F. Length of proof is 85. Level of proof is 31. ---------------- PROOF ---------------- 1 [] sl| -mb| -sb| -sm| -ml|sc|mc|sd|md|mm. 2 [copy,1,propositional] -mb| -sb| -sm| -ml|sl|sc|mc|sd|md|mm. 3 [] -sm|mb|ml. 9 [] -ml| -mc| -mm. 10 [] -ml| -mc| -sm. 11 [copy,10,propositional] -sm| -ml| -mc. 13 [] -ml| -sc| -sm. 14 [copy,13,propositional] -sm| -ml| -sc. 17 [] -md| -ml| -sm. 18 [copy,17,propositional] -sm| -ml| -md. 19 [] -md| -sl| -mm. 20 [copy,19,propositional] -sl| -md| -mm. 21 [] -md| -sl| -sm. 22 [copy,21,propositional] -sl| -sm| -md. 25 [] -sd| -mb|sc. 26 [copy,25,propositional] -mb| -sd|sc. 27 [] -sd| -sb|mc. 28 [copy,27,propositional] -sb| -sd|mc. 29 [] -sd| -sb|sc. 30 [copy,29,propositional] -sb| -sd|sc. 31 [] -mc|md|ml. 32 [copy,31,propositional] -mc|ml|md. 35 [] -mc|sd|ml. 36 [copy,35,propositional] -mc|ml|sd. 37 [] -mc|sd|sl. 38 [copy,37,propositional] -mc|sl|sd. 39 [] -mb| -md|mm. 40 [] -mb| -md|sm. 45 [] -sd|md|mm. 48 [] -sc|mc|mm. 49 [] -sl| -ml|sm. 50 [] -sb| -mb|sm. 51 [copy,50,propositional] -mb| -sb|sm. 54 [] -sd|md|sl. 55 [copy,54,propositional] -sd|sl|md. 56 [] sb| -mb|sl. 57 [copy,56,propositional] -mb|sl|sb. 58 [] -sb|mb|sl. 59 [copy,58,propositional] -sb|sl|mb. 61 [] -sl| -ml|mc. 62 [] -sd| -md|mc. 63 [] sb| -mb|sc. 64 [copy,63,propositional] -mb|sb|sc. 65 [] -sb|mb|sc. 67 [] sl| -ml|sb. 68 [copy,67,propositional] -ml|sl|sb. 69 [] -sl|ml|sb. 70 [copy,69,propositional] -sl|sb|ml. 71 [] sc| -mc|sb. 72 [copy,71,propositional] -mc|sb|sc. 73 [] -sc|mc|sb. 74 [copy,73,propositional] -sc|sb|mc. 75 [] -sc| -mb| -sb| -mm. 76 [copy,75,propositional] -mb| -sb| -sc| -mm. 77 [] -sc| -mb| -sb| -sm. 78 [copy,77,propositional] -mb| -sb| -sm| -sc. 79 [] -sc|sb|mb| -mm. 80 [copy,79,propositional] -sc| -mm|mb|sb. 83 [] -mm| -mc| -sc| -md| -sd. 84 [copy,83,propositional] -sc| -mc| -sd| -md| -mm. 85 [] -mm|sc|mc|sd|md. 88 [] -sl| -mb| -sb|sd|md. 89 [] -sl|sb|mb| -md| -sd. 90 [copy,89,propositional] -sl| -sd| -md|mb|sb. 91 [] -sb| -mc| -sc| -ml| -sl. 92 [copy,91,propositional] -sl| -sb| -ml| -sc| -mc. 95 [] sm|mm|ml. 96 [copy,95,propositional] sm|ml|mm. 97 [] sc|mc|ml. 98 [copy,97,propositional] ml|sc|mc. 101 [] sl|ml|md. 102 [] sb|mb|sd. 103 [copy,102,propositional] mb|sb|sd. 104 [] sm|mm|sc. 105 [copy,104,propositional] sm|sc|mm. 106 [] sd|md|mb. 107 [copy,106,propositional] mb|sd|md. 111 [hyper,96,3] mb|ml|mm. 112 [hyper,98,74] sb|ml|mc. 113 [hyper,98,48] ml|mc|mm. 116 [hyper,101,70] sb|ml|md. 121 [hyper,107,55] sl|mb|md. 122 [hyper,107,45] mb|md|mm. 123 [hyper,112,59] sl|mb|ml|mc. 124 [hyper,112,28,107] mb|ml|mc|md. 126 [hyper,124,61,121] mb|mc|md. 128 [hyper,126,62,103] mb|sb|mc. 132 [hyper,126,20,123,113] mb|ml|mc. 134 [hyper,128,59] sl|mb|mc. 136 [hyper,134,61,132] mb|mc. 137 [hyper,136,72] mb|sb|sc. 140 [hyper,136,36] mb|ml|sd. 141 [hyper,136,32] mb|ml|md. 143 [hyper,137,80,111] mb|sb|ml. 146 [hyper,141,9,136,122] mb|md. 147 [hyper,143,65] mb|ml|sc. 149 [hyper,147,84,136,140,146,111] mb|ml. 150 [hyper,149,68] sl|mb|sb. 153 [hyper,150,90,103,146] mb|sb. 154 [hyper,153,65] mb|sc. 155 [hyper,153,59] sl|mb. 157 [hyper,155,92,153,149,154,136] mb. 158 [hyper,157,88,101,116] ml|sd|md. 160 [hyper,157,76,112,98,113] ml|mc. 161 [hyper,157,64] sb|sc. 162 [hyper,157,57] sl|sb. 164 [hyper,161,74] sb|mc. 165 [hyper,162,70] sb|ml. 166 [hyper,164,51,157] sm|mc. 167 [hyper,164,2,157,105,160] sl|sc|mc|sd|md|mm. 169 [hyper,158,26,157] ml|sc|md. 170 [hyper,165,51,157] sm|ml. 171 [hyper,167,88,157,164] sc|mc|sd|md|mm. 172 [hyper,169,78,157,165,170] ml|md. 173 [hyper,172,49,162] sb|sm|md. 175 [hyper,173,14,172,161] sb|md. 176 [hyper,175,51,157] sm|md. 178 [hyper,171,45] sc|mc|md|mm. 179 [hyper,178,78,157,175,176] mc|md|mm. 180 [hyper,179,85] sc|mc|sd|md. 182 [hyper,180,30,175] sc|mc|md. 183 [hyper,182,78,157,175,176] mc|md. 187 [hyper,183,18,166,160] mc. 190 [hyper,187,38] sl|sd. 193 [hyper,187,11,176,172] md. 195 [hyper,193,40,157] sm. 196 [hyper,193,39,157] mm. 197 [hyper,195,22,162,193] sb. 198 [hyper,190,22,195,193] sd. 199 [hyper,198,30,197] sc. 201 [hyper,199,84,187,198,193,196] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 70 clauses generated 796 clauses kept 156 clauses forward subsumed 702 clauses back subsumed 133 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8298 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/lifsch.out0100664000076400007640000001532510103522153016770 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8273. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). formula_list(usable). -(exists x x1 all y exists z z1 ((-p(y,y)|p(x,x)| -s(z,x))& (s(x,y)| -s(y,z)|q(z1,z1))& (q(x1,y)| -q(y,z1)|s(x1,x1)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] p($f1(x,x1),$f1(x,x1))| -s(x,$f1(x,x1))| -q(x1,$f1(x,x1)). 0 [] p($f1(x,x1),$f1(x,x1))| -s(x,$f1(x,x1))|q($f1(x,x1),z1). 0 [] p($f1(x,x1),$f1(x,x1))| -s(x,$f1(x,x1))| -s(x1,x1). 0 [] p($f1(x,x1),$f1(x,x1))|s($f1(x,x1),z)| -q(x1,$f1(x,x1)). 0 [] p($f1(x,x1),$f1(x,x1))|s($f1(x,x1),z)|q($f1(x,x1),z1). 0 [] p($f1(x,x1),$f1(x,x1))|s($f1(x,x1),z)| -s(x1,x1). 0 [] p($f1(x,x1),$f1(x,x1))| -q(z1,z1)| -q(x1,$f1(x,x1)). 0 [] p($f1(x,x1),$f1(x,x1))| -q(z1,z1)|q($f1(x,x1),z1). 0 [] p($f1(x,x1),$f1(x,x1))| -q(z1,z1)| -s(x1,x1). 0 [] -p(x,x)| -s(x,$f1(x,x1))| -q(x1,$f1(x,x1)). 0 [] -p(x,x)| -s(x,$f1(x,x1))|q($f1(x,x1),z1). 0 [] -p(x,x)| -s(x,$f1(x,x1))| -s(x1,x1). 0 [] -p(x,x)|s($f1(x,x1),z)| -q(x1,$f1(x,x1)). 0 [] -p(x,x)|s($f1(x,x1),z)|q($f1(x,x1),z1). 0 [] -p(x,x)|s($f1(x,x1),z)| -s(x1,x1). 0 [] -p(x,x)| -q(z1,z1)| -q(x1,$f1(x,x1)). 0 [] -p(x,x)| -q(z1,z1)|q($f1(x,x1),z1). 0 [] -p(x,x)| -q(z1,z1)| -s(x1,x1). 0 [] s(z,x)| -s(x,$f1(x,x1))| -q(x1,$f1(x,x1)). 0 [] s(z,x)| -s(x,$f1(x,x1))|q($f1(x,x1),z1). 0 [] s(z,x)| -s(x,$f1(x,x1))| -s(x1,x1). 0 [] s(z,x)|s($f1(x,x1),z)| -q(x1,$f1(x,x1)). 0 [] s(z,x)|s($f1(x,x1),z)|q($f1(x,x1),z1). 0 [] s(z,x)|s($f1(x,x1),z)| -s(x1,x1). 0 [] s(z,x)| -q(z1,z1)| -q(x1,$f1(x,x1)). 0 [] s(z,x)| -q(z1,z1)|q($f1(x,x1),z1). 0 [] s(z,x)| -q(z1,z1)| -s(x1,x1). end_of_list. SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. dependent: set(hyper_res). dependent: set(factor). dependent: set(unit_deletion). ------------> process usable: ** KEPT (pick-wt=17): 1 [] p($f1(x,y),$f1(x,y))| -s(x,$f1(x,y))| -q(y,$f1(x,y)). ** KEPT (pick-wt=17): 2 [] p($f1(x,y),$f1(x,y))| -s(x,$f1(x,y))|q($f1(x,y),z). ** KEPT (pick-wt=15): 3 [] p($f1(x,y),$f1(x,y))| -s(x,$f1(x,y))| -s(y,y). ** KEPT (pick-wt=17): 4 [] p($f1(x,y),$f1(x,y))|s($f1(x,y),z)| -q(y,$f1(x,y)). ** KEPT (pick-wt=15): 5 [] p($f1(x,y),$f1(x,y))|s($f1(x,y),z)| -s(y,y). ** KEPT (pick-wt=15): 6 [] p($f1(x,y),$f1(x,y))| -q(z,z)| -q(y,$f1(x,y)). ** KEPT (pick-wt=15): 7 [] p($f1(x,y),$f1(x,y))| -q(z,z)|q($f1(x,y),z). ** KEPT (pick-wt=13): 8 [] p($f1(x,y),$f1(x,y))| -q(z,z)| -s(y,y). ** KEPT (pick-wt=13): 9 [] -p(x,x)| -s(x,$f1(x,y))| -q(y,$f1(x,y)). ** KEPT (pick-wt=13): 10 [] -p(x,x)| -s(x,$f1(x,y))|q($f1(x,y),z). ** KEPT (pick-wt=11): 11 [] -p(x,x)| -s(x,$f1(x,y))| -s(y,y). ** KEPT (pick-wt=13): 12 [] -p(x,x)|s($f1(x,y),z)| -q(y,$f1(x,y)). ** KEPT (pick-wt=13): 13 [] -p(x,x)|s($f1(x,y),z)|q($f1(x,y),u). ** KEPT (pick-wt=11): 14 [] -p(x,x)|s($f1(x,y),z)| -s(y,y). ** KEPT (pick-wt=11): 15 [] -p(x,x)| -q(y,y)| -q(z,$f1(x,z)). ** KEPT (pick-wt=11): 16 [] -p(x,x)| -q(y,y)|q($f1(x,z),y). ** KEPT (pick-wt=9): 17 [] -p(x,x)| -q(y,y)| -s(z,z). ** KEPT (pick-wt=13): 18 [] s(x,y)| -s(y,$f1(y,z))| -q(z,$f1(y,z)). ** KEPT (pick-wt=13): 19 [] s(x,y)| -s(y,$f1(y,z))|q($f1(y,z),u). ** KEPT (pick-wt=11): 20 [] s(x,y)| -s(y,$f1(y,z))| -s(z,z). ** KEPT (pick-wt=13): 21 [] s(x,y)|s($f1(y,z),x)| -q(z,$f1(y,z)). ** KEPT (pick-wt=11): 22 [] s(x,y)|s($f1(y,z),x)| -s(z,z). ** KEPT (pick-wt=11): 23 [] s(x,y)| -q(z,z)| -q(u,$f1(y,u)). ** KEPT (pick-wt=11): 24 [] s(x,y)| -q(z,z)|q($f1(y,u),z). ** KEPT (pick-wt=9): 25 [] s(x,y)| -q(z,z)| -s(u,u). ------------> process sos: ** KEPT (pick-wt=17): 26 [] p($f1(x,y),$f1(x,y))|s($f1(x,y),z)|q($f1(x,y),u). ** KEPT (pick-wt=13): 27 [] s(x,y)|s($f1(y,z),x)|q($f1(y,z),u). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=17) 26 [] p($f1(x,y),$f1(x,y))|s($f1(x,y),z)|q($f1(x,y),u). given clause #2: (wt=13) 27 [] s(x,y)|s($f1(y,z),x)|q($f1(y,z),u). given clause #3: (wt=17) 29 [hyper,26,20,26,factor_simp,factor_simp] p($f1(x,y),$f1(x,y))|q($f1(x,y),z)|s(u,$f1(x,y)). given clause #4: (wt=12) 60 [hyper,29,2,factor_simp,factor_simp] p($f1(x,y),$f1(x,y))|q($f1(x,y),z). given clause #5: (wt=10) 63 [hyper,60,23,60,factor_simp] p($f1(x,y),$f1(x,y))|s(z,u). given clause #6: (wt=18) 34 [hyper,27,22] s($f1(x,y),x)|q($f1(x,y),z)|s(u,v)|s($f1(v,x),u). given clause #7: (wt=7) 65 [hyper,63,8,60,factor_simp,factor_simp] p($f1(x,y),$f1(x,y)). given clause #8: (wt=14) 111 [hyper,65,13] s($f1($f1(x,y),z),u)|q($f1($f1(x,y),z),v). given clause #9: (wt=7) 117 [hyper,111,11,65,111,factor_simp] q($f1($f1(x,y),z),u). -------- PROOF -------- -----> EMPTY CLAUSE at 0.02 sec ----> 122 [hyper,117,15,65,117] $F. Length of proof is 6. Level of proof is 6. ---------------- PROOF ---------------- 2 [] p($f1(x,y),$f1(x,y))| -s(x,$f1(x,y))|q($f1(x,y),z). 8 [] p($f1(x,y),$f1(x,y))| -q(z,z)| -s(y,y). 11 [] -p(x,x)| -s(x,$f1(x,y))| -s(y,y). 13 [] -p(x,x)|s($f1(x,y),z)|q($f1(x,y),u). 15 [] -p(x,x)| -q(y,y)| -q(z,$f1(x,z)). 20 [] s(x,y)| -s(y,$f1(y,z))| -s(z,z). 23 [] s(x,y)| -q(z,z)| -q(u,$f1(y,u)). 26 [] p($f1(x,y),$f1(x,y))|s($f1(x,y),z)|q($f1(x,y),u). 29 [hyper,26,20,26,factor_simp,factor_simp] p($f1(x,y),$f1(x,y))|q($f1(x,y),z)|s(u,$f1(x,y)). 60 [hyper,29,2,factor_simp,factor_simp] p($f1(x,y),$f1(x,y))|q($f1(x,y),z). 63 [hyper,60,23,60,factor_simp] p($f1(x,y),$f1(x,y))|s(z,u). 65 [hyper,63,8,60,factor_simp,factor_simp] p($f1(x,y),$f1(x,y)). 111 [hyper,65,13] s($f1($f1(x,y),z),u)|q($f1($f1(x,y),z),v). 117 [hyper,111,11,65,111,factor_simp] q($f1($f1(x,y),z),u). 122 [hyper,117,15,65,117] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 9 clauses generated 283 clauses kept 121 clauses forward subsumed 188 clauses back subsumed 83 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8273 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/sam.in0100644000076400007640000000177705470212344016114 0ustar mccunemccune% % SAM's Lemma in the P-formulation with hyperresolution % This is not a complete axiomatization, because closure % and function symbols are not included. % set(auto). list(usable). join(1,x,1). join(x,1,1). join(0,x,x). join(x,0,x). meet(0,x,0). meet(x,0,0). meet(1,x,x). meet(x,1,x). meet(x,x,x). join(x,x,x). -meet(x,y,z) | meet(y,x,z). -join(x,y,z) | join(y,x,z). -meet(x,y,z) | join(x,z,x). -join(x,y,z) | meet(x,z,x). -meet(x,y,xy) | -meet(y,z,yz) | -meet(x,yz,xyz) | meet(xy,z,xyz). -meet(x,y,xy) | -meet(y,z,yz) | -meet(xy,z,xyz) | meet(x,yz,xyz). -join(x,y,xy) | -join(y,z,yz) | -join(x,yz,xyz) | join(xy,z,xyz). -join(x,y,xy) | -join(y,z,yz) | -join(xy,z,xyz) | join(x,yz,xyz). -meet(x,z,x) | -join(x,y,x1) | -meet(y,z,y1) | -meet(z,x1,z1) | join(x,y1,z1). -meet(x,z,x) | -join(x,y,x1) | -meet(y,z,y1) | -join(x,y1,z1) | meet(z,x1,z1). -meet(a2,b2,r1). meet(a,b,c). join(c,r2,1). meet(c,r2,0). meet(r2,b,e). join(a,b,c2). join(c2,r1,1). meet(c2,r1,0). meet(r2,a,d). join(r1,e,a2). join(r1,d,b2). end_of_list. otter-3.3f/examples/auto/steam.out0100664000076400007640000002536010103522154016632 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8308. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). formula_list(usable). all x (Wolf(x)->animal(x)). all x (Fox(x)->animal(x)). all x (Bird(x)->animal(x)). all x (Caterpillar(x)->animal(x)). all x (Snail(x)->animal(x)). all x (Grain(x)->plant(x)). exists x Wolf(x). exists x Fox(x). exists x Bird(x). exists x Caterpillar(x). exists x Snail(x). exists x Grain(x). all x (animal(x)-> (all y (plant(y)->eats(x,y)))| (all z (animal(z)&Smaller(z,x)& (exists u (plant(u)&eats(z,u)))->eats(x,z)))). all x y (Caterpillar(x)&Bird(y)->Smaller(x,y)). all x y (Snail(x)&Bird(y)->Smaller(x,y)). all x y (Bird(x)&Fox(y)->Smaller(x,y)). all x y (Fox(x)&Wolf(y)->Smaller(x,y)). all x y (Bird(x)&Caterpillar(y)->eats(x,y)). all x (Caterpillar(x)-> (exists y (plant(y)&eats(x,y)))). all x (Snail(x)-> (exists y (plant(y)&eats(x,y)))). all x y (Wolf(x)&Fox(y)-> -eats(x,y)). all x y (Wolf(x)&Grain(y)-> -eats(x,y)). all x y (Bird(x)&Snail(y)-> -eats(x,y)). -(exists x y (-$answer(eats(x,y))&animal(x)&animal(y)&eats(x,y)& (all z (Grain(z)->eats(y,z))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -Wolf(x)|animal(x). 0 [] -Fox(x)|animal(x). 0 [] -Bird(x)|animal(x). 0 [] -Caterpillar(x)|animal(x). 0 [] -Snail(x)|animal(x). 0 [] -Grain(x)|plant(x). 0 [] Wolf($c1). 0 [] Fox($c2). 0 [] Bird($c3). 0 [] Caterpillar($c4). 0 [] Snail($c5). 0 [] Grain($c6). 0 [] -animal(x)| -plant(y)|eats(x,y)| -animal(z)| -Smaller(z,x)| -plant(u)| -eats(z,u)|eats(x,z). 0 [] -Caterpillar(x)| -Bird(y)|Smaller(x,y). 0 [] -Snail(x)| -Bird(y)|Smaller(x,y). 0 [] -Bird(x)| -Fox(y)|Smaller(x,y). 0 [] -Fox(x)| -Wolf(y)|Smaller(x,y). 0 [] -Bird(x)| -Caterpillar(y)|eats(x,y). 0 [] -Caterpillar(x)|plant($f1(x)). 0 [] -Caterpillar(x)|eats(x,$f1(x)). 0 [] -Snail(x)|plant($f2(x)). 0 [] -Snail(x)|eats(x,$f2(x)). 0 [] -Wolf(x)| -Fox(y)| -eats(x,y). 0 [] -Wolf(x)| -Grain(y)| -eats(x,y). 0 [] -Bird(x)| -Snail(y)| -eats(x,y). 0 [] $answer(eats(x,y))| -animal(x)| -animal(y)| -eats(x,y)|Grain($f3(x,y)). 0 [] $answer(eats(x,y))| -animal(x)| -animal(y)| -eats(x,y)| -eats(y,$f3(x,y)). end_of_list. SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=8. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. dependent: set(hyper_res). dependent: set(factor). dependent: set(unit_deletion). ------------> process usable: ** KEPT (pick-wt=4): 1 [] -Wolf(x)|animal(x). ** KEPT (pick-wt=4): 2 [] -Fox(x)|animal(x). ** KEPT (pick-wt=4): 3 [] -Bird(x)|animal(x). ** KEPT (pick-wt=4): 4 [] -Caterpillar(x)|animal(x). ** KEPT (pick-wt=4): 5 [] -Snail(x)|animal(x). ** KEPT (pick-wt=4): 6 [] -Grain(x)|plant(x). ** KEPT (pick-wt=20): 7 [] -animal(x)| -plant(y)|eats(x,y)| -animal(z)| -Smaller(z,x)| -plant(u)| -eats(z,u)|eats(x,z). ** KEPT (pick-wt=7): 8 [] -Caterpillar(x)| -Bird(y)|Smaller(x,y). ** KEPT (pick-wt=7): 9 [] -Snail(x)| -Bird(y)|Smaller(x,y). ** KEPT (pick-wt=7): 10 [] -Bird(x)| -Fox(y)|Smaller(x,y). ** KEPT (pick-wt=7): 11 [] -Fox(x)| -Wolf(y)|Smaller(x,y). ** KEPT (pick-wt=7): 12 [] -Bird(x)| -Caterpillar(y)|eats(x,y). ** KEPT (pick-wt=5): 13 [] -Caterpillar(x)|plant($f1(x)). ** KEPT (pick-wt=6): 14 [] -Caterpillar(x)|eats(x,$f1(x)). ** KEPT (pick-wt=5): 15 [] -Snail(x)|plant($f2(x)). ** KEPT (pick-wt=6): 16 [] -Snail(x)|eats(x,$f2(x)). ** KEPT (pick-wt=7): 17 [] -Wolf(x)| -Fox(y)| -eats(x,y). ** KEPT (pick-wt=7): 18 [] -Wolf(x)| -Grain(y)| -eats(x,y). ** KEPT (pick-wt=7): 19 [] -Bird(x)| -Snail(y)| -eats(x,y). ** KEPT (pick-wt=11): 20 [] $answer(eats(x,y))| -animal(x)| -animal(y)| -eats(x,y)|Grain($f3(x,y)). ** KEPT (pick-wt=12): 21 [] $answer(eats(x,y))| -animal(x)| -animal(y)| -eats(x,y)| -eats(y,$f3(x,y)). ------------> process sos: ** KEPT (pick-wt=2): 29 [] Wolf($c1). ** KEPT (pick-wt=2): 30 [] Fox($c2). ** KEPT (pick-wt=2): 31 [] Bird($c3). ** KEPT (pick-wt=2): 32 [] Caterpillar($c4). ** KEPT (pick-wt=2): 33 [] Snail($c5). ** KEPT (pick-wt=2): 34 [] Grain($c6). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 29 [] Wolf($c1). given clause #2: (wt=2) 30 [] Fox($c2). given clause #3: (wt=2) 31 [] Bird($c3). given clause #4: (wt=2) 32 [] Caterpillar($c4). given clause #5: (wt=2) 33 [] Snail($c5). given clause #6: (wt=2) 34 [] Grain($c6). given clause #7: (wt=2) 35 [hyper,29,1] animal($c1). given clause #8: (wt=2) 37 [hyper,30,2] animal($c2). given clause #9: (wt=2) 39 [hyper,31,3] animal($c3). given clause #10: (wt=2) 44 [hyper,32,4] animal($c4). given clause #11: (wt=3) 36 [hyper,30,11,29] Smaller($c2,$c1). given clause #12: (wt=2) 48 [hyper,33,5] animal($c5). given clause #13: (wt=2) 49 [hyper,34,6] plant($c6). given clause #14: (wt=3) 38 [hyper,31,10,30] Smaller($c3,$c2). given clause #15: (wt=3) 41 [hyper,32,13] plant($f1($c4)). given clause #16: (wt=4) 40 [hyper,32,14] eats($c4,$f1($c4)). given clause #17: (wt=3) 42 [hyper,32,12,31] eats($c3,$c4). given clause #18: (wt=3) 43 [hyper,32,8,31] Smaller($c4,$c3). given clause #19: (wt=3) 46 [hyper,33,15] plant($f2($c5)). given clause #20: (wt=3) 47 [hyper,33,9,31] Smaller($c5,$c3). given clause #21: (wt=4) 45 [hyper,33,16] eats($c5,$f2($c5)). given clause #22: (wt=4) 50 [hyper,42,20,39,44] $answer(eats($c3,$c4))|Grain($f3($c3,$c4)). given clause #23: (wt=4) 54 [hyper,50,6] $answer(eats($c3,$c4))|plant($f3($c3,$c4)). given clause #24: (wt=6) 52 [hyper,45,7,39,49,48,47,46] eats($c3,$c6)|eats($c3,$c5). given clause #25: (wt=3) 61 [hyper,52,19,31,33] eats($c3,$c6). given clause #26: (wt=7) 51 [hyper,45,23,39,46,48,47] eats($c3,$f2($c5))|eats($c3,$c5). given clause #27: (wt=4) 67 [hyper,51,19,31,33] eats($c3,$f2($c5)). given clause #28: (wt=6) 62 [hyper,61,23,37,49,39,38] eats($c2,$c6)|eats($c2,$c3). given clause #29: (wt=7) 53 [hyper,45,7,39,41,48,47,46] eats($c3,$f1($c4))|eats($c3,$c5). given clause #30: (wt=4) 74 [hyper,53,19,31,33] eats($c3,$f1($c4)). given clause #31: (wt=8) 55 [hyper,54,7,39,48,47,46,45] $answer(eats($c3,$c4))|eats($c3,$f3($c3,$c4))|eats($c3,$c5). given clause #32: (wt=5) 76 [hyper,55,19,31,33] $answer(eats($c3,$c4))|eats($c3,$f3($c3,$c4)). given clause #33: (wt=7) 64 [hyper,61,7,37,46,39,38,49] eats($c2,$f2($c5))|eats($c2,$c3). given clause #34: (wt=7) 65 [hyper,61,7,37,41,39,38,49] eats($c2,$f1($c4))|eats($c2,$c3). given clause #35: (wt=7) 72 [hyper,62,20,37,39] eats($c2,$c6)|$answer(eats($c2,$c3))|Grain($f3($c2,$c3)). given clause #36: (wt=8) 63 [hyper,61,7,37,54,39,38,49] eats($c2,$f3($c3,$c4))|eats($c2,$c3)|$answer(eats($c3,$c4)). given clause #37: (wt=7) 79 [hyper,72,6] eats($c2,$c6)|$answer(eats($c2,$c3))|plant($f3($c2,$c3)). given clause #38: (wt=8) 77 [hyper,64,20,37,39] eats($c2,$f2($c5))|$answer(eats($c2,$c3))|Grain($f3($c2,$c3)). given clause #39: (wt=8) 78 [hyper,65,20,37,39] eats($c2,$f1($c4))|$answer(eats($c2,$c3))|Grain($f3($c2,$c3)). given clause #40: (wt=8) 82 [hyper,77,6] eats($c2,$f2($c5))|$answer(eats($c2,$c3))|plant($f3($c2,$c3)). given clause #41: (wt=9) 68 [hyper,62,23,35,49,37,36] eats($c2,$c3)|eats($c1,$c6)|eats($c1,$c2). given clause #42: (wt=6) 86 [hyper,68,18,29,34] eats($c2,$c3)|eats($c1,$c2). given clause #43: (wt=3) 91 [hyper,86,17,29,30] eats($c2,$c3). given clause #44: (wt=4) 92 [hyper,91,20,37,39] $answer(eats($c2,$c3))|Grain($f3($c2,$c3)). given clause #45: (wt=4) 93 [hyper,92,6] $answer(eats($c2,$c3))|plant($f3($c2,$c3)). given clause #46: (wt=8) 94 [hyper,93,7,39,48,47,46,45] $answer(eats($c2,$c3))|eats($c3,$f3($c2,$c3))|eats($c3,$c5). given clause #47: (wt=3) 95 [hyper,94,21,37,39,91,factor_simp] $answer(eats($c2,$c3))|eats($c3,$c5). -------- PROOF -------- 99 [hyper,95,19,31,33] $answer(eats($c2,$c3)). -----> EMPTY CLAUSE at 0.02 sec ----> 99 [hyper,95,19,31,33] $answer(eats($c2,$c3)). Length of proof is 21. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -Wolf(x)|animal(x). 2 [] -Fox(x)|animal(x). 3 [] -Bird(x)|animal(x). 5 [] -Snail(x)|animal(x). 6 [] -Grain(x)|plant(x). 7 [] -animal(x)| -plant(y)|eats(x,y)| -animal(z)| -Smaller(z,x)| -plant(u)| -eats(z,u)|eats(x,z). 9 [] -Snail(x)| -Bird(y)|Smaller(x,y). 10 [] -Bird(x)| -Fox(y)|Smaller(x,y). 11 [] -Fox(x)| -Wolf(y)|Smaller(x,y). 15 [] -Snail(x)|plant($f2(x)). 16 [] -Snail(x)|eats(x,$f2(x)). 17 [] -Wolf(x)| -Fox(y)| -eats(x,y). 18 [] -Wolf(x)| -Grain(y)| -eats(x,y). 19 [] -Bird(x)| -Snail(y)| -eats(x,y). 20 [] $answer(eats(x,y))| -animal(x)| -animal(y)| -eats(x,y)|Grain($f3(x,y)). 21 [] $answer(eats(x,y))| -animal(x)| -animal(y)| -eats(x,y)| -eats(y,$f3(x,y)). 23 [factor,7.2.6] -animal(x)| -plant(y)|eats(x,y)| -animal(z)| -Smaller(z,x)| -eats(z,y)|eats(x,z). 29 [] Wolf($c1). 30 [] Fox($c2). 31 [] Bird($c3). 33 [] Snail($c5). 34 [] Grain($c6). 35 [hyper,29,1] animal($c1). 36 [hyper,30,11,29] Smaller($c2,$c1). 37 [hyper,30,2] animal($c2). 38 [hyper,31,10,30] Smaller($c3,$c2). 39 [hyper,31,3] animal($c3). 45 [hyper,33,16] eats($c5,$f2($c5)). 46 [hyper,33,15] plant($f2($c5)). 47 [hyper,33,9,31] Smaller($c5,$c3). 48 [hyper,33,5] animal($c5). 49 [hyper,34,6] plant($c6). 52 [hyper,45,7,39,49,48,47,46] eats($c3,$c6)|eats($c3,$c5). 61 [hyper,52,19,31,33] eats($c3,$c6). 62 [hyper,61,23,37,49,39,38] eats($c2,$c6)|eats($c2,$c3). 68 [hyper,62,23,35,49,37,36] eats($c2,$c3)|eats($c1,$c6)|eats($c1,$c2). 86 [hyper,68,18,29,34] eats($c2,$c3)|eats($c1,$c2). 91 [hyper,86,17,29,30] eats($c2,$c3). 92 [hyper,91,20,37,39] $answer(eats($c2,$c3))|Grain($f3($c2,$c3)). 93 [hyper,92,6] $answer(eats($c2,$c3))|plant($f3($c2,$c3)). 94 [hyper,93,7,39,48,47,46,45] $answer(eats($c2,$c3))|eats($c3,$f3($c2,$c3))|eats($c3,$c5). 95 [hyper,94,21,37,39,91,factor_simp] $answer(eats($c2,$c3))|eats($c3,$c5). 99 [hyper,95,19,31,33] $answer(eats($c2,$c3)). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 47 clauses generated 161 clauses kept 98 clauses forward subsumed 85 clauses back subsumed 37 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8308 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/wang1.in0100644000076400007640000000111405470212344016332 0ustar mccunemccune% % This is the Wang exq1 problem % set(auto). list(usable). y=m | p(y,m) | v1=m | v1=y | -p(y,v1) | -p(v1,y). y=b | -p(y,b) | v=b | v=y | -p(y,v) | -p(v,y). y=k | y=m | y=b | -p(y,k). y=m | -p(y,m) | f(y)!=m. y=m | -p(y,m) | f(y)!=y. y=m | -p(y,m) | p(y,f(y)). y=m | -p(y,m) | p(f(y),y). y=b | p(y,b) | g(y)!=b. y=b | p(y,b) | g(y)!=y. y=b | p(y,b) | p(y,g(y)). y=b | p(y,b) | p(g(y),y). y=k | y!=m | p(y,k). y=k | y!=b | p(y,k). x=x. x!=y | y=x. x!=y | y!=z | x=z. x!=y | -p(x,z) | p(y,z). x!=y | -p(z,x) | p(z,y). x!=y | f(x)=f(y). x!=y | g(x)=g(y). m!=b. b!=k. k!=m. end_of_list. otter-3.3f/examples/auto/group.out0100664000076400007640000001066510103522153016656 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8268. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] f(e,x)=x. 0 [] f(g(x),x)=e. 0 [] f(f(x,y),z)=f(x,f(y,z)). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). There is no negative clause, so all clause lists will be printed at the end of the search. dependent: set(print_lists_at_end). ------------> process usable: ------------> process sos: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=5): 2 [] f(e,x)=x. ---> New Demodulator: 3 [new_demod,2] f(e,x)=x. ** KEPT (pick-wt=6): 4 [] f(g(x),x)=e. ---> New Demodulator: 5 [new_demod,4] f(g(x),x)=e. ** KEPT (pick-wt=11): 6 [] f(f(x,y),z)=f(x,f(y,z)). ---> New Demodulator: 7 [new_demod,6] f(f(x,y),z)=f(x,f(y,z)). Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back demodulation with 3. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 1 [] x=x. given clause #2: (wt=5) 2 [] f(e,x)=x. given clause #3: (wt=6) 4 [] f(g(x),x)=e. given clause #4: (wt=11) 6 [] f(f(x,y),z)=f(x,f(y,z)). given clause #5: (wt=8) 8 [para_into,6.1.1.1,4.1.1,demod,3,flip.1] f(g(x),f(x,y))=y. given clause #6: (wt=9) 10 [para_into,8.1.1.2,8.1.1] f(g(g(x)),y)=f(x,y). given clause #7: (wt=5) 14 [para_into,8.1.1.2,4.1.1,demod,11] f(x,e)=x. given clause #8: (wt=4) 24 [para_into,14.1.1,4.1.1,flip.1] g(e)=e. given clause #9: (wt=5) 22 [para_into,14.1.1,10.1.1,demod,15,flip.1] g(g(x))=x. given clause #10: (wt=6) 20 [para_into,10.1.1,4.1.1,flip.1] f(x,g(x))=e. given clause #11: (wt=12) 12 [para_into,8.1.1.2,6.1.1] f(g(f(x,y)),f(x,f(y,z)))=z. given clause #12: (wt=8) 18 [para_into,10.1.1,8.1.1,flip.1] f(x,f(g(x),y))=y. given clause #13: (wt=9) 30 [para_into,12.1.1.2.2,20.1.1,demod,15] f(g(f(x,y)),x)=g(y). given clause #14: (wt=10) 44 [para_into,30.1.1.1.1,8.1.1,flip.1] g(f(x,y))=f(g(y),g(x)). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ list(usable). 1 [] x=x. 2 [] f(e,x)=x. 4 [] f(g(x),x)=e. 6 [] f(f(x,y),z)=f(x,f(y,z)). 8 [para_into,6.1.1.1,4.1.1,demod,3,flip.1] f(g(x),f(x,y))=y. 14 [para_into,8.1.1.2,4.1.1,demod,11] f(x,e)=x. 24 [para_into,14.1.1,4.1.1,flip.1] g(e)=e. 22 [para_into,14.1.1,10.1.1,demod,15,flip.1] g(g(x))=x. 20 [para_into,10.1.1,4.1.1,flip.1] f(x,g(x))=e. 18 [para_into,10.1.1,8.1.1,flip.1] f(x,f(g(x),y))=y. 44 [para_into,30.1.1.1.1,8.1.1,flip.1] g(f(x,y))=f(g(y),g(x)). end_of_list. list(sos). end_of_list. list(demodulators). 3 [new_demod,2] f(e,x)=x. 5 [new_demod,4] f(g(x),x)=e. 7 [new_demod,6] f(f(x,y),z)=f(x,f(y,z)). 9 [new_demod,8] f(g(x),f(x,y))=y. 15 [new_demod,14] f(x,e)=x. 19 [new_demod,18] f(x,f(g(x),y))=y. 21 [new_demod,20] f(x,g(x))=e. 23 [new_demod,22] g(g(x))=x. 25 [new_demod,24] g(e)=e. 45 [new_demod,44] g(f(x,y))=f(g(y),g(x)). end_of_list. -------------- statistics ------------- clauses given 14 clauses generated 128 clauses kept 23 clauses forward subsumed 122 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8268 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/cn19.out0100664000076400007640000002415610103522153016274 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8253. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] -P(i(x,y))| -P(x)|P(y). 0 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 0 [] P(i(i(n(x),x),x)). 0 [] P(i(x,i(n(x),y))). 0 [] -P(i(i(i(a,b),c),i(b,c)))|$Ans(CN_19). end_of_list. SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -P(i(x,y))| -P(x)|P(y). ** KEPT (pick-wt=10): 2 [] -P(i(i(i(a,b),c),i(b,c)))|$Ans(CN_19). ------------> process sos: ** KEPT (pick-wt=12): 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). ** KEPT (pick-wt=7): 4 [] P(i(i(n(x),x),x)). ** KEPT (pick-wt=7): 5 [] P(i(x,i(n(x),y))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). given clause #2: (wt=7) 4 [] P(i(i(n(x),x),x)). given clause #3: (wt=7) 5 [] P(i(x,i(n(x),y))). given clause #4: (wt=10) 8 [hyper,5,1,5] P(i(n(i(x,i(n(x),y))),z)). given clause #5: (wt=10) 10 [hyper,5,1,4] P(i(n(i(i(n(x),x),x)),y)). given clause #6: (wt=16) 6 [hyper,3,1,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #7: (wt=11) 7 [hyper,4,1,3] P(i(i(x,y),i(i(n(x),x),y))). given clause #8: (wt=10) 28 [hyper,7,1,5] P(i(i(n(x),x),i(n(x),y))). given clause #9: (wt=11) 9 [hyper,5,1,3] P(i(i(i(n(x),y),z),i(x,z))). given clause #10: (wt=4) 40 [hyper,9,1,4] P(i(x,x)). given clause #11: (wt=15) 11 [hyper,5,1,3] P(i(n(i(i(x,y),i(i(y,z),i(x,z)))),u)). given clause #12: (wt=7) 42 [hyper,40,1,5] P(i(n(i(x,x)),y)). given clause #13: (wt=10) 39 [hyper,9,1,5] P(i(x,i(n(i(n(x),y)),z))). given clause #14: (wt=10) 47 [hyper,42,1,5] P(i(n(i(n(i(x,x)),y)),z)). given clause #15: (wt=11) 35 [hyper,9,1,6] P(i(i(x,n(y)),i(y,i(x,z)))). given clause #16: (wt=13) 12 [hyper,8,1,5] P(i(n(i(n(i(x,i(n(x),y))),z)),u)). given clause #17: (wt=9) 67 [hyper,35,1,9] P(i(x,i(y,i(n(x),z)))). given clause #18: (wt=9) 72 [hyper,35,1,42] P(i(x,i(n(i(y,y)),z))). given clause #19: (wt=11) 38 [hyper,9,1,7] P(i(x,i(i(n(n(x)),n(x)),y))). given clause #20: (wt=12) 71 [hyper,35,1,47] P(i(x,i(n(i(n(i(y,y)),z)),u))). given clause #21: (wt=13) 14 [hyper,10,1,5] P(i(n(i(n(i(i(n(x),x),x)),y)),z)). given clause #22: (wt=12) 74 [hyper,35,1,10] P(i(x,i(n(i(i(n(y),y),y)),z))). given clause #23: (wt=12) 75 [hyper,35,1,8] P(i(x,i(n(i(y,i(n(y),z))),u))). given clause #24: (wt=12) 81 [hyper,67,1,9] P(i(x,i(y,i(n(i(n(x),z)),u)))). given clause #25: (wt=12) 82 [hyper,67,1,7] P(i(i(n(x),x),i(y,i(n(x),z)))). given clause #26: (wt=16) 16 [hyper,6,1,6] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). given clause #27: (wt=12) 84 [hyper,67,1,5] P(i(n(i(x,i(y,i(n(x),z)))),u)). given clause #28: (wt=12) 98 [hyper,72,1,5] P(i(n(i(x,i(n(i(y,y)),z))),u)). given clause #29: (wt=13) 29 [hyper,7,1,4] P(i(i(n(i(n(x),x)),i(n(x),x)),x)). given clause #30: (wt=13) 32 [hyper,28,1,5] P(i(n(i(i(n(x),x),i(n(x),y))),z)). given clause #31: (wt=19) 17 [hyper,6,1,5] P(i(n(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),v)). given clause #32: (wt=13) 46 [hyper,42,1,7] P(i(i(n(n(i(x,x))),n(i(x,x))),y)). given clause #33: (wt=13) 50 [hyper,39,1,9] P(i(x,i(n(i(n(i(n(x),y)),z)),u))). given clause #34: (wt=13) 51 [hyper,39,1,7] P(i(i(n(x),x),i(n(i(n(x),y)),z))). given clause #35: (wt=13) 53 [hyper,39,1,5] P(i(n(i(x,i(n(i(n(x),y)),z))),u)). given clause #36: (wt=20) 18 [hyper,6,1,3] P(i(i(i(i(x,y),z),u),i(i(i(i(y,v),i(x,v)),z),u))). given clause #37: (wt=13) 55 [hyper,39,1,42] P(i(n(i(n(i(n(i(x,x)),y)),z)),u)). given clause #38: (wt=13) 85 [hyper,67,1,3] P(i(i(i(x,i(n(y),z)),u),i(y,u))). given clause #39: (wt=12) 305 [hyper,85,1,5] P(i(x,i(n(i(y,i(n(x),z))),u))). given clause #40: (wt=13) 99 [hyper,72,1,3] P(i(i(i(n(i(x,x)),y),z),i(u,z))). given clause #41: (wt=15) 19 [hyper,6,1,5] P(i(i(x,y),i(n(i(i(y,z),i(x,z))),u))). given clause #42: (wt=6) 370 [hyper,99,1,4] P(i(x,i(y,y))). given clause #43: (wt=9) 413 [hyper,370,1,5] P(i(n(i(x,i(y,y))),z)). given clause #44: (wt=10) 412 [hyper,370,1,16] P(i(i(x,y),i(z,i(x,y)))). given clause #45: (wt=8) 433 [hyper,412,1,370] P(i(x,i(y,i(z,z)))). given clause #46: (wt=16) 20 [hyper,6,1,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). given clause #47: (wt=9) 455 [hyper,412,1,5] P(i(x,i(y,i(n(y),z)))). given clause #48: (wt=9) 456 [hyper,412,1,4] P(i(x,i(i(n(y),y),y))). given clause #49: (wt=10) 414 [hyper,370,1,3] P(i(i(i(x,x),y),i(z,y))). given clause #50: (wt=10) 458 [hyper,433,1,412] P(i(x,i(y,i(z,i(u,u))))). given clause #51: (wt=16) 21 [hyper,7,1,7] P(i(i(n(i(x,y)),i(x,y)),i(i(n(x),x),y))). given clause #52: (wt=11) 366 [hyper,99,1,82] P(i(x,i(y,i(n(i(z,z)),u)))). given clause #53: (wt=11) 407 [hyper,370,1,67] P(i(x,i(n(i(y,i(z,z))),u))). given clause #54: (wt=11) 421 [hyper,412,1,85] P(i(x,i(y,i(z,i(n(x),u))))). given clause #55: (wt=11) 441 [hyper,412,1,67] P(i(x,i(y,i(z,i(n(y),u))))). given clause #56: (wt=17) 22 [hyper,7,1,6] P(i(i(x,y),i(i(n(i(y,z)),i(y,z)),i(x,z)))). given clause #57: (wt=11) 466 [hyper,433,1,5] P(i(n(i(x,i(y,i(z,z)))),u)). given clause #58: (wt=11) 517 [hyper,455,1,412] P(i(x,i(y,i(z,i(n(z),u))))). given clause #59: (wt=11) 529 [hyper,456,1,412] P(i(x,i(y,i(i(n(z),z),z)))). given clause #60: (wt=12) 409 [hyper,370,1,39] P(i(n(i(n(i(x,i(y,y))),z)),u)). given clause #61: (wt=14) 23 [hyper,7,1,5] P(i(n(i(i(x,y),i(i(n(x),x),y))),z)). given clause #62: (wt=12) 419 [hyper,412,1,412] P(i(x,i(i(y,z),i(u,i(y,z))))). given clause #63: (wt=12) 444 [hyper,412,1,39] P(i(x,i(y,i(n(i(n(y),z)),u)))). given clause #64: (wt=12) 448 [hyper,412,1,28] P(i(x,i(i(n(y),y),i(n(y),z)))). given clause #65: (wt=12) 467 [hyper,433,1,3] P(i(i(i(x,i(y,y)),z),i(u,z))). given clause #66: (wt=15) 24 [hyper,7,1,3] P(i(i(i(i(n(x),x),y),z),i(i(x,y),z))). given clause #67: (wt=12) 527 [hyper,455,1,5] P(i(n(i(x,i(y,i(n(y),z)))),u)). given clause #68: (wt=12) 539 [hyper,456,1,5] P(i(n(i(x,i(i(n(y),y),y))),z)). given clause #69: (wt=12) 541 [hyper,414,1,412] P(i(x,i(i(i(y,y),z),i(u,z)))). given clause #70: (wt=12) 551 [hyper,458,1,412] P(i(x,i(y,i(z,i(u,i(v,v)))))). given clause #71: (wt=19) 25 [hyper,7,1,10] P(i(i(n(n(i(i(n(x),x),x))),n(i(i(n(x),x),x))),y)). given clause #72: (wt=13) 183 [hyper,16,1,72] P(i(i(x,n(i(y,y))),i(z,i(x,u)))). given clause #73: (wt=13) 304 [hyper,85,1,16] P(i(x,i(i(y,n(x)),i(z,i(y,u))))). given clause #74: (wt=13) 306 [hyper,85,1,3] P(i(x,i(i(i(n(x),y),z),i(u,z)))). given clause #75: (wt=13) 411 [hyper,370,1,19] P(i(n(i(i(i(x,x),y),i(z,y))),u)). given clause #76: (wt=19) 26 [hyper,7,1,8] P(i(i(n(n(i(x,i(n(x),y)))),n(i(x,i(n(x),y)))),z)). given clause #77: (wt=13) 431 [hyper,412,1,5] P(i(n(i(i(x,y),i(z,i(x,y)))),u)). given clause #78: (wt=13) 445 [hyper,412,1,38] P(i(x,i(y,i(i(n(n(y)),n(y)),z)))). given clause #79: (wt=13) 446 [hyper,412,1,35] P(i(x,i(i(y,n(z)),i(z,i(y,u))))). given clause #80: (wt=13) 452 [hyper,412,1,9] P(i(x,i(i(i(n(y),z),u),i(y,u)))). given clause #81: (wt=27) 27 [hyper,7,1,6] P(i(i(n(i(i(i(x,y),i(z,y)),u)),i(i(i(x,y),i(z,y)),u)),i(i(z,x),u))). given clause #82: (wt=13) 453 [hyper,412,1,7] P(i(x,i(i(y,z),i(i(n(y),y),z)))). given clause #83: (wt=13) 461 [hyper,433,1,67] P(i(x,i(n(i(y,i(z,i(u,u)))),v))). given clause #84: (wt=13) 526 [hyper,455,1,16] P(i(i(x,y),i(z,i(x,i(n(y),u))))). given clause #85: (wt=13) 528 [hyper,455,1,3] P(i(i(i(x,i(n(x),y)),z),i(u,z))). given clause #86: (wt=17) 30 [hyper,7,1,3] P(i(i(n(i(x,y)),i(x,y)),i(i(y,z),i(x,z)))). given clause #87: (wt=13) 538 [hyper,456,1,16] P(i(i(x,i(n(y),y)),i(z,i(x,y)))). given clause #88: (wt=8) 1315 [hyper,538,1,85] P(i(x,i(y,i(z,x)))). given clause #89: (wt=8) 1341 [hyper,1315,1,538] P(i(x,i(y,i(z,y)))). -------- PROOF -------- 1424 [binary,1423.1,2.1] $Ans(CN_19). ----> UNIT CONFLICT at 0.09 sec ----> 1424 [binary,1423.1,2.1] $Ans(CN_19). Length of proof is 19. Level of proof is 12. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] -P(i(i(i(a,b),c),i(b,c)))|$Ans(CN_19). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(n(x),x),x)). 5 [] P(i(x,i(n(x),y))). 6 [hyper,3,1,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 7 [hyper,4,1,3] P(i(i(x,y),i(i(n(x),x),y))). 9 [hyper,5,1,3] P(i(i(i(n(x),y),z),i(x,z))). 16 [hyper,6,1,6] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 30 [hyper,7,1,3] P(i(i(n(i(x,y)),i(x,y)),i(i(y,z),i(x,z)))). 35 [hyper,9,1,6] P(i(i(x,n(y)),i(y,i(x,z)))). 40 [hyper,9,1,4] P(i(x,x)). 42 [hyper,40,1,5] P(i(n(i(x,x)),y)). 67 [hyper,35,1,9] P(i(x,i(y,i(n(x),z)))). 72 [hyper,35,1,42] P(i(x,i(n(i(y,y)),z))). 85 [hyper,67,1,3] P(i(i(i(x,i(n(y),z)),u),i(y,u))). 99 [hyper,72,1,3] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 370 [hyper,99,1,4] P(i(x,i(y,y))). 412 [hyper,370,1,16] P(i(i(x,y),i(z,i(x,y)))). 456 [hyper,412,1,4] P(i(x,i(i(n(y),y),y))). 538 [hyper,456,1,16] P(i(i(x,i(n(y),y)),i(z,i(x,y)))). 1315 [hyper,538,1,85] P(i(x,i(y,i(z,x)))). 1341 [hyper,1315,1,538] P(i(x,i(y,i(z,y)))). 1423 [hyper,1341,1,30] P(i(i(i(x,y),z),i(y,z))). 1424 [binary,1423.1,2.1] $Ans(CN_19). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 89 clauses generated 4909 clauses kept 1423 clauses forward subsumed 3491 clauses back subsumed 27 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.09 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8253 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/ec_yq.in0100644000076400007640000000036305515260753016431 0ustar mccunemccune% % Equivalential calculus (EC): YQF -> YQL (both are single axioms) % set(auto). list(usable). -P(e(x,y)) | -P(x) | P(y). % condensed detachment P(e(e(x,y),e(e(x,z),e(z,y)))). % YQF -P(e(e(a,b),e(e(c,b),e(a,c)))). % YQL end_of_list. otter-3.3f/examples/auto/ring_x2.out0100664000076400007640000003140010103522154017061 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8288. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] j(0,x)=x. 0 [] j(g(x),x)=0. 0 [] j(j(x,y),z)=j(x,j(y,z)). 0 [] j(x,y)=j(y,x). 0 [] f(f(x,y),z)=f(x,f(y,z)). 0 [] f(x,j(y,z))=j(f(x,y),f(x,z)). 0 [] f(j(y,z),x)=j(f(y,x),f(z,x)). 0 [] f(x,x)=x. 0 [] f(a,b)!=f(b,a). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=7): 2 [copy,1,flip.1] f(b,a)!=f(a,b). ------------> process sos: ** KEPT (pick-wt=3): 3 [] x=x. ** KEPT (pick-wt=5): 4 [] j(0,x)=x. ---> New Demodulator: 5 [new_demod,4] j(0,x)=x. ** KEPT (pick-wt=6): 6 [] j(g(x),x)=0. ---> New Demodulator: 7 [new_demod,6] j(g(x),x)=0. ** KEPT (pick-wt=11): 8 [] j(j(x,y),z)=j(x,j(y,z)). ---> New Demodulator: 9 [new_demod,8] j(j(x,y),z)=j(x,j(y,z)). ** KEPT (pick-wt=7): 10 [] j(x,y)=j(y,x). ** KEPT (pick-wt=11): 11 [] f(f(x,y),z)=f(x,f(y,z)). ---> New Demodulator: 12 [new_demod,11] f(f(x,y),z)=f(x,f(y,z)). ** KEPT (pick-wt=13): 14 [copy,13,flip.1] j(f(x,y),f(x,z))=f(x,j(y,z)). ---> New Demodulator: 15 [new_demod,14] j(f(x,y),f(x,z))=f(x,j(y,z)). ** KEPT (pick-wt=13): 17 [copy,16,flip.1] j(f(x,y),f(z,y))=f(j(x,z),y). ---> New Demodulator: 18 [new_demod,17] j(f(x,y),f(z,y))=f(j(x,z),y). ** KEPT (pick-wt=5): 19 [] f(x,x)=x. ---> New Demodulator: 20 [new_demod,19] f(x,x)=x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x=x. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] j(x,y)=j(y,x). >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 20. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 3 [] x=x. given clause #2: (wt=5) 4 [] j(0,x)=x. given clause #3: (wt=5) 19 [] f(x,x)=x. given clause #4: (wt=6) 6 [] j(g(x),x)=0. given clause #5: (wt=7) 10 [] j(x,y)=j(y,x). given clause #6: (wt=11) 8 [] j(j(x,y),z)=j(x,j(y,z)). given clause #7: (wt=5) 23 [para_into,10.1.1,4.1.1,flip.1] j(x,0)=x. given clause #8: (wt=4) 30 [para_into,23.1.1,6.1.1,flip.1] g(0)=0. given clause #9: (wt=6) 21 [para_into,10.1.1,6.1.1,flip.1] j(x,g(x))=0. given clause #10: (wt=8) 26 [para_into,8.1.1.1,6.1.1,demod,5,flip.1] j(g(x),j(x,y))=y. given clause #11: (wt=11) 11 [] f(f(x,y),z)=f(x,f(y,z)). given clause #12: (wt=5) 42 [para_into,26.1.1.2,6.1.1,demod,24] g(g(x))=x. given clause #13: (wt=8) 34 [para_from,21.1.1,8.1.1.1,demod,5,flip.1] j(x,j(g(x),y))=y. given clause #14: (wt=8) 38 [para_into,26.1.1.2,10.1.1] j(g(x),j(y,x))=y. given clause #15: (wt=8) 44 [para_into,26.1.1,10.1.1,demod,9] j(x,j(y,g(x)))=y. given clause #16: (wt=13) 14 [copy,13,flip.1] j(f(x,y),f(x,z))=f(x,j(y,z)). given clause #17: (wt=9) 46 [para_into,11.1.1.1,19.1.1,flip.1] f(x,f(x,y))=f(x,y). given clause #18: (wt=9) 52 [para_into,38.1.1.2,38.1.1] j(g(j(x,y)),x)=g(y). given clause #19: (wt=10) 89 [para_into,52.1.1.1.1,38.1.1,flip.1] g(j(x,y))=j(g(x),g(y)). given clause #20: (wt=11) 25 [para_into,8.1.1.1,10.1.1,demod,9] j(x,j(y,z))=j(y,j(x,z)). given clause #21: (wt=13) 17 [copy,16,flip.1] j(f(x,y),f(z,y))=f(j(x,z),y). given clause #22: (wt=11) 28 [para_into,8.1.1,10.1.1] j(x,j(y,z))=j(y,j(z,x)). given clause #23: (wt=11) 29 [copy,28,flip.1] j(x,j(y,z))=j(z,j(x,y)). given clause #24: (wt=11) 48 [para_into,11.1.1,19.1.1,flip.1] f(x,f(y,f(x,y)))=f(x,y). given clause #25: (wt=11) 68 [para_into,14.1.1.1,19.1.1] j(x,f(x,y))=f(x,j(x,y)). given clause #26: (wt=12) 58 [para_into,38.1.1.2,8.1.1] j(g(x),j(y,j(z,x)))=j(y,z). given clause #27: (wt=9) 156 [para_into,68.1.1.2,19.1.1,flip.1] f(x,j(x,x))=j(x,x). given clause #28: (wt=11) 70 [para_into,14.1.1.2,19.1.1] j(f(x,y),x)=f(x,j(y,x)). given clause #29: (wt=11) 72 [para_into,14.1.1,10.1.1,demod,15] f(x,j(y,z))=f(x,j(z,y)). given clause #30: (wt=11) 98 [para_into,25.1.1,10.1.1,demod,9] j(x,j(y,z))=j(x,j(z,y)). given clause #31: (wt=12) 60 [para_from,38.1.1,8.1.1.1,demod,9,flip.1] j(g(x),j(y,j(x,z)))=j(y,z). given clause #32: (wt=11) 102 [para_into,17.1.1.1,19.1.1] j(x,f(y,x))=f(j(x,y),x). given clause #33: (wt=9) 282 [para_into,102.1.1.2,19.1.1,flip.1] f(j(x,x),x)=j(x,x). given clause #34: (wt=11) 108 [para_into,17.1.1.2,19.1.1] j(f(x,y),y)=f(j(x,y),y). given clause #35: (wt=11) 112 [para_into,17.1.1,14.1.1] f(x,j(y,y))=f(j(x,x),y). given clause #36: (wt=12) 62 [para_into,44.1.1.2,8.1.1] j(x,j(y,j(z,g(x))))=j(y,z). given clause #37: (wt=9) 365 [para_into,112.1.1.2,23.1.1,flip.1] f(j(x,x),0)=f(x,0). given clause #38: (wt=11) 113 [para_into,17.1.1,10.1.1,demod,18] f(j(x,y),z)=f(j(y,x),z). given clause #39: (wt=11) 116 [copy,112,flip.1] f(j(x,x),y)=f(x,j(y,y)). given clause #40: (wt=9) 442 [para_into,116.1.1.1,23.1.1,flip.1] f(0,j(x,x))=f(0,x). given clause #41: (wt=12) 66 [para_from,44.1.1,8.1.1.1,demod,9,flip.1] j(x,j(y,j(g(x),z)))=j(y,z). given clause #42: (wt=11) 131 [para_into,28.1.1.2,10.1.1] j(x,j(y,z))=j(z,j(y,x)). given clause #43: (wt=11) 241 [para_into,72.1.1,19.1.1,flip.1] f(j(x,y),j(y,x))=j(x,y). given clause #44: (wt=11) 277 [para_into,102.1.1.2,156.1.1,demod,9,9,208,20] j(x,j(x,j(x,x)))=j(x,x). given clause #45: (wt=4) 542 [para_from,277.1.1,38.1.1.2,demod,541,24,541,24] g(x)=x. given clause #46: (wt=17) 77 [para_from,14.1.1,8.1.1.1] j(f(x,j(y,z)),u)=j(f(x,y),j(f(x,z),u)). given clause #47: (wt=5) 540 [para_from,277.1.1,58.1.1.2,demod,90,9,27,7,flip.1] j(x,x)=0. given clause #48: (wt=5) 563 [back_demod,454,demod,541,541,558,558,20,541,flip.1] f(0,x)=0. given clause #49: (wt=5) 569 [back_demod,418,demod,541,564,20,564,flip.1] f(x,0)=0. given clause #50: (wt=7) 544 [para_from,277.1.1,131.1.1.2,demod,541,24,541,24,flip.1] j(x,j(x,y))=y. given clause #51: (wt=15) 79 [para_into,46.1.1.2,11.1.1,demod,12,12] f(x,f(y,f(x,f(y,z))))=f(x,f(y,z)). given clause #52: (wt=7) 546 [para_from,277.1.1,29.1.1.2,demod,541,24,541,24,flip.1] j(x,j(y,x))=y. given clause #53: (wt=9) 571 [back_demod,344,demod,541,570,flip.1] f(x,f(j(x,y),y))=0. given clause #54: (wt=9) 573 [back_demod,291,demod,541,570,flip.1] f(x,f(j(y,x),y))=0. given clause #55: (wt=9) 678 [para_into,571.1.1.2.1,546.1.1] f(x,f(y,j(y,x)))=0. given clause #56: (wt=13) 81 [para_from,46.1.1,14.1.1.2,demod,15,flip.1] f(x,j(y,f(x,z)))=f(x,j(y,z)). given clause #57: (wt=9) 680 [para_into,571.1.1.2.1,544.1.1] f(x,f(y,j(x,y)))=0. given clause #58: (wt=9) 718 [para_into,573.1.1.2.1,546.1.1] f(j(x,y),f(x,y))=0. given clause #59: (wt=9) 720 [para_into,573.1.1.2.1,544.1.1] f(j(x,y),f(y,x))=0. given clause #60: (wt=9) 884 [para_from,718.1.1,102.1.1.2,demod,24,115,545,flip.1] f(x,f(y,x))=f(y,x). given clause #61: (wt=13) 83 [para_from,46.1.1,14.1.1.1,demod,15,flip.1] f(x,j(f(x,y),z))=f(x,j(y,z)). given clause #62: (wt=11) 603 [back_demod,66,demod,543] j(x,j(y,j(x,z)))=j(y,z). given clause #63: (wt=11) 605 [back_demod,62,demod,543] j(x,j(y,j(z,x)))=j(y,z). given clause #64: (wt=11) 716 [para_from,571.1.1,11.1.1.1,demod,564,12,flip.1] f(x,f(j(x,y),f(y,z)))=0. given clause #65: (wt=11) 750 [para_from,573.1.1,11.1.1.1,demod,564,12,flip.1] f(x,f(j(y,x),f(y,z)))=0. given clause #66: (wt=15) 95 [para_into,25.1.1.2,25.1.1] j(x,j(y,j(z,u)))=j(z,j(x,j(y,u))). given clause #67: (wt=11) 772 [para_into,678.1.1.2,11.1.1,demod,159] f(x,f(y,f(z,j(z,x))))=0. given clause #68: (wt=11) 784 [para_from,678.1.1,70.1.1.1,demod,5,78,20,109,flip.1] f(x,j(y,f(j(y,x),x)))=x. -------- PROOF -------- ----> UNIT CONFLICT at 0.08 sec ----> 1223 [binary,1222.1,2.1] $F. Length of proof is 50. Level of proof is 13. ---------------- PROOF ---------------- 1 [] f(a,b)!=f(b,a). 2 [copy,1,flip.1] f(b,a)!=f(a,b). 5,4 [] j(0,x)=x. 7,6 [] j(g(x),x)=0. 9,8 [] j(j(x,y),z)=j(x,j(y,z)). 10 [] j(x,y)=j(y,x). 12,11 [] f(f(x,y),z)=f(x,f(y,z)). 13 [] f(x,j(y,z))=j(f(x,y),f(x,z)). 15,14 [copy,13,flip.1] j(f(x,y),f(x,z))=f(x,j(y,z)). 16 [] f(j(x,y),z)=j(f(x,z),f(y,z)). 17 [copy,16,flip.1] j(f(x,y),f(z,y))=f(j(x,z),y). 20,19 [] f(x,x)=x. 24,23 [para_into,10.1.1,4.1.1,flip.1] j(x,0)=x. 27,26 [para_into,8.1.1.1,6.1.1,demod,5,flip.1] j(g(x),j(x,y))=y. 28 [para_into,8.1.1,10.1.1] j(x,j(y,z))=j(y,j(z,x)). 29 [copy,28,flip.1] j(x,j(y,z))=j(z,j(x,y)). 38 [para_into,26.1.1.2,10.1.1] j(g(x),j(y,x))=y. 47,46 [para_into,11.1.1.1,19.1.1,flip.1] f(x,f(x,y))=f(x,y). 48 [para_into,11.1.1,19.1.1,flip.1] f(x,f(y,f(x,y)))=f(x,y). 52 [para_into,38.1.1.2,38.1.1] j(g(j(x,y)),x)=g(y). 58 [para_into,38.1.1.2,8.1.1] j(g(x),j(y,j(z,x)))=j(y,z). 69,68 [para_into,14.1.1.1,19.1.1] j(x,f(x,y))=f(x,j(x,y)). 71,70 [para_into,14.1.1.2,19.1.1] j(f(x,y),x)=f(x,j(y,x)). 78,77 [para_from,14.1.1,8.1.1.1] j(f(x,j(y,z)),u)=j(f(x,y),j(f(x,z),u)). 90,89 [para_into,52.1.1.1.1,38.1.1,flip.1] g(j(x,y))=j(g(x),g(y)). 100 [para_into,17.1.1.1,46.1.1] j(f(x,y),f(z,f(x,y)))=f(j(x,z),f(x,y)). 103,102 [para_into,17.1.1.1,19.1.1] j(x,f(y,x))=f(j(x,y),x). 109,108 [para_into,17.1.1.2,19.1.1] j(f(x,y),y)=f(j(x,y),y). 112 [para_into,17.1.1,14.1.1] f(x,j(y,y))=f(j(x,x),y). 115,114 [back_demod,100,demod,103] f(j(f(x,y),z),f(x,y))=f(j(x,z),f(x,y)). 116 [copy,112,flip.1] f(j(x,x),y)=f(x,j(y,y)). 131 [para_into,28.1.1.2,10.1.1] j(x,j(y,z))=j(z,j(y,x)). 156 [para_into,68.1.1.2,19.1.1,flip.1] f(x,j(x,x))=j(x,x). 208,207 [para_from,156.1.1,17.1.1.1,demod,103,9] f(j(x,j(x,y)),j(x,x))=f(j(x,y),j(x,x)). 277 [para_into,102.1.1.2,156.1.1,demod,9,9,208,20] j(x,j(x,j(x,x)))=j(x,x). 281 [para_into,102.1.1.2,46.1.1,demod,15,71,12] f(x,j(y,y))=f(x,f(j(y,x),f(x,y))). 287,286 [para_into,102.1.1,14.1.1,demod,103,71,12,flip.1] f(x,f(j(y,x),f(x,y)))=f(x,f(j(y,x),y)). 291 [back_demod,281,demod,287] f(x,j(y,y))=f(x,f(j(y,x),y)). 331 [para_into,108.1.1.1,46.1.1,demod,15,69,12] f(x,j(y,y))=f(x,f(j(x,y),f(x,y))). 341,340 [para_into,108.1.1,14.1.1,demod,109,69,12,flip.1] f(x,f(j(x,y),f(x,y)))=f(x,f(j(x,y),y)). 344 [back_demod,331,demod,341] f(x,j(y,y))=f(x,f(j(x,y),y)). 365 [para_into,112.1.1.2,23.1.1,flip.1] f(j(x,x),0)=f(x,0). 418 [para_from,365.1.1,11.1.1.1,demod,12,flip.1] f(j(x,x),f(0,y))=f(x,f(0,y)). 442 [para_into,116.1.1.1,23.1.1,flip.1] f(0,j(x,x))=f(0,x). 454 [para_from,116.1.1,48.1.1.2.2] f(j(x,x),f(y,f(x,j(y,y))))=f(j(x,x),y). 464 [para_into,442.1.1.2,17.1.1] f(0,f(j(x,x),y))=f(0,f(x,y)). 541,540 [para_from,277.1.1,58.1.1.2,demod,90,9,27,7,flip.1] j(x,x)=0. 545,544 [para_from,277.1.1,131.1.1.2,demod,541,24,541,24,flip.1] j(x,j(x,y))=y. 546 [para_from,277.1.1,29.1.1.2,demod,541,24,541,24,flip.1] j(x,j(y,x))=y. 558,557 [back_demod,464,demod,541,47,flip.1] f(0,f(x,y))=f(0,y). 564,563 [back_demod,454,demod,541,541,558,558,20,541,flip.1] f(0,x)=0. 570,569 [back_demod,418,demod,541,564,20,564,flip.1] f(x,0)=0. 571 [back_demod,344,demod,541,570,flip.1] f(x,f(j(x,y),y))=0. 573 [back_demod,291,demod,541,570,flip.1] f(x,f(j(y,x),y))=0. 678 [para_into,571.1.1.2.1,546.1.1] f(x,f(y,j(y,x)))=0. 719,718 [para_into,573.1.1.2.1,546.1.1] f(j(x,y),f(x,y))=0. 784 [para_from,678.1.1,70.1.1.1,demod,5,78,20,109,flip.1] f(x,j(y,f(j(y,x),x)))=x. 885,884 [para_from,718.1.1,102.1.1.2,demod,24,115,545,flip.1] f(x,f(y,x))=f(y,x). 1222 [para_into,784.1.1.2.2.1,68.1.1,demod,12,719,570,24,12,885] f(x,y)=f(y,x). 1223 [binary,1222.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 68 clauses generated 2527 clauses kept 745 clauses forward subsumed 2347 clauses back subsumed 12 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.08 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) That finishes the proof of the theorem. Process 8288 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/robbins.in0100644000076400007640000000065205515263014016761 0ustar mccunemccune% Robbins algebra % % If a Robbins algebra has an element c such that x+c=c, % then it is Boolean. % % Commutativity, associativity, and Huntington's axiom % axiomatize Boolean algebra. set(auto). list(usable). x = x. x+y = y+x. (x+y)+z = x+y+z. n(n(x+y)+n(x+n(y))) = x. % Robbins axiom x+C = C. % hypothesis---exists a 1 n(A+n(B))+n(n(A)+n(B)) != B. % denial of Huntington axiom end_of_list. otter-3.3f/examples/auto/ec_yq.out0100664000076400007640000001441510103522153016617 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:35 2004 The command was "../../bin/otter". The process ID is 8263. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] -P(e(x,y))| -P(x)|P(y). 0 [] P(e(e(x,y),e(e(x,z),e(z,y)))). 0 [] -P(e(e(a,b),e(e(c,b),e(a,c)))). end_of_list. SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -P(e(x,y))| -P(x)|P(y). ** KEPT (pick-wt=12): 2 [] -P(e(e(a,b),e(e(c,b),e(a,c)))). ------------> process sos: ** KEPT (pick-wt=12): 3 [] P(e(e(x,y),e(e(x,z),e(z,y)))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 3 [] P(e(e(x,y),e(e(x,z),e(z,y)))). given clause #2: (wt=16) 4 [hyper,3,1,3] P(e(e(e(x,y),z),e(z,e(e(x,u),e(u,y))))). given clause #3: (wt=16) 7 [hyper,4,1,3] P(e(e(e(x,y),e(y,z)),e(e(x,u),e(u,z)))). given clause #4: (wt=12) 8 [hyper,7,1,7] P(e(e(e(x,x),y),e(y,e(z,z)))). given clause #5: (wt=12) 11 [hyper,7,1,3] P(e(e(x,y),e(y,e(z,e(x,z))))). given clause #6: (wt=20) 5 [hyper,4,1,4] P(e(e(x,e(e(y,z),e(z,u))),e(e(e(y,u),v),e(v,x)))). given clause #7: (wt=12) 12 [hyper,8,1,8] P(e(e(e(x,x),e(y,y)),e(z,z))). given clause #8: (wt=4) 33 [hyper,12,1,12] P(e(x,x)). given clause #9: (wt=8) 35 [hyper,12,1,8] P(e(e(x,x),e(y,y))). given clause #10: (wt=8) 39 [hyper,33,1,11] P(e(x,e(y,e(x,y)))). given clause #11: (wt=20) 6 [hyper,4,1,3] P(e(e(e(e(x,y),z),u),e(u,e(z,e(e(x,v),e(v,y)))))). given clause #12: (wt=8) 40 [hyper,33,1,7] P(e(e(x,y),e(y,x))). given clause #13: (wt=8) 50 [hyper,39,1,33] P(e(x,e(e(y,y),x))). given clause #14: (wt=8) 79 [hyper,40,1,39] P(e(e(x,e(y,x)),y)). given clause #15: (wt=8) 86 [hyper,50,1,40] P(e(e(e(x,x),y),y)). given clause #16: (wt=20) 9 [hyper,7,1,4] P(e(e(e(x,y),e(y,z)),e(e(e(x,u),v),e(v,e(u,z))))). given clause #17: (wt=12) 15 [hyper,8,1,7] P(e(e(e(x,y),e(y,x)),e(z,z))). given clause #18: (wt=12) 18 [hyper,11,1,8] P(e(e(x,e(y,e(x,y))),e(z,z))). given clause #19: (wt=12) 27 [hyper,5,1,7] P(e(e(x,y),e(y,e(e(z,z),x)))). given clause #20: (wt=12) 41 [hyper,35,1,11] P(e(e(x,x),e(y,e(e(z,z),y)))). given clause #21: (wt=20) 10 [hyper,7,1,3] P(e(e(e(e(x,y),e(y,z)),u),e(u,e(e(x,v),e(v,z))))). given clause #22: (wt=12) 42 [hyper,35,1,4] P(e(e(x,x),e(e(y,z),e(z,y)))). given clause #23: (wt=12) 43 [hyper,39,1,39] P(e(x,e(e(y,e(z,e(y,z))),x))). given clause #24: (wt=12) 44 [hyper,39,1,11] P(e(e(x,e(y,x)),e(z,e(y,z)))). given clause #25: (wt=12) 45 [hyper,39,1,8] P(e(e(x,e(e(y,y),x)),e(z,z))). given clause #26: (wt=16) 13 [hyper,8,1,4] P(e(e(x,e(y,y)),e(e(e(z,z),u),e(u,x)))). given clause #27: (wt=12) 46 [hyper,39,1,7] P(e(e(x,y),e(y,e(e(x,z),z)))). given clause #28: (wt=8) 263 [hyper,46,1,86] P(e(x,e(e(x,y),y))). given clause #29: (wt=8) 304 [hyper,263,1,40] P(e(e(e(x,y),y),x)). given clause #30: (wt=12) 47 [hyper,39,1,5] P(e(e(e(x,e(x,y)),z),e(z,y))). given clause #31: (wt=16) 14 [hyper,8,1,3] P(e(e(e(e(x,x),y),z),e(z,e(y,e(u,u))))). given clause #32: (wt=8) 352 [hyper,47,1,86] P(e(e(x,e(x,y)),y)). given clause #33: (wt=8) 372 [hyper,47,1,40] P(e(e(e(x,y),x),y)). given clause #34: (wt=8) 399 [hyper,14,1,304] P(e(x,e(x,e(y,y)))). given clause #35: (wt=8) 419 [hyper,352,1,40] P(e(x,e(y,e(y,x)))). given clause #36: (wt=16) 16 [hyper,8,1,4] P(e(e(e(x,y),e(e(x,z),e(z,y))),e(u,u))). given clause #37: (wt=8) 431 [hyper,372,1,40] P(e(x,e(e(y,x),y))). given clause #38: (wt=8) 445 [hyper,399,1,40] P(e(e(x,e(y,y)),x)). given clause #39: (wt=12) 49 [hyper,39,1,35] P(e(x,e(e(e(y,y),e(z,z)),x))). given clause #40: (wt=12) 73 [hyper,40,1,39] P(e(x,e(e(e(y,z),e(z,y)),x))). given clause #41: (wt=16) 17 [hyper,11,1,11] P(e(e(x,e(y,e(z,y))),e(u,e(e(z,x),u)))). given clause #42: (wt=12) 74 [hyper,40,1,11] P(e(e(x,y),e(z,e(e(y,x),z)))). given clause #43: (wt=12) 77 [hyper,40,1,4] P(e(e(x,y),e(e(y,z),e(z,x)))). given clause #44: (wt=12) 78 [hyper,40,1,3] P(e(e(e(x,y),z),e(z,e(y,x)))). given clause #45: (wt=12) 80 [hyper,40,1,12] P(e(e(x,x),e(e(y,y),e(z,z)))). given clause #46: (wt=16) 19 [hyper,11,1,4] P(e(e(x,e(y,e(z,y))),e(e(z,u),e(u,x)))). given clause #47: (wt=12) 81 [hyper,40,1,11] P(e(e(x,e(y,e(z,y))),e(z,x))). given clause #48: (wt=12) 82 [hyper,40,1,8] P(e(e(x,e(y,y)),e(e(z,z),x))). given clause #49: (wt=12) 85 [hyper,40,1,3] P(e(e(e(x,y),e(y,z)),e(x,z))). -------- PROOF -------- ----> UNIT CONFLICT at 0.05 sec ----> 946 [binary,945.1,2.1] $F. Length of proof is 9. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] -P(e(e(a,b),e(e(c,b),e(a,c)))). 3 [] P(e(e(x,y),e(e(x,z),e(z,y)))). 4 [hyper,3,1,3] P(e(e(e(x,y),z),e(z,e(e(x,u),e(u,y))))). 7 [hyper,4,1,3] P(e(e(e(x,y),e(y,z)),e(e(x,u),e(u,z)))). 8 [hyper,7,1,7] P(e(e(e(x,x),y),e(y,e(z,z)))). 12 [hyper,8,1,8] P(e(e(e(x,x),e(y,y)),e(z,z))). 33 [hyper,12,1,12] P(e(x,x)). 40 [hyper,33,1,7] P(e(e(x,y),e(y,x))). 78 [hyper,40,1,3] P(e(e(e(x,y),z),e(z,e(y,x)))). 85 [hyper,40,1,3] P(e(e(e(x,y),e(y,z)),e(x,z))). 945 [hyper,85,1,78] P(e(e(x,y),e(e(z,y),e(x,z)))). 946 [binary,945.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 49 clauses generated 1839 clauses kept 945 clauses forward subsumed 897 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8263 finished Mon Aug 2 15:30:35 2004 otter-3.3f/examples/auto/wang1.out0100664000076400007640000002221110103522154016526 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8318. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] y=m|p(y,m)|v1=m|v1=y| -p(y,v1)| -p(v1,y). 0 [] y=b| -p(y,b)|v=b|v=y| -p(y,v)| -p(v,y). 0 [] y=k|y=m|y=b| -p(y,k). 0 [] y=m| -p(y,m)|f(y)!=m. 0 [] y=m| -p(y,m)|f(y)!=y. 0 [] y=m| -p(y,m)|p(y,f(y)). 0 [] y=m| -p(y,m)|p(f(y),y). 0 [] y=b|p(y,b)|g(y)!=b. 0 [] y=b|p(y,b)|g(y)!=y. 0 [] y=b|p(y,b)|p(y,g(y)). 0 [] y=b|p(y,b)|p(g(y),y). 0 [] y=k|y!=m|p(y,k). 0 [] y=k|y!=b|p(y,k). 0 [] x=x. 0 [] x!=y|y=x. 0 [] x!=y|y!=z|x=z. 0 [] x!=y| -p(x,z)|p(y,z). 0 [] x!=y| -p(z,x)|p(z,y). 0 [] x!=y|f(x)=f(y). 0 [] x!=y|g(x)=g(y). 0 [] m!=b. 0 [] b!=k. 0 [] k!=m. end_of_list. SCAN INPUT: prop=0, horn=0, equality=1, symmetry=1, max_lits=6. This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: set(unit_deletion). dependent: set(factor). There is a clause for symmetry of equality, so it is assumed that equality is fully axiomatized; therefore, paramodulation is disabled. dependent: clear(para_from). dependent: clear(para_into). ------------> process usable: ** KEPT (pick-wt=18): 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). ** KEPT (pick-wt=18): 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). ** KEPT (pick-wt=12): 3 [] x=k|x=m|x=b| -p(x,k). ** KEPT (pick-wt=10): 4 [] x=m| -p(x,m)|f(x)!=m. ** KEPT (pick-wt=10): 5 [] x=m| -p(x,m)|f(x)!=x. ** KEPT (pick-wt=10): 6 [] x=m| -p(x,m)|p(x,f(x)). ** KEPT (pick-wt=10): 7 [] x=m| -p(x,m)|p(f(x),x). ** KEPT (pick-wt=10): 8 [] x=b|p(x,b)|g(x)!=b. ** KEPT (pick-wt=10): 9 [] x=b|p(x,b)|g(x)!=x. ** KEPT (pick-wt=9): 10 [] x=k|x!=m|p(x,k). ** KEPT (pick-wt=9): 11 [] x=k|x!=b|p(x,k). ** KEPT (pick-wt=6): 12 [] x!=y|y=x. ** KEPT (pick-wt=9): 13 [] x!=y|y!=z|x=z. ** KEPT (pick-wt=9): 14 [] x!=y| -p(x,z)|p(y,z). ** KEPT (pick-wt=9): 15 [] x!=y| -p(z,x)|p(z,y). ** KEPT (pick-wt=8): 16 [] x!=y|f(x)=f(y). ** KEPT (pick-wt=8): 17 [] x!=y|g(x)=g(y). ** KEPT (pick-wt=3): 18 [] m!=b. ** KEPT (pick-wt=3): 20 [copy,19,flip.1] k!=b. ** KEPT (pick-wt=3): 22 [copy,21,flip.1] m!=k. ------------> process sos: ** KEPT (pick-wt=10): 28 [] x=b|p(x,b)|p(x,g(x)). ** KEPT (pick-wt=10): 29 [] x=b|p(x,b)|p(g(x),x). ** KEPT (pick-wt=3): 30 [] x=x. Following clause subsumed by 30 during input processing: 0 [copy,30,flip.1] x=x. 30 back subsumes 27. 30 back subsumes 26. 30 back subsumes 25. 30 back subsumes 24. 30 back subsumes 23. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=10) 28 [] x=b|p(x,b)|p(x,g(x)). given clause #2: (wt=3) 30 [] x=x. given clause #3: (wt=3) 31 [hyper,30,11,unit_del,20] p(b,k). given clause #4: (wt=3) 32 [hyper,30,10,unit_del,22] p(m,k). given clause #5: (wt=7) 33 [hyper,31,1,28,unit_del,22,18,20,20] p(k,m)|p(k,g(k)). given clause #6: (wt=10) 29 [] x=b|p(x,b)|p(g(x),x). given clause #7: (wt=4) 38 [hyper,33,2,28,32,unit_del,20,18,22,20,factor_simp] p(k,g(k)). given clause #8: (wt=7) 40 [hyper,29,1,31,unit_del,20,18,22,20] p(g(k),k)|p(b,m). given clause #9: (wt=7) 41 [hyper,29,1,31,unit_del,20,22,18,20] p(g(k),k)|p(k,m). given clause #10: (wt=4) 68 [hyper,41,2,29,32,unit_del,20,18,22,20,factor_simp] p(g(k),k). given clause #11: (wt=20) 39 [hyper,29,2,29,28,factor_simp,factor_simp,factor_simp,factor_simp] g(x)=b|p(g(g(x)),g(x))|x=b|g(x)=x|p(x,b). given clause #12: (wt=11) 63 [hyper,41,1,38,unit_del,22,factor_simp] p(k,m)|g(k)=m|g(k)=k. given clause #13: (wt=12) 69 [hyper,68,3] g(k)=k|g(k)=m|g(k)=b. given clause #14: (wt=11) 83 [hyper,69,15,38] g(k)=m|g(k)=b|p(k,k). given clause #15: (wt=11) 88 [hyper,69,9,unit_del,20] g(k)=m|g(k)=b|p(k,b). given clause #16: (wt=13) 42 [hyper,29,7,unit_del,18] p(m,b)|g(m)=m|p(f(g(m)),g(m)). given clause #17: (wt=11) 92 [hyper,69,15,38] g(k)=k|g(k)=b|p(k,m). given clause #18: (wt=11) 97 [hyper,69,15,38] g(k)=k|g(k)=m|p(k,b). given clause #19: (wt=8) 107 [hyper,97,2,63,32,unit_del,20,18,22,factor_simp,factor_simp] g(k)=k|g(k)=m. given clause #20: (wt=7) 110 [hyper,107,15,38] g(k)=m|p(k,k). given clause #21: (wt=13) 43 [hyper,29,6,unit_del,18] p(m,b)|g(m)=m|p(g(m),f(g(m))). given clause #22: (wt=7) 111 [hyper,107,9,unit_del,20] g(k)=m|p(k,b). given clause #23: (wt=7) 114 [hyper,107,15,38] g(k)=k|p(k,m). given clause #24: (wt=7) 123 [hyper,111,1,31,unit_del,18,22,20] g(k)=m|p(b,m). given clause #25: (wt=7) 124 [hyper,111,1,31,unit_del,22,18,20] g(k)=m|p(k,m). given clause #26: (wt=20) 45 [hyper,29,2,28,28,factor_simp,factor_simp,factor_simp,factor_simp] x=b|p(x,b)|g(x)=b|g(x)=x|p(g(x),g(g(x))). given clause #27: (wt=3) 150 [back_demod,114,demod,142,unit_del,22] p(k,m). given clause #28: (wt=4) 141 [hyper,124,2,111,32,unit_del,20,18,22,factor_simp] g(k)=m. given clause #29: (wt=4) 143 [back_demod,131,demod,142,unit_del,22] p(m,g(m)). given clause #30: (wt=4) 144 [back_demod,130,demod,142,unit_del,22] p(g(m),m). given clause #31: (wt=20) 46 [hyper,29,1,28,factor_simp,factor_simp] x=b|p(x,b)|x=m|p(x,m)|g(x)=m|g(x)=x. given clause #32: (wt=4) 148 [back_demod,126,demod,142,unit_del,22] p(k,f(k)). given clause #33: (wt=4) 149 [back_demod,125,demod,142,unit_del,22] p(f(k),k). given clause #34: (wt=10) 146 [back_demod,128,demod,142,unit_del,22] g(m)=m|p(f(g(m)),g(m)). given clause #35: (wt=10) 147 [back_demod,127,demod,142,unit_del,22] g(m)=m|p(g(m),f(g(m))). given clause #36: (wt=21) 47 [hyper,29,1,28,factor_simp,factor_simp] x=b|p(x,b)|g(x)=m|p(g(x),m)|x=m|g(x)=x. given clause #37: (wt=12) 165 [hyper,149,3] f(k)=k|f(k)=m|f(k)=b. given clause #38: (wt=8) 192 [hyper,165,5,150,unit_del,22] f(k)=m|f(k)=b. given clause #39: (wt=3) 211 [hyper,192,15,148,demod,210,unit_del,18] p(k,b). -------- PROOF -------- -----> EMPTY CLAUSE at 0.11 sec ----> 213 [hyper,211,2,150,32,unit_del,20,18,22] $F. Length of proof is 25. Level of proof is 15. ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=k|x!=m|p(x,k). 11 [] x=k|x!=b|p(x,k). 15 [] x!=y| -p(z,x)|p(z,y). 18 [] m!=b. 19 [] b!=k. 20 [copy,19,flip.1] k!=b. 21 [] k!=m. 22 [copy,21,flip.1] m!=k. 28 [] x=b|p(x,b)|p(x,g(x)). 29 [] x=b|p(x,b)|p(g(x),x). 30 [] x=x. 31 [hyper,30,11,unit_del,20] p(b,k). 32 [hyper,30,10,unit_del,22] p(m,k). 33 [hyper,31,1,28,unit_del,22,18,20,20] p(k,m)|p(k,g(k)). 38 [hyper,33,2,28,32,unit_del,20,18,22,20,factor_simp] p(k,g(k)). 41 [hyper,29,1,31,unit_del,20,22,18,20] p(g(k),k)|p(k,m). 63 [hyper,41,1,38,unit_del,22,factor_simp] p(k,m)|g(k)=m|g(k)=k. 68 [hyper,41,2,29,32,unit_del,20,18,22,20,factor_simp] p(g(k),k). 69 [hyper,68,3] g(k)=k|g(k)=m|g(k)=b. 97 [hyper,69,15,38] g(k)=k|g(k)=m|p(k,b). 107 [hyper,97,2,63,32,unit_del,20,18,22,factor_simp,factor_simp] g(k)=k|g(k)=m. 111 [hyper,107,9,unit_del,20] g(k)=m|p(k,b). 114 [hyper,107,15,38] g(k)=k|p(k,m). 124 [hyper,111,1,31,unit_del,22,18,20] g(k)=m|p(k,m). 125 [hyper,114,7,unit_del,22] g(k)=k|p(f(k),k). 126 [hyper,114,6,unit_del,22] g(k)=k|p(k,f(k)). 142,141 [hyper,124,2,111,32,unit_del,20,18,22,factor_simp] g(k)=m. 148 [back_demod,126,demod,142,unit_del,22] p(k,f(k)). 149 [back_demod,125,demod,142,unit_del,22] p(f(k),k). 150 [back_demod,114,demod,142,unit_del,22] p(k,m). 165 [hyper,149,3] f(k)=k|f(k)=m|f(k)=b. 192 [hyper,165,5,150,unit_del,22] f(k)=m|f(k)=b. 210,209 [hyper,192,4,150,unit_del,22] f(k)=b. 211 [hyper,192,15,148,demod,210,unit_del,18] p(k,b). 213 [hyper,211,2,150,32,unit_del,20,18,22] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 39 clauses generated 1494 clauses kept 208 clauses forward subsumed 1356 clauses back subsumed 95 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.11 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8318 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/w_sk.out0100664000076400007640000001401110103522154016453 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8323. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] a(a(a(S,x),y),z)=a(a(x,z),a(y,z)). 0 [] a(a(K,x),y)=x. end_of_list. formula_list(usable). -(exists W all x y (a(a(W,x),y)=a(a(x,y),y)& -$ans(W))). end_of_list. -------> usable clausifies to: list(usable). 0 [] a(a(x1,$f2(x1)),$f1(x1))!=a(a($f2(x1),$f1(x1)),$f1(x1))|$ans(x1). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=16): 2 [copy,1,flip.1] a(a($f2(x),$f1(x)),$f1(x))!=a(a(x,$f2(x)),$f1(x))|$ans(x). ------------> process sos: ** KEPT (pick-wt=3): 3 [] x=x. ** KEPT (pick-wt=15): 4 [] a(a(a(S,x),y),z)=a(a(x,z),a(y,z)). ** KEPT (pick-wt=7): 5 [] a(a(K,x),y)=x. ---> New Demodulator: 6 [new_demod,5] a(a(K,x),y)=x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x=x. ** KEPT (pick-wt=15): 7 [copy,4,flip.1] a(a(x,y),a(z,y))=a(a(a(S,x),z),y). >>>> Starting back demodulation with 6. Following clause subsumed by 4 during input processing: 0 [copy,7,flip.1] a(a(a(S,x),y),z)=a(a(x,z),a(y,z)). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 3 [] x=x. given clause #2: (wt=7) 5 [] a(a(K,x),y)=x. given clause #3: (wt=15) 4 [] a(a(a(S,x),y),z)=a(a(x,z),a(y,z)). given clause #4: (wt=15) 7 [copy,4,flip.1] a(a(x,y),a(z,y))=a(a(a(S,x),z),y). given clause #5: (wt=9) 15 [para_into,7.1.1,5.1.1,flip.1] a(a(a(S,K),x),y)=y. given clause #6: (wt=25) 8 [para_into,7.1.1.1,7.1.1] a(a(a(a(S,x),y),z),a(u,a(y,z)))=a(a(a(S,a(x,z)),u),a(y,z)). given clause #7: (wt=11) 26 [para_into,15.1.1.1,7.1.1] a(a(a(a(S,S),x),K),y)=y. given clause #8: (wt=13) 28 [para_into,15.1.1,7.1.1] a(a(a(S,a(S,K)),x),y)=a(x,y). given clause #9: (wt=13) 62 [para_into,26.1.1.1.1,7.1.1] a(a(a(a(a(S,S),x),S),K),y)=y. given clause #10: (wt=15) 9 [para_into,7.1.1.1,5.1.1,flip.1] a(a(a(S,a(K,x)),y),z)=a(x,a(y,z)). given clause #11: (wt=23) 11 [para_into,7.1.1.1,4.1.1] a(a(a(x,y),a(z,y)),a(u,y))=a(a(a(S,a(a(S,x),z)),u),y). given clause #12: (wt=15) 13 [para_into,7.1.1.2,5.1.1] a(a(x,y),z)=a(a(a(S,x),a(K,z)),y). given clause #13: (wt=15) 21 [copy,13,flip.1] a(a(a(S,x),a(K,y)),z)=a(a(x,z),y). given clause #14: (wt=15) 64 [para_into,26.1.1,7.1.1] a(a(a(S,a(a(S,S),x)),y),K)=a(y,K). given clause #15: (wt=15) 86 [para_into,62.1.1.1.1.1,7.1.1] a(a(a(a(a(a(S,S),x),S),S),K),y)=y. given clause #16: (wt=25) 12 [para_into,7.1.1.2,7.1.1] a(a(x,a(y,z)),a(a(a(S,u),y),z))=a(a(a(S,x),a(u,z)),a(y,z)). given clause #17: (wt=15) 226 [para_from,13.1.1,26.1.1.1] a(a(a(a(S,a(S,S)),a(K,K)),x),y)=y. given clause #18: (wt=15) 248 [para_into,21.1.1.1,7.1.1] a(a(a(a(S,S),K),x),y)=a(a(x,y),x). given clause #19: (wt=15) 254 [copy,248,flip.1] a(a(x,y),x)=a(a(a(a(S,S),K),x),y). given clause #20: (wt=17) 30 [para_from,15.1.1,7.1.1.2] a(a(x,y),y)=a(a(a(S,x),a(a(S,K),z)),y). given clause #21: (wt=23) 14 [para_into,7.1.1.2,4.1.1] a(a(x,y),a(a(z,y),a(u,y)))=a(a(a(S,x),a(a(S,z),u)),y). given clause #22: (wt=17) 31 [para_from,15.1.1,7.1.1.1] a(x,a(y,x))=a(a(a(S,a(a(S,K),z)),y),x). given clause #23: (wt=15) 897 [para_into,31.1.1,5.1.1,flip.1] a(a(a(S,a(a(S,K),x)),y),a(K,z))=z. given clause #24: (wt=15) 1041 [para_into,897.1.1,7.1.1] a(a(a(S,a(S,a(a(S,K),x))),K),y)=y. given clause #25: (wt=17) 32 [copy,30,flip.1] a(a(a(S,x),a(a(S,K),y)),z)=a(a(x,z),z). -------- PROOF -------- 1157 [binary,1156.1,2.1] $ans(a(a(S,S),a(K,a(a(S,K),z)))). ----> UNIT CONFLICT at 0.11 sec ----> 1157 [binary,1156.1,2.1] $ans(a(a(S,S),a(K,a(a(S,K),z)))). Length of proof is 8. Level of proof is 6. ---------------- PROOF ---------------- 1 [] a(a(x,$f2(x)),$f1(x))!=a(a($f2(x),$f1(x)),$f1(x))|$ans(x). 2 [copy,1,flip.1] a(a($f2(x),$f1(x)),$f1(x))!=a(a(x,$f2(x)),$f1(x))|$ans(x). 4 [] a(a(a(S,x),y),z)=a(a(x,z),a(y,z)). 5 [] a(a(K,x),y)=x. 7 [copy,4,flip.1] a(a(x,y),a(z,y))=a(a(a(S,x),z),y). 13 [para_into,7.1.1.2,5.1.1] a(a(x,y),z)=a(a(a(S,x),a(K,z)),y). 15 [para_into,7.1.1,5.1.1,flip.1] a(a(a(S,K),x),y)=y. 30 [para_from,15.1.1,7.1.1.2] a(a(x,y),y)=a(a(a(S,x),a(a(S,K),z)),y). 32 [copy,30,flip.1] a(a(a(S,x),a(a(S,K),y)),z)=a(a(x,z),z). 1141 [para_into,32.1.1.1,13.1.1] a(a(a(a(S,S),a(K,a(a(S,K),x))),y),z)=a(a(y,z),z). 1156 [copy,1141,flip.1] a(a(x,y),y)=a(a(a(a(S,S),a(K,a(a(S,K),z))),x),y). 1157 [binary,1156.1,2.1] $ans(a(a(S,S),a(K,a(a(S,K),z)))). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 25 clauses generated 922 clauses kept 1036 clauses forward subsumed 812 clauses back subsumed 0 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.11 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8323 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/group.in0100644000076400007640000000024505470212343016454 0ustar mccunemccune% % Search for a complete set of reductions for free groups. % set(auto). list(usable). x = x. f(e,x) = x. f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). end_of_list. otter-3.3f/examples/auto/index.html0100644000076400007640000000362107714267401016776 0ustar mccunemccune /home/mccune/otter-3.3/examples/auto

/home/mccune/otter-3.3/examples/auto

These problems are easy for Otter. All use the autonomous mode.

otter < cn19.in > cn19.out

otter < comm.in > comm.out

otter < ec_yq.in > ec_yq.out

otter < group.in > group.out

otter < lifsch.in > lifsch.out

otter < mv25.in > mv25.out

otter < pigeon.in > pigeon.out

otter < ring_x2.in > ring_x2.out

otter < robbins.in > robbins.out

otter < salt.in > salt.out

otter < sam.in > sam.out

otter < steam.in > steam.out

otter < tba_gg.in > tba_gg.out

otter < wang1.in > wang1.out

otter < w_sk.in > w_sk.out

otter < x2_quant.in > x2_quant.out

otter < z11.in > z11.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/auto/README0100644000076400007640000000010007313711033015634 0ustar mccunemccuneThese problems are easy for Otter. All use the autonomous mode. otter-3.3f/examples/auto/cn19.in0100644000076400007640000000066005470212343016073 0ustar mccunemccune% The sentential calculus (CN). % % {CN1, CN2, CN3} (Lukasiewicz), along with condensed detachment, % axiomatizes the sentential calculus (the classical propositional calculus). % set(auto). list(usable). -P(i(x,y)) | -P(x) | P(y). % condensed detachment P(i(i(x,y),i(i(y,z),i(x,z)))). % CN1 P(i(i(n(x),x),x)). % CN2 P(i(x,i(n(x),y))). % CN3 -P(i(i(i(a,b),c),i(b,c))) | $Ans(CN_19). end_of_list. otter-3.3f/examples/auto/z11.in0100644000076400007640000000060305470212344015732 0ustar mccunemccune% If a group has relations ab=c, bc=d, cd=h, dh=a, ha=b, it is % cyclic with order 11. The following input will not cause a proof, % but the result follows easily from examination of the lists near the % end of the output. set(auto). list(usable). x = x. f(e,x) = x. f(g(x),x) = e. f(f(x,y),z) = f(x,f(y,z)). f(a,b) = c. f(b,c) = d. f(c,d) = h. f(d,h) = a. f(h,a) = b. end_of_list. otter-3.3f/examples/auto/sam.out0100664000076400007640000003366710103522154016312 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8303. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] join(1,x,1). 0 [] join(x,1,1). 0 [] join(0,x,x). 0 [] join(x,0,x). 0 [] meet(0,x,0). 0 [] meet(x,0,0). 0 [] meet(1,x,x). 0 [] meet(x,1,x). 0 [] meet(x,x,x). 0 [] join(x,x,x). 0 [] -meet(x,y,z)|meet(y,x,z). 0 [] -join(x,y,z)|join(y,x,z). 0 [] -meet(x,y,z)|join(x,z,x). 0 [] -join(x,y,z)|meet(x,z,x). 0 [] -meet(x,y,xy)| -meet(y,z,yz)| -meet(x,yz,xyz)|meet(xy,z,xyz). 0 [] -meet(x,y,xy)| -meet(y,z,yz)| -meet(xy,z,xyz)|meet(x,yz,xyz). 0 [] -join(x,y,xy)| -join(y,z,yz)| -join(x,yz,xyz)|join(xy,z,xyz). 0 [] -join(x,y,xy)| -join(y,z,yz)| -join(xy,z,xyz)|join(x,yz,xyz). 0 [] -meet(x,z,x)| -join(x,y,x1)| -meet(y,z,y1)| -meet(z,x1,z1)|join(x,y1,z1). 0 [] -meet(x,z,x)| -join(x,y,x1)| -meet(y,z,y1)| -join(x,y1,z1)|meet(z,x1,z1). 0 [] -meet(a2,b2,r1). 0 [] meet(a,b,c). 0 [] join(c,r2,1). 0 [] meet(c,r2,0). 0 [] meet(r2,b,e). 0 [] join(a,b,c2). 0 [] join(c2,r1,1). 0 [] meet(c2,r1,0). 0 [] meet(r2,a,d). 0 [] join(r1,e,a2). 0 [] join(r1,d,b2). end_of_list. SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -meet(x,y,z)|meet(y,x,z). ** KEPT (pick-wt=8): 2 [] -join(x,y,z)|join(y,x,z). ** KEPT (pick-wt=8): 3 [] -meet(x,y,z)|join(x,z,x). ** KEPT (pick-wt=8): 4 [] -join(x,y,z)|meet(x,z,x). ** KEPT (pick-wt=16): 5 [] -meet(x,y,z)| -meet(y,u,v)| -meet(x,v,w)|meet(z,u,w). ** KEPT (pick-wt=16): 6 [] -meet(x,y,z)| -meet(y,u,v)| -meet(z,u,w)|meet(x,v,w). ** KEPT (pick-wt=16): 7 [] -join(x,y,z)| -join(y,u,v)| -join(x,v,w)|join(z,u,w). ** KEPT (pick-wt=16): 8 [] -join(x,y,z)| -join(y,u,v)| -join(z,u,w)|join(x,v,w). ** KEPT (pick-wt=20): 9 [] -meet(x,y,x)| -join(x,z,u)| -meet(z,y,v)| -meet(y,u,w)|join(x,v,w). ** KEPT (pick-wt=20): 10 [] -meet(x,y,x)| -join(x,z,u)| -meet(z,y,v)| -join(x,v,w)|meet(y,u,w). ** KEPT (pick-wt=4): 11 [] -meet(a2,b2,r1). ------------> process sos: ** KEPT (pick-wt=4): 12 [] join(1,x,1). ** KEPT (pick-wt=4): 13 [] join(x,1,1). ** KEPT (pick-wt=4): 14 [] join(0,x,x). ** KEPT (pick-wt=4): 15 [] join(x,0,x). ** KEPT (pick-wt=4): 16 [] meet(0,x,0). ** KEPT (pick-wt=4): 17 [] meet(x,0,0). ** KEPT (pick-wt=4): 18 [] meet(1,x,x). ** KEPT (pick-wt=4): 19 [] meet(x,1,x). ** KEPT (pick-wt=4): 20 [] meet(x,x,x). ** KEPT (pick-wt=4): 21 [] join(x,x,x). ** KEPT (pick-wt=4): 22 [] meet(a,b,c). ** KEPT (pick-wt=4): 23 [] join(c,r2,1). ** KEPT (pick-wt=4): 24 [] meet(c,r2,0). ** KEPT (pick-wt=4): 25 [] meet(r2,b,e). ** KEPT (pick-wt=4): 26 [] join(a,b,c2). ** KEPT (pick-wt=4): 27 [] join(c2,r1,1). ** KEPT (pick-wt=4): 28 [] meet(c2,r1,0). ** KEPT (pick-wt=4): 29 [] meet(r2,a,d). ** KEPT (pick-wt=4): 30 [] join(r1,e,a2). ** KEPT (pick-wt=4): 31 [] join(r1,d,b2). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=4) 12 [] join(1,x,1). given clause #2: (wt=4) 13 [] join(x,1,1). given clause #3: (wt=4) 14 [] join(0,x,x). given clause #4: (wt=4) 15 [] join(x,0,x). given clause #5: (wt=4) 16 [] meet(0,x,0). given clause #6: (wt=4) 17 [] meet(x,0,0). given clause #7: (wt=4) 18 [] meet(1,x,x). given clause #8: (wt=4) 19 [] meet(x,1,x). given clause #9: (wt=4) 20 [] meet(x,x,x). given clause #10: (wt=4) 21 [] join(x,x,x). given clause #11: (wt=4) 22 [] meet(a,b,c). given clause #12: (wt=4) 23 [] join(c,r2,1). given clause #13: (wt=4) 24 [] meet(c,r2,0). given clause #14: (wt=4) 25 [] meet(r2,b,e). given clause #15: (wt=4) 26 [] join(a,b,c2). given clause #16: (wt=4) 27 [] join(c2,r1,1). given clause #17: (wt=4) 28 [] meet(c2,r1,0). given clause #18: (wt=4) 29 [] meet(r2,a,d). given clause #19: (wt=4) 30 [] join(r1,e,a2). given clause #20: (wt=4) 31 [] join(r1,d,b2). given clause #21: (wt=4) 32 [hyper,22,10,16,14,14] meet(b,a,c). given clause #22: (wt=4) 33 [hyper,22,6,20,22] meet(a,c,c). given clause #23: (wt=4) 34 [hyper,22,5,22,20] meet(c,b,c). given clause #24: (wt=4) 35 [hyper,22,3] join(a,c,a). given clause #25: (wt=4) 36 [hyper,23,2] join(r2,c,1). given clause #26: (wt=4) 37 [hyper,24,10,16,14,21] meet(r2,c,0). given clause #27: (wt=4) 38 [hyper,25,10,16,14,14] meet(b,r2,e). given clause #28: (wt=4) 39 [hyper,25,6,20,25] meet(r2,e,e). given clause #29: (wt=4) 40 [hyper,25,6,24,16] meet(c,e,0). given clause #30: (wt=4) 41 [hyper,25,5,25,20] meet(e,b,e). given clause #31: (wt=4) 42 [hyper,25,3] join(r2,e,r2). given clause #32: (wt=4) 43 [hyper,26,8,21,26] join(a,c2,c2). given clause #33: (wt=4) 44 [hyper,26,7,26,21] join(c2,b,c2). given clause #34: (wt=4) 45 [hyper,26,4] meet(a,c2,a). given clause #35: (wt=4) 46 [hyper,26,2] join(b,a,c2). given clause #36: (wt=4) 47 [hyper,27,2] join(r1,c2,1). given clause #37: (wt=4) 48 [hyper,28,10,16,14,21] meet(r1,c2,0). given clause #38: (wt=4) 49 [hyper,29,10,16,14,14] meet(a,r2,d). given clause #39: (wt=4) 50 [hyper,29,6,20,29] meet(r2,d,d). given clause #40: (wt=4) 51 [hyper,29,6,24,16] meet(c,d,0). given clause #41: (wt=4) 52 [hyper,29,5,29,20] meet(d,a,d). given clause #42: (wt=4) 53 [hyper,29,3] join(r2,d,r2). given clause #43: (wt=4) 54 [hyper,30,8,21,30] join(r1,a2,a2). given clause #44: (wt=4) 55 [hyper,30,8,27,12] join(c2,a2,1). given clause #45: (wt=4) 56 [hyper,30,7,30,21] join(a2,e,a2). given clause #46: (wt=4) 57 [hyper,30,4] meet(r1,a2,r1). given clause #47: (wt=4) 58 [hyper,30,2] join(e,r1,a2). given clause #48: (wt=4) 59 [hyper,31,8,21,31] join(r1,b2,b2). given clause #49: (wt=4) 60 [hyper,31,8,27,12] join(c2,b2,1). given clause #50: (wt=4) 61 [hyper,31,7,31,21] join(b2,d,b2). given clause #51: (wt=4) 62 [hyper,31,4] meet(r1,b2,r1). given clause #52: (wt=4) 63 [hyper,31,2] join(d,r1,b2). given clause #53: (wt=4) 64 [hyper,32,6,20,32] meet(b,c,c). given clause #54: (wt=4) 65 [hyper,32,5,32,20] meet(c,a,c). given clause #55: (wt=4) 66 [hyper,32,3] join(b,c,b). given clause #56: (wt=4) 67 [hyper,34,9,23,25,19] join(c,e,b). given clause #57: (wt=4) 68 [hyper,34,9,13,18,19] join(c,b,b). given clause #58: (wt=4) 69 [hyper,35,7,23,13] join(a,r2,1). given clause #59: (wt=4) 70 [hyper,35,2] join(c,a,a). given clause #60: (wt=4) 71 [hyper,37,5,29,33] meet(d,c,0). given clause #61: (wt=4) 72 [hyper,37,5,29,22] meet(d,b,0). given clause #62: (wt=4) 73 [hyper,37,5,25,32] meet(e,a,0). given clause #63: (wt=4) 74 [hyper,38,6,20,38] meet(b,e,e). given clause #64: (wt=4) 75 [hyper,38,6,22,24] meet(a,e,0). given clause #65: (wt=4) 76 [hyper,38,5,38,20] meet(e,r2,e). given clause #66: (wt=4) 77 [hyper,38,5,37,17] meet(e,c,0). given clause #67: (wt=4) 78 [hyper,38,3] join(b,e,b). given clause #68: (wt=4) 79 [hyper,41,9,13,18,19] join(e,b,b). given clause #69: (wt=4) 80 [hyper,42,2] join(e,r2,r2). given clause #70: (wt=4) 81 [hyper,43,2] join(c2,a,c2). given clause #71: (wt=4) 82 [hyper,44,2] join(b,c2,c2). given clause #72: (wt=4) 83 [hyper,45,10,45,21,21] meet(c2,a,a). given clause #73: (wt=4) 84 [hyper,45,5,32,32] meet(c,c2,c). given clause #74: (wt=4) 85 [hyper,45,5,29,29] meet(d,c2,d). given clause #75: (wt=4) 86 [hyper,45,5,28,17] meet(a,r1,0). given clause #76: (wt=4) 87 [hyper,46,7,46,35] join(c2,c,c2). given clause #77: (wt=4) 88 [hyper,46,4] meet(b,c2,b). given clause #78: (wt=4) 89 [hyper,49,6,20,49] meet(a,d,d). given clause #79: (wt=4) 90 [hyper,49,6,32,24] meet(b,d,0). given clause #80: (wt=4) 91 [hyper,49,5,49,20] meet(d,r2,d). given clause #81: (wt=4) 92 [hyper,49,3] join(a,d,a). given clause #82: (wt=4) 93 [hyper,52,9,13,18,19] join(d,a,a). given clause #83: (wt=4) 94 [hyper,53,2] join(d,r2,r2). given clause #84: (wt=4) 95 [hyper,54,2] join(a2,r1,a2). given clause #85: (wt=4) 96 [hyper,55,2] join(a2,c2,1). given clause #86: (wt=4) 97 [hyper,56,2] join(e,a2,a2). given clause #87: (wt=4) 98 [hyper,57,10,57,21,21] meet(a2,r1,r1). given clause #88: (wt=4) 99 [hyper,58,4] meet(e,a2,e). given clause #89: (wt=4) 100 [hyper,59,2] join(b2,r1,b2). given clause #90: (wt=4) 101 [hyper,60,2] join(b2,c2,1). given clause #91: (wt=4) 102 [hyper,61,2] join(d,b2,b2). given clause #92: (wt=4) 103 [hyper,62,10,62,21,21] meet(b2,r1,r1). given clause #93: (wt=4) 104 [hyper,63,4] meet(d,b2,d). given clause #94: (wt=4) 105 [hyper,65,9,23,29,19] join(c,d,a). given clause #95: (wt=4) 106 [hyper,66,7,23,13] join(b,r2,1). given clause #96: (wt=4) 107 [hyper,67,8,36,12] join(r2,b,1). given clause #97: (wt=4) 108 [hyper,67,7,35,26] join(a,e,c2). given clause #98: (wt=4) 109 [hyper,67,2] join(e,c,b). given clause #99: (wt=4) 110 [hyper,68,8,46,46] join(c,c2,c2). given clause #100: (wt=4) 111 [hyper,69,7,46,13] join(c2,r2,1). given clause #101: (wt=4) 112 [hyper,69,2] join(r2,a,1). given clause #102: (wt=4) 113 [hyper,72,6,38,16] meet(d,e,0). given clause #103: (wt=4) 114 [hyper,73,6,49,16] meet(e,d,0). given clause #104: (wt=4) 115 [hyper,78,7,44,44] join(c2,e,c2). given clause #105: (wt=4) 116 [hyper,79,8,46,46] join(e,c2,c2). given clause #106: (wt=4) 117 [hyper,83,6,48,16] meet(r1,a,0). given clause #107: (wt=4) 118 [hyper,83,6,49,49] meet(c2,d,d). given clause #108: (wt=4) 119 [hyper,83,6,33,33] meet(c2,c,c). given clause #109: (wt=4) 120 [hyper,84,5,28,17] meet(c,r1,0). given clause #110: (wt=4) 121 [hyper,85,10,63,48,15] meet(c2,b2,d). given clause #111: (wt=4) 122 [hyper,85,9,13,18,19] join(d,c2,c2). given clause #112: (wt=4) 123 [hyper,85,5,28,17] meet(d,r1,0). given clause #113: (wt=4) 124 [hyper,88,10,88,21,21] meet(c2,b,b). given clause #114: (wt=4) 125 [hyper,88,5,41,41] meet(e,c2,e). given clause #115: (wt=4) 126 [hyper,88,5,28,17] meet(b,r1,0). given clause #116: (wt=4) 127 [hyper,92,7,81,81] join(c2,d,c2). given clause #117: (wt=4) 128 [hyper,99,10,99,21,21] meet(a2,e,e). given clause #118: (wt=4) 129 [hyper,104,10,104,21,21] meet(b2,d,d). given clause #119: (wt=4) 130 [hyper,105,7,66,46] join(b,d,c2). given clause #120: (wt=4) 131 [hyper,105,2] join(d,c,a). given clause #121: (wt=4) 132 [hyper,107,8,82,12] join(r2,c2,1). given clause #122: (wt=4) 133 [hyper,108,8,97,55] join(a,a2,1). given clause #123: (wt=4) 134 [hyper,108,2] join(e,a,c2). given clause #124: (wt=4) 135 [hyper,117,10,52,63,15] meet(a,b2,d). given clause #125: (wt=4) 136 [hyper,117,6,89,16] meet(r1,d,0). given clause #126: (wt=4) 137 [hyper,117,6,33,16] meet(r1,c,0). given clause #127: (wt=4) 138 [hyper,121,10,16,14,14] meet(b2,c2,d). given clause #128: (wt=4) 139 [hyper,121,5,88,90] meet(b,b2,0). given clause #129: (wt=4) 140 [hyper,121,5,84,51] meet(c,b2,0). given clause #130: (wt=4) 141 [hyper,124,6,48,16] meet(r1,b,0). given clause #131: (wt=4) 142 [hyper,124,6,74,74] meet(c2,e,e). given clause #132: (wt=4) 143 [hyper,125,10,58,48,15] meet(c2,a2,e). given clause #133: (wt=4) 144 [hyper,125,5,121,114] meet(e,b2,0). given clause #134: (wt=4) 145 [hyper,125,5,28,17] meet(e,r1,0). given clause #135: (wt=4) 146 [hyper,130,8,102,60] join(b,b2,1). given clause #136: (wt=4) 147 [hyper,130,2] join(d,b,c2). given clause #137: (wt=4) 148 [hyper,133,2] join(a2,a,1). given clause #138: (wt=4) 149 [hyper,135,10,104,93,21] meet(b2,a,d). given clause #139: (wt=4) 150 [hyper,138,6,124,72] meet(b2,b,0). given clause #140: (wt=4) 151 [hyper,138,6,119,71] meet(b2,c,0). given clause #141: (wt=4) 152 [hyper,141,10,41,58,15] meet(b,a2,e). given clause #142: (wt=4) 153 [hyper,141,6,74,16] meet(r1,e,0). given clause #143: (wt=4) 154 [hyper,142,6,138,113] meet(b2,e,0). given clause #144: (wt=4) 155 [hyper,143,10,99,116,21] meet(a2,c2,e). given clause #145: (wt=4) 156 [hyper,143,5,85,113] meet(d,a2,0). -------- PROOF -------- ----> UNIT CONFLICT at 0.07 sec ----> 166 [binary,165.1,11.1] $F. Length of proof is 16. Level of proof is 6. ---------------- PROOF ---------------- 2 [] -join(x,y,z)|join(y,x,z). 4 [] -join(x,y,z)|meet(x,z,x). 5 [] -meet(x,y,z)| -meet(y,u,v)| -meet(x,v,w)|meet(z,u,w). 6 [] -meet(x,y,z)| -meet(y,u,v)| -meet(z,u,w)|meet(x,v,w). 10 [] -meet(x,y,x)| -join(x,z,u)| -meet(z,y,v)| -join(x,v,w)|meet(y,u,w). 11 [] -meet(a2,b2,r1). 14 [] join(0,x,x). 15 [] join(x,0,x). 16 [] meet(0,x,0). 20 [] meet(x,x,x). 21 [] join(x,x,x). 22 [] meet(a,b,c). 24 [] meet(c,r2,0). 25 [] meet(r2,b,e). 26 [] join(a,b,c2). 28 [] meet(c2,r1,0). 29 [] meet(r2,a,d). 30 [] join(r1,e,a2). 31 [] join(r1,d,b2). 37 [hyper,24,10,16,14,21] meet(r2,c,0). 38 [hyper,25,10,16,14,14] meet(b,r2,e). 41 [hyper,25,5,25,20] meet(e,b,e). 45 [hyper,26,4] meet(a,c2,a). 46 [hyper,26,2] join(b,a,c2). 48 [hyper,28,10,16,14,21] meet(r1,c2,0). 57 [hyper,30,4] meet(r1,a2,r1). 58 [hyper,30,2] join(e,r1,a2). 72 [hyper,37,5,29,22] meet(d,b,0). 85 [hyper,45,5,29,29] meet(d,c2,d). 88 [hyper,46,4] meet(b,c2,b). 113 [hyper,72,6,38,16] meet(d,e,0). 125 [hyper,88,5,41,41] meet(e,c2,e). 143 [hyper,125,10,58,48,15] meet(c2,a2,e). 156 [hyper,143,5,85,113] meet(d,a2,0). 165 [hyper,156,10,57,31,15] meet(a2,b2,r1). 166 [binary,165.1,11.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 145 clauses generated 7058 clauses kept 165 clauses forward subsumed 6924 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.07 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8303 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/tba_gg.out0100664000076400007640000001215510103522154016742 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8313. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] f(f(v,w,x),y,f(v,w,z))=f(v,w,f(x,y,z)). 0 [] f(y,x,x)=x. 0 [] f(x,x,y)=x. 0 [] f(g(y),y,x)=x. 0 [] f(x,y,g(y))=x. 0 [] g(g(a))!=a. end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=5): 1 [] g(g(a))!=a. ------------> process sos: ** KEPT (pick-wt=3): 2 [] x=x. ** KEPT (pick-wt=18): 3 [] f(f(x,y,z),u,f(x,y,v))=f(x,y,f(z,u,v)). ---> New Demodulator: 4 [new_demod,3] f(f(x,y,z),u,f(x,y,v))=f(x,y,f(z,u,v)). ** KEPT (pick-wt=6): 5 [] f(x,y,y)=y. ---> New Demodulator: 6 [new_demod,5] f(x,y,y)=y. ** KEPT (pick-wt=6): 7 [] f(x,x,y)=x. ---> New Demodulator: 8 [new_demod,7] f(x,x,y)=x. ** KEPT (pick-wt=7): 9 [] f(g(x),x,y)=y. ---> New Demodulator: 10 [new_demod,9] f(g(x),x,y)=y. ** KEPT (pick-wt=7): 11 [] f(x,y,g(y))=x. ---> New Demodulator: 12 [new_demod,11] f(x,y,g(y))=x. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x=x. >>>> Starting back demodulation with 4. >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 2 [] x=x. given clause #2: (wt=6) 5 [] f(x,y,y)=y. given clause #3: (wt=6) 7 [] f(x,x,y)=x. given clause #4: (wt=7) 9 [] f(g(x),x,y)=y. given clause #5: (wt=7) 11 [] f(x,y,g(y))=x. given clause #6: (wt=18) 3 [] f(f(x,y,z),u,f(x,y,v))=f(x,y,f(z,u,v)). given clause #7: (wt=6) 14 [para_into,3.1.1.1,7.1.1,demod,8,8] f(x,y,x)=x. given clause #8: (wt=15) 16 [para_into,3.1.1.1,5.1.1] f(x,y,f(z,x,u))=f(z,x,f(x,y,u)). given clause #9: (wt=12) 37 [para_into,16.1.1.3,14.1.1,flip.1] f(x,y,f(y,z,x))=f(y,z,x). given clause #10: (wt=13) 39 [para_into,16.1.1.3,11.1.1] f(x,y,z)=f(z,x,f(x,y,g(x))). given clause #11: (wt=16) 13 [para_into,3.1.1.1,11.1.1] f(x,y,f(x,z,u))=f(x,z,f(g(z),y,u)). given clause #12: (wt=10) 60 [para_into,39.1.1,5.1.1,flip.1] f(x,y,f(y,x,g(y)))=x. given clause #13: (wt=10) 71 [para_into,13.1.1.3,14.1.1,demod,15,flip.1] f(x,y,f(g(y),z,x))=x. given clause #14: (wt=10) 80 [para_into,13.1.1,7.1.1,flip.1] f(x,y,f(g(y),x,z))=x. given clause #15: (wt=10) 120 [para_into,80.1.1.3,37.1.1] f(x,y,f(x,z,g(y)))=x. given clause #16: (wt=30) 17 [para_into,3.1.1.1,3.1.1] f(f(x,y,f(z,u,v)),w,f(f(x,y,z),u,v6))=f(f(x,y,z),u,f(f(x,y,v),w,v6)). given clause #17: (wt=10) 126 [para_into,80.1.1,39.1.1,demod,57] f(g(x),y,f(y,x,z))=y. given clause #18: (wt=7) 242 [para_into,126.1.1.3,5.1.1] f(g(x),y,x)=y. -------- PROOF -------- ----> UNIT CONFLICT at 0.02 sec ----> 266 [binary,264.1,1.1] $F. Length of proof is 8. Level of proof is 6. ---------------- PROOF ---------------- 1 [] g(g(a))!=a. 3 [] f(f(x,y,z),u,f(x,y,v))=f(x,y,f(z,u,v)). 5 [] f(x,y,y)=y. 7 [] f(x,x,y)=x. 11 [] f(x,y,g(y))=x. 13 [para_into,3.1.1.1,11.1.1] f(x,y,f(x,z,u))=f(x,z,f(g(z),y,u)). 16 [para_into,3.1.1.1,5.1.1] f(x,y,f(z,x,u))=f(z,x,f(x,y,u)). 39 [para_into,16.1.1.3,11.1.1] f(x,y,z)=f(z,x,f(x,y,g(x))). 57,56 [para_into,39.1.1,16.1.1,flip.1] f(f(x,y,z),y,f(y,u,g(y)))=f(x,y,f(y,u,z)). 80 [para_into,13.1.1,7.1.1,flip.1] f(x,y,f(g(y),x,z))=x. 126 [para_into,80.1.1,39.1.1,demod,57] f(g(x),y,f(y,x,z))=y. 242 [para_into,126.1.1.3,5.1.1] f(g(x),y,x)=y. 264 [para_into,242.1.1,11.1.1] g(g(x))=x. 266 [binary,264.1,1.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 18 clauses generated 379 clauses kept 165 clauses forward subsumed 308 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8313 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/auto/mv25.in0100644000076400007640000000073105470212343016111 0ustar mccunemccune% The (infinitely) Many-Valued sentential calculus (MV). % % {MV-1,MV-2,MV-3,MV-5} axiomatizes MV. % set(auto). list(usable). -P(i(x,y)) | -P(x) | P(y). % condensed detachment P(i(x,i(y,x))). % MV-1 P(i(i(x,y),i(i(y,z),i(x,z)))). % MV-2 P(i(i(i(x,y),y),i(i(y,x),x))). % MV-3 P(i(i(n(x),n(y)),i(y,x))). % MV-5 % -P(i(n(n(a)),a)) | $ANS(MV_24). -P(i(i(a,b),i(i(c,a),i(c,b)))) | $ANS(MV_25). % -P(i(a,n(n(a)))) | $ANS(MV_29). end_of_list. otter-3.3f/examples/misc/0040755000076400007640000000000010103530360014744 5ustar mccunemccuneotter-3.3f/examples/misc/sax1.in0100644000076400007640000000073205515522043016161 0ustar mccunemccune% % is a single axiom for groups in terms % of product and inverse. % set(knuth_bendix). assign(max_proofs, 3). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(stats_level, 1). list(usable). x = x. end_of_list. list(passive). f(a,g(a)) != f(b,g(b)) | $Ans(R_inverse). f(a,f(b,g(b))) != a | $Ans(R_ident). f(f(a,b),c) != f(a,f(b,c)) | $Ans(assoc). end_of_list. list(sos). f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x)))) = u. % (3.1.1) end_of_list. otter-3.3f/examples/misc/dem_alu.in0100644000076400007640000000336410041250571016711 0ustar mccunemccune% % Canonicalizing an exclusive-or/and expression with % lex-dependent demodulation. % % This example comes from a verification problem of Smith, % Kljaich, Wojcik, and Chisholm. % op(500, xfy, #). % exclusive or op(400, xfy, *). % and lex([0, 1, cin, a0, b0, a1, b1, a2, b2, a3, b3, *(_,_), #(_,_)]). set(demod_inf). clear(demod_history). assign(demod_limit, -1). assign(max_given, 1). clear(for_sub). clear(back_sub). list(demodulators). % The following is a set of reductions for Boolean rings. % Under the following conditions, it produces a canonical form. % 1. The lex term must be lex([, *(_,_), #(_,_)]). % 2. If variables are in the term being rewritten, set(lex_order_vars). 0#x=x. x#0=x. x#x=0. x#x#y=y. x#y=y#x. y#x#z=x#y#z. 0*x=0. x*0=0. 1*x=x. x*1=x. x*x=x. x*x*y=x*y. x*y=y*x. y*x*z=x*y*z. x * (y#z) = (x*y) # (x*z). end_of_list. list(sos). p( (a2#b2#1#a2*b2)# (a3#b3)#1# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a1#b1#1#a1*b1)* (1#a2*b2)# (a1#b1#1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2) ). end_of_list. otter-3.3f/examples/misc/sax2.in0100644000076400007640000000101205515521034016151 0ustar mccunemccune% % ((xy)z)(xz)' = y is a single axiom for Abelian groups in terms % of product and inverse. % set(knuth_bendix). assign(max_proofs, 4). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(stats_level, 1). list(usable). x = x. end_of_list. list(passive). f(a,g(a)) != f(b,g(b)) | $Ans(R_inverse). f(a,f(b,g(b))) != a | $Ans(R_ident). f(f(a,b),c) != f(a,f(b,c)) | $Ans(assoc). f(a,b) != f(b,a) | $Ans(commute). end_of_list. list(sos). f(f(f(x,y),z),g(f(x,z))) = y. % 421 (3.2.1) end_of_list. otter-3.3f/examples/misc/mv.in0100644000076400007640000000140210041250571015714 0ustar mccunemccune% The (infinitely) Many-Valued sentential calculus (MV). % % {MV-1,MV-2,MV-3,MV-5} axiomatizes MV. % % Derive MV-24, MV-25, and MV-29 by condensed detachment. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs, 3). clear(print_kept). set(order_history). assign(fpa_literals, 0). % Disable FPA indexing, because it doesn't help much. list(usable). -P(i(x,y)) | -P(x) | P(y). % condensed detachment end_of_list. list(sos). P(i(x,i(y,x))). % MV-1 P(i(i(x,y),i(i(y,z),i(x,z)))). % MV-2 P(i(i(i(x,y),y),i(i(y,x),x))). % MV-3 P(i(i(n(x),n(y)),i(y,x))). % MV-5 end_of_list. list(passive). -P(i(n(n(a)),a)) | $ANS(MV_24). -P(i(i(a,b),i(i(c,a),i(c,b)))) | $ANS(MV_25). -P(i(a,n(n(a)))) | $ANS(MV_29). end_of_list. otter-3.3f/examples/misc/andrews.in0100644000076400007640000000146110041250571016742 0ustar mccunemccune% Challenge problem from Peter Andrews (1979) % % Although this problem is more easily solved by direct simplification % of the quantified formula (Champeaux, J. ACM 1986 and SIGART Newsletter), % it makes a good test problem for resolution theorem provers. Otter % can do this problem, because it translates equivalences in two ways, % depending on the context, producing only 128 clauses. (Also, FormEd % can prove it by direct simplification.) % set(binary_res). set(process_input). clear(print_kept). clear(print_back_sub). formula_list(sos). % Andrews challenge problem -( ( (exists x all y (p(x) <-> p(y))) <-> ((exists u q(u)) <-> (all v p(v))) ) <-> ( (exists w all z (q(z) <-> q(w))) <-> ((exists x1 p(x1)) <-> (all x2 q(x2))) ) ). end_of_list. otter-3.3f/examples/misc/dem_alu.out0100664000076400007640000000766010103522155017116 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8371. op(500,xfy,#). op(400,xfy,*). lex([0,1,cin,a0,b0,a1,b1,a2,b2,a3,b3,_*_,_#_]). set(demod_inf). clear(demod_history). assign(demod_limit,-1). assign(max_given,1). clear(for_sub). clear(back_sub). list(demodulators). 1 [] 0#x=x. 2 [] x#0=x. 3 [] x#x=0. 4 [] x#x#y=y. 5 [] x#y=y#x. 6 [] y#x#z=x#y#z. 7 [] 0*x=0. 8 [] x*0=0. 9 [] 1*x=x. 10 [] x*1=x. 11 [] x*x=x. 12 [] x*x*y=x*y. 13 [] x*y=y*x. 14 [] y*x*z=x*y*z. 15 [] x* (y#z)=x*y#x*z. end_of_list. list(sos). 16 [] p((a2#b2#1#a2*b2)# (a3#b3)#1# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a1#b1#1#a1*b1)* (1#a2*b2)# (a1#b1#1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)). end_of_list. lex dependent demodulator: 5 [] x#y=y#x. lex dependent demodulator: 6 [] y#x#z=x#y#z. lex dependent demodulator: 13 [] x*y=y*x. lex dependent demodulator: 14 [] y*x*z=x*y*z. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=482) 16 [] p((a2#b2#1#a2*b2)# (a3#b3)#1# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a1#b1#1#a1*b1)* (1#a2*b2)# (a1#b1#1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)). Search stopped by max_given option. ** KEPT (pick-wt=116): 17 [16,demod] p(a3#b3#cin*a0*a1*a2#cin*a0*a1*b2#cin*a0*b1*a2#cin*a0*b1*b2#cin*b0*a1*a2#cin*b0*a1*b2#cin*b0*b1*a2#cin*b0*b1*b2#a0*b0*a1*a2#a0*b0*a1*b2#a0*b0*b1*a2#a0*b0*b1*b2#a1*b1*a2#a1*b1*b2#a2*b2). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 1 clauses generated 1 demod_inf generated 1 demod & eval rewrites 44775 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 1 new demodulators 0 empty clauses 0 clauses back demodulated 0 clauses back subsumed 0 usable size 1 sos size 1 demodulators size 15 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.15 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8371 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/stage1.out0100664000076400007640000005547110103522155016677 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8401. set(para_into). clear(para_from_left). clear(para_into_left). set(para_ones_rule). clear(back_sub). clear(print_proofs). assign(max_proofs,-1). assign(max_given,30). list(usable). 1 [] x=x. 2 [] a(a(a(B,x),y),z)=a(x,a(y,z)). 3 [] a(a(W,x),y)=a(a(x,y),y). end_of_list. list(sos). 4 [] y!=a(f,y)|$Ans(y). end_of_list. assign(max_weight,1). weight_list(purge_gen). weight(x,-1000). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=5) 4 [] y!=a(f,y)|$Ans(y). ** KEPT (pick-wt=11): 5 [para_into,4.1.2,2.1.2] a(x,y)!=a(a(a(B,f),x),y)|$Ans(a(x,y)). ----> UNIT CONFLICT at 0.00 sec ----> 6 [binary,5.1,3.1] $Ans(a(a(W,a(B,f)),a(W,a(B,f)))). given clause #2: (wt=11) 5 [para_into,4.1.2,2.1.2] a(x,y)!=a(a(a(B,f),x),y)|$Ans(a(x,y)). ** KEPT (pick-wt=11): 7 [para_into,5.1.2.1,3.1.2] a(f,x)!=a(a(a(W,B),f),x)|$Ans(a(f,x)). ** KEPT (pick-wt=17): 8 [para_into,5.1.2.1,2.1.2] a(a(x,y),z)!=a(a(a(a(B,a(B,f)),x),y),z)|$Ans(a(a(x,y),z)). ----> UNIT CONFLICT at 0.00 sec ----> 9 [binary,8.1,3.1] $Ans(a(a(W,a(a(B,a(B,f)),W)),a(a(B,a(B,f)),W))). ** KEPT (pick-wt=11): 10 [para_into,5.1.2,3.1.2] a(x,x)!=a(a(W,a(B,f)),x)|$Ans(a(x,x)). ----> UNIT CONFLICT at 0.00 sec ----> 11 [binary,10.1,1.1] $Ans(a(a(W,a(B,f)),a(W,a(B,f)))). ** KEPT (pick-wt=17): 12 [para_into,5.1.2,2.1.2] a(x,a(y,z))!=a(a(a(B,a(a(B,f),x)),y),z)|$Ans(a(x,a(y,z))). given clause #3: (wt=11) 7 [para_into,5.1.2.1,3.1.2] a(f,x)!=a(a(a(W,B),f),x)|$Ans(a(f,x)). ** KEPT (pick-wt=17): 13 [para_into,7.1.2,2.1.2] a(f,a(x,y))!=a(a(a(B,a(a(W,B),f)),x),y)|$Ans(a(f,a(x,y))). given clause #4: (wt=11) 10 [para_into,5.1.2,3.1.2] a(x,x)!=a(a(W,a(B,f)),x)|$Ans(a(x,x)). ** KEPT (pick-wt=13): 14 [para_into,10.1.2.1,2.1.2] a(x,x)!=a(a(a(a(B,W),B),f),x)|$Ans(a(x,x)). ----> UNIT CONFLICT at 0.00 sec ----> 15 [binary,14.1,1.1] $Ans(a(a(a(a(B,W),B),f),a(a(a(B,W),B),f))). ** KEPT (pick-wt=19): 16 [para_into,10.1.2,2.1.2] a(a(x,y),a(x,y))!=a(a(a(B,a(W,a(B,f))),x),y)|$Ans(a(a(x,y),a(x,y))). given clause #5: (wt=13) 14 [para_into,10.1.2.1,2.1.2] a(x,x)!=a(a(a(a(B,W),B),f),x)|$Ans(a(x,x)). ** KEPT (pick-wt=21): 17 [para_into,14.1.2,2.1.2] a(a(x,y),a(x,y))!=a(a(a(B,a(a(a(B,W),B),f)),x),y)|$Ans(a(a(x,y),a(x,y))). given clause #6: (wt=17) 8 [para_into,5.1.2.1,2.1.2] a(a(x,y),z)!=a(a(a(a(B,a(B,f)),x),y),z)|$Ans(a(a(x,y),z)). ** KEPT (pick-wt=19): 18 [para_into,8.1.2.1.1.1,2.1.2] a(a(x,y),z)!=a(a(a(a(a(a(B,B),B),f),x),y),z)|$Ans(a(a(x,y),z)). ----> UNIT CONFLICT at 0.00 sec ----> 19 [binary,18.1,3.1] $Ans(a(a(W,a(a(a(a(B,B),B),f),W)),a(a(a(a(B,B),B),f),W))). ** KEPT (pick-wt=19): 20 [para_into,8.1.2.1.1,3.1.2] a(a(a(B,f),x),y)!=a(a(a(a(W,B),a(B,f)),x),y)|$Ans(a(a(a(B,f),x),y)). ** KEPT (pick-wt=23): 21 [para_into,8.1.2.1.1,2.1.2] a(a(a(x,y),z),u)!=a(a(a(a(a(B,a(B,a(B,f))),x),y),z),u)|$Ans(a(a(a(x,y),z),u)). ** KEPT (pick-wt=17): 22 [para_into,8.1.2.1,3.1.2] a(a(x,x),y)!=a(a(a(W,a(B,a(B,f))),x),y)|$Ans(a(a(x,x),y)). ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,1.1] $Ans(a(a(a(W,a(B,a(B,f))),a(W,a(B,a(B,f)))),y)). ** KEPT (pick-wt=23): 24 [para_into,8.1.2.1,2.1.2] a(a(x,a(y,z)),u)!=a(a(a(a(B,a(a(B,a(B,f)),x)),y),z),u)|$Ans(a(a(x,a(y,z)),u)). ----> UNIT CONFLICT at 0.00 sec ----> 25 [binary,24.1,3.1] $Ans(a(a(W,a(a(B,a(a(B,a(B,f)),W)),a(B,a(a(B,a(B,f)),W)))),a(B,a(a(B,a(B,f)),W)))). ** KEPT (pick-wt=17): 26 [para_into,8.1.2,3.1.2] a(a(x,y),y)!=a(a(W,a(a(B,a(B,f)),x)),y)|$Ans(a(a(x,y),y)). ----> UNIT CONFLICT at 0.00 sec ----> 27 [binary,26.1,1.1] $Ans(a(a(W,a(a(B,a(B,f)),W)),a(a(B,a(B,f)),W))). ** KEPT (pick-wt=23): 28 [para_into,8.1.2,2.1.2] a(a(x,y),a(z,u))!=a(a(a(B,a(a(a(B,a(B,f)),x),y)),z),u)|$Ans(a(a(x,y),a(z,u))). given clause #7: (wt=17) 12 [para_into,5.1.2,2.1.2] a(x,a(y,z))!=a(a(a(B,a(a(B,f),x)),y),z)|$Ans(a(x,a(y,z))). ** KEPT (pick-wt=19): 29 [para_into,12.1.2.1.1,2.1.2] a(x,a(y,z))!=a(a(a(a(a(B,B),a(B,f)),x),y),z)|$Ans(a(x,a(y,z))). ** KEPT (pick-wt=21): 30 [para_into,12.1.2.1,3.1.2] a(x,a(a(a(B,f),x),y))!=a(a(a(W,B),a(a(B,f),x)),y)|$Ans(a(x,a(a(a(B,f),x),y))). ** KEPT (pick-wt=23): 31 [para_into,12.1.2.1,2.1.2] a(x,a(a(y,z),u))!=a(a(a(a(B,a(B,a(a(B,f),x))),y),z),u)|$Ans(a(x,a(a(y,z),u))). ** KEPT (pick-wt=17): 32 [para_into,12.1.2,3.1.2] a(x,a(y,y))!=a(a(W,a(B,a(a(B,f),x))),y)|$Ans(a(x,a(y,y))). ** KEPT (pick-wt=23): 33 [para_into,12.1.2,2.1.2] a(x,a(y,a(z,u)))!=a(a(a(B,a(a(B,a(a(B,f),x)),y)),z),u)|$Ans(a(x,a(y,a(z,u)))). given clause #8: (wt=17) 13 [para_into,7.1.2,2.1.2] a(f,a(x,y))!=a(a(a(B,a(a(W,B),f)),x),y)|$Ans(a(f,a(x,y))). ** KEPT (pick-wt=19): 34 [para_into,13.1.2.1.1,2.1.2] a(f,a(x,y))!=a(a(a(a(a(B,B),a(W,B)),f),x),y)|$Ans(a(f,a(x,y))). ** KEPT (pick-wt=21): 35 [para_into,13.1.2.1,3.1.2] a(f,a(a(a(W,B),f),x))!=a(a(a(W,B),a(a(W,B),f)),x)|$Ans(a(f,a(a(a(W,B),f),x))). ** KEPT (pick-wt=23): 36 [para_into,13.1.2.1,2.1.2] a(f,a(a(x,y),z))!=a(a(a(a(B,a(B,a(a(W,B),f))),x),y),z)|$Ans(a(f,a(a(x,y),z))). ** KEPT (pick-wt=17): 37 [para_into,13.1.2,3.1.2] a(f,a(x,x))!=a(a(W,a(B,a(a(W,B),f))),x)|$Ans(a(f,a(x,x))). ** KEPT (pick-wt=23): 38 [para_into,13.1.2,2.1.2] a(f,a(x,a(y,z)))!=a(a(a(B,a(a(B,a(a(W,B),f)),x)),y),z)|$Ans(a(f,a(x,a(y,z)))). given clause #9: (wt=17) 22 [para_into,8.1.2.1,3.1.2] a(a(x,x),y)!=a(a(a(W,a(B,a(B,f))),x),y)|$Ans(a(a(x,x),y)). ** KEPT (pick-wt=19): 39 [para_into,22.1.2.1.1,2.1.2] a(a(x,x),y)!=a(a(a(a(a(B,W),B),a(B,f)),x),y)|$Ans(a(a(x,x),y)). ----> UNIT CONFLICT at 0.00 sec ----> 40 [binary,39.1,1.1] $Ans(a(a(a(a(a(B,W),B),a(B,f)),a(a(a(B,W),B),a(B,f))),y)). ** KEPT (pick-wt=25): 41 [para_into,22.1.2.1,3.1.2] a(a(a(B,a(B,f)),a(B,a(B,f))),x)!=a(a(a(W,W),a(B,a(B,f))),x)|$Ans(a(a(a(B,a(B,f)),a(B,a(B,f))),x)). ** KEPT (pick-wt=25): 42 [para_into,22.1.2.1,2.1.2] a(a(a(x,y),a(x,y)),z)!=a(a(a(a(B,a(W,a(B,a(B,f)))),x),y),z)|$Ans(a(a(a(x,y),a(x,y)),z)). ** KEPT (pick-wt=17): 43 [para_into,22.1.2,3.1.2] a(a(x,x),x)!=a(a(W,a(W,a(B,a(B,f)))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=23): 44 [para_into,22.1.2,2.1.2] a(a(x,x),a(y,z))!=a(a(a(B,a(a(W,a(B,a(B,f))),x)),y),z)|$Ans(a(a(x,x),a(y,z))). given clause #10: (wt=17) 26 [para_into,8.1.2,3.1.2] a(a(x,y),y)!=a(a(W,a(a(B,a(B,f)),x)),y)|$Ans(a(a(x,y),y)). ** KEPT (pick-wt=19): 45 [para_into,26.1.2.1,2.1.2] a(a(x,y),y)!=a(a(a(a(B,W),a(B,a(B,f))),x),y)|$Ans(a(a(x,y),y)). ----> UNIT CONFLICT at 0.00 sec ----> 46 [binary,45.1,1.1] $Ans(a(a(a(a(B,W),a(B,a(B,f))),a(a(B,W),a(B,a(B,f)))),a(a(B,W),a(B,a(B,f))))). ** KEPT (pick-wt=29): 47 [para_into,26.1.2,3.1.2] a(a(x,a(a(B,a(B,f)),x)),a(a(B,a(B,f)),x))!=a(a(W,W),a(a(B,a(B,f)),x))|$Ans(a(a(x,a(a(B,a(B,f)),x)),a(a(B,a(B,f)),x))). ** KEPT (pick-wt=25): 48 [para_into,26.1.2,2.1.2] a(a(x,a(y,z)),a(y,z))!=a(a(a(B,a(W,a(a(B,a(B,f)),x))),y),z)|$Ans(a(a(x,a(y,z)),a(y,z))). given clause #11: (wt=17) 32 [para_into,12.1.2,3.1.2] a(x,a(y,y))!=a(a(W,a(B,a(a(B,f),x))),y)|$Ans(a(x,a(y,y))). ** KEPT (pick-wt=19): 49 [para_into,32.1.2.1,2.1.2] a(x,a(y,y))!=a(a(a(a(B,W),B),a(a(B,f),x)),y)|$Ans(a(x,a(y,y))). ** KEPT (pick-wt=29): 50 [para_into,32.1.2,3.1.2] a(x,a(a(B,a(a(B,f),x)),a(B,a(a(B,f),x))))!=a(a(W,W),a(B,a(a(B,f),x)))|$Ans(a(x,a(a(B,a(a(B,f),x)),a(B,a(a(B,f),x))))). ** KEPT (pick-wt=25): 51 [para_into,32.1.2,2.1.2] a(x,a(a(y,z),a(y,z)))!=a(a(a(B,a(W,a(B,a(a(B,f),x)))),y),z)|$Ans(a(x,a(a(y,z),a(y,z)))). given clause #12: (wt=17) 37 [para_into,13.1.2,3.1.2] a(f,a(x,x))!=a(a(W,a(B,a(a(W,B),f))),x)|$Ans(a(f,a(x,x))). ** KEPT (pick-wt=19): 52 [para_into,37.1.2.1,2.1.2] a(f,a(x,x))!=a(a(a(a(B,W),B),a(a(W,B),f)),x)|$Ans(a(f,a(x,x))). ** KEPT (pick-wt=25): 53 [para_into,37.1.2,2.1.2] a(f,a(a(x,y),a(x,y)))!=a(a(a(B,a(W,a(B,a(a(W,B),f)))),x),y)|$Ans(a(f,a(a(x,y),a(x,y)))). given clause #13: (wt=17) 43 [para_into,22.1.2,3.1.2] a(a(x,x),x)!=a(a(W,a(W,a(B,a(B,f)))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=19): 54 [para_into,43.1.2.1,2.1.2] a(a(x,x),x)!=a(a(a(a(B,W),W),a(B,a(B,f))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=27): 55 [para_into,43.1.2,2.1.2] a(a(a(x,y),a(x,y)),a(x,y))!=a(a(a(B,a(W,a(W,a(B,a(B,f))))),x),y)|$Ans(a(a(a(x,y),a(x,y)),a(x,y))). given clause #14: (wt=19) 16 [para_into,10.1.2,2.1.2] a(a(x,y),a(x,y))!=a(a(a(B,a(W,a(B,f))),x),y)|$Ans(a(a(x,y),a(x,y))). ** KEPT (pick-wt=21): 56 [para_into,16.1.2.1.1,2.1.2] a(a(x,y),a(x,y))!=a(a(a(a(a(B,B),W),a(B,f)),x),y)|$Ans(a(a(x,y),a(x,y))). ** KEPT (pick-wt=27): 57 [para_into,16.1.2.1,3.1.2] a(a(a(W,a(B,f)),x),a(a(W,a(B,f)),x))!=a(a(a(W,B),a(W,a(B,f))),x)|$Ans(a(a(a(W,a(B,f)),x),a(a(W,a(B,f)),x))). ** KEPT (pick-wt=27): 58 [para_into,16.1.2.1,2.1.2] a(a(a(x,y),z),a(a(x,y),z))!=a(a(a(a(B,a(B,a(W,a(B,f)))),x),y),z)|$Ans(a(a(a(x,y),z),a(a(x,y),z))). ** KEPT (pick-wt=19): 59 [para_into,16.1.2,3.1.2] a(a(x,x),a(x,x))!=a(a(W,a(B,a(W,a(B,f)))),x)|$Ans(a(a(x,x),a(x,x))). ** KEPT (pick-wt=27): 60 [para_into,16.1.2,2.1.2] a(a(x,a(y,z)),a(x,a(y,z)))!=a(a(a(B,a(a(B,a(W,a(B,f))),x)),y),z)|$Ans(a(a(x,a(y,z)),a(x,a(y,z)))). given clause #15: (wt=19) 18 [para_into,8.1.2.1.1.1,2.1.2] a(a(x,y),z)!=a(a(a(a(a(a(B,B),B),f),x),y),z)|$Ans(a(a(x,y),z)). ** KEPT (pick-wt=19): 61 [para_into,18.1.2.1.1.1.1,3.1.2] a(a(x,y),z)!=a(a(a(a(a(a(W,B),B),f),x),y),z)|$Ans(a(a(x,y),z)). ----> UNIT CONFLICT at 0.01 sec ----> 62 [binary,61.1,3.1] $Ans(a(a(W,a(a(a(a(W,B),B),f),W)),a(a(a(a(W,B),B),f),W))). ** KEPT (pick-wt=19): 63 [para_into,18.1.2.1.1,3.1.2] a(a(f,x),y)!=a(a(a(a(W,a(a(B,B),B)),f),x),y)|$Ans(a(a(f,x),y)). ** KEPT (pick-wt=25): 64 [para_into,18.1.2.1.1,2.1.2] a(a(a(x,y),z),u)!=a(a(a(a(a(B,a(a(a(B,B),B),f)),x),y),z),u)|$Ans(a(a(a(x,y),z),u)). ** KEPT (pick-wt=19): 65 [para_into,18.1.2.1,3.1.2] a(a(x,x),y)!=a(a(a(W,a(a(a(B,B),B),f)),x),y)|$Ans(a(a(x,x),y)). ----> UNIT CONFLICT at 0.01 sec ----> 66 [binary,65.1,1.1] $Ans(a(a(a(W,a(a(a(B,B),B),f)),a(W,a(a(a(B,B),B),f))),y)). ** KEPT (pick-wt=25): 67 [para_into,18.1.2.1,2.1.2] a(a(x,a(y,z)),u)!=a(a(a(a(B,a(a(a(a(B,B),B),f),x)),y),z),u)|$Ans(a(a(x,a(y,z)),u)). ----> UNIT CONFLICT at 0.01 sec ----> 68 [binary,67.1,3.1] $Ans(a(a(W,a(a(B,a(a(a(a(B,B),B),f),W)),a(B,a(a(a(a(B,B),B),f),W)))),a(B,a(a(a(a(B,B),B),f),W)))). ** KEPT (pick-wt=19): 69 [para_into,18.1.2,3.1.2] a(a(x,y),y)!=a(a(W,a(a(a(a(B,B),B),f),x)),y)|$Ans(a(a(x,y),y)). ----> UNIT CONFLICT at 0.01 sec ----> 70 [binary,69.1,1.1] $Ans(a(a(W,a(a(a(a(B,B),B),f),W)),a(a(a(a(B,B),B),f),W))). ** KEPT (pick-wt=25): 71 [para_into,18.1.2,2.1.2] a(a(x,y),a(z,u))!=a(a(a(B,a(a(a(a(a(B,B),B),f),x),y)),z),u)|$Ans(a(a(x,y),a(z,u))). given clause #16: (wt=19) 20 [para_into,8.1.2.1.1,3.1.2] a(a(a(B,f),x),y)!=a(a(a(a(W,B),a(B,f)),x),y)|$Ans(a(a(a(B,f),x),y)). ** KEPT (pick-wt=21): 72 [para_into,20.1.2.1.1,2.1.2] a(a(a(B,f),x),y)!=a(a(a(a(a(B,a(W,B)),B),f),x),y)|$Ans(a(a(a(B,f),x),y)). ** KEPT (pick-wt=21): 73 [para_into,20.1.2.1,3.1.2] a(a(a(B,f),a(B,f)),x)!=a(a(a(W,a(W,B)),a(B,f)),x)|$Ans(a(a(a(B,f),a(B,f)),x)). ** KEPT (pick-wt=25): 74 [para_into,20.1.2.1,2.1.2] a(a(a(B,f),a(x,y)),z)!=a(a(a(a(B,a(a(W,B),a(B,f))),x),y),z)|$Ans(a(a(a(B,f),a(x,y)),z)). ** KEPT (pick-wt=19): 75 [para_into,20.1.2,3.1.2] a(a(a(B,f),x),x)!=a(a(W,a(a(W,B),a(B,f))),x)|$Ans(a(a(a(B,f),x),x)). ** KEPT (pick-wt=25): 76 [para_into,20.1.2,2.1.2] a(a(a(B,f),x),a(y,z))!=a(a(a(B,a(a(a(W,B),a(B,f)),x)),y),z)|$Ans(a(a(a(B,f),x),a(y,z))). given clause #17: (wt=19) 29 [para_into,12.1.2.1.1,2.1.2] a(x,a(y,z))!=a(a(a(a(a(B,B),a(B,f)),x),y),z)|$Ans(a(x,a(y,z))). ** KEPT (pick-wt=21): 77 [para_into,29.1.2.1.1.1,2.1.2] a(x,a(y,z))!=a(a(a(a(a(a(B,a(B,B)),B),f),x),y),z)|$Ans(a(x,a(y,z))). ** KEPT (pick-wt=21): 78 [para_into,29.1.2.1.1,3.1.2] a(a(B,f),a(x,y))!=a(a(a(a(W,a(B,B)),a(B,f)),x),y)|$Ans(a(a(B,f),a(x,y))). ** KEPT (pick-wt=25): 79 [para_into,29.1.2.1.1,2.1.2] a(a(x,y),a(z,u))!=a(a(a(a(a(B,a(a(B,B),a(B,f))),x),y),z),u)|$Ans(a(a(x,y),a(z,u))). ** KEPT (pick-wt=19): 80 [para_into,29.1.2.1,3.1.2] a(x,a(x,y))!=a(a(a(W,a(a(B,B),a(B,f))),x),y)|$Ans(a(x,a(x,y))). ** KEPT (pick-wt=25): 81 [para_into,29.1.2.1,2.1.2] a(x,a(a(y,z),u))!=a(a(a(a(B,a(a(a(B,B),a(B,f)),x)),y),z),u)|$Ans(a(x,a(a(y,z),u))). ** KEPT (pick-wt=19): 82 [para_into,29.1.2,3.1.2] a(x,a(y,y))!=a(a(W,a(a(a(B,B),a(B,f)),x)),y)|$Ans(a(x,a(y,y))). ** KEPT (pick-wt=25): 83 [para_into,29.1.2,2.1.2] a(x,a(y,a(z,u)))!=a(a(a(B,a(a(a(a(B,B),a(B,f)),x),y)),z),u)|$Ans(a(x,a(y,a(z,u)))). given clause #18: (wt=19) 34 [para_into,13.1.2.1.1,2.1.2] a(f,a(x,y))!=a(a(a(a(a(B,B),a(W,B)),f),x),y)|$Ans(a(f,a(x,y))). ** KEPT (pick-wt=21): 84 [para_into,34.1.2.1.1.1,2.1.2] a(f,a(x,y))!=a(a(a(a(a(a(B,a(B,B)),W),B),f),x),y)|$Ans(a(f,a(x,y))). ** KEPT (pick-wt=19): 85 [para_into,34.1.2.1,3.1.2] a(f,a(f,x))!=a(a(a(W,a(a(B,B),a(W,B))),f),x)|$Ans(a(f,a(f,x))). ** KEPT (pick-wt=25): 86 [para_into,34.1.2.1,2.1.2] a(f,a(a(x,y),z))!=a(a(a(a(B,a(a(a(B,B),a(W,B)),f)),x),y),z)|$Ans(a(f,a(a(x,y),z))). ** KEPT (pick-wt=19): 87 [para_into,34.1.2,3.1.2] a(f,a(x,x))!=a(a(W,a(a(a(B,B),a(W,B)),f)),x)|$Ans(a(f,a(x,x))). ** KEPT (pick-wt=25): 88 [para_into,34.1.2,2.1.2] a(f,a(x,a(y,z)))!=a(a(a(B,a(a(a(a(B,B),a(W,B)),f),x)),y),z)|$Ans(a(f,a(x,a(y,z)))). given clause #19: (wt=19) 39 [para_into,22.1.2.1.1,2.1.2] a(a(x,x),y)!=a(a(a(a(a(B,W),B),a(B,f)),x),y)|$Ans(a(a(x,x),y)). ** KEPT (pick-wt=21): 89 [para_into,39.1.2.1.1,2.1.2] a(a(x,x),y)!=a(a(a(a(a(B,a(a(B,W),B)),B),f),x),y)|$Ans(a(a(x,x),y)). ----> UNIT CONFLICT at 0.01 sec ----> 90 [binary,89.1,1.1] $Ans(a(a(a(a(a(B,a(a(B,W),B)),B),f),a(a(a(B,a(a(B,W),B)),B),f)),y)). ** KEPT (pick-wt=23): 91 [para_into,39.1.2.1,3.1.2] a(a(a(B,f),a(B,f)),x)!=a(a(a(W,a(a(B,W),B)),a(B,f)),x)|$Ans(a(a(a(B,f),a(B,f)),x)). ** KEPT (pick-wt=27): 92 [para_into,39.1.2.1,2.1.2] a(a(a(x,y),a(x,y)),z)!=a(a(a(a(B,a(a(a(B,W),B),a(B,f))),x),y),z)|$Ans(a(a(a(x,y),a(x,y)),z)). ** KEPT (pick-wt=19): 93 [para_into,39.1.2,3.1.2] a(a(x,x),x)!=a(a(W,a(a(a(B,W),B),a(B,f))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=25): 94 [para_into,39.1.2,2.1.2] a(a(x,x),a(y,z))!=a(a(a(B,a(a(a(a(B,W),B),a(B,f)),x)),y),z)|$Ans(a(a(x,x),a(y,z))). given clause #20: (wt=19) 45 [para_into,26.1.2.1,2.1.2] a(a(x,y),y)!=a(a(a(a(B,W),a(B,a(B,f))),x),y)|$Ans(a(a(x,y),y)). ** KEPT (pick-wt=21): 95 [para_into,45.1.2.1.1,2.1.2] a(a(x,y),y)!=a(a(a(a(a(B,a(B,W)),B),a(B,f)),x),y)|$Ans(a(a(x,y),y)). ----> UNIT CONFLICT at 0.01 sec ----> 96 [binary,95.1,1.1] $Ans(a(a(a(a(a(B,a(B,W)),B),a(B,f)),a(a(a(B,a(B,W)),B),a(B,f))),a(a(a(B,a(B,W)),B),a(B,f)))). ** KEPT (pick-wt=23): 97 [para_into,45.1.2.1,3.1.2] a(a(a(B,a(B,f)),x),x)!=a(a(a(W,a(B,W)),a(B,a(B,f))),x)|$Ans(a(a(a(B,a(B,f)),x),x)). ** KEPT (pick-wt=25): 98 [para_into,45.1.2.1,2.1.2] a(a(a(x,y),z),z)!=a(a(a(a(B,a(a(B,W),a(B,a(B,f)))),x),y),z)|$Ans(a(a(a(x,y),z),z)). ----> UNIT CONFLICT at 0.01 sec ----> 99 [binary,98.1,1.1] $Ans(a(a(a(a(B,a(a(B,W),a(B,a(B,f)))),a(B,a(a(B,W),a(B,a(B,f))))),a(B,a(a(B,W),a(B,a(B,f))))),a(B,a(a(B,W),a(B,a(B,f)))))). ** KEPT (pick-wt=19): 100 [para_into,45.1.2,3.1.2] a(a(x,x),x)!=a(a(W,a(a(B,W),a(B,a(B,f)))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=27): 101 [para_into,45.1.2,2.1.2] a(a(x,a(y,z)),a(y,z))!=a(a(a(B,a(a(a(B,W),a(B,a(B,f))),x)),y),z)|$Ans(a(a(x,a(y,z)),a(y,z))). given clause #21: (wt=19) 49 [para_into,32.1.2.1,2.1.2] a(x,a(y,y))!=a(a(a(a(B,W),B),a(a(B,f),x)),y)|$Ans(a(x,a(y,y))). ** KEPT (pick-wt=21): 102 [para_into,49.1.2.1,2.1.2] a(x,a(y,y))!=a(a(a(a(B,a(a(B,W),B)),a(B,f)),x),y)|$Ans(a(x,a(y,y))). ** KEPT (pick-wt=27): 103 [para_into,49.1.2,3.1.2] a(x,a(a(a(B,f),x),a(a(B,f),x)))!=a(a(W,a(a(B,W),B)),a(a(B,f),x))|$Ans(a(x,a(a(a(B,f),x),a(a(B,f),x)))). ** KEPT (pick-wt=27): 104 [para_into,49.1.2,2.1.2] a(x,a(a(y,z),a(y,z)))!=a(a(a(B,a(a(a(B,W),B),a(a(B,f),x))),y),z)|$Ans(a(x,a(a(y,z),a(y,z)))). given clause #22: (wt=19) 52 [para_into,37.1.2.1,2.1.2] a(f,a(x,x))!=a(a(a(a(B,W),B),a(a(W,B),f)),x)|$Ans(a(f,a(x,x))). ** KEPT (pick-wt=21): 105 [para_into,52.1.2.1,2.1.2] a(f,a(x,x))!=a(a(a(a(B,a(a(B,W),B)),a(W,B)),f),x)|$Ans(a(f,a(x,x))). ** KEPT (pick-wt=27): 106 [para_into,52.1.2,2.1.2] a(f,a(a(x,y),a(x,y)))!=a(a(a(B,a(a(a(B,W),B),a(a(W,B),f))),x),y)|$Ans(a(f,a(a(x,y),a(x,y)))). given clause #23: (wt=19) 54 [para_into,43.1.2.1,2.1.2] a(a(x,x),x)!=a(a(a(a(B,W),W),a(B,a(B,f))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=19): 107 [para_into,54.1.2.1.1,3.1.2] a(a(x,x),x)!=a(a(a(a(W,B),W),a(B,a(B,f))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=21): 108 [para_into,54.1.2.1,2.1.2] a(a(x,x),x)!=a(a(a(a(B,a(a(B,W),W)),B),a(B,f)),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=29): 109 [para_into,54.1.2,2.1.2] a(a(a(x,y),a(x,y)),a(x,y))!=a(a(a(B,a(a(a(B,W),W),a(B,a(B,f)))),x),y)|$Ans(a(a(a(x,y),a(x,y)),a(x,y))). given clause #24: (wt=19) 59 [para_into,16.1.2,3.1.2] a(a(x,x),a(x,x))!=a(a(W,a(B,a(W,a(B,f)))),x)|$Ans(a(a(x,x),a(x,x))). ** KEPT (pick-wt=21): 110 [para_into,59.1.2.1,2.1.2] a(a(x,x),a(x,x))!=a(a(a(a(B,W),B),a(W,a(B,f))),x)|$Ans(a(a(x,x),a(x,x))). ** KEPT (pick-wt=31): 111 [para_into,59.1.2,2.1.2] a(a(a(x,y),a(x,y)),a(a(x,y),a(x,y)))!=a(a(a(B,a(W,a(B,a(W,a(B,f))))),x),y)|$Ans(a(a(a(x,y),a(x,y)),a(a(x,y),a(x,y)))). given clause #25: (wt=19) 61 [para_into,18.1.2.1.1.1.1,3.1.2] a(a(x,y),z)!=a(a(a(a(a(a(W,B),B),f),x),y),z)|$Ans(a(a(x,y),z)). ** KEPT (pick-wt=19): 112 [para_into,61.1.2.1.1.1.1,3.1.2] a(a(x,y),z)!=a(a(a(a(a(a(W,W),B),f),x),y),z)|$Ans(a(a(x,y),z)). ----> UNIT CONFLICT at 0.01 sec ----> 113 [binary,112.1,3.1] $Ans(a(a(W,a(a(a(a(W,W),B),f),W)),a(a(a(a(W,W),B),f),W))). ** KEPT (pick-wt=19): 114 [para_into,61.1.2.1.1,3.1.2] a(a(f,x),y)!=a(a(a(a(W,a(a(W,B),B)),f),x),y)|$Ans(a(a(f,x),y)). ** KEPT (pick-wt=25): 115 [para_into,61.1.2.1.1,2.1.2] a(a(a(x,y),z),u)!=a(a(a(a(a(B,a(a(a(W,B),B),f)),x),y),z),u)|$Ans(a(a(a(x,y),z),u)). ** KEPT (pick-wt=19): 116 [para_into,61.1.2.1,3.1.2] a(a(x,x),y)!=a(a(a(W,a(a(a(W,B),B),f)),x),y)|$Ans(a(a(x,x),y)). ----> UNIT CONFLICT at 0.01 sec ----> 117 [binary,116.1,1.1] $Ans(a(a(a(W,a(a(a(W,B),B),f)),a(W,a(a(a(W,B),B),f))),y)). ** KEPT (pick-wt=25): 118 [para_into,61.1.2.1,2.1.2] a(a(x,a(y,z)),u)!=a(a(a(a(B,a(a(a(a(W,B),B),f),x)),y),z),u)|$Ans(a(a(x,a(y,z)),u)). ----> UNIT CONFLICT at 0.01 sec ----> 119 [binary,118.1,3.1] $Ans(a(a(W,a(a(B,a(a(a(a(W,B),B),f),W)),a(B,a(a(a(a(W,B),B),f),W)))),a(B,a(a(a(a(W,B),B),f),W)))). ** KEPT (pick-wt=19): 120 [para_into,61.1.2,3.1.2] a(a(x,y),y)!=a(a(W,a(a(a(a(W,B),B),f),x)),y)|$Ans(a(a(x,y),y)). ----> UNIT CONFLICT at 0.01 sec ----> 121 [binary,120.1,1.1] $Ans(a(a(W,a(a(a(a(W,B),B),f),W)),a(a(a(a(W,B),B),f),W))). ** KEPT (pick-wt=25): 122 [para_into,61.1.2,2.1.2] a(a(x,y),a(z,u))!=a(a(a(B,a(a(a(a(a(W,B),B),f),x),y)),z),u)|$Ans(a(a(x,y),a(z,u))). given clause #26: (wt=19) 63 [para_into,18.1.2.1.1,3.1.2] a(a(f,x),y)!=a(a(a(a(W,a(a(B,B),B)),f),x),y)|$Ans(a(a(f,x),y)). ** KEPT (pick-wt=21): 123 [para_into,63.1.2.1.1.1,2.1.2] a(a(f,x),y)!=a(a(a(a(a(a(B,W),a(B,B)),B),f),x),y)|$Ans(a(a(f,x),y)). ** KEPT (pick-wt=19): 124 [para_into,63.1.2.1,3.1.2] a(a(f,f),x)!=a(a(a(W,a(W,a(a(B,B),B))),f),x)|$Ans(a(a(f,f),x)). ** KEPT (pick-wt=25): 125 [para_into,63.1.2.1,2.1.2] a(a(f,a(x,y)),z)!=a(a(a(a(B,a(a(W,a(a(B,B),B)),f)),x),y),z)|$Ans(a(a(f,a(x,y)),z)). ** KEPT (pick-wt=19): 126 [para_into,63.1.2,3.1.2] a(a(f,x),x)!=a(a(W,a(a(W,a(a(B,B),B)),f)),x)|$Ans(a(a(f,x),x)). ** KEPT (pick-wt=25): 127 [para_into,63.1.2,2.1.2] a(a(f,x),a(y,z))!=a(a(a(B,a(a(a(W,a(a(B,B),B)),f),x)),y),z)|$Ans(a(a(f,x),a(y,z))). given clause #27: (wt=19) 65 [para_into,18.1.2.1,3.1.2] a(a(x,x),y)!=a(a(a(W,a(a(a(B,B),B),f)),x),y)|$Ans(a(a(x,x),y)). ** KEPT (pick-wt=21): 128 [para_into,65.1.2.1.1,2.1.2] a(a(x,x),y)!=a(a(a(a(a(B,W),a(a(B,B),B)),f),x),y)|$Ans(a(a(x,x),y)). ----> UNIT CONFLICT at 0.01 sec ----> 129 [binary,128.1,1.1] $Ans(a(a(a(a(a(B,W),a(a(B,B),B)),f),a(a(a(B,W),a(a(B,B),B)),f)),y)). ** KEPT (pick-wt=31): 130 [para_into,65.1.2.1,3.1.2] a(a(a(a(a(B,B),B),f),a(a(a(B,B),B),f)),x)!=a(a(a(W,W),a(a(a(B,B),B),f)),x)|$Ans(a(a(a(a(a(B,B),B),f),a(a(a(B,B),B),f)),x)). ** KEPT (pick-wt=27): 131 [para_into,65.1.2.1,2.1.2] a(a(a(x,y),a(x,y)),z)!=a(a(a(a(B,a(W,a(a(a(B,B),B),f))),x),y),z)|$Ans(a(a(a(x,y),a(x,y)),z)). ** KEPT (pick-wt=19): 132 [para_into,65.1.2,3.1.2] a(a(x,x),x)!=a(a(W,a(W,a(a(a(B,B),B),f))),x)|$Ans(a(a(x,x),x)). ** KEPT (pick-wt=25): 133 [para_into,65.1.2,2.1.2] a(a(x,x),a(y,z))!=a(a(a(B,a(a(W,a(a(a(B,B),B),f)),x)),y),z)|$Ans(a(a(x,x),a(y,z))). given clause #28: (wt=19) 69 [para_into,18.1.2,3.1.2] a(a(x,y),y)!=a(a(W,a(a(a(a(B,B),B),f),x)),y)|$Ans(a(a(x,y),y)). ** KEPT (pick-wt=21): 134 [para_into,69.1.2.1,2.1.2] a(a(x,y),y)!=a(a(a(a(B,W),a(a(a(B,B),B),f)),x),y)|$Ans(a(a(x,y),y)). ----> UNIT CONFLICT at 0.01 sec ----> 135 [binary,134.1,1.1] $Ans(a(a(a(a(B,W),a(a(a(B,B),B),f)),a(a(B,W),a(a(a(B,B),B),f))),a(a(B,W),a(a(a(B,B),B),f)))). ** KEPT (pick-wt=35): 136 [para_into,69.1.2,3.1.2] a(a(x,a(a(a(a(B,B),B),f),x)),a(a(a(a(B,B),B),f),x))!=a(a(W,W),a(a(a(a(B,B),B),f),x))|$Ans(a(a(x,a(a(a(a(B,B),B),f),x)),a(a(a(a(B,B),B),f),x))). ** KEPT (pick-wt=27): 137 [para_into,69.1.2,2.1.2] a(a(x,a(y,z)),a(y,z))!=a(a(a(B,a(W,a(a(a(a(B,B),B),f),x))),y),z)|$Ans(a(a(x,a(y,z)),a(y,z))). given clause #29: (wt=19) 75 [para_into,20.1.2,3.1.2] a(a(a(B,f),x),x)!=a(a(W,a(a(W,B),a(B,f))),x)|$Ans(a(a(a(B,f),x),x)). ** KEPT (pick-wt=21): 138 [para_into,75.1.2.1,2.1.2] a(a(a(B,f),x),x)!=a(a(a(a(B,W),a(W,B)),a(B,f)),x)|$Ans(a(a(a(B,f),x),x)). ** KEPT (pick-wt=27): 139 [para_into,75.1.2,2.1.2] a(a(a(B,f),a(x,y)),a(x,y))!=a(a(a(B,a(W,a(a(W,B),a(B,f)))),x),y)|$Ans(a(a(a(B,f),a(x,y)),a(x,y))). given clause #30: (wt=19) 80 [para_into,29.1.2.1,3.1.2] a(x,a(x,y))!=a(a(a(W,a(a(B,B),a(B,f))),x),y)|$Ans(a(x,a(x,y))). Search stopped by max_given option. ** KEPT (pick-wt=21): 140 [para_into,80.1.2.1.1,2.1.2] a(x,a(x,y))!=a(a(a(a(a(B,W),a(B,B)),a(B,f)),x),y)|$Ans(a(x,a(x,y))). ** KEPT (pick-wt=31): 141 [para_into,80.1.2.1,3.1.2] a(a(a(B,B),a(B,f)),a(a(a(B,B),a(B,f)),x))!=a(a(a(W,W),a(a(B,B),a(B,f))),x)|$Ans(a(a(a(B,B),a(B,f)),a(a(a(B,B),a(B,f)),x))). ** KEPT (pick-wt=27): 142 [para_into,80.1.2.1,2.1.2] a(a(x,y),a(a(x,y),z))!=a(a(a(a(B,a(W,a(a(B,B),a(B,f)))),x),y),z)|$Ans(a(a(x,y),a(a(x,y),z))). ** KEPT (pick-wt=19): 143 [para_into,80.1.2,3.1.2] a(x,a(x,x))!=a(a(W,a(W,a(a(B,B),a(B,f)))),x)|$Ans(a(x,a(x,x))). ** KEPT (pick-wt=25): 144 [para_into,80.1.2,2.1.2] a(x,a(x,a(y,z)))!=a(a(a(B,a(a(W,a(a(B,B),a(B,f))),x)),y),z)|$Ans(a(x,a(x,a(y,z)))). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 30 clauses generated 126 para_into generated 126 demod & eval rewrites 0 clauses wt,lit,sk delete 9 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 117 new demodulators 0 empty clauses 23 clauses back demodulated 0 clauses back subsumed 0 usable size 33 sos size 88 demodulators size 0 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8401 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/str_bws.in.287520100644000076400007640000000144205472203240017452 0ustar mccunemccune% % Combinatory Logic. % Find a fixed point combinator in the fragment {B, W, S}. % UR-resolution. % set(ur_res). clear(print_kept). set(bird_print). % Output (but not input) in combinatory logic notation. assign(fpa_literals, 3). % to save memory assign(max_mem, 1500). % 1.5 Megabytes list(usable). x = x. x != y | y = x. x != y | y != z | x = z. x != y | a(x,z) = a(y,z). x != y | a(z,x) = a(z,y). a(a(a(B,x),y),z) = a(x,a(y,z)). a(a(W,x),y) = a(a(x,y),y). a(a(a(S,x),y),z) = a(a(x,z),a(y,z)). end_of_list. % Deny the existence of a fixed point combinator. % If a refutation is found, $Ans contains a fixed point combinator. formula_list(sos). -(exists y all x (a(y,x) = a(x,a(y,x)) & -$Ans(y))). end_of_list. list(demodulators). a(a(a(B,x),y),z) = a(x,a(y,z)). end_of_list. otter-3.3f/examples/misc/cn.in0100644000076400007640000000175210041250571015702 0ustar mccunemccune% The sentential calculus (CN). % % {CN1, CN2, CN3} (Lukasiewicz), along with condensed detachment, % axiomatizes the sentential calculus (the classical propositional calculus). % % Show that CN16, CN18, and CN19 can be derived. set(hyper_res). clear(back_sub). assign(pick_given_ratio, 3). assign(max_proofs, 3). assign(max_weight, 16). clear(print_kept). set(order_history). % The symbols -> and - have built-in declarations, and they are used for % clauses and formulas. When redeclaring them for use with terms, we % must be careful that they will still work for clauses and formulas. op(800, yfx, ->). % left association list(usable). -P(x -> y) | -P(x) | P(y). % condensed detachment end_of_list. list(sos). P(x -> y -> (y -> z -> (x -> z))). % CN1 P(-x -> x -> x). % CN2 P(x -> (-x -> y)). % CN3 end_of_list. list(passive). -P(a -> a) | $Ans(CN_16). -P(b -> (a -> b)) | $Ans(CN_18). -P(a -> b -> c -> (b -> c)) | $Ans(CN_19). end_of_list. otter-3.3f/examples/misc/str_bws.in0100644000076400007640000000136610041250571016766 0ustar mccunemccune% % Combinatory Logic. % Find a fixed point combinator in the fragment {B, W, S}. % UR-resolution. % set(ur_res). clear(print_kept). set(bird_print). % Output (but not input) in combinatory logic notation. assign(fpa_literals, 3). % to save memory list(usable). x = x. x != y | y = x. x != y | y != z | x = z. x != y | a(x,z) = a(y,z). x != y | a(z,x) = a(z,y). a(a(a(B,x),y),z) = a(x,a(y,z)). a(a(W,x),y) = a(a(x,y),y). a(a(a(S,x),y),z) = a(a(x,z),a(y,z)). end_of_list. % Deny the existence of a fixed point combinator. % If a refutation is found, $Ans contains a fixed point combinator. formula_list(sos). -(exists y all x (a(y,x) = a(x,a(y,x)) & -$Ans(y))). end_of_list. list(demodulators). a(a(a(B,x),y),z) = a(x,a(y,z)). end_of_list. otter-3.3f/examples/misc/andrews.out0100664000076400007640000011021210103522154017136 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8361. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(process_input). clear(print_kept). clear(print_back_sub). formula_list(sos). -(((exists x all y (p(x)<->p(y)))<-> ((exists u q(u))<-> (all v p(v))))<-> ((exists w all z (q(z)<->q(w)))<-> ((exists x1 p(x1))<-> (all x2 q(x2))))). end_of_list. -------> sos clausifies to: list(sos). 0 [] p(x)|p($f1(x))| -q(u)|p(v)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] p(x)|p($f1(x))| -q(u)|p(v)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] p(x)|p($f1(x))| -q(u)|p(v)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] p(x)|p($f1(x))| -q(u)|p(v)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] p(x)|p($f1(x))| -q(u)|p(v)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] p(x)|p($f1(x))| -q(u)|p(v)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] p(x)|p($f1(x))| -q(u)|p(v)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] p(x)|p($f1(x))| -q(u)|p(v)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] -p(x)| -p($f1(x))| -q(u)|p(v)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] -p($c3)|p(y)|q($c4)|p(x3)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] -p($c3)|p(y)|q($c4)|p(x3)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] -p($c3)|p(y)|q($c4)|p(x3)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] -p($c3)|p(y)|q($c4)|p(x3)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] -p($c3)|p(y)|q($c4)|p(x3)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] -p($c3)|p(y)|q($c4)|p(x3)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] -p($c3)|p(y)|q($c4)|p(x3)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] -p($c3)|p(y)|q($c4)|p(x3)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] -p($c3)|p(y)| -q(x4)| -p($c5)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] p($c3)| -p(y)|q($c4)|p(x3)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] p($c3)| -p(y)|q($c4)|p(x3)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] p($c3)| -p(y)|q($c4)|p(x3)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] p($c3)| -p(y)|q($c4)|p(x3)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] p($c3)| -p(y)|q($c4)|p(x3)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] p($c3)| -p(y)|q($c4)|p(x3)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] p($c3)| -p(y)|q($c4)|p(x3)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] p($c3)| -p(y)|q($c4)|p(x3)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)|q($f2(w))|q(w)| -p(x1)|q(x2). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)|q($f2(w))|q(w)|p($c6)| -q($c7). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)| -q($f2(w))| -q(w)| -p(x1)|q(x2). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)| -q($f2(w))| -q(w)|p($c6)| -q($c7). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)| -q(z)|q($c8)|p($c9)|q(x5). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)| -q(z)|q($c8)| -p(x6)| -q($c10). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)|q(z)| -q($c8)|p($c9)|q(x5). 0 [] p($c3)| -p(y)| -q(x4)| -p($c5)|q(z)| -q($c8)| -p(x6)| -q($c10). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] -p($c11)|p(x7)| -q(x8)|p(x9)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] -p($c11)|p(x7)|q($c12)| -p($c13)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] p($c11)| -p(x7)| -q(x8)|p(x9)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] p($c11)| -p(x7)|q($c12)| -p($c13)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] p(x10)|p($f3(x10))|q($c14)|p(x11)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] p(x10)|p($f3(x10))| -q(x12)| -p($c15)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] -p(x10)| -p($f3(x10))|q($c14)|p(x11)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)| -q(x13)|q($c16)| -p(x14)|q(x15). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)| -q(x13)|q($c16)|p($c17)| -q($c18). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)|q(x13)| -q($c16)| -p(x14)|q(x15). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)|q(x13)| -q($c16)|p($c17)| -q($c18). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)|q($f4(x16))|q(x16)|p($c19)|q(x17). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)|q($f4(x16))|q(x16)| -p(x18)| -q($c20). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)| -q($f4(x16))| -q(x16)|p($c19)|q(x17). 0 [] -p(x10)| -p($f3(x10))| -q(x12)| -p($c15)| -q($f4(x16))| -q(x16)| -p(x18)| -q($c20). end_of_list. ------------> process usable: ------------> process sos: ** KEPT (pick-wt=14): 2 [copy,1,factor_simp,factor_simp] p(x)|p($f1(x))| -q(y)|q($f2(z))|q(z)| -p(u). ** KEPT (pick-wt=14): 4 [copy,3,factor_simp,factor_simp] p(x)|p($f1(x))| -q($c7)|q($f2(y))|q(y)|p($c6). ** KEPT (pick-wt=14): 6 [copy,5,factor_simp,factor_simp] p(x)|p($f1(x))| -q($f2(y))| -q(y)| -p(z)|q(u). ** KEPT (pick-wt=14): 8 [copy,7,factor_simp,factor_simp] p(x)|p($f1(x))| -q($f2(y))| -q(y)|p($c6)| -q($c7). ** KEPT (pick-wt=11): 10 [copy,9,factor_simp,factor_simp,factor_simp] p(x)|p($f1(x))| -q(y)|q($c8)|p($c9). ** KEPT (pick-wt=11): 12 [copy,11,factor_simp,factor_simp,factor_simp] p(x)|p($f1(x))| -q($c10)|q($c8)| -p(y). ** KEPT (pick-wt=11): 14 [copy,13,factor_simp,factor_simp,factor_simp] p(x)|p($f1(x))| -q($c8)|q(y)|p($c9). ** KEPT (pick-wt=13): 16 [copy,15,factor_simp,factor_simp] p(x)|p($f1(x))| -q($c8)|q(y)| -p(z)| -q($c10). ** KEPT (pick-wt=14): 18 [copy,17,factor_simp,factor_simp] p(x)|p($f1(x))|q($c1)| -p($c2)|q($f2(y))|q(y). Following clause subsumed by 18 during input processing: 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)|q($f2(y))|q(y)|p($c6)| -q($c7). Following clause subsumed by 6 during input processing: 0 [factor_simp,factor_simp] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($f2(y))| -q(y). Following clause subsumed by 8 during input processing: 0 [] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($f2(y))| -q(y)|p($c6)| -q($c7). Following clause subsumed by 10 during input processing: 0 [factor_simp] p(x)|p($f1(x))|q($c1)| -p($c2)| -q(y)|q($c8)|p($c9). Following clause subsumed by 12 during input processing: 0 [factor_simp,factor_simp] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($c10)|q($c8). Following clause subsumed by 14 during input processing: 0 [factor_simp,factor_simp] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($c8)|p($c9). Following clause subsumed by 16 during input processing: 0 [factor_simp,factor_simp] p(x)|p($f1(x))|q($c1)| -p($c2)| -q($c8)| -q($c10). ** KEPT (pick-wt=14): 20 [copy,19,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q(y)|p(z)|q($f2(u))|q(u). Following clause subsumed by 20 during input processing: 0 [factor_simp,factor_simp] -p(x)| -p($f1(x))| -q($c7)|p($c6)|q($f2(u))|q(u). ** KEPT (pick-wt=14): 22 [copy,21,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q($f2(y))|p(z)| -q(y)|q(u). ** KEPT (pick-wt=14): 24 [copy,23,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q($f2(y))|p($c6)| -q(y)| -q($c7). ** KEPT (pick-wt=11): 26 [copy,25,factor_simp,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q(y)|p($c9)|q($c8). ** KEPT (pick-wt=11): 28 [copy,27,factor_simp,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q($c10)|p(y)|q($c8). ** KEPT (pick-wt=11): 30 [copy,29,factor_simp,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q($c8)|p($c9)|q(y). ** KEPT (pick-wt=13): 32 [copy,31,factor_simp,factor_simp] -p(x)| -p($f1(x))| -q($c8)|p(y)|q(z)| -q($c10). ** KEPT (pick-wt=14): 34 [copy,33,factor_simp,factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q($f2(y))|q(y). Following clause subsumed by 34 during input processing: 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q($f2(y))|q(y)|p($c6)| -q($c7). ** KEPT (pick-wt=14): 36 [copy,35,factor_simp,factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($f2(y))| -q(y). Following clause subsumed by 36 during input processing: 0 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($f2(y))| -q(y)|p($c6)| -q($c7). Following clause subsumed by 26 during input processing: 0 [factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q(y)|q($c8)|p($c9). ** KEPT (pick-wt=13): 38 [copy,37,factor_simp,factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($c10)|q($c8). Following clause subsumed by 30 during input processing: 0 [factor_simp,factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($c8)|p($c9). ** KEPT (pick-wt=13): 40 [copy,39,factor_simp,factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)| -q($c8)| -q($c10). ** KEPT (pick-wt=11): 42 [copy,41,factor_simp,factor_simp,factor_simp] -p($c3)|p(x)|q($c4)|q($f2(y))|q(y). Following clause subsumed by 42 during input processing: 0 [factor_simp,factor_simp] -p($c3)|p($c6)|q($c4)|q($f2(z))|q(z)| -q($c7). ** KEPT (pick-wt=11): 44 [copy,43,factor_simp,factor_simp,factor_simp] -p($c3)|p(x)|q($c4)| -q($f2(y))| -q(y). Following clause subsumed by 44 during input processing: 0 [factor_simp,factor_simp] -p($c3)|p($c6)|q($c4)| -q($f2(z))| -q(z)| -q($c7). ** KEPT (pick-wt=10): 46 [copy,45,factor_simp,factor_simp,factor_simp] -p($c3)|p($c9)|q($c4)| -q(x)|q($c8). ** KEPT (pick-wt=10): 48 [copy,47,factor_simp,factor_simp,factor_simp] -p($c3)|p(x)|q($c4)| -q($c10)|q($c8). ** KEPT (pick-wt=8): 50 [copy,49,factor_simp,factor_simp,factor_simp,factor_simp] -p($c3)|p($c9)|q($c4)| -q($c8). ** KEPT (pick-wt=10): 52 [copy,51,factor_simp,factor_simp,factor_simp] -p($c3)|p(x)|q($c4)| -q($c8)| -q($c10). ** KEPT (pick-wt=13): 54 [copy,53,factor_simp,factor_simp] -p($c3)|p(x)| -q(y)| -p($c5)|q($f2(z))|q(z). Following clause subsumed by 54 during input processing: 0 [factor_simp,factor_simp] -p($c3)|p($c6)| -q($c7)| -p($c5)|q($f2(z))|q(z). ** KEPT (pick-wt=13): 56 [copy,55,factor_simp,factor_simp] -p($c3)|p(x)| -q($f2(y))| -p($c5)| -q(y)|q(z). ** KEPT (pick-wt=13): 58 [copy,57,factor_simp,factor_simp] -p($c3)|p($c6)| -q($f2(x))| -p($c5)| -q(x)| -q($c7). ** KEPT (pick-wt=10): 60 [copy,59,factor_simp,factor_simp,factor_simp] -p($c3)|p($c9)| -q(x)| -p($c5)|q($c8). ** KEPT (pick-wt=10): 62 [copy,61,factor_simp,factor_simp,factor_simp] -p($c3)|p(x)| -q($c10)| -p($c5)|q($c8). ** KEPT (pick-wt=10): 64 [copy,63,factor_simp,factor_simp,factor_simp] -p($c3)|p($c9)| -q($c8)| -p($c5)|q(x). ** KEPT (pick-wt=12): 66 [copy,65,factor_simp,factor_simp] -p($c3)|p(x)| -q($c8)| -p($c5)|q(y)| -q($c10). ** KEPT (pick-wt=11): 68 [copy,67,factor_simp,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)|q($f2(y))|q(y). Following clause subsumed by 68 during input processing: 0 [factor_simp] p($c3)| -p(x)|q($c4)|q($f2(z))|q(z)|p($c6)| -q($c7). ** KEPT (pick-wt=11): 70 [copy,69,factor_simp,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)| -q($f2(y))| -q(y). Following clause subsumed by 70 during input processing: 0 [factor_simp] p($c3)| -p(x)|q($c4)| -q($f2(z))| -q(z)|p($c6)| -q($c7). ** KEPT (pick-wt=12): 72 [copy,71,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)| -q(y)|q($c8)|p($c9). ** KEPT (pick-wt=10): 74 [copy,73,factor_simp,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)| -q($c10)|q($c8). ** KEPT (pick-wt=10): 76 [copy,75,factor_simp,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)| -q($c8)|p($c9). ** KEPT (pick-wt=10): 78 [copy,77,factor_simp,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)| -q($c8)| -q($c10). ** KEPT (pick-wt=11): 80 [copy,79,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q(x)|q($f2(y))|q(y). Following clause subsumed by 80 during input processing: 0 [factor_simp,factor_simp] p($c3)| -p($c5)| -q($c7)|q($f2(z))|q(z)|p($c6). ** KEPT (pick-wt=11): 82 [copy,81,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q($f2(x))| -q(x)|q(y). ** KEPT (pick-wt=13): 84 [copy,83,factor_simp,factor_simp] p($c3)| -p($c5)| -q($f2(x))| -q(x)|p($c6)| -q($c7). ** KEPT (pick-wt=10): 86 [copy,85,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q(x)|q($c8)|p($c9). ** KEPT (pick-wt=8): 88 [copy,87,factor_simp,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q($c10)|q($c8). ** KEPT (pick-wt=10): 90 [copy,89,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q($c8)|q(x)|p($c9). ** KEPT (pick-wt=10): 92 [copy,91,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q($c8)|q(x)| -q($c10). ** KEPT (pick-wt=8): 94 [copy,93,factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q(y)|q($c16). Following clause subsumed by 94 during input processing: 0 [factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p($c17)| -q($c18)|q($c16). ** KEPT (pick-wt=8): 96 [copy,95,factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q($c16)|q(y). Following clause subsumed by 96 during input processing: 0 [factor_simp,factor_simp,factor_simp] -p($c11)|p($c17)| -q($c16)|q(u)| -q($c18). ** KEPT (pick-wt=11): 98 [copy,97,factor_simp,factor_simp,factor_simp] -p($c11)|p($c19)| -q(x)|q($f4(y))|q(y). ** KEPT (pick-wt=11): 100 [copy,99,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q($c20)|q($f4(y))|q(y). ** KEPT (pick-wt=11): 102 [copy,101,factor_simp,factor_simp,factor_simp] -p($c11)|p($c19)| -q($f4(x))| -q(x)|q(y). ** KEPT (pick-wt=11): 104 [copy,103,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q($f4(y))| -q(y)| -q($c20). Following clause subsumed by 94 during input processing: 0 [factor_simp,factor_simp] -p($c11)|p(x)|q($c12)| -p($c13)| -q(y)|q($c16). Following clause subsumed by 94 during input processing: 0 [factor_simp,factor_simp] -p($c11)|p($c17)|q($c12)| -p($c13)| -q($c18)|q($c16). Following clause subsumed by 96 during input processing: 0 [factor_simp,factor_simp,factor_simp] -p($c11)|p(x)|q($c12)| -p($c13)| -q($c16). Following clause subsumed by 96 during input processing: 0 [factor_simp,factor_simp] -p($c11)|p($c17)|q($c12)| -p($c13)| -q($c16)| -q($c18). ** KEPT (pick-wt=13): 106 [copy,105,factor_simp,factor_simp] -p($c11)|p($c19)|q($c12)| -p($c13)|q($f4(x))|q(x). Following clause subsumed by 100 during input processing: 0 [factor_simp] -p($c11)|p(x)|q($c12)| -p($c13)|q($f4(y))|q(y)| -q($c20). Following clause subsumed by 102 during input processing: 0 [factor_simp,factor_simp] -p($c11)|p($c19)|q($c12)| -p($c13)| -q($f4(y))| -q(y). Following clause subsumed by 104 during input processing: 0 [factor_simp] -p($c11)|p(x)|q($c12)| -p($c13)| -q($f4(y))| -q(y)| -q($c20). ** KEPT (pick-wt=8): 108 [copy,107,factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q(y)|q($c16). Following clause subsumed by 108 during input processing: 0 [factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($c18)|q($c16)|p($c17). ** KEPT (pick-wt=8): 110 [copy,109,factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($c16)|q(y). Following clause subsumed by 110 during input processing: 0 [factor_simp,factor_simp] p($c11)| -p(x)| -q($c16)|q(u)|p($c17)| -q($c18). ** KEPT (pick-wt=13): 112 [copy,111,factor_simp,factor_simp] p($c11)| -p(x)| -q(y)|q($f4(z))|q(z)|p($c19). ** KEPT (pick-wt=11): 114 [copy,113,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($c20)|q($f4(y))|q(y). ** KEPT (pick-wt=13): 116 [copy,115,factor_simp,factor_simp] p($c11)| -p(x)| -q($f4(y))| -q(y)|p($c19)|q(z). ** KEPT (pick-wt=11): 118 [copy,117,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($f4(y))| -q(y)| -q($c20). Following clause subsumed by 108 during input processing: 0 [factor_simp,factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)| -q(y)|q($c16). Following clause subsumed by 108 during input processing: 0 [factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)| -q($c18)|q($c16)|p($c17). Following clause subsumed by 110 during input processing: 0 [factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)| -q($c16). Following clause subsumed by 110 during input processing: 0 [factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)| -q($c16)|p($c17)| -q($c18). ** KEPT (pick-wt=13): 120 [copy,119,factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)|q($f4(x))|q(x)|p($c19). Following clause subsumed by 114 during input processing: 0 [factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)|q($f4(y))|q(y)| -q($c20). Following clause subsumed by 116 during input processing: 0 [factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)| -q($f4(y))| -q(y)|p($c19). Following clause subsumed by 118 during input processing: 0 [factor_simp,factor_simp] p($c11)| -p($c13)|q($c12)| -q($f4(y))| -q(y)| -q($c20). ** KEPT (pick-wt=13): 122 [copy,121,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)| -q(y)|q($c16)| -p(z). ** KEPT (pick-wt=13): 124 [copy,123,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)| -q($c18)|q($c16)|p($c17). ** KEPT (pick-wt=11): 126 [copy,125,factor_simp,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)| -q($c16)| -p(y). ** KEPT (pick-wt=13): 128 [copy,127,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)| -q($c16)|p($c17)| -q($c18). ** KEPT (pick-wt=14): 130 [copy,129,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)|q($f4(y))|q(y)|p($c19). ** KEPT (pick-wt=16): 132 [copy,131,factor_simp] p(x)|p($f3(x))|q($c14)|q($f4(y))|q(y)| -p(z)| -q($c20). ** KEPT (pick-wt=14): 134 [copy,133,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)| -q($f4(y))| -q(y)|p($c19). ** KEPT (pick-wt=16): 136 [copy,135,factor_simp] p(x)|p($f3(x))|q($c14)| -q($f4(y))| -q(y)| -p(z)| -q($c20). ** KEPT (pick-wt=11): 138 [copy,137,factor_simp,factor_simp,factor_simp] p(x)|p($f3(x))| -q(y)| -p($c15)|q($c16). Following clause subsumed by 138 during input processing: 0 [factor_simp,factor_simp] p(x)|p($f3(x))| -q($c18)| -p($c15)|q($c16)|p($c17). ** KEPT (pick-wt=11): 140 [copy,139,factor_simp,factor_simp,factor_simp] p(x)|p($f3(x))| -q($c16)| -p($c15)|q(y). Following clause subsumed by 140 during input processing: 0 [factor_simp] p(x)|p($f3(x))| -q($c16)| -p($c15)|q(z)|p($c17)| -q($c18). ** KEPT (pick-wt=16): 142 [copy,141,factor_simp] p(x)|p($f3(x))| -q(y)| -p($c15)|q($f4(z))|q(z)|p($c19). ** KEPT (pick-wt=14): 144 [copy,143,factor_simp,factor_simp] p(x)|p($f3(x))| -q($c20)| -p($c15)|q($f4(y))|q(y). ** KEPT (pick-wt=16): 146 [copy,145,factor_simp] p(x)|p($f3(x))| -q($f4(y))| -p($c15)| -q(y)|p($c19)|q(z). ** KEPT (pick-wt=14): 148 [copy,147,factor_simp,factor_simp] p(x)|p($f3(x))| -q($f4(y))| -p($c15)| -q(y)| -q($c20). ** KEPT (pick-wt=13): 150 [copy,149,factor_simp,factor_simp] -p(x)| -p($f3(x))|q($c14)|p(y)| -q(z)|q($c16). Following clause subsumed by 150 during input processing: 0 [factor_simp,factor_simp] -p(x)| -p($f3(x))|q($c14)|p($c17)| -q($c18)|q($c16). ** KEPT (pick-wt=11): 152 [copy,151,factor_simp,factor_simp,factor_simp] -p(x)| -p($f3(x))|q($c14)|p(y)| -q($c16). Following clause subsumed by 152 during input processing: 0 [factor_simp,factor_simp] -p(x)| -p($f3(x))|q($c14)|p($c17)| -q($c16)| -q($c18). ** KEPT (pick-wt=14): 154 [copy,153,factor_simp,factor_simp] -p(x)| -p($f3(x))|q($c14)|p($c19)|q($f4(y))|q(y). ** KEPT (pick-wt=16): 156 [copy,155,factor_simp] -p(x)| -p($f3(x))|q($c14)|p(y)|q($f4(z))|q(z)| -q($c20). ** KEPT (pick-wt=14): 158 [copy,157,factor_simp,factor_simp] -p(x)| -p($f3(x))|q($c14)|p($c19)| -q($f4(y))| -q(y). ** KEPT (pick-wt=16): 160 [copy,159,factor_simp] -p(x)| -p($f3(x))|q($c14)|p(y)| -q($f4(z))| -q(z)| -q($c20). ** KEPT (pick-wt=11): 162 [copy,161,factor_simp,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q(y)| -p($c15)|q($c16). Following clause subsumed by 162 during input processing: 0 [factor_simp,factor_simp] -p(x)| -p($f3(x))| -q($c18)| -p($c15)|q($c16)|p($c17). ** KEPT (pick-wt=11): 164 [copy,163,factor_simp,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q($c16)| -p($c15)|q(y). Following clause subsumed by 164 during input processing: 0 [factor_simp] -p(x)| -p($f3(x))| -q($c16)| -p($c15)|q(z)|p($c17)| -q($c18). ** KEPT (pick-wt=16): 166 [copy,165,factor_simp] -p(x)| -p($f3(x))| -q(y)| -p($c15)|q($f4(z))|q(z)|p($c19). ** KEPT (pick-wt=14): 168 [copy,167,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q($c20)| -p($c15)|q($f4(y))|q(y). ** KEPT (pick-wt=16): 170 [copy,169,factor_simp] -p(x)| -p($f3(x))| -q($f4(y))| -p($c15)| -q(y)|p($c19)|q(z). ** KEPT (pick-wt=14): 172 [copy,171,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q($f4(y))| -p($c15)| -q(y)| -q($c20). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=8) 50 [copy,49,factor_simp,factor_simp,factor_simp,factor_simp] -p($c3)|p($c9)|q($c4)| -q($c8). given clause #2: (wt=8) 88 [copy,87,factor_simp,factor_simp,factor_simp,factor_simp] p($c3)| -p($c5)| -q($c10)|q($c8). given clause #3: (wt=8) 94 [copy,93,factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q(y)|q($c16). given clause #4: (wt=8) 96 [copy,95,factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q($c16)|q(y). given clause #5: (wt=8) 108 [copy,107,factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q(y)|q($c16). given clause #6: (wt=8) 110 [copy,109,factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($c16)|q(y). given clause #7: (wt=8) 217 [binary,96.3,94.4,factor_simp,factor_simp] -p($c11)|p(x)|q(y)| -q(z). given clause #8: (wt=8) 218 [binary,110.3,108.4,factor_simp,factor_simp] p($c11)| -p(x)|q(y)| -q(z). given clause #9: (wt=8) 219 [binary,218.1,217.1,factor_simp,factor_simp] -p(x)|q(y)| -q(z)|p(u). given clause #10: (wt=9) 176 [factor,10.1.5] p($c9)|p($f1($c9))| -q(x)|q($c8). given clause #11: (wt=6) 221 [binary,176.2,219.1,factor_simp,factor_simp,factor_simp] p($c9)| -q(x)|q($c8). given clause #12: (wt=6) 222 [binary,221.1,219.1,factor_simp,factor_simp] -q(x)|q($c8)|p(y). given clause #13: (wt=9) 177 [factor,14.1.5] p($c9)|p($f1($c9))| -q($c8)|q(x). given clause #14: (wt=6) 224 [binary,177.2,219.1,factor_simp,factor_simp,factor_simp] p($c9)| -q($c8)|q(x). given clause #15: (wt=6) 226 [binary,224.1,219.1,factor_simp,factor_simp] -q($c8)|q(x)|p(y). given clause #16: (wt=6) 228 [binary,226.1,222.2,factor_simp] q(x)|p(y)| -q(z). given clause #17: (wt=9) 185 [factor,42.3.5] -p($c3)|p(x)|q($c4)|q($f2($c4)). given clause #18: (wt=6) 230 [binary,185.4,228.3,factor_simp,factor_simp] -p($c3)|p(x)|q($c4). given clause #19: (wt=6) 231 [binary,230.3,228.3,factor_simp] -p($c3)|p(x)|q(y). given clause #20: (wt=9) 187 [factor,68.3.5] p($c3)| -p(x)|q($c4)|q($f2($c4)). given clause #21: (wt=6) 234 [binary,187.4,228.3,factor_simp,factor_simp] p($c3)| -p(x)|q($c4). given clause #22: (wt=6) 235 [binary,234.1,231.1,factor_simp] -p(x)|q($c4)|p(y). given clause #23: (wt=6) 237 [binary,235.2,228.3,factor_simp] -p(x)|p(y)|q(z). given clause #24: (wt=9) 189 [factor,104.4.5] -p($c11)|p(x)| -q($f4($c20))| -q($c20). given clause #25: (wt=6) 238 [binary,189.3,237.3,factor_simp,factor_simp] -p($c11)|p(x)| -q($c20). given clause #26: (wt=4) 240 [binary,238.3,237.3,factor_simp,factor_simp] -p($c11)|p(x). given clause #27: (wt=9) 191 [factor,118.4.5] p($c11)| -p(x)| -q($f4($c20))| -q($c20). given clause #28: (wt=6) 242 [binary,191.3,237.3,factor_simp,factor_simp] p($c11)| -p(x)| -q($c20). given clause #29: (wt=4) 245 [binary,242.3,237.3,factor_simp,factor_simp] p($c11)| -p(x). given clause #30: (wt=4) 246 [binary,245.1,240.1] -p(x)|p(y). given clause #31: (wt=9) 206 [factor,162.1.4] -p($c15)| -p($f3($c15))| -q(x)|q($c16). given clause #32: (wt=6) 248 [binary,206.2,246.2,factor_simp] -p($c15)| -q(x)|q($c16). given clause #33: (wt=4) 250 [binary,248.1,228.2,factor_simp,factor_simp] -q(x)|q($c16). given clause #34: (wt=9) 207 [factor,164.1.4] -p($c15)| -p($f3($c15))| -q($c16)|q(x). given clause #35: (wt=6) 252 [binary,207.2,246.2,factor_simp] -p($c15)| -q($c16)|q(x). given clause #36: (wt=4) 255 [binary,252.1,228.2,factor_simp,factor_simp] -q($c16)|q(x). given clause #37: (wt=4) 257 [binary,255.1,250.2] q(x)| -q(y). given clause #38: (wt=10) 213 [factor,174.4.5] p($c6)|p($f1($c6))| -q($f2($c7))| -q($c7). given clause #39: (wt=7) 259 [binary,213.2,246.1,factor_simp] p($c6)| -q($f2($c7))| -q($c7). given clause #40: (wt=4) 263 [binary,259.2,257.1,factor_simp] p($c6)| -q($c7). given clause #41: (wt=4) 265 [binary,263.1,246.1] -q($c7)|p(x). given clause #42: (wt=4) 267 [binary,265.1,257.1] p(x)| -q(y). given clause #43: (wt=10) 214 [factor,180.3.5] -p($c2)| -p($f1($c2))|q($c1)|q($f2($c1)). given clause #44: (wt=7) 269 [binary,214.2,246.2,factor_simp] -p($c2)|q($c1)|q($f2($c1)). given clause #45: (wt=4) 274 [binary,269.3,257.2,factor_simp] -p($c2)|q($c1). given clause #46: (wt=4) 275 [binary,274.1,246.2] q($c1)| -p(x). given clause #47: (wt=4) 277 [binary,275.1,257.2] -p(x)|q(y). given clause #48: (wt=10) 215 [factor,195.3.5] p($c19)|p($f3($c19))|q($c14)|q($f4($c14)). given clause #49: (wt=7) 279 [binary,215.2,277.1,factor_simp] p($c19)|q($c14)|q($f4($c14)). given clause #50: (wt=4) 284 [binary,279.3,267.2,factor_simp] p($c19)|q($c14). given clause #51: (wt=2) 285 [binary,284.1,277.1,factor_simp] q($c14). given clause #52: (wt=2) 287 [binary,285.1,267.2] p(x). given clause #53: (wt=2) 288 [binary,285.1,257.2] q(x). given clause #54: (wt=10) 216 [factor,211.4.5] -p($c15)| -p($f3($c15))| -q($f4($c20))| -q($c20). -------- PROOF -------- -----> EMPTY CLAUSE at 0.06 sec ----> 289 [binary,216.1,287.1,unit_del,287,288,288] $F. Length of proof is 68. Level of proof is 23. ---------------- PROOF ---------------- 7 [] p(x)|p($f1(x))| -q(y)|p(z)| -q($f2(u))| -q(u)|p($c6)| -q($c7). 8 [copy,7,factor_simp,factor_simp] p(x)|p($f1(x))| -q($f2(y))| -q(y)|p($c6)| -q($c7). 9 [] p(x)|p($f1(x))| -q(y)|p(z)| -q(u)|q($c8)|p($c9)|q(v). 10 [copy,9,factor_simp,factor_simp,factor_simp] p(x)|p($f1(x))| -q(y)|q($c8)|p($c9). 13 [] p(x)|p($f1(x))| -q(y)|p(z)|q(u)| -q($c8)|p($c9)|q(v). 14 [copy,13,factor_simp,factor_simp,factor_simp] p(x)|p($f1(x))| -q($c8)|q(y)|p($c9). 33 [] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q($f2(y))|q(y)| -p(z)|q(u). 34 [copy,33,factor_simp,factor_simp] -p(x)| -p($f1(x))|q($c1)| -p($c2)|q($f2(y))|q(y). 41 [] -p($c3)|p(x)|q($c4)|p(y)|q($f2(z))|q(z)| -p(u)|q(v). 42 [copy,41,factor_simp,factor_simp,factor_simp] -p($c3)|p(x)|q($c4)|q($f2(y))|q(y). 67 [] p($c3)| -p(x)|q($c4)|p(y)|q($f2(z))|q(z)| -p(u)|q(v). 68 [copy,67,factor_simp,factor_simp,factor_simp] p($c3)| -p(x)|q($c4)|q($f2(y))|q(y). 93 [] -p($c11)|p(x)| -q(y)|p(z)| -q(u)|q($c16)| -p(v)|q(w). 94 [copy,93,factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q(y)|q($c16). 95 [] -p($c11)|p(x)| -q(y)|p(z)|q(u)| -q($c16)| -p(v)|q(w). 96 [copy,95,factor_simp,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q($c16)|q(y). 103 [] -p($c11)|p(x)| -q(y)|p(z)| -q($f4(u))| -q(u)| -p(v)| -q($c20). 104 [copy,103,factor_simp,factor_simp,factor_simp] -p($c11)|p(x)| -q($f4(y))| -q(y)| -q($c20). 107 [] p($c11)| -p(x)| -q(y)|p(z)| -q(u)|q($c16)| -p(v)|q(w). 108 [copy,107,factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q(y)|q($c16). 109 [] p($c11)| -p(x)| -q(y)|p(z)|q(u)| -q($c16)| -p(v)|q(w). 110 [copy,109,factor_simp,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($c16)|q(y). 117 [] p($c11)| -p(x)| -q(y)|p(z)| -q($f4(u))| -q(u)| -p(v)| -q($c20). 118 [copy,117,factor_simp,factor_simp,factor_simp] p($c11)| -p(x)| -q($f4(y))| -q(y)| -q($c20). 129 [] p(x)|p($f3(x))|q($c14)|p(y)|q($f4(z))|q(z)|p($c19)|q(u). 130 [copy,129,factor_simp,factor_simp] p(x)|p($f3(x))|q($c14)|q($f4(y))|q(y)|p($c19). 161 [] -p(x)| -p($f3(x))| -q(y)| -p($c15)| -q(z)|q($c16)| -p(u)|q(v). 162 [copy,161,factor_simp,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q(y)| -p($c15)|q($c16). 163 [] -p(x)| -p($f3(x))| -q(y)| -p($c15)|q(z)| -q($c16)| -p(u)|q(v). 164 [copy,163,factor_simp,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q($c16)| -p($c15)|q(y). 171 [] -p(x)| -p($f3(x))| -q(y)| -p($c15)| -q($f4(z))| -q(z)| -p(u)| -q($c20). 172 [copy,171,factor_simp,factor_simp] -p(x)| -p($f3(x))| -q($f4(y))| -p($c15)| -q(y)| -q($c20). 174 [factor,8.1.5] p($c6)|p($f1($c6))| -q($f2(x))| -q(x)| -q($c7). 176 [factor,10.1.5] p($c9)|p($f1($c9))| -q(x)|q($c8). 177 [factor,14.1.5] p($c9)|p($f1($c9))| -q($c8)|q(x). 180 [factor,34.1.4] -p($c2)| -p($f1($c2))|q($c1)|q($f2(x))|q(x). 185 [factor,42.3.5] -p($c3)|p(x)|q($c4)|q($f2($c4)). 187 [factor,68.3.5] p($c3)| -p(x)|q($c4)|q($f2($c4)). 189 [factor,104.4.5] -p($c11)|p(x)| -q($f4($c20))| -q($c20). 191 [factor,118.4.5] p($c11)| -p(x)| -q($f4($c20))| -q($c20). 195 [factor,130.1.6] p($c19)|p($f3($c19))|q($c14)|q($f4(x))|q(x). 206 [factor,162.1.4] -p($c15)| -p($f3($c15))| -q(x)|q($c16). 207 [factor,164.1.4] -p($c15)| -p($f3($c15))| -q($c16)|q(x). 211 [factor,172.1.4] -p($c15)| -p($f3($c15))| -q($f4(x))| -q(x)| -q($c20). 213 [factor,174.4.5] p($c6)|p($f1($c6))| -q($f2($c7))| -q($c7). 214 [factor,180.3.5] -p($c2)| -p($f1($c2))|q($c1)|q($f2($c1)). 215 [factor,195.3.5] p($c19)|p($f3($c19))|q($c14)|q($f4($c14)). 216 [factor,211.4.5] -p($c15)| -p($f3($c15))| -q($f4($c20))| -q($c20). 217 [binary,96.3,94.4,factor_simp,factor_simp] -p($c11)|p(x)|q(y)| -q(z). 218 [binary,110.3,108.4,factor_simp,factor_simp] p($c11)| -p(x)|q(y)| -q(z). 219 [binary,218.1,217.1,factor_simp,factor_simp] -p(x)|q(y)| -q(z)|p(u). 221 [binary,176.2,219.1,factor_simp,factor_simp,factor_simp] p($c9)| -q(x)|q($c8). 222 [binary,221.1,219.1,factor_simp,factor_simp] -q(x)|q($c8)|p(y). 224 [binary,177.2,219.1,factor_simp,factor_simp,factor_simp] p($c9)| -q($c8)|q(x). 226 [binary,224.1,219.1,factor_simp,factor_simp] -q($c8)|q(x)|p(y). 228 [binary,226.1,222.2,factor_simp] q(x)|p(y)| -q(z). 230 [binary,185.4,228.3,factor_simp,factor_simp] -p($c3)|p(x)|q($c4). 231 [binary,230.3,228.3,factor_simp] -p($c3)|p(x)|q(y). 234 [binary,187.4,228.3,factor_simp,factor_simp] p($c3)| -p(x)|q($c4). 235 [binary,234.1,231.1,factor_simp] -p(x)|q($c4)|p(y). 237 [binary,235.2,228.3,factor_simp] -p(x)|p(y)|q(z). 238 [binary,189.3,237.3,factor_simp,factor_simp] -p($c11)|p(x)| -q($c20). 240 [binary,238.3,237.3,factor_simp,factor_simp] -p($c11)|p(x). 242 [binary,191.3,237.3,factor_simp,factor_simp] p($c11)| -p(x)| -q($c20). 245 [binary,242.3,237.3,factor_simp,factor_simp] p($c11)| -p(x). 246 [binary,245.1,240.1] -p(x)|p(y). 248 [binary,206.2,246.2,factor_simp] -p($c15)| -q(x)|q($c16). 250 [binary,248.1,228.2,factor_simp,factor_simp] -q(x)|q($c16). 252 [binary,207.2,246.2,factor_simp] -p($c15)| -q($c16)|q(x). 255 [binary,252.1,228.2,factor_simp,factor_simp] -q($c16)|q(x). 257 [binary,255.1,250.2] q(x)| -q(y). 259 [binary,213.2,246.1,factor_simp] p($c6)| -q($f2($c7))| -q($c7). 263 [binary,259.2,257.1,factor_simp] p($c6)| -q($c7). 265 [binary,263.1,246.1] -q($c7)|p(x). 267 [binary,265.1,257.1] p(x)| -q(y). 269 [binary,214.2,246.2,factor_simp] -p($c2)|q($c1)|q($f2($c1)). 274 [binary,269.3,257.2,factor_simp] -p($c2)|q($c1). 275 [binary,274.1,246.2] q($c1)| -p(x). 277 [binary,275.1,257.2] -p(x)|q(y). 279 [binary,215.2,277.1,factor_simp] p($c19)|q($c14)|q($f4($c14)). 284 [binary,279.3,267.2,factor_simp] p($c19)|q($c14). 285 [binary,284.1,277.1,factor_simp] q($c14). 287 [binary,285.1,267.2] p(x). 288 [binary,285.1,257.2] q(x). 289 [binary,216.1,287.1,unit_del,287,288,288] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 54 clauses generated 349 binary_res generated 301 factors generated 48 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 22 clauses forward subsumed 252 (subsumed by sos) 95 unit deletions 3 factor simplifications 593 clauses kept 202 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 196 usable size 3 sos size 3 demodulators size 0 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.06 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8361 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/misc/kb_bench.in0100644000076400007640000000143405472201532017037 0ustar mccunemccune% % Consider an associative system with 8 left identities % and 8 right inverses. % Search for a complete set of reductions. % set(knuth_bendix). set(print_lists_at_end). set(really_delete_clauses). clear(print_kept). clear(print_new_demod). clear(print_back_demod). set(para_skip_skolem). skolem([g1(x),g2(x),g3(x),g4(x),g5(x),g6(x),g7(x),g8(x)]). lex([ e1,e2,e3,e4,e5,e6,e7,e8, f(x,x), g1(x),g2(x),g3(x),g4(x),g5(x),g6(x),g7(x),g8(x) ]). list(usable). x = x. end_of_list. list(sos). f(f(x,y),z) = f(x,f(y,z)). f(e1,x) = x. f(e2,x) = x. f(e3,x) = x. f(e4,x) = x. f(e5,x) = x. f(e6,x) = x. f(e7,x) = x. f(e8,x) = x. f(x,g1(x)) = e1. f(x,g2(x)) = e2. f(x,g3(x)) = e3. f(x,g4(x)) = e4. f(x,g5(x)) = e5. f(x,g6(x)) = e6. f(x,g7(x)) = e7. f(x,g8(x)) = e8. end_of_list. otter-3.3f/examples/misc/stage2.in0100644000076400007640000000544105472202432016473 0ustar mccunemccune% % This is Stage 2 of the Kernel Method. % Wos & McCune, "Searching for Fixed Point Combinators ...", ANL-88-10. % % Stage 1 searches for kernels (reducible fixed points of an % arbitrary combinator). % Stage 2 attempts to expand a kernel into a fixed point combinator. % % This is the "sound" version of Stage 2, in which each proof % represents a fixed point combinator. (In the original, "unsound" % version, the user had to filter out answers containing a Skolem % constant.) % % "grep UNIT " to see the finxed-point combinators. % set(para_into). clear(para_from_left). set(para_ones_rule). set(bird_print). clear(back_sub). clear(print_proofs). assign(max_proofs, -1). assign(max_given, 30). % set(para_into_vars). % set(para_from_vars). list(usable). x = x. % regular isolators (including replicators) a(a(a(B,x),y),z) = a(x,a(y,z)). % a(a(L,x),y) = a(x,a(y,y)). % a(I,x) = x. % a(a(K,x),y) = x. % a(a(a(Q1,x),y),z) = a(x,a(z,y)). % irregular isolators (including replicators) % a(M,x) = a(x,x). % a(a(O,x),y) = a(y,a(x,y)). % a(a(T,x),y) = a(y,x). % a(a(a(Q,x),y),z) = a(y,a(x,z)). % regular replicators (non-isolating) a(a(W,x),y) = a(a(x,y),y). % a(a(a(N,x),y),z) = a(a(a(x,z),y),z). % a(a(a(H,x),y),z) = a(a(a(x,y),z),y). % a(a(a(S,x),y),z) = a(a(x,z),a(y,z)). % irregular replicators (non-isolating) % a(a(W1,x),y) = a(a(y,x),x). % others (non-isolating non-replicating) % a(a(a(C,x),y),z) = a(a(x,z),y). % a(a(a(R,x),y),z) = a(a(y,z),x). -FIXED(a(y,g(y)), g(y)) | $Ans(y). % Deny: Exists T All x FIXED(Tx,x). end_of_list. list(sos). % FIXED(a(a(W,a(B,xf)),a(W,a(B,xf))), xf). % FIXED(a(a(W,a(a(B,a(B,xf)),W)),a(a(B,a(B,xf)),W)), xf). % FIXED(a(a(W,a(B,xf)),a(W,a(B,xf))), xf). % FIXED(a(a(a(a(B,W),B),xf),a(a(a(B,W),B),xf)), xf). % FIXED(a(a(W,a(a(a(a(B,B),B),xf),W)),a(a(a(a(B,B),B),xf),W)), xf). FIXED(a(a(a(W,a(B,a(B,xf))),a(W,a(B,a(B,xf)))),x), xf). % FIXED(a(a(W,a(a(B,a(a(B,a(B,xf)),W)),a(B,a(a(B,a(B,xf)),W)))),a(B,a(a(B,a(B,xf)),W))), xf). % FIXED(a(a(W,a(a(B,a(B,xf)),W)),a(a(B,a(B,xf)),W)), xf). % FIXED(a(a(a(a(a(B,W),B),a(B,xf)),a(a(a(B,W),B),a(B,xf))),x), xf). % FIXED(a(a(a(a(B,W),a(B,a(B,xf))),a(a(B,W),a(B,a(B,xf)))),a(a(B,W),a(B,a(B,xf)))), xf). % FIXED(a(a(W,a(a(a(a(W,B),B),xf),W)),a(a(a(a(W,B),B),xf),W)), xf). % FIXED(a(a(a(W,a(a(a(B,B),B),xf)),a(W,a(a(a(B,B),B),xf))),x), xf). % FIXED(a(a(W,a(a(B,a(a(a(a(B,B),B),xf),W)),a(B,a(a(a(a(B,B),B),xf),W)))),a(B,a(a(a(a(B,B),B),xf),W))), xf). % FIXED(a(a(W,a(a(a(a(B,B),B),xf),W)),a(a(a(a(B,B),B),xf),W)), xf). % FIXED(a(a(a(a(a(B,a(a(B,W),B)),B),xf),a(a(a(B,a(a(B,W),B)),B),xf)),x), xf). % FIXED(a(a(a(a(a(B,a(B,W)),B),a(B,xf)),a(a(a(B,a(B,W)),B),a(B,xf))),a(a(a(B,a(B,W)),B),a(B,xf))), xf). % FIXED(a(a(a(a(B,a(a(B,W),a(B,a(B,xf)))),a(B,a(a(B,W),a(B,a(B,xf))))),a(B,a(a(B,W),a(B,a(B,xf))))),a(B,a(a(B,W),a(B,a(B,xf))))), xf). end_of_list. otter-3.3f/examples/misc/dem_alu.in.287520100644000076400007640000000344005472203557017410 0ustar mccunemccune% % Canonicalizing an exclusive-or/and expression with % lex-dependent demodulation. % % This example comes from a verification problem of Smith, % Kljaich, Wojcik, and Chisholm. % op(500, xfy, #). % exclusive or op(400, xfy, *). % and lex([0, 1, cin, a0, b0, a1, b1, a2, b2, a3, b3, *(_,_), #(_,_)]). set(demod_inf). clear(demod_history). assign(demod_limit, -1). assign(max_given, 1). clear(for_sub). clear(back_sub). assign(max_mem, 1500). % 1.5 Megabytes list(demodulators). % The following is a set of reductions for Boolean rings. % Under the following conditions, it produces a canonical form. % 1. The lex term must be lex([, *(_,_), #(_,_)]). % 2. If variables are in the term being rewritten, set(lex_order_vars). 0#x=x. x#0=x. x#x=0. x#x#y=y. x#y=y#x. y#x#z=x#y#z. 0*x=0. x*0=0. 1*x=x. x*1=x. x*x=x. x*x*y=x*y. x*y=y*x. y*x*z=x*y*z. x * (y#z) = (x*y) # (x*z). end_of_list. list(sos). p( (a2#b2#1#a2*b2)# (a3#b3)#1# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (1#a2*b2)# (a0#b0#1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (a1#b1#1#a1*b1)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2)* (cin#1)# (1#a0*b0)* (1#a1*b1)* (1#a2*b2)* (cin#1)# (a1#b1#1#a1*b1)* (1#a2*b2)# (a1#b1#1#a1*b1)* (a2#b2#1#a2*b2)* (1#a2*b2) ). end_of_list. otter-3.3f/examples/misc/andrews.in.287520100644000076400007640000000153505515270720017442 0ustar mccunemccune% Challenge problem from Peter Andrews (1979) % % Although this problem is more easily solved by direct simplification % of the quantified formula (Champeaux, J. ACM 1986 and SIGART Newsletter), % it makes a good test problem for resolution theorem provers. Otter % can do this problem, because it translates equivalences in two ways, % depending on the context, producing only 128 clauses. (Also, FormEd % can prove it by direct simplification.) % set(binary_res). set(process_input). clear(print_kept). clear(print_back_sub). assign(max_mem, 1500). % 1.5 Megabytes formula_list(sos). % Andrews challenge problem -( ( (exists x all y (p(x) <-> p(y))) <-> ((exists u q(u)) <-> (all v p(v))) ) <-> ( (exists w all z (q(z) <-> q(w))) <-> ((exists x1 p(x1)) <-> (all x2 q(x2))) ) ). end_of_list. otter-3.3f/examples/misc/cn.out0100664000076400007640000002624610103522154016110 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:36 2004 The command was "../../bin/otter". The process ID is 8366. set(hyper_res). clear(back_sub). assign(pick_given_ratio,3). assign(max_proofs,3). assign(max_weight,16). clear(print_kept). set(order_history). op(800,yfx,->). list(usable). 1 [] -P(x->y)| -P(x)|P(y). end_of_list. list(sos). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). end_of_list. list(passive). 5 [] -P(a->a)|$Ans(CN_16). 6 [] -P(b-> (a->b))|$Ans(CN_18). 7 [] -P(a->b->c-> (b->c))|$Ans(CN_19). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 2 [] P(x->y-> (y->z-> (x->z))). given clause #2: (wt=7) 3 [] P(-x->x->x). given clause #3: (wt=7) 4 [] P(x-> (-x->y)). given clause #4: (wt=10) 10 [hyper,1,4,4] P(-(x-> (-x->y))->z). given clause #5: (wt=16) 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)). given clause #6: (wt=10) 12 [hyper,1,4,3] P(-(-x->x->x)->y). given clause #7: (wt=11) 9 [hyper,1,2,3] P(x->y-> (-x->x->y)). given clause #8: (wt=10) 24 [hyper,1,9,4] P(-x->x-> (-x->y)). given clause #9: (wt=11) 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). -------- PROOF -------- 35 [binary,34.1,5.1] $Ans(CN_16). ----> UNIT CONFLICT at 0.00 sec ----> 35 [binary,34.1,5.1] $Ans(CN_16). Length of proof is 2. Level of proof is 2. ---------------- PROOF ---------------- 1 [] -P(x->y)| -P(x)|P(y). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). 5 [] -P(a->a)|$Ans(CN_16). 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). 34 [hyper,1,11,3] P(x->x). 35 [binary,34.1,5.1] $Ans(CN_16). ------------ end of proof ------------- given clause #10: (wt=4) 34 [hyper,1,11,3] P(x->x). given clause #11: (wt=7) 37 [hyper,1,4,34] P(-(x->x)->y). given clause #12: (wt=10) 33 [hyper,1,11,4] P(x-> (-(-x->y)->z)). given clause #13: (wt=15) 13 [hyper,1,4,2] P(-(x->y-> (y->z-> (x->z)))->u). given clause #14: (wt=10) 39 [hyper,1,4,37] P(-(-(x->x)->y)->z). given clause #15: (wt=11) 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))). given clause #16: (wt=9) 52 [hyper,1,11,29] P(x-> (y-> (-x->z))). given clause #17: (wt=13) 14 [hyper,1,4,10] P(-(-(x-> (-x->y))->z)->u). given clause #18: (wt=9) 56 [hyper,1,29,37] P(x-> (-(y->y)->z)). given clause #19: (wt=11) 32 [hyper,1,11,9] P(x-> (-(-x)-> -x->y)). given clause #20: (wt=11) 36 [hyper,1,11,2] P(x-> (y->z-> (-x->z))). given clause #21: (wt=14) 15 [hyper,1,2,10] P(x->y-> (-(z-> (-z->u))->y)). given clause #22: (wt=11) 40 [hyper,1,2,37] P(x->y-> (-(z->z)->y)). given clause #23: (wt=12) 55 [hyper,1,29,39] P(x-> (-(-(y->y)->z)->u)). given clause #24: (wt=12) 57 [hyper,1,29,12] P(x-> (-(-y->y->y)->z)). given clause #25: (wt=16) 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))). given clause #26: (wt=12) 58 [hyper,1,29,10] P(x-> (-(y-> (-y->z))->u)). given clause #27: (wt=12) 61 [hyper,1,11,52] P(x-> (y-> (-(-x->z)->u))). given clause #28: (wt=12) 62 [hyper,1,9,52] P(-x->x-> (y-> (-x->z))). given clause #29: (wt=15) 17 [hyper,1,8,4] P(x->y-> (-(y->z-> (x->z))->u)). given clause #30: (wt=12) 63 [hyper,1,4,52] P(-(x-> (y-> (-x->z)))->u). given clause #31: (wt=12) 75 [hyper,1,4,56] P(-(x-> (-(y->y)->z))->u). given clause #32: (wt=13) 19 [hyper,1,4,12] P(-(-(-x->x->x)->y)->z). given clause #33: (wt=16) 18 [hyper,1,8,2] P(x->y-> (x->z->u-> (y->z->u))). given clause #34: (wt=13) 25 [hyper,1,9,3] P(-(-x->x)-> (-x->x)->x). given clause #35: (wt=13) 27 [hyper,1,4,24] P(-(-x->x-> (-x->y))->z). given clause #36: (wt=13) 38 [hyper,1,9,37] P(-(-(x->x))-> -(x->x)->y). given clause #37: (wt=14) 20 [hyper,1,2,12] P(x->y-> (-(-z->z->z)->y)). given clause #38: (wt=13) 42 [hyper,1,11,33] P(x-> (-(-(-x->y)->z)->u)). given clause #39: (wt=13) 43 [hyper,1,9,33] P(-x->x-> (-(-x->y)->z)). given clause #40: (wt=13) 44 [hyper,1,4,33] P(-(x-> (-(-x->y)->z))->u). given clause #41: (wt=16) 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)). given clause #42: (wt=13) 46 [hyper,1,33,37] P(-(-(-(x->x)->y)->z)->u). given clause #43: (wt=13) 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)). given clause #44: (wt=12) 122 [hyper,1,64,4] P(x-> (-(y-> (-x->z))->u)). given clause #45: (wt=14) 22 [hyper,1,4,9] P(-(x->y-> (-x->x->y))->z). given clause #46: (wt=13) 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)). given clause #47: (wt=6) 132 [hyper,1,76,3] P(x-> (y->y)). given clause #48: (wt=9) 131 [hyper,1,76,21] P(x-> (-y->y->y)). given clause #49: (wt=15) 23 [hyper,1,2,9] P(-x->x->y->z-> (x->y->z)). given clause #50: (wt=9) 141 [hyper,1,4,132] P(-(x-> (y->y))->z). given clause #51: (wt=10) 140 [hyper,1,16,132] P(x->y-> (z-> (x->y))). given clause #52: (wt=8) 162 [hyper,1,140,132] P(x-> (y-> (z->z))). given clause #53: (wt=16) 26 [hyper,1,9,24] P(-(-x->x)-> (-x->x)-> (-x->y)). given clause #54: (wt=9) 181 [hyper,1,140,4] P(x-> (y-> (-y->z))). given clause #55: (wt=10) 142 [hyper,1,2,132] P(x->x->y-> (z->y)). given clause #56: (wt=10) 183 [hyper,1,140,162] P(x-> (y-> (z-> (u->u)))). given clause #57: (wt=14) 28 [hyper,1,2,24] P(-x->y->z-> (-x->x->z)). given clause #58: (wt=11) 129 [hyper,1,76,62] P(x-> (y-> (-(z->z)->u))). given clause #59: (wt=11) 135 [hyper,1,52,132] P(x-> (-(y-> (z->z))->u)). given clause #60: (wt=11) 154 [hyper,1,64,140] P(x-> (y-> (z-> (-x->u)))). given clause #61: (wt=14) 30 [hyper,1,4,11] P(-(-x->y->z-> (x->z))->u). given clause #62: (wt=11) 163 [hyper,1,140,131] P(x-> (y-> (-z->z->z))). given clause #63: (wt=11) 171 [hyper,1,140,52] P(x-> (y-> (z-> (-y->u)))). given clause #64: (wt=11) 190 [hyper,1,4,162] P(-(x-> (y-> (z->z)))->u). given clause #65: (wt=15) 31 [hyper,1,2,11] P(x->y->z-> (-x->u->y->z)). given clause #66: (wt=10) 249 [hyper,1,31,3] P(-(-x)->y->x->x). given clause #67: (wt=11) 192 [hyper,1,140,181] P(x-> (y-> (z-> (-z->u)))). given clause #68: (wt=12) 137 [hyper,1,33,132] P(-(-(x-> (y->y))->z)->u). given clause #69: (wt=16) 41 [hyper,1,33,33] P(-(-(x-> (-(-x->y)->z))->u)->v). given clause #70: (wt=12) 147 [hyper,1,4,131] P(-(x-> (-y->y->y))->z). given clause #71: (wt=12) 153 [hyper,1,140,140] P(x-> (y->z-> (u-> (y->z)))). given clause #72: (wt=12) 174 [hyper,1,140,33] P(x-> (y-> (-(-y->z)->u))). given clause #73: (wt=14) 45 [hyper,1,2,33] P(-(-x->y)->z->u-> (x->u)). given clause #74: (wt=12) 178 [hyper,1,140,24] P(x-> (-y->y-> (-y->z))). given clause #75: (wt=12) 191 [hyper,1,2,162] P(x-> (y->y)->z-> (u->z)). given clause #76: (wt=12) 197 [hyper,1,4,181] P(-(x-> (y-> (-y->z)))->u). given clause #77: (wt=16) 47 [hyper,1,33,24] P(-(-(-x->x-> (-x->y))->z)->u). given clause #78: (wt=12) 199 [hyper,1,140,142] P(x-> (y->y->z-> (u->z))). given clause #79: (wt=12) 202 [hyper,1,140,183] P(x-> (y-> (z-> (u-> (v->v))))). given clause #80: (wt=12) 251 [hyper,1,140,249] P(x-> (-(-y)->z->y->y)). given clause #81: (wt=16) 48 [hyper,1,33,12] P(-(-(-(-x->x->x)->y)->z)->u). given clause #82: (wt=12) 256 [hyper,1,8,249] P(x-> -(-(x->y))-> (x->y)). given clause #83: (wt=13) 87 [hyper,1,16,56] P(x-> -(y->y)-> (z-> (x->u))). given clause #84: (wt=13) 89 [hyper,1,16,52] P(x->y-> (z-> (x-> (-z->u)))). given clause #85: (wt=16) 49 [hyper,1,33,10] P(-(-(-(x-> (-x->y))->z)->u)->v). given clause #86: (wt=13) 121 [hyper,1,64,16] P(x-> (y-> -x-> (z-> (y->u)))). given clause #87: (wt=13) 123 [hyper,1,64,2] P(x-> (-x->y->z-> (u->z))). given clause #88: (wt=13) 139 [hyper,1,17,132] P(-(x->x->y-> (z->y))->u). given clause #89: (wt=16) 50 [hyper,1,33,39] P(-(-(-(-(x->x)->y)->z)->u)->v). given clause #90: (wt=13) 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))). given clause #91: (wt=8) 308 [hyper,1,64,146] P(x-> (y-> (z->x))). given clause #92: (wt=8) 322 [hyper,1,146,308] P(x-> (y-> (z->y))). -------- PROOF -------- 361 [binary,360.1,6.1] $Ans(CN_18). ----> UNIT CONFLICT at 0.04 sec ----> 361 [binary,360.1,6.1] $Ans(CN_18). Length of proof is 17. Level of proof is 10. ---------------- PROOF ---------------- 1 [] -P(x->y)| -P(x)|P(y). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). 6 [] -P(b-> (a->b))|$Ans(CN_18). 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)). 9 [hyper,1,2,3] P(x->y-> (-x->x->y)). 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))). 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)). 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))). 34 [hyper,1,11,3] P(x->x). 37 [hyper,1,4,34] P(-(x->x)->y). 52 [hyper,1,11,29] P(x-> (y-> (-x->z))). 56 [hyper,1,29,37] P(x-> (-(y->y)->z)). 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)). 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)). 131 [hyper,1,76,21] P(x-> (-y->y->y)). 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))). 308 [hyper,1,64,146] P(x-> (y-> (z->x))). 322 [hyper,1,146,308] P(x-> (y-> (z->y))). 360 [hyper,1,322,322] P(x-> (y->x)). 361 [binary,360.1,6.1] $Ans(CN_18). ------------ end of proof ------------- given clause #93: (wt=14) 51 [hyper,1,2,39] P(x->y-> (-(-(z->z)->u)->y)). given clause #94: (wt=6) 360 [hyper,1,322,322] P(x-> (y->x)). -------- PROOF -------- 387 [binary,386.1,7.1] $Ans(CN_19). ----> UNIT CONFLICT at 0.05 sec ----> 387 [binary,386.1,7.1] $Ans(CN_19). Length of proof is 18. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -P(x->y)| -P(x)|P(y). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). 7 [] -P(a->b->c-> (b->c))|$Ans(CN_19). 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)). 9 [hyper,1,2,3] P(x->y-> (-x->x->y)). 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))). 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)). 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))). 34 [hyper,1,11,3] P(x->x). 37 [hyper,1,4,34] P(-(x->x)->y). 52 [hyper,1,11,29] P(x-> (y-> (-x->z))). 56 [hyper,1,29,37] P(x-> (-(y->y)->z)). 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)). 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)). 131 [hyper,1,76,21] P(x-> (-y->y->y)). 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))). 308 [hyper,1,64,146] P(x-> (y-> (z->x))). 322 [hyper,1,146,308] P(x-> (y-> (z->y))). 360 [hyper,1,322,322] P(x-> (y->x)). 386 [hyper,1,2,360] P(x->y->z-> (y->z)). 387 [binary,386.1,7.1] $Ans(CN_19). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 94 clauses generated 5345 hyper_res generated 5345 demod & eval rewrites 0 clauses wt,lit,sk delete 1477 tautologies deleted 0 clauses forward subsumed 3491 (subsumed by sos) 447 unit deletions 0 factor simplifications 0 clauses kept 377 new demodulators 0 empty clauses 3 clauses back demodulated 0 clauses back subsumed 0 usable size 95 sos size 286 demodulators size 0 passive size 3 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8366 finished Mon Aug 2 15:30:36 2004 otter-3.3f/examples/misc/stage2.out0100664000076400007640000002713410103522155016673 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8406. set(para_into). clear(para_from_left). set(para_ones_rule). set(bird_print). clear(back_sub). clear(print_proofs). assign(max_proofs,-1). assign(max_given,30). list(usable). 1 [] x=x. 2 [] B x y z=x (y z). 3 [] W x y=x y y. 4 [] -FIXED(y g(y),g(y))|$Ans(y). end_of_list. list(sos). 5 [] FIXED(W (B (B xf)) (W (B (B xf))) x,xf). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=19) 5 [] FIXED(W (B (B xf)) (W (B (B xf))) x,xf). ** KEPT (pick-wt=21): 6 [para_into,5.1.1.1.1,2.1.2] FIXED(B W B (B x) (W (B (B x))) y,x). ** KEPT (pick-wt=21): 7 [para_into,5.1.1.1,2.1.2] FIXED(B (W (B (B x))) W (B (B x)) y,x). ** KEPT (pick-wt=19): 8 [para_into,5.1.1,3.1.2] FIXED(W (W (B (B x))) (W (B (B x))),x). ** KEPT (pick-wt=23): 9 [para_into,5.1.1,2.1.2] FIXED(B (W (B (B x)) (W (B (B x)))) y z,x). given clause #2: (wt=19) 8 [para_into,5.1.1,3.1.2] FIXED(W (W (B (B x))) (W (B (B x))),x). ** KEPT (pick-wt=21): 10 [para_into,8.1.1.1,2.1.2] FIXED(B W W (B (B x)) (W (B (B x))),x). ** KEPT (pick-wt=13): 11 [para_into,8.1.1,3.1.2] FIXED(W W (W (B (B x))),x). ** KEPT (pick-wt=21): 12 [para_into,8.1.1,2.1.2] FIXED(B (W (W (B (B x)))) W (B (B x)),x). given clause #3: (wt=13) 11 [para_into,8.1.1,3.1.2] FIXED(W W (W (B (B x))),x). ** KEPT (pick-wt=15): 13 [para_into,11.1.1,2.1.2] FIXED(B (W W) W (B (B x)),x). given clause #4: (wt=15) 13 [para_into,11.1.1,2.1.2] FIXED(B (W W) W (B (B x)),x). ** KEPT (pick-wt=17): 14 [para_into,13.1.1.1.1,2.1.2] FIXED(B B W W W (B (B x)),x). ** KEPT (pick-wt=17): 15 [para_into,13.1.1,2.1.2] FIXED(B (B (W W) W) B (B x),x). given clause #5: (wt=17) 14 [para_into,13.1.1.1.1,2.1.2] FIXED(B B W W W (B (B x)),x). ** KEPT (pick-wt=17): 16 [para_into,14.1.1.1.1,3.1.2] FIXED(W (B B) W W (B (B x)),x). ** KEPT (pick-wt=17): 17 [para_into,14.1.1.1,3.1.2] FIXED(W (B B W) W (B (B x)),x). ** KEPT (pick-wt=19): 18 [para_into,14.1.1,2.1.2] FIXED(B (B B W W W) B (B x),x). given clause #6: (wt=17) 15 [para_into,13.1.1,2.1.2] FIXED(B (B (W W) W) B (B x),x). ** KEPT (pick-wt=19): 19 [para_into,15.1.1.1.1,2.1.2] FIXED(B B (B (W W)) W B (B x),x). ** KEPT (pick-wt=19): 20 [para_into,15.1.1,2.1.2] FIXED(B (B (B (W W) W) B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 21 [binary,20.1,4.1] $Ans(B (B (B (W W) W) B) B). given clause #7: (wt=17) 16 [para_into,14.1.1.1.1,3.1.2] FIXED(W (B B) W W (B (B x)),x). ** KEPT (pick-wt=19): 22 [para_into,16.1.1.1.1.1,2.1.2] FIXED(B W B B W W (B (B x)),x). ** KEPT (pick-wt=17): 23 [para_into,16.1.1.1,3.1.2] FIXED(W (W (B B)) W (B (B x)),x). ** KEPT (pick-wt=19): 24 [para_into,16.1.1,2.1.2] FIXED(B (W (B B) W W) B (B x),x). given clause #8: (wt=17) 17 [para_into,14.1.1.1,3.1.2] FIXED(W (B B W) W (B (B x)),x). ** KEPT (pick-wt=19): 25 [para_into,17.1.1.1.1,2.1.2] FIXED(B W (B B) W W (B (B x)),x). ** KEPT (pick-wt=19): 26 [para_into,17.1.1,2.1.2] FIXED(B (W (B B W) W) B (B x),x). given clause #9: (wt=17) 23 [para_into,16.1.1.1,3.1.2] FIXED(W (W (B B)) W (B (B x)),x). ** KEPT (pick-wt=19): 27 [para_into,23.1.1.1.1,2.1.2] FIXED(B W W (B B) W (B (B x)),x). ** KEPT (pick-wt=19): 28 [para_into,23.1.1,2.1.2] FIXED(B (W (W (B B)) W) B (B x),x). given clause #10: (wt=19) 18 [para_into,14.1.1,2.1.2] FIXED(B (B B W W W) B (B x),x). ** KEPT (pick-wt=21): 29 [para_into,18.1.1.1.1,2.1.2] FIXED(B B (B B W W) W B (B x),x). ** KEPT (pick-wt=21): 30 [para_into,18.1.1,2.1.2] FIXED(B (B (B B W W W) B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,4.1] $Ans(B (B (B B W W W) B) B). given clause #11: (wt=19) 19 [para_into,15.1.1.1.1,2.1.2] FIXED(B B (B (W W)) W B (B x),x). ** KEPT (pick-wt=21): 32 [para_into,19.1.1.1.1.1,2.1.2] FIXED(B (B B) B (W W) W B (B x),x). ** KEPT (pick-wt=21): 33 [para_into,19.1.1,2.1.2] FIXED(B (B B (B (W W)) W B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 34 [binary,33.1,4.1] $Ans(B (B B (B (W W)) W B) B). given clause #12: (wt=19) 20 [para_into,15.1.1,2.1.2] FIXED(B (B (B (W W) W) B) B x,x). ** KEPT (pick-wt=21): 35 [para_into,20.1.1.1.1,2.1.2] FIXED(B B (B (B (W W) W)) B B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 36 [binary,35.1,4.1] $Ans(B B (B (B (W W) W)) B B). ** KEPT (pick-wt=19): 37 [para_into,20.1.1,3.1.2] FIXED(W (B (B (B (W W) W) B)) B,B). ** KEPT (pick-wt=25): 38 [para_into,20.1.1,2.1.2] FIXED(B (B (B (B (W W) W) B) B) x y,x y). given clause #13: (wt=19) 22 [para_into,16.1.1.1.1.1,2.1.2] FIXED(B W B B W W (B (B x)),x). ** KEPT (pick-wt=19): 39 [para_into,22.1.1.1.1.1,3.1.2] FIXED(W (B W) B W W (B (B x)),x). ** KEPT (pick-wt=19): 40 [para_into,22.1.1.1,3.1.2] FIXED(W (B W B B) W (B (B x)),x). ** KEPT (pick-wt=21): 41 [para_into,22.1.1,2.1.2] FIXED(B (B W B B W W) B (B x),x). given clause #14: (wt=19) 24 [para_into,16.1.1,2.1.2] FIXED(B (W (B B) W W) B (B x),x). ** KEPT (pick-wt=21): 42 [para_into,24.1.1.1.1,2.1.2] FIXED(B B (W (B B) W) W B (B x),x). ** KEPT (pick-wt=21): 43 [para_into,24.1.1,2.1.2] FIXED(B (B (W (B B) W W) B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 44 [binary,43.1,4.1] $Ans(B (B (W (B B) W W) B) B). given clause #15: (wt=19) 25 [para_into,17.1.1.1.1,2.1.2] FIXED(B W (B B) W W (B (B x)),x). ** KEPT (pick-wt=21): 45 [para_into,25.1.1.1.1.1,2.1.2] FIXED(B (B W) B B W W (B (B x)),x). ** KEPT (pick-wt=19): 46 [para_into,25.1.1.1,3.1.2] FIXED(W (B W (B B)) W (B (B x)),x). ** KEPT (pick-wt=21): 47 [para_into,25.1.1,2.1.2] FIXED(B (B W (B B) W W) B (B x),x). given clause #16: (wt=19) 26 [para_into,17.1.1,2.1.2] FIXED(B (W (B B W) W) B (B x),x). ** KEPT (pick-wt=21): 48 [para_into,26.1.1.1.1,2.1.2] FIXED(B B (W (B B W)) W B (B x),x). ** KEPT (pick-wt=21): 49 [para_into,26.1.1,2.1.2] FIXED(B (B (W (B B W) W) B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 50 [binary,49.1,4.1] $Ans(B (B (W (B B W) W) B) B). given clause #17: (wt=19) 27 [para_into,23.1.1.1.1,2.1.2] FIXED(B W W (B B) W (B (B x)),x). ** KEPT (pick-wt=19): 51 [para_into,27.1.1.1.1.1,3.1.2] FIXED(W B W (B B) W (B (B x)),x). ** KEPT (pick-wt=21): 52 [para_into,27.1.1.1.1,2.1.2] FIXED(B (B W W) B B W (B (B x)),x). ** KEPT (pick-wt=21): 53 [para_into,27.1.1,2.1.2] FIXED(B (B W W (B B) W) B (B x),x). given clause #18: (wt=19) 28 [para_into,23.1.1,2.1.2] FIXED(B (W (W (B B)) W) B (B x),x). ** KEPT (pick-wt=21): 54 [para_into,28.1.1.1.1,2.1.2] FIXED(B B (W (W (B B))) W B (B x),x). ** KEPT (pick-wt=21): 55 [para_into,28.1.1,2.1.2] FIXED(B (B (W (W (B B)) W) B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 56 [binary,55.1,4.1] $Ans(B (B (W (W (B B)) W) B) B). given clause #19: (wt=19) 37 [para_into,20.1.1,3.1.2] FIXED(W (B (B (B (W W) W) B)) B,B). ** KEPT (pick-wt=21): 57 [para_into,37.1.1.1,2.1.2] FIXED(B W B (B (B (W W) W) B) B,B). given clause #20: (wt=19) 39 [para_into,22.1.1.1.1.1,3.1.2] FIXED(W (B W) B W W (B (B x)),x). ** KEPT (pick-wt=21): 58 [para_into,39.1.1.1.1.1.1,2.1.2] FIXED(B W B W B W W (B (B x)),x). ** KEPT (pick-wt=19): 59 [para_into,39.1.1.1,3.1.2] FIXED(W (W (B W) B) W (B (B x)),x). ** KEPT (pick-wt=21): 60 [para_into,39.1.1,2.1.2] FIXED(B (W (B W) B W W) B (B x),x). given clause #21: (wt=19) 40 [para_into,22.1.1.1,3.1.2] FIXED(W (B W B B) W (B (B x)),x). ** KEPT (pick-wt=21): 61 [para_into,40.1.1.1.1,2.1.2] FIXED(B W (B W B) B W (B (B x)),x). ** KEPT (pick-wt=21): 62 [para_into,40.1.1,2.1.2] FIXED(B (W (B W B B) W) B (B x),x). given clause #22: (wt=19) 46 [para_into,25.1.1.1,3.1.2] FIXED(W (B W (B B)) W (B (B x)),x). ** KEPT (pick-wt=21): 63 [para_into,46.1.1.1.1,2.1.2] FIXED(B W (B W) (B B) W (B (B x)),x). ** KEPT (pick-wt=21): 64 [para_into,46.1.1,2.1.2] FIXED(B (W (B W (B B)) W) B (B x),x). given clause #23: (wt=19) 51 [para_into,27.1.1.1.1.1,3.1.2] FIXED(W B W (B B) W (B (B x)),x). ** KEPT (pick-wt=21): 65 [para_into,51.1.1.1.1,2.1.2] FIXED(B (W B W) B B W (B (B x)),x). ** KEPT (pick-wt=21): 66 [para_into,51.1.1,2.1.2] FIXED(B (W B W (B B) W) B (B x),x). given clause #24: (wt=19) 59 [para_into,39.1.1.1,3.1.2] FIXED(W (W (B W) B) W (B (B x)),x). ** KEPT (pick-wt=21): 67 [para_into,59.1.1.1.1,2.1.2] FIXED(B W (W (B W)) B W (B (B x)),x). ** KEPT (pick-wt=21): 68 [para_into,59.1.1,2.1.2] FIXED(B (W (W (B W) B) W) B (B x),x). given clause #25: (wt=21) 6 [para_into,5.1.1.1.1,2.1.2] FIXED(B W B (B x) (W (B (B x))) y,x). ** KEPT (pick-wt=23): 69 [para_into,6.1.1.1.1,2.1.2] FIXED(B (B W B) B x (W (B (B x))) y,x). ** KEPT (pick-wt=23): 70 [para_into,6.1.1.1,2.1.2] FIXED(B (B W B (B x)) W (B (B x)) y,x). ** KEPT (pick-wt=21): 71 [para_into,6.1.1,3.1.2] FIXED(W (B W B (B x)) (W (B (B x))),x). ** KEPT (pick-wt=25): 72 [para_into,6.1.1,2.1.2] FIXED(B (B W B (B x) (W (B (B x)))) y z,x). given clause #26: (wt=21) 7 [para_into,5.1.1.1,2.1.2] FIXED(B (W (B (B x))) W (B (B x)) y,x). ** KEPT (pick-wt=23): 73 [para_into,7.1.1.1.1.1,2.1.2] FIXED(B B W (B (B x)) W (B (B x)) y,x). ** KEPT (pick-wt=23): 74 [para_into,7.1.1.1,2.1.2] FIXED(B (B (W (B (B x))) W) B (B x) y,x). ** KEPT (pick-wt=21): 75 [para_into,7.1.1,3.1.2] FIXED(W (B (W (B (B x))) W) (B (B x)),x). ** KEPT (pick-wt=25): 76 [para_into,7.1.1,2.1.2] FIXED(B (B (W (B (B x))) W (B (B x))) y z,x). given clause #27: (wt=21) 10 [para_into,8.1.1.1,2.1.2] FIXED(B W W (B (B x)) (W (B (B x))),x). ** KEPT (pick-wt=21): 77 [para_into,10.1.1.1.1,3.1.2] FIXED(W B W (B (B x)) (W (B (B x))),x). ** KEPT (pick-wt=23): 78 [para_into,10.1.1.1,2.1.2] FIXED(B (B W W) B (B x) (W (B (B x))),x). ** KEPT (pick-wt=23): 79 [para_into,10.1.1,2.1.2] FIXED(B (B W W (B (B x))) W (B (B x)),x). given clause #28: (wt=21) 12 [para_into,8.1.1,2.1.2] FIXED(B (W (W (B (B x)))) W (B (B x)),x). ** KEPT (pick-wt=23): 80 [para_into,12.1.1.1.1,2.1.2] FIXED(B B W (W (B (B x))) W (B (B x)),x). ** KEPT (pick-wt=23): 81 [para_into,12.1.1,2.1.2] FIXED(B (B (W (W (B (B x)))) W) B (B x),x). given clause #29: (wt=21) 29 [para_into,18.1.1.1.1,2.1.2] FIXED(B B (B B W W) W B (B x),x). ** KEPT (pick-wt=23): 82 [para_into,29.1.1.1.1.1,2.1.2] FIXED(B (B B) (B B W) W W B (B x),x). ** KEPT (pick-wt=23): 83 [para_into,29.1.1,2.1.2] FIXED(B (B B (B B W W) W B) B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 84 [binary,83.1,4.1] $Ans(B (B B (B B W W) W B) B). given clause #30: (wt=21) 30 [para_into,18.1.1,2.1.2] FIXED(B (B (B B W W W) B) B x,x). Search stopped by max_given option. ** KEPT (pick-wt=23): 85 [para_into,30.1.1.1.1,2.1.2] FIXED(B B (B (B B W W W)) B B x,x). ----> UNIT CONFLICT at 0.00 sec ----> 86 [binary,85.1,4.1] $Ans(B B (B (B B W W W)) B B). ** KEPT (pick-wt=21): 87 [para_into,30.1.1,3.1.2] FIXED(W (B (B (B B W W W) B)) B,B). ** KEPT (pick-wt=27): 88 [para_into,30.1.1,2.1.2] FIXED(B (B (B (B B W W W) B) B) x y,x y). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 30 clauses generated 74 para_into generated 74 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 74 new demodulators 0 empty clauses 9 clauses back demodulated 0 clauses back subsumed 0 usable size 34 sos size 45 demodulators size 0 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8406 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/stage1.in0100644000076400007640000000263605472202002016466 0ustar mccunemccune% % This is Stage 1 of the Kernel Method. % Wos & McCune, "Searching for Fixed Point Combinators ...", ANL-88-10. % % Stage 1 searches for kernels (reducible fixed points of an % arbitrary combinator). % Stage 2 attempts to expand a kernel into a fixed point combinator. % set(para_into). clear(para_from_left). clear(para_into_left). set(para_ones_rule). clear(back_sub). clear(print_proofs). assign(max_proofs, -1). assign(max_given, 30). % set(para_into_vars). % set(para_from_vars). list(usable). x = x. % regular isolators (including replicators) a(a(a(B,x),y),z) = a(x,a(y,z)). % a(a(L,x),y) = a(x,a(y,y)). % a(I,x) = x. % a(a(K,x),y) = x. % a(a(a(Q1,x),y),z) = a(x,a(z,y)). % irregular isolators (including replicators) % a(M,x) = a(x,x). % a(a(O,x),y) = a(y,a(x,y)). % a(a(T,x),y) = a(y,x). % a(a(a(Q,x),y),z) = a(y,a(x,z)). % regular replicators (non-isolating) a(a(W,x),y) = a(a(x,y),y). % a(a(a(N,x),y),z) = a(a(a(x,z),y),z). % a(a(a(H,x),y),z) = a(a(a(x,y),z),y). % a(a(a(S,x),y),z) = a(a(x,z),a(y,z)). % irregular replicators (non-isolating) % a(a(W1,x),y) = a(a(y,x),x). % others (non-isolating non-replicating) % a(a(a(C,x),y),z) = a(a(x,z),y). % a(a(a(R,x),y),z) = a(a(y,z),x). end_of_list. list(sos). y != a(f,y) | $Ans(y). % denial of the weak fixed point property end_of_list. % The following discards ground clauses. assign(max_weight, 1). weight_list(purge_gen). weight(x, -1000). end_of_list. otter-3.3f/examples/misc/mv.out0100664000076400007640000002705110103522155016126 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8386. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs,3). clear(print_kept). set(order_history). assign(fpa_literals,0). list(usable). 1 [] -P(i(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). end_of_list. list(passive). 6 [] -P(i(n(n(a)),a))|$ANS(MV_24). 7 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). 8 [] -P(i(a,n(n(a))))|$ANS(MV_29). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=6) 2 [] P(i(x,i(y,x))). given clause #2: (wt=8) 9 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). given clause #3: (wt=10) 5 [] P(i(i(n(x),n(y)),i(y,x))). given clause #4: (wt=10) 10 [hyper,1,2,9] P(i(x,i(y,i(z,i(u,z))))). given clause #5: (wt=12) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). given clause #6: (wt=10) 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). given clause #7: (wt=7) 21 [hyper,1,18,5] P(i(n(x),i(x,y))). given clause #8: (wt=8) 23 [hyper,1,18,2] P(i(x,i(y,i(z,x)))). given clause #9: (wt=12) 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). given clause #10: (wt=8) 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). given clause #11: (wt=9) 25 [hyper,1,2,21] P(i(x,i(n(y),i(y,z)))). given clause #12: (wt=10) 22 [hyper,1,18,3] P(i(x,i(i(x,y),i(z,y)))). given clause #13: (wt=12) 11 [hyper,1,2,5] P(i(x,i(i(n(y),n(z)),i(z,y)))). given clause #14: (wt=10) 27 [hyper,1,18,23] P(i(x,i(y,i(z,i(u,x))))). given clause #15: (wt=10) 29 [hyper,1,2,23] P(i(x,i(y,i(z,i(u,y))))). given clause #16: (wt=10) 40 [hyper,1,4,9] P(i(i(i(x,i(y,x)),z),z)). given clause #17: (wt=12) 12 [hyper,1,2,10] P(i(x,i(y,i(z,i(u,i(v,u)))))). given clause #18: (wt=4) 96 [hyper,1,18,40] P(i(x,x)). given clause #19: (wt=6) 106 [hyper,1,2,96] P(i(x,i(y,y))). given clause #20: (wt=8) 102 [hyper,1,36,96] P(i(i(i(x,x),y),y)). given clause #21: (wt=16) 13 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #22: (wt=8) 104 [hyper,1,23,96] P(i(x,i(y,i(z,z)))). given clause #23: (wt=10) 43 [hyper,1,18,36] P(i(x,i(i(i(y,x),z),z))). given clause #24: (wt=10) 45 [hyper,1,2,36] P(i(x,i(y,i(i(y,z),z)))). given clause #25: (wt=14) 14 [hyper,1,2,3] P(i(x,i(i(y,z),i(i(z,u),i(y,u))))). given clause #26: (wt=10) 103 [hyper,1,27,96] P(i(x,i(y,i(z,i(u,u))))). given clause #27: (wt=10) 105 [hyper,1,22,96] P(i(i(i(x,x),y),i(z,y))). given clause #28: (wt=10) 107 [hyper,1,36,106] P(i(i(i(x,i(y,y)),z),z)). given clause #29: (wt=14) 15 [hyper,1,3,10] P(i(i(i(x,i(y,i(z,y))),u),i(v,u))). given clause #30: (wt=10) 115 [hyper,1,2,102] P(i(x,i(i(i(y,y),z),z))). given clause #31: (wt=10) 124 [hyper,1,13,40] P(i(i(x,y),i(x,i(z,y)))). given clause #32: (wt=9) 205 [hyper,1,124,21] P(i(n(x),i(y,i(x,z)))). given clause #33: (wt=12) 16 [hyper,1,3,9] P(i(i(i(x,i(y,x)),z),i(u,z))). given clause #34: (wt=10) 203 [hyper,1,124,36] P(i(x,i(y,i(i(x,z),z)))). given clause #35: (wt=11) 24 [hyper,1,3,21] P(i(i(i(x,y),z),i(n(x),z))). given clause #36: (wt=7) 280 [hyper,1,24,102] P(i(n(i(x,x)),y)). given clause #37: (wt=14) 17 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). given clause #38: (wt=8) 289 [hyper,1,24,5] P(i(n(n(x)),i(y,x))). given clause #39: (wt=9) 278 [hyper,1,24,107] P(i(n(i(x,i(y,y))),z)). given clause #40: (wt=9) 279 [hyper,1,24,105] P(i(n(i(x,x)),i(y,z))). given clause #41: (wt=14) 19 [hyper,1,3,18] P(i(i(i(x,y),z),i(i(i(u,x),y),z))). given clause #42: (wt=9) 282 [hyper,1,24,40] P(i(n(i(x,i(y,x))),z)). given clause #43: (wt=9) 286 [hyper,1,24,18] P(i(n(i(x,y)),i(y,z))). given clause #44: (wt=9) 298 [hyper,1,2,280] P(i(x,i(n(i(y,y)),z))). given clause #45: (wt=12) 20 [hyper,1,2,18] P(i(x,i(i(i(y,z),u),i(z,u)))). given clause #46: (wt=10) 271 [hyper,1,24,24] P(i(n(i(x,y)),i(n(x),z))). given clause #47: (wt=10) 316 [hyper,1,17,102] P(i(i(n(x),n(i(y,y))),x)). -------- PROOF -------- 413 [binary,412.1,6.1] $ANS(MV_24). ----> UNIT CONFLICT at 0.01 sec ----> 413 [binary,412.1,6.1] $ANS(MV_24). Length of proof is 11. Level of proof is 6. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 6 [] -P(i(n(n(a)),a))|$ANS(MV_24). 9 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). 17 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 21 [hyper,1,18,5] P(i(n(x),i(x,y))). 24 [hyper,1,3,21] P(i(i(i(x,y),z),i(n(x),z))). 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). 40 [hyper,1,4,9] P(i(i(i(x,i(y,x)),z),z)). 96 [hyper,1,18,40] P(i(x,x)). 102 [hyper,1,36,96] P(i(i(i(x,x),y),y)). 316 [hyper,1,17,102] P(i(i(n(x),n(i(y,y))),x)). 412 [hyper,1,24,316] P(i(n(n(x)),x)). 413 [binary,412.1,6.1] $ANS(MV_24). ------------ end of proof ------------- given clause #48: (wt=6) 412 [hyper,1,24,316] P(i(n(n(x)),x)). -------- PROOF -------- 429 [binary,428.1,8.1] $ANS(MV_29). ----> UNIT CONFLICT at 0.01 sec ----> 429 [binary,428.1,8.1] $ANS(MV_29). Length of proof is 12. Level of proof is 7. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 8 [] -P(i(a,n(n(a))))|$ANS(MV_29). 9 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). 17 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 21 [hyper,1,18,5] P(i(n(x),i(x,y))). 24 [hyper,1,3,21] P(i(i(i(x,y),z),i(n(x),z))). 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). 40 [hyper,1,4,9] P(i(i(i(x,i(y,x)),z),z)). 96 [hyper,1,18,40] P(i(x,x)). 102 [hyper,1,36,96] P(i(i(i(x,x),y),y)). 316 [hyper,1,17,102] P(i(i(n(x),n(i(y,y))),x)). 412 [hyper,1,24,316] P(i(n(n(x)),x)). 428 [hyper,1,5,412] P(i(x,n(n(x)))). 429 [binary,428.1,8.1] $ANS(MV_29). ------------ end of proof ------------- given clause #49: (wt=12) 26 [hyper,1,23,23] P(i(x,i(y,i(z,i(u,i(v,z)))))). given clause #50: (wt=6) 421 [hyper,1,316,412] P(n(n(i(x,x)))). given clause #51: (wt=6) 428 [hyper,1,5,412] P(i(x,n(n(x)))). given clause #52: (wt=8) 431 [hyper,1,2,412] P(i(x,i(n(n(y)),y))). given clause #53: (wt=12) 28 [hyper,1,3,23] P(i(i(i(x,i(y,z)),u),i(z,u))). given clause #54: (wt=8) 442 [hyper,1,2,421] P(i(x,n(n(i(y,y))))). given clause #55: (wt=8) 443 [hyper,1,428,428] P(n(n(i(x,n(n(x)))))). given clause #56: (wt=8) 445 [hyper,1,124,428] P(i(x,i(y,n(n(x))))). given clause #57: (wt=11) 30 [hyper,1,23,21] P(i(x,i(y,i(n(z),i(z,u))))). given clause #58: (wt=8) 446 [hyper,1,107,428] P(n(n(i(x,i(y,y))))). given clause #59: (wt=8) 448 [hyper,1,40,428] P(n(n(i(x,i(y,x))))). given clause #60: (wt=8) 455 [hyper,1,18,428] P(i(x,n(n(i(y,x))))). given clause #61: (wt=14) 31 [hyper,1,23,18] P(i(x,i(y,i(i(i(z,u),v),i(u,v))))). given clause #62: (wt=8) 461 [hyper,1,2,428] P(i(x,i(y,n(n(y))))). given clause #63: (wt=8) 462 [hyper,1,428,421] P(n(n(n(n(i(x,x)))))). given clause #64: (wt=8) 463 [hyper,1,428,412] P(n(n(i(n(n(x)),x)))). given clause #65: (wt=14) 32 [hyper,1,23,10] P(i(x,i(y,i(z,i(u,i(v,i(w,v))))))). given clause #66: (wt=8) 649 [hyper,1,5,455] P(i(n(i(x,n(y))),y)). given clause #67: (wt=9) 451 [hyper,1,24,428] P(i(n(x),n(n(i(x,y))))). given clause #68: (wt=7) 753 [hyper,1,5,451] P(i(n(i(x,y)),x)). given clause #69: (wt=14) 33 [hyper,1,23,5] P(i(x,i(y,i(i(n(z),n(u)),i(u,z))))). given clause #70: (wt=7) 769 [hyper,1,5,753] P(i(x,i(n(x),y))). given clause #71: (wt=9) 469 [hyper,1,428,280] P(n(n(i(n(i(x,x)),y)))). given clause #72: (wt=9) 492 [hyper,1,428,21] P(n(n(i(n(x),i(x,y))))). given clause #73: (wt=16) 34 [hyper,1,23,3] P(i(x,i(y,i(i(z,u),i(i(u,v),i(z,v)))))). given clause #74: (wt=9) 543 [hyper,1,21,443] P(i(n(i(x,n(n(x)))),y)). given clause #75: (wt=9) 714 [hyper,1,21,462] P(i(n(n(n(i(x,x)))),y)). given clause #76: (wt=9) 725 [hyper,1,21,463] P(i(n(i(n(n(x)),x)),y)). given clause #77: (wt=16) 35 [hyper,1,23,4] P(i(x,i(y,i(i(i(z,u),u),i(i(u,z),z))))). given clause #78: (wt=9) 761 [hyper,1,428,753] P(n(n(i(n(i(x,y)),x)))). given clause #79: (wt=9) 763 [hyper,1,124,753] P(i(n(i(x,y)),i(z,x))). given clause #80: (wt=9) 771 [hyper,1,2,753] P(i(x,i(n(i(y,z)),y))). given clause #81: (wt=16) 37 [hyper,1,3,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). given clause #82: (wt=9) 781 [hyper,1,428,769] P(n(n(i(x,i(n(x),y))))). given clause #83: (wt=9) 783 [hyper,1,124,769] P(i(x,i(y,i(n(x),z)))). given clause #84: (wt=9) 792 [hyper,1,18,769] P(i(x,i(n(i(y,x)),z))). given clause #85: (wt=14) 38 [hyper,1,2,4] P(i(x,i(i(i(y,z),z),i(i(z,y),y)))). given clause #86: (wt=9) 797 [hyper,1,2,769] P(i(x,i(y,i(n(y),z)))). given clause #87: (wt=10) 332 [hyper,1,124,289] P(i(n(n(x)),i(y,i(z,x)))). given clause #88: (wt=10) 339 [hyper,1,2,289] P(i(x,i(n(n(y)),i(z,y)))). given clause #89: (wt=12) 39 [hyper,1,4,10] P(i(i(i(x,i(y,i(z,y))),u),u)). given clause #90: (wt=10) 424 [hyper,1,36,412] P(i(i(i(n(n(x)),x),y),y)). given clause #91: (wt=10) 426 [hyper,1,23,412] P(i(x,i(y,i(n(n(z)),z)))). given clause #92: (wt=10) 430 [hyper,1,3,412] P(i(i(x,y),i(n(n(x)),y))). given clause #93: (wt=12) 41 [hyper,1,36,36] P(i(i(i(x,i(i(x,y),y)),z),z)). given clause #94: (wt=8) 1257 [hyper,1,424,430] P(i(n(n(n(n(x)))),x)). given clause #95: (wt=8) 1336 [hyper,1,5,1257] P(i(x,n(n(n(n(x)))))). given clause #96: (wt=9) 1272 [hyper,1,430,753] P(i(n(n(n(i(x,y)))),x)). given clause #97: (wt=12) 42 [hyper,1,23,36] P(i(x,i(y,i(z,i(i(z,u),u))))). given clause #98: (wt=9) 1296 [hyper,1,430,21] P(i(n(n(n(x))),i(x,y))). given clause #99: (wt=9) 1460 [hyper,1,5,1272] P(i(x,n(n(i(n(x),y))))). given clause #100: (wt=9) 1513 [hyper,1,5,1460] P(i(n(i(n(n(x)),y)),x)). given clause #101: (wt=12) 44 [hyper,1,3,36] P(i(i(i(i(x,y),y),z),i(x,z))). -------- PROOF -------- 1658 [binary,1657.1,7.1] $ANS(MV_25). ----> UNIT CONFLICT at 0.06 sec ----> 1658 [binary,1657.1,7.1] $ANS(MV_25). Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 7 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). 13 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). 44 [hyper,1,3,36] P(i(i(i(i(x,y),y),z),i(x,z))). 1657 [hyper,1,44,13] P(i(i(x,y),i(i(z,x),i(z,y)))). 1658 [binary,1657.1,7.1] $ANS(MV_25). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 101 clauses generated 6237 hyper_res generated 6237 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 4590 (subsumed by sos) 599 unit deletions 0 factor simplifications 0 clauses kept 1647 new demodulators 0 empty clauses 3 clauses back demodulated 0 clauses back subsumed 0 usable size 102 sos size 1550 demodulators size 0 passive size 3 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.06 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8386 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/index.html0100644000076400007640000000252407714267401016762 0ustar mccunemccune /home/mccune/otter-3.3/examples/misc

/home/mccune/otter-3.3/examples/misc

Miscellaneous easy problems.

otter < andrews.in > andrews.out

otter < cn.in > cn.out

otter < dem_alu.in > dem_alu.out

otter < ec.in > ec.out

otter < kb_bench.in > kb_bench.out

otter < mv.in > mv.out

otter < sax1.in > sax1.out

otter < sax2.in > sax2.out

otter < stage1.in > stage1.out

otter < stage2.in > stage2.out

otter < str_bws.in > str_bws.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/misc/sax2.out0100664000076400007640000003500610103522155016360 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8396. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). assign(max_proofs,4). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(stats_level,1). list(usable). 0 [] x=x. end_of_list. list(passive). 1 [] f(a,g(a))!=f(b,g(b))|$Ans(R_inverse). 2 [] f(a,f(b,g(b)))!=a|$Ans(R_ident). 3 [] f(f(a,b),c)!=f(a,f(b,c))|$Ans(assoc). 4 [] f(a,b)!=f(b,a)|$Ans(commute). end_of_list. list(sos). 0 [] f(f(f(x,y),z),g(f(x,z)))=y. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 5 [] x=x. Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] x=x. ------------> process sos: ** KEPT (pick-wt=12): 6 [] f(f(f(x,y),z),g(f(x,z)))=y. ---> New Demodulator: 7 [new_demod,6] f(f(f(x,y),z),g(f(x,z)))=y. >>>> Starting back demodulation with 7. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 6 [] f(f(f(x,y),z),g(f(x,z)))=y. given clause #2: (wt=13) 10 [para_into,6.1.1.1,6.1.1] f(x,g(f(f(y,x),g(f(y,z)))))=z. given clause #3: (wt=17) 8 [para_into,6.1.1.1.1,6.1.1] f(f(x,y),g(f(f(f(z,x),u),y)))=g(f(z,u)). given clause #4: (wt=13) 45 [para_into,8.1.1,10.1.1,flip.1] g(f(x,f(y,g(f(f(x,y),z)))))=z. given clause #5: (wt=13) 71 [para_into,45.1.1.1.2,8.1.1] g(f(f(x,y),g(f(x,f(y,z)))))=z. given clause #6: (wt=14) 43 [para_into,8.1.1.2.1,6.1.1] f(f(x,g(f(y,z))),g(x))=g(f(y,z)). given clause #7: (wt=8) 98 [para_into,43.1.1.1.2,71.1.1,demod,72] f(f(x,y),g(x))=y. given clause #8: (wt=8) 234 [back_demod,182,demod,190] f(x,f(y,g(x)))=y. given clause #9: (wt=8) 236 [back_demod,180,demod,190] f(f(x,g(y)),y)=x. -------- PROOF -------- 244 [binary,243.1,4.1] $Ans(commute). ----> UNIT CONFLICT at 0.01 sec ----> 244 [binary,243.1,4.1] $Ans(commute). Length of proof is 26. Level of proof is 9. ---------------- PROOF ---------------- 4 [] f(a,b)!=f(b,a)|$Ans(commute). 6 [] f(f(f(x,y),z),g(f(x,z)))=y. 8 [para_into,6.1.1.1.1,6.1.1] f(f(x,y),g(f(f(f(z,x),u),y)))=g(f(z,u)). 10 [para_into,6.1.1.1,6.1.1] f(x,g(f(f(y,x),g(f(y,z)))))=z. 26 [para_from,10.1.1,6.1.1.1.1] f(f(x,y),g(f(z,y)))=g(f(f(u,z),g(f(u,x)))). 27 [copy,26,flip.1] g(f(f(x,y),g(f(x,z))))=f(f(z,u),g(f(y,u))). 34 [para_into,8.1.1.2.1.1.1,10.1.1] f(f(g(f(f(x,y),g(f(x,z)))),u),g(f(f(z,v),u)))=g(f(y,v)). 37 [para_into,8.1.1.2.1.1,10.1.1] f(f(x,y),g(f(z,y)))=g(f(u,g(f(f(v,f(u,x)),g(f(v,z)))))). 43 [para_into,8.1.1.2.1,6.1.1] f(f(x,g(f(y,z))),g(x))=g(f(y,z)). 45 [para_into,8.1.1,10.1.1,flip.1] g(f(x,f(y,g(f(f(x,y),z)))))=z. 47 [copy,34,flip.1] g(f(x,y))=f(f(g(f(f(z,x),g(f(z,u)))),v),g(f(f(u,y),v))). 65,64 [para_into,45.1.1.1.2.2.1,10.1.1,flip.1] g(f(f(x,f(y,z)),g(f(x,u))))=g(f(y,f(z,g(u)))). 72,71 [para_into,45.1.1.1.2,8.1.1] g(f(f(x,y),g(f(x,f(y,z)))))=z. 76 [back_demod,37,demod,65] f(f(x,y),g(f(z,y)))=g(f(u,g(f(u,f(x,g(z)))))). 83 [para_from,45.1.1,6.1.1.2] f(f(f(x,y),f(z,g(f(f(x,z),u)))),u)=y. 98 [para_into,43.1.1.1.2,71.1.1,demod,72] f(f(x,y),g(x))=y. 103,102 [para_into,43.1.1.1,10.1.1,flip.1] g(f(f(x,y),g(f(x,z))))=f(z,g(y)). 107,106 [para_into,43.1.1.1,6.1.1] f(x,g(f(f(y,x),z)))=g(f(y,z)). 115,114 [back_demod,64,demod,103,flip.1] g(f(x,f(y,g(z))))=f(z,g(f(x,y))). 118 [back_demod,47,demod,103] g(f(x,y))=f(f(f(z,g(x)),u),g(f(f(z,y),u))). 123,122 [back_demod,27,demod,103,flip.1] f(f(x,y),g(f(z,y)))=f(x,g(z)). 156 [back_demod,83,demod,107] f(f(f(x,y),g(f(x,z))),z)=y. 161,160 [back_demod,76,demod,123,115,115,flip.1] f(f(x,y),g(f(x,z)))=f(y,g(z)). 163,162 [copy,118,flip.1,demod,123,161,flip.1] g(f(x,y))=f(g(x),g(y)). 180 [back_demod,156,demod,163] f(f(f(x,y),f(g(x),g(z))),z)=y. 190,189 [back_demod,160,demod,163] f(f(x,y),f(g(x),g(z)))=f(y,g(z)). 236 [back_demod,180,demod,190] f(f(x,g(y)),y)=x. 243 [para_into,236.1.1.1,98.1.1] f(x,y)=f(y,x). 244 [binary,243.1,4.1] $Ans(commute). ------------ end of proof ------------- given clause #10: (wt=5) 245 [para_into,236.1.1,98.1.1] g(g(x))=x. given clause #11: (wt=7) 243 [para_into,236.1.1.1,98.1.1] f(x,y)=f(y,x). given clause #12: (wt=8) 247 [back_demod,239,demod,246,246] f(g(x),f(x,y))=y. given clause #13: (wt=8) 265 [para_from,236.1.1,98.1.1.1,demod,163,246] f(x,f(g(x),y))=y. given clause #14: (wt=8) 269 [para_from,245.1.1,234.1.1.2.2] f(g(x),f(y,x))=y. given clause #15: (wt=8) 271 [para_from,245.1.1,98.1.1.2] f(f(g(x),y),x)=y. given clause #16: (wt=8) 273 [para_from,245.1.1,236.1.1.1.2] f(f(x,y),g(y))=x. given clause #17: (wt=10) 162 [copy,118,flip.1,demod,123,161,flip.1] g(f(x,y))=f(g(x),g(y)). given clause #18: (wt=13) 124 [back_demod,22,demod,103] f(f(f(x,y),f(z,g(x))),g(z))=y. given clause #19: (wt=12) 291 [para_into,124.1.1.1.1,269.1.1,demod,246] f(f(x,f(y,z)),g(y))=f(x,z). -------- PROOF -------- 315 [binary,313.1,3.1] $Ans(assoc). ----> UNIT CONFLICT at 0.02 sec ----> 315 [binary,313.1,3.1] $Ans(assoc). Length of proof is 37. Level of proof is 12. ---------------- PROOF ---------------- 3 [] f(f(a,b),c)!=f(a,f(b,c))|$Ans(assoc). 6 [] f(f(f(x,y),z),g(f(x,z)))=y. 8 [para_into,6.1.1.1.1,6.1.1] f(f(x,y),g(f(f(f(z,x),u),y)))=g(f(z,u)). 10 [para_into,6.1.1.1,6.1.1] f(x,g(f(f(y,x),g(f(y,z)))))=z. 18 [para_into,10.1.1.2.1.2.1,10.1.1] f(x,g(f(f(y,x),g(z))))=g(f(f(u,y),g(f(u,z)))). 21 [copy,18,flip.1] g(f(f(x,y),g(f(x,z))))=f(u,g(f(f(y,u),g(z)))). 22 [para_from,10.1.1,6.1.1.2.1] f(f(f(x,y),g(f(f(z,x),g(f(z,u))))),g(u))=y. 26 [para_from,10.1.1,6.1.1.1.1] f(f(x,y),g(f(z,y)))=g(f(f(u,z),g(f(u,x)))). 27 [copy,26,flip.1] g(f(f(x,y),g(f(x,z))))=f(f(z,u),g(f(y,u))). 34 [para_into,8.1.1.2.1.1.1,10.1.1] f(f(g(f(f(x,y),g(f(x,z)))),u),g(f(f(z,v),u)))=g(f(y,v)). 37 [para_into,8.1.1.2.1.1,10.1.1] f(f(x,y),g(f(z,y)))=g(f(u,g(f(f(v,f(u,x)),g(f(v,z)))))). 43 [para_into,8.1.1.2.1,6.1.1] f(f(x,g(f(y,z))),g(x))=g(f(y,z)). 45 [para_into,8.1.1,10.1.1,flip.1] g(f(x,f(y,g(f(f(x,y),z)))))=z. 47 [copy,34,flip.1] g(f(x,y))=f(f(g(f(f(z,x),g(f(z,u)))),v),g(f(f(u,y),v))). 65,64 [para_into,45.1.1.1.2.2.1,10.1.1,flip.1] g(f(f(x,f(y,z)),g(f(x,u))))=g(f(y,f(z,g(u)))). 72,71 [para_into,45.1.1.1.2,8.1.1] g(f(f(x,y),g(f(x,f(y,z)))))=z. 76 [back_demod,37,demod,65] f(f(x,y),g(f(z,y)))=g(f(u,g(f(u,f(x,g(z)))))). 83 [para_from,45.1.1,6.1.1.2] f(f(f(x,y),f(z,g(f(f(x,z),u)))),u)=y. 98 [para_into,43.1.1.1.2,71.1.1,demod,72] f(f(x,y),g(x))=y. 103,102 [para_into,43.1.1.1,10.1.1,flip.1] g(f(f(x,y),g(f(x,z))))=f(z,g(y)). 107,106 [para_into,43.1.1.1,6.1.1] f(x,g(f(f(y,x),z)))=g(f(y,z)). 115,114 [back_demod,64,demod,103,flip.1] g(f(x,f(y,g(z))))=f(z,g(f(x,y))). 118 [back_demod,47,demod,103] g(f(x,y))=f(f(f(z,g(x)),u),g(f(f(z,y),u))). 123,122 [back_demod,27,demod,103,flip.1] f(f(x,y),g(f(z,y)))=f(x,g(z)). 124 [back_demod,22,demod,103] f(f(f(x,y),f(z,g(x))),g(z))=y. 127,126 [back_demod,21,demod,103,107,flip.1] g(f(x,g(y)))=f(y,g(x)). 131 [back_demod,10,demod,127] f(x,f(f(y,z),g(f(y,x))))=z. 156 [back_demod,83,demod,107] f(f(f(x,y),g(f(x,z))),z)=y. 161,160 [back_demod,76,demod,123,115,115,flip.1] f(f(x,y),g(f(x,z)))=f(y,g(z)). 163,162 [copy,118,flip.1,demod,123,161,flip.1] g(f(x,y))=f(g(x),g(y)). 180 [back_demod,156,demod,163] f(f(f(x,y),f(g(x),g(z))),z)=y. 182 [back_demod,131,demod,163] f(x,f(f(y,z),f(g(y),g(x))))=z. 190,189 [back_demod,160,demod,163] f(f(x,y),f(g(x),g(z)))=f(y,g(z)). 234 [back_demod,182,demod,190] f(x,f(y,g(x)))=y. 236 [back_demod,180,demod,190] f(f(x,g(y)),y)=x. 246,245 [para_into,236.1.1,98.1.1] g(g(x))=x. 269 [para_from,245.1.1,234.1.1.2.2] f(g(x),f(y,x))=y. 291 [para_into,124.1.1.1.1,269.1.1,demod,246] f(f(x,f(y,z)),g(y))=f(x,z). 313 [para_into,291.1.1.1.2,269.1.1,demod,246] f(f(x,y),z)=f(x,f(y,z)). 315 [binary,313.1,3.1] $Ans(assoc). ------------ end of proof ------------- -------- PROOF -------- 325 [binary,324.1,1.1] $Ans(R_inverse). ----> UNIT CONFLICT at 0.02 sec ----> 325 [binary,324.1,1.1] $Ans(R_inverse). Length of proof is 37. Level of proof is 12. ---------------- PROOF ---------------- 1 [] f(a,g(a))!=f(b,g(b))|$Ans(R_inverse). 6 [] f(f(f(x,y),z),g(f(x,z)))=y. 8 [para_into,6.1.1.1.1,6.1.1] f(f(x,y),g(f(f(f(z,x),u),y)))=g(f(z,u)). 10 [para_into,6.1.1.1,6.1.1] f(x,g(f(f(y,x),g(f(y,z)))))=z. 18 [para_into,10.1.1.2.1.2.1,10.1.1] f(x,g(f(f(y,x),g(z))))=g(f(f(u,y),g(f(u,z)))). 21 [copy,18,flip.1] g(f(f(x,y),g(f(x,z))))=f(u,g(f(f(y,u),g(z)))). 22 [para_from,10.1.1,6.1.1.2.1] f(f(f(x,y),g(f(f(z,x),g(f(z,u))))),g(u))=y. 26 [para_from,10.1.1,6.1.1.1.1] f(f(x,y),g(f(z,y)))=g(f(f(u,z),g(f(u,x)))). 27 [copy,26,flip.1] g(f(f(x,y),g(f(x,z))))=f(f(z,u),g(f(y,u))). 34 [para_into,8.1.1.2.1.1.1,10.1.1] f(f(g(f(f(x,y),g(f(x,z)))),u),g(f(f(z,v),u)))=g(f(y,v)). 37 [para_into,8.1.1.2.1.1,10.1.1] f(f(x,y),g(f(z,y)))=g(f(u,g(f(f(v,f(u,x)),g(f(v,z)))))). 43 [para_into,8.1.1.2.1,6.1.1] f(f(x,g(f(y,z))),g(x))=g(f(y,z)). 45 [para_into,8.1.1,10.1.1,flip.1] g(f(x,f(y,g(f(f(x,y),z)))))=z. 47 [copy,34,flip.1] g(f(x,y))=f(f(g(f(f(z,x),g(f(z,u)))),v),g(f(f(u,y),v))). 65,64 [para_into,45.1.1.1.2.2.1,10.1.1,flip.1] g(f(f(x,f(y,z)),g(f(x,u))))=g(f(y,f(z,g(u)))). 72,71 [para_into,45.1.1.1.2,8.1.1] g(f(f(x,y),g(f(x,f(y,z)))))=z. 76 [back_demod,37,demod,65] f(f(x,y),g(f(z,y)))=g(f(u,g(f(u,f(x,g(z)))))). 83 [para_from,45.1.1,6.1.1.2] f(f(f(x,y),f(z,g(f(f(x,z),u)))),u)=y. 98 [para_into,43.1.1.1.2,71.1.1,demod,72] f(f(x,y),g(x))=y. 103,102 [para_into,43.1.1.1,10.1.1,flip.1] g(f(f(x,y),g(f(x,z))))=f(z,g(y)). 107,106 [para_into,43.1.1.1,6.1.1] f(x,g(f(f(y,x),z)))=g(f(y,z)). 115,114 [back_demod,64,demod,103,flip.1] g(f(x,f(y,g(z))))=f(z,g(f(x,y))). 118 [back_demod,47,demod,103] g(f(x,y))=f(f(f(z,g(x)),u),g(f(f(z,y),u))). 123,122 [back_demod,27,demod,103,flip.1] f(f(x,y),g(f(z,y)))=f(x,g(z)). 124 [back_demod,22,demod,103] f(f(f(x,y),f(z,g(x))),g(z))=y. 127,126 [back_demod,21,demod,103,107,flip.1] g(f(x,g(y)))=f(y,g(x)). 131 [back_demod,10,demod,127] f(x,f(f(y,z),g(f(y,x))))=z. 156 [back_demod,83,demod,107] f(f(f(x,y),g(f(x,z))),z)=y. 161,160 [back_demod,76,demod,123,115,115,flip.1] f(f(x,y),g(f(x,z)))=f(y,g(z)). 163,162 [copy,118,flip.1,demod,123,161,flip.1] g(f(x,y))=f(g(x),g(y)). 180 [back_demod,156,demod,163] f(f(f(x,y),f(g(x),g(z))),z)=y. 182 [back_demod,131,demod,163] f(x,f(f(y,z),f(g(y),g(x))))=z. 190,189 [back_demod,160,demod,163] f(f(x,y),f(g(x),g(z)))=f(y,g(z)). 234 [back_demod,182,demod,190] f(x,f(y,g(x)))=y. 236 [back_demod,180,demod,190] f(f(x,g(y)),y)=x. 246,245 [para_into,236.1.1,98.1.1] g(g(x))=x. 269 [para_from,245.1.1,234.1.1.2.2] f(g(x),f(y,x))=y. 291 [para_into,124.1.1.1.1,269.1.1,demod,246] f(f(x,f(y,z)),g(y))=f(x,z). 324 [para_into,291.1.1.1,234.1.1] f(x,g(x))=f(y,g(y)). 325 [binary,324.1,1.1] $Ans(R_inverse). ------------ end of proof ------------- -------- PROOF -------- 340 [binary,338.1,2.1] $Ans(R_ident). ----> UNIT CONFLICT at 0.02 sec ----> 340 [binary,338.1,2.1] $Ans(R_ident). Length of proof is 40. Level of proof is 13. ---------------- PROOF ---------------- 2 [] f(a,f(b,g(b)))!=a|$Ans(R_ident). 6 [] f(f(f(x,y),z),g(f(x,z)))=y. 8 [para_into,6.1.1.1.1,6.1.1] f(f(x,y),g(f(f(f(z,x),u),y)))=g(f(z,u)). 10 [para_into,6.1.1.1,6.1.1] f(x,g(f(f(y,x),g(f(y,z)))))=z. 18 [para_into,10.1.1.2.1.2.1,10.1.1] f(x,g(f(f(y,x),g(z))))=g(f(f(u,y),g(f(u,z)))). 21 [copy,18,flip.1] g(f(f(x,y),g(f(x,z))))=f(u,g(f(f(y,u),g(z)))). 22 [para_from,10.1.1,6.1.1.2.1] f(f(f(x,y),g(f(f(z,x),g(f(z,u))))),g(u))=y. 26 [para_from,10.1.1,6.1.1.1.1] f(f(x,y),g(f(z,y)))=g(f(f(u,z),g(f(u,x)))). 27 [copy,26,flip.1] g(f(f(x,y),g(f(x,z))))=f(f(z,u),g(f(y,u))). 34 [para_into,8.1.1.2.1.1.1,10.1.1] f(f(g(f(f(x,y),g(f(x,z)))),u),g(f(f(z,v),u)))=g(f(y,v)). 37 [para_into,8.1.1.2.1.1,10.1.1] f(f(x,y),g(f(z,y)))=g(f(u,g(f(f(v,f(u,x)),g(f(v,z)))))). 43 [para_into,8.1.1.2.1,6.1.1] f(f(x,g(f(y,z))),g(x))=g(f(y,z)). 45 [para_into,8.1.1,10.1.1,flip.1] g(f(x,f(y,g(f(f(x,y),z)))))=z. 47 [copy,34,flip.1] g(f(x,y))=f(f(g(f(f(z,x),g(f(z,u)))),v),g(f(f(u,y),v))). 65,64 [para_into,45.1.1.1.2.2.1,10.1.1,flip.1] g(f(f(x,f(y,z)),g(f(x,u))))=g(f(y,f(z,g(u)))). 72,71 [para_into,45.1.1.1.2,8.1.1] g(f(f(x,y),g(f(x,f(y,z)))))=z. 76 [back_demod,37,demod,65] f(f(x,y),g(f(z,y)))=g(f(u,g(f(u,f(x,g(z)))))). 83 [para_from,45.1.1,6.1.1.2] f(f(f(x,y),f(z,g(f(f(x,z),u)))),u)=y. 98 [para_into,43.1.1.1.2,71.1.1,demod,72] f(f(x,y),g(x))=y. 103,102 [para_into,43.1.1.1,10.1.1,flip.1] g(f(f(x,y),g(f(x,z))))=f(z,g(y)). 107,106 [para_into,43.1.1.1,6.1.1] f(x,g(f(f(y,x),z)))=g(f(y,z)). 115,114 [back_demod,64,demod,103,flip.1] g(f(x,f(y,g(z))))=f(z,g(f(x,y))). 118 [back_demod,47,demod,103] g(f(x,y))=f(f(f(z,g(x)),u),g(f(f(z,y),u))). 123,122 [back_demod,27,demod,103,flip.1] f(f(x,y),g(f(z,y)))=f(x,g(z)). 124 [back_demod,22,demod,103] f(f(f(x,y),f(z,g(x))),g(z))=y. 127,126 [back_demod,21,demod,103,107,flip.1] g(f(x,g(y)))=f(y,g(x)). 131 [back_demod,10,demod,127] f(x,f(f(y,z),g(f(y,x))))=z. 156 [back_demod,83,demod,107] f(f(f(x,y),g(f(x,z))),z)=y. 161,160 [back_demod,76,demod,123,115,115,flip.1] f(f(x,y),g(f(x,z)))=f(y,g(z)). 163,162 [copy,118,flip.1,demod,123,161,flip.1] g(f(x,y))=f(g(x),g(y)). 180 [back_demod,156,demod,163] f(f(f(x,y),f(g(x),g(z))),z)=y. 182 [back_demod,131,demod,163] f(x,f(f(y,z),f(g(y),g(x))))=z. 190,189 [back_demod,160,demod,163] f(f(x,y),f(g(x),g(z)))=f(y,g(z)). 235,234 [back_demod,182,demod,190] f(x,f(y,g(x)))=y. 236 [back_demod,180,demod,190] f(f(x,g(y)),y)=x. 246,245 [para_into,236.1.1,98.1.1] g(g(x))=x. 269 [para_from,245.1.1,234.1.1.2.2] f(g(x),f(y,x))=y. 273 [para_from,245.1.1,236.1.1.1.2] f(f(x,y),g(y))=x. 283 [para_from,162.1.1,273.1.1.2] f(f(x,f(y,z)),f(g(y),g(z)))=x. 291 [para_into,124.1.1.1.1,269.1.1,demod,246] f(f(x,f(y,z)),g(y))=f(x,z). 314,313 [para_into,291.1.1.1.2,269.1.1,demod,246] f(f(x,y),z)=f(x,f(y,z)). 338 [back_demod,283,demod,314,314,235] f(x,f(y,g(y)))=x. 340 [binary,338.1,2.1] $Ans(R_ident). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 19 clauses generated 280 clauses kept 190 clauses forward subsumed 273 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8396 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/README0100644000076400007640000000003507313710545015635 0ustar mccunemccuneMiscellaneous easy problems. otter-3.3f/examples/misc/kb_bench.out0100664000076400007640000005275310103522155017246 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8381. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(print_lists_at_end). set(really_delete_clauses). clear(print_kept). clear(print_new_demod). clear(print_back_demod). set(para_skip_skolem). skolem([g1(x),g2(x),g3(x),g4(x),g5(x),g6(x),g7(x),g8(x)]). lex([e1,e2,e3,e4,e5,e6,e7,e8,f(x,x),g1(x),g2(x),g3(x),g4(x),g5(x),g6(x),g7(x),g8(x)]). list(usable). 0 [] x=x. end_of_list. list(sos). 0 [] f(f(x,y),z)=f(x,f(y,z)). 0 [] f(e1,x)=x. 0 [] f(e2,x)=x. 0 [] f(e3,x)=x. 0 [] f(e4,x)=x. 0 [] f(e5,x)=x. 0 [] f(e6,x)=x. 0 [] f(e7,x)=x. 0 [] f(e8,x)=x. 0 [] f(x,g1(x))=e1. 0 [] f(x,g2(x))=e2. 0 [] f(x,g3(x))=e3. 0 [] f(x,g4(x))=e4. 0 [] f(x,g5(x))=e5. 0 [] f(x,g6(x))=e6. 0 [] f(x,g7(x))=e7. 0 [] f(x,g8(x))=e8. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. ------------> process sos: ** KEPT (pick-wt=11): 2 [] f(f(x,y),z)=f(x,f(y,z)). ---> New Demodulator: 3 [new_demod,2] f(f(x,y),z)=f(x,f(y,z)). ** KEPT (pick-wt=5): 4 [] f(e1,x)=x. ---> New Demodulator: 5 [new_demod,4] f(e1,x)=x. ** KEPT (pick-wt=5): 6 [] f(e2,x)=x. ---> New Demodulator: 7 [new_demod,6] f(e2,x)=x. ** KEPT (pick-wt=5): 8 [] f(e3,x)=x. ---> New Demodulator: 9 [new_demod,8] f(e3,x)=x. ** KEPT (pick-wt=5): 10 [] f(e4,x)=x. ---> New Demodulator: 11 [new_demod,10] f(e4,x)=x. ** KEPT (pick-wt=5): 12 [] f(e5,x)=x. ---> New Demodulator: 13 [new_demod,12] f(e5,x)=x. ** KEPT (pick-wt=5): 14 [] f(e6,x)=x. ---> New Demodulator: 15 [new_demod,14] f(e6,x)=x. ** KEPT (pick-wt=5): 16 [] f(e7,x)=x. ---> New Demodulator: 17 [new_demod,16] f(e7,x)=x. ** KEPT (pick-wt=5): 18 [] f(e8,x)=x. ---> New Demodulator: 19 [new_demod,18] f(e8,x)=x. ** KEPT (pick-wt=6): 20 [] f(x,g1(x))=e1. ---> New Demodulator: 21 [new_demod,20] f(x,g1(x))=e1. ** KEPT (pick-wt=6): 22 [] f(x,g2(x))=e2. ---> New Demodulator: 23 [new_demod,22] f(x,g2(x))=e2. ** KEPT (pick-wt=6): 24 [] f(x,g3(x))=e3. ---> New Demodulator: 25 [new_demod,24] f(x,g3(x))=e3. ** KEPT (pick-wt=6): 26 [] f(x,g4(x))=e4. ---> New Demodulator: 27 [new_demod,26] f(x,g4(x))=e4. ** KEPT (pick-wt=6): 28 [] f(x,g5(x))=e5. ---> New Demodulator: 29 [new_demod,28] f(x,g5(x))=e5. ** KEPT (pick-wt=6): 30 [] f(x,g6(x))=e6. ---> New Demodulator: 31 [new_demod,30] f(x,g6(x))=e6. ** KEPT (pick-wt=6): 32 [] f(x,g7(x))=e7. ---> New Demodulator: 33 [new_demod,32] f(x,g7(x))=e7. ** KEPT (pick-wt=6): 34 [] f(x,g8(x))=e8. ---> New Demodulator: 35 [new_demod,34] f(x,g8(x))=e8. >>>> Starting back demodulation with 3. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 29. >>>> Starting back demodulation with 31. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 35. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=5) 4 [] f(e1,x)=x. given clause #2: (wt=5) 6 [] f(e2,x)=x. given clause #3: (wt=5) 8 [] f(e3,x)=x. given clause #4: (wt=5) 10 [] f(e4,x)=x. given clause #5: (wt=5) 12 [] f(e5,x)=x. given clause #6: (wt=5) 14 [] f(e6,x)=x. given clause #7: (wt=5) 16 [] f(e7,x)=x. given clause #8: (wt=5) 18 [] f(e8,x)=x. given clause #9: (wt=6) 20 [] f(x,g1(x))=e1. given clause #10: (wt=4) 36 [para_into,20.1.1,18.1.1] g1(e8)=e1. given clause #11: (wt=4) 38 [para_into,20.1.1,16.1.1] g1(e7)=e1. given clause #12: (wt=4) 40 [para_into,20.1.1,14.1.1] g1(e6)=e1. given clause #13: (wt=4) 42 [para_into,20.1.1,12.1.1] g1(e5)=e1. given clause #14: (wt=4) 44 [para_into,20.1.1,10.1.1] g1(e4)=e1. given clause #15: (wt=4) 46 [para_into,20.1.1,8.1.1] g1(e3)=e1. given clause #16: (wt=4) 48 [para_into,20.1.1,6.1.1] g1(e2)=e1. given clause #17: (wt=4) 50 [para_into,20.1.1,4.1.1] g1(e1)=e1. given clause #18: (wt=6) 22 [] f(x,g2(x))=e2. given clause #19: (wt=4) 52 [para_into,22.1.1,18.1.1] g2(e8)=e2. given clause #20: (wt=4) 54 [para_into,22.1.1,16.1.1] g2(e7)=e2. given clause #21: (wt=4) 56 [para_into,22.1.1,14.1.1] g2(e6)=e2. given clause #22: (wt=4) 58 [para_into,22.1.1,12.1.1] g2(e5)=e2. given clause #23: (wt=4) 60 [para_into,22.1.1,10.1.1] g2(e4)=e2. given clause #24: (wt=4) 62 [para_into,22.1.1,8.1.1] g2(e3)=e2. given clause #25: (wt=4) 64 [para_into,22.1.1,6.1.1] g2(e2)=e2. given clause #26: (wt=4) 66 [para_into,22.1.1,4.1.1] g2(e1)=e2. given clause #27: (wt=6) 24 [] f(x,g3(x))=e3. given clause #28: (wt=4) 68 [para_into,24.1.1,18.1.1] g3(e8)=e3. given clause #29: (wt=4) 70 [para_into,24.1.1,16.1.1] g3(e7)=e3. given clause #30: (wt=4) 72 [para_into,24.1.1,14.1.1] g3(e6)=e3. given clause #31: (wt=4) 74 [para_into,24.1.1,12.1.1] g3(e5)=e3. given clause #32: (wt=4) 76 [para_into,24.1.1,10.1.1] g3(e4)=e3. given clause #33: (wt=4) 78 [para_into,24.1.1,8.1.1] g3(e3)=e3. given clause #34: (wt=4) 80 [para_into,24.1.1,6.1.1] g3(e2)=e3. given clause #35: (wt=4) 82 [para_into,24.1.1,4.1.1] g3(e1)=e3. given clause #36: (wt=6) 26 [] f(x,g4(x))=e4. given clause #37: (wt=4) 84 [para_into,26.1.1,18.1.1] g4(e8)=e4. given clause #38: (wt=4) 86 [para_into,26.1.1,16.1.1] g4(e7)=e4. given clause #39: (wt=4) 88 [para_into,26.1.1,14.1.1] g4(e6)=e4. given clause #40: (wt=4) 90 [para_into,26.1.1,12.1.1] g4(e5)=e4. given clause #41: (wt=4) 92 [para_into,26.1.1,10.1.1] g4(e4)=e4. given clause #42: (wt=4) 94 [para_into,26.1.1,8.1.1] g4(e3)=e4. given clause #43: (wt=4) 96 [para_into,26.1.1,6.1.1] g4(e2)=e4. given clause #44: (wt=4) 98 [para_into,26.1.1,4.1.1] g4(e1)=e4. given clause #45: (wt=6) 28 [] f(x,g5(x))=e5. given clause #46: (wt=4) 100 [para_into,28.1.1,18.1.1] g5(e8)=e5. given clause #47: (wt=4) 102 [para_into,28.1.1,16.1.1] g5(e7)=e5. given clause #48: (wt=4) 104 [para_into,28.1.1,14.1.1] g5(e6)=e5. given clause #49: (wt=4) 106 [para_into,28.1.1,12.1.1] g5(e5)=e5. given clause #50: (wt=4) 108 [para_into,28.1.1,10.1.1] g5(e4)=e5. given clause #51: (wt=4) 110 [para_into,28.1.1,8.1.1] g5(e3)=e5. given clause #52: (wt=4) 112 [para_into,28.1.1,6.1.1] g5(e2)=e5. given clause #53: (wt=4) 114 [para_into,28.1.1,4.1.1] g5(e1)=e5. given clause #54: (wt=6) 30 [] f(x,g6(x))=e6. given clause #55: (wt=4) 116 [para_into,30.1.1,18.1.1] g6(e8)=e6. given clause #56: (wt=4) 118 [para_into,30.1.1,16.1.1] g6(e7)=e6. given clause #57: (wt=4) 120 [para_into,30.1.1,14.1.1] g6(e6)=e6. given clause #58: (wt=4) 122 [para_into,30.1.1,12.1.1] g6(e5)=e6. given clause #59: (wt=4) 124 [para_into,30.1.1,10.1.1] g6(e4)=e6. given clause #60: (wt=4) 126 [para_into,30.1.1,8.1.1] g6(e3)=e6. given clause #61: (wt=4) 128 [para_into,30.1.1,6.1.1] g6(e2)=e6. given clause #62: (wt=4) 130 [para_into,30.1.1,4.1.1] g6(e1)=e6. given clause #63: (wt=6) 32 [] f(x,g7(x))=e7. given clause #64: (wt=4) 132 [para_into,32.1.1,18.1.1] g7(e8)=e7. given clause #65: (wt=4) 134 [para_into,32.1.1,16.1.1] g7(e7)=e7. given clause #66: (wt=4) 136 [para_into,32.1.1,14.1.1] g7(e6)=e7. given clause #67: (wt=4) 138 [para_into,32.1.1,12.1.1] g7(e5)=e7. given clause #68: (wt=4) 140 [para_into,32.1.1,10.1.1] g7(e4)=e7. given clause #69: (wt=4) 142 [para_into,32.1.1,8.1.1] g7(e3)=e7. given clause #70: (wt=4) 144 [para_into,32.1.1,6.1.1] g7(e2)=e7. given clause #71: (wt=4) 146 [para_into,32.1.1,4.1.1] g7(e1)=e7. given clause #72: (wt=6) 34 [] f(x,g8(x))=e8. given clause #73: (wt=4) 148 [para_into,34.1.1,18.1.1] g8(e8)=e8. given clause #74: (wt=4) 150 [para_into,34.1.1,16.1.1] g8(e7)=e8. given clause #75: (wt=4) 152 [para_into,34.1.1,14.1.1] g8(e6)=e8. given clause #76: (wt=4) 154 [para_into,34.1.1,12.1.1] g8(e5)=e8. given clause #77: (wt=4) 156 [para_into,34.1.1,10.1.1] g8(e4)=e8. given clause #78: (wt=4) 158 [para_into,34.1.1,8.1.1] g8(e3)=e8. given clause #79: (wt=4) 160 [para_into,34.1.1,6.1.1] g8(e2)=e8. given clause #80: (wt=4) 162 [para_into,34.1.1,4.1.1] g8(e1)=e8. given clause #81: (wt=11) 2 [] f(f(x,y),z)=f(x,f(y,z)). given clause #82: (wt=8) 164 [para_into,2.1.1.1,34.1.1,demod,19,flip.1] f(x,f(g8(x),y))=y. given clause #83: (wt=7) 198 [para_into,164.1.1.2,34.1.1,flip.1] g8(g8(x))=f(x,e8). given clause #84: (wt=7) 200 [para_into,164.1.1.2,32.1.1,flip.1] g7(g8(x))=f(x,e7). given clause #85: (wt=7) 202 [para_into,164.1.1.2,30.1.1,flip.1] g6(g8(x))=f(x,e6). given clause #86: (wt=7) 204 [para_into,164.1.1.2,28.1.1,flip.1] g5(g8(x))=f(x,e5). given clause #87: (wt=7) 206 [para_into,164.1.1.2,26.1.1,flip.1] g4(g8(x))=f(x,e4). given clause #88: (wt=7) 208 [para_into,164.1.1.2,24.1.1,flip.1] g3(g8(x))=f(x,e3). given clause #89: (wt=7) 210 [para_into,164.1.1.2,22.1.1,flip.1] g2(g8(x))=f(x,e2). given clause #90: (wt=7) 212 [para_into,164.1.1.2,20.1.1,flip.1] g1(g8(x))=f(x,e1). given clause #91: (wt=8) 166 [para_into,2.1.1.1,32.1.1,demod,17,flip.1] f(x,f(g7(x),y))=y. given clause #92: (wt=7) 222 [para_into,166.1.1.2,34.1.1,flip.1] g8(g7(x))=f(x,e8). given clause #93: (wt=7) 224 [para_into,166.1.1.2,32.1.1,flip.1] g7(g7(x))=f(x,e7). given clause #94: (wt=7) 226 [para_into,166.1.1.2,30.1.1,flip.1] g6(g7(x))=f(x,e6). given clause #95: (wt=7) 228 [para_into,166.1.1.2,28.1.1,flip.1] g5(g7(x))=f(x,e5). given clause #96: (wt=7) 230 [para_into,166.1.1.2,26.1.1,flip.1] g4(g7(x))=f(x,e4). given clause #97: (wt=7) 232 [para_into,166.1.1.2,24.1.1,flip.1] g3(g7(x))=f(x,e3). given clause #98: (wt=7) 234 [para_into,166.1.1.2,22.1.1,flip.1] g2(g7(x))=f(x,e2). given clause #99: (wt=7) 236 [para_into,166.1.1.2,20.1.1,flip.1] g1(g7(x))=f(x,e1). given clause #100: (wt=8) 168 [para_into,2.1.1.1,30.1.1,demod,15,flip.1] f(x,f(g6(x),y))=y. given clause #101: (wt=7) 248 [para_into,168.1.1.2,34.1.1,flip.1] g8(g6(x))=f(x,e8). given clause #102: (wt=7) 250 [para_into,168.1.1.2,32.1.1,flip.1] g7(g6(x))=f(x,e7). given clause #103: (wt=7) 252 [para_into,168.1.1.2,30.1.1,flip.1] g6(g6(x))=f(x,e6). given clause #104: (wt=7) 254 [para_into,168.1.1.2,28.1.1,flip.1] g5(g6(x))=f(x,e5). given clause #105: (wt=7) 256 [para_into,168.1.1.2,26.1.1,flip.1] g4(g6(x))=f(x,e4). given clause #106: (wt=7) 258 [para_into,168.1.1.2,24.1.1,flip.1] g3(g6(x))=f(x,e3). given clause #107: (wt=7) 260 [para_into,168.1.1.2,22.1.1,flip.1] g2(g6(x))=f(x,e2). given clause #108: (wt=7) 262 [para_into,168.1.1.2,20.1.1,flip.1] g1(g6(x))=f(x,e1). given clause #109: (wt=8) 170 [para_into,2.1.1.1,28.1.1,demod,13,flip.1] f(x,f(g5(x),y))=y. given clause #110: (wt=7) 276 [para_into,170.1.1.2,34.1.1,flip.1] g8(g5(x))=f(x,e8). given clause #111: (wt=7) 278 [para_into,170.1.1.2,32.1.1,flip.1] g7(g5(x))=f(x,e7). given clause #112: (wt=7) 280 [para_into,170.1.1.2,30.1.1,flip.1] g6(g5(x))=f(x,e6). given clause #113: (wt=7) 282 [para_into,170.1.1.2,28.1.1,flip.1] g5(g5(x))=f(x,e5). given clause #114: (wt=7) 284 [para_into,170.1.1.2,26.1.1,flip.1] g4(g5(x))=f(x,e4). given clause #115: (wt=7) 286 [para_into,170.1.1.2,24.1.1,flip.1] g3(g5(x))=f(x,e3). given clause #116: (wt=7) 288 [para_into,170.1.1.2,22.1.1,flip.1] g2(g5(x))=f(x,e2). given clause #117: (wt=7) 290 [para_into,170.1.1.2,20.1.1,flip.1] g1(g5(x))=f(x,e1). given clause #118: (wt=8) 172 [para_into,2.1.1.1,26.1.1,demod,11,flip.1] f(x,f(g4(x),y))=y. given clause #119: (wt=7) 306 [para_into,172.1.1.2,34.1.1,flip.1] g8(g4(x))=f(x,e8). given clause #120: (wt=7) 308 [para_into,172.1.1.2,32.1.1,flip.1] g7(g4(x))=f(x,e7). given clause #121: (wt=7) 310 [para_into,172.1.1.2,30.1.1,flip.1] g6(g4(x))=f(x,e6). given clause #122: (wt=7) 312 [para_into,172.1.1.2,28.1.1,flip.1] g5(g4(x))=f(x,e5). given clause #123: (wt=7) 314 [para_into,172.1.1.2,26.1.1,flip.1] g4(g4(x))=f(x,e4). given clause #124: (wt=7) 316 [para_into,172.1.1.2,24.1.1,flip.1] g3(g4(x))=f(x,e3). given clause #125: (wt=7) 318 [para_into,172.1.1.2,22.1.1,flip.1] g2(g4(x))=f(x,e2). given clause #126: (wt=7) 320 [para_into,172.1.1.2,20.1.1,flip.1] g1(g4(x))=f(x,e1). given clause #127: (wt=8) 174 [para_into,2.1.1.1,24.1.1,demod,9,flip.1] f(x,f(g3(x),y))=y. given clause #128: (wt=7) 338 [para_into,174.1.1.2,34.1.1,flip.1] g8(g3(x))=f(x,e8). given clause #129: (wt=7) 340 [para_into,174.1.1.2,32.1.1,flip.1] g7(g3(x))=f(x,e7). given clause #130: (wt=7) 342 [para_into,174.1.1.2,30.1.1,flip.1] g6(g3(x))=f(x,e6). given clause #131: (wt=7) 344 [para_into,174.1.1.2,28.1.1,flip.1] g5(g3(x))=f(x,e5). given clause #132: (wt=7) 346 [para_into,174.1.1.2,26.1.1,flip.1] g4(g3(x))=f(x,e4). given clause #133: (wt=7) 348 [para_into,174.1.1.2,24.1.1,flip.1] g3(g3(x))=f(x,e3). given clause #134: (wt=7) 350 [para_into,174.1.1.2,22.1.1,flip.1] g2(g3(x))=f(x,e2). given clause #135: (wt=7) 352 [para_into,174.1.1.2,20.1.1,flip.1] g1(g3(x))=f(x,e1). given clause #136: (wt=8) 176 [para_into,2.1.1.1,22.1.1,demod,7,flip.1] f(x,f(g2(x),y))=y. given clause #137: (wt=7) 372 [para_into,176.1.1.2,34.1.1,flip.1] g8(g2(x))=f(x,e8). given clause #138: (wt=7) 374 [para_into,176.1.1.2,32.1.1,flip.1] g7(g2(x))=f(x,e7). given clause #139: (wt=7) 376 [para_into,176.1.1.2,30.1.1,flip.1] g6(g2(x))=f(x,e6). given clause #140: (wt=7) 378 [para_into,176.1.1.2,28.1.1,flip.1] g5(g2(x))=f(x,e5). given clause #141: (wt=7) 380 [para_into,176.1.1.2,26.1.1,flip.1] g4(g2(x))=f(x,e4). given clause #142: (wt=7) 382 [para_into,176.1.1.2,24.1.1,flip.1] g3(g2(x))=f(x,e3). given clause #143: (wt=7) 384 [para_into,176.1.1.2,22.1.1,flip.1] g2(g2(x))=f(x,e2). given clause #144: (wt=7) 386 [para_into,176.1.1.2,20.1.1,flip.1] g1(g2(x))=f(x,e1). given clause #145: (wt=8) 178 [para_into,2.1.1.1,20.1.1,demod,5,flip.1] f(x,f(g1(x),y))=y. given clause #146: (wt=7) 408 [para_into,178.1.1.2,34.1.1,flip.1] g8(g1(x))=f(x,e8). given clause #147: (wt=7) 410 [para_into,178.1.1.2,32.1.1,flip.1] g7(g1(x))=f(x,e7). given clause #148: (wt=7) 412 [para_into,178.1.1.2,30.1.1,flip.1] g6(g1(x))=f(x,e6). given clause #149: (wt=7) 414 [para_into,178.1.1.2,28.1.1,flip.1] g5(g1(x))=f(x,e5). given clause #150: (wt=7) 416 [para_into,178.1.1.2,26.1.1,flip.1] g4(g1(x))=f(x,e4). given clause #151: (wt=7) 418 [para_into,178.1.1.2,24.1.1,flip.1] g3(g1(x))=f(x,e3). given clause #152: (wt=7) 420 [para_into,178.1.1.2,22.1.1,flip.1] g2(g1(x))=f(x,e2). given clause #153: (wt=7) 422 [para_into,178.1.1.2,20.1.1,flip.1] g1(g1(x))=f(x,e1). given clause #154: (wt=8) 216 [para_from,198.1.1,164.1.1.2.1,demod,3,19] f(g8(x),f(x,y))=y. given clause #155: (wt=7) 442 [para_into,216.1.1.2,34.1.1,demod,429,flip.1] g8(x)=f(g1(x),e8). given clause #156: (wt=7) 444 [para_into,216.1.1.2,32.1.1,demod,443,3,19,flip.1] g7(x)=f(g1(x),e7). given clause #157: (wt=7) 446 [para_into,216.1.1.2,30.1.1,demod,443,3,19,flip.1] g6(x)=f(g1(x),e6). given clause #158: (wt=7) 448 [para_into,216.1.1.2,28.1.1,demod,443,3,19,flip.1] g5(x)=f(g1(x),e5). given clause #159: (wt=7) 450 [para_into,216.1.1.2,26.1.1,demod,443,3,19,flip.1] g4(x)=f(g1(x),e4). given clause #160: (wt=7) 452 [para_into,216.1.1.2,24.1.1,demod,443,3,19,flip.1] g3(x)=f(g1(x),e3). given clause #161: (wt=7) 454 [para_into,216.1.1.2,22.1.1,demod,443,3,19,flip.1] g2(x)=f(g1(x),e2). given clause #162: (wt=7) 456 [para_into,216.1.1.2,20.1.1,demod,443,3,19] f(g1(x),e1)=g1(x). given clause #163: (wt=8) 426 [para_from,408.1.1,164.1.1.2.1,demod,3,19] f(g1(x),f(x,y))=y. given clause #164: (wt=9) 472 [back_demod,212,demod,443] g1(f(g1(x),e8))=f(x,e1). given clause #165: (wt=9) 484 [back_demod,236,demod,445] g1(f(g1(x),e7))=f(x,e1). given clause #166: (wt=9) 494 [back_demod,262,demod,447] g1(f(g1(x),e6))=f(x,e1). given clause #167: (wt=9) 502 [back_demod,290,demod,449] g1(f(g1(x),e5))=f(x,e1). given clause #168: (wt=9) 508 [back_demod,320,demod,451] g1(f(g1(x),e4))=f(x,e1). given clause #169: (wt=9) 512 [back_demod,352,demod,453] g1(f(g1(x),e3))=f(x,e1). given clause #170: (wt=9) 514 [back_demod,386,demod,455] g1(f(g1(x),e2))=f(x,e1). given clause #171: (wt=10) 194 [para_into,2.1.1,20.1.1,flip.1] f(x,f(y,g1(f(x,y))))=e1. given clause #172: (wt=7) 534 [para_into,194.1.1,426.1.1] g1(f(g1(x),x))=e1. given clause #173: (wt=8) 516 [para_into,194.1.1.2,18.1.1] f(x,g1(f(x,e8)))=e1. given clause #174: (wt=7) 542 [para_from,516.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e8))=g1(x). given clause #175: (wt=8) 518 [para_into,194.1.1.2,16.1.1] f(x,g1(f(x,e7)))=e1. given clause #176: (wt=7) 546 [para_from,518.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e7))=g1(x). given clause #177: (wt=8) 520 [para_into,194.1.1.2,14.1.1] f(x,g1(f(x,e6)))=e1. given clause #178: (wt=7) 550 [para_from,520.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e6))=g1(x). given clause #179: (wt=8) 522 [para_into,194.1.1.2,12.1.1] f(x,g1(f(x,e5)))=e1. given clause #180: (wt=7) 554 [para_from,522.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e5))=g1(x). given clause #181: (wt=8) 524 [para_into,194.1.1.2,10.1.1] f(x,g1(f(x,e4)))=e1. given clause #182: (wt=7) 558 [para_from,524.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e4))=g1(x). given clause #183: (wt=8) 526 [para_into,194.1.1.2,8.1.1] f(x,g1(f(x,e3)))=e1. given clause #184: (wt=7) 562 [para_from,526.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e3))=g1(x). given clause #185: (wt=8) 528 [para_into,194.1.1.2,6.1.1] f(x,g1(f(x,e2)))=e1. given clause #186: (wt=7) 566 [para_from,528.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e2))=g1(x). given clause #187: (wt=8) 530 [para_into,194.1.1.2,4.1.1] f(x,g1(f(x,e1)))=e1. given clause #188: (wt=7) 570 [para_from,530.1.1,426.1.1.2,demod,457,flip.1] g1(f(x,e1))=g1(x). given clause #189: (wt=9) 538 [para_from,194.1.1,426.1.1.2,demod,457,flip.1] f(x,g1(f(y,x)))=g1(y). given clause #190: (wt=10) 576 [para_from,538.1.1,426.1.1.2,flip.1] g1(f(x,y))=f(g1(y),g1(x)). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ list(usable). 1 [] x=x. 4 [] f(e1,x)=x. 6 [] f(e2,x)=x. 8 [] f(e3,x)=x. 10 [] f(e4,x)=x. 12 [] f(e5,x)=x. 14 [] f(e6,x)=x. 16 [] f(e7,x)=x. 18 [] f(e8,x)=x. 20 [] f(x,g1(x))=e1. 36 [para_into,20.1.1,18.1.1] g1(e8)=e1. 38 [para_into,20.1.1,16.1.1] g1(e7)=e1. 40 [para_into,20.1.1,14.1.1] g1(e6)=e1. 42 [para_into,20.1.1,12.1.1] g1(e5)=e1. 44 [para_into,20.1.1,10.1.1] g1(e4)=e1. 46 [para_into,20.1.1,8.1.1] g1(e3)=e1. 48 [para_into,20.1.1,6.1.1] g1(e2)=e1. 50 [para_into,20.1.1,4.1.1] g1(e1)=e1. 2 [] f(f(x,y),z)=f(x,f(y,z)). 178 [para_into,2.1.1.1,20.1.1,demod,5,flip.1] f(x,f(g1(x),y))=y. 422 [para_into,178.1.1.2,20.1.1,flip.1] g1(g1(x))=f(x,e1). 442 [para_into,216.1.1.2,34.1.1,demod,429,flip.1] g8(x)=f(g1(x),e8). 444 [para_into,216.1.1.2,32.1.1,demod,443,3,19,flip.1] g7(x)=f(g1(x),e7). 446 [para_into,216.1.1.2,30.1.1,demod,443,3,19,flip.1] g6(x)=f(g1(x),e6). 448 [para_into,216.1.1.2,28.1.1,demod,443,3,19,flip.1] g5(x)=f(g1(x),e5). 450 [para_into,216.1.1.2,26.1.1,demod,443,3,19,flip.1] g4(x)=f(g1(x),e4). 452 [para_into,216.1.1.2,24.1.1,demod,443,3,19,flip.1] g3(x)=f(g1(x),e3). 454 [para_into,216.1.1.2,22.1.1,demod,443,3,19,flip.1] g2(x)=f(g1(x),e2). 456 [para_into,216.1.1.2,20.1.1,demod,443,3,19] f(g1(x),e1)=g1(x). 426 [para_from,408.1.1,164.1.1.2.1,demod,3,19] f(g1(x),f(x,y))=y. 576 [para_from,538.1.1,426.1.1.2,flip.1] g1(f(x,y))=f(g1(y),g1(x)). end_of_list. list(sos). end_of_list. list(demodulators). 3 [new_demod,2] f(f(x,y),z)=f(x,f(y,z)). 5 [new_demod,4] f(e1,x)=x. 7 [new_demod,6] f(e2,x)=x. 9 [new_demod,8] f(e3,x)=x. 11 [new_demod,10] f(e4,x)=x. 13 [new_demod,12] f(e5,x)=x. 15 [new_demod,14] f(e6,x)=x. 17 [new_demod,16] f(e7,x)=x. 19 [new_demod,18] f(e8,x)=x. 21 [new_demod,20] f(x,g1(x))=e1. 37 [new_demod,36] g1(e8)=e1. 39 [new_demod,38] g1(e7)=e1. 41 [new_demod,40] g1(e6)=e1. 43 [new_demod,42] g1(e5)=e1. 45 [new_demod,44] g1(e4)=e1. 47 [new_demod,46] g1(e3)=e1. 49 [new_demod,48] g1(e2)=e1. 51 [new_demod,50] g1(e1)=e1. 179 [new_demod,178] f(x,f(g1(x),y))=y. 423 [new_demod,422] g1(g1(x))=f(x,e1). 427 [new_demod,426] f(g1(x),f(x,y))=y. 443 [new_demod,442] g8(x)=f(g1(x),e8). 445 [new_demod,444] g7(x)=f(g1(x),e7). 447 [new_demod,446] g6(x)=f(g1(x),e6). 449 [new_demod,448] g5(x)=f(g1(x),e5). 451 [new_demod,450] g4(x)=f(g1(x),e4). 453 [new_demod,452] g3(x)=f(g1(x),e3). 455 [new_demod,454] g2(x)=f(g1(x),e2). 457 [new_demod,456] f(g1(x),e1)=g1(x). 577 [new_demod,576] g1(f(x,y))=f(g1(y),g1(x)). end_of_list. -------------- statistics ------------- clauses given 190 clauses generated 1515 para_from generated 752 para_into generated 763 demod & eval rewrites 2625 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 1503 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 289 new demodulators 288 empty clauses 0 clauses back demodulated 258 clauses back subsumed 0 usable size 31 sos size 0 demodulators size 30 passive size 0 hot size 0 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8381 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/mv.in.287520100644000076400007640000000145605472201574016426 0ustar mccunemccune% The (infinitely) Many-Valued sentential calculus (MV). % % {MV-1,MV-2,MV-3,MV-5} axiomatizes MV. % % Derive MV-24, MV-25, and MV-29 by condensed detachment. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs, 3). clear(print_kept). set(order_history). assign(fpa_literals, 0). % Disable FPA indexing, because it doesn't help much. assign(max_mem, 1500). % 1.5 Megabytes list(usable). -P(i(x,y)) | -P(x) | P(y). % condensed detachment end_of_list. list(sos). P(i(x,i(y,x))). % MV-1 P(i(i(x,y),i(i(y,z),i(x,z)))). % MV-2 P(i(i(i(x,y),y),i(i(y,x),x))). % MV-3 P(i(i(n(x),n(y)),i(y,x))). % MV-5 end_of_list. list(passive). -P(i(n(n(a)),a)) | $ANS(MV_24). -P(i(i(a,b),i(i(c,a),i(c,b)))) | $ANS(MV_25). -P(i(a,n(n(a)))) | $ANS(MV_29). end_of_list. otter-3.3f/examples/misc/cn.in.287520100644000076400007640000000202705515274107016377 0ustar mccunemccune% The sentential calculus (CN). % % {CN1, CN2, CN3} (Lukasiewicz), along with condensed detachment, % axiomatizes the sentential calculus (the classical propositional calculus). % % Show that CN16, CN18, and CN19 can be derived. set(hyper_res). clear(back_sub). assign(pick_given_ratio, 3). assign(max_proofs, 3). assign(max_weight, 16). clear(print_kept). set(order_history). assign(max_mem, 1500). % 1.5 Megabytes % The symbols -> and - have built-in declarations, and they are used for % clauses and formulas. When redeclaring them for use with terms, we % must be careful that they will still work for clauses and formulas. op(800, yfx, ->). % left association list(usable). -P(x -> y) | -P(x) | P(y). % condensed detachment end_of_list. list(sos). P(x -> y -> (y -> z -> (x -> z))). % CN1 P(-x -> x -> x). % CN2 P(x -> (-x -> y)). % CN3 end_of_list. list(passive). -P(a -> a) | $Ans(CN_16). -P(b -> (a -> b)) | $Ans(CN_18). -P(a -> b -> c -> (b -> c)) | $Ans(CN_19). end_of_list. otter-3.3f/examples/misc/str_bws.out0100664000076400007640000003273710103522155017176 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8411. set(ur_res). clear(print_kept). set(bird_print). assign(fpa_literals,3). list(usable). 1 [] x=x. 2 [] x!=y|y=x. 3 [] x!=y|y!=z|x=z. 4 [] x!=y|x z =y z. 5 [] x!=y|z x =z y. 6 [] B x y z=x (y z). 7 [] W x y=x y y. 8 [] S x y z=x z (y z). end_of_list. formula_list(sos). -(exists y all x (y x =x (y x) & -$Ans(y))). end_of_list. -------> sos clausifies to: list(sos). 9 [] y $f1(y)!=$f1(y) (y $f1(y)) |$Ans(y). end_of_list. list(demodulators). 10 [] B x y z=x (y z). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 9 [] y $f1(y)!=$f1(y) (y $f1(y)) |$Ans(y). given clause #2: (wt=12) 14 [ur,9,2] $Ans(x)|$f1(x) (x $f1(x)) !=x $f1(x). given clause #3: (wt=25) 12 [ur,9,3,7] $Ans(W x)|x $f1(W x) $f1(W x) !=$f1(W x) (W x $f1(W x)). given clause #4: (wt=25) 18 [ur,12,2] $Ans(W x)|$f1(W x) (W x $f1(W x)) !=x $f1(W x) $f1(W x). given clause #5: (wt=28) 13 [ur,9,3,6,demod,10] $Ans(B x y)|x (y $f1(B x y)) !=$f1(B x y) (x (y $f1(B x y))). given clause #6: (wt=28) 16 [ur,12,3,7] $Ans(W W)|$f1(W W) $f1(W W) $f1(W W) !=$f1(W W) (W W $f1(W W)). given clause #7: (wt=28) 22 [ur,13,2] $Ans(B x y)|$f1(B x y) (x (y $f1(B x y))) !=x (y $f1(B x y)). given clause #8: (wt=28) 23 [ur,16,2] $Ans(W W)|$f1(W W) (W W $f1(W W)) !=$f1(W W) $f1(W W) $f1(W W). given clause #9: (wt=35) 17 [ur,12,3,6] $Ans(W (B x))|x ($f1(W (B x)) $f1(W (B x))) !=$f1(W (B x)) (W (B x) $f1(W (B x))). given clause #10: (wt=35) 27 [ur,17,2] $Ans(W (B x))|$f1(W (B x)) (W (B x) $f1(W (B x))) !=x ($f1(W (B x)) $f1(W (B x))). given clause #11: (wt=37) 11 [ur,9,3,8] $Ans(S x y)|x $f1(S x y) (y $f1(S x y)) !=$f1(S x y) (S x y $f1(S x y)). given clause #12: (wt=37) 31 [ur,11,2] $Ans(S x y)|$f1(S x y) (S x y $f1(S x y)) !=x $f1(S x y) (y $f1(S x y)). given clause #13: (wt=42) 15 [ur,12,3,8] $Ans(W (S x))|x $f1(W (S x)) ($f1(W (S x)) $f1(W (S x))) !=$f1(W (S x)) (W (S x) $f1(W (S x))). given clause #14: (wt=42) 35 [ur,15,2] $Ans(W (S x))|$f1(W (S x)) (W (S x) $f1(W (S x))) !=x $f1(W (S x)) ($f1(W (S x)) $f1(W (S x))). given clause #15: (wt=44) 21 [ur,13,3,6,demod,10] $Ans(B (B x y) z)|x (y (z $f1(B (B x y) z))) !=$f1(B (B x y) z) (x (y (z $f1(B (B x y) z)))). given clause #16: (wt=44) 29 [ur,11,3,7] $Ans(S W x)|$f1(S W x) (x $f1(S W x)) (x $f1(S W x)) !=$f1(S W x) (S W x $f1(S W x)). given clause #17: (wt=44) 39 [ur,21,2] $Ans(B (B x y) z)|$f1(B (B x y) z) (x (y (z $f1(B (B x y) z)))) !=x (y (z $f1(B (B x y) z))). given clause #18: (wt=44) 40 [ur,29,2] $Ans(S W x)|$f1(S W x) (S W x $f1(S W x)) !=$f1(S W x) (x $f1(S W x)) (x $f1(S W x)). given clause #19: (wt=47) 20 [ur,13,3,7] $Ans(B (W x) y)|x (y $f1(B (W x) y)) (y $f1(B (W x) y)) !=$f1(B (W x) y) (W x (y $f1(B (W x) y))). given clause #20: (wt=47) 30 [ur,11,3,6] $Ans(S (B x) y)|x ($f1(S (B x) y) (y $f1(S (B x) y))) !=$f1(S (B x) y) (S (B x) y $f1(S (B x) y)). given clause #21: (wt=47) 44 [ur,20,2] $Ans(B (W x) y)|$f1(B (W x) y) (W x (y $f1(B (W x) y))) !=x (y $f1(B (W x) y)) (y $f1(B (W x) y)). given clause #22: (wt=47) 48 [ur,30,2] $Ans(S (B x) y)|$f1(S (B x) y) (S (B x) y $f1(S (B x) y)) !=x ($f1(S (B x) y) (y $f1(S (B x) y))). given clause #23: (wt=54) 33 [ur,15,3,7] $Ans(W (S W))|$f1(W (S W)) ($f1(W (S W)) $f1(W (S W))) ($f1(W (S W)) $f1(W (S W))) !=$f1(W (S W)) (W (S W) $f1(W (S W))). given clause #24: (wt=54) 34 [ur,15,3,6] $Ans(W (S (B x)))|x ($f1(W (S (B x))) ($f1(W (S (B x))) $f1(W (S (B x))))) !=$f1(W (S (B x))) (W (S (B x)) $f1(W (S (B x)))). given clause #25: (wt=54) 49 [ur,33,2] $Ans(W (S W))|$f1(W (S W)) (W (S W) $f1(W (S W))) !=$f1(W (S W)) ($f1(W (S W)) $f1(W (S W))) ($f1(W (S W)) $f1(W (S W))). given clause #26: (wt=54) 53 [ur,34,2] $Ans(W (S (B x)))|$f1(W (S (B x))) (W (S (B x)) $f1(W (S (B x)))) !=x ($f1(W (S (B x))) ($f1(W (S (B x))) $f1(W (S (B x))))). given clause #27: (wt=56) 42 [ur,20,3,7] $Ans(B (W W) x)|x $f1(B (W W) x) (x $f1(B (W W) x)) (x $f1(B (W W) x)) !=$f1(B (W W) x) (W W (x $f1(B (W W) x))). given clause #28: (wt=54) 55 [ur,42,3,6] $Ans(B (W W) B)|$f1(B (W W) B) (B $f1(B (W W) B) (B $f1(B (W W) B))) !=$f1(B (W W) B) (W W (B $f1(B (W W) B))). given clause #29: (wt=36) 57 [ur,55,5] $Ans(B (W W) B)|B $f1(B (W W) B) (B $f1(B (W W) B)) !=W W (B $f1(B (W W) B)). given clause #30: (wt=14) 59 [ur,57,4] $Ans(B (W W) B)|B $f1(B (W W) B) !=W W. given clause #31: (wt=14) 61 [ur,59,2] $Ans(B (W W) B)|W W !=B $f1(B (W W) B). given clause #32: (wt=36) 60 [ur,57,2] $Ans(B (W W) B)|W W (B $f1(B (W W) B)) !=B $f1(B (W W) B) (B $f1(B (W W) B)). given clause #33: (wt=29) 62 [ur,60,3,8] $Ans(B (W W) B)|W W (B $f1(B (W W) B)) !=S B B $f1(B (W W) B). given clause #34: (wt=29) 65 [ur,62,2] $Ans(B (W W) B)|S B B $f1(B (W W) B) !=W W (B $f1(B (W W) B)). given clause #35: (wt=38) 64 [ur,62,3,7] $Ans(B (W W) B)|W (B $f1(B (W W) B)) (B $f1(B (W W) B)) !=S B B $f1(B (W W) B). given clause #36: (wt=38) 67 [ur,64,2] $Ans(B (W W) B)|S B B $f1(B (W W) B) !=W (B $f1(B (W W) B)) (B $f1(B (W W) B)). given clause #37: (wt=45) 63 [ur,60,3,7] $Ans(B (W W) B)|W (B $f1(B (W W) B)) (B $f1(B (W W) B)) !=B $f1(B (W W) B) (B $f1(B (W W) B)). given clause #38: (wt=23) 69 [ur,63,4] $Ans(B (W W) B)|W (B $f1(B (W W) B)) !=B $f1(B (W W) B). given clause #39: (wt=23) 71 [ur,69,2] $Ans(B (W W) B)|B $f1(B (W W) B) !=W (B $f1(B (W W) B)). given clause #40: (wt=45) 66 [ur,64,3,7,demod,10] $Ans(B (W W) B)|$f1(B (W W) B) (B $f1(B (W W) B) (B $f1(B (W W) B))) !=S B B $f1(B (W W) B). given clause #41: (wt=45) 68 [ur,67,3,8] $Ans(B (W W) B)|B $f1(B (W W) B) (B $f1(B (W W) B)) !=W (B $f1(B (W W) B)) (B $f1(B (W W) B)). given clause #42: (wt=45) 72 [ur,66,2] $Ans(B (W W) B)|S B B $f1(B (W W) B) !=$f1(B (W W) B) (B $f1(B (W W) B) (B $f1(B (W W) B))). given clause #43: (wt=52) 70 [ur,63,3,7,demod,10] $Ans(B (W W) B)|$f1(B (W W) B) (B $f1(B (W W) B) (B $f1(B (W W) B))) !=B $f1(B (W W) B) (B $f1(B (W W) B)). given clause #44: (wt=52) 73 [ur,72,3,8] $Ans(B (W W) B)|B $f1(B (W W) B) (B $f1(B (W W) B)) !=$f1(B (W W) B) (B $f1(B (W W) B) (B $f1(B (W W) B))). given clause #45: (wt=54) 58 [ur,55,2] $Ans(B (W W) B)|$f1(B (W W) B) (W W (B $f1(B (W W) B))) !=$f1(B (W W) B) (B $f1(B (W W) B) (B $f1(B (W W) B))). given clause #46: (wt=56) 56 [ur,42,2] $Ans(B (W W) x)|$f1(B (W W) x) (W W (x $f1(B (W W) x))) !=x $f1(B (W W) x) (x $f1(B (W W) x)) (x $f1(B (W W) x)). given clause #47: (wt=57) 26 [ur,17,3,6] $Ans(W (B (B x y)))|x (y ($f1(W (B (B x y))) $f1(W (B (B x y))))) !=$f1(W (B (B x y))) (W (B (B x y)) $f1(W (B (B x y)))). given clause #48: (wt=57) 43 [ur,20,3,6] $Ans(B (W (B x)) y)|x (y $f1(B (W (B x)) y) (y $f1(B (W (B x)) y))) !=$f1(B (W (B x)) y) (W (B x) (y $f1(B (W (B x)) y))). given clause #49: (wt=57) 77 [ur,26,2] $Ans(W (B (B x y)))|$f1(W (B (B x y))) (W (B (B x y)) $f1(W (B (B x y)))) !=x (y ($f1(W (B (B x y))) $f1(W (B (B x y))))). given clause #50: (wt=57) 81 [ur,43,2] $Ans(B (W (B x)) y)|$f1(B (W (B x)) y) (W (B x) (y $f1(B (W (B x)) y))) !=x (y $f1(B (W (B x)) y) (y $f1(B (W (B x)) y))). given clause #51: (wt=58) 28 [ur,11,3,8] $Ans(S (S x) y)|x (y $f1(S (S x) y)) ($f1(S (S x) y) (y $f1(S (S x) y))) !=$f1(S (S x) y) (S (S x) y $f1(S (S x) y)). given clause #52: (wt=58) 85 [ur,28,2] $Ans(S (S x) y)|$f1(S (S x) y) (S (S x) y $f1(S (S x) y)) !=x (y $f1(S (S x) y)) ($f1(S (S x) y) (y $f1(S (S x) y))). given clause #53: (wt=59) 19 [ur,13,3,8] $Ans(B (S x y) z)|x (z $f1(B (S x y) z)) (y (z $f1(B (S x y) z))) !=$f1(B (S x y) z) (S x y (z $f1(B (S x y) z))). given clause #54: (wt=59) 89 [ur,19,2] $Ans(B (S x y) z)|$f1(B (S x y) z) (S x y (z $f1(B (S x y) z))) !=x (z $f1(B (S x y) z)) (y (z $f1(B (S x y) z))). given clause #55: (wt=60) 38 [ur,21,3,6,demod,10] $Ans(B (B (B x y) z) u)|x (y (z (u $f1(B (B (B x y) z) u)))) !=$f1(B (B (B x y) z) u) (x (y (z (u $f1(B (B (B x y) z) u))))). given clause #56: (wt=60) 93 [ur,38,2] $Ans(B (B (B x y) z) u)|$f1(B (B (B x y) z) u) (x (y (z (u $f1(B (B (B x y) z) u))))) !=x (y (z (u $f1(B (B (B x y) z) u)))). given clause #57: (wt=63) 25 [ur,17,3,7] $Ans(W (B (W x)))|x ($f1(W (B (W x))) $f1(W (B (W x)))) ($f1(W (B (W x))) $f1(W (B (W x)))) !=$f1(W (B (W x))) (W (B (W x)) $f1(W (B (W x)))). given clause #58: (wt=63) 97 [ur,25,2] $Ans(W (B (W x)))|$f1(W (B (W x))) (W (B (W x)) $f1(W (B (W x)))) !=x ($f1(W (B (W x))) $f1(W (B (W x)))) ($f1(W (B (W x))) $f1(W (B (W x)))). given clause #59: (wt=65) 54 [ur,42,3,8] $Ans(B (W W) S)|$f1(B (W W) S) (S $f1(B (W W) S)) (S $f1(B (W W) S) (S $f1(B (W W) S))) !=$f1(B (W W) S) (W W (S $f1(B (W W) S))). given clause #60: (wt=65) 98 [ur,54,2] $Ans(B (W W) S)|$f1(B (W W) S) (W W (S $f1(B (W W) S))) !=$f1(B (W W) S) (S $f1(B (W W) S)) (S $f1(B (W W) S) (S $f1(B (W W) S))). given clause #61: (wt=69) 37 [ur,21,3,7] $Ans(B (B (W x) y) z)|x (y (z $f1(B (B (W x) y) z))) (y (z $f1(B (B (W x) y) z))) !=$f1(B (B (W x) y) z) (W x (y (z $f1(B (B (W x) y) z)))). given clause #62: (wt=69) 47 [ur,30,3,6] $Ans(S (B (B x y)) z)|x (y ($f1(S (B (B x y)) z) (z $f1(S (B (B x y)) z)))) !=$f1(S (B (B x y)) z) (S (B (B x y)) z $f1(S (B (B x y)) z)). given clause #63: (wt=69) 88 [ur,19,3,6] $Ans(B (S (B x) y) z)|x (z $f1(B (S (B x) y) z) (y (z $f1(B (S (B x) y) z)))) !=$f1(B (S (B x) y) z) (S (B x) y (z $f1(B (S (B x) y) z))). given clause #64: (wt=69) 102 [ur,37,2] $Ans(B (B (W x) y) z)|$f1(B (B (W x) y) z) (W x (y (z $f1(B (B (W x) y) z)))) !=x (y (z $f1(B (B (W x) y) z))) (y (z $f1(B (B (W x) y) z))). given clause #65: (wt=69) 106 [ur,47,2] $Ans(S (B (B x y)) z)|$f1(S (B (B x y)) z) (S (B (B x y)) z $f1(S (B (B x y)) z)) !=x (y ($f1(S (B (B x y)) z) (z $f1(S (B (B x y)) z)))). given clause #66: (wt=69) 110 [ur,88,2] $Ans(B (S (B x) y) z)|$f1(B (S (B x) y) z) (S (B x) y (z $f1(B (S (B x) y) z))) !=x (z $f1(B (S (B x) y) z) (y (z $f1(B (S (B x) y) z)))). given clause #67: (wt=70) 41 [ur,20,3,8] $Ans(B (W (S x)) y)|x (y $f1(B (W (S x)) y)) (y $f1(B (W (S x)) y) (y $f1(B (W (S x)) y))) !=$f1(B (W (S x)) y) (W (S x) (y $f1(B (W (S x)) y))). given clause #68: (wt=70) 84 [ur,28,3,6] $Ans(S (S (B x)) y)|x (y $f1(S (S (B x)) y) ($f1(S (S (B x)) y) (y $f1(S (S (B x)) y)))) !=$f1(S (S (B x)) y) (S (S (B x)) y $f1(S (S (B x)) y)). given clause #69: (wt=70) 114 [ur,41,2] $Ans(B (W (S x)) y)|$f1(B (W (S x)) y) (W (S x) (y $f1(B (W (S x)) y))) !=x (y $f1(B (W (S x)) y)) (y $f1(B (W (S x)) y) (y $f1(B (W (S x)) y))). given clause #70: (wt=70) 118 [ur,84,2] $Ans(S (S (B x)) y)|$f1(S (S (B x)) y) (S (S (B x)) y $f1(S (S (B x)) y)) !=x (y $f1(S (S (B x)) y) ($f1(S (S (B x)) y) (y $f1(S (S (B x)) y)))). given clause #71: (wt=72) 32 [ur,15,3,8] $Ans(W (S (S x)))|x ($f1(W (S (S x))) $f1(W (S (S x)))) ($f1(W (S (S x))) ($f1(W (S (S x))) $f1(W (S (S x))))) !=$f1(W (S (S x))) (W (S (S x)) $f1(W (S (S x)))). given clause #72: (wt=72) 87 [ur,19,3,7] $Ans(B (S W x) y)|y $f1(B (S W x) y) (x (y $f1(B (S W x) y))) (x (y $f1(B (S W x) y))) !=$f1(B (S W x) y) (S W x (y $f1(B (S W x) y))). given clause #73: (wt=70) 124 [ur,87,3,6] $Ans(B (S W x) B)|$f1(B (S W x) B) (x (B $f1(B (S W x) B)) (x (B $f1(B (S W x) B)))) !=$f1(B (S W x) B) (S W x (B $f1(B (S W x) B))). given clause #74: (wt=48) 126 [ur,124,5] $Ans(B (S W x) B)|x (B $f1(B (S W x) B)) (x (B $f1(B (S W x) B))) !=S W x (B $f1(B (S W x) B)). -------- PROOF -------- 132 [binary,131.1,8.1] $Ans(B (S W W) B). ----> UNIT CONFLICT at 0.02 sec ----> 132 [binary,131.1,8.1] $Ans(B (S W W) B). Length of proof is 6. Level of proof is 6. ---------------- PROOF ---------------- 2 [] x!=y|y=x. 3 [] x!=y|y!=z|x=z. 5 [] x!=y|z x =z y. 6 [] B x y z=x (y z). 7 [] W x y=x y y. 8 [] S x y z=x z (y z). 9 [] y $f1(y)!=$f1(y) (y $f1(y)) |$Ans(y). 10 [] B x y z=x (y z). 13 [ur,9,3,6,demod,10] $Ans(B x y)|x (y $f1(B x y)) !=$f1(B x y) (x (y $f1(B x y))). 19 [ur,13,3,8] $Ans(B (S x y) z)|x (z $f1(B (S x y) z)) (y (z $f1(B (S x y) z))) !=$f1(B (S x y) z) (S x y (z $f1(B (S x y) z))). 87 [ur,19,3,7] $Ans(B (S W x) y)|y $f1(B (S W x) y) (x (y $f1(B (S W x) y))) (x (y $f1(B (S W x) y))) !=$f1(B (S W x) y) (S W x (y $f1(B (S W x) y))). 124 [ur,87,3,6] $Ans(B (S W x) B)|$f1(B (S W x) B) (x (B $f1(B (S W x) B)) (x (B $f1(B (S W x) B)))) !=$f1(B (S W x) B) (S W x (B $f1(B (S W x) B))). 126 [ur,124,5] $Ans(B (S W x) B)|x (B $f1(B (S W x) B)) (x (B $f1(B (S W x) B))) !=S W x (B $f1(B (S W x) B)). 131 [ur,126,2] $Ans(B (S W x) B)|S W x (B $f1(B (S W x) B)) !=x (B $f1(B (S W x) B)) (x (B $f1(B (S W x) B))). 132 [binary,131.1,8.1] $Ans(B (S W W) B). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 74 clauses generated 393 ur_res generated 393 demod & eval rewrites 72 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 272 (subsumed by sos) 2 unit deletions 0 factor simplifications 0 clauses kept 121 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 0 usable size 82 sos size 48 demodulators size 1 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8411 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/sax1.out0100664000076400007640000004666110103522155016370 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8391. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). assign(max_proofs,3). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(stats_level,1). list(usable). 0 [] x=x. end_of_list. list(passive). 1 [] f(a,g(a))!=f(b,g(b))|$Ans(R_inverse). 2 [] f(a,f(b,g(b)))!=a|$Ans(R_ident). 3 [] f(f(a,b),c)!=f(a,f(b,c))|$Ans(assoc). end_of_list. list(sos). 0 [] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 4 [] x=x. Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] x=x. ------------> process sos: ** KEPT (pick-wt=18): 5 [] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. ---> New Demodulator: 6 [new_demod,5] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. >>>> Starting back demodulation with 6. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=18) 5 [] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. given clause #2: (wt=23) 9 [para_into,5.1.1.2.1.2.1,5.1.1] f(x,g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,x))))=u. given clause #3: (wt=28) 16 [para_into,9.1.1.2.1.1.1,5.1.1] f(x,g(f(f(y,f(z,g(z))),f(u,x))))=f(f(f(v,g(v)),g(f(y,u))),f(w,g(w))). given clause #4: (wt=24) 33 [para_into,16.1.1,9.1.1,flip.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(f(z,u))),z))),f(v,g(v)))=u. given clause #5: (wt=15) 56 [para_into,33.1.1.1.2.1,33.1.1] f(f(f(x,g(x)),g(g(y))),f(z,g(z)))=y. given clause #6: (wt=19) 71 [para_from,33.1.1,5.1.1.2.1.2] f(f(x,g(x)),g(f(y,z)))=f(f(u,g(u)),g(f(y,z))). 93 back subsumes 71. given clause #7: (wt=13) 103 [back_demod,62,demod,97] f(x,f(y,g(y)))=f(x,f(z,g(z))). -------- PROOF -------- 110 [binary,109.1,1.1] $Ans(R_inverse). ----> UNIT CONFLICT at 0.01 sec ----> 110 [binary,109.1,1.1] $Ans(R_inverse). Length of proof is 9. Level of proof is 7. ---------------- PROOF ---------------- 1 [] f(a,g(a))!=f(b,g(b))|$Ans(R_inverse). 5 [] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. 9 [para_into,5.1.1.2.1.2.1,5.1.1] f(x,g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,x))))=u. 16 [para_into,9.1.1.2.1.1.1,5.1.1] f(x,g(f(f(y,f(z,g(z))),f(u,x))))=f(f(f(v,g(v)),g(f(y,u))),f(w,g(w))). 34,33 [para_into,16.1.1,9.1.1,flip.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(f(z,u))),z))),f(v,g(v)))=u. 54 [para_into,33.1.1.1.2.1.1,16.1.1] f(f(f(x,g(x)),g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,f(w,g(w)))))),f(v6,g(v6)))=f(u,f(v7,g(v7))). 62 [copy,54,flip.1] f(x,f(y,g(y)))=f(f(f(z,g(z)),g(f(f(f(f(u,g(u)),g(f(v,x))),f(w,g(w))),f(v,f(v6,g(v6)))))),f(v7,g(v7))). 71 [para_from,33.1.1,5.1.1.2.1.2] f(f(x,g(x)),g(f(y,z)))=f(f(u,g(u)),g(f(y,z))). 97,96 [para_into,71.1.1,9.1.1,flip.1] f(f(x,g(x)),g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,f(w,g(w))))))=u. 103 [back_demod,62,demod,97] f(x,f(y,g(y)))=f(x,f(z,g(z))). 109 [para_from,103.1.1,33.1.1.1.2.1.1.2.1,demod,34] f(x,g(x))=f(y,g(y)). 110 [binary,109.1,1.1] $Ans(R_inverse). ------------ end of proof ------------- given clause #8: (wt=9) 109 [para_from,103.1.1,33.1.1.1.2.1.1.2.1,demod,34] f(x,g(x))=f(y,g(y)). given clause #9: (wt=14) 124 [para_from,109.1.1,5.1.1.2.1.2.1] f(x,g(f(g(y),f(f(z,g(z)),x))))=y. given clause #10: (wt=15) 93 [para_into,71.1.1.2.1,56.1.1,demod,57] f(f(x,g(x)),g(y))=f(f(z,g(z)),g(y)). 156 back subsumes 91. 158 back subsumes 100. given clause #11: (wt=15) 157 [para_into,93.1.1,109.1.1] f(x,g(x))=f(f(y,g(y)),g(f(z,g(z)))). given clause #12: (wt=15) 159 [copy,157,flip.1] f(f(x,g(x)),g(f(y,g(y))))=f(z,g(z)). given clause #13: (wt=11) 203 [para_from,159.1.1,33.1.1.1.2.1.1.2.1,demod,121] g(f(x,g(x)))=g(f(y,g(y))). given clause #14: (wt=16) 130 [para_into,124.1.1.2.1.2,109.1.1] f(g(f(x,g(x))),g(f(g(y),f(z,g(z)))))=y. given clause #15: (wt=16) 190 [para_from,157.1.1,9.1.1.2.1.1.1.2.1,demod,117] f(x,g(f(g(g(f(y,g(y)))),f(z,x))))=g(z). given clause #16: (wt=17) 206 [para_into,203.1.1.1.2,203.1.1] g(f(f(x,g(x)),g(f(y,g(y)))))=g(f(z,g(z))). given clause #17: (wt=17) 207 [copy,206,flip.1] g(f(x,g(x)))=g(f(f(y,g(y)),g(f(z,g(z))))). given clause #18: (wt=17) 241 [para_into,190.1.1,5.1.1,flip.1] g(f(f(x,g(x)),g(f(y,g(g(f(z,g(z))))))))=y. 391 back subsumes 93. given clause #19: (wt=13) 391 [para_from,241.1.1,93.1.1.2,demod,242] f(f(x,g(x)),y)=f(f(z,g(z)),y). 430 back subsumes 377. 431 back subsumes 320. 432 back subsumes 278. 433 back subsumes 156. 435 back subsumes 418. 436 back subsumes 347. 437 back subsumes 307. 438 back subsumes 158. 439 back subsumes 164. 440 back subsumes 179. given clause #20: (wt=18) 229 [para_into,190.1.1.2.1.2,109.1.1] f(g(x),g(f(g(g(f(y,g(y)))),f(z,g(z)))))=g(x). given clause #21: (wt=16) 441 [para_into,229.1.1.1,241.1.1,demod,242] f(x,g(f(g(g(f(y,g(y)))),f(z,g(z)))))=x. given clause #22: (wt=12) 505 [para_from,441.1.1,33.1.1.1.2.1.1,demod,117] g(g(g(f(x,g(x)))))=f(y,g(y)). given clause #23: (wt=12) 537 [copy,505,flip.1] f(x,g(x))=g(g(g(f(y,g(y))))). given clause #24: (wt=14) 568 [para_from,537.1.1,241.1.1.1] g(g(g(g(f(x,g(x))))))=g(f(y,g(y))). given clause #25: (wt=14) 625 [copy,568,flip.1] g(f(x,g(x)))=g(g(g(g(f(y,g(y)))))). given clause #26: (wt=15) 562 [para_into,537.1.1,537.1.1] g(g(g(f(x,g(x)))))=g(g(g(f(y,g(y))))). given clause #27: (wt=13) 812 [para_from,562.1.1,130.1.1.2.1.1,demod,131] g(g(f(x,g(x))))=g(g(f(y,g(y)))). given clause #28: (wt=15) 577 [para_from,537.1.1,505.1.1.1.1.1] g(g(g(g(g(g(f(x,g(x))))))))=f(y,g(y)). given clause #29: (wt=15) 630 [copy,577,flip.1] f(x,g(x))=g(g(g(g(g(g(f(y,g(y)))))))). given clause #30: (wt=16) 478 [para_into,441.1.1,109.1.1] f(x,g(x))=f(g(g(f(y,g(y)))),f(z,g(z))). given clause #31: (wt=16) 480 [copy,478,flip.1] f(g(g(f(x,g(x)))),f(y,g(y)))=f(z,g(z)). -------- PROOF -------- 1296 [binary,1294.1,2.1] $Ans(R_ident). ----> UNIT CONFLICT at 0.12 sec ----> 1296 [binary,1294.1,2.1] $Ans(R_ident). Length of proof is 33. Level of proof is 17. ---------------- PROOF ---------------- 2 [] f(a,f(b,g(b)))!=a|$Ans(R_ident). 5 [] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. 9 [para_into,5.1.1.2.1.2.1,5.1.1] f(x,g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,x))))=u. 16 [para_into,9.1.1.2.1.1.1,5.1.1] f(x,g(f(f(y,f(z,g(z))),f(u,x))))=f(f(f(v,g(v)),g(f(y,u))),f(w,g(w))). 34,33 [para_into,16.1.1,9.1.1,flip.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(f(z,u))),z))),f(v,g(v)))=u. 54 [para_into,33.1.1.1.2.1.1,16.1.1] f(f(f(x,g(x)),g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,f(w,g(w)))))),f(v6,g(v6)))=f(u,f(v7,g(v7))). 57,56 [para_into,33.1.1.1.2.1,33.1.1] f(f(f(x,g(x)),g(g(y))),f(z,g(z)))=y. 62 [copy,54,flip.1] f(x,f(y,g(y)))=f(f(f(z,g(z)),g(f(f(f(f(u,g(u)),g(f(v,x))),f(w,g(w))),f(v,f(v6,g(v6)))))),f(v7,g(v7))). 71 [para_from,33.1.1,5.1.1.2.1.2] f(f(x,g(x)),g(f(y,z)))=f(f(u,g(u)),g(f(y,z))). 93 [para_into,71.1.1.2.1,56.1.1,demod,57] f(f(x,g(x)),g(y))=f(f(z,g(z)),g(y)). 97,96 [para_into,71.1.1,9.1.1,flip.1] f(f(x,g(x)),g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,f(w,g(w))))))=u. 103 [back_demod,62,demod,97] f(x,f(y,g(y)))=f(x,f(z,g(z))). 109 [para_from,103.1.1,33.1.1.1.2.1.1.2.1,demod,34] f(x,g(x))=f(y,g(y)). 117,116 [para_from,109.1.1,33.1.1.1.2.1.1] f(f(f(x,g(x)),g(f(f(y,g(y)),z))),f(u,g(u)))=g(z). 124 [para_from,109.1.1,5.1.1.2.1.2.1] f(x,g(f(g(y),f(f(z,g(z)),x))))=y. 130 [para_into,124.1.1.2.1.2,109.1.1] f(g(f(x,g(x))),g(f(g(y),f(z,g(z)))))=y. 157 [para_into,93.1.1,109.1.1] f(x,g(x))=f(f(y,g(y)),g(f(z,g(z)))). 190 [para_from,157.1.1,9.1.1.2.1.1.1.2.1,demod,117] f(x,g(f(g(g(f(y,g(y)))),f(z,x))))=g(z). 213 [para_from,130.1.1,33.1.1.1.2.1.1.2.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(z)),g(f(u,g(u)))))),f(v,g(v)))=g(f(g(z),f(w,g(w)))). 217 [copy,213,flip.1] g(f(g(x),f(y,g(y))))=f(f(f(z,g(z)),g(f(f(f(u,g(u)),g(x)),g(f(v,g(v)))))),f(w,g(w))). 229 [para_into,190.1.1.2.1.2,109.1.1] f(g(x),g(f(g(g(f(y,g(y)))),f(z,g(z)))))=g(x). 242,241 [para_into,190.1.1,5.1.1,flip.1] g(f(f(x,g(x)),g(f(y,g(g(f(z,g(z))))))))=y. 441 [para_into,229.1.1.1,241.1.1,demod,242] f(x,g(f(g(g(f(y,g(y)))),f(z,g(z)))))=x. 478 [para_into,441.1.1,109.1.1] f(x,g(x))=f(g(g(f(y,g(y)))),f(z,g(z))). 480 [copy,478,flip.1] f(g(g(f(x,g(x)))),f(y,g(y)))=f(z,g(z)). 505 [para_from,441.1.1,33.1.1.1.2.1.1,demod,117] g(g(g(f(x,g(x)))))=f(y,g(y)). 537 [copy,505,flip.1] f(x,g(x))=g(g(g(f(y,g(y))))). 577 [para_from,537.1.1,505.1.1.1.1.1] g(g(g(g(g(g(f(x,g(x))))))))=f(y,g(y)). 630 [copy,577,flip.1] f(x,g(x))=g(g(g(g(g(g(f(y,g(y)))))))). 967 [para_from,577.1.1,130.1.1.1.1.2] f(g(f(g(g(g(g(g(f(x,g(x))))))),f(y,g(y)))),g(f(g(z),f(u,g(u)))))=z. 1059 [para_from,630.1.1,56.1.1.1.1] f(f(g(g(g(g(g(g(f(x,g(x)))))))),g(g(y))),f(z,g(z)))=y. 1189,1188 [para_from,480.1.1,441.1.1.2.1] f(x,g(f(y,g(y))))=x. 1197,1196 [back_demod,217,demod,1189,117] g(f(g(x),f(y,g(y))))=g(g(x)). 1227,1226 [back_demod,967,demod,1197,1197] f(g(g(g(g(g(g(f(x,g(x)))))))),g(g(y)))=y. 1294 [back_demod,1059,demod,1227] f(x,f(y,g(y)))=x. 1296 [binary,1294.1,2.1] $Ans(R_ident). ------------ end of proof ------------- 1439 back subsumes 1429. 1440 back subsumes 1432. given clause #32: (wt=8) 1294 [back_demod,1059,demod,1227] f(x,f(y,g(y)))=x. given clause #33: (wt=8) 1393 [back_demod,529,demod,1295,1339,1331] f(f(x,y),g(y))=x. given clause #34: (wt=5) 1528 [back_demod,1463,demod,1501] g(g(x))=x. given clause #35: (wt=8) 1395 [back_demod,513,demod,1295,1295,1339,1331] f(g(x),f(x,y))=y. given clause #36: (wt=8) 1447 [back_demod,48,demod,1295,1337,1295,1295,1295,1444,flip.1] f(x,f(g(x),y))=y. given clause #37: (wt=8) 1504 [para_into,1393.1.1.1,109.1.1,demod,1499] f(f(x,g(x)),y)=y. given clause #38: (wt=8) 1516 [back_demod,1412,demod,1505,1499] f(f(g(x),x),y)=y. given clause #39: (wt=8) 1532 [back_demod,1403,demod,1505] f(x,f(g(y),y))=x. given clause #40: (wt=8) 1550 [para_from,1528.1.1,1393.1.1.2] f(f(x,g(y)),y)=x. given clause #41: (wt=9) 1439 [back_demod,89,demod,1295,1313,1339,1293] f(x,g(x))=f(g(y),y). given clause #42: (wt=9) 1440 [back_demod,82,demod,1295,1313,1339,1293] f(g(x),x)=f(y,g(y)). given clause #43: (wt=9) 1552 [para_into,1532.1.1,1516.1.1] f(g(x),x)=f(g(y),y). given clause #44: (wt=10) 1530 [back_demod,1345,demod,1529,1527] g(f(x,y))=f(g(y),g(x)). given clause #45: (wt=13) 1546 [back_demod,1437,demod,1531,1531,1531,1529,1529,1529] f(f(g(x),g(y)),f(f(y,x),z))=z. given clause #46: (wt=13) 1554 [para_from,1530.1.1,1447.1.1.2.1] f(f(x,y),f(f(g(y),g(x)),z))=z. given clause #47: (wt=13) 1557 [para_from,1530.1.1,1504.1.1.1.2] f(f(f(x,y),f(g(y),g(x))),z)=z. given clause #48: (wt=13) 1559 [para_from,1530.1.1,1550.1.1.1.2] f(f(x,f(g(y),g(z))),f(z,y))=x. given clause #49: (wt=13) 1561 [para_from,1530.1.1,1393.1.1.2] f(f(x,f(y,z)),f(g(z),g(y)))=x. given clause #50: (wt=13) 1563 [para_from,1530.1.1,1294.1.1.2.2] f(x,f(f(y,z),f(g(z),g(y))))=x. given clause #51: (wt=13) 1569 [para_into,1546.1.1.1.1,1528.1.1] f(f(x,g(y)),f(f(y,g(x)),z))=z. given clause #52: (wt=13) 1573 [para_into,1546.1.1.1.2,1528.1.1] f(f(g(x),y),f(f(g(y),x),z))=z. given clause #53: (wt=13) 1581 [para_into,1557.1.1.1.2.1,1528.1.1] f(f(f(x,g(y)),f(y,g(x))),z)=z. given clause #54: (wt=13) 1585 [para_into,1557.1.1.1.2.2,1528.1.1] f(f(f(g(x),y),f(g(y),x)),z)=z. given clause #55: (wt=13) 1589 [para_into,1559.1.1.1.2.1,1528.1.1] f(f(x,f(y,g(z))),f(z,g(y)))=x. given clause #56: (wt=13) 1593 [para_into,1559.1.1.1.2.2,1528.1.1] f(f(x,f(g(y),z)),f(g(z),y))=x. given clause #57: (wt=13) 1614 [para_into,1563.1.1.2.2.1,1528.1.1] f(x,f(f(y,g(z)),f(z,g(y))))=x. given clause #58: (wt=13) 1618 [para_into,1563.1.1.2.2.2,1528.1.1] f(x,f(f(g(y),z),f(g(z),y)))=x. given clause #59: (wt=14) 1542 [back_demod,1443,demod,1531,1531,1531,1529,1529] f(f(g(x),g(y)),f(y,z))=f(g(x),z). given clause #60: (wt=12) 1670 [para_into,1542.1.1.1.1,1528.1.1,demod,1529] f(f(x,g(y)),f(y,z))=f(x,z). -------- PROOF -------- 1718 [binary,1716.1,3.1] $Ans(assoc). ----> UNIT CONFLICT at 0.20 sec ----> 1718 [binary,1716.1,3.1] $Ans(assoc). Length of proof is 76. Level of proof is 27. ---------------- PROOF ---------------- 3 [] f(f(a,b),c)!=f(a,f(b,c))|$Ans(assoc). 5 [] f(x,g(f(y,f(f(f(z,g(z)),g(f(u,y))),x))))=u. 9 [para_into,5.1.1.2.1.2.1,5.1.1] f(x,g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,x))))=u. 16 [para_into,9.1.1.2.1.1.1,5.1.1] f(x,g(f(f(y,f(z,g(z))),f(u,x))))=f(f(f(v,g(v)),g(f(y,u))),f(w,g(w))). 34,33 [para_into,16.1.1,9.1.1,flip.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(f(z,u))),z))),f(v,g(v)))=u. 52 [para_into,33.1.1.1.2.1.1.2.1,9.1.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(z)),u))),f(v,g(v)))=g(f(f(f(f(w,g(w)),g(f(v6,z))),f(v7,g(v7))),f(v6,u))). 54 [para_into,33.1.1.1.2.1.1,16.1.1] f(f(f(x,g(x)),g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,f(w,g(w)))))),f(v6,g(v6)))=f(u,f(v7,g(v7))). 57,56 [para_into,33.1.1.1.2.1,33.1.1] f(f(f(x,g(x)),g(g(y))),f(z,g(z)))=y. 60 [copy,52,flip.1] g(f(f(f(f(x,g(x)),g(f(y,z))),f(u,g(u))),f(y,v)))=f(f(f(w,g(w)),g(f(f(f(v6,g(v6)),g(z)),v))),f(v7,g(v7))). 62 [copy,54,flip.1] f(x,f(y,g(y)))=f(f(f(z,g(z)),g(f(f(f(f(u,g(u)),g(f(v,x))),f(w,g(w))),f(v,f(v6,g(v6)))))),f(v7,g(v7))). 71 [para_from,33.1.1,5.1.1.2.1.2] f(f(x,g(x)),g(f(y,z)))=f(f(u,g(u)),g(f(y,z))). 93 [para_into,71.1.1.2.1,56.1.1,demod,57] f(f(x,g(x)),g(y))=f(f(z,g(z)),g(y)). 97,96 [para_into,71.1.1,9.1.1,flip.1] f(f(x,g(x)),g(f(f(f(f(y,g(y)),g(f(z,u))),f(v,g(v))),f(z,f(w,g(w))))))=u. 103 [back_demod,62,demod,97] f(x,f(y,g(y)))=f(x,f(z,g(z))). 109 [para_from,103.1.1,33.1.1.1.2.1.1.2.1,demod,34] f(x,g(x))=f(y,g(y)). 117,116 [para_from,109.1.1,33.1.1.1.2.1.1] f(f(f(x,g(x)),g(f(f(y,g(y)),z))),f(u,g(u)))=g(z). 121,120 [para_from,109.1.1,33.1.1.1.2.1.1.2.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(f(z,g(z)))),u))),f(v,g(v)))=g(u). 124 [para_from,109.1.1,5.1.1.2.1.2.1] f(x,g(f(g(y),f(f(z,g(z)),x))))=y. 131,130 [para_into,124.1.1.2.1.2,109.1.1] f(g(f(x,g(x))),g(f(g(y),f(z,g(z)))))=y. 157 [para_into,93.1.1,109.1.1] f(x,g(x))=f(f(y,g(y)),g(f(z,g(z)))). 159 [copy,157,flip.1] f(f(x,g(x)),g(f(y,g(y))))=f(z,g(z)). 190 [para_from,157.1.1,9.1.1.2.1.1.1.2.1,demod,117] f(x,g(f(g(g(f(y,g(y)))),f(z,x))))=g(z). 203 [para_from,159.1.1,33.1.1.1.2.1.1.2.1,demod,121] g(f(x,g(x)))=g(f(y,g(y))). 208 [para_into,130.1.1.1.1.2,203.1.1] f(g(f(f(x,g(x)),g(f(y,g(y))))),g(f(g(z),f(u,g(u)))))=z. 213 [para_from,130.1.1,33.1.1.1.2.1.1.2.1] f(f(f(x,g(x)),g(f(f(f(y,g(y)),g(z)),g(f(u,g(u)))))),f(v,g(v)))=g(f(g(z),f(w,g(w)))). 217 [copy,213,flip.1] g(f(g(x),f(y,g(y))))=f(f(f(z,g(z)),g(f(f(f(u,g(u)),g(x)),g(f(v,g(v)))))),f(w,g(w))). 229 [para_into,190.1.1.2.1.2,109.1.1] f(g(x),g(f(g(g(f(y,g(y)))),f(z,g(z)))))=g(x). 242,241 [para_into,190.1.1,5.1.1,flip.1] g(f(f(x,g(x)),g(f(y,g(g(f(z,g(z))))))))=y. 441 [para_into,229.1.1.1,241.1.1,demod,242] f(x,g(f(g(g(f(y,g(y)))),f(z,g(z)))))=x. 478 [para_into,441.1.1,109.1.1] f(x,g(x))=f(g(g(f(y,g(y)))),f(z,g(z))). 480 [copy,478,flip.1] f(g(g(f(x,g(x)))),f(y,g(y)))=f(z,g(z)). 496 [para_from,441.1.1,16.1.1.2.1.2] f(g(f(g(g(f(x,g(x)))),f(y,g(y)))),g(f(f(z,f(u,g(u))),v)))=f(f(f(w,g(w)),g(f(z,v))),f(v6,g(v6))). 505 [para_from,441.1.1,33.1.1.1.2.1.1,demod,117] g(g(g(f(x,g(x)))))=f(y,g(y)). 529 [para_from,441.1.1,5.1.1.2.1.2.1.1] f(x,g(f(y,f(f(f(g(g(f(z,g(z)))),f(u,g(u))),g(f(v,y))),x))))=v. 536 [copy,496,flip.1] f(f(f(x,g(x)),g(f(y,z))),f(u,g(u)))=f(g(f(g(g(f(v,g(v)))),f(w,g(w)))),g(f(f(y,f(v6,g(v6))),z))). 537 [copy,505,flip.1] f(x,g(x))=g(g(g(f(y,g(y))))). 562 [para_into,537.1.1,537.1.1] g(g(g(f(x,g(x)))))=g(g(g(f(y,g(y))))). 577 [para_from,537.1.1,505.1.1.1.1.1] g(g(g(g(g(g(f(x,g(x))))))))=f(y,g(y)). 585 [para_from,537.1.1,16.1.1.2.1.2] f(g(x),g(f(f(y,f(z,g(z))),g(g(g(f(u,g(u))))))))=f(f(f(v,g(v)),g(f(y,x))),f(w,g(w))). 622 [para_from,537.1.1,16.1.1.2.1.1.2] f(x,g(f(f(y,g(g(g(f(z,g(z)))))),f(u,x))))=f(f(f(v,g(v)),g(f(y,u))),f(w,g(w))). 630 [copy,577,flip.1] f(x,g(x))=g(g(g(g(g(g(f(y,g(y)))))))). 632 [copy,585,flip.1] f(f(f(x,g(x)),g(f(y,z))),f(u,g(u)))=f(g(z),g(f(f(y,f(v,g(v))),g(g(g(f(w,g(w)))))))). 794 [para_from,562.1.1,241.1.1.1.1.2] g(f(f(g(g(f(x,g(x)))),g(g(g(f(y,g(y)))))),g(f(z,g(g(f(u,g(u))))))))=z. 812 [para_from,562.1.1,130.1.1.2.1.1,demod,131] g(g(f(x,g(x))))=g(g(f(y,g(y)))). 813 [para_from,562.1.1,103.1.1.2.2] f(x,f(g(g(f(y,g(y)))),g(g(g(f(z,g(z)))))))=f(x,f(u,g(u))). 846 [copy,813,flip.1] f(x,f(y,g(y)))=f(x,f(g(g(f(z,g(z)))),g(g(g(f(u,g(u))))))). 893 [para_from,812.1.1,441.1.1.2.1.1.1.1.2] f(x,g(f(g(g(f(g(f(y,g(y))),g(g(f(z,g(z))))))),f(u,g(u)))))=x. 967 [para_from,577.1.1,130.1.1.1.1.2] f(g(f(g(g(g(g(g(f(x,g(x))))))),f(y,g(y)))),g(f(g(z),f(u,g(u)))))=z. 982 [para_from,577.1.1,441.1.1.2.1.1.1.1.2] f(x,g(f(g(g(f(g(g(g(g(g(f(y,g(y))))))),f(z,g(z))))),f(u,g(u)))))=x. 1048 [para_from,630.1.1,241.1.1.1.1] g(f(g(g(g(g(g(g(f(x,g(x)))))))),g(f(y,g(g(f(z,g(z))))))))=y. 1059 [para_from,630.1.1,56.1.1.1.1] f(f(g(g(g(g(g(g(f(x,g(x)))))))),g(g(y))),f(z,g(z)))=y. 1096 [para_from,630.1.1,241.1.1.1.2.1.2.1.1] g(f(f(x,g(x)),g(f(y,g(g(g(g(g(g(g(g(f(z,g(z))))))))))))))=y. 1189,1188 [para_from,480.1.1,441.1.1.2.1] f(x,g(f(y,g(y))))=x. 1197,1196 [back_demod,217,demod,1189,117] g(f(g(x),f(y,g(y))))=g(g(x)). 1201,1200 [back_demod,208,demod,1189,1197] f(g(f(x,g(x))),g(g(y)))=y. 1225,1224 [back_demod,982,demod,1197,1197] f(x,g(g(g(g(g(g(g(g(f(y,g(y)))))))))))=x. 1227,1226 [back_demod,967,demod,1197,1197] f(g(g(g(g(g(g(f(x,g(x)))))))),g(g(y)))=y. 1237,1236 [back_demod,893,demod,1201,1197] f(x,g(g(g(f(y,g(y))))))=x. 1260 [back_demod,536,demod,1197] f(f(f(x,g(x)),g(f(y,z))),f(u,g(u)))=f(g(g(g(f(v,g(v))))),g(f(f(y,f(w,g(w))),z))). 1293,1292 [back_demod,1096,demod,1225] g(f(f(x,g(x)),g(y)))=y. 1295,1294 [back_demod,1059,demod,1227] f(x,f(y,g(y)))=x. 1305,1304 [back_demod,846,demod,1295,1237,flip.1] f(x,g(g(f(y,g(y)))))=x. 1331,1330 [back_demod,794,demod,1237,1305] g(f(g(g(f(x,g(x)))),g(y)))=y. 1337,1336 [back_demod,632,demod,1295,1295,1237] f(f(x,g(x)),g(f(y,z)))=f(g(z),g(y)). 1339,1338 [back_demod,622,demod,1237,1337,1295] f(x,g(f(y,f(z,x))))=f(g(z),g(y)). 1345 [copy,1260,flip.1,demod,1295,1337,1295] f(g(g(g(f(x,g(x))))),g(f(y,z)))=f(g(z),g(y)). 1393 [back_demod,529,demod,1295,1339,1331] f(f(x,y),g(y))=x. 1443 [back_demod,60,demod,1337,1295,1337,1293,1295] g(f(f(g(x),g(y)),f(y,z)))=f(g(z),x). 1463 [back_demod,1048,demod,1305] g(f(g(g(g(g(g(g(f(x,g(x)))))))),g(y)))=y. 1499,1498 [para_into,1393.1.1.1,1393.1.1] f(x,g(g(y)))=f(x,y). 1501,1500 [para_into,1393.1.1.1,630.1.1,demod,1499] f(g(g(g(g(g(g(f(x,g(x)))))))),y)=y. 1527,1526 [back_demod,1200,demod,1499] f(g(f(x,g(x))),y)=y. 1529,1528 [back_demod,1463,demod,1501] g(g(x))=x. 1531,1530 [back_demod,1345,demod,1529,1527] g(f(x,y))=f(g(y),g(x)). 1542 [back_demod,1443,demod,1531,1531,1531,1529,1529] f(f(g(x),g(y)),f(y,z))=f(g(x),z). 1550 [para_from,1528.1.1,1393.1.1.2] f(f(x,g(y)),y)=x. 1670 [para_into,1542.1.1.1.1,1528.1.1,demod,1529] f(f(x,g(y)),f(y,z))=f(x,z). 1716 [para_into,1670.1.1.1,1550.1.1,demod,1529,flip.1] f(f(x,y),z)=f(x,f(y,z)). 1718 [binary,1716.1,3.1] $Ans(assoc). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 60 clauses generated 2460 clauses kept 1244 clauses forward subsumed 3168 clauses back subsumed 16 Kbytes malloced 8789 ----------- times (seconds) ----------- user CPU time 0.20 (0 hr, 0 min, 0 sec) system CPU time 0.03 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8391 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/ec.out0100664000076400007640000001573610103522155016102 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8376. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs,2). assign(max_weight,16). clear(print_kept). set(order_history). list(usable). 1 [] -P(e(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). end_of_list. list(passive). 3 [] -P(e(e(e(a,b),e(c,a)),e(b,c)))|$Ans(EC_1). 4 [] -P(e(e(a,e(b,c)),e(e(a,b),c)))|$Ans(EC_2). end_of_list. list(demodulators). 5 [] e(e(x,x),y)=junk. 6 [] e(y,e(x,x))=junk. 7 [] e(x,junk)=junk. 8 [] e(junk,x)=junk. 9 [] P(junk)=$T. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). given clause #2: (wt=16) 10 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). given clause #3: (wt=8) 12 [hyper,1,10,2] P(e(e(x,y),e(x,y))). given clause #4: (wt=12) 13 [hyper,1,2,12] P(e(e(x,e(y,z)),e(e(y,z),x))). given clause #5: (wt=16) 11 [hyper,1,10,10] P(e(e(x,y),e(e(x,z),e(e(u,y),e(z,u))))). given clause #6: (wt=12) 14 [hyper,1,13,13] P(e(e(e(x,y),z),e(z,e(x,y)))). given clause #7: (wt=12) 15 [hyper,1,10,13] P(e(e(x,y),e(e(x,z),e(z,y)))). given clause #8: (wt=12) 18 [hyper,1,13,2] P(e(e(e(x,y),e(z,x)),e(z,y))). given clause #9: (wt=16) 16 [hyper,1,2,13] P(e(e(x,e(e(y,z),u)),e(e(u,e(y,z)),x))). given clause #10: (wt=4) 32 [hyper,1,18,14] P(e(x,x)). given clause #11: (wt=8) 31 [hyper,1,18,15] P(e(e(e(x,y),x),y)). given clause #12: (wt=8) 39 [hyper,1,15,32] P(e(e(x,y),e(y,x))). given clause #13: (wt=16) 17 [hyper,1,13,10] P(e(e(e(x,y),z),e(z,e(e(u,y),e(x,u))))). given clause #14: (wt=8) 43 [hyper,1,14,31] P(e(x,e(e(y,x),y))). given clause #15: (wt=8) 55 [hyper,1,18,43] P(e(e(x,e(x,y)),y)). given clause #16: (wt=8) 66 [hyper,1,39,55] P(e(x,e(y,e(y,x)))). given clause #17: (wt=16) 19 [hyper,1,13,11] P(e(e(e(x,y),e(e(z,u),e(y,z))),e(x,u))). given clause #18: (wt=8) 67 [hyper,1,18,55] P(e(x,e(y,e(x,y)))). given clause #19: (wt=8) 79 [hyper,1,10,66] P(e(e(e(x,y),y),x)). given clause #20: (wt=8) 94 [hyper,1,39,67] P(e(e(x,e(y,x)),y)). given clause #21: (wt=12) 20 [hyper,1,10,11] P(e(e(e(x,y),z),e(e(z,x),y))). given clause #22: (wt=8) 110 [hyper,1,39,79] P(e(x,e(e(x,y),y))). given clause #23: (wt=12) 24 [hyper,1,14,15] P(e(e(e(x,y),e(y,z)),e(x,z))). given clause #24: (wt=12) 33 [hyper,1,18,11] P(e(e(e(e(x,y),e(z,x)),z),y)). given clause #25: (wt=16) 21 [hyper,1,11,12] P(e(e(e(x,y),z),e(e(u,e(x,y)),e(z,u)))). given clause #26: (wt=12) 40 [hyper,1,11,32] P(e(e(x,y),e(e(z,x),e(y,z)))). -------- PROOF -------- 197 [binary,196.1,3.1] $Ans(EC_1). ----> UNIT CONFLICT at 0.01 sec ----> 197 [binary,196.1,3.1] $Ans(EC_1). Length of proof is 11. Level of proof is 7. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). 3 [] -P(e(e(e(a,b),e(c,a)),e(b,c)))|$Ans(EC_1). 10 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). 11 [hyper,1,10,10] P(e(e(x,y),e(e(x,z),e(e(u,y),e(z,u))))). 12 [hyper,1,10,2] P(e(e(x,y),e(x,y))). 13 [hyper,1,2,12] P(e(e(x,e(y,z)),e(e(y,z),x))). 14 [hyper,1,13,13] P(e(e(e(x,y),z),e(z,e(x,y)))). 15 [hyper,1,10,13] P(e(e(x,y),e(e(x,z),e(z,y)))). 18 [hyper,1,13,2] P(e(e(e(x,y),e(z,x)),e(z,y))). 32 [hyper,1,18,14] P(e(x,x)). 39 [hyper,1,15,32] P(e(e(x,y),e(y,x))). 40 [hyper,1,11,32] P(e(e(x,y),e(e(z,x),e(y,z)))). 196 [hyper,1,39,40] P(e(e(e(x,y),e(z,x)),e(y,z))). 197 [binary,196.1,3.1] $Ans(EC_1). ------------ end of proof ------------- given clause #27: (wt=12) 42 [hyper,1,15,31] P(e(e(e(e(x,y),x),z),e(z,y))). given clause #28: (wt=12) 46 [hyper,1,2,31] P(e(e(x,y),e(e(e(z,y),z),x))). given clause #29: (wt=16) 22 [hyper,1,2,14] P(e(e(x,e(y,e(z,u))),e(e(e(z,u),y),x))). given clause #30: (wt=12) 47 [hyper,1,15,39] P(e(e(e(x,y),z),e(z,e(y,x)))). given clause #31: (wt=12) 49 [hyper,1,2,39] P(e(e(x,e(y,z)),e(e(z,y),x))). given clause #32: (wt=12) 51 [hyper,1,17,31] P(e(x,e(e(y,z),e(e(z,x),y)))). given clause #33: (wt=16) 23 [hyper,1,15,15] P(e(e(e(x,y),z),e(z,e(e(x,u),e(u,y))))). given clause #34: (wt=12) 54 [hyper,1,43,43] P(e(e(x,e(y,e(e(z,y),z))),x)). given clause #35: (wt=12) 57 [hyper,1,15,43] P(e(e(x,y),e(y,e(e(z,x),z)))). given clause #36: (wt=12) 59 [hyper,1,2,43] P(e(e(x,e(e(y,z),y)),e(z,x))). given clause #37: (wt=16) 25 [hyper,1,2,15] P(e(e(x,e(e(y,z),e(z,u))),e(e(y,u),x))). given clause #38: (wt=12) 60 [hyper,1,43,39] P(e(e(x,e(e(y,z),e(z,y))),x)). given clause #39: (wt=12) 61 [hyper,1,43,31] P(e(e(x,e(e(e(y,z),y),z)),x)). given clause #40: (wt=12) 65 [hyper,1,43,55] P(e(e(x,e(e(y,e(y,z)),z)),x)). given clause #41: (wt=16) 26 [hyper,1,15,14] P(e(e(e(e(x,y),z),u),e(u,e(z,e(x,y))))). given clause #42: (wt=12) 68 [hyper,1,17,55] P(e(x,e(e(y,e(z,x)),e(z,y)))). given clause #43: (wt=12) 70 [hyper,1,15,55] P(e(e(e(x,e(x,y)),z),e(z,y))). given clause #44: (wt=12) 73 [hyper,1,2,55] P(e(e(x,y),e(e(z,e(z,y)),x))). -------- PROOF -------- 550 [binary,549.1,4.1] $Ans(EC_2). ----> UNIT CONFLICT at 0.03 sec ----> 550 [binary,549.1,4.1] $Ans(EC_2). Length of proof is 11. Level of proof is 9. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). 4 [] -P(e(e(a,e(b,c)),e(e(a,b),c)))|$Ans(EC_2). 10 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). 12 [hyper,1,10,2] P(e(e(x,y),e(x,y))). 13 [hyper,1,2,12] P(e(e(x,e(y,z)),e(e(y,z),x))). 14 [hyper,1,13,13] P(e(e(e(x,y),z),e(z,e(x,y)))). 15 [hyper,1,10,13] P(e(e(x,y),e(e(x,z),e(z,y)))). 18 [hyper,1,13,2] P(e(e(e(x,y),e(z,x)),e(z,y))). 31 [hyper,1,18,15] P(e(e(e(x,y),x),y)). 43 [hyper,1,14,31] P(e(x,e(e(y,x),y))). 55 [hyper,1,18,43] P(e(e(x,e(x,y)),y)). 73 [hyper,1,2,55] P(e(e(x,y),e(e(z,e(z,y)),x))). 549 [hyper,1,10,73] P(e(e(x,e(y,z)),e(e(x,y),z))). 550 [binary,549.1,4.1] $Ans(EC_2). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 44 clauses generated 1663 hyper_res generated 1663 demod & eval rewrites 62 clauses wt,lit,sk delete 270 tautologies deleted 22 clauses forward subsumed 832 (subsumed by sos) 372 unit deletions 0 factor simplifications 0 clauses kept 539 new demodulators 0 empty clauses 2 clauses back demodulated 0 clauses back subsumed 0 usable size 45 sos size 496 demodulators size 5 passive size 2 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8376 finished Mon Aug 2 15:30:37 2004 otter-3.3f/examples/misc/ec.in0100644000076400007640000000325105461320200015662 0ustar mccunemccune% Equivalential calculus (EC): YQL is a single axiom. % % {EC1, EC2} (Lesniewski) was the first axiomatization of EC. % Show that EC1 and EC2 can be derived from YQL by condensed detachment. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs,2). assign(max_weight, 16). clear(print_kept). set(order_history). list(usable). -P(e(x,y)) | -P(x) | P(y). % condensed detachment end_of_list. list(sos). P(e(e(x,y),e(e(z,y),e(x,z)))). % YQL end_of_list. list(passive). -P(e(e(e(a,b),e(c,a)),e(b,c))) | $Ans(EC_1). -P(e(e(a,e(b,c)),e(e(a,b),c))) | $Ans(EC_2). end_of_list. % The following demodulators discard clauses that contain an % instance of e(x,x) as a proper subformula. list(demodulators). e(e(x,x),y) = junk. e(y,e(x,x)) = junk. e(x,junk) = junk. e(junk,x) = junk. P(junk) = $T. end_of_list. % For reference, the 13 shortest single axioms for EC: % % P(e(e(x,y),e(e(z,y),e(x,z)))). % YQL % Lukasiewicz P1 % P(e(e(x,y),e(e(x,z),e(z,y)))). % YQF % Lukasiewicz P2 % P(e(e(x,y),e(e(z,x),e(y,z)))). % YQJ % Lukasiewicz P3 % P(e(e(e(x,y),z),e(y,e(z,x)))). % UM % Meredith P4 = P4' % P(e(x,e(e(y,e(x,z)),e(z,y)))). % XGF % Meredith P5 % P(e(e(x,e(y,z)),e(z,e(x,y)))). % WN % Meredith P7 % P(e(e(x,y),e(z,e(e(y,z),x)))). % YRM % Meredith P8 % P(e(e(x,y),e(z,e(e(z,y),x)))). % YRO % Meredith P9 % P(e(e(e(x,e(y,z)),z),e(y,x))). % PYO % Meredith P10 = P9' % P(e(e(e(x,e(y,z)),y),e(z,x))). % PYM % Meredith P11 = P8' % P(e(x,e(e(y,e(z,x)),e(z,y)))). % XGK % Kalman % P(e(x,e(e(y,z),e(e(x,z),y)))). % XHK % Winker % P(e(x,e(e(y,z),e(e(z,x),y)))). % XHN % Winker otter-3.3f/examples/Makefile0100644000076400007640000000012207706065622015464 0ustar mccunemccuneall: ./Run_all clean realclean: /bin/rm -f */*.out[0-9]* *~ */*~ Run_all.out.* otter-3.3f/examples/fringe/0040755000076400007640000000000010103530360015263 5ustar mccunemccuneotter-3.3f/examples/fringe/luka5h.out0100664000076400007640000005025710103522222017213 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8932. set(hyper_res). set(sos_queue). assign(max_weight,1). assign(equiv_hint_wt,1). set(keep_hint_subsumers). clear(print_kept). list(usable). 1 [] -P(i(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(i(x,i(y,x))) # label("Axiom 1"). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))) # label("Axiom 2"). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))) # label("Axiom 3"). 5 [] P(i(i(n(x),n(y)),i(y,x))) # label("Axiom 5"). end_of_list. list(passive). 6 [] -P(i(i(i(cx,cy),i(cy,cx)),i(cy,cx)))|$ANS(Denial_Axiom4). end_of_list. list(hints). 7 [] P(i(x,i(y,i(z,y)))) # label("Step01"). 8 [] P(i(i(i(i(x,y),i(z,y)),w),i(i(z,x),w))) # label("Step02"). 9 [] P(i(x,i(i(y,z),i(i(z,w),i(y,w))))) # label("Step03"). 10 [] P(i(i(i(x,y),z),i(y,z))) # label("Step04"). 11 [] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))) # label("Step05"). 12 [] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))) # label("Step06"). 13 [] P(i(i(i(x,i(y,x)),z),z)) # label("Step07"). 14 [] P(i(i(x,i(y,z)),i(i(w,y),i(x,i(w,z))))) # label("Step08"). 15 [] P(i(i(x,y),i(i(i(x,z),w),i(i(y,z),w)))) # label("Step09"). 16 [] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),w),w)) # label("Step10"). 17 [] P(i(n(x),i(x,y))) # label("Step11"). 18 [] P(i(x,i(i(x,y),y))) # label("Step12"). 19 [] P(i(i(i(x,i(y,x)),i(y,x)),i(i(i(x,y),y),x))) # label("Step13"). 20 [] P(i(i(n(x),n(i(y,i(z,y)))),x)) # label("Step14"). 21 [] P(i(i(n(x),n(i(i(y,z),i(i(z,w),i(y,w))))),x)) # label("Step15"). 22 [] P(i(i(x,i(y,z)),i(x,i(i(z,w),i(y,w))))) # label("Step16"). 23 [] P(i(i(x,y),i(n(y),i(x,z)))) # label("Step17"). 24 [] P(i(i(i(x,y),z),i(n(x),z))) # label("Step18"). 25 [] P(i(i(x,i(y,z)),i(y,i(x,z)))) # label("Step19"). 26 [] P(i(i(x,y),i(i(i(y,x),x),y))) # label("Step20"). 27 [] P(i(i(i(i(n(x),n(i(y,i(z,y)))),x),w),w)) # label("Step21"). 28 [] P(i(x,i(i(y,z),i(i(x,y),z)))) # label("Step22"). 29 [] P(i(i(i(n(x),i(y,z)),w),i(i(y,x),w))) # label("Step23"). 30 [] P(i(n(n(x)),x)) # label("Step24"). 31 [] P(i(i(x,y),i(i(z,x),i(z,y)))) # label("Step25"). 32 [] P(i(i(x,i(n(y),n(i(z,i(w,z))))),i(x,y))) # label("Step26"). 33 [] P(i(i(i(i(x,y),i(i(z,x),y)),w),i(z,w))) # label("Step27"). 34 [] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))) # label("Step28"). 35 [] P(i(x,n(n(x)))) # label("Step29"). 36 [] P(i(i(x,n(n(y))),i(x,y))) # label("Step30"). 37 [] P(i(i(x,i(i(y,z),w)),i(x,i(z,w)))) # label("Step31"). 38 [] P(i(i(x,i(n(y),n(z))),i(x,i(z,y)))) # label("Step32"). 39 [] P(i(i(n(x),y),i(n(y),x))) # label("Step33"). 40 [] P(i(i(n(n(x)),y),i(x,y))) # label("Step34"). 41 [] P(i(i(i(x,y),n(z)),i(z,x))) # label("Step35"). 42 [] P(i(i(x,y),i(n(y),n(x)))) # label("Step36"). 43 [] P(i(i(x,i(n(n(y)),z)),i(x,i(y,z)))) # label("Step37"). 44 [] P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))) # label("Step38"). 45 [] P(i(n(i(x,y)),n(y))) # label("Step39"). 46 [] P(i(i(i(n(x),n(y)),z),i(i(y,x),z))) # label("Step40"). 47 [] P(i(n(i(x,y)),n(i(i(y,z),n(x))))) # label("Step41"). 48 [] P(i(i(i(x,y),i(z,w)),i(y,i(n(w),n(z))))) # label("Step42"). 49 [] P(i(i(i(n(x),n(i(y,x))),n(i(y,x))),n(x))) # label("Step43"). 50 [] P(i(i(x,i(i(n(y),n(z)),w)),i(x,i(i(z,y),w)))) # label("Step44"). 51 [] P(i(i(i(n(x),n(y)),n(y)),i(i(x,y),n(x)))) # label("Step45"). 52 [] P(i(i(x,n(i(y,z))),i(x,n(i(i(z,w),n(y)))))) # label("Step46"). 53 [] P(i(i(x,i(i(n(y),n(i(z,y))),n(i(z,y)))),i(x,n(y)))) # label("Step47"). 54 [] P(i(n(x),i(n(n(y)),n(i(y,x))))) # label("Step48"). 55 [] P(i(i(i(i(x,y),y),n(i(x,y))),n(y))) # label("Step49"). 56 [] P(i(n(x),i(y,n(i(y,x))))) # label("Step50"). 57 [] P(i(i(x,i(i(i(y,z),z),n(i(y,z)))),i(x,n(z)))) # label("Step51"). 58 [] P(i(i(i(n(x),i(y,n(i(y,x)))),z),z)) # label("Step52"). 59 [] P(i(i(i(i(x,y),y),n(i(y,x))),n(x))) # label("Step53"). 60 [] P(i(i(x,i(i(i(y,z),z),n(i(z,y)))),i(x,n(y)))) # label("Step54"). 61 [] P(i(i(x,y),i(i(y,n(i(y,x))),n(x)))) # label("Step55"). 62 [] P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),n(n(y)))) # label("Step56"). 63 [] P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),y)) # label("Step57"). 64 [] P(i(i(x,i(i(y,n(i(y,z))),n(i(i(y,n(i(y,z))),n(z))))),i(x,z))) # label("Step58"). 65 [] P(i(i(i(x,n(i(x,y))),n(i(y,x))),y)) # label("Step59"). 66 [] P(i(i(x,i(i(y,n(i(y,z))),n(i(z,y)))),i(x,z))) # label("Step60"). 67 [] P(i(x,i(i(n(i(x,y)),n(i(y,x))),y))) # label("Step61"). 68 [] P(i(x,i(i(i(y,x),i(x,y)),y))) # label("Step62"). 69 [] P(i(i(i(x,y),i(y,x)),i(y,x))) # label("Step63"). end_of_list. ======= end of input processing ======= =========== start of search =========== Starting on level 1, last kept clause of level 0 is 69. Starting on level 1, last kept clause of level 0 is 69. given clause #1: (wt=6) 2 [] P(i(x,i(y,x))) # label("Axiom 1"). given clause #2: (wt=12) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))) # label("Axiom 2"). given clause #3: (wt=12) 4 [] P(i(i(i(x,y),y),i(i(y,x),x))) # label("Axiom 3"). given clause #4: (wt=10) 5 [] P(i(i(n(x),n(y)),i(y,x))) # label("Axiom 5"). Starting on level 2, last kept clause of level 1 is 75. Starting on level 2, last kept clause of level 1 is 75. given clause #5: (wt=1) 70 [hyper,2,1,2] P(i(x,i(y,i(z,y)))) # label("Step01"). given clause #6: (wt=1) 71 [hyper,3,1,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))) # label("Step02"). given clause #7: (wt=1) 72 [hyper,3,1,2] P(i(x,i(i(y,z),i(i(z,u),i(y,u))))) # label("Step03"). given clause #8: (wt=1) 73 [hyper,3,1,2] P(i(i(i(x,y),z),i(y,z))) # label("Step04"). given clause #9: (wt=1) 74 [hyper,4,1,3] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))) # label("Step05"). given clause #10: (wt=1) 75 [hyper,5,1,3] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))) # label("Step06"). Starting on level 3, last kept clause of level 2 is 82. Starting on level 3, last kept clause of level 2 is 82. given clause #11: (wt=1) 76 [hyper,70,1,4] P(i(i(i(x,i(y,x)),z),z)) # label("Step07"). given clause #12: (wt=1) 77 [hyper,71,1,71] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))) # label("Step08"). given clause #13: (wt=1) 78 [hyper,71,1,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))) # label("Step09"). given clause #14: (wt=1) 79 [hyper,72,1,4] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)) # label("Step10"). given clause #15: (wt=1) 80 [hyper,73,1,5] P(i(n(x),i(x,y))) # label("Step11"). given clause #16: (wt=1) 81 [hyper,73,1,4] P(i(x,i(i(x,y),y))) # label("Step12"). given clause #17: (wt=1) 82 [hyper,74,1,74] P(i(i(i(x,i(y,x)),i(y,x)),i(i(i(x,y),y),x))) # label("Step13"). Starting on level 4, last kept clause of level 3 is 89. Starting on level 4, last kept clause of level 3 is 89. given clause #18: (wt=1) 83 [hyper,76,1,75] P(i(i(n(x),n(i(y,i(z,y)))),x)) # label("Step14"). given clause #19: (wt=1) 84 [hyper,79,1,75] P(i(i(n(x),n(i(i(y,z),i(i(z,u),i(y,u))))),x)) # label("Step15"). given clause #20: (wt=1) 85 [hyper,79,1,71] P(i(i(x,i(y,z)),i(x,i(i(z,u),i(y,u))))) # label("Step16"). given clause #21: (wt=1) 86 [hyper,80,1,77] P(i(i(x,y),i(n(y),i(x,z)))) # label("Step17"). given clause #22: (wt=1) 87 [hyper,80,1,3] P(i(i(i(x,y),z),i(n(x),z))) # label("Step18"). given clause #23: (wt=1) 88 [hyper,81,1,77] P(i(i(x,i(y,z)),i(y,i(x,z)))) # label("Step19"). given clause #24: (wt=1) 89 [hyper,82,1,73] P(i(i(x,y),i(i(i(y,x),x),y))) # label("Step20"). Starting on level 5, last kept clause of level 4 is 94. Starting on level 5, last kept clause of level 4 is 94. given clause #25: (wt=1) 90 [hyper,83,1,81] P(i(i(i(i(n(x),n(i(y,i(z,y)))),x),u),u)) # label("Step21"). given clause #26: (wt=1) 91 [hyper,85,1,81] P(i(x,i(i(y,z),i(i(x,y),z)))) # label("Step22"). given clause #27: (wt=1) 92 [hyper,86,1,3] P(i(i(i(n(x),i(y,z)),u),i(i(y,x),u))) # label("Step23"). given clause #28: (wt=1) 93 [hyper,87,1,84] P(i(n(n(x)),x)) # label("Step24"). given clause #29: (wt=1) 94 [hyper,88,1,79] P(i(i(x,y),i(i(z,x),i(z,y)))) # label("Step25"). Starting on level 6, last kept clause of level 5 is 101. Starting on level 6, last kept clause of level 5 is 101. given clause #30: (wt=1) 95 [hyper,90,1,71] P(i(i(x,i(n(y),n(i(z,i(u,z))))),i(x,y))) # label("Step26"). given clause #31: (wt=1) 96 [hyper,91,1,3] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(z,u))) # label("Step27"). given clause #32: (wt=1) 97 [hyper,93,1,78] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))) # label("Step28"). given clause #33: (wt=1) 98 [hyper,93,1,5] P(i(x,n(n(x)))) # label("Step29"). given clause #34: (wt=1) 99 [hyper,94,1,93] P(i(i(x,n(n(y))),i(x,y))) # label("Step30"). given clause #35: (wt=1) 100 [hyper,94,1,73] P(i(i(x,i(i(y,z),u)),i(x,i(z,u)))) # label("Step31"). given clause #36: (wt=1) 101 [hyper,94,1,5] P(i(i(x,i(n(y),n(z))),i(x,i(z,y)))) # label("Step32"). Starting on level 7, last kept clause of level 6 is 104. Starting on level 7, last kept clause of level 6 is 104. given clause #37: (wt=1) 102 [hyper,95,1,92] P(i(i(n(x),y),i(n(y),x))) # label("Step33"). given clause #38: (wt=1) 103 [hyper,98,1,3] P(i(i(n(n(x)),y),i(x,y))) # label("Step34"). given clause #39: (wt=1) 104 [hyper,101,1,87] P(i(i(i(x,y),n(z)),i(z,x))) # label("Step35"). Starting on level 8, last kept clause of level 7 is 106. Starting on level 8, last kept clause of level 7 is 106. given clause #40: (wt=1) 105 [hyper,102,1,97] P(i(i(x,y),i(n(y),n(x)))) # label("Step36"). given clause #41: (wt=1) 106 [hyper,103,1,94] P(i(i(x,i(n(n(y)),z)),i(x,i(y,z)))) # label("Step37"). Starting on level 9, last kept clause of level 8 is 110. Starting on level 9, last kept clause of level 8 is 110. given clause #42: (wt=1) 107 [hyper,105,1,94] P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))) # label("Step38"). given clause #43: (wt=1) 108 [hyper,105,1,76] P(i(n(i(x,y)),n(y))) # label("Step39"). given clause #44: (wt=1) 109 [hyper,105,1,3] P(i(i(i(n(x),n(y)),z),i(i(y,x),z))) # label("Step40"). given clause #45: (wt=1) 110 [hyper,105,1,104] P(i(n(i(x,y)),n(i(i(y,z),n(x))))) # label("Step41"). Starting on level 10, last kept clause of level 9 is 115. Starting on level 10, last kept clause of level 9 is 115. given clause #46: (wt=1) 111 [hyper,107,1,100] P(i(i(i(x,y),i(z,u)),i(y,i(n(u),n(z))))) # label("Step42"). given clause #47: (wt=1) 112 [hyper,108,1,89] P(i(i(i(n(x),n(i(y,x))),n(i(y,x))),n(x))) # label("Step43"). given clause #48: (wt=1) 113 [hyper,109,1,94] P(i(i(x,i(i(n(y),n(z)),u)),i(x,i(i(z,y),u)))) # label("Step44"). given clause #49: (wt=1) 114 [hyper,109,1,74] P(i(i(i(n(x),n(y)),n(y)),i(i(x,y),n(x)))) # label("Step45"). given clause #50: (wt=1) 115 [hyper,110,1,94] P(i(i(x,n(i(y,z))),i(x,n(i(i(z,u),n(y)))))) # label("Step46"). Starting on level 11, last kept clause of level 10 is 117. Starting on level 11, last kept clause of level 10 is 117. given clause #51: (wt=1) 116 [hyper,112,1,94] P(i(i(x,i(i(n(y),n(i(z,y))),n(i(z,y)))),i(x,n(y)))) # label("Step47"). given clause #52: (wt=1) 117 [hyper,114,1,111] P(i(n(x),i(n(n(y)),n(i(y,x))))) # label("Step48"). Starting on level 12, last kept clause of level 11 is 119. Starting on level 12, last kept clause of level 11 is 119. given clause #53: (wt=1) 118 [hyper,116,1,75] P(i(i(i(i(x,y),y),n(i(x,y))),n(y))) # label("Step49"). given clause #54: (wt=1) 119 [hyper,117,1,106] P(i(n(x),i(y,n(i(y,x))))) # label("Step50"). Starting on level 13, last kept clause of level 12 is 121. Starting on level 13, last kept clause of level 12 is 121. given clause #55: (wt=1) 120 [hyper,118,1,94] P(i(i(x,i(i(i(y,z),z),n(i(y,z)))),i(x,n(z)))) # label("Step51"). given clause #56: (wt=1) 121 [hyper,119,1,81] P(i(i(i(n(x),i(y,n(i(y,x)))),z),z)) # label("Step52"). Starting on level 14, last kept clause of level 13 is 122. Starting on level 14, last kept clause of level 13 is 122. given clause #57: (wt=1) 122 [hyper,120,1,74] P(i(i(i(i(x,y),y),n(i(y,x))),n(x))) # label("Step53"). Starting on level 15, last kept clause of level 14 is 123. Starting on level 15, last kept clause of level 14 is 123. given clause #58: (wt=1) 123 [hyper,122,1,94] P(i(i(x,i(i(i(y,z),z),n(i(z,y)))),i(x,n(y)))) # label("Step54"). Starting on level 16, last kept clause of level 15 is 124. Starting on level 16, last kept clause of level 15 is 124. given clause #59: (wt=1) 124 [hyper,123,1,96] P(i(i(x,y),i(i(y,n(i(y,x))),n(x)))) # label("Step55"). Starting on level 17, last kept clause of level 16 is 125. Starting on level 17, last kept clause of level 16 is 125. given clause #60: (wt=1) 125 [hyper,124,1,121] P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),n(n(y)))) # label("Step56"). Starting on level 18, last kept clause of level 17 is 126. Starting on level 18, last kept clause of level 17 is 126. given clause #61: (wt=1) 126 [hyper,125,1,99] P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),y)) # label("Step57"). Starting on level 19, last kept clause of level 18 is 127. Starting on level 19, last kept clause of level 18 is 127. given clause #62: (wt=1) 127 [hyper,126,1,94] P(i(i(x,i(i(y,n(i(y,z))),n(i(i(y,n(i(y,z))),n(z))))),i(x,z))) # label("Step58"). Starting on level 20, last kept clause of level 19 is 128. Starting on level 20, last kept clause of level 19 is 128. given clause #63: (wt=1) 128 [hyper,127,1,115] P(i(i(i(x,n(i(x,y))),n(i(y,x))),y)) # label("Step59"). Starting on level 21, last kept clause of level 20 is 129. Starting on level 21, last kept clause of level 20 is 129. given clause #64: (wt=1) 129 [hyper,128,1,94] P(i(i(x,i(i(y,n(i(y,z))),n(i(z,y)))),i(x,z))) # label("Step60"). Starting on level 22, last kept clause of level 21 is 130. Starting on level 22, last kept clause of level 21 is 130. given clause #65: (wt=1) 130 [hyper,129,1,96] P(i(x,i(i(n(i(x,y)),n(i(y,x))),y))) # label("Step61"). Starting on level 23, last kept clause of level 22 is 131. Starting on level 23, last kept clause of level 22 is 131. given clause #66: (wt=1) 131 [hyper,130,1,113] P(i(x,i(i(i(y,x),i(x,y)),y))) # label("Step62"). -------- PROOF -------- 133 [binary,132.1,6.1] $ANS(Denial_Axiom4). ----> UNIT CONFLICT at 0.08 sec ----> 133 [binary,132.1,6.1] $ANS(Denial_Axiom4). Length of proof is 63. Level of proof is 23. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))) # label("Axiom 1"). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))) # label("Axiom 2"). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))) # label("Axiom 3"). 5 [] P(i(i(n(x),n(y)),i(y,x))) # label("Axiom 5"). 6 [] -P(i(i(i(cx,cy),i(cy,cx)),i(cy,cx)))|$ANS(Denial_Axiom4). 70 [hyper,2,1,2] P(i(x,i(y,i(z,y)))) # label("Step01"). 71 [hyper,3,1,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))) # label("Step02"). 72 [hyper,3,1,2] P(i(x,i(i(y,z),i(i(z,u),i(y,u))))) # label("Step03"). 73 [hyper,3,1,2] P(i(i(i(x,y),z),i(y,z))) # label("Step04"). 74 [hyper,4,1,3] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))) # label("Step05"). 75 [hyper,5,1,3] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))) # label("Step06"). 76 [hyper,70,1,4] P(i(i(i(x,i(y,x)),z),z)) # label("Step07"). 77 [hyper,71,1,71] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))) # label("Step08"). 78 [hyper,71,1,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))) # label("Step09"). 79 [hyper,72,1,4] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)) # label("Step10"). 80 [hyper,73,1,5] P(i(n(x),i(x,y))) # label("Step11"). 81 [hyper,73,1,4] P(i(x,i(i(x,y),y))) # label("Step12"). 82 [hyper,74,1,74] P(i(i(i(x,i(y,x)),i(y,x)),i(i(i(x,y),y),x))) # label("Step13"). 83 [hyper,76,1,75] P(i(i(n(x),n(i(y,i(z,y)))),x)) # label("Step14"). 84 [hyper,79,1,75] P(i(i(n(x),n(i(i(y,z),i(i(z,u),i(y,u))))),x)) # label("Step15"). 85 [hyper,79,1,71] P(i(i(x,i(y,z)),i(x,i(i(z,u),i(y,u))))) # label("Step16"). 86 [hyper,80,1,77] P(i(i(x,y),i(n(y),i(x,z)))) # label("Step17"). 87 [hyper,80,1,3] P(i(i(i(x,y),z),i(n(x),z))) # label("Step18"). 88 [hyper,81,1,77] P(i(i(x,i(y,z)),i(y,i(x,z)))) # label("Step19"). 89 [hyper,82,1,73] P(i(i(x,y),i(i(i(y,x),x),y))) # label("Step20"). 90 [hyper,83,1,81] P(i(i(i(i(n(x),n(i(y,i(z,y)))),x),u),u)) # label("Step21"). 91 [hyper,85,1,81] P(i(x,i(i(y,z),i(i(x,y),z)))) # label("Step22"). 92 [hyper,86,1,3] P(i(i(i(n(x),i(y,z)),u),i(i(y,x),u))) # label("Step23"). 93 [hyper,87,1,84] P(i(n(n(x)),x)) # label("Step24"). 94 [hyper,88,1,79] P(i(i(x,y),i(i(z,x),i(z,y)))) # label("Step25"). 95 [hyper,90,1,71] P(i(i(x,i(n(y),n(i(z,i(u,z))))),i(x,y))) # label("Step26"). 96 [hyper,91,1,3] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(z,u))) # label("Step27"). 97 [hyper,93,1,78] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))) # label("Step28"). 98 [hyper,93,1,5] P(i(x,n(n(x)))) # label("Step29"). 99 [hyper,94,1,93] P(i(i(x,n(n(y))),i(x,y))) # label("Step30"). 100 [hyper,94,1,73] P(i(i(x,i(i(y,z),u)),i(x,i(z,u)))) # label("Step31"). 101 [hyper,94,1,5] P(i(i(x,i(n(y),n(z))),i(x,i(z,y)))) # label("Step32"). 102 [hyper,95,1,92] P(i(i(n(x),y),i(n(y),x))) # label("Step33"). 103 [hyper,98,1,3] P(i(i(n(n(x)),y),i(x,y))) # label("Step34"). 104 [hyper,101,1,87] P(i(i(i(x,y),n(z)),i(z,x))) # label("Step35"). 105 [hyper,102,1,97] P(i(i(x,y),i(n(y),n(x)))) # label("Step36"). 106 [hyper,103,1,94] P(i(i(x,i(n(n(y)),z)),i(x,i(y,z)))) # label("Step37"). 107 [hyper,105,1,94] P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))) # label("Step38"). 108 [hyper,105,1,76] P(i(n(i(x,y)),n(y))) # label("Step39"). 109 [hyper,105,1,3] P(i(i(i(n(x),n(y)),z),i(i(y,x),z))) # label("Step40"). 110 [hyper,105,1,104] P(i(n(i(x,y)),n(i(i(y,z),n(x))))) # label("Step41"). 111 [hyper,107,1,100] P(i(i(i(x,y),i(z,u)),i(y,i(n(u),n(z))))) # label("Step42"). 112 [hyper,108,1,89] P(i(i(i(n(x),n(i(y,x))),n(i(y,x))),n(x))) # label("Step43"). 113 [hyper,109,1,94] P(i(i(x,i(i(n(y),n(z)),u)),i(x,i(i(z,y),u)))) # label("Step44"). 114 [hyper,109,1,74] P(i(i(i(n(x),n(y)),n(y)),i(i(x,y),n(x)))) # label("Step45"). 115 [hyper,110,1,94] P(i(i(x,n(i(y,z))),i(x,n(i(i(z,u),n(y)))))) # label("Step46"). 116 [hyper,112,1,94] P(i(i(x,i(i(n(y),n(i(z,y))),n(i(z,y)))),i(x,n(y)))) # label("Step47"). 117 [hyper,114,1,111] P(i(n(x),i(n(n(y)),n(i(y,x))))) # label("Step48"). 118 [hyper,116,1,75] P(i(i(i(i(x,y),y),n(i(x,y))),n(y))) # label("Step49"). 119 [hyper,117,1,106] P(i(n(x),i(y,n(i(y,x))))) # label("Step50"). 120 [hyper,118,1,94] P(i(i(x,i(i(i(y,z),z),n(i(y,z)))),i(x,n(z)))) # label("Step51"). 121 [hyper,119,1,81] P(i(i(i(n(x),i(y,n(i(y,x)))),z),z)) # label("Step52"). 122 [hyper,120,1,74] P(i(i(i(i(x,y),y),n(i(y,x))),n(x))) # label("Step53"). 123 [hyper,122,1,94] P(i(i(x,i(i(i(y,z),z),n(i(z,y)))),i(x,n(y)))) # label("Step54"). 124 [hyper,123,1,96] P(i(i(x,y),i(i(y,n(i(y,x))),n(x)))) # label("Step55"). 125 [hyper,124,1,121] P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),n(n(y)))) # label("Step56"). 126 [hyper,125,1,99] P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),y)) # label("Step57"). 127 [hyper,126,1,94] P(i(i(x,i(i(y,n(i(y,z))),n(i(i(y,n(i(y,z))),n(z))))),i(x,z))) # label("Step58"). 128 [hyper,127,1,115] P(i(i(i(x,n(i(x,y))),n(i(y,x))),y)) # label("Step59"). 129 [hyper,128,1,94] P(i(i(x,i(i(y,n(i(y,z))),n(i(z,y)))),i(x,z))) # label("Step60"). 130 [hyper,129,1,96] P(i(x,i(i(n(i(x,y)),n(i(y,x))),y))) # label("Step61"). 131 [hyper,130,1,113] P(i(x,i(i(i(y,x),i(x,y)),y))) # label("Step62"). 132 [hyper,131,1,88] P(i(i(i(x,y),i(y,x)),i(y,x))) # label("Step63"). 133 [binary,132.1,6.1] $ANS(Denial_Axiom4). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 66 clauses generated 2234 hyper_res generated 2234 demod & eval rewrites 0 clauses wt,lit,sk delete 2081 tautologies deleted 0 clauses forward subsumed 90 (subsumed by sos) 14 unit deletions 0 factor simplifications 0 clauses kept 63 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 0 usable size 67 sos size 1 demodulators size 0 passive size 1 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.08 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8932 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/lexical1.out0100664000076400007640000000550710103522222017522 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8917. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(lex_order_vars). assign(max_given,1). lex([a,b,c,d,e,f(x),add(x,x)]). special_unary([neg(x)]). list(usable). 1 [] -dum|P1(add(c,add(add(a,b),add(e,d)))). 2 [] -dum|P2(add(neg(c),add(add(neg(a),neg(b)),add(neg(e),neg(d))))). 3 [] -dum|P3(add(c,add(add(a,neg(b)),add(e,neg(d))))). 4 [] -dum|P4(add(add(neg(a),b),add(neg(b),add(add(b,neg(b)),add(a,b))))). 5 [] -dum|P5(add(x,add(add(c,add(add(a,neg(y)),neg(b))),add(f(y),b)))). end_of_list. list(sos). 6 [] dum. end_of_list. list(demodulators). 7 [] EQ(add(x,y),add(y,x)). 8 [] EQ(add(x,add(y,z)),add(y,add(x,z))). 9 [] EQ(add(add(x,y),z),add(x,add(y,z))). end_of_list. lex dependent demodulator: 7 [] EQ(add(x,y),add(y,x)). lex dependent demodulator: 8 [] EQ(add(x,add(y,z)),add(y,add(x,z))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=1) 6 [] dum. Search stopped by max_given option. ** KEPT (pick-wt=17): 10 [binary,6.1,5.1,demod,7,7,8,7,8,8,7,7,8,7,8,8,8,7,8,8] P5(add(x,add(neg(y),add(a,add(b,add(neg(b),add(c,f(y)))))))). ** KEPT (pick-wt=17): 11 [binary,6.1,4.1,demod,7,8,7,8,7,8,8,8,8,7,8,7,8,8] P4(add(a,add(neg(a),add(b,add(b,add(b,add(neg(b),neg(b)))))))). ** KEPT (pick-wt=12): 12 [binary,6.1,3.1,demod,7,8,7,8,7,8,8,8,8] P3(add(a,add(neg(b),add(c,add(neg(d),e))))). ** KEPT (pick-wt=15): 13 [binary,6.1,2.1,demod,7,8,7,8,7,8,8,8,8] P2(add(neg(a),add(neg(b),add(neg(c),add(neg(d),neg(e)))))). ** KEPT (pick-wt=10): 14 [binary,6.1,1.1,demod,7,8,7,8,7,8,8,8,8] P1(add(a,add(b,add(c,add(d,e))))). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 1 clauses generated 5 binary_res generated 5 factors generated 0 demod & eval rewrites 57 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 5 new demodulators 0 empty clauses 0 clauses back demodulated 0 clauses back subsumed 0 usable size 6 sos size 5 demodulators size 3 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8917 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/gl8.in0100644000076400007640000000121205737100334016311 0ustar mccunemccune% This is Theorem 8 from the appendix of "Automated Reasoning about Cubic % Curves", by R. Padmanabhan and W. McCune, to appear in _Computers and % Mathematics with Applications_. % % No nontrivial (gL)-algebra contains a majority function in its clone % of operations. set(para_from). set(para_into). set(para_from_vars). % set(para_into_vars). set(order_eq). set(geometric_rule). set(geometric_rewrite_before). set(lrpo). lex([a,b,f(x,x,x)]). assign(max_mem, 1500). clear(print_kept). clear(print_back_sub). list(usable). x = x. end_of_list. list(sos). f(x,x,y)=x. f(x,y,x)=x. f(y,x,x)=x. end_of_list. list(passive). a != b. end_of_list. otter-3.3f/examples/fringe/x3tricks.in0100644000076400007640000001714106007677046017413 0ustar mccunemccune% ------------------------------------------------------------------------- % Lex Demo 4 % % This is a more substantial problem based on the x^3 = x problem from % ring theory (x^3 = x implies commutativity). % % In this demo we prove only the intermediate lemma: 3xy + 3yx = E. % % In addition to lex() and special_unary(), this demo makes use of % several Otter features (e.g., age factors, conditional demodulation) % and representation tricks (e.g., coefficients, templates for polynomial % subtraction). % % Contributed by Bob Veroff. % ------------------------------------------------------------------------- % inference rules set(hyper_res). clear(order_hyper). set(para_into). set(para_from). set(para_from_left). clear(para_from_right). set(para_into_left). clear(para_into_right). % equality set(order_eq). set(dynamic_demod). assign(dynamic_demod_depth,1). assign(dynamic_demod_rhs,5). set(back_demod). clear(symbol_elim). set(lex_order_vars). % processing assign(demod_limit,250). assign(max_weight, 999). assign(max_literals, 1). % printing clear(print_kept). clear(print_back_sub). clear(print_new_demod). clear(print_back_demod). % search assign(age_factor,1). % lexical ordering of terms lex([A,B,E,MULT(x,x),INV(x),Coeff(x,x),ADD(x,x)]). special_unary([INV(x),Coeff(x,x)]). list(usable). % ring axioms EQ(ADD(x,y),ADD(y,x)). EQ(ADD(ADD(x,y),z),ADD(x,ADD(y,z))). EQ(MULT(MULT(x,y),z),MULT(x,MULT(y,z))). EQ(MULT(ADD(x,y),z),ADD(MULT(x,z),MULT(y,z))). EQ(MULT(x,ADD(y,z)),ADD(MULT(x,y),MULT(x,z))). EQ(ADD(x,E),x). EQ(ADD(E,x),x). EQ(ADD(INV(x),x),E). EQ(ADD(x,INV(x)),E). EQ(x,x). % key lemmas EQ(MULT(INV(x),y),INV(MULT(x,y))). EQ(MULT(x,INV(y)),INV(MULT(x,y))). EQ(INV(ADD(x,y)),ADD(INV(x),INV(y))). % term identification for polynomial subtraction % identify terms without coefficients TID(ADD(x,v),x,v). TID(ADD(x1,ADD(x,v)),x,ADD(x1,v)). TID(ADD(x1,ADD(x2,ADD(x,v))),x,ADD(x1,ADD(x2,v))). TID(ADD(x1,ADD(x2,ADD(x3,ADD(x,v)))),x, ADD(x1,ADD(x2,ADD(x3,v)))). TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x,v))))),x, ADD(x1,ADD(x2,ADD(x3,ADD(x4,v))))). TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,ADD(x,v)))))),x, ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,v)))))). TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,ADD(x6,ADD(x,v))))))),x, ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,ADD(x6,v))))))). % identify terms with coefficients TID(Coeff(x,z),x,Coeff(x,$DIFF(z,1))) | $NOT($INT(z)). TID(ADD(Coeff(x,z),v),x,ADD(Coeff(x,$DIFF(z,1)),v)) | $NOT($INT(z)). TID(ADD(x1,ADD(Coeff(x,z),v)),x,ADD(x1,ADD(Coeff(x,$DIFF(z,1)),v))) | $NOT($INT(z)). TID(ADD(x1,ADD(x2,ADD(Coeff(x,z),v))),x, ADD(x1,ADD(x2,ADD(Coeff(x,$DIFF(z,1)),v)))) | $NOT($INT(z)). TID(ADD(x1,ADD(x2,ADD(x3,ADD(Coeff(x,z),v)))),x, ADD(x1,ADD(x2,ADD(x3,ADD(Coeff(x,$DIFF(z,1)),v))))) | $NOT($INT(z)). TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,z),v))))),x, ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,$DIFF(z,1)),v)))))) | $NOT($INT(z)). TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,z),v))))),x, ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,$DIFF(z,1)),v)))))) | $NOT($INT(z)). % subtraction templates IDENT(x,x). -EQ(w,v) | -TID(w,x1,w1) | -TID(v,x2,v1) | -$RENAME(x1,x2) | -IDENT(x1,x2) | EQ(ADD(INV(w1),v1),E). -EQ(w,E) | -EQ(v,E) | -TID(w,x1,w1) | -TID(v,x2,v1) | -$RENAME(x1,x2) | -IDENT(x1,x2) | EQ(ADD(INV(w1),v1),E). % recognize cycles -EQ(Coeff(x,y),E) | EQ(IsCycle(x),y). end_of_list. list(sos). % special hypothesis EQ(MULT(x,MULT(x,x)),x). % denial -EQ(ADD(Coeff(MULT(A,B),3),Coeff(MULT(B,A),3)),E). end_of_list. list(demodulators). % special conditional demodulator for cycles $GT(x,IsCycle(z)) -> EQ(Coeff(z,x),Coeff(z,$MOD(x,IsCycle(z)))). % special hypothesis EQ(MULT(x,MULT(x,x)),x). % commutativity of addition EQ(ADD(x,y),ADD(y,x)). EQ(ADD(x,ADD(y,z)),ADD(y,ADD(x,z))). % associativity EQ(ADD(ADD(x,y),z),ADD(x,ADD(y,z))). EQ(MULT(MULT(x,y),z),MULT(x,MULT(y,z))). % distributivity EQ(MULT(ADD(x,y),z),ADD(MULT(x,z),MULT(y,z))). EQ(MULT(x,ADD(y,z)),ADD(MULT(x,y),MULT(x,z))). % identity EQ(ADD(x,E),x). EQ(ADD(E,x),x). EQ(MULT(E,x),E). EQ(MULT(x,E),E). EQ(INV(E),E). % INV simplification and canonicalization EQ(INV(INV(x)),x). EQ(MULT(x,INV(y)),INV(MULT(x,y))). EQ(MULT(INV(x),y),INV(MULT(x,y))). EQ(INV(ADD(x,y)),ADD(INV(x),INV(y))). EQ(INV(Coeff(x,y)),Coeff(INV(x),y)). % INV cancellation EQ(ADD(x,INV(x)),E). EQ(ADD(x,ADD(INV(x),y)),y). % coefficients EQ(ADD(x,x),Coeff(x,2)). $INT(y) -> EQ(ADD(x,Coeff(x,y)),Coeff(x,$SUM(y,1))). $AND($INT(y),$INT(z)) -> EQ(ADD(Coeff(x,y),Coeff(x,z)),Coeff(x,$SUM(y,z))). EQ(ADD(x,ADD(x,y)),ADD(Coeff(x,2),y)). $INT(y) -> EQ(ADD(x,ADD(Coeff(x,y),z)),ADD(Coeff(x,$SUM(y,1)),z)). $AND($INT(y),$INT(z)) -> EQ(ADD(Coeff(x,y),ADD(Coeff(x,z),v)),ADD(Coeff(x,$SUM(y,z)),v)). % nested coefficients $AND($INT(y),$INT(z)) -> EQ(Coeff(Coeff(x,y),z),Coeff(x,$PROD(y,z))). % simplification and canonicalization with coefficients EQ(Coeff(E,x),E). EQ(Coeff(x,0),E). EQ(Coeff(x,1),x). EQ(MULT(x,Coeff(y,z)),Coeff(MULT(x,y),z)). EQ(MULT(Coeff(x,z),y),Coeff(MULT(x,y),z)). EQ(Coeff(ADD(x,y),z),ADD(Coeff(x,z),Coeff(y,z))). % ordinary INV cancellation with coefficients $INT(y) -> EQ(ADD(x,Coeff(INV(x),y)),Coeff(INV(x),$DIFF(y,1))). $INT(y) -> EQ(ADD(INV(x),Coeff(x,y)),Coeff(x,$DIFF(y,1))). EQ(ADD(Coeff(x,y),Coeff(INV(x),y)),E). $AND($INT(y),$AND($INT(z),$GT(y,z))) -> EQ(ADD(Coeff(x,y),Coeff(INV(x),z)),Coeff(x,$DIFF(y,z))). $AND($INT(y),$AND($INT(z),$GT(z,y))) -> EQ(ADD(Coeff(x,y),Coeff(INV(x),z)),Coeff(INV(x),$DIFF(z,y))). $INT(y) -> EQ(ADD(x,ADD(Coeff(INV(x),y),zzz)),ADD(Coeff(INV(x),$DIFF(y,1)),zzz)). $INT(y) -> EQ(ADD(INV(x),ADD(Coeff(x,y),zzz)),ADD(Coeff(x,$DIFF(y,1)),zzz)). EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),y),zzz)),zzz). $AND($INT(y),$AND($INT(z),$GT(y,z))) -> EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),z),zzz)),ADD(Coeff(x,$DIFF(y,z)),zzz)). $AND($INT(y),$AND($INT(z),$GT(z,y))) -> EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),z),zzz)),ADD(Coeff(INV(x),$DIFF(z,y)),zzz)). % ******************** % Literal Demodulators % ******************** % subtraction by demodulation (complex terms) EQ(EQ(ADD(x,y),ADD(u,v)),EQ(ADD(INV(ADD(u,v)),ADD(x,y)),E)). EQ(EQ(ADD(x,y),MULT(u,v)),EQ(ADD(INV(MULT(u,v)),ADD(x,y)),E)). EQ(EQ(ADD(x,y),INV(u)),EQ(ADD(u,ADD(x,y)),E)). EQ(EQ(ADD(x,y),Coeff(u,v)),EQ(ADD(INV(Coeff(u,v)),ADD(x,y)),E)). % prefer non inverse form EQ(EQ(INV(x),E),EQ(x,E)). % normalize so leftmost term non INV EQ(EQ(ADD(INV(x),y),E),EQ(ADD(x,INV(y)),E)). EQ(EQ(ADD(Coeff(INV(x),y),z),E),EQ(ADD(Coeff(x,y),INV(z)),E)). % literal demodulation takes place before equality ordering EQ(EQ(MULT(u,v),ADD(x,y)),EQ(ADD(INV(MULT(u,v)),ADD(x,y)),E)). EQ(EQ(INV(u),ADD(x,y)),EQ(ADD(u,ADD(x,y)),E)). EQ(EQ(Coeff(u,v),ADD(x,y)),EQ(ADD(INV(Coeff(u,v)),ADD(x,y)),E)). EQ(EQ(E,INV(x)),EQ(x,E)). EQ(EQ(E,ADD(INV(x),y)),EQ(ADD(x,INV(y)),E)). EQ(EQ(E,ADD(Coeff(INV(x),y),z)),EQ(ADD(Coeff(x,y),INV(z)),E)). end_of_list. weight_list(pick_given). weight(EQ(Coeff($(1),$(1)),E), -100). end_of_list. weight_list(purge_gen). weight(MULT($(1),MULT($(1),MULT($(1),MULT($(1),$(1))))), 9999). weight(ADD($(1),ADD($(1),ADD($(1),ADD($(1),ADD($(1),ADD($(1),$(1))))))), 9999). weight(Coeff(Coeff($(1),$(1)),$(1)),9999). weight(TID($(1),$(1),$(1)),9999). end_of_list. weight_list(terms). % for equality ordering, want polynomial = term weight(ADD($(1),$(1)),+10). end_of_list. otter-3.3f/examples/fringe/lexical2.in0100644000076400007640000000245306007700674017336 0ustar mccunemccune% ------------------------------------------------------------------------- % Lex Demo 2 % % Demonstrate lex() and special_unary(). % % Include other demodulators, such as cancellation. % % Contributed by Bob Veroff. % ------------------------------------------------------------------------- % inference rule set(binary_res). % include variables in lexical ordering set(lex_order_vars). % processing assign(max_given, 1). % lexical ordering of terms lex([0,a,b,c,d,e,add(x,x)]). special_unary([neg(x)]). list(usable). % negated complex terms -dum | P1(neg(add(c,add(neg(add(a,neg(b))),add(e,neg(d)))))). % simple cancellation -dum | P2(add(add(neg(a),b),add(neg(b),add(add(b,neg(b)),add(a,b))))). % combine previous two examples -dum | P3(add(add(neg(a),b),neg(add(neg(b),add(add(b,neg(b)),add(a,b)))))). end_of_list. list(sos). dum. end_of_list. list(demodulators). % commutativity EQ(add(x,y),add(y,x)). EQ(add(x,add(y,z)),add(y,add(x,z))). % associativity EQ(add(add(x,y),z),add(x,add(y,z))). % move negation inside EQ(neg(add(x,y)),add(neg(x),neg(y))). % identity EQ(add(0,x),x). % simplification EQ(neg(neg(x)),x). % cancellation (we can assume neg(x) is to the right of x) EQ(add(x,neg(x)),0). EQ(add(x,add(neg(x),y)),y). end_of_list. otter-3.3f/examples/fringe/if.in0100644000076400007640000000711106007762736016234 0ustar mccunemccune% This input file can be used to rewrite Boolean expressions into % canonical if-then-else form. It should rewrite tautologies to 1 % and unsatisfiable expressions to 0. The result is like an OBDD % (ordered binary decision diagram); it is not very fast, because it % is done with ordinary rewriting, not with the fast OBDD algorithms % (structure sharing, caching, etc.). % % The propositional "variables" in the expressions to be % rewritten can be either (Otter) variables, constants, or a % mixture. If variables are included, the flag lex_order_vars % must be set % % The built-in ordering relation has variables < constants, with % variables ordered by variable number and constants ordered by % the C library strcmp() function. The constant ordering can be % changed with a lex command, e.g., lex([b,c,a]) means that b < c < a, % variables are still smaller, and other constants are bigger. % % There is something tricky going on here, but I think it is % correct. There are two if-then-else operators: if(x,y,z) is % the external form, and ite(x,y,z) is the internal form. The % internal form has the property that it NEVER has propositional % variables in the second or third argument. This property % speeds up the rewriting. If the expression to be rewritten % has if-then-else, if(x,y,z) should be used. These are rewritten % right away to the ite(x,y,z) form, and the rest of the rewriting is % done in terms of ite(x,y,z). % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Declare Boolean operations as infix or prefix. % This is for parsing and printing only. % Note that the defaults for & and | are overridden. op(400, fx, ~). op(450, xfy, #). % exclusive or op(450, xfy, |). op(460, xfy, &). op(470, xfx, -->). op(480, xfx, <-->). make_evaluable(_>_, $LGT(_,_)). list(demodulators). % Define ordinary Boolean operations in terms of if(_,_,_). if(x,y,z) = ite(x,ite(y,1,0),ite(z,1,0)). x & y = ite(x,ite(y,1,0),0). x | y = ite(x,1,ite(y,1,0)). ~x = ite(x,0,1). x --> y = ~x | y. x <--> y = (x --> y) & (y --> x). x # y = ~(x <--> y). % These can speed things up, because they are applied first. x <--> x = 1. x --> x = 1. x & x = x. x | x = x. x # x = 0. % The rest of the rules rewrite ite-expressions into canonical form. % basic simplification ite(x,y,y) = y. ite(1,x,y) = x. ite(0,x,y) = y. % move if-expressions out of conditions ite(ite(x,y,z),u,v) = ite(x,ite(y,u,v),ite(z,u,v)). % collapse conditions ite(x,ite(x,y,z),w) = ite(x,y,w). ite(x,w,ite(x,y,z)) = ite(x,w,z). % sort on conditions (x1 > x2) -> ite(x1,ite(x2,y,z),w) = ite(x2,ite(x1,y,w),ite(x1,z,w)). (x1 > x2) -> ite(x1,w,ite(x2,y,z)) = ite(x2,ite(x1,w,y),ite(x1,w,z)). end_of_list. set(demod_inf). % the "inference rule" clear(demod_history). % we don't want to see a list of 44775 integers assign(demod_limit, -1). % no limit set(sos_queue). assign(max_given, 4). set(lex_order_vars). set(pretty_print). % Here are the expressions to be rewritten. list(sos). P1((A & (B | C)) <--> ((A & B) | (A & C))). % Distributivity (=1) P2(~(~x | ~y) | ~(~x | y) <--> x). % Huntington identity (=1) P3(if(D,if(C,if(A,B,I),if(E,F,G)),H)). P4( ((a2# (b2# (1# (a2&b2))))# ((a3#b3)# (1# (a0# (b0# (1# (a0&b0))))))) <--> if(a0,if(a2,if(a3,if(b3,1,0),if(b3,0,1)),if(a3,if(b2,if(b3,1,0), if(b3,0,1)),if(b2,if(b3,0,1),if(b3,1,0)))),if(a2,if(a3,if(b0, if(b3,1,0),if(b3,0,1)),if(b0,if(b3,0,1),if(b3,1,0))),if(a3, if(b0,if(b2,if(b3,1,0),if(b3,0,1)),if(b2,if(b3,0,1),if(b3,1,0))), if(b0,if(b2,if(b3,0,1),if(b3,1,0)),if(b2,if(b3,1,0),if(b3,0,1)))))) ). end_of_list. otter-3.3f/examples/fringe/lexical3.out0100664000076400007640000000471210103522222017521 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8927. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(lex_order_vars). assign(max_given,1). lex([a,b,c,d,e,C1,C2,C3,C4,C5,C6,neg(x),coeff(x,x),add(x,x)]). special_unary([neg(x),coeff(x,x)]). list(usable). 1 [] -dum|P(add(a,add(b,add(coeff(neg(c),C6),add(neg(a),add(neg(b),add(coeff(c,C5),add(coeff(a,C1),add(coeff(b,C2),add(neg(c),add(coeff(neg(a),C3),add(coeff(neg(b),C4),add(c,coeff(neg(a),C2)))))))))))))). end_of_list. list(sos). 2 [] dum. end_of_list. list(demodulators). 3 [] EQ(add(x,y),add(y,x)). 4 [] EQ(add(x,add(y,z)),add(y,add(x,z))). 5 [] EQ(add(add(x,y),z),add(x,add(y,z))). end_of_list. lex dependent demodulator: 3 [] EQ(add(x,y),add(y,x)). lex dependent demodulator: 4 [] EQ(add(x,add(y,z)),add(y,add(x,z))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=1) 2 [] dum. Search stopped by max_given option. ** KEPT (pick-wt=47): 6 [binary,2.1,1.1,demod,3,4,4,4,4,4,3,4,4,4,4,4,4,4,4,3,4,4,4,4,4,4,4,4,4,4,4,4,3,4,4,4,4] P(add(a,add(neg(a),add(coeff(a,C1),add(coeff(neg(a),C2),add(coeff(neg(a),C3),add(b,add(neg(b),add(coeff(b,C2),add(coeff(neg(b),C4),add(c,add(neg(c),add(coeff(c,C5),coeff(neg(c),C6)))))))))))))). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 1 clauses generated 1 binary_res generated 1 factors generated 0 demod & eval rewrites 33 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 1 new demodulators 0 empty clauses 0 clauses back demodulated 0 clauses back subsumed 0 usable size 2 sos size 1 demodulators size 3 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8927 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/lexical2.out0100664000076400007640000000507610103522222017524 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8922. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(lex_order_vars). assign(max_given,1). lex([0,a,b,c,d,e,add(x,x)]). special_unary([neg(x)]). list(usable). 1 [] -dum|P1(neg(add(c,add(neg(add(a,neg(b))),add(e,neg(d)))))). 2 [] -dum|P2(add(add(neg(a),b),add(neg(b),add(add(b,neg(b)),add(a,b))))). 3 [] -dum|P3(add(add(neg(a),b),neg(add(neg(b),add(add(b,neg(b)),add(a,b)))))). end_of_list. list(sos). 4 [] dum. end_of_list. list(demodulators). 5 [] EQ(add(x,y),add(y,x)). 6 [] EQ(add(x,add(y,z)),add(y,add(x,z))). 7 [] EQ(add(add(x,y),z),add(x,add(y,z))). 8 [] EQ(neg(add(x,y)),add(neg(x),neg(y))). 9 [] EQ(add(0,x),x). 10 [] EQ(neg(neg(x)),x). 11 [] EQ(add(x,neg(x)),0). 12 [] EQ(add(x,add(neg(x),y)),y). end_of_list. lex dependent demodulator: 5 [] EQ(add(x,y),add(y,x)). lex dependent demodulator: 6 [] EQ(add(x,add(y,z)),add(y,add(x,z))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=1) 4 [] dum. Search stopped by max_given option. ** KEPT (pick-wt=8): 13 [binary,4.1,3.1,demod,11,9,6,5,11,5,9,5] P3(add(neg(a),add(neg(a),b))). ** KEPT (pick-wt=2): 14 [binary,4.1,2.1,demod,11,9,6,5,11,5,9,5,12] P2(b). ** KEPT (pick-wt=13): 15 [binary,4.1,1.1,demod,8,10,5,6,5,6,5,6,6,6,6,8,10,8,8,8,10] P1(add(a,add(neg(b),add(neg(c),add(d,neg(e)))))). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 1 clauses generated 3 binary_res generated 3 factors generated 0 demod & eval rewrites 34 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 3 new demodulators 0 empty clauses 0 clauses back demodulated 0 clauses back subsumed 0 usable size 4 sos size 3 demodulators size 8 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8922 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/mfl_13.out0100664000076400007640000002723110103522222017077 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8937. op(400,xfx,*). set(para_into). set(para_from). set(order_eq). set(dynamic_demod). set(process_input). set(demod_out_in). set(lrpo). lex([$T,A,B,C,D,E,1,_*_,rs(_,_),ls(_,_),_=_]). assign(max_weight,20). assign(pick_given_ratio,3). assign(max_proofs,2). assign(max_mem,20000). clear(print_kept). clear(print_new_demod). list(usable). 0 [] x=x. 0 [] x*rs(x,y)=y. 0 [] rs(x,x*y)=y. 0 [] ls(x,y)*y=x. 0 [] ls(x*y,y)=x. 0 [] 1*x=x. 0 [] x*1=x. end_of_list. list(sos). 0 [] (x*y)* (z*x)= (x* (y*z))*x. 0 [] A* (B* (A*C))!= ((A*B)*A)*C|$ANS(Moufang_3). end_of_list. list(demodulators). 1 [] EQ(((x*y)*z)*y=x* (y* (z*y)),$T). 2 [] EQ(x* (y* (z*y))= ((x*y)*z)*y,$T). end_of_list. list(hot). 3 [] (x*y)* (z*x)= (x* (y*z))*x. 4 [] x*rs(x,y)=y. 5 [] rs(x,x*y)=y. 6 [] ls(x,y)*y=x. 7 [] ls(x*y,y)=x. 8 [] 1*x=x. 9 [] x*1=x. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 10 [] x=x. ** KEPT (pick-wt=7): 11 [] x*rs(x,y)=y. ---> New Demodulator: 12 [new_demod,11] x*rs(x,y)=y. ** KEPT (pick-wt=7): 13 [] rs(x,x*y)=y. ---> New Demodulator: 14 [new_demod,13] rs(x,x*y)=y. ** KEPT (pick-wt=7): 15 [] ls(x,y)*y=x. ---> New Demodulator: 16 [new_demod,15] ls(x,y)*y=x. ** KEPT (pick-wt=7): 17 [] ls(x*y,y)=x. ---> New Demodulator: 18 [new_demod,17] ls(x*y,y)=x. ** KEPT (pick-wt=5): 19 [] 1*x=x. ---> New Demodulator: 20 [new_demod,19] 1*x=x. ** KEPT (pick-wt=5): 21 [] x*1=x. ---> New Demodulator: 22 [new_demod,21] x*1=x. ------------> process sos: ** KEPT (pick-wt=15): 24 [copy,23,flip.1] (x* (y*z))*x= (x*y)* (z*x). ---> New Demodulator: 25 [new_demod,24] (x* (y*z))*x= (x*y)* (z*x). ** KEPT (pick-wt=15): 27 [copy,26,flip.1] ((A*B)*A)*C!=A* (B* (A*C))|$ANS(Moufang_3). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=15) 24 [copy,23,flip.1] (x* (y*z))*x= (x*y)* (z*x). 73 back subsumes 52. 83 back subsumes 45. given clause #2: (wt=7) 128 (heat=1) [para_into,116.1.1.2.1,9.1.1,demod,72,20] rs(x,x)*y=y. 138 back subsumes 126. given clause #3: (wt=5) 138 [para_into,128.1.1,21.1.1] rs(x,x)=1. given clause #4: (wt=5) 140 [para_into,128.1.1,11.1.1,demod,139,flip.1] rs(1,x)=x. given clause #5: (wt=15) 27 [copy,26,flip.1] ((A*B)*A)*C!=A* (B* (A*C))|$ANS(Moufang_3). given clause #6: (wt=5) 142 [para_from,128.1.1,17.1.1.1,demod,139] ls(x,x)=1. given clause #7: (wt=9) 81 (heat=1) [para_into,36.1.1.2,9.1.1,demod,20,22] rs(1,x)*y=x*y. given clause #8: (wt=9) 90 (heat=1) [para_into,38.1.1.2,9.1.1,demod,20,20] x*ls(y,1)=x*y. 145 back subsumes 118. given clause #9: (wt=11) 28 [para_into,24.1.1.1.2,19.1.1,demod,22] (x*y)*x=x* (y*x). given clause #10: (wt=5) 145 [para_into,90.1.1,128.1.1,demod,129] ls(x,1)=x. given clause #11: (wt=11) 42 (heat=1) [para_into,28.1.1.1,4.1.1,flip.1] x* (rs(x,y)*x)=y*x. 178 back subsumes 166. 188 back subsumes 178. given clause #12: (wt=7) 202 (heat=1) [para_into,176.1.1.2,8.1.1,demod,139,flip.1] rs(x,1)*x=1. given clause #13: (wt=15) 30 [para_into,24.1.1.1.2,15.1.1,demod,29,flip.1] (x*ls(y,z))* (z*x)=x* (y*x). given clause #14: (wt=7) 213 [para_from,202.1.1,17.1.1.1] ls(1,x)=rs(x,1). given clause #15: (wt=7) 215 [para_from,202.1.1,13.1.1.2] rs(rs(x,1),1)=x. given clause #16: (wt=7) 248 (heat=1) [para_into,246.1.1,9.1.1,demod,22] rs(ls(x,y),x)=y. given clause #17: (wt=15) 32 [para_into,24.1.1.1.2,11.1.1,demod,29,flip.1] (x*y)* (rs(y,z)*x)=x* (z*x). given clause #18: (wt=9) 194 (heat=1) [para_into,174.1.1.1,8.1.1] ls(x,rs(x,1)*x)=x. given clause #19: (wt=9) 221 (heat=1) [para_from,207.1.1,5.1.1.2,demod,14,flip.1] (x*rs(y,1))*y=x. 304 back subsumes 237. 304 back subsumes 235. given clause #20: (wt=9) 244 (heat=1) [para_from,211.1.2,7.1.1.1,demod,47] rs(x,1)* (x*y)=y. given clause #21: (wt=19) 34 [para_into,24.1.2.1,15.1.1,demod,29] ls(x,y)* ((y*z)*ls(x,y))=x* (z*ls(x,y)). given clause #22: (wt=9) 255 (heat=1) [para_from,250.1.1,7.1.1.1,demod,47] rs(x,1)*y=rs(x,y). 444 back subsumes 421. given clause #23: (wt=9) 262 [para_into,221.1.1.1.2,248.1.1,demod,214] (x*y)*rs(y,1)=x. given clause #24: (wt=9) 266 [para_into,221.1.1.1,15.1.1,flip.1] ls(x,rs(y,1))=x*y. given clause #25: (wt=15) 36 [para_into,24.1.2.1,11.1.1,demod,29] x* ((rs(x,y)*z)*x)=y* (z*x). given clause #26: (wt=9) 270 (heat=1) [para_into,262.1.1.1,6.1.1,flip.1] ls(x,y)=x*rs(y,1). given clause #27: (wt=9) 272 (heat=1) [para_into,262.1.1.1,4.1.1] x*rs(rs(y,x),1)=y. given clause #28: (wt=9) 278 (heat=1) [para_from,262.1.1,5.1.1.2] rs(x*y,x)=rs(y,1). given clause #29: (wt=15) 38 [para_into,24.1.2.2,15.1.1,demod,29] x* ((y*ls(z,x))*x)= (x*y)*z. -------- PROOF -------- 586 [binary,584.1,144.1] $ANS(Moufang_3). ----> UNIT CONFLICT at 0.08 sec ----> 586 [binary,584.1,144.1] $ANS(Moufang_3). Length of proof is 34. Level of proof is 14. ---------------- PROOF ---------------- 4 [] x*rs(x,y)=y. 5 [] rs(x,x*y)=y. 6 [] ls(x,y)*y=x. 7 [] ls(x*y,y)=x. 8 [] 1*x=x. 9 [] x*1=x. 11 [] x*rs(x,y)=y. 14,13 [] rs(x,x*y)=y. 15 [] ls(x,y)*y=x. 17 [] ls(x*y,y)=x. 20,19 [] 1*x=x. 22,21 [] x*1=x. 23 [] (x*y)* (z*x)= (x* (y*z))*x. 24 [copy,23,flip.1] (x* (y*z))*x= (x*y)* (z*x). 26 [] A* (B* (A*C))!= ((A*B)*A)*C|$ANS(Moufang_3). 27 [copy,26,flip.1] ((A*B)*A)*C!=A* (B* (A*C))|$ANS(Moufang_3). 29,28 [para_into,24.1.1.1.2,19.1.1,demod,22] (x*y)*x=x* (y*x). 30 [para_into,24.1.1.1.2,15.1.1,demod,29,flip.1] (x*ls(y,z))* (z*x)=x* (y*x). 32 [para_into,24.1.1.1.2,11.1.1,demod,29,flip.1] (x*y)* (rs(y,z)*x)=x* (z*x). 36 [para_into,24.1.2.1,11.1.1,demod,29] x* ((rs(x,y)*z)*x)=y* (z*x). 38 [para_into,24.1.2.2,15.1.1,demod,29] x* ((y*ls(z,x))*x)= (x*y)*z. 42 (heat=1) [para_into,28.1.1.1,4.1.1,flip.1] x* (rs(x,y)*x)=y*x. 47,46 (heat=1) [para_from,28.1.1,7.1.1.1] ls(x* (y*x),x)=x*y. 72,71 (heat=1) [para_from,32.1.1,5.1.1.2] rs(x*y,x* (z*x))=rs(y,z)*x. 82,81 (heat=1) [para_into,36.1.1.2,9.1.1,demod,20,22] rs(1,x)*y=x*y. 116 [para_from,24.1.1,13.1.1.2] rs(x* (y*z),(x*y)* (z*x))=x. 129,128 (heat=1) [para_into,116.1.1.2.1,9.1.1,demod,72,20] rs(x,x)*y=y. 139,138 [para_into,128.1.1,21.1.1] rs(x,x)=1. 144 [para_from,81.1.2,27.1.2.2.2,demod,29,82] (A* (B*A))*C!=A* (B* (A*C))|$ANS(Moufang_3). 176 [para_from,42.1.1,13.1.1.2] rs(x,y*x)=rs(x,y)*x. 202 (heat=1) [para_into,176.1.1.2,8.1.1,demod,139,flip.1] rs(x,1)*x=1. 207 [para_from,202.1.1,24.1.2.2,demod,29,22] x* ((y*rs(x,1))*x)=x*y. 211 [para_from,202.1.1,24.1.2.1,demod,29,20] rs(x,1)* ((x*y)*rs(x,1))=y*rs(x,1). 214,213 [para_from,202.1.1,17.1.1.1] ls(1,x)=rs(x,1). 221 (heat=1) [para_from,207.1.1,5.1.1.2,demod,14,flip.1] (x*rs(y,1))*y=x. 244 (heat=1) [para_from,211.1.2,7.1.1.1,demod,47] rs(x,1)* (x*y)=y. 246 [para_from,30.1.1,13.1.1.2,demod,72] rs(ls(x,y),x)*z=y*z. 248 (heat=1) [para_into,246.1.1,9.1.1,demod,22] rs(ls(x,y),x)=y. 262 [para_into,221.1.1.1.2,248.1.1,demod,214] (x*y)*rs(y,1)=x. 271,270 (heat=1) [para_into,262.1.1.1,6.1.1,flip.1] ls(x,y)=x*rs(y,1). 272 (heat=1) [para_into,262.1.1.1,4.1.1] x*rs(rs(y,x),1)=y. 316 [para_into,244.1.1.1,248.1.1,demod,271,20] x* (rs(x,1)*y)=y. 331,330 (heat=1) [para_into,316.1.1.2,4.1.1,flip.1] rs(rs(x,1),y)=x*y. 380 [para_from,244.1.1,17.1.1.1,demod,271] x*rs(y*x,1)=rs(y,1). 396,395 (heat=1) [para_from,380.1.1,5.1.1.2,flip.1] rs(x*y,1)=rs(y,rs(x,1)). 526,525 [para_from,272.1.1,244.1.1.2,flip.1] rs(rs(x,y),1)=rs(y,1)*x. 573 [para_from,38.1.2,221.1.1.1,demod,271] (x* ((y* (rs(z,1)*rs(x,1)))*x))*z=x*y. 584 (heat=1) [para_into,573.1.1.1.2.1,6.1.1,demod,271,396,331,526,129] (x* (y*x))*z=x* (y* (x*z)). 586 [binary,584.1,144.1] $ANS(Moufang_3). ------------ end of proof ------------- given clause #30: (wt=9) 316 [para_into,244.1.1.1,248.1.1,demod,271,20] x* (rs(x,1)*y)=y. given clause #31: (wt=9) 330 (heat=1) [para_into,316.1.1.2,4.1.1,flip.1] rs(rs(x,1),y)=x*y. -------- PROOF -------- 615 [binary,614.1,10.1] $ANS(Moufang_3). ----> UNIT CONFLICT at 0.09 sec ----> 615 [binary,614.1,10.1] $ANS(Moufang_3). Length of proof is 32. Level of proof is 15. ---------------- PROOF ---------------- 4 [] x*rs(x,y)=y. 5 [] rs(x,x*y)=y. 6 [] ls(x,y)*y=x. 7 [] ls(x*y,y)=x. 8 [] 1*x=x. 9 [] x*1=x. 10 [] x=x. 11 [] x*rs(x,y)=y. 14,13 [] rs(x,x*y)=y. 15 [] ls(x,y)*y=x. 17 [] ls(x*y,y)=x. 20,19 [] 1*x=x. 22,21 [] x*1=x. 23 [] (x*y)* (z*x)= (x* (y*z))*x. 24 [copy,23,flip.1] (x* (y*z))*x= (x*y)* (z*x). 26 [] A* (B* (A*C))!= ((A*B)*A)*C|$ANS(Moufang_3). 27 [copy,26,flip.1] ((A*B)*A)*C!=A* (B* (A*C))|$ANS(Moufang_3). 29,28 [para_into,24.1.1.1.2,19.1.1,demod,22] (x*y)*x=x* (y*x). 30 [para_into,24.1.1.1.2,15.1.1,demod,29,flip.1] (x*ls(y,z))* (z*x)=x* (y*x). 32 [para_into,24.1.1.1.2,11.1.1,demod,29,flip.1] (x*y)* (rs(y,z)*x)=x* (z*x). 38 [para_into,24.1.2.2,15.1.1,demod,29] x* ((y*ls(z,x))*x)= (x*y)*z. 42 (heat=1) [para_into,28.1.1.1,4.1.1,flip.1] x* (rs(x,y)*x)=y*x. 47,46 (heat=1) [para_from,28.1.1,7.1.1.1] ls(x* (y*x),x)=x*y. 72,71 (heat=1) [para_from,32.1.1,5.1.1.2] rs(x*y,x* (z*x))=rs(y,z)*x. 116 [para_from,24.1.1,13.1.1.2] rs(x* (y*z),(x*y)* (z*x))=x. 129,128 (heat=1) [para_into,116.1.1.2.1,9.1.1,demod,72,20] rs(x,x)*y=y. 139,138 [para_into,128.1.1,21.1.1] rs(x,x)=1. 176 [para_from,42.1.1,13.1.1.2] rs(x,y*x)=rs(x,y)*x. 202 (heat=1) [para_into,176.1.1.2,8.1.1,demod,139,flip.1] rs(x,1)*x=1. 207 [para_from,202.1.1,24.1.2.2,demod,29,22] x* ((y*rs(x,1))*x)=x*y. 211 [para_from,202.1.1,24.1.2.1,demod,29,20] rs(x,1)* ((x*y)*rs(x,1))=y*rs(x,1). 214,213 [para_from,202.1.1,17.1.1.1] ls(1,x)=rs(x,1). 221 (heat=1) [para_from,207.1.1,5.1.1.2,demod,14,flip.1] (x*rs(y,1))*y=x. 244 (heat=1) [para_from,211.1.2,7.1.1.1,demod,47] rs(x,1)* (x*y)=y. 246 [para_from,30.1.1,13.1.1.2,demod,72] rs(ls(x,y),x)*z=y*z. 248 (heat=1) [para_into,246.1.1,9.1.1,demod,22] rs(ls(x,y),x)=y. 262 [para_into,221.1.1.1.2,248.1.1,demod,214] (x*y)*rs(y,1)=x. 271,270 (heat=1) [para_into,262.1.1.1,6.1.1,flip.1] ls(x,y)=x*rs(y,1). 272 (heat=1) [para_into,262.1.1.1,4.1.1] x*rs(rs(y,x),1)=y. 316 [para_into,244.1.1.1,248.1.1,demod,271,20] x* (rs(x,1)*y)=y. 331,330 (heat=1) [para_into,316.1.1.2,4.1.1,flip.1] rs(rs(x,1),y)=x*y. 380 [para_from,244.1.1,17.1.1.1,demod,271] x*rs(y*x,1)=rs(y,1). 396,395 (heat=1) [para_from,380.1.1,5.1.1.2,flip.1] rs(x*y,1)=rs(y,rs(x,1)). 526,525 [para_from,272.1.1,244.1.1.2,flip.1] rs(rs(x,y),1)=rs(y,1)*x. 573 [para_from,38.1.2,221.1.1.1,demod,271] (x* ((y* (rs(z,1)*rs(x,1)))*x))*z=x*y. 585,584 (heat=1) [para_into,573.1.1.1.2.1,6.1.1,demod,271,396,331,526,129] (x* (y*x))*z=x* (y* (x*z)). 614 [para_from,330.1.2,27.1.2.2.2,demod,29,585,331] A* (B* (A*C))!=A* (B* (A*C))|$ANS(Moufang_3). 615 [binary,614.1,10.1] $ANS(Moufang_3). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 31 clauses generated 3887 (hot clauses generated) 1918 para_from generated 1809 para_into generated 2078 demod & eval rewrites 8511 clauses wt,lit,sk delete 885 tautologies deleted 0 clauses forward subsumed 2676 (subsumed by sos) 348 unit deletions 0 factor simplifications 0 clauses kept 335 (hot clauses kept) 247 new demodulators 267 empty clauses 2 clauses back demodulated 0 clauses back subsumed 9 usable size 38 sos size 288 demodulators size 269 passive size 0 hot size 7 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.09 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8937 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/gl8.out0100664000076400007640000000527010103522222016507 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8907. set(para_from). set(para_into). set(para_from_vars). set(order_eq). set(geometric_rule). set(geometric_rewrite_before). set(lrpo). lex([a,b,f(x,x,x)]). assign(max_mem,1500). clear(print_kept). clear(print_back_sub). list(usable). 1 [] x=x. end_of_list. list(sos). 2 [] f(x,x,y)=x. 3 [] f(x,y,x)=x. 4 [] f(y,x,x)=x. end_of_list. list(passive). 5 [] a!=b. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=6) 2 [] f(x,x,y)=x. given clause #2: (wt=6) 3 [] f(x,y,x)=x. given clause #3: (wt=6) 4 [] f(y,x,x)=x. given clause #4: (wt=12) 6 [para_into,2.1.1,2.1.2] f(f(x,x,y),f(x,x,y),z)=x. given clause #5: (wt=18) 16 [para_into,6.1.1.1,6.1.1,gL-id] f(x,f(f(y,y,z),f(y,y,z),u),v)=f(x,y,z). given clause #6: (wt=6) 65 [para_into,16.1.1,3.1.1,flip.1] f(x,y,z)=x. -------- PROOF -------- ----> UNIT CONFLICT at 0.01 sec ----> 83 [binary,82.1,5.1] $F. Length of proof is 4. Level of proof is 4. ---------------- PROOF ---------------- 2 [] f(x,x,y)=x. 3 [] f(x,y,x)=x. 4 [] f(y,x,x)=x. 5 [] a!=b. 6 [para_into,2.1.1,2.1.2] f(f(x,x,y),f(x,x,y),z)=x. 16 [para_into,6.1.1.1,6.1.1,gL-id] f(x,f(f(y,y,z),f(y,y,z),u),v)=f(x,y,z). 65 [para_into,16.1.1,3.1.1,flip.1] f(x,y,z)=x. 82 [para_into,65.1.1,4.1.1] x=y. 83 [binary,82.1,5.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 6 clauses generated 138 para_from generated 42 para_into generated 94 gL rule generated 2 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 61 (subsumed by sos) 34 unit deletions 0 factor simplifications 0 clauses kept 77 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 7 usable size 5 sos size 69 demodulators size 0 passive size 1 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8907 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/mfl_13.in0100644000076400007640000000273407313705217016715 0ustar mccunemccune% The problem is % % Loop, Moufang-1 -> Moufang-3 % % where the proof does not go through Moufang-2. % The strategy involves the hot list and literal demodulation. % % This input file was contributed by Larry Wos (wos@mcs.anl.gov). op(400,xfx, *). % make all association explicit set(para_into). set(para_from). set(order_eq). set(dynamic_demod). set(process_input). set(demod_out_in). set(lrpo). lex([$T,A,B,C,D,E,1,_*_,rs(_,_),ls(_,_),=(_,_)]). assign(max_weight,20). assign(pick_given_ratio,3). assign(max_proofs,2). assign(max_mem,20000). clear(print_kept). clear(print_new_demod). list(usable). x = x. x * rs(x,y) = y. % right solvable rs(x,x * y) = y. % right solution is unique (implies left cancellation) ls(x,y) * y = x. % left solvable ls(x * y,y) = x. % left solution is unique (implies right cancellation) 1 * x = x. x * 1 = x. end_of_list. list(sos). (x * y) * (z * x) = (x * (y * z)) * x. % Moufang_1 A * (B * (A * C)) != ((A * B) * A) * C | $ANS(Moufang_3). end_of_list. list(demodulators). % Blocking use of Moufang 2. EQ(( ((x * y) * z) * y = x * (y * (z * y)) ), $T). EQ(( x * (y * (z * y)) = ((x * y) * z) * y ), $T). end_of_list. list(hot). (x * y) * (z * x) = (x * (y * z)) * x. % Moufang_1 x * rs(x,y) = y. % right solvable rs(x,x * y) = y. % right solution is unique (implies left cancellation) ls(x,y) * y = x. % left solvable ls(x * y,y) = x. % left solution is unique (implies right cancellation) 1 * x = x. x * 1 = x. end_of_list. otter-3.3f/examples/fringe/gl4.out0100664000076400007640000001405110103522222016500 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8902. set(para_from). set(para_into). set(order_eq). set(geometric_rule). set(geometric_rewrite_before). set(lrpo). lex([A,B,C,D,E,F,e,f(x,x),g(x)]). assign(pick_given_ratio,1). assign(max_weight,17). clear(print_kept). list(usable). 1 [] x=x. end_of_list. list(sos). 2 [] f(x,f(e,x))=e. end_of_list. list(passive). 3 [] f(f(A,B),f(C,D))!=f(f(A,C),f(B,D)). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=7) 2 [] f(x,f(e,x))=e. given clause #2: (wt=7) 5 [para_into,2.1.1.2,2.1.1] f(f(e,e),e)=e. given clause #3: (wt=11) 4 [para_into,2.1.1.2.1,2.1.2] f(x,f(f(y,f(e,y)),x))=e. given clause #4: (wt=11) 6 [para_into,2.1.2,2.1.2,gL-id] f(x,f(y,x))=f(z,f(y,z)). 30 back subsumes 13. 33 back subsumes 14. 36 back subsumes 12. given clause #5: (wt=11) 7 [para_into,5.1.1.1.1,5.1.2] f(f(f(f(e,e),e),e),e)=e. given clause #6: (wt=11) 8 [para_into,5.1.1.1.1,2.1.2] f(f(f(x,f(e,x)),e),e)=e. 55 back subsumes 42. given clause #7: (wt=11) 9 [para_into,5.1.1.1.2,5.1.2] f(f(e,f(f(e,e),e)),e)=e. 67 back subsumes 9. given clause #8: (wt=11) 10 [para_into,5.1.1.1.2,2.1.2] f(f(e,f(x,f(e,x))),e)=e. 73 back subsumes 66. given clause #9: (wt=11) 11 [para_into,5.1.1.2,5.1.2] f(f(e,e),f(f(e,e),e))=e. given clause #10: (wt=11) 15 [para_from,5.1.2,2.1.1.2.1] f(x,f(f(f(e,e),e),x))=e. 91 back subsumes 69. 94 back subsumes 50. 95 back subsumes 48. given clause #11: (wt=15) 16 [para_into,4.1.1.2.1.2.1,5.1.2] f(x,f(f(y,f(f(f(e,e),e),y)),x))=e. given clause #12: (wt=11) 29 [para_into,6.1.1.2,5.1.1,flip.1] f(x,f(f(e,e),x))=f(e,e). 99 back subsumes 98. 122 back subsumes 68. 123 back subsumes 90. 124 back subsumes 81. 125 back subsumes 39. given clause #13: (wt=15) 17 [para_into,4.1.1.2.1.2.1,2.1.2] f(x,f(f(y,f(f(z,f(e,z)),y)),x))=e. given clause #14: (wt=11) 30 [para_into,6.1.1.2,2.1.1] f(f(e,x),e)=f(y,f(x,y)). 127 back subsumes 87. 128 back subsumes 71. 130 back subsumes 85. 143 back subsumes 108. 147 back subsumes 65. 148 back subsumes 41. 149 back subsumes 88. 150 back subsumes 130. 151 back subsumes 89. 152 back subsumes 74. 153 back subsumes 11. given clause #15: (wt=15) 18 [para_into,4.1.1.2.1.2,4.1.1] f(x,f(f(f(f(y,f(e,y)),e),e),x))=e. given clause #16: (wt=11) 33 [para_into,6.1.2.2,2.1.1] f(x,f(y,x))=f(f(e,y),e). 158 back subsumes 86. 160 back subsumes 106. given clause #17: (wt=15) 19 [para_into,4.1.1.2,4.1.1] f(f(f(x,f(e,x)),f(y,f(e,y))),e)=e. given clause #18: (wt=11) 36 [para_from,6.1.1,2.1.1.2] f(f(x,e),f(y,f(x,y)))=e. 166 back subsumes 82. 169 back subsumes 51. 173 back subsumes 83. 174 back subsumes 61. 175 back subsumes 62. 177 back subsumes 105. given clause #19: (wt=15) 20 [para_into,4.1.2,5.1.2] f(x,f(f(y,f(e,y)),x))=f(f(e,e),e). given clause #20: (wt=11) 67 [para_into,9.1.1.1,6.1.2] f(f(x,f(f(e,e),x)),e)=e. 181 back subsumes 52. 182 back subsumes 63. 183 back subsumes 64. 184 back subsumes 182. 189 back subsumes 178. 189 back subsumes 176. given clause #21: (wt=15) 21 [para_into,4.1.2,2.1.2] f(x,f(f(y,f(e,y)),x))=f(z,f(e,z)). given clause #22: (wt=11) 84 [para_into,11.1.2,5.1.2,gL-id] f(x,f(f(e,e),e))=f(x,e). 199 back subsumes 197. given clause #23: (wt=15) 22 [para_from,4.1.2,5.1.2] f(f(e,e),e)=f(x,f(f(y,f(e,y)),x)). given clause #24: (wt=11) 102 [para_into,29.1.1.2,11.1.1,gL-id] f(f(f(e,e),e),x)=f(e,x). 219 back subsumes 217. 222 back subsumes 137. 223 back subsumes 135. given clause #25: (wt=15) 23 [para_from,4.1.2,2.1.2] f(x,f(e,x))=f(y,f(f(z,f(e,z)),y)). given clause #26: (wt=11) 116 [para_from,29.1.1,2.1.1.2] f(f(f(e,e),e),f(e,e))=e. given clause #27: (wt=15) 24 [para_from,4.1.2,5.1.1.2] f(f(e,e),f(x,f(f(y,f(e,y)),x)))=e. given clause #28: (wt=11) 126 [para_from,29.1.2,2.1.1.2] f(e,f(x,f(f(e,e),x)))=e. given clause #29: (wt=15) 25 [para_from,4.1.2,5.1.1.1.2] f(f(e,f(x,f(f(y,f(e,y)),x))),e)=e. given clause #30: (wt=11) 141 [para_from,30.1.1,29.1.1.2,gL-id] f(x,f(y,f(e,y)))=f(x,e). 238 back subsumes 200. 239 back subsumes 236. 240 back subsumes 201. 252 back subsumes 232. given clause #31: (wt=15) 26 [para_from,4.1.2,5.1.1.1.1] f(f(f(x,f(f(y,f(e,y)),x)),e),e)=e. given clause #32: (wt=11) 153 [para_from,30.1.2,2.1.1.2] f(f(x,e),f(f(e,x),e))=e. 266 back subsumes 205. given clause #33: (wt=15) 27 [para_into,6.1.1.2,6.1.2] f(f(x,y),f(z,f(x,z)))=f(u,f(y,u)). -------- PROOF -------- ----> UNIT CONFLICT at 0.04 sec ----> 270 [binary,269.1,3.1] $F. Length of proof is 3. Level of proof is 3. ---------------- PROOF ---------------- 2 [] f(x,f(e,x))=e. 3 [] f(f(A,B),f(C,D))!=f(f(A,C),f(B,D)). 6 [para_into,2.1.2,2.1.2,gL-id] f(x,f(y,x))=f(z,f(y,z)). 27 [para_into,6.1.1.2,6.1.2] f(f(x,y),f(z,f(x,z)))=f(u,f(y,u)). 269 [gL,27] f(f(x,y),f(z,u))=f(f(x,z),f(y,u)). 270 [binary,269.1,3.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 33 clauses generated 4623 para_from generated 2120 para_into generated 2481 gL rule generated 22 demod & eval rewrites 0 clauses wt,lit,sk delete 3053 tautologies deleted 0 clauses forward subsumed 1304 (subsumed by sos) 734 unit deletions 0 factor simplifications 0 clauses kept 266 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 48 usable size 32 sos size 188 demodulators size 0 passive size 1 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8902 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/rob_ocd.in0100644000076400007640000000636707700375747017264 0ustar mccunemccune% % If a Robbins algebra has elements C and D such that C+D=C, then it % is Boolean. This input file uses the proof of a similar theorem % to guide the search. % % Special features used: list(hints), label attributes, build_proof_object. % %%%%%%%%%%%%%%%%%%%%% Basic options op(400, xfx, +). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(pick_given_ratio, 4). assign(max_mem, 20000). %%%%%%%%%%%%%%%%%%%%% Standard for equational problems set(knuth_bendix). %%%%%%%%%%%%%%%%%%%%% Modifications to strategy set(build_proof_object_2). set(dynamic_demod_lex_dep). assign(max_weight, 30). lex([A, B, E, c, d, e, f, g(x), n(x), +(x,x)]). %%%%%%%%%%%%%%%%%%%%% Clauses list(usable). x = x. x + y = y + x. (x + y) + z = x + (y + z). x + (y + z) = y + (x + z). % commuted form of associativity end_of_list. list(sos). n(n(x + y) + n(x + n(y))) = x. % Robbins axiom c + d = c. % hypothesis n(A + n(B)) + n(n(A) + n(B)) != B. % denial of Huntington axiom end_of_list. % Subtract 20 from the pick-weight of kept clauses that subsume any hint. assign(bsub_hint_wt, -20). % The hints list conatins a proof of the (slightly weaker) theorem that % from the same hypotheses, we can derive a 0 such that x+0=x. Label % attributes on hints are inherited by the clauses to which the hints % apply. list(hints). n(n(x+ (y+z))+n(y+n(x+z)))=y # label(step_1). n(n(x+y)+n(y+n(x)))=y # label(step_2). n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x # label(step_3). n(n(x+y)+n(n(y)+x))=x # label(step_4). c+ (d+x)=c+x # label(step_5). n(n(x+c)+n(c+n(x+d)))=c # label(step_6). n(n(x+ (y+z))+n(z+n(x+y)))=z # label(step_7). n(n(x+ (y+z))+n(y+n(z+x)))=y # label(step_8). n(n(c)+n(d+n(c)))=d # label(step_9). n(n(x+y)+n(n(x)+y))=y # label(step_10). n(n(x+n(y))+n(y+x))=x # label(step_11). n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x # label(step_12). n(n(x+c)+n(c+n(d+x)))=c # label(step_13). n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y # label(step_14). n(n(x+ (y+z))+n(z+n(y+x)))=z # label(step_15). n(n(x+ (y+z))+n(n(z+x)+y))=y # label(step_16). n(d+n(c+n(d+n(c))))=n(d+n(c)) # label(step_17). n(d+n(n(c)+ (n(n(d+n(c))+x)+n(n(d+n(c))+n(x)))))=n(c) # label(step_18). n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x) # label(step_19). n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y # label(step_20). n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x # label(step_21). n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d # label(step_22). n(n(d+n(c))+n(c+n(d+n(c))))=d # label(step_23). n(n(c+n(d+n(c)))+n(c+n(c+n(d+n(c)))))=c # label(step_24). n(d+n(d+ (n(c)+n(c+n(d+n(c))))))=n(c) # label(step_25). n(c+n(d+n(c)))=n(c) # label(step_26). n(n(c)+n(c+n(c)))=c # label(step_27). n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c) # label(step_28). n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c # label(step_29). n(c+ (c+n(c+n(c))))=n(c) # label(step_30). d+n(c+n(c))=d # label(step_31). n(n(x+d)+n(x+ (n(d)+n(c+n(c)))))=x+n(c+n(c)) # label(step_32). x+n(c+n(c))=x # label(step_33). end_of_list. otter-3.3f/examples/fringe/ec_yql.out0100664000076400007640000003541110103522221017270 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:13 2004 The command was "../../bin/otter". The process ID is 8897. set(hyper_res). set(ancestor_subsume). assign(max_weight,28). clear(print_kept). set(order_history). assign(max_proofs,2). list(usable). 1 [] -P(e(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). end_of_list. list(passive). 3 [] -P(e(a,e(e(b,e(a,c)),e(c,b))))|$ANSWER(P5_XGF). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). given clause #2: (wt=16) 4 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). given clause #3: (wt=8) 7 [hyper,1,4,2] P(e(e(x,y),e(x,y))). given clause #4: (wt=12) 8 [hyper,1,2,7] P(e(e(x,e(y,z)),e(e(y,z),x))). given clause #5: (wt=12) 9 [hyper,1,8,8] P(e(e(e(x,y),z),e(z,e(x,y)))). given clause #6: (wt=12) 10 [hyper,1,4,8] P(e(e(x,y),e(e(x,z),e(z,y)))). 17 back subsumes 16. given clause #7: (wt=8) 18 [hyper,1,4,10] P(e(e(x,x),e(y,y))). 23 back subsumes 7. given clause #8: (wt=4) 23 [hyper,1,18,18] P(e(x,x)). 26 back subsumes 9. 26 back subsumes 8. given clause #9: (wt=8) 26 [hyper,1,10,23] P(e(e(x,y),e(y,x))). 27 back subsumes 21. 27 back subsumes 20. 28 back subsumes 14. 28 back subsumes 11. given clause #10: (wt=12) 13 [hyper,1,8,2] P(e(e(e(x,y),e(z,x)),e(z,y))). given clause #11: (wt=8) 32 [hyper,1,13,10] P(e(e(e(x,y),x),y)). given clause #12: (wt=8) 33 [hyper,1,26,32] P(e(x,e(e(y,x),y))). given clause #13: (wt=8) 38 [hyper,1,13,33] P(e(e(x,e(x,y)),y)). given clause #14: (wt=8) 43 [hyper,1,33,23] P(e(e(x,e(y,y)),x)). given clause #15: (wt=8) 50 [hyper,1,26,38] P(e(x,e(y,e(y,x)))). given clause #16: (wt=8) 51 [hyper,1,13,38] P(e(x,e(y,e(x,y)))). given clause #17: (wt=8) 56 [hyper,1,26,43] P(e(x,e(x,e(y,y)))). given clause #18: (wt=8) 63 [hyper,1,4,50] P(e(e(e(x,y),y),x)). given clause #19: (wt=8) 78 [hyper,1,26,51] P(e(e(x,e(y,x)),y)). given clause #20: (wt=8) 87 [hyper,1,51,23] P(e(x,e(e(y,y),x))). given clause #21: (wt=8) 97 [hyper,1,13,56] P(e(e(e(x,x),y),y)). given clause #22: (wt=8) 116 [hyper,1,26,63] P(e(x,e(e(x,y),y))). given clause #23: (wt=12) 17 [hyper,1,8,10] P(e(e(e(x,y),e(y,z)),e(x,z))). 188 back subsumes 51. 192 back subsumes 38. 193 back subsumes 188. given clause #24: (wt=8) 192 [hyper,1,17,32] P(e(e(x,e(x,y)),y)). 194 back subsumes 52. 195 back subsumes 53. 196 back subsumes 54. given clause #25: (wt=8) 193 [hyper,1,17,10] P(e(x,e(y,e(x,y)))). 197 back subsumes 75. 198 back subsumes 78. 199 back subsumes 116. 200 back subsumes 79. 201 back subsumes 80. 202 back subsumes 83. 203 back subsumes 85. 204 back subsumes 86. 205 back subsumes 87. 206 back subsumes 88. 207 back subsumes 185. 208 back subsumes 89. 209 back subsumes 90. 210 back subsumes 91. 211 back subsumes 92. given clause #26: (wt=8) 198 [hyper,1,26,193] P(e(e(x,e(y,x)),y)). 212 back subsumes 121. 213 back subsumes 124. 214 back subsumes 125. 215 back subsumes 126. given clause #27: (wt=8) 199 [hyper,1,17,193] P(e(x,e(e(x,y),y))). 216 back subsumes 157. 217 back subsumes 160. 218 back subsumes 159. 219 back subsumes 162. 220 back subsumes 63. 221 back subsumes 163. 222 back subsumes 164. 223 back subsumes 167. 224 back subsumes 170. 225 back subsumes 173. 226 back subsumes 165. 227 back subsumes 169. 228 back subsumes 172. 229 back subsumes 174. 230 back subsumes 175. 231 back subsumes 176. 232 back subsumes 97. 233 back subsumes 177. 234 back subsumes 182. 235 back subsumes 178. 236 back subsumes 179. 237 back subsumes 180. 238 back subsumes 181. given clause #28: (wt=8) 205 [hyper,1,193,23] P(e(x,e(e(y,y),x))). 239 back subsumes 127. 240 back subsumes 166. 241 back subsumes 129. 242 back subsumes 56. 243 back subsumes 132. 244 back subsumes 133. 245 back subsumes 158. 246 back subsumes 134. 247 back subsumes 137. 248 back subsumes 140. 249 back subsumes 142. 250 back subsumes 143. 251 back subsumes 144. 252 back subsumes 183. 253 back subsumes 145. 254 back subsumes 146. 255 back subsumes 147. 256 back subsumes 148. given clause #29: (wt=8) 220 [hyper,1,26,199] P(e(e(e(x,y),y),x)). 257 back subsumes 135. 258 back subsumes 168. 259 back subsumes 113. 260 back subsumes 117. 261 back subsumes 118. 262 back subsumes 119. given clause #30: (wt=8) 232 [hyper,1,199,23] P(e(e(e(x,x),y),y)). 263 back subsumes 149. 264 back subsumes 226. 265 back subsumes 151. 266 back subsumes 154. 267 back subsumes 155. 268 back subsumes 156. given clause #31: (wt=8) 242 [hyper,1,17,205] P(e(x,e(x,e(y,y)))). 269 back subsumes 93. 270 back subsumes 136. 271 back subsumes 227. 272 back subsumes 94. 273 back subsumes 98. 274 back subsumes 99. 275 back subsumes 150. 276 back subsumes 112. 277 back subsumes 128. 278 back subsumes 218. 279 back subsumes 120. 280 back subsumes 100. 281 back subsumes 106. 282 back subsumes 107. 283 back subsumes 184. 284 back subsumes 108. 285 back subsumes 109. 286 back subsumes 110. 287 back subsumes 111. given clause #32: (wt=12) 24 [hyper,1,10,18] P(e(e(e(x,x),y),e(y,e(z,z)))). 294 back subsumes 282. 297 back subsumes 275. 298 back subsumes 277. 299 back subsumes 102. 300 back subsumes 281. 301 back subsumes 287. given clause #33: (wt=12) 25 [hyper,1,2,18] P(e(e(x,e(y,y)),e(e(z,z),x))). 308 back subsumes 251. 311 back subsumes 139. 312 back subsumes 250. 313 back subsumes 256. given clause #34: (wt=12) 27 [hyper,1,10,26] P(e(e(e(x,y),z),e(z,e(y,x)))). 330 back subsumes 50. given clause #35: (wt=8) 330 [hyper,1,27,32] P(e(x,e(y,e(y,x)))). 336 back subsumes 60. 337 back subsumes 328. 338 back subsumes 62. 339 back subsumes 64. 340 back subsumes 68. 341 back subsumes 318. 342 back subsumes 69. 343 back subsumes 306. 344 back subsumes 292. 345 back subsumes 70. 346 back subsumes 186. 347 back subsumes 71. 348 back subsumes 72. 349 back subsumes 73. 350 back subsumes 74. given clause #36: (wt=12) 28 [hyper,1,2,26] P(e(e(x,e(y,z)),e(e(z,y),x))). given clause #37: (wt=12) 34 [hyper,1,10,32] P(e(e(e(e(x,y),x),z),e(z,y))). 375 back subsumes 220. 379 back subsumes 249. 380 back subsumes 105. 392 back subsumes 43. given clause #38: (wt=8) 375 [hyper,1,34,34] P(e(e(e(x,y),y),x)). 396 back subsumes 259. 397 back subsumes 115. 398 back subsumes 263. 399 back subsumes 260. 400 back subsumes 261. 401 back subsumes 262. given clause #39: (wt=8) 392 [hyper,1,34,24] P(e(e(x,e(y,y)),x)). 402 back subsumes 228. 403 back subsumes 82. 404 back subsumes 57. 405 back subsumes 58. 406 back subsumes 59. given clause #40: (wt=12) 36 [hyper,1,2,32] P(e(e(x,y),e(e(e(z,y),z),x))). 434 back subsumes 329. 437 back subsumes 299. given clause #41: (wt=12) 37 [hyper,1,33,33] P(e(e(x,e(y,e(e(z,y),z))),x)). 450 back subsumes 229. 453 back subsumes 67. given clause #42: (wt=12) 39 [hyper,1,10,33] P(e(e(x,y),e(y,e(e(z,x),z)))). 467 back subsumes 141. given clause #43: (wt=12) 40 [hyper,1,2,33] P(e(e(x,e(e(y,z),y)),e(z,x))). given clause #44: (wt=12) 41 [hyper,1,33,32] P(e(e(x,e(e(e(y,z),y),z)),x)). given clause #45: (wt=12) 42 [hyper,1,33,26] P(e(e(x,e(e(y,z),e(z,y))),x)). given clause #46: (wt=12) 44 [hyper,1,33,18] P(e(e(x,e(e(y,y),e(z,z))),x)). given clause #47: (wt=12) 49 [hyper,1,33,38] P(e(e(x,e(e(y,e(y,z)),z)),x)). given clause #48: (wt=12) 55 [hyper,1,33,43] P(e(e(x,e(e(y,e(z,z)),y)),x)). 616 back subsumes 65. 625 back subsumes 471. 626 back subsumes 506. given clause #49: (wt=12) 61 [hyper,1,33,50] P(e(e(x,e(y,e(z,e(z,y)))),x)). given clause #50: (wt=12) 66 [hyper,1,50,38] P(e(x,e(x,e(e(y,e(y,z)),z)))). given clause #51: (wt=12) 76 [hyper,1,50,51] P(e(x,e(x,e(y,e(z,e(y,z)))))). given clause #52: (wt=12) 77 [hyper,1,33,51] P(e(e(x,e(y,e(z,e(y,z)))),x)). 755 back subsumes 723. 758 back subsumes 717. 759 back subsumes 715. 760 back subsumes 724. 772 back subsumes 678. given clause #53: (wt=12) 81 [hyper,1,51,50] P(e(x,e(e(y,e(z,e(z,y))),x))). given clause #54: (wt=12) 84 [hyper,1,51,33] P(e(x,e(e(y,e(e(z,y),z)),x))). given clause #55: (wt=12) 95 [hyper,1,50,56] P(e(x,e(x,e(y,e(y,e(z,z)))))). 892 back subsumes 796. 916 back subsumes 842. given clause #56: (wt=12) 96 [hyper,1,33,56] P(e(e(x,e(y,e(y,e(z,z)))),x)). 934 back subsumes 893. 938 back subsumes 898. 941 back subsumes 892. 942 back subsumes 890. 943 back subsumes 899. 944 back subsumes 923. 945 back subsumes 920. 946 back subsumes 917. 949 back subsumes 916. 953 back subsumes 95. 958 back subsumes 718. 961 back subsumes 673. 965 back subsumes 474. given clause #57: (wt=12) 101 [hyper,1,56,50] P(e(e(x,e(y,e(y,x))),e(z,z))). given clause #58: (wt=12) 103 [hyper,1,56,38] P(e(e(e(x,e(x,y)),y),e(z,z))). given clause #59: (wt=12) 104 [hyper,1,56,33] P(e(e(x,e(e(y,x),y)),e(z,z))). given clause #60: (wt=12) 114 [hyper,1,50,63] P(e(x,e(x,e(e(e(y,z),z),y)))). 1050 back subsumes 841. given clause #61: (wt=12) 122 [hyper,1,50,78] P(e(x,e(x,e(e(y,e(z,y)),z)))). 1113 back subsumes 846. given clause #62: (wt=12) 123 [hyper,1,33,78] P(e(e(x,e(e(y,e(z,y)),z)),x)). -------- PROOF -------- 1162 [binary,1161.1,3.1] $ANSWER(P5_XGF). ----> UNIT CONFLICT at 0.07 sec ----> 1162 [binary,1161.1,3.1] $ANSWER(P5_XGF). Length of proof is 15. Level of proof is 13. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). 3 [] -P(e(a,e(e(b,e(a,c)),e(c,b))))|$ANSWER(P5_XGF). 4 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). 7 [hyper,1,4,2] P(e(e(x,y),e(x,y))). 8 [hyper,1,2,7] P(e(e(x,e(y,z)),e(e(y,z),x))). 10 [hyper,1,4,8] P(e(e(x,y),e(e(x,z),e(z,y)))). 13 [hyper,1,8,2] P(e(e(e(x,y),e(z,x)),e(z,y))). 18 [hyper,1,4,10] P(e(e(x,x),e(y,y))). 23 [hyper,1,18,18] P(e(x,x)). 26 [hyper,1,10,23] P(e(e(x,y),e(y,x))). 32 [hyper,1,13,10] P(e(e(e(x,y),x),y)). 33 [hyper,1,26,32] P(e(x,e(e(y,x),y))). 38 [hyper,1,13,33] P(e(e(x,e(x,y)),y)). 51 [hyper,1,13,38] P(e(x,e(y,e(x,y)))). 78 [hyper,1,26,51] P(e(e(x,e(y,x)),y)). 123 [hyper,1,33,78] P(e(e(x,e(e(y,e(z,y)),z)),x)). 1161 [hyper,1,123,4] P(e(x,e(e(y,e(x,z)),e(z,y)))). 1162 [binary,1161.1,3.1] $ANSWER(P5_XGF). ------------ end of proof ------------- 1131 back subsumes 1089. 1134 back subsumes 1085. 1137 back subsumes 1090. 1140 back subsumes 800. 1141 back subsumes 1083. 1142 back subsumes 1091. 1152 back subsumes 897. 1153 back subsumes 722. 1156 back subsumes 677. given clause #63: (wt=12) 130 [hyper,1,50,87] P(e(x,e(x,e(y,e(e(z,z),y))))). 1216 back subsumes 844. given clause #64: (wt=12) 131 [hyper,1,33,87] P(e(e(x,e(y,e(e(z,z),y))),x)). 1234 back subsumes 1188. 1236 back subsumes 1190. 1239 back subsumes 1186. 1242 back subsumes 1191. 1245 back subsumes 798. 1246 back subsumes 1184. 1247 back subsumes 1192. 1257 back subsumes 1087. 1258 back subsumes 895. 1259 back subsumes 720. 1262 back subsumes 675. given clause #65: (wt=12) 138 [hyper,1,87,50] P(e(e(x,x),e(y,e(z,e(z,y))))). 1279 back subsumes 630. given clause #66: (wt=12) 152 [hyper,1,50,97] P(e(x,e(x,e(e(e(y,y),z),z)))). 1340 back subsumes 843. given clause #67: (wt=12) 153 [hyper,1,33,97] P(e(e(x,e(e(e(y,y),z),z)),x)). 1358 back subsumes 1308. 1360 back subsumes 1309. 1362 back subsumes 1311. 1365 back subsumes 1307. 1368 back subsumes 1312. 1371 back subsumes 797. 1372 back subsumes 1305. 1373 back subsumes 1313. 1374 back subsumes 1347. 1375 back subsumes 1344. 1376 back subsumes 1341. 1379 back subsumes 1340. 1383 back subsumes 152. 1388 back subsumes 1187. 1389 back subsumes 1086. 1390 back subsumes 894. 1391 back subsumes 719. 1394 back subsumes 674. given clause #68: (wt=12) 161 [hyper,1,50,116] P(e(x,e(x,e(y,e(e(y,z),z))))). 1458 back subsumes 845. given clause #69: (wt=12) 171 [hyper,1,116,50] P(e(e(e(x,e(y,e(y,x))),z),z)). 1489 back subsumes 969. 1493 back subsumes 799. given clause #70: (wt=12) 194 [hyper,1,10,192] P(e(e(e(x,e(x,y)),z),e(z,y))). 1514 back subsumes 1500. 1523 back subsumes 248. 1524 back subsumes 103. 1528 back subsumes 1514. given clause #71: (wt=12) 196 [hyper,1,2,192] P(e(e(x,y),e(e(z,e(z,y)),x))). 1568 back subsumes 793. 1572 back subsumes 1515. 1574 back subsumes 1508. 1575 back subsumes 1502. 1576 back subsumes 1503. 1578 back subsumes 1505. 1580 back subsumes 1511. 1581 back subsumes 1516. 1608 back subsumes 473. 1614 back subsumes 656. given clause #72: (wt=12) 197 [hyper,1,193,193] P(e(x,e(e(y,e(z,e(y,z))),x))). 1638 back subsumes 77. 1641 back subsumes 76. 1645 back subsumes 771. 1646 back subsumes 1028. 1647 back subsumes 770. 1648 back subsumes 938. 1649 back subsumes 1368. 1650 back subsumes 1242. 1651 back subsumes 1429. 1652 back subsumes 1137. 1655 back subsumes 755. 1656 back subsumes 772. 1685 back subsumes 776. 1686 back subsumes 775. 1689 back subsumes 774. 1692 back subsumes 280. 1693 back subsumes 773. given clause #73: (wt=12) 200 [hyper,1,10,193] P(e(e(x,y),e(y,e(z,e(x,z))))). 1724 back subsumes 1081. 1734 back subsumes 1711. 1763 back subsumes 509. 1766 back subsumes 363. 1769 back subsumes 239. 1771 back subsumes 214. given clause #74: (wt=12) 201 [hyper,1,2,193] P(e(e(x,e(y,e(z,y))),e(z,x))). -------- PROOF -------- 1828 [binary,1827.1,3.1] $ANSWER(P5_XGF). ----> UNIT CONFLICT at 0.13 sec ----> 1828 [binary,1827.1,3.1] $ANSWER(P5_XGF). Length of proof is 9. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). 3 [] -P(e(a,e(e(b,e(a,c)),e(c,b))))|$ANSWER(P5_XGF). 4 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). 7 [hyper,1,4,2] P(e(e(x,y),e(x,y))). 8 [hyper,1,2,7] P(e(e(x,e(y,z)),e(e(y,z),x))). 10 [hyper,1,4,8] P(e(e(x,y),e(e(x,z),e(z,y)))). 13 [hyper,1,8,2] P(e(e(e(x,y),e(z,x)),e(z,y))). 17 [hyper,1,8,10] P(e(e(e(x,y),e(y,z)),e(x,z))). 193 [hyper,1,17,10] P(e(x,e(y,e(x,y)))). 201 [hyper,1,2,193] P(e(e(x,e(y,e(z,y))),e(z,x))). 1827 [hyper,1,201,13] P(e(x,e(e(y,e(x,z)),e(z,y)))). 1828 [binary,1827.1,3.1] $ANSWER(P5_XGF). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 74 clauses generated 3270 hyper_res generated 3270 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 1447 cl not subsumed due to ancestor_subsume 259 (subsumed by sos) 634 unit deletions 0 factor simplifications 0 clauses kept 1823 new demodulators 0 empty clauses 2 clauses back demodulated 0 clauses back subsumed 257 usable size 56 sos size 1512 demodulators size 0 passive size 1 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.13 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8897 finished Mon Aug 2 15:31:13 2004 otter-3.3f/examples/fringe/ec_yql.in.288970100644000076400007640000000340506006207253017577 0ustar mccunemccune% This is a problem in the equivalential calculus (EC): YQL -> XGF. % The strategy uses ancestor subsumption to find a shorter proof. % This input file was contributed by Larry Wos. set(hyper_res). set(ancestor_subsume). assign(max_weight,28). clear(print_kept). set(order_history). assign(max_proofs, 2). assign(max_mem, 1500). list(usable). -P(e(x,y)) | -P(x) | P(y). % condensed detacment end_of_list. list(sos). % Following are all of the shortest single axioms for EC. P(e(e(x,y),e(e(z,y),e(x,z)))). % P1_YQL % P(e(e(x,y),e(e(x,z),e(z,y)))). % P2_YQF % P(e(e(x,y),e(e(z,x),e(y,z)))). % P3_YQJ % P(e(e(e(x,y),z),e(y,e(z,x)))). % P4_UM % P(e(x,e(e(y,e(x,z)),e(z,y)))). % P5_XGF % P(e(e(x,e(y,z)),e(z,e(x,y)))). % P7_WN % P(e(e(x,y),e(z,e(e(y,z),x)))). % P8_YRM % P(e(e(x,y),e(z,e(e(z,y),x)))). % P9_YRO % P(e(e(e(x,e(y,z)),z),e(y,x))). % PYO % P(e(e(e(x,e(y,z)),y),e(z,x))). % PYM % P(e(x,e(e(y,e(z,x)),e(z,y)))). % XGK % P(e(x,e(e(y,z),e(e(x,z),y)))). % XHK % P(e(x,e(e(y,z),e(e(z,x),y)))). % XHN end_of_list. list(passive). % Here are denials of the thirteen shortest single axioms for EC. % -P(e(e(a,b),e(e(c,b),e(a,c)))) | $ANSWER(P1_YQL). % -P(e(e(a,b),e(e(a,c),e(c,b)))) | $ANSWER(P2_YQF). % -P(e(e(a,b),e(e(c,a),e(b,c)))) | $ANSWER(P3_YQJ). % -P(e(e(e(a,b),c),e(b,e(c,a)))) | $ANSWER(P4_UM). -P(e(a,e(e(b,e(a,c)),e(c,b)))) | $ANSWER(P5_XGF). % -P(e(e(a,e(b,c)),e(c,e(a,b)))) | $ANSWER(P7_WN). % -P(e(e(a,b),e(c,e(e(b,c),a)))) | $ANSWER(P8_YRM). % -P(e(e(a,b),e(c,e(e(c,b),a)))) | $ANSWER(P9_YRO). % -P(e(e(e(a,e(b,c)),c),e(b,a))) | $ANSWER(PYO). % -P(e(e(e(a,e(b,c)),b),e(c,a))) | $ANSWER(PYM). % -P(e(a,e(e(b,e(c,a)),e(c,b)))) | $ANSWER(XGK). % -P(e(a,e(e(b,c),e(e(a,c),b)))) | $ANSWER(XHK). % -P(e(a,e(e(b,c),e(e(c,a),b)))) | $ANSWER(XHN). end_of_list. otter-3.3f/examples/fringe/rob_ocd.out0100664000076400007640000011763610103522223017437 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:15 2004 The command was "../../bin/otter". The process ID is 8947. op(400,xfx,+). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(pick_given_ratio,4). assign(max_mem,20000). set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(build_proof_object_2). dependent: set(order_history). set(dynamic_demod_lex_dep). assign(max_weight,30). lex([A,B,E,c,d,e,f,g(x),n(x),x+x]). list(usable). 0 [] x=x. 0 [] x+y=y+x. 0 [] (x+y)+z=x+ (y+z). 0 [] x+ (y+z)=y+ (x+z). end_of_list. list(sos). 0 [] n(n(x+y)+n(x+n(y)))=x. 0 [] c+d=c. 0 [] n(A+n(B))+n(n(A)+n(B))!=B. end_of_list. assign(bsub_hint_wt,-20). list(hints). 1 [] n(n(x+ (y+z))+n(y+n(x+z)))=y # label(step_1). 2 [] n(n(x+y)+n(y+n(x)))=y # label(step_2). 3 [] n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x # label(step_3). 4 [] n(n(x+y)+n(n(y)+x))=x # label(step_4). 5 [] c+ (d+x)=c+x # label(step_5). 6 [] n(n(x+c)+n(c+n(x+d)))=c # label(step_6). 7 [] n(n(x+ (y+z))+n(z+n(x+y)))=z # label(step_7). 8 [] n(n(x+ (y+z))+n(y+n(z+x)))=y # label(step_8). 9 [] n(n(c)+n(d+n(c)))=d # label(step_9). 10 [] n(n(x+y)+n(n(x)+y))=y # label(step_10). 11 [] n(n(x+n(y))+n(y+x))=x # label(step_11). 12 [] n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x # label(step_12). 13 [] n(n(x+c)+n(c+n(d+x)))=c # label(step_13). 14 [] n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y # label(step_14). 15 [] n(n(x+ (y+z))+n(z+n(y+x)))=z # label(step_15). 16 [] n(n(x+ (y+z))+n(n(z+x)+y))=y # label(step_16). 17 [] n(d+n(c+n(d+n(c))))=n(d+n(c)) # label(step_17). 18 [] n(d+n(n(c)+ (n(n(d+n(c))+x)+n(n(d+n(c))+n(x)))))=n(c) # label(step_18). 19 [] n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x) # label(step_19). 20 [] n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y # label(step_20). 21 [] n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x # label(step_21). 22 [] n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d # label(step_22). 23 [] n(n(d+n(c))+n(c+n(d+n(c))))=d # label(step_23). 24 [] n(n(c+n(d+n(c)))+n(c+n(c+n(d+n(c)))))=c # label(step_24). 25 [] n(d+n(d+ (n(c)+n(c+n(d+n(c))))))=n(c) # label(step_25). 26 [] n(c+n(d+n(c)))=n(c) # label(step_26). 27 [] n(n(c)+n(c+n(c)))=c # label(step_27). 28 [] n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c) # label(step_28). 29 [] n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c # label(step_29). 30 [] n(c+ (c+n(c+n(c))))=n(c) # label(step_30). 31 [] d+n(c+n(c))=d # label(step_31). 32 [] n(n(x+d)+n(x+ (n(d)+n(c+n(c)))))=x+n(c+n(c)) # label(step_32). 33 [] x+n(c+n(c))=x # label(step_33). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 34 [] x=x. ** KEPT (pick-wt=7): 35 [] x+y=y+x. ---> New Demodulator: (lex-dependent) 36 [new_demod,35] x+y=y+x. ** KEPT (pick-wt=11): 37 [] (x+y)+z=x+ (y+z). ---> New Demodulator: 38 [new_demod,37] (x+y)+z=x+ (y+z). ** KEPT (pick-wt=11): 39 [] x+ (y+z)=y+ (x+z). ---> New Demodulator: (lex-dependent) 40 [new_demod,39] x+ (y+z)=y+ (x+z). Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] x=x. Following clause subsumed by 35 during input processing: 0 [copy,35,flip.1] x+y=y+x. >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 38. Following clause subsumed by 39 during input processing: 0 [copy,39,flip.1] x+ (y+z)=y+ (x+z). >>>> Starting back demodulation with 40. ------------> process sos: ** KEPT (pick-wt=13): 41 [] n(n(x+y)+n(x+n(y)))=x. ---> New Demodulator: 42 [new_demod,41] n(n(x+y)+n(x+n(y)))=x. ** KEPT (pick-wt=5): 43 [] c+d=c. ---> New Demodulator: 44 [new_demod,43] c+d=c. ** KEPT (pick-wt=14): 45 [] n(A+n(B))+n(n(A)+n(B))!=B. >>>> Starting back demodulation with 42. >>>> Starting back demodulation with 44. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=13) 41 [] n(n(x+y)+n(x+n(y)))=x. given clause #2: (wt=-20) 46 [para_into,41.1.1.1.1.1,39.1.1] n(n(x+ (y+z))+n(y+n(x+z)))=y # label(step_1). given clause #3: (wt=-20) 50 [para_into,41.1.1.1.1.1,35.1.1] n(n(x+y)+n(y+n(x)))=y # label(step_2). given clause #4: (wt=-20) 54 [para_into,41.1.1.1.2.1.2,41.1.1,demod,36] n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x # label(step_3). given clause #5: (wt=-20) 56 [para_into,41.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(y)+x))=x # label(step_4). given clause #6: (wt=5) 43 [] c+d=c. given clause #7: (wt=-20) 64 [para_into,46.1.1.1.1.1.2,35.1.1] n(n(x+ (y+z))+n(z+n(x+y)))=z # label(step_7). given clause #8: (wt=-20) 70 [para_into,46.1.1.1.2.1.2.1,35.1.1] n(n(x+ (y+z))+n(y+n(z+x)))=y # label(step_8). given clause #9: (wt=-20) 102 [para_into,50.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(x)+y))=y # label(step_10). given clause #10: (wt=-20) 106 [para_into,50.1.1.1,35.1.1] n(n(x+n(y))+n(y+x))=x # label(step_11). given clause #11: (wt=14) 45 [] n(A+n(B))+n(n(A)+n(B))!=B. given clause #12: (wt=-20) 158 [para_into,56.1.1.1.2.1.1,50.1.1] n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x # label(step_12). given clause #13: (wt=-20) 196 [para_from,43.1.1,46.1.1.1.1.1.2] n(n(x+c)+n(c+n(x+d)))=c # label(step_6). given clause #14: (wt=-20) 204 [para_from,43.1.1,50.1.1.1.1.1] n(n(c)+n(d+n(c)))=d # label(step_9). given clause #15: (wt=-20) 206 [para_from,43.1.1,37.1.1.1,flip.1] c+ (d+x)=c+x # label(step_5). given clause #16: (wt=19) 48 [para_into,41.1.1.1.1.1,37.1.1,demod,38] n(n(x+ (y+z))+n(x+ (y+n(z))))=x+y. given clause #17: (wt=-20) 214 [para_into,64.1.1.1.1.1,39.1.1] n(n(x+ (y+z))+n(z+n(y+x)))=z # label(step_15). given clause #18: (wt=-20) 244 [para_into,70.1.1.1.1.1.2,43.1.1] n(n(x+c)+n(c+n(d+x)))=c # label(step_13). given clause #19: (wt=-20) 272 [para_into,70.1.1.1.2.1,35.1.1] n(n(x+ (y+z))+n(n(z+x)+y))=y # label(step_16). given clause #20: (wt=-20) 338 [para_into,102.1.1.1.2,102.1.1,demod,38,36] n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x) # label(step_19). given clause #21: (wt=20) 52 [para_into,41.1.1.1.1,41.1.1] n(x+n(n(x+y)+n(n(x+n(y)))))=n(x+y). 896 back subsumes 860. 896 back subsumes 824. given clause #22: (wt=-20) 376 [para_into,106.1.1.1.2.1,39.1.1,demod,38] n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y # label(step_20). given clause #23: (wt=-20) 378 [para_from,106.1.1,54.1.1.1.2.1.2.2,demod,40,36,36] n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x # label(step_21). given clause #24: (wt=-20) 432 [para_into,158.1.1.1.2.1,43.1.1,demod,36] n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d # label(step_22). given clause #25: (wt=-20) 496 [para_from,204.1.1,102.1.1.1.2,demod,36] n(d+n(c+n(d+n(c))))=n(d+n(c)) # label(step_17). given clause #26: (wt=18) 58 [para_into,41.1.1.1.2,41.1.1,demod,40,36,36] n(x+n(x+ (n(y)+n(x+y))))=n(x+y). given clause #27: (wt=-20) 528 [para_from,204.1.1,54.1.1.1.1] n(d+n(n(c)+ (n(n(d+n(c))+x)+n(n(d+n(c))+n(x)))))=n(c) # label(step_18). given clause #28: (wt=-20) 548 [para_from,206.1.1,64.1.1.1.1.1.2,demod,38] n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y # label(step_14). given clause #29: (wt=-20) 832 [para_into,338.1.1.1.2.1.2.2,204.1.1,demod,36,207,205] n(n(d+n(c))+n(c+n(d+n(c))))=d # label(step_23). given clause #30: (wt=-20) 1278 [para_from,832.1.1,272.1.1.1.2,demod,36,40,36,1043,flip.1] n(c+n(d+n(c)))=n(c) # label(step_26). given clause #31: (wt=21) 60 [para_into,46.1.1.1.1.1.2,39.1.1] n(n(x+ (y+ (z+u)))+n(z+n(x+ (y+u))))=z. given clause #32: (wt=-20) 1298 [back_demod,1112,demod,1279,1279] n(n(c)+n(c+n(c)))=c # label(step_27). given clause #33: (wt=-20) 1404 [para_from,1298.1.1,378.1.1.1.1,demod,40] n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c) # label(step_28). given clause #34: (wt=-20) 1420 [para_from,1298.1.1,338.1.1.1.2.1.2.2,demod,36,1299] n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c # label(step_29). given clause #35: (wt=-20) 1482 [para_from,1420.1.1,272.1.1.1.2,demod,36,40,36,1405,flip.1] n(c+ (c+n(c+n(c))))=n(c) # label(step_30). given clause #36: (wt=23) 62 [para_into,46.1.1.1.1.1.2,37.1.1,demod,38] n(n(x+ (y+ (z+u)))+n(y+ (z+n(x+u))))=y+z. given clause #37: (wt=-20) 1520 [para_from,1482.1.1,548.1.1.1.1,demod,36,433,flip.1] d+n(c+n(c))=d # label(step_31). given clause #38: (wt=-20) 1642 [para_from,1520.1.1,54.1.1.1.2.1.2.2.1,demod,40,207,36,1629] x+n(c+n(c))=x # label(step_31). given clause #39: (wt=5) 1646 [para_from,1520.1.1,46.1.1.1.2.1,demod,207,36,1643] n(n(d))=d. given clause #40: (wt=5) 1682 [back_demod,1522,demod,1643,1643,1643] n(n(c))=c. given clause #41: (wt=17) 66 [para_into,46.1.1.1.1.1,35.1.1,demod,38] n(n(x+ (y+z))+n(x+n(z+y)))=x. given clause #42: (wt=7) 1684 [back_demod,1482,demod,1643] n(c+c)=n(c). given clause #43: (wt=9) 198 [para_from,43.1.1,39.1.1.2,flip.1] c+ (x+d)=x+c. given clause #44: (wt=9) 896 [para_into,52.1.1.1.2.1.1.1,35.1.1,demod,113] n(x+y)=n(y+x). given clause #45: (wt=9) 1698 [para_into,1642.1.1,35.1.1] n(c+n(c))+x=x. given clause #46: (wt=21) 68 [para_into,46.1.1.1.2.1.2.1,39.1.1] n(n(x+ (y+ (z+u)))+n(y+n(z+ (x+u))))=y. given clause #47: (wt=7) 1961 [para_from,1698.1.1,52.1.1.1,demod,1699,1699,1753,1699] n(n(n(x)))=n(x). given clause #48: (wt=5) 2031 [para_into,1961.1.1.1.1,378.1.1,demod,379] n(n(x))=x. -------- PROOF -------- ----> UNIT CONFLICT at 0.47 sec ----> 2174 [binary,2173.1,34.1] $F. Length of proof is 37. Level of proof is 17. ---------------- PROOF ---------------- 34 [] x=x. 36,35 [] x+y=y+x. 38,37 [] (x+y)+z=x+ (y+z). 40,39 [] x+ (y+z)=y+ (x+z). 41 [] n(n(x+y)+n(x+n(y)))=x. 43 [] c+d=c. 45 [] n(A+n(B))+n(n(A)+n(B))!=B. 46 [para_into,41.1.1.1.1.1,39.1.1] n(n(x+ (y+z))+n(y+n(x+z)))=y # label(step_1). 50 [para_into,41.1.1.1.1.1,35.1.1] n(n(x+y)+n(y+n(x)))=y # label(step_2). 52 [para_into,41.1.1.1.1,41.1.1] n(x+n(n(x+y)+n(n(x+n(y)))))=n(x+y). 54 [para_into,41.1.1.1.2.1.2,41.1.1,demod,36] n(n(x+y)+n(x+ (n(y+z)+n(y+n(z)))))=x # label(step_3). 56 [para_into,41.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(y)+x))=x # label(step_4). 64 [para_into,46.1.1.1.1.1.2,35.1.1] n(n(x+ (y+z))+n(z+n(x+y)))=z # label(step_7). 70 [para_into,46.1.1.1.2.1.2.1,35.1.1] n(n(x+ (y+z))+n(y+n(z+x)))=y # label(step_8). 102 [para_into,50.1.1.1.2.1,35.1.1] n(n(x+y)+n(n(x)+y))=y # label(step_10). 106 [para_into,50.1.1.1,35.1.1] n(n(x+n(y))+n(y+x))=x # label(step_11). 158 [para_into,56.1.1.1.2.1.1,50.1.1] n(n(x+ (n(y+z)+n(z+n(y))))+n(z+x))=x # label(step_12). 205,204 [para_from,43.1.1,50.1.1.1.1.1] n(n(c)+n(d+n(c)))=d # label(step_9). 207,206 [para_from,43.1.1,37.1.1.1,flip.1] c+ (d+x)=c+x # label(step_5). 244 [para_into,70.1.1.1.1.1.2,43.1.1] n(n(x+c)+n(c+n(d+x)))=c # label(step_13). 272 [para_into,70.1.1.1.2.1,35.1.1] n(n(x+ (y+z))+n(n(z+x)+y))=y # label(step_16). 338 [para_into,102.1.1.1.2,102.1.1,demod,38,36] n(x+n(y+ (x+n(n(y)+x))))=n(n(y)+x) # label(step_19). 376 [para_into,106.1.1.1.2.1,39.1.1,demod,38] n(n(x+ (y+n(z)))+n(x+ (z+y)))=x+y # label(step_20). 379,378 [para_from,106.1.1,54.1.1.1.2.1.2.2,demod,40,36,36] n(n(x+n(y+n(z)))+n(x+ (y+n(z+ (y+n(y+n(z)))))))=x # label(step_21). 433,432 [para_into,158.1.1.1.2.1,43.1.1,demod,36] n(n(c)+n(d+ (n(x+c)+n(c+n(x)))))=d # label(step_22). 496 [para_from,204.1.1,102.1.1.1.2,demod,36] n(d+n(c+n(d+n(c))))=n(d+n(c)) # label(step_17). 548 [para_from,206.1.1,64.1.1.1.1.1.2,demod,38] n(n(x+ (c+y))+n(d+ (y+n(x+c))))=d+y # label(step_14). 832 [para_into,338.1.1.1.2.1.2.2,204.1.1,demod,36,207,205] n(n(d+n(c))+n(c+n(d+n(c))))=d # label(step_23). 1043,1042 [para_into,378.1.1.1.1,204.1.1,demod,207,40] n(d+n(d+ (n(c)+n(c+n(d+n(c))))))=n(c) # label(step_25). 1112 [para_from,496.1.1,244.1.1.1.2.1.2,demod,36,36] n(n(c+n(d+n(c)))+n(c+n(c+n(d+n(c)))))=c # label(step_24). 1279,1278 [para_from,832.1.1,272.1.1.1.2,demod,36,40,36,1043,flip.1] n(c+n(d+n(c)))=n(c) # label(step_26). 1299,1298 [back_demod,1112,demod,1279,1279] n(n(c)+n(c+n(c)))=c # label(step_27). 1405,1404 [para_from,1298.1.1,378.1.1.1.1,demod,40] n(c+n(c+ (n(c)+n(c+ (c+n(c+n(c)))))))=n(c) # label(step_28). 1420 [para_from,1298.1.1,338.1.1.1.2.1.2.2,demod,36,1299] n(n(c+n(c))+n(c+ (c+n(c+n(c)))))=c # label(step_29). 1482 [para_from,1420.1.1,272.1.1.1.2,demod,36,40,36,1405,flip.1] n(c+ (c+n(c+n(c))))=n(c) # label(step_30). 1520 [para_from,1482.1.1,548.1.1.1.1,demod,36,433,flip.1] d+n(c+n(c))=d # label(step_31). 1629,1628 [para_from,1520.1.1,376.1.1.1.2.1.2,demod,36,36] n(n(x+d)+n(x+ (n(d)+n(c+n(c)))))=x+n(c+n(c)) # label(step_32). 1643,1642 [para_from,1520.1.1,54.1.1.1.2.1.2.2.1,demod,40,207,36,1629] x+n(c+n(c))=x # label(step_31). 1699,1698 [para_into,1642.1.1,35.1.1] n(c+n(c))+x=x. 1753,1752 [para_from,1642.1.1,338.1.1.1.2.1.2.2.1,demod,1699,1699,1643] n(n(x+n(n(x))))=n(n(x)). 1961 [para_from,1698.1.1,52.1.1.1,demod,1699,1699,1753,1699] n(n(n(x)))=n(x). 2032,2031 [para_into,1961.1.1.1.1,378.1.1,demod,379] n(n(x))=x. 2144,2143 [para_into,2031.1.1.1,102.1.1,flip.1] n(x+y)+n(n(x)+y)=n(y). 2173 [back_demod,45,demod,2144,2032] B!=B. 2174 [binary,2173.1,34.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (= v0 v0) (34)) (2 (input) (= (+ v0 v1) (+ v1 v0)) (35)) (3 (input) (= (+ (+ v0 v1) v2) (+ v0 (+ v1 v2))) (37)) (4 (input) (= (+ v0 (+ v1 v2)) (+ v1 (+ v0 v2))) (39)) (5 (input) (= (n (+ (n (+ v0 v1)) (n (+ v0 (n v1))))) v0) (41)) (6 (input) (= (+ (c) (d)) (c)) (43)) (7 (input) (not (= (+ (n (+ (A) (n (B)))) (n (+ (n (A)) (n (B))))) (B))) (45)) (8 (instantiate 4 ((v0 . v64))) (= (+ v64 (+ v1 v2)) (+ v1 (+ v64 v2))) NIL) (9 (instantiate 5 ((v0 . v64)(v1 . (+ v1 v2)))) (= (n (+ (n (+ v64 (+ v1 v2))) (n (+ v64 (n (+ v1 v2)))))) v64) NIL) (10 (paramod 8 (1) 9 (1 1 1 1)) (= (n (+ (n (+ v1 (+ v64 v2))) (n (+ v64 (n (+ v1 v2)))))) v64) NIL) (11 (instantiate 10 ((v1 . v0)(v64 . v1))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ v1 (n (+ v0 v2)))))) v1) (46)) (12 (instantiate 2 ((v0 . v64)(v1 . v65))) (= (+ v64 v65) (+ v65 v64)) NIL) (13 (instantiate 5 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v64 (n v65))))) v64) NIL) (14 (paramod 12 (1) 13 (1 1 1 1)) (= (n (+ (n (+ v65 v64)) (n (+ v64 (n v65))))) v64) NIL) (15 (instantiate 14 ((v64 . v1)(v65 . v0))) (= (n (+ (n (+ v0 v1)) (n (+ v1 (n v0))))) v1) (50)) (16 (instantiate 5 ((v0 . (n (+ v0 v1)))(v1 . (n (+ v0 (n v1)))))) (= (n (+ (n (+ (n (+ v0 v1)) (n (+ v0 (n v1))))) (n (+ (n (+ v0 v1)) (n (n (+ v0 (n v1)))))))) (n (+ v0 v1))) NIL) (17 (paramod 5 (1) 16 (1 1 1)) (= (n (+ v0 (n (+ (n (+ v0 v1)) (n (n (+ v0 (n v1)))))))) (n (+ v0 v1))) (52)) (18 (instantiate 5 ((v0 . v64)(v1 . (+ (n (+ v0 v1)) (n (+ v0 (n v1))))))) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))) (n (+ v64 (n (+ (n (+ v0 v1)) (n (+ v0 (n v1))))))))) v64) NIL) (19 (paramod 5 (1) 18 (1 1 2 1 2)) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))) (n (+ v64 v0)))) v64) NIL) (20 (instantiate 2 ((v0 . (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))))(v1 . (n (+ v64 v0))))) (= (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))) (n (+ v64 v0))) (+ (n (+ v64 v0)) (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))))) NIL) (21 (paramod 20 (1) 19 (1 1)) (= (n (+ (n (+ v64 v0)) (n (+ v64 (+ (n (+ v0 v1)) (n (+ v0 (n v1)))))))) v64) NIL) (22 (instantiate 21 ((v0 . v1)(v1 . v2)(v64 . v0))) (= (n (+ (n (+ v0 v1)) (n (+ v0 (+ (n (+ v1 v2)) (n (+ v1 (n v2)))))))) v0) (54)) (23 (instantiate 2 ((v0 . v64)(v1 . (n v65)))) (= (+ v64 (n v65)) (+ (n v65) v64)) NIL) (24 (instantiate 5 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v64 (n v65))))) v64) NIL) (25 (paramod 23 (1) 24 (1 1 2 1)) (= (n (+ (n (+ v64 v65)) (n (+ (n v65) v64)))) v64) NIL) (26 (instantiate 25 ((v64 . v0)(v65 . v1))) (= (n (+ (n (+ v0 v1)) (n (+ (n v1) v0)))) v0) (56)) (27 (instantiate 2 ((v0 . v65)(v1 . v66))) (= (+ v65 v66) (+ v66 v65)) NIL) (28 (instantiate 11 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v64 v66)))))) v65) NIL) (29 (paramod 27 (1) 28 (1 1 1 1 2)) (= (n (+ (n (+ v64 (+ v66 v65))) (n (+ v65 (n (+ v64 v66)))))) v65) NIL) (30 (instantiate 29 ((v64 . v0)(v65 . v2)(v66 . v1))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ v2 (n (+ v0 v1)))))) v2) (64)) (31 (instantiate 2 ((v0 . v64)(v1 . v66))) (= (+ v64 v66) (+ v66 v64)) NIL) (32 (instantiate 11 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v64 v66)))))) v65) NIL) (33 (paramod 31 (1) 32 (1 1 2 1 2 1)) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v66 v64)))))) v65) NIL) (34 (instantiate 33 ((v64 . v0)(v65 . v1)(v66 . v2))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ v1 (n (+ v2 v0)))))) v1) (70)) (35 (instantiate 2 ((v0 . v65)(v1 . (n v64)))) (= (+ v65 (n v64)) (+ (n v64) v65)) NIL) (36 (instantiate 15 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v65 (n v64))))) v65) NIL) (37 (paramod 35 (1) 36 (1 1 2 1)) (= (n (+ (n (+ v64 v65)) (n (+ (n v64) v65)))) v65) NIL) (38 (instantiate 37 ((v64 . v0)(v65 . v1))) (= (n (+ (n (+ v0 v1)) (n (+ (n v0) v1)))) v1) (102)) (39 (instantiate 2 ((v0 . (n (+ v64 v65)))(v1 . (n (+ v65 (n v64)))))) (= (+ (n (+ v64 v65)) (n (+ v65 (n v64)))) (+ (n (+ v65 (n v64))) (n (+ v64 v65)))) NIL) (40 (instantiate 15 ((v0 . v64)(v1 . v65))) (= (n (+ (n (+ v64 v65)) (n (+ v65 (n v64))))) v65) NIL) (41 (paramod 39 (1) 40 (1 1)) (= (n (+ (n (+ v65 (n v64))) (n (+ v64 v65)))) v65) NIL) (42 (instantiate 41 ((v64 . v1)(v65 . v0))) (= (n (+ (n (+ v0 (n v1))) (n (+ v1 v0)))) v0) (106)) (43 (instantiate 26 ((v0 . v64)(v1 . (+ (n (+ v0 v1)) (n (+ v1 (n v0))))))) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v1 (n v0)))))) (n (+ (n (+ (n (+ v0 v1)) (n (+ v1 (n v0))))) v64)))) v64) NIL) (44 (paramod 15 (1) 43 (1 1 2 1 1)) (= (n (+ (n (+ v64 (+ (n (+ v0 v1)) (n (+ v1 (n v0)))))) (n (+ v1 v64)))) v64) NIL) (45 (instantiate 44 ((v0 . v1)(v1 . v2)(v64 . v0))) (= (n (+ (n (+ v0 (+ (n (+ v1 v2)) (n (+ v2 (n v1)))))) (n (+ v2 v0)))) v0) (158)) (46 (instantiate 15 ((v0 . (c))(v1 . (d)))) (= (n (+ (n (+ (c) (d))) (n (+ (d) (n (c)))))) (d)) NIL) (47 (paramod 6 (1) 46 (1 1 1 1)) (= (n (+ (n (c)) (n (+ (d) (n (c)))))) (d)) (204)) (48 (instantiate 3 ((v0 . (c))(v1 . (d))(v2 . v66))) (= (+ (+ (c) (d)) v66) (+ (c) (+ (d) v66))) NIL) (49 (paramod 6 (1) 48 (1 1)) (= (+ (c) v66) (+ (c) (+ (d) v66))) NIL) (50 (flip 49 ()) (= (+ (c) (+ (d) v66)) (+ (c) v66)) NIL) (51 (instantiate 50 ((v66 . v0))) (= (+ (c) (+ (d) v0)) (+ (c) v0)) (206)) (52 (instantiate 34 ((v0 . v64)(v1 . (c))(v2 . (d)))) (= (n (+ (n (+ v64 (+ (c) (d)))) (n (+ (c) (n (+ (d) v64)))))) (c)) NIL) (53 (paramod 6 (1) 52 (1 1 1 1 2)) (= (n (+ (n (+ v64 (c))) (n (+ (c) (n (+ (d) v64)))))) (c)) NIL) (54 (instantiate 53 ((v64 . v0))) (= (n (+ (n (+ v0 (c))) (n (+ (c) (n (+ (d) v0)))))) (c)) (244)) (55 (instantiate 2 ((v0 . v65)(v1 . (n (+ v66 v64))))) (= (+ v65 (n (+ v66 v64))) (+ (n (+ v66 v64)) v65)) NIL) (56 (instantiate 34 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ v65 (n (+ v66 v64)))))) v65) NIL) (57 (paramod 55 (1) 56 (1 1 2 1)) (= (n (+ (n (+ v64 (+ v65 v66))) (n (+ (n (+ v66 v64)) v65)))) v65) NIL) (58 (instantiate 57 ((v64 . v0)(v65 . v1)(v66 . v2))) (= (n (+ (n (+ v0 (+ v1 v2))) (n (+ (n (+ v2 v0)) v1)))) v1) (272)) (59 (instantiate 38 ((v0 . (+ v0 v1))(v1 . (n (+ (n v0) v1))))) (= (n (+ (n (+ (+ v0 v1) (n (+ (n v0) v1)))) (n (+ (n (+ v0 v1)) (n (+ (n v0) v1)))))) (n (+ (n v0) v1))) NIL) (60 (paramod 38 (1) 59 (1 1 2)) (= (n (+ (n (+ (+ v0 v1) (n (+ (n v0) v1)))) v1)) (n (+ (n v0) v1))) NIL) (61 (instantiate 3 ((v0 . v0)(v1 . v1)(v2 . (n (+ (n v0) v1))))) (= (+ (+ v0 v1) (n (+ (n v0) v1))) (+ v0 (+ v1 (n (+ (n v0) v1))))) NIL) (62 (paramod 61 (1) 60 (1 1 1 1)) (= (n (+ (n (+ v0 (+ v1 (n (+ (n v0) v1))))) v1)) (n (+ (n v0) v1))) NIL) (63 (instantiate 2 ((v0 . (n (+ v0 (+ v1 (n (+ (n v0) v1))))))(v1 . v1))) (= (+ (n (+ v0 (+ v1 (n (+ (n v0) v1))))) v1) (+ v1 (n (+ v0 (+ v1 (n (+ (n v0) v1))))))) NIL) (64 (paramod 63 (1) 62 (1 1)) (= (n (+ v1 (n (+ v0 (+ v1 (n (+ (n v0) v1))))))) (n (+ (n v0) v1))) NIL) (65 (instantiate 64 ((v0 . v1)(v1 . v0))) (= (n (+ v0 (n (+ v1 (+ v0 (n (+ (n v1) v0))))))) (n (+ (n v1) v0))) (338)) (66 (instantiate 4 ((v0 . v65))) (= (+ v65 (+ v1 v2)) (+ v1 (+ v65 v2))) NIL) (67 (instantiate 42 ((v0 . (+ v1 v2))(v1 . v65))) (= (n (+ (n (+ (+ v1 v2) (n v65))) (n (+ v65 (+ v1 v2))))) (+ v1 v2)) NIL) (68 (paramod 66 (1) 67 (1 1 2 1)) (= (n (+ (n (+ (+ v1 v2) (n v65))) (n (+ v1 (+ v65 v2))))) (+ v1 v2)) NIL) (69 (instantiate 3 ((v0 . v1)(v1 . v2)(v2 . (n v65)))) (= (+ (+ v1 v2) (n v65)) (+ v1 (+ v2 (n v65)))) NIL) (70 (paramod 69 (1) 68 (1 1 1 1)) (= (n (+ (n (+ v1 (+ v2 (n v65)))) (n (+ v1 (+ v65 v2))))) (+ v1 v2)) NIL) (71 (instantiate 70 ((v1 . v0)(v2 . v1)(v65 . v2))) (= (n (+ (n (+ v0 (+ v1 (n v2)))) (n (+ v0 (+ v2 v1))))) (+ v0 v1)) (376)) (72 (instantiate 22 ((v0 . v64)(v1 . (n (+ v0 (n v1))))(v2 . (+ v1 v0)))) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ (n (+ v0 (n v1))) (+ v1 v0))) (n (+ (n (+ v0 (n v1))) (n (+ v1 v0))))))))) v64) NIL) (73 (paramod 42 (1) 72 (1 1 2 1 2 2)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ (n (+ v0 (n v1))) (+ v1 v0))) v0))))) v64) NIL) (74 (instantiate 4 ((v0 . (n (+ v0 (n v1))))(v1 . v1)(v2 . v0))) (= (+ (n (+ v0 (n v1))) (+ v1 v0)) (+ v1 (+ (n (+ v0 (n v1))) v0))) NIL) (75 (paramod 74 (1) 73 (1 1 2 1 2 1 1)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ v1 (+ (n (+ v0 (n v1))) v0))) v0))))) v64) NIL) (76 (instantiate 2 ((v0 . (n (+ v0 (n v1))))(v1 . v0))) (= (+ (n (+ v0 (n v1))) v0) (+ v0 (n (+ v0 (n v1))))) NIL) (77 (paramod 76 (1) 75 (1 1 2 1 2 1 1 2)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ (n (+ v1 (+ v0 (n (+ v0 (n v1)))))) v0))))) v64) NIL) (78 (instantiate 2 ((v0 . (n (+ v1 (+ v0 (n (+ v0 (n v1)))))))(v1 . v0))) (= (+ (n (+ v1 (+ v0 (n (+ v0 (n v1)))))) v0) (+ v0 (n (+ v1 (+ v0 (n (+ v0 (n v1)))))))) NIL) (79 (paramod 78 (1) 77 (1 1 2 1 2)) (= (n (+ (n (+ v64 (n (+ v0 (n v1))))) (n (+ v64 (+ v0 (n (+ v1 (+ v0 (n (+ v0 (n v1))))))))))) v64) NIL) (80 (instantiate 79 ((v0 . v1)(v1 . v2)(v64 . v0))) (= (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2))))))))))) v0) (378)) (81 (instantiate 45 ((v0 . (d))(v1 . v65)(v2 . (c)))) (= (n (+ (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))) (n (+ (c) (d))))) (d)) NIL) (82 (paramod 6 (1) 81 (1 1 2 1)) (= (n (+ (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))) (n (c)))) (d)) NIL) (83 (instantiate 2 ((v0 . (n (+ (d) (+ (n (+ v65 (c))) (n (+ (c) (n v65)))))))(v1 . 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(n (+ (c) (n (c))))))) (= (+ v64 (n (+ (c) (n (c))))) (+ (n (+ (c) (n (c)))) v64)) NIL) (171 (instantiate 169 ((v0 . v64))) (= (+ v64 (n (+ (c) (n (c))))) v64) NIL) (172 (paramod 170 (1) 171 (1)) (= (+ (n (+ (c) (n (c)))) v64) v64) NIL) (173 (instantiate 172 ((v64 . v0))) (= (+ (n (+ (c) (n (c)))) v0) v0) (1698)) (174 (instantiate 169 ((v0 . (n v65)))) (= (+ (n v65) (n (+ (c) (n (c))))) (n v65)) NIL) (175 (instantiate 65 ((v0 . (n (+ (c) (n (c)))))(v1 . v65))) (= (n (+ (n (+ (c) (n (c)))) (n (+ v65 (+ (n (+ (c) (n (c)))) (n (+ (n v65) (n (+ (c) (n (c))))))))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL) (176 (paramod 174 (1) 175 (1 1 2 1 2 2 1)) (= (n (+ (n (+ (c) (n (c)))) (n (+ v65 (+ (n (+ (c) (n (c)))) (n (n v65))))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL) (177 (instantiate 173 ((v0 . (n (n v65))))) (= (+ (n (+ (c) (n (c)))) (n (n v65))) (n (n v65))) NIL) (178 (paramod 177 (1) 176 (1 1 2 1 2)) (= (n (+ (n (+ (c) (n (c)))) (n (+ v65 (n (n v65)))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL) (179 (instantiate 173 ((v0 . (n (+ v65 (n (n v65))))))) (= (+ (n (+ (c) (n (c)))) (n (+ v65 (n (n v65))))) (n (+ v65 (n (n v65))))) NIL) (180 (paramod 179 (1) 178 (1 1)) (= (n (n (+ v65 (n (n v65))))) (n (+ (n v65) (n (+ (c) (n (c))))))) NIL) (181 (instantiate 169 ((v0 . (n v65)))) (= (+ (n v65) (n (+ (c) (n (c))))) (n v65)) NIL) (182 (paramod 181 (1) 180 (2 1)) (= (n (n (+ v65 (n (n v65))))) (n (n v65))) NIL) (183 (instantiate 182 ((v65 . v0))) (= (n (n (+ v0 (n (n v0))))) (n (n v0))) (1752)) (184 (instantiate 173 ((v0 . (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))))) (= (+ (n (+ (c) (n (c)))) (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) NIL) (185 (instantiate 17 ((v0 . (n (+ (c) (n (c)))))(v1 . v65))) (= (n (+ (n (+ (c) (n (c)))) (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65)))))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL) (186 (paramod 184 (1) 185 (1 1)) (= (n (n (+ (n (+ (n (+ (c) (n (c)))) v65)) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL) (187 (instantiate 173 ((v0 . v65))) (= (+ (n (+ (c) (n (c)))) v65) v65) NIL) (188 (paramod 187 (1) 186 (1 1 1 1 1)) (= (n (n (+ (n v65) (n (n (+ (n (+ (c) (n (c)))) (n v65))))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL) (189 (instantiate 173 ((v0 . (n v65)))) (= (+ (n (+ (c) (n (c)))) (n v65)) (n v65)) NIL) (190 (paramod 189 (1) 188 (1 1 1 2 1 1)) (= (n (n (+ (n v65) (n (n (n v65)))))) (n (+ (n (+ (c) (n (c)))) v65))) NIL) (191 (instantiate 183 ((v0 . (n v65)))) (= (n (n (+ (n v65) (n (n (n v65)))))) (n (n (n v65)))) NIL) (192 (paramod 191 (1) 190 (1)) (= (n (n (n v65))) (n (+ (n (+ (c) (n (c)))) v65))) NIL) (193 (instantiate 173 ((v0 . v65))) (= (+ (n (+ (c) (n (c)))) v65) v65) NIL) (194 (paramod 193 (1) 192 (2 1)) (= (n (n (n v65))) (n v65)) NIL) (195 (instantiate 194 ((v65 . v0))) (= (n (n (n v0))) (n v0)) (1961)) (196 (instantiate 195 ((v0 . (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2))))))))))))) (= (n (n (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2))))))))))))) (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2)))))))))))) NIL) (197 (paramod 80 (1) 196 (1 1 1)) (= (n (n v0)) (n (+ (n (+ v0 (n (+ v1 (n v2))))) (n (+ v0 (+ v1 (n (+ v2 (+ v1 (n (+ v1 (n v2)))))))))))) NIL) (198 (paramod 80 (1) 197 (2)) (= (n (n v0)) v0) (2031)) (199 (instantiate 198 ((v0 . (+ (n (+ v0 v1)) (n (+ (n v0) v1)))))) (= (n (n (+ (n (+ v0 v1)) (n (+ (n v0) v1))))) (+ (n (+ v0 v1)) (n (+ (n v0) v1)))) NIL) (200 (paramod 38 (1) 199 (1 1)) (= (n v1) (+ (n (+ v0 v1)) (n (+ (n v0) v1)))) NIL) (201 (flip 200 ()) (= (+ (n (+ v0 v1)) (n (+ (n v0) v1))) (n v1)) (2143)) (202 (instantiate 201 ((v0 . (A))(v1 . (n (B))))) (= (+ (n (+ (A) (n (B)))) (n (+ (n (A)) (n (B))))) (n (n (B)))) NIL) (203 (paramod 202 (1) 7 (1 1)) (not (= (n (n (B))) (B))) NIL) (204 (instantiate 198 ((v0 . (B)))) (= (n (n (B))) (B)) NIL) (205 (paramod 204 (1) 203 (1 1)) (not (= (B) (B))) (2173)) (206 (instantiate 1 ((v0 . (B)))) (= (B) (B)) NIL) (207 (resolve 205 () 206 ()) false (2174)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 48 clauses generated 3063 para_from generated 1790 para_into generated 1273 demod & eval rewrites 6647 clauses wt,lit,sk delete 773 tautologies deleted 0 clauses forward subsumed 1669 (subsumed by sos) 16 unit deletions 0 factor simplifications 0 clauses kept 1073 new demodulators 1067 empty clauses 1 clauses back demodulated 423 clauses back subsumed 2 usable size 24 sos size 624 demodulators size 645 passive size 0 hot size 0 Kbytes malloced 7812 ----------- times (seconds) ----------- user CPU time 0.48 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8947 finished Mon Aug 2 15:31:15 2004 otter-3.3f/examples/fringe/x3tricks.out0100664000076400007640000003336410103522223017575 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:15 2004 The command was "../../bin/otter". The process ID is 8952. set(hyper_res). clear(order_hyper). set(para_into). set(para_from). WARNING: set(para_from_left) flag already set. set(para_from_left). clear(para_from_right). WARNING: set(para_into_left) flag already set. set(para_into_left). clear(para_into_right). set(order_eq). set(dynamic_demod). assign(dynamic_demod_depth,1). assign(dynamic_demod_rhs,5). set(back_demod). WARNING: clear(symbol_elim) flag already clear. clear(symbol_elim). set(lex_order_vars). assign(demod_limit,250). assign(max_weight,999). assign(max_literals,1). clear(print_kept). clear(print_back_sub). clear(print_new_demod). clear(print_back_demod). assign(age_factor,1). lex([A,B,E,MULT(x,x),INV(x),Coeff(x,x),ADD(x,x)]). special_unary([INV(x),Coeff(x,x)]). list(usable). 1 [] EQ(ADD(x,y),ADD(y,x)). 2 [] EQ(ADD(ADD(x,y),z),ADD(x,ADD(y,z))). 3 [] EQ(MULT(MULT(x,y),z),MULT(x,MULT(y,z))). 4 [] EQ(MULT(ADD(x,y),z),ADD(MULT(x,z),MULT(y,z))). 5 [] EQ(MULT(x,ADD(y,z)),ADD(MULT(x,y),MULT(x,z))). 6 [] EQ(ADD(x,E),x). 7 [] EQ(ADD(E,x),x). 8 [] EQ(ADD(INV(x),x),E). 9 [] EQ(ADD(x,INV(x)),E). 10 [] EQ(x,x). 11 [] EQ(MULT(INV(x),y),INV(MULT(x,y))). 12 [] EQ(MULT(x,INV(y)),INV(MULT(x,y))). 13 [] EQ(INV(ADD(x,y)),ADD(INV(x),INV(y))). 14 [] TID(ADD(x,v),x,v). 15 [] TID(ADD(x1,ADD(x,v)),x,ADD(x1,v)). 16 [] TID(ADD(x1,ADD(x2,ADD(x,v))),x,ADD(x1,ADD(x2,v))). 17 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(x,v)))),x,ADD(x1,ADD(x2,ADD(x3,v)))). 18 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x,v))))),x,ADD(x1,ADD(x2,ADD(x3,ADD(x4,v))))). 19 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,ADD(x,v)))))),x,ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,v)))))). 20 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,ADD(x6,ADD(x,v))))))),x,ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(x5,ADD(x6,v))))))). 21 [] TID(Coeff(x,z),x,Coeff(x,$DIFF(z,1)))|$NOT($INT(z)). 22 [] TID(ADD(Coeff(x,z),v),x,ADD(Coeff(x,$DIFF(z,1)),v))|$NOT($INT(z)). 23 [] TID(ADD(x1,ADD(Coeff(x,z),v)),x,ADD(x1,ADD(Coeff(x,$DIFF(z,1)),v)))|$NOT($INT(z)). 24 [] TID(ADD(x1,ADD(x2,ADD(Coeff(x,z),v))),x,ADD(x1,ADD(x2,ADD(Coeff(x,$DIFF(z,1)),v))))|$NOT($INT(z)). 25 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(Coeff(x,z),v)))),x,ADD(x1,ADD(x2,ADD(x3,ADD(Coeff(x,$DIFF(z,1)),v)))))|$NOT($INT(z)). 26 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,z),v))))),x,ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,$DIFF(z,1)),v))))))|$NOT($INT(z)). 27 [] TID(ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,z),v))))),x,ADD(x1,ADD(x2,ADD(x3,ADD(x4,ADD(Coeff(x,$DIFF(z,1)),v))))))|$NOT($INT(z)). 28 [] IDENT(x,x). 29 [] -EQ(w,v)| -TID(w,x1,w1)| -TID(v,x2,v1)| -$RENAME(x1,x2)| -IDENT(x1,x2)|EQ(ADD(INV(w1),v1),E). 30 [] -EQ(w,E)| -EQ(v,E)| -TID(w,x1,w1)| -TID(v,x2,v1)| -$RENAME(x1,x2)| -IDENT(x1,x2)|EQ(ADD(INV(w1),v1),E). 31 [] -EQ(Coeff(x,y),E)|EQ(IsCycle(x),y). end_of_list. list(sos). 32 [] EQ(MULT(x,MULT(x,x)),x). 33 [] -EQ(ADD(Coeff(MULT(A,B),3),Coeff(MULT(B,A),3)),E). end_of_list. list(demodulators). 34 [] $GT(x,IsCycle(z))->EQ(Coeff(z,x),Coeff(z,$MOD(x,IsCycle(z)))). 35 [] EQ(MULT(x,MULT(x,x)),x). 36 [] EQ(ADD(x,y),ADD(y,x)). 37 [] EQ(ADD(x,ADD(y,z)),ADD(y,ADD(x,z))). 38 [] EQ(ADD(ADD(x,y),z),ADD(x,ADD(y,z))). 39 [] EQ(MULT(MULT(x,y),z),MULT(x,MULT(y,z))). 40 [] EQ(MULT(ADD(x,y),z),ADD(MULT(x,z),MULT(y,z))). 41 [] EQ(MULT(x,ADD(y,z)),ADD(MULT(x,y),MULT(x,z))). 42 [] EQ(ADD(x,E),x). 43 [] EQ(ADD(E,x),x). 44 [] EQ(MULT(E,x),E). 45 [] EQ(MULT(x,E),E). 46 [] EQ(INV(E),E). 47 [] EQ(INV(INV(x)),x). 48 [] EQ(MULT(x,INV(y)),INV(MULT(x,y))). 49 [] EQ(MULT(INV(x),y),INV(MULT(x,y))). 50 [] EQ(INV(ADD(x,y)),ADD(INV(x),INV(y))). 51 [] EQ(INV(Coeff(x,y)),Coeff(INV(x),y)). 52 [] EQ(ADD(x,INV(x)),E). 53 [] EQ(ADD(x,ADD(INV(x),y)),y). 54 [] EQ(ADD(x,x),Coeff(x,2)). 55 [] $INT(y)->EQ(ADD(x,Coeff(x,y)),Coeff(x,$SUM(y,1))). 56 [] $AND($INT(y),$INT(z))->EQ(ADD(Coeff(x,y),Coeff(x,z)),Coeff(x,$SUM(y,z))). 57 [] EQ(ADD(x,ADD(x,y)),ADD(Coeff(x,2),y)). 58 [] $INT(y)->EQ(ADD(x,ADD(Coeff(x,y),z)),ADD(Coeff(x,$SUM(y,1)),z)). 59 [] $AND($INT(y),$INT(z))->EQ(ADD(Coeff(x,y),ADD(Coeff(x,z),v)),ADD(Coeff(x,$SUM(y,z)),v)). 60 [] $AND($INT(y),$INT(z))->EQ(Coeff(Coeff(x,y),z),Coeff(x,$PROD(y,z))). 61 [] EQ(Coeff(E,x),E). 62 [] EQ(Coeff(x,0),E). 63 [] EQ(Coeff(x,1),x). 64 [] EQ(MULT(x,Coeff(y,z)),Coeff(MULT(x,y),z)). 65 [] EQ(MULT(Coeff(x,z),y),Coeff(MULT(x,y),z)). 66 [] EQ(Coeff(ADD(x,y),z),ADD(Coeff(x,z),Coeff(y,z))). 67 [] $INT(y)->EQ(ADD(x,Coeff(INV(x),y)),Coeff(INV(x),$DIFF(y,1))). 68 [] $INT(y)->EQ(ADD(INV(x),Coeff(x,y)),Coeff(x,$DIFF(y,1))). 69 [] EQ(ADD(Coeff(x,y),Coeff(INV(x),y)),E). 70 [] $AND($INT(y),$AND($INT(z),$GT(y,z)))->EQ(ADD(Coeff(x,y),Coeff(INV(x),z)),Coeff(x,$DIFF(y,z))). 71 [] $AND($INT(y),$AND($INT(z),$GT(z,y)))->EQ(ADD(Coeff(x,y),Coeff(INV(x),z)),Coeff(INV(x),$DIFF(z,y))). 72 [] $INT(y)->EQ(ADD(x,ADD(Coeff(INV(x),y),zzz)),ADD(Coeff(INV(x),$DIFF(y,1)),zzz)). 73 [] $INT(y)->EQ(ADD(INV(x),ADD(Coeff(x,y),zzz)),ADD(Coeff(x,$DIFF(y,1)),zzz)). 74 [] EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),y),zzz)),zzz). 75 [] $AND($INT(y),$AND($INT(z),$GT(y,z)))->EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),z),zzz)),ADD(Coeff(x,$DIFF(y,z)),zzz)). 76 [] $AND($INT(y),$AND($INT(z),$GT(z,y)))->EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),z),zzz)),ADD(Coeff(INV(x),$DIFF(z,y)),zzz)). 77 [] EQ(EQ(ADD(x,y),ADD(u,v)),EQ(ADD(INV(ADD(u,v)),ADD(x,y)),E)). 78 [] EQ(EQ(ADD(x,y),MULT(u,v)),EQ(ADD(INV(MULT(u,v)),ADD(x,y)),E)). 79 [] EQ(EQ(ADD(x,y),INV(u)),EQ(ADD(u,ADD(x,y)),E)). 80 [] EQ(EQ(ADD(x,y),Coeff(u,v)),EQ(ADD(INV(Coeff(u,v)),ADD(x,y)),E)). 81 [] EQ(EQ(INV(x),E),EQ(x,E)). 82 [] EQ(EQ(ADD(INV(x),y),E),EQ(ADD(x,INV(y)),E)). 83 [] EQ(EQ(ADD(Coeff(INV(x),y),z),E),EQ(ADD(Coeff(x,y),INV(z)),E)). 84 [] EQ(EQ(MULT(u,v),ADD(x,y)),EQ(ADD(INV(MULT(u,v)),ADD(x,y)),E)). 85 [] EQ(EQ(INV(u),ADD(x,y)),EQ(ADD(u,ADD(x,y)),E)). 86 [] EQ(EQ(Coeff(u,v),ADD(x,y)),EQ(ADD(INV(Coeff(u,v)),ADD(x,y)),E)). 87 [] EQ(EQ(E,INV(x)),EQ(x,E)). 88 [] EQ(EQ(E,ADD(INV(x),y)),EQ(ADD(x,INV(y)),E)). 89 [] EQ(EQ(E,ADD(Coeff(INV(x),y),z)),EQ(ADD(Coeff(x,y),INV(z)),E)). end_of_list. weight_list(pick_given). weight(EQ(Coeff($(1),$(1)),E),-100). end_of_list. weight_list(purge_gen). weight(MULT($(1),MULT($(1),MULT($(1),MULT($(1),$(1))))),9999). weight(ADD($(1),ADD($(1),ADD($(1),ADD($(1),ADD($(1),ADD($(1),$(1))))))),9999). weight(Coeff(Coeff($(1),$(1)),$(1)),9999). weight(TID($(1),$(1),$(1)),9999). end_of_list. weight_list(terms). weight(ADD($(1),$(1)),+10). end_of_list. lex dependent demodulator: 36 [] EQ(ADD(x,y),ADD(y,x)). lex dependent demodulator: 37 [] EQ(ADD(x,ADD(y,z)),ADD(y,ADD(x,z))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=7) 32 [] EQ(MULT(x,MULT(x,x)),x). given clause #2: (wt=12) 92 [para_from,32.1.1,3.1.1.1,demod,39,flip.1] EQ(MULT(x,MULT(x,MULT(x,y))),MULT(x,y)). given clause #3: (wt=13) 33 [] -EQ(ADD(Coeff(MULT(A,B),3),Coeff(MULT(B,A),3)),E). given clause #4: (wt=38) 90 [para_into,32.1.1.2,5.1.1,demod,40,40,37,36,37,36,37,41,40,35,41,40,41,40,40,35,36,36,37,36,37,36,37,36,37,36,37,37,37,37,37,37,37,37,37,36,37,36,37,37,37,37,37,37,77,50,36,37,36,37,37,53,37,53] EQ(ADD(MULT(x,MULT(x,y)),ADD(MULT(x,MULT(y,x)),ADD(MULT(x,MULT(y,y)),ADD(MULT(y,MULT(x,x)),ADD(MULT(y,MULT(x,y)),MULT(y,MULT(y,x))))))),E). given clause #5: (wt=-94) 100 [para_into,90.1.1.1,32.1.1,demod,35,35,35,35,35,54,55,55,55,55] EQ(Coeff(x,6),E). given clause #6: (wt=9) 104 [hyper,100,31] EQ(IsCycle(x),6). given clause #7: (wt=15) 96 [para_into,90.1.1.1.2,32.1.1,demod,39,35,39,35,35,39,35,35,39,35,39,35,39,35,54,36,58,37,54,37,55] EQ(ADD(Coeff(x,3),Coeff(MULT(x,x),3)),E). given clause #8: (wt=19) 106 [hyper,96,30,100,21,22,eval,28,demod,51,37,76,83,51,propositional] EQ(ADD(Coeff(x,3),Coeff(INV(MULT(x,x)),3)),E). given clause #9: (wt=22) 112 [para_from,96.1.1,5.1.1.2,demod,45,64,64,flip.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(MULT(x,MULT(y,y)),3)),E). given clause #10: (wt=22) 114 [para_from,96.1.1,4.1.1.1,demod,44,65,65,39,flip.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(MULT(x,MULT(x,y)),3)),E). given clause #11: (wt=24) 110 [para_into,96.1.1.2.1,3.1.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(MULT(x,MULT(y,MULT(x,y))),3)),E). given clause #12: (wt=24) 120 [para_from,106.1.1,5.1.1.2,demod,45,64,64,48,flip.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(INV(MULT(x,MULT(y,y))),3)),E). given clause #13: (wt=24) 122 [para_from,106.1.1,4.1.1.1,demod,44,65,65,49,39,flip.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(INV(MULT(x,MULT(x,y))),3)),E). given clause #14: (wt=26) 118 [para_into,106.1.1.2.1.1,3.1.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(INV(MULT(x,MULT(y,MULT(x,y)))),3)),E). given clause #15: (wt=28) 126 [para_into,112.1.1.1.1,3.1.1,demod,39] EQ(ADD(Coeff(MULT(x,MULT(y,z)),3),Coeff(MULT(x,MULT(y,MULT(z,z))),3)),E). given clause #16: (wt=28) 128 [para_from,112.1.1,4.1.1.1,demod,44,65,39,65,39,39,flip.1] EQ(ADD(Coeff(MULT(x,MULT(y,z)),3),Coeff(MULT(x,MULT(y,MULT(y,z))),3)),E). given clause #17: (wt=28) 130 [hyper,114,30,112,22,22,eval,28,demod,50,51,51,36,37,36,37,36,37,74,propositional] EQ(ADD(Coeff(MULT(x,MULT(x,y)),3),Coeff(INV(MULT(x,MULT(y,y))),3)),E). given clause #18: (wt=29) 134 [para_from,114.1.1,4.1.1.1,demod,44,65,39,65,39,39,36,flip.1] EQ(ADD(Coeff(MULT(x,MULT(x,MULT(y,z))),3),Coeff(MULT(x,MULT(y,z)),3)),E). given clause #19: (wt=29) 144 [hyper,120,30,114,22,22,eval,28,demod,50,51,51,36,37,36,37,37,74,83,51,47,propositional] EQ(ADD(Coeff(MULT(x,MULT(x,y)),3),Coeff(MULT(x,MULT(y,y)),3)),E). given clause #20: (wt=30) 108 [para_into,96.1.1.2.1,5.1.1,demod,66,40,40,37,36,37,36,37,66,66,66,37,37,37,36,37,36,97,42,36,37,37] EQ(ADD(Coeff(x,3),ADD(Coeff(MULT(x,x),3),ADD(Coeff(MULT(x,y),3),Coeff(MULT(y,x),3)))),E). -------- PROOF -------- ----> UNIT CONFLICT at 0.13 sec ----> 194 [binary,192.1,33.1] $F. Length of proof is 7. Level of proof is 5. ---------------- PROOF ---------------- 4 [] EQ(MULT(ADD(x,y),z),ADD(MULT(x,z),MULT(y,z))). 5 [] EQ(MULT(x,ADD(y,z)),ADD(MULT(x,y),MULT(x,z))). 21 [] TID(Coeff(x,z),x,Coeff(x,$DIFF(z,1)))|$NOT($INT(z)). 22 [] TID(ADD(Coeff(x,z),v),x,ADD(Coeff(x,$DIFF(z,1)),v))|$NOT($INT(z)). 23 [] TID(ADD(x1,ADD(Coeff(x,z),v)),x,ADD(x1,ADD(Coeff(x,$DIFF(z,1)),v)))|$NOT($INT(z)). 28 [] IDENT(x,x). 30 [] -EQ(w,E)| -EQ(v,E)| -TID(w,x1,w1)| -TID(v,x2,v1)| -$RENAME(x1,x2)| -IDENT(x1,x2)|EQ(ADD(INV(w1),v1),E). 32 [] EQ(MULT(x,MULT(x,x)),x). 33 [] -EQ(ADD(Coeff(MULT(A,B),3),Coeff(MULT(B,A),3)),E). 35 [] EQ(MULT(x,MULT(x,x)),x). 36 [] EQ(ADD(x,y),ADD(y,x)). 37 [] EQ(ADD(x,ADD(y,z)),ADD(y,ADD(x,z))). 39 [] EQ(MULT(MULT(x,y),z),MULT(x,MULT(y,z))). 40 [] EQ(MULT(ADD(x,y),z),ADD(MULT(x,z),MULT(y,z))). 41 [] EQ(MULT(x,ADD(y,z)),ADD(MULT(x,y),MULT(x,z))). 42 [] EQ(ADD(x,E),x). 43 [] EQ(ADD(E,x),x). 44 [] EQ(MULT(E,x),E). 47 [] EQ(INV(INV(x)),x). 49 [] EQ(MULT(INV(x),y),INV(MULT(x,y))). 50 [] EQ(INV(ADD(x,y)),ADD(INV(x),INV(y))). 51 [] EQ(INV(Coeff(x,y)),Coeff(INV(x),y)). 53 [] EQ(ADD(x,ADD(INV(x),y)),y). 54 [] EQ(ADD(x,x),Coeff(x,2)). 55 [] $INT(y)->EQ(ADD(x,Coeff(x,y)),Coeff(x,$SUM(y,1))). 57 [] EQ(ADD(x,ADD(x,y)),ADD(Coeff(x,2),y)). 58 [] $INT(y)->EQ(ADD(x,ADD(Coeff(x,y),z)),ADD(Coeff(x,$SUM(y,1)),z)). 60 [] $AND($INT(y),$INT(z))->EQ(Coeff(Coeff(x,y),z),Coeff(x,$PROD(y,z))). 65 [] EQ(MULT(Coeff(x,z),y),Coeff(MULT(x,y),z)). 66 [] EQ(Coeff(ADD(x,y),z),ADD(Coeff(x,z),Coeff(y,z))). 74 [] EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),y),zzz)),zzz). 76 [] $AND($INT(y),$AND($INT(z),$GT(z,y)))->EQ(ADD(Coeff(x,y),ADD(Coeff(INV(x),z),zzz)),ADD(Coeff(INV(x),$DIFF(z,y)),zzz)). 77 [] EQ(EQ(ADD(x,y),ADD(u,v)),EQ(ADD(INV(ADD(u,v)),ADD(x,y)),E)). 83 [] EQ(EQ(ADD(Coeff(INV(x),y),z),E),EQ(ADD(Coeff(x,y),INV(z)),E)). 90 [para_into,32.1.1.2,5.1.1,demod,40,40,37,36,37,36,37,41,40,35,41,40,41,40,40,35,36,36,37,36,37,36,37,36,37,36,37,37,37,37,37,37,37,37,37,36,37,36,37,37,37,37,37,37,77,50,36,37,36,37,37,53,37,53] EQ(ADD(MULT(x,MULT(x,y)),ADD(MULT(x,MULT(y,x)),ADD(MULT(x,MULT(y,y)),ADD(MULT(y,MULT(x,x)),ADD(MULT(y,MULT(x,y)),MULT(y,MULT(y,x))))))),E). 97,96 [para_into,90.1.1.1.2,32.1.1,demod,39,35,39,35,35,39,35,35,39,35,39,35,39,35,54,36,58,37,54,37,55] EQ(ADD(Coeff(x,3),Coeff(MULT(x,x),3)),E). 101,100 [para_into,90.1.1.1,32.1.1,demod,35,35,35,35,35,54,55,55,55,55] EQ(Coeff(x,6),E). 106 [hyper,96,30,100,21,22,eval,28,demod,51,37,76,83,51,propositional] EQ(ADD(Coeff(x,3),Coeff(INV(MULT(x,x)),3)),E). 108 [para_into,96.1.1.2.1,5.1.1,demod,66,40,40,37,36,37,36,37,66,66,66,37,37,37,36,37,36,97,42,36,37,37] EQ(ADD(Coeff(x,3),ADD(Coeff(MULT(x,x),3),ADD(Coeff(MULT(x,y),3),Coeff(MULT(y,x),3)))),E). 122 [para_from,106.1.1,4.1.1.1,demod,44,65,65,49,39,flip.1] EQ(ADD(Coeff(MULT(x,y),3),Coeff(INV(MULT(x,MULT(x,y))),3)),E). 192 [hyper,108,30,122,22,23,eval,28,demod,35,36,50,51,47,51,37,37,37,36,37,36,37,37,37,74,57,60,101,43,propositional] EQ(ADD(Coeff(MULT(x,y),3),Coeff(MULT(y,x),3)),E). 194 [binary,192.1,33.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 20 clauses generated 1097 hyper_res generated 317 para_from generated 402 para_into generated 378 demod & eval rewrites 15496 clauses wt,lit,sk delete 416 tautologies deleted 36 clauses forward subsumed 594 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 52 new demodulators 52 empty clauses 1 clauses back demodulated 1 clauses back subsumed 0 usable size 50 sos size 34 demodulators size 108 passive size 0 hot size 0 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.14 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8952 finished Mon Aug 2 15:31:15 2004 otter-3.3f/examples/fringe/olsax_hints.in0100644000076400007640000001026207654037574020176 0ustar mccunemccune% This proves that an equation is a single axiom for ortholattices % in terms of the Sheffer stroke. % % It uses hints (hints2) to guide Otter to a particular proof. % In other words, this is a job to check a proof rather than find a proof. set(knuth_bendix). set(back_unit_deletion). assign(max_weight, 0). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). clear(sigint_interact). list(usable). x = x. end_of_list. list(sos). f(f(f(f(y,x),f(x,z)),u),f(x,f(f(x,f(f(y,y),y)),z))) = x. % OL single axiom end_of_list. list(sos). % denial of SS OL 3-basis. f(f(X,X),f(X,Y)) != X | f(X,f(X,X)) != f(Y,f(Y,Y)) | f(X,f(f(Y,Z),f(Y,Z))) != f(Z,f(f(Y,X),f(Y,X))). end_of_list. assign(bsub_hint_add_wt, -1000). set(keep_hint_subsumers). set(degrade_hints2). list(hints2). f(f(f(f(x,y),f(y,z)),u),f(y,f(f(y,f(f(x,x),x)),z)))=y. f(f(X,X),f(X,Y))!=X|f(X,f(X,X))!=f(Y,f(Y,Y))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). f(f(X,X),f(X,Y))!=X|f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). f(f(x,y),f(x,f(f(x,f(f(f(f(z,x),f(x,u)),f(f(z,x),f(x,u))),f(f(z,x),f(x,u)))),f(f(x,f(f(z,z),z)),u))))=x. f(x,f(f(x,y),f(f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))),u)))=f(x,y). f(f(x,y),f(f(f(x,y),f(y,z)),y))=f(f(x,y),f(y,z)). f(x,f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))))=f(x,y). f(f(f(f(x,y),f(y,z)),y),f(y,y))=y. f(f(x,x),f(x,x))=x. f(x,f(f(x,f(f(x,x),y)),f(x,x)))=f(x,f(f(x,x),y)). f(x,f(f(x,y),f(x,f(x,x))))=f(x,y). f(f(f(f(x,y),f(y,f(y,f(y,y)))),z),f(y,f(f(x,x),x)))=y. f(x,f(f(x,y),f(x,y)))=f(x,y). f(f(x,y),f(x,x))=x. f(f(f(f(x,y),f(y,z)),u),f(y,y))=y. f(x,f(f(x,x),y))=f(x,x). f(f(f(x,x),y),x)=f(x,x). f(f(x,x),f(x,y))=x. f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(f(f(x,y),f(y,z)),y). f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). f(f(f(x,y),f(x,y)),x)=f(x,y). f(f(f(x,y),f(y,z)),y)=f(y,f(f(x,y),f(y,z))). f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(y,f(f(x,y),f(y,z))). f(f(f(f(x,y),f(x,z)),u),f(x,x))=x. f(f(f(x,f(f(x,y),z)),u),f(f(x,y),f(x,y)))=f(x,y). f(f(x,y),f(y,y))=y. f(x,f(f(y,x),f(y,x)))=f(y,x). f(f(x,x),f(y,x))=x. f(x,f(y,f(x,x)))=f(x,x). f(f(x,y),f(x,f(f(z,z),z)))=x. f(f(f(x,f(f(y,x),z)),u),f(f(y,x),f(y,x)))=f(y,x). f(f(x,f(f(y,z),f(z,u))),f(z,z))=z. f(f(f(f(x,y),f(z,y)),u),f(y,y))=y. f(x,f(f(x,y),f(f(z,z),z)))=f(x,y). f(x,x)=f(x,f(f(y,y),y)). f(x,f(f(y,y),y))=f(x,x). f(x,f(y,f(y,y)))=f(x,x). f(x,x)=f(x,f(y,f(y,y))). f(x,f(f(x,y),f(z,f(z,z))))=f(x,y). f(f(x,f(y,f(y,y))),f(z,x))=x. f(f(x,f(f(y,z),f(y,u))),f(y,y))=y. f(f(x,f(y,f(f(z,y),u))),f(f(z,y),f(z,y)))=f(z,y). f(f(f(f(x,y),f(z,y)),u),f(y,f(f(v,v),v)))=y. f(f(f(x,f(x,x)),f(y,f(y,y))),z)=f(x,f(x,x)). f(x,f(x,x))=f(y,f(y,y)). f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). f(f(f(x,y),z),f(f(x,f(f(y,u),f(y,v))),f(x,f(f(y,u),f(y,v)))))=f(x,f(f(y,u),f(y,v))). f(f(f(x,y),z),f(f(y,x),f(y,x)))=f(y,x). f(f(x,y),f(y,x))=f(f(y,x),f(y,x)). f(f(x,y),f(f(f(y,x),z),f(f(u,u),u)))=f(f(y,x),z). f(x,f(f(y,x),f(x,y)))=f(y,x). f(x,y)=f(y,x). f(f(f(x,y),z),f(f(y,x),f(x,y)))=f(y,x). f(f(f(x,y),z),f(f(x,y),f(y,x)))=f(y,x). f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,u),f(z,v)),y)))=f(f(f(z,u),f(z,v)),y). f(f(x,y),z)=f(f(y,x),z). f(x,f(y,z))=f(f(z,y),x). f(f(x,y),z)=f(z,f(y,x)). f(x,f(f(y,z),u))=f(f(f(z,y),u),x). f(f(f(x,y),z),u)=f(u,f(f(y,x),z)). f(f(f(f(x,y),z),u),f(f(f(y,x),z),f(f(x,y),z)))=f(z,f(x,y)). f(f(x,y),f(z,u))=f(f(y,x),f(u,z)). f(f(f(x,y),f(z,u)),v)=f(v,f(f(u,z),f(y,x))). f(f(f(f(x,y),f(z,u)),v),f(f(f(y,x),f(u,z)),f(f(z,u),f(x,y))))=f(f(z,u),f(x,y)). f(f(f(f(x,f(y,f(f(z,y),u))),z),v),f(f(z,y),f(z,y)))=f(z,y). f(f(x,f(f(f(y,f(f(z,y),u)),v),z)),f(f(z,y),f(z,y)))=f(z,y). f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,v),f(z,u)),y)))=f(f(f(z,v),f(z,u)),y). f(f(f(f(f(x,y),f(x,z)),u),f(f(f(x,z),f(x,y)),u)),f(f(u,x),v))=f(f(f(x,z),f(x,y)),u). f(f(f(x,f(f(y,x),z)),f(x,u)),y)=f(y,x). f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(f(f(u,y),f(v,y)),x). f(f(f(x,y),f(z,y)),f(f(u,v),f(u,y)))=f(f(f(x,y),f(z,y)),u). f(f(f(x,y),f(z,y)),f(f(u,y),f(u,v)))=f(f(f(x,y),f(z,y)),u). f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(x,f(f(u,y),f(v,y))). f(f(f(x,y),f(x,y)),z)=f(x,f(f(z,y),f(z,y))). f(x,f(f(y,z),f(y,z)))=f(z,f(f(x,y),f(x,y))). f(x,f(f(y,z),f(y,z)))=f(y,f(f(x,z),f(x,z))). f(x,f(f(y,z),f(y,z)))=f(z,f(f(y,x),f(y,x))). end_of_list. otter-3.3f/examples/fringe/bring.out0100664000076400007640000005704610103522221017125 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:13 2004 The command was "../../bin/otter". The process ID is 8892. op(400,fx,~). op(450,xfy,#). op(450,xfy,|). op(460,xfy,&). op(470,xfx,-->). op(480,xfx,<-->). make_evaluable(_>_,$LGT(_,_)). set(lex_order_vars). lex([0,1,A,B,C,cin,a0,b0,a1,b1,a2,b2,a3,b3,_&_,_#_]). list(demodulators). 1 [] x|y=x#y# (x&y). 2 [] ~x=1#x. 3 [] x-->y= ~x|y. 4 [] x<-->y= (x-->y)& (y-->x). 5 [] if(x,y,z)= (x-->y)& (~x-->z). 6 [] 0#x=x. 7 [] x#0=x. 8 [] x#x=0. 9 [] x#x#y=y. 10 [] 0&x=0. 11 [] x&0=0. 12 [] 1&x=x. 13 [] x&1=x. 14 [] x&x=x. 15 [] x&x&y=x&y. 16 [] x&y#z= (x&y)# (x&z). 17 [] x#y=y#x. 18 [] x#y#z=y#x#z. 19 [] x&y=y&x. 20 [] y&x&z=x&y&z. end_of_list. set(demod_inf). clear(demod_history). assign(demod_limit,-1). set(sos_queue). assign(max_given,3). list(sos). 21 [] P1(A&B|C<--> (A&B)| (A&C)). 22 [] P2(~(~x| ~y)| ~(~x|y)<-->x). 23 [] P3((a2#b2#1# (a2&b2))# (a3#b3)#1# (a0#b0#1# (a0&b0)&1# (a0&b0)&a1#b1#1# (a1&b1)&1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2)&cin#1)# (a0#b0#1# (a0&b0)&1# (a0&b0)&a1#b1#1# (a1&b1)&1# (a1&b1)&1# (a2&b2)&cin#1)# (a0#b0#1# (a0&b0)&1# (a0&b0)&1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2)&cin#1)# (a0#b0#1# (a0&b0)&1# (a0&b0)&1# (a1&b1)&1# (a2&b2)&cin#1)# (a0#b0#1# (a0&b0)&a1#b1#1# (a1&b1)&1# (a1&b1)&1# (a2&b2))# (a0#b0#1# (a0&b0)&a1#b1#1# (a1&b1)&1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2))# (a0#b0#1# (a0&b0)&1# (a1&b1)&1# (a2&b2))# (a0#b0#1# (a0&b0)&1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2))# (1# (a0&b0)&a1#b1#1# (a1&b1)&1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2)&cin#1)# (1# (a0&b0)&a1#b1#1# (a1&b1)&1# (a1&b1)&1# (a2&b2)&cin#1)# (1# (a0&b0)&1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2)&cin#1)# (1# (a0&b0)&1# (a1&b1)&1# (a2&b2)&cin#1)# (a1#b1#1# (a1&b1)&1# (a2&b2))# (a1#b1#1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2))). end_of_list. set(pretty_print). lex dependent demodulator: 17 [] x#y=y#x. lex dependent demodulator: 18 [] x#y#z=y#x#z. lex dependent demodulator: 19 [] x&y=y&x. lex dependent demodulator: 20 [] y&x&z=x&y&z. ======= end of input processing ======= =========== start of search =========== Starting on level 1, last kept clause of level 0 is 23. Starting on level 1, last kept clause of level 0 is 23. given clause #1: (wt=14) 21 [] P1(A&B|C<--> (A&B)| (A&C)). ** KEPT (pick-wt=2): 24 [21,demod] P1(1). given clause #2: (wt=15) 22 [] P2(~(~x| ~y)| ~(~x|y)<-->x). ** KEPT (pick-wt=2): 25 [22,demod] P2(1). given clause #3: (wt=482) 23 [] P3( #( a2#b2#1# (a2&b2), #( a3#b3, #( 1, #( &( a0#b0#1# (a0&b0), &( 1# (a0&b0), &( a1#b1#1# (a1&b1), 1# (a1&b1)&a2#b2#1# (a2&b2)&1# (a2&b2)&cin#1 ) ) ), #( &( a0#b0#1# (a0&b0), &( 1# (a0&b0), a1#b1#1# (a1&b1)&1# (a1&b1)&1# (a2&b2)&cin#1 ) ), #( &( a0#b0#1# (a0&b0), &( 1# (a0&b0), &( 1# (a1&b1), a2#b2#1# (a2&b2)&1# (a2&b2)&cin#1 ) ) ), #( &( a0#b0#1# (a0&b0), 1# (a0&b0)&1# (a1&b1)&1# (a2&b2)&cin#1 ), #( &( a0#b0#1# (a0&b0), a1#b1#1# (a1&b1)&1# (a1&b1)&1# (a2&b2) ), #( &( a0#b0#1# (a0&b0), &( a1#b1#1# (a1&b1), &( 1# (a1&b1), a2#b2#1# (a2&b2)&1# (a2&b2) ) ) ), #( &( a0#b0#1# (a0&b0), 1# (a1&b1)&1# (a2&b2) ), #( &( a0#b0#1# (a0&b0), &( 1# (a1&b1), &( a2#b2#1# (a2&b2), 1# (a2&b2) ) ) ), #( &( 1# (a0&b0), &( a1#b1#1# (a1&b1), &( 1# (a1&b1), &( #( a2, #( b2, #( 1, &( a2, b2 ) ) ) ), &( #( 1, &( a2, b2 ) ), cin#1 ) ) ) ) ), #( &( 1# (a0&b0), &( #( a1, #( b1, #( 1, &( a1, b1 ) ) ) ), &( 1# (a1&b1), &( #( 1, &( a2, b2 ) ), cin#1 ) ) ) ), #( &( 1# (a0&b0), &( 1# (a1&b1), &( #( a2, #( b2, #( 1, &( a2, b2 ) ) ) ), &( #( 1, &( a2, b2 ) ), #( cin, 1 ) ) ) ) ), #( &( 1# (a0&b0), &( #( 1, &( a1, b1 ) ), &( #( 1, &( a2, b2 ) ), #( cin, 1 ) ) ) ), #( &( #( a1, #( b1, #( 1, &( a1, b1 ) ) ) ), #( 1, &( a2, b2 ) ) ), &( #( a1, #( b1, #( 1, &( a1, b1 ) ) ) ), &( #( a2, #( b2, #( 1, &( a2, b2 ) ) ) ), #( 1, &( a2, b2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). Search stopped by max_given option. ** KEPT (pick-wt=116): 26 [23,demod] P3( #( a3, #( b3, #( cin&a0&a1&a2, #( cin&a0&a1&b2, #( cin&a0&b1&a2, #( cin&a0&b1&b2, #( cin&b0&a1&a2, #( cin&b0&a1&b2, #( cin&b0&b1&a2, #( cin&b0&b1&b2, #( a0&b0&a1&a2, #( a0&b0&a1&b2, #( a0&b0&b1&a2, #( a0&b0&b1&b2, #( a1&b1&a2, #( a1&b1&b2, a2&b2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 3 clauses generated 3 demod_inf generated 3 demod & eval rewrites 45084 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 3 new demodulators 0 empty clauses 0 clauses back demodulated 0 clauses back subsumed 0 usable size 3 sos size 3 demodulators size 20 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.17 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8892 finished Mon Aug 2 15:31:13 2004 otter-3.3f/examples/fringe/index.html0100644000076400007640000000324707714267401017304 0ustar mccunemccune /home/mccune/otter-3.3/examples/fringe

/home/mccune/otter-3.3/examples/fringe

These problems illustrate some of Otter's esoteric features: hints, rewriting, tricks with orderings, algebraic geometry.

otter < bring.in > bring.out

otter < ec_yql.in > ec_yql.out

otter < gl4.in > gl4.out

otter < gl8.in > gl8.out

otter < if.in > if.out

otter < lexical1.in > lexical1.out

otter < lexical2.in > lexical2.out

otter < lexical3.in > lexical3.out

otter < luka5h.in > luka5h.out

otter < mfl_13.in > mfl_13.out

otter < olsax_hints.in > olsax_hints.out

otter < rob_ocd.in > rob_ocd.out

otter < x3tricks.in > x3tricks.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/fringe/if.out0100664000076400007640000001251710103522222016415 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8912. op(400,fx,~). op(450,xfy,#). op(450,xfy,|). op(460,xfy,&). op(470,xfx,-->). op(480,xfx,<-->). make_evaluable(_>_,$LGT(_,_)). list(demodulators). 1 [] if(x,y,z)=ite(x,ite(y,1,0),ite(z,1,0)). 2 [] x&y=ite(x,ite(y,1,0),0). 3 [] x|y=ite(x,1,ite(y,1,0)). 4 [] ~x=ite(x,0,1). 5 [] x-->y= ~x|y. 6 [] x<-->y= (x-->y)& (y-->x). 7 [] x#y= ~(x<-->y). 8 [] x<-->x=1. 9 [] x-->x=1. 10 [] x&x=x. 11 [] x|x=x. 12 [] x#x=0. 13 [] ite(x,y,y)=y. 14 [] ite(1,x,y)=x. 15 [] ite(0,x,y)=y. 16 [] ite(ite(x,y,z),u,v)=ite(x,ite(y,u,v),ite(z,u,v)). 17 [] ite(x,ite(x,y,z),w)=ite(x,y,w). 18 [] ite(x,w,ite(x,y,z))=ite(x,w,z). 19 [] x1>x2->ite(x1,ite(x2,y,z),w)=ite(x2,ite(x1,y,w),ite(x1,z,w)). 20 [] x1>x2->ite(x1,w,ite(x2,y,z))=ite(x2,ite(x1,w,y),ite(x1,w,z)). end_of_list. set(demod_inf). clear(demod_history). assign(demod_limit,-1). set(sos_queue). assign(max_given,4). set(lex_order_vars). set(pretty_print). list(sos). 21 [] P1(A&B|C<--> (A&B)| (A&C)). 22 [] P2(~(~x| ~y)| ~(~x|y)<-->x). 23 [] P3(if(D,if(C,if(A,B,I),if(E,F,G)),H)). 24 [] P4( <-->( (a2#b2#1# (a2&b2))# (a3#b3)#1#a0#b0#1# (a0&b0), if( a0, if( a2, if(a3,if(b3,1,0),if(b3,0,1)), if( a3, if(b2,if(b3,1,0),if(b3,0,1)), if(b2,if(b3,0,1),if(b3,1,0)) ) ), if( a2, if( a3, if(b0,if(b3,1,0),if(b3,0,1)), if(b0,if(b3,0,1),if(b3,1,0)) ), if( a3, if( b0, if(b2,if(b3,1,0),if(b3,0,1)), if(b2,if(b3,0,1),if(b3,1,0)) ), if( b0, if(b2,if(b3,0,1),if(b3,1,0)), if(b2,if(b3,1,0),if(b3,0,1)) ) ) ) ) ) ). end_of_list. ======= end of input processing ======= =========== start of search =========== Starting on level 1, last kept clause of level 0 is 24. Starting on level 1, last kept clause of level 0 is 24. given clause #1: (wt=14) 21 [] P1(A&B|C<--> (A&B)| (A&C)). ** KEPT (pick-wt=2): 25 [21,demod] P1(1). given clause #2: (wt=15) 22 [] P2(~(~x| ~y)| ~(~x|y)<-->x). ** KEPT (pick-wt=2): 26 [22,demod] P2(1). given clause #3: (wt=14) 23 [] P3(if(D,if(C,if(A,B,I),if(E,F,G)),H)). ** KEPT (pick-wt=83): 27 [23,demod] P3( ite( A, ite( B, ite( C, ite(D,1,ite(H,1,0)), ite(D,ite(E,ite(F,1,0),ite(G,1,0)),ite(H,1,0)) ), ite( C, ite(D,0,ite(H,1,0)), ite(D,ite(E,ite(F,1,0),ite(G,1,0)),ite(H,1,0)) ) ), ite( C, ite(D,ite(I,1,0),ite(H,1,0)), ite(D,ite(E,ite(F,1,0),ite(G,1,0)),ite(H,1,0)) ) ) ). given clause #4: (wt=133) 24 [] P4( <-->( (a2#b2#1# (a2&b2))# (a3#b3)#1#a0#b0#1# (a0&b0), if( a0, if( a2, if(a3,if(b3,1,0),if(b3,0,1)), if( a3, if(b2,if(b3,1,0),if(b3,0,1)), if(b2,if(b3,0,1),if(b3,1,0)) ) ), if( a2, if( a3, if(b0,if(b3,1,0),if(b3,0,1)), if(b0,if(b3,0,1),if(b3,1,0)) ), if( a3, if( b0, if(b2,if(b3,1,0),if(b3,0,1)), if(b2,if(b3,0,1),if(b3,1,0)) ), if( b0, if(b2,if(b3,0,1),if(b3,1,0)), if(b2,if(b3,1,0),if(b3,0,1)) ) ) ) ) ) ). Search stopped by max_given option. ** KEPT (pick-wt=2): 28 [24,demod] P4(1). Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 4 clauses generated 4 demod_inf generated 4 demod & eval rewrites 4145 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 4 new demodulators 0 empty clauses 0 clauses back demodulated 0 clauses back subsumed 0 usable size 4 sos size 4 demodulators size 20 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8912 finished Mon Aug 2 15:31:14 2004 otter-3.3f/examples/fringe/gl4.in.288970100644000076400007640000000121105737100313017001 0ustar mccunemccune% This is Theorem 4 from the appendix of "Automated Reasoning about Cubic % Curves", by R. Padmanabhan and W. McCune, to appear in _Computers and % Mathematics with Applications_. set(para_from). set(para_into). % set(para_from_vars). % set(para_into_vars). set(order_eq). set(geometric_rule). set(geometric_rewrite_before). set(lrpo). lex([A,B,C,D,E,F,e,f(x,x),g(x)]). assign(pick_given_ratio, 1). assign(max_weight, 17). assign(max_mem, 1500). clear(print_kept). list(usable). x = x. end_of_list. list(sos). % f(e,e)=e. f(x,f(e,x)) = e. % f(f(x,e),x) = e. end_of_list. list(passive). f(f(A,B),f(C,D)) != f(f(A,C),f(B,D)). end_of_list. otter-3.3f/examples/fringe/gl4.in0100644000076400007640000000116210041250711016276 0ustar mccunemccune% This is Theorem 4 from the appendix of "Automated Reasoning about Cubic % Curves", by R. Padmanabhan and W. McCune, to appear in _Computers and % Mathematics with Applications_. set(para_from). set(para_into). % set(para_from_vars). % set(para_into_vars). set(order_eq). set(geometric_rule). set(geometric_rewrite_before). set(lrpo). lex([A,B,C,D,E,F,e,f(x,x),g(x)]). assign(pick_given_ratio, 1). assign(max_weight, 17). clear(print_kept). list(usable). x = x. end_of_list. list(sos). % f(e,e)=e. f(x,f(e,x)) = e. % f(f(x,e),x) = e. end_of_list. list(passive). f(f(A,B),f(C,D)) != f(f(A,C),f(B,D)). end_of_list. otter-3.3f/examples/fringe/README0100644000076400007640000000017207313706120016150 0ustar mccunemccuneThese problems illustrate some of Otter's esoteric features: hints, rewriting, tricks with orderings, algebraic geometry. otter-3.3f/examples/fringe/luka5h.in0100644000076400007640000001572006007676175017035 0ustar mccunemccune% ------------------------------------------------------------------------- % "Luka 5" Problem for many-valued sentential calculus. % % The five axioms % % P(i(x,i(y,x))) # Axiom 1. % P(i(i(x,y),i(i(y,z),i(x,z)))) # Axiom 2. % P(i(i(i(x,y),y),i(i(y,x),x))) # Axiom 3. % P(i(i(i(x,y),i(y,x)),i(y,x))) # Axiom 4. % P(i(i(n(x),n(y)),i(y,x))) # Axiom 5. % % together with the inference rule condensed detachment are known to be a % complete system for the many-valued sentential calculus (page 144 of [1]). % % The problem is to show that Axiom 4 is dependent on the four remaining % axioms. % % This experiment uses hints to check a known proof consisting of 63 steps. % This is done by including the 63 steps as hints and by keeping a % generated clause if and only if it subsumes a hint. % % REFERENCES: % % [1] Lukasiewicz, J., "Investigations into the sentential calculus", % pp. 131-152 in Jan Lukasiewicz: Selected Works, ed. L. Borkowski, % North Holland Publishing, Amsterdam (1970). % % Contributed by Bob Veroff % ------------------------------------------------------------------------- % general processing set(hyper_res). set(sos_queue). assign(max_weight, 1). % keep nothing in general % hints assign(equiv_hint_wt, 1). set(keep_hint_subsumers). % printing clear(print_kept). list(usable). % condensed detachment -P(i(x,y)) | -P(x) | P(y). end_of_list. list(sos). % Thesis 18 (Scott) P(i(x,i(y,x))) # label("Axiom 1"). % Thesis 1 (Scott) P(i(i(x,y),i(i(y,z),i(x,z)))) # label("Axiom 2"). % Thesis 27 (Scott) P(i(i(i(x,y),y),i(i(y,x),x))) # label("Axiom 3"). % Thesis 49 (Scott) P(i(i(n(x),n(y)),i(y,x))) # label("Axiom 5"). end_of_list. list(passive). % Axiom 4 is not one of Scott's 71 theses. -P(i(i(i(cx,cy),i(cy,cx)),i(cy,cx))) | $ANS(Denial_Axiom4). end_of_list. list(hints). % 63 steps of the known proof P(i(x,i(y,i(z,y)))) # label("Step01"). P(i(i(i(i(x,y),i(z,y)),w),i(i(z,x),w))) # label("Step02"). P(i(x,i(i(y,z),i(i(z,w),i(y,w))))) # label("Step03"). P(i(i(i(x,y),z),i(y,z))) # label("Step04"). P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))) # label("Step05"). P(i(i(i(x,y),z),i(i(n(y),n(x)),z))) # label("Step06"). P(i(i(i(x,i(y,x)),z),z)) # label("Step07"). P(i(i(x,i(y,z)),i(i(w,y),i(x,i(w,z))))) # label("Step08"). P(i(i(x,y),i(i(i(x,z),w),i(i(y,z),w)))) # label("Step09"). P(i(i(i(i(x,y),i(i(y,z),i(x,z))),w),w)) # label("Step10"). P(i(n(x),i(x,y))) # label("Step11"). P(i(x,i(i(x,y),y))) # label("Step12"). P(i(i(i(x,i(y,x)),i(y,x)),i(i(i(x,y),y),x))) # label("Step13"). P(i(i(n(x),n(i(y,i(z,y)))),x)) # label("Step14"). P(i(i(n(x),n(i(i(y,z),i(i(z,w),i(y,w))))),x)) # label("Step15"). P(i(i(x,i(y,z)),i(x,i(i(z,w),i(y,w))))) # label("Step16"). P(i(i(x,y),i(n(y),i(x,z)))) # label("Step17"). P(i(i(i(x,y),z),i(n(x),z))) # label("Step18"). P(i(i(x,i(y,z)),i(y,i(x,z)))) # label("Step19"). P(i(i(x,y),i(i(i(y,x),x),y))) # label("Step20"). P(i(i(i(i(n(x),n(i(y,i(z,y)))),x),w),w)) # label("Step21"). P(i(x,i(i(y,z),i(i(x,y),z)))) # label("Step22"). P(i(i(i(n(x),i(y,z)),w),i(i(y,x),w))) # label("Step23"). P(i(n(n(x)),x)) # label("Step24"). P(i(i(x,y),i(i(z,x),i(z,y)))) # label("Step25"). P(i(i(x,i(n(y),n(i(z,i(w,z))))),i(x,y))) # label("Step26"). P(i(i(i(i(x,y),i(i(z,x),y)),w),i(z,w))) # label("Step27"). P(i(i(i(n(n(x)),y),z),i(i(x,y),z))) # label("Step28"). P(i(x,n(n(x)))) # label("Step29"). P(i(i(x,n(n(y))),i(x,y))) # label("Step30"). P(i(i(x,i(i(y,z),w)),i(x,i(z,w)))) # label("Step31"). P(i(i(x,i(n(y),n(z))),i(x,i(z,y)))) # label("Step32"). P(i(i(n(x),y),i(n(y),x))) # label("Step33"). P(i(i(n(n(x)),y),i(x,y))) # label("Step34"). P(i(i(i(x,y),n(z)),i(z,x))) # label("Step35"). P(i(i(x,y),i(n(y),n(x)))) # label("Step36"). P(i(i(x,i(n(n(y)),z)),i(x,i(y,z)))) # label("Step37"). P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))) # label("Step38"). P(i(n(i(x,y)),n(y))) # label("Step39"). P(i(i(i(n(x),n(y)),z),i(i(y,x),z))) # label("Step40"). P(i(n(i(x,y)),n(i(i(y,z),n(x))))) # label("Step41"). P(i(i(i(x,y),i(z,w)),i(y,i(n(w),n(z))))) # label("Step42"). P(i(i(i(n(x),n(i(y,x))),n(i(y,x))),n(x))) # label("Step43"). P(i(i(x,i(i(n(y),n(z)),w)),i(x,i(i(z,y),w)))) # label("Step44"). P(i(i(i(n(x),n(y)),n(y)),i(i(x,y),n(x)))) # label("Step45"). P(i(i(x,n(i(y,z))),i(x,n(i(i(z,w),n(y)))))) # label("Step46"). P(i(i(x,i(i(n(y),n(i(z,y))),n(i(z,y)))),i(x,n(y)))) # label("Step47"). P(i(n(x),i(n(n(y)),n(i(y,x))))) # label("Step48"). P(i(i(i(i(x,y),y),n(i(x,y))),n(y))) # label("Step49"). P(i(n(x),i(y,n(i(y,x))))) # label("Step50"). P(i(i(x,i(i(i(y,z),z),n(i(y,z)))),i(x,n(z)))) # label("Step51"). P(i(i(i(n(x),i(y,n(i(y,x)))),z),z)) # label("Step52"). P(i(i(i(i(x,y),y),n(i(y,x))),n(x))) # label("Step53"). P(i(i(x,i(i(i(y,z),z),n(i(z,y)))),i(x,n(y)))) # label("Step54"). P(i(i(x,y),i(i(y,n(i(y,x))),n(x)))) # label("Step55"). P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),n(n(y)))) # label("Step56"). P(i(i(i(x,n(i(x,y))),n(i(i(x,n(i(x,y))),n(y)))),y)) # label("Step57"). P(i(i(x,i(i(y,n(i(y,z))),n(i(i(y,n(i(y,z))),n(z))))),i(x,z))) # label("Step58"). P(i(i(i(x,n(i(x,y))),n(i(y,x))),y)) # label("Step59"). P(i(i(x,i(i(y,n(i(y,z))),n(i(z,y)))),i(x,z))) # label("Step60"). P(i(x,i(i(n(i(x,y)),n(i(y,x))),y))) # label("Step61"). P(i(x,i(i(i(y,x),i(x,y)),y))) # label("Step62"). P(i(i(i(x,y),i(y,x)),i(y,x))) # label("Step63"). end_of_list. otter-3.3f/examples/fringe/lexical1.in0100644000076400007640000000246306007700644017333 0ustar mccunemccune% ------------------------------------------------------------------------- % Lex Demo 1 % % Demonstrate lex() and special_unary(). % % Canonicalization with respect to commutativity and associativity only. % % Contributed by Bob Veroff. % ------------------------------------------------------------------------- % inference rule set(binary_res). % include variables in lexical ordering set(lex_order_vars). % processing assign(max_given, 1). % lexical ordering of terms lex([a,b,c,d,e,f(x),add(x,x)]). special_unary([neg(x)]). list(usable). % nonnegated constants only -dum | P1(add(c,add(add(a,b),add(e,d)))). % negated constants only -dum | P2(add(neg(c),add(add(neg(a),neg(b)),add(neg(e),neg(d))))). % mixed negated and nonnegated constants (but distinct from each other) -dum | P3(add(c,add(add(a,neg(b)),add(e,neg(d))))). % negated and nonnegated occurrences of same constant -dum | P4(add(add(neg(a),b),add(neg(b),add(add(b,neg(b)),add(a,b))))). % include variables and other functions -dum | P5(add(x,add(add(c,add(add(a,neg(y)),neg(b))),add(f(y),b)))). end_of_list. list(sos). dum. end_of_list. list(demodulators). % commutativity EQ(add(x,y),add(y,x)). EQ(add(x,add(y,z)),add(y,add(x,z))). % associativity EQ(add(add(x,y),z),add(x,add(y,z))). end_of_list. otter-3.3f/examples/fringe/bring.in0100644000076400007640000000743106007760744016741 0ustar mccunemccune% This input file uses Boolean ring rules to rewrite % Boolean expressions into canonical form in terms of % {and,xor,0,1}. It should rewrite % tautologies to 1 and unsatisfiable expressions to 0. % % The propositional "variables" in the expressions to be % rewritten can be either (Otter) variables, constants, or a % mixture. If variables are included, the flag lex_order_vars % must be set. % % A lex command of the form lex([, _&_, _#_)]) % must be present. All constants in the expressions to be rewritten % must occur in the lex command. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Declare Boolean operations as infix or prefix. % This is for parsing and printing only. % Note that the defaults for & and | are overridden. op(400, fx, ~). op(450, xfy, #). % exclusive or op(450, xfy, |). op(460, xfy, &). op(470, xfx, -->). op(480, xfx, <-->). make_evaluable(_>_, $LGT(_,_)). set(lex_order_vars). lex([0, 1, A, B, C, cin, a0, b0, a1, b1, a2, b2, a3, b3, _&_, _#_]). list(demodulators). % Define ordinary Boolean operations in terms of {0,1,&,#}. x | y = x # (y # (x & y)). ~x = 1 # x. x --> y = ~x | y. x <--> y = (x --> y) & (y --> x). if(x,y,z) = (x --> y) & (~x --> z). % The rest of the rules rewrite Boolean ring terms into canonical form. 0 # x = x. x # 0 = x. x # x = 0. x # (x # y) = y. 0 & x = 0. x & 0 = 0. 1 & x = x. x & 1 = x. x & x = x. x & (x & y) = x & y. x & (y # z) = (x & y) # (x & z). % To handle sorting of associative/commutative expressions, % we can use either the built-in lex-dependent demodulation % or conditional demodulation. Take your pick. The lex-dependent % alternative is three times faster for the P3 expression below. % lex-dependent demodulators x # y = y # x. x # (y # z) = y # (x # z). x & y = y & x. y & (x & z) = x & (y & z). % conditional demodulators % (x > y) -> (x # y = y # x). % (x > y) -> (x # (y # z) = y # (x # z)). % (x > y) -> (x & y = y & x). % (x > y) -> (x & (y & z) = y & (x & z)). end_of_list. set(demod_inf). % the "inference rule" clear(demod_history). % we don't want to see a list of 44775 integers assign(demod_limit, -1). % no limit set(sos_queue). assign(max_given, 3). % Here are the expressions to be rewritten. list(sos). P1((A & (B | C)) <--> ((A & B) | (A & C))). % Distributivity P2(~(~x | ~y) | ~(~x | y) <--> x). % Huntington identity P3(#(#(a2,#(b2,#(1,&(a2,b2)))),#(#(a3,b3),#(1,#(&(#(a0,#(b0,#(1,&(a0,b0)))), &(#(1,&(a0,b0)),&(#(a1,#(b1,#(1,&(a1,b1)))),&(#(1,&(a1,b1)),&(#(a2,#(b2,#(1, &(a2,b2)))),&(#(1,&(a2,b2)),#(cin,1))))))),#(&(#(a0,#(b0,#(1,&(a0,b0)))), &(#(1,&(a0,b0)),&(#(a1,#(b1,#(1,&(a1,b1)))),&(#(1,&(a1,b1)),&(#(1,&(a2,b2)), #(cin,1)))))),#(&(#(a0,#(b0,#(1,&(a0,b0)))),&(#(1,&(a0,b0)),&(#(1,&(a1,b1)), &(#(a2,#(b2,#(1,&(a2,b2)))),&(#(1,&(a2,b2)),#(cin,1)))))),#(&(#(a0,#(b0,#(1, &(a0,b0)))),&(#(1,&(a0,b0)),&(#(1,&(a1,b1)),&(#(1,&(a2,b2)),#(cin,1))))), #(&(#(a0,#(b0,#(1,&(a0,b0)))),&(#(a1,#(b1,#(1,&(a1,b1)))),&(#(1,&(a1,b1)), #(1,&(a2,b2))))),#(&(#(a0,#(b0,#(1,&(a0,b0)))),&(#(a1,#(b1,#(1,&(a1,b1)))), &(#(1,&(a1,b1)),&(#(a2,#(b2,#(1,&(a2,b2)))),#(1,&(a2,b2)))))),#(&(#(a0,#(b0, #(1,&(a0,b0)))),&(#(1,&(a1,b1)),#(1,&(a2,b2)))),#(&(#(a0,#(b0,#(1,&(a0, b0)))),&(#(1,&(a1,b1)),&(#(a2,#(b2,#(1,&(a2,b2)))),#(1,&(a2,b2))))),#(&(#(1, &(a0,b0)),&(#(a1,#(b1,#(1,&(a1,b1)))),&(#(1,&(a1,b1)),&(#(a2,#(b2,#(1, &(a2,b2)))),&(#(1,&(a2,b2)),#(cin,1)))))),#(&(#(1,&(a0,b0)),&(#(a1,#(b1, #(1,&(a1,b1)))),&(#(1,&(a1,b1)),&(#(1,&(a2,b2)),#(cin,1))))),#(&(#(1,&(a0, b0)),&(#(1,&(a1,b1)),&(#(a2,#(b2,#(1,&(a2,b2)))),&(#(1,&(a2,b2)),#(cin, 1))))),#(&(#(1,&(a0,b0)),&(#(1,&(a1,b1)),&(#(1,&(a2,b2)),#(cin,1)))), #(&(#(a1,#(b1,#(1,&(a1,b1)))),#(1,&(a2,b2))),&(#(a1,#(b1,#(1,&(a1,b1)))), &(#(a2,#(b2,#(1,&(a2,b2)))),#(1,&(a2,b2))))))))))))))))))))). end_of_list. set(pretty_print). otter-3.3f/examples/fringe/lexical3.in0100644000076400007640000000230306007700667017333 0ustar mccunemccune% ------------------------------------------------------------------------- % Lex Demo 3 % % Demonstrate lex() and an advanced use of special_unary(). % % Function coeff(x,y) is special "unary"; its lexical order is determined % by its first argument. % % Canonicalization with respect to commutativity and associativity only. % % Contributed by Bob Veroff. % ------------------------------------------------------------------------- % inference rule set(binary_res). % include variables in lexical ordering set(lex_order_vars). % processing assign(max_given, 1). % lexical ordering of terms lex([a,b,c,d,e,C1,C2,C3,C4,C5,C6,neg(x),coeff(x,x),add(x,x)]). special_unary([neg(x),coeff(x,x)]). list(usable). % a mixture of constants, negated constants, with and with coefficients -dum | P(add(a,add(b,add(coeff(neg(c),C6),add(neg(a),add(neg(b),add(coeff(c,C5),add(coeff(a,C1),add(coeff(b,C2),add(neg(c),add(coeff(neg(a),C3),add(coeff(neg(b),C4),add(c,coeff(neg(a),C2)))))))))))))). end_of_list. list(sos). dum. end_of_list. list(demodulators). % commutativity EQ(add(x,y),add(y,x)). EQ(add(x,add(y,z)),add(y,add(x,z))). % associativity EQ(add(add(x,y),z),add(x,add(y,z))). end_of_list. otter-3.3f/examples/fringe/ec_yql.in0100644000076400007640000000335610041250711017073 0ustar mccunemccune% This is a problem in the equivalential calculus (EC): YQL -> XGF. % The strategy uses ancestor subsumption to find a shorter proof. % This input file was contributed by Larry Wos. set(hyper_res). set(ancestor_subsume). assign(max_weight,28). clear(print_kept). set(order_history). assign(max_proofs, 2). list(usable). -P(e(x,y)) | -P(x) | P(y). % condensed detacment end_of_list. list(sos). % Following are all of the shortest single axioms for EC. P(e(e(x,y),e(e(z,y),e(x,z)))). % P1_YQL % P(e(e(x,y),e(e(x,z),e(z,y)))). % P2_YQF % P(e(e(x,y),e(e(z,x),e(y,z)))). % P3_YQJ % P(e(e(e(x,y),z),e(y,e(z,x)))). % P4_UM % P(e(x,e(e(y,e(x,z)),e(z,y)))). % P5_XGF % P(e(e(x,e(y,z)),e(z,e(x,y)))). % P7_WN % P(e(e(x,y),e(z,e(e(y,z),x)))). % P8_YRM % P(e(e(x,y),e(z,e(e(z,y),x)))). % P9_YRO % P(e(e(e(x,e(y,z)),z),e(y,x))). % PYO % P(e(e(e(x,e(y,z)),y),e(z,x))). % PYM % P(e(x,e(e(y,e(z,x)),e(z,y)))). % XGK % P(e(x,e(e(y,z),e(e(x,z),y)))). % XHK % P(e(x,e(e(y,z),e(e(z,x),y)))). % XHN end_of_list. list(passive). % Here are denials of the thirteen shortest single axioms for EC. % -P(e(e(a,b),e(e(c,b),e(a,c)))) | $ANSWER(P1_YQL). % -P(e(e(a,b),e(e(a,c),e(c,b)))) | $ANSWER(P2_YQF). % -P(e(e(a,b),e(e(c,a),e(b,c)))) | $ANSWER(P3_YQJ). % -P(e(e(e(a,b),c),e(b,e(c,a)))) | $ANSWER(P4_UM). -P(e(a,e(e(b,e(a,c)),e(c,b)))) | $ANSWER(P5_XGF). % -P(e(e(a,e(b,c)),e(c,e(a,b)))) | $ANSWER(P7_WN). % -P(e(e(a,b),e(c,e(e(b,c),a)))) | $ANSWER(P8_YRM). % -P(e(e(a,b),e(c,e(e(c,b),a)))) | $ANSWER(P9_YRO). % -P(e(e(e(a,e(b,c)),c),e(b,a))) | $ANSWER(PYO). % -P(e(e(e(a,e(b,c)),b),e(c,a))) | $ANSWER(PYM). % -P(e(a,e(e(b,e(c,a)),e(c,b)))) | $ANSWER(XGK). % -P(e(a,e(e(b,c),e(e(a,c),b)))) | $ANSWER(XHK). % -P(e(a,e(e(b,c),e(e(c,a),b)))) | $ANSWER(XHN). end_of_list. otter-3.3f/examples/fringe/olsax_hints.out0100664000076400007640000006740610103522223020362 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:14 2004 The command was "../../bin/otter". The process ID is 8942. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(back_unit_deletion). dependent: set(unit_deletion). assign(max_weight,0). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). clear(sigint_interact). list(usable). 0 [] x=x. end_of_list. list(sos). 0 [] f(f(f(f(y,x),f(x,z)),u),f(x,f(f(x,f(f(y,y),y)),z)))=x. end_of_list. list(sos). 0 [] f(f(X,X),f(X,Y))!=X|f(X,f(X,X))!=f(Y,f(Y,Y))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). end_of_list. assign(bsub_hint_add_wt,-1000). set(keep_hint_subsumers). set(degrade_hints2). list(hints2). 1 [] f(f(f(f(x,y),f(y,z)),u),f(y,f(f(y,f(f(x,x),x)),z)))=y. 2 [] f(f(X,X),f(X,Y))!=X|f(X,f(X,X))!=f(Y,f(Y,Y))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 3 [] f(f(X,X),f(X,Y))!=X|f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 4 [] f(f(x,y),f(x,f(f(x,f(f(f(f(z,x),f(x,u)),f(f(z,x),f(x,u))),f(f(z,x),f(x,u)))),f(f(x,f(f(z,z),z)),u))))=x. 5 [] f(x,f(f(x,y),f(f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))),u)))=f(x,y). 6 [] f(f(x,y),f(f(f(x,y),f(y,z)),y))=f(f(x,y),f(y,z)). 7 [] f(x,f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))))=f(x,y). 8 [] f(f(f(f(x,y),f(y,z)),y),f(y,y))=y. 9 [] f(f(x,x),f(x,x))=x. 10 [] f(x,f(f(x,f(f(x,x),y)),f(x,x)))=f(x,f(f(x,x),y)). 11 [] f(x,f(f(x,y),f(x,f(x,x))))=f(x,y). 12 [] f(f(f(f(x,y),f(y,f(y,f(y,y)))),z),f(y,f(f(x,x),x)))=y. 13 [] f(x,f(f(x,y),f(x,y)))=f(x,y). 14 [] f(f(x,y),f(x,x))=x. 15 [] f(f(f(f(x,y),f(y,z)),u),f(y,y))=y. 16 [] f(x,f(f(x,x),y))=f(x,x). 17 [] f(f(f(x,x),y),x)=f(x,x). 18 [] f(f(x,x),f(x,y))=x. 19 [] f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(f(f(x,y),f(y,z)),y). 20 [] f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 21 [] f(f(f(x,y),f(x,y)),x)=f(x,y). 22 [] f(f(f(x,y),f(y,z)),y)=f(y,f(f(x,y),f(y,z))). 23 [] f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(y,f(f(x,y),f(y,z))). 24 [] f(f(f(f(x,y),f(x,z)),u),f(x,x))=x. 25 [] f(f(f(x,f(f(x,y),z)),u),f(f(x,y),f(x,y)))=f(x,y). 26 [] f(f(x,y),f(y,y))=y. 27 [] f(x,f(f(y,x),f(y,x)))=f(y,x). 28 [] f(f(x,x),f(y,x))=x. 29 [] f(x,f(y,f(x,x)))=f(x,x). 30 [] f(f(x,y),f(x,f(f(z,z),z)))=x. 31 [] f(f(f(x,f(f(y,x),z)),u),f(f(y,x),f(y,x)))=f(y,x). 32 [] f(f(x,f(f(y,z),f(z,u))),f(z,z))=z. 33 [] f(f(f(f(x,y),f(z,y)),u),f(y,y))=y. 34 [] f(x,f(f(x,y),f(f(z,z),z)))=f(x,y). 35 [] f(x,x)=f(x,f(f(y,y),y)). 36 [] f(x,f(f(y,y),y))=f(x,x). 37 [] f(x,f(y,f(y,y)))=f(x,x). 38 [] f(x,x)=f(x,f(y,f(y,y))). 39 [] f(x,f(f(x,y),f(z,f(z,z))))=f(x,y). 40 [] f(f(x,f(y,f(y,y))),f(z,x))=x. 41 [] f(f(x,f(f(y,z),f(y,u))),f(y,y))=y. 42 [] f(f(x,f(y,f(f(z,y),u))),f(f(z,y),f(z,y)))=f(z,y). 43 [] f(f(f(f(x,y),f(z,y)),u),f(y,f(f(v,v),v)))=y. 44 [] f(f(f(x,f(x,x)),f(y,f(y,y))),z)=f(x,f(x,x)). 45 [] f(x,f(x,x))=f(y,f(y,y)). 46 [] f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 47 [] f(f(f(x,y),z),f(f(x,f(f(y,u),f(y,v))),f(x,f(f(y,u),f(y,v)))))=f(x,f(f(y,u),f(y,v))). 48 [] f(f(f(x,y),z),f(f(y,x),f(y,x)))=f(y,x). 49 [] f(f(x,y),f(y,x))=f(f(y,x),f(y,x)). 50 [] f(f(x,y),f(f(f(y,x),z),f(f(u,u),u)))=f(f(y,x),z). 51 [] f(x,f(f(y,x),f(x,y)))=f(y,x). 52 [] f(x,y)=f(y,x). 53 [] f(f(f(x,y),z),f(f(y,x),f(x,y)))=f(y,x). 54 [] f(f(f(x,y),z),f(f(x,y),f(y,x)))=f(y,x). 55 [] f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,u),f(z,v)),y)))=f(f(f(z,u),f(z,v)),y). 56 [] f(f(x,y),z)=f(f(y,x),z). 57 [] f(x,f(y,z))=f(f(z,y),x). 58 [] f(f(x,y),z)=f(z,f(y,x)). 59 [] f(x,f(f(y,z),u))=f(f(f(z,y),u),x). 60 [] f(f(f(x,y),z),u)=f(u,f(f(y,x),z)). 61 [] f(f(f(f(x,y),z),u),f(f(f(y,x),z),f(f(x,y),z)))=f(z,f(x,y)). 62 [] f(f(x,y),f(z,u))=f(f(y,x),f(u,z)). 63 [] f(f(f(x,y),f(z,u)),v)=f(v,f(f(u,z),f(y,x))). 64 [] f(f(f(f(x,y),f(z,u)),v),f(f(f(y,x),f(u,z)),f(f(z,u),f(x,y))))=f(f(z,u),f(x,y)). 65 [] f(f(f(f(x,f(y,f(f(z,y),u))),z),v),f(f(z,y),f(z,y)))=f(z,y). 66 [] f(f(x,f(f(f(y,f(f(z,y),u)),v),z)),f(f(z,y),f(z,y)))=f(z,y). 67 [] f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,v),f(z,u)),y)))=f(f(f(z,v),f(z,u)),y). 68 [] f(f(f(f(f(x,y),f(x,z)),u),f(f(f(x,z),f(x,y)),u)),f(f(u,x),v))=f(f(f(x,z),f(x,y)),u). 69 [] f(f(f(x,f(f(y,x),z)),f(x,u)),y)=f(y,x). 70 [] f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(f(f(u,y),f(v,y)),x). 71 [] f(f(f(x,y),f(z,y)),f(f(u,v),f(u,y)))=f(f(f(x,y),f(z,y)),u). 72 [] f(f(f(x,y),f(z,y)),f(f(u,y),f(u,v)))=f(f(f(x,y),f(z,y)),u). 73 [] f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(x,f(f(u,y),f(v,y))). 74 [] f(f(f(x,y),f(x,y)),z)=f(x,f(f(z,y),f(z,y))). 75 [] f(x,f(f(y,z),f(y,z)))=f(z,f(f(x,y),f(x,y))). 76 [] f(x,f(f(y,z),f(y,z)))=f(y,f(f(x,z),f(x,z))). 77 [] f(x,f(f(y,z),f(y,z)))=f(z,f(f(y,x),f(y,x))). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 78 [] x=x. Following clause subsumed by 78 during input processing: 0 [copy,78,flip.1] x=x. >>>> Starting back unit deletion with 78. ------------> process sos: +++ bsub adjust, cl 1, new wt -500 ** KEPT (pick-wt=-977): 79 [] f(f(f(f(x,y),f(y,z)),u),f(y,f(f(y,f(f(x,x),x)),z)))=y. ---> New Demodulator: 80 [new_demod,79] f(f(f(f(x,y),f(y,z)),u),f(y,f(f(y,f(f(x,x),x)),z)))=y. +++ bsub adjust, cl 3, new wt -500 ** KEPT (pick-wt=-961): 82 [copy,81,flip.2] f(f(X,X),f(X,Y))!=X|f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). >>>> Starting back demodulation with 80. >> BACK DEMODULATING HINT 1 WITH 80. >>>> Starting back unit deletion with 79. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=-977) 79 [] f(f(f(f(x,y),f(y,z)),u),f(y,f(f(y,f(f(x,x),x)),z)))=y. +++ bsub adjust, cl 4, new wt -500 +++ bsub adjust, cl 5, new wt -500 >> BACK DEMODULATING HINT 4 WITH 84. >> BACK DEMODULATING HINT 5 WITH 86. given clause #2: (wt=-973) 85 [para_into,79.1.1.1,79.1.1] f(x,f(f(x,y),f(f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))),u)))=f(x,y). +++ bsub adjust, cl 6, new wt -500 +++ bsub adjust, cl 7, new wt -500 >> BACK DEMODULATING HINT 6 WITH 88. >> BACK DEMODULATING HINT 7 WITH 90. given clause #3: (wt=-979) 87 [para_into,85.1.1.2.2,79.1.1] f(f(x,y),f(f(f(x,y),f(y,z)),y))=f(f(x,y),f(y,z)). +++ bsub adjust, cl 8, new wt -500 >> BACK DEMODULATING HINT 8 WITH 92. given clause #4: (wt=-985) 91 [para_into,87.1.1.2.1,79.1.1,demod,80] f(f(f(f(x,y),f(y,z)),y),f(y,y))=y. +++ bsub adjust, cl 9, new wt -500 >> BACK DEMODULATING HINT 9 WITH 94. +++ bsub adjust, cl 10, new wt -500 >> BACK DEMODULATING HINT 10 WITH 96. given clause #5: (wt=-991) 93 [para_into,91.1.1.1.1,91.1.1] f(f(x,x),f(x,x))=x. given clause #6: (wt=-979) 89 [para_into,85.1.1.2,85.1.1] f(x,f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))))=f(x,y). +++ bsub adjust, cl 11, new wt -500 >> BACK DEMODULATING HINT 11 WITH 98. given clause #7: (wt=-985) 97 [para_into,89.1.1.2.2.1,93.1.1] f(x,f(f(x,y),f(x,f(x,x))))=f(x,y). +++ bsub adjust, cl 12, new wt -500 >> BACK DEMODULATING HINT 12 WITH 100. given clause #8: (wt=-979) 95 [para_from,91.1.1,87.1.1.1,demod,92,92] f(x,f(f(x,f(f(x,x),y)),f(x,x)))=f(x,f(f(x,x),y)). given clause #9: (wt=-977) 99 [para_from,97.1.1,79.1.1.2] f(f(f(f(x,y),f(y,f(y,f(y,y)))),z),f(y,f(f(x,x),x)))=y. given clause #10: (wt=-961) 82 [copy,81,flip.2] f(f(X,X),f(X,Y))!=X|f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). given clause #11: (wt=-957) 83 [para_into,79.1.1.1.1,79.1.1] f(f(x,y),f(x,f(f(x,f(f(f(f(z,x),f(x,u)),f(f(z,x),f(x,u))),f(f(z,x),f(x,u)))),f(f(x,f(f(z,z),z)),u))))=x. +++ bsub adjust, cl 13, new wt -500 >> BACK DEMODULATING HINT 13 WITH 102. given clause #12: (wt=-987) 101 [para_from,83.1.1,85.1.1.2.2] f(x,f(f(x,y),f(x,y)))=f(x,y). +++ bsub adjust, cl 14, new wt -500 +++ bsub adjust, cl 15, new wt -500 +++ bsub adjust, cl 16, new wt -500 >> BACK DEMODULATING HINT 14 WITH 104. >> BACK DEMODULATING HINT 10 WITH 104. >> BACK DEMODULATING HINT 9 WITH 104. >> BACK DEMODULATING HINT 15 WITH 106. >> BACK DEMODULATING HINT 8 WITH 106. >> BACK DEMODULATING HINT 16 WITH 108. >> BACK DEMODULATING HINT 10 WITH 108. given clause #13: (wt=-991) 103 [para_into,101.1.1.2.1,83.1.1,demod,84,84] f(f(x,y),f(x,x))=x. +++ bsub adjust, cl 17, new wt -500 >> BACK DEMODULATING HINT 17 WITH 110. given clause #14: (wt=-989) 107 [back_demod,95,demod,104,flip.1] f(x,f(f(x,x),y))=f(x,x). +++ bsub adjust, cl 18, new wt -500 +++ bsub adjust, cl 19, new wt -500 +++ bsub adjust, cl 20, new wt -500 >> BACK DEMODULATING HINT 18 WITH 112. >> BACK DEMODULATING HINT 9 WITH 112. >> BACK DEMODULATING HINT 3 WITH 112. NEW HINT: 116 [bsub_wt=2147483647, bsub_add_wt=-500] X!=X|f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). >> BACK DEMODULATING HINT 2 WITH 112. >> BACK DEMODULATING HINT 23 WITH 114. >> BACK DEMODULATING HINT 19 WITH 114. >> BACK DEMODULATING HINT 4 WITH 114. NEW HINT: 117 [bsub_wt=2147483647, bsub_add_wt=-500] f(f(x,y),f(x,f(f(x,f(f(f(f(z,x),f(x,u)),x),f(f(z,x),f(x,u)))),f(f(x,f(f(z,z),z)),u))))=x. given clause #15: (wt=-991) 111 [para_into,107.1.1.2.1,103.1.1,demod,104] f(f(x,x),f(x,y))=x. +++ bsub adjust, cl 21, new wt -500 >> BACK DEMODULATING HINT 21 WITH 119. +++ bsub adjust, cl 10, new wt -250 >> BACK DEMODULATING HINT 10 WITH 121. given clause #16: (wt=-989) 109 [para_into,103.1.1.2,103.1.1] f(f(f(x,x),y),x)=f(x,x). +++ bsub adjust, cl 22, new wt -500 +++ bsub adjust, cl 23, new wt -500 >> BACK DEMODULATING HINT 117 WITH 123. NEW HINT: 126 [bsub_wt=2147483647, bsub_add_wt=-500] f(f(x,y),f(x,f(f(x,f(f(x,f(f(z,x),f(x,u))),f(f(z,x),f(x,u)))),f(f(x,f(f(z,z),z)),u))))=x. >> BACK DEMODULATING HINT 22 WITH 123. >> BACK DEMODULATING HINT 19 WITH 123. >> BACK DEMODULATING HINT 8 WITH 123. >> BACK DEMODULATING HINT 6 WITH 123. NEW HINT: 127 [bsub_wt=2147483647, bsub_add_wt=-500] f(f(x,y),f(y,f(f(x,y),f(y,z))))=f(f(x,y),f(y,z)). >> BACK DEMODULATING HINT 23 WITH 125. >> BACK DEMODULATING HINT 19 WITH 125. >> BACK DEMODULATING HINT 4 WITH 125. given clause #17: (wt=-987) 118 [para_into,111.1.1.2,103.1.1] f(f(f(x,y),f(x,y)),x)=f(x,y). given clause #18: (wt=-985) 105 [para_into,101.1.1.2.1,79.1.1,demod,80,80] f(f(f(f(x,y),f(y,z)),u),f(y,y))=y. +++ bsub adjust, cl 24, new wt -500 +++ bsub adjust, cl 25, new wt -500 +++ bsub adjust, cl 26, new wt -500 >> BACK DEMODULATING HINT 24 WITH 129. >> BACK DEMODULATING HINT 25 WITH 131. >> BACK DEMODULATING HINT 26 WITH 133. >> BACK DEMODULATING HINT 9 WITH 133. >> BACK DEMODULATING HINT 8 WITH 133. +++ bsub adjust, cl 127, new wt -250 >> BACK DEMODULATING HINT 127 WITH 135. given clause #19: (wt=-991) 132 [para_into,105.1.1.1,103.1.1] f(f(x,y),f(y,y))=y. +++ bsub adjust, cl 27, new wt -500 +++ bsub adjust, cl 28, new wt -500 >> BACK DEMODULATING HINT 27 WITH 137. >> BACK DEMODULATING HINT 28 WITH 139. >> BACK DEMODULATING HINT 9 WITH 139. given clause #20: (wt=-991) 138 [para_from,132.1.1,118.1.1.1.2,demod,133,133] f(f(x,x),f(y,x))=x. +++ bsub adjust, cl 29, new wt -500 +++ bsub adjust, cl 30, new wt -500 >> BACK DEMODULATING HINT 29 WITH 141. >> BACK DEMODULATING HINT 12 WITH 141. >> BACK DEMODULATING HINT 10 WITH 141. >> BACK DEMODULATING HINT 30 WITH 143. +++ bsub adjust, cl 31, new wt -500 >> BACK DEMODULATING HINT 31 WITH 145. given clause #21: (wt=-989) 140 [para_into,138.1.1.1,138.1.1] f(x,f(y,f(x,x)))=f(x,x). given clause #22: (wt=-987) 136 [para_from,132.1.1,103.1.1.1] f(x,f(f(y,x),f(y,x)))=f(y,x). +++ bsub adjust, cl 32, new wt -500 +++ bsub adjust, cl 33, new wt -500 >> BACK DEMODULATING HINT 32 WITH 147. >> BACK DEMODULATING HINT 33 WITH 149. given clause #23: (wt=-987) 142 [back_demod,99,demod,141,133] f(f(x,y),f(x,f(f(z,z),z)))=x. +++ bsub adjust, cl 34, new wt -500 >> BACK DEMODULATING HINT 34 WITH 151. >> BACK DEMODULATING HINT 7 WITH 151. +++ bsub adjust, cl 35, new wt -500 +++ bsub adjust, cl 36, new wt -500 given clause #24: (wt=-989) 152 [para_from,142.1.1,138.1.1.2,demod,143] f(x,x)=f(x,f(f(y,y),y)). +++ bsub adjust, cl 12, new wt -250 >> BACK DEMODULATING HINT 12 WITH 155. given clause #25: (wt=-989) 153 [copy,152,flip.1] f(x,f(f(y,y),y))=f(x,x). +++ bsub adjust, cl 37, new wt -500 +++ bsub adjust, cl 38, new wt -500 given clause #26: (wt=-989) 156 [para_into,153.1.1.2.1,138.1.1] f(x,f(y,f(y,y)))=f(x,x). given clause #27: (wt=-989) 157 [copy,156,flip.1] f(x,x)=f(x,f(y,f(y,y))). +++ bsub adjust, cl 39, new wt -500 +++ bsub adjust, cl 40, new wt -500 >> BACK DEMODULATING HINT 39 WITH 159. >> BACK DEMODULATING HINT 11 WITH 159. >> BACK DEMODULATING HINT 40 WITH 161. given clause #28: (wt=-987) 160 [para_from,157.1.1,138.1.1.1] f(f(x,f(y,f(y,y))),f(z,x))=x. given clause #29: (wt=-985) 128 [para_into,105.1.1.1.1.1,118.1.1] f(f(f(f(x,y),f(x,z)),u),f(x,x))=x. +++ bsub adjust, cl 41, new wt -500 >> BACK DEMODULATING HINT 41 WITH 163. given clause #30: (wt=-985) 146 [para_from,136.1.1,105.1.1.1] f(f(x,f(f(y,z),f(z,u))),f(z,z))=z. +++ bsub adjust, cl 42, new wt -500 >> BACK DEMODULATING HINT 42 WITH 165. given clause #31: (wt=-985) 148 [para_from,136.1.1,105.1.1.1.1.2] f(f(f(f(x,y),f(z,y)),u),f(y,y))=y. +++ bsub adjust, cl 43, new wt -500 >> BACK DEMODULATING HINT 43 WITH 167. given clause #32: (wt=-985) 150 [para_into,142.1.1.1,142.1.1] f(x,f(f(x,y),f(f(z,z),z)))=f(x,y). given clause #33: (wt=-985) 158 [para_from,157.1.1,101.1.1.2] f(x,f(f(x,y),f(z,f(z,z))))=f(x,y). +++ bsub adjust, cl 44, new wt -500 >> BACK DEMODULATING HINT 44 WITH 169. given clause #34: (wt=-985) 162 [para_into,128.1.1.1,136.1.1] f(f(x,f(f(y,z),f(y,u))),f(y,y))=y. given clause #35: (wt=-981) 122 [para_into,109.1.1.1,79.1.1,demod,114,flip.1] f(f(f(x,y),f(y,z)),y)=f(y,f(f(x,y),f(y,z))). given clause #36: (wt=-981) 166 [para_into,148.1.1.2,152.1.1] f(f(f(f(x,y),f(z,y)),u),f(y,f(f(v,v),v)))=y. given clause #37: (wt=-981) 168 [para_into,158.1.1,160.1.1,flip.1] f(f(f(x,f(x,x)),f(y,f(y,y))),z)=f(x,f(x,x)). +++ bsub adjust, cl 45, new wt -500 +++ bsub adjust, cl 116, new wt -250 given clause #38: (wt=-989) 170 [para_into,168.1.1,132.1.1] f(x,f(x,x))=f(y,f(y,y)). given clause #39: (wt=-979) 130 [para_into,105.1.1.1.1.1,111.1.1] f(f(f(x,f(f(x,y),z)),u),f(f(x,y),f(x,y)))=f(x,y). +++ bsub adjust, cl 47, new wt -500 >> BACK DEMODULATING HINT 47 WITH 173. given clause #40: (wt=-979) 144 [para_from,138.1.1,105.1.1.1.1.1] f(f(f(x,f(f(y,x),z)),u),f(f(y,x),f(y,x)))=f(y,x). +++ bsub adjust, cl 48, new wt -500 >> BACK DEMODULATING HINT 48 WITH 175. +++ bsub adjust, cl 10, new wt -125 >> BACK DEMODULATING HINT 10 WITH 177. given clause #41: (wt=-983) 174 [para_into,144.1.1.1.1.2,142.1.1] f(f(f(x,y),z),f(f(y,x),f(y,x)))=f(y,x). +++ bsub adjust, cl 49, new wt -500 +++ bsub adjust, cl 50, new wt -500 >> BACK DEMODULATING HINT 50 WITH 180. given clause #42: (wt=-985) 178 [para_from,174.1.1,109.1.1.1] f(f(x,y),f(y,x))=f(f(y,x),f(y,x)). +++ bsub adjust, cl 51, new wt -500 +++ bsub adjust, cl 52, new wt -500 >> BACK DEMODULATING HINT 51 WITH 182. given clause #43: (wt=-993) 183 [para_into,178.1.1.2,178.1.1,demod,104,125,182] f(x,y)=f(y,x). +++ bsub adjust, cl 53, new wt -500 +++ bsub adjust, cl 54, new wt -500 >> BACK DEMODULATING HINT 53 WITH 185. >> BACK DEMODULATING HINT 54 WITH 187. given clause #44: (wt=-987) 181 [para_into,178.1.1.1,178.1.1,demod,112,125,flip.1] f(x,f(f(y,x),f(x,y)))=f(y,x). given clause #45: (wt=-983) 184 [para_from,183.1.1,174.1.1.2.2] f(f(f(x,y),z),f(f(y,x),f(x,y)))=f(y,x). given clause #46: (wt=-983) 186 [para_from,183.1.1,174.1.1.2.1] f(f(f(x,y),z),f(f(x,y),f(y,x)))=f(y,x). given clause #47: (wt=-979) 164 [para_into,146.1.1.1.2.1,160.1.1] f(f(x,f(y,f(f(z,y),u))),f(f(z,y),f(z,y)))=f(z,y). +++ bsub adjust, cl 55, new wt -500 >> BACK DEMODULATING HINT 55 WITH 189. given clause #48: (wt=-979) 179 [para_from,174.1.1,142.1.1.1] f(f(x,y),f(f(f(y,x),z),f(f(u,u),u)))=f(f(y,x),z). +++ bsub adjust, cl 56, new wt -500 given clause #49: (wt=-989) 190 [para_into,179.1.1.2.1.1,183.1.1,demod,151] f(f(x,y),z)=f(f(y,x),z). +++ bsub adjust, cl 57, new wt -500 +++ bsub adjust, cl 58, new wt -500 given clause #50: (wt=-989) 191 [para_into,190.1.1,183.1.1] f(x,f(y,z))=f(f(z,y),x). +++ bsub adjust, cl 59, new wt -500 +++ bsub adjust, cl 60, new wt -500 +++ bsub adjust, cl 61, new wt -500 >> BACK DEMODULATING HINT 61 WITH 196. given clause #51: (wt=-989) 192 [copy,191,flip.1] f(f(x,y),z)=f(z,f(y,x)). +++ bsub adjust, cl 62, new wt -500 given clause #52: (wt=-985) 193 [para_into,191.1.1.2,191.1.1] f(x,f(f(y,z),u))=f(f(f(z,y),u),x). given clause #53: (wt=-985) 194 [copy,193,flip.1] f(f(f(x,y),z),u)=f(u,f(f(y,x),z)). +++ bsub adjust, cl 63, new wt -500 given clause #54: (wt=-985) 197 [para_into,192.1.1,191.1.1] f(f(x,y),f(z,u))=f(f(y,x),f(u,z)). +++ bsub adjust, cl 64, new wt -500 >> BACK DEMODULATING HINT 64 WITH 200. given clause #55: (wt=-981) 198 [para_into,194.1.1.1,191.1.1] f(f(f(x,y),f(z,u)),v)=f(v,f(f(u,z),f(y,x))). given clause #56: (wt=-975) 124 [back_demod,113,demod,123] f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(y,f(f(x,y),f(y,z))). given clause #57: (wt=-975) 195 [para_from,191.1.1,184.1.1.2.1] f(f(f(f(x,y),z),u),f(f(f(y,x),z),f(f(x,y),z)))=f(z,f(x,y)). given clause #58: (wt=-967) 199 [para_from,197.1.1,186.1.1.2.1] f(f(f(f(x,y),f(z,u)),v),f(f(f(y,x),f(u,z)),f(f(z,u),f(x,y))))=f(f(z,u),f(x,y)). given clause #59: (wt=-965) 172 [para_into,130.1.1.1.1.2,162.1.1] f(f(f(x,y),z),f(f(x,f(f(y,u),f(y,v))),f(x,f(f(y,u),f(y,v)))))=f(x,f(f(y,u),f(y,v))). +++ bsub adjust, cl 65, new wt -500 >> BACK DEMODULATING HINT 65 WITH 202. given clause #60: (wt=-975) 201 [para_into,172.1.1.2.1,164.1.1,demod,165,165] f(f(f(f(x,f(y,f(f(z,y),u))),z),v),f(f(z,y),f(z,y)))=f(z,y). +++ bsub adjust, cl 66, new wt -500 >> BACK DEMODULATING HINT 66 WITH 204. given clause #61: (wt=-975) 203 [para_into,201.1.1.1,194.1.1] f(f(x,f(f(f(y,f(f(z,y),u)),v),z)),f(f(z,y),f(z,y)))=f(z,y). given clause #62: (wt=-965) 188 [para_into,164.1.1.1.2.2,128.1.1] f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,u),f(z,v)),y)))=f(f(f(z,u),f(z,v)),y). +++ bsub adjust, cl 67, new wt -500 >> BACK DEMODULATING HINT 67 WITH 206. given clause #63: (wt=-965) 205 [para_into,188.1.1.2.1.1,183.1.1] f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,v),f(z,u)),y)))=f(f(f(z,v),f(z,u)),y). +++ bsub adjust, cl 68, new wt -500 >> BACK DEMODULATING HINT 68 WITH 208. given clause #64: (wt=-965) 207 [para_into,205.1.1,192.1.1] f(f(f(f(f(x,y),f(x,z)),u),f(f(f(x,z),f(x,y)),u)),f(f(u,x),v))=f(f(f(x,z),f(x,y)),u). +++ bsub adjust, cl 69, new wt -500 >> BACK DEMODULATING HINT 69 WITH 210. given clause #65: (wt=-983) 209 [para_into,207.1.1,203.1.1,flip.1] f(f(f(x,f(f(y,x),z)),f(x,u)),y)=f(y,x). +++ bsub adjust, cl 70, new wt -500 given clause #66: (wt=-975) 211 [para_into,209.1.1.1.1.2,166.1.1] f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(f(f(u,y),f(v,y)),x). +++ bsub adjust, cl 71, new wt -500 +++ bsub adjust, cl 72, new wt -500 +++ bsub adjust, cl 21, new wt -250 +++ bsub adjust, cl 21, new wt -125 >> BACK DEMODULATING HINT 71 WITH 213. >> BACK DEMODULATING HINT 72 WITH 215. >> BACK DEMODULATING HINT 21 WITH 217. >> BACK DEMODULATING HINT 21 WITH 219. +++ bsub adjust, cl 73, new wt -500 >> BACK DEMODULATING HINT 73 WITH 221. >> BACK DEMODULATING HINT 70 WITH 221. given clause #67: (wt=-975) 212 [para_into,211.1.1,192.1.1] f(f(f(x,y),f(z,y)),f(f(u,v),f(u,y)))=f(f(f(x,y),f(z,y)),u). given clause #68: (wt=-975) 214 [para_into,211.1.1,183.1.1] f(f(f(x,y),f(z,y)),f(f(u,y),f(u,v)))=f(f(f(x,y),f(z,y)),u). given clause #69: (wt=-975) 220 [para_from,211.1.1,199.1.1.2.2,demod,215,213,196,flip.1] f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(x,f(f(u,y),f(v,y))). +++ bsub adjust, cl 74, new wt -500 +++ bsub adjust, cl 13, new wt -250 +++ bsub adjust, cl 13, new wt -125 >> BACK DEMODULATING HINT 13 WITH 224. >> BACK DEMODULATING HINT 13 WITH 226. given clause #70: (wt=-981) 222 [para_into,220.1.1,214.1.1] f(f(f(x,y),f(x,y)),z)=f(x,f(f(z,y),f(z,y))). +++ bsub adjust, cl 75, new wt -500 +++ bsub adjust, cl 76, new wt -500 given clause #71: (wt=-981) 227 [para_into,222.1.1,198.1.1] f(x,f(f(y,z),f(y,z)))=f(z,f(f(x,y),f(x,y))). given clause #72: (wt=-981) 228 [para_into,222.1.1,192.1.1] f(x,f(f(y,z),f(y,z)))=f(y,f(f(x,z),f(x,z))). -------- PROOF -------- +++ bsub adjust, cl 77, new wt -500 ----> UNIT CONFLICT at 0.77 sec ----> 230 [binary,229.1,171.1] $F. Length of proof is 75. Level of proof is 26. ---------------- PROOF ---------------- 78 [] x=x. 80,79 [] f(f(f(f(x,y),f(y,z)),u),f(y,f(f(y,f(f(x,x),x)),z)))=y. 81 [] f(f(X,X),f(X,Y))!=X|f(X,f(X,X))!=f(Y,f(Y,Y))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 82 [copy,81,flip.2] f(f(X,X),f(X,Y))!=X|f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 84,83 [para_into,79.1.1.1.1,79.1.1] f(f(x,y),f(x,f(f(x,f(f(f(f(z,x),f(x,u)),f(f(z,x),f(x,u))),f(f(z,x),f(x,u)))),f(f(x,f(f(z,z),z)),u))))=x. 85 [para_into,79.1.1.1,79.1.1] f(x,f(f(x,y),f(f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))),u)))=f(x,y). 87 [para_into,85.1.1.2.2,79.1.1] f(f(x,y),f(f(f(x,y),f(y,z)),y))=f(f(x,y),f(y,z)). 89 [para_into,85.1.1.2,85.1.1] f(x,f(f(x,y),f(f(f(z,x),f(z,x)),f(z,x))))=f(x,y). 92,91 [para_into,87.1.1.2.1,79.1.1,demod,80] f(f(f(f(x,y),f(y,z)),y),f(y,y))=y. 93 [para_into,91.1.1.1.1,91.1.1] f(f(x,x),f(x,x))=x. 95 [para_from,91.1.1,87.1.1.1,demod,92,92] f(x,f(f(x,f(f(x,x),y)),f(x,x)))=f(x,f(f(x,x),y)). 97 [para_into,89.1.1.2.2.1,93.1.1] f(x,f(f(x,y),f(x,f(x,x))))=f(x,y). 99 [para_from,97.1.1,79.1.1.2] f(f(f(f(x,y),f(y,f(y,f(y,y)))),z),f(y,f(f(x,x),x)))=y. 101 [para_from,83.1.1,85.1.1.2.2] f(x,f(f(x,y),f(x,y)))=f(x,y). 104,103 [para_into,101.1.1.2.1,83.1.1,demod,84,84] f(f(x,y),f(x,x))=x. 105 [para_into,101.1.1.2.1,79.1.1,demod,80,80] f(f(f(f(x,y),f(y,z)),u),f(y,y))=y. 107 [back_demod,95,demod,104,flip.1] f(x,f(f(x,x),y))=f(x,x). 109 [para_into,103.1.1.2,103.1.1] f(f(f(x,x),y),x)=f(x,x). 112,111 [para_into,107.1.1.2.1,103.1.1,demod,104] f(f(x,x),f(x,y))=x. 114,113 [para_into,107.1.1.2,79.1.1,flip.1] f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(f(f(x,y),f(y,z)),y). 115 [back_demod,82,demod,112,unit_del,78] f(Y,f(Y,Y))!=f(X,f(X,X))|f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 118 [para_into,111.1.1.2,103.1.1] f(f(f(x,y),f(x,y)),x)=f(x,y). 123,122 [para_into,109.1.1.1,79.1.1,demod,114,flip.1] f(f(f(x,y),f(y,z)),y)=f(y,f(f(x,y),f(y,z))). 125,124 [back_demod,113,demod,123] f(f(f(x,y),f(y,z)),f(f(x,y),f(y,z)))=f(y,f(f(x,y),f(y,z))). 128 [para_into,105.1.1.1.1.1,118.1.1] f(f(f(f(x,y),f(x,z)),u),f(x,x))=x. 130 [para_into,105.1.1.1.1.1,111.1.1] f(f(f(x,f(f(x,y),z)),u),f(f(x,y),f(x,y)))=f(x,y). 133,132 [para_into,105.1.1.1,103.1.1] f(f(x,y),f(y,y))=y. 136 [para_from,132.1.1,103.1.1.1] f(x,f(f(y,x),f(y,x)))=f(y,x). 138 [para_from,132.1.1,118.1.1.1.2,demod,133,133] f(f(x,x),f(y,x))=x. 141,140 [para_into,138.1.1.1,138.1.1] f(x,f(y,f(x,x)))=f(x,x). 143,142 [back_demod,99,demod,141,133] f(f(x,y),f(x,f(f(z,z),z)))=x. 144 [para_from,138.1.1,105.1.1.1.1.1] f(f(f(x,f(f(y,x),z)),u),f(f(y,x),f(y,x)))=f(y,x). 146 [para_from,136.1.1,105.1.1.1] f(f(x,f(f(y,z),f(z,u))),f(z,z))=z. 148 [para_from,136.1.1,105.1.1.1.1.2] f(f(f(f(x,y),f(z,y)),u),f(y,y))=y. 151,150 [para_into,142.1.1.1,142.1.1] f(x,f(f(x,y),f(f(z,z),z)))=f(x,y). 152 [para_from,142.1.1,138.1.1.2,demod,143] f(x,x)=f(x,f(f(y,y),y)). 153 [copy,152,flip.1] f(x,f(f(y,y),y))=f(x,x). 156 [para_into,153.1.1.2.1,138.1.1] f(x,f(y,f(y,y)))=f(x,x). 157 [copy,156,flip.1] f(x,x)=f(x,f(y,f(y,y))). 158 [para_from,157.1.1,101.1.1.2] f(x,f(f(x,y),f(z,f(z,z))))=f(x,y). 160 [para_from,157.1.1,138.1.1.1] f(f(x,f(y,f(y,y))),f(z,x))=x. 162 [para_into,128.1.1.1,136.1.1] f(f(x,f(f(y,z),f(y,u))),f(y,y))=y. 165,164 [para_into,146.1.1.1.2.1,160.1.1] f(f(x,f(y,f(f(z,y),u))),f(f(z,y),f(z,y)))=f(z,y). 166 [para_into,148.1.1.2,152.1.1] f(f(f(f(x,y),f(z,y)),u),f(y,f(f(v,v),v)))=y. 168 [para_into,158.1.1,160.1.1,flip.1] f(f(f(x,f(x,x)),f(y,f(y,y))),z)=f(x,f(x,x)). 170 [para_into,168.1.1,132.1.1] f(x,f(x,x))=f(y,f(y,y)). 171 [back_unit_del,170.1,115.1] f(X,f(f(Y,Z),f(Y,Z)))!=f(Z,f(f(Y,X),f(Y,X))). 172 [para_into,130.1.1.1.1.2,162.1.1] f(f(f(x,y),z),f(f(x,f(f(y,u),f(y,v))),f(x,f(f(y,u),f(y,v)))))=f(x,f(f(y,u),f(y,v))). 174 [para_into,144.1.1.1.1.2,142.1.1] f(f(f(x,y),z),f(f(y,x),f(y,x)))=f(y,x). 178 [para_from,174.1.1,109.1.1.1] f(f(x,y),f(y,x))=f(f(y,x),f(y,x)). 179 [para_from,174.1.1,142.1.1.1] f(f(x,y),f(f(f(y,x),z),f(f(u,u),u)))=f(f(y,x),z). 182,181 [para_into,178.1.1.1,178.1.1,demod,112,125,flip.1] f(x,f(f(y,x),f(x,y)))=f(y,x). 183 [para_into,178.1.1.2,178.1.1,demod,104,125,182] f(x,y)=f(y,x). 184 [para_from,183.1.1,174.1.1.2.2] f(f(f(x,y),z),f(f(y,x),f(x,y)))=f(y,x). 186 [para_from,183.1.1,174.1.1.2.1] f(f(f(x,y),z),f(f(x,y),f(y,x)))=f(y,x). 188 [para_into,164.1.1.1.2.2,128.1.1] f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,u),f(z,v)),y)))=f(f(f(z,u),f(z,v)),y). 190 [para_into,179.1.1.2.1.1,183.1.1,demod,151] f(f(x,y),z)=f(f(y,x),z). 191 [para_into,190.1.1,183.1.1] f(x,f(y,z))=f(f(z,y),x). 192 [copy,191,flip.1] f(f(x,y),z)=f(z,f(y,x)). 193 [para_into,191.1.1.2,191.1.1] f(x,f(f(y,z),u))=f(f(f(z,y),u),x). 194 [copy,193,flip.1] f(f(f(x,y),z),u)=f(u,f(f(y,x),z)). 196,195 [para_from,191.1.1,184.1.1.2.1] f(f(f(f(x,y),z),u),f(f(f(y,x),z),f(f(x,y),z)))=f(z,f(x,y)). 197 [para_into,192.1.1,191.1.1] f(f(x,y),f(z,u))=f(f(y,x),f(u,z)). 198 [para_into,194.1.1.1,191.1.1] f(f(f(x,y),f(z,u)),v)=f(v,f(f(u,z),f(y,x))). 199 [para_from,197.1.1,186.1.1.2.1] f(f(f(f(x,y),f(z,u)),v),f(f(f(y,x),f(u,z)),f(f(z,u),f(x,y))))=f(f(z,u),f(x,y)). 201 [para_into,172.1.1.2.1,164.1.1,demod,165,165] f(f(f(f(x,f(y,f(f(z,y),u))),z),v),f(f(z,y),f(z,y)))=f(z,y). 203 [para_into,201.1.1.1,194.1.1] f(f(x,f(f(f(y,f(f(z,y),u)),v),z)),f(f(z,y),f(z,y)))=f(z,y). 205 [para_into,188.1.1.2.1.1,183.1.1] f(f(x,f(y,z)),f(f(f(f(z,u),f(z,v)),y),f(f(f(z,v),f(z,u)),y)))=f(f(f(z,v),f(z,u)),y). 207 [para_into,205.1.1,192.1.1] f(f(f(f(f(x,y),f(x,z)),u),f(f(f(x,z),f(x,y)),u)),f(f(u,x),v))=f(f(f(x,z),f(x,y)),u). 209 [para_into,207.1.1,203.1.1,flip.1] f(f(f(x,f(f(y,x),z)),f(x,u)),y)=f(y,x). 211 [para_into,209.1.1.1.1.2,166.1.1] f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(f(f(u,y),f(v,y)),x). 213,212 [para_into,211.1.1,192.1.1] f(f(f(x,y),f(z,y)),f(f(u,v),f(u,y)))=f(f(f(x,y),f(z,y)),u). 215,214 [para_into,211.1.1,183.1.1] f(f(f(x,y),f(z,y)),f(f(u,y),f(u,v)))=f(f(f(x,y),f(z,y)),u). 220 [para_from,211.1.1,199.1.1.2.2,demod,215,213,196,flip.1] f(f(f(x,y),f(x,z)),f(f(u,y),f(v,y)))=f(x,f(f(u,y),f(v,y))). 222 [para_into,220.1.1,214.1.1] f(f(f(x,y),f(x,y)),z)=f(x,f(f(z,y),f(z,y))). 227 [para_into,222.1.1,198.1.1] f(x,f(f(y,z),f(y,z)))=f(z,f(f(x,y),f(x,y))). 228 [para_into,222.1.1,192.1.1] f(x,f(f(y,z),f(y,z)))=f(y,f(f(x,z),f(x,z))). 229 [para_into,228.1.1,227.1.1] f(x,f(f(y,z),f(y,z)))=f(z,f(f(y,x),f(y,x))). 230 [binary,229.1,171.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 72 clauses generated 16883 para_from generated 7276 para_into generated 9606 back unit del. gen. 1 demod & eval rewrites 18607 clauses wt,lit,sk delete 16501 tautologies deleted 0 clauses forward subsumed 332 (subsumed by sos) 39 unit deletions 1 factor simplifications 0 clauses kept 85 new demodulators 62 empty clauses 1 clauses back demodulated 13 clauses back subsumed 3 usable size 59 sos size 10 demodulators size 51 passive size 0 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.77 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) That finishes the proof of the theorem. Process 8942 finished Mon Aug 2 15:31:15 2004 otter-3.3f/examples/wos/0040755000076400007640000000000010103530360014621 5ustar mccunemccuneotter-3.3f/examples/wos/grp_exp4.in0100644000076400007640000001434505517330133016716 0ustar mccunemccune% Input File for Studying Exponent 4 Groups with OTTER 3.0 % set(ur_res). set(knuth_bendix). clear(eq_units_both_ways). set(process_input). set(index_for_back_demod). set(para_into_units_only). set(para_from_units_only). set(lrpo). lex([e,a,b,f(x,x),g(x)]). assign(pick_given_ratio, 3). assign(max_proofs, 4). assign(demod_limit, 500). assign(max_mem, 24000). assign(max_weight, 51). % assign(max_seconds, 60). assign(change_limit_after, 10). assign(new_max_weight, 41). clear(print_kept). clear(print_new_demod). clear(print_back_demod). weight_list(pick_and_purge). % Following are proof steps with cancellation, but not the back_demods. weight(f(e,f(e,f(e,f(f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,y),e)), 2). weight(f(e,f(e,f(e,f(f(f(x,x),f(f(x,e),e)),e))))=f(x,f(f(x,x),e)), 2). weight(f(e,f(e,f(e,f(x,f(f(f(x,f(x,x)),e),e)))))=e, 2). weight(f(e,f(e,f(f(e,f(x,f(y,f(y,y)))),y)))=x, 2). weight(f(e,f(e,f(f(f(x,f(f(x,x),e)),e),f(f(f(x,f(f(x,x),e)),e),f(f(x,f(f(x,x),e)),e)))))=x, 2). weight(f(e,f(e,f(y,f(f(f(y,f(y,y)),e),e))))=e, 2). weight(f(e,f(f(e,f(e,f(f(x,e),e))),y))=f(x,f(e,y)), 2). weight(f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x, 2). weight(f(e,f(f(e,f(e,f(x,e))),e))=x, 2). weight(f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x, 2). weight(f(e,f(f(e,f(f(f(x,f(f(x,x),e)),e),f(f(f(x,f(f(x,x),e)),e),f(f(x,f(f(x,x),e)),e)))),y))=f(x,f(e,y)), 2). weight(f(e,f(f(f(x,f(e,f(e,y))),e),e))=f(f(e,f(f(x,e),e)),y), 2). weight(f(e,f(y,f(f(f(y,f(y,y)),e),e)))=e, 2). weight(f(f(e,f(x,f(e,y))),f(y,f(y,y)))=f(e,f(f(x,e),e)), 2). weight(f(f(e,f(x,f(y,f(y,y)))),y)=f(e,f(f(x,e),e)), 2). weight(f(f(e,x),e)=f(e,f(x,e)), 2). weight(f(f(e,x),f(e,y))=f(e,f(x,y)), 2). weight(f(f(e,x),y)=f(e,f(x,f(e,f(e,f(f(y,e),e))))), 2). weight(f(f(f(x,f(x,x)),e),e)=f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))), 2). weight(f(f(f(x,x),e),f(f(f(x,e),f(f(f(x,e),e),e)),e))=e, 2). weight(f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)), 2). weight(f(f(f(x,x),f(f(x,x),f(x,x))),e)=f(x,f(f(x,e),e)), 2). weight(f(f(x,e),f(f(f(x,e),f(f(x,f(f(x,e),e)),e)),e))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))), 2). weight(f(f(x,e),f(f(x,x),f(f(x,e),e)))=e, 2). weight(f(f(x,e),f(y,e))=f(f(x,y),e), 2). weight(f(f(x,f(e,f(e,f(y,f(y,y))))),f(e,y))=f(f(x,e),e), 2). weight(f(f(x,f(e,f(e,y))),f(y,f(y,y)))=f(f(x,e),e), 2). weight(f(f(x,f(e,f(y,f(y,y)))),y)=f(f(x,e),e), 2). weight(f(f(x,f(e,y)),e)=f(f(x,e),f(e,f(y,e))), 2). weight(f(f(x,f(f(x,e),e)),e)=f(f(f(x,x),f(x,x)),f(f(f(x,x),e),e)), 2). weight(f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)), 2). weight(f(f(x,f(x,x)),f(e,f(f(x,e),e)))=e, 2). weight(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x))))=f(e,x), 2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),e))=f(x,f(f(x,e),e)), 2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,e),e),y)))=f(x,f(f(x,f(f(x,e),e)),f(e,y))), 2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z)))=f(x,f(y,f(e,z))), 2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),y))=f(x,f(f(x,e),y)), 2). weight(f(f(x,x),f(f(x,f(f(x,e),e)),e))=e, 2). weight(f(f(x,x),f(f(x,f(f(x,e),e)),f(e,f(f(y,e),e))))=y, 2). weight(f(f(x,y),e)=f(f(x,e),f(y,e)), 2). weight(f(f(x,y),z)=f(f(x,e),f(y,f(f(e,f(e,f(z,u))),f(u,f(u,u))))), 2). weight(f(x,e)=x, 2). weight(f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))), 2). weight(f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e))=e, 2). weight(f(x,f(f(x,f(f(x,x),e)),e))=e, 2). weight(f(x,f(f(x,f(f(x,x),e)),f(f(f(f(y,f(y,y)),e),e),f(f(f(f(y,f(y,y)),e),e),f(f(f(y,f(y,y)),e),e)))))=y, 2). weight(f(x,f(f(x,f(f(x,x),e)),f(f(f(y,f(f(y,y),e)),e),f(f(f(y,f(f(y,y),e)),e),f(f(y,f(f(y,y),e)),e)))))=y, 2). weight(f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y), 2). weight(f(x,f(f(x,f(f(x,x),f(y,e))),e))=y, 2). weight(f(x,f(f(x,f(f(x,x),f(y,f(z,f(z,z))))),f(e,z)))=y, 2). weight(f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))), 2). weight(f(x,f(f(x,f(x,f(f(x,e),e))),e))=f(f(x,x),f(x,x)), 2). weight(f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))), 2). weight(f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))), 2). weight(f(y,f(f(f(y,f(y,y)),e),e))=e, 2). % Following are proof steps with cancellation, just the back_demods. weight(f(e,f(e,f(e,f(f(f(x,f(f(x,e),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,y),e)), 2). weight(f(e,f(e,f(e,f(f(x,e),e))))=x, 2). weight(f(e,f(e,f(e,x)))=x, 2). weight(f(e,f(e,f(f(f(x,x),f(f(x,e),e)),f(f(f(x,x),f(f(x,e),e)),f(f(x,x),f(f(x,e),e))))))=x, 2). weight(f(e,f(e,x))=x, 2). weight(f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x, 2). weight(f(e,f(f(e,f(f(f(x,x),f(f(x,e),e)),f(f(f(x,x),f(f(x,e),e)),f(f(x,x),f(f(x,e),e))))),y))=f(x,f(e,y)), 2). weight(f(e,f(f(f(x,e),e),f(e,f(e,f(f(y,e),e)))))=f(f(e,f(f(x,e),e)),y), 2). weight(f(e,f(x,x))=f(x,x), 2). weight(f(e,y)=y, 2). weight(f(f(e,x),y)=f(e,f(x,f(e,f(e,y)))), 2). weight(f(f(x,f(f(x,e),e)),f(e,y))=f(f(x,e),f(f(f(x,e),e),y)), 2). weight(f(f(x,f(x,f(y,z))),f(z,f(z,z)))=f(x,f(x,y)), 2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))), 2). weight(f(f(x,x),f(f(x,e),f(f(f(x,e),e),f(f(y,e),e))))=y, 2). weight(f(f(x,x),f(x,f(x,y)))=y, 2). weight(f(f(x,x),f(x,x))=e, 2). weight(f(f(x,y),f(e,z))=f(f(x,e),f(y,z)), 2). weight(f(f(x,y),f(e,z))=f(x,f(y,z)), 2). weight(f(f(x,y),z)=f(x,f(y,f(e,f(e,z)))), 2). weight(f(f(x,y),z)=f(x,f(y,z)), 2). weight(f(x,f(f(x,f(f(x,x),e)),f(e,f(f(y,e),e))))=y, 2). weight(f(x,f(f(x,x),f(f(x,e),e)))=e, 2). weight(f(x,f(f(x,y),f(e,z)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))), 2). weight(f(x,f(x,f(x,x)))=e, 2). end_of_list. list(usable). (x = x). end_of_list. % list(usable). % f(x,y) != f(x,z) | y = z. % f(y,x) != f(z,x) | y = z. % f(x,y) != u | f(x,z) != u | y = z. % f(y,x) != u | f(z,x) != u | y = z. % end_of_list. list(sos). f(y,f(f(y,f(f(y,y),f(x,z))),f(z,f(z,z)))) = x. f(e,e) = e. end_of_list. list(passive). % (f(a,f(a,f(a,a))) != f(b,f(b,f(b,b)))) | $ANS(X4_Y4). % (f(a,f(b,f(b,f(b,b)))) != a) | $ANS(R_ident). % (f(b,f(b,f(b,f(b,a)))) != a) | $ANS(L_ident_if_assoc). (f(f(a,b),c) != f(a,f(b,c))) | $ANS(assoc). (f(a,f(a,f(a,a))) != e) | $ANS(exp4). (f(e,a) != a) | $ANS(lid). (f(a,e) != a) | $ANS(rid). end_of_list. list(demodulators). % (f(x,y) = f(x,z)) = (y = z). % (f(y,x) = f(z,x)) = (y = z). end_of_list. otter-3.3f/examples/wos/grp_exp3.in0100644000076400007640000000406106005317124016705 0ustar mccunemccune% Input File for Studying Exponent 3 Groups with OTTER 3.0 set(knuth_bendix). clear(eq_units_both_ways). set(process_input). set(index_for_back_demod). % Following 8 are knuth-bendix options % set(dynamic_demod_all). % clear(para_from_right). % set(back_demod). % set(para_from). % set(para_into). % clear(para_into_right). % set(dynamic_demod). % set(order_eq). set(lrpo). lex([e,f(x,x),g(x)]). % lrpo_lr_status([f(x,x)]). assign(pick_given_ratio, 3). assign(max_proofs, 4). assign(max_mem, 12000). % set(control_memory). % set(sos_queue). assign(max_weight, 80). % assign(max_seconds, 3600). % assign(report, 300). assign(demod_limit, -1). assign(change_limit_after, 12). assign(new_max_weight, 25). clear(print_kept). clear(print_new_demod). clear(print_back_demod). weight_list(pick_and_purge). % following is the union of proof steps for exp3. weight(EQ(f(e,e),e), 2). weight(EQ(f(e,f(x,f(x,f(x,e)))),e), 2). weight(EQ(f(f(x,e),f(f(x,e),f(x,e))),e), 2). weight(EQ(f(f(x,e),f(f(x,e),f(x,f(f(f(e,f(x,e)),y),f(y,y))))),f(x,e)), 2). weight(EQ(f(f(x,y),e),f(x,f(y,f(z,f(z,f(z,e)))))), 2). weight(EQ(f(f(x,y),f(e,z)),f(x,f(y,z))), 2). weight(EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e), 2). weight(EQ(f(x,e),x), 2). weight(EQ(f(x,f(f(x,f(f(x,y),f(e,f(f(e,z),f(e,z))))),z)),y), 2). weight(EQ(f(x,f(f(x,f(f(x,y),f(e,f(z,z)))),f(f(e,f(f(e,z),u)),f(e,f(u,u))))),y), 2). weight(EQ(f(x,f(f(x,f(f(x,y),z)),f(f(e,z),f(e,z)))),y), 2). weight(EQ(f(x,f(f(y,z),u)),f(f(x,y),f(f(e,z),u))), 2). weight(EQ(f(x,f(x,f(f(x,f(y,f(z,e))),f(f(f(e,e),u),f(u,u))))),f(y,z)), 2). weight(EQ(f(x,f(x,f(f(y,z),f(z,z)))),f(x,f(x,f(y,e)))), 2). weight(EQ(f(x,f(x,f(x,e))),e), 2). weight(EQ(f(x,f(x,f(x,f(y,e)))),y), 2). weight(EQ(f(x,f(x,f(x,f(y,f(z,e))))),f(y,z)), 2). weight(EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)), 2). end_of_list. list(usable). EQ(x,x). end_of_list. list(sos). EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). end_of_list. list(passive). -EQ(f(e,a),a) | $ANS(lid). -EQ(f(a,e),a) | $ANS(rid). -EQ(f(a,f(a,a)),e) | $ANS(exp3). -EQ(f(f(a,b),c), f(a,f(b,c))) | $ANS(assoc). end_of_list. otter-3.3f/examples/wos/cursory.in0100644000076400007640000001253106005317122016663 0ustar mccunemccune% Input File for Cursory Proof Checking set(hyper_res). assign(max_weight,2). % set(control_memory). assign(max_proofs, -1). clear(print_kept). % set(very_verbose). % set(ancestor_subsume). clear(back_sub). % assign(max_seconds, 600). assign(max_mem,22000). % assign(report, 900). % assign(max_distinct_vars, 4). % assign(pick_given_ratio, 3). set(order_history). set(input_sos_first). % set(sos_queue). weight_list(pick_and_purge). % Following are the steps of a 42-step proof, including duplicates, % of the deducibility of the Church axiom system from that of Lukasiewicz. weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2). weight(P(i(i(x,y),i(i(n(x),x),y))),2). weight(P(i(i(i(n(x),y),z),i(x,z))),2). weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2). weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2). weight(P(i(i(x,n(y)),i(y,i(x,z)))),2). weight(P(i(x,x)),2). weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2). weight(P(i(n(i(x,x)),y)),2). weight(P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))),2). weight(P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))),2). weight(P(i(x,i(n(i(y,y)),z))),2). weight(P(i(i(i(n(i(x,x)),y),z),i(u,z))),2). weight(P(i(x,i(y,y))),2). weight(P(i(i(i(x,x),y),i(z,y))),2). weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2). weight(P(i(x,i(i(n(y),y),y))),2). weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2). weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2). weight(P(i(i(n(x),y),i(i(y,x),x))),2). weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2). weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2). weight(P(i(i(n(x),y),i(i(y,x),x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2). weight(P(i(x,i(y,x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(P(i(i(i(x,y),z),i(y,z))),2). weight(P(i(x,i(y,x))),2). weight(P(i(x,i(i(x,y),y))),2). weight(P(i(i(i(x,y),z),i(y,z))),2). weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2). weight(P(i(n(x),i(x,y))),2). weight(P(i(x,i(i(x,y),y))),2). weight(P(i(i(x,y),i(i(n(y),x),y))),2). weight(P(i(i(n(x),y),i(n(y),x))),2). weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2). weight(P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))),2). weight(P(i(n(i(x,y)),x)),2). weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2). weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),2). weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2). end_of_list. list(usable). -P(i(x,y)) | -P(x) | P(y). % The following disjunctions are known axiom systems. % -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | % -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | % $ANSWER(step_allFrege_18_35_39_40_46_21). % 21 is dependent. % -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | % -P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | % -P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | % $ANSWER(step_allHilbert_18_21_22_3_54_30). % 30 is dependent. -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49). % -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | % -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59). % -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | % -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60). % -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | % -P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3). % -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | % -P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | % -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | % $ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). % -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | % -P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | % -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | % $ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). end_of_list. list(sos). % The following three are Luka, 1 2 3. P(i(i(x,y),i(i(y,z),i(x,z)))). P(i(i(n(x),x),x)). P(i(x,i(n(x),y))). % The following are from Frege, 18 35 21 46 39 40, with 21 dependent. % P(i(x,i(y,x))). % axiom F1. % P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). % axiom F2. % P(i(i(x,i(y,z)),i(y,i(x,z)))). % axiom F3. % P(i(i(x,y),i(n(y),n(x)))). % axiom F4. % P(i(n(n(x)),x)). % axiom F5. % P(i(x,n(n(x)))). % axiom f6. end_of_list. list(passive). % -P(i(i(p,q),i(i(q,r),i(p,r)))) | $ANSWER(step_L1). % -P(i(i(n(p),p),p)) | $ANSWER(step_L2). % -P(i(p,i(n(p),q))) | $ANSWER(step_L3). -P(i(q,i(p,q))) | $ANSWER(step_18). % -P(i(i(i(p,q),r),i(q,r))) | $ANSWER(step_19). % -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_21). % -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANSWER(step_22). % -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_30). -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANSWER(step_35). % -P(i(i(i(p,q),r),i(n(p),r))) | $ANSWER(step_37). % -P(i(n(n(p)),p)) | $ANSWER(step_39). % -P(i(p,n(n(p)))) | $ANSWER(step_40). % -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_46). -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_49). % -P(i(i(p,q),i(i(n(p),q),q))) | $ANSWER(step_54). % -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_59). % -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_60). end_of_list. list(demodulators). % (n(n(x)) = junk). (n(n(n(x))) = junk). % (i(i(x,x),y) = junk). % (i(y,i(x,x)) = junk). (i(junk,x) = junk). (i(x,junk) = junk). (n(junk) = junk). (P(junk) = $T). end_of_list. otter-3.3f/examples/wos/cursory.out0100664000076400007640000006066410103522157017100 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:39 2004 The command was "../../bin/otter". The process ID is 8502. set(hyper_res). assign(max_weight,2). assign(max_proofs,-1). clear(print_kept). clear(back_sub). assign(max_mem,22000). set(order_history). set(input_sos_first). weight_list(pick_and_purge). weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2). weight(P(i(i(x,y),i(i(n(x),x),y))),2). weight(P(i(i(i(n(x),y),z),i(x,z))),2). weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2). weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2). weight(P(i(i(x,n(y)),i(y,i(x,z)))),2). weight(P(i(x,x)),2). weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2). weight(P(i(n(i(x,x)),y)),2). weight(P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))),2). weight(P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))),2). weight(P(i(x,i(n(i(y,y)),z))),2). weight(P(i(i(i(n(i(x,x)),y),z),i(u,z))),2). weight(P(i(x,i(y,y))),2). weight(P(i(i(i(x,x),y),i(z,y))),2). weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2). weight(P(i(x,i(i(n(y),y),y))),2). weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2). weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2). weight(P(i(i(n(x),y),i(i(y,x),x))),2). weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2). weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2). weight(P(i(i(n(x),y),i(i(y,x),x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2). weight(P(i(x,i(y,x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(P(i(i(i(x,y),z),i(y,z))),2). weight(P(i(x,i(y,x))),2). weight(P(i(x,i(i(x,y),y))),2). weight(P(i(i(i(x,y),z),i(y,z))),2). weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2). weight(P(i(n(x),i(x,y))),2). weight(P(i(x,i(i(x,y),y))),2). weight(P(i(i(x,y),i(i(n(y),x),y))),2). weight(P(i(i(n(x),y),i(n(y),x))),2). weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2). weight(P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))),2). weight(P(i(n(i(x,y)),x)),2). weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2). weight(P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))),2). weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2). end_of_list. list(usable). 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49). 3 [] $ANSWER(step_allWos_x_19_37_60). end_of_list. list(sos). 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 5 [] P(i(i(n(x),x),x)). 6 [] P(i(x,i(n(x),y))). end_of_list. list(passive). 7 [] -P(i(q,i(p,q)))|$ANSWER(step_18). 8 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANSWER(step_35). 9 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_49). end_of_list. list(demodulators). 10 [] n(n(n(x)))=junk. 11 [] i(junk,x)=junk. 12 [] i(x,junk)=junk. 13 [] n(junk)=junk. 14 [] P(junk)=$T. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=-2147483647) 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). given clause #2: (wt=-2147483647) 5 [] P(i(i(n(x),x),x)). given clause #3: (wt=-2147483647) 6 [] P(i(x,i(n(x),y))). given clause #4: (wt=2) 15 [hyper,1,4,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #5: (wt=2) 16 [hyper,1,4,5] P(i(i(x,y),i(i(n(x),x),y))). given clause #6: (wt=2) 17 [hyper,1,4,6] P(i(i(i(n(x),y),z),i(x,z))). given clause #7: (wt=2) 18 [hyper,1,15,15] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). given clause #8: (wt=2) 19 [hyper,1,15,4] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). given clause #9: (wt=2) 20 [hyper,1,16,6] P(i(i(n(x),x),i(n(x),y))). given clause #10: (wt=2) 21 [hyper,1,15,17] P(i(i(x,n(y)),i(y,i(x,z)))). given clause #11: (wt=2) 22 [hyper,1,17,5] P(i(x,x)). given clause #12: (wt=2) 23 [hyper,1,18,19] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). given clause #13: (wt=2) 24 [hyper,1,6,22] P(i(n(i(x,x)),y)). given clause #14: (wt=2) 25 [hyper,1,23,16] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). given clause #15: (wt=2) 26 [hyper,1,21,24] P(i(x,i(n(i(y,y)),z))). given clause #16: (wt=2) 27 [hyper,1,4,25] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). given clause #17: (wt=2) 28 [hyper,1,4,26] P(i(i(i(n(i(x,x)),y),z),i(u,z))). given clause #18: (wt=2) 29 [hyper,1,28,5] P(i(x,i(y,y))). given clause #19: (wt=2) 30 [hyper,1,4,29] P(i(i(i(x,x),y),i(z,y))). given clause #20: (wt=2) 31 [hyper,1,27,30] P(i(i(n(x),y),i(z,i(i(y,x),x)))). given clause #21: (wt=2) 32 [hyper,1,23,30] P(i(i(x,y),i(i(i(z,z),u),i(i(y,v),u)))). given clause #22: (wt=2) 33 [hyper,1,30,16] P(i(x,i(i(n(y),y),y))). given clause #23: (wt=2) 34 [hyper,1,4,31] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). given clause #24: (wt=2) 35 [hyper,1,18,32] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(x,i(i(v,w),z))))). given clause #25: (wt=2) 36 [hyper,1,34,5] P(i(i(n(x),y),i(i(y,x),x))). given clause #26: (wt=2) 37 [hyper,1,18,36] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). -------- PROOF -------- 40 [binary,39.1,9.1] $ANSWER(step_49). ----> UNIT CONFLICT at 0.01 sec ----> 40 [binary,39.1,9.1] $ANSWER(step_49). Length of proof is 20. Level of proof is 12. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 5 [] P(i(i(n(x),x),x)). 6 [] P(i(x,i(n(x),y))). 9 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_49). 15 [hyper,1,4,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 16 [hyper,1,4,5] P(i(i(x,y),i(i(n(x),x),y))). 17 [hyper,1,4,6] P(i(i(i(n(x),y),z),i(x,z))). 18 [hyper,1,15,15] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 19 [hyper,1,15,4] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 21 [hyper,1,15,17] P(i(i(x,n(y)),i(y,i(x,z)))). 22 [hyper,1,17,5] P(i(x,x)). 23 [hyper,1,18,19] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 24 [hyper,1,6,22] P(i(n(i(x,x)),y)). 25 [hyper,1,23,16] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 26 [hyper,1,21,24] P(i(x,i(n(i(y,y)),z))). 27 [hyper,1,4,25] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 28 [hyper,1,4,26] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 29 [hyper,1,28,5] P(i(x,i(y,y))). 30 [hyper,1,4,29] P(i(i(i(x,x),y),i(z,y))). 31 [hyper,1,27,30] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 34 [hyper,1,4,31] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 36 [hyper,1,34,5] P(i(i(n(x),y),i(i(y,x),x))). 37 [hyper,1,18,36] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 39 [hyper,1,37,6] P(i(i(n(x),n(y)),i(y,x))). 40 [binary,39.1,9.1] $ANSWER(step_49). ------------ end of proof ------------- given clause #27: (wt=2) 38 [hyper,1,17,36] P(i(x,i(i(y,x),x))). given clause #28: (wt=2) 39 [hyper,1,37,6] P(i(i(n(x),n(y)),i(y,x))). -------- PROOF -------- 44 [binary,43.1,7.1] $ANSWER(step_18). ----> UNIT CONFLICT at 0.01 sec ----> 44 [binary,43.1,7.1] $ANSWER(step_18). Length of proof is 21. Level of proof is 13. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 5 [] P(i(i(n(x),x),x)). 6 [] P(i(x,i(n(x),y))). 7 [] -P(i(q,i(p,q)))|$ANSWER(step_18). 15 [hyper,1,4,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 16 [hyper,1,4,5] P(i(i(x,y),i(i(n(x),x),y))). 17 [hyper,1,4,6] P(i(i(i(n(x),y),z),i(x,z))). 18 [hyper,1,15,15] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 19 [hyper,1,15,4] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 21 [hyper,1,15,17] P(i(i(x,n(y)),i(y,i(x,z)))). 22 [hyper,1,17,5] P(i(x,x)). 23 [hyper,1,18,19] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 24 [hyper,1,6,22] P(i(n(i(x,x)),y)). 25 [hyper,1,23,16] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 26 [hyper,1,21,24] P(i(x,i(n(i(y,y)),z))). 27 [hyper,1,4,25] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 28 [hyper,1,4,26] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 29 [hyper,1,28,5] P(i(x,i(y,y))). 30 [hyper,1,4,29] P(i(i(i(x,x),y),i(z,y))). 31 [hyper,1,27,30] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 34 [hyper,1,4,31] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 36 [hyper,1,34,5] P(i(i(n(x),y),i(i(y,x),x))). 37 [hyper,1,18,36] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 39 [hyper,1,37,6] P(i(i(n(x),n(y)),i(y,x))). 43 [hyper,1,17,39] P(i(x,i(y,x))). 44 [binary,43.1,7.1] $ANSWER(step_18). ------------ end of proof ------------- given clause #29: (wt=2) 41 [hyper,1,18,38] P(i(i(x,i(y,z)),i(z,i(x,z)))). given clause #30: (wt=2) 42 [hyper,1,16,38] P(i(i(n(x),x),i(i(y,x),x))). given clause #31: (wt=2) 43 [hyper,1,17,39] P(i(x,i(y,x))). given clause #32: (wt=2) 45 [hyper,1,27,41] P(i(i(n(x),y),i(z,i(i(x,z),z)))). given clause #33: (wt=2) 46 [hyper,1,4,41] P(i(i(i(x,i(y,x)),z),i(i(y,i(u,x)),z))). given clause #34: (wt=2) 47 [hyper,1,18,42] P(i(i(x,i(y,z)),i(i(n(z),z),i(x,z)))). given clause #35: (wt=2) 48 [hyper,1,4,43] P(i(i(i(x,y),z),i(y,z))). given clause #36: (wt=2) 49 [hyper,1,34,45] P(i(i(n(x),y),i(z,i(i(u,z),z)))). given clause #37: (wt=2) 50 [hyper,1,4,45] P(i(i(i(x,i(i(y,x),x)),z),i(i(n(y),u),z))). given clause #38: (wt=2) 51 [hyper,1,46,41] P(i(i(x,i(y,z)),i(z,i(z,z)))). given clause #39: (wt=2) 52 [hyper,1,46,37] P(i(i(x,i(y,z)),i(i(n(z),x),i(z,z)))). given clause #40: (wt=2) 53 [hyper,1,46,18] P(i(i(x,i(y,z)),i(i(u,x),i(z,i(u,z))))). given clause #41: (wt=2) 54 [hyper,1,46,47] P(i(i(x,i(y,z)),i(i(n(z),z),i(z,z)))). given clause #42: (wt=2) 55 [hyper,1,27,48] P(i(i(n(x),y),i(z,i(i(y,x),z)))). given clause #43: (wt=2) 56 [hyper,1,48,39] P(i(n(x),i(x,y))). given clause #44: (wt=2) 57 [hyper,1,48,36] P(i(x,i(i(x,y),y))). given clause #45: (wt=2) 58 [hyper,1,48,6] P(i(x,i(n(i(y,x)),z))). given clause #46: (wt=2) 59 [hyper,1,4,49] P(i(i(i(x,i(i(y,x),x)),z),i(i(n(u),v),z))). given clause #47: (wt=2) 60 [hyper,1,4,51] P(i(i(i(x,i(x,x)),y),i(i(z,i(u,x)),y))). given clause #48: (wt=2) 61 [hyper,1,46,53] P(i(i(x,i(y,z)),i(i(u,z),i(z,i(u,z))))). given clause #49: (wt=2) 62 [hyper,1,53,4] P(i(i(x,i(y,z)),i(i(y,u),i(x,i(y,u))))). given clause #50: (wt=2) 63 [hyper,1,4,55] P(i(i(i(x,i(i(y,z),x)),u),i(i(n(z),y),u))). given clause #51: (wt=2) 64 [hyper,1,53,56] P(i(i(x,n(y)),i(z,i(x,z)))). given clause #52: (wt=2) 65 [hyper,1,47,56] P(i(i(n(x),x),i(n(y),x))). given clause #53: (wt=2) 66 [hyper,1,37,56] P(i(i(n(x),y),i(n(y),x))). given clause #54: (wt=2) 67 [hyper,1,18,57] P(i(i(x,i(y,z)),i(y,i(x,z)))). given clause #55: (wt=2) 68 [hyper,1,16,57] P(i(i(n(x),x),i(i(x,y),y))). given clause #56: (wt=2) 69 [hyper,1,4,58] P(i(i(i(n(i(x,y)),z),u),i(y,u))). given clause #57: (wt=2) 70 [hyper,1,60,62] P(i(i(x,i(y,z)),i(i(z,u),i(z,i(z,u))))). given clause #58: (wt=2) 71 [hyper,1,46,62] P(i(i(x,i(y,z)),i(i(x,u),i(z,i(x,u))))). given clause #59: (wt=2) 72 [hyper,1,66,56] P(i(n(i(x,y)),x)). given clause #60: (wt=2) 73 [hyper,1,46,67] P(i(i(x,i(y,z)),i(x,i(z,z)))). given clause #61: (wt=2) 74 [hyper,1,27,67] P(i(i(n(x),y),i(i(y,x),i(i(x,z),z)))). given clause #62: (wt=2) 75 [hyper,1,4,67] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). given clause #63: (wt=2) 76 [hyper,1,67,36] P(i(i(x,y),i(i(n(y),x),y))). given clause #64: (wt=2) 77 [hyper,1,18,68] P(i(i(x,i(y,z)),i(i(n(y),y),i(x,z)))). given clause #65: (wt=2) 78 [hyper,1,43,72] P(i(x,i(n(i(y,z)),y))). given clause #66: (wt=2) 79 [hyper,1,4,73] P(i(i(i(x,i(y,y)),z),i(i(x,i(u,y)),z))). given clause #67: (wt=2) 80 [hyper,1,4,74] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(y),x),u))). given clause #68: (wt=2) 81 [hyper,1,75,73] P(i(i(x,i(y,z)),i(y,i(z,z)))). given clause #69: (wt=2) 82 [hyper,1,75,71] P(i(i(x,i(y,z)),i(i(y,u),i(z,i(y,u))))). given clause #70: (wt=2) 83 [hyper,1,75,62] P(i(i(x,i(y,z)),i(i(x,u),i(y,i(x,u))))). given clause #71: (wt=2) 84 [hyper,1,75,53] P(i(i(x,i(y,z)),i(i(u,y),i(z,i(u,z))))). given clause #72: (wt=2) 85 [hyper,1,75,52] P(i(i(x,i(y,z)),i(i(n(z),y),i(z,z)))). given clause #73: (wt=2) 86 [hyper,1,75,47] P(i(i(x,i(y,z)),i(i(n(z),z),i(y,z)))). given clause #74: (wt=2) 87 [hyper,1,75,41] P(i(i(x,i(y,z)),i(z,i(y,z)))). given clause #75: (wt=2) 88 [hyper,1,75,37] P(i(i(x,i(y,z)),i(i(n(z),x),i(y,z)))). given clause #76: (wt=2) 89 [hyper,1,75,18] P(i(i(x,i(y,z)),i(i(u,x),i(y,i(u,z))))). given clause #77: (wt=2) 90 [hyper,1,23,76] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). given clause #78: (wt=2) 91 [hyper,1,46,77] P(i(i(x,i(y,z)),i(i(n(x),x),i(z,z)))). given clause #79: (wt=2) 92 [hyper,1,4,78] P(i(i(i(n(i(x,y)),x),z),i(u,z))). given clause #80: (wt=2) 93 [hyper,1,79,62] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(z,u))))). given clause #81: (wt=2) 94 [hyper,1,79,18] P(i(i(x,i(y,z)),i(i(u,z),i(x,i(u,z))))). given clause #82: (wt=2) 95 [hyper,1,80,48] P(i(i(n(x),y),i(x,i(i(x,z),z)))). given clause #83: (wt=2) 96 [hyper,1,80,30] P(i(i(n(x),x),i(y,i(i(x,z),z)))). given clause #84: (wt=2) 97 [hyper,1,4,81] P(i(i(i(x,i(y,y)),z),i(i(u,i(x,y)),z))). given clause #85: (wt=2) 98 [hyper,1,84,15] P(i(i(x,i(y,z)),i(u,i(x,u)))). given clause #86: (wt=2) 99 [hyper,1,86,15] P(i(i(n(x),x),i(i(y,z),x))). given clause #87: (wt=2) 100 [hyper,1,4,87] P(i(i(i(x,i(y,x)),z),i(i(u,i(y,x)),z))). given clause #88: (wt=2) 101 [hyper,1,89,4] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))). given clause #89: (wt=2) 102 [hyper,1,4,90] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(y),z),u))). given clause #90: (wt=2) 103 [hyper,1,90,72] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). -------- PROOF -------- 127 [binary,126.1,8.1] $ANSWER(step_35). ----> UNIT CONFLICT at 0.09 sec ----> 127 [binary,126.1,8.1] $ANSWER(step_35). Length of proof is 32. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 5 [] P(i(i(n(x),x),x)). 6 [] P(i(x,i(n(x),y))). 8 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANSWER(step_35). 15 [hyper,1,4,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 16 [hyper,1,4,5] P(i(i(x,y),i(i(n(x),x),y))). 17 [hyper,1,4,6] P(i(i(i(n(x),y),z),i(x,z))). 18 [hyper,1,15,15] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 19 [hyper,1,15,4] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 21 [hyper,1,15,17] P(i(i(x,n(y)),i(y,i(x,z)))). 22 [hyper,1,17,5] P(i(x,x)). 23 [hyper,1,18,19] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 24 [hyper,1,6,22] P(i(n(i(x,x)),y)). 25 [hyper,1,23,16] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 26 [hyper,1,21,24] P(i(x,i(n(i(y,y)),z))). 27 [hyper,1,4,25] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 28 [hyper,1,4,26] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 29 [hyper,1,28,5] P(i(x,i(y,y))). 30 [hyper,1,4,29] P(i(i(i(x,x),y),i(z,y))). 31 [hyper,1,27,30] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 34 [hyper,1,4,31] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 36 [hyper,1,34,5] P(i(i(n(x),y),i(i(y,x),x))). 37 [hyper,1,18,36] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 39 [hyper,1,37,6] P(i(i(n(x),n(y)),i(y,x))). 43 [hyper,1,17,39] P(i(x,i(y,x))). 48 [hyper,1,4,43] P(i(i(i(x,y),z),i(y,z))). 56 [hyper,1,48,39] P(i(n(x),i(x,y))). 57 [hyper,1,48,36] P(i(x,i(i(x,y),y))). 66 [hyper,1,37,56] P(i(i(n(x),y),i(n(y),x))). 67 [hyper,1,18,57] P(i(i(x,i(y,z)),i(y,i(x,z)))). 72 [hyper,1,66,56] P(i(n(i(x,y)),x)). 75 [hyper,1,4,67] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 76 [hyper,1,67,36] P(i(i(x,y),i(i(n(y),x),y))). 90 [hyper,1,23,76] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 103 [hyper,1,90,72] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 126 [hyper,1,75,103] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 127 [binary,126.1,8.1] $ANSWER(step_35). ------------ end of proof ------------- given clause #91: (wt=2) 104 [hyper,1,90,24] P(i(i(x,i(y,y)),i(i(z,x),i(y,y)))). given clause #92: (wt=2) 105 [hyper,1,75,91] P(i(i(x,i(y,z)),i(i(n(y),y),i(z,z)))). given clause #93: (wt=2) 106 [hyper,1,75,93] P(i(i(x,i(y,z)),i(i(z,u),i(y,i(z,u))))). given clause #94: (wt=2) 107 [hyper,1,75,94] P(i(i(x,i(y,z)),i(i(u,z),i(y,i(u,z))))). given clause #95: (wt=2) 108 [hyper,1,63,95] P(i(i(n(x),y),i(z,i(i(z,u),u)))). given clause #96: (wt=2) 109 [hyper,1,4,95] P(i(i(i(x,i(i(x,y),y)),z),i(i(n(x),u),z))). given clause #97: (wt=2) 110 [hyper,1,4,96] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(y),y),u))). given clause #98: (wt=2) 111 [hyper,1,97,98] P(i(i(x,i(y,z)),i(u,i(y,u)))). given clause #99: (wt=2) 112 [hyper,1,60,98] P(i(i(x,i(y,z)),i(u,i(z,u)))). given clause #100: (wt=2) 113 [hyper,1,27,98] P(i(i(n(x),y),i(z,i(i(x,u),z)))). given clause #101: (wt=2) 114 [hyper,1,4,98] P(i(i(i(x,i(y,x)),z),i(i(y,i(u,v)),z))). given clause #102: (wt=2) 115 [hyper,1,18,99] P(i(i(x,i(y,z)),i(i(n(u),u),i(x,u)))). given clause #103: (wt=2) 116 [hyper,1,100,35] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(z,i(i(v,w),z))))). given clause #104: (wt=2) 117 [hyper,1,100,23] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(u,i(i(v,z),u))))). given clause #105: (wt=2) 118 [hyper,1,100,101] P(i(i(x,i(y,z)),i(i(z,u),i(z,i(y,u))))). given clause #106: (wt=2) 119 [hyper,1,75,101] P(i(i(x,i(y,z)),i(i(z,u),i(y,i(x,u))))). given clause #107: (wt=2) 120 [hyper,1,46,101] P(i(i(x,i(y,z)),i(i(z,u),i(z,i(x,u))))). given clause #108: (wt=2) 121 [hyper,1,102,98] P(i(i(n(x),y),i(z,i(i(u,x),z)))). given clause #109: (wt=2) 122 [hyper,1,102,87] P(i(i(n(x),y),i(x,i(i(y,z),x)))). given clause #110: (wt=2) 123 [hyper,1,102,67] P(i(i(n(x),y),i(i(y,z),i(i(z,x),x)))). given clause #111: (wt=2) 124 [hyper,1,97,103] P(i(i(x,i(y,z)),i(i(z,y),i(z,z)))). given clause #112: (wt=2) 125 [hyper,1,79,103] P(i(i(x,i(y,z)),i(i(z,x),i(z,z)))). given clause #113: (wt=2) 126 [hyper,1,75,103] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). -------- PROOF -------- 151 [hyper,2,43,126,39] $ANSWER(step_allBEH_Church_FL_18_35_49). -----> EMPTY CLAUSE at 0.14 sec ----> 151 [hyper,2,43,126,39] $ANSWER(step_allBEH_Church_FL_18_35_49). Length of proof is 32. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49). 4 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 5 [] P(i(i(n(x),x),x)). 6 [] P(i(x,i(n(x),y))). 15 [hyper,1,4,4] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 16 [hyper,1,4,5] P(i(i(x,y),i(i(n(x),x),y))). 17 [hyper,1,4,6] P(i(i(i(n(x),y),z),i(x,z))). 18 [hyper,1,15,15] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 19 [hyper,1,15,4] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 21 [hyper,1,15,17] P(i(i(x,n(y)),i(y,i(x,z)))). 22 [hyper,1,17,5] P(i(x,x)). 23 [hyper,1,18,19] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 24 [hyper,1,6,22] P(i(n(i(x,x)),y)). 25 [hyper,1,23,16] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 26 [hyper,1,21,24] P(i(x,i(n(i(y,y)),z))). 27 [hyper,1,4,25] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 28 [hyper,1,4,26] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 29 [hyper,1,28,5] P(i(x,i(y,y))). 30 [hyper,1,4,29] P(i(i(i(x,x),y),i(z,y))). 31 [hyper,1,27,30] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 34 [hyper,1,4,31] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 36 [hyper,1,34,5] P(i(i(n(x),y),i(i(y,x),x))). 37 [hyper,1,18,36] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 39 [hyper,1,37,6] P(i(i(n(x),n(y)),i(y,x))). 43 [hyper,1,17,39] P(i(x,i(y,x))). 48 [hyper,1,4,43] P(i(i(i(x,y),z),i(y,z))). 56 [hyper,1,48,39] P(i(n(x),i(x,y))). 57 [hyper,1,48,36] P(i(x,i(i(x,y),y))). 66 [hyper,1,37,56] P(i(i(n(x),y),i(n(y),x))). 67 [hyper,1,18,57] P(i(i(x,i(y,z)),i(y,i(x,z)))). 72 [hyper,1,66,56] P(i(n(i(x,y)),x)). 75 [hyper,1,4,67] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 76 [hyper,1,67,36] P(i(i(x,y),i(i(n(y),x),y))). 90 [hyper,1,23,76] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 103 [hyper,1,90,72] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 126 [hyper,1,75,103] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 151 [hyper,2,43,126,39] $ANSWER(step_allBEH_Church_FL_18_35_49). ------------ end of proof ------------- given clause #114: (wt=2) 128 [hyper,1,100,104] P(i(i(x,i(y,y)),i(i(z,y),i(y,y)))). given clause #115: (wt=2) 129 [hyper,1,97,104] P(i(i(x,i(y,z)),i(i(u,y),i(z,z)))). given clause #116: (wt=2) 130 [hyper,1,79,104] P(i(i(x,i(y,z)),i(i(u,x),i(z,z)))). given clause #117: (wt=2) 131 [hyper,1,60,104] P(i(i(x,i(y,z)),i(i(u,z),i(z,z)))). given clause #118: (wt=2) 132 [hyper,1,4,108] P(i(i(i(x,i(i(x,y),y)),z),i(i(n(u),v),z))). given clause #119: (wt=2) 133 [hyper,1,102,111] P(i(i(n(x),y),i(z,i(i(y,u),z)))). given clause #120: (wt=2) 134 [hyper,1,59,111] P(i(i(n(x),y),i(z,i(i(u,v),z)))). given clause #121: (wt=2) 135 [hyper,1,4,111] P(i(i(i(x,i(y,x)),z),i(i(u,i(y,v)),z))). given clause #122: (wt=2) 136 [hyper,1,4,112] P(i(i(i(x,i(y,x)),z),i(i(u,i(v,y)),z))). given clause #123: (wt=2) 137 [hyper,1,4,113] P(i(i(i(x,i(i(y,z),x)),u),i(i(n(y),v),u))). given clause #124: (wt=2) 138 [hyper,1,114,112] P(i(i(x,i(y,z)),i(u,i(v,u)))). given clause #125: (wt=2) 139 [hyper,1,114,105] P(i(i(x,i(y,z)),i(i(n(x),x),i(u,u)))). given clause #126: (wt=2) 140 [hyper,1,114,104] P(i(i(x,i(y,z)),i(i(u,x),i(x,x)))). given clause #127: (wt=2) 141 [hyper,1,114,101] P(i(i(x,i(y,z)),i(i(u,v),i(u,i(x,v))))). given clause #128: (wt=2) 142 [hyper,1,114,91] P(i(i(x,i(y,z)),i(i(n(u),u),i(u,u)))). given clause #129: (wt=2) 143 [hyper,1,114,85] P(i(i(x,i(y,z)),i(i(n(u),x),i(u,u)))). given clause #130: (wt=2) 144 [hyper,1,114,84] P(i(i(x,i(y,z)),i(i(u,x),i(v,i(u,v))))). given clause #131: (wt=2) 145 [hyper,1,114,81] P(i(i(x,i(y,z)),i(x,i(u,u)))). given clause #132: (wt=2) 146 [hyper,1,114,115] P(i(i(x,i(y,z)),i(i(n(u),u),i(v,u)))). given clause #133: (wt=2) 147 [hyper,1,4,121] P(i(i(i(x,i(i(y,z),x)),u),i(i(n(z),v),u))). given clause #134: (wt=2) 148 [hyper,1,4,122] P(i(i(i(x,i(i(y,z),x)),u),i(i(n(x),y),u))). given clause #135: (wt=2) 149 [hyper,1,4,123] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(z),x),u))). given clause #136: (wt=2) 150 [hyper,1,114,124] P(i(i(x,i(y,z)),i(i(u,x),i(u,u)))). given clause #137: (wt=2) 152 [hyper,1,15,126] P(i(i(x,y),i(i(i(y,z),x),i(i(y,z),z)))). given clause #138: (wt=2) 153 [hyper,1,114,129] P(i(i(x,i(y,z)),i(i(u,x),i(v,v)))). given clause #139: (wt=2) 154 [hyper,1,114,130] P(i(i(x,i(y,z)),i(i(u,v),i(v,v)))). given clause #140: (wt=2) 155 [hyper,1,4,133] P(i(i(i(x,i(i(y,z),x)),u),i(i(n(v),y),u))). given clause #141: (wt=2) 156 [hyper,1,4,134] P(i(i(i(x,i(i(y,z),x)),u),i(i(n(v),w),u))). given clause #142: (wt=2) 157 [hyper,1,135,129] P(i(i(x,i(y,z)),i(i(u,y),i(v,v)))). given clause #143: (wt=2) 158 [hyper,1,135,118] P(i(i(x,i(y,z)),i(i(u,v),i(u,i(y,v))))). given clause #144: (wt=2) 159 [hyper,1,135,117] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(w,i(i(v,z),w))))). given clause #145: (wt=2) 160 [hyper,1,135,116] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(w,i(i(v,v6),w))))). given clause #146: (wt=2) 161 [hyper,1,135,84] P(i(i(x,i(y,z)),i(i(u,y),i(v,i(u,v))))). given clause #147: (wt=2) 162 [hyper,1,135,81] P(i(i(x,i(y,z)),i(y,i(u,u)))). given clause #148: (wt=2) 163 [hyper,1,136,129] P(i(i(x,i(y,z)),i(i(u,z),i(v,v)))). given clause #149: (wt=2) 164 [hyper,1,136,118] P(i(i(x,i(y,z)),i(i(u,v),i(u,i(z,v))))). given clause #150: (wt=2) 165 [hyper,1,136,84] P(i(i(x,i(y,z)),i(i(u,z),i(v,i(u,v))))). given clause #151: (wt=2) 166 [hyper,1,136,81] P(i(i(x,i(y,z)),i(z,i(u,u)))). given clause #152: (wt=2) 167 [hyper,1,4,138] P(i(i(i(x,i(y,x)),z),i(i(u,i(v,w)),z))). given clause #153: (wt=2) 168 [hyper,1,136,139] P(i(i(x,i(y,z)),i(i(n(u),u),i(v,v)))). given clause #154: (wt=2) 169 [hyper,1,136,141] P(i(i(x,i(y,z)),i(i(u,v),i(u,i(w,v))))). given clause #155: (wt=2) 170 [hyper,1,136,143] P(i(i(x,i(y,z)),i(i(n(u),v),i(u,u)))). given clause #156: (wt=2) 171 [hyper,1,136,144] P(i(i(x,i(y,z)),i(i(u,v),i(w,i(u,w))))). given clause #157: (wt=2) 172 [hyper,1,136,145] P(i(i(x,i(y,z)),i(u,i(v,v)))). given clause #158: (wt=2) 173 [hyper,1,4,145] P(i(i(i(x,i(y,y)),z),i(i(x,i(u,v)),z))). given clause #159: (wt=2) 174 [hyper,1,18,152] P(i(i(x,i(i(y,z),u)),i(i(u,y),i(x,i(i(y,z),z))))). given clause #160: (wt=2) 175 [hyper,1,4,162] P(i(i(i(x,i(y,y)),z),i(i(u,i(x,v)),z))). given clause #161: (wt=2) 176 [hyper,1,4,166] P(i(i(i(x,i(y,y)),z),i(i(u,i(v,x)),z))). given clause #162: (wt=2) 177 [hyper,1,4,172] P(i(i(i(x,i(y,y)),z),i(i(u,i(v,w)),z))). given clause #163: (wt=2) 178 [hyper,1,135,174] P(i(i(x,i(i(y,z),u)),i(i(v,y),i(v,i(i(y,z),z))))). given clause #164: (wt=2) 179 [hyper,1,174,30] P(i(i(x,y),i(i(i(z,z),x),i(i(y,u),u)))). given clause #165: (wt=2) 180 [hyper,1,18,179] P(i(i(x,i(i(y,y),z)),i(i(z,u),i(x,i(i(u,v),v))))). given clause #166: (wt=2) 181 [hyper,1,135,180] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(u,i(i(v,w),w))))). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ -------------- statistics ------------- clauses given 166 clauses generated 22083 hyper_res generated 22083 demod & eval rewrites 0 clauses wt,lit,sk delete 18426 tautologies deleted 0 clauses forward subsumed 3493 (subsumed by sos) 415 unit deletions 0 factor simplifications 0 clauses kept 163 new demodulators 0 empty clauses 4 clauses back demodulated 0 clauses back subsumed 0 usable size 169 sos size 0 demodulators size 5 passive size 3 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.32 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8502 finished Mon Aug 2 15:30:39 2004 otter-3.3f/examples/wos/twoval.in0100644000076400007640000002213506005317040016471 0ustar mccunemccune% Input File for Studying Two-Valued Sentential Calculus with OTTER 3.0 set(hyper_res). assign(max_weight,20). assign(max_proofs, -1). clear(print_kept). % clear(for_sub). clear(back_sub). % assign(max_seconds, 1200). assign(max_mem, 24000). % assign(report, 900). % assign(max_distinct_vars, 4). % assign(pick_given_ratio, 3). assign(max_given, 618). set(order_history). set(input_sos_first). % set(sos_queue). weight_list(pick_and_purge). % Following are templates corresponding to the 68 theses to be proved. weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2). weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2). weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2). weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2). weight(P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))),2). weight(P(i(i(i(n(x),y),z),i(x,z))),2). weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2). weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2). weight(P(i(x,i(i(n(y),y),y))),2). weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2). weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2). weight(P(i(i(n(x),y),i(i(y,x),x))),2). weight(P(i(x,x)),2). weight(P(i(x,i(i(y,x),x))),2). weight(P(i(x,i(y,x))),2). weight(P(i(i(i(x,y),z),i(y,z))),2). weight(P(i(x,i(i(x,y),y))),2). weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2). weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2). weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2). weight(P(i(i(i(x,y),x),x)),2). weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))),2). weight(P(i(i(i(x,y),z),i(i(z,x),x))),2). weight(P(i(i(i(x,y),y),i(i(y,x),x))),2). weight(P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))),2). weight(P(i(i(i(x,y),z),i(i(x,z),z))),2). weight(P(i(i(x,i(x,y)),i(x,y))),2). weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))),2). weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2). weight(P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))),2). weight(P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))),2). weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2). weight(P(i(n(x),i(x,y))),2). weight(P(i(i(i(x,y),z),i(n(x),z))),2). weight(P(i(i(x,n(x)),n(x))),2). weight(P(i(n(n(x)),x)),2). weight(P(i(x,n(n(x)))),2). weight(P(i(i(x,y),i(n(n(x)),y))),2). weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2). weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2). weight(P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))),2). weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2). weight(P(i(i(x,y),i(n(y),n(x)))),2). weight(P(i(i(x,n(y)),i(y,n(x)))),2). weight(P(i(i(n(x),y),i(n(y),x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(P(i(i(i(n(x),y),z),i(i(n(y),x),z))),2). weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2). weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2). weight(P(i(i(n(x),y),i(i(x,y),y))),2). weight(P(i(i(x,y),i(i(n(x),y),y))),2). weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2). weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2). weight(P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))),2). weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2). weight(P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))),2). weight(P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))),2). weight(P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))),2). weight(P(i(i(n(n(x)),y),i(x,y))),2). weight(P(i(x,i(y,y))),2). weight(P(i(n(i(x,x)),y)),2). weight(P(i(i(n(x),n(i(y,y))),x)),2). weight(P(i(n(i(x,y)),x)),2). weight(P(i(n(i(x,y)),n(y))),2). weight(P(i(n(i(x,n(y))),y)),2). weight(P(i(x,i(n(y),n(i(x,y))))),2). weight(P(i(x,i(y,n(i(x,n(y)))))),2). weight(P(n(i(i(x,x),n(i(y,y))))),2). end_of_list. list(usable). % The following clause is used with hyperresolution for condensed detachment. -P(i(x,y)) | -P(x) | P(y). % The following disjunctions, except those mentioning Scott, % are the negation of known axiom systems. -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21). % 21 is dependent. -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | -P(i(i(q,r),i(i(p,q),i(p,r)))) | -P(i(p,i(n(p),q))) | -P(i(i(p,q),i(i(n(p),q),q))) | -P(i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_allHilbert_18_21_22_3_54_30). % 30 is dependent. -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49). -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59). -P(i(i(i(p,q),r),i(q,r))) | -P(i(i(i(p,q),r),i(n(p),r))) | -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60). -P(i(i(p,q),i(i(q,r),i(p,r)))) | -P(i(i(n(p),p),p)) | -P(i(p,i(n(p),q))) | $ANSWER(step_allLuka_1_2_3). -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | -P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(p,q),i(n(q),n(p)))) | $ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). -P(i(p,p)) | -P(i(p,i(q,p))) | -P(i(i(p,i(q,r)),i(q,i(p,r)))) | -P(i(i(i(p,q),p),p)) | -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(i(n(n(p)),p)) | -P(i(p,n(n(p)))) | -P(i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). end_of_list. list(sos). % The following three are Luka, 1 2 3. P(i(i(x,y),i(i(y,z),i(x,z)))). P(i(i(n(x),x),x)). P(i(x,i(n(x),y))). % The following are from Frege, 18 35 21 46 39 40, with 21 dependent. % P(i(x,i(y,x))). % axiom F1. % P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). % axiom F2. % P(i(i(x,i(y,z)),i(y,i(x,z)))). % axiom F3. % P(i(i(x,y),i(n(y),n(x)))). % axiom F4. % P(i(n(n(x)),x)). % axiom F5. % P(i(x,n(n(x)))). % axiom f6. end_of_list. list(passive). -P(i(i(i(i(q,r),i(p,r)),s),i(i(p,q),s))) | $ANS(neg_th_04). -P(i(i(p,i(q,r)),i(i(s,q),i(p,i(s,r))))) | $ANS(neg_th_05). -P(i(i(p,q),i(i(i(p,r),s),i(i(q,r),s)))) | $ANS(neg_th_06). -P(i(i(t,i(i(p,r),s)),i(i(p,q),i(t,i(i(q,r),s))))) | $ANS(neg_th_07). -P(i(i(q,r),i(i(p,q),i(i(r,s),i(p,s))))) | $ANS(neg_th_08). -P(i(i(i(n(p),q),r),i(p,r))) | $ANS(neg_th_09). -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p)))) | $ANS(neg_th_10). -P(i(i(q,i(i(n(p),p),p)),i(i(n(p),p),p))) | $ANS(neg_th_11). -P(i(t,i(i(n(p),p),p))) | $ANS(neg_th_12). -P(i(i(n(p),q),i(t,i(i(q,p),p)))) | $ANS(neg_th_13). -P(i(i(i(t,i(i(q,p),p)),r),i(i(n(p),q),r))) | $ANS(neg_th_14). -P(i(i(n(p),q),i(i(q,p),p))) | $ANS(neg_th_15). -P(i(p,p)) | $ANS(neg_th_16). -P(i(p,i(i(q,p),p))) | $ANS(neg_th_17). -P(i(q,i(p,q))) | $ANS(neg_th_18). -P(i(i(i(p,q),r),i(q,r))) | $ANS(neg_th_19). -P(i(p,i(i(p,q),q))) | $ANS(neg_th_20). -P(i(i(p,i(q,r)),i(q,i(p,r)))) | $ANS(neg_th_21). -P(i(i(q,r),i(i(p,q),i(p,r)))) | $ANS(neg_th_22). -P(i(i(i(q,i(p,r)),s),i(i(p,i(q,r)),s))) | $ANS(neg_th_23). -P(i(i(i(p,q),p),p)) | $ANS(neg_th_24). -P(i(i(i(p,r),s),i(i(p,q),i(i(q,r),s)))) | $ANS(neg_th_25). -P(i(i(i(p,q),r),i(i(r,p),p))) | $ANS(neg_th_26). -P(i(i(i(p,q),q),i(i(q,p),p))) | $ANS(neg_th_27). -P(i(i(i(i(r,p),p),s),i(i(i(p,q),r),s))) | $ANS(neg_th_28). -P(i(i(i(p,q),r),i(i(p,r),r))) | $ANS(neg_th_29). -P(i(i(p,i(p,q)),i(p,q))) | $ANS(neg_th_30). -P(i(i(p,s),i(i(i(p,q),r),i(i(s,r),r)))) | $ANS(neg_th_31). -P(i(i(i(p,q),r),i(i(p,s),i(i(s,r),r)))) | $ANS(neg_th_32). -P(i(i(p,s),i(i(s,i(q,i(p,r))),i(q,i(p,r))))) | $ANS(neg_th_33). -P(i(i(s,i(q,i(p,r))),i(i(p,s),i(q,i(p,r))))) | $ANS(neg_th_34). -P(i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANS(neg_th_35). -P(i(n(p),i(p,q))) | $ANS(neg_th_36). -P(i(i(i(p,q),r),i(n(p),r))) | $ANS(neg_th_37). -P(i(i(p,n(p)),n(p))) | $ANS(neg_th_38). -P(i(n(n(p)),p)) | $ANS(neg_th_39). -P(i(p,n(n(p)))) | $ANS(neg_th_40). -P(i(i(p,q),i(n(n(p)),q))) | $ANS(neg_th_41). -P(i(i(i(n(n(p)),q),r),i(i(p,q),r))) | $ANS(neg_th_42). -P(i(i(p,q),i(i(q,n(p)),n(p)))) | $ANS(neg_th_43). -P(i(i(s,i(q,n(p))),i(i(p,q),i(s,n(p))))) | $ANS(neg_th_44). -P(i(i(s,i(q,p)),i(i(n(p),q),i(s,p)))) | $ANS(neg_th_45). -P(i(i(p,q),i(n(q),n(p)))) | $ANS(neg_th_46). -P(i(i(p,n(q)),i(q,n(p)))) | $ANS(neg_th_47). -P(i(i(n(p),q),i(n(q),p))) | $ANS(neg_th_48). -P(i(i(n(p),n(q)),i(q,p))) | $ANS(neg_th_49). -P(i(i(i(n(q),p),r),i(i(n(p),q),r))) | $ANS(neg_th_50). -P(i(i(p,i(q,r)),i(p,i(n(r),n(q))))) | $ANS(neg_th_51). -P(i(i(p,i(q,n(r))),i(p,i(r,n(q))))) | $ANS(neg_th_52). -P(i(i(n(p),q),i(i(p,q),q))) | $ANS(neg_th_53). -P(i(i(p,q),i(i(n(p),q),q))) | $ANS(neg_th_54). -P(i(i(p,q),i(i(p,n(q)),n(p)))) | $ANS(neg_th_55). -P(i(i(i(i(p,q),q),r),i(i(n(p),q),r))) | $ANS(neg_th_56). -P(i(i(n(p),r),i(i(p,q),i(i(q,r),r)))) | $ANS(neg_th_57). -P(i(i(i(i(p,q),i(i(q,r),r)),s),i(i(n(p),r),s))) | $ANS(neg_th_58). -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANS(neg_th_59). -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANS(neg_th_60). -P(i(i(p,r),i(i(q,r),i(i(n(p),q),r)))) | $ANS(neg_th_61). -P(i(i(n(n(p)),q),i(p,q))) | $ANS(neg_th_62). -P(i(q,i(p,p))) | $ANS(neg_th_63). -P(i(n(i(p,p)),q)) | $ANS(neg_th_64). -P(i(i(n(q),n(i(p,p))),q)) | $ANS(neg_th_65). -P(i(n(i(p,q)),p)) | $ANS(neg_th_66). -P(i(n(i(p,q)),n(q))) | $ANS(neg_th_67). -P(i(n(i(p,n(q))),q)) | $ANS(neg_th_68). -P(i(p,i(n(q),n(i(p,q))))) | $ANS(neg_th_69). -P(i(p,i(q,n(i(p,n(q)))))) | $ANS(neg_th_70). -P(n(i(i(p,p),n(i(q,q))))) | $ANS(neg_th_71). end_of_list. % list(demodulators). % (n(n(x)) = junk). % (n(n(n(x))) = junk). % (i(i(x,x),y) = junk). % (i(y,i(x,x)) = junk). % (i(n(i(x,x)),y) = junk). % (i(y,n(i(x,x))) = junk). % (i(junk,x) = junk). % (i(x,junk) = junk). % (n(junk) = junk). % (P(junk) = $T). % end_of_list. otter-3.3f/examples/wos/README.more0100644000076400007640000000437007313710612016454 0ustar mccunemccuneThis subdirectory serves two purposes. First, its members sup- plement the test problems supplied by Bill McCune. Second, its members provide a beginning for studying various fields of mathematics and logic. Currently, as of 01-21-94, all members are input files and summaries of the corresponding output files. For additional input files, output files, statistics, research topics, and more, see the book to be published by Larry Wos, "Automating the Search for Elegant Proofs: An Experimenter's Notebook". The following briefly describes the possible use for the respec- tive input files. The files feature the use of the resonance strategy, but other strategies are used. They contain options commented out with % that can be used by removing the %. grp_exp3.in --- can be used to study a given single axiom for groups of exponent 3, those groups in which the third power of all elements x is the identity e. grp_exp4.in --- can be used to study a given single axiom for groups of exponent 4, those in which the fourth power of every element x is the identity e. robbins.in --- can be used to study Robbins algebra in the context of proving such an algebra is Boolean when one adjoins to its ax- ioms the equation c+c = c. twoval.in --- can be used to study two-valued or propositional cal- culus. mayval.in --- can be used to study may-valued calculus. The file includes a very difficult theorem to prove, MV5. If one wishes to attempt its proof, one must change the assigned limit on max_proofs from 4 to 5. cursory.in --- can be used to proof check a given proof, but in a cursory manner rather than in a rigorous manner. In cursory proof checking, OTTER is not forced to produce a proof that is consistent with the precise history of the given proof being checked. In rigorous proof checking, by supplying the pre- cise history of the proof being checked (with appropriate demodu- lators), OTTER is forced to attempt to duplicate the given proof. rigorous.in --- can be used to rigorously check a given proof. See the comments accompanying cursory.proof.checking.in for pertinent detail. Welcome are questions on these files, e-mailed to wos@mcs.anl.gov or phone 312-493-0767 (home), or 708-252-7224 (office). Even more welcome are open questions and unsolved problems. otter-3.3f/examples/wos/rigorous.out0100664000076400007640000011416710103522200017226 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:56 2004 The command was "../../bin/otter". The process ID is 8522. set(hyper_res). assign(max_mem,8000). assign(max_weight,80). assign(max_proofs,-1). set(input_sos_first). set(order_history). weight_list(pick_and_purge). weight(P(rew($(0),$(0)),$(1)),99). end_of_list. list(usable). 1 [] -P(u,i(x,y))| -P(v,x)|P(rew(u,v),y). 2 [] -P(x,i(q,i(p,q)))| -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(z,i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49). 3 [] -P(x,i(q,i(p,q)))| -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(z,i(n(n(p)),p))| -P(u,i(p,n(n(p))))| -P(v,i(i(p,q),i(n(q),n(p))))| -P(w,i(i(p,i(q,r)),i(q,i(p,r))))|$ANSWER(step_allFrege_18_35_39_40_46_21). 4 [] -P(x,i(q,i(p,q)))| -P(y,i(i(p,i(q,r)),i(q,i(p,r))))| -P(z,i(i(q,r),i(i(p,q),i(p,r))))| -P(u,i(p,i(n(p),q)))| -P(v,i(i(p,q),i(i(n(p),q),q)))| -P(w,i(i(p,i(p,q)),i(p,q)))|$ANSWER(step_allHilbert_18_21_22_3_54_30). 5 [] -P(x,i(i(i(p,q),r),i(q,r)))| -P(y,i(i(i(p,q),r),i(n(p),r)))| -P(z,i(i(n(p),r),i(i(q,r),i(i(p,q),r))))|$ANSWER(step_allLuka_x_19_37_59). 6 [] -P(x,i(i(i(p,q),r),i(q,r)))| -P(y,i(i(i(p,q),r),i(n(p),r)))| -P(z,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r)))))|$ANSWER(step_allWos_x_19_37_60). end_of_list. list(sos). 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). 8 [] P(c2,i(i(n(x),x),x)). 9 [] P(c3,i(x,i(n(x),y))). end_of_list. list(passive). end_of_list. list(demodulators). 10 [] EQ(rew(c1,c1),c4). 11 [] EQ(rew(c4,c4),c5). 12 [] EQ(rew(c4,c1),c6). 13 [] EQ(rew(c5,c6),c7). 14 [] EQ(rew(c7,c1),c8). 15 [] EQ(rew(c1,c3),c9). 16 [] EQ(rew(c9,c6),c10). 17 [] EQ(rew(c10,c2),c10a). 18 [] EQ(rew(c10a,c2),c11). 19 [] EQ(rew(c9,c11),c12). 20 [] EQ(rew(c7,c12),c13). 21 [] EQ(rew(c1,c13),c14). 22 [] EQ(rew(c14,c2),c15). 23 [] EQ(rew(c9,c2),c16). 24 [] EQ(rew(c9,c15),c17). 25 [] EQ(rew(c5,c17),c17a). 26 [] EQ(rew(c17a,c3),c18). 27 [] EQ(rew(c1,c18),c19). 28 [] EQ(rew(c19,c15),c20). 29 [] EQ(rew(c5,c20),c21). 30 [] EQ(rew(c21,c1),c22). 31 [] EQ(rew(c1,c21),c23). 32 [] EQ(rew(c23,c15),c24a). 33 [] EQ(rew(c24a,c3),c24). 34 [] EQ(rew(c21,c6),c25). 35 [] EQ(rew(c25,c24),c26). 36 [] EQ(rew(c1,c26),c28). 37 [] EQ(rew(c28,c26),c29). 38 [] EQ(rew(c29,c16),c30). 39 [] EQ(rew(c7,c29),c31). 40 [] EQ(rew(c21,c31),c32). 41 [] EQ(rew(c32,c18),c33). 42 [] EQ(rew(c21,c33),c34). 43 [] EQ(rew(c34,c22),c35). 44 [] EQ(rew(c21,c3),c36). 45 [] EQ(rew(c1,c36),c37). 46 [] EQ(rew(c26,c2),c38). 47 [] EQ(rew(c37,c2),c39). 48 [] EQ(rew(c9,c38),c40). 49 [] EQ(rew(c1,c39),c41). 50 [] EQ(rew(c1,c41),c42). 51 [] EQ(rew(c42,c15),c43). 52 [] EQ(rew(c5,c43),c44). 53 [] EQ(rew(c5,c15),c45). 54 [] EQ(rew(c44,c36),c46). 55 [] EQ(rew(c44,c3),c47). 56 [] EQ(rew(c45,c36),c48). 57 [] EQ(rew(c45,c3),c49). 58 [] EQ(rew(c1,c48),c50). 59 [] EQ(rew(c22,c46),c51). 60 [] EQ(rew(c22,c47),c52). 61 [] EQ(rew(c50,c15),c53). 62 [] EQ(rew(c21,c53),c54). 63 [] EQ(rew(c44,c47),c55). 64 [] EQ(rew(c1,c53),c56). 65 [] EQ(rew(c56,c32),c57). 66 [] EQ(rew(c1,c57),c58). 67 [] EQ(rew(c58,c21),c59). 68 [] EQ(rew(c22,c59),c60). 69 [] EQ(rew(c60,c41),c61). 70 [] EQ(rew(c1,c40),c62). 71 [] EQ(rew(c21,c18),c63). 72 [] EQ(rew(c48,c63),c64). 73 [] EQ(rew(c61,c16),c64a). 74 [] EQ(rew(c64a,c64),c65). 75 [] EQ(rew(c48,c36),c66). 76 [] EQ(rew(c46,c18),c67). 77 [] EQ(rew(c48,c18),c68). 78 [] EQ(rew(c51,c20),c69). 79 [] EQ(rew(c52,c20),c70). 80 [] EQ(rew(c70,c16),c70a). 81 [] EQ(rew(c70a,c16),c71). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=-2147483647) 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). ** KEPT (pick-wt=17): 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #2: (wt=-2147483647) 8 [] P(c2,i(i(n(x),x),x)). given clause #3: (wt=-2147483647) 9 [] P(c3,i(x,i(n(x),y))). ** KEPT (pick-wt=12): 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). given clause #4: (wt=12) 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). ** KEPT (pick-wt=5): 84 [hyper,1,83,8,demod,23] P(c16,i(x,x)). given clause #5: (wt=5) 84 [hyper,1,83,8,demod,23] P(c16,i(x,x)). given clause #6: (wt=17) 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). ** KEPT (pick-wt=17): 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). ** KEPT (pick-wt=17): 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). given clause #7: (wt=17) 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). given clause #8: (wt=17) 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). ** KEPT (pick-wt=21): 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). ** KEPT (pick-wt=16): 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). given clause #9: (wt=16) 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). ** KEPT (pick-wt=19): 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). given clause #10: (wt=19) 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). ** KEPT (pick-wt=17): 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). given clause #11: (wt=17) 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). ** KEPT (pick-wt=10): 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). given clause #12: (wt=10) 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). given clause #13: (wt=21) 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). ** KEPT (pick-wt=14): 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). ** KEPT (pick-wt=17): 93 [hyper,1,87,7,demod,14] P(c8,i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))). given clause #14: (wt=14) 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). ** KEPT (pick-wt=18): 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). given clause #15: (wt=17) 93 [hyper,1,87,7,demod,14] P(c8,i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))). given clause #16: (wt=18) 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). ** KEPT (pick-wt=12): 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). given clause #17: (wt=12) 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). ** KEPT (pick-wt=16): 96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). ** KEPT (pick-wt=9): 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). given clause #18: (wt=9) 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). ** KEPT (pick-wt=13): 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). given clause #19: (wt=13) 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). ** KEPT (pick-wt=7): 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). given clause #20: (wt=7) 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). ** KEPT (pick-wt=11): 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). given clause #21: (wt=11) 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). ** KEPT (pick-wt=9): 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). given clause #22: (wt=9) 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). ** KEPT (pick-wt=13): 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). given clause #23: (wt=13) 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). ** KEPT (pick-wt=17): 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). ** KEPT (pick-wt=7): 104 [hyper,1,102,99,demod,71] P(c63,i(x,i(y,y))). ** KEPT (pick-wt=17): 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). ** KEPT (pick-wt=8): 106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))). ** KEPT (pick-wt=13): 107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))). given clause #24: (wt=7) 104 [hyper,1,102,99,demod,71] P(c63,i(x,i(y,y))). given clause #25: (wt=8) 106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))). ** KEPT (pick-wt=12): 108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))). given clause #26: (wt=12) 108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))). ** KEPT (pick-wt=7): 109 [hyper,1,108,8,demod,47] P(c39,i(n(n(x)),x)). given clause #27: (wt=7) 109 [hyper,1,108,8,demod,47] P(c39,i(n(n(x)),x)). ** KEPT (pick-wt=11): 110 [hyper,1,7,109,demod,49] P(c41,i(i(x,y),i(n(n(x)),y))). given clause #28: (wt=11) 110 [hyper,1,7,109,demod,49] P(c41,i(i(x,y),i(n(n(x)),y))). ** KEPT (pick-wt=15): 111 [hyper,1,7,110,demod,50] P(c42,i(i(i(n(n(x)),y),z),i(i(x,y),z))). given clause #29: (wt=13) 107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))). given clause #30: (wt=15) 111 [hyper,1,7,110,demod,50] P(c42,i(i(i(n(n(x)),y),z),i(i(x,y),z))). ** KEPT (pick-wt=13): 112 [hyper,1,111,95,demod,51] P(c43,i(i(x,y),i(i(y,n(x)),n(x)))). given clause #31: (wt=13) 112 [hyper,1,111,95,demod,51] P(c43,i(i(x,y),i(i(y,n(x)),n(x)))). ** KEPT (pick-wt=17): 113 [hyper,1,85,112,demod,52] P(c44,i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))). given clause #32: (wt=16) 96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). ** KEPT (pick-wt=11): 114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))). ** KEPT (pick-wt=11): 115 [hyper,1,96,9,demod,57] P(c49,i(i(n(x),n(y)),i(y,x))). given clause #33: (wt=11) 114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))). ** KEPT (pick-wt=15): 116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))). ** KEPT (pick-wt=8): 117 [hyper,1,114,106,demod,75] P(c66,i(n(i(x,y)),x)). ** KEPT (pick-wt=8): 118 [hyper,1,114,104,demod,72] P(c64,i(n(i(x,x)),y)). ** KEPT (pick-wt=9): 119 [hyper,1,114,99,demod,77] P(c68,i(n(i(x,n(y))),y)). given clause #34: (wt=8) 117 [hyper,1,114,106,demod,75] P(c66,i(n(i(x,y)),x)). given clause #35: (wt=8) 118 [hyper,1,114,104,demod,72] P(c64,i(n(i(x,x)),y)). given clause #36: (wt=9) 119 [hyper,1,114,99,demod,77] P(c68,i(n(i(x,n(y))),y)). given clause #37: (wt=11) 115 [hyper,1,96,9,demod,57] P(c49,i(i(n(x),n(y)),i(y,x))). given clause #38: (wt=15) 116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))). ** KEPT (pick-wt=12): 120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))). given clause #39: (wt=12) 120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))). ** KEPT (pick-wt=12): 121 [hyper,1,102,120,demod,62] P(c54,i(i(x,y),i(i(n(x),y),y))). ** KEPT (pick-wt=16): 122 [hyper,1,7,120,demod,64] P(c56,i(i(i(i(x,y),y),z),i(i(n(x),y),z))). given clause #40: (wt=12) 121 [hyper,1,102,120,demod,62] P(c54,i(i(x,y),i(i(n(x),y),y))). given clause #41: (wt=16) 122 [hyper,1,7,120,demod,64] P(c56,i(i(i(i(x,y),y),z),i(i(n(x),y),z))). given clause #42: (wt=17) 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). ** KEPT (pick-wt=16): 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). given clause #43: (wt=16) 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). ** KEPT (pick-wt=9): 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). given clause #44: (wt=9) 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). given clause #45: (wt=17) 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). ** KEPT (pick-wt=13): 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). given clause #46: (wt=13) 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). ** KEPT (pick-wt=17): 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). ** KEPT (pick-wt=9): 127 [hyper,1,125,8,demod,46] P(c38,i(i(x,n(x)),n(x))). given clause #47: (wt=9) 127 [hyper,1,125,8,demod,46] P(c38,i(i(x,n(x)),n(x))). ** KEPT (pick-wt=7): 128 [hyper,1,83,127,demod,48] P(c40,i(x,n(n(x)))). given clause #48: (wt=7) 128 [hyper,1,83,127,demod,48] P(c40,i(x,n(n(x)))). ** KEPT (pick-wt=11): 129 [hyper,1,7,128,demod,70] P(c62,i(i(n(n(x)),y),i(x,y))). given clause #49: (wt=11) 129 [hyper,1,7,128,demod,70] P(c62,i(i(n(n(x)),y),i(x,y))). given clause #50: (wt=17) 113 [hyper,1,85,112,demod,52] P(c44,i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))). ** KEPT (pick-wt=11): 130 [hyper,1,113,106,demod,54] P(c46,i(i(x,y),i(n(y),n(x)))). ** KEPT (pick-wt=11): 131 [hyper,1,113,9,demod,55] P(c47,i(i(x,n(y)),i(y,n(x)))). given clause #51: (wt=11) 130 [hyper,1,113,106,demod,54] P(c46,i(i(x,y),i(n(y),n(x)))). ** KEPT (pick-wt=15): 132 [hyper,1,107,130,demod,59] P(c51,i(i(x,i(y,z)),i(x,i(n(z),n(y))))). ** KEPT (pick-wt=9): 133 [hyper,1,130,99,demod,76] P(c67,i(n(i(x,y)),n(y))). given clause #52: (wt=9) 133 [hyper,1,130,99,demod,76] P(c67,i(n(i(x,y)),n(y))). given clause #53: (wt=11) 131 [hyper,1,113,9,demod,55] P(c47,i(i(x,n(y)),i(y,n(x)))). ** KEPT (pick-wt=13): 134 [hyper,1,113,131,demod,63] P(c55,i(i(x,y),i(i(x,n(y)),n(x)))). ** KEPT (pick-wt=15): 135 [hyper,1,107,131,demod,60] P(c52,i(i(x,i(y,n(z))),i(x,i(z,n(y))))). given clause #54: (wt=13) 134 [hyper,1,113,131,demod,63] P(c55,i(i(x,y),i(i(x,n(y)),n(x)))). given clause #55: (wt=15) 132 [hyper,1,107,130,demod,59] P(c51,i(i(x,i(y,z)),i(x,i(n(z),n(y))))). ** KEPT (pick-wt=11): 136 [hyper,1,132,101,demod,78] P(c69,i(x,i(n(y),n(i(x,y))))). given clause #56: (wt=11) 136 [hyper,1,132,101,demod,78] P(c69,i(x,i(n(y),n(i(x,y))))). given clause #57: (wt=15) 135 [hyper,1,107,131,demod,60] P(c52,i(i(x,i(y,n(z))),i(x,i(z,n(y))))). ** KEPT (pick-wt=11): 137 [hyper,1,135,101,demod,79] P(c70,i(x,i(y,n(i(x,n(y)))))). given clause #58: (wt=11) 137 [hyper,1,135,101,demod,79] P(c70,i(x,i(y,n(i(x,n(y)))))). ** KEPT (pick-wt=11): 138 [hyper,1,137,84,demod,80] P(c70a,i(x,n(i(i(y,y),n(x))))). given clause #59: (wt=11) 138 [hyper,1,137,84,demod,80] P(c70a,i(x,n(i(i(y,y),n(x))))). ** KEPT (pick-wt=11): 139 [hyper,1,138,84,demod,81] P(c71,n(i(i(x,x),n(i(y,y))))). given clause #60: (wt=11) 139 [hyper,1,138,84,demod,81] P(c71,n(i(i(x,x),n(i(y,y))))). given clause #61: (wt=17) 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). ** KEPT (pick-wt=13): 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). given clause #62: (wt=13) 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). ** KEPT (pick-wt=17): 141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). ** KEPT (pick-wt=11): 142 [hyper,1,140,84,demod,38] P(c30,i(i(x,i(x,y)),i(x,y))). given clause #63: (wt=11) 142 [hyper,1,140,84,demod,38] P(c30,i(i(x,i(x,y)),i(x,y))). -------- PROOF -------- 143 [hyper,4,99,102,107,9,121,142] $ANSWER(step_allHilbert_18_21_22_3_54_30). ** KEPT (pick-wt=0): 143 [hyper,4,99,102,107,9,121,142] $ANSWER(step_allHilbert_18_21_22_3_54_30). -----> EMPTY CLAUSE at 0.04 sec ----> 143 [hyper,4,99,102,107,9,121,142] $ANSWER(step_allHilbert_18_21_22_3_54_30). Length of proof is 34. Level of proof is 22. ---------------- PROOF ---------------- 1 [] -P(u,i(x,y))| -P(v,x)|P(rew(u,v),y). 4 [] -P(x,i(q,i(p,q)))| -P(y,i(i(p,i(q,r)),i(q,i(p,r))))| -P(z,i(i(q,r),i(i(p,q),i(p,r))))| -P(u,i(p,i(n(p),q)))| -P(v,i(i(p,q),i(i(n(p),q),q)))| -P(w,i(i(p,i(p,q)),i(p,q)))|$ANSWER(step_allHilbert_18_21_22_3_54_30). 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). 8 [] P(c2,i(i(n(x),x),x)). 9 [] P(c3,i(x,i(n(x),y))). 10 [] EQ(rew(c1,c1),c4). 11 [] EQ(rew(c4,c4),c5). 12 [] EQ(rew(c4,c1),c6). 13 [] EQ(rew(c5,c6),c7). 15 [] EQ(rew(c1,c3),c9). 16 [] EQ(rew(c9,c6),c10). 17 [] EQ(rew(c10,c2),c10a). 18 [] EQ(rew(c10a,c2),c11). 19 [] EQ(rew(c9,c11),c12). 20 [] EQ(rew(c7,c12),c13). 21 [] EQ(rew(c1,c13),c14). 22 [] EQ(rew(c14,c2),c15). 23 [] EQ(rew(c9,c2),c16). 24 [] EQ(rew(c9,c15),c17). 25 [] EQ(rew(c5,c17),c17a). 26 [] EQ(rew(c17a,c3),c18). 27 [] EQ(rew(c1,c18),c19). 28 [] EQ(rew(c19,c15),c20). 29 [] EQ(rew(c5,c20),c21). 30 [] EQ(rew(c21,c1),c22). 31 [] EQ(rew(c1,c21),c23). 32 [] EQ(rew(c23,c15),c24a). 33 [] EQ(rew(c24a,c3),c24). 34 [] EQ(rew(c21,c6),c25). 35 [] EQ(rew(c25,c24),c26). 36 [] EQ(rew(c1,c26),c28). 37 [] EQ(rew(c28,c26),c29). 38 [] EQ(rew(c29,c16),c30). 44 [] EQ(rew(c21,c3),c36). 53 [] EQ(rew(c5,c15),c45). 56 [] EQ(rew(c45,c36),c48). 58 [] EQ(rew(c1,c48),c50). 61 [] EQ(rew(c50,c15),c53). 62 [] EQ(rew(c21,c53),c54). 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). 84 [hyper,1,83,8,demod,23] P(c16,i(x,x)). 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). 96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))). 107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))). 114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))). 116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))). 120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))). 121 [hyper,1,102,120,demod,62] P(c54,i(i(x,y),i(i(n(x),y),y))). 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). 142 [hyper,1,140,84,demod,38] P(c30,i(i(x,i(x,y)),i(x,y))). 143 [hyper,4,99,102,107,9,121,142] $ANSWER(step_allHilbert_18_21_22_3_54_30). ------------ end of proof ------------- given clause #64: (wt=17) 141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). ** KEPT (pick-wt=17): 144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). given clause #65: (wt=17) 144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). ** KEPT (pick-wt=16): 145 [hyper,1,122,144,demod,65] P(c57,i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). ** KEPT (pick-wt=19): 146 [hyper,1,144,99,demod,41] P(c33,i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))). given clause #66: (wt=16) 145 [hyper,1,122,144,demod,65] P(c57,i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). ** KEPT (pick-wt=20): 147 [hyper,1,7,145,demod,66] P(c58,i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))). given clause #67: (wt=19) 146 [hyper,1,144,99,demod,41] P(c33,i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))). ** KEPT (pick-wt=19): 148 [hyper,1,102,146,demod,42] P(c34,i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))). given clause #68: (wt=19) 148 [hyper,1,102,146,demod,42] P(c34,i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))). ** KEPT (pick-wt=15): 149 [hyper,1,148,107,demod,43] P(c35,i(i(x,i(y,z)),i(i(x,y),i(x,z)))). given clause #69: (wt=15) 149 [hyper,1,148,107,demod,43] P(c35,i(i(x,i(y,z)),i(i(x,y),i(x,z)))). -------- PROOF -------- 150 [hyper,3,99,149,109,128,130,102] $ANSWER(step_allFrege_18_35_39_40_46_21). ** KEPT (pick-wt=0): 150 [hyper,3,99,149,109,128,130,102] $ANSWER(step_allFrege_18_35_39_40_46_21). -----> EMPTY CLAUSE at 0.04 sec ----> 150 [hyper,3,99,149,109,128,130,102] $ANSWER(step_allFrege_18_35_39_40_46_21). Length of proof is 41. Level of proof is 26. ---------------- PROOF ---------------- 1 [] -P(u,i(x,y))| -P(v,x)|P(rew(u,v),y). 3 [] -P(x,i(q,i(p,q)))| -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(z,i(n(n(p)),p))| -P(u,i(p,n(n(p))))| -P(v,i(i(p,q),i(n(q),n(p))))| -P(w,i(i(p,i(q,r)),i(q,i(p,r))))|$ANSWER(step_allFrege_18_35_39_40_46_21). 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). 8 [] P(c2,i(i(n(x),x),x)). 9 [] P(c3,i(x,i(n(x),y))). 10 [] EQ(rew(c1,c1),c4). 11 [] EQ(rew(c4,c4),c5). 12 [] EQ(rew(c4,c1),c6). 13 [] EQ(rew(c5,c6),c7). 15 [] EQ(rew(c1,c3),c9). 16 [] EQ(rew(c9,c6),c10). 17 [] EQ(rew(c10,c2),c10a). 18 [] EQ(rew(c10a,c2),c11). 19 [] EQ(rew(c9,c11),c12). 20 [] EQ(rew(c7,c12),c13). 21 [] EQ(rew(c1,c13),c14). 22 [] EQ(rew(c14,c2),c15). 24 [] EQ(rew(c9,c15),c17). 25 [] EQ(rew(c5,c17),c17a). 26 [] EQ(rew(c17a,c3),c18). 27 [] EQ(rew(c1,c18),c19). 28 [] EQ(rew(c19,c15),c20). 29 [] EQ(rew(c5,c20),c21). 30 [] EQ(rew(c21,c1),c22). 31 [] EQ(rew(c1,c21),c23). 32 [] EQ(rew(c23,c15),c24a). 33 [] EQ(rew(c24a,c3),c24). 34 [] EQ(rew(c21,c6),c25). 35 [] EQ(rew(c25,c24),c26). 36 [] EQ(rew(c1,c26),c28). 37 [] EQ(rew(c28,c26),c29). 39 [] EQ(rew(c7,c29),c31). 40 [] EQ(rew(c21,c31),c32). 41 [] EQ(rew(c32,c18),c33). 42 [] EQ(rew(c21,c33),c34). 43 [] EQ(rew(c34,c22),c35). 44 [] EQ(rew(c21,c3),c36). 45 [] EQ(rew(c1,c36),c37). 46 [] EQ(rew(c26,c2),c38). 47 [] EQ(rew(c37,c2),c39). 48 [] EQ(rew(c9,c38),c40). 49 [] EQ(rew(c1,c39),c41). 50 [] EQ(rew(c1,c41),c42). 51 [] EQ(rew(c42,c15),c43). 52 [] EQ(rew(c5,c43),c44). 54 [] EQ(rew(c44,c36),c46). 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))). 107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))). 108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))). 109 [hyper,1,108,8,demod,47] P(c39,i(n(n(x)),x)). 110 [hyper,1,7,109,demod,49] P(c41,i(i(x,y),i(n(n(x)),y))). 111 [hyper,1,7,110,demod,50] P(c42,i(i(i(n(n(x)),y),z),i(i(x,y),z))). 112 [hyper,1,111,95,demod,51] P(c43,i(i(x,y),i(i(y,n(x)),n(x)))). 113 [hyper,1,85,112,demod,52] P(c44,i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))). 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 127 [hyper,1,125,8,demod,46] P(c38,i(i(x,n(x)),n(x))). 128 [hyper,1,83,127,demod,48] P(c40,i(x,n(n(x)))). 130 [hyper,1,113,106,demod,54] P(c46,i(i(x,y),i(n(y),n(x)))). 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). 141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). 144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). 146 [hyper,1,144,99,demod,41] P(c33,i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))). 148 [hyper,1,102,146,demod,42] P(c34,i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))). 149 [hyper,1,148,107,demod,43] P(c35,i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 150 [hyper,3,99,149,109,128,130,102] $ANSWER(step_allFrege_18_35_39_40_46_21). ------------ end of proof ------------- -------- PROOF -------- 151 [hyper,2,99,149,115] $ANSWER(step_allBEH_Church_FL_18_35_49). ** KEPT (pick-wt=0): 151 [hyper,2,99,149,115] $ANSWER(step_allBEH_Church_FL_18_35_49). -----> EMPTY CLAUSE at 0.04 sec ----> 151 [hyper,2,99,149,115] $ANSWER(step_allBEH_Church_FL_18_35_49). Length of proof is 33. Level of proof is 26. ---------------- PROOF ---------------- 1 [] -P(u,i(x,y))| -P(v,x)|P(rew(u,v),y). 2 [] -P(x,i(q,i(p,q)))| -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(z,i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49). 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). 8 [] P(c2,i(i(n(x),x),x)). 9 [] P(c3,i(x,i(n(x),y))). 10 [] EQ(rew(c1,c1),c4). 11 [] EQ(rew(c4,c4),c5). 12 [] EQ(rew(c4,c1),c6). 13 [] EQ(rew(c5,c6),c7). 15 [] EQ(rew(c1,c3),c9). 16 [] EQ(rew(c9,c6),c10). 17 [] EQ(rew(c10,c2),c10a). 18 [] EQ(rew(c10a,c2),c11). 19 [] EQ(rew(c9,c11),c12). 20 [] EQ(rew(c7,c12),c13). 21 [] EQ(rew(c1,c13),c14). 22 [] EQ(rew(c14,c2),c15). 24 [] EQ(rew(c9,c15),c17). 25 [] EQ(rew(c5,c17),c17a). 26 [] EQ(rew(c17a,c3),c18). 27 [] EQ(rew(c1,c18),c19). 28 [] EQ(rew(c19,c15),c20). 29 [] EQ(rew(c5,c20),c21). 30 [] EQ(rew(c21,c1),c22). 31 [] EQ(rew(c1,c21),c23). 32 [] EQ(rew(c23,c15),c24a). 33 [] EQ(rew(c24a,c3),c24). 34 [] EQ(rew(c21,c6),c25). 35 [] EQ(rew(c25,c24),c26). 36 [] EQ(rew(c1,c26),c28). 37 [] EQ(rew(c28,c26),c29). 39 [] EQ(rew(c7,c29),c31). 40 [] EQ(rew(c21,c31),c32). 41 [] EQ(rew(c32,c18),c33). 42 [] EQ(rew(c21,c33),c34). 43 [] EQ(rew(c34,c22),c35). 53 [] EQ(rew(c5,c15),c45). 57 [] EQ(rew(c45,c3),c49). 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). 96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))). 115 [hyper,1,96,9,demod,57] P(c49,i(i(n(x),n(y)),i(y,x))). 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). 141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). 144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). 146 [hyper,1,144,99,demod,41] P(c33,i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))). 148 [hyper,1,102,146,demod,42] P(c34,i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))). 149 [hyper,1,148,107,demod,43] P(c35,i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 151 [hyper,2,99,149,115] $ANSWER(step_allBEH_Church_FL_18_35_49). ------------ end of proof ------------- given clause #70: (wt=20) 147 [hyper,1,7,145,demod,66] P(c58,i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))). ** KEPT (pick-wt=16): 152 [hyper,1,147,102,demod,67] P(c59,i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). given clause #71: (wt=16) 152 [hyper,1,147,102,demod,67] P(c59,i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). -------- PROOF -------- 153 [hyper,5,100,108,152] $ANSWER(step_allLuka_x_19_37_59). ** KEPT (pick-wt=0): 153 [hyper,5,100,108,152] $ANSWER(step_allLuka_x_19_37_59). -----> EMPTY CLAUSE at 0.05 sec ----> 153 [hyper,5,100,108,152] $ANSWER(step_allLuka_x_19_37_59). Length of proof is 37. Level of proof is 26. ---------------- PROOF ---------------- 1 [] -P(u,i(x,y))| -P(v,x)|P(rew(u,v),y). 5 [] -P(x,i(i(i(p,q),r),i(q,r)))| -P(y,i(i(i(p,q),r),i(n(p),r)))| -P(z,i(i(n(p),r),i(i(q,r),i(i(p,q),r))))|$ANSWER(step_allLuka_x_19_37_59). 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). 8 [] P(c2,i(i(n(x),x),x)). 9 [] P(c3,i(x,i(n(x),y))). 10 [] EQ(rew(c1,c1),c4). 11 [] EQ(rew(c4,c4),c5). 12 [] EQ(rew(c4,c1),c6). 13 [] EQ(rew(c5,c6),c7). 15 [] EQ(rew(c1,c3),c9). 16 [] EQ(rew(c9,c6),c10). 17 [] EQ(rew(c10,c2),c10a). 18 [] EQ(rew(c10a,c2),c11). 19 [] EQ(rew(c9,c11),c12). 20 [] EQ(rew(c7,c12),c13). 21 [] EQ(rew(c1,c13),c14). 22 [] EQ(rew(c14,c2),c15). 24 [] EQ(rew(c9,c15),c17). 25 [] EQ(rew(c5,c17),c17a). 26 [] EQ(rew(c17a,c3),c18). 27 [] EQ(rew(c1,c18),c19). 28 [] EQ(rew(c19,c15),c20). 29 [] EQ(rew(c5,c20),c21). 31 [] EQ(rew(c1,c21),c23). 32 [] EQ(rew(c23,c15),c24a). 33 [] EQ(rew(c24a,c3),c24). 34 [] EQ(rew(c21,c6),c25). 35 [] EQ(rew(c25,c24),c26). 36 [] EQ(rew(c1,c26),c28). 37 [] EQ(rew(c28,c26),c29). 39 [] EQ(rew(c7,c29),c31). 40 [] EQ(rew(c21,c31),c32). 44 [] EQ(rew(c21,c3),c36). 45 [] EQ(rew(c1,c36),c37). 53 [] EQ(rew(c5,c15),c45). 56 [] EQ(rew(c45,c36),c48). 58 [] EQ(rew(c1,c48),c50). 61 [] EQ(rew(c50,c15),c53). 64 [] EQ(rew(c1,c53),c56). 65 [] EQ(rew(c56,c32),c57). 66 [] EQ(rew(c1,c57),c58). 67 [] EQ(rew(c58,c21),c59). 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). 96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))). 108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))). 114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))). 116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))). 120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))). 122 [hyper,1,7,120,demod,64] P(c56,i(i(i(i(x,y),y),z),i(i(n(x),y),z))). 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). 141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). 144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). 145 [hyper,1,122,144,demod,65] P(c57,i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). 147 [hyper,1,7,145,demod,66] P(c58,i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))). 152 [hyper,1,147,102,demod,67] P(c59,i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). 153 [hyper,5,100,108,152] $ANSWER(step_allLuka_x_19_37_59). ------------ end of proof ------------- ** KEPT (pick-wt=20): 154 [hyper,1,107,152,demod,68] P(c60,i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))). given clause #72: (wt=20) 154 [hyper,1,107,152,demod,68] P(c60,i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))). -------- PROOF -------- 155 [hyper,6,100,108,154] $ANSWER(step_allWos_x_19_37_60). ** KEPT (pick-wt=0): 155 [hyper,6,100,108,154] $ANSWER(step_allWos_x_19_37_60). -----> EMPTY CLAUSE at 0.05 sec ----> 155 [hyper,6,100,108,154] $ANSWER(step_allWos_x_19_37_60). Length of proof is 39. Level of proof is 27. ---------------- PROOF ---------------- 1 [] -P(u,i(x,y))| -P(v,x)|P(rew(u,v),y). 6 [] -P(x,i(i(i(p,q),r),i(q,r)))| -P(y,i(i(i(p,q),r),i(n(p),r)))| -P(z,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r)))))|$ANSWER(step_allWos_x_19_37_60). 7 [] P(c1,i(i(x,y),i(i(y,z),i(x,z)))). 8 [] P(c2,i(i(n(x),x),x)). 9 [] P(c3,i(x,i(n(x),y))). 10 [] EQ(rew(c1,c1),c4). 11 [] EQ(rew(c4,c4),c5). 12 [] EQ(rew(c4,c1),c6). 13 [] EQ(rew(c5,c6),c7). 15 [] EQ(rew(c1,c3),c9). 16 [] EQ(rew(c9,c6),c10). 17 [] EQ(rew(c10,c2),c10a). 18 [] EQ(rew(c10a,c2),c11). 19 [] EQ(rew(c9,c11),c12). 20 [] EQ(rew(c7,c12),c13). 21 [] EQ(rew(c1,c13),c14). 22 [] EQ(rew(c14,c2),c15). 24 [] EQ(rew(c9,c15),c17). 25 [] EQ(rew(c5,c17),c17a). 26 [] EQ(rew(c17a,c3),c18). 27 [] EQ(rew(c1,c18),c19). 28 [] EQ(rew(c19,c15),c20). 29 [] EQ(rew(c5,c20),c21). 30 [] EQ(rew(c21,c1),c22). 31 [] EQ(rew(c1,c21),c23). 32 [] EQ(rew(c23,c15),c24a). 33 [] EQ(rew(c24a,c3),c24). 34 [] EQ(rew(c21,c6),c25). 35 [] EQ(rew(c25,c24),c26). 36 [] EQ(rew(c1,c26),c28). 37 [] EQ(rew(c28,c26),c29). 39 [] EQ(rew(c7,c29),c31). 40 [] EQ(rew(c21,c31),c32). 44 [] EQ(rew(c21,c3),c36). 45 [] EQ(rew(c1,c36),c37). 53 [] EQ(rew(c5,c15),c45). 56 [] EQ(rew(c45,c36),c48). 58 [] EQ(rew(c1,c48),c50). 61 [] EQ(rew(c50,c15),c53). 64 [] EQ(rew(c1,c53),c56). 65 [] EQ(rew(c56,c32),c57). 66 [] EQ(rew(c1,c57),c58). 67 [] EQ(rew(c58,c21),c59). 68 [] EQ(rew(c22,c59),c60). 82 [hyper,1,7,7,demod,10] P(c4,i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,7,9,demod,15] P(c9,i(i(i(n(x),y),z),i(x,z))). 85 [hyper,1,82,82,demod,11] P(c5,i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 86 [hyper,1,82,7,demod,12] P(c6,i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 87 [hyper,1,85,86,demod,13] P(c7,i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 88 [hyper,1,83,86,demod,16] P(c10,i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). 89 [hyper,1,88,8,demod,17] P(c10a,i(i(i(n(i(i(n(x),x),x)),y),z),i(i(u,y),z))). 90 [hyper,1,89,8,demod,18] P(c11,i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))). 91 [hyper,1,83,90,demod,19] P(c12,i(x,i(i(n(y),y),y))). 92 [hyper,1,87,91,demod,20] P(c13,i(i(n(x),y),i(z,i(i(y,x),x)))). 94 [hyper,1,7,92,demod,21] P(c14,i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 95 [hyper,1,94,8,demod,22] P(c15,i(i(n(x),y),i(i(y,x),x))). 96 [hyper,1,85,95,demod,53] P(c45,i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 97 [hyper,1,83,95,demod,24] P(c17,i(x,i(i(y,x),x))). 98 [hyper,1,85,97,demod,25] P(c17a,i(i(x,i(y,z)),i(z,i(x,z)))). 99 [hyper,1,98,9,demod,26] P(c18,i(x,i(y,x))). 100 [hyper,1,7,99,demod,27] P(c19,i(i(i(x,y),z),i(y,z))). 101 [hyper,1,100,95,demod,28] P(c20,i(x,i(i(x,y),y))). 102 [hyper,1,85,101,demod,29] P(c21,i(i(x,i(y,z)),i(y,i(x,z)))). 103 [hyper,1,7,102,demod,31] P(c23,i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 105 [hyper,1,102,86,demod,34] P(c25,i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 106 [hyper,1,102,9,demod,44] P(c36,i(n(x),i(x,y))). 107 [hyper,1,102,7,demod,30] P(c22,i(i(x,y),i(i(z,x),i(z,y)))). 108 [hyper,1,7,106,demod,45] P(c37,i(i(i(x,y),z),i(n(x),z))). 114 [hyper,1,96,106,demod,56] P(c48,i(i(n(x),y),i(n(y),x))). 116 [hyper,1,7,114,demod,58] P(c50,i(i(i(n(x),y),z),i(i(n(y),x),z))). 120 [hyper,1,116,95,demod,61] P(c53,i(i(n(x),y),i(i(x,y),y))). 122 [hyper,1,7,120,demod,64] P(c56,i(i(i(i(x,y),y),z),i(i(n(x),y),z))). 123 [hyper,1,103,95,demod,32] P(c24a,i(i(x,i(n(y),z)),i(i(i(x,z),y),y))). 124 [hyper,1,123,9,demod,33] P(c24,i(i(i(x,y),x),x)). 125 [hyper,1,105,124,demod,35] P(c26,i(i(i(x,y),z),i(i(z,x),x))). 126 [hyper,1,7,125,demod,36] P(c28,i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 140 [hyper,1,126,125,demod,37] P(c29,i(i(i(x,y),z),i(i(x,z),z))). 141 [hyper,1,87,140,demod,39] P(c31,i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). 144 [hyper,1,102,141,demod,40] P(c32,i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). 145 [hyper,1,122,144,demod,65] P(c57,i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). 147 [hyper,1,7,145,demod,66] P(c58,i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))). 152 [hyper,1,147,102,demod,67] P(c59,i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). 154 [hyper,1,107,152,demod,68] P(c60,i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))). 155 [hyper,6,100,108,154] $ANSWER(step_allWos_x_19_37_60). ------------ end of proof ------------- ** KEPT (pick-wt=16): 156 [hyper,1,154,110,demod,69] P(c61,i(i(x,y),i(i(z,y),i(i(n(x),z),y)))). given clause #73: (wt=16) 156 [hyper,1,154,110,demod,69] P(c61,i(i(x,y),i(i(z,y),i(i(n(x),z),y)))). ** KEPT (pick-wt=12): 157 [hyper,1,156,84,demod,73] P(c64a,i(i(x,y),i(i(n(y),x),y))). given clause #74: (wt=12) 157 [hyper,1,156,84,demod,73] P(c64a,i(i(x,y),i(i(n(y),x),y))). ** KEPT (pick-wt=11): 158 [hyper,1,157,118,demod,74] P(c65,i(i(n(x),n(i(y,y))),x)). given clause #75: (wt=11) 158 [hyper,1,157,118,demod,74] P(c65,i(i(n(x),n(i(y,y))),x)). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ -------------- statistics ------------- clauses given 75 clauses generated 3790 hyper_res generated 3790 demod & eval rewrites 74 clauses wt,lit,sk delete 3711 tautologies deleted 0 clauses forward subsumed 2 (subsumed by sos) 2 unit deletions 0 factor simplifications 0 clauses kept 72 new demodulators 0 empty clauses 5 clauses back demodulated 0 clauses back subsumed 0 usable size 81 sos size 0 demodulators size 72 passive size 0 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8522 finished Mon Aug 2 15:30:56 2004 otter-3.3f/examples/wos/grp_exp4.out0100664000076400007640000016321210103522160017105 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:39 2004 The command was "../../bin/otter". The process ID is 8512. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(eq_units_both_ways). WARNING: set(process_input) flag already set. set(process_input). WARNING: set(index_for_back_demod) flag already set. set(index_for_back_demod). set(para_into_units_only). set(para_from_units_only). WARNING: set(lrpo) flag already set. set(lrpo). lex([e,a,b,f(x,x),g(x)]). assign(pick_given_ratio,3). assign(max_proofs,4). assign(demod_limit,500). assign(max_mem,24000). assign(max_weight,51). assign(change_limit_after,10). assign(new_max_weight,41). clear(print_kept). clear(print_new_demod). clear(print_back_demod). weight_list(pick_and_purge). weight(f(e,f(e,f(e,f(f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,y),e)),2). weight(f(e,f(e,f(e,f(f(f(x,x),f(f(x,e),e)),e))))=f(x,f(f(x,x),e)),2). weight(f(e,f(e,f(e,f(x,f(f(f(x,f(x,x)),e),e)))))=e,2). weight(f(e,f(e,f(f(e,f(x,f(y,f(y,y)))),y)))=x,2). weight(f(e,f(e,f(f(f(x,f(f(x,x),e)),e),f(f(f(x,f(f(x,x),e)),e),f(f(x,f(f(x,x),e)),e)))))=x,2). weight(f(e,f(e,f(y,f(f(f(y,f(y,y)),e),e))))=e,2). weight(f(e,f(f(e,f(e,f(f(x,e),e))),y))=f(x,f(e,y)),2). weight(f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x,2). weight(f(e,f(f(e,f(e,f(x,e))),e))=x,2). weight(f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x,2). weight(f(e,f(f(e,f(f(f(x,f(f(x,x),e)),e),f(f(f(x,f(f(x,x),e)),e),f(f(x,f(f(x,x),e)),e)))),y))=f(x,f(e,y)),2). weight(f(e,f(f(f(x,f(e,f(e,y))),e),e))=f(f(e,f(f(x,e),e)),y),2). weight(f(e,f(y,f(f(f(y,f(y,y)),e),e)))=e,2). weight(f(f(e,f(x,f(e,y))),f(y,f(y,y)))=f(e,f(f(x,e),e)),2). weight(f(f(e,f(x,f(y,f(y,y)))),y)=f(e,f(f(x,e),e)),2). weight(f(f(e,x),e)=f(e,f(x,e)),2). weight(f(f(e,x),f(e,y))=f(e,f(x,y)),2). weight(f(f(e,x),y)=f(e,f(x,f(e,f(e,f(f(y,e),e))))),2). weight(f(f(f(x,f(x,x)),e),e)=f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))),2). weight(f(f(f(x,x),e),f(f(f(x,e),f(f(f(x,e),e),e)),e))=e,2). weight(f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)),2). weight(f(f(f(x,x),f(f(x,x),f(x,x))),e)=f(x,f(f(x,e),e)),2). weight(f(f(x,e),f(f(f(x,e),f(f(x,f(f(x,e),e)),e)),e))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))),2). weight(f(f(x,e),f(f(x,x),f(f(x,e),e)))=e,2). weight(f(f(x,e),f(y,e))=f(f(x,y),e),2). weight(f(f(x,f(e,f(e,f(y,f(y,y))))),f(e,y))=f(f(x,e),e),2). weight(f(f(x,f(e,f(e,y))),f(y,f(y,y)))=f(f(x,e),e),2). weight(f(f(x,f(e,f(y,f(y,y)))),y)=f(f(x,e),e),2). weight(f(f(x,f(e,y)),e)=f(f(x,e),f(e,f(y,e))),2). weight(f(f(x,f(f(x,e),e)),e)=f(f(f(x,x),f(x,x)),f(f(f(x,x),e),e)),2). weight(f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)),2). weight(f(f(x,f(x,x)),f(e,f(f(x,e),e)))=e,2). weight(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x))))=f(e,x),2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),e))=f(x,f(f(x,e),e)),2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,e),e),y)))=f(x,f(f(x,f(f(x,e),e)),f(e,y))),2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z)))=f(x,f(y,f(e,z))),2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),y))=f(x,f(f(x,e),y)),2). weight(f(f(x,x),f(f(x,f(f(x,e),e)),e))=e,2). weight(f(f(x,x),f(f(x,f(f(x,e),e)),f(e,f(f(y,e),e))))=y,2). weight(f(f(x,y),e)=f(f(x,e),f(y,e)),2). weight(f(f(x,y),z)=f(f(x,e),f(y,f(f(e,f(e,f(z,u))),f(u,f(u,u))))),2). weight(f(x,e)=x,2). weight(f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))),2). weight(f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e))=e,2). weight(f(x,f(f(x,f(f(x,x),e)),e))=e,2). weight(f(x,f(f(x,f(f(x,x),e)),f(f(f(f(y,f(y,y)),e),e),f(f(f(f(y,f(y,y)),e),e),f(f(f(y,f(y,y)),e),e)))))=y,2). weight(f(x,f(f(x,f(f(x,x),e)),f(f(f(y,f(f(y,y),e)),e),f(f(f(y,f(f(y,y),e)),e),f(f(y,f(f(y,y),e)),e)))))=y,2). weight(f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y),2). weight(f(x,f(f(x,f(f(x,x),f(y,e))),e))=y,2). weight(f(x,f(f(x,f(f(x,x),f(y,f(z,f(z,z))))),f(e,z)))=y,2). weight(f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))),2). weight(f(x,f(f(x,f(x,f(f(x,e),e))),e))=f(f(x,x),f(x,x)),2). weight(f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))),2). weight(f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))),2). weight(f(y,f(f(f(y,f(y,y)),e),e))=e,2). weight(f(e,f(e,f(e,f(f(f(x,f(f(x,e),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,y),e)),2). weight(f(e,f(e,f(e,f(f(x,e),e))))=x,2). weight(f(e,f(e,f(e,x)))=x,2). weight(f(e,f(e,f(f(f(x,x),f(f(x,e),e)),f(f(f(x,x),f(f(x,e),e)),f(f(x,x),f(f(x,e),e))))))=x,2). weight(f(e,f(e,x))=x,2). weight(f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x,2). weight(f(e,f(f(e,f(f(f(x,x),f(f(x,e),e)),f(f(f(x,x),f(f(x,e),e)),f(f(x,x),f(f(x,e),e))))),y))=f(x,f(e,y)),2). weight(f(e,f(f(f(x,e),e),f(e,f(e,f(f(y,e),e)))))=f(f(e,f(f(x,e),e)),y),2). weight(f(e,f(x,x))=f(x,x),2). weight(f(e,y)=y,2). weight(f(f(e,x),y)=f(e,f(x,f(e,f(e,y)))),2). weight(f(f(x,f(f(x,e),e)),f(e,y))=f(f(x,e),f(f(f(x,e),e),y)),2). weight(f(f(x,f(x,f(y,z))),f(z,f(z,z)))=f(x,f(x,y)),2). weight(f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))),2). weight(f(f(x,x),f(f(x,e),f(f(f(x,e),e),f(f(y,e),e))))=y,2). weight(f(f(x,x),f(x,f(x,y)))=y,2). weight(f(f(x,x),f(x,x))=e,2). weight(f(f(x,y),f(e,z))=f(f(x,e),f(y,z)),2). weight(f(f(x,y),f(e,z))=f(x,f(y,z)),2). weight(f(f(x,y),z)=f(x,f(y,f(e,f(e,z)))),2). weight(f(f(x,y),z)=f(x,f(y,z)),2). weight(f(x,f(f(x,f(f(x,x),e)),f(e,f(f(y,e),e))))=y,2). weight(f(x,f(f(x,x),f(f(x,e),e)))=e,2). weight(f(x,f(f(x,y),f(e,z)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))),2). weight(f(x,f(x,f(x,x)))=e,2). end_of_list. list(usable). 0 [] x=x. end_of_list. list(sos). 0 [] f(y,f(f(y,f(f(y,y),f(x,z))),f(z,f(z,z))))=x. 0 [] f(e,e)=e. end_of_list. list(passive). 1 [] f(f(a,b),c)!=f(a,f(b,c))|$ANS(assoc). 2 [] f(a,f(a,f(a,a)))!=e|$ANS(exp4). 3 [] f(e,a)!=a|$ANS(lid). 4 [] f(a,e)!=a|$ANS(rid). end_of_list. list(demodulators). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 5 [] x=x. ------------> process sos: ** KEPT (pick-wt=19): 6 [] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. ---> New Demodulator: 7 [new_demod,6] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. ** KEPT (pick-wt=5): 8 [] f(e,e)=e. ---> New Demodulator: 9 [new_demod,8] f(e,e)=e. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=19) 6 [] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. given clause #2: (wt=2) 10 [para_into,6.1.1.2.1.2,6.1.1] f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))). given clause #3: (wt=5) 8 [] f(e,e)=e. given clause #4: (wt=2) 16 [para_from,8.1.1,10.1.1.2.2.1.2,demod,9,9,9,9,9,9,9] f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))). given clause #5: (wt=51) 11 [para_into,10.1.1.2.1,6.1.1] f(x,f(y,f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z))). given clause #6: (wt=2) 17 [para_from,8.1.1,6.1.1.2.2.2,demod,9] f(x,f(f(x,f(f(x,x),f(y,e))),e))=y. given clause #7: (wt=2) 19 [para_from,8.1.1,6.1.1.2.1.2.2,demod,9,9] f(x,f(f(x,f(f(x,x),e)),e))=e. given clause #8: (wt=2) 21 [para_from,8.1.1,6.1.1.2.1.2.1] f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x. given clause #9: (wt=27) 12 [para_into,10.1.1,6.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(y,f(z,f(z,z)))),z)))=y. given clause #10: (wt=2) 41 [para_into,19.1.1.2.1,16.1.1] f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e))=e. reducing weight limit to 41. given clause #11: (wt=2) 45 [para_from,19.1.1,17.1.1.2.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),e))=f(x,f(f(x,e),e)). given clause #12: (wt=2) 49 [para_from,19.1.1,10.1.1.2.1] f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))). given clause #13: (wt=29) 14 [para_from,8.1.1,10.1.1.2.1,demod,9,9,9,9] f(e,f(e,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x))))))=f(e,f(e,f(e,x))). given clause #14: (wt=2) 50 [para_from,19.1.1,6.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),e)),f(f(f(y,f(f(y,y),e)),e),f(f(f(y,f(f(y,y),e)),e),f(f(y,f(f(y,y),e)),e)))))=y. given clause #15: (wt=2) 54 [para_into,21.1.1.2.1.2.2,19.1.1,demod,9,9] f(e,f(e,f(f(f(x,f(f(x,x),e)),e),f(f(f(x,f(f(x,x),e)),e),f(f(x,f(f(x,x),e)),e)))))=x. given clause #16: (wt=2) 58 [para_into,21.1.1.2.1.2.2,16.1.1] f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. given clause #17: (wt=39) 23 [para_into,16.1.1.2.1,16.1.1] f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,y),e),e))). given clause #18: (wt=2) 66 [para_into,21.1.1.2.2.2,8.1.1,demod,9,63,63] f(e,f(e,f(e,f(f(x,e),e))))=x. given clause #19: (wt=2) 70 [para_into,21.1.1,10.1.1,demod,9,9,9,9] f(e,f(e,f(f(e,f(x,f(y,f(y,y)))),y)))=x. given clause #20: (wt=2) 79 [para_from,45.1.1,19.1.1.2.1] f(f(x,x),f(f(x,f(f(x,e),e)),e))=e. given clause #21: (wt=35) 24 [para_into,16.1.1.2.1,6.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e)))=f(x,f(y,e)). given clause #22: (wt=2) 81 [para_from,45.1.1,17.1.1.2.1.2] f(x,f(f(x,f(x,f(f(x,e),e))),e))=f(f(x,x),f(x,x)). given clause #23: (wt=13) 94 [para_into,23.1.1.2.1.1,8.1.1,demod,9,9,9,63,63,67,9,9,9,9,flip.1] f(e,f(e,f(f(f(e,x),e),e)))=x. given clause #24: (wt=2) 132 [para_into,94.1.1.2.2.1.1,16.1.1,demod,9,9,9,9,130,130,67,flip.1] f(f(e,x),e)=f(e,f(x,e)). given clause #25: (wt=39) 26 [para_from,16.1.1,6.1.1.2.1.2,demod,9,9] f(x,f(f(x,f(f(f(x,x),f(x,x)),f(f(f(f(x,x),f(x,x)),f(f(x,x),f(x,x))),f(y,e)))),e))=f(f(x,x),y). given clause #26: (wt=2) 137 [back_demod,49,demod,128,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))). given clause #27: (wt=2) 147 [para_from,132.1.1,17.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y). given clause #28: (wt=2) 157 [para_from,137.1.1,17.1.1.2.1,demod,9,9,flip.1] f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)). given clause #29: (wt=43) 28 [para_from,16.1.1,6.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),f(f(y,y),f(f(f(y,y),f(y,y)),f(z,e))))),f(f(f(y,z),e),f(f(f(y,z),e),f(f(y,z),e)))))=y. given clause #30: (wt=2) 167 [back_demod,19,demod,158] f(x,f(f(x,x),f(f(x,e),e)))=e. given clause #31: (wt=2) 173 [para_into,147.1.1.2.1.2.2,23.1.1,demod,9,9,9,9,133,133,67,9,9,9,9] f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))). 207 back subsumes 102. given clause #32: (wt=2) 177 [para_into,157.1.1.1,45.1.1] f(f(x,f(f(x,e),e)),e)=f(f(f(x,x),f(x,x)),f(f(f(x,x),e),e)). given clause #33: (wt=47) 30 [para_into,11.1.1,10.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z))),u)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,u))). 224 back subsumes 112. given clause #34: (wt=2) 178 [para_into,157.1.1.1,16.1.1] f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)). given clause #35: (wt=2) 182 [para_from,157.1.1,66.1.1.2.2.2.1] f(e,f(e,f(e,f(f(f(x,x),f(f(x,e),e)),e))))=f(x,f(f(x,x),e)). given clause #36: (wt=2) 193 [para_into,173.1.1.2.1.2,6.1.1,flip.1] f(e,f(e,f(e,f(f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,y),e)). given clause #37: (wt=47) 39 [para_from,17.1.1,6.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),y)),f(f(f(z,f(f(z,z),f(y,e))),e),f(f(f(z,f(f(z,z),f(y,e))),e),f(f(z,f(f(z,z),f(y,e))),e)))))=z. given clause #38: (wt=15) 231 [para_from,178.1.1,173.1.1.2,demod,67] f(f(x,x),f(f(x,x),f(f(x,e),e)))=x. given clause #39: (wt=19) 227 [para_from,30.1.1,6.1.1.2.1,demod,7,flip.1] f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z)))=y. 288 back subsumes 284. given clause #40: (wt=15) 269 [para_into,227.1.1.1.2.2.1,8.1.1,demod,9] f(f(e,f(e,f(e,x))),f(x,f(x,x)))=e. given clause #41: (wt=51) 52 [para_into,21.1.1.2.1.2.2,21.1.1] f(e,f(f(e,f(e,x)),f(f(f(e,f(e,f(x,y))),f(y,f(y,y))),f(f(f(e,f(e,f(x,y))),f(y,f(y,y))),f(f(e,f(e,f(x,y))),f(y,f(y,y)))))))=e. given clause #42: (wt=15) 282 [para_into,227.1.1.2.2,8.1.1,demod,9] f(f(x,f(f(x,x),f(f(x,y),e))),e)=y. given clause #43: (wt=15) 317 [back_demod,282,demod,312] f(f(x,x),f(f(x,f(f(x,y),e)),e))=y. given clause #44: (wt=17) 248 [para_into,227.1.1.1.2.1,8.1.1] f(f(e,f(e,f(f(e,x),y))),f(y,f(y,y)))=x. given clause #45: (wt=41) 74 [para_from,21.1.1,10.1.1.2.1,demod,9,9,9,9] f(e,f(x,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(e,f(e,f(f(f(e,f(e,f(x,z))),f(z,f(z,z))),y))). given clause #46: (wt=19) 301 [para_from,269.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,e),y)))=f(e,f(e,f(e,y))). given clause #47: (wt=19) 305 [back_demod,244,demod,300,300,67] f(f(x,e),f(f(x,e),f(x,e)))=f(x,f(f(x,x),e)). given clause #48: (wt=19) 311 [para_into,282.1.1.1.2.2,282.1.1] f(f(x,f(f(x,x),y)),e)=f(f(x,x),f(f(x,y),e)). 415 back subsumes 238. given clause #49: (wt=37) 75 [para_from,41.1.1,17.1.1.2.1.2,flip.1] f(f(f(x,x),f(x,x)),f(f(f(f(x,x),f(x,x)),f(f(x,x),f(x,x))),f(f(x,x),e)))=f(x,f(f(x,e),e)). given clause #50: (wt=19) 387 [para_from,305.1.1,269.1.1.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,x),e)))=e. given clause #51: (wt=17) 416 [para_into,387.1.1.1,66.1.1] f(x,f(f(x,e),f(f(f(x,e),f(x,e)),e)))=e. given clause #52: (wt=21) 139 [para_into,132.1.1.1,21.1.1,flip.1] f(e,f(f(f(e,f(e,f(x,y))),f(y,f(y,y))),e))=f(x,e). given clause #53: (wt=37) 85 [para_from,14.1.1,16.1.1.2.1,demod,63,63,63,9,9,9,9,63,flip.1] f(e,f(e,f(e,f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))),e))))=f(e,f(e,f(e,f(e,f(x,e))))). given clause #54: (wt=21) 186 [para_into,167.1.1.2.2.1,132.1.1,demod,133] f(f(e,x),f(f(f(e,x),f(e,x)),f(e,f(f(x,e),e))))=e. given clause #55: (wt=21) 285 [para_from,227.1.1,21.1.1.2.1.2.2,demod,136] f(e,f(e,f(f(e,x),y)))=f(z,f(f(z,z),f(f(z,x),y))). given clause #56: (wt=21) 293 [para_into,269.1.1.1,66.1.1] f(x,f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))))=e. given clause #57: (wt=37) 89 [para_into,54.1.1.2.2.1.1,45.1.1,demod,46,46] f(e,f(e,f(f(f(x,f(f(x,e),e)),e),f(f(f(x,f(f(x,e),e)),e),f(f(x,f(f(x,e),e)),e)))))=f(x,x). given clause #58: (wt=17) 500 [para_from,293.1.1,227.1.1.1.2.2,demod,275] f(f(x,x),f(f(x,e),f(f(f(x,y),e),e)))=y. given clause #59: (wt=17) 504 [back_demod,454,demod,503] f(f(e,x),f(e,f(f(x,x),f(f(x,e),e))))=e. given clause #60: (wt=21) 327 [back_demod,173,demod,312] f(x,f(f(x,x),f(f(x,y),e)))=f(e,f(e,f(e,f(y,e)))). given clause #61: (wt=31) 93 [para_from,58.1.1,21.1.1.2.1.2,demod,61] f(e,f(e,f(x,f(f(x,y),e))))=f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))). given clause #62: (wt=21) 340 [para_into,317.1.1.2.1,45.1.1] f(f(f(x,x),f(x,x)),f(f(x,f(f(x,e),e)),e))=f(x,x). given clause #63: (wt=21) 353 [para_from,248.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,y),z)))=f(e,f(e,f(f(e,y),z))). given clause #64: (wt=17) 634 [para_into,353.1.1.2,231.1.1,flip.1] f(e,f(e,f(f(e,x),f(f(x,e),e))))=f(x,x). given clause #65: (wt=41) 103 [para_from,66.1.1,6.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),y)),f(f(e,f(e,f(f(y,e),e))),f(f(e,f(e,f(f(y,e),e))),f(e,f(e,f(f(y,e),e)))))))=e. given clause #66: (wt=19) 671 [para_into,634.1.1,285.1.1] f(x,f(f(x,x),f(f(x,y),f(f(y,e),e))))=f(y,y). given clause #67: (wt=2) 703 [para_from,671.1.1,16.1.1.2.1,demod,328,flip.1] f(e,f(e,f(e,f(f(f(x,y),f(f(y,e),e)),e))))=f(x,f(f(y,y),e)). given clause #68: (wt=2) 718 [para_from,703.1.1,132.1.1.1,demod,133,133,67] f(f(x,f(f(y,y),e)),e)=f(f(x,y),f(f(y,e),e)). given clause #69: (wt=25) 107 [para_from,70.1.1,16.1.1.2.1,demod,9,9,9,9,63,flip.1] f(e,f(e,f(e,f(f(f(e,f(x,f(y,f(y,y)))),y),e))))=f(e,f(x,e)). given clause #70: (wt=19) 722 [para_into,718.1.1,132.1.1] f(e,f(f(f(x,x),e),e))=f(f(e,x),f(f(x,e),e)). given clause #71: (wt=21) 371 [back_demod,319,demod,366] f(f(x,x),f(f(x,e),f(y,e)))=f(f(x,x),f(f(x,y),e)). given clause #72: (wt=2) 793 [para_from,371.1.1,317.1.1.2.1.2.1,demod,318] f(f(x,y),e)=f(f(x,e),f(y,e)). 907 back subsumes 371. given clause #73: (wt=27) 116 [para_from,24.1.1,17.1.1.2.1] f(f(x,x),f(f(x,f(y,e)),e))=f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))). given clause #74: (wt=2) 900 [para_from,793.1.1,703.1.1.2.2.2.1.1,demod,9,9,67,9,9] f(f(x,e),f(y,e))=f(f(x,y),e). given clause #75: (wt=2) 917 [back_demod,58,demod,899] f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. given clause #76: (wt=2) 965 [para_into,900.1.1.2,132.1.1,flip.1] f(f(x,f(e,y)),e)=f(f(x,e),f(e,f(y,e))). given clause #77: (wt=37) 119 [para_from,81.1.1,17.1.1.2.1.2] f(x,f(f(x,f(f(f(x,x),f(x,x)),f(f(x,x),f(x,x)))),e))=f(f(x,x),f(f(x,x),f(f(f(x,x),e),e))). given clause #78: (wt=2) 1033 [back_demod,190,demod,966,966,9,67,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),y))=f(x,f(f(x,e),y)). 1216 back subsumes 177. given clause #79: (wt=2) 1076 [para_from,900.1.1,81.1.1.2.1.2] f(f(x,e),f(f(f(x,e),f(f(x,f(f(x,e),e)),e)),e))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))). given clause #80: (wt=2) 1130 [para_into,917.1.1.2.2.1.1,671.1.1,demod,834,1014,635,672,672] f(e,f(f(e,f(e,f(x,f(f(y,e),f(y,e))))),f(f(f(y,y),e),f(f(f(y,y),e),f(f(y,y),e)))))=x. -------- PROOF -------- 1244 [binary,1242.1,4.1] $ANS(rid). ----> UNIT CONFLICT at 0.49 sec ----> 1244 [binary,1242.1,4.1] $ANS(rid). Length of proof is 57. Level of proof is 18. ---------------- PROOF ---------------- 4 [] f(a,e)!=a|$ANS(rid). 7,6 [] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. 9,8 [] f(e,e)=e. 10 [para_into,6.1.1.2.1.2,6.1.1] f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))). 11 [para_into,10.1.1.2.1,6.1.1] f(x,f(y,f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z))). 16 [para_from,8.1.1,10.1.1.2.2.1.2,demod,9,9,9,9,9,9,9] f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))). 17 [para_from,8.1.1,6.1.1.2.2.2,demod,9] f(x,f(f(x,f(f(x,x),f(y,e))),e))=y. 19 [para_from,8.1.1,6.1.1.2.1.2.2,demod,9,9] f(x,f(f(x,f(f(x,x),e)),e))=e. 22,21 [para_from,8.1.1,6.1.1.2.1.2.1] f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x. 23 [para_into,16.1.1.2.1,16.1.1] f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,y),e),e))). 24 [para_into,16.1.1.2.1,6.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e)))=f(x,f(y,e)). 30 [para_into,11.1.1,10.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z))),u)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,u))). 49 [para_from,19.1.1,10.1.1.2.1] f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))). 58 [para_into,21.1.1.2.1.2.2,16.1.1] f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 63,62 [para_into,21.1.1.2.1.2,17.1.1,demod,9,9,9] f(e,f(f(e,x),e))=f(e,f(e,f(x,e))). 67,66 [para_into,21.1.1.2.2.2,8.1.1,demod,9,63,63] f(e,f(e,f(e,f(f(x,e),e))))=x. 94 [para_into,23.1.1.2.1.1,8.1.1,demod,9,9,9,63,63,67,9,9,9,9,flip.1] f(e,f(e,f(f(f(e,x),e),e)))=x. 122,121 [para_into,94.1.1.2.2.1.1,94.1.1,flip.1] f(e,f(f(f(e,x),e),e))=f(e,f(e,f(f(x,e),e))). 128,127 [para_into,94.1.1.2.2.1.1,49.1.1,demod,9,9,9,9,9,9,9,9,122,122,122,67,flip.1] f(e,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))))=f(e,f(e,x)). 130,129 [para_into,94.1.1.2.2.1.1,23.1.1,demod,9,9,9,9,122,67,9,9,9,9,flip.1] f(f(e,f(e,f(x,e))),e)=f(e,f(e,f(f(x,e),e))). 133,132 [para_into,94.1.1.2.2.1.1,16.1.1,demod,9,9,9,9,130,130,67,flip.1] f(f(e,x),e)=f(e,f(x,e)). 136,135 [para_into,94.1.1.2.2.1.1,10.1.1,demod,9,9,9,9,133,133,133,133,67,flip.1] f(f(e,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y)))))=f(e,f(x,y)). 137 [back_demod,49,demod,128,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))). 147 [para_from,132.1.1,17.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y). 157 [para_from,137.1.1,17.1.1.2.1,demod,9,9,flip.1] f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)). 173 [para_into,147.1.1.2.1.2.2,23.1.1,demod,9,9,9,9,133,133,67,9,9,9,9] f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))). 178 [para_into,157.1.1.1,16.1.1] f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)). 200,199 [para_into,173.1.1,16.1.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),y),e)))=f(e,f(e,f(e,f(y,e)))). 227 [para_from,30.1.1,6.1.1.2.1,demod,7,flip.1] f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z)))=y. 231 [para_from,178.1.1,173.1.1.2,demod,67] f(f(x,x),f(f(x,x),f(f(x,e),e)))=x. 244 [para_from,231.1.1,24.1.1.2.2.1.1.2,demod,200] f(e,f(e,f(e,f(f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))),e))))=f(x,f(f(x,x),e)). 248 [para_into,227.1.1.1.2.1,8.1.1] f(f(e,f(e,f(f(e,x),y))),f(y,f(y,y)))=x. 254 [para_into,227.1.1.1.2.2.1,173.1.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,f(f(x,x),y)),e). 269 [para_into,227.1.1.1.2.2.1,8.1.1,demod,9] f(f(e,f(e,f(e,x))),f(x,f(x,x)))=e. 275,274 [para_into,227.1.1.1.2.2,227.1.1] f(f(x,f(f(x,x),y)),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z)))))=f(f(x,x),f(f(x,y),z)). 282 [para_into,227.1.1.2.2,8.1.1,demod,9] f(f(x,f(f(x,x),f(f(x,y),e))),e)=y. 285 [para_from,227.1.1,21.1.1.2.1.2.2,demod,136] f(e,f(e,f(f(e,x),y)))=f(z,f(f(z,z),f(f(z,x),y))). 300,299 [para_from,269.1.1,24.1.1.2.2.1.1.2.2,demod,275,200,133,133,133] f(e,f(e,f(e,f(f(f(x,e),y),e))))=f(x,f(e,f(e,f(e,f(y,e))))). 301 [para_from,269.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,e),y)))=f(e,f(e,f(e,y))). 305 [back_demod,244,demod,300,300,67] f(f(x,e),f(f(x,e),f(x,e)))=f(x,f(f(x,x),e)). 312,311 [para_into,282.1.1.1.2.2,282.1.1] f(f(x,f(f(x,x),y)),e)=f(f(x,x),f(f(x,y),e)). 318,317 [back_demod,282,demod,312] f(f(x,x),f(f(x,f(f(x,y),e)),e))=y. 319 [back_demod,254,demod,312] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,y),e)). 328,327 [back_demod,173,demod,312] f(x,f(f(x,x),f(f(x,y),e)))=f(e,f(e,f(e,f(y,e)))). 353 [para_from,248.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,y),z)))=f(e,f(e,f(f(e,y),z))). 366,365 [para_from,301.1.1,227.1.1.1.2.2.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,y))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,e),y)). 371 [back_demod,319,demod,366] f(f(x,x),f(f(x,e),f(y,e)))=f(f(x,x),f(f(x,y),e)). 487 [para_from,285.1.1,132.1.1.1,demod,312,133] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(f(e,y),z),e))). 635,634 [para_into,353.1.1.2,231.1.1,flip.1] f(e,f(e,f(f(e,x),f(f(x,e),e))))=f(x,x). 672,671 [para_into,634.1.1,285.1.1] f(x,f(f(x,x),f(f(x,y),f(f(y,e),e))))=f(y,y). 703 [para_from,671.1.1,16.1.1.2.1,demod,328,flip.1] f(e,f(e,f(e,f(f(f(x,y),f(f(y,e),e)),e))))=f(x,f(f(y,y),e)). 793 [para_from,371.1.1,317.1.1.2.1.2.1,demod,318] f(f(x,y),e)=f(f(x,e),f(y,e)). 834,833 [para_into,793.1.1,311.1.1,flip.1] f(f(x,e),f(f(f(x,x),y),e))=f(f(x,x),f(f(x,y),e)). 899,898 [para_from,793.1.1,16.1.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e)))=f(x,f(f(x,e),f(y,e))). 900 [para_from,793.1.1,703.1.1.2.2.2.1.1,demod,9,9,67,9,9] f(f(x,e),f(y,e))=f(f(x,y),e). 917 [back_demod,58,demod,899] f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 958,957 [para_into,900.1.1.1,132.1.1,flip.1] f(f(f(e,x),y),e)=f(f(e,f(x,e)),f(y,e)). 1014,1013 [back_demod,487,demod,958] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(e,f(y,e)),f(z,e)))). 1130 [para_into,917.1.1.2.2.1.1,671.1.1,demod,834,1014,635,672,672] f(e,f(f(e,f(e,f(x,f(f(y,e),f(y,e))))),f(f(f(y,y),e),f(f(f(y,y),e),f(f(y,y),e)))))=x. 1242 [para_into,1130.1.1.2.1.2.2,305.1.1,demod,22,flip.1] f(x,e)=x. 1244 [binary,1242.1,4.1] $ANS(rid). ------------ end of proof ------------- -------- PROOF -------- 1405 [binary,1403.1,2.1] $ANS(exp4). ----> UNIT CONFLICT at 0.52 sec ----> 1405 [binary,1403.1,2.1] $ANS(exp4). Length of proof is 61. Level of proof is 20. ---------------- PROOF ---------------- 2 [] f(a,f(a,f(a,a)))!=e|$ANS(exp4). 7,6 [] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. 9,8 [] f(e,e)=e. 10 [para_into,6.1.1.2.1.2,6.1.1] f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))). 11 [para_into,10.1.1.2.1,6.1.1] f(x,f(y,f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z))). 16 [para_from,8.1.1,10.1.1.2.2.1.2,demod,9,9,9,9,9,9,9] f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))). 17 [para_from,8.1.1,6.1.1.2.2.2,demod,9] f(x,f(f(x,f(f(x,x),f(y,e))),e))=y. 19 [para_from,8.1.1,6.1.1.2.1.2.2,demod,9,9] f(x,f(f(x,f(f(x,x),e)),e))=e. 22,21 [para_from,8.1.1,6.1.1.2.1.2.1] f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x. 23 [para_into,16.1.1.2.1,16.1.1] f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,y),e),e))). 24 [para_into,16.1.1.2.1,6.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e)))=f(x,f(y,e)). 30 [para_into,11.1.1,10.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z))),u)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,u))). 49 [para_from,19.1.1,10.1.1.2.1] f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))). 58 [para_into,21.1.1.2.1.2.2,16.1.1] f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 63,62 [para_into,21.1.1.2.1.2,17.1.1,demod,9,9,9] f(e,f(f(e,x),e))=f(e,f(e,f(x,e))). 67,66 [para_into,21.1.1.2.2.2,8.1.1,demod,9,63,63] f(e,f(e,f(e,f(f(x,e),e))))=x. 94 [para_into,23.1.1.2.1.1,8.1.1,demod,9,9,9,63,63,67,9,9,9,9,flip.1] f(e,f(e,f(f(f(e,x),e),e)))=x. 122,121 [para_into,94.1.1.2.2.1.1,94.1.1,flip.1] f(e,f(f(f(e,x),e),e))=f(e,f(e,f(f(x,e),e))). 128,127 [para_into,94.1.1.2.2.1.1,49.1.1,demod,9,9,9,9,9,9,9,9,122,122,122,67,flip.1] f(e,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))))=f(e,f(e,x)). 130,129 [para_into,94.1.1.2.2.1.1,23.1.1,demod,9,9,9,9,122,67,9,9,9,9,flip.1] f(f(e,f(e,f(x,e))),e)=f(e,f(e,f(f(x,e),e))). 133,132 [para_into,94.1.1.2.2.1.1,16.1.1,demod,9,9,9,9,130,130,67,flip.1] f(f(e,x),e)=f(e,f(x,e)). 136,135 [para_into,94.1.1.2.2.1.1,10.1.1,demod,9,9,9,9,133,133,133,133,67,flip.1] f(f(e,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y)))))=f(e,f(x,y)). 137 [back_demod,49,demod,128,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))). 147 [para_from,132.1.1,17.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y). 157 [para_from,137.1.1,17.1.1.2.1,demod,9,9,flip.1] f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)). 173 [para_into,147.1.1.2.1.2.2,23.1.1,demod,9,9,9,9,133,133,67,9,9,9,9] f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))). 178 [para_into,157.1.1.1,16.1.1] f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)). 200,199 [para_into,173.1.1,16.1.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),y),e)))=f(e,f(e,f(e,f(y,e)))). 227 [para_from,30.1.1,6.1.1.2.1,demod,7,flip.1] f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z)))=y. 231 [para_from,178.1.1,173.1.1.2,demod,67] f(f(x,x),f(f(x,x),f(f(x,e),e)))=x. 244 [para_from,231.1.1,24.1.1.2.2.1.1.2,demod,200] f(e,f(e,f(e,f(f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))),e))))=f(x,f(f(x,x),e)). 248 [para_into,227.1.1.1.2.1,8.1.1] f(f(e,f(e,f(f(e,x),y))),f(y,f(y,y)))=x. 254 [para_into,227.1.1.1.2.2.1,173.1.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,f(f(x,x),y)),e). 269 [para_into,227.1.1.1.2.2.1,8.1.1,demod,9] f(f(e,f(e,f(e,x))),f(x,f(x,x)))=e. 275,274 [para_into,227.1.1.1.2.2,227.1.1] f(f(x,f(f(x,x),y)),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z)))))=f(f(x,x),f(f(x,y),z)). 282 [para_into,227.1.1.2.2,8.1.1,demod,9] f(f(x,f(f(x,x),f(f(x,y),e))),e)=y. 285 [para_from,227.1.1,21.1.1.2.1.2.2,demod,136] f(e,f(e,f(f(e,x),y)))=f(z,f(f(z,z),f(f(z,x),y))). 300,299 [para_from,269.1.1,24.1.1.2.2.1.1.2.2,demod,275,200,133,133,133] f(e,f(e,f(e,f(f(f(x,e),y),e))))=f(x,f(e,f(e,f(e,f(y,e))))). 301 [para_from,269.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,e),y)))=f(e,f(e,f(e,y))). 305 [back_demod,244,demod,300,300,67] f(f(x,e),f(f(x,e),f(x,e)))=f(x,f(f(x,x),e)). 312,311 [para_into,282.1.1.1.2.2,282.1.1] f(f(x,f(f(x,x),y)),e)=f(f(x,x),f(f(x,y),e)). 318,317 [back_demod,282,demod,312] f(f(x,x),f(f(x,f(f(x,y),e)),e))=y. 319 [back_demod,254,demod,312] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,y),e)). 328,327 [back_demod,173,demod,312] f(x,f(f(x,x),f(f(x,y),e)))=f(e,f(e,f(e,f(y,e)))). 353 [para_from,248.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,y),z)))=f(e,f(e,f(f(e,y),z))). 366,365 [para_from,301.1.1,227.1.1.1.2.2.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,y))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,e),y)). 371 [back_demod,319,demod,366] f(f(x,x),f(f(x,e),f(y,e)))=f(f(x,x),f(f(x,y),e)). 387 [para_from,305.1.1,269.1.1.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,x),e)))=e. 487 [para_from,285.1.1,132.1.1.1,demod,312,133] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(f(e,y),z),e))). 635,634 [para_into,353.1.1.2,231.1.1,flip.1] f(e,f(e,f(f(e,x),f(f(x,e),e))))=f(x,x). 672,671 [para_into,634.1.1,285.1.1] f(x,f(f(x,x),f(f(x,y),f(f(y,e),e))))=f(y,y). 703 [para_from,671.1.1,16.1.1.2.1,demod,328,flip.1] f(e,f(e,f(e,f(f(f(x,y),f(f(y,e),e)),e))))=f(x,f(f(y,y),e)). 793 [para_from,371.1.1,317.1.1.2.1.2.1,demod,318] f(f(x,y),e)=f(f(x,e),f(y,e)). 834,833 [para_into,793.1.1,311.1.1,flip.1] f(f(x,e),f(f(f(x,x),y),e))=f(f(x,x),f(f(x,y),e)). 881 [para_from,793.1.1,387.1.1.2.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,e),f(x,e))))=e. 899,898 [para_from,793.1.1,16.1.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e)))=f(x,f(f(x,e),f(y,e))). 900 [para_from,793.1.1,703.1.1.2.2.2.1.1,demod,9,9,67,9,9] f(f(x,e),f(y,e))=f(f(x,y),e). 917 [back_demod,58,demod,899] f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 958,957 [para_into,900.1.1.1,132.1.1,flip.1] f(f(f(e,x),y),e)=f(f(e,f(x,e)),f(y,e)). 1014,1013 [back_demod,487,demod,958] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(e,f(y,e)),f(z,e)))). 1130 [para_into,917.1.1.2.2.1.1,671.1.1,demod,834,1014,635,672,672] f(e,f(f(e,f(e,f(x,f(f(y,e),f(y,e))))),f(f(f(y,y),e),f(f(f(y,y),e),f(f(y,y),e)))))=x. 1243,1242 [para_into,1130.1.1.2.1.2.2,305.1.1,demod,22,flip.1] f(x,e)=x. 1250,1249 [para_into,1130.1.1.2.2.1.1,8.1.1,demod,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243] f(e,f(e,f(e,x)))=x. 1403 [back_demod,881,demod,1243,1250,1243,1243] f(x,f(x,f(x,x)))=e. 1405 [binary,1403.1,2.1] $ANS(exp4). ------------ end of proof ------------- -------- PROOF -------- 1460 [binary,1458.1,3.1] $ANS(lid). ----> UNIT CONFLICT at 0.53 sec ----> 1460 [binary,1458.1,3.1] $ANS(lid). Length of proof is 122. Level of proof is 28. ---------------- PROOF ---------------- 3 [] f(e,a)!=a|$ANS(lid). 7,6 [] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. 9,8 [] f(e,e)=e. 10 [para_into,6.1.1.2.1.2,6.1.1] f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))). 11 [para_into,10.1.1.2.1,6.1.1] f(x,f(y,f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z))). 16 [para_from,8.1.1,10.1.1.2.2.1.2,demod,9,9,9,9,9,9,9] f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))). 17 [para_from,8.1.1,6.1.1.2.2.2,demod,9] f(x,f(f(x,f(f(x,x),f(y,e))),e))=y. 19 [para_from,8.1.1,6.1.1.2.1.2.2,demod,9,9] f(x,f(f(x,f(f(x,x),e)),e))=e. 22,21 [para_from,8.1.1,6.1.1.2.1.2.1] f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x. 23 [para_into,16.1.1.2.1,16.1.1] f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,y),e),e))). 24 [para_into,16.1.1.2.1,6.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e)))=f(x,f(y,e)). 30 [para_into,11.1.1,10.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z))),u)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,u))). 45 [para_from,19.1.1,17.1.1.2.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),e))=f(x,f(f(x,e),e)). 49 [para_from,19.1.1,10.1.1.2.1] f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))). 58 [para_into,21.1.1.2.1.2.2,16.1.1] f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 61,60 [para_into,21.1.1.2.1.2,21.1.1] f(e,f(f(e,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(e,f(e,f(x,y))). 63,62 [para_into,21.1.1.2.1.2,17.1.1,demod,9,9,9] f(e,f(f(e,x),e))=f(e,f(e,f(x,e))). 67,66 [para_into,21.1.1.2.2.2,8.1.1,demod,9,63,63] f(e,f(e,f(e,f(f(x,e),e))))=x. 70 [para_into,21.1.1,10.1.1,demod,9,9,9,9] f(e,f(e,f(f(e,f(x,f(y,f(y,y)))),y)))=x. 81 [para_from,45.1.1,17.1.1.2.1.2] f(x,f(f(x,f(x,f(f(x,e),e))),e))=f(f(x,x),f(x,x)). 93 [para_from,58.1.1,21.1.1.2.1.2,demod,61] f(e,f(e,f(x,f(f(x,y),e))))=f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))). 94 [para_into,23.1.1.2.1.1,8.1.1,demod,9,9,9,63,63,67,9,9,9,9,flip.1] f(e,f(e,f(f(f(e,x),e),e)))=x. 107 [para_from,70.1.1,16.1.1.2.1,demod,9,9,9,9,63,flip.1] f(e,f(e,f(e,f(f(f(e,f(x,f(y,f(y,y)))),y),e))))=f(e,f(x,e)). 122,121 [para_into,94.1.1.2.2.1.1,94.1.1,flip.1] f(e,f(f(f(e,x),e),e))=f(e,f(e,f(f(x,e),e))). 128,127 [para_into,94.1.1.2.2.1.1,49.1.1,demod,9,9,9,9,9,9,9,9,122,122,122,67,flip.1] f(e,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))))=f(e,f(e,x)). 130,129 [para_into,94.1.1.2.2.1.1,23.1.1,demod,9,9,9,9,122,67,9,9,9,9,flip.1] f(f(e,f(e,f(x,e))),e)=f(e,f(e,f(f(x,e),e))). 133,132 [para_into,94.1.1.2.2.1.1,16.1.1,demod,9,9,9,9,130,130,67,flip.1] f(f(e,x),e)=f(e,f(x,e)). 136,135 [para_into,94.1.1.2.2.1.1,10.1.1,demod,9,9,9,9,133,133,133,133,67,flip.1] f(f(e,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y)))))=f(e,f(x,y)). 137 [back_demod,49,demod,128,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))). 147 [para_from,132.1.1,17.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y). 158,157 [para_from,137.1.1,17.1.1.2.1,demod,9,9,flip.1] f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)). 167 [back_demod,19,demod,158] f(x,f(f(x,x),f(f(x,e),e)))=e. 173 [para_into,147.1.1.2.1.2.2,23.1.1,demod,9,9,9,9,133,133,67,9,9,9,9] f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))). 178 [para_into,157.1.1.1,16.1.1] f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)). 186 [para_into,167.1.1.2.2.1,132.1.1,demod,133] f(f(e,x),f(f(f(e,x),f(e,x)),f(e,f(f(x,e),e))))=e. 190 [para_into,173.1.1.2.1.2,173.1.1,demod,67] f(x,f(f(x,f(e,f(e,f(e,f(y,e))))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),y)). 200,199 [para_into,173.1.1,16.1.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),y),e)))=f(e,f(e,f(e,f(y,e)))). 205 [para_from,173.1.1,10.1.1.2.1,demod,136,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),y)),e),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 227 [para_from,30.1.1,6.1.1.2.1,demod,7,flip.1] f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z)))=y. 231 [para_from,178.1.1,173.1.1.2,demod,67] f(f(x,x),f(f(x,x),f(f(x,e),e)))=x. 244 [para_from,231.1.1,24.1.1.2.2.1.1.2,demod,200] f(e,f(e,f(e,f(f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))),e))))=f(x,f(f(x,x),e)). 248 [para_into,227.1.1.1.2.1,8.1.1] f(f(e,f(e,f(f(e,x),y))),f(y,f(y,y)))=x. 254 [para_into,227.1.1.1.2.2.1,173.1.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,f(f(x,x),y)),e). 257,256 [para_into,227.1.1.1.2.2.1,167.1.1] f(f(x,f(f(x,x),f(e,y))),f(y,f(y,y)))=f(f(x,x),f(f(x,e),e)). 269 [para_into,227.1.1.1.2.2.1,8.1.1,demod,9] f(f(e,f(e,f(e,x))),f(x,f(x,x)))=e. 275,274 [para_into,227.1.1.1.2.2,227.1.1] f(f(x,f(f(x,x),y)),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z)))))=f(f(x,x),f(f(x,y),z)). 282 [para_into,227.1.1.2.2,8.1.1,demod,9] f(f(x,f(f(x,x),f(f(x,y),e))),e)=y. 285 [para_from,227.1.1,21.1.1.2.1.2.2,demod,136] f(e,f(e,f(f(e,x),y)))=f(z,f(f(z,z),f(f(z,x),y))). 293 [para_into,269.1.1.1,66.1.1] f(x,f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))))=e. 300,299 [para_from,269.1.1,24.1.1.2.2.1.1.2.2,demod,275,200,133,133,133] f(e,f(e,f(e,f(f(f(x,e),y),e))))=f(x,f(e,f(e,f(e,f(y,e))))). 301 [para_from,269.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,e),y)))=f(e,f(e,f(e,y))). 305 [back_demod,244,demod,300,300,67] f(f(x,e),f(f(x,e),f(x,e)))=f(x,f(f(x,x),e)). 312,311 [para_into,282.1.1.1.2.2,282.1.1] f(f(x,f(f(x,x),y)),e)=f(f(x,x),f(f(x,y),e)). 318,317 [back_demod,282,demod,312] f(f(x,x),f(f(x,f(f(x,y),e)),e))=y. 319 [back_demod,254,demod,312] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,y),e)). 321 [back_demod,205,demod,312] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(f(x,y),e)),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 328,327 [back_demod,173,demod,312] f(x,f(f(x,x),f(f(x,y),e)))=f(e,f(e,f(e,f(y,e)))). 340 [para_into,317.1.1.2.1,45.1.1] f(f(f(x,x),f(x,x)),f(f(x,f(f(x,e),e)),e))=f(x,x). 353 [para_from,248.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,y),z)))=f(e,f(e,f(f(e,y),z))). 366,365 [para_from,301.1.1,227.1.1.1.2.2.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,y))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,e),y)). 371 [back_demod,319,demod,366] f(f(x,x),f(f(x,e),f(y,e)))=f(f(x,x),f(f(x,y),e)). 387 [para_from,305.1.1,269.1.1.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,x),e)))=e. 454 [para_from,186.1.1,6.1.1.2.1] f(f(e,x),f(e,f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e)))))=e. 487 [para_from,285.1.1,132.1.1.1,demod,312,133] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(f(e,y),z),e))). 490 [para_from,285.1.1,317.1.1.2.1.2.1,demod,9,312,133] f(e,f(e,f(f(f(x,x),f(f(x,f(f(x,y),z)),e)),e)))=f(e,f(f(e,y),z)). 503,502 [para_from,293.1.1,227.1.1.1.2.2.1,demod,257,flip.1] f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e)))=f(f(x,x),f(f(x,e),e)). 504 [back_demod,454,demod,503] f(f(e,x),f(e,f(f(x,x),f(f(x,e),e))))=e. 555 [para_from,504.1.1,248.1.1.1.2.2,demod,9,9] f(e,f(f(e,f(f(x,x),f(f(x,e),e))),f(f(e,f(f(x,x),f(f(x,e),e))),f(e,f(f(x,x),f(f(x,e),e))))))=x. 577 [para_into,327.1.1.2.2.1,6.1.1,flip.1] f(e,f(e,f(e,f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,x),f(y,e))). 591 [para_from,93.1.1,16.1.1.2.1,demod,133,133,312,9,9,9,9,133] f(e,f(e,f(e,f(f(f(x,x),f(x,x)),f(f(f(x,x),f(y,e)),e)))))=f(e,f(e,f(e,f(f(x,f(f(x,y),e)),e)))). 600,599 [para_into,353.1.1.2.2.1,327.1.1,flip.1] f(e,f(e,f(f(e,f(f(x,x),f(f(x,y),e))),z)))=f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))). 610,609 [para_into,353.1.1.2.2.1,231.1.1,demod,600,9,9,9,9] f(f(x,x),f(f(f(x,x),f(x,x)),f(x,y)))=f(x,f(f(x,x),f(e,y))). 635,634 [para_into,353.1.1.2,231.1.1,flip.1] f(e,f(e,f(f(e,x),f(f(x,e),e))))=f(x,x). 653 [para_from,353.1.1,16.1.1.2.1,demod,133,133,328] f(x,f(e,f(e,f(f(f(e,y),z),e))))=f(e,f(e,f(e,f(f(f(x,y),z),e)))). 672,671 [para_into,634.1.1,285.1.1] f(x,f(f(x,x),f(f(x,y),f(f(y,e),e))))=f(y,y). 687 [para_from,634.1.1,10.1.1.2.1,demod,9,9,9,9] f(e,f(f(x,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(e,f(e,f(f(e,f(f(e,x),f(f(x,e),e))),y))). 688 [para_into,671.1.1.2.2.1,231.1.1,demod,610] f(x,f(f(x,x),f(e,f(f(f(f(x,x),f(f(x,e),e)),e),e))))=f(f(f(x,x),f(f(x,e),e)),f(f(x,x),f(f(x,e),e))). 703 [para_from,671.1.1,16.1.1.2.1,demod,328,flip.1] f(e,f(e,f(e,f(f(f(x,y),f(f(y,e),e)),e))))=f(x,f(f(y,y),e)). 718 [para_from,703.1.1,132.1.1.1,demod,133,133,67] f(f(x,f(f(y,y),e)),e)=f(f(x,y),f(f(y,e),e)). 722 [para_into,718.1.1,132.1.1] f(e,f(f(f(x,x),e),e))=f(f(e,x),f(f(x,e),e)). 748 [para_into,107.1.1.2.2.2.1.1,58.1.1,demod,133,133,312] f(e,f(e,f(e,f(f(x,f(f(x,y),e)),e))))=f(e,f(e,f(e,f(f(f(x,x),f(x,x)),f(f(f(x,x),f(y,e)),e))))). 763 [para_from,722.1.1,285.1.1.2.2.1,flip.1] f(x,f(f(x,x),f(f(x,f(f(f(y,y),e),e)),z)))=f(e,f(e,f(f(f(e,y),f(f(y,e),e)),z))). 793 [para_from,371.1.1,317.1.1.2.1.2.1,demod,318] f(f(x,y),e)=f(f(x,e),f(y,e)). 830 [para_into,793.1.1.1,6.1.1,flip.1] f(f(x,e),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e))=f(y,e). 834,833 [para_into,793.1.1,311.1.1,flip.1] f(f(x,e),f(f(f(x,x),y),e))=f(f(x,x),f(f(x,y),e)). 842 [para_from,793.1.1,340.1.1.2] f(f(f(x,x),f(x,x)),f(f(x,e),f(f(f(x,e),e),e)))=f(x,x). 881 [para_from,793.1.1,387.1.1.2.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,e),f(x,e))))=e. 899,898 [para_from,793.1.1,16.1.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e)))=f(x,f(f(x,e),f(y,e))). 900 [para_from,793.1.1,703.1.1.2.2.2.1.1,demod,9,9,67,9,9] f(f(x,e),f(y,e))=f(f(x,y),e). 917 [back_demod,58,demod,899] f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 955,954 [para_into,900.1.1.1,311.1.1,flip.1] f(f(f(x,f(f(x,x),y)),z),e)=f(f(f(x,x),f(f(x,y),e)),f(z,e)). 958,957 [para_into,900.1.1.1,132.1.1,flip.1] f(f(f(e,x),y),e)=f(f(e,f(x,e)),f(y,e)). 966,965 [para_into,900.1.1.2,132.1.1,flip.1] f(f(x,f(e,y)),e)=f(f(x,e),f(e,f(y,e))). 974 [back_demod,830,demod,955] f(f(x,e),f(f(f(x,x),f(f(x,f(y,z)),e)),f(f(z,f(z,z)),e)))=f(y,e). 978 [back_demod,577,demod,955] f(e,f(e,f(e,f(f(f(x,x),f(f(x,f(y,z)),e)),f(f(z,f(z,z)),e)))))=f(x,f(f(x,x),f(y,e))). 997 [back_demod,653,demod,958,flip.1] f(e,f(e,f(e,f(f(f(x,y),z),e))))=f(x,f(e,f(e,f(f(e,f(y,e)),f(z,e))))). 1014,1013 [back_demod,487,demod,958] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(e,f(y,e)),f(z,e)))). 1034,1033 [back_demod,190,demod,966,966,9,67,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),y))=f(x,f(f(x,e),y)). 1040 [back_demod,490,demod,1014,966,9,958] f(e,f(e,f(e,f(e,f(f(e,f(f(x,e),e)),f(f(y,e),e))))))=f(e,f(f(e,x),y)). 1060 [back_demod,321,demod,1034] f(x,f(f(x,e),f(f(f(x,x),f(f(x,y),e)),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 1076 [para_from,900.1.1,81.1.1.2.1.2] f(f(x,e),f(f(f(x,e),f(f(x,f(f(x,e),e)),e)),e))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))). 1081 [para_from,900.1.1,718.1.1.1.2.1] f(f(x,f(f(f(y,y),e),e)),e)=f(f(x,f(y,e)),f(f(f(y,e),e),e)). 1109 [para_from,900.1.1,311.1.1.1.2.1] f(f(f(x,e),f(f(f(x,x),e),y)),e)=f(f(f(x,e),f(x,e)),f(f(f(x,e),y),e)). 1130 [para_into,917.1.1.2.2.1.1,671.1.1,demod,834,1014,635,672,672] f(e,f(f(e,f(e,f(x,f(f(y,e),f(y,e))))),f(f(f(y,y),e),f(f(f(y,y),e),f(f(y,y),e)))))=x. 1195,1194 [para_into,1033.1.1,353.1.1,flip.1] f(x,f(f(x,e),f(f(f(x,x),y),z)))=f(e,f(e,f(f(e,y),z))). 1199,1198 [back_demod,1060,demod,1195] f(e,f(e,f(f(e,f(f(x,y),e)),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 1207 [back_demod,1040,demod,1199,9,9,9] f(e,f(e,f(x,f(e,f(e,f(f(y,e),e))))))=f(e,f(f(e,x),y)). 1232 [para_into,1076.1.1.2,793.1.1] f(f(x,e),f(f(f(x,e),e),f(f(f(x,f(f(x,e),e)),e),e)))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))). 1243,1242 [para_into,1130.1.1.2.1.2.2,305.1.1,demod,22,flip.1] f(x,e)=x. 1250,1249 [para_into,1130.1.1.2.2.1.1,8.1.1,demod,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243] f(e,f(e,f(e,x)))=x. 1266,1265 [back_demod,1232,demod,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,flip.1] f(f(x,x),f(x,x))=f(x,f(x,f(x,x))). 1287,1286 [back_demod,1207,demod,1243,1243,flip.1] f(e,f(f(e,x),y))=f(e,f(e,f(x,f(e,f(e,y))))). 1345,1344 [back_demod,1109,demod,1243,1243,1243,1243,1243,1243,1243,flip.1] f(f(x,x),f(x,y))=f(x,f(f(x,x),y)). 1355,1354 [back_demod,1081,demod,1243,1243,1243,1243,1243,1243,1243,flip.1] f(f(x,y),y)=f(x,f(y,y)). 1376,1375 [back_demod,997,demod,1243,1250,1243,1243,1287,1250] f(f(x,y),z)=f(x,f(y,f(e,f(e,z)))). 1382,1381 [back_demod,978,demod,1243,1345,1376,1243,1376,1376,1250,1376,1250,1376,1376,1250,1376,1250,1250,1243,1376] f(x,f(x,f(x,f(e,f(e,f(y,f(z,f(z,f(z,z)))))))))=f(x,f(x,f(x,f(e,f(e,y))))). 1384,1383 [back_demod,974,demod,1243,1243,1345,1376,1243,1376,1376,1250,1376,1250,1376,1376,1250,1376,1250,1382,1243] f(x,f(x,f(x,f(x,f(e,f(e,y))))))=y. 1404,1403 [back_demod,881,demod,1243,1250,1243,1243] f(x,f(x,f(x,x)))=e. 1419,1418 [back_demod,842,demod,1266,1404,1243,1243,1243,1243] f(e,f(x,x))=f(x,x). 1426,1425 [back_demod,763,demod,1243,1243,1376,1376,1250,1345,1376,1384,1243,1243,1355,1419,1376,flip.1] f(e,f(e,f(x,f(x,f(e,f(e,y))))))=f(x,f(x,f(e,y))). 1430,1429 [back_demod,748,demod,1243,1243,1250,1266,1404,1243,1376,1243,1426,flip.1] f(e,f(e,f(x,f(x,f(e,y)))))=f(x,f(x,y)). 1440,1439 [back_demod,688,demod,1243,1243,1355,1243,1243,1376,1250,1404,1243,1243,1243,1355,1243,1243,1355,1376,1376,1250,flip.1] f(x,f(x,f(x,f(e,f(x,f(x,x))))))=f(x,x). 1442,1441 [back_demod,687,demod,1376,1376,1250,1440,1355,1266,1404,1243,1376,1243,1243,1355,1419,1419,1376,1430] f(e,f(x,f(x,f(e,f(e,y)))))=f(x,f(x,f(e,y))). 1453,1452 [back_demod,591,demod,1266,1404,1243,1376,1243,1442,1430,1243,1243,1250] f(e,f(x,f(x,y)))=f(x,f(x,y)). 1458 [back_demod,555,demod,1243,1243,1355,1453,1243,1243,1355,1453,1243,1243,1355,1453,1376,1453,1453,1345,1266,1404,1243,1355,1266,1404,1243] f(e,x)=x. 1460 [binary,1458.1,3.1] $ANS(lid). ------------ end of proof ------------- -------- PROOF -------- 1477 [binary,1475.1,1.1] $ANS(assoc). 1420 back subsumes 1389. ----> UNIT CONFLICT at 0.59 sec ----> 1477 [binary,1475.1,1.1] $ANS(assoc). Length of proof is 123. Level of proof is 29. ---------------- PROOF ---------------- 1 [] f(f(a,b),c)!=f(a,f(b,c))|$ANS(assoc). 7,6 [] f(x,f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))))=y. 9,8 [] f(e,e)=e. 10 [para_into,6.1.1.2.1.2,6.1.1] f(x,f(f(x,y),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,z))). 11 [para_into,10.1.1.2.1,6.1.1] f(x,f(y,f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,u))),f(u,f(u,u))),z))). 16 [para_from,8.1.1,10.1.1.2.2.1.2,demod,9,9,9,9,9,9,9] f(x,f(f(x,y),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))). 17 [para_from,8.1.1,6.1.1.2.2.2,demod,9] f(x,f(f(x,f(f(x,x),f(y,e))),e))=y. 19 [para_from,8.1.1,6.1.1.2.1.2.2,demod,9,9] f(x,f(f(x,f(f(x,x),e)),e))=e. 22,21 [para_from,8.1.1,6.1.1.2.1.2.1] f(e,f(f(e,f(e,f(x,y))),f(y,f(y,y))))=x. 23 [para_into,16.1.1.2.1,16.1.1] f(x,f(f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,y),e),e))). 24 [para_into,16.1.1.2.1,6.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e)))=f(x,f(y,e)). 30 [para_into,11.1.1,10.1.1,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z))),u)))=f(f(x,x),f(f(f(x,x),f(x,x)),f(y,u))). 45 [para_from,19.1.1,17.1.1.2.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),e))=f(x,f(f(x,e),e)). 49 [para_from,19.1.1,10.1.1.2.1] f(x,f(e,f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y))). 58 [para_into,21.1.1.2.1.2.2,16.1.1] f(e,f(f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 61,60 [para_into,21.1.1.2.1.2,21.1.1] f(e,f(f(e,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(e,f(e,f(x,y))). 63,62 [para_into,21.1.1.2.1.2,17.1.1,demod,9,9,9] f(e,f(f(e,x),e))=f(e,f(e,f(x,e))). 67,66 [para_into,21.1.1.2.2.2,8.1.1,demod,9,63,63] f(e,f(e,f(e,f(f(x,e),e))))=x. 70 [para_into,21.1.1,10.1.1,demod,9,9,9,9] f(e,f(e,f(f(e,f(x,f(y,f(y,y)))),y)))=x. 81 [para_from,45.1.1,17.1.1.2.1.2] f(x,f(f(x,f(x,f(f(x,e),e))),e))=f(f(x,x),f(x,x)). 93 [para_from,58.1.1,21.1.1.2.1.2,demod,61] f(e,f(e,f(x,f(f(x,y),e))))=f(e,f(e,f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e))))). 94 [para_into,23.1.1.2.1.1,8.1.1,demod,9,9,9,63,63,67,9,9,9,9,flip.1] f(e,f(e,f(f(f(e,x),e),e)))=x. 107 [para_from,70.1.1,16.1.1.2.1,demod,9,9,9,9,63,flip.1] f(e,f(e,f(e,f(f(f(e,f(x,f(y,f(y,y)))),y),e))))=f(e,f(x,e)). 122,121 [para_into,94.1.1.2.2.1.1,94.1.1,flip.1] f(e,f(f(f(e,x),e),e))=f(e,f(e,f(f(x,e),e))). 128,127 [para_into,94.1.1.2.2.1.1,49.1.1,demod,9,9,9,9,9,9,9,9,122,122,122,67,flip.1] f(e,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))))=f(e,f(e,x)). 130,129 [para_into,94.1.1.2.2.1.1,23.1.1,demod,9,9,9,9,122,67,9,9,9,9,flip.1] f(f(e,f(e,f(x,e))),e)=f(e,f(e,f(f(x,e),e))). 133,132 [para_into,94.1.1.2.2.1.1,16.1.1,demod,9,9,9,9,130,130,67,flip.1] f(f(e,x),e)=f(e,f(x,e)). 136,135 [para_into,94.1.1.2.2.1.1,10.1.1,demod,9,9,9,9,133,133,133,133,67,flip.1] f(f(e,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y)))))=f(e,f(x,y)). 137 [back_demod,49,demod,128,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),e)),e),y)))=f(x,f(e,f(e,y))). 147 [para_from,132.1.1,17.1.1.2.1.2.2] f(x,f(f(x,f(f(x,x),f(e,f(y,e)))),e))=f(e,y). 158,157 [para_from,137.1.1,17.1.1.2.1,demod,9,9,flip.1] f(f(x,f(f(x,x),e)),e)=f(f(x,x),f(f(x,e),e)). 167 [back_demod,19,demod,158] f(x,f(f(x,x),f(f(x,e),e)))=e. 173 [para_into,147.1.1.2.1.2.2,23.1.1,demod,9,9,9,9,133,133,67,9,9,9,9] f(x,f(f(x,f(f(x,x),y)),e))=f(e,f(e,f(e,f(y,e)))). 178 [para_into,157.1.1.1,16.1.1] f(f(f(x,x),f(f(f(x,x),f(x,x)),f(x,e))),e)=f(f(x,x),f(f(x,e),e)). 186 [para_into,167.1.1.2.2.1,132.1.1,demod,133] f(f(e,x),f(f(f(e,x),f(e,x)),f(e,f(f(x,e),e))))=e. 190 [para_into,173.1.1.2.1.2,173.1.1,demod,67] f(x,f(f(x,f(e,f(e,f(e,f(y,e))))),e))=f(f(x,x),f(f(f(x,x),f(x,x)),y)). 200,199 [para_into,173.1.1,16.1.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),y),e)))=f(e,f(e,f(e,f(y,e)))). 205 [para_from,173.1.1,10.1.1.2.1,demod,136,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,f(f(x,x),y)),e),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 227 [para_from,30.1.1,6.1.1.2.1,demod,7,flip.1] f(f(x,f(f(x,x),f(f(x,y),z))),f(z,f(z,z)))=y. 231 [para_from,178.1.1,173.1.1.2,demod,67] f(f(x,x),f(f(x,x),f(f(x,e),e)))=x. 244 [para_from,231.1.1,24.1.1.2.2.1.1.2,demod,200] f(e,f(e,f(e,f(f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))),e))))=f(x,f(f(x,x),e)). 248 [para_into,227.1.1.1.2.1,8.1.1] f(f(e,f(e,f(f(e,x),y))),f(y,f(y,y)))=x. 254 [para_into,227.1.1.1.2.2.1,173.1.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,f(f(x,x),y)),e). 257,256 [para_into,227.1.1.1.2.2.1,167.1.1] f(f(x,f(f(x,x),f(e,y))),f(y,f(y,y)))=f(f(x,x),f(f(x,e),e)). 269 [para_into,227.1.1.1.2.2.1,8.1.1,demod,9] f(f(e,f(e,f(e,x))),f(x,f(x,x)))=e. 275,274 [para_into,227.1.1.1.2.2,227.1.1] f(f(x,f(f(x,x),y)),f(f(z,f(z,z)),f(f(z,f(z,z)),f(z,f(z,z)))))=f(f(x,x),f(f(x,y),z)). 282 [para_into,227.1.1.2.2,8.1.1,demod,9] f(f(x,f(f(x,x),f(f(x,y),e))),e)=y. 285 [para_from,227.1.1,21.1.1.2.1.2.2,demod,136] f(e,f(e,f(f(e,x),y)))=f(z,f(f(z,z),f(f(z,x),y))). 293 [para_into,269.1.1.1,66.1.1] f(x,f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e))))=e. 300,299 [para_from,269.1.1,24.1.1.2.2.1.1.2.2,demod,275,200,133,133,133] f(e,f(e,f(e,f(f(f(x,e),y),e))))=f(x,f(e,f(e,f(e,f(y,e))))). 301 [para_from,269.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,e),y)))=f(e,f(e,f(e,y))). 305 [back_demod,244,demod,300,300,67] f(f(x,e),f(f(x,e),f(x,e)))=f(x,f(f(x,x),e)). 312,311 [para_into,282.1.1.1.2.2,282.1.1] f(f(x,f(f(x,x),y)),e)=f(f(x,x),f(f(x,y),e)). 318,317 [back_demod,282,demod,312] f(f(x,x),f(f(x,f(f(x,y),e)),e))=y. 319 [back_demod,254,demod,312] f(f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,y),e)). 321 [back_demod,205,demod,312] f(f(x,x),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(f(x,y),e)),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 328,327 [back_demod,173,demod,312] f(x,f(f(x,x),f(f(x,y),e)))=f(e,f(e,f(e,f(y,e)))). 340 [para_into,317.1.1.2.1,45.1.1] f(f(f(x,x),f(x,x)),f(f(x,f(f(x,e),e)),e))=f(x,x). 353 [para_from,248.1.1,6.1.1.2.1.2.2,demod,275] f(x,f(f(x,x),f(f(x,y),z)))=f(e,f(e,f(f(e,y),z))). 366,365 [para_from,301.1.1,227.1.1.1.2.2.1] f(f(x,f(f(x,x),f(f(e,f(e,f(e,y))),z))),f(z,f(z,z)))=f(f(x,x),f(f(x,e),y)). 371 [back_demod,319,demod,366] f(f(x,x),f(f(x,e),f(y,e)))=f(f(x,x),f(f(x,y),e)). 387 [para_from,305.1.1,269.1.1.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,x),e)))=e. 454 [para_from,186.1.1,6.1.1.2.1] f(f(e,x),f(e,f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e)))))=e. 487 [para_from,285.1.1,132.1.1.1,demod,312,133] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(f(e,y),z),e))). 490 [para_from,285.1.1,317.1.1.2.1.2.1,demod,9,312,133] f(e,f(e,f(f(f(x,x),f(f(x,f(f(x,y),z)),e)),e)))=f(e,f(f(e,y),z)). 503,502 [para_from,293.1.1,227.1.1.1.2.2.1,demod,257,flip.1] f(f(f(x,e),e),f(f(f(x,e),e),f(f(x,e),e)))=f(f(x,x),f(f(x,e),e)). 504 [back_demod,454,demod,503] f(f(e,x),f(e,f(f(x,x),f(f(x,e),e))))=e. 555 [para_from,504.1.1,248.1.1.1.2.2,demod,9,9] f(e,f(f(e,f(f(x,x),f(f(x,e),e))),f(f(e,f(f(x,x),f(f(x,e),e))),f(e,f(f(x,x),f(f(x,e),e))))))=x. 577 [para_into,327.1.1.2.2.1,6.1.1,flip.1] f(e,f(e,f(e,f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e))))=f(x,f(f(x,x),f(y,e))). 591 [para_from,93.1.1,16.1.1.2.1,demod,133,133,312,9,9,9,9,133] f(e,f(e,f(e,f(f(f(x,x),f(x,x)),f(f(f(x,x),f(y,e)),e)))))=f(e,f(e,f(e,f(f(x,f(f(x,y),e)),e)))). 600,599 [para_into,353.1.1.2.2.1,327.1.1,flip.1] f(e,f(e,f(f(e,f(f(x,x),f(f(x,y),e))),z)))=f(x,f(f(x,x),f(f(e,f(e,f(e,f(y,e)))),z))). 610,609 [para_into,353.1.1.2.2.1,231.1.1,demod,600,9,9,9,9] f(f(x,x),f(f(f(x,x),f(x,x)),f(x,y)))=f(x,f(f(x,x),f(e,y))). 635,634 [para_into,353.1.1.2,231.1.1,flip.1] f(e,f(e,f(f(e,x),f(f(x,e),e))))=f(x,x). 653 [para_from,353.1.1,16.1.1.2.1,demod,133,133,328] f(x,f(e,f(e,f(f(f(e,y),z),e))))=f(e,f(e,f(e,f(f(f(x,y),z),e)))). 672,671 [para_into,634.1.1,285.1.1] f(x,f(f(x,x),f(f(x,y),f(f(y,e),e))))=f(y,y). 687 [para_from,634.1.1,10.1.1.2.1,demod,9,9,9,9] f(e,f(f(x,x),f(f(y,f(y,y)),f(f(y,f(y,y)),f(y,f(y,y))))))=f(e,f(e,f(f(e,f(f(e,x),f(f(x,e),e))),y))). 688 [para_into,671.1.1.2.2.1,231.1.1,demod,610] f(x,f(f(x,x),f(e,f(f(f(f(x,x),f(f(x,e),e)),e),e))))=f(f(f(x,x),f(f(x,e),e)),f(f(x,x),f(f(x,e),e))). 703 [para_from,671.1.1,16.1.1.2.1,demod,328,flip.1] f(e,f(e,f(e,f(f(f(x,y),f(f(y,e),e)),e))))=f(x,f(f(y,y),e)). 718 [para_from,703.1.1,132.1.1.1,demod,133,133,67] f(f(x,f(f(y,y),e)),e)=f(f(x,y),f(f(y,e),e)). 722 [para_into,718.1.1,132.1.1] f(e,f(f(f(x,x),e),e))=f(f(e,x),f(f(x,e),e)). 748 [para_into,107.1.1.2.2.2.1.1,58.1.1,demod,133,133,312] f(e,f(e,f(e,f(f(x,f(f(x,y),e)),e))))=f(e,f(e,f(e,f(f(f(x,x),f(x,x)),f(f(f(x,x),f(y,e)),e))))). 763 [para_from,722.1.1,285.1.1.2.2.1,flip.1] f(x,f(f(x,x),f(f(x,f(f(f(y,y),e),e)),z)))=f(e,f(e,f(f(f(e,y),f(f(y,e),e)),z))). 793 [para_from,371.1.1,317.1.1.2.1.2.1,demod,318] f(f(x,y),e)=f(f(x,e),f(y,e)). 830 [para_into,793.1.1.1,6.1.1,flip.1] f(f(x,e),f(f(f(x,f(f(x,x),f(y,z))),f(z,f(z,z))),e))=f(y,e). 834,833 [para_into,793.1.1,311.1.1,flip.1] f(f(x,e),f(f(f(x,x),y),e))=f(f(x,x),f(f(x,y),e)). 842 [para_from,793.1.1,340.1.1.2] f(f(f(x,x),f(x,x)),f(f(x,e),f(f(f(x,e),e),e)))=f(x,x). 881 [para_from,793.1.1,387.1.1.2.2] f(f(e,f(e,f(e,f(x,e)))),f(x,f(f(x,e),f(x,e))))=e. 899,898 [para_from,793.1.1,16.1.1.2,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),f(y,e)))=f(x,f(f(x,e),f(y,e))). 900 [para_from,793.1.1,703.1.1.2.2.2.1.1,demod,9,9,67,9,9] f(f(x,e),f(y,e))=f(f(x,y),e). 917 [back_demod,58,demod,899] f(e,f(f(e,f(e,f(x,f(f(x,e),f(y,e))))),f(f(f(x,y),e),f(f(f(x,y),e),f(f(x,y),e)))))=x. 955,954 [para_into,900.1.1.1,311.1.1,flip.1] f(f(f(x,f(f(x,x),y)),z),e)=f(f(f(x,x),f(f(x,y),e)),f(z,e)). 958,957 [para_into,900.1.1.1,132.1.1,flip.1] f(f(f(e,x),y),e)=f(f(e,f(x,e)),f(y,e)). 966,965 [para_into,900.1.1.2,132.1.1,flip.1] f(f(x,f(e,y)),e)=f(f(x,e),f(e,f(y,e))). 974 [back_demod,830,demod,955] f(f(x,e),f(f(f(x,x),f(f(x,f(y,z)),e)),f(f(z,f(z,z)),e)))=f(y,e). 978 [back_demod,577,demod,955] f(e,f(e,f(e,f(f(f(x,x),f(f(x,f(y,z)),e)),f(f(z,f(z,z)),e)))))=f(x,f(f(x,x),f(y,e))). 997 [back_demod,653,demod,958,flip.1] f(e,f(e,f(e,f(f(f(x,y),z),e))))=f(x,f(e,f(e,f(f(e,f(y,e)),f(z,e))))). 1014,1013 [back_demod,487,demod,958] f(f(x,x),f(f(x,f(f(x,y),z)),e))=f(e,f(e,f(f(e,f(y,e)),f(z,e)))). 1034,1033 [back_demod,190,demod,966,966,9,67,flip.1] f(f(x,x),f(f(f(x,x),f(x,x)),y))=f(x,f(f(x,e),y)). 1040 [back_demod,490,demod,1014,966,9,958] f(e,f(e,f(e,f(e,f(f(e,f(f(x,e),e)),f(f(y,e),e))))))=f(e,f(f(e,x),y)). 1060 [back_demod,321,demod,1034] f(x,f(f(x,e),f(f(f(x,x),f(f(x,y),e)),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 1076 [para_from,900.1.1,81.1.1.2.1.2] f(f(x,e),f(f(f(x,e),f(f(x,f(f(x,e),e)),e)),e))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))). 1081 [para_from,900.1.1,718.1.1.1.2.1] f(f(x,f(f(f(y,y),e),e)),e)=f(f(x,f(y,e)),f(f(f(y,e),e),e)). 1109 [para_from,900.1.1,311.1.1.1.2.1] f(f(f(x,e),f(f(f(x,x),e),y)),e)=f(f(f(x,e),f(x,e)),f(f(f(x,e),y),e)). 1130 [para_into,917.1.1.2.2.1.1,671.1.1,demod,834,1014,635,672,672] f(e,f(f(e,f(e,f(x,f(f(y,e),f(y,e))))),f(f(f(y,y),e),f(f(f(y,y),e),f(f(y,y),e)))))=x. 1195,1194 [para_into,1033.1.1,353.1.1,flip.1] f(x,f(f(x,e),f(f(f(x,x),y),z)))=f(e,f(e,f(f(e,y),z))). 1199,1198 [back_demod,1060,demod,1195] f(e,f(e,f(f(e,f(f(x,y),e)),z)))=f(x,f(e,f(f(e,f(e,f(y,e))),z))). 1207 [back_demod,1040,demod,1199,9,9,9] f(e,f(e,f(x,f(e,f(e,f(f(y,e),e))))))=f(e,f(f(e,x),y)). 1232 [para_into,1076.1.1.2,793.1.1] f(f(x,e),f(f(f(x,e),e),f(f(f(x,f(f(x,e),e)),e),e)))=f(f(f(x,e),f(x,e)),f(f(x,e),f(x,e))). 1243,1242 [para_into,1130.1.1.2.1.2.2,305.1.1,demod,22,flip.1] f(x,e)=x. 1250,1249 [para_into,1130.1.1.2.2.1.1,8.1.1,demod,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243] f(e,f(e,f(e,x)))=x. 1266,1265 [back_demod,1232,demod,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,1243,flip.1] f(f(x,x),f(x,x))=f(x,f(x,f(x,x))). 1287,1286 [back_demod,1207,demod,1243,1243,flip.1] f(e,f(f(e,x),y))=f(e,f(e,f(x,f(e,f(e,y))))). 1345,1344 [back_demod,1109,demod,1243,1243,1243,1243,1243,1243,1243,flip.1] f(f(x,x),f(x,y))=f(x,f(f(x,x),y)). 1355,1354 [back_demod,1081,demod,1243,1243,1243,1243,1243,1243,1243,flip.1] f(f(x,y),y)=f(x,f(y,y)). 1376,1375 [back_demod,997,demod,1243,1250,1243,1243,1287,1250] f(f(x,y),z)=f(x,f(y,f(e,f(e,z)))). 1382,1381 [back_demod,978,demod,1243,1345,1376,1243,1376,1376,1250,1376,1250,1376,1376,1250,1376,1250,1250,1243,1376] f(x,f(x,f(x,f(e,f(e,f(y,f(z,f(z,f(z,z)))))))))=f(x,f(x,f(x,f(e,f(e,y))))). 1384,1383 [back_demod,974,demod,1243,1243,1345,1376,1243,1376,1376,1250,1376,1250,1376,1376,1250,1376,1250,1382,1243] f(x,f(x,f(x,f(x,f(e,f(e,y))))))=y. 1404,1403 [back_demod,881,demod,1243,1250,1243,1243] f(x,f(x,f(x,x)))=e. 1419,1418 [back_demod,842,demod,1266,1404,1243,1243,1243,1243] f(e,f(x,x))=f(x,x). 1426,1425 [back_demod,763,demod,1243,1243,1376,1376,1250,1345,1376,1384,1243,1243,1355,1419,1376,flip.1] f(e,f(e,f(x,f(x,f(e,f(e,y))))))=f(x,f(x,f(e,y))). 1430,1429 [back_demod,748,demod,1243,1243,1250,1266,1404,1243,1376,1243,1426,flip.1] f(e,f(e,f(x,f(x,f(e,y)))))=f(x,f(x,y)). 1440,1439 [back_demod,688,demod,1243,1243,1355,1243,1243,1376,1250,1404,1243,1243,1243,1355,1243,1243,1355,1376,1376,1250,flip.1] f(x,f(x,f(x,f(e,f(x,f(x,x))))))=f(x,x). 1442,1441 [back_demod,687,demod,1376,1376,1250,1440,1355,1266,1404,1243,1376,1243,1243,1355,1419,1419,1376,1430] f(e,f(x,f(x,f(e,f(e,y)))))=f(x,f(x,f(e,y))). 1453,1452 [back_demod,591,demod,1266,1404,1243,1376,1243,1442,1430,1243,1243,1250] f(e,f(x,f(x,y)))=f(x,f(x,y)). 1459,1458 [back_demod,555,demod,1243,1243,1355,1453,1243,1243,1355,1453,1243,1243,1355,1453,1376,1453,1453,1345,1266,1404,1243,1355,1266,1404,1243] f(e,x)=x. 1475 [back_demod,1375,demod,1459,1459] f(f(x,y),z)=f(x,f(y,z)). 1477 [binary,1475.1,1.1] $ANS(assoc). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 80 clauses generated 4577 para_from generated 2170 para_into generated 2407 demod & eval rewrites 25809 clauses wt,lit,sk delete 2041 tautologies deleted 0 clauses forward subsumed 2517 (subsumed by sos) 109 unit deletions 0 factor simplifications 0 clauses kept 823 new demodulators 646 empty clauses 4 clauses back demodulated 801 clauses back subsumed 7 usable size 1 sos size 14 demodulators size 13 passive size 4 hot size 0 Kbytes malloced 4882 ----------- times (seconds) ----------- user CPU time 0.59 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) That finishes the proof of the theorem. Process 8512 finished Mon Aug 2 15:30:40 2004 otter-3.3f/examples/wos/rigorous.in0100644000076400007640000001530506005317051017031 0ustar mccunemccune% Input File for Rigorous Proof Checking the deducibility of various % axiom systems of two-valued sentential calculus set(hyper_res). % clear(print_kept). % assign(report, 60). assign(max_mem, 8000). assign(max_weight, 80). assign(max_proofs, -1). set(input_sos_first). set(order_history). weight_list(pick_and_purge). weight(P(rew($(0),$(0)),$(1)), 99). end_of_list. list(usable). -P(u,i(x,y)) | -P(v,x) | P(rew(u,v),y). -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(z,i(i(n(p),n(q)),i(q,p))) | $ANSWER(step_allBEH_Church_FL_18_35_49). -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | -P(z,i(n(n(p)),p)) | -P(u,i(p,n(n(p)))) | -P(v,i(i(p,q),i(n(q),n(p)))) | -P(w,i(i(p,i(q,r)),i(q,i(p,r)))) | $ANSWER(step_allFrege_18_35_39_40_46_21). % 21 is dependent. -P(x,i(q,i(p,q))) | -P(y,i(i(p,i(q,r)),i(q,i(p,r)))) | -P(z,i(i(q,r),i(i(p,q),i(p,r)))) | -P(u,i(p,i(n(p),q))) | -P(v,i(i(p,q),i(i(n(p),q),q))) | -P(w,i(i(p,i(p,q)),i(p,q))) | $ANSWER(step_allHilbert_18_21_22_3_54_30). % 30 is dependent. -P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | -P(z,i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANSWER(step_allLuka_x_19_37_59). -P(x,i(i(i(p,q),r),i(q,r))) | -P(y,i(i(i(p,q),r),i(n(p),r))) | -P(z,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANSWER(step_allWos_x_19_37_60). end_of_list. list(sos). P(c1,i(i(x,y),i(i(y,z),i(x,z)))). P(c2,i(i(n(x),x),x)). P(c3,i(x,i(n(x),y))). end_of_list. list(passive). % -P(x,i(i(i(i(q,r),i(p,r)),s),i(i(p,q),s))) | $ANS(neg_th_04). % -P(x,i(i(p,i(q,r)),i(i(s,q),i(p,i(s,r))))) | $ANS(neg_th_05). % -P(x,i(i(p,q),i(i(i(p,r),s),i(i(q,r),s)))) | $ANS(neg_th_06). % -P(x,i(i(t,i(i(p,r),s)),i(i(p,q),i(t,i(i(q,r),s))))) | $ANS(neg_th_07). % -P(x,i(i(q,r),i(i(p,q),i(i(r,s),i(p,s))))) | $ANS(neg_th_08). % -P(x,i(i(i(n(p),q),r),i(p,r))) | $ANS(neg_th_09). % -P(x,i(p,i(i(i(n(p),p),p),i(i(q,p),p)))) | $ANS(neg_th_10). % -P(x,i(i(q,i(i(n(p),p),p)),i(i(n(p),p),p))) | $ANS(neg_th_11). % -P(x,i(t,i(i(n(p),p),p))) | $ANS(neg_th_12). % -P(x,i(i(n(p),q),i(t,i(i(q,p),p)))) | $ANS(neg_th_13). % -P(x,i(i(i(t,i(i(q,p),p)),r),i(i(n(p),q),r))) | $ANS(neg_th_14). % -P(x,i(i(n(p),q),i(i(q,p),p))) | $ANS(neg_th_15). % -P(x,i(p,p)) | $ANS(neg_th_16). % -P(x,i(p,i(i(q,p),p))) | $ANS(neg_th_17). % -P(x,i(q,i(p,q))) | $ANS(neg_th_18). % -P(x,i(i(i(p,q),r),i(q,r))) | $ANS(neg_th_19). % -P(x,i(p,i(i(p,q),q))) | $ANS(neg_th_20). % -P(x,i(i(p,i(q,r)),i(q,i(p,r)))) | $ANS(neg_th_21). % -P(x,i(i(q,r),i(i(p,q),i(p,r)))) | $ANS(neg_th_22). % -P(x,i(i(i(q,i(p,r)),s),i(i(p,i(q,r)),s))) | $ANS(neg_th_23). % -P(x,i(i(i(p,q),p),p)) | $ANS(neg_th_24). % -P(x,i(i(i(p,r),s),i(i(p,q),i(i(q,r),s)))) | $ANS(neg_th_25). % -P(x,i(i(i(p,q),r),i(i(r,p),p))) | $ANS(neg_th_26). % -P(x,i(i(i(p,q),q),i(i(q,p),p))) | $ANS(neg_th_27). % -P(x,i(i(i(i(r,p),p),s),i(i(i(p,q),r),s))) | $ANS(neg_th_28). % -P(x,i(i(i(p,q),r),i(i(p,r),r))) | $ANS(neg_th_29). % -P(x,i(i(p,i(p,q)),i(p,q))) | $ANS(neg_th_30). % -P(x,i(i(p,s),i(i(i(p,q),r),i(i(s,r),r)))) | $ANS(neg_th_31). % -P(x,i(i(i(p,q),r),i(i(p,s),i(i(s,r),r)))) | $ANS(neg_th_32). % -P(x,i(i(p,s),i(i(s,i(q,i(p,r))),i(q,i(p,r))))) | $ANS(neg_th_33). % -P(x,i(i(s,i(q,i(p,r))),i(i(p,s),i(q,i(p,r))))) | $ANS(neg_th_34). % -P(x,i(i(p,i(q,r)),i(i(p,q),i(p,r)))) | $ANS(neg_th_35). % -P(x,i(n(p),i(p,q))) | $ANS(neg_th_36). % -P(x,i(i(i(p,q),r),i(n(p),r))) | $ANS(neg_th_37). % -P(x,i(i(p,n(p)),n(p))) | $ANS(neg_th_38). % -P(x,i(n(n(p)),p)) | $ANS(neg_th_39). % -P(x,i(p,n(n(p)))) | $ANS(neg_th_40). % -P(x,i(i(p,q),i(n(n(p)),q))) | $ANS(neg_th_41). % -P(x,i(i(i(n(n(p)),q),r),i(i(p,q),r))) | $ANS(neg_th_42). % -P(x,i(i(p,q),i(i(q,n(p)),n(p)))) | $ANS(neg_th_43). % -P(x,i(i(s,i(q,n(p))),i(i(p,q),i(s,n(p))))) | $ANS(neg_th_44). % -P(x,i(i(s,i(q,p)),i(i(n(p),q),i(s,p)))) | $ANS(neg_th_45). % -P(x,i(i(p,q),i(n(q),n(p)))) | $ANS(neg_th_46). % -P(x,i(i(p,n(q)),i(q,n(p)))) | $ANS(neg_th_47). % -P(x,i(i(n(p),q),i(n(q),p))) | $ANS(neg_th_48). % -P(x,i(i(n(p),n(q)),i(q,p))) | $ANS(neg_th_49). % -P(x,i(i(i(n(q),p),r),i(i(n(p),q),r))) | $ANS(neg_th_50). % -P(x,i(i(p,i(q,r)),i(p,i(n(r),n(q))))) | $ANS(neg_th_51). % -P(x,i(i(p,i(q,n(r))),i(p,i(r,n(q))))) | $ANS(neg_th_52). % -P(x,i(i(n(p),q),i(i(p,q),q))) | $ANS(neg_th_53). % -P(x,i(i(p,q),i(i(n(p),q),q))) | $ANS(neg_th_54). % -P(x,i(i(p,q),i(i(p,n(q)),n(p)))) | $ANS(neg_th_55). % -P(x,i(i(i(i(p,q),q),r),i(i(n(p),q),r))) | $ANS(neg_th_56). % -P(x,i(i(n(p),r),i(i(p,q),i(i(q,r),r)))) | $ANS(neg_th_57). % -P(x,i(i(i(i(p,q),i(i(q,r),r)),s),i(i(n(p),r),s))) | $ANS(neg_th_58). % -P(x,i(i(n(p),r),i(i(q,r),i(i(p,q),r)))) | $ANS(neg_th_59). % -P(x,i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r))))) | $ANS(neg_th_60). % -P(x,i(i(p,r),i(i(q,r),i(i(n(p),q),r)))) | $ANS(neg_th_61). % -P(x,i(i(n(n(p)),q),i(p,q))) | $ANS(neg_th_62). % -P(x,i(q,i(p,p))) | $ANS(neg_th_63). % -P(x,i(n(i(p,p)),q)) | $ANS(neg_th_64). % -P(x,i(i(n(q),n(i(p,p))),q)) | $ANS(neg_th_65). % -P(x,i(n(i(p,q)),p)) | $ANS(neg_th_66). % -P(x,i(n(i(p,q)),n(q))) | $ANS(neg_th_67). % -P(x,i(n(i(p,n(q))),q)) | $ANS(neg_th_68). % -P(x,i(p,i(n(q),n(i(p,q))))) | $ANS(neg_th_69). % -P(x,i(p,i(q,n(i(p,n(q)))))) | $ANS(neg_th_70). % -P(x,n(i(i(p,p),n(i(q,q))))) | $ANS(neg_th_71). end_of_list. list(demodulators). % Following essentially mirrrors the Lukasiewicz proof with history. EQ(rew(c1,c1),c4). EQ(rew(c4,c4),c5). EQ(rew(c4,c1),c6). EQ(rew(c5,c6),c7). EQ(rew(c7,c1),c8). EQ(rew(c1,c3),c9). EQ(rew(c9,c6),c10). EQ(rew(c10,c2),c10a). EQ(rew(c10a,c2),c11). EQ(rew(c9,c11),c12). EQ(rew(c7,c12),c13). EQ(rew(c1,c13),c14). EQ(rew(c14,c2),c15). EQ(rew(c9,c2),c16). EQ(rew(c9,c15),c17). EQ(rew(c5,c17),c17a). EQ(rew(c17a,c3),c18). EQ(rew(c1,c18),c19). EQ(rew(c19,c15),c20). EQ(rew(c5,c20),c21). EQ(rew(c21,c1),c22). EQ(rew(c1,c21),c23). EQ(rew(c23,c15),c24a). EQ(rew(c24a,c3),c24). EQ(rew(c21,c6),c25). EQ(rew(c25,c24),c26). EQ(rew(c1,c26),c28). EQ(rew(c28,c26),c29). EQ(rew(c29,c16),c30). EQ(rew(c7,c29),c31). EQ(rew(c21,c31),c32). EQ(rew(c32,c18),c33). EQ(rew(c21,c33),c34). EQ(rew(c34,c22),c35). EQ(rew(c21,c3),c36). EQ(rew(c1,c36),c37). EQ(rew(c26,c2),c38). EQ(rew(c37,c2),c39). EQ(rew(c9,c38),c40). EQ(rew(c1,c39),c41). EQ(rew(c1,c41),c42). EQ(rew(c42,c15),c43). EQ(rew(c5,c43),c44). EQ(rew(c5,c15),c45). EQ(rew(c44,c36),c46). EQ(rew(c44,c3),c47). EQ(rew(c45,c36),c48). EQ(rew(c45,c3),c49). EQ(rew(c1,c48),c50). EQ(rew(c22,c46),c51). EQ(rew(c22,c47),c52). EQ(rew(c50,c15),c53). EQ(rew(c21,c53),c54). EQ(rew(c44,c47),c55). EQ(rew(c1,c53),c56). EQ(rew(c56,c32),c57). EQ(rew(c1,c57),c58). EQ(rew(c58,c21),c59). EQ(rew(c22,c59),c60). EQ(rew(c60,c41),c61). EQ(rew(c1,c40),c62). EQ(rew(c21,c18),c63). EQ(rew(c48,c63),c64). EQ(rew(c61,c16),c64a). EQ(rew(c64a,c64),c65). EQ(rew(c48,c36),c66). EQ(rew(c46,c18),c67). EQ(rew(c48,c18),c68). EQ(rew(c51,c20),c69). EQ(rew(c52,c20),c70). EQ(rew(c70,c16),c70a). EQ(rew(c70a,c16),c71). end_of_list. otter-3.3f/examples/wos/rob_occ.in0100644000076400007640000000547506005317011016571 0ustar mccunemccune% Input File for Studying Robbins Algebra with OTTER 3.0 set(knuth_bendix). clear(eq_units_both_ways). set(index_for_back_demod). set(dynamic_demod_lex_dep). set(lrpo). set(process_input). set(display_terms). clear(print_kept). clear(print_new_demod). clear(print_back_demod). % assign(report, 60). assign(max_weight, 20). assign(max_mem, 8000). lex([A, B, C, D, E, F, g(x), n(x), +(x,x)]). weight_list(pick_and_purge). weight(EQ(+(C,C),C), 2). % following are steps from a proof of +(c,c)=c, the union of c and c = c. weight(EQ(+(C,+(C,x)),+(C,x)), 2). weight(EQ(+(C,+(x,C)),+(C,x)), 2). weight(EQ(+(C,+(x,+(y,C))),+(C,+(x,y))), 2). weight(EQ(+(C,+(x,+(C,y))),+(C,+(x,y))), 2). weight(EQ(n(+(n(+(C,x)),n(+(C,n(+(x,C)))))),C), 2). weight(EQ(n(+(n(+(C,x)),n(+(C,n(+(C,x)))))),C), 2). weight(EQ(n(+(n(C),n(+(C,n(C))))),C), 2). weight(EQ(n(+(n(+(x,y)),n(+(y,n(x))))),y), 2). weight(EQ(n(+(n(+(x,y)),n(+(n(y),x)))),x), 2). weight(EQ(n(+(C,n(+(n(C),+(C,n(C)))))),n(C)), 2). weight(EQ(+(C,+(x,y)),+(C,+(y,x))), 2). weight(EQ(n(+(n(+(C,+(x,y))),n(+(C,n(+(y,x)))))),C), 2). weight(EQ(n(+(n(+(C,x)),n(+(n(C),+(x,C))))),+(x,C)), 2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(z,n(+(x,y)))))),z), 2). weight(EQ(n(+(n(+(x,y)),n(+(n(x),y)))),y), 2). weight(EQ(n(+(n(+(x,n(y))),n(+(y,x)))),x), 2). weight(EQ(n(+(n(+(n(x),y)),n(+(y,x)))),y), 2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,y)),z)))),z), 2). weight(EQ(n(+(n(+(x,C)),n(+(C,n(+(C,x)))))),C), 2). weight(EQ(n(+(C,n(+(C,+(n(+(C,x)),n(+(x,C))))))),n(+(x,C))), 2). weight(EQ(n(+(n(C),n(+(C,+(n(C),n(+(C,n(C)))))))),C), 2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(y,n(+(x,z)))))),y), 2). weight(EQ(n(+(n(C),n(+(n(C),+(C,n(C)))))),C), 2). weight(EQ(n(+(n(C),+(C,n(C)))),n(+(C,n(C)))), 2). weight(EQ(n(+(C,n(+(C,n(C))))),n(C)), 2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,z)),y)))),y), 2). weight(EQ(n(+(x,C)),n(+(C,x))), 2). weight(EQ(n(+(x,+(y,C))),n(+(C,+(x,y)))), 2). weight(EQ(n(+(n(+(C,x)),n(+(C,+(n(C),x))))),+(x,C)), 2). weight(EQ(n(+(n(+(C,x)),n(+(n(C),+(x,n(+(C,n(C)))))))),x), 2). weight(EQ(+(C,n(+(C,n(C)))),C), 2). weight(EQ(+(C,+(x,n(+(C,n(C))))),+(C,x)), 2). weight(EQ(+(x,n(+(C,n(C)))),x), 2). weight(EQ(+(n(+(C,n(C))),x),x), 2). weight(EQ(n(+(n(x),n(+(C,+(x,n(C)))))),x), 2). weight(EQ(n(+(n(x),n(n(x)))),n(+(C,n(C)))), 2). weight(EQ(n(+(x,n(x))),n(+(C,n(C)))), 2). weight(EQ(n(n(+(x,n(n(x))))),n(n(x))), 2). weight(EQ(n(n(x)),x), 2). weight(EQ(+(n(+(y,x)),n(+(n(y),x))),n(x)), 2). end_of_list. list(usable). EQ(x,x). EQ(+(x,y),+(y,x)). EQ(+(+(x,y),z),+(x,+(y,z))). end_of_list. list(sos). EQ(n(+(n(+(x,y)),n(+(x,n(y))))),x). % Robbins axiom EQ(+(C,C),C). % hypothesis -EQ(+(n(+(A,n(B))),n(+(n(A),n(B)))),B). % denial of Huntington axiom end_of_list. % list(demodulators). % (+(x,y) = +(y,x)). % (+(+(x,y),z) = +(x,+(y,z))). % (n(+(n(+(x,y)),n(+(x,n(y))))) = x). % Robbins axiom % (+(C,C) = C). % hypothesis % end_of_list. otter-3.3f/examples/wos/index.html0100644000076400007640000000215707714267401016641 0ustar mccunemccune /home/mccune/otter-3.3/examples/wos

/home/mccune/otter-3.3/examples/wos

These problems were contributed by Larry Wos in 1994. Most illustrate the resonance strategy.

otter < cursory.in > cursory.out

otter < grp_exp3.in > grp_exp3.out

otter < grp_exp4.in > grp_exp4.out

otter < manyval.in > manyval.out

otter < rigorous.in > rigorous.out

otter < rob_occ.in > rob_occ.out

otter < twoval.in > twoval.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/wos/rob_occ.out0100664000076400007640000003243710103522200016762 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:56 2004 The command was "../../bin/otter". The process ID is 8527. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(eq_units_both_ways). WARNING: set(index_for_back_demod) flag already set. set(index_for_back_demod). set(dynamic_demod_lex_dep). WARNING: set(lrpo) flag already set. set(lrpo). WARNING: set(process_input) flag already set. set(process_input). set(display_terms). clear(print_kept). clear(print_new_demod). clear(print_back_demod). assign(max_weight,20). assign(max_mem,8000). lex($cons(A,$cons(B,$cons(C,$cons(D,$cons(E,$cons(F,$cons(g(x),$cons(n(x),$cons(+(x,x),$nil)))))))))). weight_list(pick_and_purge). weight(EQ(+(C,C),C),2). weight(EQ(+(C,+(C,x)),+(C,x)),2). weight(EQ(+(C,+(x,C)),+(C,x)),2). weight(EQ(+(C,+(x,+(y,C))),+(C,+(x,y))),2). weight(EQ(+(C,+(x,+(C,y))),+(C,+(x,y))),2). weight(EQ(n(+(n(+(C,x)),n(+(C,n(+(x,C)))))),C),2). weight(EQ(n(+(n(+(C,x)),n(+(C,n(+(C,x)))))),C),2). weight(EQ(n(+(n(C),n(+(C,n(C))))),C),2). weight(EQ(n(+(n(+(x,y)),n(+(y,n(x))))),y),2). weight(EQ(n(+(n(+(x,y)),n(+(n(y),x)))),x),2). weight(EQ(n(+(C,n(+(n(C),+(C,n(C)))))),n(C)),2). weight(EQ(+(C,+(x,y)),+(C,+(y,x))),2). weight(EQ(n(+(n(+(C,+(x,y))),n(+(C,n(+(y,x)))))),C),2). weight(EQ(n(+(n(+(C,x)),n(+(n(C),+(x,C))))),+(x,C)),2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(z,n(+(x,y)))))),z),2). weight(EQ(n(+(n(+(x,y)),n(+(n(x),y)))),y),2). weight(EQ(n(+(n(+(x,n(y))),n(+(y,x)))),x),2). weight(EQ(n(+(n(+(n(x),y)),n(+(y,x)))),y),2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,y)),z)))),z),2). weight(EQ(n(+(n(+(x,C)),n(+(C,n(+(C,x)))))),C),2). weight(EQ(n(+(C,n(+(C,+(n(+(C,x)),n(+(x,C))))))),n(+(x,C))),2). weight(EQ(n(+(n(C),n(+(C,+(n(C),n(+(C,n(C)))))))),C),2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(y,n(+(x,z)))))),y),2). weight(EQ(n(+(n(C),n(+(n(C),+(C,n(C)))))),C),2). weight(EQ(n(+(n(C),+(C,n(C)))),n(+(C,n(C)))),2). weight(EQ(n(+(C,n(+(C,n(C))))),n(C)),2). weight(EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,z)),y)))),y),2). weight(EQ(n(+(x,C)),n(+(C,x))),2). weight(EQ(n(+(x,+(y,C))),n(+(C,+(x,y)))),2). weight(EQ(n(+(n(+(C,x)),n(+(C,+(n(C),x))))),+(x,C)),2). weight(EQ(n(+(n(+(C,x)),n(+(n(C),+(x,n(+(C,n(C)))))))),x),2). weight(EQ(+(C,n(+(C,n(C)))),C),2). weight(EQ(+(C,+(x,n(+(C,n(C))))),+(C,x)),2). weight(EQ(+(x,n(+(C,n(C)))),x),2). weight(EQ(+(n(+(C,n(C))),x),x),2). weight(EQ(n(+(n(x),n(+(C,+(x,n(C)))))),x),2). weight(EQ(n(+(n(x),n(n(x)))),n(+(C,n(C)))),2). weight(EQ(n(+(x,n(x))),n(+(C,n(C)))),2). weight(EQ(n(n(+(x,n(n(x))))),n(n(x))),2). weight(EQ(n(n(x)),x),2). weight(EQ(+(n(+(y,x)),n(+(n(y),x))),n(x)),2). end_of_list. list(usable). 0 [] EQ(x,x). 0 [] EQ(+(x,y),+(y,x)). 0 [] EQ(+(+(x,y),z),+(x,+(y,z))). end_of_list. list(sos). 0 [] EQ(n(+(n(+(x,y)),n(+(x,n(y))))),x). 0 [] EQ(+(C,C),C). 0 [] -(EQ(+(n(+(A,n(B))),n(+(n(A),n(B)))),B)). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] EQ(x,x). ** KEPT (pick-wt=7): 2 [] EQ(+(x,y),+(y,x)). ---> New Demodulator: (lex-dependent) 3 [new_demod,2] EQ(+(x,y),+(y,x)). ** KEPT (pick-wt=11): 4 [] EQ(+(+(x,y),z),+(x,+(y,z))). ---> New Demodulator: 5 [new_demod,4] EQ(+(+(x,y),z),+(x,+(y,z))). >>>> Starting back demodulation with 3. >>>> Starting back demodulation with 5. ------------> process sos: ** KEPT (pick-wt=2): 6 [] EQ(n(+(n(+(x,y)),n(+(x,n(y))))),x). ---> New Demodulator: 7 [new_demod,6] EQ(n(+(n(+(x,y)),n(+(x,n(y))))),x). ** KEPT (pick-wt=2): 8 [] EQ(+(C,C),C). ---> New Demodulator: 9 [new_demod,8] EQ(+(C,C),C). ** KEPT (pick-wt=14): 10 [] -(EQ(+(n(+(A,n(B))),n(+(n(A),n(B)))),B)). >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 6 [] EQ(n(+(n(+(x,y)),n(+(x,n(y))))),x). given clause #2: (wt=2) 8 [] EQ(+(C,C),C). given clause #3: (wt=2) 13 [para_into,6.1.1.1.1.1,2.1.1] EQ(n(+(n(+(x,y)),n(+(y,n(x))))),y). given clause #4: (wt=2) 17 [para_into,6.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,y)),n(+(n(y),x)))),x). given clause #5: (wt=2) 21 [para_from,8.1.1,6.1.1.1.1.1] EQ(n(+(n(C),n(+(C,n(C))))),C). given clause #6: (wt=2) 23 [para_from,8.1.1,4.1.1.1,flip.1] EQ(+(C,+(C,x)),+(C,x)). given clause #7: (wt=2) 25 [para_into,13.1.1.1.1.1,4.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(z,n(+(x,y)))))),z). given clause #8: (wt=2) 29 [para_into,13.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,y)),n(+(n(x),y)))),y). given clause #9: (wt=2) 33 [para_into,13.1.1.1,2.1.1] EQ(n(+(n(+(x,n(y))),n(+(y,x)))),x). given clause #10: (wt=2) 51 [para_into,17.1.1.1,2.1.1] EQ(n(+(n(+(n(x),y)),n(+(y,x)))),y). given clause #11: (wt=2) 61 [para_from,21.1.1,13.1.1.1.2,demod,3,3] EQ(n(+(C,n(+(n(C),+(C,n(C)))))),n(C)). given clause #12: (wt=2) 73 [para_into,23.1.1.2,2.1.1] EQ(+(C,+(x,C)),+(C,x)). given clause #13: (wt=2) 75 [para_from,23.1.1,17.1.1.1.1.1,demod,3] EQ(n(+(n(+(C,x)),n(+(C,n(+(C,x)))))),C). given clause #14: (wt=2) 81 [para_into,25.1.1.1.1.1.2,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(y,n(+(x,z)))))),y). given clause #15: (wt=2) 83 [para_into,25.1.1.1.1.1,2.1.1,demod,5] EQ(n(+(n(+(x,+(y,z))),n(+(y,n(+(z,x)))))),y). given clause #16: (wt=2) 85 [para_into,25.1.1.1.2.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(z,n(+(y,x)))))),z). given clause #17: (wt=2) 87 [para_into,25.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,y)),z)))),z). given clause #18: (wt=2) 123 [para_from,61.1.1,29.1.1.1.1,demod,120,3,flip.1] EQ(n(+(n(C),+(C,n(C)))),n(+(C,n(C)))). given clause #19: (wt=2) 129 [back_demod,61,demod,124] EQ(n(+(C,n(+(C,n(C))))),n(C)). given clause #20: (wt=2) 131 [para_into,73.1.1.2,4.1.1] EQ(+(C,+(x,+(y,C))),+(C,+(x,y))). given clause #21: (wt=2) 133 [para_from,73.1.1,51.1.1.1.2.1,demod,3,3] EQ(n(+(n(+(C,x)),n(+(C,n(+(x,C)))))),C). given clause #22: (wt=2) 135 [para_from,73.1.1,33.1.1.1.2.1,demod,3,3] EQ(n(+(n(+(C,x)),n(+(n(C),+(x,C))))),+(x,C)). given clause #23: (wt=2) 139 [para_from,73.1.1,4.1.1.1,demod,5,5,flip.1] EQ(+(C,+(x,+(C,y))),+(C,+(x,y))). given clause #24: (wt=2) 143 [para_into,75.1.1.1.1.1,2.1.1] EQ(n(+(n(+(x,C)),n(+(C,n(+(C,x)))))),C). given clause #25: (wt=2) 153 [para_into,81.1.1.1.1.1,2.1.1,demod,5] EQ(n(+(n(+(x,+(y,z))),n(+(x,n(+(z,y)))))),x). given clause #26: (wt=2) 157 [para_into,81.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,z)),y)))),y). given clause #27: (wt=2) 167 [para_into,83.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(n(+(z,x)),y)))),y). given clause #28: (wt=2) 173 [para_into,85.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(n(+(y,x)),z)))),z). given clause #29: (wt=2) 199 [para_into,131.1.1.2,2.1.1,demod,5,140] EQ(+(C,+(x,y)),+(C,+(y,x))). given clause #30: (wt=2) 227 [para_into,153.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(n(+(z,y)),x)))),x). given clause #31: (wt=2) 233 [para_into,157.1.1.1.2.1.1,21.1.1,demod,3] EQ(n(+(n(+(C,x)),n(+(n(C),+(x,n(+(C,n(C)))))))),x). given clause #32: (wt=9) 221 [para_from,143.1.1,85.1.1.1.2,demod,3,212] EQ(n(+(C,x)),n(+(x,C))). given clause #33: (wt=13) 261 [para_into,221.1.1.1,199.1.1,demod,3] EQ(n(+(C,+(x,y))),n(+(C,+(y,x)))). given clause #34: (wt=14) 10 [] -(EQ(+(n(+(A,n(B))),n(+(n(A),n(B)))),B)). given clause #35: (wt=14) 89 [para_into,25.1.1.1.2,21.1.1,demod,3] EQ(n(+(C,n(+(C,+(n(C),n(C)))))),n(C)). given clause #36: (wt=14) 267 [para_from,89.1.1,33.1.1.1.2,demod,3,142,flip.1] EQ(n(+(C,+(n(C),n(C)))),n(+(C,n(C)))). given clause #37: (wt=15) 79 [para_into,25.1.1.1.1.1.2,8.1.1] EQ(n(+(n(+(x,C)),n(+(C,n(+(x,C)))))),C). given clause #38: (wt=15) 127 [para_from,61.1.1,17.1.1.1.1,demod,124,3] EQ(n(+(n(C),n(+(C,n(n(+(C,n(C)))))))),C). given clause #39: (wt=15) 219 [para_into,143.1.1.1,2.1.1] EQ(n(+(n(+(C,n(+(C,x)))),n(+(x,C)))),C). given clause #40: (wt=15) 247 [para_into,199.1.1.2,4.1.1] EQ(+(C,+(x,+(y,z))),+(C,+(z,+(x,y)))). given clause #41: (wt=15) 249 [para_from,199.1.1,139.1.1.2.2,demod,140] EQ(+(C,+(x,+(y,z))),+(C,+(x,+(z,y)))). given clause #42: (wt=15) 255 [para_from,199.1.1,4.1.1.1,demod,5,5,5] EQ(+(C,+(x,+(y,z))),+(C,+(y,+(x,z)))). given clause #43: (wt=15) 283 [para_into,247.1.1.2.2,199.1.1,demod,140,5,198] EQ(+(C,+(x,+(y,z))),+(C,+(z,+(y,x)))). given clause #44: (wt=15) 285 [para_into,247.1.1.2.2,139.1.1,demod,140,5,5,132,140] EQ(+(C,+(x,+(y,z))),+(C,+(y,+(z,x)))). given clause #45: (wt=16) 69 [para_from,21.1.1,17.1.1.1.1,demod,3] EQ(n(+(C,n(+(n(C),n(n(+(C,n(C)))))))),n(C)). given clause #46: (wt=17) 77 [para_from,23.1.1,13.1.1.1.1.1,demod,3] EQ(n(+(n(+(C,x)),n(+(n(C),+(C,x))))),+(C,x)). given clause #47: (wt=2) 337 [para_into,77.1.1.1.1,129.1.1,demod,260,flip.1] EQ(+(C,n(+(C,n(C)))),C). given clause #48: (wt=2) 339 [para_from,337.1.1,139.1.1.2.2,demod,74,flip.1] EQ(+(C,+(x,n(+(C,n(C))))),+(C,x)). given clause #49: (wt=2) 351 [para_from,339.1.1,33.1.1.1.2.1,demod,3,3,234,flip.1] EQ(+(x,n(+(C,n(C)))),x). given clause #50: (wt=2) 365 [para_into,351.1.1,2.1.1] EQ(+(n(+(C,n(C))),x),x). given clause #51: (wt=2) 379 [para_from,351.1.1,81.1.1.1.2.1,demod,3] EQ(n(+(n(x),n(+(C,+(x,n(C)))))),x). given clause #52: (wt=2) 385 [para_from,351.1.1,33.1.1.1.2.1,demod,366,3] EQ(n(+(n(x),n(n(x)))),n(+(C,n(C)))). given clause #53: (wt=2) 403 [para_into,385.1.1.1.1,379.1.1,demod,380] EQ(n(+(x,n(x))),n(+(C,n(C)))). given clause #54: (wt=2) 451 [para_from,403.1.1,51.1.1.1.1,demod,3,366,448,flip.1] EQ(n(n(x)),x). -------- PROOF -------- ----> UNIT CONFLICT at 0.14 sec ----> 519 [binary,518.1,1.1] $F. Length of proof is 30. Level of proof is 16. ---------------- PROOF ---------------- 1 [] EQ(x,x). 3,2 [] EQ(+(x,y),+(y,x)). 5,4 [] EQ(+(+(x,y),z),+(x,+(y,z))). 6 [] EQ(n(+(n(+(x,y)),n(+(x,n(y))))),x). 8 [] EQ(+(C,C),C). 10 [] -(EQ(+(n(+(A,n(B))),n(+(n(A),n(B)))),B)). 13 [para_into,6.1.1.1.1.1,2.1.1] EQ(n(+(n(+(x,y)),n(+(y,n(x))))),y). 17 [para_into,6.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,y)),n(+(n(y),x)))),x). 21 [para_from,8.1.1,6.1.1.1.1.1] EQ(n(+(n(C),n(+(C,n(C))))),C). 24,23 [para_from,8.1.1,4.1.1.1,flip.1] EQ(+(C,+(C,x)),+(C,x)). 25 [para_into,13.1.1.1.1.1,4.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(z,n(+(x,y)))))),z). 29 [para_into,13.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,y)),n(+(n(x),y)))),y). 33 [para_into,13.1.1.1,2.1.1] EQ(n(+(n(+(x,n(y))),n(+(y,x)))),x). 51 [para_into,17.1.1.1,2.1.1] EQ(n(+(n(+(n(x),y)),n(+(y,x)))),y). 61 [para_from,21.1.1,13.1.1.1.2,demod,3,3] EQ(n(+(C,n(+(n(C),+(C,n(C)))))),n(C)). 74,73 [para_into,23.1.1.2,2.1.1] EQ(+(C,+(x,C)),+(C,x)). 77 [para_from,23.1.1,13.1.1.1.1.1,demod,3] EQ(n(+(n(+(C,x)),n(+(n(C),+(C,x))))),+(C,x)). 81 [para_into,25.1.1.1.1.1.2,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(y,n(+(x,z)))))),y). 120,119 [para_from,61.1.1,25.1.1.1.2,demod,3,24,3] EQ(n(+(n(C),n(+(n(C),+(C,n(C)))))),C). 124,123 [para_from,61.1.1,29.1.1.1.1,demod,120,3,flip.1] EQ(n(+(n(C),+(C,n(C)))),n(+(C,n(C)))). 129 [back_demod,61,demod,124] EQ(n(+(C,n(+(C,n(C))))),n(C)). 139 [para_from,73.1.1,4.1.1.1,demod,5,5,flip.1] EQ(+(C,+(x,+(C,y))),+(C,+(x,y))). 157 [para_into,81.1.1.1.2.1,2.1.1] EQ(n(+(n(+(x,+(y,z))),n(+(n(+(x,z)),y)))),y). 234,233 [para_into,157.1.1.1.2.1.1,21.1.1,demod,3] EQ(n(+(n(+(C,x)),n(+(n(C),+(x,n(+(C,n(C)))))))),x). 260,259 [para_into,233.1.1.1.1.1,8.1.1] EQ(n(+(n(C),n(+(n(C),+(C,n(+(C,n(C)))))))),C). 337 [para_into,77.1.1.1.1,129.1.1,demod,260,flip.1] EQ(+(C,n(+(C,n(C)))),C). 339 [para_from,337.1.1,139.1.1.2.2,demod,74,flip.1] EQ(+(C,+(x,n(+(C,n(C))))),+(C,x)). 352,351 [para_from,339.1.1,33.1.1.1.2.1,demod,3,3,234,flip.1] EQ(+(x,n(+(C,n(C)))),x). 366,365 [para_into,351.1.1,2.1.1] EQ(+(n(+(C,n(C))),x),x). 380,379 [para_from,351.1.1,81.1.1.1.2.1,demod,3] EQ(n(+(n(x),n(+(C,+(x,n(C)))))),x). 385 [para_from,351.1.1,33.1.1.1.2.1,demod,366,3] EQ(n(+(n(x),n(n(x)))),n(+(C,n(C)))). 403 [para_into,385.1.1.1.1,379.1.1,demod,380] EQ(n(+(x,n(x))),n(+(C,n(C)))). 448,447 [para_from,403.1.1,51.1.1.1.2,demod,3,352] EQ(n(n(+(x,n(n(x))))),x). 452,451 [para_from,403.1.1,51.1.1.1.1,demod,3,366,448,flip.1] EQ(n(n(x)),x). 509,508 [para_into,451.1.1.1,29.1.1,flip.1] EQ(+(n(+(x,y)),n(+(n(x),y))),n(y)). 518 [back_demod,10,demod,509,452] -(EQ(B,B)). 519 [binary,518.1,1.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 54 clauses generated 3114 para_from generated 1853 para_into generated 1261 demod & eval rewrites 4872 clauses wt,lit,sk delete 1340 tautologies deleted 0 clauses forward subsumed 1635 (subsumed by sos) 95 unit deletions 0 factor simplifications 0 clauses kept 261 new demodulators 257 empty clauses 1 clauses back demodulated 116 clauses back subsumed 0 usable size 23 sos size 122 demodulators size 142 passive size 0 hot size 0 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.14 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8527 finished Mon Aug 2 15:30:56 2004 otter-3.3f/examples/wos/manyval.out0100664000076400007640000062635510103522200017033 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:40 2004 The command was "../../bin/otter". The process ID is 8517. set(hyper_res). assign(max_weight,22). assign(change_limit_after,1000). assign(new_max_weight,16). assign(max_proofs,4). clear(print_kept). clear(back_sub). assign(max_mem,24000). assign(max_distinct_vars,4). assign(pick_given_ratio,3). set(order_history). set(input_sos_first). weight_list(pick_given). weight(P(i(n(n(x)),x)),2). weight(P(i(x,n(n(x)))),2). weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2). weight(P(i(i(x,y),i(n(y),n(x)))),2). weight(P(i(i(i(x,y),i(y,x)),i(y,x))),2). weight(P(i(x,i(y,x))),2). weight(P(i(i(x,y),i(i(y,z),i(x,z)))),2). weight(P(i(i(i(x,y),y),i(i(y,x),x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(i($(1),$(2)),1). end_of_list. list(usable). 1 [] -P(i(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). end_of_list. list(passive). 6 [] -P(i(n(n(a)),a))|$ANS(lemma_24). 7 [] -P(i(a,n(n(a))))|$ANS(lemma_29). 8 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(lemma_25). 9 [] -P(i(i(a,b),i(n(b),n(a))))|$ANS(lemma_36). 10 [] -P(i(i(i(a,b),i(b,a)),i(b,a)))|$ANS(thm_MV5). end_of_list. list(demodulators). 11 [] n(n(n(x)))=junk. 12 [] i(i(x,x),y)=junk. 13 [] i(y,i(x,x))=junk. 14 [] i(n(i(x,x)),y)=junk. 15 [] i(y,n(i(x,x)))=junk. 16 [] i(junk,x)=junk. 17 [] i(x,junk)=junk. 18 [] n(junk)=junk. 19 [] P(junk)=$T. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=-2147483647) 2 [] P(i(x,i(y,x))). given clause #2: (wt=-2147483647) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). given clause #3: (wt=-2147483647) 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). given clause #4: (wt=-2147483647) 5 [] P(i(i(n(x),n(y)),i(y,x))). given clause #5: (wt=23) 20 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). given clause #6: (wt=17) 23 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). given clause #7: (wt=12) 33 [hyper,1,23,5] P(i(n(x),i(x,y))). given clause #8: (wt=17) 28 [hyper,1,4,20] P(i(i(i(x,i(y,x)),z),z)). given clause #9: (wt=32) 21 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #10: (wt=5) 39 [hyper,1,23,28] P(i(x,x)). given clause #11: (wt=17) 34 [hyper,1,23,4] P(i(x,i(i(x,y),y))). given clause #12: (wt=18) 51 [hyper,1,34,33] P(i(i(i(n(x),i(x,y)),z),z)). given clause #13: (wt=65) 22 [hyper,1,2,3] P(i(x,i(i(y,z),i(i(z,u),i(y,u))))). given clause #14: (wt=19) 37 [hyper,1,3,33] P(i(i(i(x,y),z),i(n(x),z))). given clause #15: (wt=13) 73 [hyper,1,37,5] P(i(n(n(x)),i(y,x))). given clause #16: (wt=15) 70 [hyper,1,37,28] P(i(n(i(x,i(y,x))),z)). given clause #17: (wt=32) 24 [hyper,1,3,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). given clause #18: (wt=15) 71 [hyper,1,37,23] P(i(n(i(x,y)),i(y,z))). given clause #19: (wt=16) 68 [hyper,1,37,51] P(i(n(i(n(x),i(x,y))),z)). given clause #20: (wt=17) 62 [hyper,1,37,37] P(i(n(i(x,y)),i(n(x),z))). given clause #21: (wt=47) 25 [hyper,1,2,4] P(i(x,i(i(i(y,z),z),i(i(z,y),y)))). given clause #22: (wt=19) 75 [hyper,1,34,73] P(i(i(i(n(n(x)),i(y,x)),z),z)). given clause #23: (wt=17) 105 [hyper,1,37,75] P(i(n(i(n(n(x)),i(y,x))),z)). given clause #24: (wt=19) 89 [hyper,1,24,37] P(i(i(i(x,y),y),i(n(y),x))). given clause #25: (wt=29) 26 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). given clause #26: (wt=13) 116 [hyper,1,23,89] P(i(x,i(n(x),y))). given clause #27: (wt=17) 114 [hyper,1,37,89] P(i(n(i(x,y)),i(n(y),x))). given clause #28: (wt=17) 141 [hyper,1,116,116] P(i(n(i(x,i(n(x),y))),z)). given clause #29: (wt=35) 27 [hyper,1,2,5] P(i(x,i(i(n(y),n(z)),i(z,y)))). given clause #30: (wt=18) 148 [hyper,1,3,116] P(i(i(i(n(x),y),z),i(x,z))). given clause #31: (wt=16) 180 [hyper,1,37,148] P(i(n(i(n(x),y)),i(x,z))). given clause #32: (wt=19) 143 [hyper,1,34,116] P(i(i(i(x,i(n(x),y)),z),z)). given clause #33: (wt=23) 29 [hyper,1,3,20] P(i(i(i(x,i(y,x)),z),i(u,z))). given clause #34: (wt=19) 146 [hyper,1,23,116] P(i(x,i(n(i(y,x)),z))). given clause #35: (wt=19) 153 [hyper,1,116,71] P(i(n(i(n(i(x,y)),i(y,z))),u)). given clause #36: (wt=19) 154 [hyper,1,116,70] P(i(n(i(n(i(x,i(y,x))),z)),u)). given clause #37: (wt=47) 30 [hyper,1,2,20] P(i(x,i(y,i(z,i(u,z))))). given clause #38: (wt=20) 49 [hyper,1,3,34] P(i(i(i(i(x,y),y),z),i(x,z))). -------- PROOF -------- 242 [binary,241.1,8.1] $ANS(lemma_25). ----> UNIT CONFLICT at 0.01 sec ----> 242 [binary,241.1,8.1] $ANS(lemma_25). Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 8 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(lemma_25). 21 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 23 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 34 [hyper,1,23,4] P(i(x,i(i(x,y),y))). 49 [hyper,1,3,34] P(i(i(i(i(x,y),y),z),i(x,z))). 241 [hyper,1,49,21] P(i(i(x,y),i(i(z,x),i(z,y)))). 242 [binary,241.1,8.1] $ANS(lemma_25). ------------ end of proof ------------- given clause #39: (wt=2) 241 [hyper,1,49,21] P(i(i(x,y),i(i(z,x),i(z,y)))). given clause #40: (wt=18) 229 [hyper,1,37,49] P(i(n(i(i(x,y),y)),i(x,z))). given clause #41: (wt=29) 31 [hyper,1,3,23] P(i(i(i(x,y),z),i(i(i(u,x),y),z))). given clause #42: (wt=20) 138 [hyper,1,26,5] P(i(i(n(n(x)),n(n(y))),i(x,y))). given clause #43: (wt=20) 142 [hyper,1,37,116] P(i(n(x),i(n(i(x,y)),z))). given clause #44: (wt=20) 155 [hyper,1,116,68] P(i(n(i(n(i(n(x),i(x,y))),z)),u)). given clause #45: (wt=35) 32 [hyper,1,2,23] P(i(x,i(i(i(y,z),u),i(z,u)))). given clause #46: (wt=20) 190 [hyper,1,116,180] P(i(n(i(n(i(n(x),y)),i(x,z))),u)). given clause #47: (wt=21) 74 [hyper,1,37,4] P(i(n(i(x,y)),i(i(y,x),x))). given clause #48: (wt=21) 76 [hyper,1,3,73] P(i(i(i(x,y),z),i(n(n(y)),z))). -------- PROOF -------- 338 [binary,337.1,6.1] $ANS(lemma_24). ----> UNIT CONFLICT at 0.02 sec ----> 338 [binary,337.1,6.1] $ANS(lemma_24). Length of proof is 11. Level of proof is 7. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 6 [] -P(i(n(n(a)),a))|$ANS(lemma_24). 23 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 24 [hyper,1,3,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). 33 [hyper,1,23,5] P(i(n(x),i(x,y))). 34 [hyper,1,23,4] P(i(x,i(i(x,y),y))). 37 [hyper,1,3,33] P(i(i(i(x,y),z),i(n(x),z))). 73 [hyper,1,37,5] P(i(n(n(x)),i(y,x))). 76 [hyper,1,3,73] P(i(i(i(x,y),z),i(n(n(y)),z))). 89 [hyper,1,24,37] P(i(i(i(x,y),y),i(n(y),x))). 116 [hyper,1,23,89] P(i(x,i(n(x),y))). 143 [hyper,1,34,116] P(i(i(i(x,i(n(x),y)),z),z)). 337 [hyper,1,76,143] P(i(n(n(x)),x)). 338 [binary,337.1,6.1] $ANS(lemma_24). ------------ end of proof ------------- given clause #49: (wt=29) 35 [hyper,1,23,3] P(i(x,i(i(x,y),i(z,y)))). given clause #50: (wt=2) 337 [hyper,1,76,143] P(i(n(n(x)),x)). -------- PROOF -------- 368 [binary,367.1,7.1] $ANS(lemma_29). ----> UNIT CONFLICT at 0.02 sec ----> 368 [binary,367.1,7.1] $ANS(lemma_29). Length of proof is 12. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 7 [] -P(i(a,n(n(a))))|$ANS(lemma_29). 23 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 24 [hyper,1,3,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). 33 [hyper,1,23,5] P(i(n(x),i(x,y))). 34 [hyper,1,23,4] P(i(x,i(i(x,y),y))). 37 [hyper,1,3,33] P(i(i(i(x,y),z),i(n(x),z))). 73 [hyper,1,37,5] P(i(n(n(x)),i(y,x))). 76 [hyper,1,3,73] P(i(i(i(x,y),z),i(n(n(y)),z))). 89 [hyper,1,24,37] P(i(i(i(x,y),y),i(n(y),x))). 116 [hyper,1,23,89] P(i(x,i(n(x),y))). 143 [hyper,1,34,116] P(i(i(i(x,i(n(x),y)),z),z)). 337 [hyper,1,76,143] P(i(n(n(x)),x)). 367 [hyper,1,5,337] P(i(x,n(n(x)))). 368 [binary,367.1,7.1] $ANS(lemma_29). ------------ end of proof ------------- given clause #51: (wt=2) 367 [hyper,1,5,337] P(i(x,n(n(x)))). given clause #52: (wt=7) 418 [hyper,1,367,39] P(n(n(i(x,x)))). given clause #53: (wt=23) 36 [hyper,1,23,2] P(i(x,i(y,i(z,x)))). given clause #54: (wt=9) 392 [hyper,1,367,337] P(n(n(i(n(n(x)),x)))). given clause #55: (wt=11) 364 [hyper,1,116,337] P(i(n(i(n(n(x)),x)),y)). given clause #56: (wt=11) 370 [hyper,1,367,367] P(n(n(i(x,n(n(x)))))). given clause #57: (wt=25) 38 [hyper,1,2,33] P(i(x,i(n(y),i(y,z)))). given clause #58: (wt=13) 366 [hyper,1,34,337] P(i(i(i(n(n(x)),x),y),y)). given clause #59: (wt=13) 375 [hyper,1,116,367] P(i(n(i(x,n(n(x)))),y)). given clause #60: (wt=13) 385 [hyper,1,28,367] P(n(n(i(x,i(y,x))))). given clause #61: (wt=38) 40 [hyper,1,3,28] P(i(i(x,y),i(i(i(z,i(u,z)),x),y))). given clause #62: (wt=13) 440 [hyper,1,34,418] P(i(i(n(n(i(x,x))),y),y)). given clause #63: (wt=13) 467 [hyper,1,367,364] P(n(n(i(n(i(n(n(x)),x)),y)))). given clause #64: (wt=14) 378 [hyper,1,51,367] P(n(n(i(n(x),i(x,y))))). given clause #65: (wt=35) 41 [hyper,1,2,28] P(i(x,i(i(i(y,i(z,y)),u),u))). given clause #66: (wt=15) 327 [hyper,1,49,76] P(i(x,i(n(n(y)),y))). given clause #67: (wt=15) 374 [hyper,1,143,367] P(n(n(i(x,i(n(x),y))))). given clause #68: (wt=15) 377 [hyper,1,75,367] P(n(n(i(n(n(x)),i(y,x))))). given clause #69: (wt=62) 42 [hyper,1,28,21] P(i(i(x,y),i(z,i(i(y,u),i(x,u))))). given clause #70: (wt=15) 382 [hyper,1,34,367] P(i(i(i(x,n(n(x))),y),y)). given clause #71: (wt=15) 388 [hyper,1,23,367] P(i(x,n(n(i(y,x))))). given clause #72: (wt=11) 618 [hyper,1,5,388] P(i(n(i(x,n(y))),y)). given clause #73: (wt=62) 43 [hyper,1,21,21] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). given clause #74: (wt=13) 665 [hyper,1,367,618] P(n(n(i(n(i(x,n(y))),y)))). given clause #75: (wt=15) 441 [hyper,1,2,418] P(i(x,n(n(i(y,y))))). given clause #76: (wt=15) 462 [hyper,1,142,392] P(i(n(i(n(i(n(n(x)),x)),y)),z)). given clause #77: (wt=26) 44 [hyper,1,21,28] P(i(i(x,y),i(x,i(z,y)))). given clause #78: (wt=15) 465 [hyper,1,34,392] P(i(i(n(n(i(n(n(x)),x))),y),y)). given clause #79: (wt=15) 482 [hyper,1,367,366] P(n(n(i(i(i(n(n(x)),x),y),y)))). given clause #80: (wt=15) 494 [hyper,1,367,375] P(n(n(i(n(i(x,n(n(x)))),y)))). given clause #81: (wt=50) 45 [hyper,1,21,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). given clause #82: (wt=15) 527 [hyper,1,367,440] P(n(n(i(i(n(n(i(x,x))),y),y)))). given clause #83: (wt=15) 668 [hyper,1,116,618] P(i(n(i(n(i(x,n(y))),y)),z)). given clause #84: (wt=16) 380 [hyper,1,37,367] P(i(n(x),n(n(i(x,y))))). given clause #85: (wt=23) 46 [hyper,1,34,34] P(i(i(i(x,i(i(x,y),y)),z),z)). given clause #86: (wt=9) 831 [hyper,1,5,380] P(i(n(i(x,y)),x)). given clause #87: (wt=11) 848 [hyper,1,367,831] P(n(n(i(n(i(x,y)),x)))). given clause #88: (wt=13) 851 [hyper,1,116,831] P(i(n(i(n(i(x,y)),x)),z)). given clause #89: (wt=23) 47 [hyper,1,23,34] P(i(x,i(i(i(y,x),z),z))). given clause #90: (wt=15) 853 [hyper,1,44,831] P(i(n(i(x,y)),i(z,x))). given clause #91: (wt=15) 859 [hyper,1,34,831] P(i(i(i(n(i(x,y)),x),z),z)). given clause #92: (wt=15) 863 [hyper,1,380,848] P(n(n(i(n(i(n(i(x,y)),x)),z)))). given clause #93: (wt=44) 48 [hyper,1,21,34] P(i(i(x,y),i(i(i(i(y,z),i(x,z)),u),u))). given clause #94: (wt=16) 390 [hyper,1,3,367] P(i(i(n(n(x)),y),i(x,y))). given clause #95: (wt=17) 372 [hyper,1,148,367] P(i(x,n(n(i(n(x),y))))). given clause #96: (wt=11) 1010 [hyper,1,5,372] P(i(n(i(n(n(x)),y)),x)). given clause #97: (wt=35) 50 [hyper,1,2,34] P(i(x,i(y,i(i(y,z),z)))). given clause #98: (wt=13) 1058 [hyper,1,367,1010] P(n(n(i(n(i(n(n(x)),y)),x)))). given clause #99: (wt=15) 1061 [hyper,1,116,1010] P(i(n(i(n(i(n(n(x)),y)),x)),z)). given clause #100: (wt=17) 376 [hyper,1,76,367] P(i(n(n(x)),n(n(i(y,x))))). given clause #101: (wt=23) 52 [hyper,1,34,28] P(i(i(i(i(i(x,i(y,x)),z),z),u),u)). given clause #102: (wt=11) 1106 [hyper,1,5,376] P(i(n(i(x,y)),n(y))). given clause #103: (wt=13) 1114 [hyper,1,367,1106] P(n(n(i(n(i(x,y)),n(y))))). given clause #104: (wt=15) 1117 [hyper,1,116,1106] P(i(n(i(n(i(x,y)),n(y))),z)). given clause #105: (wt=23) 53 [hyper,1,34,23] P(i(i(i(i(i(x,y),z),i(y,z)),u),u)). given clause #106: (wt=17) 412 [hyper,1,367,71] P(n(n(i(n(i(x,y)),i(y,z))))). given clause #107: (wt=17) 413 [hyper,1,367,70] P(n(n(i(n(i(x,i(y,x))),z)))). given clause #108: (wt=17) 472 [hyper,1,34,364] P(i(i(i(n(i(n(n(x)),x)),y),z),z)). given clause #109: (wt=29) 54 [hyper,1,34,20] P(i(i(i(x,i(y,i(z,y))),u),u)). given clause #110: (wt=17) 476 [hyper,1,142,370] P(i(n(i(n(i(x,n(n(x)))),y)),z)). given clause #111: (wt=17) 479 [hyper,1,34,370] P(i(i(n(n(i(x,n(n(x))))),y),y)). given clause #112: (wt=17) 485 [hyper,1,116,366] P(i(n(i(i(i(n(n(x)),x),y),y)),z)). given clause #113: (wt=23) 55 [hyper,1,34,5] P(i(i(i(i(n(x),n(y)),i(y,x)),z),z)). given clause #114: (wt=17) 530 [hyper,1,116,440] P(i(n(i(i(n(n(i(x,x))),y),y)),z)). given clause #115: (wt=17) 550 [hyper,1,367,327] P(n(n(i(x,i(n(n(y)),y))))). given clause #116: (wt=17) 579 [hyper,1,367,382] P(n(n(i(i(i(x,n(n(x))),y),y)))). given clause #117: (wt=29) 56 [hyper,1,34,4] P(i(i(i(i(i(x,y),y),i(i(y,x),x)),z),z)). given clause #118: (wt=17) 590 [hyper,1,24,382] P(i(i(i(n(n(x)),x),x),n(n(x)))). given clause #119: (wt=17) 593 [hyper,1,440,388] P(n(n(i(x,n(n(i(y,y))))))). given clause #120: (wt=17) 596 [hyper,1,367,388] P(n(n(i(x,n(n(i(y,x))))))). given clause #121: (wt=38) 57 [hyper,1,34,3] P(i(i(i(i(x,y),i(i(y,z),i(x,z))),u),u)). given clause #122: (wt=17) 673 [hyper,1,34,618] P(i(i(i(n(i(x,n(y))),y),z),z)). given clause #123: (wt=17) 723 [hyper,1,367,462] P(n(n(i(n(i(n(i(n(n(x)),x)),y)),z)))). given clause #124: (wt=17) 739 [hyper,1,44,618] P(i(n(i(x,n(y))),i(z,y))). given clause #125: (wt=24) 58 [hyper,1,34,51] P(i(i(i(i(i(n(x),i(x,y)),z),z),u),u)). given clause #126: (wt=17) 759 [hyper,1,367,465] P(n(n(i(i(n(n(i(n(n(x)),x))),y),y)))). given clause #127: (wt=17) 814 [hyper,1,367,668] P(n(n(i(n(i(n(i(x,n(y))),y)),z)))). given clause #128: (wt=17) 865 [hyper,1,142,848] P(i(n(i(n(i(n(i(x,y)),x)),z)),u)). given clause #129: (wt=28) 59 [hyper,1,21,51] P(i(i(x,n(y)),i(x,i(y,z)))). given clause #130: (wt=17) 868 [hyper,1,34,848] P(i(i(n(n(i(n(i(x,y)),x))),z),z)). given clause #131: (wt=17) 919 [hyper,1,367,853] P(n(n(i(n(i(x,y)),i(z,x))))). given clause #132: (wt=17) 928 [hyper,1,367,859] P(n(n(i(i(i(n(i(x,y)),x),z),z)))). given clause #133: (wt=40) 60 [hyper,1,3,51] P(i(i(x,y),i(i(i(n(z),i(z,u)),x),y))). given clause #134: (wt=17) 1057 [hyper,1,372,1010] P(n(n(i(n(i(n(i(n(n(x)),y)),x)),z)))). given clause #135: (wt=17) 1065 [hyper,1,44,1010] P(i(n(i(n(n(x)),y)),i(z,x))). given clause #136: (wt=17) 1071 [hyper,1,34,1010] P(i(i(i(n(i(n(n(x)),y)),x),z),z)). given clause #137: (wt=37) 61 [hyper,1,2,51] P(i(x,i(i(i(n(y),i(y,z)),u),u))). given clause #138: (wt=17) 1113 [hyper,1,372,1106] P(n(n(i(n(i(n(i(x,y)),n(y))),z)))). given clause #139: (wt=17) 1126 [hyper,1,34,1106] P(i(i(i(n(i(x,y)),n(y)),z),z)). given clause #140: (wt=18) 362 [hyper,1,241,337] P(i(i(x,n(n(y))),i(x,y))). given clause #141: (wt=25) 63 [hyper,1,34,37] P(i(i(i(i(i(x,y),z),i(n(x),z)),u),u)). given clause #142: (wt=17) 1452 [hyper,1,362,440] P(i(i(n(n(i(x,x))),n(n(y))),y)). given clause #143: (wt=17) 1454 [hyper,1,362,366] P(i(i(i(n(n(x)),x),n(n(y))),y)). given clause #144: (wt=18) 369 [hyper,1,3,337] P(i(i(x,y),i(n(n(x)),y))). given clause #145: (wt=24) 64 [hyper,1,28,37] P(i(n(x),i(y,i(x,z)))). given clause #146: (wt=15) 1547 [hyper,1,369,440] P(i(n(n(i(n(n(i(x,x))),y))),y)). given clause #147: (wt=15) 1550 [hyper,1,369,366] P(i(n(n(i(i(n(n(x)),x),y))),y)). given clause #148: (wt=17) 1541 [hyper,1,369,859] P(i(n(n(i(i(n(i(x,y)),x),z))),z)). given clause #149: (wt=28) 65 [hyper,1,21,37] P(i(i(x,y),i(n(y),i(x,z)))). given clause #150: (wt=17) 1546 [hyper,1,369,465] P(i(n(n(i(n(n(i(n(n(x)),x))),y))),y)). given clause #151: (wt=17) 1549 [hyper,1,369,382] P(i(n(n(i(i(x,n(n(x))),y))),y)). given clause #152: (wt=17) 1595 [hyper,1,367,1547] P(n(n(i(n(n(i(n(n(i(x,x))),y))),y)))). given clause #153: (wt=30) 66 [hyper,1,3,37] P(i(i(i(n(x),y),z),i(i(i(x,u),y),z))). given clause #154: (wt=17) 1616 [hyper,1,367,1550] P(n(n(i(n(n(i(i(n(n(x)),x),y))),y)))). given clause #155: (wt=18) 396 [hyper,1,367,180] P(n(n(i(n(i(n(x),y)),i(x,z))))). given clause #156: (wt=18) 414 [hyper,1,367,68] P(n(n(i(n(i(n(x),i(x,y))),z)))). given clause #157: (wt=39) 67 [hyper,1,2,37] P(i(x,i(i(i(y,z),u),i(n(y),u)))). given clause #158: (wt=18) 820 [hyper,1,367,380] P(n(n(i(n(x),n(n(i(x,y))))))). given clause #159: (wt=18) 963 [hyper,1,367,390] P(n(n(i(i(n(n(x)),y),i(x,y))))). given clause #160: (wt=18) 1548 [hyper,1,369,390] P(i(n(n(i(n(n(x)),y))),i(x,y))). given clause #161: (wt=24) 69 [hyper,1,37,34] P(i(n(x),i(i(i(x,y),z),z))). given clause #162: (wt=19) 328 [hyper,1,37,76] P(i(n(i(x,y)),i(n(n(y)),z))). given clause #163: (wt=19) 340 [hyper,1,76,4] P(i(n(n(x)),i(i(x,y),y))). given clause #164: (wt=19) 363 [hyper,1,146,337] P(i(n(i(x,i(n(n(y)),y))),z)). given clause #165: (wt=30) 72 [hyper,1,37,21] P(i(n(i(i(x,y),i(z,y))),i(i(z,x),u))). given clause #166: (wt=19) 365 [hyper,1,35,337] P(i(i(i(n(n(x)),x),y),i(z,y))). given clause #167: (wt=19) 391 [hyper,1,2,367] P(i(x,i(y,n(n(y))))). given clause #168: (wt=19) 404 [hyper,1,367,141] P(n(n(i(n(i(x,i(n(x),y))),z)))). given clause #169: (wt=27) 77 [hyper,1,2,73] P(i(x,i(n(n(y)),i(z,y)))). given clause #170: (wt=19) 406 [hyper,1,367,114] P(n(n(i(n(i(x,y)),i(n(y),x))))). given clause #171: (wt=19) 407 [hyper,1,367,105] P(n(n(i(n(i(n(n(x)),i(y,x))),z)))). given clause #172: (wt=19) 415 [hyper,1,367,62] P(n(n(i(n(i(x,y)),i(n(x),z))))). given clause #173: (wt=21) 78 [hyper,1,34,70] P(i(i(i(n(i(x,i(y,x))),z),u),u)). given clause #174: (wt=19) 421 [hyper,1,367,34] P(n(n(i(x,i(i(x,y),y))))). given clause #175: (wt=19) 426 [hyper,1,367,28] P(n(n(i(i(i(x,i(y,x)),z),z)))). given clause #176: (wt=19) 431 [hyper,1,367,23] P(n(n(i(i(i(x,y),z),i(y,z))))). given clause #177: (wt=34) 79 [hyper,1,3,70] P(i(i(x,y),i(n(i(z,i(u,z))),y))). given clause #178: (wt=19) 435 [hyper,1,367,5] P(n(n(i(i(n(x),n(y)),i(y,x))))). given clause #179: (wt=19) 438 [hyper,1,146,418] P(i(n(i(x,n(n(i(y,y))))),z)). given clause #180: (wt=19) 439 [hyper,1,35,418] P(i(i(n(n(i(x,x))),y),i(z,y))). given clause #181: (wt=31) 80 [hyper,1,2,70] P(i(x,i(n(i(y,i(z,y))),u))). given clause #182: (wt=19) 466 [hyper,1,2,392] P(i(x,n(n(i(n(n(y)),y))))). given clause #183: (wt=19) 488 [hyper,1,34,366] P(i(i(i(i(i(n(n(x)),x),y),y),z),z)). given clause #184: (wt=19) 491 [hyper,1,24,366] P(i(i(i(x,n(n(x))),n(n(x))),x)). given clause #185: (wt=30) 81 [hyper,1,37,24] P(i(n(i(i(x,y),y)),i(i(i(y,x),x),z))). given clause #186: (wt=19) 499 [hyper,1,34,375] P(i(i(i(n(i(x,n(n(x)))),y),z),z)). given clause #187: (wt=19) 505 [hyper,1,34,385] P(i(i(n(n(i(x,i(y,x)))),z),z)). given clause #188: (wt=19) 534 [hyper,1,34,440] P(i(i(i(i(n(n(i(x,x))),y),y),z),z)). given clause #189: (wt=38) 82 [hyper,1,34,24] P(i(i(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z)),u),u)). given clause #190: (wt=19) 539 [hyper,1,142,467] P(i(n(i(n(i(n(i(n(n(x)),x)),y)),z)),u)). given clause #191: (wt=19) 542 [hyper,1,34,467] P(i(i(n(n(i(n(i(n(n(x)),x)),y))),z),z)). given clause #192: (wt=19) 582 [hyper,1,116,382] P(i(n(i(i(i(x,n(n(x))),y),y)),z)). given clause #193: (wt=41) 83 [hyper,1,28,24] P(i(i(i(x,y),y),i(z,i(i(y,x),x)))). given clause #194: (wt=19) 601 [hyper,1,138,388] P(i(x,i(y,n(n(x))))). given clause #195: (wt=19) 602 [hyper,1,116,388] P(i(n(i(x,n(n(i(y,x))))),z)). given clause #196: (wt=19) 619 [hyper,1,3,388] P(i(i(n(n(i(x,y))),z),i(y,z))). given clause #197: (wt=41) 84 [hyper,1,24,24] P(i(i(i(x,i(y,x)),i(y,x)),i(i(i(x,y),y),x))). given clause #198: (wt=19) 712 [hyper,1,142,665] P(i(n(i(n(i(n(i(x,n(y))),y)),z)),u)). given clause #199: (wt=19) 715 [hyper,1,34,665] P(i(i(n(n(i(n(i(x,n(y))),y))),z),z)). given clause #200: (wt=19) 762 [hyper,1,116,465] P(i(n(i(i(n(n(i(n(n(x)),x))),y),y)),z)). given clause #201: (wt=44) 85 [hyper,1,21,24] P(i(i(x,i(y,z)),i(i(i(z,y),y),i(x,z)))). given clause #202: (wt=19) 834 [hyper,1,380,527] P(n(n(i(n(i(i(n(n(i(x,x))),y),y)),z)))). given clause #203: (wt=19) 835 [hyper,1,380,494] P(n(n(i(n(i(n(i(x,n(n(x)))),y)),z)))). given clause #204: (wt=19) 836 [hyper,1,380,482] P(n(n(i(n(i(i(i(n(n(x)),x),y),y)),z)))). given clause #205: (wt=41) 86 [hyper,1,3,24] P(i(i(i(i(i(x,y),y),z),u),i(i(i(i(y,x),x),z),u))). given clause #206: (wt=19) 861 [hyper,1,2,831] P(i(x,i(n(i(y,z)),y))). given clause #207: (wt=19) 872 [hyper,1,34,851] P(i(i(i(n(i(n(i(x,y)),x)),z),u),u)). given clause #208: (wt=19) 921 [hyper,1,116,853] P(i(n(i(n(i(x,y)),i(z,x))),u)). given clause #209: (wt=65) 87 [hyper,1,2,24] P(i(x,i(i(i(i(y,z),z),u),i(i(i(z,y),y),u)))). given clause #210: (wt=19) 930 [hyper,1,116,859] P(i(n(i(i(i(n(i(x,y)),x),z),z)),u)). given clause #211: (wt=19) 937 [hyper,1,380,863] P(n(n(i(n(i(n(i(n(i(x,y)),x)),z)),u)))). given clause #212: (wt=19) 986 [hyper,1,367,372] P(n(n(i(x,n(n(i(n(x),y))))))). given clause #213: (wt=24) 88 [hyper,1,24,51] P(i(i(i(i(x,y),n(x)),n(x)),i(x,y))). given clause #214: (wt=19) 1079 [hyper,1,142,1058] P(i(n(i(n(i(n(i(n(n(x)),y)),x)),z)),u)). given clause #215: (wt=19) 1083 [hyper,1,34,1058] P(i(i(n(n(i(n(i(n(n(x)),y)),x))),z),z)). given clause #216: (wt=19) 1093 [hyper,1,367,376] P(n(n(i(n(n(x)),n(n(i(y,x))))))). given clause #217: (wt=35) 90 [hyper,1,24,34] P(i(i(i(x,y),y),i(i(i(i(y,x),x),z),z))). given clause #218: (wt=19) 1121 [hyper,1,44,1106] P(i(n(i(x,y)),i(z,n(y)))). given clause #219: (wt=19) 1131 [hyper,1,142,1114] P(i(n(i(n(i(n(i(x,y)),n(y))),z)),u)). given clause #220: (wt=19) 1135 [hyper,1,34,1114] P(i(i(n(n(i(n(i(x,y)),n(y)))),z),z)). given clause #221: (wt=50) 91 [hyper,1,24,21] P(i(i(i(i(x,y),i(z,y)),i(z,y)),i(i(x,z),i(x,y)))). given clause #222: (wt=19) 1153 [hyper,1,367,472] P(n(n(i(i(i(n(i(n(n(x)),x)),y),z),z)))). given clause #223: (wt=19) 1171 [hyper,1,367,479] P(n(n(i(i(n(n(i(x,n(n(x))))),y),y)))). given clause #224: (wt=19) 1235 [hyper,1,367,590] P(n(n(i(i(i(n(n(x)),x),x),n(n(x)))))). given clause #225: (wt=47) 92 [hyper,1,24,3] P(i(i(i(x,y),y),i(i(x,z),i(i(y,x),z)))). given clause #226: (wt=19) 1272 [hyper,1,367,673] P(n(n(i(i(i(n(i(x,n(y))),y),z),z)))). given clause #227: (wt=19) 1285 [hyper,1,367,739] P(n(n(i(n(i(x,n(y))),i(z,y))))). given clause #228: (wt=19) 1307 [hyper,1,673,59] P(i(n(i(x,n(n(y)))),i(y,z))). given clause #229: (wt=21) 93 [hyper,1,34,71] P(i(i(i(n(i(x,y)),i(y,z)),u),u)). given clause #230: (wt=19) 1338 [hyper,1,367,868] P(n(n(i(i(n(n(i(n(i(x,y)),x))),z),z)))). given clause #231: (wt=19) 1390 [hyper,1,367,1065] P(n(n(i(n(i(n(n(x)),y)),i(z,x))))). given clause #232: (wt=19) 1400 [hyper,1,367,1071] P(n(n(i(i(i(n(i(n(n(x)),y)),x),z),z)))). given clause #233: (wt=25) 94 [hyper,1,3,71] P(i(i(i(x,y),z),i(n(i(u,x)),z))). given clause #234: (wt=19) 1414 [hyper,1,367,1126] P(n(n(i(i(i(n(i(x,y)),n(y)),z),z)))). given clause #235: (wt=19) 1447 [hyper,1,362,859] P(i(i(i(n(i(x,y)),x),n(n(z))),z)). given clause #236: (wt=19) 1451 [hyper,1,362,465] P(i(i(n(n(i(n(n(x)),x))),n(n(y))),y)). given clause #237: (wt=31) 95 [hyper,1,2,71] P(i(x,i(n(i(y,z)),i(z,u)))). given clause #238: (wt=19) 1453 [hyper,1,362,382] P(i(i(i(x,n(n(x))),n(n(y))),y)). given clause #239: (wt=19) 1471 [hyper,1,367,1452] P(n(n(i(i(n(n(i(x,x))),n(n(y))),y)))). given clause #240: (wt=19) 1491 [hyper,1,367,1454] P(n(n(i(i(i(n(n(x)),x),n(n(y))),y)))). given clause #241: (wt=22) 96 [hyper,1,34,68] P(i(i(i(n(i(n(x),i(x,y))),z),u),u)). given clause #242: (wt=19) 1521 [hyper,1,55,369] P(i(n(n(i(n(x),n(y)))),i(y,x))). given clause #243: (wt=19) 1522 [hyper,1,53,369] P(i(n(n(i(i(x,y),z))),i(y,z))). given clause #244: (wt=19) 1523 [hyper,1,52,369] P(i(n(n(i(i(x,i(y,x)),z))),z)). given clause #245: (wt=36) 97 [hyper,1,3,68] P(i(i(x,y),i(n(i(n(z),i(z,u))),y))). given clause #246: (wt=19) 1536 [hyper,1,369,1454] P(i(n(n(i(i(n(n(x)),x),n(n(y))))),y)). given clause #247: (wt=19) 1537 [hyper,1,369,1452] P(i(n(n(i(n(n(i(x,x))),n(n(y))))),y)). given clause #248: (wt=19) 1538 [hyper,1,369,1126] P(i(n(n(i(i(n(i(x,y)),n(y)),z))),z)). given clause #249: (wt=33) 98 [hyper,1,2,68] P(i(x,i(n(i(n(y),i(y,z))),u))). given clause #250: (wt=19) 1539 [hyper,1,369,1071] P(i(n(n(i(i(n(i(n(n(x)),y)),x),z))),z)). given clause #251: (wt=19) 1540 [hyper,1,369,868] P(i(n(n(i(n(n(i(n(i(x,y)),x))),z))),z)). given clause #252: (wt=19) 1542 [hyper,1,369,673] P(i(n(n(i(i(n(i(x,n(y))),y),z))),z)). given clause #253: (wt=23) 99 [hyper,1,34,62] P(i(i(i(n(i(x,y)),i(n(x),z)),u),u)). given clause #254: (wt=19) 1543 [hyper,1,369,590] P(i(n(n(i(i(n(n(x)),x),x))),n(n(x)))). given clause #255: (wt=19) 1544 [hyper,1,369,479] P(i(n(n(i(n(n(i(x,n(n(x))))),y))),y)). given clause #256: (wt=19) 1545 [hyper,1,369,472] P(i(n(n(i(i(n(i(n(n(x)),x)),y),z))),z)). given clause #257: (wt=26) 100 [hyper,1,3,62] P(i(i(i(n(x),y),z),i(n(i(x,u)),z))). given clause #258: (wt=19) 1598 [hyper,1,116,1547] P(i(n(i(n(n(i(n(n(i(x,x))),y))),y)),z)). given clause #259: (wt=19) 1619 [hyper,1,116,1550] P(i(n(i(n(n(i(i(n(n(x)),x),y))),y)),z)). given clause #260: (wt=19) 1637 [hyper,1,367,1541] P(n(n(i(n(n(i(i(n(i(x,y)),x),z))),z)))). given clause #261: (wt=35) 101 [hyper,1,2,62] P(i(x,i(n(i(y,z)),i(n(y),u)))). given clause #262: (wt=19) 1690 [hyper,1,65,146] P(i(n(i(n(i(x,y)),z)),i(y,u))). given clause #263: (wt=19) 1713 [hyper,1,367,1546] P(n(n(i(n(n(i(n(n(i(n(n(x)),x))),y))),y)))). given clause #264: (wt=19) 1736 [hyper,1,367,1549] P(n(n(i(n(n(i(i(x,n(n(x))),y))),y)))). given clause #265: (wt=53) 102 [hyper,1,34,25] P(i(i(i(x,i(i(i(y,z),z),i(i(z,y),y))),u),u)). given clause #266: (wt=19) 1771 [hyper,1,55,66] P(i(i(i(x,y),n(z)),i(z,x))). given clause #267: (wt=13) 2930 [hyper,1,1771,372] P(i(n(i(n(i(x,y)),z)),x)). given clause #268: (wt=15) 2929 [hyper,1,1771,388] P(i(n(i(x,i(y,z))),y)). given clause #269: (wt=35) 103 [hyper,1,3,25] P(i(i(i(i(i(x,y),y),i(i(y,x),x)),z),i(u,z))). given clause #270: (wt=15) 2934 [hyper,1,367,2930] P(n(n(i(n(i(n(i(x,y)),z)),x)))). given clause #271: (wt=15) 2935 [hyper,1,362,2930] P(i(n(i(n(i(n(n(x)),y)),z)),x)). given clause #272: (wt=17) 2937 [hyper,1,116,2930] P(i(n(i(n(i(n(i(x,y)),z)),x)),u)). given clause #273: (wt=95) 104 [hyper,1,2,25] P(i(x,i(y,i(i(i(z,u),u),i(i(u,z),z))))). given clause #274: (wt=17) 2948 [hyper,1,367,2929] P(n(n(i(n(i(x,i(y,z))),y)))). given clause #275: (wt=17) 2973 [hyper,1,367,2935] P(n(n(i(n(i(n(i(n(n(x)),y)),z)),x)))). given clause #276: (wt=19) 2540 [hyper,1,382,94] P(i(n(i(x,y)),n(n(i(y,z))))). given clause #277: (wt=25) 106 [hyper,1,34,75] P(i(i(i(i(i(n(n(x)),i(y,x)),z),z),u),u)). given clause #278: (wt=19) 2933 [hyper,1,372,2930] P(n(n(i(n(i(n(i(n(i(x,y)),z)),x)),u)))). given clause #279: (wt=19) 2941 [hyper,1,44,2930] P(i(n(i(n(i(x,y)),z)),i(u,x))). given clause #280: (wt=19) 2942 [hyper,1,34,2930] P(i(i(i(n(i(n(i(x,y)),z)),x),u),u)). given clause #281: (wt=28) 107 [hyper,1,24,75] P(i(i(i(i(x,y),n(n(y))),n(n(y))),i(x,y))). given clause #282: (wt=19) 2949 [hyper,1,362,2929] P(i(n(i(x,i(n(n(y)),z))),y)). given clause #283: (wt=19) 2951 [hyper,1,116,2929] P(i(n(i(n(i(x,i(y,z))),y)),u)). given clause #284: (wt=19) 2975 [hyper,1,116,2935] P(i(n(i(n(i(n(i(n(n(x)),y)),z)),x)),u)). given clause #285: (wt=30) 108 [hyper,1,21,75] P(i(i(x,n(n(y))),i(x,i(z,y)))). given clause #286: (wt=20) 394 [hyper,1,367,229] P(n(n(i(n(i(i(x,y),y)),i(x,z))))). given clause #287: (wt=20) 400 [hyper,1,367,148] P(n(n(i(i(i(n(x),y),z),i(x,z))))). given clause #288: (wt=20) 416 [hyper,1,367,51] P(n(n(i(i(i(n(x),i(x,y)),z),z)))). given clause #289: (wt=42) 109 [hyper,1,3,75] P(i(i(x,y),i(i(i(n(n(z)),i(u,z)),x),y))). given clause #290: (wt=20) 547 [hyper,1,34,378] P(i(i(n(n(i(n(x),i(x,y)))),z),z)). given clause #291: (wt=20) 823 [hyper,1,116,380] P(i(n(i(n(x),n(n(i(x,y))))),z)). given clause #292: (wt=20) 966 [hyper,1,116,390] P(i(n(i(i(n(n(x)),y),i(x,y))),z)). given clause #293: (wt=39) 110 [hyper,1,2,75] P(i(x,i(i(i(n(n(y)),i(z,y)),u),u))). given clause #294: (wt=20) 1011 [hyper,1,3,372] P(i(i(n(n(i(n(x),y))),z),i(x,z))). given clause #295: (wt=20) 1425 [hyper,1,367,362] P(n(n(i(i(x,n(n(y))),i(x,y))))). given clause #296: (wt=20) 1511 [hyper,1,369,369] P(i(n(n(i(x,y))),i(n(n(x)),y))). given clause #297: (wt=23) 111 [hyper,1,34,105] P(i(i(i(n(i(n(n(x)),i(y,x))),z),u),u)). given clause #298: (wt=20) 1512 [hyper,1,367,369] P(n(n(i(i(x,y),i(n(n(x)),y))))). given clause #299: (wt=20) 1518 [hyper,1,58,369] P(i(n(n(i(i(n(x),i(x,y)),z))),z)). given clause #300: (wt=20) 1551 [hyper,1,369,362] P(i(n(n(i(x,n(n(y))))),i(x,y))). given clause #301: (wt=38) 112 [hyper,1,3,105] P(i(i(x,y),i(n(i(n(n(z)),i(u,z))),y))). given clause #302: (wt=20) 1553 [hyper,1,369,148] P(i(n(n(i(i(n(x),y),z))),i(x,z))). given clause #303: (wt=20) 1818 [hyper,1,367,1548] P(n(n(i(n(n(i(n(n(x)),y))),i(x,y))))). given clause #304: (wt=20) 2940 [hyper,1,59,2930] P(i(n(i(n(i(n(x),y)),z)),i(x,u))). given clause #305: (wt=35) 113 [hyper,1,2,105] P(i(x,i(n(i(n(n(y)),i(z,y))),u))). given clause #306: (wt=21) 150 [hyper,1,116,105] P(i(n(i(n(i(n(n(x)),i(y,x))),z)),u)). given clause #307: (wt=21) 156 [hyper,1,116,62] P(i(n(i(n(i(x,y)),i(n(x),z))),u)). given clause #308: (wt=21) 159 [hyper,1,116,34] P(i(n(i(x,i(i(x,y),y))),z)). given clause #309: (wt=25) 115 [hyper,1,34,89] P(i(i(i(i(i(x,y),y),i(n(y),x)),z),z)). given clause #310: (wt=21) 160 [hyper,1,116,28] P(i(n(i(i(i(x,i(y,x)),z),z)),u)). given clause #311: (wt=21) 164 [hyper,1,116,23] P(i(n(i(i(i(x,y),z),i(y,z))),u)). given clause #312: (wt=21) 166 [hyper,1,116,5] P(i(n(i(i(n(x),n(y)),i(y,x))),z)). given clause #313: (wt=30) 117 [hyper,1,3,89] P(i(i(i(n(x),y),z),i(i(i(y,x),x),z))). given clause #314: (wt=21) 167 [hyper,1,116,114] P(i(n(i(n(i(x,y)),i(n(y),x))),z)). given clause #315: (wt=21) 171 [hyper,1,116,141] P(i(n(i(n(i(x,i(n(x),y))),z)),u)). given clause #316: (wt=21) 184 [hyper,1,24,148] P(i(i(i(x,n(y)),n(y)),i(y,x))). given clause #317: (wt=39) 118 [hyper,1,2,89] P(i(x,i(i(i(y,z),z),i(n(z),y)))). given clause #318: (wt=21) 188 [hyper,1,148,116] P(i(x,i(n(i(n(x),y)),z))). given clause #319: (wt=21) 222 [hyper,1,3,146] P(i(i(i(n(i(x,y)),z),u),i(y,u))). given clause #320: (wt=21) 303 [hyper,1,31,5] P(i(i(i(x,n(y)),n(z)),i(z,y))). given clause #321: (wt=27) 119 [hyper,1,89,25] P(i(n(i(i(i(x,y),y),i(i(y,x),x))),z)). given clause #322: (wt=15) 3444 [hyper,1,303,372] P(i(n(i(n(i(x,n(y))),z)),y)). given clause #323: (wt=17) 3452 [hyper,1,367,3444] P(n(n(i(n(i(n(i(x,n(y))),z)),y)))). given clause #324: (wt=19) 3443 [hyper,1,303,388] P(i(n(i(x,i(y,n(z)))),z)). given clause #325: (wt=36) 120 [hyper,1,89,22] P(i(n(i(i(x,y),i(i(y,z),i(x,z)))),u)). given clause #326: (wt=19) 3454 [hyper,1,116,3444] P(i(n(i(n(i(n(i(x,n(y))),z)),y)),u)). given clause #327: (wt=21) 325 [hyper,1,143,76] P(i(n(n(x)),i(n(i(y,x)),z))). given clause #328: (wt=21) 379 [hyper,1,49,367] P(i(x,n(n(i(i(x,y),y))))). given clause #329: (wt=27) 121 [hyper,1,37,26] P(i(n(i(x,y)),i(i(n(y),n(x)),z))). given clause #330: (wt=13) 3527 [hyper,1,5,379] P(i(n(i(i(n(x),y),y)),x)). given clause #331: (wt=15) 3487 [hyper,1,1771,379] P(i(n(i(i(i(x,y),z),z)),x)). given clause #332: (wt=15) 3747 [hyper,1,367,3527] P(n(n(i(n(i(i(n(x),y),y)),x)))). given clause #333: (wt=35) 122 [hyper,1,34,26] P(i(i(i(i(i(x,y),z),i(i(n(y),n(x)),z)),u),u)). given clause #334: (wt=17) 3497 [hyper,1,303,379] P(i(n(i(i(i(x,n(y)),z),z)),y)). given clause #335: (wt=17) 3751 [hyper,1,116,3527] P(i(n(i(n(i(i(n(x),y),y)),x)),z)). given clause #336: (wt=17) 3772 [hyper,1,367,3487] P(n(n(i(n(i(i(i(x,y),z),z)),x)))). given clause #337: (wt=29) 123 [hyper,1,28,26] P(i(i(n(x),n(y)),i(z,i(y,x)))). given clause #338: (wt=17) 3773 [hyper,1,362,3487] P(i(n(i(i(i(n(n(x)),y),z),z)),x)). given clause #339: (wt=19) 3746 [hyper,1,372,3527] P(n(n(i(n(i(n(i(i(n(x),y),y)),x)),z)))). given clause #340: (wt=19) 3759 [hyper,1,44,3527] P(i(n(i(i(n(x),y),y)),i(z,x))). given clause #341: (wt=35) 124 [hyper,1,26,26] P(i(i(n(x),n(i(y,z))),i(i(n(z),n(y)),x))). given clause #342: (wt=19) 3765 [hyper,1,34,3527] P(i(i(i(n(i(i(n(x),y),y)),x),z),z)). given clause #343: (wt=19) 3775 [hyper,1,116,3487] P(i(n(i(n(i(i(i(x,y),z),z)),x)),u)). given clause #344: (wt=19) 3800 [hyper,1,367,3497] P(n(n(i(n(i(i(i(x,n(y)),z),z)),y)))). given clause #345: (wt=29) 125 [hyper,1,24,26] P(i(i(i(x,y),y),i(i(n(x),n(y)),x))). given clause #346: (wt=19) 3849 [hyper,1,367,3773] P(n(n(i(n(i(i(i(n(n(x)),y),z),z)),x)))). given clause #347: (wt=20) 3755 [hyper,1,59,3527] P(i(n(i(i(n(n(x)),y),y)),i(x,z))). given clause #348: (wt=21) 381 [hyper,1,35,367] P(i(i(i(x,n(n(x))),y),i(z,y))). given clause #349: (wt=38) 126 [hyper,1,21,26] P(i(i(x,y),i(i(n(z),n(y)),i(x,z)))). given clause #350: (wt=21) 383 [hyper,1,31,367] P(i(i(i(x,y),z),n(n(i(y,z))))). given clause #351: (wt=21) 386 [hyper,1,26,367] P(i(i(n(x),n(y)),n(n(i(y,x))))). given clause #352: (wt=19) 4202 [hyper,1,100,386] P(i(n(i(x,y)),n(n(i(z,x))))). given clause #353: (wt=35) 127 [hyper,1,3,26] P(i(i(i(i(n(x),n(y)),z),u),i(i(i(y,x),z),u))). given clause #354: (wt=21) 398 [hyper,1,367,154] P(n(n(i(n(i(n(i(x,i(y,x))),z)),u)))). given clause #355: (wt=21) 399 [hyper,1,367,153] P(n(n(i(n(i(n(i(x,y)),i(y,z))),u)))). given clause #356: (wt=21) 401 [hyper,1,367,146] P(n(n(i(x,i(n(i(y,x)),z))))). given clause #357: (wt=59) 128 [hyper,1,2,26] P(i(x,i(i(i(y,z),u),i(i(n(z),n(y)),u)))). given clause #358: (wt=21) 402 [hyper,1,367,143] P(n(n(i(i(i(x,i(n(x),y)),z),z)))). given clause #359: (wt=21) 408 [hyper,1,367,89] P(n(n(i(i(i(x,y),y),i(n(y),x))))). given clause #360: (wt=21) 410 [hyper,1,367,75] P(n(n(i(i(i(n(n(x)),i(y,x)),z),z)))). given clause #361: (wt=25) 129 [hyper,1,26,89] P(i(i(n(x),n(i(y,x))),i(n(x),y))). given clause #362: (wt=21) 419 [hyper,1,367,37] P(n(n(i(i(i(x,y),z),i(n(x),z))))). given clause #363: (wt=21) 464 [hyper,1,35,392] P(i(i(n(n(i(n(n(x)),x))),y),i(z,y))). given clause #364: (wt=21) 489 [hyper,1,31,366] P(i(i(i(x,i(n(n(y)),y)),z),z)). given clause #365: (wt=33) 130 [hyper,1,26,75] P(i(i(n(x),n(i(n(n(y)),i(z,y)))),x)). given clause #366: (wt=21) 490 [hyper,1,26,366] P(i(i(n(x),n(i(n(n(y)),y))),x)). given clause #367: (wt=21) 507 [hyper,1,366,40] P(i(i(i(x,i(y,x)),n(n(z))),z)). given clause #368: (wt=21) 517 [hyper,1,40,367] P(i(i(i(x,i(y,x)),z),n(n(z)))). given clause #369: (wt=31) 131 [hyper,1,26,51] P(i(i(n(x),n(i(n(y),i(y,z)))),x)). given clause #370: (wt=21) 535 [hyper,1,31,440] P(i(i(i(x,n(n(i(y,y)))),z),z)). given clause #371: (wt=21) 557 [hyper,1,34,374] P(i(i(n(n(i(x,i(n(x),y)))),z),z)). given clause #372: (wt=21) 562 [hyper,1,34,377] P(i(i(n(n(i(n(n(x)),i(y,x)))),z),z)). given clause #373: (wt=25) 132 [hyper,1,26,37] P(i(i(n(x),n(i(y,z))),i(n(y),x))). given clause #374: (wt=21) 587 [hyper,1,34,382] P(i(i(i(i(i(x,n(n(x))),y),y),z),z)). given clause #375: (wt=21) 595 [hyper,1,382,388] P(n(n(i(x,i(y,n(n(y))))))). given clause #376: (wt=21) 611 [hyper,1,34,388] P(i(i(i(x,n(n(i(y,x)))),z),z)). given clause #377: (wt=29) 133 [hyper,1,26,34] P(i(i(n(x),n(y)),i(i(i(y,x),z),z))). given clause #378: (wt=21) 623 [hyper,1,388,392] P(n(n(i(x,n(n(i(n(n(y)),y))))))). given clause #379: (wt=21) 725 [hyper,1,34,462] P(i(i(i(n(i(n(i(n(n(x)),x)),y)),z),u),u)). given clause #380: (wt=21) 768 [hyper,1,34,465] P(i(i(i(i(n(n(i(n(n(x)),x))),y),y),z),z)). given clause #381: (wt=29) 134 [hyper,1,26,28] P(i(i(n(x),n(i(y,i(z,y)))),x)). given clause #382: (wt=21) 774 [hyper,1,142,482] P(i(n(i(n(i(i(i(n(n(x)),x),y),y)),z)),u)). given clause #383: (wt=21) 777 [hyper,1,34,482] P(i(i(n(n(i(i(i(n(n(x)),x),y),y))),z),z)). given clause #384: (wt=21) 781 [hyper,1,142,494] P(i(n(i(n(i(n(i(x,n(n(x)))),y)),z)),u)). given clause #385: (wt=41) 135 [hyper,1,26,24] P(i(i(n(x),n(i(i(y,z),z))),i(i(i(z,y),y),x))). given clause #386: (wt=21) 784 [hyper,1,34,494] P(i(i(n(n(i(n(i(x,n(n(x)))),y))),z),z)). given clause #387: (wt=21) 808 [hyper,1,142,527] P(i(n(i(n(i(i(n(n(i(x,x))),y),y)),z)),u)). given clause #388: (wt=21) 811 [hyper,1,34,527] P(i(i(n(n(i(i(n(n(i(x,x))),y),y))),z),z)). given clause #389: (wt=23) 136 [hyper,1,26,23] P(i(i(n(x),n(i(y,z))),i(z,x))). given clause #390: (wt=21) 816 [hyper,1,34,668] P(i(i(i(n(i(n(i(x,n(y))),y)),z),u),u)). given clause #391: (wt=21) 832 [hyper,1,3,380] P(i(i(n(n(i(x,y))),z),i(n(x),z))). given clause #392: (wt=21) 847 [hyper,1,388,831] P(n(n(i(x,i(n(i(y,z)),y))))). given clause #393: (wt=47) 137 [hyper,1,26,21] P(i(i(n(x),n(i(i(y,z),i(u,z)))),i(i(u,y),x))). given clause #394: (wt=21) 858 [hyper,1,35,831] P(i(i(i(n(i(x,y)),x),z),i(u,z))). given clause #395: (wt=21) 924 [hyper,1,34,853] P(i(i(i(n(i(x,y)),i(z,x)),u),u)). given clause #396: (wt=21) 931 [hyper,1,34,859] P(i(i(i(i(i(n(i(x,y)),x),z),z),u),u)). given clause #397: (wt=29) 139 [hyper,1,26,4] P(i(i(n(x),n(i(y,x))),i(i(x,y),y))). given clause #398: (wt=21) 938 [hyper,1,34,863] P(i(i(n(n(i(n(i(n(i(x,y)),x)),z))),u),u)). given clause #399: (wt=21) 969 [hyper,1,46,390] P(i(x,i(i(n(n(x)),y),y))). given clause #400: (wt=21) 977 [hyper,1,31,390] P(i(i(i(x,n(n(y))),z),i(y,z))). given clause #401: (wt=35) 140 [hyper,1,26,3] P(i(i(n(x),n(y)),i(i(x,z),i(y,z)))). given clause #402: (wt=21) 990 [hyper,1,116,372] P(i(n(i(x,n(n(i(n(x),y))))),z)). given clause #403: (wt=21) 1013 [hyper,1,372,859] P(n(n(i(n(i(i(i(n(i(x,y)),x),z),z)),u)))). given clause #404: (wt=21) 1014 [hyper,1,372,853] P(n(n(i(n(i(n(i(x,y)),i(z,x))),u)))). given clause #405: (wt=25) 144 [hyper,1,26,116] P(i(i(n(x),n(y)),i(n(i(y,x)),z))). given clause #406: (wt=21) 1015 [hyper,1,372,668] P(n(n(i(n(i(n(i(n(i(x,n(y))),y)),z)),u)))). given clause #407: (wt=21) 1016 [hyper,1,372,465] P(n(n(i(n(i(i(n(n(i(n(n(x)),x))),y),y)),z)))). given clause #408: (wt=21) 1017 [hyper,1,372,462] P(n(n(i(n(i(n(i(n(i(n(n(x)),x)),y)),z)),u)))). given clause #409: (wt=31) 145 [hyper,1,24,116] P(i(i(i(x,y),y),i(n(i(i(y,x),x)),z))). given clause #410: (wt=21) 1018 [hyper,1,372,441] P(n(n(i(n(i(x,n(n(i(y,y))))),z)))). given clause #411: (wt=21) 1020 [hyper,1,372,388] P(n(n(i(n(i(x,n(n(i(y,x))))),z)))). given clause #412: (wt=21) 1021 [hyper,1,372,382] P(n(n(i(n(i(i(i(x,n(n(x))),y),y)),z)))). given clause #413: (wt=40) 147 [hyper,1,21,116] P(i(i(x,y),i(n(i(i(y,z),i(x,z))),u))). given clause #414: (wt=21) 1023 [hyper,1,372,327] P(n(n(i(n(i(x,i(n(n(y)),y))),z)))). given clause #415: (wt=21) 1086 [hyper,1,372,1061] P(n(n(i(n(i(n(i(n(i(n(n(x)),y)),x)),z)),u)))). given clause #416: (wt=21) 1088 [hyper,1,34,1061] P(i(i(i(n(i(n(i(n(n(x)),y)),x)),z),u),u)). given clause #417: (wt=27) 149 [hyper,1,2,116] P(i(x,i(y,i(n(y),z)))). given clause #418: (wt=21) 1096 [hyper,1,116,376] P(i(n(i(n(n(x)),n(n(i(y,x))))),z)). given clause #419: (wt=21) 1138 [hyper,1,372,1117] P(n(n(i(n(i(n(i(n(i(x,y)),n(y))),z)),u)))). given clause #420: (wt=21) 1140 [hyper,1,34,1117] P(i(i(i(n(i(n(i(x,y)),n(y))),z),u),u)). given clause #421: (wt=23) 151 [hyper,1,116,89] P(i(n(i(i(i(x,y),y),i(n(y),x))),z)). given clause #422: (wt=21) 1155 [hyper,1,116,472] P(i(n(i(i(i(n(i(n(n(x)),x)),y),z),z)),u)). given clause #423: (wt=21) 1174 [hyper,1,116,479] P(i(n(i(i(n(n(i(x,n(n(x))))),y),y)),z)). given clause #424: (wt=21) 1238 [hyper,1,116,590] P(i(n(i(i(i(n(n(x)),x),x),n(n(x)))),y)). given clause #425: (wt=23) 152 [hyper,1,116,75] P(i(n(i(i(i(n(n(x)),i(y,x)),z),z)),u)). given clause #426: (wt=21) 1274 [hyper,1,116,673] P(i(n(i(i(i(n(i(x,n(y))),y),z),z)),u)). given clause #427: (wt=21) 1287 [hyper,1,116,739] P(i(n(i(n(i(x,n(y))),i(z,y))),u)). given clause #428: (wt=21) 1324 [hyper,1,59,590] P(i(i(i(n(n(x)),x),x),i(n(x),y))). given clause #429: (wt=22) 157 [hyper,1,116,51] P(i(n(i(i(i(n(x),i(x,y)),z),z)),u)). given clause #430: (wt=21) 1328 [hyper,1,59,440] P(i(i(n(n(i(x,x))),n(y)),i(y,z))). given clause #431: (wt=21) 1330 [hyper,1,59,366] P(i(i(i(n(n(x)),x),n(y)),i(y,z))). given clause #432: (wt=21) 1340 [hyper,1,116,868] P(i(n(i(i(n(n(i(n(i(x,y)),x))),z),z)),u)). given clause #433: (wt=23) 158 [hyper,1,116,37] P(i(n(i(i(i(x,y),z),i(n(x),z))),u)). given clause #434: (wt=21) 1392 [hyper,1,116,1065] P(i(n(i(n(i(n(n(x)),y)),i(z,x))),u)). given clause #435: (wt=21) 1402 [hyper,1,116,1071] P(i(n(i(i(i(n(i(n(n(x)),y)),x),z),z)),u)). given clause #436: (wt=21) 1416 [hyper,1,116,1126] P(i(n(i(i(i(n(i(x,y)),n(y)),z),z)),u)). given clause #437: (wt=33) 161 [hyper,1,116,26] P(i(n(i(i(i(x,y),z),i(i(n(y),n(x)),z))),u)). given clause #438: (wt=21) 1440 [hyper,1,31,362] P(i(i(i(x,y),n(n(z))),i(y,z))). given clause #439: (wt=21) 1444 [hyper,1,362,1126] P(i(i(i(n(i(x,y)),n(y)),n(n(z))),z)). given clause #440: (wt=21) 1445 [hyper,1,362,1071] P(i(i(i(n(i(n(n(x)),y)),x),n(n(z))),z)). given clause #441: (wt=51) 162 [hyper,1,116,25] P(i(n(i(x,i(i(i(y,z),z),i(i(z,y),y)))),u)). given clause #442: (wt=21) 1446 [hyper,1,362,868] P(i(i(n(n(i(n(i(x,y)),x))),n(n(z))),z)). given clause #443: (wt=21) 1448 [hyper,1,362,673] P(i(i(i(n(i(x,n(y))),y),n(n(z))),z)). given clause #444: (wt=21) 1449 [hyper,1,362,479] P(i(i(n(n(i(x,n(n(x))))),n(n(y))),y)). given clause #445: (wt=36) 163 [hyper,1,116,24] P(i(n(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))),u)). given clause #446: (wt=21) 1450 [hyper,1,362,472] P(i(i(i(n(i(n(n(x)),x)),y),n(n(z))),z)). given clause #447: (wt=21) 1474 [hyper,1,116,1452] P(i(n(i(i(n(n(i(x,x))),n(n(y))),y)),z)). given clause #448: (wt=21) 1494 [hyper,1,116,1454] P(i(n(i(i(i(n(n(x)),x),n(n(y))),y)),z)). given clause #449: (wt=27) 165 [hyper,1,116,20] P(i(n(i(x,i(y,i(z,y)))),u)). given clause #450: (wt=21) 1516 [hyper,1,63,369] P(i(n(n(i(i(x,y),z))),i(n(x),z))). given clause #451: (wt=21) 1524 [hyper,1,49,369] P(i(x,i(n(n(i(x,y))),y))). given clause #452: (wt=20) 5560 [hyper,1,65,1524] P(i(n(i(n(n(i(x,y))),y)),i(x,z))). given clause #453: (wt=23) 168 [hyper,1,34,114] P(i(i(i(n(i(x,y)),i(n(y),x)),z),z)). given clause #454: (wt=21) 1534 [hyper,1,26,369] P(i(i(n(x),n(y)),i(n(n(y)),x))). given clause #455: (wt=21) 1554 [hyper,1,369,143] P(i(n(n(i(i(x,i(n(x),y)),z))),z)). given clause #456: (wt=21) 1556 [hyper,1,369,89] P(i(n(n(i(i(x,y),y))),i(n(y),x))). given clause #457: (wt=26) 169 [hyper,1,3,114] P(i(i(i(n(x),y),z),i(n(i(y,x)),z))). given clause #458: (wt=20) 6004 [hyper,1,169,386] P(i(n(i(n(x),y)),n(n(i(x,y))))). given clause #459: (wt=21) 1558 [hyper,1,369,75] P(i(n(n(i(i(n(n(x)),i(y,x)),z))),z)). given clause #460: (wt=21) 1594 [hyper,1,372,1547] P(n(n(i(n(i(n(n(i(n(n(i(x,x))),y))),y)),z)))). given clause #461: (wt=35) 170 [hyper,1,2,114] P(i(x,i(n(i(y,z)),i(n(z),y)))). given clause #462: (wt=21) 1604 [hyper,1,44,1547] P(i(n(n(i(n(n(i(x,x))),y))),i(z,y))). given clause #463: (wt=21) 1610 [hyper,1,34,1547] P(i(i(i(n(n(i(n(n(i(x,x))),y))),y),z),z)). given clause #464: (wt=21) 1615 [hyper,1,372,1550] P(n(n(i(n(i(n(n(i(i(n(n(x)),x),y))),y)),z)))). given clause #465: (wt=23) 172 [hyper,1,34,141] P(i(i(i(n(i(x,i(n(x),y))),z),u),u)). given clause #466: (wt=21) 1625 [hyper,1,44,1550] P(i(n(n(i(i(n(n(x)),x),y))),i(z,y))). given clause #467: (wt=21) 1631 [hyper,1,34,1550] P(i(i(i(n(n(i(i(n(n(x)),x),y))),y),z),z)). given clause #468: (wt=21) 1638 [hyper,1,362,1541] P(i(n(n(i(i(n(i(x,y)),x),n(n(z))))),z)). given clause #469: (wt=38) 173 [hyper,1,3,141] P(i(i(x,y),i(n(i(z,i(n(z),u))),y))). given clause #470: (wt=21) 1640 [hyper,1,116,1541] P(i(n(i(n(n(i(i(n(i(x,y)),x),z))),z)),u)). given clause #471: (wt=21) 1692 [hyper,1,65,142] P(i(n(i(n(i(x,y)),z)),i(n(x),u))). given clause #472: (wt=21) 1704 [hyper,1,65,47] P(i(n(i(i(i(x,y),z),z)),i(y,u))). given clause #473: (wt=35) 174 [hyper,1,2,141] P(i(x,i(n(i(y,i(n(y),z))),u))). given clause #474: (wt=21) 1707 [hyper,1,65,36] P(i(n(i(x,i(y,z))),i(z,u))). given clause #475: (wt=21) 1714 [hyper,1,362,1546] P(i(n(n(i(n(n(i(n(n(x)),x))),n(n(y))))),y)). given clause #476: (wt=21) 1717 [hyper,1,116,1546] P(i(n(i(n(n(i(n(n(i(n(n(x)),x))),y))),y)),z)). given clause #477: (wt=39) 175 [hyper,1,116,27] P(i(n(i(x,i(i(n(y),n(z)),i(z,y)))),u)). given clause #478: (wt=21) 1737 [hyper,1,362,1549] P(i(n(n(i(i(x,n(n(x))),n(n(y))))),y)). given clause #479: (wt=21) 1740 [hyper,1,116,1549] P(i(n(i(n(n(i(i(x,n(n(x))),y))),y)),z)). given clause #480: (wt=21) 1858 [hyper,1,367,328] P(n(n(i(n(i(x,y)),i(n(n(y)),z))))). given clause #481: (wt=41) 176 [hyper,1,34,27] P(i(i(i(x,i(i(n(y),n(z)),i(z,y))),u),u)). given clause #482: (wt=21) 1869 [hyper,1,367,340] P(n(n(i(n(n(x)),i(i(x,y),y))))). given clause #483: (wt=21) 1893 [hyper,1,367,365] P(n(n(i(i(i(n(n(x)),x),y),i(z,y))))). given clause #484: (wt=21) 1970 [hyper,1,367,439] P(n(n(i(i(n(n(i(x,x))),y),i(z,y))))). given clause #485: (wt=29) 177 [hyper,1,3,27] P(i(i(i(i(n(x),n(y)),i(y,x)),z),i(u,z))). given clause #486: (wt=21) 1987 [hyper,1,369,488] P(i(n(n(i(i(i(i(n(n(x)),x),y),y),z))),z)). given clause #487: (wt=21) 1988 [hyper,1,367,488] P(n(n(i(i(i(i(i(n(n(x)),x),y),y),z),z)))). given clause #488: (wt=21) 2000 [hyper,1,367,491] P(n(n(i(i(i(x,n(n(x))),n(n(x))),x)))). given clause #489: (wt=71) 178 [hyper,1,2,27] P(i(x,i(y,i(i(n(z),n(u)),i(u,z))))). given clause #490: (wt=21) 2030 [hyper,1,369,499] P(i(n(n(i(i(n(i(x,n(n(x)))),y),z))),z)). given clause #491: (wt=21) 2031 [hyper,1,367,499] P(n(n(i(i(i(n(i(x,n(n(x)))),y),z),z)))). given clause #492: (wt=21) 2044 [hyper,1,369,505] P(i(n(n(i(n(n(i(x,i(y,x)))),z))),z)). given clause #493: (wt=22) 179 [hyper,1,116,148] P(i(n(i(i(i(n(x),y),z),i(x,z))),u)). given clause #494: (wt=21) 2045 [hyper,1,367,505] P(n(n(i(i(n(n(i(x,i(y,x)))),z),z)))). given clause #495: (wt=21) 2056 [hyper,1,369,534] P(i(n(n(i(i(i(n(n(i(x,x))),y),y),z))),z)). given clause #496: (wt=21) 2057 [hyper,1,367,534] P(n(n(i(i(i(i(n(n(i(x,x))),y),y),z),z)))). given clause #497: (wt=24) 181 [hyper,1,34,148] P(i(i(i(i(i(n(x),y),z),i(x,z)),u),u)). given clause #498: (wt=21) 2073 [hyper,1,369,542] P(i(n(n(i(n(n(i(n(i(n(n(x)),x)),y))),z))),z)). given clause #499: (wt=21) 2074 [hyper,1,367,542] P(n(n(i(i(n(n(i(n(i(n(n(x)),x)),y))),z),z)))). given clause #500: (wt=21) 2099 [hyper,1,367,601] P(n(n(i(x,i(y,n(n(x))))))). given clause #501: (wt=27) 182 [hyper,1,28,148] P(i(x,i(y,i(n(x),z)))). given clause #502: (wt=21) 2197 [hyper,1,369,619] P(i(n(n(i(n(n(i(x,y))),z))),i(y,z))). given clause #503: (wt=21) 2198 [hyper,1,367,619] P(n(n(i(i(n(n(i(x,y))),z),i(y,z))))). given clause #504: (wt=21) 2233 [hyper,1,369,715] P(i(n(n(i(n(n(i(n(i(x,n(y))),y))),z))),z)). given clause #505: (wt=25) 183 [hyper,1,26,148] P(i(i(n(x),n(i(n(y),z))),i(y,x))). given clause #506: (wt=21) 2234 [hyper,1,367,715] P(n(n(i(i(n(n(i(n(i(x,n(y))),y))),z),z)))). given clause #507: (wt=21) 2365 [hyper,1,369,872] P(i(n(n(i(i(n(i(n(i(x,y)),x)),z),u))),u)). given clause #508: (wt=21) 2366 [hyper,1,367,872] P(n(n(i(i(i(n(i(n(i(x,y)),x)),z),u),u)))). given clause #509: (wt=28) 185 [hyper,1,21,148] P(i(i(x,n(y)),i(y,i(x,z)))). given clause #510: (wt=21) 2406 [hyper,1,369,1083] P(i(n(n(i(n(n(i(n(i(n(n(x)),y)),x))),z))),z)). given clause #511: (wt=21) 2407 [hyper,1,367,1083] P(n(n(i(i(n(n(i(n(i(n(n(x)),y)),x))),z),z)))). given clause #512: (wt=21) 2446 [hyper,1,367,1121] P(n(n(i(n(i(x,y)),i(z,n(y)))))). given clause #513: (wt=31) 186 [hyper,1,3,148] P(i(i(i(x,y),z),i(i(i(n(x),u),y),z))). given clause #514: (wt=21) 2458 [hyper,1,369,1135] P(i(n(n(i(n(n(i(n(i(x,y)),n(y)))),z))),z)). given clause #515: (wt=21) 2459 [hyper,1,367,1135] P(n(n(i(i(n(n(i(n(i(x,y)),n(y)))),z),z)))). given clause #516: (wt=21) 2519 [hyper,1,367,1307] P(n(n(i(n(i(x,n(n(y)))),i(y,z))))). given clause #517: (wt=37) 187 [hyper,1,2,148] P(i(x,i(i(i(n(y),z),u),i(y,u)))). given clause #518: (wt=21) 2568 [hyper,1,367,1447] P(n(n(i(i(i(n(i(x,y)),x),n(n(z))),z)))). given clause #519: (wt=21) 2582 [hyper,1,367,1451] P(n(n(i(i(n(n(i(n(n(x)),x))),n(n(y))),y)))). given clause #520: (wt=21) 2606 [hyper,1,367,1453] P(n(n(i(i(i(x,n(n(x))),n(n(y))),y)))). given clause #521: (wt=25) 189 [hyper,1,148,34] P(i(x,i(i(i(n(x),y),z),z))). given clause #522: (wt=21) 2652 [hyper,1,367,1521] P(n(n(i(n(n(i(n(x),n(y)))),i(y,x))))). given clause #523: (wt=21) 2674 [hyper,1,367,1522] P(n(n(i(n(n(i(i(x,y),z))),i(y,z))))). given clause #524: (wt=21) 2687 [hyper,1,367,1523] P(n(n(i(n(n(i(i(x,i(y,x)),z))),z)))). given clause #525: (wt=22) 191 [hyper,1,34,180] P(i(i(i(n(i(n(x),y)),i(x,z)),u),u)). given clause #526: (wt=21) 2701 [hyper,1,367,1536] P(n(n(i(n(n(i(i(n(n(x)),x),n(n(y))))),y)))). given clause #527: (wt=21) 2723 [hyper,1,367,1537] P(n(n(i(n(n(i(n(n(i(x,x))),n(n(y))))),y)))). given clause #528: (wt=21) 2745 [hyper,1,367,1538] P(n(n(i(n(n(i(i(n(i(x,y)),n(y)),z))),z)))). given clause #529: (wt=27) 192 [hyper,1,3,180] P(i(i(i(x,y),z),i(n(i(n(x),u)),z))). given clause #530: (wt=20) 6927 [hyper,1,382,192] P(i(n(i(n(x),y)),n(n(i(x,z))))). given clause #531: (wt=21) 2761 [hyper,1,367,1539] P(n(n(i(n(n(i(i(n(i(n(n(x)),y)),x),z))),z)))). given clause #532: (wt=21) 2775 [hyper,1,367,1540] P(n(n(i(n(n(i(n(n(i(n(i(x,y)),x))),z))),z)))). given clause #533: (wt=33) 193 [hyper,1,2,180] P(i(x,i(n(i(n(y),z)),i(y,u)))). given clause #534: (wt=21) 2789 [hyper,1,367,1542] P(n(n(i(n(n(i(i(n(i(x,n(y))),y),z))),z)))). given clause #535: (wt=21) 2809 [hyper,1,367,1543] P(n(n(i(n(n(i(i(n(n(x)),x),x))),n(n(x)))))). given clause #536: (wt=21) 2830 [hyper,1,367,1544] P(n(n(i(n(n(i(n(n(i(x,n(n(x))))),y))),y)))). given clause #537: (wt=23) 194 [hyper,1,116,143] P(i(n(i(i(i(x,i(n(x),y)),z),z)),u)). given clause #538: (wt=21) 2855 [hyper,1,367,1545] P(n(n(i(n(n(i(i(n(i(n(n(x)),x)),y),z))),z)))). given clause #539: (wt=21) 2866 [hyper,1,382,100] P(i(n(i(x,y)),n(n(i(n(x),z))))). given clause #540: (wt=21) 2887 [hyper,1,367,1690] P(n(n(i(n(i(n(i(x,y)),z)),i(y,u))))). given clause #541: (wt=25) 195 [hyper,1,34,143] P(i(i(i(i(i(x,i(n(x),y)),z),z),u),u)). given clause #542: (wt=21) 2914 [hyper,1,369,1771] P(i(n(n(i(i(x,y),n(z)))),i(z,x))). given clause #543: (wt=21) 2915 [hyper,1,367,1771] P(n(n(i(i(i(x,y),n(z)),i(z,x))))). given clause #544: (wt=21) 2918 [hyper,1,94,1771] P(i(n(i(x,i(y,z))),i(u,y))). given clause #545: (wt=33) 196 [hyper,1,26,143] P(i(i(n(x),n(i(y,i(n(y),z)))),x)). given clause #546: (wt=21) 2947 [hyper,1,372,2929] P(n(n(i(n(i(n(i(x,i(y,z))),y)),u)))). given clause #547: (wt=21) 2953 [hyper,1,34,2929] P(i(i(i(n(i(x,i(y,z))),y),u),u)). given clause #548: (wt=21) 2969 [hyper,1,34,2934] P(i(i(n(n(i(n(i(n(i(x,y)),z)),x))),u),u)). given clause #549: (wt=23) 197 [hyper,1,24,143] P(i(i(i(i(n(x),y),x),x),i(n(x),y))). given clause #550: (wt=21) 2972 [hyper,1,372,2935] P(n(n(i(n(i(n(i(n(i(n(n(x)),y)),z)),x)),u)))). given clause #551: (wt=21) 2978 [hyper,1,44,2935] P(i(n(i(n(i(n(n(x)),y)),z)),i(u,x))). given clause #552: (wt=21) 2979 [hyper,1,34,2935] P(i(i(i(n(i(n(i(n(n(x)),y)),z)),x),u),u)). given clause #553: (wt=30) 198 [hyper,1,21,143] P(i(i(x,y),i(x,i(n(y),z)))). given clause #554: (wt=21) 2989 [hyper,1,367,2540] P(n(n(i(n(i(x,y)),n(n(i(y,z))))))). given clause #555: (wt=21) 2999 [hyper,1,367,2941] P(n(n(i(n(i(n(i(x,y)),z)),i(u,x))))). given clause #556: (wt=21) 3000 [hyper,1,369,2942] P(i(n(n(i(i(n(i(n(i(x,y)),z)),x),u))),u)). given clause #557: (wt=42) 199 [hyper,1,3,143] P(i(i(x,y),i(i(i(z,i(n(z),u)),x),y))). given clause #558: (wt=21) 3001 [hyper,1,367,2942] P(n(n(i(i(i(n(i(n(i(x,y)),z)),x),u),u)))). given clause #559: (wt=21) 3028 [hyper,1,367,2949] P(n(n(i(n(i(x,i(n(n(y)),z))),y)))). given clause #560: (wt=21) 3346 [hyper,1,117,362] P(i(i(i(n(n(x)),y),y),i(n(y),x))). given clause #561: (wt=39) 200 [hyper,1,2,143] P(i(x,i(i(i(y,i(n(y),z)),u),u))). given clause #562: (wt=21) 3451 [hyper,1,372,3444] P(n(n(i(n(i(n(i(n(i(x,n(y))),z)),y)),u)))). given clause #563: (wt=21) 3457 [hyper,1,44,3444] P(i(n(i(n(i(x,n(y))),z)),i(u,y))). given clause #564: (wt=21) 3458 [hyper,1,34,3444] P(i(i(i(n(i(n(i(x,n(y))),z)),y),u),u)). given clause #565: (wt=35) 201 [hyper,1,26,29] P(i(i(n(x),n(i(y,i(z,y)))),i(u,x))). given clause #566: (wt=21) 3466 [hyper,1,367,3443] P(n(n(i(n(i(x,i(y,n(z)))),z)))). given clause #567: (wt=21) 3745 [hyper,1,379,3527] P(n(n(i(i(i(n(i(i(n(x),y),y)),x),z),z)))). given clause #568: (wt=21) 3749 [hyper,1,188,3527] P(i(n(i(n(i(n(i(i(n(x),y),y)),x)),z)),u)). given clause #569: (wt=32) 202 [hyper,1,24,29] P(i(i(i(i(x,y),y),y),i(z,i(x,y)))). given clause #570: (wt=21) 3771 [hyper,1,372,3487] P(n(n(i(n(i(n(i(i(i(x,y),z),z)),x)),u)))). given clause #571: (wt=21) 3780 [hyper,1,44,3487] P(i(n(i(i(i(x,y),z),z)),i(u,x))). given clause #572: (wt=21) 3781 [hyper,1,34,3487] P(i(i(i(n(i(i(i(x,y),z),z)),x),u),u)). given clause #573: (wt=50) 203 [hyper,1,21,29] P(i(i(x,y),i(z,i(x,i(u,y))))). given clause #574: (wt=21) 3792 [hyper,1,34,3747] P(i(i(n(n(i(n(i(i(n(x),y),y)),x))),z),z)). given clause #575: (wt=21) 3802 [hyper,1,116,3497] P(i(n(i(n(i(i(i(x,n(y)),z),z)),y)),u)). given clause #576: (wt=21) 3851 [hyper,1,116,3773] P(i(n(i(n(i(i(i(n(n(x)),y),z),z)),x)),u)). given clause #577: (wt=55) 204 [hyper,1,29,148] P(i(x,i(y,i(z,i(n(y),u))))). given clause #578: (wt=21) 3864 [hyper,1,367,3759] P(n(n(i(n(i(i(n(x),y),y)),i(z,x))))). given clause #579: (wt=21) 3915 [hyper,1,369,3765] P(i(n(n(i(i(n(i(i(n(x),y),y)),x),z))),z)). given clause #580: (wt=21) 4203 [hyper,1,94,386] P(i(n(i(x,n(y))),n(n(i(z,y))))). given clause #581: (wt=55) 205 [hyper,1,29,143] P(i(x,i(y,i(z,i(n(z),u))))). given clause #582: (wt=21) 4240 [hyper,1,367,4202] P(n(n(i(n(i(x,y)),n(n(i(z,x))))))). given clause #583: (wt=21) 4888 [hyper,1,100,139] P(i(n(i(x,y)),i(i(x,z),z))). given clause #584: (wt=21) 6740 [hyper,1,55,186] P(i(i(i(n(n(x)),y),n(z)),i(z,x))). given clause #585: (wt=55) 206 [hyper,1,29,75] P(i(x,i(y,i(n(n(z)),i(u,z))))). given clause #586: (wt=21) 6749 [hyper,1,186,590] P(i(i(i(n(i(n(n(x)),x)),y),x),n(n(x)))). given clause #587: (wt=21) 6938 [hyper,1,192,386] P(i(n(i(n(n(x)),y)),n(n(i(z,x))))). given clause #588: (wt=21) 7113 [hyper,1,534,198] P(i(i(n(n(i(x,x))),y),i(n(y),z))). given clause #589: (wt=51) 207 [hyper,1,29,51] P(i(x,i(y,i(n(z),i(z,u))))). given clause #590: (wt=21) 7114 [hyper,1,488,198] P(i(i(i(n(n(x)),x),y),i(n(y),z))). given clause #591: (wt=22) 281 [hyper,1,116,229] P(i(n(i(n(i(i(x,y),y)),i(x,z))),u)). given clause #592: (wt=22) 371 [hyper,1,241,367] P(i(i(x,y),i(x,n(n(y))))). given clause #593: (wt=49) 208 [hyper,1,29,37] P(i(x,i(n(y),i(z,i(y,u))))). given clause #594: (wt=13) 7678 [hyper,1,859,371] P(i(n(i(x,y)),n(n(x)))). given clause #595: (wt=15) 7926 [hyper,1,367,7678] P(n(n(i(n(i(x,y)),n(n(x)))))). given clause #596: (wt=17) 7669 [hyper,1,3765,371] P(i(n(i(i(n(x),y),y)),n(n(x)))). given clause #597: (wt=59) 209 [hyper,1,29,26] P(i(x,i(i(n(y),n(z)),i(u,i(z,y))))). given clause #598: (wt=17) 7672 [hyper,1,2942,371] P(i(n(i(n(i(x,y)),z)),n(n(x)))). given clause #599: (wt=17) 7683 [hyper,1,534,371] P(i(i(n(n(i(x,x))),y),n(n(y)))). given clause #600: (wt=17) 7684 [hyper,1,488,371] P(i(i(i(n(n(x)),x),y),n(n(y)))). given clause #601: (wt=83) 210 [hyper,1,29,24] P(i(x,i(i(i(y,z),z),i(u,i(i(z,y),y))))). given clause #602: (wt=17) 7935 [hyper,1,116,7678] P(i(n(i(n(i(x,y)),n(n(x)))),z)). given clause #603: (wt=19) 7668 [hyper,1,3781,371] P(i(n(i(i(i(x,y),z),z)),n(n(x)))). given clause #604: (wt=19) 7670 [hyper,1,3458,371] P(i(n(i(n(i(x,n(y))),z)),n(n(y)))). given clause #605: (wt=47) 211 [hyper,1,29,23] P(i(x,i(y,i(z,i(u,y))))). given clause #606: (wt=19) 7671 [hyper,1,2953,371] P(i(n(i(x,i(y,z))),n(n(y)))). given clause #607: (wt=19) 7673 [hyper,1,1631,371] P(i(n(n(i(i(n(n(x)),x),y))),n(n(y)))). given clause #608: (wt=19) 7674 [hyper,1,1610,371] P(i(n(n(i(n(n(i(x,x))),y))),n(n(y)))). given clause #609: (wt=35) 212 [hyper,1,148,146] P(i(x,i(n(i(y,i(n(x),z))),u))). given clause #610: (wt=19) 7677 [hyper,1,931,371] P(i(i(i(n(i(x,y)),x),z),n(n(z)))). given clause #611: (wt=19) 7680 [hyper,1,768,371] P(i(i(n(n(i(n(n(x)),x))),y),n(n(y)))). given clause #612: (wt=19) 7682 [hyper,1,587,371] P(i(i(i(x,n(n(x))),y),n(n(y)))). given clause #613: (wt=31) 213 [hyper,1,143,146] P(i(n(i(x,i(y,i(n(y),z)))),u)). given clause #614: (wt=19) 7925 [hyper,1,372,7678] P(n(n(i(n(i(n(i(x,y)),n(n(x)))),z)))). given clause #615: (wt=19) 7946 [hyper,1,34,7678] P(i(i(i(n(i(x,y)),n(n(x))),z),z)). given clause #616: (wt=19) 7961 [hyper,1,367,7669] P(n(n(i(n(i(i(n(x),y),y)),n(n(x)))))). given clause #617: (wt=23) 214 [hyper,1,116,146] P(i(n(i(x,i(n(i(y,x)),z))),u)). given clause #618: (wt=19) 7991 [hyper,1,367,7672] P(n(n(i(n(i(n(i(x,y)),z)),n(n(x)))))). given clause #619: (wt=19) 8004 [hyper,1,367,7683] P(n(n(i(i(n(n(i(x,x))),y),n(n(y)))))). given clause #620: (wt=19) 8033 [hyper,1,367,7684] P(n(n(i(i(i(n(n(x)),x),y),n(n(y)))))). given clause #621: (wt=31) 215 [hyper,1,75,146] P(i(n(i(x,i(n(n(y)),i(z,y)))),u)). given clause #622: (wt=20) 7835 [hyper,1,371,390] P(i(i(n(n(x)),y),n(n(i(x,y))))). given clause #623: (wt=21) 7738 [hyper,1,371,3497] P(i(n(i(i(i(x,n(y)),z),z)),n(n(y)))). given clause #624: (wt=21) 7774 [hyper,1,371,1549] P(i(n(n(i(i(x,n(n(x))),y))),n(n(y)))). given clause #625: (wt=29) 216 [hyper,1,51,146] P(i(n(i(x,i(n(y),i(y,z)))),u)). given clause #626: (wt=21) 7776 [hyper,1,371,1546] P(i(n(n(i(n(n(i(n(n(x)),x))),y))),n(n(y)))). given clause #627: (wt=21) 7780 [hyper,1,371,1541] P(i(n(n(i(i(n(i(x,y)),x),z))),n(n(z)))). given clause #628: (wt=21) 7795 [hyper,1,371,1126] P(i(i(i(n(i(x,y)),n(y)),z),n(n(z)))). given clause #629: (wt=32) 217 [hyper,1,37,146] P(i(n(x),i(n(i(y,i(x,z))),u))). given clause #630: (wt=21) 7799 [hyper,1,371,1071] P(i(i(i(n(i(n(n(x)),y)),x),z),n(n(z)))). given clause #631: (wt=21) 7806 [hyper,1,371,868] P(i(i(n(n(i(n(i(x,y)),x))),z),n(n(z)))). given clause #632: (wt=21) 7816 [hyper,1,371,673] P(i(i(i(n(i(x,n(y))),y),z),n(n(z)))). given clause #633: (wt=25) 218 [hyper,1,34,146] P(i(i(i(x,i(n(i(y,x)),z)),u),u)). given clause #634: (wt=21) 7831 [hyper,1,371,479] P(i(i(n(n(i(x,n(n(x))))),y),n(n(y)))). given clause #635: (wt=21) 7832 [hyper,1,371,472] P(i(i(i(n(i(n(n(x)),x)),y),z),n(n(z)))). given clause #636: (wt=21) 7920 [hyper,1,1524,7678] P(i(n(n(i(i(n(i(x,y)),n(n(x))),z))),z)). given clause #637: (wt=37) 219 [hyper,1,26,146] P(i(i(n(x),n(y)),i(n(i(z,i(y,x))),u))). given clause #638: (wt=21) 7921 [hyper,1,969,7678] P(i(i(n(n(i(n(i(x,y)),n(n(x))))),z),z)). given clause #639: (wt=21) 7924 [hyper,1,379,7678] P(n(n(i(i(i(n(i(x,y)),n(n(x))),z),z)))). given clause #640: (wt=21) 7931 [hyper,1,188,7678] P(i(n(i(n(i(n(i(x,y)),n(n(x)))),z)),u)). given clause #641: (wt=49) 220 [hyper,1,24,146] P(i(i(i(x,y),y),i(n(i(z,i(i(y,x),x))),u))). given clause #642: (wt=21) 7970 [hyper,1,116,7669] P(i(n(i(n(i(i(n(x),y),y)),n(n(x)))),z)). given clause #643: (wt=21) 7993 [hyper,1,116,7672] P(i(n(i(n(i(n(i(x,y)),z)),n(n(x)))),u)). given clause #644: (wt=21) 8013 [hyper,1,116,7683] P(i(n(i(i(n(n(i(x,x))),y),n(n(y)))),z)). given clause #645: (wt=31) 221 [hyper,1,23,146] P(i(x,i(n(i(y,i(z,x))),u))). given clause #646: (wt=21) 8042 [hyper,1,116,7684] P(i(n(i(i(i(n(n(x)),x),y),n(n(y)))),z)). given clause #647: (wt=21) 8078 [hyper,1,367,7668] P(n(n(i(n(i(i(i(x,y),z),z)),n(n(x)))))). given clause #648: (wt=21) 8091 [hyper,1,367,7670] P(n(n(i(n(i(n(i(x,n(y))),z)),n(n(y)))))). given clause #649: (wt=39) 223 [hyper,1,2,146] P(i(x,i(y,i(n(i(z,y)),u)))). given clause #650: (wt=21) 8107 [hyper,1,367,7671] P(n(n(i(n(i(x,i(y,z))),n(n(y)))))). given clause #651: (wt=21) 8121 [hyper,1,367,7673] P(n(n(i(n(n(i(i(n(n(x)),x),y))),n(n(y)))))). given clause #652: (wt=21) 8156 [hyper,1,367,7674] P(n(n(i(n(n(i(n(n(i(x,x))),y))),n(n(y)))))). given clause #653: (wt=39) 224 [hyper,1,146,114] P(i(n(i(x,i(n(i(y,z)),i(n(z),y)))),u)). given clause #654: (wt=21) 8196 [hyper,1,367,7677] P(n(n(i(i(i(n(i(x,y)),x),z),n(n(z)))))). given clause #655: (wt=21) 8226 [hyper,1,367,7680] P(n(n(i(i(n(n(i(n(n(x)),x))),y),n(n(y)))))). given clause #656: (wt=21) 8257 [hyper,1,367,7682] P(n(n(i(i(i(x,n(n(x))),y),n(n(y)))))). given clause #657: (wt=43) 225 [hyper,1,146,89] P(i(n(i(x,i(i(i(y,z),z),i(n(z),y)))),u)). given clause #658: (wt=22) 395 [hyper,1,367,190] P(n(n(i(n(i(n(i(n(x),y)),i(x,z))),u)))). given clause #659: (wt=22) 397 [hyper,1,367,155] P(n(n(i(n(i(n(i(n(x),i(x,y))),z)),u)))). given clause #660: (wt=22) 403 [hyper,1,367,142] P(n(n(i(n(x),i(n(i(x,y)),z))))). given clause #661: (wt=39) 226 [hyper,1,146,34] P(i(n(i(x,i(y,i(i(y,z),z)))),u)). given clause #662: (wt=22) 405 [hyper,1,367,138] P(n(n(i(i(n(n(x)),n(n(y))),i(x,y))))). given clause #663: (wt=22) 417 [hyper,1,367,49] P(n(n(i(i(i(i(x,y),y),z),i(x,z))))). given clause #664: (wt=22) 830 [hyper,1,34,380] P(i(i(i(n(x),n(n(i(x,y)))),z),z)). given clause #665: (wt=25) 227 [hyper,1,143,49] P(i(x,i(n(i(i(x,y),y)),z))). given clause #666: (wt=22) 849 [hyper,1,241,831] P(i(i(x,n(i(y,z))),i(x,y))). given clause #667: (wt=17) 8976 [hyper,1,3765,849] P(i(n(i(i(n(n(i(x,y))),z),z)),x)). given clause #668: (wt=17) 8979 [hyper,1,2942,849] P(i(n(i(n(i(n(i(x,y)),z)),u)),x)). given clause #669: (wt=24) 228 [hyper,1,116,49] P(i(n(i(i(i(i(x,y),y),z),i(x,z))),u)). given clause #670: (wt=19) 8975 [hyper,1,3781,849] P(i(n(i(i(i(n(i(x,y)),z),u),u)),x)). given clause #671: (wt=19) 8986 [hyper,1,673,849] P(i(n(i(x,n(n(i(y,z))))),y)). given clause #672: (wt=19) 9089 [hyper,1,367,8976] P(n(n(i(n(i(i(n(n(i(x,y))),z),z)),x)))). given clause #673: (wt=26) 230 [hyper,1,34,49] P(i(i(i(i(i(i(x,y),y),z),i(x,z)),u),u)). given clause #674: (wt=19) 9090 [hyper,1,362,8976] P(i(n(i(i(n(n(i(n(n(x)),y))),z),z)),x)). given clause #675: (wt=19) 9112 [hyper,1,367,8979] P(n(n(i(n(i(n(i(n(i(x,y)),z)),u)),x)))). given clause #676: (wt=19) 9113 [hyper,1,362,8979] P(i(n(i(n(i(n(i(n(n(x)),y)),z)),u)),x)). given clause #677: (wt=71) 231 [hyper,1,29,49] P(i(x,i(y,i(z,i(i(y,u),u))))). given clause #678: (wt=21) 8974 [hyper,1,7816,849] P(n(n(i(n(i(x,n(n(i(y,z))))),y)))). given clause #679: (wt=21) 8989 [hyper,1,534,849] P(i(i(n(n(i(x,x))),n(i(y,z))),y)). given clause #680: (wt=21) 8990 [hyper,1,488,849] P(i(i(i(n(n(x)),x),n(i(y,z))),y)). given clause #681: (wt=35) 232 [hyper,1,28,49] P(i(x,i(y,i(i(x,z),z)))). given clause #682: (wt=21) 9010 [hyper,1,26,849] P(i(i(n(n(i(x,y))),n(z)),i(z,x))). given clause #683: (wt=21) 9082 [hyper,1,849,8976] P(i(n(i(i(n(n(i(n(i(x,y)),z))),u),u)),x)). given clause #684: (wt=21) 9088 [hyper,1,371,8976] P(i(n(i(i(n(n(i(x,y))),z),z)),n(n(x)))). given clause #685: (wt=29) 233 [hyper,1,26,49] P(i(i(n(x),n(i(i(y,z),z))),i(y,x))). given clause #686: (wt=21) 9102 [hyper,1,116,8976] P(i(n(i(n(i(i(n(n(i(x,y))),z),z)),x)),u)). given clause #687: (wt=21) 9111 [hyper,1,371,8979] P(i(n(i(n(i(n(i(x,y)),z)),u)),n(n(x)))). given clause #688: (wt=21) 9116 [hyper,1,367,8975] P(n(n(i(n(i(i(i(n(i(x,y)),z),u),u)),x)))). given clause #689: (wt=32) 234 [hyper,1,21,49] P(i(i(x,i(y,z)),i(y,i(x,z)))). given clause #690: (wt=21) 9117 [hyper,1,362,8975] P(i(n(i(i(i(n(i(n(n(x)),y)),z),u),u)),x)). given clause #691: (wt=21) 9154 [hyper,1,367,9090] P(n(n(i(n(i(i(n(n(i(n(n(x)),y))),z),z)),x)))). given clause #692: (wt=21) 9161 [hyper,1,367,9113] P(n(n(i(n(i(n(i(n(i(n(n(x)),y)),z)),u)),x)))). given clause #693: (wt=35) 235 [hyper,1,3,49] P(i(i(i(x,y),z),i(i(i(i(x,u),u),y),z))). given clause #694: (wt=22) 860 [hyper,1,3,831] P(i(i(x,y),i(n(i(x,z)),y))). given clause #695: (wt=15) 9695 [hyper,1,1126,860] P(i(n(i(n(i(x,y)),z)),n(y))). given clause #696: (wt=17) 9687 [hyper,1,7795,860] P(n(n(i(n(i(n(i(x,y)),z)),n(y))))). given clause #697: (wt=41) 236 [hyper,1,2,49] P(i(x,i(i(i(i(y,z),z),u),i(y,u)))). given clause #698: (wt=17) 9689 [hyper,1,3765,860] P(i(n(i(n(i(i(n(x),y),y)),z)),x)). given clause #699: (wt=17) 9702 [hyper,1,534,860] P(i(n(i(i(n(n(i(x,x))),y),z)),y)). given clause #700: (wt=17) 9703 [hyper,1,488,860] P(i(n(i(i(i(n(n(x)),x),y),z)),y)). given clause #701: (wt=43) 237 [hyper,1,49,146] P(i(x,i(n(i(y,i(i(x,z),z))),u))). given clause #702: (wt=19) 9688 [hyper,1,3781,860] P(i(n(i(n(i(i(i(x,y),z),z)),u)),x)). given clause #703: (wt=19) 9690 [hyper,1,3458,860] P(i(n(i(n(i(n(i(x,n(y))),z)),u)),y)). given clause #704: (wt=19) 9691 [hyper,1,2953,860] P(i(n(i(n(i(x,i(y,z))),u)),y)). given clause #705: (wt=29) 238 [hyper,1,49,34] P(i(x,i(i(i(i(x,y),y),z),z))). given clause #706: (wt=19) 9692 [hyper,1,1631,860] P(i(n(i(n(n(i(i(n(n(x)),x),y))),z)),y)). given clause #707: (wt=19) 9693 [hyper,1,1610,860] P(i(n(i(n(n(i(n(n(i(x,x))),y))),z)),y)). given clause #708: (wt=19) 9697 [hyper,1,931,860] P(i(n(i(i(i(n(i(x,y)),x),z),u)),z)). given clause #709: (wt=23) 239 [hyper,1,49,26] P(i(x,i(i(n(y),n(x)),y))). given clause #710: (wt=19) 9699 [hyper,1,768,860] P(i(n(i(i(n(n(i(n(n(x)),x))),y),z)),y)). given clause #711: (wt=19) 9701 [hyper,1,587,860] P(i(n(i(i(i(x,n(n(x))),y),z)),y)). given clause #712: (wt=19) 9925 [hyper,1,860,9695] P(i(n(i(n(i(n(i(x,y)),z)),u)),n(y))). given clause #713: (wt=26) 240 [hyper,1,49,24] P(i(i(x,y),i(i(i(y,x),x),y))). given clause #714: (wt=19) 9932 [hyper,1,116,9695] P(i(n(i(n(i(n(i(x,y)),z)),n(y))),u)). given clause #715: (wt=19) 9946 [hyper,1,367,9689] P(n(n(i(n(i(n(i(i(n(x),y),y)),z)),x)))). given clause #716: (wt=19) 9972 [hyper,1,367,9702] P(n(n(i(n(i(i(n(n(i(x,x))),y),z)),y)))). given clause #717: (wt=41) 243 [hyper,1,49,3] P(i(x,i(i(y,z),i(i(x,y),z)))). given clause #718: (wt=19) 10005 [hyper,1,367,9703] P(n(n(i(n(i(i(i(n(n(x)),x),y),z)),y)))). given clause #719: (wt=20) 9872 [hyper,1,860,390] P(i(n(i(i(n(n(x)),y),z)),i(x,y))). given clause #720: (wt=21) 9726 [hyper,1,55,860] P(i(n(i(i(n(x),n(y)),z)),i(y,x))). given clause #721: (wt=68) 244 [hyper,1,241,241] P(i(i(x,i(y,z)),i(x,i(i(u,y),i(u,z))))). given clause #722: (wt=21) 9727 [hyper,1,53,860] P(i(n(i(i(i(x,y),z),u)),i(y,z))). given clause #723: (wt=21) 9728 [hyper,1,52,860] P(i(n(i(i(i(x,i(y,x)),z),u)),z)). given clause #724: (wt=21) 9736 [hyper,1,860,8976] P(i(n(i(n(i(i(n(n(i(x,y))),z),z)),u)),x)). given clause #725: (wt=33) 245 [hyper,1,148,241] P(i(x,i(i(y,n(x)),i(y,z)))). given clause #726: (wt=21) 9751 [hyper,1,860,7684] P(i(n(i(i(i(n(n(x)),x),y),z)),n(n(y)))). given clause #727: (wt=21) 9752 [hyper,1,860,7683] P(i(n(i(i(n(n(i(x,x))),y),z)),n(n(y)))). given clause #728: (wt=21) 9760 [hyper,1,860,7669] P(i(n(i(n(i(i(n(x),y),y)),z)),n(n(x)))). given clause #729: (wt=36) 246 [hyper,1,116,241] P(i(n(i(i(x,y),i(i(z,x),i(z,y)))),u)). given clause #730: (wt=21) 9769 [hyper,1,860,3773] P(i(n(i(n(i(i(i(n(n(x)),y),z),z)),u)),x)). given clause #731: (wt=21) 9773 [hyper,1,860,3497] P(i(n(i(n(i(i(i(x,n(y)),z),z)),u)),y)). given clause #732: (wt=21) 9800 [hyper,1,860,1549] P(i(n(i(n(n(i(i(x,n(n(x))),y))),z)),y)). given clause #733: (wt=41) 247 [hyper,1,49,241] P(i(x,i(i(y,i(x,z)),i(y,z)))). given clause #734: (wt=21) 9802 [hyper,1,860,1546] P(i(n(i(n(n(i(n(n(i(n(n(x)),x))),y))),z)),y)). given clause #735: (wt=21) 9806 [hyper,1,860,1541] P(i(n(i(n(n(i(i(n(i(x,y)),x),z))),u)),z)). given clause #736: (wt=21) 9820 [hyper,1,860,1454] P(i(n(i(i(i(n(n(x)),x),n(n(y))),z)),y)). given clause #737: (wt=30) 248 [hyper,1,37,241] P(i(n(x),i(i(y,x),i(y,z)))). given clause #738: (wt=21) 9822 [hyper,1,860,1452] P(i(n(i(i(n(n(i(x,x))),n(n(y))),z)),y)). given clause #739: (wt=21) 9835 [hyper,1,860,1126] P(i(n(i(i(i(n(i(x,y)),n(y)),z),u)),z)). given clause #740: (wt=21) 9838 [hyper,1,860,1071] P(i(n(i(i(i(n(i(n(n(x)),y)),x),z),u)),z)). given clause #741: (wt=38) 249 [hyper,1,34,241] P(i(i(i(i(x,y),i(i(z,x),i(z,y))),u),u)). given clause #742: (wt=21) 9842 [hyper,1,860,868] P(i(n(i(i(n(n(i(n(i(x,y)),x))),z),u)),z)). given clause #743: (wt=21) 9851 [hyper,1,860,673] P(i(n(i(i(i(n(i(x,n(y))),y),z),u)),z)). given clause #744: (wt=21) 9868 [hyper,1,860,479] P(i(n(i(i(n(n(i(x,n(n(x))))),y),z)),y)). given clause #745: (wt=53) 250 [hyper,1,29,241] P(i(x,i(i(y,z),i(y,i(u,z))))). given clause #746: (wt=21) 9869 [hyper,1,860,472] P(i(n(i(i(i(n(i(n(n(x)),x)),y),z),u)),z)). given clause #747: (wt=21) 9929 [hyper,1,372,9695] P(n(n(i(n(i(n(i(n(i(x,y)),z)),n(y))),u)))). given clause #748: (wt=21) 9933 [hyper,1,34,9695] P(i(i(i(n(i(n(i(x,y)),z)),n(y)),u),u)). given clause #749: (wt=35) 251 [hyper,1,26,241] P(i(i(n(x),n(y)),i(i(z,y),i(z,x)))). given clause #750: (wt=21) 9941 [hyper,1,860,9689] P(i(n(i(n(i(n(i(i(n(x),y),y)),z)),u)),x)). given clause #751: (wt=21) 9958 [hyper,1,116,9689] P(i(n(i(n(i(n(i(i(n(x),y),y)),z)),x)),u)). given clause #752: (wt=21) 9965 [hyper,1,860,9702] P(i(n(i(n(i(i(n(n(i(x,x))),y),z)),u)),y)). given clause #753: (wt=47) 252 [hyper,1,24,241] P(i(i(i(x,y),y),i(i(z,i(y,x)),i(z,x)))). given clause #754: (wt=21) 9989 [hyper,1,116,9702] P(i(n(i(n(i(i(n(n(i(x,x))),y),z)),y)),u)). given clause #755: (wt=21) 9998 [hyper,1,860,9703] P(i(n(i(n(i(i(i(n(n(x)),x),y),z)),u)),y)). given clause #756: (wt=21) 10022 [hyper,1,116,9703] P(i(n(i(n(i(i(i(n(n(x)),x),y),z)),y)),u)). given clause #757: (wt=68) 253 [hyper,1,21,241] P(i(i(x,y),i(i(z,i(y,u)),i(z,i(x,u))))). given clause #758: (wt=21) 10039 [hyper,1,367,9688] P(n(n(i(n(i(n(i(i(i(x,y),z),z)),u)),x)))). given clause #759: (wt=21) 10041 [hyper,1,367,9690] P(n(n(i(n(i(n(i(n(i(x,n(y))),z)),u)),y)))). given clause #760: (wt=21) 10042 [hyper,1,367,9691] P(n(n(i(n(i(n(i(x,i(y,z))),u)),y)))). given clause #761: (wt=32) 254 [hyper,1,3,241] P(i(i(i(i(x,y),i(x,z)),u),i(i(y,z),u))). given clause #762: (wt=21) 10170 [hyper,1,367,9692] P(n(n(i(n(i(n(n(i(i(n(n(x)),x),y))),z)),y)))). given clause #763: (wt=21) 10206 [hyper,1,367,9693] P(n(n(i(n(i(n(n(i(n(n(i(x,x))),y))),z)),y)))). given clause #764: (wt=21) 10234 [hyper,1,367,9697] P(n(n(i(n(i(i(i(n(i(x,y)),x),z),u)),z)))). given clause #765: (wt=65) 255 [hyper,1,2,241] P(i(x,i(i(y,z),i(i(u,y),i(u,z))))). given clause #766: (wt=21) 10283 [hyper,1,65,239] P(i(n(i(i(n(x),n(y)),x)),i(y,z))). given clause #767: (wt=21) 10564 [hyper,1,367,9699] P(n(n(i(n(i(i(n(n(i(n(n(x)),x))),y),z)),y)))). given clause #768: (wt=21) 10601 [hyper,1,367,9701] P(n(n(i(n(i(i(i(x,n(n(x))),y),z)),y)))). given clause #769: (wt=36) 256 [hyper,1,241,180] P(i(i(x,n(i(n(y),z))),i(x,i(y,u)))). given clause #770: (wt=21) 10630 [hyper,1,367,9925] P(n(n(i(n(i(n(i(n(i(x,y)),z)),u)),n(y))))). given clause #771: (wt=22) 941 [hyper,1,382,48] P(i(i(i(i(n(n(x)),y),i(x,y)),z),z)). given clause #772: (wt=22) 1019 [hyper,1,372,390] P(n(n(i(n(i(i(n(n(x)),y),i(x,y))),z)))). given clause #773: (wt=40) 257 [hyper,1,241,148] P(i(i(x,i(i(n(y),z),u)),i(x,i(y,u)))). given clause #774: (wt=22) 1022 [hyper,1,372,380] P(n(n(i(n(i(n(x),n(n(i(x,y))))),z)))). given clause #775: (wt=22) 1354 [hyper,1,382,60] P(i(i(i(n(x),i(x,y)),z),n(n(z)))). given clause #776: (wt=22) 1356 [hyper,1,366,60] P(i(i(i(n(x),i(x,y)),n(n(z))),z)). given clause #777: (wt=42) 258 [hyper,1,241,146] P(i(i(x,y),i(x,i(n(i(z,y)),u)))). given clause #778: (wt=22) 1428 [hyper,1,116,362] P(i(n(i(i(x,n(n(y))),i(x,y))),z)). given clause #779: (wt=22) 1515 [hyper,1,116,369] P(i(n(i(i(x,y),i(n(n(x)),y))),z)). given clause #780: (wt=22) 1555 [hyper,1,369,138] P(i(n(n(i(n(n(x)),n(n(y))))),i(x,y))). given clause #781: (wt=42) 259 [hyper,1,241,143] P(i(i(x,i(i(y,i(n(y),z)),u)),i(x,u))). given clause #782: (wt=22) 1569 [hyper,1,369,49] P(i(n(n(i(i(i(x,y),y),z))),i(x,z))). given clause #783: (wt=22) 1779 [hyper,1,66,138] P(i(i(i(n(x),y),n(n(z))),i(x,z))). given clause #784: (wt=22) 1821 [hyper,1,116,1548] P(i(n(i(n(n(i(n(n(x)),y))),i(x,y))),z)). given clause #785: (wt=38) 260 [hyper,1,241,141] P(i(i(x,n(i(y,i(n(y),z)))),i(x,u))). given clause #786: (wt=22) 1873 [hyper,1,65,340] P(i(n(i(i(x,y),y)),i(n(n(x)),z))). given clause #787: (wt=22) 3143 [hyper,1,369,547] P(i(n(n(i(n(n(i(n(x),i(x,y)))),z))),z)). given clause #788: (wt=22) 3144 [hyper,1,367,547] P(n(n(i(i(n(n(i(n(x),i(x,y)))),z),z)))). given clause #789: (wt=38) 261 [hyper,1,241,114] P(i(i(x,n(i(y,z))),i(x,i(n(z),y)))). given clause #790: (wt=22) 3166 [hyper,1,369,1011] P(i(n(n(i(n(n(i(n(x),y))),z))),i(x,z))). given clause #791: (wt=22) 3167 [hyper,1,367,1011] P(n(n(i(i(n(n(i(n(x),y))),z),i(x,z))))). given clause #792: (wt=22) 3172 [hyper,1,66,1011] P(i(i(i(n(i(n(x),y)),z),u),i(x,u))). given clause #793: (wt=38) 262 [hyper,1,241,105] P(i(i(x,n(i(n(n(y)),i(z,y)))),i(x,u))). given clause #794: (wt=22) 3199 [hyper,1,367,1511] P(n(n(i(n(n(i(x,y))),i(n(n(x)),y))))). given clause #795: (wt=22) 3236 [hyper,1,367,1518] P(n(n(i(n(n(i(i(n(x),i(x,y)),z))),z)))). given clause #796: (wt=22) 3252 [hyper,1,367,1551] P(n(n(i(n(n(i(x,n(n(y))))),i(x,y))))). given clause #797: (wt=42) 263 [hyper,1,241,89] P(i(i(x,i(i(y,z),z)),i(x,i(n(z),y)))). given clause #798: (wt=21) 12406 [hyper,1,941,263] P(i(i(n(n(i(x,y))),y),i(n(y),x))). given clause #799: (wt=22) 3275 [hyper,1,367,1553] P(n(n(i(n(n(i(i(n(x),y),z))),i(x,z))))). given clause #800: (wt=22) 3294 [hyper,1,367,2940] P(n(n(i(n(i(n(i(n(x),y)),z)),i(x,u))))). given clause #801: (wt=42) 264 [hyper,1,241,75] P(i(i(x,i(i(n(n(y)),i(z,y)),u)),i(x,u))). given clause #802: (wt=22) 3528 [hyper,1,3,379] P(i(i(n(n(i(i(x,y),y))),z),i(x,z))). given clause #803: (wt=22) 3779 [hyper,1,59,3487] P(i(n(i(i(i(n(x),y),z),z)),i(x,u))). given clause #804: (wt=22) 3967 [hyper,1,367,3755] P(n(n(i(n(i(i(n(n(x)),y),y)),i(x,z))))). given clause #805: (wt=34) 265 [hyper,1,241,71] P(i(i(x,n(i(y,z))),i(x,i(z,u)))). given clause #806: (wt=22) 4199 [hyper,1,117,386] P(i(i(i(n(x),y),y),n(n(i(x,y))))). given clause #807: (wt=22) 4946 [hyper,1,3,969] P(i(i(i(i(n(n(x)),y),y),z),i(x,z))). given clause #808: (wt=22) 5579 [hyper,1,3,1524] P(i(i(i(n(n(i(x,y))),y),z),i(x,z))). given clause #809: (wt=34) 266 [hyper,1,241,70] P(i(i(x,n(i(y,i(z,y)))),i(x,u))). given clause #810: (wt=22) 5849 [hyper,1,367,5560] P(n(n(i(n(i(n(n(i(x,y))),y)),i(x,z))))). given clause #811: (wt=22) 6027 [hyper,1,367,6004] P(n(n(i(n(i(n(x),y)),n(n(i(x,y))))))). given clause #812: (wt=22) 6728 [hyper,1,382,186] P(i(i(i(n(x),y),z),n(n(i(x,z))))). given clause #813: (wt=36) 267 [hyper,1,241,68] P(i(i(x,n(i(n(y),i(y,z)))),i(x,u))). given clause #814: (wt=22) 6952 [hyper,1,192,49] P(i(n(i(n(i(i(x,y),y)),z)),i(x,u))). given clause #815: (wt=22) 6959 [hyper,1,367,6927] P(n(n(i(n(i(n(x),y)),n(n(i(x,z))))))). given clause #816: (wt=22) 7775 [hyper,1,371,1548] P(i(n(n(i(n(n(x)),y))),n(n(i(x,y))))). given clause #817: (wt=38) 268 [hyper,1,241,62] P(i(i(x,n(i(y,z))),i(x,i(n(y),u)))). given clause #818: (wt=21) 13056 [hyper,1,5,7775] P(i(n(i(x,y)),n(i(n(n(x)),y)))). given clause #819: (wt=22) 7837 [hyper,1,371,369] P(i(i(x,y),n(n(i(n(n(x)),y))))). given clause #820: (wt=22) 7839 [hyper,1,371,362] P(i(i(x,n(n(y))),n(n(i(x,y))))). given clause #821: (wt=40) 269 [hyper,1,241,51] P(i(i(x,i(i(n(y),i(y,z)),u)),i(x,u))). given clause #822: (wt=22) 7842 [hyper,1,371,229] P(i(n(i(i(x,y),y)),n(n(i(x,z))))). given clause #823: (wt=22) 8349 [hyper,1,367,7835] P(n(n(i(i(n(n(x)),y),n(n(i(x,y))))))). given clause #824: (wt=22) 9710 [hyper,1,181,860] P(i(n(i(i(i(n(x),y),z),u)),i(x,z))). given clause #825: (wt=44) 270 [hyper,1,241,49] P(i(i(x,i(i(i(y,z),z),u)),i(x,i(y,u)))). given clause #826: (wt=22) 9723 [hyper,1,58,860] P(i(n(i(i(i(n(x),i(x,y)),z),u)),z)). given clause #827: (wt=22) 9801 [hyper,1,860,1548] P(i(n(i(n(n(i(n(n(x)),y))),z)),i(x,y))). given clause #828: (wt=22) 9877 [hyper,1,860,369] P(i(n(i(i(x,y),z)),i(n(n(x)),y))). given clause #829: (wt=42) 271 [hyper,1,241,37] P(i(i(x,i(i(y,z),u)),i(x,i(n(y),u)))). given clause #830: (wt=22) 9879 [hyper,1,860,362] P(i(n(i(i(x,n(n(y))),z)),i(x,y))). given clause #831: (wt=22) 10885 [hyper,1,367,9872] P(n(n(i(n(i(i(n(n(x)),y),z)),i(x,y))))). given clause #832: (wt=23) 302 [hyper,1,31,23] P(i(i(i(x,i(y,z)),u),i(z,u))). given clause #833: (wt=38) 272 [hyper,1,241,34] P(i(i(x,y),i(x,i(i(y,z),z)))). given clause #834: (wt=23) 316 [hyper,1,3,142] P(i(i(i(n(i(x,y)),z),u),i(n(x),u))). given clause #835: (wt=23) 373 [hyper,1,146,367] P(i(n(i(x,i(y,n(n(y))))),z)). given clause #836: (wt=23) 409 [hyper,1,367,76] P(n(n(i(i(i(x,y),z),i(n(n(y)),z))))). given clause #837: (wt=38) 273 [hyper,1,241,28] P(i(i(x,i(i(y,i(z,y)),u)),i(x,u))). given clause #838: (wt=23) 411 [hyper,1,367,74] P(n(n(i(n(i(x,y)),i(i(y,x),x))))). given clause #839: (wt=23) 461 [hyper,1,146,392] P(i(n(i(x,n(n(i(n(n(y)),y))))),z)). given clause #840: (wt=23) 471 [hyper,1,35,364] P(i(i(i(n(i(n(n(x)),x)),y),z),i(u,z))). given clause #841: (wt=62) 274 [hyper,1,241,26] P(i(i(x,i(i(y,z),u)),i(x,i(i(n(z),n(y)),u)))). given clause #842: (wt=23) 474 [hyper,1,2,364] P(i(x,i(n(i(n(n(y)),y)),z))). given clause #843: (wt=23) 478 [hyper,1,35,370] P(i(i(n(n(i(x,n(n(x))))),y),i(z,y))). given clause #844: (wt=23) 480 [hyper,1,2,370] P(i(x,n(n(i(y,n(n(y))))))). given clause #845: (wt=68) 275 [hyper,1,241,24] P(i(i(x,i(i(i(y,z),z),u)),i(x,i(i(i(z,y),y),u)))). given clause #846: (wt=23) 672 [hyper,1,35,618] P(i(i(i(n(i(x,n(y))),y),z),i(u,z))). given clause #847: (wt=23) 675 [hyper,1,2,618] P(i(x,i(n(i(y,n(z))),z))). given clause #848: (wt=23) 850 [hyper,1,146,831] P(i(n(i(x,i(n(i(y,z)),y))),u)). given clause #849: (wt=38) 276 [hyper,1,241,23] P(i(i(x,i(i(y,z),u)),i(x,i(z,u)))). given clause #850: (wt=23) 867 [hyper,1,35,848] P(i(i(n(n(i(n(i(x,y)),x))),z),i(u,z))). given clause #851: (wt=23) 869 [hyper,1,2,848] P(i(x,n(n(i(n(i(y,z)),y))))). given clause #852: (wt=23) 889 [hyper,1,3,47] P(i(i(i(i(i(x,y),z),z),u),i(y,u))). given clause #853: (wt=38) 277 [hyper,1,241,5] P(i(i(x,i(n(y),n(z))),i(x,i(z,y)))). given clause #854: (wt=17) 14575 [hyper,1,277,371] P(i(i(n(x),y),i(n(y),x))). given clause #855: (wt=14) 14687 [hyper,1,14575,340] P(i(n(i(i(x,y),y)),n(x))). given clause #856: (wt=15) 14680 [hyper,1,14575,1524] P(i(n(i(n(n(i(n(x),y))),y)),x)). given clause #857: (wt=50) 278 [hyper,1,241,4] P(i(i(x,i(i(y,z),z)),i(x,i(i(z,y),y)))). given clause #858: (wt=16) 14704 [hyper,1,367,14687] P(n(n(i(n(i(i(x,y),y)),n(x))))). given clause #859: (wt=17) 14692 [hyper,1,14575,239] P(i(n(i(i(n(x),n(n(y))),x)),y)). given clause #860: (wt=17) 14747 [hyper,1,367,14680] P(n(n(i(n(i(n(n(i(n(x),y))),y)),x)))). given clause #861: (wt=68) 279 [hyper,1,241,3] P(i(i(x,i(y,z)),i(x,i(i(z,u),i(y,u))))). given clause #862: (wt=18) 14688 [hyper,1,14575,248] P(i(n(i(i(x,y),i(x,z))),y)). given clause #863: (wt=18) 14699 [hyper,1,860,14687] P(i(n(i(n(i(i(x,y),y)),z)),n(x))). given clause #864: (wt=18) 14725 [hyper,1,116,14687] P(i(n(i(n(i(i(x,y),y)),n(x))),z)). given clause #865: (wt=40) 280 [hyper,1,241,229] P(i(i(x,n(i(i(y,z),z))),i(x,i(y,u)))). given clause #866: (wt=19) 14603 [hyper,1,369,14575] P(i(n(n(i(n(x),y))),i(n(y),x))). given clause #867: (wt=19) 14604 [hyper,1,367,14575] P(n(n(i(i(n(x),y),i(n(y),x))))). given clause #868: (wt=19) 14633 [hyper,1,66,14575] P(i(i(i(x,y),z),i(n(z),x))). given clause #869: (wt=24) 282 [hyper,1,34,229] P(i(i(i(n(i(i(x,y),y)),i(x,z)),u),u)). given clause #870: (wt=15) 15382 [hyper,1,14633,240] P(i(n(i(i(i(x,y),y),x)),y)). given clause #871: (wt=17) 15377 [hyper,1,14633,1524] P(i(n(i(n(n(i(i(x,y),z))),z)),x)). given clause #872: (wt=17) 15389 [hyper,1,14633,133] P(i(n(i(i(i(x,y),z),z)),n(y))). given clause #873: (wt=31) 283 [hyper,1,3,229] P(i(i(i(x,y),z),i(n(i(i(x,u),u)),z))). given clause #874: (wt=17) 15390 [hyper,1,14633,123] P(i(n(i(x,i(y,z))),n(z))). given clause #875: (wt=17) 15411 [hyper,1,367,15382] P(n(n(i(n(i(i(i(x,y),y),x)),y)))). given clause #876: (wt=19) 14686 [hyper,1,14575,1511] P(i(n(i(n(n(x)),y)),n(i(x,y)))). given clause #877: (wt=37) 284 [hyper,1,2,229] P(i(x,i(n(i(i(y,z),z)),i(y,u)))). given clause #878: (wt=19) 14693 [hyper,1,14575,238] P(i(n(i(i(i(i(n(x),y),y),z),z)),x)). given clause #879: (wt=19) 14696 [hyper,1,14575,35] P(i(n(i(i(n(x),y),i(z,y))),x)). given clause #880: (wt=19) 14740 [hyper,1,860,14680] P(i(n(i(n(i(n(n(i(n(x),y))),y)),z)),x)). given clause #881: (wt=25) 285 [hyper,1,143,31] P(i(i(i(x,y),z),i(n(i(y,z)),u))). given clause #882: (wt=19) 14741 [hyper,1,849,14680] P(i(n(i(n(n(i(n(n(i(x,y))),z))),z)),x)). given clause #883: (wt=19) 14746 [hyper,1,371,14680] P(i(n(i(n(n(i(n(x),y))),y)),n(n(x)))). given clause #884: (wt=19) 14796 [hyper,1,116,14680] P(i(n(i(n(i(n(n(i(n(x),y))),y)),x)),z)). given clause #885: (wt=27) 286 [hyper,1,37,31] P(i(n(i(x,y)),i(i(i(z,x),y),u))). given clause #886: (wt=19) 15035 [hyper,1,367,14692] P(n(n(i(n(i(i(n(x),n(n(y))),x)),y)))). given clause #887: (wt=19) 15404 [hyper,1,860,15382] P(i(n(i(n(i(i(i(x,y),y),x)),z)),y)). given clause #888: (wt=19) 15410 [hyper,1,371,15382] P(i(n(i(i(i(x,y),y),x)),n(n(y)))). given clause #889: (wt=29) 287 [hyper,1,28,31] P(i(i(i(x,y),z),i(u,i(y,z)))). given clause #890: (wt=19) 15456 [hyper,1,116,15382] P(i(n(i(n(i(i(i(x,y),y),x)),y)),z)). given clause #891: (wt=19) 15485 [hyper,1,367,15377] P(n(n(i(n(i(n(n(i(i(x,y),z))),z)),x)))). given clause #892: (wt=19) 15486 [hyper,1,362,15377] P(i(n(i(n(n(i(i(n(n(x)),y),z))),z)),x)). given clause #893: (wt=35) 288 [hyper,1,26,31] P(i(i(n(x),n(i(y,z))),i(i(i(u,y),z),x))). given clause #894: (wt=19) 15519 [hyper,1,367,15389] P(n(n(i(n(i(i(i(x,y),z),z)),n(y))))). given clause #895: (wt=19) 15558 [hyper,1,367,15390] P(n(n(i(n(i(x,i(y,z))),n(z))))). given clause #896: (wt=20) 14576 [hyper,1,277,369] P(i(i(x,n(y)),i(y,n(x)))). given clause #897: (wt=29) 289 [hyper,1,24,31] P(i(i(i(x,y),y),i(i(i(z,y),x),x))). given clause #898: (wt=20) 14617 [hyper,1,234,14575] P(i(n(x),i(i(n(y),x),y))). given clause #899: (wt=13) 16171 [hyper,1,14575,14617] P(i(n(i(i(n(x),y),x)),y)). given clause #900: (wt=15) 16228 [hyper,1,367,16171] P(n(n(i(n(i(i(n(x),y),x)),y)))). given clause #901: (wt=38) 290 [hyper,1,21,31] P(i(i(x,y),i(i(i(z,y),u),i(x,u)))). given clause #902: (wt=17) 16222 [hyper,1,860,16171] P(i(n(i(n(i(i(n(x),y),x)),z)),y)). given clause #903: (wt=17) 16227 [hyper,1,371,16171] P(i(n(i(i(n(x),y),x)),n(n(y)))). given clause #904: (wt=17) 16265 [hyper,1,116,16171] P(i(n(i(n(i(i(n(x),y),x)),y)),z)). given clause #905: (wt=35) 291 [hyper,1,31,241] P(i(i(i(x,y),z),i(i(u,y),i(u,z)))). given clause #906: (wt=19) 16226 [hyper,1,372,16171] P(n(n(i(n(i(n(i(i(n(x),y),x)),y)),z)))). given clause #907: (wt=19) 16272 [hyper,1,44,16171] P(i(n(i(i(n(x),y),x)),i(z,y))). given clause #908: (wt=19) 16278 [hyper,1,34,16171] P(i(i(i(n(i(i(n(x),y),x)),y),z),z)). given clause #909: (wt=25) 292 [hyper,1,31,148] P(i(i(i(x,i(n(y),z)),u),i(y,u))). given clause #910: (wt=19) 16388 [hyper,1,367,16222] P(n(n(i(n(i(n(i(i(n(x),y),x)),z)),y)))). given clause #911: (wt=19) 16425 [hyper,1,367,16227] P(n(n(i(n(i(i(n(x),y),x)),n(n(y)))))). given clause #912: (wt=20) 14703 [hyper,1,372,14687] P(n(n(i(n(i(n(i(i(x,y),y)),n(x))),z)))). given clause #913: (wt=33) 293 [hyper,1,31,143] P(i(i(i(x,i(y,i(n(y),z))),u),u)). given clause #914: (wt=20) 14735 [hyper,1,34,14687] P(i(i(i(n(i(i(x,y),y)),n(x)),z),z)). given clause #915: (wt=20) 15215 [hyper,1,367,14688] P(n(n(i(n(i(i(x,y),i(x,z))),y)))). given clause #916: (wt=20) 15240 [hyper,1,367,14699] P(n(n(i(n(i(n(i(i(x,y),y)),z)),n(x))))). given clause #917: (wt=25) 294 [hyper,1,31,89] P(i(i(i(x,i(y,z)),z),i(n(z),y))). given clause #918: (wt=20) 15284 [hyper,1,14575,14603] P(i(n(i(n(x),y)),n(i(n(y),x)))). given clause #919: (wt=20) 15379 [hyper,1,14633,251] P(i(n(i(i(x,y),i(x,z))),n(z))). given clause #920: (wt=20) 15388 [hyper,1,14633,140] P(i(n(i(i(x,y),i(z,y))),n(x))). given clause #921: (wt=33) 295 [hyper,1,31,75] P(i(i(i(x,i(n(n(y)),i(z,y))),u),u)). given clause #922: (wt=21) 14493 [hyper,1,277,5560] P(i(n(i(n(n(i(n(x),y))),y)),i(z,x))). given clause #923: (wt=21) 14593 [hyper,1,7837,14575] P(n(n(i(n(n(i(n(x),y))),i(n(y),x))))). given clause #924: (wt=21) 14597 [hyper,1,860,14575] P(i(n(i(i(n(x),y),z)),i(n(y),x))). given clause #925: (wt=31) 296 [hyper,1,31,51] P(i(i(i(x,i(n(y),i(y,z))),u),u)). given clause #926: (wt=21) 14602 [hyper,1,371,14575] P(i(i(n(x),y),n(n(i(n(y),x))))). given clause #927: (wt=21) 14625 [hyper,1,186,14575] P(i(i(i(n(n(x)),y),z),i(n(z),x))). given clause #928: (wt=21) 14630 [hyper,1,116,14575] P(i(n(i(i(n(x),y),i(n(y),x))),z)). given clause #929: (wt=29) 297 [hyper,1,31,49] P(i(i(i(x,i(i(y,z),z)),u),i(y,u))). given clause #930: (wt=21) 14646 [hyper,1,31,14575] P(i(i(i(x,n(y)),z),i(n(z),y))). given clause #931: (wt=19) 16992 [hyper,1,14646,1524] P(i(n(i(n(n(i(i(x,n(y)),z))),z)),y)). given clause #932: (wt=19) 16993 [hyper,1,14646,969] P(i(n(i(i(n(n(i(x,n(y)))),z),z)),y)). given clause #933: (wt=25) 298 [hyper,1,31,37] P(i(i(i(x,i(y,z)),u),i(n(y),u))). given clause #934: (wt=21) 14745 [hyper,1,372,14680] P(n(n(i(n(i(n(i(n(n(i(n(x),y))),y)),x)),z)))). given clause #935: (wt=21) 14809 [hyper,1,34,14680] P(i(i(i(n(i(n(n(i(n(x),y))),y)),x),z),z)). given clause #936: (wt=21) 15029 [hyper,1,860,14692] P(i(n(i(n(i(i(n(x),n(n(y))),x)),z)),y)). given clause #937: (wt=29) 299 [hyper,1,31,34] P(i(i(i(x,y),z),i(i(i(y,z),u),u))). given clause #938: (wt=21) 15034 [hyper,1,371,14692] P(i(n(i(i(n(x),n(n(y))),x)),n(n(y)))). given clause #939: (wt=21) 15069 [hyper,1,116,14692] P(i(n(i(n(i(i(n(x),n(n(y))),x)),y)),z)). given clause #940: (wt=21) 15354 [hyper,1,369,14633] P(i(n(n(i(i(x,y),z))),i(n(z),x))). given clause #941: (wt=35) 300 [hyper,1,31,26] P(i(i(i(x,i(y,z)),u),i(i(n(z),n(y)),u))). given clause #942: (wt=21) 15355 [hyper,1,367,14633] P(n(n(i(i(i(x,y),z),i(n(z),x))))). given clause #943: (wt=21) 15383 [hyper,1,14633,239] P(i(n(i(i(n(x),n(i(y,z))),x)),y)). given clause #944: (wt=21) 15384 [hyper,1,14633,238] P(i(n(i(i(i(i(i(x,y),z),z),u),u)),x)). given clause #945: (wt=41) 301 [hyper,1,31,24] P(i(i(i(x,i(i(y,z),z)),u),i(i(i(z,y),y),u))). given clause #946: (wt=21) 15387 [hyper,1,14633,219] P(i(n(i(n(i(x,i(y,z))),u)),n(z))). given clause #947: (wt=21) 15392 [hyper,1,14633,47] P(i(n(i(i(i(x,i(y,z)),u),u)),y)). given clause #948: (wt=21) 15396 [hyper,1,14633,35] P(i(n(i(i(i(x,y),z),i(u,z))),x)). given clause #949: (wt=29) 304 [hyper,1,31,4] P(i(i(i(x,i(y,z)),z),i(i(z,y),y))). given clause #950: (wt=21) 15409 [hyper,1,372,15382] P(n(n(i(n(i(n(i(i(i(x,y),y),x)),y)),z)))). given clause #951: (wt=21) 15466 [hyper,1,44,15382] P(i(n(i(i(i(x,y),y),x)),i(z,y))). given clause #952: (wt=21) 15472 [hyper,1,34,15382] P(i(i(i(n(i(i(i(x,y),y),x)),y),z),z)). given clause #953: (wt=35) 305 [hyper,1,31,3] P(i(i(i(x,y),z),i(i(z,u),i(y,u)))). given clause #954: (wt=21) 15475 [hyper,1,7839,15377] P(n(n(i(n(i(n(n(i(i(n(n(x)),y),z))),z)),x)))). given clause #955: (wt=21) 15478 [hyper,1,860,15377] P(i(n(i(n(i(n(n(i(i(x,y),z))),z)),u)),x)). given clause #956: (wt=21) 15479 [hyper,1,849,15377] P(i(n(i(n(n(i(i(n(i(x,y)),z),u))),u)),x)). given clause #957: (wt=44) 306 [hyper,1,241,138] P(i(i(x,i(n(n(y)),n(n(z)))),i(x,i(y,z)))). given clause #958: (wt=21) 15484 [hyper,1,371,15377] P(i(n(i(n(n(i(i(x,y),z))),z)),n(n(x)))). given clause #959: (wt=21) 15504 [hyper,1,116,15377] P(i(n(i(n(i(n(n(i(i(x,y),z))),z)),x)),u)). given clause #960: (wt=21) 15514 [hyper,1,860,15389] P(i(n(i(n(i(i(i(x,y),z),z)),u)),n(y))). given clause #961: (wt=45) 307 [hyper,1,146,138] P(i(n(i(x,i(i(n(n(y)),n(n(z))),i(y,z)))),u)). given clause #962: (wt=21) 15525 [hyper,1,116,15389] P(i(n(i(n(i(i(i(x,y),z),z)),n(y))),u)). given clause #963: (wt=21) 15564 [hyper,1,116,15390] P(i(n(i(n(i(x,i(y,z))),n(z))),u)). given clause #964: (wt=21) 15588 [hyper,1,367,14686] P(n(n(i(n(i(n(n(x)),y)),n(i(x,y)))))). given clause #965: (wt=24) 308 [hyper,1,116,138] P(i(n(i(i(n(n(x)),n(n(y))),i(x,y))),z)). given clause #966: (wt=21) 15631 [hyper,1,367,14693] P(n(n(i(n(i(i(i(i(n(x),y),y),z),z)),x)))). given clause #967: (wt=21) 15661 [hyper,1,367,14696] P(n(n(i(n(i(i(n(x),y),i(z,y))),x)))). given clause #968: (wt=21) 15695 [hyper,1,367,14740] P(n(n(i(n(i(n(i(n(n(i(n(x),y))),y)),z)),x)))). given clause #969: (wt=26) 309 [hyper,1,34,138] P(i(i(i(i(n(n(x)),n(n(y))),i(x,y)),z),z)). given clause #970: (wt=21) 15746 [hyper,1,367,14741] P(n(n(i(n(i(n(n(i(n(n(i(x,y))),z))),z)),x)))). given clause #971: (wt=21) 15747 [hyper,1,362,14741] P(i(n(i(n(n(i(n(n(i(n(n(x)),y))),z))),z)),x)). given clause #972: (wt=21) 15778 [hyper,1,367,14746] P(n(n(i(n(i(n(n(i(n(x),y))),y)),n(n(x)))))). given clause #973: (wt=25) 310 [hyper,1,31,138] P(i(i(i(x,n(n(y))),n(n(z))),i(y,z))). given clause #974: (wt=21) 15845 [hyper,1,367,15404] P(n(n(i(n(i(n(i(i(i(x,y),y),x)),z)),y)))). given clause #975: (wt=21) 15877 [hyper,1,367,15410] P(n(n(i(n(i(i(i(x,y),y),x)),n(n(y)))))). given clause #976: (wt=21) 16206 [hyper,1,65,14617] P(i(n(i(i(n(x),y),x)),i(n(y),z))). given clause #977: (wt=35) 311 [hyper,1,3,138] P(i(i(i(x,y),z),i(i(n(n(x)),n(n(y))),z))). given clause #978: (wt=21) 16220 [hyper,1,1524,16171] P(i(n(n(i(i(n(i(i(n(x),y),x)),y),z))),z)). given clause #979: (wt=21) 16221 [hyper,1,969,16171] P(i(i(n(n(i(n(i(i(n(x),y),x)),y))),z),z)). given clause #980: (wt=21) 16225 [hyper,1,379,16171] P(n(n(i(i(i(n(i(i(n(x),y),x)),y),z),z)))). given clause #981: (wt=41) 312 [hyper,1,2,138] P(i(x,i(i(n(n(y)),n(n(z))),i(y,z)))). given clause #982: (wt=21) 16260 [hyper,1,188,16171] P(i(n(i(n(i(n(i(i(n(x),y),x)),y)),z)),u)). given clause #983: (wt=21) 16380 [hyper,1,860,16222] P(i(n(i(n(i(n(i(i(n(x),y),x)),z)),u)),y)). given clause #984: (wt=21) 16387 [hyper,1,371,16222] P(i(n(i(n(i(i(n(x),y),x)),z)),n(n(y)))). given clause #985: (wt=44) 313 [hyper,1,241,142] P(i(i(x,n(y)),i(x,i(n(i(y,z)),u)))). given clause #986: (wt=21) 16411 [hyper,1,116,16222] P(i(n(i(n(i(n(i(i(n(x),y),x)),z)),y)),u)). given clause #987: (wt=21) 16445 [hyper,1,116,16227] P(i(n(i(n(i(i(n(x),y),x)),n(n(y)))),z)). given clause #988: (wt=21) 16499 [hyper,1,367,16272] P(n(n(i(n(i(i(n(x),y),x)),i(z,y))))). given clause #989: (wt=24) 314 [hyper,1,116,142] P(i(n(i(n(x),i(n(i(x,y)),z))),u)). given clause #990: (wt=21) 17005 [hyper,1,14646,189] P(i(n(i(i(i(n(i(x,n(y))),z),u),u)),y)). given clause #991: (wt=21) 17022 [hyper,1,367,16992] P(n(n(i(n(i(n(n(i(i(x,n(y)),z))),z)),y)))). given clause #992: (wt=21) 17067 [hyper,1,367,16993] P(n(n(i(n(i(i(n(n(i(x,n(y)))),z),z)),y)))). given clause #993: (wt=26) 315 [hyper,1,34,142] P(i(i(i(n(x),i(n(i(x,y)),z)),u),u)). given clause #994: (wt=22) 14511 [hyper,1,277,1873] P(i(n(i(i(x,y),y)),i(z,n(x)))). given clause #995: (wt=22) 14533 [hyper,1,277,1511] P(i(n(n(i(x,n(y)))),i(y,n(x)))). given clause #996: (wt=22) 14690 [hyper,1,14575,245] P(i(n(i(i(x,n(n(y))),i(x,z))),y)). given clause #997: (wt=41) 317 [hyper,1,2,142] P(i(x,i(n(y),i(n(i(y,z)),u)))). given clause #998: (wt=22) 14697 [hyper,1,1524,14687] P(i(n(n(i(i(n(i(i(x,y),y)),n(x)),z))),z)). given clause #999: (wt=22) 14698 [hyper,1,969,14687] P(i(i(n(n(i(n(i(i(x,y),y)),n(x)))),z),z)). given clause #1000: (wt=22) 14702 [hyper,1,379,14687] P(n(n(i(i(i(n(i(i(x,y),y)),n(x)),z),z)))). reducing weight limit to 16. given clause #1001: (wt=46) 318 [hyper,1,241,74] P(i(i(x,n(i(y,z))),i(x,i(i(z,y),y)))). given clause #1002: (wt=22) 14720 [hyper,1,188,14687] P(i(n(i(n(i(n(i(i(x,y),y)),n(x))),z)),u)). given clause #1003: (wt=22) 14800 [hyper,1,59,14680] P(i(n(i(n(n(i(n(n(x)),y))),y)),i(x,z))). given clause #1004: (wt=22) 15208 [hyper,1,860,14688] P(i(n(i(n(i(i(x,y),i(x,z))),u)),y)). given clause #1005: (wt=47) 319 [hyper,1,146,74] P(i(n(i(x,i(n(i(y,z)),i(i(z,y),y)))),u)). given clause #1006: (wt=22) 15214 [hyper,1,371,14688] P(i(n(i(i(x,y),i(x,z))),n(n(y)))). given clause #1007: (wt=22) 15226 [hyper,1,116,14688] P(i(n(i(n(i(i(x,y),i(x,z))),y)),u)). given clause #1008: (wt=22) 15235 [hyper,1,860,14699] P(i(n(i(n(i(n(i(i(x,y),y)),z)),u)),n(x))). given clause #1009: (wt=25) 320 [hyper,1,116,74] P(i(n(i(n(i(x,y)),i(i(y,x),x))),z)). given clause #1010: (wt=22) 15245 [hyper,1,116,14699] P(i(n(i(n(i(n(i(i(x,y),y)),z)),n(x))),u)). given clause #1011: (wt=22) 15983 [hyper,1,367,14576] P(n(n(i(i(x,n(y)),i(y,n(x)))))). given clause #1012: (wt=22) 16180 [hyper,1,367,14617] P(n(n(i(n(x),i(i(n(y),x),y))))). given clause #1013: (wt=27) 321 [hyper,1,34,74] P(i(i(i(n(i(x,y)),i(i(y,x),x)),z),z)). given clause #1014: (wt=22) 16639 [hyper,1,367,15284] P(n(n(i(n(i(n(x),y)),n(i(n(y),x)))))). given clause #1015: (wt=22) 16681 [hyper,1,367,15388] P(n(n(i(n(i(i(x,y),i(z,y))),n(x))))). given clause #1016: (wt=23) 979 [hyper,1,390,388] P(i(x,n(n(i(y,n(n(x))))))). given clause #1017: (wt=28) 322 [hyper,1,3,74] P(i(i(i(i(x,y),y),z),i(n(i(y,x)),z))). given clause #1018: (wt=23) 985 [hyper,1,372,372] P(n(n(i(n(i(x,n(n(i(n(x),y))))),z)))). given clause #1019: (wt=23) 995 [hyper,1,46,372] P(n(n(i(n(i(x,i(i(x,y),y))),z)))). given clause #1020: (wt=23) 1003 [hyper,1,34,372] P(i(i(i(x,n(n(i(n(x),y)))),z),z)). given clause #1021: (wt=43) 323 [hyper,1,2,74] P(i(x,i(n(i(y,z)),i(i(z,y),y)))). given clause #1022: (wt=23) 1008 [hyper,1,23,372] P(i(x,n(n(i(n(i(y,x)),z))))). given clause #1023: (wt=23) 1030 [hyper,1,372,141] P(n(n(i(n(i(n(i(x,i(n(x),y))),z)),u)))). given clause #1024: (wt=23) 1032 [hyper,1,372,105] P(n(n(i(n(i(n(i(n(n(x)),i(y,x))),z)),u)))). given clause #1025: (wt=46) 324 [hyper,1,241,76] P(i(i(x,i(i(y,z),u)),i(x,i(n(n(z)),u)))). given clause #1026: (wt=23) 1036 [hyper,1,372,62] P(n(n(i(n(i(n(i(x,y)),i(n(x),z))),u)))). given clause #1027: (wt=23) 1046 [hyper,1,372,28] P(n(n(i(n(i(i(i(x,i(y,x)),z),z)),u)))). given clause #1028: (wt=23) 1051 [hyper,1,372,23] P(n(n(i(n(i(i(i(x,y),z),i(y,z))),u)))). given clause #1029: (wt=25) 326 [hyper,1,116,76] P(i(n(i(i(i(x,y),z),i(n(n(y)),z))),u)). given clause #1030: (wt=23) 1053 [hyper,1,372,5] P(n(n(i(n(i(i(n(x),n(y)),i(y,x))),z)))). given clause #1031: (wt=23) 1070 [hyper,1,35,1010] P(i(i(i(n(i(n(n(x)),y)),x),z),i(u,z))). given clause #1032: (wt=23) 1073 [hyper,1,2,1010] P(i(x,i(n(i(n(n(y)),z)),y))). given clause #1033: (wt=27) 329 [hyper,1,34,76] P(i(i(i(i(i(x,y),z),i(n(n(y)),z)),u),u)). given clause #1034: (wt=23) 1092 [hyper,1,372,376] P(n(n(i(n(i(n(n(x)),n(n(i(y,x))))),z)))). given clause #1035: (wt=23) 1105 [hyper,1,34,376] P(i(i(i(n(n(x)),n(n(i(y,x)))),z),z)). given clause #1036: (wt=23) 1107 [hyper,1,3,376] P(i(i(n(n(i(x,y))),z),i(n(n(y)),z))). given clause #1037: (wt=27) 330 [hyper,1,31,76] P(i(i(i(x,i(y,z)),u),i(n(n(z)),u))). given clause #1038: (wt=23) 1125 [hyper,1,35,1106] P(i(i(i(n(i(x,y)),n(y)),z),i(u,z))). given clause #1039: (wt=23) 1127 [hyper,1,3,1106] P(i(i(n(x),y),i(n(i(z,x)),y))). given clause #1040: (wt=23) 1128 [hyper,1,2,1106] P(i(x,i(n(i(y,z)),n(z)))). given clause #1041: (wt=51) 331 [hyper,1,29,76] P(i(x,i(n(n(y)),i(z,i(u,y))))). given clause #1042: (wt=23) 1147 [hyper,1,34,412] P(i(i(n(n(i(n(i(x,y)),i(y,z)))),u),u)). given clause #1043: (wt=23) 1150 [hyper,1,34,413] P(i(i(n(n(i(n(i(x,i(y,x))),z))),u),u)). given clause #1044: (wt=23) 1152 [hyper,1,372,472] P(n(n(i(n(i(i(i(n(i(n(n(x)),x)),y),z),z)),u)))). given clause #1045: (wt=25) 332 [hyper,1,28,76] P(i(n(n(x)),i(y,i(z,x)))). given clause #1046: (wt=23) 1156 [hyper,1,34,472] P(i(i(i(i(i(n(i(n(n(x)),x)),y),z),z),u),u)). given clause #1047: (wt=23) 1164 [hyper,1,372,476] P(n(n(i(n(i(n(i(n(i(x,n(n(x)))),y)),z)),u)))). given clause #1048: (wt=23) 1166 [hyper,1,34,476] P(i(i(i(n(i(n(i(x,n(n(x)))),y)),z),u),u)). given clause #1049: (wt=27) 333 [hyper,1,26,76] P(i(i(n(x),n(i(y,z))),i(n(n(z)),x))). given clause #1050: (wt=23) 1170 [hyper,1,372,479] P(n(n(i(n(i(i(n(n(i(x,n(n(x))))),y),y)),z)))). given clause #1051: (wt=23) 1183 [hyper,1,34,479] P(i(i(i(i(n(n(i(x,n(n(x))))),y),y),z),z)). given clause #1052: (wt=23) 1187 [hyper,1,372,485] P(n(n(i(n(i(n(i(i(i(n(n(x)),x),y),y)),z)),u)))). given clause #1053: (wt=31) 334 [hyper,1,3,76] P(i(i(i(n(n(x)),y),z),i(i(i(u,x),y),z))). given clause #1054: (wt=23) 1189 [hyper,1,34,485] P(i(i(i(n(i(i(i(n(n(x)),x),y),y)),z),u),u)). given clause #1055: (wt=23) 1203 [hyper,1,372,530] P(n(n(i(n(i(n(i(i(n(n(i(x,x))),y),y)),z)),u)))). given clause #1056: (wt=23) 1205 [hyper,1,34,530] P(i(i(i(n(i(i(n(n(i(x,x))),y),y)),z),u),u)). given clause #1057: (wt=43) 335 [hyper,1,2,76] P(i(x,i(i(i(y,z),u),i(n(n(z)),u)))). given clause #1058: (wt=23) 1210 [hyper,1,142,550] P(i(n(i(n(i(x,i(n(n(y)),y))),z)),u)). given clause #1059: (wt=23) 1214 [hyper,1,34,550] P(i(i(n(n(i(x,i(n(n(y)),y)))),z),z)). given clause #1060: (wt=23) 1218 [hyper,1,142,579] P(i(n(i(n(i(i(i(x,n(n(x))),y),y)),z)),u)). given clause #1061: (wt=33) 336 [hyper,1,76,146] P(i(n(n(x)),i(n(i(y,i(z,x))),u))). given clause #1062: (wt=23) 1222 [hyper,1,34,579] P(i(i(n(n(i(i(i(x,n(n(x))),y),y))),z),z)). given clause #1063: (wt=23) 1234 [hyper,1,372,590] P(n(n(i(n(i(i(i(n(n(x)),x),x),n(n(x)))),y)))). given clause #1064: (wt=23) 1247 [hyper,1,34,590] P(i(i(i(i(i(n(n(x)),x),x),n(n(x))),y),y)). given clause #1065: (wt=25) 339 [hyper,1,76,34] P(i(n(n(x)),i(i(i(y,x),z),z))). given clause #1066: (wt=23) 1254 [hyper,1,142,593] P(i(n(i(n(i(x,n(n(i(y,y))))),z)),u)). given clause #1067: (wt=23) 1258 [hyper,1,34,593] P(i(i(n(n(i(x,n(n(i(y,y)))))),z),z)). given clause #1068: (wt=23) 1262 [hyper,1,142,596] P(i(n(i(n(i(x,n(n(i(y,x))))),z)),u)). given clause #1069: (wt=31) 341 [hyper,1,76,3] P(i(n(n(x)),i(i(x,y),i(z,y)))). given clause #1070: (wt=23) 1266 [hyper,1,34,596] P(i(i(n(n(i(x,n(n(i(y,x)))))),z),z)). given clause #1071: (wt=23) 1271 [hyper,1,372,673] P(n(n(i(n(i(i(i(n(i(x,n(y))),y),z),z)),u)))). given clause #1072: (wt=23) 1275 [hyper,1,34,673] P(i(i(i(i(i(n(i(x,n(y))),y),z),z),u),u)). given clause #1073: (wt=62) 342 [hyper,1,241,35] P(i(i(x,y),i(x,i(i(y,z),i(u,z))))). given clause #1074: (wt=23) 1281 [hyper,1,34,723] P(i(i(n(n(i(n(i(n(i(n(n(x)),x)),y)),z))),u),u)). given clause #1075: (wt=23) 1284 [hyper,1,372,739] P(n(n(i(n(i(n(i(x,n(y))),i(z,y))),u)))). given clause #1076: (wt=23) 1290 [hyper,1,34,739] P(i(i(i(n(i(x,n(y))),i(z,y)),u),u)). given clause #1077: (wt=37) 343 [hyper,1,148,35] P(i(x,i(i(i(n(x),y),z),i(u,z)))). given clause #1078: (wt=23) 1298 [hyper,1,142,759] P(i(n(i(n(i(i(n(n(i(n(n(x)),x))),y),y)),z)),u)). given clause #1079: (wt=23) 1302 [hyper,1,34,759] P(i(i(n(n(i(i(n(n(i(n(n(x)),x))),y),y))),z),z)). given clause #1080: (wt=23) 1305 [hyper,1,34,814] P(i(i(n(n(i(n(i(n(i(x,n(y))),y)),z))),u),u)). given clause #1081: (wt=25) 344 [hyper,1,143,35] P(i(i(i(x,i(n(x),y)),z),i(u,z))). given clause #1082: (wt=23) 1322 [hyper,1,59,859] P(i(i(i(n(i(x,y)),x),n(z)),i(z,u))). given clause #1083: (wt=23) 1327 [hyper,1,59,465] P(i(i(n(n(i(n(n(x)),x))),n(y)),i(y,z))). given clause #1084: (wt=23) 1329 [hyper,1,59,382] P(i(i(i(x,n(n(x))),n(y)),i(y,z))). given clause #1085: (wt=33) 345 [hyper,1,116,35] P(i(n(i(x,i(i(x,y),i(z,y)))),u)). given clause #1086: (wt=23) 1337 [hyper,1,372,868] P(n(n(i(n(i(i(n(n(i(n(i(x,y)),x))),z),z)),u)))). given clause #1087: (wt=23) 1342 [hyper,1,34,868] P(i(i(i(i(n(n(i(n(i(x,y)),x))),z),z),u),u)). given clause #1088: (wt=23) 1346 [hyper,1,34,919] P(i(i(n(n(i(n(i(x,y)),i(z,x)))),u),u)). given clause #1089: (wt=37) 346 [hyper,1,76,35] P(i(n(n(x)),i(i(i(y,x),z),i(u,z)))). given clause #1090: (wt=23) 1349 [hyper,1,34,928] P(i(i(n(n(i(i(i(n(i(x,y)),x),z),z))),u),u)). given clause #1091: (wt=23) 1386 [hyper,1,34,1057] P(i(i(n(n(i(n(i(n(i(n(n(x)),y)),x)),z))),u),u)). given clause #1092: (wt=23) 1389 [hyper,1,372,1065] P(n(n(i(n(i(n(i(n(n(x)),y)),i(z,x))),u)))). given clause #1093: (wt=25) 347 [hyper,1,75,35] P(i(i(i(n(n(x)),i(y,x)),z),i(u,z))). given clause #1094: (wt=23) 1395 [hyper,1,34,1065] P(i(i(i(n(i(n(n(x)),y)),i(z,x)),u),u)). given clause #1095: (wt=23) 1399 [hyper,1,372,1071] P(n(n(i(n(i(i(i(n(i(n(n(x)),y)),x),z),z)),u)))). given clause #1096: (wt=23) 1404 [hyper,1,34,1071] P(i(i(i(i(i(n(i(n(n(x)),y)),x),z),z),u),u)). given clause #1097: (wt=24) 348 [hyper,1,51,35] P(i(i(i(n(x),i(x,y)),z),i(u,z))). given clause #1098: (wt=23) 1410 [hyper,1,34,1113] P(i(i(n(n(i(n(i(n(i(x,y)),n(y))),z))),u),u)). given clause #1099: (wt=23) 1413 [hyper,1,372,1126] P(n(n(i(n(i(i(i(n(i(x,y)),n(y)),z),z)),u)))). given clause #1100: (wt=23) 1418 [hyper,1,34,1126] P(i(i(i(i(i(n(i(x,y)),n(y)),z),z),u),u)). given clause #1101: (wt=41) 349 [hyper,1,49,35] P(i(x,i(i(i(i(x,y),y),z),i(u,z)))). given clause #1102: (wt=23) 1455 [hyper,1,362,143] P(i(i(i(x,i(n(x),y)),n(n(z))),z)). given clause #1103: (wt=23) 1456 [hyper,1,362,75] P(i(i(i(n(n(x)),i(y,x)),n(n(z))),z)). given clause #1104: (wt=23) 1470 [hyper,1,372,1452] P(n(n(i(n(i(i(n(n(i(x,x))),n(n(y))),y)),z)))). given clause #1105: (wt=36) 350 [hyper,1,37,35] P(i(n(x),i(i(i(x,y),z),i(u,z)))). given clause #1106: (wt=23) 1479 [hyper,1,44,1452] P(i(i(n(n(i(x,x))),n(n(y))),i(z,y))). given clause #1107: (wt=23) 1485 [hyper,1,34,1452] P(i(i(i(i(n(n(i(x,x))),n(n(y))),y),z),z)). given clause #1108: (wt=23) 1490 [hyper,1,372,1454] P(n(n(i(n(i(i(i(n(n(x)),x),n(n(y))),y)),z)))). given clause #1109: (wt=35) 351 [hyper,1,34,35] P(i(i(i(x,i(i(x,y),i(z,y))),u),u)). given clause #1110: (wt=23) 1499 [hyper,1,44,1454] P(i(i(i(n(n(x)),x),n(n(y))),i(z,y))). given clause #1111: (wt=23) 1505 [hyper,1,34,1454] P(i(i(i(i(i(n(n(x)),x),n(n(y))),y),z),z)). given clause #1112: (wt=23) 1557 [hyper,1,369,76] P(i(n(n(i(i(x,y),z))),i(n(n(y)),z))). given clause #1113: (wt=41) 352 [hyper,1,26,35] P(i(i(n(x),n(y)),i(i(i(y,x),z),i(u,z)))). given clause #1114: (wt=23) 1600 [hyper,1,59,1547] P(i(n(n(i(n(n(i(x,x))),n(y)))),i(y,z))). given clause #1115: (wt=23) 1621 [hyper,1,59,1550] P(i(n(n(i(i(n(n(x)),x),n(y)))),i(y,z))). given clause #1116: (wt=23) 1636 [hyper,1,372,1541] P(n(n(i(n(i(n(n(i(i(n(i(x,y)),x),z))),z)),u)))). given clause #1117: (wt=47) 353 [hyper,1,24,35] P(i(i(i(x,y),y),i(i(i(i(y,x),x),z),i(u,z)))). given clause #1118: (wt=23) 1642 [hyper,1,44,1541] P(i(n(n(i(i(n(i(x,y)),x),z))),i(u,z))). given clause #1119: (wt=23) 1643 [hyper,1,34,1541] P(i(i(i(n(n(i(i(n(i(x,y)),x),z))),z),u),u)). given clause #1120: (wt=23) 1674 [hyper,1,65,853] P(i(n(i(x,y)),i(n(i(y,z)),u))). given clause #1121: (wt=35) 354 [hyper,1,23,35] P(i(x,i(i(i(y,x),z),i(u,z)))). given clause #1122: (wt=23) 1683 [hyper,1,65,369] P(i(n(i(n(n(x)),y)),i(i(x,y),z))). given clause #1123: (wt=23) 1697 [hyper,1,65,71] P(i(n(i(x,y)),i(n(i(z,x)),u))). given clause #1124: (wt=23) 1698 [hyper,1,65,64] P(i(n(i(x,i(y,z))),i(n(y),u))). given clause #1125: (wt=26) 355 [hyper,1,3,35] P(i(i(i(i(x,y),i(z,y)),u),i(x,u))). given clause #1126: (wt=23) 1712 [hyper,1,372,1546] P(n(n(i(n(i(n(n(i(n(n(i(n(n(x)),x))),y))),y)),z)))). given clause #1127: (wt=23) 1724 [hyper,1,44,1546] P(i(n(n(i(n(n(i(n(n(x)),x))),y))),i(z,y))). given clause #1128: (wt=23) 1730 [hyper,1,34,1546] P(i(i(i(n(n(i(n(n(i(n(n(x)),x))),y))),y),z),z)). given clause #1129: (wt=59) 356 [hyper,1,2,35] P(i(x,i(y,i(i(y,z),i(u,z))))). given clause #1130: (wt=23) 1735 [hyper,1,372,1549] P(n(n(i(n(i(n(n(i(i(x,n(n(x))),y))),y)),z)))). given clause #1131: (wt=23) 1747 [hyper,1,44,1549] P(i(n(n(i(i(x,n(n(x))),y))),i(z,y))). given clause #1132: (wt=23) 1753 [hyper,1,34,1549] P(i(i(i(n(n(i(i(x,n(n(x))),y))),y),z),z)). given clause #1133: (wt=32) 357 [hyper,1,35,138] P(i(i(i(i(n(n(x)),n(n(y))),i(x,y)),z),i(u,z))). given clause #1134: (wt=23) 1759 [hyper,1,142,1595] P(i(n(i(n(i(n(n(i(n(n(i(x,x))),y))),y)),z)),u)). given clause #1135: (wt=23) 1764 [hyper,1,34,1595] P(i(i(n(n(i(n(n(i(n(n(i(x,x))),y))),y))),z),z)). given clause #1136: (wt=23) 1766 [hyper,1,382,66] P(i(i(i(x,y),z),n(n(i(n(x),z))))). given clause #1137: (wt=29) 358 [hyper,1,35,114] P(i(i(i(n(i(x,y)),i(n(y),x)),z),i(u,z))). given clause #1138: (wt=23) 1777 [hyper,1,66,362] P(i(i(i(x,y),n(n(z))),i(n(x),z))). given clause #1139: (wt=23) 1785 [hyper,1,142,1616] P(i(n(i(n(i(n(n(i(i(n(n(x)),x),y))),y)),z)),u)). given clause #1140: (wt=23) 1790 [hyper,1,34,1616] P(i(i(n(n(i(n(n(i(i(n(n(x)),x),y))),y))),z),z)). given clause #1141: (wt=31) 359 [hyper,1,35,89] P(i(i(i(i(i(x,y),y),i(n(y),x)),z),i(u,z))). given clause #1142: (wt=23) 1841 [hyper,1,65,69] P(i(n(i(i(i(x,y),z),z)),i(n(x),u))). given clause #1143: (wt=23) 1860 [hyper,1,116,328] P(i(n(i(n(i(x,y)),i(n(n(y)),z))),u)). given clause #1144: (wt=23) 1872 [hyper,1,116,340] P(i(n(i(n(n(x)),i(i(x,y),y))),z)). given clause #1145: (wt=33) 360 [hyper,1,35,74] P(i(i(i(n(i(x,y)),i(i(y,x),x)),z),i(u,z))). given clause #1146: (wt=23) 1895 [hyper,1,116,365] P(i(n(i(i(i(n(n(x)),x),y),i(z,y))),u)). given clause #1147: (wt=23) 1934 [hyper,1,369,78] P(i(n(n(i(i(n(i(x,i(y,x))),z),u))),u)). given clause #1148: (wt=23) 1935 [hyper,1,367,78] P(n(n(i(i(i(n(i(x,i(y,x))),z),u),u)))). given clause #1149: (wt=29) 361 [hyper,1,35,34] P(i(i(i(x,i(i(x,y),y)),z),i(u,z))). given clause #1150: (wt=23) 1972 [hyper,1,116,439] P(i(n(i(i(n(n(i(x,x))),y),i(z,y))),u)). given clause #1151: (wt=23) 1989 [hyper,1,362,488] P(i(i(i(i(i(n(n(x)),x),y),y),n(n(z))),z)). given clause #1152: (wt=23) 1991 [hyper,1,116,488] P(i(n(i(i(i(i(i(n(n(x)),x),y),y),z),z)),u)). given clause #1153: (wt=27) 384 [hyper,1,29,367] P(i(x,n(n(i(y,i(z,y)))))). given clause #1154: (wt=23) 2003 [hyper,1,116,491] P(i(n(i(i(i(x,n(n(x))),n(n(x))),x)),y)). given clause #1155: (wt=23) 2032 [hyper,1,362,499] P(i(i(i(n(i(x,n(n(x)))),y),n(n(z))),z)). given clause #1156: (wt=23) 2034 [hyper,1,116,499] P(i(n(i(i(i(n(i(x,n(n(x)))),y),z),z)),u)). given clause #1157: (wt=27) 387 [hyper,1,24,367] P(i(i(i(x,y),y),n(n(i(i(y,x),x))))). given clause #1158: (wt=23) 2046 [hyper,1,362,505] P(i(i(n(n(i(x,i(y,x)))),n(n(z))),z)). given clause #1159: (wt=23) 2048 [hyper,1,116,505] P(i(n(i(i(n(n(i(x,i(y,x)))),z),z)),u)). given clause #1160: (wt=23) 2058 [hyper,1,362,534] P(i(i(i(i(n(n(i(x,x))),y),y),n(n(z))),z)). given clause #1161: (wt=36) 389 [hyper,1,21,367] P(i(i(x,y),n(n(i(i(y,z),i(x,z)))))). given clause #1162: (wt=23) 2060 [hyper,1,116,534] P(i(n(i(i(i(i(n(n(i(x,x))),y),y),z),z)),u)). given clause #1163: (wt=23) 2075 [hyper,1,362,542] P(i(i(n(n(i(n(i(n(n(x)),x)),y))),n(n(z))),z)). given clause #1164: (wt=23) 2077 [hyper,1,116,542] P(i(n(i(i(n(n(i(n(i(n(n(x)),x)),y))),z),z)),u)). given clause #1165: (wt=34) 393 [hyper,1,367,241] P(n(n(i(i(x,y),i(i(z,x),i(z,y)))))). given clause #1166: (wt=23) 2102 [hyper,1,116,601] P(i(n(i(x,i(y,n(n(x))))),z)). given clause #1167: (wt=23) 2200 [hyper,1,116,619] P(i(n(i(i(n(n(i(x,y))),z),i(y,z))),u)). given clause #1168: (wt=23) 2235 [hyper,1,362,715] P(i(i(n(n(i(n(i(x,n(y))),y))),n(n(z))),z)). given clause #1169: (wt=31) 420 [hyper,1,367,35] P(n(n(i(x,i(i(x,y),i(z,y)))))). given clause #1170: (wt=23) 2237 [hyper,1,116,715] P(i(n(i(i(n(n(i(n(i(x,n(y))),y))),z),z)),u)). given clause #1171: (wt=23) 2367 [hyper,1,362,872] P(i(i(i(n(i(n(i(x,y)),x)),z),n(n(u))),u)). given clause #1172: (wt=23) 2408 [hyper,1,362,1083] P(i(i(n(n(i(n(i(n(n(x)),y)),x))),n(n(z))),z)). given clause #1173: (wt=37) 422 [hyper,1,367,32] P(n(n(i(x,i(i(i(y,z),u),i(z,u)))))). given clause #1174: (wt=23) 2410 [hyper,1,116,1083] P(i(n(i(i(n(n(i(n(i(n(n(x)),y)),x))),z),z)),u)). given clause #1175: (wt=23) 2448 [hyper,1,116,1121] P(i(n(i(n(i(x,y)),i(z,n(y)))),u)). given clause #1176: (wt=23) 2460 [hyper,1,362,1135] P(i(i(n(n(i(n(i(x,y)),n(y)))),n(n(z))),z)). given clause #1177: (wt=31) 423 [hyper,1,367,31] P(n(n(i(i(i(x,y),z),i(i(i(u,x),y),z))))). given clause #1178: (wt=23) 2462 [hyper,1,116,1135] P(i(n(i(i(n(n(i(n(i(x,y)),n(y)))),z),z)),u)). given clause #1179: (wt=23) 2521 [hyper,1,116,1307] P(i(n(i(n(i(x,n(n(y)))),i(y,z))),u)). given clause #1180: (wt=23) 2529 [hyper,1,369,93] P(i(n(n(i(i(n(i(x,y)),i(y,z)),u))),u)). given clause #1181: (wt=49) 424 [hyper,1,367,30] P(n(n(i(x,i(y,i(z,i(u,z))))))). given clause #1182: (wt=23) 2530 [hyper,1,367,93] P(n(n(i(i(i(n(i(x,y)),i(y,z)),u),u)))). given clause #1183: (wt=23) 2553 [hyper,1,94,148] P(i(n(i(x,i(n(y),z))),i(y,u))). given clause #1184: (wt=23) 2557 [hyper,1,94,89] P(i(n(i(x,i(y,z))),i(n(z),y))). given clause #1185: (wt=25) 425 [hyper,1,367,29] P(n(n(i(i(i(x,i(y,x)),z),i(u,z))))). given clause #1186: (wt=23) 2570 [hyper,1,116,1447] P(i(n(i(i(i(n(i(x,y)),x),n(n(z))),z)),u)). given clause #1187: (wt=23) 2585 [hyper,1,116,1451] P(i(n(i(i(n(n(i(n(n(x)),x))),n(n(y))),y)),z)). given clause #1188: (wt=23) 2609 [hyper,1,116,1453] P(i(n(i(i(i(x,n(n(x))),n(n(y))),y)),z)). given clause #1189: (wt=37) 427 [hyper,1,367,27] P(n(n(i(x,i(i(n(y),n(z)),i(z,y)))))). given clause #1190: (wt=23) 2655 [hyper,1,116,1521] P(i(n(i(n(n(i(n(x),n(y)))),i(y,x))),z)). given clause #1191: (wt=23) 2676 [hyper,1,116,1522] P(i(n(i(n(n(i(i(x,y),z))),i(y,z))),u)). given clause #1192: (wt=23) 2688 [hyper,1,362,1523] P(i(n(n(i(i(x,i(y,x)),n(n(z))))),z)). given clause #1193: (wt=31) 428 [hyper,1,367,26] P(n(n(i(i(i(x,y),z),i(i(n(y),n(x)),z))))). given clause #1194: (wt=23) 2690 [hyper,1,116,1523] P(i(n(i(n(n(i(i(x,i(y,x)),z))),z)),u)). given clause #1195: (wt=23) 2704 [hyper,1,116,1536] P(i(n(i(n(n(i(i(n(n(x)),x),n(n(y))))),y)),z)). given clause #1196: (wt=23) 2726 [hyper,1,116,1537] P(i(n(i(n(n(i(n(n(i(x,x))),n(n(y))))),y)),z)). given clause #1197: (wt=49) 429 [hyper,1,367,25] P(n(n(i(x,i(i(i(y,z),z),i(i(z,y),y)))))). given clause #1198: (wt=23) 2746 [hyper,1,362,1538] P(i(n(n(i(i(n(i(x,y)),n(y)),n(n(z))))),z)). given clause #1199: (wt=23) 2748 [hyper,1,116,1538] P(i(n(i(n(n(i(i(n(i(x,y)),n(y)),z))),z)),u)). given clause #1200: (wt=23) 2762 [hyper,1,362,1539] P(i(n(n(i(i(n(i(n(n(x)),y)),x),n(n(z))))),z)). given clause #1201: (wt=34) 430 [hyper,1,367,24] P(n(n(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))))). given clause #1202: (wt=23) 2764 [hyper,1,116,1539] P(i(n(i(n(n(i(i(n(i(n(n(x)),y)),x),z))),z)),u)). given clause #1203: (wt=23) 2776 [hyper,1,362,1540] P(i(n(n(i(n(n(i(n(i(x,y)),x))),n(n(z))))),z)). given clause #1204: (wt=23) 2778 [hyper,1,116,1540] P(i(n(i(n(n(i(n(n(i(n(i(x,y)),x))),z))),z)),u)). given clause #1205: (wt=67) 432 [hyper,1,367,22] P(n(n(i(x,i(i(y,z),i(i(z,u),i(y,u))))))). given clause #1206: (wt=23) 2790 [hyper,1,362,1542] P(i(n(n(i(i(n(i(x,n(y))),y),n(n(z))))),z)). given clause #1207: (wt=23) 2792 [hyper,1,116,1542] P(i(n(i(n(n(i(i(n(i(x,n(y))),y),z))),z)),u)). given clause #1208: (wt=23) 2812 [hyper,1,116,1543] P(i(n(i(n(n(i(i(n(n(x)),x),x))),n(n(x)))),y)). given clause #1209: (wt=34) 433 [hyper,1,367,21] P(n(n(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))))). given clause #1210: (wt=23) 2814 [hyper,1,59,1543] P(i(n(n(i(i(n(n(x)),x),x))),i(n(x),y))). given clause #1211: (wt=23) 2831 [hyper,1,362,1544] P(i(n(n(i(n(n(i(x,n(n(x))))),n(n(y))))),y)). given clause #1212: (wt=23) 2834 [hyper,1,116,1544] P(i(n(i(n(n(i(n(n(i(x,n(n(x))))),y))),y)),z)). given clause #1213: (wt=25) 434 [hyper,1,367,20] P(n(n(i(x,i(y,i(z,y)))))). given clause #1214: (wt=23) 2856 [hyper,1,362,1545] P(i(n(n(i(i(n(i(n(n(x)),x)),y),n(n(z))))),z)). given clause #1215: (wt=23) 2858 [hyper,1,116,1545] P(i(n(i(n(n(i(i(n(i(n(n(x)),x)),y),z))),z)),u)). given clause #1216: (wt=23) 2917 [hyper,1,116,1771] P(i(n(i(i(i(x,y),n(z)),i(z,x))),u)). given clause #1217: (wt=25) 436 [hyper,1,367,4] P(n(n(i(i(i(x,y),y),i(i(y,x),x))))). given clause #1218: (wt=23) 2983 [hyper,1,34,2948] P(i(i(n(n(i(n(i(x,i(y,z))),y))),u),u)). given clause #1219: (wt=23) 2985 [hyper,1,34,2973] P(i(i(n(n(i(n(i(n(i(n(n(x)),y)),z)),x))),u),u)). given clause #1220: (wt=23) 2991 [hyper,1,116,2540] P(i(n(i(n(i(x,y)),n(n(i(y,z))))),u)). given clause #1221: (wt=34) 437 [hyper,1,367,3] P(n(n(i(i(x,y),i(i(y,z),i(x,z)))))). given clause #1222: (wt=23) 3002 [hyper,1,362,2942] P(i(i(i(n(i(n(i(x,y)),z)),x),n(n(u))),u)). given clause #1223: (wt=23) 3030 [hyper,1,116,2949] P(i(n(i(n(i(x,i(n(n(y)),z))),y)),u)). given clause #1224: (wt=23) 3097 [hyper,1,382,109] P(i(i(i(n(n(x)),i(y,x)),z),n(n(z)))). given clause #1225: (wt=25) 442 [hyper,1,367,36] P(n(n(i(x,i(y,i(z,x)))))). given clause #1226: (wt=23) 3322 [hyper,1,382,117] P(i(i(i(x,y),y),n(n(i(n(y),x))))). given clause #1227: (wt=23) 3349 [hyper,1,117,138] P(i(i(i(n(n(x)),n(y)),n(y)),i(y,x))). given clause #1228: (wt=23) 3386 [hyper,1,367,188] P(n(n(i(x,i(n(i(n(x),y)),z))))). given clause #1229: (wt=50) 443 [hyper,1,241,36] P(i(i(x,y),i(x,i(z,i(u,y))))). given clause #1230: (wt=23) 3417 [hyper,1,369,222] P(i(n(n(i(i(n(i(x,y)),z),u))),i(y,u))). given clause #1231: (wt=23) 3418 [hyper,1,367,222] P(n(n(i(i(i(n(i(x,y)),z),u),i(y,u))))). given clause #1232: (wt=23) 3428 [hyper,1,369,303] P(i(n(n(i(i(x,n(y)),n(z)))),i(z,y))). given clause #1233: (wt=55) 444 [hyper,1,148,36] P(i(x,i(y,i(z,i(n(x),u))))). given clause #1234: (wt=23) 3429 [hyper,1,367,303] P(n(n(i(i(i(x,n(y)),n(z)),i(z,y))))). given clause #1235: (wt=23) 3433 [hyper,1,86,303] P(i(i(i(i(n(x),y),y),n(z)),i(z,x))). given clause #1236: (wt=17) 18887 [hyper,1,3433,7839] P(i(n(i(i(n(x),n(n(y))),y)),x)). given clause #1237: (wt=27) 445 [hyper,1,116,36] P(i(n(i(x,i(y,i(z,x)))),u)). given clause #1238: (wt=19) 18898 [hyper,1,367,18887] P(n(n(i(n(i(i(n(x),n(n(y))),y)),x)))). given clause #1239: (wt=21) 18891 [hyper,1,860,18887] P(i(n(i(n(i(i(n(x),n(n(y))),y)),z)),x)). given clause #1240: (wt=21) 18892 [hyper,1,849,18887] P(i(n(i(i(n(n(i(x,y))),n(n(z))),z)),x)). given clause #1241: (wt=49) 446 [hyper,1,76,36] P(i(n(n(x)),i(y,i(z,i(u,x))))). given clause #1242: (wt=21) 18897 [hyper,1,371,18887] P(i(n(i(i(n(x),n(n(y))),y)),n(n(x)))). given clause #1243: (wt=21) 18913 [hyper,1,116,18887] P(i(n(i(n(i(i(n(x),n(n(y))),y)),x)),z)). given clause #1244: (wt=23) 3456 [hyper,1,59,3444] P(i(n(i(n(i(x,n(n(y)))),z)),i(y,u))). given clause #1245: (wt=71) 447 [hyper,1,49,36] P(i(x,i(y,i(z,i(i(x,u),u))))). given clause #1246: (wt=23) 3462 [hyper,1,34,3452] P(i(i(n(n(i(n(i(n(i(x,n(y))),z)),y))),u),u)). given clause #1247: (wt=23) 3468 [hyper,1,116,3443] P(i(n(i(n(i(x,i(y,n(z)))),z)),u)). given clause #1248: (wt=23) 3477 [hyper,1,367,325] P(n(n(i(n(n(x)),i(n(i(y,x)),z))))). given clause #1249: (wt=48) 448 [hyper,1,37,36] P(i(n(x),i(y,i(z,i(x,u))))). given clause #1250: (wt=23) 3481 [hyper,1,65,325] P(i(n(i(n(i(x,y)),z)),i(n(n(y)),u))). given clause #1251: (wt=23) 3495 [hyper,1,369,379] P(i(n(n(x)),n(n(i(i(x,y),y))))). given clause #1252: (wt=23) 3496 [hyper,1,367,379] P(n(n(i(x,n(n(i(i(x,y),y))))))). given clause #1253: (wt=29) 449 [hyper,1,34,36] P(i(i(i(x,i(y,i(z,x))),u),u)). given clause #1254: (wt=23) 3531 [hyper,1,379,3444] P(n(n(i(i(i(n(i(n(i(x,n(y))),z)),y),u),u)))). given clause #1255: (wt=23) 3536 [hyper,1,379,2935] P(n(n(i(i(i(n(i(n(i(n(n(x)),y)),z)),x),u),u)))). given clause #1256: (wt=23) 3537 [hyper,1,379,2934] P(n(n(i(i(n(n(i(n(i(n(i(x,y)),z)),x))),u),u)))). given clause #1257: (wt=53) 450 [hyper,1,26,36] P(i(i(n(x),n(y)),i(z,i(u,i(y,x))))). given clause #1258: (wt=23) 3538 [hyper,1,379,2929] P(n(n(i(i(i(n(i(x,i(y,z))),y),u),u)))). given clause #1259: (wt=23) 3551 [hyper,1,379,1550] P(n(n(i(i(i(n(n(i(i(n(n(x)),x),y))),y),z),z)))). given clause #1260: (wt=23) 3554 [hyper,1,379,1547] P(n(n(i(i(i(n(n(i(n(n(i(x,x))),y))),y),z),z)))). given clause #1261: (wt=77) 451 [hyper,1,24,36] P(i(i(i(x,y),y),i(z,i(u,i(i(y,x),x))))). given clause #1262: (wt=23) 3593 [hyper,1,379,1117] P(n(n(i(i(i(n(i(n(i(x,y)),n(y))),z),u),u)))). given clause #1263: (wt=23) 3599 [hyper,1,379,1061] P(n(n(i(i(i(n(i(n(i(n(n(x)),y)),x)),z),u),u)))). given clause #1264: (wt=23) 3608 [hyper,1,379,863] P(n(n(i(i(n(n(i(n(i(n(i(x,y)),x)),z))),u),u)))). given clause #1265: (wt=47) 452 [hyper,1,23,36] P(i(x,i(y,i(z,i(u,x))))). given clause #1266: (wt=23) 3610 [hyper,1,379,859] P(n(n(i(i(i(i(i(n(i(x,y)),x),z),z),u),u)))). given clause #1267: (wt=23) 3611 [hyper,1,379,853] P(n(n(i(i(i(n(i(x,y)),i(z,x)),u),u)))). given clause #1268: (wt=23) 3624 [hyper,1,379,668] P(n(n(i(i(i(n(i(n(i(x,n(y))),y)),z),u),u)))). given clause #1269: (wt=31) 453 [hyper,1,36,418] P(i(x,i(y,n(n(i(z,z)))))). given clause #1270: (wt=23) 3638 [hyper,1,379,527] P(n(n(i(i(n(n(i(i(n(n(i(x,x))),y),y))),z),z)))). given clause #1271: (wt=23) 3641 [hyper,1,379,494] P(n(n(i(i(n(n(i(n(i(x,n(n(x)))),y))),z),z)))). given clause #1272: (wt=23) 3644 [hyper,1,379,482] P(n(n(i(i(n(n(i(i(i(n(n(x)),x),y),y))),z),z)))). given clause #1273: (wt=39) 454 [hyper,1,36,367] P(i(x,i(y,i(z,n(n(z)))))). given clause #1274: (wt=23) 3649 [hyper,1,379,465] P(n(n(i(i(i(i(n(n(i(n(n(x)),x))),y),y),z),z)))). given clause #1275: (wt=23) 3650 [hyper,1,379,462] P(n(n(i(i(i(n(i(n(i(n(n(x)),x)),y)),z),u),u)))). given clause #1276: (wt=23) 3651 [hyper,1,379,441] P(n(n(i(i(i(x,n(n(i(y,y)))),z),z)))). given clause #1277: (wt=31) 455 [hyper,1,36,337] P(i(x,i(y,i(n(n(z)),z)))). given clause #1278: (wt=23) 3670 [hyper,1,379,388] P(n(n(i(i(i(x,n(n(i(y,x)))),z),z)))). given clause #1279: (wt=23) 3671 [hyper,1,379,382] P(n(n(i(i(i(i(i(x,n(n(x))),y),y),z),z)))). given clause #1280: (wt=23) 3673 [hyper,1,379,377] P(n(n(i(i(n(n(i(n(n(x)),i(y,x)))),z),z)))). given clause #1281: (wt=83) 456 [hyper,1,36,138] P(i(x,i(y,i(i(n(n(z)),n(n(u))),i(z,u))))). given clause #1282: (wt=23) 3675 [hyper,1,379,374] P(n(n(i(i(n(n(i(x,i(n(x),y)))),z),z)))). given clause #1283: (wt=23) 3683 [hyper,1,379,327] P(n(n(i(i(i(x,i(n(n(y)),y)),z),z)))). given clause #1284: (wt=23) 3770 [hyper,1,379,3487] P(n(n(i(i(i(n(i(i(i(x,y),z),z)),x),u),u)))). given clause #1285: (wt=71) 457 [hyper,1,36,114] P(i(x,i(y,i(n(i(z,u)),i(n(u),z))))). given clause #1286: (wt=23) 3776 [hyper,1,108,3487] P(i(n(i(i(i(n(n(x)),y),z),z)),i(u,x))). given clause #1287: (wt=23) 3785 [hyper,1,379,3747] P(n(n(i(i(n(n(i(n(i(i(n(x),y),y)),x))),z),z)))). given clause #1288: (wt=23) 3787 [hyper,1,69,3747] P(i(i(i(n(i(n(i(i(n(x),y),y)),x)),z),u),u)). given clause #1289: (wt=79) 458 [hyper,1,36,89] P(i(x,i(y,i(i(i(z,u),u),i(n(u),z))))). given clause #1290: (wt=23) 3799 [hyper,1,372,3497] P(n(n(i(n(i(n(i(i(i(x,n(y)),z),z)),y)),u)))). given clause #1291: (wt=23) 3806 [hyper,1,44,3497] P(i(n(i(i(i(x,n(y)),z),z)),i(u,y))). given clause #1292: (wt=23) 3807 [hyper,1,34,3497] P(i(i(i(n(i(i(i(x,n(y)),z),z)),y),u),u)). given clause #1293: (wt=87) 459 [hyper,1,36,74] P(i(x,i(y,i(n(i(z,u)),i(i(u,z),z))))). given clause #1294: (wt=23) 3813 [hyper,1,372,3751] P(n(n(i(n(i(n(i(n(i(i(n(x),y),y)),x)),z)),u)))). given clause #1295: (wt=23) 3817 [hyper,1,34,3772] P(i(i(n(n(i(n(i(i(i(x,y),z),z)),x))),u),u)). given clause #1296: (wt=23) 3848 [hyper,1,372,3773] P(n(n(i(n(i(n(i(i(i(n(n(x)),y),z),z)),x)),u)))). given clause #1297: (wt=71) 460 [hyper,1,36,34] P(i(x,i(y,i(z,i(i(z,u),u))))). given clause #1298: (wt=23) 3854 [hyper,1,34,3773] P(i(i(i(n(i(i(i(n(n(x)),y),z),z)),x),u),u)). given clause #1299: (wt=23) 3866 [hyper,1,116,3759] P(i(n(i(n(i(i(n(x),y),y)),i(z,x))),u)). given clause #1300: (wt=23) 3916 [hyper,1,362,3765] P(i(i(i(n(i(i(n(x),y),y)),x),n(n(z))),z)). given clause #1301: (wt=39) 463 [hyper,1,36,392] P(i(x,i(y,n(n(i(n(n(z)),z)))))). given clause #1302: (wt=23) 3918 [hyper,1,116,3765] P(i(n(i(i(i(n(i(i(n(x),y),y)),x),z),z)),u)). given clause #1303: (wt=23) 3981 [hyper,1,367,381] P(n(n(i(i(i(x,n(n(x))),y),i(z,y))))). given clause #1304: (wt=23) 4158 [hyper,1,369,383] P(i(n(n(i(i(x,y),z))),n(n(i(y,z))))). given clause #1305: (wt=26) 468 [hyper,1,241,364] P(i(i(x,n(i(n(n(y)),y))),i(x,z))). given clause #1306: (wt=23) 4159 [hyper,1,367,383] P(n(n(i(i(i(x,y),z),n(n(i(y,z))))))). given clause #1307: (wt=23) 4189 [hyper,1,3765,386] P(n(n(i(x,i(i(n(n(x)),y),y))))). given clause #1308: (wt=23) 4194 [hyper,1,369,386] P(i(n(n(i(n(x),n(y)))),n(n(i(y,x))))). given clause #1309: (wt=27) 469 [hyper,1,146,364] P(i(n(i(x,i(n(i(n(n(y)),y)),z))),u)). given clause #1310: (wt=23) 4195 [hyper,1,367,386] P(n(n(i(i(n(x),n(y)),n(n(i(y,x))))))). given clause #1311: (wt=23) 4204 [hyper,1,66,386] P(i(i(i(x,y),n(z)),n(n(i(z,x))))). given clause #1312: (wt=23) 4242 [hyper,1,116,4202] P(i(n(i(n(i(x,y)),n(n(i(z,x))))),u)). given clause #1313: (wt=47) 470 [hyper,1,36,364] P(i(x,i(y,i(n(i(n(n(z)),z)),u)))). given clause #1314: (wt=23) 4259 [hyper,1,127,1771] P(i(i(i(x,y),n(z)),i(z,n(y)))). given clause #1315: (wt=21) 19064 [hyper,1,4259,979] P(i(n(i(x,n(n(i(y,z))))),n(z))). given clause #1316: (wt=23) 4304 [hyper,1,117,129] P(i(i(i(n(i(x,y)),y),y),i(n(y),x))). given clause #1317: (wt=26) 473 [hyper,1,3,364] P(i(i(x,y),i(n(i(n(n(z)),z)),y))). given clause #1318: (wt=23) 4331 [hyper,1,367,464] P(n(n(i(i(n(n(i(n(n(x)),x))),y),i(z,y))))). given clause #1319: (wt=23) 4344 [hyper,1,369,489] P(i(n(n(i(i(x,i(n(n(y)),y)),z))),z)). given clause #1320: (wt=23) 4390 [hyper,1,369,490] P(i(n(n(i(n(x),n(i(n(n(y)),y))))),x)). given clause #1321: (wt=27) 475 [hyper,1,146,370] P(i(n(i(x,n(n(i(y,n(n(y))))))),z)). given clause #1322: (wt=23) 4391 [hyper,1,367,490] P(n(n(i(i(n(x),n(i(n(n(y)),y))),x)))). given clause #1323: (wt=23) 4399 [hyper,1,66,490] P(i(i(i(x,y),n(i(n(n(z)),z))),x)). given clause #1324: (wt=23) 4415 [hyper,1,490,1550] P(n(i(i(n(n(x)),x),n(i(n(n(y)),y))))). given clause #1325: (wt=47) 477 [hyper,1,36,370] P(i(x,i(y,n(n(i(z,n(n(z)))))))). given clause #1326: (wt=23) 4417 [hyper,1,490,1547] P(n(i(n(n(i(x,x))),n(i(n(n(y)),y))))). given clause #1327: (wt=23) 4432 [hyper,1,367,507] P(n(n(i(i(i(x,i(y,x)),n(n(z))),z)))). given clause #1328: (wt=23) 4443 [hyper,1,369,517] P(i(n(n(i(i(x,i(y,x)),z))),n(n(z)))). given clause #1329: (wt=27) 481 [hyper,1,367,38] P(n(n(i(x,i(n(y),i(y,z)))))). given clause #1330: (wt=23) 4444 [hyper,1,367,517] P(n(n(i(i(i(x,i(y,x)),z),n(n(z)))))). given clause #1331: (wt=23) 4498 [hyper,1,369,535] P(i(n(n(i(i(x,n(n(i(y,y)))),z))),z)). given clause #1332: (wt=23) 4513 [hyper,1,369,557] P(i(n(n(i(n(n(i(x,i(n(x),y)))),z))),z)). given clause #1333: (wt=30) 483 [hyper,1,241,366] P(i(i(x,i(i(n(n(y)),y),z)),i(x,z))). given clause #1334: (wt=21) 19144 [hyper,1,3765,483] P(i(n(i(i(n(i(i(n(n(x)),x),y)),z),z)),y)). given clause #1335: (wt=22) 19157 [hyper,1,483,14576] P(i(i(x,n(i(n(n(y)),y))),n(x))). given clause #1336: (wt=23) 4530 [hyper,1,369,562] P(i(n(n(i(n(n(i(n(n(x)),i(y,x)))),z))),z)). given clause #1337: (wt=31) 484 [hyper,1,146,366] P(i(n(i(x,i(i(i(n(n(y)),y),z),z))),u)). given clause #1338: (wt=23) 4582 [hyper,1,369,587] P(i(n(n(i(i(i(i(x,n(n(x))),y),y),z))),z)). given clause #1339: (wt=23) 4607 [hyper,1,369,611] P(i(n(n(i(i(x,n(n(i(y,x)))),z))),z)). given clause #1340: (wt=23) 4670 [hyper,1,369,725] P(i(n(n(i(i(n(i(n(i(n(n(x)),x)),y)),z),u))),u)). given clause #1341: (wt=55) 486 [hyper,1,36,366] P(i(x,i(y,i(i(i(n(n(z)),z),u),u)))). given clause #1342: (wt=23) 4677 [hyper,1,369,768] P(i(n(n(i(i(i(n(n(i(n(n(x)),x))),y),y),z))),z)). given clause #1343: (wt=23) 4723 [hyper,1,369,777] P(i(n(n(i(n(n(i(i(i(n(n(x)),x),y),y))),z))),z)). given clause #1344: (wt=23) 4769 [hyper,1,369,784] P(i(n(n(i(n(n(i(n(i(x,n(n(x)))),y))),z))),z)). given clause #1345: (wt=25) 487 [hyper,1,35,366] P(i(i(i(i(i(n(n(x)),x),y),y),z),i(u,z))). given clause #1346: (wt=23) 4784 [hyper,1,369,811] P(i(n(n(i(n(n(i(i(n(n(i(x,x))),y),y))),z))),z)). given clause #1347: (wt=23) 4810 [hyper,1,26,136] P(i(i(n(n(i(x,y))),n(n(z))),i(y,z))). given clause #1348: (wt=23) 4825 [hyper,1,369,816] P(i(n(n(i(i(n(i(n(i(x,n(y))),y)),z),u))),u)). given clause #1349: (wt=30) 492 [hyper,1,3,366] P(i(i(x,y),i(i(i(n(n(z)),z),x),y))). given clause #1350: (wt=23) 4834 [hyper,1,369,832] P(i(n(n(i(n(n(i(x,y))),z))),i(n(x),z))). given clause #1351: (wt=23) 4835 [hyper,1,367,832] P(n(n(i(i(n(n(i(x,y))),z),i(n(x),z))))). given clause #1352: (wt=23) 4861 [hyper,1,367,858] P(n(n(i(i(i(n(i(x,y)),x),z),i(u,z))))). given clause #1353: (wt=27) 493 [hyper,1,2,366] P(i(x,i(i(i(n(n(y)),y),z),z))). given clause #1354: (wt=23) 4867 [hyper,1,369,924] P(i(n(n(i(i(n(i(x,y)),i(z,x)),u))),u)). given clause #1355: (wt=23) 4871 [hyper,1,369,931] P(i(n(n(i(i(i(i(n(i(x,y)),x),z),z),u))),u)). given clause #1356: (wt=23) 4889 [hyper,1,94,139] P(i(n(i(x,n(y))),i(i(y,z),z))). given clause #1357: (wt=30) 495 [hyper,1,241,375] P(i(i(x,n(i(y,n(n(y))))),i(x,z))). given clause #1358: (wt=23) 4905 [hyper,1,369,938] P(i(n(n(i(n(n(i(n(i(n(i(x,y)),x)),z))),u))),u)). given clause #1359: (wt=23) 5078 [hyper,1,369,977] P(i(n(n(i(i(x,n(n(y))),z))),i(y,z))). given clause #1360: (wt=23) 5079 [hyper,1,367,977] P(n(n(i(i(i(x,n(n(y))),z),i(y,z))))). given clause #1361: (wt=31) 496 [hyper,1,146,375] P(i(n(i(x,i(n(i(y,n(n(y)))),z))),u)). given clause #1362: (wt=23) 5269 [hyper,1,369,1088] P(i(n(n(i(i(n(i(n(i(n(n(x)),y)),x)),z),u))),u)). given clause #1363: (wt=23) 5286 [hyper,1,369,1140] P(i(n(n(i(i(n(i(n(i(x,y)),n(y))),z),u))),u)). given clause #1364: (wt=23) 5321 [hyper,1,367,1324] P(n(n(i(i(i(n(n(x)),x),x),i(n(x),y))))). given clause #1365: (wt=55) 497 [hyper,1,36,375] P(i(x,i(y,i(n(i(z,n(n(z)))),u)))). given clause #1366: (wt=23) 5351 [hyper,1,367,1328] P(n(n(i(i(n(n(i(x,x))),n(y)),i(y,z))))). given clause #1367: (wt=23) 5367 [hyper,1,367,1330] P(n(n(i(i(i(n(n(x)),x),n(y)),i(y,z))))). given clause #1368: (wt=23) 5383 [hyper,1,369,1440] P(i(n(n(i(i(x,y),n(n(z))))),i(y,z))). given clause #1369: (wt=25) 498 [hyper,1,35,375] P(i(i(i(n(i(x,n(n(x)))),y),z),i(u,z))). given clause #1370: (wt=23) 5384 [hyper,1,367,1440] P(n(n(i(i(i(x,y),n(n(z))),i(y,z))))). given clause #1371: (wt=23) 5402 [hyper,1,367,1444] P(n(n(i(i(i(n(i(x,y)),n(y)),n(n(z))),z)))). given clause #1372: (wt=23) 5418 [hyper,1,367,1445] P(n(n(i(i(i(n(i(n(n(x)),y)),x),n(n(z))),z)))). given clause #1373: (wt=30) 500 [hyper,1,3,375] P(i(i(x,y),i(n(i(z,n(n(z)))),y))). given clause #1374: (wt=23) 5432 [hyper,1,367,1446] P(n(n(i(i(n(n(i(n(i(x,y)),x))),n(n(z))),z)))). given clause #1375: (wt=23) 5447 [hyper,1,367,1448] P(n(n(i(i(i(n(i(x,n(y))),y),n(n(z))),z)))). given clause #1376: (wt=23) 5463 [hyper,1,367,1449] P(n(n(i(i(n(n(i(x,n(n(x))))),n(n(y))),y)))). given clause #1377: (wt=27) 501 [hyper,1,2,375] P(i(x,i(n(i(y,n(n(y)))),z))). given clause #1378: (wt=23) 5492 [hyper,1,367,1450] P(n(n(i(i(i(n(i(n(n(x)),x)),y),n(n(z))),z)))). given clause #1379: (wt=23) 5518 [hyper,1,367,1516] P(n(n(i(n(n(i(i(x,y),z))),i(n(x),z))))). given clause #1380: (wt=23) 5541 [hyper,1,369,1524] P(i(n(n(x)),i(n(n(i(x,y))),y))). given clause #1381: (wt=31) 502 [hyper,1,146,385] P(i(n(i(x,n(n(i(y,i(z,y)))))),u)). given clause #1382: (wt=16) 19291 [hyper,1,14575,5541] P(i(n(i(n(n(i(x,y))),y)),n(x))). given clause #1383: (wt=18) 19290 [hyper,1,14602,5541] P(n(n(i(n(i(n(n(i(x,y))),y)),n(x))))). given clause #1384: (wt=20) 19315 [hyper,1,860,19291] P(i(n(i(n(i(n(n(i(x,y))),y)),z)),n(x))). given clause #1385: (wt=55) 503 [hyper,1,36,385] P(i(x,i(y,n(n(i(z,i(u,z))))))). given clause #1386: (wt=20) 19322 [hyper,1,116,19291] P(i(n(i(n(i(n(n(i(x,y))),y)),n(x))),z)). given clause #1387: (wt=22) 19325 [hyper,1,34,19291] P(i(i(i(n(i(n(n(i(x,y))),y)),n(x)),z),z)). given clause #1388: (wt=23) 5542 [hyper,1,367,1524] P(n(n(i(x,i(n(n(i(x,y))),y))))). given clause #1389: (wt=25) 504 [hyper,1,35,385] P(i(i(n(n(i(x,i(y,x)))),z),i(u,z))). given clause #1390: (wt=23) 5590 [hyper,1,1524,3747] P(i(n(n(i(n(n(i(n(i(i(n(x),y),y)),x))),z))),z)). given clause #1391: (wt=23) 5593 [hyper,1,1524,3487] P(i(n(n(i(i(n(i(i(i(x,y),z),z)),x),u))),u)). given clause #1392: (wt=23) 5595 [hyper,1,1524,3444] P(i(n(n(i(i(n(i(n(i(x,n(y))),z)),y),u))),u)). given clause #1393: (wt=40) 506 [hyper,1,367,40] P(n(n(i(i(x,y),i(i(i(z,i(u,z)),x),y))))). given clause #1394: (wt=23) 5600 [hyper,1,1524,2935] P(i(n(n(i(i(n(i(n(i(n(n(x)),y)),z)),x),u))),u)). given clause #1395: (wt=23) 5601 [hyper,1,1524,2934] P(i(n(n(i(n(n(i(n(i(n(i(x,y)),z)),x))),u))),u)). given clause #1396: (wt=23) 5602 [hyper,1,1524,2929] P(i(n(n(i(i(n(i(x,i(y,z))),y),u))),u)). given clause #1397: (wt=39) 508 [hyper,1,148,40] P(i(x,i(i(i(y,i(z,y)),n(x)),u))). given clause #1398: (wt=23) 5615 [hyper,1,1524,1550] P(i(n(n(i(i(n(n(i(i(n(n(x)),x),y))),y),z))),z)). given clause #1399: (wt=23) 5618 [hyper,1,1524,1547] P(i(n(n(i(i(n(n(i(n(n(i(x,x))),y))),y),z))),z)). given clause #1400: (wt=23) 5882 [hyper,1,369,1534] P(i(n(n(i(n(x),n(y)))),i(n(n(y)),x))). given clause #1401: (wt=25) 509 [hyper,1,143,40] P(i(i(i(x,i(y,x)),z),i(n(z),u))). given clause #1402: (wt=23) 5883 [hyper,1,367,1534] P(n(n(i(i(n(x),n(y)),i(n(n(y)),x))))). given clause #1403: (wt=23) 5892 [hyper,1,66,1534] P(i(i(i(x,y),n(z)),i(n(n(z)),x))). given clause #1404: (wt=23) 5929 [hyper,1,367,1554] P(n(n(i(n(n(i(i(x,i(n(x),y)),z))),z)))). given clause #1405: (wt=27) 510 [hyper,1,75,40] P(i(i(i(x,i(y,x)),n(n(z))),i(u,z))). given clause #1406: (wt=23) 5960 [hyper,1,367,1556] P(n(n(i(n(n(i(i(x,y),y))),i(n(y),x))))). given clause #1407: (wt=23) 6055 [hyper,1,367,1558] P(n(n(i(n(n(i(i(n(n(x)),i(y,x)),z))),z)))). given clause #1408: (wt=23) 6096 [hyper,1,367,1604] P(n(n(i(n(n(i(n(n(i(x,x))),y))),i(z,y))))). given clause #1409: (wt=25) 511 [hyper,1,51,40] P(i(i(i(x,i(y,x)),n(z)),i(z,u))). given clause #1410: (wt=23) 6132 [hyper,1,367,1625] P(n(n(i(n(n(i(i(n(n(x)),x),y))),i(z,y))))). given clause #1411: (wt=23) 6165 [hyper,1,367,1638] P(n(n(i(n(n(i(i(n(i(x,y)),x),n(n(z))))),z)))). given clause #1412: (wt=23) 6173 [hyper,1,367,1692] P(n(n(i(n(i(n(i(x,y)),z)),i(n(x),u))))). given clause #1413: (wt=47) 512 [hyper,1,49,40] P(i(x,i(i(i(y,i(z,y)),i(x,u)),u))). given clause #1414: (wt=23) 6175 [hyper,1,367,1704] P(n(n(i(n(i(i(i(x,y),z),z)),i(y,u))))). given clause #1415: (wt=23) 6178 [hyper,1,367,1707] P(n(n(i(n(i(x,i(y,z))),i(z,u))))). given clause #1416: (wt=23) 6186 [hyper,1,367,1714] P(n(n(i(n(n(i(n(n(i(n(n(x)),x))),n(n(y))))),y)))). given clause #1417: (wt=36) 513 [hyper,1,37,40] P(i(n(x),i(i(i(y,i(z,y)),x),u))). given clause #1418: (wt=23) 6211 [hyper,1,367,1737] P(n(n(i(n(n(i(i(x,n(n(x))),n(n(y))))),y)))). given clause #1419: (wt=23) 6274 [hyper,1,367,1987] P(n(n(i(n(n(i(i(i(i(n(n(x)),x),y),y),z))),z)))). given clause #1420: (wt=23) 6318 [hyper,1,367,2030] P(n(n(i(n(n(i(i(n(i(x,n(n(x)))),y),z))),z)))). given clause #1421: (wt=41) 514 [hyper,1,26,40] P(i(i(n(x),n(y)),i(i(i(z,i(u,z)),y),x))). given clause #1422: (wt=23) 6353 [hyper,1,367,2044] P(n(n(i(n(n(i(n(n(i(x,i(y,x)))),z))),z)))). given clause #1423: (wt=23) 6390 [hyper,1,367,2056] P(n(n(i(n(n(i(i(i(n(n(i(x,x))),y),y),z))),z)))). given clause #1424: (wt=23) 6425 [hyper,1,367,2073] P(n(n(i(n(n(i(n(n(i(n(i(n(n(x)),x)),y))),z))),z)))). given clause #1425: (wt=53) 515 [hyper,1,24,40] P(i(i(i(x,y),y),i(i(i(z,i(u,z)),i(y,x)),x))). given clause #1426: (wt=23) 6504 [hyper,1,367,2197] P(n(n(i(n(n(i(n(n(i(x,y))),z))),i(y,z))))). given clause #1427: (wt=23) 6527 [hyper,1,367,2233] P(n(n(i(n(n(i(n(n(i(n(i(x,n(y))),y))),z))),z)))). given clause #1428: (wt=23) 6598 [hyper,1,367,2365] P(n(n(i(n(n(i(i(n(i(n(i(x,y)),x)),z),u))),u)))). given clause #1429: (wt=33) 516 [hyper,1,40,375] P(i(i(i(x,i(y,x)),n(i(z,n(n(z))))),u)). given clause #1430: (wt=23) 6699 [hyper,1,367,2406] P(n(n(i(n(n(i(n(n(i(n(i(n(n(x)),y)),x))),z))),z)))). given clause #1431: (wt=23) 6735 [hyper,1,115,186] P(i(i(i(n(i(x,y)),z),y),i(n(y),x))). given clause #1432: (wt=23) 6742 [hyper,1,186,1771] P(i(i(i(n(i(x,y)),z),n(u)),i(u,x))). given clause #1433: (wt=33) 518 [hyper,1,40,366] P(i(i(i(x,i(y,x)),i(i(n(n(z)),z),u)),u)). given clause #1434: (wt=23) 6799 [hyper,1,367,2458] P(n(n(i(n(n(i(n(n(i(n(i(x,y)),n(y)))),z))),z)))). given clause #1435: (wt=23) 6939 [hyper,1,192,383] P(i(n(i(n(i(x,y)),z)),n(n(i(y,u))))). given clause #1436: (wt=23) 6946 [hyper,1,192,139] P(i(n(i(n(n(x)),y)),i(i(x,z),z))). given clause #1437: (wt=29) 519 [hyper,1,40,364] P(i(i(i(x,i(y,x)),n(i(n(n(z)),z))),u)). given clause #1438: (wt=23) 6991 [hyper,1,367,2866] P(n(n(i(n(i(x,y)),n(n(i(n(x),z))))))). given clause #1439: (wt=23) 7005 [hyper,1,367,2914] P(n(n(i(n(n(i(i(x,y),n(z)))),i(z,x))))). given clause #1440: (wt=23) 7019 [hyper,1,367,2918] P(n(n(i(n(i(x,i(y,z))),i(u,y))))). given clause #1441: (wt=41) 520 [hyper,1,40,138] P(i(i(i(x,i(y,x)),i(n(n(z)),n(n(u)))),i(z,u))). given clause #1442: (wt=23) 7102 [hyper,1,367,2978] P(n(n(i(n(i(n(i(n(n(x)),y)),z)),i(u,x))))). given clause #1443: (wt=23) 7105 [hyper,1,1631,198] P(i(n(n(i(i(n(n(x)),x),y))),i(n(y),z))). given clause #1444: (wt=23) 7106 [hyper,1,1610,198] P(i(n(n(i(n(n(i(x,x))),y))),i(n(y),z))). given clause #1445: (wt=33) 521 [hyper,1,40,114] P(i(i(i(x,i(y,x)),n(i(z,u))),i(n(u),z))). given clause #1446: (wt=23) 7109 [hyper,1,931,198] P(i(i(i(n(i(x,y)),x),z),i(n(z),u))). given clause #1447: (wt=23) 7110 [hyper,1,768,198] P(i(i(n(n(i(n(n(x)),x))),y),i(n(y),z))). given clause #1448: (wt=23) 7112 [hyper,1,587,198] P(i(i(i(x,n(n(x))),y),i(n(y),z))). given clause #1449: (wt=37) 522 [hyper,1,40,89] P(i(i(i(x,i(y,x)),i(i(z,u),u)),i(n(u),z))). given clause #1450: (wt=23) 7260 [hyper,1,367,3000] P(n(n(i(n(n(i(i(n(i(n(i(x,y)),z)),x),u))),u)))). given clause #1451: (wt=23) 7278 [hyper,1,382,199] P(i(i(i(x,i(n(x),y)),z),n(n(z)))). given clause #1452: (wt=23) 7343 [hyper,1,369,3346] P(i(n(n(i(i(n(n(x)),y),y))),i(n(y),x))). given clause #1453: (wt=37) 523 [hyper,1,40,74] P(i(i(i(x,i(y,x)),n(i(z,u))),i(i(u,z),z))). given clause #1454: (wt=23) 7344 [hyper,1,367,3346] P(n(n(i(i(i(n(n(x)),y),y),i(n(y),x))))). given clause #1455: (wt=23) 7373 [hyper,1,367,3457] P(n(n(i(n(i(n(i(x,n(y))),z)),i(u,y))))). given clause #1456: (wt=23) 7412 [hyper,1,367,3780] P(n(n(i(n(i(i(i(x,y),z),z)),i(u,x))))). given clause #1457: (wt=29) 524 [hyper,1,40,34] P(i(i(i(x,i(y,x)),z),i(i(z,u),u))). given clause #1458: (wt=23) 7499 [hyper,1,367,3915] P(n(n(i(n(n(i(i(n(i(i(n(x),y),y)),x),z))),z)))). given clause #1459: (wt=23) 7532 [hyper,1,367,4203] P(n(n(i(n(i(x,n(y))),n(n(i(z,y))))))). given clause #1460: (wt=23) 7549 [hyper,1,367,4888] P(n(n(i(n(i(x,y)),i(i(x,z),z))))). given clause #1461: (wt=35) 525 [hyper,1,40,5] P(i(i(i(x,i(y,x)),i(n(z),n(u))),i(u,z))). given clause #1462: (wt=23) 7565 [hyper,1,369,6740] P(i(n(n(i(i(n(n(x)),y),n(z)))),i(z,x))). given clause #1463: (wt=23) 7566 [hyper,1,367,6740] P(n(n(i(i(i(n(n(x)),y),n(z)),i(z,x))))). given clause #1464: (wt=23) 7584 [hyper,1,369,6749] P(i(n(n(i(i(n(i(n(n(x)),x)),y),x))),n(n(x)))). given clause #1465: (wt=41) 526 [hyper,1,40,4] P(i(i(i(x,i(y,x)),i(i(z,u),u)),i(i(u,z),z))). given clause #1466: (wt=23) 7585 [hyper,1,367,6749] P(n(n(i(i(i(n(i(n(n(x)),x)),y),x),n(n(x)))))). given clause #1467: (wt=23) 7616 [hyper,1,367,6938] P(n(n(i(n(i(n(n(x)),y)),n(n(i(z,x))))))). given clause #1468: (wt=23) 7629 [hyper,1,367,7113] P(n(n(i(i(n(n(i(x,x))),y),i(n(y),z))))). given clause #1469: (wt=30) 528 [hyper,1,241,440] P(i(i(x,i(n(n(i(y,y))),z)),i(x,z))). given clause #1470: (wt=21) 19412 [hyper,1,3765,528] P(i(n(i(i(n(i(n(n(i(x,x))),y)),z),z)),y)). given clause #1471: (wt=23) 7648 [hyper,1,367,7114] P(n(n(i(i(i(n(n(x)),x),y),i(n(y),z))))). given clause #1472: (wt=23) 7735 [hyper,1,371,3765] P(i(i(i(n(i(i(n(x),y),y)),x),z),n(n(z)))). given clause #1473: (wt=31) 529 [hyper,1,146,440] P(i(n(i(x,i(i(n(n(i(y,y))),z),z))),u)). given clause #1474: (wt=23) 7736 [hyper,1,371,3759] P(i(n(i(i(n(x),y),y)),n(n(i(z,x))))). given clause #1475: (wt=23) 7741 [hyper,1,371,3443] P(i(n(i(x,i(y,n(z)))),n(n(z)))). given clause #1476: (wt=23) 7748 [hyper,1,371,2942] P(i(i(i(n(i(n(i(x,y)),z)),x),u),n(n(u)))). given clause #1477: (wt=33) 531 [hyper,1,40,440] P(i(i(i(x,i(y,x)),i(n(n(i(z,z))),u)),u)). given clause #1478: (wt=23) 7749 [hyper,1,371,2941] P(i(n(i(n(i(x,y)),z)),n(n(i(u,x))))). given clause #1479: (wt=23) 7777 [hyper,1,371,1545] P(i(n(n(i(i(n(i(n(n(x)),x)),y),z))),n(n(z)))). given clause #1480: (wt=23) 7778 [hyper,1,371,1544] P(i(n(n(i(n(n(i(x,n(n(x))))),y))),n(n(y)))). given clause #1481: (wt=55) 532 [hyper,1,36,440] P(i(x,i(y,i(i(n(n(i(z,z))),u),u)))). given clause #1482: (wt=23) 7779 [hyper,1,371,1542] P(i(n(n(i(i(n(i(x,n(y))),y),z))),n(n(z)))). given clause #1483: (wt=23) 7781 [hyper,1,371,1540] P(i(n(n(i(n(n(i(n(i(x,y)),x))),z))),n(n(z)))). given clause #1484: (wt=23) 7782 [hyper,1,371,1539] P(i(n(n(i(i(n(i(n(n(x)),y)),x),z))),n(n(z)))). given clause #1485: (wt=25) 533 [hyper,1,35,440] P(i(i(i(i(n(n(i(x,x))),y),y),z),i(u,z))). given clause #1486: (wt=23) 7783 [hyper,1,371,1538] P(i(n(n(i(i(n(i(x,y)),n(y)),z))),n(n(z)))). given clause #1487: (wt=23) 7792 [hyper,1,371,1307] P(i(n(i(x,n(n(y)))),n(n(i(y,z))))). given clause #1488: (wt=23) 7794 [hyper,1,371,1135] P(i(i(n(n(i(n(i(x,y)),n(y)))),z),n(n(z)))). given clause #1489: (wt=30) 536 [hyper,1,3,440] P(i(i(x,y),i(i(n(n(i(z,z))),x),y))). given clause #1490: (wt=23) 7796 [hyper,1,371,1121] P(i(n(i(x,y)),n(n(i(z,n(y)))))). given clause #1491: (wt=23) 7798 [hyper,1,371,1083] P(i(i(n(n(i(n(i(n(n(x)),y)),x))),z),n(n(z)))). given clause #1492: (wt=23) 7805 [hyper,1,371,872] P(i(i(i(n(i(n(i(x,y)),x)),z),u),n(n(u)))). given clause #1493: (wt=27) 537 [hyper,1,2,440] P(i(x,i(i(n(n(i(y,y))),z),z))). given clause #1494: (wt=23) 7815 [hyper,1,371,715] P(i(i(n(n(i(n(i(x,n(y))),y))),z),n(n(z)))). given clause #1495: (wt=23) 7817 [hyper,1,371,619] P(i(i(n(n(i(x,y))),z),n(n(i(y,z))))). given clause #1496: (wt=23) 7823 [hyper,1,371,542] P(i(i(n(n(i(n(i(n(n(x)),x)),y))),z),n(n(z)))). given clause #1497: (wt=31) 538 [hyper,1,146,467] P(i(n(i(x,n(n(i(n(i(n(n(y)),y)),z))))),u)). given clause #1498: (wt=23) 7825 [hyper,1,371,534] P(i(i(i(i(n(n(i(x,x))),y),y),z),n(n(z)))). given clause #1499: (wt=23) 7826 [hyper,1,371,505] P(i(i(n(n(i(x,i(y,x)))),z),n(n(z)))). given clause #1500: (wt=23) 7827 [hyper,1,371,499] P(i(i(i(n(i(x,n(n(x)))),y),z),n(n(z)))). given clause #1501: (wt=55) 540 [hyper,1,36,467] P(i(x,i(y,n(n(i(n(i(n(n(z)),z)),u)))))). given clause #1502: (wt=23) 7830 [hyper,1,371,488] P(i(i(i(i(i(n(n(x)),x),y),y),z),n(n(z)))). given clause #1503: (wt=23) 7834 [hyper,1,371,439] P(i(i(n(n(i(x,x))),y),n(n(i(z,y))))). given clause #1504: (wt=23) 7838 [hyper,1,371,365] P(i(i(i(n(n(x)),x),y),n(n(i(z,y))))). given clause #1505: (wt=25) 541 [hyper,1,35,467] P(i(i(n(n(i(n(i(n(n(x)),x)),y))),z),i(u,z))). given clause #1506: (wt=23) 7840 [hyper,1,371,328] P(i(n(i(x,y)),n(n(i(n(n(y)),z))))). given clause #1507: (wt=23) 7930 [hyper,1,189,7678] P(i(i(i(n(i(n(i(x,y)),n(n(x)))),z),u),u)). given clause #1508: (wt=23) 7941 [hyper,1,44,7678] P(i(n(i(x,y)),i(z,n(n(x))))). given clause #1509: (wt=27) 543 [hyper,1,2,467] P(i(x,n(n(i(n(i(n(n(y)),y)),z))))). given clause #1510: (wt=23) 7948 [hyper,1,1524,7926] P(i(n(n(i(n(n(i(n(i(x,y)),n(n(x))))),z))),z)). given clause #1511: (wt=23) 7950 [hyper,1,379,7926] P(n(n(i(i(n(n(i(n(i(x,y)),n(n(x))))),z),z)))). given clause #1512: (wt=23) 7960 [hyper,1,372,7669] P(n(n(i(n(i(n(i(i(n(x),y),y)),n(n(x)))),z)))). given clause #1513: (wt=33) 544 [hyper,1,146,378] P(i(n(i(x,n(n(i(n(y),i(y,z)))))),u)). given clause #1514: (wt=23) 7981 [hyper,1,34,7669] P(i(i(i(n(i(i(n(x),y),y)),n(n(x))),z),z)). given clause #1515: (wt=23) 7990 [hyper,1,372,7672] P(n(n(i(n(i(n(i(n(i(x,y)),z)),n(n(x)))),u)))). given clause #1516: (wt=23) 7995 [hyper,1,34,7672] P(i(i(i(n(i(n(i(x,y)),z)),n(n(x))),u),u)). given clause #1517: (wt=59) 545 [hyper,1,36,378] P(i(x,i(y,n(n(i(n(z),i(z,u))))))). given clause #1518: (wt=23) 8003 [hyper,1,372,7683] P(n(n(i(n(i(i(n(n(i(x,x))),y),n(n(y)))),z)))). given clause #1519: (wt=23) 8024 [hyper,1,34,7683] P(i(i(i(i(n(n(i(x,x))),y),n(n(y))),z),z)). given clause #1520: (wt=23) 8032 [hyper,1,372,7684] P(n(n(i(n(i(i(i(n(n(x)),x),y),n(n(y)))),z)))). given clause #1521: (wt=26) 546 [hyper,1,35,378] P(i(i(n(n(i(n(x),i(x,y)))),z),i(u,z))). given clause #1522: (wt=23) 8053 [hyper,1,34,7684] P(i(i(i(i(i(n(n(x)),x),y),n(n(y))),z),z)). given clause #1523: (wt=23) 8070 [hyper,1,372,7935] P(n(n(i(n(i(n(i(n(i(x,y)),n(n(x)))),z)),u)))). given clause #1524: (wt=23) 8080 [hyper,1,116,7668] P(i(n(i(n(i(i(i(x,y),z),z)),n(n(x)))),u)). given clause #1525: (wt=29) 548 [hyper,1,2,378] P(i(x,n(n(i(n(y),i(y,z)))))). given clause #1526: (wt=23) 8093 [hyper,1,116,7670] P(i(n(i(n(i(n(i(x,n(y))),z)),n(n(y)))),u)). given clause #1527: (wt=23) 8109 [hyper,1,116,7671] P(i(n(i(n(i(x,i(y,z))),n(n(y)))),u)). given clause #1528: (wt=23) 8134 [hyper,1,116,7673] P(i(n(i(n(n(i(i(n(n(x)),x),y))),n(n(y)))),z)). given clause #1529: (wt=37) 549 [hyper,1,367,41] P(n(n(i(x,i(i(i(y,i(z,y)),u),u))))). given clause #1530: (wt=23) 8169 [hyper,1,116,7674] P(i(n(i(n(n(i(n(n(i(x,x))),y))),n(n(y)))),z)). given clause #1531: (wt=23) 8198 [hyper,1,116,7677] P(i(n(i(i(i(n(i(x,y)),x),z),n(n(z)))),u)). given clause #1532: (wt=23) 8236 [hyper,1,116,7680] P(i(n(i(i(n(n(i(n(n(x)),x))),y),n(n(y)))),z)). given clause #1533: (wt=35) 551 [hyper,1,146,327] P(i(n(i(x,i(y,i(n(n(z)),z)))),u)). given clause #1534: (wt=23) 8266 [hyper,1,116,7682] P(i(n(i(i(i(x,n(n(x))),y),n(n(y)))),z)). given clause #1535: (wt=23) 8303 [hyper,1,371,7946] P(i(i(i(n(i(x,y)),n(n(x))),z),n(n(z)))). given clause #1536: (wt=23) 8304 [hyper,1,362,7946] P(i(i(i(n(i(x,y)),n(n(x))),n(n(z))),z)). given clause #1537: (wt=63) 552 [hyper,1,36,327] P(i(x,i(y,i(z,i(n(n(u)),u))))). given clause #1538: (wt=23) 8309 [hyper,1,116,7946] P(i(n(i(i(i(n(i(x,y)),n(n(x))),z),z)),u)). given clause #1539: (wt=23) 8381 [hyper,1,367,7738] P(n(n(i(n(i(i(i(x,n(y)),z),z)),n(n(y)))))). given clause #1540: (wt=23) 8395 [hyper,1,367,7774] P(n(n(i(n(n(i(i(x,n(n(x))),y))),n(n(y)))))). given clause #1541: (wt=27) 553 [hyper,1,35,327] P(i(i(i(x,i(n(n(y)),y)),z),i(u,z))). given clause #1542: (wt=23) 8430 [hyper,1,367,7776] P(n(n(i(n(n(i(n(n(i(n(n(x)),x))),y))),n(n(y)))))). given clause #1543: (wt=23) 8458 [hyper,1,367,7780] P(n(n(i(n(n(i(i(n(i(x,y)),x),z))),n(n(z)))))). given clause #1544: (wt=23) 8476 [hyper,1,367,7795] P(n(n(i(i(i(n(i(x,y)),n(y)),z),n(n(z)))))). given clause #1545: (wt=35) 554 [hyper,1,146,374] P(i(n(i(x,n(n(i(y,i(n(y),z)))))),u)). given clause #1546: (wt=23) 8511 [hyper,1,367,7799] P(n(n(i(i(i(n(i(n(n(x)),y)),x),z),n(n(z)))))). given clause #1547: (wt=23) 8546 [hyper,1,367,7806] P(n(n(i(i(n(n(i(n(i(x,y)),x))),z),n(n(z)))))). given clause #1548: (wt=23) 8566 [hyper,1,367,7816] P(n(n(i(i(i(n(i(x,n(y))),y),z),n(n(z)))))). given clause #1549: (wt=63) 555 [hyper,1,36,374] P(i(x,i(y,n(n(i(z,i(n(z),u))))))). given clause #1550: (wt=23) 8610 [hyper,1,367,7831] P(n(n(i(i(n(n(i(x,n(n(x))))),y),n(n(y)))))). given clause #1551: (wt=23) 8646 [hyper,1,367,7832] P(n(n(i(i(i(n(i(n(n(x)),x)),y),z),n(n(z)))))). given clause #1552: (wt=23) 8678 [hyper,1,367,7920] P(n(n(i(n(n(i(i(n(i(x,y)),n(n(x))),z))),z)))). given clause #1553: (wt=27) 556 [hyper,1,35,374] P(i(i(n(n(i(x,i(n(x),y)))),z),i(u,z))). given clause #1554: (wt=23) 8977 [hyper,1,3458,849] P(i(n(i(n(i(x,n(n(i(y,z))))),u)),y)). given clause #1555: (wt=23) 8978 [hyper,1,2953,849] P(i(n(i(x,i(n(i(y,z)),u))),y)). given clause #1556: (wt=23) 8980 [hyper,1,1631,849] P(i(n(n(i(i(n(n(x)),x),n(i(y,z))))),y)). given clause #1557: (wt=31) 558 [hyper,1,2,374] P(i(x,n(n(i(y,i(n(y),z)))))). given clause #1558: (wt=23) 8981 [hyper,1,1610,849] P(i(n(n(i(n(n(i(x,x))),n(i(y,z))))),y)). given clause #1559: (wt=23) 8984 [hyper,1,931,849] P(i(i(i(n(i(x,y)),x),n(i(z,u))),z)). given clause #1560: (wt=23) 8985 [hyper,1,768,849] P(i(i(n(n(i(n(n(x)),x))),n(i(y,z))),y)). given clause #1561: (wt=35) 559 [hyper,1,146,377] P(i(n(i(x,n(n(i(n(n(y)),i(z,y)))))),u)). given clause #1562: (wt=23) 8988 [hyper,1,587,849] P(i(i(i(x,n(n(x))),n(i(y,z))),y)). given clause #1563: (wt=23) 9000 [hyper,1,117,849] P(i(i(i(n(i(x,y)),z),z),i(n(z),x))). given clause #1564: (wt=23) 9087 [hyper,1,372,8976] P(n(n(i(n(i(n(i(i(n(n(i(x,y))),z),z)),x)),u)))). given clause #1565: (wt=63) 560 [hyper,1,36,377] P(i(x,i(y,n(n(i(n(n(z)),i(u,z))))))). given clause #1566: (wt=23) 9106 [hyper,1,44,8976] P(i(n(i(i(n(n(i(x,y))),z),z)),i(u,x))). given clause #1567: (wt=23) 9107 [hyper,1,34,8976] P(i(i(i(n(i(i(n(n(i(x,y))),z),z)),x),u),u)). given clause #1568: (wt=23) 9115 [hyper,1,371,8975] P(i(n(i(i(i(n(i(x,y)),z),u),u)),n(n(x)))). given clause #1569: (wt=27) 561 [hyper,1,35,377] P(i(i(n(n(i(n(n(x)),i(y,x)))),z),i(u,z))). given clause #1570: (wt=23) 9125 [hyper,1,371,8986] P(i(n(i(x,n(n(i(y,z))))),n(n(y)))). given clause #1571: (wt=23) 9126 [hyper,1,362,8986] P(i(n(i(x,n(n(i(n(n(y)),z))))),y)). given clause #1572: (wt=23) 9135 [hyper,1,116,8986] P(i(n(i(n(i(x,n(n(i(y,z))))),y)),u)). given clause #1573: (wt=31) 563 [hyper,1,2,377] P(i(x,n(n(i(n(n(y)),i(z,y)))))). given clause #1574: (wt=23) 9157 [hyper,1,116,9090] P(i(n(i(n(i(i(n(n(i(n(n(x)),y))),z),z)),x)),u)). given clause #1575: (wt=23) 9181 [hyper,1,367,8989] P(n(n(i(i(n(n(i(x,x))),n(i(y,z))),y)))). given clause #1576: (wt=23) 9204 [hyper,1,367,8990] P(n(n(i(i(i(n(n(x)),x),n(i(y,z))),y)))). given clause #1577: (wt=64) 564 [hyper,1,367,42] P(n(n(i(i(x,y),i(z,i(i(y,u),i(x,u))))))). given clause #1578: (wt=23) 9336 [hyper,1,369,9010] P(i(n(n(i(n(n(i(x,y))),n(z)))),i(z,x))). given clause #1579: (wt=23) 9337 [hyper,1,367,9010] P(n(n(i(i(n(n(i(x,y))),n(z)),i(z,x))))). given clause #1580: (wt=23) 9352 [hyper,1,367,9082] P(n(n(i(n(i(i(n(n(i(n(i(x,y)),z))),u),u)),x)))). given clause #1581: (wt=37) 565 [hyper,1,366,42] P(i(x,i(i(y,z),i(n(n(y)),z)))). given clause #1582: (wt=23) 9353 [hyper,1,362,9082] P(i(n(i(i(n(n(i(n(i(n(n(x)),y)),z))),u),u)),x)). given clause #1583: (wt=23) 9361 [hyper,1,367,9088] P(n(n(i(n(i(i(n(n(i(x,y))),z),z)),n(n(x)))))). given clause #1584: (wt=23) 9428 [hyper,1,367,9111] P(n(n(i(n(i(n(i(n(i(x,y)),z)),u)),n(n(x)))))). given clause #1585: (wt=61) 566 [hyper,1,76,42] P(i(n(n(x)),i(y,i(i(x,z),i(u,z))))). given clause #1586: (wt=23) 9599 [hyper,1,367,9117] P(n(n(i(n(i(i(i(n(i(n(n(x)),y)),z),u),u)),x)))). given clause #1587: (wt=23) 9709 [hyper,1,195,860] P(i(n(i(i(i(x,i(n(x),y)),z),u)),z)). given clause #1588: (wt=23) 9715 [hyper,1,115,860] P(i(n(i(i(i(x,y),y),z)),i(n(y),x))). given clause #1589: (wt=83) 567 [hyper,1,49,42] P(i(x,i(y,i(i(z,u),i(i(x,z),u))))). given clause #1590: (wt=23) 9716 [hyper,1,106,860] P(i(n(i(i(i(n(n(x)),i(y,x)),z),u)),z)). given clause #1591: (wt=23) 9722 [hyper,1,63,860] P(i(n(i(i(i(x,y),z),u)),i(n(x),z))). given clause #1592: (wt=23) 9731 [hyper,1,860,9090] P(i(n(i(n(i(i(n(n(i(n(n(x)),y))),z),z)),u)),x)). given clause #1593: (wt=65) 568 [hyper,1,26,42] P(i(i(n(x),n(y)),i(z,i(i(x,u),i(y,u))))). given clause #1594: (wt=23) 9737 [hyper,1,860,7946] P(i(n(i(i(i(n(i(x,y)),n(n(x))),z),u)),z)). given clause #1595: (wt=23) 9753 [hyper,1,860,7682] P(i(n(i(i(i(x,n(n(x))),y),z)),n(n(y)))). given clause #1596: (wt=23) 9754 [hyper,1,860,7680] P(i(n(i(i(n(n(i(n(n(x)),x))),y),z)),n(n(y)))). given clause #1597: (wt=89) 569 [hyper,1,24,42] P(i(i(i(x,y),y),i(z,i(i(x,u),i(i(y,x),u))))). given clause #1598: (wt=23) 9755 [hyper,1,860,7677] P(i(n(i(i(i(n(i(x,y)),x),z),u)),n(n(z)))). given clause #1599: (wt=23) 9756 [hyper,1,860,7674] P(i(n(i(n(n(i(n(n(i(x,x))),y))),z)),n(n(y)))). given clause #1600: (wt=23) 9757 [hyper,1,860,7673] P(i(n(i(n(n(i(i(n(n(x)),x),y))),z)),n(n(y)))). given clause #1601: (wt=59) 570 [hyper,1,23,42] P(i(x,i(y,i(i(x,z),i(u,z))))). given clause #1602: (wt=23) 9758 [hyper,1,860,7671] P(i(n(i(n(i(x,i(y,z))),u)),n(n(y)))). given clause #1603: (wt=23) 9759 [hyper,1,860,7670] P(i(n(i(n(i(n(i(x,n(y))),z)),u)),n(n(y)))). given clause #1604: (wt=23) 9761 [hyper,1,860,7668] P(i(n(i(n(i(i(i(x,y),z),z)),u)),n(n(x)))). given clause #1605: (wt=61) 571 [hyper,1,42,440] P(i(x,i(i(y,z),i(i(n(n(i(u,u))),y),z)))). given clause #1606: (wt=23) 9770 [hyper,1,860,3765] P(i(n(i(i(i(n(i(i(n(x),y),y)),x),z),u)),z)). given clause #1607: (wt=23) 9771 [hyper,1,860,3759] P(i(n(i(n(i(i(n(x),y),y)),z)),i(u,x))). given clause #1608: (wt=23) 9774 [hyper,1,860,3443] P(i(n(i(n(i(x,i(y,n(z)))),u)),z)). given clause #1609: (wt=33) 572 [hyper,1,42,367] P(i(x,i(i(n(n(y)),z),i(y,z)))). given clause #1610: (wt=23) 9776 [hyper,1,860,2949] P(i(n(i(n(i(x,i(n(n(y)),z))),u)),y)). given clause #1611: (wt=23) 9787 [hyper,1,860,1771] P(i(n(i(i(i(x,y),n(z)),u)),i(z,x))). given clause #1612: (wt=23) 9803 [hyper,1,860,1545] P(i(n(i(n(n(i(i(n(i(n(n(x)),x)),y),z))),u)),z)). given clause #1613: (wt=61) 573 [hyper,1,42,366] P(i(x,i(i(y,z),i(i(i(n(n(u)),u),y),z)))). given clause #1614: (wt=23) 9804 [hyper,1,860,1544] P(i(n(i(n(n(i(n(n(i(x,n(n(x))))),y))),z)),y)). given clause #1615: (wt=23) 9805 [hyper,1,860,1542] P(i(n(i(n(n(i(i(n(i(x,n(y))),y),z))),u)),z)). given clause #1616: (wt=23) 9807 [hyper,1,860,1540] P(i(n(i(n(n(i(n(n(i(n(i(x,y)),x))),z))),u)),z)). given clause #1617: (wt=39) 574 [hyper,1,42,327] P(i(x,i(i(i(n(n(y)),y),z),i(u,z)))). given clause #1618: (wt=23) 9808 [hyper,1,860,1539] P(i(n(i(n(n(i(i(n(i(n(n(x)),y)),x),z))),u)),z)). given clause #1619: (wt=23) 9809 [hyper,1,860,1538] P(i(n(i(n(n(i(i(n(i(x,y)),n(y)),z))),u)),z)). given clause #1620: (wt=23) 9810 [hyper,1,860,1537] P(i(n(i(n(n(i(n(n(i(x,x))),n(n(y))))),z)),y)). given clause #1621: (wt=71) 575 [hyper,1,42,138] P(i(x,i(i(i(y,z),u),i(i(n(n(y)),n(n(z))),u)))). given clause #1622: (wt=23) 9811 [hyper,1,860,1536] P(i(n(i(n(n(i(i(n(n(x)),x),n(n(y))))),z)),y)). given clause #1623: (wt=23) 9814 [hyper,1,860,1523] P(i(n(i(n(n(i(i(x,i(y,x)),z))),u)),z)). given clause #1624: (wt=23) 9815 [hyper,1,860,1522] P(i(n(i(n(n(i(i(x,y),z))),u)),i(y,z))). given clause #1625: (wt=53) 576 [hyper,1,42,114] P(i(x,i(i(i(n(y),z),u),i(n(i(z,y)),u)))). given clause #1626: (wt=23) 9816 [hyper,1,860,1521] P(i(n(i(n(n(i(n(x),n(y)))),z)),i(y,x))). given clause #1627: (wt=23) 9821 [hyper,1,860,1453] P(i(n(i(i(i(x,n(n(x))),n(n(y))),z)),y)). given clause #1628: (wt=23) 9823 [hyper,1,860,1451] P(i(n(i(i(n(n(i(n(n(x)),x))),n(n(y))),z)),y)). given clause #1629: (wt=61) 577 [hyper,1,42,89] P(i(x,i(i(i(n(y),z),u),i(i(i(z,y),y),u)))). given clause #1630: (wt=23) 9827 [hyper,1,860,1447] P(i(n(i(i(i(n(i(x,y)),x),n(n(z))),u)),z)). given clause #1631: (wt=23) 9834 [hyper,1,860,1135] P(i(n(i(i(n(n(i(n(i(x,y)),n(y)))),z),u)),z)). given clause #1632: (wt=23) 9836 [hyper,1,860,1121] P(i(n(i(n(i(x,y)),z)),i(u,n(y)))). given clause #1633: (wt=57) 578 [hyper,1,42,74] P(i(x,i(i(i(i(y,z),z),u),i(n(i(z,y)),u)))). given clause #1634: (wt=23) 9837 [hyper,1,860,1083] P(i(n(i(i(n(n(i(n(i(n(n(x)),y)),x))),z),u)),z)). given clause #1635: (wt=23) 9850 [hyper,1,860,715] P(i(n(i(i(n(n(i(n(i(x,n(y))),y))),z),u)),z)). given clause #1636: (wt=23) 9852 [hyper,1,860,619] P(i(n(i(i(n(n(i(x,y))),z),u)),i(y,z))). given clause #1637: (wt=34) 580 [hyper,1,241,382] P(i(i(x,i(i(y,n(n(y))),z)),i(x,z))). given clause #1638: (wt=23) 9858 [hyper,1,860,542] P(i(n(i(i(n(n(i(n(i(n(n(x)),x)),y))),z),u)),z)). given clause #1639: (wt=23) 9860 [hyper,1,860,534] P(i(n(i(i(i(i(n(n(i(x,x))),y),y),z),u)),z)). given clause #1640: (wt=23) 9863 [hyper,1,860,505] P(i(n(i(i(n(n(i(x,i(y,x)))),z),u)),z)). given clause #1641: (wt=35) 581 [hyper,1,146,382] P(i(n(i(x,i(i(i(y,n(n(y))),z),z))),u)). given clause #1642: (wt=23) 9864 [hyper,1,860,499] P(i(n(i(i(i(n(i(x,n(n(x)))),y),z),u)),z)). given clause #1643: (wt=23) 9867 [hyper,1,860,488] P(i(n(i(i(i(i(i(n(n(x)),x),y),y),z),u)),z)). given clause #1644: (wt=23) 9871 [hyper,1,860,439] P(i(n(i(i(n(n(i(x,x))),y),z)),i(u,y))). given clause #1645: (wt=69) 583 [hyper,1,42,382] P(i(x,i(i(y,z),i(i(i(u,n(n(u))),y),z)))). given clause #1646: (wt=23) 9878 [hyper,1,860,365] P(i(n(i(i(i(n(n(x)),x),y),z)),i(u,y))). given clause #1647: (wt=23) 9923 [hyper,1,1524,9695] P(i(n(n(i(i(n(i(n(i(x,y)),z)),n(y)),u))),u)). given clause #1648: (wt=23) 9924 [hyper,1,969,9695] P(i(i(n(n(i(n(i(n(i(x,y)),z)),n(y)))),u),u)). given clause #1649: (wt=37) 584 [hyper,1,40,382] P(i(i(i(x,i(y,x)),i(i(z,n(n(z))),u)),u)). given clause #1650: (wt=23) 9928 [hyper,1,379,9695] P(n(n(i(i(i(n(i(n(i(x,y)),z)),n(y)),u),u)))). given clause #1651: (wt=23) 9945 [hyper,1,372,9689] P(n(n(i(n(i(n(i(n(i(i(n(x),y),y)),z)),x)),u)))). given clause #1652: (wt=23) 9960 [hyper,1,34,9689] P(i(i(i(n(i(n(i(i(n(x),y),y)),z)),x),u),u)). given clause #1653: (wt=63) 585 [hyper,1,36,382] P(i(x,i(y,i(i(i(z,n(n(z))),u),u)))). given clause #1654: (wt=23) 9971 [hyper,1,372,9702] P(n(n(i(n(i(n(i(i(n(n(i(x,x))),y),z)),y)),u)))). given clause #1655: (wt=23) 9993 [hyper,1,34,9702] P(i(i(i(n(i(i(n(n(i(x,x))),y),z)),y),u),u)). given clause #1656: (wt=23) 10004 [hyper,1,372,9703] P(n(n(i(n(i(n(i(i(i(n(n(x)),x),y),z)),y)),u)))). given clause #1657: (wt=27) 586 [hyper,1,35,382] P(i(i(i(i(i(x,n(n(x))),y),y),z),i(u,z))). given clause #1658: (wt=23) 10026 [hyper,1,34,9703] P(i(i(i(n(i(i(i(n(n(x)),x),y),z)),y),u),u)). given clause #1659: (wt=23) 10162 [hyper,1,860,9692] P(i(n(i(n(i(n(n(i(i(n(n(x)),x),y))),z)),u)),y)). given clause #1660: (wt=23) 10189 [hyper,1,116,9692] P(i(n(i(n(i(n(n(i(i(n(n(x)),x),y))),z)),y)),u)). given clause #1661: (wt=25) 588 [hyper,1,31,382] P(i(i(i(x,i(y,n(n(y)))),z),z)). given clause #1662: (wt=23) 10198 [hyper,1,860,9693] P(i(n(i(n(i(n(n(i(n(n(i(x,x))),y))),z)),u)),y)). given clause #1663: (wt=23) 10225 [hyper,1,116,9693] P(i(n(i(n(i(n(n(i(n(n(i(x,x))),y))),z)),y)),u)). given clause #1664: (wt=23) 10296 [hyper,1,3,239] P(i(i(i(i(n(x),n(y)),x),z),i(y,z))). given clause #1665: (wt=25) 589 [hyper,1,26,382] P(i(i(n(x),n(i(y,n(n(y))))),x)). given clause #1666: (wt=23) 10556 [hyper,1,860,9699] P(i(n(i(n(i(i(n(n(i(n(n(x)),x))),y),z)),u)),y)). given clause #1667: (wt=23) 10584 [hyper,1,116,9699] P(i(n(i(n(i(i(n(n(i(n(n(x)),x))),y),z)),y)),u)). given clause #1668: (wt=23) 10593 [hyper,1,860,9701] P(i(n(i(n(i(i(i(x,n(n(x))),y),z)),u)),y)). given clause #1669: (wt=34) 591 [hyper,1,3,382] P(i(i(x,y),i(i(i(z,n(n(z))),x),y))). given clause #1670: (wt=23) 10622 [hyper,1,116,9701] P(i(n(i(n(i(i(i(x,n(n(x))),y),z)),y)),u)). given clause #1671: (wt=23) 10906 [hyper,1,367,9726] P(n(n(i(n(i(i(n(x),n(y)),z)),i(y,x))))). given clause #1672: (wt=23) 11047 [hyper,1,367,9727] P(n(n(i(n(i(i(i(x,y),z),u)),i(y,z))))). given clause #1673: (wt=31) 592 [hyper,1,2,382] P(i(x,i(i(i(y,n(n(y))),z),z))). given clause #1674: (wt=23) 11051 [hyper,1,367,9728] P(n(n(i(n(i(i(i(x,i(y,x)),z),u)),z)))). given clause #1675: (wt=23) 11053 [hyper,1,367,9736] P(n(n(i(n(i(n(i(i(n(n(i(x,y))),z),z)),u)),x)))). given clause #1676: (wt=23) 11145 [hyper,1,367,9751] P(n(n(i(n(i(i(i(n(n(x)),x),y),z)),n(n(y)))))). given clause #1677: (wt=33) 594 [hyper,1,388,388] P(n(n(i(x,i(y,n(n(i(z,y)))))))). given clause #1678: (wt=23) 11165 [hyper,1,367,9752] P(n(n(i(n(i(i(n(n(i(x,x))),y),z)),n(n(y)))))). given clause #1679: (wt=23) 11184 [hyper,1,367,9760] P(n(n(i(n(i(n(i(i(n(x),y),y)),z)),n(n(x)))))). given clause #1680: (wt=23) 11192 [hyper,1,367,9769] P(n(n(i(n(i(n(i(i(i(n(n(x)),y),z),z)),u)),x)))). given clause #1681: (wt=34) 597 [hyper,1,241,388] P(i(i(x,y),i(x,n(n(i(z,y)))))). given clause #1682: (wt=23) 11194 [hyper,1,367,9773] P(n(n(i(n(i(n(i(i(i(x,n(y)),z),z)),u)),y)))). given clause #1683: (wt=23) 11205 [hyper,1,367,9800] P(n(n(i(n(i(n(n(i(i(x,n(n(x))),y))),z)),y)))). given clause #1684: (wt=23) 11377 [hyper,1,367,9802] P(n(n(i(n(i(n(n(i(n(n(i(n(n(x)),x))),y))),z)),y)))). given clause #1685: (wt=31) 598 [hyper,1,148,388] P(i(x,n(n(i(y,i(n(x),z)))))). given clause #1686: (wt=23) 11404 [hyper,1,367,9806] P(n(n(i(n(i(n(n(i(i(n(i(x,y)),x),z))),u)),z)))). given clause #1687: (wt=23) 11412 [hyper,1,367,9820] P(n(n(i(n(i(i(i(n(n(x)),x),n(n(y))),z)),y)))). given clause #1688: (wt=23) 11450 [hyper,1,367,9822] P(n(n(i(n(i(i(n(n(i(x,x))),n(n(y))),z)),y)))). given clause #1689: (wt=35) 599 [hyper,1,146,388] P(i(n(i(x,i(y,n(n(i(z,y)))))),u)). given clause #1690: (wt=23) 11461 [hyper,1,367,9835] P(n(n(i(n(i(i(i(n(i(x,y)),n(y)),z),u)),z)))). given clause #1691: (wt=23) 11464 [hyper,1,367,9838] P(n(n(i(n(i(i(i(n(i(n(n(x)),y)),x),z),u)),z)))). given clause #1692: (wt=23) 11469 [hyper,1,367,9842] P(n(n(i(n(i(i(n(n(i(n(i(x,y)),x))),z),u)),z)))). given clause #1693: (wt=29) 600 [hyper,1,143,388] P(n(n(i(x,i(y,i(n(y),z)))))). given clause #1694: (wt=23) 11472 [hyper,1,367,9851] P(n(n(i(n(i(i(i(n(i(x,n(y))),y),z),u)),z)))). given clause #1695: (wt=23) 11483 [hyper,1,367,9868] P(n(n(i(n(i(i(n(n(i(x,n(n(x))))),y),z)),y)))). given clause #1696: (wt=23) 11514 [hyper,1,367,9869] P(n(n(i(n(i(i(i(n(i(n(n(x)),x)),y),z),u)),z)))). given clause #1697: (wt=29) 603 [hyper,1,76,388] P(i(n(n(x)),n(n(i(y,i(z,x)))))). given clause #1698: (wt=23) 11588 [hyper,1,367,9941] P(n(n(i(n(i(n(i(n(i(i(n(x),y),y)),z)),u)),x)))). given clause #1699: (wt=23) 11591 [hyper,1,367,9965] P(n(n(i(n(i(n(i(i(n(n(i(x,x))),y),z)),u)),y)))). given clause #1700: (wt=23) 11622 [hyper,1,367,9998] P(n(n(i(n(i(n(i(i(i(n(n(x)),x),y),z)),u)),y)))). given clause #1701: (wt=29) 604 [hyper,1,75,388] P(n(n(i(x,i(n(n(y)),i(z,y)))))). given clause #1702: (wt=23) 11761 [hyper,1,367,10283] P(n(n(i(n(i(i(n(x),n(y)),x)),i(y,z))))). given clause #1703: (wt=23) 12490 [hyper,1,263,1548] P(i(n(n(i(n(n(i(x,y))),y))),i(n(y),x))). given clause #1704: (wt=23) 12579 [hyper,1,367,12406] P(n(n(i(i(n(n(i(x,y))),y),i(n(y),x))))). given clause #1705: (wt=39) 605 [hyper,1,49,388] P(i(x,n(n(i(y,i(i(x,z),z)))))). given clause #1706: (wt=23) 12698 [hyper,1,3765,265] P(i(n(i(i(n(n(i(x,y))),z),z)),i(y,u))). given clause #1707: (wt=23) 13017 [hyper,1,386,7775] P(n(n(i(n(i(x,y)),n(i(n(n(x)),y)))))). given clause #1708: (wt=23) 13808 [hyper,1,1126,272] P(i(n(i(x,y)),i(i(n(y),z),z))). given clause #1709: (wt=39) 606 [hyper,1,42,388] P(i(x,i(i(n(n(i(y,z))),u),i(z,u)))). given clause #1710: (wt=23) 14357 [hyper,1,276,5560] P(i(n(i(n(n(i(i(x,y),z))),z)),i(y,u))). given clause #1711: (wt=23) 14376 [hyper,1,276,1011] P(i(i(n(n(i(n(i(x,y)),z))),u),i(y,u))). given clause #1712: (wt=23) 14471 [hyper,1,277,10283] P(i(n(i(i(n(x),n(n(y))),x)),i(z,y))). given clause #1713: (wt=27) 607 [hyper,1,40,388] P(i(i(i(x,i(y,x)),z),n(n(i(u,z))))). given clause #1714: (wt=23) 14549 [hyper,1,277,1011] P(i(i(n(n(i(n(n(x)),y))),n(z)),i(z,x))). given clause #1715: (wt=23) 14559 [hyper,1,277,619] P(i(i(n(n(i(x,n(y)))),n(z)),i(z,y))). given clause #1716: (wt=23) 14601 [hyper,1,372,14575] P(n(n(i(n(i(i(n(x),y),i(n(y),x))),z)))). given clause #1717: (wt=28) 608 [hyper,1,37,388] P(i(n(x),n(n(i(y,i(x,z)))))). given clause #1718: (wt=23) 14616 [hyper,1,235,14575] P(i(i(i(i(n(x),y),y),z),i(n(z),x))). given clause #1719: (wt=17) 20044 [hyper,1,14616,860] P(i(n(i(n(i(i(n(x),y),z)),y)),x)). given clause #1720: (wt=17) 20054 [hyper,1,14616,371] P(i(n(i(i(n(x),y),n(n(y)))),x)). given clause #1721: (wt=63) 609 [hyper,1,36,388] P(i(x,i(y,i(z,n(n(i(u,z))))))). given clause #1722: (wt=19) 20081 [hyper,1,367,20044] P(n(n(i(n(i(n(i(i(n(x),y),z)),y)),x)))). given clause #1723: (wt=19) 20105 [hyper,1,367,20054] P(n(n(i(n(i(i(n(x),y),n(n(y)))),x)))). given clause #1724: (wt=21) 20042 [hyper,1,14616,1524] P(i(n(i(n(n(i(i(i(n(x),y),y),z))),z)),x)). given clause #1725: (wt=27) 610 [hyper,1,35,388] P(i(i(i(x,n(n(i(y,x)))),z),i(u,z))). given clause #1726: (wt=21) 20043 [hyper,1,14616,969] P(i(n(i(i(n(n(i(i(n(x),y),y))),z),z)),x)). given clause #1727: (wt=21) 20045 [hyper,1,14616,849] P(i(n(i(i(n(x),n(i(y,z))),y)),x)). given clause #1728: (wt=21) 20068 [hyper,1,14616,198] P(i(n(i(i(n(x),y),i(n(y),z))),x)). given clause #1729: (wt=33) 612 [hyper,1,31,388] P(i(i(i(x,y),z),n(n(i(u,i(y,z)))))). given clause #1730: (wt=21) 20073 [hyper,1,14616,59] P(i(n(i(i(n(x),n(y)),i(y,z))),x)). given clause #1731: (wt=21) 20077 [hyper,1,860,20044] P(i(n(i(n(i(n(i(i(n(x),y),z)),y)),u)),x)). given clause #1732: (wt=21) 20078 [hyper,1,849,20044] P(i(n(i(n(i(i(n(n(i(x,y))),z),u)),z)),x)). given clause #1733: (wt=51) 613 [hyper,1,29,388] P(i(x,n(n(i(y,i(z,i(u,z))))))). given clause #1734: (wt=21) 20080 [hyper,1,371,20044] P(i(n(i(n(i(i(n(x),y),z)),y)),n(n(x)))). given clause #1735: (wt=21) 20088 [hyper,1,116,20044] P(i(n(i(n(i(n(i(i(n(x),y),z)),y)),x)),u)). given clause #1736: (wt=21) 20096 [hyper,1,860,20054] P(i(n(i(n(i(i(n(x),y),n(n(y)))),z)),x)). given clause #1737: (wt=33) 614 [hyper,1,26,388] P(i(i(n(x),n(y)),n(n(i(z,i(y,x)))))). given clause #1738: (wt=21) 20097 [hyper,1,849,20054] P(i(n(i(i(n(n(i(x,y))),z),n(n(z)))),x)). given clause #1739: (wt=21) 20104 [hyper,1,371,20054] P(i(n(i(i(n(x),y),n(n(y)))),n(n(x)))). given clause #1740: (wt=21) 20122 [hyper,1,116,20054] P(i(n(i(n(i(i(n(x),y),n(n(y)))),x)),z)). given clause #1741: (wt=45) 615 [hyper,1,24,388] P(i(i(i(x,y),y),n(n(i(z,i(i(y,x),x)))))). given clause #1742: (wt=23) 14645 [hyper,1,34,14575] P(i(i(i(i(n(x),y),i(n(y),x)),z),z)). given clause #1743: (wt=23) 14682 [hyper,1,14575,1522] P(i(n(i(x,y)),n(i(i(z,x),y)))). given clause #1744: (wt=23) 14683 [hyper,1,14575,1521] P(i(n(i(x,y)),n(i(n(y),n(x))))). given clause #1745: (wt=27) 616 [hyper,1,23,388] P(i(x,n(n(i(y,i(z,x)))))). given clause #1746: (wt=23) 14695 [hyper,1,14575,232] P(i(n(i(x,i(i(n(y),z),z))),y)). given clause #1747: (wt=23) 14738 [hyper,1,1524,14680] P(i(n(n(i(i(n(i(n(n(i(n(x),y))),y)),x),z))),z)). given clause #1748: (wt=23) 14739 [hyper,1,969,14680] P(i(i(n(n(i(n(i(n(n(i(n(x),y))),y)),x))),z),z)). given clause #1749: (wt=66) 617 [hyper,1,21,388] P(i(i(x,y),n(n(i(z,i(i(y,u),i(x,u))))))). given clause #1750: (wt=23) 14744 [hyper,1,379,14680] P(n(n(i(i(i(n(i(n(n(i(n(x),y))),y)),x),z),z)))). given clause #1751: (wt=23) 14783 [hyper,1,188,14680] P(i(n(i(n(i(n(i(n(n(i(n(x),y))),y)),x)),z)),u)). given clause #1752: (wt=23) 15033 [hyper,1,372,14692] P(n(n(i(n(i(n(i(i(n(x),n(n(y))),x)),y)),z)))). given clause #1753: (wt=31) 620 [hyper,1,2,388] P(i(x,i(y,n(n(i(z,y)))))). given clause #1754: (wt=23) 15081 [hyper,1,34,14692] P(i(i(i(n(i(i(n(x),n(n(y))),x)),y),z),z)). given clause #1755: (wt=23) 15287 [hyper,1,860,14603] P(i(n(i(n(n(i(n(x),y))),z)),i(n(y),x))). given clause #1756: (wt=23) 15292 [hyper,1,371,14603] P(i(n(n(i(n(x),y))),n(n(i(n(y),x))))). given clause #1757: (wt=29) 621 [hyper,1,388,467] P(n(n(i(x,n(n(i(n(i(n(n(y)),y)),z))))))). given clause #1758: (wt=23) 15316 [hyper,1,116,14603] P(i(n(i(n(n(i(n(x),y))),i(n(y),x))),z)). given clause #1759: (wt=23) 15345 [hyper,1,7837,14633] P(n(n(i(n(n(i(i(x,y),z))),i(n(z),x))))). given clause #1760: (wt=23) 15348 [hyper,1,860,14633] P(i(n(i(i(i(x,y),z),u)),i(n(z),x))). given clause #1761: (wt=29) 622 [hyper,1,388,440] P(n(n(i(x,i(i(n(n(i(y,y))),z),z))))). given clause #1762: (wt=23) 15353 [hyper,1,371,14633] P(i(i(i(x,y),z),n(n(i(n(z),x))))). given clause #1763: (wt=23) 15365 [hyper,1,186,14633] P(i(i(i(n(i(x,y)),z),u),i(n(u),x))). given clause #1764: (wt=23) 15366 [hyper,1,127,14633] P(i(i(i(x,y),z),i(n(z),n(y)))). given clause #1765: (wt=29) 624 [hyper,1,388,385] P(n(n(i(x,n(n(i(y,i(z,y)))))))). given clause #1766: (wt=19) 20358 [hyper,1,15366,1524] P(i(n(i(n(n(i(i(x,y),z))),z)),n(y))). given clause #1767: (wt=19) 20359 [hyper,1,15366,969] P(i(n(i(i(n(n(i(x,y))),z),z)),n(y))). given clause #1768: (wt=20) 20388 [hyper,1,15366,90] P(i(n(i(i(i(i(x,y),y),z),z)),n(x))). given clause #1769: (wt=33) 625 [hyper,1,388,382] P(n(n(i(x,i(i(i(y,n(n(y))),z),z))))). given clause #1770: (wt=21) 20384 [hyper,1,15366,189] P(i(n(i(i(i(n(i(x,y)),z),u),u)),n(y))). given clause #1771: (wt=21) 20398 [hyper,1,367,20358] P(n(n(i(n(i(n(n(i(i(x,y),z))),z)),n(y))))). given clause #1772: (wt=21) 20403 [hyper,1,367,20359] P(n(n(i(n(i(i(n(n(i(x,y))),z),z)),n(y))))). given clause #1773: (wt=31) 626 [hyper,1,388,378] P(n(n(i(x,n(n(i(n(y),i(y,z)))))))). given clause #1774: (wt=22) 20407 [hyper,1,367,20388] P(n(n(i(n(i(i(i(i(x,y),y),z),z)),n(x))))). given clause #1775: (wt=23) 15368 [hyper,1,116,14633] P(i(n(i(i(i(x,y),z),i(n(z),x))),u)). given clause #1776: (wt=23) 15402 [hyper,1,1524,15382] P(i(n(n(i(i(n(i(i(i(x,y),y),x)),y),z))),z)). given clause #1777: (wt=33) 627 [hyper,1,388,377] P(n(n(i(x,n(n(i(n(n(y)),i(z,y)))))))). given clause #1778: (wt=23) 15403 [hyper,1,969,15382] P(i(i(n(n(i(n(i(i(i(x,y),y),x)),y))),z),z)). given clause #1779: (wt=23) 15408 [hyper,1,379,15382] P(n(n(i(i(i(n(i(i(i(x,y),y),x)),y),z),z)))). given clause #1780: (wt=23) 15412 [hyper,1,362,15382] P(i(n(i(i(i(x,n(n(y))),n(n(y))),x)),y)). given clause #1781: (wt=29) 628 [hyper,1,388,375] P(n(n(i(x,i(n(i(y,n(n(y)))),z))))). given clause #1782: (wt=23) 15443 [hyper,1,198,15382] P(i(n(i(i(i(x,y),y),x)),i(n(y),z))). given clause #1783: (wt=23) 15445 [hyper,1,188,15382] P(i(n(i(n(i(n(i(i(i(x,y),y),x)),y)),z)),u)). given clause #1784: (wt=23) 15483 [hyper,1,372,15377] P(n(n(i(n(i(n(i(n(n(i(i(x,y),z))),z)),x)),u)))). given clause #1785: (wt=33) 629 [hyper,1,388,374] P(n(n(i(x,n(n(i(y,i(n(y),z)))))))). given clause #1786: (wt=23) 15508 [hyper,1,44,15377] P(i(n(i(n(n(i(i(x,y),z))),z)),i(u,x))). given clause #1787: (wt=23) 15509 [hyper,1,34,15377] P(i(i(i(n(i(n(n(i(i(x,y),z))),z)),x),u),u)). given clause #1788: (wt=23) 15518 [hyper,1,372,15389] P(n(n(i(n(i(n(i(i(i(x,y),z),z)),n(y))),u)))). given clause #1789: (wt=25) 630 [hyper,1,388,370] P(n(n(i(x,n(n(i(y,n(n(y))))))))). given clause #1790: (wt=23) 15527 [hyper,1,34,15389] P(i(i(i(n(i(i(i(x,y),z),z)),n(y)),u),u)). given clause #1791: (wt=23) 15557 [hyper,1,372,15390] P(n(n(i(n(i(n(i(x,i(y,z))),n(z))),u)))). given clause #1792: (wt=23) 15566 [hyper,1,34,15390] P(i(i(i(n(i(x,i(y,z))),n(z)),u),u)). given clause #1793: (wt=29) 631 [hyper,1,388,366] P(n(n(i(x,i(i(i(n(n(y)),y),z),z))))). given clause #1794: (wt=23) 15583 [hyper,1,860,14686] P(i(n(i(n(i(n(n(x)),y)),z)),n(i(x,y)))). given clause #1795: (wt=23) 15608 [hyper,1,116,14686] P(i(n(i(n(i(n(n(x)),y)),n(i(x,y)))),z)). given clause #1796: (wt=23) 15624 [hyper,1,860,14693] P(i(n(i(n(i(i(i(i(n(x),y),y),z),z)),u)),x)). given clause #1797: (wt=25) 632 [hyper,1,388,364] P(n(n(i(x,i(n(i(n(n(y)),y)),z))))). given clause #1798: (wt=23) 15625 [hyper,1,849,14693] P(i(n(i(i(i(i(n(n(i(x,y))),z),z),u),u)),x)). given clause #1799: (wt=23) 15630 [hyper,1,371,14693] P(i(n(i(i(i(i(n(x),y),y),z),z)),n(n(x)))). given clause #1800: (wt=23) 15647 [hyper,1,116,14693] P(i(n(i(n(i(i(i(i(n(x),y),y),z),z)),x)),u)). given clause #1801: (wt=33) 633 [hyper,1,388,327] P(n(n(i(x,i(y,i(n(n(z)),z)))))). given clause #1802: (wt=23) 15655 [hyper,1,860,14696] P(i(n(i(n(i(i(n(x),y),i(z,y))),u)),x)). given clause #1803: (wt=23) 15656 [hyper,1,849,14696] P(i(n(i(i(n(n(i(x,y))),z),i(u,z))),x)). given clause #1804: (wt=23) 15678 [hyper,1,116,14696] P(i(n(i(n(i(i(n(x),y),i(z,y))),x)),u)). given clause #1805: (wt=67) 634 [hyper,1,388,241] P(n(n(i(x,i(i(y,z),i(i(u,y),i(u,z))))))). given clause #1806: (wt=23) 15687 [hyper,1,860,14740] P(i(n(i(n(i(n(i(n(n(i(n(x),y))),y)),z)),u)),x)). given clause #1807: (wt=23) 15688 [hyper,1,849,14740] P(i(n(i(n(i(n(n(i(n(n(i(x,y))),z))),z)),u)),x)). given clause #1808: (wt=23) 15694 [hyper,1,371,14740] P(i(n(i(n(i(n(n(i(n(x),y))),y)),z)),n(n(x)))). given clause #1809: (wt=39) 635 [hyper,1,388,229] P(n(n(i(x,i(n(i(i(y,z),z)),i(y,u)))))). given clause #1810: (wt=23) 15715 [hyper,1,116,14740] P(i(n(i(n(i(n(i(n(n(i(n(x),y))),y)),z)),x)),u)). given clause #1811: (wt=23) 15736 [hyper,1,7839,14741] P(n(n(i(n(i(n(n(i(n(n(i(n(n(x)),y))),z))),z)),x)))). given clause #1812: (wt=23) 15739 [hyper,1,849,14741] P(i(n(i(n(n(i(n(n(i(n(i(x,y)),z))),u))),u)),x)). given clause #1813: (wt=35) 636 [hyper,1,388,180] P(n(n(i(x,i(n(i(n(y),z)),i(y,u)))))). given clause #1814: (wt=23) 15745 [hyper,1,371,14741] P(i(n(i(n(n(i(n(n(i(x,y))),z))),z)),n(n(x)))). given clause #1815: (wt=23) 15766 [hyper,1,116,14741] P(i(n(i(n(i(n(n(i(n(n(i(x,y))),z))),z)),x)),u)). given clause #1816: (wt=23) 15797 [hyper,1,116,14746] P(i(n(i(n(i(n(n(i(n(x),y))),y)),n(n(x)))),z)). given clause #1817: (wt=39) 637 [hyper,1,388,148] P(n(n(i(x,i(i(i(n(y),z),u),i(y,u)))))). given clause #1818: (wt=23) 15836 [hyper,1,860,15404] P(i(n(i(n(i(n(i(i(i(x,y),y),x)),z)),u)),y)). given clause #1819: (wt=23) 15844 [hyper,1,371,15404] P(i(n(i(n(i(i(i(x,y),y),x)),z)),n(n(y)))). given clause #1820: (wt=23) 15862 [hyper,1,116,15404] P(i(n(i(n(i(n(i(i(i(x,y),y),x)),z)),y)),u)). given clause #1821: (wt=41) 638 [hyper,1,388,146] P(n(n(i(x,i(y,i(n(i(z,y)),u)))))). given clause #1822: (wt=23) 15902 [hyper,1,116,15410] P(i(n(i(n(i(i(i(x,y),y),x)),n(n(y)))),z)). given clause #1823: (wt=23) 15934 [hyper,1,860,15486] P(i(n(i(n(i(n(n(i(i(n(n(x)),y),z))),z)),u)),x)). given clause #1824: (wt=23) 15946 [hyper,1,116,15486] P(i(n(i(n(i(n(n(i(i(n(n(x)),y),z))),z)),x)),u)). given clause #1825: (wt=41) 639 [hyper,1,388,143] P(n(n(i(x,i(i(i(y,i(n(y),z)),u),u))))). given clause #1826: (wt=23) 16218 [hyper,1,3,14617] P(i(i(i(i(n(x),y),x),z),i(n(y),z))). given clause #1827: (wt=23) 16256 [hyper,1,227,16171] P(i(n(i(i(i(n(i(i(n(x),y),x)),y),z),z)),u)). given clause #1828: (wt=23) 16259 [hyper,1,189,16171] P(i(i(i(n(i(n(i(i(n(x),y),x)),y)),z),u),u)). given clause #1829: (wt=43) 640 [hyper,1,388,142] P(n(n(i(x,i(n(y),i(n(i(y,z)),u)))))). given clause #1830: (wt=23) 16281 [hyper,1,1524,16228] P(i(n(n(i(n(n(i(n(i(i(n(x),y),x)),y))),z))),z)). given clause #1831: (wt=23) 16283 [hyper,1,379,16228] P(n(n(i(i(n(n(i(n(i(i(n(x),y),x)),y))),z),z)))). given clause #1832: (wt=23) 16377 [hyper,1,7839,16222] P(n(n(i(n(i(n(i(i(n(x),n(n(y))),x)),z)),y)))). given clause #1833: (wt=37) 641 [hyper,1,388,141] P(n(n(i(x,i(n(i(y,i(n(y),z))),u))))). given clause #1834: (wt=23) 16386 [hyper,1,372,16222] P(n(n(i(n(i(n(i(n(i(i(n(x),y),x)),z)),y)),u)))). given clause #1835: (wt=23) 16415 [hyper,1,44,16222] P(i(n(i(n(i(i(n(x),y),x)),z)),i(u,y))). given clause #1836: (wt=23) 16416 [hyper,1,34,16222] P(i(i(i(n(i(n(i(i(n(x),y),x)),z)),y),u),u)). given clause #1837: (wt=43) 642 [hyper,1,388,138] P(n(n(i(x,i(i(n(n(y)),n(n(z))),i(y,z)))))). given clause #1838: (wt=23) 16424 [hyper,1,372,16227] P(n(n(i(n(i(n(i(i(n(x),y),x)),n(n(y)))),z)))). given clause #1839: (wt=23) 16456 [hyper,1,34,16227] P(i(i(i(n(i(i(n(x),y),x)),n(n(y))),z),z)). given clause #1840: (wt=23) 16464 [hyper,1,372,16265] P(n(n(i(n(i(n(i(n(i(i(n(x),y),x)),y)),z)),u)))). given clause #1841: (wt=37) 643 [hyper,1,388,114] P(n(n(i(x,i(n(i(y,z)),i(n(z),y)))))). given clause #1842: (wt=23) 16491 [hyper,1,14575,16272] P(i(n(i(x,y)),i(i(n(z),y),z))). given clause #1843: (wt=23) 16498 [hyper,1,371,16272] P(i(n(i(i(n(x),y),x)),n(n(i(z,y))))). given clause #1844: (wt=23) 16506 [hyper,1,116,16272] P(i(n(i(n(i(i(n(x),y),x)),i(z,y))),u)). given clause #1845: (wt=37) 644 [hyper,1,388,105] P(n(n(i(x,i(n(i(n(n(y)),i(z,y))),u))))). given clause #1846: (wt=23) 16512 [hyper,1,7837,16278] P(n(n(i(n(n(i(i(n(i(i(n(x),y),x)),y),z))),z)))). given clause #1847: (wt=23) 16515 [hyper,1,860,16278] P(i(n(i(i(i(n(i(i(n(x),y),x)),y),z),u)),z)). given clause #1848: (wt=23) 16521 [hyper,1,371,16278] P(i(i(i(n(i(i(n(x),y),x)),y),z),n(n(z)))). given clause #1849: (wt=41) 645 [hyper,1,388,89] P(n(n(i(x,i(i(i(y,z),z),i(n(z),y)))))). given clause #1850: (wt=23) 16522 [hyper,1,362,16278] P(i(i(i(n(i(i(n(x),y),x)),y),n(n(z))),z)). given clause #1851: (wt=23) 16705 [hyper,1,367,14493] P(n(n(i(n(i(n(n(i(n(x),y))),y)),i(z,x))))). given clause #1852: (wt=23) 16736 [hyper,1,367,14597] P(n(n(i(n(i(i(n(x),y),z)),i(n(y),x))))). given clause #1853: (wt=45) 646 [hyper,1,388,76] P(n(n(i(x,i(i(i(y,z),u),i(n(n(z)),u)))))). given clause #1854: (wt=23) 16764 [hyper,1,367,14602] P(n(n(i(i(n(x),y),n(n(i(n(y),x))))))). given clause #1855: (wt=23) 16900 [hyper,1,369,14625] P(i(n(n(i(i(n(n(x)),y),z))),i(n(z),x))). given clause #1856: (wt=23) 16901 [hyper,1,367,14625] P(n(n(i(i(i(n(n(x)),y),z),i(n(z),x))))). given clause #1857: (wt=41) 647 [hyper,1,388,75] P(n(n(i(x,i(i(i(n(n(y)),i(z,y)),u),u))))). given clause #1858: (wt=23) 16927 [hyper,1,14625,238] P(i(n(i(i(i(i(i(n(n(x)),y),z),z),u),u)),x)). given clause #1859: (wt=23) 16935 [hyper,1,14625,35] P(i(n(i(i(i(n(n(x)),y),z),i(u,z))),x)). given clause #1860: (wt=23) 16970 [hyper,1,369,14646] P(i(n(n(i(i(x,n(y)),z))),i(n(z),y))). given clause #1861: (wt=45) 648 [hyper,1,388,74] P(n(n(i(x,i(n(i(y,z)),i(i(z,y),y)))))). given clause #1862: (wt=23) 16971 [hyper,1,367,14646] P(n(n(i(i(i(x,n(y)),z),i(n(z),y))))). given clause #1863: (wt=23) 16974 [hyper,1,254,14646] P(i(i(n(x),y),i(n(i(z,y)),x))). given clause #1864: (wt=23) 16994 [hyper,1,14646,601] P(i(n(i(x,n(n(i(y,n(z)))))),z)). given clause #1865: (wt=33) 649 [hyper,1,388,71] P(n(n(i(x,i(n(i(y,z)),i(z,u)))))). given clause #1866: (wt=23) 16995 [hyper,1,14646,290] P(i(n(i(i(i(x,n(y)),z),i(u,z))),y)). given clause #1867: (wt=23) 17002 [hyper,1,14646,238] P(i(n(i(i(i(i(i(x,n(y)),z),z),u),u)),y)). given clause #1868: (wt=23) 17006 [hyper,1,14646,126] P(i(n(i(i(n(x),n(n(y))),i(z,x))),y)). given clause #1869: (wt=33) 650 [hyper,1,388,70] P(n(n(i(x,i(n(i(y,i(z,y))),u))))). given clause #1870: (wt=23) 17014 [hyper,1,860,16992] P(i(n(i(n(i(n(n(i(i(x,n(y)),z))),z)),u)),y)). given clause #1871: (wt=23) 17021 [hyper,1,371,16992] P(i(n(i(n(n(i(i(x,n(y)),z))),z)),n(n(y)))). given clause #1872: (wt=23) 17048 [hyper,1,116,16992] P(i(n(i(n(i(n(n(i(i(x,n(y)),z))),z)),y)),u)). given clause #1873: (wt=35) 651 [hyper,1,388,68] P(n(n(i(x,i(n(i(n(y),i(y,z))),u))))). given clause #1874: (wt=23) 17059 [hyper,1,860,16993] P(i(n(i(n(i(i(n(n(i(x,n(y)))),z),z)),u)),y)). given clause #1875: (wt=23) 17066 [hyper,1,371,16993] P(i(n(i(i(n(n(i(x,n(y)))),z),z)),n(n(y)))). given clause #1876: (wt=23) 17093 [hyper,1,116,16993] P(i(n(i(n(i(i(n(n(i(x,n(y)))),z),z)),y)),u)). given clause #1877: (wt=37) 652 [hyper,1,388,62] P(n(n(i(x,i(n(i(y,z)),i(n(y),u)))))). given clause #1878: (wt=23) 17237 [hyper,1,367,15383] P(n(n(i(n(i(i(n(x),n(i(y,z))),x)),y)))). given clause #1879: (wt=23) 17266 [hyper,1,367,15384] P(n(n(i(n(i(i(i(i(i(x,y),z),z),u),u)),x)))). given clause #1880: (wt=23) 17284 [hyper,1,367,15387] P(n(n(i(n(i(n(i(x,i(y,z))),u)),n(z))))). given clause #1881: (wt=39) 653 [hyper,1,388,51] P(n(n(i(x,i(i(i(n(y),i(y,z)),u),u))))). given clause #1882: (wt=23) 17288 [hyper,1,367,15392] P(n(n(i(n(i(i(i(x,i(y,z)),u),u)),y)))). given clause #1883: (wt=23) 17293 [hyper,1,367,15396] P(n(n(i(n(i(i(i(x,y),z),i(u,z))),x)))). given clause #1884: (wt=23) 17323 [hyper,1,367,15466] P(n(n(i(n(i(i(i(x,y),y),x)),i(z,y))))). given clause #1885: (wt=43) 654 [hyper,1,388,49] P(n(n(i(x,i(i(i(i(y,z),z),u),i(y,u)))))). given clause #1886: (wt=23) 17372 [hyper,1,367,15478] P(n(n(i(n(i(n(i(n(n(i(i(x,y),z))),z)),u)),x)))). given clause #1887: (wt=23) 17378 [hyper,1,367,15479] P(n(n(i(n(i(n(n(i(i(n(i(x,y)),z),u))),u)),x)))). given clause #1888: (wt=23) 17379 [hyper,1,362,15479] P(i(n(i(n(n(i(i(n(i(n(n(x)),y)),z),u))),u)),x)). given clause #1889: (wt=53) 655 [hyper,1,388,38] P(n(n(i(x,i(y,i(n(z),i(z,u))))))). given clause #1890: (wt=23) 17546 [hyper,1,367,15484] P(n(n(i(n(i(n(n(i(i(x,y),z))),z)),n(n(x)))))). given clause #1891: (wt=23) 17560 [hyper,1,367,15514] P(n(n(i(n(i(n(i(i(i(x,y),z),z)),u)),n(y))))). given clause #1892: (wt=23) 17691 [hyper,1,367,16206] P(n(n(i(n(i(i(n(x),y),x)),i(n(y),z))))). given clause #1893: (wt=41) 656 [hyper,1,388,37] P(n(n(i(x,i(i(i(y,z),u),i(n(y),u)))))). given clause #1894: (wt=23) 17975 [hyper,1,367,16380] P(n(n(i(n(i(n(i(n(i(i(n(x),y),x)),z)),u)),y)))). given clause #1895: (wt=23) 17983 [hyper,1,367,16387] P(n(n(i(n(i(n(i(i(n(x),y),x)),z)),n(n(y)))))). given clause #1896: (wt=23) 18050 [hyper,1,367,17005] P(n(n(i(n(i(i(i(n(i(x,n(y))),z),u),u)),y)))). given clause #1897: (wt=49) 657 [hyper,1,388,36] P(n(n(i(x,i(y,i(z,i(u,y))))))). given clause #1898: (wt=23) 18082 [hyper,1,14575,14533] P(i(n(i(x,n(y))),n(i(y,n(x))))). given clause #1899: (wt=23) 18312 [hyper,1,3,979] P(i(i(n(n(i(x,n(n(y))))),z),i(y,z))). given clause #1900: (wt=23) 18442 [hyper,1,16278,1127] P(i(n(i(x,i(i(n(y),z),y))),z)). given clause #1901: (wt=61) 658 [hyper,1,388,35] P(n(n(i(x,i(y,i(i(y,z),i(u,z))))))). given clause #1902: (wt=23) 18445 [hyper,1,14735,1127] P(i(n(i(x,i(i(y,z),z))),n(y))). given clause #1903: (wt=23) 18644 [hyper,1,14575,346] P(i(n(i(i(i(x,y),z),i(u,z))),n(y))). given clause #1904: (wt=23) 18916 [hyper,1,44,18887] P(i(n(i(i(n(x),n(n(y))),y)),i(z,x))). given clause #1905: (wt=37) 659 [hyper,1,388,34] P(n(n(i(x,i(y,i(i(y,z),z)))))). given clause #1906: (wt=23) 18918 [hyper,1,34,18887] P(i(i(i(n(i(i(n(x),n(n(y))),y)),x),z),z)). given clause #1907: (wt=23) 18925 [hyper,1,367,18897] P(n(n(i(n(i(i(n(x),n(n(y))),y)),n(n(x)))))). given clause #1908: (wt=23) 19071 [hyper,1,367,19064] P(n(n(i(n(i(x,n(n(i(y,z))))),n(z))))). given clause #1909: (wt=73) 660 [hyper,1,388,27] P(n(n(i(x,i(y,i(i(n(z),n(u)),i(u,z))))))). given clause #1910: (wt=23) 19212 [hyper,1,1126,492] P(i(i(i(n(n(x)),x),n(i(y,z))),n(z))). given clause #1911: (wt=23) 19480 [hyper,1,1126,536] P(i(i(n(n(i(x,x))),n(i(y,z))),n(z))). given clause #1912: (wt=23) 19658 [hyper,1,3765,580] P(i(n(i(i(n(i(i(x,n(n(x))),y)),z),z)),y)). given clause #1913: (wt=61) 661 [hyper,1,388,26] P(n(n(i(x,i(i(i(y,z),u),i(i(n(z),n(y)),u)))))). given clause #1914: (wt=23) 20041 [hyper,1,14616,14576] P(i(n(i(x,n(i(n(y),n(x))))),y)). given clause #1915: (wt=23) 20046 [hyper,1,14616,597] P(i(n(i(i(n(x),y),n(n(i(z,y))))),x)). given clause #1916: (wt=23) 20071 [hyper,1,14616,108] P(i(n(i(i(n(x),n(n(y))),i(z,y))),x)). given clause #1917: (wt=97) 662 [hyper,1,388,25] P(n(n(i(x,i(y,i(i(i(z,u),u),i(i(u,z),z))))))). given clause #1918: (wt=23) 20091 [hyper,1,44,20044] P(i(n(i(n(i(i(n(x),y),z)),y)),i(u,x))). given clause #1919: (wt=23) 20125 [hyper,1,44,20054] P(i(n(i(i(n(x),y),n(n(y)))),i(z,x))). given clause #1920: (wt=23) 20127 [hyper,1,34,20054] P(i(i(i(n(i(i(n(x),y),n(n(y)))),x),z),z)). given clause #1921: (wt=67) 663 [hyper,1,388,24] P(n(n(i(x,i(i(i(i(y,z),z),u),i(i(i(z,y),y),u)))))). given clause #1922: (wt=23) 20159 [hyper,1,367,20045] P(n(n(i(n(i(i(n(x),n(i(y,z))),y)),x)))). given clause #1923: (wt=23) 20179 [hyper,1,367,20068] P(n(n(i(n(i(i(n(x),y),i(n(y),z))),x)))). given clause #1924: (wt=23) 20209 [hyper,1,367,20073] P(n(n(i(n(i(i(n(x),n(y)),i(y,z))),x)))). given clause #1925: (wt=25) 664 [hyper,1,388,618] P(n(n(i(x,i(n(i(y,n(z))),z))))). given clause #1926: (wt=23) 20249 [hyper,1,367,20104] P(n(n(i(n(i(i(n(x),y),n(n(y)))),n(n(x)))))). given clause #1927: (wt=23) 20380 [hyper,1,15366,239] P(i(n(i(i(n(x),n(i(y,z))),x)),n(z))). given clause #1928: (wt=23) 20381 [hyper,1,15366,238] P(i(n(i(i(i(i(i(x,y),z),z),u),u)),n(y))). given clause #1929: (wt=26) 666 [hyper,1,241,618] P(i(i(x,n(i(y,n(z)))),i(x,z))). given clause #1930: (wt=21) 20787 [hyper,1,14809,666] P(i(n(i(n(n(i(n(n(i(x,n(y)))),z))),z)),y)). given clause #1931: (wt=23) 20382 [hyper,1,15366,234] P(i(n(i(x,i(y,z))),n(i(x,z)))). given clause #1932: (wt=23) 20385 [hyper,1,15366,126] P(i(n(i(i(n(x),n(y)),i(z,x))),n(y))). given clause #1933: (wt=27) 667 [hyper,1,146,618] P(i(n(i(x,i(n(i(y,n(z))),z))),u)). given clause #1934: (wt=23) 20390 [hyper,1,15366,84] P(i(n(i(i(i(x,y),y),x)),n(i(y,x)))). given clause #1935: (wt=23) 20392 [hyper,1,15366,47] P(i(n(i(i(i(x,i(y,z)),u),u)),n(z))). given clause #1936: (wt=23) 20397 [hyper,1,849,20358] P(i(n(i(n(n(i(i(x,i(y,z)),u))),u)),y)). given clause #1937: (wt=53) 669 [hyper,1,42,618] P(i(x,i(i(y,z),i(n(i(u,n(y))),z)))). given clause #1938: (wt=23) 20402 [hyper,1,849,20359] P(i(n(i(i(n(n(i(x,i(y,z)))),u),u)),y)). given clause #1939: (wt=23) 20438 [hyper,1,277,16218] P(i(i(i(i(n(x),y),x),n(z)),i(z,y))). given clause #1940: (wt=15) 20887 [hyper,1,20438,7837] P(i(n(i(n(n(i(n(x),y))),x)),y)). given clause #1941: (wt=29) 670 [hyper,1,40,618] P(i(i(i(x,i(y,x)),n(i(z,n(u)))),u)). given clause #1942: (wt=17) 20911 [hyper,1,367,20887] P(n(n(i(n(i(n(n(i(n(x),y))),x)),y)))). given clause #1943: (wt=19) 20895 [hyper,1,20438,379] P(i(n(i(i(i(i(n(x),y),x),z),z)),y)). given clause #1944: (wt=19) 20900 [hyper,1,860,20887] P(i(n(i(n(i(n(n(i(n(x),y))),x)),z)),y)). given clause #1945: (wt=47) 671 [hyper,1,36,618] P(i(x,i(y,i(n(i(z,n(u))),u)))). given clause #1946: (wt=19) 20910 [hyper,1,371,20887] P(i(n(i(n(n(i(n(x),y))),x)),n(n(y)))). given clause #1947: (wt=19) 20912 [hyper,1,362,20887] P(i(n(i(n(n(i(n(x),n(n(y))))),x)),y)). given clause #1948: (wt=19) 20930 [hyper,1,116,20887] P(i(n(i(n(i(n(n(i(n(x),y))),x)),y)),z)). given clause #1949: (wt=26) 674 [hyper,1,3,618] P(i(i(x,y),i(n(i(z,n(x))),y))). given clause #1950: (wt=21) 20898 [hyper,1,7839,20887] P(n(n(i(n(i(n(n(i(n(x),n(n(y))))),x)),y)))). given clause #1951: (wt=21) 20934 [hyper,1,44,20887] P(i(n(i(n(n(i(n(x),y))),x)),i(z,y))). given clause #1952: (wt=21) 20936 [hyper,1,34,20887] P(i(i(i(n(i(n(n(i(n(x),y))),x)),y),z),z)). given clause #1953: (wt=64) 676 [hyper,1,367,43] P(n(n(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))))). given clause #1954: (wt=21) 20943 [hyper,1,367,20895] P(n(n(i(n(i(i(i(i(n(x),y),x),z),z)),y)))). given clause #1955: (wt=21) 20951 [hyper,1,367,20910] P(n(n(i(n(i(n(n(i(n(x),y))),x)),n(n(y)))))). given clause #1956: (wt=23) 20784 [hyper,1,20127,666] P(i(n(i(i(n(n(i(x,n(y)))),z),n(n(z)))),y)). given clause #1957: (wt=36) 677 [hyper,1,366,43] P(i(i(x,y),i(n(n(i(y,z))),i(x,z)))). given clause #1958: (wt=21) 21049 [hyper,1,14646,677] P(i(n(i(n(n(i(n(x),y))),i(z,y))),x)). given clause #1959: (wt=22) 21047 [hyper,1,15366,677] P(i(n(i(n(n(i(x,y))),i(z,y))),n(x))). given clause #1960: (wt=23) 20785 [hyper,1,18918,666] P(i(n(i(i(n(n(i(x,n(y)))),n(n(z))),z)),y)). given clause #1961: (wt=58) 678 [hyper,1,76,43] P(i(n(n(i(x,y))),i(i(z,x),i(u,i(z,y))))). given clause #1962: (wt=23) 20901 [hyper,1,849,20887] P(i(n(i(n(n(i(n(x),n(i(y,z))))),x)),y)). given clause #1963: (wt=23) 20921 [hyper,1,198,20887] P(i(n(i(n(n(i(n(x),y))),x)),i(n(y),z))). given clause #1964: (wt=23) 20933 [hyper,1,59,20887] P(i(n(i(n(n(i(n(x),n(y)))),x)),i(y,z))). given clause #1965: (wt=89) 679 [hyper,1,49,43] P(i(x,i(i(y,z),i(i(x,i(z,u)),i(y,u))))). given clause #1966: (wt=23) 20942 [hyper,1,371,20895] P(i(n(i(i(i(i(n(x),y),x),z),z)),n(n(y)))). given clause #1967: (wt=23) 20944 [hyper,1,362,20895] P(i(n(i(i(i(i(n(x),n(n(y))),x),z),z)),y)). given clause #1968: (wt=23) 20972 [hyper,1,14616,674] P(i(n(i(n(i(x,n(i(n(y),z)))),z)),y)). given clause #1969: (wt=62) 680 [hyper,1,26,43] P(i(i(n(i(x,y)),n(z)),i(i(u,x),i(z,i(u,y))))). given clause #1970: (wt=23) 21042 [hyper,1,367,20934] P(n(n(i(n(i(n(n(i(n(x),y))),x)),i(z,y))))). given clause #1971: (wt=23) 21102 [hyper,1,367,21049] P(n(n(i(n(i(n(n(i(n(x),y))),i(z,y))),x)))). given clause #1972: (wt=23) 21110 [hyper,1,849,21047] P(i(n(i(n(n(i(i(x,y),z))),i(u,z))),x)). given clause #1973: (wt=98) 681 [hyper,1,24,43] P(i(i(i(i(x,y),z),z),i(i(u,x),i(i(z,i(x,y)),i(u,y))))). given clause #1974: (wt=24) 943 [hyper,1,366,48] P(i(i(i(i(x,y),i(n(n(x)),y)),z),z)). given clause #1975: (wt=24) 1000 [hyper,1,37,372] P(i(n(x),n(n(i(n(i(x,y)),z))))). given clause #1976: (wt=24) 1025 [hyper,1,372,229] P(n(n(i(n(i(n(i(i(x,y),y)),i(x,z))),u)))). given clause #1977: (wt=56) 682 [hyper,1,23,43] P(i(i(x,y),i(i(z,x),i(u,i(z,y))))). given clause #1978: (wt=24) 1026 [hyper,1,372,148] P(n(n(i(n(i(i(i(n(x),y),z),i(x,z))),u)))). given clause #1979: (wt=24) 1037 [hyper,1,372,51] P(n(n(i(n(i(i(i(n(x),i(x,y)),z),z)),u)))). given clause #1980: (wt=24) 1424 [hyper,1,372,362] P(n(n(i(n(i(i(x,n(n(y))),i(x,y))),z)))). given clause #1981: (wt=68) 683 [hyper,1,21,43] P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))). given clause #1982: (wt=24) 1439 [hyper,1,34,362] P(i(i(i(i(x,n(n(y))),i(x,y)),z),z)). given clause #1983: (wt=24) 1510 [hyper,1,372,369] P(n(n(i(n(i(i(x,y),i(n(n(x)),y))),z)))). given clause #1984: (wt=24) 1699 [hyper,1,65,62] P(i(n(i(n(x),y)),i(n(i(x,z)),u))). given clause #1985: (wt=50) 684 [hyper,1,43,618] P(i(i(x,y),i(n(i(z,n(i(y,u)))),i(x,u)))). given clause #1986: (wt=24) 1708 [hyper,1,65,35] P(i(n(i(i(x,y),i(z,y))),i(x,u))). given clause #1987: (wt=24) 1793 [hyper,1,34,396] P(i(i(n(n(i(n(i(n(x),y)),i(x,z)))),u),u)). given clause #1988: (wt=24) 1796 [hyper,1,34,414] P(i(i(n(n(i(n(i(n(x),i(x,y))),z))),u),u)). given clause #1989: (wt=54) 685 [hyper,1,43,440] P(i(i(x,y),i(i(n(n(i(z,z))),i(y,u)),i(x,u)))). given clause #1990: (wt=24) 1800 [hyper,1,142,820] P(i(n(i(n(i(n(x),n(n(i(x,y))))),z)),u)). given clause #1991: (wt=24) 1805 [hyper,1,34,820] P(i(i(n(n(i(n(x),n(n(i(x,y)))))),z),z)). given clause #1992: (wt=24) 1809 [hyper,1,142,963] P(i(n(i(n(i(i(n(n(x)),y),i(x,y))),z)),u)). given clause #1993: (wt=58) 686 [hyper,1,43,382] P(i(i(x,y),i(i(i(z,n(n(z))),i(y,u)),i(x,u)))). given clause #1994: (wt=24) 1814 [hyper,1,34,963] P(i(i(n(n(i(i(n(n(x)),y),i(x,y)))),z),z)). given clause #1995: (wt=24) 1817 [hyper,1,372,1548] P(n(n(i(n(i(n(n(i(n(n(x)),y))),i(x,y))),z)))). given clause #1996: (wt=24) 1833 [hyper,1,34,1548] P(i(i(i(n(n(i(n(n(x)),y))),i(x,y)),z),z)). given clause #1997: (wt=54) 687 [hyper,1,43,366] P(i(i(x,y),i(i(i(n(n(z)),z),i(y,u)),i(x,u)))). given clause #1998: (wt=24) 1885 [hyper,1,3,340] P(i(i(i(i(x,y),y),z),i(n(n(x)),z))). given clause #1999: (wt=24) 2644 [hyper,1,369,96] P(i(n(n(i(i(n(i(n(x),i(x,y))),z),u))),u)). given clause #2000: (wt=24) 2645 [hyper,1,367,96] P(n(n(i(i(i(n(i(n(x),i(x,y))),z),u),u)))). given clause #2001: (wt=30) 688 [hyper,1,43,327] P(i(i(x,n(n(y))),i(z,i(x,y)))). given clause #2002: (wt=24) 2824 [hyper,1,5,1543] P(i(n(x),n(i(i(n(n(x)),x),x)))). given clause #2003: (wt=24) 2926 [hyper,1,26,1771] P(i(i(n(n(x)),n(i(y,z))),i(x,y))). given clause #2004: (wt=24) 3145 [hyper,1,362,547] P(i(i(n(n(i(n(x),i(x,y)))),n(n(z))),z)). given clause #2005: (wt=62) 689 [hyper,1,43,241] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))). given clause #2006: (wt=24) 3147 [hyper,1,116,547] P(i(n(i(i(n(n(i(n(x),i(x,y)))),z),z)),u)). given clause #2007: (wt=24) 3169 [hyper,1,116,1011] P(i(n(i(i(n(n(i(n(x),y))),z),i(x,z))),u)). given clause #2008: (wt=24) 3202 [hyper,1,116,1511] P(i(n(i(n(n(i(x,y))),i(n(n(x)),y))),z)). given clause #2009: (wt=40) 690 [hyper,1,43,229] P(i(i(x,y),i(n(i(i(y,z),z)),i(x,u)))). given clause #2010: (wt=24) 3237 [hyper,1,362,1518] P(i(n(n(i(i(n(x),i(x,y)),n(n(z))))),z)). given clause #2011: (wt=24) 3239 [hyper,1,116,1518] P(i(n(i(n(n(i(i(n(x),i(x,y)),z))),z)),u)). given clause #2012: (wt=24) 3255 [hyper,1,116,1551] P(i(n(i(n(n(i(x,n(n(y))))),i(x,y))),z)). given clause #2013: (wt=36) 691 [hyper,1,43,180] P(i(i(x,y),i(n(i(n(y),z)),i(x,u)))). given clause #2014: (wt=24) 3277 [hyper,1,116,1553] P(i(n(i(n(n(i(i(n(x),y),z))),i(x,z))),u)). given clause #2015: (wt=24) 3332 [hyper,1,49,117] P(i(n(x),i(i(i(y,x),x),y))). given clause #2016: (wt=24) 3669 [hyper,1,379,390] P(n(n(i(i(i(i(n(n(x)),y),i(x,y)),z),z)))). given clause #2017: (wt=40) 692 [hyper,1,43,148] P(i(i(x,y),i(i(i(n(y),z),u),i(x,u)))). given clause #2018: (wt=24) 3672 [hyper,1,379,380] P(n(n(i(i(i(n(x),n(n(i(x,y)))),z),z)))). given clause #2019: (wt=24) 3689 [hyper,1,379,180] P(n(n(i(i(i(n(i(n(x),y)),i(x,z)),u),u)))). given clause #2020: (wt=24) 3969 [hyper,1,116,3755] P(i(n(i(n(i(i(n(n(x)),y),y)),i(x,z))),u)). given clause #2021: (wt=34) 693 [hyper,1,43,146] P(i(i(x,n(i(y,z))),i(z,i(x,u)))). given clause #2022: (wt=24) 4163 [hyper,1,86,383] P(i(i(i(i(x,y),y),z),n(n(i(x,z))))). given clause #2023: (wt=24) 4215 [hyper,1,26,386] P(i(i(n(n(x)),n(n(y))),n(n(i(x,y))))). given clause #2024: (wt=24) 5125 [hyper,1,140,3487] P(i(i(i(i(i(n(x),y),z),z),u),i(x,u))). given clause #2025: (wt=36) 694 [hyper,1,43,142] P(i(i(x,n(i(y,z))),i(n(y),i(x,u)))). given clause #2026: (wt=24) 5388 [hyper,1,86,1440] P(i(i(i(i(x,y),y),n(n(z))),i(x,z))). given clause #2027: (wt=24) 5767 [hyper,1,1524,390] P(i(n(n(i(i(i(n(n(x)),y),i(x,y)),z))),z)). given clause #2028: (wt=24) 5771 [hyper,1,1524,380] P(i(n(n(i(i(n(x),n(n(i(x,y)))),z))),z)). given clause #2029: (wt=44) 695 [hyper,1,43,138] P(i(i(x,y),i(i(n(n(y)),n(n(z))),i(x,z)))). given clause #2030: (wt=24) 5786 [hyper,1,1524,180] P(i(n(n(i(i(n(i(n(x),y)),i(x,z)),u))),u)). given clause #2031: (wt=24) 5852 [hyper,1,116,5560] P(i(n(i(n(i(n(n(i(x,y))),y)),i(x,z))),u)). given clause #2032: (wt=24) 6032 [hyper,1,116,6004] P(i(n(i(n(i(n(x),y)),n(n(i(x,y))))),z)). given clause #2033: (wt=36) 696 [hyper,1,43,114] P(i(i(x,n(y)),i(n(i(z,y)),i(x,z)))). given clause #2034: (wt=24) 6570 [hyper,1,26,183] P(i(i(n(n(i(n(x),y))),n(n(z))),i(x,z))). given clause #2035: (wt=24) 6788 [hyper,1,186,49] P(i(i(i(n(i(i(x,y),y)),z),u),i(x,u))). given clause #2036: (wt=24) 6961 [hyper,1,116,6927] P(i(n(i(n(i(n(x),y)),n(n(i(x,z))))),u)). given clause #2037: (wt=40) 697 [hyper,1,43,89] P(i(i(x,n(y)),i(i(i(z,y),y),i(x,z)))). given clause #2038: (wt=21) 21546 [hyper,1,14646,697] P(i(n(i(i(i(x,y),y),i(z,x))),y)). given clause #2039: (wt=23) 21560 [hyper,1,367,21546] P(n(n(i(n(i(i(i(x,y),y),i(z,x))),y)))). given clause #2040: (wt=24) 7215 [hyper,1,198,390] P(i(i(n(n(x)),y),i(n(i(x,y)),z))). given clause #2041: (wt=42) 698 [hyper,1,43,76] P(i(i(x,n(n(y))),i(i(i(z,y),u),i(x,u)))). given clause #2042: (wt=24) 7689 [hyper,1,369,371] P(i(n(n(i(x,y))),i(x,n(n(y))))). given clause #2043: (wt=21) 21578 [hyper,1,14575,7689] P(i(n(i(x,n(n(y)))),n(i(x,y)))). given clause #2044: (wt=22) 21612 [hyper,1,280,21578] P(i(n(i(i(x,y),n(n(y)))),i(x,z))). given clause #2045: (wt=40) 699 [hyper,1,43,74] P(i(i(x,i(y,z)),i(n(i(z,y)),i(x,z)))). given clause #2046: (wt=23) 21577 [hyper,1,14602,7689] P(n(n(i(n(i(x,n(n(y)))),n(i(x,y)))))). given clause #2047: (wt=24) 7690 [hyper,1,367,371] P(n(n(i(i(x,y),i(x,n(n(y))))))). given clause #2048: (wt=24) 7729 [hyper,1,371,5560] P(i(n(i(n(n(i(x,y))),y)),n(n(i(x,z))))). given clause #2049: (wt=34) 700 [hyper,1,43,71] P(i(i(x,y),i(n(i(z,y)),i(x,u)))). given clause #2050: (wt=24) 7737 [hyper,1,371,3755] P(i(n(i(i(n(n(x)),y),y)),n(n(i(x,z))))). given clause #2051: (wt=24) 7750 [hyper,1,371,2940] P(i(n(i(n(i(n(x),y)),z)),n(n(i(x,u))))). given clause #2052: (wt=24) 7772 [hyper,1,371,1553] P(i(n(n(i(i(n(x),y),z))),n(n(i(x,z))))). given clause #2053: (wt=36) 701 [hyper,1,43,62] P(i(i(x,n(y)),i(n(i(y,z)),i(x,u)))). given clause #2054: (wt=24) 7773 [hyper,1,371,1551] P(i(n(n(i(x,n(n(y))))),n(n(i(x,y))))). given clause #2055: (wt=24) 7786 [hyper,1,371,1518] P(i(n(n(i(i(n(x),i(x,y)),z))),n(n(z)))). given clause #2056: (wt=24) 7788 [hyper,1,371,1511] P(i(n(n(i(x,y))),n(n(i(n(n(x)),y))))). given clause #2057: (wt=44) 702 [hyper,1,43,49] P(i(i(x,y),i(i(i(i(y,z),z),u),i(x,u)))). given clause #2058: (wt=24) 7800 [hyper,1,371,1011] P(i(i(n(n(i(n(x),y))),z),n(n(i(x,z))))). given clause #2059: (wt=24) 7822 [hyper,1,371,547] P(i(i(n(n(i(n(x),i(x,y)))),z),n(n(z)))). given clause #2060: (wt=24) 7947 [hyper,1,3,7678] P(i(i(n(n(x)),y),i(n(i(x,z)),y))). given clause #2061: (wt=52) 703 [hyper,1,43,38] P(i(i(x,n(y)),i(z,i(x,i(y,u))))). given clause #2062: (wt=24) 8061 [hyper,1,7684,60] P(n(n(i(i(i(n(x),i(x,y)),n(n(z))),z)))). given clause #2063: (wt=24) 8146 [hyper,1,5,7673] P(i(n(x),n(i(i(n(n(y)),y),x)))). given clause #2064: (wt=24) 8181 [hyper,1,5,7674] P(i(n(x),n(i(n(n(i(y,y))),x)))). given clause #2065: (wt=40) 704 [hyper,1,43,37] P(i(i(x,n(y)),i(i(i(y,z),u),i(x,u)))). given clause #2066: (wt=24) 8199 [hyper,1,57,7677] P(n(n(i(i(x,y),i(n(i(x,z)),y))))). given clause #2067: (wt=24) 8208 [hyper,1,7677,241] P(n(n(i(i(x,n(i(y,z))),i(x,y))))). given clause #2068: (wt=24) 8285 [hyper,1,7682,186] P(n(n(i(i(i(n(x),y),z),n(n(i(x,z))))))). given clause #2069: (wt=56) 705 [hyper,1,43,35] P(i(i(x,i(y,z)),i(y,i(x,i(u,z))))). given clause #2070: (wt=24) 8292 [hyper,1,7682,60] P(n(n(i(i(i(n(x),i(x,y)),z),n(n(z)))))). given clause #2071: (wt=24) 8358 [hyper,1,116,7835] P(i(n(i(i(n(n(x)),y),n(n(i(x,y))))),z)). given clause #2072: (wt=24) 8994 [hyper,1,369,849] P(i(n(n(i(x,n(i(y,z))))),i(x,y))). given clause #2073: (wt=62) 706 [hyper,1,43,27] P(i(i(x,i(n(y),n(z))),i(u,i(x,i(z,y))))). given clause #2074: (wt=24) 9105 [hyper,1,59,8976] P(i(n(i(i(n(n(i(n(x),y))),z),z)),i(x,u))). given clause #2075: (wt=24) 9705 [hyper,1,369,860] P(i(n(n(i(x,y))),i(n(i(x,z)),y))). given clause #2076: (wt=21) 21880 [hyper,1,14575,9705] P(i(n(i(n(i(x,y)),z)),n(i(x,z)))). given clause #2077: (wt=50) 707 [hyper,1,43,26] P(i(i(x,i(n(y),n(z))),i(i(i(z,y),u),i(x,u)))). given clause #2078: (wt=22) 21889 [hyper,1,280,21880] P(i(n(i(n(i(i(x,y),z)),y)),i(x,u))). given clause #2079: (wt=23) 21879 [hyper,1,14602,9705] P(n(n(i(n(i(n(i(x,y)),z)),n(i(x,z)))))). given clause #2080: (wt=24) 9707 [hyper,1,230,860] P(i(n(i(i(i(i(x,y),y),z),u)),i(x,z))). given clause #2081: (wt=86) 708 [hyper,1,43,25] P(i(i(x,i(i(y,z),z)),i(u,i(x,i(i(z,y),y))))). given clause #2082: (wt=24) 9740 [hyper,1,860,7835] P(i(n(i(i(n(n(x)),y),z)),n(n(i(x,y))))). given clause #2083: (wt=24) 9765 [hyper,1,860,5560] P(i(n(i(n(i(n(n(i(x,y))),y)),z)),i(x,u))). given clause #2084: (wt=24) 9772 [hyper,1,860,3755] P(i(n(i(n(i(i(n(n(x)),y),y)),z)),i(x,u))). given clause #2085: (wt=56) 709 [hyper,1,43,24] P(i(i(x,i(i(y,z),z)),i(i(i(i(z,y),y),u),i(x,u)))). given clause #2086: (wt=24) 9798 [hyper,1,860,1553] P(i(n(i(n(n(i(i(n(x),y),z))),u)),i(x,z))). given clause #2087: (wt=24) 9799 [hyper,1,860,1551] P(i(n(i(n(n(i(x,n(n(y))))),z)),i(x,y))). given clause #2088: (wt=24) 9817 [hyper,1,860,1518] P(i(n(i(n(n(i(i(n(x),i(x,y)),z))),u)),z)). given clause #2089: (wt=29) 710 [hyper,1,388,665] P(n(n(i(x,n(n(i(n(i(y,n(z))),z))))))). given clause #2090: (wt=24) 9819 [hyper,1,860,1511] P(i(n(i(n(n(i(x,y))),z)),i(n(n(x)),y))). given clause #2091: (wt=24) 9839 [hyper,1,860,1011] P(i(n(i(i(n(n(i(n(x),y))),z),u)),i(x,z))). given clause #2092: (wt=24) 9857 [hyper,1,860,547] P(i(n(i(i(n(n(i(n(x),i(x,y)))),z),u)),z)). given clause #2093: (wt=31) 711 [hyper,1,146,665] P(i(n(i(x,n(n(i(n(i(y,n(z))),z))))),u)). given clause #2094: (wt=24) 9894 [hyper,1,860,138] P(i(n(i(i(n(n(x)),n(n(y))),z)),i(x,y))). given clause #2095: (wt=24) 10064 [hyper,1,65,238] P(i(n(i(i(i(i(x,y),y),z),z)),i(x,u))). given clause #2096: (wt=24) 10880 [hyper,1,860,9872] P(i(n(i(n(i(i(n(n(x)),y),z)),u)),i(x,y))). given clause #2097: (wt=55) 713 [hyper,1,36,665] P(i(x,i(y,n(n(i(n(i(z,n(u))),u)))))). given clause #2098: (wt=24) 10891 [hyper,1,116,9872] P(i(n(i(n(i(i(n(n(x)),y),z)),i(x,y))),u)). given clause #2099: (wt=24) 11823 [hyper,1,7677,257] P(n(n(i(n(i(i(i(n(x),y),z),u)),i(x,z))))). given clause #2100: (wt=24) 11842 [hyper,1,257,5560] P(i(n(i(n(n(i(i(n(x),y),z))),z)),i(x,u))). given clause #2101: (wt=25) 714 [hyper,1,35,665] P(i(i(n(n(i(n(i(x,n(y))),y))),z),i(u,z))). given clause #2102: (wt=24) 11846 [hyper,1,257,1553] P(i(n(n(i(i(n(i(n(x),y)),z),u))),i(x,u))). given clause #2103: (wt=24) 11847 [hyper,1,257,1551] P(i(n(n(i(i(n(x),y),n(n(z))))),i(x,z))). given clause #2104: (wt=24) 11860 [hyper,1,257,1011] P(i(i(n(n(i(n(i(n(x),y)),z))),u),i(x,u))). given clause #2105: (wt=27) 716 [hyper,1,2,665] P(i(x,n(n(i(n(i(y,n(z))),z))))). given clause #2106: (wt=24) 11986 [hyper,1,367,1555] P(n(n(i(n(n(i(n(n(x)),n(n(y))))),i(x,y))))). given clause #2107: (wt=24) 12071 [hyper,1,367,1569] P(n(n(i(n(n(i(i(i(x,y),y),z))),i(x,z))))). given clause #2108: (wt=24) 12094 [hyper,1,367,1779] P(n(n(i(i(i(n(x),y),n(n(z))),i(x,z))))). given clause #2109: (wt=33) 717 [hyper,1,388,441] P(n(n(i(x,i(y,n(n(i(z,z)))))))). given clause #2110: (wt=24) 12135 [hyper,1,367,1873] P(n(n(i(n(i(i(x,y),y)),i(n(n(x)),z))))). given clause #2111: (wt=24) 12161 [hyper,1,367,3143] P(n(n(i(n(n(i(n(n(i(n(x),i(x,y)))),z))),z)))). given clause #2112: (wt=24) 12327 [hyper,1,367,3166] P(n(n(i(n(n(i(n(n(i(n(x),y))),z))),i(x,z))))). given clause #2113: (wt=35) 718 [hyper,1,146,441] P(i(n(i(x,i(y,n(n(i(z,z)))))),u)). given clause #2114: (wt=24) 12350 [hyper,1,367,3172] P(n(n(i(i(i(n(i(n(x),y)),z),u),i(x,u))))). given clause #2115: (wt=24) 12669 [hyper,1,369,3528] P(i(n(n(i(n(n(i(i(x,y),y))),z))),i(x,z))). given clause #2116: (wt=24) 12670 [hyper,1,367,3528] P(n(n(i(i(n(n(i(i(x,y),y))),z),i(x,z))))). given clause #2117: (wt=39) 719 [hyper,1,42,441] P(i(x,i(i(n(n(i(y,y))),z),i(u,z)))). given clause #2118: (wt=24) 12692 [hyper,1,367,3779] P(n(n(i(n(i(i(i(n(x),y),z),z)),i(x,u))))). given clause #2119: (wt=24) 12768 [hyper,1,369,4946] P(i(n(n(i(i(i(n(n(x)),y),y),z))),i(x,z))). given clause #2120: (wt=24) 12769 [hyper,1,367,4946] P(n(n(i(i(i(i(n(n(x)),y),y),z),i(x,z))))). given clause #2121: (wt=63) 720 [hyper,1,36,441] P(i(x,i(y,i(z,n(n(i(u,u))))))). given clause #2122: (wt=24) 12841 [hyper,1,369,5579] P(i(n(n(i(i(n(n(i(x,y))),y),z))),i(x,z))). given clause #2123: (wt=24) 12842 [hyper,1,367,5579] P(n(n(i(i(i(n(n(i(x,y))),y),z),i(x,z))))). given clause #2124: (wt=24) 13006 [hyper,1,367,6952] P(n(n(i(n(i(n(i(i(x,y),y)),z)),i(x,u))))). given clause #2125: (wt=27) 721 [hyper,1,35,441] P(i(i(i(x,n(n(i(y,y)))),z),i(u,z))). given clause #2126: (wt=24) 13020 [hyper,1,367,7775] P(n(n(i(n(n(i(n(n(x)),y))),n(n(i(x,y))))))). given clause #2127: (wt=24) 13124 [hyper,1,367,7837] P(n(n(i(i(x,y),n(n(i(n(n(x)),y))))))). given clause #2128: (wt=24) 13373 [hyper,1,367,7839] P(n(n(i(i(x,n(n(y))),n(n(i(x,y))))))). given clause #2129: (wt=33) 722 [hyper,1,388,462] P(n(n(i(x,i(n(i(n(i(n(n(y)),y)),z)),u))))). given clause #2130: (wt=24) 13520 [hyper,1,7677,269] P(n(n(i(n(i(i(i(n(x),i(x,y)),z),u)),z)))). given clause #2131: (wt=24) 13561 [hyper,1,367,7842] P(n(n(i(n(i(i(x,y),y)),n(n(i(x,z))))))). given clause #2132: (wt=24) 13655 [hyper,1,367,9801] P(n(n(i(n(i(n(n(i(n(n(x)),y))),z)),i(x,y))))). given clause #2133: (wt=34) 724 [hyper,1,241,462] P(i(i(x,n(i(n(i(n(n(y)),y)),z))),i(x,u))). given clause #2134: (wt=24) 13681 [hyper,1,367,9877] P(n(n(i(n(i(i(x,y),z)),i(n(n(x)),y))))). given clause #2135: (wt=24) 13758 [hyper,1,367,9879] P(n(n(i(n(i(i(x,n(n(y))),z)),i(x,y))))). given clause #2136: (wt=24) 14472 [hyper,1,277,9877] P(i(n(i(i(x,n(y)),z)),i(y,n(x)))). given clause #2137: (wt=34) 726 [hyper,1,3,462] P(i(i(x,y),i(n(i(n(i(n(n(z)),z)),u)),y))). given clause #2138: (wt=24) 14634 [hyper,1,65,14575] P(i(n(i(n(x),y)),i(i(n(y),x),z))). given clause #2139: (wt=24) 14669 [hyper,1,14575,1556] P(i(n(i(n(x),y)),n(i(i(y,x),x)))). given clause #2140: (wt=24) 14685 [hyper,1,14575,1516] P(i(n(i(n(x),y)),n(i(i(x,z),y)))). given clause #2141: (wt=31) 727 [hyper,1,2,462] P(i(x,i(n(i(n(i(n(n(y)),y)),z)),u))). given clause #2142: (wt=24) 14716 [hyper,1,227,14687] P(i(n(i(i(i(n(i(i(x,y),y)),n(x)),z),z)),u)). given clause #2143: (wt=24) 14719 [hyper,1,189,14687] P(i(i(i(n(i(n(i(i(x,y),y)),n(x))),z),u),u)). given clause #2144: (wt=24) 14789 [hyper,1,140,14680] P(i(i(i(n(n(i(n(n(x)),y))),y),z),i(x,z))). given clause #2145: (wt=55) 728 [hyper,1,388,44] P(n(n(i(x,i(i(y,z),i(y,i(u,z))))))). given clause #2146: (wt=24) 15015 [hyper,1,1524,14704] P(i(n(n(i(n(n(i(n(i(i(x,y),y)),n(x)))),z))),z)). given clause #2147: (wt=24) 15017 [hyper,1,379,14704] P(n(n(i(i(n(n(i(n(i(i(x,y),y)),n(x)))),z),z)))). given clause #2148: (wt=24) 15205 [hyper,1,7839,14688] P(n(n(i(n(i(i(x,n(n(y))),i(x,z))),y)))). given clause #2149: (wt=28) 729 [hyper,1,367,44] P(n(n(i(i(x,y),i(x,i(z,y)))))). given clause #2150: (wt=24) 15213 [hyper,1,372,14688] P(n(n(i(n(i(n(i(i(x,y),i(x,z))),y)),u)))). given clause #2151: (wt=24) 15229 [hyper,1,44,14688] P(i(n(i(i(x,y),i(x,z))),i(u,y))). given clause #2152: (wt=24) 15230 [hyper,1,34,14688] P(i(i(i(n(i(i(x,y),i(x,z))),y),u),u)). given clause #2153: (wt=56) 730 [hyper,1,241,44] P(i(i(x,i(y,z)),i(x,i(y,i(u,z))))). given clause #2154: (wt=24) 15239 [hyper,1,372,14699] P(n(n(i(n(i(n(i(n(i(i(x,y),y)),z)),n(x))),u)))). given clause #2155: (wt=24) 15248 [hyper,1,34,14699] P(i(i(i(n(i(n(i(i(x,y),y)),z)),n(x)),u),u)). given clause #2156: (wt=24) 15256 [hyper,1,372,14725] P(n(n(i(n(i(n(i(n(i(i(x,y),y)),n(x))),z)),u)))). given clause #2157: (wt=30) 731 [hyper,1,116,44] P(i(n(i(i(x,y),i(x,i(z,y)))),u)). given clause #2158: (wt=24) 15304 [hyper,1,234,14603] P(i(n(x),i(n(n(i(n(y),x))),y))). given clause #2159: (wt=24) 15363 [hyper,1,234,14633] P(i(n(x),i(i(i(y,z),x),y))). given clause #2160: (wt=15) 22121 [hyper,1,14575,15363] P(i(n(i(i(i(x,y),z),x)),z)). given clause #2161: (wt=56) 732 [hyper,1,43,44] P(i(i(x,y),i(i(y,z),i(x,i(u,z))))). given clause #2162: (wt=17) 22120 [hyper,1,14602,15363] P(n(n(i(n(i(i(i(x,y),z),x)),z)))). given clause #2163: (wt=19) 22176 [hyper,1,860,22121] P(i(n(i(n(i(i(i(x,y),z),x)),u)),z)). given clause #2164: (wt=19) 22188 [hyper,1,371,22121] P(i(n(i(i(i(x,y),z),x)),n(n(z)))). given clause #2165: (wt=32) 733 [hyper,1,34,44] P(i(i(i(i(x,y),i(x,i(z,y))),u),u)). given clause #2166: (wt=19) 22189 [hyper,1,362,22121] P(i(n(i(i(i(x,y),n(n(z))),x)),z)). given clause #2167: (wt=19) 22198 [hyper,1,116,22121] P(i(n(i(n(i(i(i(x,y),z),x)),z)),u)). given clause #2168: (wt=21) 22175 [hyper,1,7839,22121] P(n(n(i(n(i(i(i(x,y),n(n(z))),x)),z)))). given clause #2169: (wt=29) 734 [hyper,1,31,44] P(i(i(i(x,y),z),i(y,i(u,z)))). given clause #2170: (wt=21) 22187 [hyper,1,372,22121] P(n(n(i(n(i(n(i(i(i(x,y),z),x)),z)),u)))). given clause #2171: (wt=21) 22201 [hyper,1,44,22121] P(i(n(i(i(i(x,y),z),x)),i(u,z))). given clause #2172: (wt=21) 22202 [hyper,1,34,22121] P(i(i(i(n(i(i(i(x,y),z),x)),z),u),u)). given clause #2173: (wt=29) 735 [hyper,1,26,44] P(i(i(n(x),n(y)),i(y,i(z,x)))). given clause #2174: (wt=21) 22239 [hyper,1,367,22176] P(n(n(i(n(i(n(i(i(i(x,y),z),x)),u)),z)))). given clause #2175: (wt=21) 22242 [hyper,1,367,22188] P(n(n(i(n(i(i(i(x,y),z),x)),n(n(z)))))). given clause #2176: (wt=23) 22164 [hyper,1,65,15363] P(i(n(i(i(i(x,y),z),x)),i(n(z),u))). given clause #2177: (wt=35) 736 [hyper,1,24,44] P(i(i(i(x,y),y),i(i(y,x),i(z,x)))). given clause #2178: (wt=23) 22177 [hyper,1,849,22121] P(i(n(i(i(i(x,y),n(i(z,u))),x)),z)). given clause #2179: (wt=23) 22200 [hyper,1,59,22121] P(i(n(i(i(i(x,y),n(z)),x)),i(z,u))). given clause #2180: (wt=23) 22238 [hyper,1,371,22176] P(i(n(i(n(i(i(i(x,y),z),x)),u)),n(n(z)))). given clause #2181: (wt=56) 737 [hyper,1,21,44] P(i(i(x,y),i(i(y,z),i(u,i(x,z))))). given clause #2182: (wt=23) 22240 [hyper,1,362,22176] P(i(n(i(n(i(i(i(x,y),n(n(z))),x)),u)),z)). given clause #2183: (wt=23) 22243 [hyper,1,116,22188] P(i(n(i(n(i(i(i(x,y),z),x)),n(n(z)))),u)). given clause #2184: (wt=23) 22251 [hyper,1,116,22189] P(i(n(i(n(i(i(i(x,y),n(n(z))),x)),z)),u)). given clause #2185: (wt=29) 738 [hyper,1,3,44] P(i(i(i(x,i(y,z)),u),i(i(x,z),u))). given clause #2186: (wt=23) 22261 [hyper,1,367,22201] P(n(n(i(n(i(i(i(x,y),z),x)),i(u,z))))). given clause #2187: (wt=24) 15391 [hyper,1,14633,48] P(i(n(i(i(i(i(x,y),i(z,y)),u),u)),z)). given clause #2188: (wt=24) 15973 [hyper,1,7837,14576] P(n(n(i(n(n(i(x,n(y)))),i(y,n(x)))))). given clause #2189: (wt=31) 740 [hyper,1,44,388] P(i(x,i(y,n(n(i(z,x)))))). given clause #2190: (wt=24) 15982 [hyper,1,371,14576] P(i(i(x,n(y)),n(n(i(y,n(x)))))). given clause #2191: (wt=21) 22429 [hyper,1,20438,15982] P(i(n(i(x,n(i(n(n(x)),y)))),y)). given clause #2192: (wt=23) 22515 [hyper,1,367,22429] P(n(n(i(n(i(x,n(i(n(n(x)),y)))),y)))). given clause #2193: (wt=62) 741 [hyper,1,44,241] P(i(i(x,y),i(z,i(i(u,x),i(u,y))))). given clause #2194: (wt=24) 16022 [hyper,1,116,14576] P(i(n(i(i(x,n(y)),i(y,n(x)))),z)). given clause #2195: (wt=24) 16174 [hyper,1,860,14617] P(i(n(i(n(x),y)),i(i(n(z),x),z))). given clause #2196: (wt=24) 16179 [hyper,1,371,14617] P(i(n(x),n(n(i(i(n(y),x),y))))). given clause #2197: (wt=30) 742 [hyper,1,44,229] P(i(n(i(i(x,y),y)),i(z,i(x,u)))). given clause #2198: (wt=24) 16204 [hyper,1,116,14617] P(i(n(i(n(x),i(i(n(y),x),y))),z)). given clause #2199: (wt=24) 16576 [hyper,1,7837,14735] P(n(n(i(n(n(i(i(n(i(i(x,y),y)),n(x)),z))),z)))). given clause #2200: (wt=24) 16579 [hyper,1,860,14735] P(i(n(i(i(i(n(i(i(x,y),y)),n(x)),z),u)),z)). given clause #2201: (wt=28) 743 [hyper,1,44,180] P(i(n(i(n(x),y)),i(z,i(x,u)))). given clause #2202: (wt=24) 16585 [hyper,1,371,14735] P(i(i(i(n(i(i(x,y),y)),n(x)),z),n(n(z)))). given clause #2203: (wt=24) 16586 [hyper,1,362,14735] P(i(i(i(n(i(i(x,y),y)),n(x)),n(n(z))),z)). given clause #2204: (wt=24) 16634 [hyper,1,860,15284] P(i(n(i(n(i(n(x),y)),z)),n(i(n(y),x)))). given clause #2205: (wt=30) 744 [hyper,1,44,148] P(i(i(i(n(x),y),z),i(u,i(x,z)))). given clause #2206: (wt=24) 16660 [hyper,1,116,15284] P(i(n(i(n(i(n(x),y)),n(i(n(y),x)))),z)). given clause #2207: (wt=24) 16676 [hyper,1,860,15388] P(i(n(i(n(i(i(x,y),i(z,y))),u)),n(x))). given clause #2208: (wt=24) 16688 [hyper,1,116,15388] P(i(n(i(n(i(i(x,y),i(z,y))),n(x))),u)). given clause #2209: (wt=39) 745 [hyper,1,44,146] P(i(x,i(y,i(n(i(z,x)),u)))). given clause #2210: (wt=24) 17181 [hyper,1,14575,15354] P(i(n(i(n(x),y)),n(i(i(y,z),x)))). given clause #2211: (wt=24) 18070 [hyper,1,367,14511] P(n(n(i(n(i(i(x,y),y)),i(z,n(x)))))). given clause #2212: (wt=24) 18246 [hyper,1,367,15208] P(n(n(i(n(i(n(i(i(x,y),i(x,z))),u)),y)))). given clause #2213: (wt=40) 746 [hyper,1,44,142] P(i(n(x),i(y,i(n(i(x,z)),u)))). given clause #2214: (wt=24) 18247 [hyper,1,367,15214] P(n(n(i(n(i(i(x,y),i(x,z))),n(n(y)))))). given clause #2215: (wt=24) 18915 [hyper,1,59,18887] P(i(n(i(i(n(n(x)),n(n(y))),y)),i(x,z))). given clause #2216: (wt=24) 19158 [hyper,1,483,14533] P(i(n(n(i(x,n(i(n(n(y)),y))))),n(x))). given clause #2217: (wt=32) 747 [hyper,1,44,138] P(i(i(n(n(x)),n(n(y))),i(z,i(x,y)))). given clause #2218: (wt=24) 19169 [hyper,1,367,19157] P(n(n(i(i(x,n(i(n(n(y)),y))),n(x))))). given clause #2219: (wt=24) 19307 [hyper,1,65,5541] P(i(n(i(n(n(i(x,y))),y)),i(n(n(x)),z))). given clause #2220: (wt=24) 19323 [hyper,1,44,19291] P(i(n(i(n(n(i(x,y))),y)),i(z,n(x)))). given clause #2221: (wt=31) 748 [hyper,1,44,114] P(i(n(i(x,y)),i(z,i(n(y),x)))). given clause #2222: (wt=24) 20072 [hyper,1,14616,65] P(i(n(i(n(x),i(i(n(y),x),z))),y)). given clause #2223: (wt=24) 20090 [hyper,1,59,20044] P(i(n(i(n(i(i(n(n(x)),y),z)),y)),i(x,u))). given clause #2224: (wt=24) 20124 [hyper,1,59,20054] P(i(n(i(i(n(n(x)),y),n(n(y)))),i(x,z))). given clause #2225: (wt=33) 749 [hyper,1,44,89] P(i(i(i(x,y),y),i(z,i(n(y),x)))). given clause #2226: (wt=24) 21112 [hyper,1,367,21047] P(n(n(i(n(i(n(n(i(x,y))),i(z,y))),n(x))))). given clause #2227: (wt=24) 21628 [hyper,1,367,21612] P(n(n(i(n(i(i(x,y),n(n(y)))),i(x,z))))). given clause #2228: (wt=24) 21902 [hyper,1,367,21889] P(n(n(i(n(i(n(i(i(x,y),z)),y)),i(x,u))))). given clause #2229: (wt=37) 750 [hyper,1,44,76] P(i(i(i(x,y),z),i(u,i(n(n(y)),z)))). given clause #2230: (wt=25) 769 [hyper,1,31,465] P(i(i(i(x,n(n(i(n(n(y)),y)))),z),z)). given clause #2231: (wt=25) 788 [hyper,1,366,45] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). -- HEY mccune, WE HAVE A PROOF!! -- 22685 [binary,22684.1,9.1] $ANS(lemma_36). ----> UNIT CONFLICT at 15.64 sec ----> 22685 [binary,22684.1,9.1] $ANS(lemma_36). Length of proof is 23. Level of proof is 12. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 9 [] -P(i(i(a,b),i(n(b),n(a))))|$ANS(lemma_36). 21 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 23 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 24 [hyper,1,3,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). 33 [hyper,1,23,5] P(i(n(x),i(x,y))). 34 [hyper,1,23,4] P(i(x,i(i(x,y),y))). 37 [hyper,1,3,33] P(i(i(i(x,y),z),i(n(x),z))). 45 [hyper,1,21,3] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 49 [hyper,1,3,34] P(i(i(i(i(x,y),y),z),i(x,z))). 73 [hyper,1,37,5] P(i(n(n(x)),i(y,x))). 76 [hyper,1,3,73] P(i(i(i(x,y),z),i(n(n(y)),z))). 89 [hyper,1,24,37] P(i(i(i(x,y),y),i(n(y),x))). 116 [hyper,1,23,89] P(i(x,i(n(x),y))). 143 [hyper,1,34,116] P(i(i(i(x,i(n(x),y)),z),z)). 241 [hyper,1,49,21] P(i(i(x,y),i(i(z,x),i(z,y)))). 277 [hyper,1,241,5] P(i(i(x,i(n(y),n(z))),i(x,i(z,y)))). 337 [hyper,1,76,143] P(i(n(n(x)),x)). 366 [hyper,1,34,337] P(i(i(i(n(n(x)),x),y),y)). 367 [hyper,1,5,337] P(i(x,n(n(x)))). 371 [hyper,1,241,367] P(i(i(x,y),i(x,n(n(y))))). 788 [hyper,1,366,45] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 14575 [hyper,1,277,371] P(i(i(n(x),y),i(n(y),x))). 14645 [hyper,1,34,14575] P(i(i(i(i(n(x),y),i(n(y),x)),z),z)). 22684 [hyper,1,14645,788] P(i(i(x,y),i(n(y),n(x)))). 22685 [binary,22684.1,9.1] $ANS(lemma_36). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 2231 clauses generated 727008 hyper_res generated 727008 demod & eval rewrites 158772 clauses wt,lit,sk delete 264285 tautologies deleted 34174 clauses forward subsumed 405887 (subsumed by sos) 78513 unit deletions 0 factor simplifications 0 clauses kept 22662 new demodulators 0 empty clauses 4 clauses back demodulated 0 clauses back subsumed 0 usable size 2232 sos size 20435 demodulators size 9 passive size 5 hot size 0 Kbytes malloced 15625 ----------- times (seconds) ----------- user CPU time 15.64 (0 hr, 0 min, 15 sec) system CPU time 0.12 (0 hr, 0 min, 0 sec) wall-clock time 16 (0 hr, 0 min, 16 sec) That finishes the proof of the theorem. Process 8517 finished Mon Aug 2 15:30:56 2004 otter-3.3f/examples/wos/README0100644000076400007640000000013607313704504015512 0ustar mccunemccuneThese problems were contributed by Larry Wos in 1994. Most illustrate the resonance strategy. otter-3.3f/examples/wos/manyval.in0100644000076400007640000000344205752465761016652 0ustar mccunemccune% Input File for Studying Many-Valued Sentential Calculus with OTTER 3.0 set(hyper_res). assign(max_weight, 22). assign(change_limit_after, 1000). assign(new_max_weight, 16). % The following is set to 4 rather than 5, for MV5 is very difficult to prove. assign(max_proofs, 4). clear(print_kept). clear(back_sub). assign(max_mem, 24000). % assign(report, 900). assign(max_distinct_vars, 4). assign(pick_given_ratio, 3). set(order_history). set(input_sos_first). weight_list(pick_given). % Following are four lemmas to prove. weight(P(i(n(n(x)),x)), 2). weight(P(i(x,n(n(x)))), 2). weight(P(i(i(x,y),i(i(z,x),i(z,y)))), 2). weight(P(i(i(x,y),i(n(y),n(x)))), 2). % The following is a difficult theorem to prove. weight(P(i(i(i(x,y),i(y,x)),i(y,x))), 2). % Following are the axioms for many-valued. weight(P(i(x,i(y,x))), 2). weight(P(i(i(x,y),i(i(y,z),i(x,z)))), 2). weight(P(i(i(i(x,y),y),i(i(y,x),x))), 2). weight(P(i(i(n(x),n(y)),i(y,x))), 2). % Following is for recursive tail strategy. weight(i($(1),$(2)),1). end_of_list. list(usable). -P(i(x,y)) | -P(x) | P(y). end_of_list. list(sos). P(i(x,i(y,x))). P(i(i(x,y),i(i(y,z),i(x,z)))). P(i(i(i(x,y),y),i(i(y,x),x))). P(i(i(n(x),n(y)),i(y,x))). end_of_list. list(passive). % The following four clauses are negations of four lemmas to prove. -P(i(n(n(a)),a)) | $ANS(lemma_24). -P(i(a,n(n(a)))) | $ANS(lemma_29). -P(i(i(a,b),i(i(c,a),i(c,b)))) | $ANS(lemma_25). -P(i(i(a,b),i(n(b),n(a)))) | $ANS(lemma_36). % The following clause is the negation of a difficult theorem to prove. -P(i(i(i(a,b),i(b,a)),i(b,a))) | $ANS(thm_MV5). end_of_list. list(demodulators). (n(n(n(x))) = junk). (i(i(x,x),y) = junk). (i(y,i(x,x)) = junk). (i(n(i(x,x)),y) = junk). (i(y,n(i(x,x))) = junk). (i(junk,x) = junk). (i(x,junk) = junk). (n(junk) = junk). (P(junk) = $T). end_of_list. otter-3.3f/examples/wos/twoval.out0100664000076400007640000072220410103522210016667 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:56 2004 The command was "../../bin/otter". The process ID is 8532. set(hyper_res). assign(max_weight,20). assign(max_proofs,-1). clear(print_kept). clear(back_sub). assign(max_mem,24000). assign(max_given,618). set(order_history). set(input_sos_first). weight_list(pick_and_purge). weight(P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))),2). weight(P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))),2). weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))),2). weight(P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))),2). weight(P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))),2). weight(P(i(i(i(n(x),y),z),i(x,z))),2). weight(P(i(x,i(i(i(n(x),x),x),i(i(y,x),x)))),2). weight(P(i(i(x,i(i(n(y),y),y)),i(i(n(y),y),y))),2). weight(P(i(x,i(i(n(y),y),y))),2). weight(P(i(i(n(x),y),i(z,i(i(y,x),x)))),2). weight(P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))),2). weight(P(i(i(n(x),y),i(i(y,x),x))),2). weight(P(i(x,x)),2). weight(P(i(x,i(i(y,x),x))),2). weight(P(i(x,i(y,x))),2). weight(P(i(i(i(x,y),z),i(y,z))),2). weight(P(i(x,i(i(x,y),y))),2). weight(P(i(i(x,i(y,z)),i(y,i(x,z)))),2). weight(P(i(i(x,y),i(i(z,x),i(z,y)))),2). weight(P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))),2). weight(P(i(i(i(x,y),x),x)),2). weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))),2). weight(P(i(i(i(x,y),z),i(i(z,x),x))),2). weight(P(i(i(i(x,y),y),i(i(y,x),x))),2). weight(P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))),2). weight(P(i(i(i(x,y),z),i(i(x,z),z))),2). weight(P(i(i(x,i(x,y)),i(x,y))),2). weight(P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))),2). weight(P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))),2). weight(P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))),2). weight(P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))),2). weight(P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))),2). weight(P(i(n(x),i(x,y))),2). weight(P(i(i(i(x,y),z),i(n(x),z))),2). weight(P(i(i(x,n(x)),n(x))),2). weight(P(i(n(n(x)),x)),2). weight(P(i(x,n(n(x)))),2). weight(P(i(i(x,y),i(n(n(x)),y))),2). weight(P(i(i(i(n(n(x)),y),z),i(i(x,y),z))),2). weight(P(i(i(x,y),i(i(y,n(x)),n(x)))),2). weight(P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))),2). weight(P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))),2). weight(P(i(i(x,y),i(n(y),n(x)))),2). weight(P(i(i(x,n(y)),i(y,n(x)))),2). weight(P(i(i(n(x),y),i(n(y),x))),2). weight(P(i(i(n(x),n(y)),i(y,x))),2). weight(P(i(i(i(n(x),y),z),i(i(n(y),x),z))),2). weight(P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))),2). weight(P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))),2). weight(P(i(i(n(x),y),i(i(x,y),y))),2). weight(P(i(i(x,y),i(i(n(x),y),y))),2). weight(P(i(i(x,y),i(i(x,n(y)),n(x)))),2). weight(P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))),2). weight(P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))),2). weight(P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))),2). weight(P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))),2). weight(P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))),2). weight(P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))),2). weight(P(i(i(n(n(x)),y),i(x,y))),2). weight(P(i(x,i(y,y))),2). weight(P(i(n(i(x,x)),y)),2). weight(P(i(i(n(x),n(i(y,y))),x)),2). weight(P(i(n(i(x,y)),x)),2). weight(P(i(n(i(x,y)),n(y))),2). weight(P(i(n(i(x,n(y))),y)),2). weight(P(i(x,i(n(y),n(i(x,y))))),2). weight(P(i(x,i(y,n(i(x,n(y)))))),2). weight(P(n(i(i(x,x),n(i(y,y))))),2). end_of_list. list(usable). 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(n(n(p)),p))| -P(i(p,n(n(p))))| -P(i(i(p,q),i(n(q),n(p))))| -P(i(i(p,i(q,r)),i(q,i(p,r))))|$ANSWER(step_allFrege_18_35_39_40_46_21). 3 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(q,i(p,r))))| -P(i(i(q,r),i(i(p,q),i(p,r))))| -P(i(p,i(n(p),q)))| -P(i(i(p,q),i(i(n(p),q),q)))| -P(i(i(p,i(p,q)),i(p,q)))|$ANSWER(step_allHilbert_18_21_22_3_54_30). 4 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49). 5 [] -P(i(i(i(p,q),r),i(q,r)))| -P(i(i(i(p,q),r),i(n(p),r)))| -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r))))|$ANSWER(step_allLuka_x_19_37_59). 6 [] -P(i(i(i(p,q),r),i(q,r)))| -P(i(i(i(p,q),r),i(n(p),r)))| -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r)))))|$ANSWER(step_allWos_x_19_37_60). 7 [] -P(i(i(p,q),i(i(q,r),i(p,r))))| -P(i(i(n(p),p),p))| -P(i(p,i(n(p),q)))|$ANSWER(step_allLuka_1_2_3). 8 [] -P(i(p,p))| -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(q,i(p,r))))| -P(i(i(i(p,q),p),p))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(n(n(p)),p))| -P(i(p,n(n(p))))| -P(i(i(p,q),i(n(q),n(p))))|$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). 9 [] -P(i(p,p))| -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(q,i(p,r))))| -P(i(i(i(p,q),p),p))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(n(n(p)),p))| -P(i(p,n(n(p))))| -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). end_of_list. list(sos). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). end_of_list. list(passive). 13 [] -P(i(i(i(i(q,r),i(p,r)),s),i(i(p,q),s)))|$ANS(neg_th_04). 14 [] -P(i(i(p,i(q,r)),i(i(s,q),i(p,i(s,r)))))|$ANS(neg_th_05). 15 [] -P(i(i(p,q),i(i(i(p,r),s),i(i(q,r),s))))|$ANS(neg_th_06). 16 [] -P(i(i(t,i(i(p,r),s)),i(i(p,q),i(t,i(i(q,r),s)))))|$ANS(neg_th_07). 17 [] -P(i(i(q,r),i(i(p,q),i(i(r,s),i(p,s)))))|$ANS(neg_th_08). 18 [] -P(i(i(i(n(p),q),r),i(p,r)))|$ANS(neg_th_09). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 20 [] -P(i(i(q,i(i(n(p),p),p)),i(i(n(p),p),p)))|$ANS(neg_th_11). 21 [] -P(i(t,i(i(n(p),p),p)))|$ANS(neg_th_12). 22 [] -P(i(i(n(p),q),i(t,i(i(q,p),p))))|$ANS(neg_th_13). 23 [] -P(i(i(i(t,i(i(q,p),p)),r),i(i(n(p),q),r)))|$ANS(neg_th_14). 24 [] -P(i(i(n(p),q),i(i(q,p),p)))|$ANS(neg_th_15). 25 [] -P(i(p,p))|$ANS(neg_th_16). 26 [] -P(i(p,i(i(q,p),p)))|$ANS(neg_th_17). 27 [] -P(i(q,i(p,q)))|$ANS(neg_th_18). 28 [] -P(i(i(i(p,q),r),i(q,r)))|$ANS(neg_th_19). 29 [] -P(i(p,i(i(p,q),q)))|$ANS(neg_th_20). 30 [] -P(i(i(p,i(q,r)),i(q,i(p,r))))|$ANS(neg_th_21). 31 [] -P(i(i(q,r),i(i(p,q),i(p,r))))|$ANS(neg_th_22). 32 [] -P(i(i(i(q,i(p,r)),s),i(i(p,i(q,r)),s)))|$ANS(neg_th_23). 33 [] -P(i(i(i(p,q),p),p))|$ANS(neg_th_24). 34 [] -P(i(i(i(p,r),s),i(i(p,q),i(i(q,r),s))))|$ANS(neg_th_25). 35 [] -P(i(i(i(p,q),r),i(i(r,p),p)))|$ANS(neg_th_26). 36 [] -P(i(i(i(p,q),q),i(i(q,p),p)))|$ANS(neg_th_27). 37 [] -P(i(i(i(i(r,p),p),s),i(i(i(p,q),r),s)))|$ANS(neg_th_28). 38 [] -P(i(i(i(p,q),r),i(i(p,r),r)))|$ANS(neg_th_29). 39 [] -P(i(i(p,i(p,q)),i(p,q)))|$ANS(neg_th_30). 40 [] -P(i(i(p,s),i(i(i(p,q),r),i(i(s,r),r))))|$ANS(neg_th_31). 41 [] -P(i(i(i(p,q),r),i(i(p,s),i(i(s,r),r))))|$ANS(neg_th_32). 42 [] -P(i(i(p,s),i(i(s,i(q,i(p,r))),i(q,i(p,r)))))|$ANS(neg_th_33). 43 [] -P(i(i(s,i(q,i(p,r))),i(i(p,s),i(q,i(p,r)))))|$ANS(neg_th_34). 44 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANS(neg_th_35). 45 [] -P(i(n(p),i(p,q)))|$ANS(neg_th_36). 46 [] -P(i(i(i(p,q),r),i(n(p),r)))|$ANS(neg_th_37). 47 [] -P(i(i(p,n(p)),n(p)))|$ANS(neg_th_38). 48 [] -P(i(n(n(p)),p))|$ANS(neg_th_39). 49 [] -P(i(p,n(n(p))))|$ANS(neg_th_40). 50 [] -P(i(i(p,q),i(n(n(p)),q)))|$ANS(neg_th_41). 51 [] -P(i(i(i(n(n(p)),q),r),i(i(p,q),r)))|$ANS(neg_th_42). 52 [] -P(i(i(p,q),i(i(q,n(p)),n(p))))|$ANS(neg_th_43). 53 [] -P(i(i(s,i(q,n(p))),i(i(p,q),i(s,n(p)))))|$ANS(neg_th_44). 54 [] -P(i(i(s,i(q,p)),i(i(n(p),q),i(s,p))))|$ANS(neg_th_45). 55 [] -P(i(i(p,q),i(n(q),n(p))))|$ANS(neg_th_46). 56 [] -P(i(i(p,n(q)),i(q,n(p))))|$ANS(neg_th_47). 57 [] -P(i(i(n(p),q),i(n(q),p)))|$ANS(neg_th_48). 58 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANS(neg_th_49). 59 [] -P(i(i(i(n(q),p),r),i(i(n(p),q),r)))|$ANS(neg_th_50). 60 [] -P(i(i(p,i(q,r)),i(p,i(n(r),n(q)))))|$ANS(neg_th_51). 61 [] -P(i(i(p,i(q,n(r))),i(p,i(r,n(q)))))|$ANS(neg_th_52). 62 [] -P(i(i(n(p),q),i(i(p,q),q)))|$ANS(neg_th_53). 63 [] -P(i(i(p,q),i(i(n(p),q),q)))|$ANS(neg_th_54). 64 [] -P(i(i(p,q),i(i(p,n(q)),n(p))))|$ANS(neg_th_55). 65 [] -P(i(i(i(i(p,q),q),r),i(i(n(p),q),r)))|$ANS(neg_th_56). 66 [] -P(i(i(n(p),r),i(i(p,q),i(i(q,r),r))))|$ANS(neg_th_57). 67 [] -P(i(i(i(i(p,q),i(i(q,r),r)),s),i(i(n(p),r),s)))|$ANS(neg_th_58). 68 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r))))|$ANS(neg_th_59). 69 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r)))))|$ANS(neg_th_60). 70 [] -P(i(i(p,r),i(i(q,r),i(i(n(p),q),r))))|$ANS(neg_th_61). 71 [] -P(i(i(n(n(p)),q),i(p,q)))|$ANS(neg_th_62). 72 [] -P(i(q,i(p,p)))|$ANS(neg_th_63). 73 [] -P(i(n(i(p,p)),q))|$ANS(neg_th_64). 74 [] -P(i(i(n(q),n(i(p,p))),q))|$ANS(neg_th_65). 75 [] -P(i(n(i(p,q)),p))|$ANS(neg_th_66). 76 [] -P(i(n(i(p,q)),n(q)))|$ANS(neg_th_67). 77 [] -P(i(n(i(p,n(q))),q))|$ANS(neg_th_68). 78 [] -P(i(p,i(n(q),n(i(p,q)))))|$ANS(neg_th_69). 79 [] -P(i(p,i(q,n(i(p,n(q))))))|$ANS(neg_th_70). 80 [] -P(n(i(i(p,p),n(i(q,q)))))|$ANS(neg_th_71). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=-2147483647) 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). -------- PROOF -------- 82 [binary,81.1,13.1] $ANS(neg_th_04). ----> UNIT CONFLICT at 0.01 sec ----> 82 [binary,81.1,13.1] $ANS(neg_th_04). Length of proof is 1. Level of proof is 1. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 13 [] -P(i(i(i(i(q,r),i(p,r)),s),i(i(p,q),s)))|$ANS(neg_th_04). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 82 [binary,81.1,13.1] $ANS(neg_th_04). ------------ end of proof ------------- given clause #2: (wt=-2147483647) 11 [] P(i(i(n(x),x),x)). given clause #3: (wt=-2147483647) 12 [] P(i(x,i(n(x),y))). -------- PROOF -------- 84 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3). -----> EMPTY CLAUSE at 0.01 sec ----> 84 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3). Length of proof is 0. Level of proof is 0. ---------------- PROOF ---------------- 7 [] -P(i(i(p,q),i(i(q,r),i(p,r))))| -P(i(i(n(p),p),p))| -P(i(p,i(n(p),q)))|$ANSWER(step_allLuka_1_2_3). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 84 [hyper,7,10,11,12] $ANSWER(step_allLuka_1_2_3). ------------ end of proof ------------- -------- PROOF -------- 87 [binary,86.1,18.1] $ANS(neg_th_09). ----> UNIT CONFLICT at 0.01 sec ----> 87 [binary,86.1,18.1] $ANS(neg_th_09). Length of proof is 1. Level of proof is 1. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 12 [] P(i(x,i(n(x),y))). 18 [] -P(i(i(i(n(p),q),r),i(p,r)))|$ANS(neg_th_09). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 87 [binary,86.1,18.1] $ANS(neg_th_09). ------------ end of proof ------------- given clause #4: (wt=2) 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). -------- PROOF -------- 91 [binary,90.1,14.1] $ANS(neg_th_05). ----> UNIT CONFLICT at 0.01 sec ----> 91 [binary,90.1,14.1] $ANS(neg_th_05). Length of proof is 2. Level of proof is 2. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 14 [] -P(i(i(p,i(q,r)),i(i(s,q),i(p,i(s,r)))))|$ANS(neg_th_05). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 91 [binary,90.1,14.1] $ANS(neg_th_05). ------------ end of proof ------------- -------- PROOF -------- 96 [binary,95.1,15.1] $ANS(neg_th_06). ----> UNIT CONFLICT at 0.01 sec ----> 96 [binary,95.1,15.1] $ANS(neg_th_06). Length of proof is 2. Level of proof is 2. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 15 [] -P(i(i(p,q),i(i(i(p,r),s),i(i(q,r),s))))|$ANS(neg_th_06). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 96 [binary,95.1,15.1] $ANS(neg_th_06). ------------ end of proof ------------- given clause #5: (wt=2) 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). given clause #6: (wt=2) 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). -------- PROOF -------- 111 [binary,110.1,25.1] $ANS(neg_th_16). ----> UNIT CONFLICT at 0.01 sec ----> 111 [binary,110.1,25.1] $ANS(neg_th_16). Length of proof is 2. Level of proof is 2. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 25 [] -P(i(p,p))|$ANS(neg_th_16). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 110 [hyper,1,86,11] P(i(x,x)). 111 [binary,110.1,25.1] $ANS(neg_th_16). ------------ end of proof ------------- given clause #7: (wt=2) 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). -------- PROOF -------- 116 [binary,115.1,17.1] $ANS(neg_th_08). ----> UNIT CONFLICT at 0.01 sec ----> 116 [binary,115.1,17.1] $ANS(neg_th_08). Length of proof is 3. Level of proof is 3. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 17 [] -P(i(i(q,r),i(i(p,q),i(i(r,s),i(p,s)))))|$ANS(neg_th_08). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 115 [hyper,1,81,90] P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))). 116 [binary,115.1,17.1] $ANS(neg_th_08). ------------ end of proof ------------- given clause #8: (wt=2) 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). -------- PROOF -------- 123 [binary,122.1,16.1] $ANS(neg_th_07). ----> UNIT CONFLICT at 0.01 sec ----> 123 [binary,122.1,16.1] $ANS(neg_th_07). Length of proof is 4. Level of proof is 3. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 16 [] -P(i(i(t,i(i(p,r),s)),i(i(p,q),i(t,i(i(q,r),s)))))|$ANS(neg_th_07). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 123 [binary,122.1,16.1] $ANS(neg_th_07). ------------ end of proof ------------- -------- PROOF -------- 125 [binary,124.1,19.1] $ANS(neg_th_10). ----> UNIT CONFLICT at 0.02 sec ----> 125 [binary,124.1,19.1] $ANS(neg_th_10). Length of proof is 4. Level of proof is 3. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 12 [] P(i(x,i(n(x),y))). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 124 [hyper,1,86,95] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). 125 [binary,124.1,19.1] $ANS(neg_th_10). ------------ end of proof ------------- given clause #9: (wt=2) 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). given clause #10: (wt=2) 110 [hyper,1,86,11] P(i(x,x)). -------- PROOF -------- 137 [binary,136.1,73.1] $ANS(neg_th_64). ----> UNIT CONFLICT at 0.02 sec ----> 137 [binary,136.1,73.1] $ANS(neg_th_64). Length of proof is 3. Level of proof is 3. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 73 [] -P(i(n(i(p,p)),q))|$ANS(neg_th_64). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 110 [hyper,1,86,11] P(i(x,x)). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 137 [binary,136.1,73.1] $ANS(neg_th_64). ------------ end of proof ------------- given clause #11: (wt=2) 115 [hyper,1,81,90] P(i(i(x,y),i(i(z,x),i(i(y,u),i(z,u))))). given clause #12: (wt=2) 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). given clause #13: (wt=2) 124 [hyper,1,86,95] P(i(x,i(i(i(n(x),y),z),i(i(u,y),z)))). given clause #14: (wt=2) 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). given clause #15: (wt=2) 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). given clause #16: (wt=2) 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). given clause #17: (wt=2) 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). given clause #18: (wt=2) 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). given clause #19: (wt=2) 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). given clause #20: (wt=10) 85 [hyper,1,12,12] P(i(n(i(x,i(n(x),y))),z)). given clause #21: (wt=10) 88 [hyper,1,12,11] P(i(n(i(i(n(x),x),x)),y)). given clause #22: (wt=10) 109 [hyper,1,86,12] P(i(x,i(n(i(n(x),y)),z))). given clause #23: (wt=10) 175 [hyper,1,12,136] P(i(n(i(n(i(x,x)),y)),z)). given clause #24: (wt=11) 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). given clause #25: (wt=9) 248 [hyper,1,86,105] P(i(x,i(y,i(n(x),z)))). given clause #26: (wt=9) 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). given clause #27: (wt=11) 108 [hyper,1,86,83] P(i(x,i(i(n(n(x)),n(x)),y))). given clause #28: (wt=11) 112 [hyper,1,86,10] P(i(x,i(i(y,z),i(n(x),z)))). given clause #29: (wt=11) 176 [hyper,1,10,136] P(i(i(x,y),i(n(i(z,z)),y))). given clause #30: (wt=12) 180 [hyper,1,86,151] P(i(x,i(i(x,y),i(i(z,x),y)))). given clause #31: (wt=12) 242 [hyper,1,135,105] P(i(i(n(x),x),i(y,i(n(x),z)))). given clause #32: (wt=12) 252 [hyper,1,105,175] P(i(x,i(n(i(n(i(y,y)),z)),u))). given clause #33: (wt=12) 254 [hyper,1,105,88] P(i(x,i(n(i(i(n(y),y),y)),z))). given clause #34: (wt=12) 255 [hyper,1,105,85] P(i(x,i(n(i(y,i(n(y),z))),u))). given clause #35: (wt=12) 267 [hyper,1,86,248] P(i(x,i(y,i(n(i(n(x),z)),u)))). given clause #36: (wt=12) 269 [hyper,1,12,248] P(i(n(i(x,i(y,i(n(x),z)))),u)). given clause #37: (wt=12) 291 [hyper,1,12,253] P(i(n(i(x,i(n(i(y,y)),z))),u)). given clause #38: (wt=13) 102 [hyper,1,83,11] P(i(i(n(i(n(x),x)),i(n(x),x)),x)). given clause #39: (wt=13) 114 [hyper,1,86,90] P(i(x,i(i(y,z),i(n(x),i(y,u))))). given clause #40: (wt=13) 134 [hyper,1,12,101] P(i(n(i(i(n(x),x),i(n(x),y))),z)). given clause #41: (wt=13) 168 [hyper,1,135,12] P(i(i(n(x),x),i(n(i(n(x),y)),z))). given clause #42: (wt=13) 173 [hyper,1,90,136] P(i(i(x,y),i(n(i(z,z)),i(x,u)))). given clause #43: (wt=13) 174 [hyper,1,83,136] P(i(i(n(n(i(x,x))),n(i(x,x))),y)). given clause #44: (wt=13) 208 [hyper,1,12,85] P(i(n(i(n(i(x,i(n(x),y))),z)),u)). given clause #45: (wt=13) 215 [hyper,1,12,88] P(i(n(i(n(i(i(n(x),x),x)),y)),z)). given clause #46: (wt=13) 223 [hyper,1,86,109] P(i(x,i(n(i(n(i(n(x),y)),z)),u))). given clause #47: (wt=13) 225 [hyper,1,12,109] P(i(n(i(x,i(n(i(n(x),y)),z))),u)). given clause #48: (wt=13) 227 [hyper,1,109,136] P(i(n(i(n(i(n(i(x,x)),y)),z)),u)). given clause #49: (wt=13) 266 [hyper,1,90,248] P(i(i(x,y),i(z,i(x,i(n(z),u))))). given clause #50: (wt=13) 270 [hyper,1,10,248] P(i(i(i(x,i(n(y),z)),u),i(y,u))). -------- PROOF -------- 437 [binary,436.1,19.1] $ANS(neg_th_10). ----> UNIT CONFLICT at 0.05 sec ----> 437 [binary,436.1,19.1] $ANS(neg_th_10). Length of proof is 6. Level of proof is 5. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 12 [] P(i(x,i(n(x),y))). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 248 [hyper,1,86,105] P(i(x,i(y,i(n(x),z)))). 270 [hyper,1,10,248] P(i(i(i(x,i(n(y),z)),u),i(y,u))). 436 [hyper,1,270,10] P(i(x,i(i(i(n(x),y),z),i(u,z)))). 437 [binary,436.1,19.1] $ANS(neg_th_10). ------------ end of proof ------------- given clause #51: (wt=11) 426 [hyper,1,270,266] P(i(x,i(y,i(z,i(n(y),u))))). given clause #52: (wt=12) 435 [hyper,1,270,12] P(i(x,i(n(i(y,i(n(x),z))),u))). given clause #53: (wt=13) 290 [hyper,1,90,253] P(i(i(x,n(i(y,y))),i(z,i(x,u)))). given clause #54: (wt=13) 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). -------- PROOF -------- 504 [binary,503.1,72.1] $ANS(neg_th_63). ----> UNIT CONFLICT at 0.05 sec ----> 504 [binary,503.1,72.1] $ANS(neg_th_63). Length of proof is 8. Level of proof is 6. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 72 [] -P(i(q,i(p,p)))|$ANS(neg_th_63). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 504 [binary,503.1,72.1] $ANS(neg_th_63). ------------ end of proof ------------- given clause #55: (wt=2) 503 [hyper,1,292,11] P(i(x,i(y,y))). given clause #56: (wt=2) 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). -------- PROOF -------- 527 [binary,526.1,22.1] $ANS(neg_th_13). ----> UNIT CONFLICT at 0.06 sec ----> 527 [binary,526.1,22.1] $ANS(neg_th_13). Length of proof is 16. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 22 [] -P(i(i(n(p),q),i(t,i(i(q,p),p))))|$ANS(neg_th_13). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 527 [binary,526.1,22.1] $ANS(neg_th_13). ------------ end of proof ------------- -------- PROOF -------- 542 [binary,541.1,21.1] $ANS(neg_th_12). ----> UNIT CONFLICT at 0.06 sec ----> 542 [binary,541.1,21.1] $ANS(neg_th_12). Length of proof is 11. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 21 [] -P(i(t,i(i(n(p),p),p)))|$ANS(neg_th_12). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 542 [binary,541.1,21.1] $ANS(neg_th_12). ------------ end of proof ------------- -------- PROOF -------- 543 [binary,541.1,20.1] $ANS(neg_th_11). ----> UNIT CONFLICT at 0.06 sec ----> 543 [binary,541.1,20.1] $ANS(neg_th_11). Length of proof is 11. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 20 [] -P(i(i(q,i(i(n(p),p),p)),i(i(n(p),p),p)))|$ANS(neg_th_11). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 543 [binary,541.1,20.1] $ANS(neg_th_11). ------------ end of proof ------------- given clause #57: (wt=2) 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). -------- PROOF -------- 551 [binary,550.1,19.1] $ANS(neg_th_10). ----> UNIT CONFLICT at 0.06 sec ----> 551 [binary,550.1,19.1] $ANS(neg_th_10). Length of proof is 20. Level of proof is 9. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 550 [hyper,1,86,525] P(i(x,i(y,i(i(z,x),x)))). 551 [binary,550.1,19.1] $ANS(neg_th_10). ------------ end of proof ------------- given clause #58: (wt=2) 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). -------- PROOF -------- 566 [binary,565.1,23.1] $ANS(neg_th_14). ----> UNIT CONFLICT at 0.06 sec ----> 566 [binary,565.1,23.1] $ANS(neg_th_14). Length of proof is 17. Level of proof is 9. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 23 [] -P(i(i(i(t,i(i(q,p),p)),r),i(i(n(p),q),r)))|$ANS(neg_th_14). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 566 [binary,565.1,23.1] $ANS(neg_th_14). ------------ end of proof ------------- given clause #59: (wt=2) 528 [hyper,1,122,519] P(i(i(x,y),i(i(i(z,z),u),i(i(y,v),u)))). given clause #60: (wt=2) 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). given clause #61: (wt=2) 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). given clause #62: (wt=2) 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). -------- PROOF -------- 627 [binary,626.1,24.1] $ANS(neg_th_15). ----> UNIT CONFLICT at 0.07 sec ----> 627 [binary,626.1,24.1] $ANS(neg_th_15). Length of proof is 18. Level of proof is 10. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 24 [] -P(i(i(n(p),q),i(i(q,p),p)))|$ANS(neg_th_15). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 627 [binary,626.1,24.1] $ANS(neg_th_15). ------------ end of proof ------------- given clause #63: (wt=2) 584 [hyper,1,90,528] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(x,i(i(v,w),z))))). given clause #64: (wt=2) 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). -------- PROOF -------- 650 [binary,649.1,26.1] $ANS(neg_th_17). ----> UNIT CONFLICT at 0.07 sec ----> 650 [binary,649.1,26.1] $ANS(neg_th_17). Length of proof is 22. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 26 [] -P(i(p,i(i(q,p),p)))|$ANS(neg_th_17). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 650 [binary,649.1,26.1] $ANS(neg_th_17). ------------ end of proof ------------- given clause #65: (wt=2) 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). -------- PROOF -------- 666 [binary,665.1,54.1] $ANS(neg_th_45). ----> UNIT CONFLICT at 0.08 sec ----> 666 [binary,665.1,54.1] $ANS(neg_th_45). Length of proof is 19. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 54 [] -P(i(i(s,i(q,p)),i(i(n(p),q),i(s,p))))|$ANS(neg_th_45). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 666 [binary,665.1,54.1] $ANS(neg_th_45). ------------ end of proof ------------- given clause #66: (wt=2) 639 [hyper,1,584,10] P(i(i(x,y),i(i(z,u),i(i(y,v),i(z,u))))). given clause #67: (wt=2) 648 [hyper,1,90,612] P(i(i(x,i(y,z)),i(i(n(z),z),i(x,z)))). given clause #68: (wt=2) 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). given clause #69: (wt=2) 653 [hyper,1,10,612] P(i(i(i(i(x,y),y),z),i(i(n(y),y),z))). given clause #70: (wt=2) 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). -------- PROOF -------- 764 [binary,763.1,58.1] $ANS(neg_th_49). ----> UNIT CONFLICT at 0.09 sec ----> 764 [binary,763.1,58.1] $ANS(neg_th_49). Length of proof is 20. Level of proof is 12. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 58 [] -P(i(i(n(p),n(q)),i(q,p)))|$ANS(neg_th_49). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 764 [binary,763.1,58.1] $ANS(neg_th_49). ------------ end of proof ------------- given clause #71: (wt=2) 669 [hyper,1,10,626] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))). given clause #72: (wt=2) 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). given clause #73: (wt=2) 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). -------- PROOF -------- 809 [binary,808.1,27.1] $ANS(neg_th_18). ----> UNIT CONFLICT at 0.10 sec ----> 809 [binary,808.1,27.1] $ANS(neg_th_18). Length of proof is 25. Level of proof is 13. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 27 [] -P(i(q,i(p,q)))|$ANS(neg_th_18). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 809 [binary,808.1,27.1] $ANS(neg_th_18). ------------ end of proof ------------- -------- PROOF -------- 810 [binary,808.1,26.1] $ANS(neg_th_17). ----> UNIT CONFLICT at 0.10 sec ----> 810 [binary,808.1,26.1] $ANS(neg_th_17). Length of proof is 25. Level of proof is 13. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 26 [] -P(i(p,i(i(q,p),p)))|$ANS(neg_th_17). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 810 [binary,808.1,26.1] $ANS(neg_th_17). ------------ end of proof ------------- given clause #74: (wt=2) 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). given clause #75: (wt=2) 805 [hyper,1,10,716] P(i(i(i(x,i(y,x)),z),i(i(y,i(u,x)),z))). given clause #76: (wt=2) 807 [hyper,1,716,626] P(i(x,i(i(n(x),y),x))). given clause #77: (wt=2) 808 [hyper,1,716,541] P(i(x,i(y,x))). -------- PROOF -------- 882 [binary,881.1,28.1] $ANS(neg_th_19). ----> UNIT CONFLICT at 0.11 sec ----> 882 [binary,881.1,28.1] $ANS(neg_th_19). Length of proof is 26. Level of proof is 14. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 28 [] -P(i(i(i(p,q),r),i(q,r)))|$ANS(neg_th_19). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 882 [binary,881.1,28.1] $ANS(neg_th_19). ------------ end of proof ------------- given clause #78: (wt=2) 844 [hyper,1,805,90] P(i(i(x,i(y,z)),i(i(u,x),i(z,i(u,z))))). given clause #79: (wt=2) 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). -------- PROOF -------- 937 [binary,936.1,19.1] $ANS(neg_th_10). ----> UNIT CONFLICT at 0.12 sec ----> 937 [binary,936.1,19.1] $ANS(neg_th_10). Length of proof is 27. Level of proof is 15. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 936 [hyper,1,881,808] P(i(x,i(y,i(z,x)))). 937 [binary,936.1,19.1] $ANS(neg_th_10). ------------ end of proof ------------- -------- PROOF -------- 939 [binary,938.1,45.1] $ANS(neg_th_36). ----> UNIT CONFLICT at 0.12 sec ----> 939 [binary,938.1,45.1] $ANS(neg_th_36). Length of proof is 33. Level of proof is 15. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 45 [] -P(i(n(p),i(p,q)))|$ANS(neg_th_36). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 939 [binary,938.1,45.1] $ANS(neg_th_36). ------------ end of proof ------------- -------- PROOF -------- 942 [binary,941.1,29.1] $ANS(neg_th_20). ----> UNIT CONFLICT at 0.12 sec ----> 942 [binary,941.1,29.1] $ANS(neg_th_20). Length of proof is 31. Level of proof is 15. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 29 [] -P(i(p,i(i(p,q),q)))|$ANS(neg_th_20). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 942 [binary,941.1,29.1] $ANS(neg_th_20). ------------ end of proof ------------- given clause #80: (wt=2) 938 [hyper,1,881,763] P(i(n(x),i(x,y))). -------- PROOF -------- 962 [binary,961.1,57.1] $ANS(neg_th_48). ----> UNIT CONFLICT at 0.12 sec ----> 962 [binary,961.1,57.1] $ANS(neg_th_48). Length of proof is 34. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 57 [] -P(i(i(n(p),q),i(n(q),p)))|$ANS(neg_th_48). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 962 [binary,961.1,57.1] $ANS(neg_th_48). ------------ end of proof ------------- -------- PROOF -------- 964 [binary,963.1,33.1] $ANS(neg_th_24). ----> UNIT CONFLICT at 0.12 sec ----> 964 [binary,963.1,33.1] $ANS(neg_th_24). Length of proof is 34. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 33 [] -P(i(i(i(p,q),p),p))|$ANS(neg_th_24). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 964 [binary,963.1,33.1] $ANS(neg_th_24). ------------ end of proof ------------- -------- PROOF -------- 982 [binary,981.1,46.1] $ANS(neg_th_37). ----> UNIT CONFLICT at 0.12 sec ----> 982 [binary,981.1,46.1] $ANS(neg_th_37). Length of proof is 34. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 46 [] -P(i(i(i(p,q),r),i(n(p),r)))|$ANS(neg_th_37). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 981 [hyper,1,10,938] P(i(i(i(x,y),z),i(n(x),z))). 982 [binary,981.1,46.1] $ANS(neg_th_37). ------------ end of proof ------------- given clause #81: (wt=2) 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). -------- PROOF -------- 1007 [binary,1006.1,30.1] $ANS(neg_th_21). ----> UNIT CONFLICT at 0.12 sec ----> 1007 [binary,1006.1,30.1] $ANS(neg_th_21). Length of proof is 32. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 30 [] -P(i(i(p,i(q,r)),i(q,i(p,r))))|$ANS(neg_th_21). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1007 [binary,1006.1,30.1] $ANS(neg_th_21). ------------ end of proof ------------- given clause #82: (wt=2) 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). -------- PROOF -------- 1076 [binary,1075.1,48.1] $ANS(neg_th_39). ----> UNIT CONFLICT at 0.13 sec ----> 1076 [binary,1075.1,48.1] $ANS(neg_th_39). Length of proof is 36. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 48 [] -P(i(n(n(p)),p))|$ANS(neg_th_39). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1076 [binary,1075.1,48.1] $ANS(neg_th_39). ------------ end of proof ------------- -------- PROOF -------- 1090 [binary,1089.1,59.1] $ANS(neg_th_50). ----> UNIT CONFLICT at 0.13 sec ----> 1090 [binary,1089.1,59.1] $ANS(neg_th_50). Length of proof is 35. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 59 [] -P(i(i(i(n(q),p),r),i(i(n(p),q),r)))|$ANS(neg_th_50). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1090 [binary,1089.1,59.1] $ANS(neg_th_50). ------------ end of proof ------------- -------- PROOF -------- 1093 [binary,1092.1,75.1] $ANS(neg_th_66). ----> UNIT CONFLICT at 0.13 sec ----> 1093 [binary,1092.1,75.1] $ANS(neg_th_66). Length of proof is 35. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 75 [] -P(i(n(i(p,q)),p))|$ANS(neg_th_66). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1093 [binary,1092.1,75.1] $ANS(neg_th_66). ------------ end of proof ------------- -------- PROOF -------- 1095 [binary,1094.1,77.1] $ANS(neg_th_68). ----> UNIT CONFLICT at 0.13 sec ----> 1095 [binary,1094.1,77.1] $ANS(neg_th_68). Length of proof is 35. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 77 [] -P(i(n(i(p,n(q))),q))|$ANS(neg_th_68). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1094 [hyper,1,961,808] P(i(n(i(x,n(y))),y)). 1095 [binary,1094.1,77.1] $ANS(neg_th_68). ------------ end of proof ------------- given clause #83: (wt=2) 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). -------- PROOF -------- 1120 [binary,1119.1,39.1] $ANS(neg_th_30). ----> UNIT CONFLICT at 0.13 sec ----> 1120 [binary,1119.1,39.1] $ANS(neg_th_30). Length of proof is 35. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 39 [] -P(i(i(p,i(p,q)),i(p,q)))|$ANS(neg_th_30). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1119 [hyper,1,81,963] P(i(i(x,i(x,y)),i(x,y))). 1120 [binary,1119.1,39.1] $ANS(neg_th_30). ------------ end of proof ------------- given clause #84: (wt=2) 981 [hyper,1,10,938] P(i(i(i(x,y),z),i(n(x),z))). given clause #85: (wt=2) 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). -------- PROOF -------- 1193 [binary,1192.1,32.1] $ANS(neg_th_23). ----> UNIT CONFLICT at 0.14 sec ----> 1193 [binary,1192.1,32.1] $ANS(neg_th_23). Length of proof is 33. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 32 [] -P(i(i(i(q,i(p,r)),s),i(i(p,i(q,r)),s)))|$ANS(neg_th_23). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1193 [binary,1192.1,32.1] $ANS(neg_th_23). ------------ end of proof ------------- -------- PROOF -------- 1213 [binary,1212.1,34.1] $ANS(neg_th_25). ----> UNIT CONFLICT at 0.14 sec ----> 1213 [binary,1212.1,34.1] $ANS(neg_th_25). Length of proof is 33. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 34 [] -P(i(i(i(p,r),s),i(i(p,q),i(i(q,r),s))))|$ANS(neg_th_25). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1213 [binary,1212.1,34.1] $ANS(neg_th_25). ------------ end of proof ------------- -------- PROOF -------- 1217 [binary,1216.1,31.1] $ANS(neg_th_22). ----> UNIT CONFLICT at 0.14 sec ----> 1217 [binary,1216.1,31.1] $ANS(neg_th_22). Length of proof is 33. Level of proof is 17. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 31 [] -P(i(i(q,r),i(i(p,q),i(p,r))))|$ANS(neg_th_22). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1217 [binary,1216.1,31.1] $ANS(neg_th_22). ------------ end of proof ------------- given clause #86: (wt=2) 1008 [hyper,1,83,941] P(i(i(n(x),x),i(i(x,y),y))). given clause #87: (wt=2) 1075 [hyper,1,671,961] P(i(n(n(x)),x)). -------- PROOF -------- 1237 [binary,1236.1,49.1] $ANS(neg_th_40). ----> UNIT CONFLICT at 0.15 sec ----> 1237 [binary,1236.1,49.1] $ANS(neg_th_40). Length of proof is 37. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 49 [] -P(i(p,n(n(p))))|$ANS(neg_th_40). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1236 [hyper,1,763,1075] P(i(x,n(n(x)))). 1237 [binary,1236.1,49.1] $ANS(neg_th_40). ------------ end of proof ------------- -------- PROOF -------- 1240 [binary,1239.1,47.1] $ANS(neg_th_38). ----> UNIT CONFLICT at 0.15 sec ----> 1240 [binary,1239.1,47.1] $ANS(neg_th_38). Length of proof is 37. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 47 [] -P(i(i(p,n(p)),n(p)))|$ANS(neg_th_38). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1239 [hyper,1,626,1075] P(i(i(x,n(x)),n(x))). 1240 [binary,1239.1,47.1] $ANS(neg_th_38). ------------ end of proof ------------- -------- PROOF -------- 1257 [binary,1256.1,51.1] $ANS(neg_th_42). ----> UNIT CONFLICT at 0.15 sec ----> 1257 [binary,1256.1,51.1] $ANS(neg_th_42). Length of proof is 37. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 51 [] -P(i(i(i(n(n(p)),q),r),i(i(p,q),r)))|$ANS(neg_th_42). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1257 [binary,1256.1,51.1] $ANS(neg_th_42). ------------ end of proof ------------- -------- PROOF -------- 1262 [binary,1261.1,50.1] $ANS(neg_th_41). ----> UNIT CONFLICT at 0.15 sec ----> 1262 [binary,1261.1,50.1] $ANS(neg_th_41). Length of proof is 37. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 50 [] -P(i(i(p,q),i(n(n(p)),q)))|$ANS(neg_th_41). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1261 [hyper,1,10,1075] P(i(i(x,y),i(n(n(x)),y))). 1262 [binary,1261.1,50.1] $ANS(neg_th_41). ------------ end of proof ------------- given clause #88: (wt=2) 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). -------- PROOF -------- 1278 [binary,1277.1,71.1] $ANS(neg_th_62). ----> UNIT CONFLICT at 0.15 sec ----> 1278 [binary,1277.1,71.1] $ANS(neg_th_62). Length of proof is 36. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 71 [] -P(i(i(n(n(p)),q),i(p,q)))|$ANS(neg_th_62). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1277 [hyper,1,1089,763] P(i(i(n(n(x)),y),i(x,y))). 1278 [binary,1277.1,71.1] $ANS(neg_th_62). ------------ end of proof ------------- -------- PROOF -------- 1281 [binary,1280.1,62.1] $ANS(neg_th_53). ----> UNIT CONFLICT at 0.15 sec ----> 1281 [binary,1280.1,62.1] $ANS(neg_th_53). Length of proof is 36. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 62 [] -P(i(i(n(p),q),i(i(p,q),q)))|$ANS(neg_th_53). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 1281 [binary,1280.1,62.1] $ANS(neg_th_53). ------------ end of proof ------------- given clause #89: (wt=2) 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). given clause #90: (wt=2) 1094 [hyper,1,961,808] P(i(n(i(x,n(y))),y)). given clause #91: (wt=2) 1119 [hyper,1,81,963] P(i(i(x,i(x,y)),i(x,y))). given clause #92: (wt=2) 1183 [hyper,1,188,1006] P(i(i(n(x),x),i(i(y,x),i(i(x,z),z)))). given clause #93: (wt=2) 1184 [hyper,1,182,1006] P(i(i(n(x),y),i(i(y,x),i(i(x,z),z)))). given clause #94: (wt=2) 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). given clause #95: (wt=2) 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). -------- PROOF -------- 1512 [binary,1511.1,74.1] $ANS(neg_th_65). ----> UNIT CONFLICT at 0.18 sec ----> 1512 [binary,1511.1,74.1] $ANS(neg_th_65). Length of proof is 34. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 74 [] -P(i(i(n(q),n(i(p,p))),q))|$ANS(neg_th_65). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1511 [hyper,1,1201,136] P(i(i(n(x),n(i(y,y))),x)). 1512 [binary,1511.1,74.1] $ANS(neg_th_65). ------------ end of proof ------------- given clause #96: (wt=2) 1203 [hyper,1,1006,528] P(i(i(i(x,x),y),i(i(z,u),i(i(u,v),y)))). given clause #97: (wt=2) 1210 [hyper,1,1006,115] P(i(i(x,y),i(i(y,z),i(i(z,u),i(x,u))))). given clause #98: (wt=2) 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). -------- PROOF -------- 1631 [binary,1630.1,36.1] $ANS(neg_th_27). ----> UNIT CONFLICT at 0.19 sec ----> 1631 [binary,1630.1,36.1] $ANS(neg_th_27). Length of proof is 38. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 36 [] -P(i(i(i(p,q),q),i(i(q,p),p)))|$ANS(neg_th_27). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1630 [hyper,1,1212,963] P(i(i(i(x,y),z),i(i(z,x),x))). 1631 [binary,1630.1,36.1] $ANS(neg_th_27). ------------ end of proof ------------- -------- PROOF -------- 1632 [binary,1630.1,35.1] $ANS(neg_th_26). ----> UNIT CONFLICT at 0.19 sec ----> 1632 [binary,1630.1,35.1] $ANS(neg_th_26). Length of proof is 38. Level of proof is 18. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 35 [] -P(i(i(i(p,q),r),i(i(r,p),p)))|$ANS(neg_th_26). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1630 [hyper,1,1212,963] P(i(i(i(x,y),z),i(i(z,x),x))). 1632 [binary,1630.1,35.1] $ANS(neg_th_26). ------------ end of proof ------------- given clause #99: (wt=2) 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). given clause #100: (wt=2) 1230 [hyper,1,90,1008] P(i(i(x,i(y,z)),i(i(n(y),y),i(x,z)))). given clause #101: (wt=2) 1233 [hyper,1,10,1008] P(i(i(i(i(x,y),y),z),i(i(n(x),x),z))). given clause #102: (wt=2) 1236 [hyper,1,763,1075] P(i(x,n(n(x)))). given clause #103: (wt=2) 1239 [hyper,1,626,1075] P(i(i(x,n(x)),n(x))). -------- PROOF -------- 1958 [binary,1957.1,52.1] $ANS(neg_th_43). ----> UNIT CONFLICT at 0.22 sec ----> 1958 [binary,1957.1,52.1] $ANS(neg_th_43). Length of proof is 41. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 52 [] -P(i(i(p,q),i(i(q,n(p)),n(p))))|$ANS(neg_th_43). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1239 [hyper,1,626,1075] P(i(i(x,n(x)),n(x))). 1957 [hyper,1,1212,1239] P(i(i(x,y),i(i(y,n(x)),n(x)))). 1958 [binary,1957.1,52.1] $ANS(neg_th_43). ------------ end of proof ------------- given clause #104: (wt=2) 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). -------- PROOF -------- 2006 [binary,2005.1,55.1] $ANS(neg_th_46). ----> UNIT CONFLICT at 0.22 sec ----> 2006 [binary,2005.1,55.1] $ANS(neg_th_46). Length of proof is 38. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 55 [] -P(i(i(p,q),i(n(q),n(p))))|$ANS(neg_th_46). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 2006 [binary,2005.1,55.1] $ANS(neg_th_46). ------------ end of proof ------------- -------- PROOF -------- 2009 [binary,2008.1,56.1] $ANS(neg_th_47). ----> UNIT CONFLICT at 0.22 sec ----> 2009 [binary,2008.1,56.1] $ANS(neg_th_47). Length of proof is 38. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 56 [] -P(i(i(p,n(q)),i(q,n(p))))|$ANS(neg_th_47). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2008 [hyper,1,1256,763] P(i(i(x,n(y)),i(y,n(x)))). 2009 [binary,2008.1,56.1] $ANS(neg_th_47). ------------ end of proof ------------- given clause #105: (wt=2) 1261 [hyper,1,10,1075] P(i(i(x,y),i(n(n(x)),y))). given clause #106: (wt=2) 1277 [hyper,1,1089,763] P(i(i(n(n(x)),y),i(x,y))). given clause #107: (wt=2) 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). -------- PROOF -------- 2151 [binary,2150.1,63.1] $ANS(neg_th_54). ----> UNIT CONFLICT at 0.23 sec ----> 2151 [binary,2150.1,63.1] $ANS(neg_th_54). Length of proof is 40. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 63 [] -P(i(i(p,q),i(i(n(p),q),q)))|$ANS(neg_th_54). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 2150 [hyper,1,1256,1280] P(i(i(x,y),i(i(n(x),y),y))). 2151 [binary,2150.1,63.1] $ANS(neg_th_54). ------------ end of proof ------------- -------- PROOF -------- 2175 [binary,2174.1,65.1] $ANS(neg_th_56). ----> UNIT CONFLICT at 0.24 sec ----> 2175 [binary,2174.1,65.1] $ANS(neg_th_56). Length of proof is 37. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 65 [] -P(i(i(i(i(p,q),q),r),i(i(n(p),q),r)))|$ANS(neg_th_56). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 2174 [hyper,1,10,1280] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))). 2175 [binary,2174.1,65.1] $ANS(neg_th_56). ------------ end of proof ------------- given clause #108: (wt=2) 1282 [hyper,1,1089,526] P(i(i(n(x),y),i(z,i(i(x,y),y)))). given clause #109: (wt=2) 1288 [hyper,1,1089,151] P(i(i(n(x),y),i(i(y,z),i(i(x,y),z)))). given clause #110: (wt=2) 1358 [hyper,1,81,1119] P(i(i(i(x,y),x),i(i(x,y),y))). given clause #111: (wt=2) 1371 [hyper,1,10,1183] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(y),y),u))). given clause #112: (wt=2) 1373 [hyper,1,1089,1184] P(i(i(n(x),y),i(i(x,y),i(i(y,z),z)))). given clause #113: (wt=2) 1381 [hyper,1,270,1184] P(i(x,i(i(i(n(x),y),z),i(i(z,u),u)))). given clause #114: (wt=2) 1386 [hyper,1,10,1184] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(y),x),u))). given clause #115: (wt=2) 1391 [hyper,1,1184,938] P(i(i(i(x,y),x),i(i(x,z),z))). given clause #116: (wt=2) 1394 [hyper,1,1184,503] P(i(i(i(x,x),y),i(i(y,z),z))). given clause #117: (wt=2) 1407 [hyper,1,1184,12] P(i(i(i(n(n(x)),y),x),i(i(x,z),z))). given clause #118: (wt=2) 1430 [hyper,1,1192,665] P(i(i(x,i(y,z)),i(i(n(z),x),i(y,z)))). given clause #119: (wt=2) 1452 [hyper,1,1192,90] P(i(i(x,i(y,z)),i(i(u,x),i(y,i(u,z))))). given clause #120: (wt=2) 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). -------- PROOF -------- 2581 [binary,2580.1,68.1] $ANS(neg_th_59). ----> UNIT CONFLICT at 0.29 sec ----> 2581 [binary,2580.1,68.1] $ANS(neg_th_59). Length of proof is 40. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 68 [] -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r))))|$ANS(neg_th_59). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2580 [hyper,1,1089,1471] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). 2581 [binary,2580.1,68.1] $ANS(neg_th_59). ------------ end of proof ------------- given clause #121: (wt=2) 1482 [hyper,1,1201,1092] P(i(i(n(x),n(i(x,y))),x)). given clause #122: (wt=2) 1511 [hyper,1,1201,136] P(i(i(n(x),n(i(y,y))),x)). given clause #123: (wt=2) 1527 [hyper,1,669,1203] P(i(i(n(x),x),i(i(y,z),i(i(z,u),x)))). given clause #124: (wt=2) 1611 [hyper,1,1210,11] P(i(i(x,y),i(i(y,z),i(i(n(x),x),z)))). given clause #125: (wt=2) 1618 [hyper,1,669,1212] P(i(i(n(x),y),i(i(y,z),i(i(z,x),x)))). -------- PROOF -------- 2731 [binary,2730.1,66.1] $ANS(neg_th_57). ----> UNIT CONFLICT at 0.32 sec ----> 2731 [binary,2730.1,66.1] $ANS(neg_th_57). Length of proof is 41. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 66 [] -P(i(i(n(p),r),i(i(p,q),i(i(q,r),r))))|$ANS(neg_th_57). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 669 [hyper,1,10,626] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1618 [hyper,1,669,1212] P(i(i(n(x),y),i(i(y,z),i(i(z,x),x)))). 2730 [hyper,1,1089,1618] P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). 2731 [binary,2730.1,66.1] $ANS(neg_th_57). ------------ end of proof ------------- given clause #126: (wt=2) 1625 [hyper,1,1212,1201] P(i(i(x,y),i(i(y,z),i(i(n(z),x),z)))). given clause #127: (wt=2) 1630 [hyper,1,1212,963] P(i(i(i(x,y),z),i(i(z,x),x))). -------- PROOF -------- 2875 [binary,2874.1,37.1] $ANS(neg_th_28). ----> UNIT CONFLICT at 0.33 sec ----> 2875 [binary,2874.1,37.1] $ANS(neg_th_28). Length of proof is 39. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 37 [] -P(i(i(i(i(r,p),p),s),i(i(i(p,q),r),s)))|$ANS(neg_th_28). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1630 [hyper,1,1212,963] P(i(i(i(x,y),z),i(i(z,x),x))). 2874 [hyper,1,10,1630] P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 2875 [binary,2874.1,37.1] $ANS(neg_th_28). ------------ end of proof ------------- given clause #128: (wt=2) 1658 [hyper,1,1212,1216] P(i(i(x,y),i(i(y,z),i(i(u,x),i(u,z))))). given clause #129: (wt=2) 1660 [hyper,1,1192,1216] P(i(i(x,i(y,z)),i(i(u,y),i(u,i(x,z))))). given clause #130: (wt=2) 1665 [hyper,1,805,1216] P(i(i(x,i(y,z)),i(i(u,z),i(u,i(x,z))))). given clause #131: (wt=2) 1673 [hyper,1,122,1216] P(i(i(x,y),i(i(z,u),i(i(y,z),i(x,u))))). given clause #132: (wt=2) 1677 [hyper,1,90,1216] P(i(i(x,i(y,z)),i(i(z,u),i(x,i(y,u))))). given clause #133: (wt=2) 1680 [hyper,1,10,1216] P(i(i(i(i(x,y),i(x,z)),u),i(i(y,z),u))). given clause #134: (wt=2) 1686 [hyper,1,1216,1184] P(i(i(x,i(n(y),z)),i(x,i(i(z,y),i(i(y,u),u))))). given clause #135: (wt=2) 1687 [hyper,1,1216,1183] P(i(i(x,i(n(y),y)),i(x,i(i(z,y),i(i(y,u),u))))). given clause #136: (wt=2) 1730 [hyper,1,1216,177] P(i(i(x,i(n(y),y)),i(x,i(i(y,z),i(i(u,y),z))))). given clause #137: (wt=2) 1734 [hyper,1,1216,151] P(i(i(x,i(n(y),z)),i(x,i(i(y,u),i(i(z,y),u))))). given clause #138: (wt=2) 1805 [hyper,1,1233,1212] P(i(i(n(x),x),i(i(x,y),i(i(y,z),z)))). given clause #139: (wt=2) 1809 [hyper,1,1233,808] P(i(i(n(x),x),i(y,i(i(x,z),z)))). given clause #140: (wt=2) 1822 [hyper,1,1233,10] P(i(i(n(x),x),i(i(y,z),i(i(x,y),z)))). given clause #141: (wt=2) 1957 [hyper,1,1212,1239] P(i(i(x,y),i(i(y,n(x)),n(x)))). -------- PROOF -------- 3494 [binary,3493.1,53.1] $ANS(neg_th_44). ----> UNIT CONFLICT at 0.41 sec ----> 3494 [binary,3493.1,53.1] $ANS(neg_th_44). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 53 [] -P(i(i(s,i(q,n(p))),i(i(p,q),i(s,n(p)))))|$ANS(neg_th_44). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1239 [hyper,1,626,1075] P(i(i(x,n(x)),n(x))). 1957 [hyper,1,1212,1239] P(i(i(x,y),i(i(y,n(x)),n(x)))). 3493 [hyper,1,90,1957] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))). 3494 [binary,3493.1,53.1] $ANS(neg_th_44). ------------ end of proof ------------- given clause #142: (wt=2) 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). -------- PROOF -------- 3557 [binary,3556.1,60.1] $ANS(neg_th_51). ----> UNIT CONFLICT at 0.42 sec ----> 3557 [binary,3556.1,60.1] $ANS(neg_th_51). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 60 [] -P(i(i(p,i(q,r)),i(p,i(n(r),n(q)))))|$ANS(neg_th_51). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 3556 [hyper,1,1216,2005] P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))). 3557 [binary,3556.1,60.1] $ANS(neg_th_51). ------------ end of proof ------------- -------- PROOF -------- 3637 [binary,3636.1,76.1] $ANS(neg_th_67). ----> UNIT CONFLICT at 0.42 sec ----> 3637 [binary,3636.1,76.1] $ANS(neg_th_67). Length of proof is 39. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 76 [] -P(i(n(i(p,q)),n(q)))|$ANS(neg_th_67). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 3636 [hyper,1,2005,808] P(i(n(i(x,y)),n(y))). 3637 [binary,3636.1,76.1] $ANS(neg_th_67). ------------ end of proof ------------- given clause #143: (wt=2) 2008 [hyper,1,1256,763] P(i(i(x,n(y)),i(y,n(x)))). -------- PROOF -------- 3709 [binary,3708.1,61.1] $ANS(neg_th_52). ----> UNIT CONFLICT at 0.43 sec ----> 3709 [binary,3708.1,61.1] $ANS(neg_th_52). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 61 [] -P(i(i(p,i(q,n(r))),i(p,i(r,n(q)))))|$ANS(neg_th_52). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2008 [hyper,1,1256,763] P(i(i(x,n(y)),i(y,n(x)))). 3708 [hyper,1,1216,2008] P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))). 3709 [binary,3708.1,61.1] $ANS(neg_th_52). ------------ end of proof ------------- given clause #144: (wt=2) 2150 [hyper,1,1256,1280] P(i(i(x,y),i(i(n(x),y),y))). -------- PROOF -------- 3752 [hyper,3,808,1006,1216,12,2150,1119] $ANSWER(step_allHilbert_18_21_22_3_54_30). -----> EMPTY CLAUSE at 0.43 sec ----> 3752 [hyper,3,808,1006,1216,12,2150,1119] $ANSWER(step_allHilbert_18_21_22_3_54_30). Length of proof is 45. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 3 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(q,i(p,r))))| -P(i(i(q,r),i(i(p,q),i(p,r))))| -P(i(p,i(n(p),q)))| -P(i(i(p,q),i(i(n(p),q),q)))| -P(i(i(p,i(p,q)),i(p,q)))|$ANSWER(step_allHilbert_18_21_22_3_54_30). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1119 [hyper,1,81,963] P(i(i(x,i(x,y)),i(x,y))). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 2150 [hyper,1,1256,1280] P(i(i(x,y),i(i(n(x),y),y))). 3752 [hyper,3,808,1006,1216,12,2150,1119] $ANSWER(step_allHilbert_18_21_22_3_54_30). ------------ end of proof ------------- given clause #145: (wt=2) 2155 [hyper,1,1212,1280] P(i(i(n(x),y),i(i(y,z),i(i(x,z),z)))). -------- PROOF -------- 3858 [binary,3857.1,38.1] $ANS(neg_th_29). ----> UNIT CONFLICT at 0.44 sec ----> 3858 [binary,3857.1,38.1] $ANS(neg_th_29). Length of proof is 41. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 38 [] -P(i(i(i(p,q),r),i(i(p,r),r)))|$ANS(neg_th_29). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 2155 [hyper,1,1212,1280] P(i(i(n(x),y),i(i(y,z),i(i(x,z),z)))). 3857 [hyper,1,2155,938] P(i(i(i(x,y),z),i(i(x,z),z))). 3858 [binary,3857.1,38.1] $ANS(neg_th_29). ------------ end of proof ------------- given clause #146: (wt=2) 2171 [hyper,1,90,1280] P(i(i(x,i(y,z)),i(i(n(y),z),i(x,z)))). given clause #147: (wt=2) 2174 [hyper,1,10,1280] P(i(i(i(i(x,y),y),z),i(i(n(x),y),z))). given clause #148: (wt=2) 2176 [hyper,1,1280,941] P(i(i(x,i(i(n(x),y),y)),i(i(n(x),y),y))). given clause #149: (wt=2) 2195 [hyper,1,10,1282] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(y),z),u))). given clause #150: (wt=2) 2205 [hyper,1,1256,1288] P(i(i(x,y),i(i(y,z),i(i(n(x),y),z)))). given clause #151: (wt=2) 2208 [hyper,1,1216,1288] P(i(i(x,i(n(y),z)),i(x,i(i(z,u),i(i(y,z),u))))). given clause #152: (wt=2) 2221 [hyper,1,10,1288] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(z),x),u))). given clause #153: (wt=2) 2233 [hyper,1,1212,1358] P(i(i(i(x,y),z),i(i(z,x),i(i(x,y),y)))). given clause #154: (wt=2) 2243 [hyper,1,122,1358] P(i(i(x,y),i(i(i(x,z),x),i(i(y,z),z)))). given clause #155: (wt=2) 2250 [hyper,1,10,1358] P(i(i(i(i(x,y),y),z),i(i(i(x,y),x),z))). given clause #156: (wt=2) 2267 [hyper,1,1216,1373] P(i(i(x,i(n(y),z)),i(x,i(i(y,z),i(i(z,u),u))))). given clause #157: (wt=2) 2279 [hyper,1,10,1373] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),y),u))). given clause #158: (wt=2) 2350 [hyper,1,1212,1391] P(i(i(i(x,y),z),i(i(z,x),i(i(x,u),u)))). given clause #159: (wt=2) 2358 [hyper,1,584,1391] P(i(i(x,y),i(i(i(z,u),z),i(i(y,v),z)))). given clause #160: (wt=2) 2362 [hyper,1,122,1391] P(i(i(x,y),i(i(i(x,z),x),i(i(y,u),u)))). given clause #161: (wt=2) 2369 [hyper,1,10,1391] P(i(i(i(i(x,y),y),z),i(i(i(x,u),x),z))). given clause #162: (wt=2) 2375 [hyper,1,1212,1394] P(i(i(i(x,x),y),i(i(y,z),i(i(z,u),u)))). given clause #163: (wt=2) 2385 [hyper,1,122,1394] P(i(i(x,y),i(i(i(z,z),x),i(i(y,u),u)))). given clause #164: (wt=2) 2392 [hyper,1,10,1394] P(i(i(i(i(x,y),y),z),i(i(i(u,u),x),z))). given clause #165: (wt=2) 2576 [hyper,1,1216,1471] P(i(i(x,i(n(y),z)),i(x,i(i(u,y),i(i(z,u),y))))). -------- PROOF -------- 4783 [binary,4782.1,70.1] $ANS(neg_th_61). ----> UNIT CONFLICT at 0.59 sec ----> 4783 [binary,4782.1,70.1] $ANS(neg_th_61). Length of proof is 45. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 70 [] -P(i(i(p,r),i(i(q,r),i(i(n(p),q),r))))|$ANS(neg_th_61). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 2576 [hyper,1,1216,1471] P(i(i(x,i(n(y),z)),i(x,i(i(u,y),i(i(z,u),y))))). 4782 [hyper,1,2576,2005] P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))). 4783 [binary,4782.1,70.1] $ANS(neg_th_61). ------------ end of proof ------------- given clause #166: (wt=2) 2580 [hyper,1,1089,1471] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). -------- PROOF -------- 4796 [hyper,5,881,981,2580] $ANSWER(step_allLuka_x_19_37_59). -----> EMPTY CLAUSE at 0.59 sec ----> 4796 [hyper,5,881,981,2580] $ANSWER(step_allLuka_x_19_37_59). Length of proof is 41. Level of proof is 19. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 5 [] -P(i(i(i(p,q),r),i(q,r)))| -P(i(i(i(p,q),r),i(n(p),r)))| -P(i(i(n(p),r),i(i(q,r),i(i(p,q),r))))|$ANSWER(step_allLuka_x_19_37_59). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 981 [hyper,1,10,938] P(i(i(i(x,y),z),i(n(x),z))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2580 [hyper,1,1089,1471] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). 4796 [hyper,5,881,981,2580] $ANSWER(step_allLuka_x_19_37_59). ------------ end of proof ------------- -------- PROOF -------- 4807 [binary,4806.1,69.1] $ANS(neg_th_60). ----> UNIT CONFLICT at 0.59 sec ----> 4807 [binary,4806.1,69.1] $ANS(neg_th_60). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 69 [] -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r)))))|$ANS(neg_th_60). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2580 [hyper,1,1089,1471] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). 4806 [hyper,1,1216,2580] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))). 4807 [binary,4806.1,69.1] $ANS(neg_th_60). ------------ end of proof ------------- given clause #167: (wt=2) 2592 [hyper,1,10,1471] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(y),z),u))). given clause #168: (wt=2) 2594 [hyper,1,1471,1094] P(i(i(x,i(y,n(z))),i(i(z,x),i(y,n(z))))). given clause #169: (wt=2) 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). -------- PROOF -------- 4979 [binary,4978.1,44.1] $ANS(neg_th_35). ----> UNIT CONFLICT at 0.62 sec ----> 4979 [binary,4978.1,44.1] $ANS(neg_th_35). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 44 [] -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))|$ANS(neg_th_35). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 4978 [hyper,1,1192,2595] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 4979 [binary,4978.1,44.1] $ANS(neg_th_35). ------------ end of proof ------------- given clause #170: (wt=2) 2667 [hyper,1,1216,1527] P(i(i(x,i(n(y),y)),i(x,i(i(z,u),i(i(u,v),y))))). given clause #171: (wt=2) 2676 [hyper,1,10,1527] P(i(i(i(i(x,y),i(i(y,z),u)),v),i(i(n(u),u),v))). given clause #172: (wt=2) 2688 [hyper,1,1006,1611] P(i(i(x,y),i(i(z,x),i(i(n(z),z),y)))). given clause #173: (wt=2) 2727 [hyper,1,1216,1618] P(i(i(x,i(n(y),z)),i(x,i(i(z,u),i(i(u,y),y))))). given clause #174: (wt=2) 2730 [hyper,1,1089,1618] P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). -------- PROOF -------- 5266 [binary,5265.1,67.1] $ANS(neg_th_58). ----> UNIT CONFLICT at 0.66 sec ----> 5266 [binary,5265.1,67.1] $ANS(neg_th_58). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 67 [] -P(i(i(i(i(p,q),i(i(q,r),r)),s),i(i(n(p),r),s)))|$ANS(neg_th_58). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 669 [hyper,1,10,626] P(i(i(i(i(x,y),y),z),i(i(n(y),x),z))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1618 [hyper,1,669,1212] P(i(i(n(x),y),i(i(y,z),i(i(z,x),x)))). 2730 [hyper,1,1089,1618] P(i(i(n(x),y),i(i(x,z),i(i(z,y),y)))). 5265 [hyper,1,10,2730] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))). 5266 [binary,5265.1,67.1] $ANS(neg_th_58). ------------ end of proof ------------- given clause #175: (wt=2) 2739 [hyper,1,10,1618] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(z),x),u))). given clause #176: (wt=2) 2751 [hyper,1,1618,12] P(i(i(i(n(n(x)),y),z),i(i(z,x),x))). given clause #177: (wt=2) 2762 [hyper,1,1006,1625] P(i(i(x,y),i(i(z,x),i(i(n(y),z),y)))). given clause #178: (wt=2) 2800 [hyper,1,1625,941] P(i(i(i(i(x,y),y),z),i(i(n(z),x),z))). given clause #179: (wt=2) 2826 [hyper,1,1625,180] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(u),x),u))). given clause #180: (wt=2) 2840 [hyper,1,1625,12] P(i(i(i(n(x),y),z),i(i(n(z),x),z))). given clause #181: (wt=2) 2852 [hyper,1,1212,1630] P(i(i(i(x,y),z),i(i(z,u),i(i(u,x),x)))). given clause #182: (wt=2) 2866 [hyper,1,122,1630] P(i(i(x,y),i(i(i(z,u),x),i(i(y,z),z)))). given clause #183: (wt=2) 2874 [hyper,1,10,1630] P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). -------- PROOF -------- 5693 [binary,5692.1,41.1] $ANS(neg_th_32). ----> UNIT CONFLICT at 0.74 sec ----> 5693 [binary,5692.1,41.1] $ANS(neg_th_32). Length of proof is 41. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 41 [] -P(i(i(i(p,q),r),i(i(p,s),i(i(s,r),r))))|$ANS(neg_th_32). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1630 [hyper,1,1212,963] P(i(i(i(x,y),z),i(i(z,x),x))). 2852 [hyper,1,1212,1630] P(i(i(i(x,y),z),i(i(z,u),i(i(u,x),x)))). 2874 [hyper,1,10,1630] P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 5692 [hyper,1,2874,2852] P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). 5693 [binary,5692.1,41.1] $ANS(neg_th_32). ------------ end of proof ------------- given clause #184: (wt=2) 2937 [hyper,1,1006,1658] P(i(i(x,y),i(i(z,x),i(i(u,z),i(u,y))))). given clause #185: (wt=2) 3027 [hyper,1,805,1660] P(i(i(x,i(y,z)),i(i(u,x),i(u,i(z,z))))). given clause #186: (wt=2) 3129 [hyper,1,1192,1665] P(i(i(x,i(y,z)),i(i(u,z),i(u,i(y,z))))). given clause #187: (wt=2) 3134 [hyper,1,805,1665] P(i(i(x,i(y,z)),i(i(u,z),i(u,i(z,z))))). given clause #188: (wt=2) 3153 [hyper,1,1006,1673] P(i(i(x,y),i(i(z,u),i(i(u,x),i(z,y))))). given clause #189: (wt=2) 3232 [hyper,1,1192,1677] P(i(i(x,i(y,z)),i(i(z,u),i(y,i(x,u))))). given clause #190: (wt=2) 3247 [hyper,1,1677,1630] P(i(i(x,y),i(i(i(x,z),u),i(i(u,x),y)))). given clause #191: (wt=2) 3258 [hyper,1,1677,1394] P(i(i(x,y),i(i(i(z,z),u),i(i(u,x),y)))). given clause #192: (wt=2) 3259 [hyper,1,1677,1391] P(i(i(x,y),i(i(i(z,u),z),i(i(z,x),y)))). given clause #193: (wt=2) 3265 [hyper,1,1677,1216] P(i(i(i(x,y),z),i(i(u,y),i(i(x,u),z)))). given clause #194: (wt=2) 3269 [hyper,1,1677,1201] P(i(i(x,y),i(i(z,x),i(i(n(x),z),y)))). given clause #195: (wt=2) 3338 [hyper,1,1680,10] P(i(i(x,y),i(i(i(z,y),u),i(i(z,x),u)))). given clause #196: (wt=2) 3364 [hyper,1,1687,981] P(i(i(i(x,y),x),i(i(z,x),i(i(x,u),u)))). given clause #197: (wt=2) 3368 [hyper,1,1687,519] P(i(i(i(x,x),y),i(i(z,y),i(i(y,u),u)))). given clause #198: (wt=2) 3380 [hyper,1,1730,981] P(i(i(i(x,y),x),i(i(x,z),i(i(u,x),z)))). given clause #199: (wt=2) 3395 [hyper,1,1734,981] P(i(i(i(x,y),z),i(i(x,u),i(i(z,x),u)))). given clause #200: (wt=2) 3399 [hyper,1,1734,519] P(i(i(i(x,x),y),i(i(z,u),i(i(y,z),u)))). given clause #201: (wt=2) 3415 [hyper,1,1216,1805] P(i(i(x,i(n(y),y)),i(x,i(i(y,z),i(i(z,u),u))))). given clause #202: (wt=2) 3423 [hyper,1,10,1805] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),x),u))). given clause #203: (wt=2) 3443 [hyper,1,10,1809] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(y),y),u))). given clause #204: (wt=2) 3451 [hyper,1,1216,1822] P(i(i(x,i(n(y),y)),i(x,i(i(z,u),i(i(y,z),u))))). given clause #205: (wt=2) 3459 [hyper,1,10,1822] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(z),z),u))). given clause #206: (wt=2) 3493 [hyper,1,90,1957] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))). -------- PROOF -------- 6956 [binary,6955.1,64.1] $ANS(neg_th_55). ----> UNIT CONFLICT at 0.97 sec ----> 6956 [binary,6955.1,64.1] $ANS(neg_th_55). Length of proof is 45. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 64 [] -P(i(i(p,q),i(i(p,n(q)),n(p))))|$ANS(neg_th_55). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1239 [hyper,1,626,1075] P(i(i(x,n(x)),n(x))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1957 [hyper,1,1212,1239] P(i(i(x,y),i(i(y,n(x)),n(x)))). 2008 [hyper,1,1256,763] P(i(i(x,n(y)),i(y,n(x)))). 3493 [hyper,1,90,1957] P(i(i(x,i(y,n(z))),i(i(z,y),i(x,n(z))))). 6955 [hyper,1,3493,2008] P(i(i(x,y),i(i(x,n(y)),n(x)))). 6956 [binary,6955.1,64.1] $ANS(neg_th_55). ------------ end of proof ------------- given clause #207: (wt=2) 3556 [hyper,1,1216,2005] P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))). -------- PROOF -------- 7105 [binary,7104.1,78.1] $ANS(neg_th_69). ----> UNIT CONFLICT at 0.98 sec ----> 7105 [binary,7104.1,78.1] $ANS(neg_th_69). Length of proof is 43. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 78 [] -P(i(p,i(n(q),n(i(p,q)))))|$ANS(neg_th_69). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 3556 [hyper,1,1216,2005] P(i(i(x,i(y,z)),i(x,i(n(z),n(y))))). 7104 [hyper,1,3556,941] P(i(x,i(n(y),n(i(x,y))))). 7105 [binary,7104.1,78.1] $ANS(neg_th_69). ------------ end of proof ------------- given clause #208: (wt=2) 3636 [hyper,1,2005,808] P(i(n(i(x,y)),n(y))). given clause #209: (wt=2) 3701 [hyper,1,1452,2008] P(i(i(x,i(y,n(z))),i(z,i(x,n(y))))). given clause #210: (wt=2) 3708 [hyper,1,1216,2008] P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))). -------- PROOF -------- 7361 [binary,7360.1,79.1] $ANS(neg_th_70). ----> UNIT CONFLICT at 1.01 sec ----> 7361 [binary,7360.1,79.1] $ANS(neg_th_70). Length of proof is 43. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 79 [] -P(i(p,i(q,n(i(p,n(q))))))|$ANS(neg_th_70). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 2008 [hyper,1,1256,763] P(i(i(x,n(y)),i(y,n(x)))). 3708 [hyper,1,1216,2008] P(i(i(x,i(y,n(z))),i(x,i(z,n(y))))). 7360 [hyper,1,3708,941] P(i(x,i(y,n(i(x,n(y)))))). 7361 [binary,7360.1,79.1] $ANS(neg_th_70). ------------ end of proof ------------- given clause #211: (wt=2) 3757 [hyper,1,1677,2150] P(i(i(x,y),i(i(z,x),i(i(n(z),x),y)))). given clause #212: (wt=2) 3766 [hyper,1,1212,2150] P(i(i(x,y),i(i(y,z),i(i(n(x),z),z)))). given clause #213: (wt=2) 3778 [hyper,1,122,2150] P(i(i(n(x),y),i(i(x,z),i(i(y,z),z)))). given clause #214: (wt=2) 3841 [hyper,1,1216,2155] P(i(i(x,i(n(y),z)),i(x,i(i(z,u),i(i(y,u),u))))). given clause #215: (wt=2) 3853 [hyper,1,10,2155] P(i(i(i(i(x,y),i(i(z,y),y)),u),i(i(n(z),x),u))). given clause #216: (wt=2) 3857 [hyper,1,2155,938] P(i(i(i(x,y),z),i(i(x,z),z))). -------- PROOF -------- 7695 [binary,7694.1,40.1] $ANS(neg_th_31). ----> UNIT CONFLICT at 1.07 sec ----> 7695 [binary,7694.1,40.1] $ANS(neg_th_31). Length of proof is 42. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 40 [] -P(i(i(p,s),i(i(i(p,q),r),i(i(s,r),r))))|$ANS(neg_th_31). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 2155 [hyper,1,1212,1280] P(i(i(n(x),y),i(i(y,z),i(i(x,z),z)))). 3857 [hyper,1,2155,938] P(i(i(i(x,y),z),i(i(x,z),z))). 7694 [hyper,1,122,3857] P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). 7695 [binary,7694.1,40.1] $ANS(neg_th_31). ------------ end of proof ------------- given clause #217: (wt=2) 3867 [hyper,1,2155,12] P(i(i(i(n(n(x)),y),z),i(i(x,z),z))). given clause #218: (wt=2) 3883 [hyper,1,1192,2171] P(i(i(x,i(y,z)),i(i(n(x),z),i(y,z)))). given clause #219: (wt=2) 4124 [hyper,1,2208,981] P(i(i(i(x,y),z),i(i(z,u),i(i(x,z),u)))). given clause #220: (wt=2) 4160 [hyper,1,1452,2233] P(i(i(x,i(i(y,z),u)),i(i(u,y),i(x,i(i(y,z),z))))). given clause #221: (wt=2) 4167 [hyper,1,1006,2233] P(i(i(x,y),i(i(i(y,z),x),i(i(y,z),z)))). given clause #222: (wt=2) 4174 [hyper,1,81,2233] P(i(i(x,y),i(i(i(x,z),y),i(i(y,z),z)))). given clause #223: (wt=2) 4192 [hyper,1,2233,1216] P(i(i(i(i(x,y),i(x,z)),y),i(i(y,z),z))). given clause #224: (wt=2) 4220 [hyper,1,2233,10] P(i(i(i(i(x,y),i(z,y)),z),i(i(z,x),x))). given clause #225: (wt=2) 4234 [hyper,1,1006,2243] P(i(i(i(x,y),x),i(i(x,z),i(i(z,y),y)))). given clause #226: (wt=2) 4241 [hyper,1,90,2243] P(i(i(x,i(i(y,z),y)),i(i(y,u),i(x,i(i(u,z),z))))). given clause #227: (wt=2) 4292 [hyper,1,2250,1630] P(i(i(i(x,y),x),i(i(y,x),x))). given clause #228: (wt=2) 4304 [hyper,1,2250,981] P(i(i(i(x,y),x),i(n(x),y))). given clause #229: (wt=2) 4322 [hyper,1,2250,10] P(i(i(i(x,y),x),i(i(y,z),i(i(x,y),z)))). given clause #230: (wt=2) 4334 [hyper,1,2267,981] P(i(i(i(x,y),z),i(i(x,z),i(i(z,u),u)))). given clause #231: (wt=2) 4373 [hyper,1,1452,2350] P(i(i(x,i(i(y,z),u)),i(i(u,y),i(x,i(i(y,v),v))))). given clause #232: (wt=2) 4381 [hyper,1,1006,2350] P(i(i(x,y),i(i(i(y,z),x),i(i(y,u),u)))). given clause #233: (wt=2) 4389 [hyper,1,81,2350] P(i(i(x,y),i(i(i(x,z),y),i(i(y,u),u)))). given clause #234: (wt=2) 4417 [hyper,1,2350,1216] P(i(i(i(i(x,y),i(x,z)),y),i(i(y,u),u))). given clause #235: (wt=2) 4455 [hyper,1,1119,2358] P(i(i(i(x,y),x),i(i(x,z),x))). given clause #236: (wt=2) 4457 [hyper,1,1006,2358] P(i(i(i(x,y),x),i(i(z,u),i(i(u,v),x)))). given clause #237: (wt=2) 4459 [hyper,1,963,2358] P(i(i(i(x,y),x),i(i(z,u),x))). given clause #238: (wt=2) 4465 [hyper,1,90,2358] P(i(i(x,i(i(y,z),y)),i(i(u,v),i(x,i(i(v,w),y))))). given clause #239: (wt=2) 4481 [hyper,1,1006,2362] P(i(i(i(x,y),x),i(i(x,z),i(i(z,u),u)))). given clause #240: (wt=2) 4488 [hyper,1,90,2362] P(i(i(x,i(i(y,z),y)),i(i(y,u),i(x,i(i(u,v),v))))). given clause #241: (wt=2) 4554 [hyper,1,2369,981] P(i(i(i(x,y),x),i(n(x),z))). given clause #242: (wt=2) 4559 [hyper,1,2369,519] P(i(i(i(x,y),x),i(z,x))). given clause #243: (wt=2) 4575 [hyper,1,2369,10] P(i(i(i(x,y),x),i(i(z,u),i(i(x,z),u)))). given clause #244: (wt=2) 4580 [hyper,1,1452,2375] P(i(i(x,i(i(y,y),z)),i(i(z,u),i(x,i(i(u,v),v))))). given clause #245: (wt=2) 4611 [hyper,1,2375,1261] P(i(i(i(n(n(x)),x),y),i(i(y,z),z))). given clause #246: (wt=2) 4754 [hyper,1,2392,981] P(i(i(i(x,x),y),i(n(y),z))). given clause #247: (wt=2) 4782 [hyper,1,2576,2005] P(i(i(x,y),i(i(z,y),i(i(n(x),z),y)))). given clause #248: (wt=2) 4788 [hyper,1,2576,981] P(i(i(i(x,y),z),i(i(u,x),i(i(z,u),x)))). given clause #249: (wt=2) 4806 [hyper,1,1216,2580] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))). -------- PROOF -------- 9164 [hyper,6,881,981,4806] $ANSWER(step_allWos_x_19_37_60). -----> EMPTY CLAUSE at 1.41 sec ----> 9164 [hyper,6,881,981,4806] $ANSWER(step_allWos_x_19_37_60). Length of proof is 43. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 6 [] -P(i(i(i(p,q),r),i(q,r)))| -P(i(i(i(p,q),r),i(n(p),r)))| -P(i(i(s,i(n(p),r)),i(s,i(i(q,r),i(i(p,q),r)))))|$ANSWER(step_allWos_x_19_37_60). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 981 [hyper,1,10,938] P(i(i(i(x,y),z),i(n(x),z))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2580 [hyper,1,1089,1471] P(i(i(n(x),y),i(i(z,y),i(i(x,z),y)))). 4806 [hyper,1,1216,2580] P(i(i(x,i(n(y),z)),i(x,i(i(u,z),i(i(y,u),z))))). 9164 [hyper,6,881,981,4806] $ANSWER(step_allWos_x_19_37_60). ------------ end of proof ------------- given clause #250: (wt=2) 4817 [hyper,1,10,2580] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(z),y),u))). given clause #251: (wt=2) 4921 [hyper,1,2594,808] P(i(i(x,n(x)),i(y,n(x)))). given clause #252: (wt=2) 4967 [hyper,1,1452,2595] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))). -------- PROOF -------- 9289 [binary,9288.1,43.1] $ANS(neg_th_34). ----> UNIT CONFLICT at 1.44 sec ----> 9289 [binary,9288.1,43.1] $ANS(neg_th_34). Length of proof is 44. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 43 [] -P(i(i(s,i(q,i(p,r))),i(i(p,s),i(q,i(p,r)))))|$ANS(neg_th_34). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1452 [hyper,1,1192,90] P(i(i(x,i(y,z)),i(i(u,x),i(y,i(u,z))))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 4967 [hyper,1,1452,2595] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(x,i(z,u))))). 9288 [hyper,1,1192,4967] P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))). 9289 [binary,9288.1,43.1] $ANS(neg_th_34). ------------ end of proof ------------- given clause #253: (wt=2) 4978 [hyper,1,1192,2595] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). -------- PROOF -------- 9396 [hyper,9,110,808,1006,963,4978,1075,1236,763] $ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). -----> EMPTY CLAUSE at 1.46 sec ----> 9396 [hyper,9,110,808,1006,963,4978,1075,1236,763] $ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). Length of proof is 46. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 9 [] -P(i(p,p))| -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(q,i(p,r))))| -P(i(i(i(p,q),p),p))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(n(n(p)),p))| -P(i(p,n(n(p))))| -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1236 [hyper,1,763,1075] P(i(x,n(n(x)))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 4978 [hyper,1,1192,2595] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 9396 [hyper,9,110,808,1006,963,4978,1075,1236,763] $ANSWER(step_allScott_orig0_16_18_21_24_35_39_40_49). ------------ end of proof ------------- -------- PROOF -------- 9397 [hyper,8,110,808,1006,963,4978,1075,1236,2005] $ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). -----> EMPTY CLAUSE at 1.46 sec ----> 9397 [hyper,8,110,808,1006,963,4978,1075,1236,2005] $ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). Length of proof is 48. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 8 [] -P(i(p,p))| -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(q,i(p,r))))| -P(i(i(i(p,q),p),p))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(n(n(p)),p))| -P(i(p,n(n(p))))| -P(i(i(p,q),i(n(q),n(p))))|$ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1236 [hyper,1,763,1075] P(i(x,n(n(x)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 4978 [hyper,1,1192,2595] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 9397 [hyper,8,110,808,1006,963,4978,1075,1236,2005] $ANSWER(step_allScott_orig_16_18_21_24_35_39_40_46). ------------ end of proof ------------- -------- PROOF -------- 9398 [hyper,4,808,4978,763] $ANSWER(step_allBEH_Church_FL_18_35_49). -----> EMPTY CLAUSE at 1.46 sec ----> 9398 [hyper,4,808,4978,763] $ANSWER(step_allBEH_Church_FL_18_35_49). Length of proof is 42. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 4 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(i(n(p),n(q)),i(q,p)))|$ANSWER(step_allBEH_Church_FL_18_35_49). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 4978 [hyper,1,1192,2595] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 9398 [hyper,4,808,4978,763] $ANSWER(step_allBEH_Church_FL_18_35_49). ------------ end of proof ------------- -------- PROOF -------- 9399 [hyper,2,808,4978,1075,1236,2005,1006] $ANSWER(step_allFrege_18_35_39_40_46_21). -----> EMPTY CLAUSE at 1.46 sec ----> 9399 [hyper,2,808,4978,1075,1236,2005,1006] $ANSWER(step_allFrege_18_35_39_40_46_21). Length of proof is 47. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] -P(i(p,i(q,p)))| -P(i(i(p,i(q,r)),i(i(p,q),i(p,r))))| -P(i(n(n(p)),p))| -P(i(p,n(n(p))))| -P(i(i(p,q),i(n(q),n(p))))| -P(i(i(p,i(q,r)),i(q,i(p,r))))|$ANSWER(step_allFrege_18_35_39_40_46_21). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1092 [hyper,1,961,938] P(i(n(i(x,y)),x)). 1192 [hyper,1,10,1006] P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u))). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1236 [hyper,1,763,1075] P(i(x,n(n(x)))). 1256 [hyper,1,95,1075] P(i(i(i(n(n(x)),y),z),i(i(x,y),z))). 1471 [hyper,1,122,1201] P(i(i(n(x),y),i(i(z,x),i(i(y,z),x)))). 2005 [hyper,1,1256,961] P(i(i(x,y),i(n(y),n(x)))). 2595 [hyper,1,1471,1092] P(i(i(x,i(y,z)),i(i(y,x),i(y,z)))). 4978 [hyper,1,1192,2595] P(i(i(x,i(y,z)),i(i(x,y),i(x,z)))). 9399 [hyper,2,808,4978,1075,1236,2005,1006] $ANSWER(step_allFrege_18_35_39_40_46_21). ------------ end of proof ------------- given clause #254: (wt=2) 5123 [hyper,1,2676,1006] P(i(i(n(x),x),i(i(y,z),i(i(u,y),x)))). given clause #255: (wt=2) 5125 [hyper,1,2676,881] P(i(i(n(x),x),i(y,i(i(y,z),x)))). given clause #256: (wt=2) 5127 [hyper,1,2676,519] P(i(i(n(x),x),i(y,i(i(z,u),x)))). given clause #257: (wt=2) 5256 [hyper,1,1216,2730] P(i(i(x,i(n(y),z)),i(x,i(i(y,u),i(i(u,z),z))))). given clause #258: (wt=2) 5265 [hyper,1,10,2730] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),z),u))). given clause #259: (wt=2) 5514 [hyper,1,1452,2852] P(i(i(x,i(i(y,z),u)),i(i(u,v),i(x,i(i(v,y),y))))). given clause #260: (wt=2) 5529 [hyper,1,81,2852] P(i(i(x,y),i(i(i(x,z),u),i(i(u,y),y)))). given clause #261: (wt=2) 5535 [hyper,1,2852,2595] P(i(i(i(i(x,y),i(x,z)),u),i(i(u,y),y))). given clause #262: (wt=2) 5692 [hyper,1,2874,2852] P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). -------- PROOF -------- 9889 [binary,9888.1,42.1] $ANS(neg_th_33). ----> UNIT CONFLICT at 1.57 sec ----> 9889 [binary,9888.1,42.1] $ANS(neg_th_33). Length of proof is 42. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 42 [] -P(i(i(p,s),i(i(s,i(q,i(p,r))),i(q,i(p,r)))))|$ANS(neg_th_33). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 963 [hyper,1,626,938] P(i(i(i(x,y),x),x)). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1630 [hyper,1,1212,963] P(i(i(i(x,y),z),i(i(z,x),x))). 2852 [hyper,1,1212,1630] P(i(i(i(x,y),z),i(i(z,u),i(i(u,x),x)))). 2874 [hyper,1,10,1630] P(i(i(i(i(x,y),y),z),i(i(i(y,u),x),z))). 5692 [hyper,1,2874,2852] P(i(i(i(x,y),z),i(i(x,u),i(i(u,z),z)))). 9888 [hyper,1,5692,1006] P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))). 9889 [binary,9888.1,42.1] $ANS(neg_th_33). ------------ end of proof ------------- given clause #263: (wt=2) 5722 [hyper,1,2874,981] P(i(i(i(x,y),z),i(n(z),x))). given clause #264: (wt=2) 5777 [hyper,1,2937,1630] P(i(i(x,i(i(y,z),u)),i(i(v,x),i(v,i(i(u,y),y))))). given clause #265: (wt=2) 5780 [hyper,1,2937,1394] P(i(i(x,i(i(y,y),z)),i(i(u,x),i(u,i(i(z,v),v))))). given clause #266: (wt=2) 5781 [hyper,1,2937,1391] P(i(i(x,i(i(y,z),y)),i(i(u,x),i(u,i(i(y,v),v))))). given clause #267: (wt=2) 5785 [hyper,1,2937,1239] P(i(i(x,i(y,n(y))),i(i(z,x),i(z,n(y))))). given clause #268: (wt=2) 5789 [hyper,1,2937,1119] P(i(i(x,i(y,i(y,z))),i(i(u,x),i(u,i(y,z))))). given clause #269: (wt=2) 5857 [hyper,1,1192,3027] P(i(i(x,i(y,z)),i(i(u,y),i(u,i(z,z))))). given clause #270: (wt=2) 5951 [hyper,1,3153,1119] P(i(i(x,y),i(i(y,i(z,i(z,u))),i(x,i(z,u))))). given clause #271: (wt=2) 6157 [hyper,1,90,3247] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(u,y),v))))). given clause #272: (wt=2) 6212 [hyper,1,90,3258] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(x,i(i(z,u),v))))). given clause #273: (wt=2) 6299 [hyper,1,90,3259] P(i(i(x,i(i(y,z),y)),i(i(u,v),i(x,i(i(y,u),v))))). given clause #274: (wt=2) 6366 [hyper,1,1452,3265] P(i(i(x,i(i(y,z),u)),i(i(v,z),i(x,i(i(y,v),u))))). given clause #275: (wt=2) 6404 [hyper,1,3265,2150] P(i(i(x,y),i(i(z,x),i(i(n(z),y),y)))). given clause #276: (wt=2) 6468 [hyper,1,1006,3269] P(i(i(x,y),i(i(y,z),i(i(n(y),x),z)))). given clause #277: (wt=2) 6603 [hyper,1,1452,3364] P(i(i(x,i(i(y,z),y)),i(i(u,y),i(x,i(i(y,v),v))))). given clause #278: (wt=2) 6619 [hyper,1,1452,3368] P(i(i(x,i(i(y,y),z)),i(i(u,z),i(x,i(i(z,v),v))))). given clause #279: (wt=2) 6642 [hyper,1,1452,3380] P(i(i(x,i(i(y,z),y)),i(i(y,u),i(x,i(i(v,y),u))))). given clause #280: (wt=2) 6646 [hyper,1,1006,3380] P(i(i(x,y),i(i(i(x,z),x),i(i(u,x),y)))). given clause #281: (wt=2) 6955 [hyper,1,3493,2008] P(i(i(x,y),i(i(x,n(y)),n(x)))). given clause #282: (wt=2) 7020 [hyper,1,1192,3556] P(i(i(x,i(y,z)),i(y,i(n(z),n(x))))). given clause #283: (wt=2) 7104 [hyper,1,3556,941] P(i(x,i(n(y),n(i(x,y))))). given clause #284: (wt=2) 7214 [hyper,1,1192,3701] P(i(i(x,i(y,n(z))),i(z,i(y,n(x))))). given clause #285: (wt=2) 7267 [hyper,1,3701,941] P(i(x,i(y,n(i(y,n(x)))))). given clause #286: (wt=2) 7320 [hyper,1,1192,3708] P(i(i(x,i(y,n(z))),i(y,i(z,n(x))))). given clause #287: (wt=2) 7360 [hyper,1,3708,941] P(i(x,i(y,n(i(x,n(y)))))). given clause #288: (wt=2) 7502 [hyper,1,3766,941] P(i(i(i(i(x,y),y),z),i(i(n(x),z),z))). given clause #289: (wt=2) 7528 [hyper,1,3766,180] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),u),u))). given clause #290: (wt=2) 7560 [hyper,1,1216,3778] P(i(i(x,i(n(y),z)),i(x,i(i(y,u),i(i(z,u),u))))). given clause #291: (wt=2) 7571 [hyper,1,10,3778] P(i(i(i(i(x,y),i(i(z,y),y)),u),i(i(n(x),z),u))). given clause #292: (wt=2) 7595 [hyper,1,3841,981] P(i(i(i(x,y),z),i(i(z,u),i(i(x,u),u)))). given clause #293: (wt=2) 7655 [hyper,1,3265,3857] P(i(i(x,y),i(i(i(z,u),x),i(i(z,y),y)))). given clause #294: (wt=2) 7660 [hyper,1,2937,3857] P(i(i(x,i(i(y,z),u)),i(i(v,x),i(v,i(i(y,u),u))))). given clause #295: (wt=2) 7673 [hyper,1,1677,3857] P(i(i(x,y),i(i(i(z,u),x),i(i(z,x),y)))). given clause #296: (wt=2) 7694 [hyper,1,122,3857] P(i(i(x,y),i(i(i(x,z),u),i(i(y,u),u)))). given clause #297: (wt=2) 7702 [hyper,1,10,3857] P(i(i(i(i(x,y),y),z),i(i(i(x,u),y),z))). given clause #298: (wt=2) 7718 [hyper,1,3857,1201] P(i(i(x,i(i(n(y),x),y)),i(i(n(y),x),y))). given clause #299: (wt=2) 7729 [hyper,1,3857,83] P(i(i(x,i(i(n(x),x),y)),i(i(n(x),x),y))). given clause #300: (wt=2) 7902 [hyper,1,1452,4124] P(i(i(x,i(i(y,z),u)),i(i(u,v),i(x,i(i(y,u),v))))). given clause #301: (wt=2) 8028 [hyper,1,4167,808] P(i(i(i(i(x,y),z),y),i(i(i(x,y),z),z))). given clause #302: (wt=2) 8056 [hyper,1,90,4174] P(i(i(x,i(i(y,z),u)),i(i(y,u),i(x,i(i(u,z),z))))). given clause #303: (wt=2) 8160 [hyper,1,3265,4292] P(i(i(x,y),i(i(i(y,z),x),i(i(z,y),y)))). given clause #304: (wt=2) 8165 [hyper,1,2937,4292] P(i(i(x,i(i(y,z),y)),i(i(u,x),i(u,i(i(z,y),y))))). given clause #305: (wt=2) 8195 [hyper,1,10,4292] P(i(i(i(i(x,y),y),z),i(i(i(y,x),y),z))). given clause #306: (wt=2) 8216 [hyper,1,2576,4304] P(i(i(i(x,y),x),i(i(z,x),i(i(y,z),x)))). given clause #307: (wt=2) 8282 [hyper,1,1452,4334] P(i(i(x,i(i(y,z),u)),i(i(y,u),i(x,i(i(u,v),v))))). given clause #308: (wt=2) 8425 [hyper,1,4381,808] P(i(i(i(i(x,y),z),y),i(i(i(x,y),u),u))). given clause #309: (wt=2) 8505 [hyper,1,3265,4455] P(i(i(x,y),i(i(i(y,z),x),i(i(y,u),y)))). given clause #310: (wt=2) 8510 [hyper,1,2937,4455] P(i(i(x,i(i(y,z),y)),i(i(u,x),i(u,i(i(y,v),y))))). given clause #311: (wt=2) 8519 [hyper,1,1677,4455] P(i(i(x,y),i(i(i(x,z),x),i(i(x,u),y)))). given clause #312: (wt=2) 8543 [hyper,1,10,4455] P(i(i(i(i(x,y),x),z),i(i(i(x,u),x),z))). given clause #313: (wt=2) 8565 [hyper,1,3265,4459] P(i(i(x,y),i(i(i(y,z),x),i(i(u,v),y)))). given clause #314: (wt=2) 8570 [hyper,1,2937,4459] P(i(i(x,i(i(y,z),y)),i(i(u,x),i(u,i(i(v,w),y))))). given clause #315: (wt=2) 8581 [hyper,1,1677,4459] P(i(i(x,y),i(i(i(x,z),x),i(i(u,v),y)))). given clause #316: (wt=2) 8603 [hyper,1,81,4459] P(i(i(x,i(x,y)),i(i(z,u),i(x,y)))). given clause #317: (wt=2) 8605 [hyper,1,10,4459] P(i(i(i(i(x,y),z),u),i(i(i(z,v),z),u))). given clause #318: (wt=2) 8679 [hyper,1,2576,4554] P(i(i(i(x,y),x),i(i(z,x),i(i(u,z),x)))). given clause #319: (wt=2) 8769 [hyper,1,81,4559] P(i(i(x,i(x,y)),i(z,i(x,y)))). given clause #320: (wt=2) 8950 [hyper,1,2576,4754] P(i(i(i(x,x),y),i(i(z,y),i(i(u,z),y)))). given clause #321: (wt=2) 9029 [hyper,1,1006,4782] P(i(i(x,y),i(i(z,y),i(i(n(z),x),y)))). given clause #322: (wt=2) 9070 [hyper,1,2874,4788] P(i(i(i(x,y),z),i(i(u,z),i(i(x,u),z)))). given clause #323: (wt=2) 9082 [hyper,1,1452,4788] P(i(i(x,i(i(y,z),u)),i(i(v,y),i(x,i(i(u,v),y))))). given clause #324: (wt=2) 9089 [hyper,1,1006,4788] P(i(i(x,y),i(i(i(y,z),u),i(i(u,x),y)))). given clause #325: (wt=2) 9255 [hyper,1,1452,4921] P(i(i(x,i(y,n(y))),i(z,i(x,n(y))))). given clause #326: (wt=2) 9260 [hyper,1,1216,4921] P(i(i(x,i(y,n(y))),i(x,i(z,n(y))))). given clause #327: (wt=2) 9288 [hyper,1,1192,4967] P(i(i(x,i(y,i(z,u))),i(i(z,x),i(y,i(z,u))))). given clause #328: (wt=2) 9291 [hyper,1,1006,4967] P(i(i(x,y),i(i(z,i(y,i(x,u))),i(z,i(x,u))))). given clause #329: (wt=2) 9292 [hyper,1,881,4967] P(i(i(x,i(y,z)),i(i(y,x),i(u,i(y,z))))). given clause #330: (wt=2) 9368 [hyper,1,4967,1216] P(i(i(x,i(x,y)),i(i(y,z),i(x,z)))). given clause #331: (wt=2) 9414 [hyper,1,1452,4978] P(i(i(x,i(y,i(z,u))),i(i(y,z),i(x,i(y,u))))). given clause #332: (wt=2) 9457 [hyper,1,4978,1119] P(i(i(i(x,i(x,y)),x),i(i(x,i(x,y)),y))). given clause #333: (wt=2) 9490 [hyper,1,1216,5123] P(i(i(x,i(n(y),y)),i(x,i(i(z,u),i(i(v,z),y))))). given clause #334: (wt=2) 9499 [hyper,1,10,5123] P(i(i(i(i(x,y),i(i(z,x),u)),v),i(i(n(u),u),v))). given clause #335: (wt=2) 9541 [hyper,1,10,5125] P(i(i(i(x,i(i(x,y),z)),u),i(i(n(z),z),u))). given clause #336: (wt=2) 9583 [hyper,1,10,5127] P(i(i(i(x,i(i(y,z),u)),v),i(i(n(u),u),v))). given clause #337: (wt=2) 9706 [hyper,1,5514,10] P(i(i(i(x,y),z),i(i(x,u),i(i(z,u),u)))). given clause #338: (wt=2) 9730 [hyper,1,90,5529] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(u,v),v))))). given clause #339: (wt=2) 9872 [hyper,1,1452,5692] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,u),u))))). given clause #340: (wt=2) 9888 [hyper,1,5692,1006] P(i(i(x,y),i(i(y,i(z,i(x,u))),i(z,i(x,u))))). given clause #341: (wt=2) 10219 [hyper,1,1192,5785] P(i(i(x,i(y,n(x))),i(i(z,y),i(z,n(x))))). given clause #342: (wt=2) 10263 [hyper,1,1192,5789] P(i(i(x,i(y,i(x,z))),i(i(u,y),i(u,i(x,z))))). given clause #343: (wt=2) 10265 [hyper,1,881,5789] P(i(i(x,i(x,y)),i(i(z,u),i(z,i(x,y))))). given clause #344: (wt=2) 10530 [hyper,1,6366,3857] P(i(i(x,y),i(i(i(z,u),y),i(i(z,x),y)))). given clause #345: (wt=2) 10922 [hyper,1,90,6955] P(i(i(x,i(y,n(z))),i(i(y,z),i(x,n(y))))). given clause #346: (wt=2) 11425 [hyper,1,7214,4921] P(i(x,i(y,n(i(x,n(x)))))). given clause #347: (wt=2) 11754 [hyper,1,7320,4921] P(i(x,i(y,n(i(y,n(y)))))). given clause #348: (wt=2) 12107 [hyper,1,1452,7595] P(i(i(x,i(i(y,z),u)),i(i(u,v),i(x,i(i(y,v),v))))). given clause #349: (wt=2) 12139 [hyper,1,7595,5127] P(i(i(i(x,i(i(y,z),u)),v),i(i(n(u),v),v))). given clause #350: (wt=2) 12140 [hyper,1,7595,4978] P(i(i(i(i(x,y),i(x,z)),u),i(i(x,u),u))). given clause #351: (wt=2) 12154 [hyper,1,7595,3857] P(i(i(i(i(x,y),y),z),i(i(i(x,u),z),z))). given clause #352: (wt=2) 12155 [hyper,1,7595,3778] P(i(i(i(i(x,y),i(i(z,y),y)),u),i(i(n(x),u),u))). given clause #353: (wt=2) 12177 [hyper,1,7595,2730] P(i(i(i(i(x,y),i(i(y,z),z)),u),i(i(n(x),u),u))). given clause #354: (wt=2) 12179 [hyper,1,7595,2595] P(i(i(i(i(x,y),i(x,z)),u),i(i(y,u),u))). given clause #355: (wt=2) 12181 [hyper,1,7595,2580] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(z),u),u))). given clause #356: (wt=2) 12189 [hyper,1,7595,2155] P(i(i(i(i(x,y),i(i(z,y),y)),u),i(i(n(z),u),u))). given clause #357: (wt=2) 12190 [hyper,1,7595,1809] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(y),u),u))). given clause #358: (wt=2) 12415 [hyper,1,7702,7702] P(i(i(i(i(x,y),z),y),i(i(i(x,u),y),y))). given clause #359: (wt=2) 12454 [hyper,1,7702,7502] P(i(i(i(i(x,y),z),y),i(i(n(x),y),y))). given clause #360: (wt=2) 12471 [hyper,1,7702,2874] P(i(i(i(i(x,y),z),y),i(i(i(y,u),x),y))). given clause #361: (wt=2) 12473 [hyper,1,7702,2800] P(i(i(i(i(x,y),z),y),i(i(n(y),x),y))). given clause #362: (wt=2) 12477 [hyper,1,7702,2392] P(i(i(i(i(x,y),z),y),i(i(i(u,u),x),y))). given clause #363: (wt=2) 12479 [hyper,1,7702,2369] P(i(i(i(i(x,y),z),y),i(i(i(x,u),x),y))). given clause #364: (wt=2) 12489 [hyper,1,7702,1233] P(i(i(i(i(x,y),z),y),i(i(n(x),x),y))). given clause #365: (wt=2) 12684 [hyper,1,90,8160] P(i(i(x,i(i(y,z),u)),i(i(u,y),i(x,i(i(z,y),y))))). given clause #366: (wt=2) 12777 [hyper,1,1452,8216] P(i(i(x,i(i(y,z),y)),i(i(u,y),i(x,i(i(z,u),y))))). given clause #367: (wt=2) 12898 [hyper,1,90,8505] P(i(i(x,i(i(y,z),u)),i(i(u,y),i(x,i(i(y,v),y))))). given clause #368: (wt=2) 12971 [hyper,1,90,8519] P(i(i(x,i(i(y,z),y)),i(i(y,u),i(x,i(i(y,v),u))))). given clause #369: (wt=2) 13022 [hyper,1,8543,3265] P(i(i(i(x,y),x),i(i(z,u),i(i(x,z),x)))). given clause #370: (wt=2) 13080 [hyper,1,90,8565] P(i(i(x,i(i(y,z),u)),i(i(u,y),i(x,i(i(v,w),y))))). given clause #371: (wt=2) 13172 [hyper,1,90,8581] P(i(i(x,i(i(y,z),y)),i(i(y,u),i(x,i(i(v,w),u))))). given clause #372: (wt=2) 13205 [hyper,1,1452,8603] P(i(i(x,i(y,i(y,z))),i(i(u,v),i(x,i(y,z))))). given clause #373: (wt=2) 13272 [hyper,1,1452,8679] P(i(i(x,i(i(y,z),y)),i(i(u,y),i(x,i(i(v,u),y))))). given clause #374: (wt=2) 13325 [hyper,1,10,8769] P(i(i(i(x,i(y,z)),u),i(i(y,i(y,z)),u))). given clause #375: (wt=2) 13336 [hyper,1,1452,8950] P(i(i(x,i(i(y,y),z)),i(i(u,z),i(x,i(i(v,u),z))))). given clause #376: (wt=2) 13350 [hyper,1,8950,881] P(i(i(x,i(y,i(z,y))),i(i(u,x),i(y,i(z,y))))). given clause #377: (wt=2) 13351 [hyper,1,8950,808] P(i(i(x,i(y,i(z,z))),i(i(u,x),i(y,i(z,z))))). given clause #378: (wt=2) 13411 [hyper,1,1452,9070] P(i(i(x,i(i(y,z),u)),i(i(v,u),i(x,i(i(y,v),u))))). given clause #379: (wt=2) 13620 [hyper,1,1192,9255] P(i(i(x,i(y,n(x))),i(z,i(y,n(x))))). given clause #380: (wt=2) 13679 [hyper,1,1192,9260] P(i(i(x,i(y,n(x))),i(y,i(z,n(x))))). given clause #381: (wt=2) 13725 [hyper,1,81,9288] P(i(i(x,y),i(i(z,i(y,i(z,u))),i(x,i(z,u))))). given clause #382: (wt=2) 13749 [hyper,1,9288,3232] P(i(i(x,i(y,i(x,z))),i(i(z,u),i(x,i(y,u))))). given clause #383: (wt=2) 13759 [hyper,1,9288,1677] P(i(i(x,i(x,i(y,z))),i(i(z,u),i(x,i(y,u))))). given clause #384: (wt=2) 13760 [hyper,1,9288,1660] P(i(i(x,i(y,i(z,u))),i(i(x,z),i(x,i(y,u))))). given clause #385: (wt=2) 13765 [hyper,1,9288,1452] P(i(i(x,i(y,i(x,z))),i(i(u,y),i(x,i(u,z))))). given clause #386: (wt=2) 13801 [hyper,1,9288,90] P(i(i(x,i(x,i(y,z))),i(i(u,y),i(x,i(u,z))))). given clause #387: (wt=2) 13845 [hyper,1,1192,9292] P(i(i(x,i(y,z)),i(i(x,y),i(u,i(x,z))))). given clause #388: (wt=2) 13875 [hyper,1,9292,2008] P(i(i(x,i(y,n(x))),i(z,i(x,n(y))))). given clause #389: (wt=2) 13937 [hyper,1,1452,9368] P(i(i(x,i(y,i(y,z))),i(i(z,u),i(x,i(y,u))))). given clause #390: (wt=2) 13968 [hyper,1,1192,9414] P(i(i(x,i(y,i(z,u))),i(i(x,z),i(y,i(x,u))))). given clause #391: (wt=2) 13970 [hyper,1,1006,9414] P(i(i(x,y),i(i(z,i(x,i(y,u))),i(z,i(x,u))))). given clause #392: (wt=2) 14055 [hyper,1,9490,4754] P(i(i(i(x,x),y),i(i(z,u),i(i(v,z),y)))). given clause #393: (wt=2) 14523 [hyper,1,1680,10263] P(i(i(x,i(i(y,x),z)),i(i(u,y),i(u,i(i(y,x),z))))). given clause #394: (wt=2) 14641 [hyper,1,1192,10922] P(i(i(x,i(y,n(z))),i(i(x,z),i(y,n(x))))). given clause #395: (wt=2) 14654 [hyper,1,10922,4921] P(i(i(x,y),i(i(y,n(y)),n(x)))). given clause #396: (wt=2) 15542 [hyper,1,12898,1630] P(i(i(x,y),i(i(i(x,z),y),i(i(y,u),y)))). given clause #397: (wt=2) 15600 [hyper,1,1452,13022] P(i(i(x,i(i(y,z),y)),i(i(u,v),i(x,i(i(y,u),y))))). given clause #398: (wt=2) 15677 [hyper,1,13080,1630] P(i(i(x,y),i(i(i(x,z),y),i(i(u,v),y)))). given clause #399: (wt=2) 15747 [hyper,1,1192,13205] P(i(i(x,i(y,i(x,z))),i(i(u,v),i(y,i(x,z))))). given clause #400: (wt=2) 15749 [hyper,1,881,13205] P(i(i(x,i(x,y)),i(i(z,u),i(v,i(x,y))))). given clause #401: (wt=2) 15831 [hyper,1,13325,13205] P(i(i(x,i(x,i(x,y))),i(i(z,u),i(v,i(x,y))))). given clause #402: (wt=2) 15832 [hyper,1,13325,10922] P(i(i(x,i(x,n(y))),i(i(x,y),i(z,n(x))))). given clause #403: (wt=2) 15833 [hyper,1,13325,10263] P(i(i(x,i(x,i(y,z))),i(i(u,x),i(u,i(y,z))))). given clause #404: (wt=2) 15834 [hyper,1,13325,10219] P(i(i(x,i(x,n(y))),i(i(z,x),i(z,n(y))))). given clause #405: (wt=2) 15837 [hyper,1,13325,9414] P(i(i(x,i(x,i(y,z))),i(i(x,y),i(u,i(x,z))))). given clause #406: (wt=2) 15838 [hyper,1,13325,9260] P(i(i(x,i(x,n(x))),i(y,i(z,n(x))))). given clause #407: (wt=2) 15840 [hyper,1,13325,7320] P(i(i(x,i(x,n(y))),i(x,i(y,n(z))))). given clause #408: (wt=2) 15842 [hyper,1,13325,7020] P(i(i(x,i(x,y)),i(x,i(n(y),n(z))))). given clause #409: (wt=2) 15846 [hyper,1,13325,4978] P(i(i(x,i(x,y)),i(i(z,x),i(z,y)))). given clause #410: (wt=2) 15847 [hyper,1,13325,4967] P(i(i(x,i(x,i(y,z))),i(i(y,x),i(u,i(y,z))))). given clause #411: (wt=2) 15850 [hyper,1,13325,3708] P(i(i(x,i(x,n(y))),i(z,i(y,n(x))))). given clause #412: (wt=2) 15851 [hyper,1,13325,3701] P(i(i(x,i(x,n(y))),i(y,i(z,n(x))))). given clause #413: (wt=2) 15852 [hyper,1,13325,3556] P(i(i(x,i(x,y)),i(z,i(n(y),n(x))))). given clause #414: (wt=2) 15853 [hyper,1,13325,3493] P(i(i(x,i(x,n(y))),i(i(y,x),i(z,n(y))))). given clause #415: (wt=2) 15857 [hyper,1,13325,3232] P(i(i(x,i(x,y)),i(i(y,z),i(x,i(u,z))))). given clause #416: (wt=2) 15865 [hyper,1,13325,2171] P(i(i(x,i(x,y)),i(i(n(x),y),i(z,y)))). given clause #417: (wt=2) 15870 [hyper,1,13325,1677] P(i(i(x,i(x,y)),i(i(y,z),i(u,i(x,z))))). given clause #418: (wt=2) 15872 [hyper,1,13325,1660] P(i(i(x,i(x,y)),i(i(z,x),i(z,i(u,y))))). given clause #419: (wt=2) 15876 [hyper,1,13325,1452] P(i(i(x,i(x,y)),i(i(z,u),i(x,i(z,y))))). given clause #420: (wt=2) 15878 [hyper,1,13325,1230] P(i(i(x,i(x,y)),i(i(n(x),x),i(z,y)))). given clause #421: (wt=2) 15880 [hyper,1,13325,1006] P(i(i(x,i(x,y)),i(x,i(z,y)))). given clause #422: (wt=2) 15882 [hyper,1,13325,665] P(i(i(x,i(x,y)),i(i(n(y),x),i(z,y)))). given clause #423: (wt=2) 15891 [hyper,1,13325,90] P(i(i(x,i(x,y)),i(i(z,x),i(u,i(z,y))))). given clause #424: (wt=2) 15941 [hyper,1,1192,13350] P(i(i(x,i(y,i(z,x))),i(i(u,y),i(x,i(z,x))))). given clause #425: (wt=2) 15950 [hyper,1,81,13350] P(i(i(x,y),i(i(z,i(y,i(u,x))),i(x,i(u,x))))). given clause #426: (wt=2) 15979 [hyper,1,81,13351] P(i(i(x,y),i(i(z,i(y,i(u,u))),i(x,i(u,u))))). given clause #427: (wt=2) 16120 [hyper,1,13325,13749] P(i(i(x,i(x,i(y,z))),i(i(z,u),i(y,i(x,u))))). given clause #428: (wt=2) 16129 [hyper,1,1192,13749] P(i(i(x,i(y,i(y,z))),i(i(z,u),i(y,i(x,u))))). given clause #429: (wt=2) 16130 [hyper,1,1006,13749] P(i(i(x,y),i(i(z,i(u,i(z,x))),i(z,i(u,y))))). given clause #430: (wt=2) 16142 [hyper,1,1006,13759] P(i(i(x,y),i(i(z,i(z,i(u,x))),i(z,i(u,y))))). given clause #431: (wt=2) 16145 [hyper,1,13325,13760] P(i(i(x,i(x,i(y,z))),i(i(u,y),i(u,i(x,z))))). given clause #432: (wt=2) 16154 [hyper,1,1192,13760] P(i(i(x,i(y,i(z,u))),i(i(y,z),i(y,i(x,u))))). given clause #433: (wt=2) 16155 [hyper,1,1006,13760] P(i(i(x,y),i(i(x,i(z,i(y,u))),i(x,i(z,u))))). given clause #434: (wt=2) 16188 [hyper,1,13325,13765] P(i(i(x,i(x,i(y,z))),i(i(u,x),i(y,i(u,z))))). given clause #435: (wt=2) 16197 [hyper,1,1192,13765] P(i(i(x,i(y,i(y,z))),i(i(u,x),i(y,i(u,z))))). given clause #436: (wt=2) 16198 [hyper,1,1006,13765] P(i(i(x,y),i(i(z,i(y,i(z,u))),i(z,i(x,u))))). given clause #437: (wt=2) 16209 [hyper,1,1006,13801] P(i(i(x,y),i(i(z,i(z,i(y,u))),i(z,i(x,u))))). given clause #438: (wt=2) 16251 [hyper,1,805,13845] P(i(i(x,i(y,z)),i(i(z,x),i(u,i(z,z))))). given clause #439: (wt=2) 16344 [hyper,1,1192,13875] P(i(i(x,i(y,n(y))),i(z,i(y,n(x))))). given clause #440: (wt=2) 16355 [hyper,1,13325,13937] P(i(i(x,i(x,i(x,y))),i(i(y,z),i(u,i(x,z))))). given clause #441: (wt=2) 16368 [hyper,1,1192,13937] P(i(i(x,i(y,i(x,z))),i(i(z,u),i(y,i(x,u))))). given clause #442: (wt=2) 16370 [hyper,1,1006,13937] P(i(i(x,y),i(i(z,i(u,i(u,x))),i(z,i(u,y))))). given clause #443: (wt=2) 16411 [hyper,1,1006,13968] P(i(i(x,y),i(i(x,i(z,i(y,u))),i(z,i(x,u))))). given clause #444: (wt=2) 16464 [hyper,1,1452,14055] P(i(i(x,i(i(y,y),z)),i(i(u,v),i(x,i(i(w,u),z))))). given clause #445: (wt=2) 16583 [hyper,1,13325,14641] P(i(i(x,i(x,n(y))),i(i(z,y),i(x,n(z))))). given clause #446: (wt=2) 16722 [hyper,1,90,14654] P(i(i(x,i(y,n(y))),i(i(z,y),i(x,n(z))))). given clause #447: (wt=2) 16822 [hyper,1,90,15542] P(i(i(x,i(i(y,z),u)),i(i(y,u),i(x,i(i(u,v),u))))). given clause #448: (wt=2) 16831 [hyper,1,15542,1075] P(i(i(i(n(n(x)),y),x),i(i(x,z),x))). given clause #449: (wt=2) 16903 [hyper,1,90,15677] P(i(i(x,i(i(y,z),u)),i(i(y,u),i(x,i(i(v,w),u))))). given clause #450: (wt=2) 16915 [hyper,1,15677,1075] P(i(i(i(n(n(x)),y),x),i(i(z,u),x))). given clause #451: (wt=2) 16943 [hyper,1,1680,15747] P(i(i(x,i(i(y,x),z)),i(i(u,v),i(y,i(i(y,x),z))))). given clause #452: (wt=2) 16986 [hyper,1,805,15749] P(i(i(x,i(y,x)),i(i(z,u),i(v,i(x,x))))). given clause #453: (wt=2) 17024 [hyper,1,13801,15831] P(i(i(x,y),i(i(z,i(z,i(z,u))),i(x,i(z,u))))). given clause #454: (wt=2) 17131 [hyper,1,1006,15837] P(i(i(x,y),i(i(x,i(x,i(y,z))),i(u,i(x,z))))). given clause #455: (wt=2) 17287 [hyper,1,1452,15846] P(i(i(x,i(y,i(y,z))),i(i(u,y),i(x,i(u,z))))). given clause #456: (wt=2) 17317 [hyper,1,1006,15847] P(i(i(x,y),i(i(y,i(y,i(x,z))),i(u,i(x,z))))). given clause #457: (wt=2) 17529 [hyper,1,9288,15857] P(i(i(x,i(x,i(x,y))),i(i(y,z),i(x,i(u,z))))). given clause #458: (wt=2) 17681 [hyper,1,9288,15872] P(i(i(x,i(y,i(y,z))),i(i(x,y),i(x,i(u,z))))). given clause #459: (wt=2) 17731 [hyper,1,9288,15876] P(i(i(x,i(x,i(x,y))),i(i(z,u),i(x,i(z,y))))). given clause #460: (wt=2) 17833 [hyper,1,3265,15880] P(i(i(x,i(y,z)),i(i(y,x),i(y,i(u,z))))). given clause #461: (wt=2) 17879 [hyper,1,10,15880] P(i(i(i(x,i(y,z)),u),i(i(x,i(x,z)),u))). given clause #462: (wt=2) 18005 [hyper,1,1006,15941] P(i(i(x,y),i(i(z,i(y,i(u,z))),i(z,i(u,z))))). given clause #463: (wt=2) 18019 [hyper,1,1006,15950] P(i(i(x,i(y,i(z,u))),i(i(u,y),i(u,i(z,u))))). given clause #464: (wt=2) 18047 [hyper,1,1006,16120] P(i(i(x,y),i(i(z,i(z,i(u,x))),i(u,i(z,y))))). given clause #465: (wt=2) 18076 [hyper,1,1006,16129] P(i(i(x,y),i(i(z,i(u,i(u,x))),i(u,i(z,y))))). given clause #466: (wt=2) 18244 [hyper,1,1006,16145] P(i(i(x,y),i(i(z,i(z,i(y,u))),i(x,i(z,u))))). given clause #467: (wt=2) 18250 [hyper,1,13325,16154] P(i(i(x,i(x,i(y,z))),i(i(x,y),i(x,i(u,z))))). given clause #468: (wt=2) 18264 [hyper,1,1006,16154] P(i(i(x,y),i(i(z,i(x,i(y,u))),i(x,i(z,u))))). given clause #469: (wt=2) 18265 [hyper,1,881,16154] P(i(i(x,i(y,z)),i(i(x,y),i(x,i(u,z))))). given clause #470: (wt=2) 18341 [hyper,1,1006,16188] P(i(i(x,y),i(i(y,i(y,i(z,u))),i(z,i(x,u))))). given clause #471: (wt=2) 18367 [hyper,1,1006,16197] P(i(i(x,y),i(i(y,i(z,i(z,u))),i(z,i(x,u))))). given clause #472: (wt=2) 18370 [hyper,1,81,16197] P(i(i(x,y),i(i(z,i(y,i(x,u))),i(x,i(z,u))))). given clause #473: (wt=2) 18496 [hyper,1,16197,16251] P(i(i(x,i(y,i(z,u))),i(i(u,y),i(x,i(u,u))))). given clause #474: (wt=2) 18499 [hyper,1,13325,16251] P(i(i(x,i(x,y)),i(i(y,z),i(u,i(y,y))))). given clause #475: (wt=2) 18541 [hyper,1,1192,16251] P(i(i(x,i(y,z)),i(i(z,y),i(u,i(z,z))))). given clause #476: (wt=2) 18568 [hyper,1,13325,16344] P(i(i(x,i(x,n(x))),i(y,i(x,n(z))))). given clause #477: (wt=2) 18652 [hyper,1,1006,16355] P(i(i(x,y),i(i(z,i(z,i(z,x))),i(u,i(z,y))))). given clause #478: (wt=2) 18659 [hyper,1,1680,16368] P(i(i(x,i(i(y,x),z)),i(i(z,u),i(y,i(i(y,x),u))))). given clause #479: (wt=2) 18662 [hyper,1,1006,16368] P(i(i(x,y),i(i(z,i(u,i(z,x))),i(u,i(z,y))))). given clause #480: (wt=2) 18875 [hyper,1,13325,16722] P(i(i(x,i(x,n(x))),i(i(y,x),i(z,n(y))))). given clause #481: (wt=2) 18911 [hyper,1,1192,16722] P(i(i(x,i(y,n(x))),i(i(z,x),i(y,n(z))))). given clause #482: (wt=2) 19140 [hyper,1,16197,16986] P(i(i(x,i(y,i(z,y))),i(i(u,v),i(x,i(y,y))))). given clause #483: (wt=2) 19153 [hyper,1,13325,16986] P(i(i(x,i(x,y)),i(i(z,u),i(v,i(y,y))))). given clause #484: (wt=2) 19156 [hyper,1,9368,16986] P(i(i(i(x,i(y,y)),z),i(i(y,i(u,y)),z))). given clause #485: (wt=2) 19168 [hyper,1,1192,16986] P(i(i(x,i(y,y)),i(i(z,u),i(v,i(y,y))))). given clause #486: (wt=2) 19173 [hyper,1,805,16986] P(i(i(x,i(y,z)),i(i(u,v),i(w,i(z,z))))). given clause #487: (wt=2) 19207 [hyper,1,13325,17287] P(i(i(x,i(x,i(x,y))),i(i(z,x),i(u,i(z,y))))). given clause #488: (wt=2) 19220 [hyper,1,1192,17287] P(i(i(x,i(y,i(x,z))),i(i(u,x),i(y,i(u,z))))). given clause #489: (wt=2) 19222 [hyper,1,1006,17287] P(i(i(x,y),i(i(z,i(y,i(y,u))),i(z,i(x,u))))). given clause #490: (wt=2) 19278 [hyper,1,1006,17529] P(i(i(x,y),i(i(z,i(z,i(z,x))),i(z,i(u,y))))). given clause #491: (wt=2) 19280 [hyper,1,13325,17681] P(i(i(x,i(x,i(x,y))),i(i(z,x),i(z,i(u,y))))). given clause #492: (wt=2) 19289 [hyper,1,1192,17681] P(i(i(x,i(y,i(x,z))),i(i(y,x),i(y,i(u,z))))). given clause #493: (wt=2) 19290 [hyper,1,1006,17681] P(i(i(x,y),i(i(x,i(y,i(y,z))),i(x,i(u,z))))). given clause #494: (wt=2) 19307 [hyper,1,1006,17731] P(i(i(x,y),i(i(z,i(z,i(z,u))),i(z,i(x,u))))). given clause #495: (wt=2) 19311 [hyper,1,13325,17833] P(i(i(x,i(x,y)),i(i(x,z),i(x,i(u,y))))). given clause #496: (wt=2) 19314 [hyper,1,9288,17833] P(i(i(x,i(y,i(x,z))),i(i(x,y),i(x,i(u,z))))). given clause #497: (wt=2) 19370 [hyper,1,17833,2008] P(i(i(x,i(y,n(x))),i(x,i(z,n(y))))). given clause #498: (wt=2) 19526 [hyper,1,16915,18005] P(i(i(x,y),i(i(z,i(u,i(v,z))),i(z,i(v,z))))). given clause #499: (wt=2) 19534 [hyper,1,17879,18019] P(i(i(x,i(x,i(y,z))),i(i(z,u),i(z,i(y,z))))). given clause #500: (wt=2) 19718 [hyper,1,1006,18250] P(i(i(x,y),i(i(x,i(x,i(y,z))),i(x,i(u,z))))). given clause #501: (wt=2) 19870 [hyper,1,1006,18370] P(i(i(x,i(y,i(z,u))),i(i(z,y),i(z,i(x,u))))). given clause #502: (wt=2) 20242 [hyper,1,9368,19153] P(i(i(i(x,i(y,y)),z),i(i(u,i(u,y)),z))). given clause #503: (wt=2) 20311 [hyper,1,9368,19168] P(i(i(i(x,i(y,y)),z),i(i(u,i(y,y)),z))). given clause #504: (wt=2) 20333 [hyper,1,9368,19173] P(i(i(i(x,i(y,y)),z),i(i(u,i(v,y)),z))). given clause #505: (wt=2) 20355 [hyper,1,1006,19207] P(i(i(x,y),i(i(y,i(y,i(y,z))),i(u,i(x,z))))). given clause #506: (wt=2) 20365 [hyper,1,1006,19220] P(i(i(x,y),i(i(y,i(z,i(y,u))),i(z,i(x,u))))). given clause #507: (wt=2) 20457 [hyper,1,1006,19280] P(i(i(x,y),i(i(y,i(y,i(y,z))),i(x,i(u,z))))). given clause #508: (wt=2) 20467 [hyper,1,1006,19289] P(i(i(x,y),i(i(y,i(x,i(y,z))),i(x,i(u,z))))). given clause #509: (wt=2) 20507 [hyper,1,13325,19314] P(i(i(x,i(x,i(y,z))),i(i(y,x),i(y,i(u,z))))). given clause #510: (wt=2) 20515 [hyper,1,1192,19314] P(i(i(x,i(y,i(y,z))),i(i(y,x),i(y,i(u,z))))). given clause #511: (wt=2) 20516 [hyper,1,1006,19314] P(i(i(x,y),i(i(x,i(y,i(x,z))),i(x,i(u,z))))). given clause #512: (wt=2) 20519 [hyper,1,17879,19370] P(i(i(x,i(x,n(x))),i(x,i(y,n(z))))). given clause #513: (wt=2) 20548 [hyper,1,1192,19370] P(i(i(x,i(y,n(y))),i(y,i(z,n(x))))). given clause #514: (wt=2) 20576 [hyper,1,13801,19526] P(i(i(x,y),i(i(y,i(z,i(u,y))),i(x,i(u,y))))). given clause #515: (wt=2) 20583 [hyper,1,1006,19534] P(i(i(x,y),i(i(z,i(z,i(u,x))),i(x,i(u,x))))). given clause #516: (wt=2) 20602 [hyper,1,17879,19870] P(i(i(x,i(x,i(y,z))),i(i(y,u),i(y,i(x,z))))). given clause #517: (wt=2) 20611 [hyper,1,1192,19870] P(i(i(x,i(y,i(z,u))),i(i(z,x),i(z,i(y,u))))). given clause #518: (wt=2) 20996 [hyper,1,1006,20507] P(i(i(x,y),i(i(y,i(y,i(x,z))),i(x,i(u,z))))). given clause #519: (wt=2) 21024 [hyper,1,1006,20515] P(i(i(x,y),i(i(y,i(x,i(x,z))),i(x,i(u,z))))). given clause #520: (wt=2) 21218 [hyper,1,1006,20611] P(i(i(x,y),i(i(y,i(z,i(x,u))),i(x,i(z,u))))). given clause #521: (wt=6) 1122 [hyper,1,963,174] P(n(n(i(x,x)))). given clause #522: (wt=8) 520 [hyper,1,519,519] P(i(x,i(y,i(z,z)))). given clause #523: (wt=8) 797 [hyper,1,270,716] P(i(x,i(y,i(z,y)))). given clause #524: (wt=8) 936 [hyper,1,881,808] P(i(x,i(y,i(z,x)))). -------- PROOF -------- 21576 [binary,21575.1,19.1] $ANS(neg_th_10). ----> UNIT CONFLICT at 6.15 sec ----> 21576 [binary,21575.1,19.1] $ANS(neg_th_10). Length of proof is 44. Level of proof is 21. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 936 [hyper,1,881,808] P(i(x,i(y,i(z,x)))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1089 [hyper,1,10,961] P(i(i(i(n(x),y),z),i(i(n(y),x),z))). 1212 [hyper,1,1006,95] P(i(i(i(x,y),z),i(i(x,u),i(i(u,y),z)))). 1216 [hyper,1,1006,10] P(i(i(x,y),i(i(z,x),i(z,y)))). 1280 [hyper,1,1089,626] P(i(i(n(x),y),i(i(x,y),y))). 2155 [hyper,1,1212,1280] P(i(i(n(x),y),i(i(y,z),i(i(x,z),z)))). 3841 [hyper,1,1216,2155] P(i(i(x,i(n(y),z)),i(x,i(i(z,u),i(i(y,u),u))))). 21575 [hyper,1,3841,936] P(i(x,i(i(i(y,x),z),i(i(u,z),z)))). 21576 [binary,21575.1,19.1] $ANS(neg_th_10). ------------ end of proof ------------- given clause #525: (wt=8) 1078 [hyper,1,519,961] P(i(x,i(n(n(y)),y))). given clause #526: (wt=2) 21966 [hyper,1,7595,1078] P(i(i(i(n(n(x)),x),y),i(i(z,y),y))). given clause #527: (wt=8) 1142 [hyper,1,981,763] P(i(n(n(x)),i(y,x))). given clause #528: (wt=8) 1323 [hyper,1,763,1094] P(i(x,i(y,n(n(x))))). given clause #529: (wt=8) 1823 [hyper,1,1236,1236] P(n(n(i(x,n(n(x)))))). given clause #530: (wt=8) 1834 [hyper,1,961,1236] P(i(n(n(n(n(x)))),x)). given clause #531: (wt=8) 1836 [hyper,1,881,1236] P(i(x,n(n(i(y,x))))). given clause #532: (wt=8) 1837 [hyper,1,808,1236] P(i(x,i(y,n(n(y))))). given clause #533: (wt=8) 1845 [hyper,1,519,1236] P(i(x,n(n(i(y,y))))). given clause #534: (wt=8) 1880 [hyper,1,1236,1075] P(n(n(i(n(n(x)),x)))). given clause #535: (wt=8) 1890 [hyper,1,1236,808] P(n(n(i(x,i(y,x))))). given clause #536: (wt=8) 1909 [hyper,1,1236,503] P(n(n(i(x,i(y,y))))). given clause #537: (wt=8) 2140 [hyper,1,1277,1236] P(i(x,n(n(n(n(x)))))). given clause #538: (wt=8) 3736 [hyper,1,2008,1239] P(i(x,n(i(x,n(x))))). given clause #539: (wt=2) 23913 [hyper,1,671,3736] P(n(i(i(x,x),n(i(x,x))))). given clause #540: (wt=8) 21331 [hyper,1,1236,1122] P(n(n(n(n(i(x,x)))))). given clause #541: (wt=9) 518 [hyper,1,12,503] P(i(n(i(x,i(y,y))),z)). given clause #542: (wt=9) 540 [hyper,1,519,105] P(i(x,i(y,i(n(y),z)))). given clause #543: (wt=9) 701 [hyper,1,648,541] P(i(i(n(x),x),i(y,x))). given clause #544: (wt=9) 862 [hyper,1,626,808] P(i(i(i(x,n(y)),y),y)). given clause #545: (wt=9) 880 [hyper,1,12,808] P(i(n(i(x,i(y,x))),z)). given clause #546: (wt=9) 958 [hyper,1,881,12] P(i(x,i(n(i(y,x)),z))). given clause #547: (wt=9) 960 [hyper,1,808,938] P(i(x,i(n(y),i(y,z)))). given clause #548: (wt=9) 1104 [hyper,1,961,12] P(i(n(i(n(n(x)),y)),x)). given clause #549: (wt=9) 1138 [hyper,1,981,961] P(i(n(n(x)),i(n(y),x))). given clause #550: (wt=9) 1140 [hyper,1,981,881] P(i(n(i(x,y)),i(y,z))). given clause #551: (wt=9) 1141 [hyper,1,981,808] P(i(n(x),i(y,i(x,z)))). given clause #552: (wt=9) 1157 [hyper,1,981,174] P(i(n(n(n(i(x,x)))),y)). given clause #553: (wt=9) 1164 [hyper,1,981,102] P(i(n(n(i(n(x),x))),x)). given clause #554: (wt=9) 1255 [hyper,1,105,1075] P(i(x,i(n(n(n(x))),y))). given clause #555: (wt=9) 1260 [hyper,1,12,1075] P(i(n(i(n(n(x)),x)),y)). given clause #556: (wt=9) 1300 [hyper,1,808,1092] P(i(x,i(n(i(y,z)),y))). given clause #557: (wt=9) 1483 [hyper,1,1201,1075] P(i(i(n(x),n(n(x))),x)). given clause #558: (wt=9) 1833 [hyper,1,981,1236] P(i(n(x),n(n(i(x,y))))). given clause #559: (wt=9) 1841 [hyper,1,626,1236] P(i(i(n(n(n(x))),x),x)). given clause #560: (wt=9) 1862 [hyper,1,86,1236] P(i(x,n(n(i(n(x),y))))). given clause #561: (wt=9) 1863 [hyper,1,83,1236] P(i(i(n(x),x),n(n(x)))). given clause #562: (wt=9) 1865 [hyper,1,12,1236] P(i(n(i(x,n(n(x)))),y)). given clause #563: (wt=9) 1878 [hyper,1,1236,1092] P(n(n(i(n(i(x,y)),x)))). given clause #564: (wt=9) 1887 [hyper,1,1236,938] P(n(n(i(n(x),i(x,y))))). given clause #565: (wt=9) 1935 [hyper,1,1236,136] P(n(n(i(n(i(x,x)),y)))). given clause #566: (wt=9) 1952 [hyper,1,1236,12] P(n(n(i(x,i(n(x),y))))). given clause #567: (wt=9) 1953 [hyper,1,1236,11] P(n(n(i(i(n(x),x),x)))). given clause #568: (wt=9) 1969 [hyper,1,105,1239] P(i(x,i(i(x,n(x)),y))). given clause #569: (wt=9) 2064 [hyper,1,1261,1092] P(i(n(n(n(i(x,y)))),x)). given clause #570: (wt=9) 2071 [hyper,1,1261,938] P(i(n(n(n(x))),i(x,y))). given clause #571: (wt=9) 3633 [hyper,1,2005,938] P(i(n(i(x,y)),n(n(x)))). given clause #572: (wt=9) 3687 [hyper,1,2005,11] P(i(n(x),n(i(n(x),x)))). given clause #573: (wt=9) 5046 [hyper,1,2595,938] P(i(i(x,n(x)),i(x,y))). given clause #574: (wt=9) 8758 [hyper,1,981,4559] P(i(n(i(x,y)),i(z,x))). given clause #575: (wt=9) 10031 [hyper,1,5722,1006] P(i(n(i(x,i(y,z))),y)). given clause #576: (wt=10) 517 [hyper,1,90,503] P(i(i(x,y),i(z,i(x,y)))). given clause #577: (wt=10) 550 [hyper,1,86,525] P(i(x,i(y,i(i(z,x),x)))). given clause #578: (wt=10) 567 [hyper,1,526,503] P(i(x,i(i(i(y,y),z),z))). given clause #579: (wt=10) 685 [hyper,1,626,12] P(i(i(i(n(n(x)),y),x),x)). given clause #580: (wt=10) 795 [hyper,1,519,716] P(i(x,i(y,i(i(z,y),y)))). given clause #581: (wt=10) 944 [hyper,1,881,526] P(i(x,i(y,i(i(x,z),z)))). given clause #582: (wt=2) 27701 [hyper,1,1625,944] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(u),y),u))). given clause #583: (wt=10) 959 [hyper,1,881,10] P(i(x,i(i(x,y),i(z,y)))). -------- PROOF -------- 28030 [binary,28029.1,19.1] $ANS(neg_th_10). ----> UNIT CONFLICT at 7.40 sec ----> 28030 [binary,28029.1,19.1] $ANS(neg_th_10). Length of proof is 28. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 19 [] -P(i(p,i(i(i(n(p),p),p),i(i(q,p),p))))|$ANS(neg_th_10). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 959 [hyper,1,881,10] P(i(x,i(i(x,y),i(z,y)))). 28029 [hyper,1,881,959] P(i(x,i(i(i(y,x),z),i(u,z)))). 28030 [binary,28029.1,19.1] $ANS(neg_th_10). ------------ end of proof ------------- given clause #584: (wt=10) 965 [hyper,1,526,938] P(i(x,i(i(i(y,z),y),y))). given clause #585: (wt=10) 980 [hyper,1,12,938] P(i(n(i(n(x),i(x,y))),z)). given clause #586: (wt=10) 984 [hyper,1,881,941] P(i(x,i(i(i(y,x),z),z))). given clause #587: (wt=10) 985 [hyper,1,808,941] P(i(x,i(y,i(i(y,z),z)))). given clause #588: (wt=10) 1015 [hyper,1,941,808] P(i(i(i(x,i(y,x)),z),z)). given clause #589: (wt=10) 1032 [hyper,1,941,503] P(i(i(i(x,i(y,y)),z),z)). given clause #590: (wt=10) 1091 [hyper,1,961,941] P(i(n(i(i(n(x),y),y)),x)). given clause #591: (wt=10) 1123 [hyper,1,981,981] P(i(n(i(x,y)),i(n(x),z))). given clause #592: (wt=10) 1166 [hyper,1,981,86] P(i(n(i(n(x),y)),i(x,z))). given clause #593: (wt=10) 1167 [hyper,1,981,83] P(i(n(x),i(i(n(x),x),y))). given clause #594: (wt=10) 1169 [hyper,1,981,12] P(i(n(x),i(n(i(x,y)),z))). given clause #595: (wt=10) 1172 [hyper,1,881,1006] P(i(i(x,y),i(x,i(z,y)))). given clause #596: (wt=10) 1195 [hyper,1,1006,961] P(i(n(x),i(i(n(y),x),y))). given clause #597: (wt=10) 1197 [hyper,1,1006,763] P(i(x,i(i(n(y),n(x)),y))). given clause #598: (wt=10) 1218 [hyper,1,981,1008] P(i(n(n(x)),i(i(x,y),y))). given clause #599: (wt=10) 1234 [hyper,1,1006,1075] P(i(x,i(n(n(i(x,y))),y))). given clause #600: (wt=10) 1235 [hyper,1,941,1075] P(i(i(i(n(n(x)),x),y),y)). given clause #601: (wt=10) 1242 [hyper,1,526,1075] P(i(x,i(i(y,n(y)),n(y)))). given clause #602: (wt=10) 1318 [hyper,1,12,1092] P(i(n(i(n(i(x,y)),x)),z)). given clause #603: (wt=10) 1322 [hyper,1,808,1094] P(i(x,i(n(i(y,n(z))),z))). given clause #604: (wt=10) 1345 [hyper,1,1006,1119] P(i(x,i(i(x,i(x,y)),y))). given clause #605: (wt=10) 1522 [hyper,1,1201,11] P(i(i(n(x),i(n(x),x)),x)). given clause #606: (wt=10) 1692 [hyper,1,1216,1075] P(i(i(x,n(n(y))),i(x,y))). given clause #607: (wt=10) 1825 [hyper,1,1216,1236] P(i(i(x,y),i(x,n(n(y))))). given clause #608: (wt=10) 1835 [hyper,1,941,1236] P(i(i(i(x,n(n(x))),y),y)). given clause #609: (wt=10) 1877 [hyper,1,1236,1094] P(n(n(i(n(i(x,n(y))),y)))). given clause #610: (wt=10) 1884 [hyper,1,1236,963] P(n(n(i(i(i(x,y),x),x)))). given clause #611: (wt=10) 1886 [hyper,1,1236,941] P(n(n(i(x,i(i(x,y),y))))). given clause #612: (wt=10) 1894 [hyper,1,1236,671] P(n(n(i(i(i(x,x),y),y)))). given clause #613: (wt=10) 1955 [hyper,1,1236,1239] P(n(n(i(i(x,n(x)),n(x))))). given clause #614: (wt=10) 2051 [hyper,1,1261,1239] P(i(n(n(i(x,n(x)))),n(x))). given clause #615: (wt=10) 2063 [hyper,1,1261,1094] P(i(n(n(n(i(x,n(y))))),y)). given clause #616: (wt=10) 2069 [hyper,1,1261,963] P(i(n(n(i(i(x,y),x))),x)). given clause #617: (wt=10) 2075 [hyper,1,1261,671] P(i(n(n(i(i(x,x),y))),y)). -------- PROOF -------- 32258 [binary,32257.1,80.1] $ANS(neg_th_71). ----> UNIT CONFLICT at 8.29 sec ----> 32258 [binary,32257.1,80.1] $ANS(neg_th_71). Length of proof is 43. Level of proof is 20. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 10 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 11 [] P(i(i(n(x),x),x)). 12 [] P(i(x,i(n(x),y))). 80 [] -P(n(i(i(p,p),n(i(q,q)))))|$ANS(neg_th_71). 81 [hyper,1,10,10] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 83 [hyper,1,10,11] P(i(i(x,y),i(i(n(x),x),y))). 86 [hyper,1,10,12] P(i(i(i(n(x),y),z),i(x,z))). 90 [hyper,1,81,81] P(i(i(x,i(y,z)),i(i(u,y),i(x,i(u,z))))). 95 [hyper,1,81,10] P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u)))). 101 [hyper,1,83,12] P(i(i(n(x),x),i(n(x),y))). 105 [hyper,1,81,86] P(i(i(x,n(y)),i(y,i(x,z)))). 110 [hyper,1,86,11] P(i(x,x)). 122 [hyper,1,90,95] P(i(i(x,i(i(y,z),u)),i(i(y,v),i(x,i(i(v,z),u))))). 135 [hyper,1,10,101] P(i(i(i(n(x),y),z),i(i(n(x),x),z))). 136 [hyper,1,12,110] P(i(n(i(x,x)),y)). 151 [hyper,1,122,83] P(i(i(n(x),y),i(i(x,z),i(i(y,x),z)))). 177 [hyper,1,135,151] P(i(i(n(x),x),i(i(x,y),i(i(z,x),y)))). 182 [hyper,1,10,151] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),z),u))). 188 [hyper,1,10,177] P(i(i(i(i(x,y),i(i(z,x),y)),u),i(i(n(x),x),u))). 253 [hyper,1,105,136] P(i(x,i(n(i(y,y)),z))). 292 [hyper,1,10,253] P(i(i(i(n(i(x,x)),y),z),i(u,z))). 503 [hyper,1,292,11] P(i(x,i(y,y))). 519 [hyper,1,10,503] P(i(i(i(x,x),y),i(z,y))). 525 [hyper,1,188,519] P(i(i(n(x),x),i(y,i(i(z,x),x)))). 526 [hyper,1,182,519] P(i(i(n(x),y),i(z,i(i(y,x),x)))). 541 [hyper,1,519,83] P(i(x,i(i(n(y),y),y))). 554 [hyper,1,10,525] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),z),u))). 565 [hyper,1,10,526] P(i(i(i(x,i(i(y,z),z)),u),i(i(n(z),y),u))). 612 [hyper,1,554,11] P(i(i(n(x),x),i(i(y,x),x))). 626 [hyper,1,565,11] P(i(i(n(x),y),i(i(y,x),x))). 649 [hyper,1,86,612] P(i(x,i(i(y,x),x))). 665 [hyper,1,90,626] P(i(i(x,i(y,z)),i(i(n(z),y),i(x,z)))). 671 [hyper,1,626,503] P(i(i(i(x,x),y),y)). 716 [hyper,1,90,649] P(i(i(x,i(y,z)),i(z,i(x,z)))). 763 [hyper,1,665,12] P(i(i(n(x),n(y)),i(y,x))). 808 [hyper,1,716,541] P(i(x,i(y,x))). 881 [hyper,1,10,808] P(i(i(i(x,y),z),i(y,z))). 938 [hyper,1,881,763] P(i(n(x),i(x,y))). 941 [hyper,1,881,626] P(i(x,i(i(x,y),y))). 961 [hyper,1,665,938] P(i(i(n(x),y),i(n(y),x))). 1006 [hyper,1,90,941] P(i(i(x,i(y,z)),i(y,i(x,z)))). 1075 [hyper,1,671,961] P(i(n(n(x)),x)). 1201 [hyper,1,1006,626] P(i(i(x,y),i(i(n(y),x),y))). 1261 [hyper,1,10,1075] P(i(i(x,y),i(n(n(x)),y))). 1511 [hyper,1,1201,136] P(i(i(n(x),n(i(y,y))),x)). 2075 [hyper,1,1261,671] P(i(n(n(i(i(x,x),y))),y)). 32257 [hyper,1,1511,2075] P(n(i(i(x,x),n(i(y,y))))). 32258 [binary,32257.1,80.1] $ANS(neg_th_71). ------------ end of proof ------------- given clause #618: (wt=2) 32257 [hyper,1,1511,2075] P(n(i(i(x,x),n(i(y,y))))). Search stopped by max_given option. Search stopped by max_given option. ============ end of search ============ -------------- statistics ------------- clauses given 618 clauses generated 220845 hyper_res generated 220845 demod & eval rewrites 0 clauses wt,lit,sk delete 112070 tautologies deleted 0 clauses forward subsumed 76607 (subsumed by sos) 47139 unit deletions 0 factor simplifications 0 clauses kept 32160 new demodulators 0 empty clauses 82 clauses back demodulated 0 clauses back subsumed 0 usable size 627 sos size 31545 demodulators size 0 passive size 68 hot size 0 Kbytes malloced 20507 ----------- times (seconds) ----------- user CPU time 8.30 (0 hr, 0 min, 8 sec) system CPU time 0.08 (0 hr, 0 min, 0 sec) wall-clock time 8 (0 hr, 0 min, 8 sec) That finishes the proof of the theorem. Process 8532 finished Mon Aug 2 15:31:04 2004 otter-3.3f/examples/wos/grp_exp3.out0100664000076400007640000002321410103522157017107 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:39 2004 The command was "../../bin/otter". The process ID is 8507. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(eq_units_both_ways). WARNING: set(process_input) flag already set. set(process_input). WARNING: set(index_for_back_demod) flag already set. set(index_for_back_demod). WARNING: set(lrpo) flag already set. set(lrpo). lex([e,f(x,x),g(x)]). assign(pick_given_ratio,3). assign(max_proofs,4). assign(max_mem,12000). assign(max_weight,80). assign(demod_limit,-1). assign(change_limit_after,12). assign(new_max_weight,25). clear(print_kept). clear(print_new_demod). clear(print_back_demod). weight_list(pick_and_purge). weight(EQ(f(e,e),e),2). weight(EQ(f(e,f(x,f(x,f(x,e)))),e),2). weight(EQ(f(f(x,e),f(f(x,e),f(x,e))),e),2). weight(EQ(f(f(x,e),f(f(x,e),f(x,f(f(f(e,f(x,e)),y),f(y,y))))),f(x,e)),2). weight(EQ(f(f(x,y),e),f(x,f(y,f(z,f(z,f(z,e)))))),2). weight(EQ(f(f(x,y),f(e,z)),f(x,f(y,z))),2). weight(EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e),2). weight(EQ(f(x,e),x),2). weight(EQ(f(x,f(f(x,f(f(x,y),f(e,f(f(e,z),f(e,z))))),z)),y),2). weight(EQ(f(x,f(f(x,f(f(x,y),f(e,f(z,z)))),f(f(e,f(f(e,z),u)),f(e,f(u,u))))),y),2). weight(EQ(f(x,f(f(x,f(f(x,y),z)),f(f(e,z),f(e,z)))),y),2). weight(EQ(f(x,f(f(y,z),u)),f(f(x,y),f(f(e,z),u))),2). weight(EQ(f(x,f(x,f(f(x,f(y,f(z,e))),f(f(f(e,e),u),f(u,u))))),f(y,z)),2). weight(EQ(f(x,f(x,f(f(y,z),f(z,z)))),f(x,f(x,f(y,e)))),2). weight(EQ(f(x,f(x,f(x,e))),e),2). weight(EQ(f(x,f(x,f(x,f(y,e)))),y),2). weight(EQ(f(x,f(x,f(x,f(y,f(z,e))))),f(y,z)),2). weight(EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)),2). end_of_list. list(usable). 0 [] EQ(x,x). end_of_list. list(sos). 0 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). end_of_list. list(passive). 1 [] -EQ(f(e,a),a)|$ANS(lid). 2 [] -EQ(f(a,e),a)|$ANS(rid). 3 [] -EQ(f(a,f(a,a)),e)|$ANS(exp3). 4 [] -EQ(f(f(a,b),c),f(a,f(b,c)))|$ANS(assoc). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 5 [] EQ(x,x). ------------> process sos: ** KEPT (pick-wt=17): 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). ---> New Demodulator: 7 [new_demod,6] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). >>>> Starting back demodulation with 7. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=17) 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). given clause #2: (wt=2) 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). given clause #3: (wt=2) 22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). given clause #4: (wt=2) 34 [para_into,22.1.1.1,22.1.1,demod,23] EQ(f(x,f(f(y,z),u)),f(f(x,y),f(f(e,z),u))). given clause #5: (wt=15) 24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). given clause #6: (wt=15) 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). given clause #7: (wt=2) 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). given clause #8: (wt=2) 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). -------- PROOF -------- 155 [binary,153.1,2.1] $ANS(rid). ----> UNIT CONFLICT at 0.01 sec ----> 155 [binary,153.1,2.1] $ANS(rid). Length of proof is 8. Level of proof is 6. ---------------- PROOF ---------------- 2 [] -EQ(f(a,e),a)|$ANS(rid). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 155 [binary,153.1,2.1] $ANS(rid). ------------ end of proof ------------- -------- PROOF -------- 178 [binary,176.1,3.1] $ANS(exp3). ----> UNIT CONFLICT at 0.01 sec ----> 178 [binary,176.1,3.1] $ANS(exp3). Length of proof is 10. Level of proof is 7. ---------------- PROOF ---------------- 3 [] -EQ(f(a,f(a,a)),e)|$ANS(exp3). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 25,24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 141 [para_into,99.1.1.2.2,24.1.1] EQ(f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),y)),e). 154,153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 176 [back_demod,141,demod,154,154,25,154,154,25] EQ(f(x,f(x,x)),e). 178 [binary,176.1,3.1] $ANS(exp3). ------------ end of proof ------------- -------- PROOF -------- 201 [binary,199.1,1.1] $ANS(lid). ----> UNIT CONFLICT at 0.01 sec ----> 201 [binary,199.1,1.1] $ANS(lid). Length of proof is 12. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -EQ(f(e,a),a)|$ANS(lid). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 25,24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 109 [para_from,79.1.1,24.1.1.1.2.2] EQ(f(f(f(x,e),f(f(x,e),x)),f(x,e)),f(x,e)). 141 [para_into,99.1.1.2.2,24.1.1] EQ(f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),y)),e). 154,153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 177,176 [back_demod,141,demod,154,154,25,154,154,25] EQ(f(x,f(x,x)),e). 199 [back_demod,109,demod,154,154,177,154,154] EQ(f(e,x),x). 201 [binary,199.1,1.1] $ANS(lid). ------------ end of proof ------------- -------- PROOF -------- 220 [binary,218.1,4.1] $ANS(assoc). ----> UNIT CONFLICT at 0.02 sec ----> 220 [binary,218.1,4.1] $ANS(assoc). Length of proof is 17. Level of proof is 9. ---------------- PROOF ---------------- 4 [] -EQ(f(f(a,b),c),f(a,f(b,c)))|$ANS(assoc). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 25,24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 28 [back_demod,11,demod,23] EQ(f(x,f(y,f(e,f(e,f(f(z,z),f(z,z)))))),f(f(x,y),z)). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 109 [para_from,79.1.1,24.1.1.1.2.2] EQ(f(f(f(x,e),f(f(x,e),x)),f(x,e)),f(x,e)). 119,118 [para_from,79.1.1,32.1.1.2.2.1.1] EQ(f(x,f(x,f(f(y,z),f(z,z)))),f(x,f(x,f(y,e)))). 130 [back_demod,28,demod,119] EQ(f(x,f(y,f(e,f(e,f(z,e))))),f(f(x,y),z)). 141 [para_into,99.1.1.2.2,24.1.1] EQ(f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),y)),e). 154,153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 177,176 [back_demod,141,demod,154,154,25,154,154,25] EQ(f(x,f(x,x)),e). 185 [back_demod,130,demod,154,flip.1] EQ(f(f(x,y),z),f(x,f(y,f(e,f(e,z))))). 200,199 [back_demod,109,demod,154,154,177,154,154] EQ(f(e,x),x). 218 [back_demod,185,demod,200,200] EQ(f(f(x,y),z),f(x,f(y,z))). 220 [binary,218.1,4.1] $ANS(assoc). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 8 clauses generated 124 para_from generated 49 para_into generated 75 demod & eval rewrites 1119 clauses wt,lit,sk delete 2 tautologies deleted 0 clauses forward subsumed 110 (subsumed by sos) 9 unit deletions 0 factor simplifications 0 clauses kept 115 new demodulators 97 empty clauses 4 clauses back demodulated 101 clauses back subsumed 0 usable size 1 sos size 13 demodulators size 13 passive size 4 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8507 finished Mon Aug 2 15:30:39 2004 otter-3.3f/examples/Loop/0040755000076400007640000000000010012247374014733 5ustar mccunemccuneotter-3.3f/examples/Loop/temp0100644000076400007640000017311110012253620015613 0ustar mccunemccuneStarted otter-ploop Tue Feb 10 15:36:21 CST 2004 on theorem.mcs.anl.gov. Here is the fixed part of the input (file head). ============================ set(auto). assign(max_seconds, 10). assign(max_weight, 50). list(usable). x = x. f(a,b) != f(b,a) | $Ans(commute). end_of_list. % sos to be given on command line ============================ f(f(x,x),f(x,y)) = x. % Job 1 Search stopped because sos empty. clauses kept 4 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,x),f(y,x)) = x. % Job 2 Search stopped because sos empty. clauses kept 5 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(y,y)),f(x,x)) = x. % Job 3 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(y,y),y),f(x,x)) = x. % Job 4 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(x,f(y,z)),f(x,z)) = x. % Job 5 Search stopped by max_seconds option. clauses kept 2499 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(y,z)),f(z,x)) = x. % Job 6 Search stopped by max_seconds option. clauses kept 1196 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(y,z)),f(x,y)) = x. % Job 7 Search stopped by max_seconds option. clauses kept 200 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(x,f(y,z)),f(y,x)) = x. % Job 8 Search stopped by max_seconds option. clauses kept 1170 user CPU time 10.17 (0 hr, 0 min, 10 sec) f(f(f(y,z),x),f(x,z)) = x. % Job 9 Search stopped by max_seconds option. clauses kept 140 user CPU time 10.22 (0 hr, 0 min, 10 sec) f(f(f(y,z),x),f(z,x)) = x. % Job 10 Search stopped by max_seconds option. clauses kept 199 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(f(y,z),x),f(x,y)) = x. % Job 11 Search stopped by max_seconds option. clauses kept 1522 user CPU time 10.14 (0 hr, 0 min, 10 sec) f(f(f(y,z),x),f(y,x)) = x. % Job 12 Search stopped by max_seconds option. clauses kept 2252 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,y))),f(x,z)) = x. % Job 13 Search stopped by max_seconds option. clauses kept 3008 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,y),y)),f(x,z)) = x. % Job 14 Search stopped by max_seconds option. clauses kept 3068 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,y))),f(z,x)) = x. % Job 15 Search stopped because sos empty. clauses kept 10 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(f(y,y),y)),f(z,x)) = x. % Job 16 Search stopped because sos empty. clauses kept 8 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,y)),x),f(x,z)) = x. % Job 17 Search stopped because sos empty. clauses kept 8 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(y,y),y),x),f(x,z)) = x. % Job 18 Search stopped because sos empty. clauses kept 8 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,y)),x),f(z,x)) = x. % Job 19 Search stopped because sos empty. clauses kept 26 user CPU time 0.47 (0 hr, 0 min, 0 sec) f(f(f(f(y,y),y),x),f(z,x)) = x. % Job 20 Search stopped by max_seconds option. clauses kept 358 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,y),y)),f(x,z)) = x. % Job 21 Search stopped because sos empty. clauses kept 9 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(f(x,y),y)),f(z,x)) = x. % Job 22 Search stopped because sos empty. clauses kept 43 user CPU time 1.22 (0 hr, 0 min, 1 sec) f(f(f(f(x,y),z),z),f(x,x)) = x. % Job 23 Search stopped by max_seconds option. clauses kept 367 user CPU time 10.15 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,y))),f(x,z)) = x. % Job 24 Search stopped because sos empty. clauses kept 66 user CPU time 0.22 (0 hr, 0 min, 0 sec) f(f(x,f(f(y,x),y)),f(x,z)) = x. % Job 25 Search stopped by max_seconds option. clauses kept 398 user CPU time 10.28 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,y))),f(z,x)) = x. % Job 26 Search stopped because sos empty. clauses kept 5 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(x,f(f(y,x),y)),f(z,x)) = x. % Job 27 Search stopped because sos empty. clauses kept 45 user CPU time 1.97 (0 hr, 0 min, 1 sec) f(f(x,f(y,f(y,x))),f(x,z)) = x. % Job 28 Search stopped by max_seconds option. clauses kept 315 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),y),x),f(x,z)) = x. % Job 29 Search stopped because sos empty. clauses kept 11 user CPU time 0.03 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(y,x))),f(z,x)) = x. % Job 30 Search stopped by max_seconds option. clauses kept 97 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),y),x),f(z,x)) = x. % Job 31 Search stopped because sos empty. clauses kept 14 user CPU time 0.07 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),z),z),f(x,x)) = x. % Job 32 Search stopped by max_seconds option. clauses kept 2865 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(y,f(f(x,z),y)),f(x,x)) = x. % Job 33 Search stopped because sos empty. clauses kept 21 user CPU time 0.18 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,z)),y),f(x,x)) = x. % Job 34 Search stopped because sos empty. clauses kept 68 user CPU time 2.84 (0 hr, 0 min, 2 sec) f(f(f(y,f(x,y)),x),f(x,z)) = x. % Job 35 Search stopped because sos empty. clauses kept 34 user CPU time 0.35 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),x),f(x,z)) = x. % Job 36 Search stopped because sos empty. clauses kept 13 user CPU time 0.14 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,y)),x),f(z,x)) = x. % Job 37 Search stopped because sos empty. clauses kept 9 user CPU time 0.03 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),x),f(z,x)) = x. % Job 38 Search stopped by max_seconds option. clauses kept 409 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(y,f(f(z,x),y)),f(x,x)) = x. % Job 39 Search stopped because sos empty. clauses kept 11 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(f(y,f(z,x)),y),f(x,x)) = x. % Job 40 Search stopped because sos empty. clauses kept 45 user CPU time 0.35 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,x)),x),f(x,z)) = x. % Job 41 Search stopped because sos empty. clauses kept 13 user CPU time 0.14 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,x)),x),f(z,x)) = x. % Job 42 Search stopped by max_seconds option. clauses kept 299 user CPU time 10.18 (0 hr, 0 min, 10 sec) f(f(y,f(y,f(x,z))),f(x,x)) = x. % Job 43 Search stopped because sos empty. clauses kept 69 user CPU time 5.12 (0 hr, 0 min, 5 sec) f(f(y,f(y,f(z,x))),f(x,x)) = x. % Job 44 Search stopped because sos empty. clauses kept 45 user CPU time 0.50 (0 hr, 0 min, 0 sec) f(f(x,f(f(x,x),y)),f(x,z)) = x. % Job 45 Search stopped because sos empty. clauses kept 6 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(f(x,x),y)),f(z,x)) = x. % Job 46 Search stopped because sos empty. clauses kept 5 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),x),f(x,z)) = x. % Job 47 Search stopped because sos empty. clauses kept 5 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),x),f(z,x)) = x. % Job 48 Search stopped because sos empty. clauses kept 12 user CPU time 0.06 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(x,x))),f(x,z)) = x. % Job 49 Search stopped because sos empty. clauses kept 15 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(x,x))),f(z,x)) = x. % Job 50 Search stopped because sos empty. clauses kept 7 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,x)),x),f(x,z)) = x. % Job 51 Search stopped because sos empty. clauses kept 17 user CPU time 0.08 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,x)),x),f(z,x)) = x. % Job 52 Search stopped because sos empty. clauses kept 17 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(y,y))),f(z,f(z,z))) = x. % Job 53 Search stopped because sos empty. clauses kept 14 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(x,f(f(y,y),y)),f(z,f(z,z))) = x. % Job 54 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(y,y))),f(f(z,z),z)) = x. % Job 55 Search stopped because sos empty. clauses kept 143 user CPU time 6.02 (0 hr, 0 min, 6 sec) f(f(x,f(f(y,y),y)),f(f(z,z),z)) = x. % Job 56 Search stopped because sos empty. clauses kept 4 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,y)),x),f(z,f(z,z))) = x. % Job 57 Search stopped because sos empty. clauses kept 67 user CPU time 0.37 (0 hr, 0 min, 0 sec) f(f(f(f(y,y),y),x),f(z,f(z,z))) = x. % Job 58 Search stopped because sos empty. clauses kept 4 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,y)),x),f(f(z,z),z)) = x. % Job 59 Search stopped by max_seconds option. clauses kept 2987 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(f(y,y),y),x),f(f(z,z),z)) = x. % Job 60 Search stopped because sos empty. clauses kept 3 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(x,y),y),y),f(x,f(z,y))) = x. % Job 61 Search stopped by max_seconds option. clauses kept 248 user CPU time 10.29 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),y),y),f(x,f(y,z))) = x. % Job 62 Search stopped because sos empty. clauses kept 11 user CPU time 0.05 (0 hr, 0 min, 0 sec) f(f(f(f(x,y),y),y),f(f(z,y),x)) = x. % Job 63 Search stopped because sos empty. clauses kept 34 user CPU time 0.53 (0 hr, 0 min, 0 sec) f(f(f(f(x,y),y),y),f(f(y,z),x)) = x. % Job 64 Search stopped because sos empty. clauses kept 7 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,y),y)),f(x,f(z,y))) = x. % Job 65 ----> UNIT CONFLICT at 0.14 sec ----> 573 [binary,572.1,2.1] $Ans(commute). Search stopped by max_proofs option. clauses kept 287 user CPU time 0.16 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,y)),y),f(x,f(z,y))) = x. % Job 66 ----> UNIT CONFLICT at 6.50 sec ----> 2427 [binary,2426.1,2.1] $Ans(commute). Search stopped by max_proofs option. clauses kept 1214 user CPU time 6.51 (0 hr, 0 min, 6 sec) f(f(f(f(y,x),y),y),f(x,f(z,y))) = x. % Job 67 Search stopped because sos empty. clauses kept 23 user CPU time 0.37 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,y),y)),f(x,f(y,z))) = x. % Job 68 Search stopped because sos empty. clauses kept 11 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,y)),y),f(x,f(y,z))) = x. % Job 69 Search stopped because sos empty. clauses kept 28 user CPU time 0.16 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),y),f(x,f(y,z))) = x. % Job 70 Search stopped because sos empty. clauses kept 8 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,y),y)),f(f(z,y),x)) = x. % Job 71 Search stopped because sos empty. clauses kept 30 user CPU time 0.18 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,y)),y),f(f(z,y),x)) = x. % Job 72 Search stopped because sos empty. clauses kept 18 user CPU time 0.13 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),y),f(f(z,y),x)) = x. % Job 73 Search stopped because sos empty. clauses kept 35 user CPU time 0.34 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,y),y)),f(f(y,z),x)) = x. % Job 74 Search stopped because sos empty. clauses kept 15 user CPU time 0.10 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,y)),y),f(f(y,z),x)) = x. % Job 75 Search stopped because sos empty. clauses kept 8 user CPU time 0.03 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),y),f(f(y,z),x)) = x. % Job 76 Search stopped because sos empty. clauses kept 12 user CPU time 0.05 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,y))),f(x,f(z,y))) = x. % Job 77 Search stopped because sos empty. clauses kept 44 user CPU time 1.11 (0 hr, 0 min, 1 sec) f(f(y,f(f(y,x),y)),f(x,f(z,y))) = x. % Job 78 Search stopped by max_seconds option. clauses kept 1643 user CPU time 10.17 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,x)),y),f(x,f(z,y))) = x. % Job 79 Search stopped because sos empty. clauses kept 23 user CPU time 0.37 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,y))),f(x,f(y,z))) = x. % Job 80 Search stopped because sos empty. clauses kept 71 user CPU time 4.50 (0 hr, 0 min, 4 sec) f(f(y,f(f(y,x),y)),f(x,f(y,z))) = x. % Job 81 Search stopped by max_seconds option. clauses kept 155 user CPU time 10.36 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,x)),y),f(x,f(y,z))) = x. % Job 82 Search stopped because sos empty. clauses kept 8 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,y))),f(f(z,y),x)) = x. % Job 83 Search stopped because sos empty. clauses kept 13 user CPU time 0.05 (0 hr, 0 min, 0 sec) f(f(y,f(f(y,x),y)),f(f(z,y),x)) = x. % Job 84 Search stopped because sos empty. clauses kept 17 user CPU time 0.12 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,x)),y),f(f(z,y),x)) = x. % Job 85 Search stopped by max_seconds option. clauses kept 134 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(y,f(y,f(x,y))),f(f(y,z),x)) = x. % Job 86 Search stopped because sos empty. clauses kept 10 user CPU time 0.06 (0 hr, 0 min, 0 sec) f(f(y,f(f(y,x),y)),f(f(y,z),x)) = x. % Job 87 Search stopped because sos empty. clauses kept 15 user CPU time 0.15 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,x)),y),f(f(y,z),x)) = x. % Job 88 Search stopped because sos empty. clauses kept 7 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(y,x))),f(x,f(z,y))) = x. % Job 89 Search stopped because sos empty. clauses kept 25 user CPU time 0.43 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(y,x))),f(x,f(y,z))) = x. % Job 90 Search stopped because sos empty. clauses kept 32 user CPU time 0.29 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(y,x))),f(f(z,y),x)) = x. % Job 91 Search stopped because sos empty. clauses kept 12 user CPU time 0.09 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(y,x))),f(f(y,z),x)) = x. % Job 92 Search stopped by max_seconds option. clauses kept 2296 user CPU time 10.14 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,y),y)),f(z,f(z,z))) = x. % Job 93 Search stopped because sos empty. clauses kept 124 user CPU time 1.67 (0 hr, 0 min, 1 sec) f(f(x,f(f(x,y),y)),f(f(z,z),z)) = x. % Job 94 Search stopped by max_seconds option. clauses kept 2970 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,y))),f(z,f(z,z))) = x. % Job 95 Search stopped by max_seconds option. clauses kept 2581 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,x),y)),f(z,f(z,z))) = x. % Job 96 Search stopped because sos empty. clauses kept 9 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(x,y))),f(f(z,z),z)) = x. % Job 97 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(f(y,x),y)),f(f(z,z),z)) = x. % Job 98 Search stopped by max_seconds option. clauses kept 2150 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,x))),f(z,f(z,z))) = x. % Job 99 Search stopped by max_seconds option. clauses kept 2807 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),y),x),f(z,f(z,z))) = x. % Job 100 Search stopped because sos empty. clauses kept 8 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(y,x))),f(f(z,z),z)) = x. % Job 101 Search stopped because sos empty. clauses kept 6 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(x,y),y),x),f(f(z,z),z)) = x. % Job 102 Search stopped because sos empty. clauses kept 8 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(f(x,y),z),z),f(x,f(y,z))) = x. % Job 103 Search stopped because sos empty. clauses kept 24 user CPU time 0.94 (0 hr, 0 min, 0 sec) f(f(f(f(x,y),z),z),f(x,f(z,y))) = x. % Job 104 Search stopped because sos empty. clauses kept 32 user CPU time 1.59 (0 hr, 0 min, 1 sec) f(f(f(f(x,y),z),z),f(f(y,z),x)) = x. % Job 105 Search stopped because sos empty. clauses kept 53 user CPU time 5.68 (0 hr, 0 min, 5 sec) f(f(f(f(x,y),z),z),f(f(z,y),x)) = x. % Job 106 Search stopped because sos empty. clauses kept 47 user CPU time 3.04 (0 hr, 0 min, 3 sec) f(f(f(y,f(x,y)),x),f(z,f(z,z))) = x. % Job 107 Search stopped because sos empty. clauses kept 4 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),x),f(z,f(z,z))) = x. % Job 108 Search stopped because sos empty. clauses kept 5 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,y)),x),f(f(z,z),z)) = x. % Job 109 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),y),x),f(f(z,z),z)) = x. % Job 110 Search stopped because sos empty. clauses kept 9 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),z),z),f(x,f(y,z))) = x. % Job 111 Search stopped by max_seconds option. clauses kept 266 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),z),z),f(x,f(z,y))) = x. % Job 112 Search stopped because sos empty. clauses kept 64 user CPU time 6.34 (0 hr, 0 min, 6 sec) f(f(f(f(y,x),z),z),f(f(y,z),x)) = x. % Job 113 Search stopped by max_seconds option. clauses kept 411 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),z),z),f(f(z,y),x)) = x. % Job 114 Search stopped because sos empty. clauses kept 35 user CPU time 2.05 (0 hr, 0 min, 2 sec) f(f(f(y,f(y,x)),x),f(z,f(z,z))) = x. % Job 115 Search stopped because sos empty. clauses kept 7 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(y,x)),x),f(f(z,z),z)) = x. % Job 116 Search stopped because sos empty. clauses kept 6 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,z),y)),f(x,f(z,y))) = x. % Job 117 Search stopped because sos empty. clauses kept 30 user CPU time 1.35 (0 hr, 0 min, 1 sec) f(f(f(y,f(x,z)),y),f(x,f(z,y))) = x. % Job 118 Search stopped because sos empty. clauses kept 48 user CPU time 3.84 (0 hr, 0 min, 3 sec) f(f(y,f(f(x,z),y)),f(x,f(y,z))) = x. % Job 119 Search stopped by max_seconds option. clauses kept 464 user CPU time 10.15 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,z)),y),f(x,f(y,z))) = x. % Job 120 Search stopped by max_seconds option. clauses kept 1176 user CPU time 10.18 (0 hr, 0 min, 10 sec) f(f(y,f(f(x,z),y)),f(f(z,y),x)) = x. % Job 121 Search stopped because sos empty. clauses kept 38 user CPU time 3.33 (0 hr, 0 min, 3 sec) f(f(f(y,f(x,z)),y),f(f(z,y),x)) = x. % Job 122 Search stopped because sos empty. clauses kept 54 user CPU time 3.84 (0 hr, 0 min, 3 sec) f(f(y,f(f(x,z),y)),f(f(y,z),x)) = x. % Job 123 Search stopped by max_seconds option. clauses kept 849 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,z)),y),f(f(y,z),x)) = x. % Job 124 Search stopped because sos empty. clauses kept 29 user CPU time 1.02 (0 hr, 0 min, 1 sec) f(f(y,f(f(z,x),y)),f(x,f(z,y))) = x. % Job 125 Search stopped by max_seconds option. clauses kept 110 user CPU time 10.19 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,x)),y),f(x,f(z,y))) = x. % Job 126 Search stopped by max_seconds option. clauses kept 1106 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(y,f(f(z,x),y)),f(x,f(y,z))) = x. % Job 127 Search stopped because sos empty. clauses kept 50 user CPU time 4.20 (0 hr, 0 min, 4 sec) f(f(f(y,f(z,x)),y),f(x,f(y,z))) = x. % Job 128 Search stopped because sos empty. clauses kept 54 user CPU time 5.29 (0 hr, 0 min, 5 sec) f(f(y,f(f(z,x),y)),f(f(z,y),x)) = x. % Job 129 Search stopped because sos empty. clauses kept 68 user CPU time 8.81 (0 hr, 0 min, 8 sec) f(f(f(y,f(z,x)),y),f(f(z,y),x)) = x. % Job 130 Search stopped by max_seconds option. clauses kept 76 user CPU time 10.31 (0 hr, 0 min, 10 sec) f(f(y,f(f(z,x),y)),f(f(y,z),x)) = x. % Job 131 Search stopped because sos empty. clauses kept 29 user CPU time 1.33 (0 hr, 0 min, 1 sec) f(f(f(y,f(z,x)),y),f(f(y,z),x)) = x. % Job 132 Search stopped because sos empty. clauses kept 31 user CPU time 1.35 (0 hr, 0 min, 1 sec) f(f(y,f(y,f(x,z))),f(x,f(z,y))) = x. % Job 133 Search stopped because sos empty. clauses kept 20 user CPU time 0.40 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,z))),f(x,f(y,z))) = x. % Job 134 Search stopped because sos empty. clauses kept 24 user CPU time 0.59 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,z))),f(f(z,y),x)) = x. % Job 135 Search stopped because sos empty. clauses kept 20 user CPU time 0.49 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,z))),f(f(y,z),x)) = x. % Job 136 Search stopped by max_seconds option. clauses kept 1236 user CPU time 10.27 (0 hr, 0 min, 10 sec) f(f(y,f(y,f(z,x))),f(x,f(z,y))) = x. % Job 137 Search stopped by max_seconds option. clauses kept 329 user CPU time 10.16 (0 hr, 0 min, 10 sec) f(f(y,f(y,f(z,x))),f(x,f(y,z))) = x. % Job 138 Search stopped because sos empty. clauses kept 76 user CPU time 3.64 (0 hr, 0 min, 3 sec) f(f(y,f(y,f(z,x))),f(f(z,y),x)) = x. % Job 139 Search stopped because sos empty. clauses kept 45 user CPU time 3.49 (0 hr, 0 min, 3 sec) f(f(y,f(y,f(z,x))),f(f(y,z),x)) = x. % Job 140 Search stopped because sos empty. clauses kept 60 user CPU time 7.10 (0 hr, 0 min, 7 sec) f(f(x,f(f(x,x),y)),f(z,f(z,z))) = x. % Job 141 Search stopped because sos empty. clauses kept 198 user CPU time 2.23 (0 hr, 0 min, 2 sec) f(f(x,f(f(x,x),y)),f(f(z,z),z)) = x. % Job 142 Search stopped because sos empty. clauses kept 87 user CPU time 0.13 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),x),f(z,f(z,z))) = x. % Job 143 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),x),f(f(z,z),z)) = x. % Job 144 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),y),f(x,f(z,y))) = x. % Job 145 Search stopped because sos empty. clauses kept 42 user CPU time 0.26 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),y),f(x,f(y,z))) = x. % Job 146 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),y),f(f(z,y),x)) = x. % Job 147 Search stopped because sos empty. clauses kept 40 user CPU time 0.73 (0 hr, 0 min, 0 sec) f(f(f(f(x,x),y),y),f(f(y,z),x)) = x. % Job 148 Search stopped because sos empty. clauses kept 8 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(x,f(y,f(x,x))),f(z,f(z,z))) = x. % Job 149 Search stopped by max_seconds option. clauses kept 1612 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,x))),f(f(z,z),z)) = x. % Job 150 Search stopped by max_seconds option. clauses kept 1466 user CPU time 10.22 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,x)),x),f(z,f(z,z))) = x. % Job 151 Search stopped because sos empty. clauses kept 4 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,x)),x),f(f(z,z),z)) = x. % Job 152 Search stopped because sos empty. clauses kept 4 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,x),y)),f(x,f(z,y))) = x. % Job 153 Search stopped by max_seconds option. clauses kept 1511 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,x)),y),f(x,f(z,y))) = x. % Job 154 Search stopped because sos empty. clauses kept 35 user CPU time 0.49 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,x),y)),f(x,f(y,z))) = x. % Job 155 Search stopped because sos empty. clauses kept 50 user CPU time 0.73 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,x)),y),f(x,f(y,z))) = x. % Job 156 Search stopped because sos empty. clauses kept 63 user CPU time 1.20 (0 hr, 0 min, 1 sec) f(f(y,f(f(x,x),y)),f(f(z,y),x)) = x. % Job 157 Search stopped because sos empty. clauses kept 12 user CPU time 0.05 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,x)),y),f(f(z,y),x)) = x. % Job 158 Search stopped because sos empty. clauses kept 34 user CPU time 0.62 (0 hr, 0 min, 0 sec) f(f(y,f(f(x,x),y)),f(f(y,z),x)) = x. % Job 159 Search stopped because sos empty. clauses kept 6 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(y,f(x,x)),y),f(f(y,z),x)) = x. % Job 160 Search stopped because sos empty. clauses kept 120 user CPU time 6.32 (0 hr, 0 min, 6 sec) f(f(y,f(y,f(x,x))),f(x,f(z,y))) = x. % Job 161 Search stopped because sos empty. clauses kept 22 user CPU time 0.21 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,x))),f(x,f(y,z))) = x. % Job 162 Search stopped because sos empty. clauses kept 107 user CPU time 8.50 (0 hr, 0 min, 8 sec) f(f(y,f(y,f(x,x))),f(f(z,y),x)) = x. % Job 163 Search stopped because sos empty. clauses kept 18 user CPU time 0.14 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(x,x))),f(f(y,z),x)) = x. % Job 164 Search stopped because sos empty. clauses kept 99 user CPU time 5.71 (0 hr, 0 min, 5 sec) f(f(x,f(y,f(z,z))),f(x,f(u,z))) = x. % Job 165 Search stopped by max_seconds option. clauses kept 2463 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,z))),f(x,f(z,u))) = x. % Job 166 Search stopped by max_seconds option. clauses kept 2813 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,z))),f(f(u,z),x)) = x. % Job 167 Search stopped by max_seconds option. clauses kept 1334 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,z))),f(f(z,u),x)) = x. % Job 168 Search stopped by max_seconds option. clauses kept 1907 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,y),z)),f(x,f(u,y))) = x. % Job 169 Search stopped by max_seconds option. clauses kept 2631 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,y),z)),f(x,f(y,u))) = x. % Job 170 Search stopped because sos empty. clauses kept 14 user CPU time 0.05 (0 hr, 0 min, 0 sec) f(f(x,f(f(y,y),z)),f(f(u,y),x)) = x. % Job 171 Search stopped by max_seconds option. clauses kept 1644 user CPU time 10.19 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,y),z)),f(f(y,u),x)) = x. % Job 172 Search stopped because sos empty. clauses kept 59 user CPU time 3.22 (0 hr, 0 min, 3 sec) f(f(f(y,f(z,z)),x),f(x,f(u,z))) = x. % Job 173 Search stopped by max_seconds option. clauses kept 1911 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,z)),x),f(x,f(z,u))) = x. % Job 174 Search stopped by max_seconds option. clauses kept 333 user CPU time 10.25 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,z)),x),f(f(u,z),x)) = x. % Job 175 Search stopped by max_seconds option. clauses kept 467 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,z)),x),f(f(z,u),x)) = x. % Job 176 Search stopped by max_seconds option. clauses kept 2225 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(f(y,y),z),x),f(x,f(u,y))) = x. % Job 177 Search stopped by max_seconds option. clauses kept 1942 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(f(f(y,y),z),x),f(x,f(y,u))) = x. % Job 178 Search stopped by max_seconds option. clauses kept 1914 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(f(f(y,y),z),x),f(f(u,y),x)) = x. % Job 179 Search stopped by max_seconds option. clauses kept 2433 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(f(y,y),z),x),f(f(y,u),x)) = x. % Job 180 Search stopped by max_seconds option. clauses kept 2122 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,u))),f(x,f(u,z))) = x. % Job 181 Search stopped by max_seconds option. clauses kept 2379 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,u))),f(f(u,z),x)) = x. % Job 182 Search stopped by max_seconds option. clauses kept 1616 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,z))),f(x,f(u,z))) = x. % Job 183 Search stopped by max_seconds option. clauses kept 2170 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,z))),f(x,f(z,u))) = x. % Job 184 Search stopped by max_seconds option. clauses kept 2279 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,z))),f(f(u,z),x)) = x. % Job 185 Search stopped by max_seconds option. clauses kept 1444 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,z))),f(f(z,u),x)) = x. % Job 186 Search stopped by max_seconds option. clauses kept 1889 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),u)),f(x,f(z,y))) = x. % Job 187 Search stopped by max_seconds option. clauses kept 2306 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),u)),f(f(z,y),x)) = x. % Job 188 Search stopped by max_seconds option. clauses kept 1766 user CPU time 10.28 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,y))),f(x,f(u,z))) = x. % Job 189 Search stopped by max_seconds option. clauses kept 2150 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),y)),f(x,f(u,z))) = x. % Job 190 Search stopped by max_seconds option. clauses kept 1971 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,y))),f(x,f(z,u))) = x. % Job 191 Search stopped by max_seconds option. clauses kept 2343 user CPU time 10.10 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),y)),f(x,f(z,u))) = x. % Job 192 Search stopped by max_seconds option. clauses kept 563 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,y))),f(f(u,z),x)) = x. % Job 193 Search stopped by max_seconds option. clauses kept 1818 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),y)),f(f(u,z),x)) = x. % Job 194 Search stopped by max_seconds option. clauses kept 1633 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,y))),f(f(z,u),x)) = x. % Job 195 Search stopped by max_seconds option. clauses kept 1474 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),y)),f(f(z,u),x)) = x. % Job 196 Search stopped by max_seconds option. clauses kept 1384 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),z)),f(x,f(u,y))) = x. % Job 197 Search stopped by max_seconds option. clauses kept 1963 user CPU time 10.21 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),z)),f(x,f(y,u))) = x. % Job 198 Search stopped by max_seconds option. clauses kept 1395 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),z)),f(f(u,y),x)) = x. % Job 199 Search stopped by max_seconds option. clauses kept 1962 user CPU time 10.10 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,z),z)),f(f(y,u),x)) = x. % Job 200 Search stopped by max_seconds option. clauses kept 1622 user CPU time 10.15 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,u)),x),f(x,f(u,z))) = x. % Job 201 Search stopped by max_seconds option. clauses kept 2185 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,u)),x),f(f(u,z),x)) = x. % Job 202 Search stopped by max_seconds option. clauses kept 2519 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,z)),x),f(x,f(u,z))) = x. % Job 203 Search stopped by max_seconds option. clauses kept 932 user CPU time 10.19 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,z)),x),f(x,f(z,u))) = x. % Job 204 Search stopped by max_seconds option. clauses kept 154 user CPU time 10.26 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,z)),x),f(f(u,z),x)) = x. % Job 205 Search stopped by max_seconds option. clauses kept 1470 user CPU time 10.22 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,z)),x),f(f(z,u),x)) = x. % Job 206 Search stopped by max_seconds option. clauses kept 1883 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),u),x),f(x,f(z,y))) = x. % Job 207 Search stopped by max_seconds option. clauses kept 2176 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),u),x),f(f(z,y),x)) = x. % Job 208 Search stopped by max_seconds option. clauses kept 2172 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,y)),x),f(x,f(u,z))) = x. % Job 209 Search stopped by max_seconds option. clauses kept 2359 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),y),x),f(x,f(u,z))) = x. % Job 210 Search stopped by max_seconds option. clauses kept 1966 user CPU time 10.26 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,y)),x),f(x,f(z,u))) = x. % Job 211 Search stopped by max_seconds option. clauses kept 1510 user CPU time 10.12 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),y),x),f(x,f(z,u))) = x. % Job 212 Search stopped by max_seconds option. clauses kept 1765 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,y)),x),f(f(u,z),x)) = x. % Job 213 Search stopped by max_seconds option. clauses kept 1649 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),y),x),f(f(u,z),x)) = x. % Job 214 Search stopped by max_seconds option. clauses kept 2069 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,y)),x),f(f(z,u),x)) = x. % Job 215 Search stopped by max_seconds option. clauses kept 1862 user CPU time 10.23 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),y),x),f(f(z,u),x)) = x. % Job 216 Search stopped by max_seconds option. clauses kept 2104 user CPU time 10.26 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),z),x),f(x,f(u,y))) = x. % Job 217 Search stopped by max_seconds option. clauses kept 2022 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),z),x),f(x,f(y,u))) = x. % Job 218 Search stopped by max_seconds option. clauses kept 1023 user CPU time 10.17 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),z),x),f(f(u,y),x)) = x. % Job 219 Search stopped by max_seconds option. clauses kept 2000 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(f(y,z),z),x),f(f(y,u),x)) = x. % Job 220 Search stopped by max_seconds option. clauses kept 2079 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,y),z)),f(x,f(u,y))) = x. % Job 221 Search stopped by max_seconds option. clauses kept 1639 user CPU time 10.09 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,y),z)),f(x,f(y,u))) = x. % Job 222 Search stopped by max_seconds option. clauses kept 271 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,y),z)),f(f(u,y),x)) = x. % Job 223 Search stopped by max_seconds option. clauses kept 1481 user CPU time 10.09 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,y),z)),f(f(y,u),x)) = x. % Job 224 Search stopped by max_seconds option. clauses kept 180 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,z))),f(x,f(u,z))) = x. % Job 225 Search stopped by max_seconds option. clauses kept 2339 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,z))),f(x,f(z,u))) = x. % Job 226 Search stopped by max_seconds option. clauses kept 1775 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,z))),f(f(u,z),x)) = x. % Job 227 Search stopped by max_seconds option. clauses kept 1188 user CPU time 10.15 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,z))),f(f(z,u),x)) = x. % Job 228 Search stopped by max_seconds option. clauses kept 1566 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,x))),f(x,f(u,z))) = x. % Job 229 Search stopped by max_seconds option. clauses kept 2553 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,x))),f(x,f(z,u))) = x. % Job 230 Search stopped by max_seconds option. clauses kept 1924 user CPU time 10.09 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,x))),f(f(u,z),x)) = x. % Job 231 Search stopped by max_seconds option. clauses kept 588 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(z,x))),f(f(z,u),x)) = x. % Job 232 Search stopped by max_seconds option. clauses kept 116 user CPU time 10.23 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,x),z)),f(x,f(u,y))) = x. % Job 233 Search stopped by max_seconds option. clauses kept 1691 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,x),z)),f(x,f(y,u))) = x. % Job 234 Search stopped by max_seconds option. clauses kept 465 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,x),z)),f(f(u,y),x)) = x. % Job 235 Search stopped by max_seconds option. clauses kept 1439 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,x),z)),f(f(y,u),x)) = x. % Job 236 Search stopped by max_seconds option. clauses kept 1119 user CPU time 10.08 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),z),x),f(x,f(u,y))) = x. % Job 237 Search stopped by max_seconds option. clauses kept 1906 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),z),x),f(x,f(y,u))) = x. % Job 238 Search stopped by max_seconds option. clauses kept 224 user CPU time 10.18 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),z),x),f(f(u,y),x)) = x. % Job 239 Search stopped by max_seconds option. clauses kept 1646 user CPU time 10.18 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),z),x),f(f(y,u),x)) = x. % Job 240 Search stopped by max_seconds option. clauses kept 890 user CPU time 10.17 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,z)),x),f(x,f(u,z))) = x. % Job 241 Search stopped because sos empty. clauses kept 116 user CPU time 8.39 (0 hr, 0 min, 8 sec) f(f(f(y,f(x,z)),x),f(x,f(z,u))) = x. % Job 242 Search stopped by max_seconds option. clauses kept 188 user CPU time 10.16 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,z)),x),f(f(u,z),x)) = x. % Job 243 Search stopped by max_seconds option. clauses kept 1073 user CPU time 10.16 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,z)),x),f(f(z,u),x)) = x. % Job 244 Search stopped by max_seconds option. clauses kept 2370 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,x)),x),f(x,f(u,z))) = x. % Job 245 Search stopped by max_seconds option. clauses kept 1513 user CPU time 10.15 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,x)),x),f(x,f(z,u))) = x. % Job 246 Search stopped by max_seconds option. clauses kept 446 user CPU time 10.18 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,x)),x),f(f(u,z),x)) = x. % Job 247 Search stopped by max_seconds option. clauses kept 1142 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(y,f(z,x)),x),f(f(z,u),x)) = x. % Job 248 Search stopped by max_seconds option. clauses kept 2149 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),z),x),f(x,f(u,y))) = x. % Job 249 Search stopped by max_seconds option. clauses kept 1731 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),z),x),f(x,f(y,u))) = x. % Job 250 Search stopped by max_seconds option. clauses kept 477 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),z),x),f(f(u,y),x)) = x. % Job 251 Search stopped by max_seconds option. clauses kept 1520 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),z),x),f(f(y,u),x)) = x. % Job 252 Search stopped by max_seconds option. clauses kept 2179 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(f(f(y,f(z,z)),z),z),f(x,x)) = x. % Job 253 Search stopped because sos empty. clauses kept 5 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(f(z,f(y,y)),y)),f(x,x)) = x. % Job 254 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(z,f(y,y))),y),f(x,x)) = x. % Job 255 Search stopped because sos empty. clauses kept 4 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(z,f(y,y)))),f(x,x)) = x. % Job 256 Search stopped because sos empty. clauses kept 4 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(f(y,y),z),y),y),f(x,x)) = x. % Job 257 Search stopped because sos empty. clauses kept 3 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(y,f(f(f(y,y),z),y)),f(x,x)) = x. % Job 258 Search stopped because sos empty. clauses kept 4 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(y,f(f(y,y),z)),y),f(x,x)) = x. % Job 259 Search stopped because sos empty. clauses kept 4 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(f(y,y),z))),f(x,x)) = x. % Job 260 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(z,f(z,z)))),f(x,x)) = x. % Job 261 Search stopped because sos empty. clauses kept 11 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(f(z,z),z))),f(x,x)) = x. % Job 262 Search stopped because sos empty. clauses kept 3 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(f(f(y,f(y,z)),z),z),f(x,x)) = x. % Job 263 Search stopped because sos empty. clauses kept 11 user CPU time 0.06 (0 hr, 0 min, 0 sec) f(f(f(f(y,f(z,y)),z),z),f(x,x)) = x. % Job 264 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(f(y,z),y),z),z),f(x,x)) = x. % Job 265 Search stopped because sos empty. clauses kept 6 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(f(z,f(z,z)),y)),f(x,x)) = x. % Job 266 Search stopped because sos empty. clauses kept 21 user CPU time 0.12 (0 hr, 0 min, 0 sec) f(f(y,f(f(f(z,z),z),y)),f(x,x)) = x. % Job 267 Search stopped because sos empty. clauses kept 3 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(z,f(z,z))),y),f(x,x)) = x. % Job 268 Search stopped because sos empty. clauses kept 12 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(y,f(f(z,z),z)),y),f(x,x)) = x. % Job 269 Search stopped because sos empty. clauses kept 4 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(f(z,f(z,y)),y)),f(x,x)) = x. % Job 270 Search stopped because sos empty. clauses kept 11 user CPU time 0.08 (0 hr, 0 min, 0 sec) f(f(f(y,f(z,f(z,y))),y),f(x,x)) = x. % Job 271 Search stopped because sos empty. clauses kept 11 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(f(f(f(y,z),z),y),y),f(x,x)) = x. % Job 272 Search stopped because sos empty. clauses kept 79 user CPU time 3.41 (0 hr, 0 min, 3 sec) f(f(y,f(f(z,f(y,z)),y)),f(x,x)) = x. % Job 273 Search stopped because sos empty. clauses kept 4 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(f(f(z,y),z),y)),f(x,x)) = x. % Job 274 Search stopped because sos empty. clauses kept 10 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(f(y,f(z,f(y,z))),y),f(x,x)) = x. % Job 275 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(f(z,y),z)),y),f(x,x)) = x. % Job 276 Search stopped because sos empty. clauses kept 6 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(z,f(z,y)))),f(x,x)) = x. % Job 277 Search stopped because sos empty. clauses kept 9 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(f(f(y,z),z),y)),f(x,x)) = x. % Job 278 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(y,f(f(y,z),z)),y),f(x,x)) = x. % Job 279 Search stopped because sos empty. clauses kept 6 user CPU time 0.02 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(z,f(y,z)))),f(x,x)) = x. % Job 280 Search stopped because sos empty. clauses kept 4 user CPU time 0.00 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(f(z,y),z))),f(x,x)) = x. % Job 281 Search stopped because sos empty. clauses kept 10 user CPU time 0.04 (0 hr, 0 min, 0 sec) f(f(y,f(y,f(f(y,z),z))),f(x,x)) = x. % Job 282 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(f(f(y,f(y,y)),z),z),f(x,x)) = x. % Job 283 Search stopped because sos empty. clauses kept 12 user CPU time 0.05 (0 hr, 0 min, 0 sec) f(f(f(f(f(y,y),y),z),z),f(x,x)) = x. % Job 284 Search stopped because sos empty. clauses kept 5 user CPU time 0.01 (0 hr, 0 min, 0 sec) f(f(x,f(f(f(y,z),u),u)),f(x,z)) = x. % Job 285 Search stopped by max_seconds option. clauses kept 2249 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),u),u)),f(z,x)) = x. % Job 286 Search stopped by max_seconds option. clauses kept 1994 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),y))),f(x,u)) = x. % Job 287 Search stopped by max_seconds option. clauses kept 2140 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,f(z,u)),y)),f(x,u)) = x. % Job 288 Search stopped by max_seconds option. clauses kept 1936 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),y))),f(u,x)) = x. % Job 289 Search stopped by max_seconds option. clauses kept 1761 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,f(z,u)),y)),f(u,x)) = x. % Job 290 Search stopped by max_seconds option. clauses kept 1561 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),u),u)),f(x,y)) = x. % Job 291 Search stopped by max_seconds option. clauses kept 1534 user CPU time 10.09 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),u),u)),f(y,x)) = x. % Job 292 Search stopped by max_seconds option. clauses kept 1578 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,f(z,u)))),f(x,u)) = x. % Job 293 Search stopped by max_seconds option. clauses kept 2164 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,f(z,u)))),f(u,x)) = x. % Job 294 Search stopped by max_seconds option. clauses kept 1484 user CPU time 10.09 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,f(z,u)))),f(x,z)) = x. % Job 295 Search stopped by max_seconds option. clauses kept 2150 user CPU time 10.14 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(y,f(z,u)))),f(z,x)) = x. % Job 296 Search stopped by max_seconds option. clauses kept 1700 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),y))),f(x,z)) = x. % Job 297 Search stopped by max_seconds option. clauses kept 1982 user CPU time 10.22 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,f(z,u)),y)),f(x,z)) = x. % Job 298 Search stopped by max_seconds option. clauses kept 381 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),y))),f(z,x)) = x. % Job 299 Search stopped by max_seconds option. clauses kept 1543 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(x,f(f(y,f(z,u)),y)),f(z,x)) = x. % Job 300 Search stopped by max_seconds option. clauses kept 1411 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),u),u),x),f(x,z)) = x. % Job 301 Search stopped by max_seconds option. clauses kept 989 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),u),u),x),f(z,x)) = x. % Job 302 Search stopped by max_seconds option. clauses kept 2076 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),y)),x),f(x,u)) = x. % Job 303 Search stopped by max_seconds option. clauses kept 1447 user CPU time 10.11 (0 hr, 0 min, 10 sec) f(f(f(f(y,f(z,u)),y),x),f(x,u)) = x. % Job 304 Search stopped by max_seconds option. clauses kept 1707 user CPU time 10.25 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),y)),x),f(u,x)) = x. % Job 305 Search stopped by max_seconds option. clauses kept 1701 user CPU time 10.01 (0 hr, 0 min, 10 sec) f(f(f(f(y,f(z,u)),y),x),f(u,x)) = x. % Job 306 Search stopped by max_seconds option. clauses kept 2093 user CPU time 10.28 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),u),u),x),f(x,y)) = x. % Job 307 Search stopped by max_seconds option. clauses kept 2289 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),u),u),x),f(y,x)) = x. % Job 308 Search stopped by max_seconds option. clauses kept 2258 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,f(z,u))),x),f(x,u)) = x. % Job 309 Search stopped by max_seconds option. clauses kept 1016 user CPU time 10.17 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,f(z,u))),x),f(u,x)) = x. % Job 310 Search stopped by max_seconds option. clauses kept 1501 user CPU time 10.29 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,f(z,u))),x),f(x,z)) = x. % Job 311 Search stopped by max_seconds option. clauses kept 161 user CPU time 10.26 (0 hr, 0 min, 10 sec) f(f(f(y,f(y,f(z,u))),x),f(z,x)) = x. % Job 312 Search stopped by max_seconds option. clauses kept 1962 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),y)),x),f(x,z)) = x. % Job 313 Search stopped by max_seconds option. clauses kept 1851 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(f(f(y,f(z,u)),y),x),f(x,z)) = x. % Job 314 Search stopped by max_seconds option. clauses kept 1567 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),y)),x),f(z,x)) = x. % Job 315 Search stopped by max_seconds option. clauses kept 1951 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(f(f(y,f(z,u)),y),x),f(z,x)) = x. % Job 316 Search stopped by max_seconds option. clauses kept 1837 user CPU time 10.07 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,f(y,z)),u)),f(x,z)) = x. % Job 317 Search stopped by max_seconds option. clauses kept 1773 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,f(y,z)),u)),f(z,x)) = x. % Job 318 Search stopped by max_seconds option. clauses kept 1405 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,f(y,z)),u)),f(x,y)) = x. % Job 319 Search stopped by max_seconds option. clauses kept 324 user CPU time 10.24 (0 hr, 0 min, 10 sec) f(f(x,f(f(x,f(y,z)),u)),f(y,x)) = x. % Job 320 Search stopped by max_seconds option. clauses kept 461 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,f(z,u)))),f(x,u)) = x. % Job 321 Search stopped by max_seconds option. clauses kept 2338 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,f(z,u)))),f(u,x)) = x. % Job 322 Search stopped by max_seconds option. clauses kept 1205 user CPU time 10.10 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,f(z,u)))),f(x,z)) = x. % Job 323 Search stopped by max_seconds option. clauses kept 700 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(x,f(z,u)))),f(z,x)) = x. % Job 324 Search stopped by max_seconds option. clauses kept 1527 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),x))),f(x,u)) = x. % Job 325 Search stopped by max_seconds option. clauses kept 2568 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),x))),f(u,x)) = x. % Job 326 Search stopped by max_seconds option. clauses kept 570 user CPU time 10.03 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),x),u)),f(x,z)) = x. % Job 327 Search stopped by max_seconds option. clauses kept 1699 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),x),u)),f(z,x)) = x. % Job 328 Search stopped by max_seconds option. clauses kept 1450 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),x))),f(x,z)) = x. % Job 329 Search stopped by max_seconds option. clauses kept 1972 user CPU time 10.00 (0 hr, 0 min, 10 sec) f(f(f(f(x,f(y,z)),u),x),f(x,z)) = x. % Job 330 Search stopped by max_seconds option. clauses kept 1765 user CPU time 10.29 (0 hr, 0 min, 10 sec) f(f(x,f(y,f(f(z,u),x))),f(z,x)) = x. % Job 331 Search stopped because sos empty. clauses kept 104 user CPU time 8.30 (0 hr, 0 min, 8 sec) f(f(f(f(x,f(y,z)),u),x),f(z,x)) = x. % Job 332 Search stopped by max_seconds option. clauses kept 1691 user CPU time 10.15 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),x),u)),f(x,y)) = x. % Job 333 Search stopped by max_seconds option. clauses kept 590 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(x,f(f(f(y,z),x),u)),f(y,x)) = x. % Job 334 Search stopped by max_seconds option. clauses kept 1533 user CPU time 10.06 (0 hr, 0 min, 10 sec) f(f(f(f(x,f(y,z)),u),x),f(x,y)) = x. % Job 335 Search stopped by max_seconds option. clauses kept 318 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(f(f(x,f(y,z)),u),x),f(y,x)) = x. % Job 336 Search stopped by max_seconds option. clauses kept 782 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,f(z,u))),x),f(x,u)) = x. % Job 337 Search stopped because sos empty. clauses kept 94 user CPU time 4.32 (0 hr, 0 min, 4 sec) f(f(f(y,f(x,f(z,u))),x),f(u,x)) = x. % Job 338 Search stopped by max_seconds option. clauses kept 1083 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,f(z,u))),x),f(x,z)) = x. % Job 339 Search stopped by max_seconds option. clauses kept 186 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(f(y,f(x,f(z,u))),x),f(z,x)) = x. % Job 340 Search stopped by max_seconds option. clauses kept 2301 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),x)),x),f(x,u)) = x. % Job 341 Search stopped by max_seconds option. clauses kept 432 user CPU time 10.27 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),x)),x),f(u,x)) = x. % Job 342 Search stopped by max_seconds option. clauses kept 1167 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),x),u),x),f(x,z)) = x. % Job 343 Search stopped by max_seconds option. clauses kept 637 user CPU time 10.13 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),x),u),x),f(z,x)) = x. % Job 344 Search stopped by max_seconds option. clauses kept 1526 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),x)),x),f(x,z)) = x. % Job 345 Search stopped by max_seconds option. clauses kept 1502 user CPU time 10.04 (0 hr, 0 min, 10 sec) f(f(f(y,f(f(z,u),x)),x),f(z,x)) = x. % Job 346 Search stopped by max_seconds option. clauses kept 2168 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),x),u),x),f(x,y)) = x. % Job 347 Search stopped by max_seconds option. clauses kept 1608 user CPU time 10.22 (0 hr, 0 min, 10 sec) f(f(f(f(f(y,z),x),u),x),f(y,x)) = x. % Job 348 Search stopped by max_seconds option. clauses kept 2242 user CPU time 10.02 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),f(x,z)),u),f(x,x)) = x. % Job 349 Search stopped by max_seconds option. clauses kept 154 user CPU time 10.25 (0 hr, 0 min, 10 sec) f(f(f(f(x,y),f(z,x)),u),f(x,x)) = x. % Job 350 Search stopped because sos empty. clauses kept 16 user CPU time 0.15 (0 hr, 0 min, 0 sec) f(f(f(f(y,x),f(x,z)),u),f(x,x)) = x. % Job 351 Search stopped by max_seconds option. clauses kept 1680 user CPU time 10.05 (0 hr, 0 min, 10 sec) f(f(y,f(f(x,z),f(x,u))),f(x,x)) = x. % Job 352 Search stopped by max_seconds option. clauses kept 1743 user CPU time 10.09 (0 hr, 0 min, 10 sec) f(f(f(f(y,x),f(z,x)),u),f(x,x)) = x. % Job 353 Search stopped by max_seconds option. clauses kept 128 user CPU time 10.22 (0 hr, 0 min, 10 sec) f(f(y,f(f(x,z),f(u,x))),f(x,x)) = x. % Job 354 Search stopped because sos empty. clauses kept 24 user CPU time 0.22 (0 hr, 0 min, 0 sec) f(f(y,f(f(z,x),f(x,u))),f(x,x)) = x. % Job 355 Search stopped because sos empty. clauses kept 149 user CPU time 4.83 (0 hr, 0 min, 4 sec) f(f(y,f(f(z,x),f(u,x))),f(x,x)) = x. % Job 356 Search stopped because sos empty. clauses kept 10 user CPU time 0.01 (0 hr, 0 min, 0 sec) Finished otter-ploop Tue Feb 10 16:13:36 CST 2004 on theorem.mcs.anl.gov otter-3.3f/examples/Loop/otter-ploop0100755000076400007640000000157410012247271017145 0ustar mccunemccune#!/usr/local/bin/perl5 -w if ($#ARGV != 0) { die "Need one arg: input file, candidates on stdin.\n"; } $input = $ARGV[0]; if (! -e $input) { die "input $input not found"; } $otter = "../../bin/otter"; if (! -x $otter) { die "binary $otter not found"; } $host=`hostname`; chop($host); $date=`date`; chop($date); print "Started otter-ploop $date on $host.\n"; print "\nHere is the fixed part of the input (file $input).\n"; print "============================\n"; print `cat $input`; print "============================\n"; $i = 0; while ($equation = ) { $i++; chop $equation; $command = "$otter -s '$equation' < $input 2> /dev/null | egrep '(ERROR|UNIT|EMPTY|^Search stopped|user CPU|clauses kept)'"; @output = `$command`; print "\n$equation % Job $i\n"; print @output; } $date=`date`; chop($date); print "\nFinished otter-ploop $date on $host\n"; otter-3.3f/examples/Loop/Sheffer-mgi-without-mirrors0100644000076400007640000003105207303461575022216 0ustar mccunemccunef(f(x,x),f(x,y)) = x. f(f(x,x),f(y,x)) = x. f(f(y,f(y,y)),f(x,x)) = x. f(f(f(y,y),y),f(x,x)) = x. f(f(x,f(y,z)),f(x,z)) = x. f(f(x,f(y,z)),f(z,x)) = x. f(f(x,f(y,z)),f(x,y)) = x. f(f(x,f(y,z)),f(y,x)) = x. f(f(f(y,z),x),f(x,z)) = x. f(f(f(y,z),x),f(z,x)) = x. f(f(f(y,z),x),f(x,y)) = x. f(f(f(y,z),x),f(y,x)) = x. f(f(x,f(y,f(y,y))),f(x,z)) = x. f(f(x,f(f(y,y),y)),f(x,z)) = x. f(f(x,f(y,f(y,y))),f(z,x)) = x. f(f(x,f(f(y,y),y)),f(z,x)) = x. f(f(f(y,f(y,y)),x),f(x,z)) = x. f(f(f(f(y,y),y),x),f(x,z)) = x. f(f(f(y,f(y,y)),x),f(z,x)) = x. f(f(f(f(y,y),y),x),f(z,x)) = x. f(f(x,f(f(x,y),y)),f(x,z)) = x. f(f(x,f(f(x,y),y)),f(z,x)) = x. f(f(f(f(x,y),z),z),f(x,x)) = x. f(f(x,f(y,f(x,y))),f(x,z)) = x. f(f(x,f(f(y,x),y)),f(x,z)) = x. f(f(x,f(y,f(x,y))),f(z,x)) = x. f(f(x,f(f(y,x),y)),f(z,x)) = x. f(f(x,f(y,f(y,x))),f(x,z)) = x. f(f(f(f(x,y),y),x),f(x,z)) = x. f(f(x,f(y,f(y,x))),f(z,x)) = x. f(f(f(f(x,y),y),x),f(z,x)) = x. f(f(f(f(y,x),z),z),f(x,x)) = x. f(f(y,f(f(x,z),y)),f(x,x)) = x. f(f(f(y,f(x,z)),y),f(x,x)) = x. f(f(f(y,f(x,y)),x),f(x,z)) = x. f(f(f(f(y,x),y),x),f(x,z)) = x. f(f(f(y,f(x,y)),x),f(z,x)) = x. f(f(f(f(y,x),y),x),f(z,x)) = x. f(f(y,f(f(z,x),y)),f(x,x)) = x. f(f(f(y,f(z,x)),y),f(x,x)) = x. f(f(f(y,f(y,x)),x),f(x,z)) = x. f(f(f(y,f(y,x)),x),f(z,x)) = x. f(f(y,f(y,f(x,z))),f(x,x)) = x. f(f(y,f(y,f(z,x))),f(x,x)) = x. f(f(x,f(f(x,x),y)),f(x,z)) = x. f(f(x,f(f(x,x),y)),f(z,x)) = x. f(f(f(f(x,x),y),x),f(x,z)) = x. f(f(f(f(x,x),y),x),f(z,x)) = x. f(f(x,f(y,f(x,x))),f(x,z)) = x. f(f(x,f(y,f(x,x))),f(z,x)) = x. f(f(f(y,f(x,x)),x),f(x,z)) = x. f(f(f(y,f(x,x)),x),f(z,x)) = x. f(f(x,f(y,f(y,y))),f(z,f(z,z))) = x. f(f(x,f(f(y,y),y)),f(z,f(z,z))) = x. f(f(x,f(y,f(y,y))),f(f(z,z),z)) = x. f(f(x,f(f(y,y),y)),f(f(z,z),z)) = x. f(f(f(y,f(y,y)),x),f(z,f(z,z))) = x. f(f(f(f(y,y),y),x),f(z,f(z,z))) = x. f(f(f(y,f(y,y)),x),f(f(z,z),z)) = x. f(f(f(f(y,y),y),x),f(f(z,z),z)) = x. f(f(f(f(x,y),y),y),f(x,f(z,y))) = x. f(f(f(f(x,y),y),y),f(x,f(y,z))) = x. f(f(f(f(x,y),y),y),f(f(z,y),x)) = x. f(f(f(f(x,y),y),y),f(f(y,z),x)) = x. f(f(y,f(f(x,y),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,y)),y),f(x,f(z,y))) = x. f(f(f(f(y,x),y),y),f(x,f(z,y))) = x. f(f(y,f(f(x,y),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,y)),y),f(x,f(y,z))) = x. f(f(f(f(y,x),y),y),f(x,f(y,z))) = x. f(f(y,f(f(x,y),y)),f(f(z,y),x)) = x. f(f(f(y,f(x,y)),y),f(f(z,y),x)) = x. f(f(f(f(y,x),y),y),f(f(z,y),x)) = x. f(f(y,f(f(x,y),y)),f(f(y,z),x)) = x. f(f(f(y,f(x,y)),y),f(f(y,z),x)) = x. f(f(f(f(y,x),y),y),f(f(y,z),x)) = x. f(f(y,f(y,f(x,y))),f(x,f(z,y))) = x. f(f(y,f(f(y,x),y)),f(x,f(z,y))) = x. f(f(f(y,f(y,x)),y),f(x,f(z,y))) = x. f(f(y,f(y,f(x,y))),f(x,f(y,z))) = x. f(f(y,f(f(y,x),y)),f(x,f(y,z))) = x. f(f(f(y,f(y,x)),y),f(x,f(y,z))) = x. f(f(y,f(y,f(x,y))),f(f(z,y),x)) = x. f(f(y,f(f(y,x),y)),f(f(z,y),x)) = x. f(f(f(y,f(y,x)),y),f(f(z,y),x)) = x. f(f(y,f(y,f(x,y))),f(f(y,z),x)) = x. f(f(y,f(f(y,x),y)),f(f(y,z),x)) = x. f(f(f(y,f(y,x)),y),f(f(y,z),x)) = x. f(f(y,f(y,f(y,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(y,x))),f(x,f(y,z))) = x. f(f(y,f(y,f(y,x))),f(f(z,y),x)) = x. f(f(y,f(y,f(y,x))),f(f(y,z),x)) = x. f(f(x,f(f(x,y),y)),f(z,f(z,z))) = x. f(f(x,f(f(x,y),y)),f(f(z,z),z)) = x. f(f(x,f(y,f(x,y))),f(z,f(z,z))) = x. f(f(x,f(f(y,x),y)),f(z,f(z,z))) = x. f(f(x,f(y,f(x,y))),f(f(z,z),z)) = x. f(f(x,f(f(y,x),y)),f(f(z,z),z)) = x. f(f(x,f(y,f(y,x))),f(z,f(z,z))) = x. f(f(f(f(x,y),y),x),f(z,f(z,z))) = x. f(f(x,f(y,f(y,x))),f(f(z,z),z)) = x. f(f(f(f(x,y),y),x),f(f(z,z),z)) = x. f(f(f(f(x,y),z),z),f(x,f(y,z))) = x. f(f(f(f(x,y),z),z),f(x,f(z,y))) = x. f(f(f(f(x,y),z),z),f(f(y,z),x)) = x. f(f(f(f(x,y),z),z),f(f(z,y),x)) = x. f(f(f(y,f(x,y)),x),f(z,f(z,z))) = x. f(f(f(f(y,x),y),x),f(z,f(z,z))) = x. f(f(f(y,f(x,y)),x),f(f(z,z),z)) = x. f(f(f(f(y,x),y),x),f(f(z,z),z)) = x. f(f(f(f(y,x),z),z),f(x,f(y,z))) = x. f(f(f(f(y,x),z),z),f(x,f(z,y))) = x. f(f(f(f(y,x),z),z),f(f(y,z),x)) = x. f(f(f(f(y,x),z),z),f(f(z,y),x)) = x. f(f(f(y,f(y,x)),x),f(z,f(z,z))) = x. f(f(f(y,f(y,x)),x),f(f(z,z),z)) = x. f(f(y,f(f(x,z),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,z)),y),f(x,f(z,y))) = x. f(f(y,f(f(x,z),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,z)),y),f(x,f(y,z))) = x. f(f(y,f(f(x,z),y)),f(f(z,y),x)) = x. f(f(f(y,f(x,z)),y),f(f(z,y),x)) = x. f(f(y,f(f(x,z),y)),f(f(y,z),x)) = x. f(f(f(y,f(x,z)),y),f(f(y,z),x)) = x. f(f(y,f(f(z,x),y)),f(x,f(z,y))) = x. f(f(f(y,f(z,x)),y),f(x,f(z,y))) = x. f(f(y,f(f(z,x),y)),f(x,f(y,z))) = x. f(f(f(y,f(z,x)),y),f(x,f(y,z))) = x. f(f(y,f(f(z,x),y)),f(f(z,y),x)) = x. f(f(f(y,f(z,x)),y),f(f(z,y),x)) = x. f(f(y,f(f(z,x),y)),f(f(y,z),x)) = x. f(f(f(y,f(z,x)),y),f(f(y,z),x)) = x. f(f(y,f(y,f(x,z))),f(x,f(z,y))) = x. f(f(y,f(y,f(x,z))),f(x,f(y,z))) = x. f(f(y,f(y,f(x,z))),f(f(z,y),x)) = x. f(f(y,f(y,f(x,z))),f(f(y,z),x)) = x. f(f(y,f(y,f(z,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(z,x))),f(x,f(y,z))) = x. f(f(y,f(y,f(z,x))),f(f(z,y),x)) = x. f(f(y,f(y,f(z,x))),f(f(y,z),x)) = x. f(f(x,f(f(x,x),y)),f(z,f(z,z))) = x. f(f(x,f(f(x,x),y)),f(f(z,z),z)) = x. f(f(f(f(x,x),y),x),f(z,f(z,z))) = x. f(f(f(f(x,x),y),x),f(f(z,z),z)) = x. f(f(f(f(x,x),y),y),f(x,f(z,y))) = x. f(f(f(f(x,x),y),y),f(x,f(y,z))) = x. f(f(f(f(x,x),y),y),f(f(z,y),x)) = x. f(f(f(f(x,x),y),y),f(f(y,z),x)) = x. f(f(x,f(y,f(x,x))),f(z,f(z,z))) = x. f(f(x,f(y,f(x,x))),f(f(z,z),z)) = x. f(f(f(y,f(x,x)),x),f(z,f(z,z))) = x. f(f(f(y,f(x,x)),x),f(f(z,z),z)) = x. f(f(y,f(f(x,x),y)),f(x,f(z,y))) = x. f(f(f(y,f(x,x)),y),f(x,f(z,y))) = x. f(f(y,f(f(x,x),y)),f(x,f(y,z))) = x. f(f(f(y,f(x,x)),y),f(x,f(y,z))) = x. f(f(y,f(f(x,x),y)),f(f(z,y),x)) = x. f(f(f(y,f(x,x)),y),f(f(z,y),x)) = x. f(f(y,f(f(x,x),y)),f(f(y,z),x)) = x. f(f(f(y,f(x,x)),y),f(f(y,z),x)) = x. f(f(y,f(y,f(x,x))),f(x,f(z,y))) = x. f(f(y,f(y,f(x,x))),f(x,f(y,z))) = x. f(f(y,f(y,f(x,x))),f(f(z,y),x)) = x. f(f(y,f(y,f(x,x))),f(f(y,z),x)) = x. f(f(x,f(y,f(z,z))),f(x,f(u,z))) = x. f(f(x,f(y,f(z,z))),f(x,f(z,u))) = x. f(f(x,f(y,f(z,z))),f(f(u,z),x)) = x. f(f(x,f(y,f(z,z))),f(f(z,u),x)) = x. f(f(x,f(f(y,y),z)),f(x,f(u,y))) = x. f(f(x,f(f(y,y),z)),f(x,f(y,u))) = x. f(f(x,f(f(y,y),z)),f(f(u,y),x)) = x. f(f(x,f(f(y,y),z)),f(f(y,u),x)) = x. f(f(f(y,f(z,z)),x),f(x,f(u,z))) = x. f(f(f(y,f(z,z)),x),f(x,f(z,u))) = x. f(f(f(y,f(z,z)),x),f(f(u,z),x)) = x. f(f(f(y,f(z,z)),x),f(f(z,u),x)) = x. f(f(f(f(y,y),z),x),f(x,f(u,y))) = x. f(f(f(f(y,y),z),x),f(x,f(y,u))) = x. f(f(f(f(y,y),z),x),f(f(u,y),x)) = x. f(f(f(f(y,y),z),x),f(f(y,u),x)) = x. f(f(x,f(y,f(z,u))),f(x,f(u,z))) = x. f(f(x,f(y,f(z,u))),f(f(u,z),x)) = x. f(f(x,f(y,f(y,z))),f(x,f(u,z))) = x. f(f(x,f(y,f(y,z))),f(x,f(z,u))) = x. f(f(x,f(y,f(y,z))),f(f(u,z),x)) = x. f(f(x,f(y,f(y,z))),f(f(z,u),x)) = x. f(f(x,f(f(y,z),u)),f(x,f(z,y))) = x. f(f(x,f(f(y,z),u)),f(f(z,y),x)) = x. f(f(x,f(y,f(z,y))),f(x,f(u,z))) = x. f(f(x,f(f(y,z),y)),f(x,f(u,z))) = x. f(f(x,f(y,f(z,y))),f(x,f(z,u))) = x. f(f(x,f(f(y,z),y)),f(x,f(z,u))) = x. f(f(x,f(y,f(z,y))),f(f(u,z),x)) = x. f(f(x,f(f(y,z),y)),f(f(u,z),x)) = x. f(f(x,f(y,f(z,y))),f(f(z,u),x)) = x. f(f(x,f(f(y,z),y)),f(f(z,u),x)) = x. f(f(x,f(f(y,z),z)),f(x,f(u,y))) = x. f(f(x,f(f(y,z),z)),f(x,f(y,u))) = x. f(f(x,f(f(y,z),z)),f(f(u,y),x)) = x. f(f(x,f(f(y,z),z)),f(f(y,u),x)) = x. f(f(f(y,f(z,u)),x),f(x,f(u,z))) = x. f(f(f(y,f(z,u)),x),f(f(u,z),x)) = x. f(f(f(y,f(y,z)),x),f(x,f(u,z))) = x. f(f(f(y,f(y,z)),x),f(x,f(z,u))) = x. f(f(f(y,f(y,z)),x),f(f(u,z),x)) = x. f(f(f(y,f(y,z)),x),f(f(z,u),x)) = x. f(f(f(f(y,z),u),x),f(x,f(z,y))) = x. f(f(f(f(y,z),u),x),f(f(z,y),x)) = x. f(f(f(y,f(z,y)),x),f(x,f(u,z))) = x. f(f(f(f(y,z),y),x),f(x,f(u,z))) = x. f(f(f(y,f(z,y)),x),f(x,f(z,u))) = x. f(f(f(f(y,z),y),x),f(x,f(z,u))) = x. f(f(f(y,f(z,y)),x),f(f(u,z),x)) = x. f(f(f(f(y,z),y),x),f(f(u,z),x)) = x. f(f(f(y,f(z,y)),x),f(f(z,u),x)) = x. f(f(f(f(y,z),y),x),f(f(z,u),x)) = x. f(f(f(f(y,z),z),x),f(x,f(u,y))) = x. f(f(f(f(y,z),z),x),f(x,f(y,u))) = x. f(f(f(f(y,z),z),x),f(f(u,y),x)) = x. f(f(f(f(y,z),z),x),f(f(y,u),x)) = x. f(f(x,f(f(x,y),z)),f(x,f(u,y))) = x. f(f(x,f(f(x,y),z)),f(x,f(y,u))) = x. f(f(x,f(f(x,y),z)),f(f(u,y),x)) = x. f(f(x,f(f(x,y),z)),f(f(y,u),x)) = x. f(f(x,f(y,f(x,z))),f(x,f(u,z))) = x. f(f(x,f(y,f(x,z))),f(x,f(z,u))) = x. f(f(x,f(y,f(x,z))),f(f(u,z),x)) = x. f(f(x,f(y,f(x,z))),f(f(z,u),x)) = x. f(f(x,f(y,f(z,x))),f(x,f(u,z))) = x. f(f(x,f(y,f(z,x))),f(x,f(z,u))) = x. f(f(x,f(y,f(z,x))),f(f(u,z),x)) = x. f(f(x,f(y,f(z,x))),f(f(z,u),x)) = x. f(f(x,f(f(y,x),z)),f(x,f(u,y))) = x. f(f(x,f(f(y,x),z)),f(x,f(y,u))) = x. f(f(x,f(f(y,x),z)),f(f(u,y),x)) = x. f(f(x,f(f(y,x),z)),f(f(y,u),x)) = x. f(f(f(f(x,y),z),x),f(x,f(u,y))) = x. f(f(f(f(x,y),z),x),f(x,f(y,u))) = x. f(f(f(f(x,y),z),x),f(f(u,y),x)) = x. f(f(f(f(x,y),z),x),f(f(y,u),x)) = x. f(f(f(y,f(x,z)),x),f(x,f(u,z))) = x. f(f(f(y,f(x,z)),x),f(x,f(z,u))) = x. f(f(f(y,f(x,z)),x),f(f(u,z),x)) = x. f(f(f(y,f(x,z)),x),f(f(z,u),x)) = x. f(f(f(y,f(z,x)),x),f(x,f(u,z))) = x. f(f(f(y,f(z,x)),x),f(x,f(z,u))) = x. f(f(f(y,f(z,x)),x),f(f(u,z),x)) = x. f(f(f(y,f(z,x)),x),f(f(z,u),x)) = x. f(f(f(f(y,x),z),x),f(x,f(u,y))) = x. f(f(f(f(y,x),z),x),f(x,f(y,u))) = x. f(f(f(f(y,x),z),x),f(f(u,y),x)) = x. f(f(f(f(y,x),z),x),f(f(y,u),x)) = x. f(f(f(f(y,f(z,z)),z),z),f(x,x)) = x. f(f(y,f(f(z,f(y,y)),y)),f(x,x)) = x. f(f(f(y,f(z,f(y,y))),y),f(x,x)) = x. f(f(y,f(y,f(z,f(y,y)))),f(x,x)) = x. f(f(f(f(f(y,y),z),y),y),f(x,x)) = x. f(f(y,f(f(f(y,y),z),y)),f(x,x)) = x. f(f(f(y,f(f(y,y),z)),y),f(x,x)) = x. f(f(y,f(y,f(f(y,y),z))),f(x,x)) = x. f(f(y,f(y,f(z,f(z,z)))),f(x,x)) = x. f(f(y,f(y,f(f(z,z),z))),f(x,x)) = x. f(f(f(f(y,f(y,z)),z),z),f(x,x)) = x. f(f(f(f(y,f(z,y)),z),z),f(x,x)) = x. f(f(f(f(f(y,z),y),z),z),f(x,x)) = x. f(f(y,f(f(z,f(z,z)),y)),f(x,x)) = x. f(f(y,f(f(f(z,z),z),y)),f(x,x)) = x. f(f(f(y,f(z,f(z,z))),y),f(x,x)) = x. f(f(f(y,f(f(z,z),z)),y),f(x,x)) = x. f(f(y,f(f(z,f(z,y)),y)),f(x,x)) = x. f(f(f(y,f(z,f(z,y))),y),f(x,x)) = x. f(f(f(f(f(y,z),z),y),y),f(x,x)) = x. f(f(y,f(f(z,f(y,z)),y)),f(x,x)) = x. f(f(y,f(f(f(z,y),z),y)),f(x,x)) = x. f(f(f(y,f(z,f(y,z))),y),f(x,x)) = x. f(f(f(y,f(f(z,y),z)),y),f(x,x)) = x. f(f(y,f(y,f(z,f(z,y)))),f(x,x)) = x. f(f(y,f(f(f(y,z),z),y)),f(x,x)) = x. f(f(f(y,f(f(y,z),z)),y),f(x,x)) = x. f(f(y,f(y,f(z,f(y,z)))),f(x,x)) = x. f(f(y,f(y,f(f(z,y),z))),f(x,x)) = x. f(f(y,f(y,f(f(y,z),z))),f(x,x)) = x. f(f(f(f(y,f(y,y)),z),z),f(x,x)) = x. f(f(f(f(f(y,y),y),z),z),f(x,x)) = x. f(f(x,f(f(f(y,z),u),u)),f(x,z)) = x. f(f(x,f(f(f(y,z),u),u)),f(z,x)) = x. f(f(x,f(y,f(f(z,u),y))),f(x,u)) = x. f(f(x,f(f(y,f(z,u)),y)),f(x,u)) = x. f(f(x,f(y,f(f(z,u),y))),f(u,x)) = x. f(f(x,f(f(y,f(z,u)),y)),f(u,x)) = x. f(f(x,f(f(f(y,z),u),u)),f(x,y)) = x. f(f(x,f(f(f(y,z),u),u)),f(y,x)) = x. f(f(x,f(y,f(y,f(z,u)))),f(x,u)) = x. f(f(x,f(y,f(y,f(z,u)))),f(u,x)) = x. f(f(x,f(y,f(y,f(z,u)))),f(x,z)) = x. f(f(x,f(y,f(y,f(z,u)))),f(z,x)) = x. f(f(x,f(y,f(f(z,u),y))),f(x,z)) = x. f(f(x,f(f(y,f(z,u)),y)),f(x,z)) = x. f(f(x,f(y,f(f(z,u),y))),f(z,x)) = x. f(f(x,f(f(y,f(z,u)),y)),f(z,x)) = x. f(f(f(f(f(y,z),u),u),x),f(x,z)) = x. f(f(f(f(f(y,z),u),u),x),f(z,x)) = x. f(f(f(y,f(f(z,u),y)),x),f(x,u)) = x. f(f(f(f(y,f(z,u)),y),x),f(x,u)) = x. f(f(f(y,f(f(z,u),y)),x),f(u,x)) = x. f(f(f(f(y,f(z,u)),y),x),f(u,x)) = x. f(f(f(f(f(y,z),u),u),x),f(x,y)) = x. f(f(f(f(f(y,z),u),u),x),f(y,x)) = x. f(f(f(y,f(y,f(z,u))),x),f(x,u)) = x. f(f(f(y,f(y,f(z,u))),x),f(u,x)) = x. f(f(f(y,f(y,f(z,u))),x),f(x,z)) = x. f(f(f(y,f(y,f(z,u))),x),f(z,x)) = x. f(f(f(y,f(f(z,u),y)),x),f(x,z)) = x. f(f(f(f(y,f(z,u)),y),x),f(x,z)) = x. f(f(f(y,f(f(z,u),y)),x),f(z,x)) = x. f(f(f(f(y,f(z,u)),y),x),f(z,x)) = x. f(f(x,f(f(x,f(y,z)),u)),f(x,z)) = x. f(f(x,f(f(x,f(y,z)),u)),f(z,x)) = x. f(f(x,f(f(x,f(y,z)),u)),f(x,y)) = x. f(f(x,f(f(x,f(y,z)),u)),f(y,x)) = x. f(f(x,f(y,f(x,f(z,u)))),f(x,u)) = x. f(f(x,f(y,f(x,f(z,u)))),f(u,x)) = x. f(f(x,f(y,f(x,f(z,u)))),f(x,z)) = x. f(f(x,f(y,f(x,f(z,u)))),f(z,x)) = x. f(f(x,f(y,f(f(z,u),x))),f(x,u)) = x. f(f(x,f(y,f(f(z,u),x))),f(u,x)) = x. f(f(x,f(f(f(y,z),x),u)),f(x,z)) = x. f(f(x,f(f(f(y,z),x),u)),f(z,x)) = x. f(f(x,f(y,f(f(z,u),x))),f(x,z)) = x. f(f(f(f(x,f(y,z)),u),x),f(x,z)) = x. f(f(x,f(y,f(f(z,u),x))),f(z,x)) = x. f(f(f(f(x,f(y,z)),u),x),f(z,x)) = x. f(f(x,f(f(f(y,z),x),u)),f(x,y)) = x. f(f(x,f(f(f(y,z),x),u)),f(y,x)) = x. f(f(f(f(x,f(y,z)),u),x),f(x,y)) = x. f(f(f(f(x,f(y,z)),u),x),f(y,x)) = x. f(f(f(y,f(x,f(z,u))),x),f(x,u)) = x. f(f(f(y,f(x,f(z,u))),x),f(u,x)) = x. f(f(f(y,f(x,f(z,u))),x),f(x,z)) = x. f(f(f(y,f(x,f(z,u))),x),f(z,x)) = x. f(f(f(y,f(f(z,u),x)),x),f(x,u)) = x. f(f(f(y,f(f(z,u),x)),x),f(u,x)) = x. f(f(f(f(f(y,z),x),u),x),f(x,z)) = x. f(f(f(f(f(y,z),x),u),x),f(z,x)) = x. f(f(f(y,f(f(z,u),x)),x),f(x,z)) = x. f(f(f(y,f(f(z,u),x)),x),f(z,x)) = x. f(f(f(f(f(y,z),x),u),x),f(x,y)) = x. f(f(f(f(f(y,z),x),u),x),f(y,x)) = x. f(f(f(f(x,y),f(x,z)),u),f(x,x)) = x. f(f(f(f(x,y),f(z,x)),u),f(x,x)) = x. f(f(f(f(y,x),f(x,z)),u),f(x,x)) = x. f(f(y,f(f(x,z),f(x,u))),f(x,x)) = x. f(f(f(f(y,x),f(z,x)),u),f(x,x)) = x. f(f(y,f(f(x,z),f(u,x))),f(x,x)) = x. f(f(y,f(f(z,x),f(x,u))),f(x,x)) = x. f(f(y,f(f(z,x),f(u,x))),f(x,x)) = x. otter-3.3f/examples/Loop/README0100644000076400007640000000113607303522630015611 0ustar mccunemccuneThis directory contains a Perl program that runs a sequence of Otter jobs. The part of the input that is fixed for all of the jobs is in a file (named "head" in this example). A second file contains candidate clauses , one line for each Otter job (named Sheffer-mgi-without-mirrors in this example). Run it like this: otter-ploop head < Sheffer-mgi-without-mirrors > Sheffer.out This example tries, for 10 seconds each, to prove commutativity from each of the candidates. (You might have to change the reference to the Otter binary in otter-ploop.) The output contains several lines for each job. otter-3.3f/examples/Loop/head0100644000076400007640000000024410012247232015545 0ustar mccunemccuneset(auto). assign(max_seconds, 10). assign(max_weight, 50). list(usable). x = x. f(a,b) != f(b,a) | $Ans(commute). end_of_list. % sos to be given on command line otter-3.3f/examples/ivy/0040755000076400007640000000000010103530360014620 5ustar mccunemccuneotter-3.3f/examples/ivy/group-x2-refute.out0100664000076400007640000001577610103522211020337 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8580. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (= (F (E) V1) V1) NIL) (2 (input) (= (F (G V2) V2) (E)) NIL) (3 (input) (= (F (F V3 V4) V5) (F V3 (F V4 V5))) NIL) (4 (input) (= (F V6 V6) (E)) NIL) (5 (input) (= V7 V7) NIL) (6 (input) (not (= (F (SK1) (SK2)) (F (SK2) (SK1)))) NIL) ) 0 [] F(E,x)=x. 0 [] F(G(x),x)=E. 0 [] F(F(x,y),z)=F(x,F(y,z)). 0 [] F(x,x)=E. 0 [] x=x. 0 [] F(SK1,SK2)!=F(SK2,SK1). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=7): 2 [copy,1,flip.1] F(SK2,SK1)!=F(SK1,SK2). ------------> process sos: ** KEPT (pick-wt=5): 3 [] F(E,x)=x. ---> New Demodulator: 4 [new_demod,3] F(E,x)=x. ** KEPT (pick-wt=6): 5 [] F(G(x),x)=E. ---> New Demodulator: 6 [new_demod,5] F(G(x),x)=E. ** KEPT (pick-wt=11): 7 [] F(F(x,y),z)=F(x,F(y,z)). ---> New Demodulator: 8 [new_demod,7] F(F(x,y),z)=F(x,F(y,z)). ** KEPT (pick-wt=5): 9 [] F(x,x)=E. ---> New Demodulator: 10 [new_demod,9] F(x,x)=E. ** KEPT (pick-wt=3): 11 [] x=x. >>>> Starting back demodulation with 4. >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] x=x. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=5) 3 [] F(E,x)=x. given clause #2: (wt=3) 11 [] x=x. given clause #3: (wt=5) 9 [] F(x,x)=E. given clause #4: (wt=6) 5 [] F(G(x),x)=E. given clause #5: (wt=11) 7 [] F(F(x,y),z)=F(x,F(y,z)). given clause #6: (wt=7) 12 [para_into,7.1.1.1,9.1.1,demod,4,flip.1] F(x,F(x,y))=y. given clause #7: (wt=4) 22 [para_into,12.1.1.2,5.1.1,demod,19] G(x)=x. given clause #8: (wt=5) 18 [para_into,12.1.1.2,9.1.1] F(x,E)=x. given clause #9: (wt=9) 16 [para_into,7.1.1,9.1.1,flip.1] F(x,F(y,F(x,y)))=E. given clause #10: (wt=7) 26 [para_from,16.1.1,12.1.1.2,demod,19,flip.1] F(x,F(y,x))=y. -------- PROOF -------- ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,2.1] $F. Length of proof is 6. Level of proof is 4. ---------------- PROOF ---------------- 1 [] F(SK1,SK2)!=F(SK2,SK1). 2 [copy,1,flip.1] F(SK2,SK1)!=F(SK1,SK2). 4,3 [] F(E,x)=x. 7 [] F(F(x,y),z)=F(x,F(y,z)). 9 [] F(x,x)=E. 12 [para_into,7.1.1.1,9.1.1,demod,4,flip.1] F(x,F(x,y))=y. 16 [para_into,7.1.1,9.1.1,flip.1] F(x,F(y,F(x,y)))=E. 19,18 [para_into,12.1.1.2,9.1.1] F(x,E)=x. 26 [para_from,16.1.1,12.1.1.2,demod,19,flip.1] F(x,F(y,x))=y. 30 [para_from,26.1.1,12.1.1.2] F(x,y)=F(y,x). 31 [binary,30.1,2.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (= (F (E) V1) V1) NIL) (2 (input) (= (F (G V2) V2) (E)) NIL) (3 (input) (= (F (F V3 V4) V5) (F V3 (F V4 V5))) NIL) (4 (input) (= (F V6 V6) (E)) NIL) (5 (input) (= V7 V7) NIL) (6 (input) (not (= (F (SK1) (SK2)) (F (SK2) (SK1)))) NIL) (7 (instantiate 6 ()) (not (= (F (SK1) (SK2)) (F (SK2) (SK1)))) (1)) (8 (flip 7 ()) (not (= (F (SK2) (SK1)) (F (SK1) (SK2)))) (2)) (9 (instantiate 1 ((V1 . v0))) (= (F (E) v0) v0) (3)) (10 (instantiate 3 ((V3 . v0)(V4 . v1)(V5 . v2))) (= (F (F v0 v1) v2) (F v0 (F v1 v2))) (7)) (11 (instantiate 4 ((V6 . v0))) (= (F v0 v0) (E)) (9)) (12 (instantiate 11 ((v0 . v65))) (= (F v65 v65) (E)) NIL) (13 (instantiate 10 ((v0 . v65)(v1 . v65)(v2 . v66))) (= (F (F v65 v65) v66) (F v65 (F v65 v66))) NIL) (14 (paramod 12 (1) 13 (1 1)) (= (F (E) v66) (F v65 (F v65 v66))) NIL) (15 (instantiate 9 ((v0 . v66))) (= (F (E) v66) v66) NIL) (16 (paramod 15 (1) 14 (1)) (= v66 (F v65 (F v65 v66))) NIL) (17 (flip 16 ()) (= (F v65 (F v65 v66)) v66) NIL) (18 (instantiate 17 ((v65 . v0)(v66 . v1))) (= (F v0 (F v0 v1)) v1) (12)) (19 (instantiate 11 ((v0 . (F v64 v65)))) (= (F (F v64 v65) (F v64 v65)) (E)) NIL) (20 (instantiate 10 ((v0 . v64)(v1 . v65)(v2 . (F v64 v65)))) (= (F (F v64 v65) (F v64 v65)) (F v64 (F v65 (F v64 v65)))) NIL) (21 (paramod 19 (1) 20 (1)) (= (E) (F v64 (F v65 (F v64 v65)))) NIL) (22 (flip 21 ()) (= (F v64 (F v65 (F v64 v65))) (E)) NIL) (23 (instantiate 22 ((v64 . v0)(v65 . v1))) (= (F v0 (F v1 (F v0 v1))) (E)) (16)) (24 (instantiate 11 ((v0 . v65))) (= (F v65 v65) (E)) NIL) (25 (instantiate 18 ((v0 . v65)(v1 . v65))) (= (F v65 (F v65 v65)) v65) NIL) (26 (paramod 24 (1) 25 (1 2)) (= (F v65 (E)) v65) NIL) (27 (instantiate 26 ((v65 . v0))) (= (F v0 (E)) v0) (18)) (28 (instantiate 23 ((v0 . v64))) (= (F v64 (F v1 (F v64 v1))) (E)) NIL) (29 (instantiate 18 ((v0 . v64)(v1 . (F v1 (F v64 v1))))) (= (F v64 (F v64 (F v1 (F v64 v1)))) (F v1 (F v64 v1))) NIL) (30 (paramod 28 (1) 29 (1 2)) (= (F v64 (E)) (F v1 (F v64 v1))) NIL) (31 (instantiate 27 ((v0 . v64))) (= (F v64 (E)) v64) NIL) (32 (paramod 31 (1) 30 (1)) (= v64 (F v1 (F v64 v1))) NIL) (33 (flip 32 ()) (= (F v1 (F v64 v1)) v64) NIL) (34 (instantiate 33 ((v1 . v0)(v64 . v1))) (= (F v0 (F v1 v0)) v1) (26)) (35 (instantiate 34 ((v0 . v64))) (= (F v64 (F v1 v64)) v1) NIL) (36 (instantiate 18 ((v0 . v64)(v1 . (F v1 v64)))) (= (F v64 (F v64 (F v1 v64))) (F v1 v64)) NIL) (37 (paramod 35 (1) 36 (1 2)) (= (F v64 v1) (F v1 v64)) NIL) (38 (instantiate 37 ((v64 . v0))) (= (F v0 v1) (F v1 v0)) (30)) (39 (instantiate 38 ((v0 . (SK2))(v1 . (SK1)))) (= (F (SK2) (SK1)) (F (SK1) (SK2))) NIL) (40 (resolve 8 () 39 ()) false (31)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 10 clauses generated 76 clauses kept 16 clauses forward subsumed 71 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8580 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/group-comm.out0100664000076400007640000007660310103522211017445 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8570. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (= (F (E) V1) V1) NIL) (2 (input) (= (F (G V2) V2) (E)) NIL) (3 (input) (= (F (F V3 V4) V5) (F V3 (F V4 V5))) NIL) (4 (input) (= (H V6 V7) (F V6 (F V7 (F (G V6) (G V7))))) NIL) (5 (input) (= (F V8 (F V8 V8)) (E)) NIL) (6 (input) (= V9 V9) NIL) (7 (input) (not (= (H (H (SK1) (SK2)) (SK2)) (E))) NIL) ) 0 [] F(E,x)=x. 0 [] F(G(x),x)=E. 0 [] F(F(x,y),z)=F(x,F(y,z)). 0 [] H(x,y)=F(x,F(y,F(G(x),G(y)))). 0 [] F(x,F(x,x))=E. 0 [] x=x. 0 [] H(H(SK1,SK2),SK2)!=E. end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=7): 1 [] H(H(SK1,SK2),SK2)!=E. ------------> process sos: ** KEPT (pick-wt=5): 2 [] F(E,x)=x. ---> New Demodulator: 3 [new_demod,2] F(E,x)=x. ** KEPT (pick-wt=6): 4 [] F(G(x),x)=E. ---> New Demodulator: 5 [new_demod,4] F(G(x),x)=E. ** KEPT (pick-wt=11): 6 [] F(F(x,y),z)=F(x,F(y,z)). ---> New Demodulator: 7 [new_demod,6] F(F(x,y),z)=F(x,F(y,z)). ** KEPT (pick-wt=13): 8 [] H(x,y)=F(x,F(y,F(G(x),G(y)))). ** KEPT (pick-wt=7): 9 [] F(x,F(x,x))=E. ---> New Demodulator: 10 [new_demod,9] F(x,F(x,x))=E. ** KEPT (pick-wt=3): 11 [] x=x. >>>> Starting back demodulation with 3. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. ** KEPT (pick-wt=13): 12 [copy,8,flip.1] F(x,F(y,F(G(x),G(y))))=H(x,y). >>>> Starting back demodulation with 10. Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] x=x. Following clause subsumed by 8 during input processing: 0 [copy,12,flip.1] H(x,y)=F(x,F(y,F(G(x),G(y)))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=5) 2 [] F(E,x)=x. given clause #2: (wt=3) 11 [] x=x. given clause #3: (wt=6) 4 [] F(G(x),x)=E. given clause #4: (wt=7) 9 [] F(x,F(x,x))=E. given clause #5: (wt=11) 6 [] F(F(x,y),z)=F(x,F(y,z)). given clause #6: (wt=13) 8 [] H(x,y)=F(x,F(y,F(G(x),G(y)))). given clause #7: (wt=8) 15 [para_into,6.1.1.1,4.1.1,demod,3,flip.1] F(G(x),F(x,y))=y. given clause #8: (wt=6) 29 [para_into,15.1.1.2,2.1.1] F(G(E),x)=x. given clause #9: (wt=7) 27 [para_into,15.1.1.2,4.1.1,demod,24] F(G(x),G(x))=x. given clause #10: (wt=5) 35 [back_demod,27,demod,34,34,7,10] F(x,E)=x. given clause #11: (wt=9) 13 [para_into,6.1.1.1,9.1.1,demod,3,7,flip.1] F(x,F(x,F(x,y)))=y. given clause #12: (wt=6) 33 [para_from,27.1.1,15.1.1.2,demod,22,flip.1] G(x)=F(x,x). given clause #13: (wt=13) 17 [para_into,6.1.1,9.1.1,demod,7,flip.1] F(x,F(y,F(x,F(y,F(x,y)))))=E. given clause #14: (wt=13) 46 [para_from,17.1.1,13.1.1.2.2,demod,36,flip.1] F(x,F(y,F(x,F(y,x))))=F(y,y). given clause #15: (wt=15) 41 [back_demod,12,demod,34,34,7,flip.1] H(x,y)=F(x,F(y,F(x,F(x,F(y,y))))). given clause #16: (wt=25) 43 [back_demod,40,demod,42,42,42,7,7,7,7,7,10,36,7,7,7,7,7,7,7,7,7,7,14,14] F(SK1,F(SK2,F(SK2,F(SK1,F(SK1,F(SK2,F(SK2,F(SK1,F(SK2,F(SK1,F(SK1,SK2)))))))))))!=E. given clause #17: (wt=15) 50 [para_from,46.1.1,13.1.1.2.2] F(x,F(x,F(y,y)))=F(y,F(x,F(y,x))). given clause #18: (wt=15) 53 [copy,50,flip.1] F(x,F(y,F(x,y)))=F(y,F(y,F(x,x))). given clause #19: (wt=17) 51 [para_from,46.1.1,6.1.1.1,demod,7,7,7,7,flip.1] F(x,F(y,F(x,F(y,F(x,z)))))=F(y,F(y,z)). given clause #20: (wt=17) 64 [para_from,53.1.1,13.1.1.2.2] F(x,F(x,F(y,F(y,F(x,x)))))=F(y,F(x,y)). given clause #21: (wt=21) 48 [para_into,46.1.1.2.2.2,6.1.1,demod,7,7] F(x,F(y,F(z,F(x,F(y,F(z,x))))))=F(y,F(z,F(y,z))). given clause #22: (wt=17) 65 [copy,64,flip.1] F(x,F(y,x))=F(y,F(y,F(x,F(x,F(y,y))))). given clause #23: (wt=19) 58 [para_from,50.1.1,6.1.1.1,demod,7,7,7,7,7] F(x,F(y,F(x,F(y,z))))=F(y,F(y,F(x,F(x,z)))). -------- PROOF -------- ----> UNIT CONFLICT at 0.01 sec ----> 159 [binary,158.1,11.1] $F. Length of proof is 19. Level of proof is 9. ---------------- PROOF ---------------- 1 [] H(H(SK1,SK2),SK2)!=E. 3,2 [] F(E,x)=x. 4 [] F(G(x),x)=E. 7,6 [] F(F(x,y),z)=F(x,F(y,z)). 8 [] H(x,y)=F(x,F(y,F(G(x),G(y)))). 10,9 [] F(x,F(x,x))=E. 11 [] x=x. 12 [copy,8,flip.1] F(x,F(y,F(G(x),G(y))))=H(x,y). 14,13 [para_into,6.1.1.1,9.1.1,demod,3,7,flip.1] F(x,F(x,F(x,y)))=y. 15 [para_into,6.1.1.1,4.1.1,demod,3,flip.1] F(G(x),F(x,y))=y. 17 [para_into,6.1.1,9.1.1,demod,7,flip.1] F(x,F(y,F(x,F(y,F(x,y)))))=E. 19 [para_from,8.1.1,1.1.1] F(H(SK1,SK2),F(SK2,F(G(H(SK1,SK2)),G(SK2))))!=E. 22,21 [para_into,15.1.1.2,15.1.1] F(G(G(x)),y)=F(x,y). 24,23 [para_into,15.1.1.2,9.1.1] F(G(x),E)=F(x,x). 27 [para_into,15.1.1.2,4.1.1,demod,24] F(G(x),G(x))=x. 34,33 [para_from,27.1.1,15.1.1.2,demod,22,flip.1] G(x)=F(x,x). 36,35 [back_demod,27,demod,34,34,7,10] F(x,E)=x. 40 [back_demod,19,demod,34,34,7] F(H(SK1,SK2),F(SK2,F(H(SK1,SK2),F(H(SK1,SK2),F(SK2,SK2)))))!=E. 42,41 [back_demod,12,demod,34,34,7,flip.1] H(x,y)=F(x,F(y,F(x,F(x,F(y,y))))). 43 [back_demod,40,demod,42,42,42,7,7,7,7,7,10,36,7,7,7,7,7,7,7,7,7,7,14,14] F(SK1,F(SK2,F(SK2,F(SK1,F(SK1,F(SK2,F(SK2,F(SK1,F(SK2,F(SK1,F(SK1,SK2)))))))))))!=E. 47,46 [para_from,17.1.1,13.1.1.2.2,demod,36,flip.1] F(x,F(y,F(x,F(y,x))))=F(y,y). 50 [para_from,46.1.1,13.1.1.2.2] F(x,F(x,F(y,y)))=F(y,F(x,F(y,x))). 51 [para_from,46.1.1,6.1.1.1,demod,7,7,7,7,flip.1] F(x,F(y,F(x,F(y,F(x,z)))))=F(y,F(y,z)). 58 [para_from,50.1.1,6.1.1.1,demod,7,7,7,7,7] F(x,F(y,F(x,F(y,z))))=F(y,F(y,F(x,F(x,z)))). 73,72 [para_into,51.1.1.2.2.2,6.1.1,demod,7,7,7] F(x,F(y,F(z,F(x,F(y,F(z,F(x,u)))))))=F(y,F(z,F(y,F(z,u)))). 158 [para_from,58.1.1,43.1.1.2.2.2.2.2.2,demod,73,14,47,10] E!=E. 159 [binary,158.1,11.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (= (F (E) V1) V1) NIL) (2 (input) (= (F (G V2) V2) (E)) NIL) (3 (input) (= (F (F V3 V4) V5) (F V3 (F V4 V5))) NIL) (4 (input) (= (H V6 V7) (F V6 (F V7 (F (G V6) (G V7))))) NIL) (5 (input) (= (F V8 (F V8 V8)) (E)) NIL) (6 (input) (= V9 V9) NIL) (7 (input) (not (= (H (H (SK1) (SK2)) (SK2)) (E))) NIL) (8 (instantiate 7 ()) (not (= (H (H (SK1) (SK2)) (SK2)) (E))) (1)) (9 (instantiate 1 ((V1 . v0))) (= (F (E) v0) v0) (2)) (10 (instantiate 2 ((V2 . v0))) (= (F (G v0) v0) (E)) (4)) (11 (instantiate 3 ((V3 . v0)(V4 . v1)(V5 . v2))) (= (F (F v0 v1) v2) (F v0 (F v1 v2))) (6)) (12 (instantiate 4 ((V6 . v0)(V7 . v1))) (= (H v0 v1) (F v0 (F v1 (F (G v0) (G v1))))) (8)) (13 (instantiate 5 ((V8 . v0))) (= (F v0 (F v0 v0)) (E)) (9)) (14 (instantiate 6 ((V9 . v0))) (= v0 v0) (11)) (15 (flip 12 ()) (= (F v0 (F v1 (F (G v0) (G v1)))) (H v0 v1)) (12)) (16 (instantiate 13 ((v0 . v64))) (= (F v64 (F v64 v64)) (E)) NIL) (17 (instantiate 11 ((v0 . v64)(v1 . (F v64 v64))(v2 . v66))) (= (F (F v64 (F v64 v64)) v66) (F v64 (F (F v64 v64) v66))) NIL) (18 (paramod 16 (1) 17 (1 1)) (= (F (E) v66) (F v64 (F (F v64 v64) v66))) NIL) (19 (instantiate 9 ((v0 . v66))) (= (F (E) v66) v66) NIL) (20 (paramod 19 (1) 18 (1)) (= v66 (F v64 (F (F v64 v64) v66))) NIL) (21 (instantiate 11 ((v0 . v64)(v1 . v64)(v2 . v66))) (= (F (F v64 v64) v66) (F v64 (F v64 v66))) NIL) (22 (paramod 21 (1) 20 (2 2)) (= v66 (F v64 (F v64 (F v64 v66)))) NIL) (23 (flip 22 ()) (= (F v64 (F v64 (F v64 v66))) v66) NIL) (24 (instantiate 23 ((v64 . v0)(v66 . v1))) (= (F v0 (F v0 (F v0 v1))) v1) (13)) (25 (instantiate 10 ((v0 . v65))) (= (F (G v65) v65) (E)) NIL) (26 (instantiate 11 ((v0 . (G v65))(v1 . v65)(v2 . v66))) (= (F (F (G v65) v65) v66) (F (G v65) (F v65 v66))) NIL) (27 (paramod 25 (1) 26 (1 1)) (= (F (E) v66) (F (G v65) (F v65 v66))) NIL) (28 (instantiate 9 ((v0 . v66))) (= (F (E) v66) v66) NIL) (29 (paramod 28 (1) 27 (1)) (= v66 (F (G v65) (F v65 v66))) NIL) (30 (flip 29 ()) (= (F (G v65) (F v65 v66)) v66) NIL) (31 (instantiate 30 ((v65 . v0)(v66 . v1))) (= (F (G v0) (F v0 v1)) v1) (15)) (32 (instantiate 13 ((v0 . (F v64 v65)))) (= (F (F v64 v65) (F (F v64 v65) (F v64 v65))) (E)) NIL) (33 (instantiate 11 ((v0 . v64)(v1 . v65)(v2 . (F (F v64 v65) (F v64 v65))))) (= (F (F v64 v65) (F (F v64 v65) (F v64 v65))) (F v64 (F v65 (F (F v64 v65) (F v64 v65))))) NIL) (34 (paramod 32 (1) 33 (1)) (= (E) (F v64 (F v65 (F (F v64 v65) (F v64 v65))))) NIL) (35 (instantiate 11 ((v0 . v64)(v1 . v65)(v2 . (F v64 v65)))) (= (F (F v64 v65) (F v64 v65)) (F v64 (F v65 (F v64 v65)))) NIL) (36 (paramod 35 (1) 34 (2 2 2)) (= (E) (F v64 (F v65 (F v64 (F v65 (F v64 v65)))))) NIL) (37 (flip 36 ()) (= (F v64 (F v65 (F v64 (F v65 (F v64 v65))))) (E)) NIL) (38 (instantiate 37 ((v64 . v0)(v65 . v1))) (= (F v0 (F v1 (F v0 (F v1 (F v0 v1))))) (E)) (17)) (39 (instantiate 12 ((v0 . (H (SK1) (SK2)))(v1 . (SK2)))) (= (H (H (SK1) (SK2)) (SK2)) (F (H (SK1) (SK2)) (F (SK2) (F (G (H (SK1) (SK2))) (G (SK2)))))) NIL) (40 (paramod 39 (1) 8 (1 1)) (not (= (F (H (SK1) (SK2)) (F (SK2) (F (G (H (SK1) (SK2))) (G (SK2))))) (E))) (19)) (41 (instantiate 31 ((v0 . (G v0))(v1 . (F v0 v1)))) (= (F (G (G v0)) (F (G v0) (F v0 v1))) (F v0 v1)) NIL) (42 (paramod 31 (1) 41 (1 2)) (= (F (G (G v0)) v1) (F v0 v1)) (21)) (43 (instantiate 13 ((v0 . v64))) (= (F v64 (F v64 v64)) (E)) NIL) (44 (instantiate 31 ((v0 . v64)(v1 . (F v64 v64)))) (= (F (G v64) (F v64 (F v64 v64))) (F v64 v64)) NIL) (45 (paramod 43 (1) 44 (1 2)) (= (F (G v64) (E)) (F v64 v64)) NIL) (46 (instantiate 45 ((v64 . v0))) (= (F (G v0) (E)) (F v0 v0)) (23)) (47 (instantiate 10 ((v0 . v65))) (= (F (G v65) v65) (E)) NIL) (48 (instantiate 31 ((v0 . (G v65))(v1 . v65))) (= (F (G (G v65)) (F (G v65) v65)) v65) NIL) (49 (paramod 47 (1) 48 (1 2)) (= (F (G (G v65)) (E)) v65) NIL) (50 (instantiate 46 ((v0 . (G v65)))) (= (F (G (G v65)) (E)) (F (G v65) (G v65))) NIL) (51 (paramod 50 (1) 49 (1)) (= (F (G v65) (G v65)) v65) NIL) (52 (instantiate 51 ((v65 . v0))) (= (F (G v0) (G v0)) v0) (27)) (53 (instantiate 31 ((v0 . (G v0))(v1 . (G v0)))) (= (F (G (G v0)) (F (G v0) (G v0))) (G v0)) NIL) (54 (paramod 52 (1) 53 (1 2)) (= (F (G (G v0)) v0) (G v0)) NIL) (55 (instantiate 42 ((v0 . v0)(v1 . v0))) (= (F (G (G v0)) v0) (F v0 v0)) NIL) (56 (paramod 55 (1) 54 (1)) (= (F v0 v0) (G v0)) NIL) (57 (flip 56 ()) (= (G v0) (F v0 v0)) (33)) (58 (paramod 57 (1) 52 (1 1)) (= (F (F v0 v0) (G v0)) v0) NIL) (59 (paramod 57 (1) 58 (1 2)) (= (F (F v0 v0) (F v0 v0)) v0) NIL) (60 (instantiate 11 ((v0 . v0)(v1 . v0)(v2 . (F v0 v0)))) (= (F (F v0 v0) (F v0 v0)) (F v0 (F v0 (F v0 v0)))) NIL) (61 (paramod 60 (1) 59 (1)) (= (F v0 (F v0 (F v0 v0))) v0) NIL) (62 (paramod 13 (1) 61 (1 2)) (= (F v0 (E)) v0) (35)) (63 (instantiate 57 ((v0 . (H (SK1) (SK2))))) (= (G (H (SK1) (SK2))) (F (H (SK1) (SK2)) (H (SK1) (SK2)))) NIL) (64 (paramod 63 (1) 40 (1 1 2 2 1)) (not (= (F (H (SK1) (SK2)) (F (SK2) (F (F (H (SK1) (SK2)) (H (SK1) (SK2))) (G (SK2))))) (E))) NIL) (65 (instantiate 57 ((v0 . (SK2)))) (= (G (SK2)) (F (SK2) (SK2))) NIL) (66 (paramod 65 (1) 64 (1 1 2 2 2)) (not (= (F (H (SK1) (SK2)) (F (SK2) (F (F (H (SK1) (SK2)) (H (SK1) (SK2))) (F (SK2) (SK2))))) (E))) NIL) (67 (instantiate 11 ((v0 . (H (SK1) (SK2)))(v1 . (H (SK1) (SK2)))(v2 . (F (SK2) (SK2))))) (= (F (F (H (SK1) (SK2)) (H (SK1) (SK2))) (F (SK2) (SK2))) (F (H (SK1) (SK2)) (F (H (SK1) (SK2)) (F (SK2) (SK2))))) NIL) (68 (paramod 67 (1) 66 (1 1 2 2)) (not (= (F (H (SK1) (SK2)) (F (SK2) (F (H (SK1) (SK2)) (F (H (SK1) (SK2)) (F (SK2) (SK2)))))) (E))) (40)) (69 (paramod 57 (1) 15 (1 2 2 1)) (= (F v0 (F v1 (F (F v0 v0) (G v1)))) (H v0 v1)) NIL) (70 (instantiate 57 ((v0 . v1))) (= (G v1) (F v1 v1)) NIL) (71 (paramod 70 (1) 69 (1 2 2 2)) (= (F v0 (F v1 (F (F v0 v0) (F v1 v1)))) (H v0 v1)) NIL) (72 (instantiate 11 ((v0 . v0)(v1 . v0)(v2 . (F v1 v1)))) (= (F (F v0 v0) (F v1 v1)) (F v0 (F v0 (F v1 v1)))) NIL) (73 (paramod 72 (1) 71 (1 2 2)) (= (F v0 (F v1 (F v0 (F v0 (F v1 v1))))) (H v0 v1)) NIL) (74 (flip 73 ()) (= (H v0 v1) (F v0 (F v1 (F v0 (F v0 (F v1 v1)))))) (41)) (75 (instantiate 74 ((v0 . (SK1))(v1 . (SK2)))) (= (H (SK1) (SK2)) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))))) NIL) (76 (paramod 75 (1) 68 (1 1 1)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (H (SK1) (SK2)) (F (H (SK1) (SK2)) (F (SK2) (SK2)))))) (E))) NIL) (77 (instantiate 74 ((v0 . (SK1))(v1 . (SK2)))) (= (H (SK1) (SK2)) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))))) NIL) (78 (paramod 77 (1) 76 (1 1 2 2 1)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (H (SK1) (SK2)) (F (SK2) (SK2)))))) (E))) NIL) (79 (instantiate 74 ((v0 . (SK1))(v1 . (SK2)))) (= (H (SK1) (SK2)) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))))) NIL) (80 (paramod 79 (1) 78 (1 1 2 2 2 1)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (SK2)))))) (E))) NIL) (81 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))))(v2 . (F (SK2) (SK2))))) (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (SK2))) (F (SK1) (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK2) (SK2))))) NIL) (82 (paramod 81 (1) 80 (1 1 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK2) (SK2))))))) (E))) NIL) (83 (instantiate 11 ((v0 . (SK2))(v1 . (F (SK1) (F (SK1) (F (SK2) (SK2)))))(v2 . (F (SK2) (SK2))))) (= (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK2) (SK2))) (F (SK2) (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK2) (SK2))))) NIL) (84 (paramod 83 (1) 82 (1 1 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK2) (SK2)))))))) (E))) NIL) (85 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK1) (F (SK2) (SK2))))(v2 . (F (SK2) (SK2))))) (= (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK2) (SK2))) (F (SK1) (F (F (SK1) (F (SK2) (SK2))) (F (SK2) (SK2))))) NIL) (86 (paramod 85 (1) 84 (1 1 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (SK1) (F (F (SK1) (F (SK2) (SK2))) (F (SK2) (SK2))))))))) (E))) NIL) (87 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK2) (SK2)))(v2 . (F (SK2) (SK2))))) (= (F (F (SK1) (F (SK2) (SK2))) (F (SK2) (SK2))) (F (SK1) (F (F (SK2) (SK2)) (F (SK2) (SK2))))) NIL) (88 (paramod 87 (1) 86 (1 1 2 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (F (SK2) (SK2)) (F (SK2) (SK2)))))))))) (E))) NIL) (89 (instantiate 11 ((v0 . (SK2))(v1 . (SK2))(v2 . (F (SK2) (SK2))))) (= (F (F (SK2) (SK2)) (F (SK2) (SK2))) (F (SK2) (F (SK2) (F (SK2) (SK2))))) NIL) (90 (paramod 89 (1) 88 (1 1 2 2 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK2) (SK2))))))))))) (E))) NIL) (91 (instantiate 13 ((v0 . (SK2)))) (= (F (SK2) (F (SK2) (SK2))) (E)) NIL) (92 (paramod 91 (1) 90 (1 1 2 2 2 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (E))))))))) (E))) NIL) (93 (instantiate 62 ((v0 . (SK2)))) (= (F (SK2) (E)) (SK2)) NIL) (94 (paramod 93 (1) 92 (1 1 2 2 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) (E))) NIL) (95 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))))(v2 . (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))) (F (SK1) (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) NIL) (96 (paramod 95 (1) 94 (1 1 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (SK1) (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))) (E))) NIL) (97 (instantiate 11 ((v0 . (SK2))(v1 . (F (SK1) (F (SK1) (F (SK2) (SK2)))))(v2 . (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) (= (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))) (F (SK2) (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) NIL) (98 (paramod 97 (1) 96 (1 1 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (SK1) (F (SK2) (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))) (E))) NIL) (99 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK1) (F (SK2) (SK2))))(v2 . (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) (= (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))) (F (SK1) (F (F (SK1) (F (SK2) (SK2))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) NIL) (100 (paramod 99 (1) 98 (1 1 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (F (SK1) (F (SK2) (SK2))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))) (E))) NIL) (101 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK2) (SK2)))(v2 . (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) (= (F (F (SK1) (F (SK2) (SK2))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))) (F (SK1) (F (F (SK2) (SK2)) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) NIL) (102 (paramod 101 (1) 100 (1 1 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (F (SK2) (SK2)) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))) (E))) NIL) (103 (instantiate 11 ((v0 . (SK2))(v1 . (SK2))(v2 . (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) (= (F (F (SK2) (SK2)) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))) NIL) (104 (paramod 103 (1) 102 (1 1 2 2 2 2 2 2)) (not (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (E))) NIL) (105 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))))(v2 . (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (= (F (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2)))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (F (SK1) (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) NIL) (106 (paramod 105 (1) 104 (1 1)) (not (= (F (SK1) (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))))) (E))) NIL) (107 (instantiate 11 ((v0 . (SK2))(v1 . (F (SK1) (F (SK1) (F (SK2) (SK2)))))(v2 . (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (= (F (F (SK2) (F (SK1) (F (SK1) (F (SK2) (SK2))))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (F (SK2) (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) NIL) (108 (paramod 107 (1) 106 (1 1 2)) (not (= (F (SK1) (F (SK2) (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (E))) NIL) (109 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK1) (F (SK2) (SK2))))(v2 . (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (= (F (F (SK1) (F (SK1) (F (SK2) (SK2)))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (F (SK1) (F (F (SK1) (F (SK2) (SK2))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) NIL) (110 (paramod 109 (1) 108 (1 1 2 2)) (not (= (F (SK1) (F (SK2) (F (SK1) (F (F (SK1) (F (SK2) (SK2))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))))))) (E))) NIL) (111 (instantiate 11 ((v0 . (SK1))(v1 . (F (SK2) (SK2)))(v2 . (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (= (F (F (SK1) (F (SK2) (SK2))) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (F (SK1) (F (F (SK2) (SK2)) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) NIL) (112 (paramod 111 (1) 110 (1 1 2 2 2)) (not (= (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (F (SK2) (SK2)) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))))) (E))) NIL) (113 (instantiate 11 ((v0 . (SK2))(v1 . (SK2))(v2 . (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (= (F (F (SK2) (SK2)) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (F (SK2) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) NIL) (114 (paramod 113 (1) 112 (1 1 2 2 2 2)) (not (= (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))))))))) (E))) NIL) (115 (instantiate 24 ((v0 . (SK2))(v1 . (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))))) (= (F (SK2) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))))) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))) NIL) (116 (paramod 115 (1) 114 (1 1 2 2 2 2)) (not (= (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))))) (E))) NIL) (117 (instantiate 24 ((v0 . (SK1))(v1 . (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (= (F (SK1) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))))) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2))))))))))) NIL) (118 (paramod 117 (1) 116 (1 1 2 2)) (not (= (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))))))))) (E))) (43)) (119 (instantiate 38 ((v0 . v64))) (= (F v64 (F v1 (F v64 (F v1 (F v64 v1))))) (E)) NIL) (120 (instantiate 24 ((v0 . v64)(v1 . (F v1 (F v64 (F v1 (F v64 v1))))))) (= (F v64 (F v64 (F v64 (F v1 (F v64 (F v1 (F v64 v1))))))) (F v1 (F v64 (F v1 (F v64 v1))))) NIL) (121 (paramod 119 (1) 120 (1 2 2)) (= (F v64 (F v64 (E))) (F v1 (F v64 (F v1 (F v64 v1))))) NIL) (122 (instantiate 62 ((v0 . v64))) (= (F v64 (E)) v64) NIL) (123 (paramod 122 (1) 121 (1 2)) (= (F v64 v64) (F v1 (F v64 (F v1 (F v64 v1))))) NIL) (124 (flip 123 ()) (= (F v1 (F v64 (F v1 (F v64 v1)))) (F v64 v64)) NIL) (125 (instantiate 124 ((v1 . v0)(v64 . v1))) (= (F v0 (F v1 (F v0 (F v1 v0)))) (F v1 v1)) (46)) (126 (instantiate 125 ((v0 . v64))) (= (F v64 (F v1 (F v64 (F v1 v64)))) (F v1 v1)) NIL) (127 (instantiate 24 ((v0 . v64)(v1 . (F v1 (F v64 (F v1 v64)))))) (= (F v64 (F v64 (F v64 (F v1 (F v64 (F v1 v64)))))) (F v1 (F v64 (F v1 v64)))) NIL) (128 (paramod 126 (1) 127 (1 2 2)) (= (F v64 (F v64 (F v1 v1))) (F v1 (F v64 (F v1 v64)))) NIL) (129 (instantiate 128 ((v64 . v0))) (= (F v0 (F v0 (F v1 v1))) (F v1 (F v0 (F v1 v0)))) (50)) (130 (instantiate 125 ((v0 . v64))) (= (F v64 (F v1 (F v64 (F v1 v64)))) (F v1 v1)) NIL) (131 (instantiate 11 ((v0 . v64)(v1 . (F v1 (F v64 (F v1 v64))))(v2 . v66))) (= (F (F v64 (F v1 (F v64 (F v1 v64)))) v66) (F v64 (F (F v1 (F v64 (F v1 v64))) v66))) NIL) (132 (paramod 130 (1) 131 (1 1)) (= (F (F v1 v1) v66) (F v64 (F (F v1 (F v64 (F v1 v64))) v66))) NIL) (133 (instantiate 11 ((v0 . v1)(v1 . v1)(v2 . v66))) (= (F (F v1 v1) v66) (F v1 (F v1 v66))) NIL) (134 (paramod 133 (1) 132 (1)) (= (F v1 (F v1 v66)) (F v64 (F (F v1 (F v64 (F v1 v64))) v66))) NIL) (135 (instantiate 11 ((v0 . v1)(v1 . (F v64 (F v1 v64)))(v2 . v66))) (= (F (F v1 (F v64 (F v1 v64))) v66) (F v1 (F (F v64 (F v1 v64)) v66))) NIL) (136 (paramod 135 (1) 134 (2 2)) (= (F v1 (F v1 v66)) (F v64 (F v1 (F (F v64 (F v1 v64)) v66)))) NIL) (137 (instantiate 11 ((v0 . v64)(v1 . (F v1 v64))(v2 . v66))) (= (F (F v64 (F v1 v64)) v66) (F v64 (F (F v1 v64) v66))) NIL) (138 (paramod 137 (1) 136 (2 2 2)) (= (F v1 (F v1 v66)) (F v64 (F v1 (F v64 (F (F v1 v64) v66))))) NIL) (139 (instantiate 11 ((v0 . v1)(v1 . v64)(v2 . v66))) (= (F (F v1 v64) v66) (F v1 (F v64 v66))) NIL) (140 (paramod 139 (1) 138 (2 2 2 2)) (= (F v1 (F v1 v66)) (F v64 (F v1 (F v64 (F v1 (F v64 v66)))))) NIL) (141 (flip 140 ()) (= (F v64 (F v1 (F v64 (F v1 (F v64 v66))))) (F v1 (F v1 v66))) NIL) (142 (instantiate 141 ((v64 . v0)(v66 . v2))) (= (F v0 (F v1 (F v0 (F v1 (F v0 v2))))) (F v1 (F v1 v2))) (51)) (143 (instantiate 129 ((v0 . v64))) (= (F v64 (F v64 (F v1 v1))) (F v1 (F v64 (F v1 v64)))) NIL) (144 (instantiate 11 ((v0 . v64)(v1 . (F v64 (F v1 v1)))(v2 . v66))) (= (F (F v64 (F v64 (F v1 v1))) v66) (F v64 (F (F v64 (F v1 v1)) v66))) NIL) (145 (paramod 143 (1) 144 (1 1)) (= (F (F v1 (F v64 (F v1 v64))) v66) (F v64 (F (F v64 (F v1 v1)) v66))) NIL) (146 (instantiate 11 ((v0 . v1)(v1 . (F v64 (F v1 v64)))(v2 . v66))) (= (F (F v1 (F v64 (F v1 v64))) v66) (F v1 (F (F v64 (F v1 v64)) v66))) NIL) (147 (paramod 146 (1) 145 (1)) (= (F v1 (F (F v64 (F v1 v64)) v66)) (F v64 (F (F v64 (F v1 v1)) v66))) NIL) (148 (instantiate 11 ((v0 . v64)(v1 . (F v1 v64))(v2 . v66))) (= (F (F v64 (F v1 v64)) v66) (F v64 (F (F v1 v64) v66))) NIL) (149 (paramod 148 (1) 147 (1 2)) (= (F v1 (F v64 (F (F v1 v64) v66))) (F v64 (F (F v64 (F v1 v1)) v66))) NIL) (150 (instantiate 11 ((v0 . v1)(v1 . v64)(v2 . v66))) (= (F (F v1 v64) v66) (F v1 (F v64 v66))) NIL) (151 (paramod 150 (1) 149 (1 2 2)) (= (F v1 (F v64 (F v1 (F v64 v66)))) (F v64 (F (F v64 (F v1 v1)) v66))) NIL) (152 (instantiate 11 ((v0 . v64)(v1 . (F v1 v1))(v2 . v66))) (= (F (F v64 (F v1 v1)) v66) (F v64 (F (F v1 v1) v66))) NIL) (153 (paramod 152 (1) 151 (2 2)) (= (F v1 (F v64 (F v1 (F v64 v66)))) (F v64 (F v64 (F (F v1 v1) v66)))) NIL) (154 (instantiate 11 ((v0 . v1)(v1 . v1)(v2 . v66))) (= (F (F v1 v1) v66) (F v1 (F v1 v66))) NIL) (155 (paramod 154 (1) 153 (2 2 2)) (= (F v1 (F v64 (F v1 (F v64 v66)))) (F v64 (F v64 (F v1 (F v1 v66))))) NIL) (156 (instantiate 155 ((v1 . v0)(v64 . v1)(v66 . v2))) (= (F v0 (F v1 (F v0 (F v1 v2)))) (F v1 (F v1 (F v0 (F v0 v2))))) (58)) (157 (instantiate 11 ((v2 . (F v64 v66)))) (= (F (F v0 v1) (F v64 v66)) (F v0 (F v1 (F v64 v66)))) NIL) (158 (instantiate 142 ((v0 . v64)(v1 . (F v0 v1))(v2 . v66))) (= (F v64 (F (F v0 v1) (F v64 (F (F v0 v1) (F v64 v66))))) (F (F v0 v1) (F (F v0 v1) v66))) NIL) (159 (paramod 157 (1) 158 (1 2 2 2)) (= (F v64 (F (F v0 v1) (F v64 (F v0 (F v1 (F v64 v66)))))) (F (F v0 v1) (F (F v0 v1) v66))) NIL) (160 (instantiate 11 ((v0 . v0)(v1 . v1)(v2 . (F v64 (F v0 (F v1 (F v64 v66))))))) (= (F (F v0 v1) (F v64 (F v0 (F v1 (F v64 v66))))) (F v0 (F v1 (F v64 (F v0 (F v1 (F v64 v66))))))) NIL) (161 (paramod 160 (1) 159 (1 2)) (= (F v64 (F v0 (F v1 (F v64 (F v0 (F v1 (F v64 v66))))))) (F (F v0 v1) (F (F v0 v1) v66))) NIL) (162 (instantiate 11 ((v0 . v0)(v1 . v1)(v2 . v66))) (= (F (F v0 v1) v66) (F v0 (F v1 v66))) NIL) (163 (paramod 162 (1) 161 (2 2)) (= (F v64 (F v0 (F v1 (F v64 (F v0 (F v1 (F v64 v66))))))) (F (F v0 v1) (F v0 (F v1 v66)))) NIL) (164 (instantiate 11 ((v0 . v0)(v1 . v1)(v2 . (F v0 (F v1 v66))))) (= (F (F v0 v1) (F v0 (F v1 v66))) (F v0 (F v1 (F v0 (F v1 v66))))) NIL) (165 (paramod 164 (1) 163 (2)) (= (F v64 (F v0 (F v1 (F v64 (F v0 (F v1 (F v64 v66))))))) (F v0 (F v1 (F v0 (F v1 v66))))) NIL) (166 (instantiate 165 ((v0 . v1)(v1 . v2)(v64 . v0)(v66 . v3))) (= (F v0 (F v1 (F v2 (F v0 (F v1 (F v2 (F v0 v3))))))) (F v1 (F v2 (F v1 (F v2 v3))))) (72)) (167 (instantiate 156 ((v0 . (SK2))(v1 . (SK1))(v2 . (F (SK1) (SK2))))) (= (F (SK2) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (SK2)))))) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (SK2))))))) NIL) (168 (paramod 167 (1) 118 (1 1 2 2 2 2 2 2)) (not (= (F (SK1) (F (SK2) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (SK2)))))))))))) (E))) NIL) (169 (instantiate 166 ((v0 . (SK2))(v1 . (SK1))(v2 . (SK1))(v3 . (F (SK2) (F (SK1) (SK2)))))) (= (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK2) (F (SK2) (F (SK1) (SK2)))))))))) (F (SK1) (F (SK1) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (SK2)))))))) NIL) (170 (paramod 169 (1) 168 (1 1 2 2)) (not (= (F (SK1) (F (SK2) (F (SK1) (F (SK1) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (SK2))))))))) (E))) NIL) (171 (instantiate 24 ((v0 . (SK1))(v1 . (F (SK2) (F (SK1) (SK2)))))) (= (F (SK1) (F (SK1) (F (SK1) (F (SK2) (F (SK1) (SK2)))))) (F (SK2) (F (SK1) (SK2)))) NIL) (172 (paramod 171 (1) 170 (1 1 2 2 2)) (not (= (F (SK1) (F (SK2) (F (SK1) (F (SK2) (F (SK1) (SK2)))))) (E))) NIL) (173 (instantiate 125 ((v0 . (SK2))(v1 . (SK1)))) (= (F (SK2) (F (SK1) (F (SK2) (F (SK1) (SK2))))) (F (SK1) (SK1))) NIL) (174 (paramod 173 (1) 172 (1 1 2)) (not (= (F (SK1) (F (SK1) (SK1))) (E))) NIL) (175 (instantiate 13 ((v0 . (SK1)))) (= (F (SK1) (F (SK1) (SK1))) (E)) NIL) (176 (paramod 175 (1) 174 (1 1)) (not (= (E) (E))) (158)) (177 (instantiate 14 ((v0 . (E)))) (= (E) (E)) NIL) (178 (resolve 176 () 177 ()) false (159)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 23 clauses generated 419 clauses kept 118 clauses forward subsumed 399 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8570 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/lifsch.in0100644000076400007640000000456006747655711016455 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (NOT (S V2 (SK1 V2 V3))) (NOT (Q V3 (SK1 V2 V3)))))) (2 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (NOT (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6)))) (3 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (NOT (S V2 (SK1 V2 V3))) (NOT (S V3 V3))))) (4 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (S (SK1 V2 V3) V5) (NOT (Q V3 (SK1 V2 V3)))))) (5 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6)))) (6 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (S (SK1 V2 V3) V5) (NOT (S V3 V3))))) (7 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (NOT (Q V6 V6)) (NOT (Q V3 (SK1 V2 V3)))))) (8 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (NOT (Q V6 V6)) (Q (SK1 V2 V3) V6)))) (9 (INPUT) (OR (P (SK1 V2 V3) (SK1 V2 V3)) (OR (NOT (Q V6 V6)) (NOT (S V3 V3))))) (10 (INPUT) (OR (NOT (P V2 V2)) (OR (NOT (S V2 (SK1 V2 V3))) (NOT (Q V3 (SK1 V2 V3)))))) (11 (INPUT) (OR (NOT (P V2 V2)) (OR (NOT (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6)))) (12 (INPUT) (OR (NOT (P V2 V2)) (OR (NOT (S V2 (SK1 V2 V3))) (NOT (S V3 V3))))) (13 (INPUT) (OR (NOT (P V2 V2)) (OR (S (SK1 V2 V3) V5) (NOT (Q V3 (SK1 V2 V3)))))) (14 (INPUT) (OR (NOT (P V2 V2)) (OR (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6)))) (15 (INPUT) (OR (NOT (P V2 V2)) (OR (S (SK1 V2 V3) V5) (NOT (S V3 V3))))) (16 (INPUT) (OR (NOT (P V2 V2)) (OR (NOT (Q V6 V6)) (NOT (Q V3 (SK1 V2 V3)))))) (17 (INPUT) (OR (NOT (P V2 V2)) (OR (NOT (Q V6 V6)) (Q (SK1 V2 V3) V6)))) (18 (INPUT) (OR (NOT (P V2 V2)) (OR (NOT (Q V6 V6)) (NOT (S V3 V3))))) (19 (INPUT) (OR (S V5 V2) (OR (NOT (S V2 (SK1 V2 V3))) (NOT (Q V3 (SK1 V2 V3)))))) (20 (INPUT) (OR (S V5 V2) (OR (NOT (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6)))) (21 (INPUT) (OR (S V5 V2) (OR (NOT (S V2 (SK1 V2 V3))) (NOT (S V3 V3))))) (22 (INPUT) (OR (S V5 V2) (OR (S (SK1 V2 V3) V5) (NOT (Q V3 (SK1 V2 V3)))))) (23 (INPUT) (OR (S V5 V2) (OR (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6)))) (24 (INPUT) (OR (S V5 V2) (OR (S (SK1 V2 V3) V5) (NOT (S V3 V3))))) (25 (INPUT) (OR (S V5 V2) (OR (NOT (Q V6 V6)) (NOT (Q V3 (SK1 V2 V3)))))) (26 (INPUT) (OR (S V5 V2) (OR (NOT (Q V6 V6)) (Q (SK1 V2 V3) V6)))) (27 (INPUT) (OR (S V5 V2) (OR (NOT (Q V6 V6)) (NOT (S V3 V3)))))) otter-3.3f/examples/ivy/steam.in0100644000076400007640000000312706747655711016314 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (OR (NOT (WOLF V1)) (ANIMAL V1))) (2 (INPUT) (OR (NOT (FOX V2)) (ANIMAL V2))) (3 (INPUT) (OR (NOT (BIRD V3)) (ANIMAL V3))) (4 (INPUT) (OR (NOT (SNAIL V4)) (ANIMAL V4))) (5 (INPUT) (OR (NOT (GRAIN V5)) (PLANT V5))) (6 (INPUT) (WOLF (SK1))) (7 (INPUT) (FOX (SK2))) (8 (INPUT) (BIRD (SK3))) (9 (INPUT) (SNAIL (SK4))) (10 (INPUT) (GRAIN (SK5))) (11 (INPUT) (OR (NOT (SNAIL V11)) (OR (NOT (BIRD V12)) (SMALLER V11 V12)))) (12 (INPUT) (OR (NOT (BIRD V13)) (OR (NOT (FOX V14)) (SMALLER V13 V14)))) (13 (INPUT) (OR (NOT (FOX V15)) (OR (NOT (WOLF V16)) (SMALLER V15 V16)))) (14 (INPUT) (OR (NOT (SNAIL V17)) (PLANT (SK6 V17)))) (15 (INPUT) (OR (NOT (SNAIL V17)) (EATS V17 (SK6 V17)))) (16 (INPUT) (OR (NOT (WOLF V19)) (OR (NOT (FOX V20)) (NOT (EATS V19 V20))))) (17 (INPUT) (OR (NOT (WOLF V21)) (OR (NOT (GRAIN V22)) (NOT (EATS V21 V22))))) (18 (INPUT) (OR (NOT (BIRD V23)) (OR (NOT (SNAIL V24)) (NOT (EATS V23 V24))))) (19 (INPUT) (OR (NOT (ANIMAL V25)) (OR (NOT (PLANT V26)) (OR (EATS V25 V26) (OR (NOT (ANIMAL V27)) (OR (NOT (SMALLER V27 V25)) (OR (NOT (PLANT V28)) (OR (NOT (EATS V27 V28)) (EATS V25 V27))))))))) (20 (INPUT) (OR (NOT (ANIMAL V29)) (OR (NOT (ANIMAL V30)) (OR (NOT (EATS V29 V30)) (GRAIN (SK7 V29 V30)))))) (21 (INPUT) (OR (NOT (ANIMAL V29)) (OR (NOT (ANIMAL V30)) (OR (NOT (EATS V29 V30)) (NOT (EATS V30 (SK7 V29 V30)))))))) otter-3.3f/examples/ivy/group-x2.out0100664000076400007640000001577610103522211017047 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8575. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (= (F (E) V1) V1) NIL) (2 (input) (= (F (G V2) V2) (E)) NIL) (3 (input) (= (F (F V3 V4) V5) (F V3 (F V4 V5))) NIL) (4 (input) (= (F V6 V6) (E)) NIL) (5 (input) (= V7 V7) NIL) (6 (input) (not (= (F (SK1) (SK2)) (F (SK2) (SK1)))) NIL) ) 0 [] F(E,x)=x. 0 [] F(G(x),x)=E. 0 [] F(F(x,y),z)=F(x,F(y,z)). 0 [] F(x,x)=E. 0 [] x=x. 0 [] F(SK1,SK2)!=F(SK2,SK1). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=7): 2 [copy,1,flip.1] F(SK2,SK1)!=F(SK1,SK2). ------------> process sos: ** KEPT (pick-wt=5): 3 [] F(E,x)=x. ---> New Demodulator: 4 [new_demod,3] F(E,x)=x. ** KEPT (pick-wt=6): 5 [] F(G(x),x)=E. ---> New Demodulator: 6 [new_demod,5] F(G(x),x)=E. ** KEPT (pick-wt=11): 7 [] F(F(x,y),z)=F(x,F(y,z)). ---> New Demodulator: 8 [new_demod,7] F(F(x,y),z)=F(x,F(y,z)). ** KEPT (pick-wt=5): 9 [] F(x,x)=E. ---> New Demodulator: 10 [new_demod,9] F(x,x)=E. ** KEPT (pick-wt=3): 11 [] x=x. >>>> Starting back demodulation with 4. >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] x=x. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=5) 3 [] F(E,x)=x. given clause #2: (wt=3) 11 [] x=x. given clause #3: (wt=5) 9 [] F(x,x)=E. given clause #4: (wt=6) 5 [] F(G(x),x)=E. given clause #5: (wt=11) 7 [] F(F(x,y),z)=F(x,F(y,z)). given clause #6: (wt=7) 12 [para_into,7.1.1.1,9.1.1,demod,4,flip.1] F(x,F(x,y))=y. given clause #7: (wt=4) 22 [para_into,12.1.1.2,5.1.1,demod,19] G(x)=x. given clause #8: (wt=5) 18 [para_into,12.1.1.2,9.1.1] F(x,E)=x. given clause #9: (wt=9) 16 [para_into,7.1.1,9.1.1,flip.1] F(x,F(y,F(x,y)))=E. given clause #10: (wt=7) 26 [para_from,16.1.1,12.1.1.2,demod,19,flip.1] F(x,F(y,x))=y. -------- PROOF -------- ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,2.1] $F. Length of proof is 6. Level of proof is 4. ---------------- PROOF ---------------- 1 [] F(SK1,SK2)!=F(SK2,SK1). 2 [copy,1,flip.1] F(SK2,SK1)!=F(SK1,SK2). 4,3 [] F(E,x)=x. 7 [] F(F(x,y),z)=F(x,F(y,z)). 9 [] F(x,x)=E. 12 [para_into,7.1.1.1,9.1.1,demod,4,flip.1] F(x,F(x,y))=y. 16 [para_into,7.1.1,9.1.1,flip.1] F(x,F(y,F(x,y)))=E. 19,18 [para_into,12.1.1.2,9.1.1] F(x,E)=x. 26 [para_from,16.1.1,12.1.1.2,demod,19,flip.1] F(x,F(y,x))=y. 30 [para_from,26.1.1,12.1.1.2] F(x,y)=F(y,x). 31 [binary,30.1,2.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (= (F (E) V1) V1) NIL) (2 (input) (= (F (G V2) V2) (E)) NIL) (3 (input) (= (F (F V3 V4) V5) (F V3 (F V4 V5))) NIL) (4 (input) (= (F V6 V6) (E)) NIL) (5 (input) (= V7 V7) NIL) (6 (input) (not (= (F (SK1) (SK2)) (F (SK2) (SK1)))) NIL) (7 (instantiate 6 ()) (not (= (F (SK1) (SK2)) (F (SK2) (SK1)))) (1)) (8 (flip 7 ()) (not (= (F (SK2) (SK1)) (F (SK1) (SK2)))) (2)) (9 (instantiate 1 ((V1 . v0))) (= (F (E) v0) v0) (3)) (10 (instantiate 3 ((V3 . v0)(V4 . v1)(V5 . v2))) (= (F (F v0 v1) v2) (F v0 (F v1 v2))) (7)) (11 (instantiate 4 ((V6 . v0))) (= (F v0 v0) (E)) (9)) (12 (instantiate 11 ((v0 . v65))) (= (F v65 v65) (E)) NIL) (13 (instantiate 10 ((v0 . v65)(v1 . v65)(v2 . v66))) (= (F (F v65 v65) v66) (F v65 (F v65 v66))) NIL) (14 (paramod 12 (1) 13 (1 1)) (= (F (E) v66) (F v65 (F v65 v66))) NIL) (15 (instantiate 9 ((v0 . v66))) (= (F (E) v66) v66) NIL) (16 (paramod 15 (1) 14 (1)) (= v66 (F v65 (F v65 v66))) NIL) (17 (flip 16 ()) (= (F v65 (F v65 v66)) v66) NIL) (18 (instantiate 17 ((v65 . v0)(v66 . v1))) (= (F v0 (F v0 v1)) v1) (12)) (19 (instantiate 11 ((v0 . (F v64 v65)))) (= (F (F v64 v65) (F v64 v65)) (E)) NIL) (20 (instantiate 10 ((v0 . v64)(v1 . v65)(v2 . (F v64 v65)))) (= (F (F v64 v65) (F v64 v65)) (F v64 (F v65 (F v64 v65)))) NIL) (21 (paramod 19 (1) 20 (1)) (= (E) (F v64 (F v65 (F v64 v65)))) NIL) (22 (flip 21 ()) (= (F v64 (F v65 (F v64 v65))) (E)) NIL) (23 (instantiate 22 ((v64 . v0)(v65 . v1))) (= (F v0 (F v1 (F v0 v1))) (E)) (16)) (24 (instantiate 11 ((v0 . v65))) (= (F v65 v65) (E)) NIL) (25 (instantiate 18 ((v0 . v65)(v1 . v65))) (= (F v65 (F v65 v65)) v65) NIL) (26 (paramod 24 (1) 25 (1 2)) (= (F v65 (E)) v65) NIL) (27 (instantiate 26 ((v65 . v0))) (= (F v0 (E)) v0) (18)) (28 (instantiate 23 ((v0 . v64))) (= (F v64 (F v1 (F v64 v1))) (E)) NIL) (29 (instantiate 18 ((v0 . v64)(v1 . (F v1 (F v64 v1))))) (= (F v64 (F v64 (F v1 (F v64 v1)))) (F v1 (F v64 v1))) NIL) (30 (paramod 28 (1) 29 (1 2)) (= (F v64 (E)) (F v1 (F v64 v1))) NIL) (31 (instantiate 27 ((v0 . v64))) (= (F v64 (E)) v64) NIL) (32 (paramod 31 (1) 30 (1)) (= v64 (F v1 (F v64 v1))) NIL) (33 (flip 32 ()) (= (F v1 (F v64 v1)) v64) NIL) (34 (instantiate 33 ((v1 . v0)(v64 . v1))) (= (F v0 (F v1 v0)) v1) (26)) (35 (instantiate 34 ((v0 . v64))) (= (F v64 (F v1 v64)) v1) NIL) (36 (instantiate 18 ((v0 . v64)(v1 . (F v1 v64)))) (= (F v64 (F v64 (F v1 v64))) (F v1 v64)) NIL) (37 (paramod 35 (1) 36 (1 2)) (= (F v64 v1) (F v1 v64)) NIL) (38 (instantiate 37 ((v64 . v0))) (= (F v0 v1) (F v1 v0)) (30)) (39 (instantiate 38 ((v0 . (SK2))(v1 . (SK1)))) (= (F (SK2) (SK1)) (F (SK1) (SK2))) NIL) (40 (resolve 8 () 39 ()) false (31)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 10 clauses generated 76 clauses kept 16 clauses forward subsumed 71 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8575 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/comb-sk-w.out0100664000076400007640000002374310103522211017154 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8565. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (= V1 V1) NIL) (2 (input) (= (A (A (A (S) V2) V3) V4) (A (A V2 V4) (A V3 V4))) NIL) (3 (input) (= (A (A (K) V5) V6) V5) NIL) (4 (input) (not (= (A (A V7 (SK1 V7)) (SK2 V7)) (A (A (SK1 V7) (SK2 V7)) (SK2 V7)))) NIL) ) 0 [] x=x. 0 [] A(A(A(S,x),y),z)=A(A(x,z),A(y,z)). 0 [] A(A(K,x),y)=x. 0 [] A(A(x,SK1(x)),SK2(x))!=A(A(SK1(x),SK2(x)),SK2(x)). end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=16): 2 [copy,1,flip.1] A(A(SK1(x),SK2(x)),SK2(x))!=A(A(x,SK1(x)),SK2(x)). ------------> process sos: ** KEPT (pick-wt=3): 3 [] x=x. ** KEPT (pick-wt=15): 4 [] A(A(A(S,x),y),z)=A(A(x,z),A(y,z)). ** KEPT (pick-wt=7): 5 [] A(A(K,x),y)=x. ---> New Demodulator: 6 [new_demod,5] A(A(K,x),y)=x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x=x. ** KEPT (pick-wt=15): 7 [copy,4,flip.1] A(A(x,y),A(z,y))=A(A(A(S,x),z),y). >>>> Starting back demodulation with 6. Following clause subsumed by 4 during input processing: 0 [copy,7,flip.1] A(A(A(S,x),y),z)=A(A(x,z),A(y,z)). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 3 [] x=x. given clause #2: (wt=7) 5 [] A(A(K,x),y)=x. given clause #3: (wt=15) 4 [] A(A(A(S,x),y),z)=A(A(x,z),A(y,z)). given clause #4: (wt=15) 7 [copy,4,flip.1] A(A(x,y),A(z,y))=A(A(A(S,x),z),y). given clause #5: (wt=9) 15 [para_into,7.1.1,5.1.1,flip.1] A(A(A(S,K),x),y)=y. given clause #6: (wt=25) 8 [para_into,7.1.1.1,7.1.1] A(A(A(A(S,x),y),z),A(u,A(y,z)))=A(A(A(S,A(x,z)),u),A(y,z)). given clause #7: (wt=11) 26 [para_into,15.1.1.1,7.1.1] A(A(A(A(S,S),x),K),y)=y. given clause #8: (wt=13) 28 [para_into,15.1.1,7.1.1] A(A(A(S,A(S,K)),x),y)=A(x,y). given clause #9: (wt=13) 62 [para_into,26.1.1.1.1,7.1.1] A(A(A(A(A(S,S),x),S),K),y)=y. given clause #10: (wt=15) 9 [para_into,7.1.1.1,5.1.1,flip.1] A(A(A(S,A(K,x)),y),z)=A(x,A(y,z)). given clause #11: (wt=23) 11 [para_into,7.1.1.1,4.1.1] A(A(A(x,y),A(z,y)),A(u,y))=A(A(A(S,A(A(S,x),z)),u),y). given clause #12: (wt=15) 13 [para_into,7.1.1.2,5.1.1] A(A(x,y),z)=A(A(A(S,x),A(K,z)),y). given clause #13: (wt=15) 21 [copy,13,flip.1] A(A(A(S,x),A(K,y)),z)=A(A(x,z),y). given clause #14: (wt=15) 64 [para_into,26.1.1,7.1.1] A(A(A(S,A(A(S,S),x)),y),K)=A(y,K). given clause #15: (wt=15) 86 [para_into,62.1.1.1.1.1,7.1.1] A(A(A(A(A(A(S,S),x),S),S),K),y)=y. given clause #16: (wt=25) 12 [para_into,7.1.1.2,7.1.1] A(A(x,A(y,z)),A(A(A(S,u),y),z))=A(A(A(S,x),A(u,z)),A(y,z)). given clause #17: (wt=15) 226 [para_from,13.1.1,26.1.1.1] A(A(A(A(S,A(S,S)),A(K,K)),x),y)=y. given clause #18: (wt=15) 248 [para_into,21.1.1.1,7.1.1] A(A(A(A(S,S),K),x),y)=A(A(x,y),x). given clause #19: (wt=15) 254 [copy,248,flip.1] A(A(x,y),x)=A(A(A(A(S,S),K),x),y). given clause #20: (wt=17) 30 [para_from,15.1.1,7.1.1.2] A(A(x,y),y)=A(A(A(S,x),A(A(S,K),z)),y). given clause #21: (wt=23) 14 [para_into,7.1.1.2,4.1.1] A(A(x,y),A(A(z,y),A(u,y)))=A(A(A(S,x),A(A(S,z),u)),y). given clause #22: (wt=17) 31 [para_from,15.1.1,7.1.1.1] A(x,A(y,x))=A(A(A(S,A(A(S,K),z)),y),x). given clause #23: (wt=15) 897 [para_into,31.1.1,5.1.1,flip.1] A(A(A(S,A(A(S,K),x)),y),A(K,z))=z. given clause #24: (wt=15) 1041 [para_into,897.1.1,7.1.1] A(A(A(S,A(S,A(A(S,K),x))),K),y)=y. given clause #25: (wt=17) 32 [copy,30,flip.1] A(A(A(S,x),A(A(S,K),y)),z)=A(A(x,z),z). -------- PROOF -------- ----> UNIT CONFLICT at 0.11 sec ----> 1157 [binary,1156.1,2.1] $F. Length of proof is 8. Level of proof is 6. ---------------- PROOF ---------------- 1 [] A(A(x,SK1(x)),SK2(x))!=A(A(SK1(x),SK2(x)),SK2(x)). 2 [copy,1,flip.1] A(A(SK1(x),SK2(x)),SK2(x))!=A(A(x,SK1(x)),SK2(x)). 4 [] A(A(A(S,x),y),z)=A(A(x,z),A(y,z)). 5 [] A(A(K,x),y)=x. 7 [copy,4,flip.1] A(A(x,y),A(z,y))=A(A(A(S,x),z),y). 13 [para_into,7.1.1.2,5.1.1] A(A(x,y),z)=A(A(A(S,x),A(K,z)),y). 15 [para_into,7.1.1,5.1.1,flip.1] A(A(A(S,K),x),y)=y. 30 [para_from,15.1.1,7.1.1.2] A(A(x,y),y)=A(A(A(S,x),A(A(S,K),z)),y). 32 [copy,30,flip.1] A(A(A(S,x),A(A(S,K),y)),z)=A(A(x,z),z). 1141 [para_into,32.1.1.1,13.1.1] A(A(A(A(S,S),A(K,A(A(S,K),x))),y),z)=A(A(y,z),z). 1156 [copy,1141,flip.1] A(A(x,y),y)=A(A(A(A(S,S),A(K,A(A(S,K),z))),x),y). 1157 [binary,1156.1,2.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (= V1 V1) NIL) (2 (input) (= (A (A (A (S) V2) V3) V4) (A (A V2 V4) (A V3 V4))) NIL) (3 (input) (= (A (A (K) V5) V6) V5) NIL) (4 (input) (not (= (A (A V7 (SK1 V7)) (SK2 V7)) (A (A (SK1 V7) (SK2 V7)) (SK2 V7)))) NIL) (5 (instantiate 4 ((V7 . v0))) (not (= (A (A v0 (SK1 v0)) (SK2 v0)) (A (A (SK1 v0) (SK2 v0)) (SK2 v0)))) (1)) (6 (flip 5 ()) (not (= (A (A (SK1 v0) (SK2 v0)) (SK2 v0)) (A (A v0 (SK1 v0)) (SK2 v0)))) (2)) (7 (instantiate 2 ((V2 . v0)(V3 . v1)(V4 . v2))) (= (A (A (A (S) v0) v1) v2) (A (A v0 v2) (A v1 v2))) (4)) (8 (instantiate 3 ((V5 . v0)(V6 . v1))) (= (A (A (K) v0) v1) v0) (5)) (9 (flip 7 ()) (= (A (A v0 v2) (A v1 v2)) (A (A (A (S) v0) v1) v2)) NIL) (10 (instantiate 9 ((v1 . v2)(v2 . v1))) (= (A (A v0 v1) (A v2 v1)) (A (A (A (S) v0) v2) v1)) (7)) (11 (instantiate 8 ((v1 . v65))) (= (A (A (K) v0) v65) v0) NIL) (12 (instantiate 10 ((v0 . v64)(v1 . v65)(v2 . (A (K) v0)))) (= (A (A v64 v65) (A (A (K) v0) v65)) (A (A (A (S) v64) (A (K) v0)) v65)) NIL) (13 (paramod 11 (1) 12 (1 2)) (= (A (A v64 v65) v0) (A (A (A (S) v64) (A (K) v0)) v65)) NIL) (14 (instantiate 13 ((v0 . v2)(v64 . v0)(v65 . v1))) (= (A (A v0 v1) v2) (A (A (A (S) v0) (A (K) v2)) v1)) (13)) (15 (instantiate 8 ((v0 . v65)(v1 . (A v66 v65)))) (= (A (A (K) v65) (A v66 v65)) v65) NIL) (16 (instantiate 10 ((v0 . (K))(v1 . v65)(v2 . v66))) (= (A (A (K) v65) (A v66 v65)) (A (A (A (S) (K)) v66) v65)) NIL) (17 (paramod 15 (1) 16 (1)) (= v65 (A (A (A (S) (K)) v66) v65)) NIL) (18 (flip 17 ()) (= (A (A (A (S) (K)) v66) v65) v65) NIL) (19 (instantiate 18 ((v65 . v1)(v66 . v0))) (= (A (A (A (S) (K)) v0) v1) v1) (15)) (20 (instantiate 19 ((v1 . v65))) (= (A (A (A (S) (K)) v0) v65) v65) NIL) (21 (instantiate 10 ((v0 . v64)(v1 . v65)(v2 . (A (A (S) (K)) v0)))) (= (A (A v64 v65) (A (A (A (S) (K)) v0) v65)) (A (A (A (S) v64) (A (A (S) (K)) v0)) v65)) NIL) (22 (paramod 20 (1) 21 (1 2)) (= (A (A v64 v65) v65) (A (A (A (S) v64) (A (A (S) (K)) v0)) v65)) NIL) (23 (instantiate 22 ((v0 . v2)(v64 . v0)(v65 . v1))) (= (A (A v0 v1) v1) (A (A (A (S) v0) (A (A (S) (K)) v2)) v1)) (30)) (24 (flip 23 ()) (= (A (A (A (S) v0) (A (A (S) (K)) v2)) v1) (A (A v0 v1) v1)) NIL) (25 (instantiate 24 ((v1 . v2)(v2 . v1))) (= (A (A (A (S) v0) (A (A (S) (K)) v1)) v2) (A (A v0 v2) v2)) (32)) (26 (instantiate 14 ((v0 . (S))(v1 . v64)(v2 . (A (A (S) (K)) v65)))) (= (A (A (S) v64) (A (A (S) (K)) v65)) (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v65))) v64)) NIL) (27 (instantiate 25 ((v0 . v64)(v1 . v65)(v2 . v66))) (= (A (A (A (S) v64) (A (A (S) (K)) v65)) v66) (A (A v64 v66) v66)) NIL) (28 (paramod 26 (1) 27 (1 1)) (= (A (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v65))) v64) v66) (A (A v64 v66) v66)) NIL) (29 (instantiate 28 ((v64 . v1)(v65 . v0)(v66 . v2))) (= (A (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v0))) v1) v2) (A (A v1 v2) v2)) (1141)) (30 (flip 29 ()) (= (A (A v1 v2) v2) (A (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v0))) v1) v2)) NIL) (31 (instantiate 30 ((v0 . v2)(v1 . v0)(v2 . v1))) (= (A (A v0 v1) v1) (A (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v2))) v0) v1)) (1156)) (32 (instantiate 6 ((v0 . (A (A (S) (S)) (A (K) (A (A (S) (K)) v66)))))) (not (= (A (A (SK1 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66)))) (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))) (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))) (A (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))) (SK1 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))) (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))))) NIL) (33 (instantiate 31 ((v0 . (SK1 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66)))))(v1 . (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66)))))(v2 . v66))) (= (A (A (SK1 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66)))) (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))) (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))) (A (A (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))) (SK1 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66))))) (SK2 (A (A (S) (S)) (A (K) (A (A (S) (K)) v66)))))) NIL) (34 (resolve 32 () 33 ()) false (1157)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 25 clauses generated 922 clauses kept 1036 clauses forward subsumed 812 clauses back subsumed 0 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.12 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8565 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/lifsch.out0100664000076400007640000005275510103522211016632 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8585. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (S V2 (SK1 V2 V3))) (not (Q V3 (SK1 V2 V3))))) NIL) (2 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6))) NIL) (3 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (S V2 (SK1 V2 V3))) (not (S V3 V3)))) NIL) (4 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (S (SK1 V2 V3) V5) (not (Q V3 (SK1 V2 V3))))) NIL) (5 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6))) NIL) (6 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (S (SK1 V2 V3) V5) (not (S V3 V3)))) NIL) (7 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (Q V6 V6)) (not (Q V3 (SK1 V2 V3))))) NIL) (8 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (Q V6 V6)) (Q (SK1 V2 V3) V6))) NIL) (9 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (Q V6 V6)) (not (S V3 V3)))) NIL) (10 (input) (or (not (P V2 V2)) (or (not (S V2 (SK1 V2 V3))) (not (Q V3 (SK1 V2 V3))))) NIL) (11 (input) (or (not (P V2 V2)) (or (not (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6))) NIL) (12 (input) (or (not (P V2 V2)) (or (not (S V2 (SK1 V2 V3))) (not (S V3 V3)))) NIL) (13 (input) (or (not (P V2 V2)) (or (S (SK1 V2 V3) V5) (not (Q V3 (SK1 V2 V3))))) NIL) (14 (input) (or (not (P V2 V2)) (or (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6))) NIL) (15 (input) (or (not (P V2 V2)) (or (S (SK1 V2 V3) V5) (not (S V3 V3)))) NIL) (16 (input) (or (not (P V2 V2)) (or (not (Q V6 V6)) (not (Q V3 (SK1 V2 V3))))) NIL) (17 (input) (or (not (P V2 V2)) (or (not (Q V6 V6)) (Q (SK1 V2 V3) V6))) NIL) (18 (input) (or (not (P V2 V2)) (or (not (Q V6 V6)) (not (S V3 V3)))) NIL) (19 (input) (or (S V5 V2) (or (not (S V2 (SK1 V2 V3))) (not (Q V3 (SK1 V2 V3))))) NIL) (20 (input) (or (S V5 V2) (or (not (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6))) NIL) (21 (input) (or (S V5 V2) (or (not (S V2 (SK1 V2 V3))) (not (S V3 V3)))) NIL) (22 (input) (or (S V5 V2) (or (S (SK1 V2 V3) V5) (not (Q V3 (SK1 V2 V3))))) NIL) (23 (input) (or (S V5 V2) (or (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6))) NIL) (24 (input) (or (S V5 V2) (or (S (SK1 V2 V3) V5) (not (S V3 V3)))) NIL) (25 (input) (or (S V5 V2) (or (not (Q V6 V6)) (not (Q V3 (SK1 V2 V3))))) NIL) (26 (input) (or (S V5 V2) (or (not (Q V6 V6)) (Q (SK1 V2 V3) V6))) NIL) (27 (input) (or (S V5 V2) (or (not (Q V6 V6)) (not (S V3 V3)))) NIL) ) 0 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))| -Q(y,SK1(x,y)). 0 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))|Q(SK1(x,y),z). 0 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))| -S(y,y). 0 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)| -Q(y,SK1(x,y)). 0 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)|Q(SK1(x,y),u). 0 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)| -S(y,y). 0 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)| -Q(y,SK1(x,y)). 0 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)|Q(SK1(x,y),z). 0 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)| -S(y,y). 0 [] -P(x,x)| -S(x,SK1(x,y))| -Q(y,SK1(x,y)). 0 [] -P(x,x)| -S(x,SK1(x,y))|Q(SK1(x,y),z). 0 [] -P(x,x)| -S(x,SK1(x,y))| -S(y,y). 0 [] -P(x,x)|S(SK1(x,y),z)| -Q(y,SK1(x,y)). 0 [] -P(x,x)|S(SK1(x,y),z)|Q(SK1(x,y),u). 0 [] -P(x,x)|S(SK1(x,y),z)| -S(y,y). 0 [] -P(x,x)| -Q(y,y)| -Q(z,SK1(x,z)). 0 [] -P(x,x)| -Q(y,y)|Q(SK1(x,z),y). 0 [] -P(x,x)| -Q(y,y)| -S(z,z). 0 [] S(x,y)| -S(y,SK1(y,z))| -Q(z,SK1(y,z)). 0 [] S(x,y)| -S(y,SK1(y,z))|Q(SK1(y,z),u). 0 [] S(x,y)| -S(y,SK1(y,z))| -S(z,z). 0 [] S(x,y)|S(SK1(y,z),x)| -Q(z,SK1(y,z)). 0 [] S(x,y)|S(SK1(y,z),x)|Q(SK1(y,z),u). 0 [] S(x,y)|S(SK1(y,z),x)| -S(z,z). 0 [] S(x,y)| -Q(z,z)| -Q(u,SK1(y,u)). 0 [] S(x,y)| -Q(z,z)|Q(SK1(y,u),z). 0 [] S(x,y)| -Q(z,z)| -S(u,u). end_of_list. SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. dependent: set(hyper_res). dependent: set(factor). dependent: set(unit_deletion). ------------> process usable: ** KEPT (pick-wt=17): 1 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))| -Q(y,SK1(x,y)). ** KEPT (pick-wt=17): 2 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))|Q(SK1(x,y),z). ** KEPT (pick-wt=15): 3 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))| -S(y,y). ** KEPT (pick-wt=17): 4 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)| -Q(y,SK1(x,y)). ** KEPT (pick-wt=15): 5 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)| -S(y,y). ** KEPT (pick-wt=15): 6 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)| -Q(y,SK1(x,y)). ** KEPT (pick-wt=15): 7 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)|Q(SK1(x,y),z). ** KEPT (pick-wt=13): 8 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)| -S(y,y). ** KEPT (pick-wt=13): 9 [] -P(x,x)| -S(x,SK1(x,y))| -Q(y,SK1(x,y)). ** KEPT (pick-wt=13): 10 [] -P(x,x)| -S(x,SK1(x,y))|Q(SK1(x,y),z). ** KEPT (pick-wt=11): 11 [] -P(x,x)| -S(x,SK1(x,y))| -S(y,y). ** KEPT (pick-wt=13): 12 [] -P(x,x)|S(SK1(x,y),z)| -Q(y,SK1(x,y)). ** KEPT (pick-wt=13): 13 [] -P(x,x)|S(SK1(x,y),z)|Q(SK1(x,y),u). ** KEPT (pick-wt=11): 14 [] -P(x,x)|S(SK1(x,y),z)| -S(y,y). ** KEPT (pick-wt=11): 15 [] -P(x,x)| -Q(y,y)| -Q(z,SK1(x,z)). ** KEPT (pick-wt=11): 16 [] -P(x,x)| -Q(y,y)|Q(SK1(x,z),y). ** KEPT (pick-wt=9): 17 [] -P(x,x)| -Q(y,y)| -S(z,z). ** KEPT (pick-wt=13): 18 [] S(x,y)| -S(y,SK1(y,z))| -Q(z,SK1(y,z)). ** KEPT (pick-wt=13): 19 [] S(x,y)| -S(y,SK1(y,z))|Q(SK1(y,z),u). ** KEPT (pick-wt=11): 20 [] S(x,y)| -S(y,SK1(y,z))| -S(z,z). ** KEPT (pick-wt=13): 21 [] S(x,y)|S(SK1(y,z),x)| -Q(z,SK1(y,z)). ** KEPT (pick-wt=11): 22 [] S(x,y)|S(SK1(y,z),x)| -S(z,z). ** KEPT (pick-wt=11): 23 [] S(x,y)| -Q(z,z)| -Q(u,SK1(y,u)). ** KEPT (pick-wt=11): 24 [] S(x,y)| -Q(z,z)|Q(SK1(y,u),z). ** KEPT (pick-wt=9): 25 [] S(x,y)| -Q(z,z)| -S(u,u). ------------> process sos: ** KEPT (pick-wt=17): 26 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)|Q(SK1(x,y),u). ** KEPT (pick-wt=13): 27 [] S(x,y)|S(SK1(y,z),x)|Q(SK1(y,z),u). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=17) 26 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)|Q(SK1(x,y),u). given clause #2: (wt=13) 27 [] S(x,y)|S(SK1(y,z),x)|Q(SK1(y,z),u). given clause #3: (wt=17) 29 [hyper,20,26.2,26.2,factor_simp,factor_simp] P(SK1(x,y),SK1(x,y))|Q(SK1(x,y),z)|S(u,SK1(x,y)). given clause #4: (wt=12) 60 [hyper,2,29.3,factor_simp,factor_simp] P(SK1(x,y),SK1(x,y))|Q(SK1(x,y),z). given clause #5: (wt=10) 63 [hyper,23,60.2,60.2,factor_simp] P(SK1(x,y),SK1(x,y))|S(z,u). given clause #6: (wt=18) 34 [hyper,22,27.1] S(SK1(x,y),x)|Q(SK1(x,y),z)|S(u,v)|S(SK1(v,x),u). given clause #7: (wt=7) 65 [hyper,8,60.2,63.2,factor_simp,factor_simp] P(SK1(x,y),SK1(x,y)). given clause #8: (wt=14) 111 [hyper,13,65.1] S(SK1(SK1(x,y),z),u)|Q(SK1(SK1(x,y),z),v). given clause #9: (wt=7) 117 [hyper,11,65.1,111.1,111.1,factor_simp] Q(SK1(SK1(x,y),z),u). -------- PROOF -------- -----> EMPTY CLAUSE at 0.03 sec ----> 122 [hyper,15,65.1,117.1,117.1] $F. Length of proof is 6. Level of proof is 6. ---------------- PROOF ---------------- 2 [] P(SK1(x,y),SK1(x,y))| -S(x,SK1(x,y))|Q(SK1(x,y),z). 8 [] P(SK1(x,y),SK1(x,y))| -Q(z,z)| -S(y,y). 11 [] -P(x,x)| -S(x,SK1(x,y))| -S(y,y). 13 [] -P(x,x)|S(SK1(x,y),z)|Q(SK1(x,y),u). 15 [] -P(x,x)| -Q(y,y)| -Q(z,SK1(x,z)). 20 [] S(x,y)| -S(y,SK1(y,z))| -S(z,z). 23 [] S(x,y)| -Q(z,z)| -Q(u,SK1(y,u)). 26 [] P(SK1(x,y),SK1(x,y))|S(SK1(x,y),z)|Q(SK1(x,y),u). 29 [hyper,20,26.2,26.2,factor_simp,factor_simp] P(SK1(x,y),SK1(x,y))|Q(SK1(x,y),z)|S(u,SK1(x,y)). 60 [hyper,2,29.3,factor_simp,factor_simp] P(SK1(x,y),SK1(x,y))|Q(SK1(x,y),z). 63 [hyper,23,60.2,60.2,factor_simp] P(SK1(x,y),SK1(x,y))|S(z,u). 65 [hyper,8,60.2,63.2,factor_simp,factor_simp] P(SK1(x,y),SK1(x,y)). 111 [hyper,13,65.1] S(SK1(SK1(x,y),z),u)|Q(SK1(SK1(x,y),z),v). 117 [hyper,11,65.1,111.1,111.1,factor_simp] Q(SK1(SK1(x,y),z),u). 122 [hyper,15,65.1,117.1,117.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (S V2 (SK1 V2 V3))) (not (Q V3 (SK1 V2 V3))))) NIL) (2 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6))) NIL) (3 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (S V2 (SK1 V2 V3))) (not (S V3 V3)))) NIL) (4 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (S (SK1 V2 V3) V5) (not (Q V3 (SK1 V2 V3))))) NIL) (5 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6))) NIL) (6 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (S (SK1 V2 V3) V5) (not (S V3 V3)))) NIL) (7 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (Q V6 V6)) (not (Q V3 (SK1 V2 V3))))) NIL) (8 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (Q V6 V6)) (Q (SK1 V2 V3) V6))) NIL) (9 (input) (or (P (SK1 V2 V3) (SK1 V2 V3)) (or (not (Q V6 V6)) (not (S V3 V3)))) NIL) (10 (input) (or (not (P V2 V2)) (or (not (S V2 (SK1 V2 V3))) (not (Q V3 (SK1 V2 V3))))) NIL) (11 (input) (or (not (P V2 V2)) (or (not (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6))) NIL) (12 (input) (or (not (P V2 V2)) (or (not (S V2 (SK1 V2 V3))) (not (S V3 V3)))) NIL) (13 (input) (or (not (P V2 V2)) (or (S (SK1 V2 V3) V5) (not (Q V3 (SK1 V2 V3))))) NIL) (14 (input) (or (not (P V2 V2)) (or (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6))) NIL) (15 (input) (or (not (P V2 V2)) (or (S (SK1 V2 V3) V5) (not (S V3 V3)))) NIL) (16 (input) (or (not (P V2 V2)) (or (not (Q V6 V6)) (not (Q V3 (SK1 V2 V3))))) NIL) (17 (input) (or (not (P V2 V2)) (or (not (Q V6 V6)) (Q (SK1 V2 V3) V6))) NIL) (18 (input) (or (not (P V2 V2)) (or (not (Q V6 V6)) (not (S V3 V3)))) NIL) (19 (input) (or (S V5 V2) (or (not (S V2 (SK1 V2 V3))) (not (Q V3 (SK1 V2 V3))))) NIL) (20 (input) (or (S V5 V2) (or (not (S V2 (SK1 V2 V3))) (Q (SK1 V2 V3) V6))) NIL) (21 (input) (or (S V5 V2) (or (not (S V2 (SK1 V2 V3))) (not (S V3 V3)))) NIL) (22 (input) (or (S V5 V2) (or (S (SK1 V2 V3) V5) (not (Q V3 (SK1 V2 V3))))) NIL) (23 (input) (or (S V5 V2) (or (S (SK1 V2 V3) V5) (Q (SK1 V2 V3) V6))) NIL) (24 (input) (or (S V5 V2) (or (S (SK1 V2 V3) V5) (not (S V3 V3)))) NIL) (25 (input) (or (S V5 V2) (or (not (Q V6 V6)) (not (Q V3 (SK1 V2 V3))))) NIL) (26 (input) (or (S V5 V2) (or (not (Q V6 V6)) (Q (SK1 V2 V3) V6))) NIL) (27 (input) (or (S V5 V2) (or (not (Q V6 V6)) (not (S V3 V3)))) NIL) (28 (instantiate 2 ((V2 . v0)(V3 . v1)(V6 . v2))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (not (S v0 (SK1 v0 v1))) (Q (SK1 v0 v1) v2))) (2)) (29 (instantiate 9 ((V2 . v0)(V3 . v1)(V6 . v2))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (not (Q v2 v2)) (not (S v1 v1)))) (8)) (30 (instantiate 12 ((V2 . v0)(V3 . v1))) (or (not (P v0 v0)) (or (not (S v0 (SK1 v0 v1))) (not (S v1 v1)))) (11)) (31 (instantiate 14 ((V2 . v0)(V3 . v1)(V5 . v2)(V6 . v3))) (or (not (P v0 v0)) (or (S (SK1 v0 v1) v2) (Q (SK1 v0 v1) v3))) (13)) (32 (instantiate 16 ((V2 . v0)(V6 . v1)(V3 . v2))) (or (not (P v0 v0)) (or (not (Q v1 v1)) (not (Q v2 (SK1 v0 v2))))) (15)) (33 (instantiate 21 ((V5 . v0)(V2 . v1)(V3 . v2))) (or (S v0 v1) (or (not (S v1 (SK1 v1 v2))) (not (S v2 v2)))) (20)) (34 (instantiate 25 ((V5 . v0)(V2 . v1)(V6 . v2)(V3 . v3))) (or (S v0 v1) (or (not (Q v2 v2)) (not (Q v3 (SK1 v1 v3))))) (23)) (35 (instantiate 5 ((V2 . v0)(V3 . v1)(V5 . v2)(V6 . v3))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (S (SK1 v0 v1) v2) (Q (SK1 v0 v1) v3))) (26)) (36 (instantiate 33 ((v1 . (SK1 v64 v65)))) (or (S v0 (SK1 v64 v65)) (or (not (S (SK1 v64 v65) (SK1 (SK1 v64 v65) v2))) (not (S v2 v2)))) NIL) (37 (instantiate 35 ((v0 . v64)(v1 . v65)(v2 . (SK1 (SK1 v64 v65) v2))(v3 . v67))) (or (P (SK1 v64 v65) (SK1 v64 v65)) (or (S (SK1 v64 v65) (SK1 (SK1 v64 v65) v2)) (Q (SK1 v64 v65) v67))) NIL) (38 (resolve 36 (2 1) 37 (2 1)) (or (S v0 (SK1 v64 v65)) (or (not (S v2 v2)) (or (P (SK1 v64 v65) (SK1 v64 v65)) (Q (SK1 v64 v65) v67)))) NIL) (39 (instantiate 38 ((v2 . v3)(v64 . v1)(v65 . v2)(v67 . v4))) (or (S v0 (SK1 v1 v2)) (or (not (S v3 v3)) (or (P (SK1 v1 v2) (SK1 v1 v2)) (Q (SK1 v1 v2) v4)))) NIL) (40 (instantiate 39 ((v3 . (SK1 v64 v65)))) (or (S v0 (SK1 v1 v2)) (or (not (S (SK1 v64 v65) (SK1 v64 v65))) (or (P (SK1 v1 v2) (SK1 v1 v2)) (Q (SK1 v1 v2) v4)))) NIL) (41 (instantiate 35 ((v0 . v64)(v1 . v65)(v2 . (SK1 v64 v65))(v3 . v67))) (or (P (SK1 v64 v65) (SK1 v64 v65)) (or (S (SK1 v64 v65) (SK1 v64 v65)) (Q (SK1 v64 v65) v67))) NIL) (42 (resolve 40 (2 1) 41 (2 1)) (or (S v0 (SK1 v1 v2)) (or (P (SK1 v1 v2) (SK1 v1 v2)) (or (Q (SK1 v1 v2) v4) (or (P (SK1 v64 v65) (SK1 v64 v65)) (Q (SK1 v64 v65) v67))))) NIL) (43 (instantiate 42 ((v4 . v3)(v64 . v4)(v65 . v5)(v67 . v6))) (or (S v0 (SK1 v1 v2)) (or (P (SK1 v1 v2) (SK1 v1 v2)) (or (Q (SK1 v1 v2) v3) (or (P (SK1 v4 v5) (SK1 v4 v5)) (Q (SK1 v4 v5) v6))))) NIL) (44 (instantiate 43 ((v1 . v4)(v2 . v5))) (or (S v0 (SK1 v4 v5)) (or (P (SK1 v4 v5) (SK1 v4 v5)) (or (Q (SK1 v4 v5) v3) (or (P (SK1 v4 v5) (SK1 v4 v5)) (Q (SK1 v4 v5) v6))))) NIL) (45 (propositional 44) (or (S v0 (SK1 v4 v5)) (or (P (SK1 v4 v5) (SK1 v4 v5)) (or (Q (SK1 v4 v5) v3) (Q (SK1 v4 v5) v6)))) NIL) (46 (instantiate 45 ((v3 . v6))) (or (S v0 (SK1 v4 v5)) (or (P (SK1 v4 v5) (SK1 v4 v5)) (or (Q (SK1 v4 v5) v6) (Q (SK1 v4 v5) v6)))) NIL) (47 (propositional 46) (or (S v0 (SK1 v4 v5)) (or (P (SK1 v4 v5) (SK1 v4 v5)) (Q (SK1 v4 v5) v6))) NIL) (48 (instantiate 47 ((v4 . v1)(v5 . v2)(v6 . v3))) (or (S v0 (SK1 v1 v2)) (or (P (SK1 v1 v2) (SK1 v1 v2)) (Q (SK1 v1 v2) v3))) (29)) (49 (instantiate 28 ((v0 . v65)(v1 . v66))) (or (P (SK1 v65 v66) (SK1 v65 v66)) (or (not (S v65 (SK1 v65 v66))) (Q (SK1 v65 v66) v2))) NIL) (50 (instantiate 48 ((v0 . v65)(v1 . v65)(v2 . v66)(v3 . v67))) (or (S v65 (SK1 v65 v66)) (or (P (SK1 v65 v66) (SK1 v65 v66)) (Q (SK1 v65 v66) v67))) NIL) (51 (resolve 49 (2 1) 50 (1)) (or (P (SK1 v65 v66) (SK1 v65 v66)) (or (Q (SK1 v65 v66) v2) (or (P (SK1 v65 v66) (SK1 v65 v66)) (Q (SK1 v65 v66) v67)))) NIL) (52 (instantiate 51 ((v65 . v0)(v66 . v1)(v67 . v3))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (Q (SK1 v0 v1) v2) (or (P (SK1 v0 v1) (SK1 v0 v1)) (Q (SK1 v0 v1) v3)))) NIL) (53 (propositional 52) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (Q (SK1 v0 v1) v2) (Q (SK1 v0 v1) v3))) NIL) (54 (instantiate 53 ((v2 . v3))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (Q (SK1 v0 v1) v3) (Q (SK1 v0 v1) v3))) NIL) (55 (propositional 54) (or (P (SK1 v0 v1) (SK1 v0 v1)) (Q (SK1 v0 v1) v3)) NIL) (56 (instantiate 55 ((v3 . v2))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (Q (SK1 v0 v1) v2)) (60)) (57 (instantiate 34 ((v2 . (SK1 v64 v65)))) (or (S v0 v1) (or (not (Q (SK1 v64 v65) (SK1 v64 v65))) (not (Q v3 (SK1 v1 v3))))) NIL) (58 (instantiate 56 ((v0 . v64)(v1 . v65)(v2 . (SK1 v64 v65)))) (or (P (SK1 v64 v65) (SK1 v64 v65)) (Q (SK1 v64 v65) (SK1 v64 v65))) NIL) (59 (resolve 57 (2 1) 58 (2)) (or (S v0 v1) (or (not (Q v3 (SK1 v1 v3))) (P (SK1 v64 v65) (SK1 v64 v65)))) NIL) (60 (instantiate 59 ((v3 . v2)(v64 . v3)(v65 . v4))) (or (S v0 v1) (or (not (Q v2 (SK1 v1 v2))) (P (SK1 v3 v4) (SK1 v3 v4)))) NIL) (61 (instantiate 60 ((v2 . (SK1 v64 v65)))) (or (S v0 v1) (or (not (Q (SK1 v64 v65) (SK1 v1 (SK1 v64 v65)))) (P (SK1 v3 v4) (SK1 v3 v4)))) NIL) (62 (instantiate 56 ((v0 . v64)(v1 . v65)(v2 . (SK1 v1 (SK1 v64 v65))))) (or (P (SK1 v64 v65) (SK1 v64 v65)) (Q (SK1 v64 v65) (SK1 v1 (SK1 v64 v65)))) NIL) (63 (resolve 61 (2 1) 62 (2)) (or (S v0 v1) (or (P (SK1 v3 v4) (SK1 v3 v4)) (P (SK1 v64 v65) (SK1 v64 v65)))) NIL) (64 (instantiate 63 ((v3 . v2)(v4 . v3)(v64 . v4)(v65 . v5))) (or (S v0 v1) (or (P (SK1 v2 v3) (SK1 v2 v3)) (P (SK1 v4 v5) (SK1 v4 v5)))) NIL) (65 (instantiate 64 ((v2 . v4)(v3 . v5))) (or (S v0 v1) (or (P (SK1 v4 v5) (SK1 v4 v5)) (P (SK1 v4 v5) (SK1 v4 v5)))) NIL) (66 (propositional 65) (or (S v0 v1) (P (SK1 v4 v5) (SK1 v4 v5))) NIL) (67 (instantiate 66 ((v4 . v2)(v5 . v3))) (or (S v0 v1) (P (SK1 v2 v3) (SK1 v2 v3))) (63)) (68 (instantiate 29 ((v2 . (SK1 v64 v65)))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (not (Q (SK1 v64 v65) (SK1 v64 v65))) (not (S v1 v1)))) NIL) (69 (instantiate 56 ((v0 . v64)(v1 . v65)(v2 . (SK1 v64 v65)))) (or (P (SK1 v64 v65) (SK1 v64 v65)) (Q (SK1 v64 v65) (SK1 v64 v65))) NIL) (70 (resolve 68 (2 1) 69 (2)) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (not (S v1 v1)) (P (SK1 v64 v65) (SK1 v64 v65)))) NIL) (71 (instantiate 70 ((v64 . v2)(v65 . v3))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (not (S v1 v1)) (P (SK1 v2 v3) (SK1 v2 v3)))) NIL) (72 (instantiate 71 ((v1 . v65))) (or (P (SK1 v0 v65) (SK1 v0 v65)) (or (not (S v65 v65)) (P (SK1 v2 v3) (SK1 v2 v3)))) NIL) (73 (instantiate 67 ((v0 . v65)(v1 . v65)(v2 . v66)(v3 . v67))) (or (S v65 v65) (P (SK1 v66 v67) (SK1 v66 v67))) NIL) (74 (resolve 72 (2 1) 73 (1)) (or (P (SK1 v0 v65) (SK1 v0 v65)) (or (P (SK1 v2 v3) (SK1 v2 v3)) (P (SK1 v66 v67) (SK1 v66 v67)))) NIL) (75 (instantiate 74 ((v65 . v1)(v66 . v4)(v67 . v5))) (or (P (SK1 v0 v1) (SK1 v0 v1)) (or (P (SK1 v2 v3) (SK1 v2 v3)) (P (SK1 v4 v5) (SK1 v4 v5)))) NIL) (76 (instantiate 75 ((v0 . v2)(v1 . v3))) (or (P (SK1 v2 v3) (SK1 v2 v3)) (or (P (SK1 v2 v3) (SK1 v2 v3)) (P (SK1 v4 v5) (SK1 v4 v5)))) NIL) (77 (propositional 76) (or (P (SK1 v2 v3) (SK1 v2 v3)) (P (SK1 v4 v5) (SK1 v4 v5))) NIL) (78 (instantiate 77 ((v2 . v4)(v3 . v5))) (or (P (SK1 v4 v5) (SK1 v4 v5)) (P (SK1 v4 v5) (SK1 v4 v5))) NIL) (79 (propositional 78) (P (SK1 v4 v5) (SK1 v4 v5)) NIL) (80 (instantiate 79 ((v4 . v0)(v5 . v1))) (P (SK1 v0 v1) (SK1 v0 v1)) (65)) (81 (instantiate 31 ((v0 . (SK1 v64 v65)))) (or (not (P (SK1 v64 v65) (SK1 v64 v65))) (or (S (SK1 (SK1 v64 v65) v1) v2) (Q (SK1 (SK1 v64 v65) v1) v3))) NIL) (82 (instantiate 80 ((v0 . v64)(v1 . v65))) (P (SK1 v64 v65) (SK1 v64 v65)) NIL) (83 (resolve 81 (1) 82 ()) (or (S (SK1 (SK1 v64 v65) v1) v2) (Q (SK1 (SK1 v64 v65) v1) v3)) NIL) (84 (instantiate 83 ((v1 . v2)(v2 . v3)(v3 . v4)(v64 . v0)(v65 . v1))) (or (S (SK1 (SK1 v0 v1) v2) v3) (Q (SK1 (SK1 v0 v1) v2) v4)) (111)) (85 (instantiate 30 ((v0 . (SK1 v64 v65)))) (or (not (P (SK1 v64 v65) (SK1 v64 v65))) (or (not (S (SK1 v64 v65) (SK1 (SK1 v64 v65) v1))) (not (S v1 v1)))) NIL) (86 (instantiate 80 ((v0 . v64)(v1 . v65))) (P (SK1 v64 v65) (SK1 v64 v65)) NIL) (87 (resolve 85 (1) 86 ()) (or (not (S (SK1 v64 v65) (SK1 (SK1 v64 v65) v1))) (not (S v1 v1))) NIL) (88 (instantiate 87 ((v1 . v2)(v64 . v0)(v65 . v1))) (or (not (S (SK1 v0 v1) (SK1 (SK1 v0 v1) v2))) (not (S v2 v2))) NIL) (89 (instantiate 88 ((v0 . (SK1 v64 v65))(v1 . v66))) (or (not (S (SK1 (SK1 v64 v65) v66) (SK1 (SK1 (SK1 v64 v65) v66) v2))) (not (S v2 v2))) NIL) (90 (instantiate 84 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . (SK1 (SK1 (SK1 v64 v65) v66) v2))(v4 . v68))) (or (S (SK1 (SK1 v64 v65) v66) (SK1 (SK1 (SK1 v64 v65) v66) v2)) (Q (SK1 (SK1 v64 v65) v66) v68)) NIL) (91 (resolve 89 (1) 90 (1)) (or (not (S v2 v2)) (Q (SK1 (SK1 v64 v65) v66) v68)) NIL) (92 (instantiate 91 ((v2 . v0)(v64 . v1)(v65 . v2)(v66 . v3)(v68 . v4))) (or (not (S v0 v0)) (Q (SK1 (SK1 v1 v2) v3) v4)) NIL) (93 (instantiate 92 ((v0 . (SK1 (SK1 v64 v65) v66)))) (or (not (S (SK1 (SK1 v64 v65) v66) (SK1 (SK1 v64 v65) v66))) (Q (SK1 (SK1 v1 v2) v3) v4)) NIL) (94 (instantiate 84 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . (SK1 (SK1 v64 v65) v66))(v4 . v68))) (or (S (SK1 (SK1 v64 v65) v66) (SK1 (SK1 v64 v65) v66)) (Q (SK1 (SK1 v64 v65) v66) v68)) NIL) (95 (resolve 93 (1) 94 (1)) (or (Q (SK1 (SK1 v1 v2) v3) v4) (Q (SK1 (SK1 v64 v65) v66) v68)) NIL) (96 (instantiate 95 ((v1 . v0)(v2 . v1)(v3 . v2)(v4 . v3)(v64 . v4)(v65 . v5)(v66 . v6)(v68 . v7))) (or (Q (SK1 (SK1 v0 v1) v2) v3) (Q (SK1 (SK1 v4 v5) v6) v7)) NIL) (97 (instantiate 96 ((v0 . v4)(v1 . v5)(v2 . v6)(v3 . v7))) (or (Q (SK1 (SK1 v4 v5) v6) v7) (Q (SK1 (SK1 v4 v5) v6) v7)) NIL) (98 (propositional 97) (Q (SK1 (SK1 v4 v5) v6) v7) NIL) (99 (instantiate 98 ((v4 . v0)(v5 . v1)(v6 . v2)(v7 . v3))) (Q (SK1 (SK1 v0 v1) v2) v3) (117)) (100 (instantiate 32 ((v0 . (SK1 v64 v65)))) (or (not (P (SK1 v64 v65) (SK1 v64 v65))) (or (not (Q v1 v1)) (not (Q v2 (SK1 (SK1 v64 v65) v2))))) NIL) (101 (instantiate 80 ((v0 . v64)(v1 . v65))) (P (SK1 v64 v65) (SK1 v64 v65)) NIL) (102 (resolve 100 (1) 101 ()) (or (not (Q v1 v1)) (not (Q v2 (SK1 (SK1 v64 v65) v2)))) NIL) (103 (instantiate 102 ((v1 . v0)(v2 . v1)(v64 . v2)(v65 . v3))) (or (not (Q v0 v0)) (not (Q v1 (SK1 (SK1 v2 v3) v1)))) NIL) (104 (instantiate 103 ((v0 . (SK1 (SK1 v64 v65) v66)))) (or (not (Q (SK1 (SK1 v64 v65) v66) (SK1 (SK1 v64 v65) v66))) (not (Q v1 (SK1 (SK1 v2 v3) v1)))) NIL) (105 (instantiate 99 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . (SK1 (SK1 v64 v65) v66)))) (Q (SK1 (SK1 v64 v65) v66) (SK1 (SK1 v64 v65) v66)) NIL) (106 (resolve 104 (1) 105 ()) (not (Q v1 (SK1 (SK1 v2 v3) v1))) NIL) (107 (instantiate 106 ((v1 . v0)(v2 . v1)(v3 . v2))) (not (Q v0 (SK1 (SK1 v1 v2) v0))) NIL) (108 (instantiate 107 ((v0 . (SK1 (SK1 v64 v65) v66)))) (not (Q (SK1 (SK1 v64 v65) v66) (SK1 (SK1 v1 v2) (SK1 (SK1 v64 v65) v66)))) NIL) (109 (instantiate 99 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . (SK1 (SK1 v1 v2) (SK1 (SK1 v64 v65) v66))))) (Q (SK1 (SK1 v64 v65) v66) (SK1 (SK1 v1 v2) (SK1 (SK1 v64 v65) v66))) NIL) (110 (resolve 108 () 109 ()) false (122)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 9 clauses generated 283 clauses kept 121 clauses forward subsumed 188 clauses back subsumed 83 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8585 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/p-and-not-p.in0100644000076400007640000000023006747663307017225 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (P)) (2 (INPUT) (NOT (P)))) otter-3.3f/examples/ivy/p-and-not-p.out0100664000076400007640000000451210103522211017400 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8590. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (P) NIL) (2 (input) (not (P)) NIL) -------- PROOF -------- ) 0 [] P. 0 [] -P. end_of_list. SCAN INPUT: prop=1, horn=1, equality=0, symmetry=0, max_lits=1. The clause set is propositional; the strategy will be ordered hyperresolution with the propositional optimizations, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: set(propositional). dependent: set(sort_literals). ------------> process usable: ** KEPT (pick-wt=1): 1 [] -P. ------------> process sos: ** KEPT (pick-wt=1): 2 [] P. ----> UNIT CONFLICT at 0.00 sec ----> 3 [binary,2.1,1.1] $F. Length of proof is 0. Level of proof is 0. ---------------- PROOF ---------------- 1 [] -P. 2 [] P. 3 [binary,2.1,1.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (P) NIL) (2 (input) (not (P)) NIL) (3 (instantiate 2 ()) (not (P)) (1)) (4 (instantiate 1 ()) (P) (2)) (5 (resolve 3 () 4 ()) false (3)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 0 clauses generated 0 clauses kept 2 clauses forward subsumed 0 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8590 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/steam.out0100664000076400007640000006430610103522211016466 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8595. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (or (not (WOLF V1)) (ANIMAL V1)) NIL) (2 (input) (or (not (FOX V2)) (ANIMAL V2)) NIL) (3 (input) (or (not (BIRD V3)) (ANIMAL V3)) NIL) (4 (input) (or (not (SNAIL V4)) (ANIMAL V4)) NIL) (5 (input) (or (not (GRAIN V5)) (PLANT V5)) NIL) (6 (input) (WOLF (SK1)) NIL) (7 (input) (FOX (SK2)) NIL) (8 (input) (BIRD (SK3)) NIL) (9 (input) (SNAIL (SK4)) NIL) (10 (input) (GRAIN (SK5)) NIL) (11 (input) (or (not (SNAIL V11)) (or (not (BIRD V12)) (SMALLER V11 V12))) NIL) (12 (input) (or (not (BIRD V13)) (or (not (FOX V14)) (SMALLER V13 V14))) NIL) (13 (input) (or (not (FOX V15)) (or (not (WOLF V16)) (SMALLER V15 V16))) NIL) (14 (input) (or (not (SNAIL V17)) (PLANT (SK6 V17))) NIL) (15 (input) (or (not (SNAIL V17)) (EATS V17 (SK6 V17))) NIL) (16 (input) (or (not (WOLF V19)) (or (not (FOX V20)) (not (EATS V19 V20)))) NIL) (17 (input) (or (not (WOLF V21)) (or (not (GRAIN V22)) (not (EATS V21 V22)))) NIL) (18 (input) (or (not (BIRD V23)) (or (not (SNAIL V24)) (not (EATS V23 V24)))) NIL) (19 (input) (or (not (ANIMAL V25)) (or (not (PLANT V26)) (or (EATS V25 V26) (or (not (ANIMAL V27)) (or (not (SMALLER V27 V25)) (or (not (PLANT V28)) (or (not (EATS V27 V28)) (EATS V25 V27)))))))) NIL) (20 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (GRAIN (SK7 V29 V30))))) NIL) (21 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (not (EATS V30 (SK7 V29 V30)))))) NIL) ) 0 [] -WOLF(x)|ANIMAL(x). 0 [] -FOX(x)|ANIMAL(x). 0 [] -BIRD(x)|ANIMAL(x). 0 [] -SNAIL(x)|ANIMAL(x). 0 [] -GRAIN(x)|PLANT(x). 0 [] WOLF(SK1). 0 [] FOX(SK2). 0 [] BIRD(SK3). 0 [] SNAIL(SK4). 0 [] GRAIN(SK5). 0 [] -SNAIL(x)| -BIRD(y)|SMALLER(x,y). 0 [] -BIRD(x)| -FOX(y)|SMALLER(x,y). 0 [] -FOX(x)| -WOLF(y)|SMALLER(x,y). 0 [] -SNAIL(x)|PLANT(SK6(x)). 0 [] -SNAIL(x)|EATS(x,SK6(x)). 0 [] -WOLF(x)| -FOX(y)| -EATS(x,y). 0 [] -WOLF(x)| -GRAIN(y)| -EATS(x,y). 0 [] -BIRD(x)| -SNAIL(y)| -EATS(x,y). 0 [] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -PLANT(u)| -EATS(z,u)|EATS(x,z). 0 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)|GRAIN(SK7(x,y)). 0 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)| -EATS(y,SK7(x,y)). end_of_list. SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=8. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. dependent: set(hyper_res). dependent: set(factor). dependent: set(unit_deletion). ------------> process usable: ** KEPT (pick-wt=4): 1 [] -WOLF(x)|ANIMAL(x). ** KEPT (pick-wt=4): 2 [] -FOX(x)|ANIMAL(x). ** KEPT (pick-wt=4): 3 [] -BIRD(x)|ANIMAL(x). ** KEPT (pick-wt=4): 4 [] -SNAIL(x)|ANIMAL(x). ** KEPT (pick-wt=4): 5 [] -GRAIN(x)|PLANT(x). ** KEPT (pick-wt=7): 6 [] -SNAIL(x)| -BIRD(y)|SMALLER(x,y). ** KEPT (pick-wt=7): 7 [] -BIRD(x)| -FOX(y)|SMALLER(x,y). ** KEPT (pick-wt=7): 8 [] -FOX(x)| -WOLF(y)|SMALLER(x,y). ** KEPT (pick-wt=5): 9 [] -SNAIL(x)|PLANT(SK6(x)). ** KEPT (pick-wt=6): 10 [] -SNAIL(x)|EATS(x,SK6(x)). ** KEPT (pick-wt=7): 11 [] -WOLF(x)| -FOX(y)| -EATS(x,y). ** KEPT (pick-wt=7): 12 [] -WOLF(x)| -GRAIN(y)| -EATS(x,y). ** KEPT (pick-wt=7): 13 [] -BIRD(x)| -SNAIL(y)| -EATS(x,y). ** KEPT (pick-wt=20): 14 [] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -PLANT(u)| -EATS(z,u)|EATS(x,z). ** KEPT (pick-wt=11): 15 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)|GRAIN(SK7(x,y)). ** KEPT (pick-wt=12): 16 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)| -EATS(y,SK7(x,y)). ------------> process sos: ** KEPT (pick-wt=2): 24 [] WOLF(SK1). ** KEPT (pick-wt=2): 25 [] FOX(SK2). ** KEPT (pick-wt=2): 26 [] BIRD(SK3). ** KEPT (pick-wt=2): 27 [] SNAIL(SK4). ** KEPT (pick-wt=2): 28 [] GRAIN(SK5). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 24 [] WOLF(SK1). given clause #2: (wt=2) 25 [] FOX(SK2). given clause #3: (wt=2) 26 [] BIRD(SK3). given clause #4: (wt=2) 27 [] SNAIL(SK4). given clause #5: (wt=2) 28 [] GRAIN(SK5). given clause #6: (wt=2) 29 [hyper,1,24.1] ANIMAL(SK1). given clause #7: (wt=2) 31 [hyper,2,25.1] ANIMAL(SK2). given clause #8: (wt=2) 33 [hyper,3,26.1] ANIMAL(SK3). given clause #9: (wt=2) 37 [hyper,4,27.1] ANIMAL(SK4). given clause #10: (wt=2) 38 [hyper,5,28.1] PLANT(SK5). given clause #11: (wt=3) 30 [hyper,8,25.1,24.1] SMALLER(SK2,SK1). given clause #12: (wt=3) 32 [hyper,7,26.1,25.1] SMALLER(SK3,SK2). given clause #13: (wt=3) 35 [hyper,9,27.1] PLANT(SK6(SK4)). given clause #14: (wt=3) 36 [hyper,6,27.1,26.1] SMALLER(SK4,SK3). given clause #15: (wt=4) 34 [hyper,10,27.1] EATS(SK4,SK6(SK4)). given clause #16: (wt=7) 39 [hyper,18,33.1,35.1,37.1,36.1,34.1] EATS(SK3,SK6(SK4))|EATS(SK3,SK4). given clause #17: (wt=4) 44 [hyper,13,26.1,27.1,39.2] EATS(SK3,SK6(SK4)). given clause #18: (wt=6) 40 [hyper,14,33.1,38.1,37.1,36.1,35.1,34.1] EATS(SK3,SK5)|EATS(SK3,SK4). given clause #19: (wt=3) 48 [hyper,13,26.1,27.1,40.2] EATS(SK3,SK5). given clause #20: (wt=6) 46 [hyper,14,31.1,38.1,33.1,32.1,35.1,44.1] EATS(SK2,SK5)|EATS(SK2,SK3). given clause #21: (wt=7) 45 [hyper,18,31.1,35.1,33.1,32.1,44.1] EATS(SK2,SK6(SK4))|EATS(SK2,SK3). given clause #22: (wt=7) 51 [hyper,15,31.1,33.1,46.2] EATS(SK2,SK5)|GRAIN(SK7(SK2,SK3)). given clause #23: (wt=7) 53 [hyper,5,51.2] EATS(SK2,SK5)|PLANT(SK7(SK2,SK3)). given clause #24: (wt=8) 52 [hyper,15,31.1,33.1,45.2] EATS(SK2,SK6(SK4))|GRAIN(SK7(SK2,SK3)). given clause #25: (wt=8) 55 [hyper,5,52.2] EATS(SK2,SK6(SK4))|PLANT(SK7(SK2,SK3)). given clause #26: (wt=9) 49 [hyper,18,29.1,38.1,31.1,30.1,46.1] EATS(SK2,SK3)|EATS(SK1,SK5)|EATS(SK1,SK2). given clause #27: (wt=6) 58 [hyper,12,24.1,28.1,49.2] EATS(SK2,SK3)|EATS(SK1,SK2). given clause #28: (wt=3) 63 [hyper,11,24.1,25.1,58.2] EATS(SK2,SK3). given clause #29: (wt=4) 64 [hyper,15,31.1,33.1,63.1] GRAIN(SK7(SK2,SK3)). given clause #30: (wt=4) 65 [hyper,5,64.1] PLANT(SK7(SK2,SK3)). given clause #31: (wt=8) 66 [hyper,14,33.1,65.1,37.1,36.1,35.1,34.1] EATS(SK3,SK7(SK2,SK3))|EATS(SK3,SK4). given clause #32: (wt=3) 67 [hyper,16,31.1,33.1,63.1,66.1] EATS(SK3,SK4). -------- PROOF -------- -----> EMPTY CLAUSE at 0.01 sec ----> 71 [hyper,13,26.1,27.1,67.1] $F. Length of proof is 21. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -WOLF(x)|ANIMAL(x). 2 [] -FOX(x)|ANIMAL(x). 3 [] -BIRD(x)|ANIMAL(x). 4 [] -SNAIL(x)|ANIMAL(x). 5 [] -GRAIN(x)|PLANT(x). 6 [] -SNAIL(x)| -BIRD(y)|SMALLER(x,y). 7 [] -BIRD(x)| -FOX(y)|SMALLER(x,y). 8 [] -FOX(x)| -WOLF(y)|SMALLER(x,y). 9 [] -SNAIL(x)|PLANT(SK6(x)). 10 [] -SNAIL(x)|EATS(x,SK6(x)). 11 [] -WOLF(x)| -FOX(y)| -EATS(x,y). 12 [] -WOLF(x)| -GRAIN(y)| -EATS(x,y). 13 [] -BIRD(x)| -SNAIL(y)| -EATS(x,y). 14 [] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -PLANT(u)| -EATS(z,u)|EATS(x,z). 15 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)|GRAIN(SK7(x,y)). 16 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)| -EATS(y,SK7(x,y)). 18 [factor,14.2.6] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -EATS(z,y)|EATS(x,z). 24 [] WOLF(SK1). 25 [] FOX(SK2). 26 [] BIRD(SK3). 27 [] SNAIL(SK4). 28 [] GRAIN(SK5). 29 [hyper,1,24.1] ANIMAL(SK1). 30 [hyper,8,25.1,24.1] SMALLER(SK2,SK1). 31 [hyper,2,25.1] ANIMAL(SK2). 32 [hyper,7,26.1,25.1] SMALLER(SK3,SK2). 33 [hyper,3,26.1] ANIMAL(SK3). 34 [hyper,10,27.1] EATS(SK4,SK6(SK4)). 35 [hyper,9,27.1] PLANT(SK6(SK4)). 36 [hyper,6,27.1,26.1] SMALLER(SK4,SK3). 37 [hyper,4,27.1] ANIMAL(SK4). 38 [hyper,5,28.1] PLANT(SK5). 39 [hyper,18,33.1,35.1,37.1,36.1,34.1] EATS(SK3,SK6(SK4))|EATS(SK3,SK4). 44 [hyper,13,26.1,27.1,39.2] EATS(SK3,SK6(SK4)). 46 [hyper,14,31.1,38.1,33.1,32.1,35.1,44.1] EATS(SK2,SK5)|EATS(SK2,SK3). 49 [hyper,18,29.1,38.1,31.1,30.1,46.1] EATS(SK2,SK3)|EATS(SK1,SK5)|EATS(SK1,SK2). 58 [hyper,12,24.1,28.1,49.2] EATS(SK2,SK3)|EATS(SK1,SK2). 63 [hyper,11,24.1,25.1,58.2] EATS(SK2,SK3). 64 [hyper,15,31.1,33.1,63.1] GRAIN(SK7(SK2,SK3)). 65 [hyper,5,64.1] PLANT(SK7(SK2,SK3)). 66 [hyper,14,33.1,65.1,37.1,36.1,35.1,34.1] EATS(SK3,SK7(SK2,SK3))|EATS(SK3,SK4). 67 [hyper,16,31.1,33.1,63.1,66.1] EATS(SK3,SK4). 71 [hyper,13,26.1,27.1,67.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (or (not (WOLF V1)) (ANIMAL V1)) NIL) (2 (input) (or (not (FOX V2)) (ANIMAL V2)) NIL) (3 (input) (or (not (BIRD V3)) (ANIMAL V3)) NIL) (4 (input) (or (not (SNAIL V4)) (ANIMAL V4)) NIL) (5 (input) (or (not (GRAIN V5)) (PLANT V5)) NIL) (6 (input) (WOLF (SK1)) NIL) (7 (input) (FOX (SK2)) NIL) (8 (input) (BIRD (SK3)) NIL) (9 (input) (SNAIL (SK4)) NIL) (10 (input) (GRAIN (SK5)) NIL) (11 (input) (or (not (SNAIL V11)) (or (not (BIRD V12)) (SMALLER V11 V12))) NIL) (12 (input) (or (not (BIRD V13)) (or (not (FOX V14)) (SMALLER V13 V14))) NIL) (13 (input) (or (not (FOX V15)) (or (not (WOLF V16)) (SMALLER V15 V16))) NIL) (14 (input) (or (not (SNAIL V17)) (PLANT (SK6 V17))) NIL) (15 (input) (or (not (SNAIL V17)) (EATS V17 (SK6 V17))) NIL) (16 (input) (or (not (WOLF V19)) (or (not (FOX V20)) (not (EATS V19 V20)))) NIL) (17 (input) (or (not (WOLF V21)) (or (not (GRAIN V22)) (not (EATS V21 V22)))) NIL) (18 (input) (or (not (BIRD V23)) (or (not (SNAIL V24)) (not (EATS V23 V24)))) NIL) (19 (input) (or (not (ANIMAL V25)) (or (not (PLANT V26)) (or (EATS V25 V26) (or (not (ANIMAL V27)) (or (not (SMALLER V27 V25)) (or (not (PLANT V28)) (or (not (EATS V27 V28)) (EATS V25 V27)))))))) NIL) (20 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (GRAIN (SK7 V29 V30))))) NIL) (21 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (not (EATS V30 (SK7 V29 V30)))))) NIL) (22 (instantiate 1 ((V1 . v0))) (or (not (WOLF v0)) (ANIMAL v0)) (1)) (23 (instantiate 2 ((V2 . v0))) (or (not (FOX v0)) (ANIMAL v0)) (2)) (24 (instantiate 3 ((V3 . v0))) (or (not (BIRD v0)) (ANIMAL v0)) (3)) (25 (instantiate 4 ((V4 . v0))) (or (not (SNAIL v0)) (ANIMAL v0)) (4)) (26 (instantiate 5 ((V5 . v0))) (or (not (GRAIN v0)) (PLANT v0)) (5)) (27 (instantiate 11 ((V11 . v0)(V12 . v1))) (or (not (SNAIL v0)) (or (not (BIRD v1)) (SMALLER v0 v1))) (6)) (28 (instantiate 12 ((V13 . v0)(V14 . v1))) (or (not (BIRD v0)) (or (not (FOX v1)) (SMALLER v0 v1))) (7)) (29 (instantiate 13 ((V15 . v0)(V16 . v1))) (or (not (FOX v0)) (or (not (WOLF v1)) (SMALLER v0 v1))) (8)) (30 (instantiate 14 ((V17 . v0))) (or (not (SNAIL v0)) (PLANT (SK6 v0))) (9)) (31 (instantiate 15 ((V17 . v0))) (or (not (SNAIL v0)) (EATS v0 (SK6 v0))) (10)) (32 (instantiate 16 ((V19 . v0)(V20 . v1))) (or (not (WOLF v0)) (or (not (FOX v1)) (not (EATS v0 v1)))) (11)) (33 (instantiate 17 ((V21 . v0)(V22 . v1))) (or (not (WOLF v0)) (or (not (GRAIN v1)) (not (EATS v0 v1)))) (12)) (34 (instantiate 18 ((V23 . v0)(V24 . v1))) (or (not (BIRD v0)) (or (not (SNAIL v1)) (not (EATS v0 v1)))) (13)) (35 (instantiate 19 ((V25 . v0)(V26 . v1)(V27 . v2)(V28 . v3))) (or (not (ANIMAL v0)) (or (not (PLANT v1)) (or (EATS v0 v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS v0 v2)))))))) (14)) (36 (instantiate 20 ((V29 . v0)(V30 . v1))) (or (not (ANIMAL v0)) (or (not (ANIMAL v1)) (or (not (EATS v0 v1)) (GRAIN (SK7 v0 v1))))) (15)) (37 (instantiate 21 ((V29 . v0)(V30 . v1))) (or (not (ANIMAL v0)) (or (not (ANIMAL v1)) (or (not (EATS v0 v1)) (not (EATS v1 (SK7 v0 v1)))))) (16)) (38 (instantiate 35 ((v1 . v3))) (or (not (ANIMAL v0)) (or (not (PLANT v3)) (or (EATS v0 v3) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS v0 v2)))))))) NIL) (39 (propositional 38) (or (not (ANIMAL v0)) (or (not (PLANT v3)) (or (EATS v0 v3) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (EATS v2 v3)) (EATS v0 v2))))))) NIL) (40 (instantiate 39 ((v3 . v1))) (or (not (ANIMAL v0)) (or (not (PLANT v1)) (or (EATS v0 v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (EATS v2 v1)) (EATS v0 v2))))))) (18)) (41 (instantiate 6 ()) (WOLF (SK1)) (24)) (42 (instantiate 7 ()) (FOX (SK2)) (25)) (43 (instantiate 8 ()) (BIRD (SK3)) (26)) (44 (instantiate 9 ()) (SNAIL (SK4)) (27)) (45 (instantiate 10 ()) (GRAIN (SK5)) (28)) (46 (instantiate 22 ((v0 . (SK1)))) (or (not (WOLF (SK1))) (ANIMAL (SK1))) NIL) (47 (resolve 46 (1) 41 ()) (ANIMAL (SK1)) (29)) (48 (instantiate 29 ((v0 . (SK2)))) (or (not (FOX (SK2))) (or (not (WOLF v1)) (SMALLER (SK2) v1))) NIL) (49 (resolve 48 (1) 42 ()) (or (not (WOLF v1)) (SMALLER (SK2) v1)) NIL) (50 (instantiate 49 ((v1 . v0))) (or (not (WOLF v0)) (SMALLER (SK2) v0)) NIL) (51 (instantiate 50 ((v0 . (SK1)))) (or (not (WOLF (SK1))) (SMALLER (SK2) (SK1))) NIL) (52 (resolve 51 (1) 41 ()) (SMALLER (SK2) (SK1)) (30)) (53 (instantiate 23 ((v0 . (SK2)))) (or (not (FOX (SK2))) (ANIMAL (SK2))) NIL) (54 (resolve 53 (1) 42 ()) (ANIMAL (SK2)) (31)) (55 (instantiate 28 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (or (not (FOX v1)) (SMALLER (SK3) v1))) NIL) (56 (resolve 55 (1) 43 ()) (or (not (FOX v1)) (SMALLER (SK3) v1)) NIL) (57 (instantiate 56 ((v1 . v0))) (or (not (FOX v0)) (SMALLER (SK3) v0)) NIL) (58 (instantiate 57 ((v0 . (SK2)))) (or (not (FOX (SK2))) (SMALLER (SK3) (SK2))) NIL) (59 (resolve 58 (1) 42 ()) (SMALLER (SK3) (SK2)) (32)) (60 (instantiate 24 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (ANIMAL (SK3))) NIL) (61 (resolve 60 (1) 43 ()) (ANIMAL (SK3)) (33)) (62 (instantiate 31 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (EATS (SK4) (SK6 (SK4)))) NIL) (63 (resolve 62 (1) 44 ()) (EATS (SK4) (SK6 (SK4))) (34)) (64 (instantiate 30 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (PLANT (SK6 (SK4)))) NIL) (65 (resolve 64 (1) 44 ()) (PLANT (SK6 (SK4))) (35)) (66 (instantiate 27 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (or (not (BIRD v1)) (SMALLER (SK4) v1))) NIL) (67 (resolve 66 (1) 44 ()) (or (not (BIRD v1)) (SMALLER (SK4) v1)) NIL) (68 (instantiate 67 ((v1 . v0))) (or (not (BIRD v0)) (SMALLER (SK4) v0)) NIL) (69 (instantiate 68 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (SMALLER (SK4) (SK3))) NIL) (70 (resolve 69 (1) 43 ()) (SMALLER (SK4) (SK3)) (36)) (71 (instantiate 25 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (ANIMAL (SK4))) NIL) (72 (resolve 71 (1) 44 ()) (ANIMAL (SK4)) (37)) (73 (instantiate 26 ((v0 . (SK5)))) (or (not (GRAIN (SK5))) (PLANT (SK5))) NIL) (74 (resolve 73 (1) 45 ()) (PLANT (SK5)) (38)) (75 (instantiate 40 ((v0 . (SK3)))) (or (not (ANIMAL (SK3))) (or (not (PLANT v1)) (or (EATS (SK3) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK3))) (or (not (EATS v2 v1)) (EATS (SK3) v2))))))) NIL) (76 (resolve 75 (1) 61 ()) (or (not (PLANT v1)) (or (EATS (SK3) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK3))) (or (not (EATS v2 v1)) (EATS (SK3) v2)))))) NIL) (77 (instantiate 76 ((v1 . v0)(v2 . v1))) (or (not (PLANT v0)) (or (EATS (SK3) v0) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (EATS v1 v0)) (EATS (SK3) v1)))))) NIL) (78 (instantiate 77 ((v0 . (SK6 (SK4))))) (or (not (PLANT (SK6 (SK4)))) (or (EATS (SK3) (SK6 (SK4))) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (EATS v1 (SK6 (SK4)))) (EATS (SK3) v1)))))) NIL) (79 (resolve 78 (1) 65 ()) (or (EATS (SK3) (SK6 (SK4))) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (EATS v1 (SK6 (SK4)))) (EATS (SK3) v1))))) NIL) (80 (instantiate 79 ((v1 . v0))) (or (EATS (SK3) (SK6 (SK4))) (or (not (ANIMAL v0)) (or (not (SMALLER v0 (SK3))) (or (not (EATS v0 (SK6 (SK4)))) (EATS (SK3) v0))))) NIL) (81 (instantiate 80 ((v0 . (SK4)))) (or (EATS (SK3) (SK6 (SK4))) (or (not (ANIMAL (SK4))) (or (not (SMALLER (SK4) (SK3))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4)))))) NIL) (82 (resolve 81 (2 1) 72 ()) (or (EATS (SK3) (SK6 (SK4))) (or (not (SMALLER (SK4) (SK3))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4))))) NIL) (83 (resolve 82 (2 1) 70 ()) (or (EATS (SK3) (SK6 (SK4))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4)))) NIL) (84 (resolve 83 (2 1) 63 ()) (or (EATS (SK3) (SK6 (SK4))) (EATS (SK3) (SK4))) (39)) (85 (instantiate 34 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (or (not (SNAIL v1)) (not (EATS (SK3) v1)))) NIL) (86 (resolve 85 (1) 43 ()) (or (not (SNAIL v1)) (not (EATS (SK3) v1))) NIL) (87 (instantiate 86 ((v1 . v0))) (or (not (SNAIL v0)) (not (EATS (SK3) v0))) NIL) (88 (instantiate 87 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (not (EATS (SK3) (SK4)))) NIL) (89 (resolve 88 (1) 44 ()) (not (EATS (SK3) (SK4))) NIL) (90 (resolve 89 () 84 (2)) (EATS (SK3) (SK6 (SK4))) (44)) (91 (instantiate 35 ((v0 . (SK2)))) (or (not (ANIMAL (SK2))) (or (not (PLANT v1)) (or (EATS (SK2) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK2))) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS (SK2) v2)))))))) NIL) (92 (resolve 91 (1) 54 ()) (or (not (PLANT v1)) (or (EATS (SK2) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK2))) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS (SK2) v2))))))) NIL) (93 (instantiate 92 ((v1 . v0)(v2 . v1)(v3 . v2))) (or (not (PLANT v0)) (or (EATS (SK2) v0) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK2))) (or (not (PLANT v2)) (or (not (EATS v1 v2)) (EATS (SK2) v1))))))) NIL) (94 (instantiate 93 ((v0 . (SK5)))) (or (not (PLANT (SK5))) (or (EATS (SK2) (SK5)) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK2))) (or (not (PLANT v2)) (or (not (EATS v1 v2)) (EATS (SK2) v1))))))) NIL) (95 (resolve 94 (1) 74 ()) (or (EATS (SK2) (SK5)) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK2))) (or (not (PLANT v2)) (or (not (EATS v1 v2)) (EATS (SK2) v1)))))) NIL) (96 (instantiate 95 ((v1 . v0)(v2 . v1))) (or (EATS (SK2) (SK5)) (or (not (ANIMAL v0)) (or (not (SMALLER v0 (SK2))) (or (not (PLANT v1)) (or (not (EATS v0 v1)) (EATS (SK2) v0)))))) NIL) (97 (instantiate 96 ((v0 . (SK3)))) (or (EATS (SK2) (SK5)) (or (not (ANIMAL (SK3))) (or (not (SMALLER (SK3) (SK2))) (or (not (PLANT v1)) (or (not (EATS (SK3) v1)) (EATS (SK2) (SK3))))))) NIL) (98 (resolve 97 (2 1) 61 ()) (or (EATS (SK2) (SK5)) (or (not (SMALLER (SK3) (SK2))) (or (not (PLANT v1)) (or (not (EATS (SK3) v1)) (EATS (SK2) (SK3)))))) NIL) (99 (instantiate 98 ((v1 . v0))) (or (EATS (SK2) (SK5)) (or (not (SMALLER (SK3) (SK2))) (or (not (PLANT v0)) (or (not (EATS (SK3) v0)) (EATS (SK2) (SK3)))))) NIL) (100 (resolve 99 (2 1) 59 ()) (or (EATS (SK2) (SK5)) (or (not (PLANT v0)) (or (not (EATS (SK3) v0)) (EATS (SK2) (SK3))))) NIL) (101 (instantiate 100 ((v0 . (SK6 (SK4))))) (or (EATS (SK2) (SK5)) (or (not (PLANT (SK6 (SK4)))) (or (not (EATS (SK3) (SK6 (SK4)))) (EATS (SK2) (SK3))))) NIL) (102 (resolve 101 (2 1) 65 ()) (or (EATS (SK2) (SK5)) (or (not (EATS (SK3) (SK6 (SK4)))) (EATS (SK2) (SK3)))) NIL) (103 (resolve 102 (2 1) 90 ()) (or (EATS (SK2) (SK5)) (EATS (SK2) (SK3))) (46)) (104 (instantiate 40 ((v0 . (SK1)))) (or (not (ANIMAL (SK1))) (or (not (PLANT v1)) (or (EATS (SK1) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK1))) (or (not (EATS v2 v1)) (EATS (SK1) v2))))))) NIL) (105 (resolve 104 (1) 47 ()) (or (not (PLANT v1)) (or (EATS (SK1) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK1))) (or (not (EATS v2 v1)) (EATS (SK1) v2)))))) NIL) (106 (instantiate 105 ((v1 . v0)(v2 . v1))) (or (not (PLANT v0)) (or (EATS (SK1) v0) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK1))) (or (not (EATS v1 v0)) (EATS (SK1) v1)))))) NIL) (107 (instantiate 106 ((v0 . (SK5)))) (or (not (PLANT (SK5))) (or (EATS (SK1) (SK5)) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK1))) (or (not (EATS v1 (SK5))) (EATS (SK1) v1)))))) NIL) (108 (resolve 107 (1) 74 ()) (or (EATS (SK1) (SK5)) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK1))) (or (not (EATS v1 (SK5))) (EATS (SK1) v1))))) NIL) (109 (instantiate 108 ((v1 . v0))) (or (EATS (SK1) (SK5)) (or (not (ANIMAL v0)) (or (not (SMALLER v0 (SK1))) (or (not (EATS v0 (SK5))) (EATS (SK1) v0))))) NIL) (110 (instantiate 109 ((v0 . (SK2)))) (or (EATS (SK1) (SK5)) (or (not (ANIMAL (SK2))) (or (not (SMALLER (SK2) (SK1))) (or (not (EATS (SK2) (SK5))) (EATS (SK1) (SK2)))))) NIL) (111 (resolve 110 (2 1) 54 ()) (or (EATS (SK1) (SK5)) (or (not (SMALLER (SK2) (SK1))) (or (not (EATS (SK2) (SK5))) (EATS (SK1) (SK2))))) NIL) (112 (resolve 111 (2 1) 52 ()) (or (EATS (SK1) (SK5)) (or (not (EATS (SK2) (SK5))) (EATS (SK1) (SK2)))) NIL) (113 (resolve 112 (2 1) 103 (1)) (or (EATS (SK1) (SK5)) (or (EATS (SK1) (SK2)) (EATS (SK2) (SK3)))) (49)) (114 (instantiate 33 ((v0 . (SK1)))) (or (not (WOLF (SK1))) (or (not (GRAIN v1)) (not (EATS (SK1) v1)))) NIL) (115 (resolve 114 (1) 41 ()) (or (not (GRAIN v1)) (not (EATS (SK1) v1))) NIL) (116 (instantiate 115 ((v1 . v0))) (or (not (GRAIN v0)) (not (EATS (SK1) v0))) NIL) (117 (instantiate 116 ((v0 . (SK5)))) (or (not (GRAIN (SK5))) (not (EATS (SK1) (SK5)))) NIL) (118 (resolve 117 (1) 45 ()) (not (EATS (SK1) (SK5))) NIL) (119 (resolve 118 () 113 (1)) (or (EATS (SK1) (SK2)) (EATS (SK2) (SK3))) (58)) (120 (instantiate 32 ((v0 . (SK1)))) (or (not (WOLF (SK1))) (or (not (FOX v1)) (not (EATS (SK1) v1)))) NIL) (121 (resolve 120 (1) 41 ()) (or (not (FOX v1)) (not (EATS (SK1) v1))) NIL) (122 (instantiate 121 ((v1 . v0))) (or (not (FOX v0)) (not (EATS (SK1) v0))) NIL) (123 (instantiate 122 ((v0 . (SK2)))) (or (not (FOX (SK2))) (not (EATS (SK1) (SK2)))) NIL) (124 (resolve 123 (1) 42 ()) (not (EATS (SK1) (SK2))) NIL) (125 (resolve 124 () 119 (1)) (EATS (SK2) (SK3)) (63)) (126 (instantiate 36 ((v0 . (SK2)))) (or (not (ANIMAL (SK2))) (or (not (ANIMAL v1)) (or (not (EATS (SK2) v1)) (GRAIN (SK7 (SK2) v1))))) NIL) (127 (resolve 126 (1) 54 ()) (or (not (ANIMAL v1)) (or (not (EATS (SK2) v1)) (GRAIN (SK7 (SK2) v1)))) NIL) (128 (instantiate 127 ((v1 . v0))) (or (not (ANIMAL v0)) (or (not (EATS (SK2) v0)) (GRAIN (SK7 (SK2) v0)))) NIL) (129 (instantiate 128 ((v0 . (SK3)))) (or (not (ANIMAL (SK3))) (or (not (EATS (SK2) (SK3))) (GRAIN (SK7 (SK2) (SK3))))) NIL) (130 (resolve 129 (1) 61 ()) (or (not (EATS (SK2) (SK3))) (GRAIN (SK7 (SK2) (SK3)))) NIL) (131 (resolve 130 (1) 125 ()) (GRAIN (SK7 (SK2) (SK3))) (64)) (132 (instantiate 26 ((v0 . (SK7 (SK2) (SK3))))) (or (not (GRAIN (SK7 (SK2) (SK3)))) (PLANT (SK7 (SK2) (SK3)))) NIL) (133 (resolve 132 (1) 131 ()) (PLANT (SK7 (SK2) (SK3))) (65)) (134 (instantiate 35 ((v0 . (SK3)))) (or (not (ANIMAL (SK3))) (or (not (PLANT v1)) (or (EATS (SK3) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK3))) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS (SK3) v2)))))))) NIL) (135 (resolve 134 (1) 61 ()) (or (not (PLANT v1)) (or (EATS (SK3) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK3))) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS (SK3) v2))))))) NIL) (136 (instantiate 135 ((v1 . v0)(v2 . v1)(v3 . v2))) (or (not (PLANT v0)) (or (EATS (SK3) v0) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (PLANT v2)) (or (not (EATS v1 v2)) (EATS (SK3) v1))))))) NIL) (137 (instantiate 136 ((v0 . (SK7 (SK2) (SK3))))) (or (not (PLANT (SK7 (SK2) (SK3)))) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (PLANT v2)) (or (not (EATS v1 v2)) (EATS (SK3) v1))))))) NIL) (138 (resolve 137 (1) 133 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (PLANT v2)) (or (not (EATS v1 v2)) (EATS (SK3) v1)))))) NIL) (139 (instantiate 138 ((v1 . v0)(v2 . v1))) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (ANIMAL v0)) (or (not (SMALLER v0 (SK3))) (or (not (PLANT v1)) (or (not (EATS v0 v1)) (EATS (SK3) v0)))))) NIL) (140 (instantiate 139 ((v0 . (SK4)))) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (ANIMAL (SK4))) (or (not (SMALLER (SK4) (SK3))) (or (not (PLANT v1)) (or (not (EATS (SK4) v1)) (EATS (SK3) (SK4))))))) NIL) (141 (resolve 140 (2 1) 72 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (SMALLER (SK4) (SK3))) (or (not (PLANT v1)) (or (not (EATS (SK4) v1)) (EATS (SK3) (SK4)))))) NIL) (142 (instantiate 141 ((v1 . v0))) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (SMALLER (SK4) (SK3))) (or (not (PLANT v0)) (or (not (EATS (SK4) v0)) (EATS (SK3) (SK4)))))) NIL) (143 (resolve 142 (2 1) 70 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (PLANT v0)) (or (not (EATS (SK4) v0)) (EATS (SK3) (SK4))))) NIL) (144 (instantiate 143 ((v0 . (SK6 (SK4))))) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (PLANT (SK6 (SK4)))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4))))) NIL) (145 (resolve 144 (2 1) 65 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4)))) NIL) (146 (resolve 145 (2 1) 63 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (EATS (SK3) (SK4))) (66)) (147 (instantiate 37 ((v0 . (SK2)))) (or (not (ANIMAL (SK2))) (or (not (ANIMAL v1)) (or (not (EATS (SK2) v1)) (not (EATS v1 (SK7 (SK2) v1)))))) NIL) (148 (resolve 147 (1) 54 ()) (or (not (ANIMAL v1)) (or (not (EATS (SK2) v1)) (not (EATS v1 (SK7 (SK2) v1))))) NIL) (149 (instantiate 148 ((v1 . v0))) (or (not (ANIMAL v0)) (or (not (EATS (SK2) v0)) (not (EATS v0 (SK7 (SK2) v0))))) NIL) (150 (instantiate 149 ((v0 . (SK3)))) (or (not (ANIMAL (SK3))) (or (not (EATS (SK2) (SK3))) (not (EATS (SK3) (SK7 (SK2) (SK3)))))) NIL) (151 (resolve 150 (1) 61 ()) (or (not (EATS (SK2) (SK3))) (not (EATS (SK3) (SK7 (SK2) (SK3))))) NIL) (152 (resolve 151 (1) 125 ()) (not (EATS (SK3) (SK7 (SK2) (SK3)))) NIL) (153 (resolve 152 () 146 (1)) (EATS (SK3) (SK4)) (67)) (154 (instantiate 34 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (or (not (SNAIL v1)) (not (EATS (SK3) v1)))) NIL) (155 (resolve 154 (1) 43 ()) (or (not (SNAIL v1)) (not (EATS (SK3) v1))) NIL) (156 (instantiate 155 ((v1 . v0))) (or (not (SNAIL v0)) (not (EATS (SK3) v0))) NIL) (157 (instantiate 156 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (not (EATS (SK3) (SK4)))) NIL) (158 (resolve 157 (1) 44 ()) (not (EATS (SK3) (SK4))) NIL) (159 (resolve 158 () 153 ()) false (71)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 32 clauses generated 83 clauses kept 70 clauses forward subsumed 29 clauses back subsumed 24 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8595 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/cd-cn19.out0100664000076400007640000007300010103522211016502 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8560. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (or (not (P (I V1 V2))) (or (not (P V1)) (P V2))) NIL) (2 (input) (P (I (I V3 V4) (I (I V4 V5) (I V3 V5)))) NIL) (3 (input) (P (I (I (N V6) V6) V6)) NIL) (4 (input) (P (I V7 (I (N V7) V8))) NIL) (5 (input) (not (P (I (I (I (SK1) (SK2)) (SK3)) (I (SK2) (SK3))))) NIL) ) 0 [] -P(I(x,y))| -P(x)|P(y). 0 [] P(I(I(x,y),I(I(y,z),I(x,z)))). 0 [] P(I(I(N(x),x),x)). 0 [] P(I(x,I(N(x),y))). 0 [] -P(I(I(I(SK1,SK2),SK3),I(SK2,SK3))). end_of_list. SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -P(I(x,y))| -P(x)|P(y). ** KEPT (pick-wt=10): 2 [] -P(I(I(I(SK1,SK2),SK3),I(SK2,SK3))). ------------> process sos: ** KEPT (pick-wt=12): 3 [] P(I(I(x,y),I(I(y,z),I(x,z)))). ** KEPT (pick-wt=7): 4 [] P(I(I(N(x),x),x)). ** KEPT (pick-wt=7): 5 [] P(I(x,I(N(x),y))). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 3 [] P(I(I(x,y),I(I(y,z),I(x,z)))). given clause #2: (wt=7) 4 [] P(I(I(N(x),x),x)). given clause #3: (wt=7) 5 [] P(I(x,I(N(x),y))). given clause #4: (wt=10) 8 [hyper,1,5.1,5.1] P(I(N(I(x,I(N(x),y))),z)). given clause #5: (wt=10) 10 [hyper,1,5.1,4.1] P(I(N(I(I(N(x),x),x)),y)). given clause #6: (wt=16) 6 [hyper,1,3.1,3.1] P(I(I(I(I(x,y),I(z,y)),u),I(I(z,x),u))). given clause #7: (wt=11) 7 [hyper,1,3.1,4.1] P(I(I(x,y),I(I(N(x),x),y))). given clause #8: (wt=10) 28 [hyper,1,7.1,5.1] P(I(I(N(x),x),I(N(x),y))). given clause #9: (wt=11) 9 [hyper,1,3.1,5.1] P(I(I(I(N(x),y),z),I(x,z))). given clause #10: (wt=4) 40 [hyper,1,9.1,4.1] P(I(x,x)). given clause #11: (wt=15) 11 [hyper,1,5.1,3.1] P(I(N(I(I(x,y),I(I(y,z),I(x,z)))),u)). given clause #12: (wt=7) 42 [hyper,1,5.1,40.1] P(I(N(I(x,x)),y)). given clause #13: (wt=10) 39 [hyper,1,9.1,5.1] P(I(x,I(N(I(N(x),y)),z))). given clause #14: (wt=10) 47 [hyper,1,5.1,42.1] P(I(N(I(N(I(x,x)),y)),z)). given clause #15: (wt=11) 35 [hyper,1,6.1,9.1] P(I(I(x,N(y)),I(y,I(x,z)))). given clause #16: (wt=13) 12 [hyper,1,5.1,8.1] P(I(N(I(N(I(x,I(N(x),y))),z)),u)). given clause #17: (wt=9) 67 [hyper,1,9.1,35.1] P(I(x,I(y,I(N(x),z)))). given clause #18: (wt=9) 72 [hyper,1,35.1,42.1] P(I(x,I(N(I(y,y)),z))). given clause #19: (wt=11) 38 [hyper,1,9.1,7.1] P(I(x,I(I(N(N(x)),N(x)),y))). given clause #20: (wt=12) 71 [hyper,1,35.1,47.1] P(I(x,I(N(I(N(I(y,y)),z)),u))). given clause #21: (wt=13) 14 [hyper,1,5.1,10.1] P(I(N(I(N(I(I(N(x),x),x)),y)),z)). given clause #22: (wt=12) 74 [hyper,1,35.1,10.1] P(I(x,I(N(I(I(N(y),y),y)),z))). given clause #23: (wt=12) 75 [hyper,1,35.1,8.1] P(I(x,I(N(I(y,I(N(y),z))),u))). given clause #24: (wt=12) 81 [hyper,1,9.1,67.1] P(I(x,I(y,I(N(I(N(x),z)),u)))). given clause #25: (wt=12) 82 [hyper,1,7.1,67.1] P(I(I(N(x),x),I(y,I(N(x),z)))). given clause #26: (wt=16) 16 [hyper,1,6.1,6.1] P(I(I(x,I(y,z)),I(I(u,y),I(x,I(u,z))))). given clause #27: (wt=12) 84 [hyper,1,5.1,67.1] P(I(N(I(x,I(y,I(N(x),z)))),u)). given clause #28: (wt=12) 98 [hyper,1,5.1,72.1] P(I(N(I(x,I(N(I(y,y)),z))),u)). given clause #29: (wt=13) 29 [hyper,1,7.1,4.1] P(I(I(N(I(N(x),x)),I(N(x),x)),x)). given clause #30: (wt=13) 32 [hyper,1,5.1,28.1] P(I(N(I(I(N(x),x),I(N(x),y))),z)). given clause #31: (wt=19) 17 [hyper,1,5.1,6.1] P(I(N(I(I(I(I(x,y),I(z,y)),u),I(I(z,x),u))),v)). given clause #32: (wt=13) 46 [hyper,1,7.1,42.1] P(I(I(N(N(I(x,x))),N(I(x,x))),y)). given clause #33: (wt=13) 50 [hyper,1,9.1,39.1] P(I(x,I(N(I(N(I(N(x),y)),z)),u))). given clause #34: (wt=13) 51 [hyper,1,7.1,39.1] P(I(I(N(x),x),I(N(I(N(x),y)),z))). given clause #35: (wt=13) 53 [hyper,1,5.1,39.1] P(I(N(I(x,I(N(I(N(x),y)),z))),u)). given clause #36: (wt=20) 18 [hyper,1,3.1,6.1] P(I(I(I(I(x,y),z),u),I(I(I(I(y,v),I(x,v)),z),u))). given clause #37: (wt=13) 55 [hyper,1,39.1,42.1] P(I(N(I(N(I(N(I(x,x)),y)),z)),u)). given clause #38: (wt=13) 85 [hyper,1,3.1,67.1] P(I(I(I(x,I(N(y),z)),u),I(y,u))). given clause #39: (wt=12) 305 [hyper,1,85.1,5.1] P(I(x,I(N(I(y,I(N(x),z))),u))). given clause #40: (wt=13) 99 [hyper,1,3.1,72.1] P(I(I(I(N(I(x,x)),y),z),I(u,z))). given clause #41: (wt=15) 19 [hyper,1,6.1,5.1] P(I(I(x,y),I(N(I(I(y,z),I(x,z))),u))). given clause #42: (wt=6) 370 [hyper,1,99.1,4.1] P(I(x,I(y,y))). given clause #43: (wt=9) 413 [hyper,1,5.1,370.1] P(I(N(I(x,I(y,y))),z)). given clause #44: (wt=10) 412 [hyper,1,16.1,370.1] P(I(I(x,y),I(z,I(x,y)))). given clause #45: (wt=8) 433 [hyper,1,412.1,370.1] P(I(x,I(y,I(z,z)))). given clause #46: (wt=16) 20 [hyper,1,6.1,3.1] P(I(I(x,y),I(I(I(x,z),u),I(I(y,z),u)))). given clause #47: (wt=9) 455 [hyper,1,412.1,5.1] P(I(x,I(y,I(N(y),z)))). given clause #48: (wt=9) 456 [hyper,1,412.1,4.1] P(I(x,I(I(N(y),y),y))). given clause #49: (wt=10) 414 [hyper,1,3.1,370.1] P(I(I(I(x,x),y),I(z,y))). given clause #50: (wt=10) 458 [hyper,1,412.1,433.1] P(I(x,I(y,I(z,I(u,u))))). given clause #51: (wt=16) 21 [hyper,1,7.1,7.1] P(I(I(N(I(x,y)),I(x,y)),I(I(N(x),x),y))). given clause #52: (wt=11) 366 [hyper,1,99.1,82.1] P(I(x,I(y,I(N(I(z,z)),u)))). given clause #53: (wt=11) 407 [hyper,1,67.1,370.1] P(I(x,I(N(I(y,I(z,z))),u))). given clause #54: (wt=11) 421 [hyper,1,85.1,412.1] P(I(x,I(y,I(z,I(N(x),u))))). given clause #55: (wt=11) 441 [hyper,1,412.1,67.1] P(I(x,I(y,I(z,I(N(y),u))))). given clause #56: (wt=17) 22 [hyper,1,6.1,7.1] P(I(I(x,y),I(I(N(I(y,z)),I(y,z)),I(x,z)))). given clause #57: (wt=11) 466 [hyper,1,5.1,433.1] P(I(N(I(x,I(y,I(z,z)))),u)). given clause #58: (wt=11) 517 [hyper,1,412.1,455.1] P(I(x,I(y,I(z,I(N(z),u))))). given clause #59: (wt=11) 529 [hyper,1,412.1,456.1] P(I(x,I(y,I(I(N(z),z),z)))). given clause #60: (wt=12) 409 [hyper,1,39.1,370.1] P(I(N(I(N(I(x,I(y,y))),z)),u)). given clause #61: (wt=14) 23 [hyper,1,5.1,7.1] P(I(N(I(I(x,y),I(I(N(x),x),y))),z)). given clause #62: (wt=12) 419 [hyper,1,412.1,412.1] P(I(x,I(I(y,z),I(u,I(y,z))))). given clause #63: (wt=12) 444 [hyper,1,412.1,39.1] P(I(x,I(y,I(N(I(N(y),z)),u)))). given clause #64: (wt=12) 448 [hyper,1,412.1,28.1] P(I(x,I(I(N(y),y),I(N(y),z)))). given clause #65: (wt=12) 467 [hyper,1,3.1,433.1] P(I(I(I(x,I(y,y)),z),I(u,z))). given clause #66: (wt=15) 24 [hyper,1,3.1,7.1] P(I(I(I(I(N(x),x),y),z),I(I(x,y),z))). given clause #67: (wt=12) 527 [hyper,1,5.1,455.1] P(I(N(I(x,I(y,I(N(y),z)))),u)). given clause #68: (wt=12) 539 [hyper,1,5.1,456.1] P(I(N(I(x,I(I(N(y),y),y))),z)). given clause #69: (wt=12) 541 [hyper,1,412.1,414.1] P(I(x,I(I(I(y,y),z),I(u,z)))). given clause #70: (wt=12) 551 [hyper,1,412.1,458.1] P(I(x,I(y,I(z,I(u,I(v,v)))))). given clause #71: (wt=19) 25 [hyper,1,7.1,10.1] P(I(I(N(N(I(I(N(x),x),x))),N(I(I(N(x),x),x))),y)). given clause #72: (wt=13) 183 [hyper,1,16.1,72.1] P(I(I(x,N(I(y,y))),I(z,I(x,u)))). given clause #73: (wt=13) 304 [hyper,1,85.1,16.1] P(I(x,I(I(y,N(x)),I(z,I(y,u))))). given clause #74: (wt=13) 306 [hyper,1,85.1,3.1] P(I(x,I(I(I(N(x),y),z),I(u,z)))). given clause #75: (wt=13) 411 [hyper,1,19.1,370.1] P(I(N(I(I(I(x,x),y),I(z,y))),u)). given clause #76: (wt=19) 26 [hyper,1,7.1,8.1] P(I(I(N(N(I(x,I(N(x),y)))),N(I(x,I(N(x),y)))),z)). given clause #77: (wt=13) 431 [hyper,1,5.1,412.1] P(I(N(I(I(x,y),I(z,I(x,y)))),u)). given clause #78: (wt=13) 445 [hyper,1,412.1,38.1] P(I(x,I(y,I(I(N(N(y)),N(y)),z)))). given clause #79: (wt=13) 446 [hyper,1,412.1,35.1] P(I(x,I(I(y,N(z)),I(z,I(y,u))))). given clause #80: (wt=13) 452 [hyper,1,412.1,9.1] P(I(x,I(I(I(N(y),z),u),I(y,u)))). given clause #81: (wt=27) 27 [hyper,1,7.1,6.1] P(I(I(N(I(I(I(x,y),I(z,y)),u)),I(I(I(x,y),I(z,y)),u)),I(I(z,x),u))). given clause #82: (wt=13) 453 [hyper,1,412.1,7.1] P(I(x,I(I(y,z),I(I(N(y),y),z)))). given clause #83: (wt=13) 461 [hyper,1,67.1,433.1] P(I(x,I(N(I(y,I(z,I(u,u)))),v))). given clause #84: (wt=13) 526 [hyper,1,16.1,455.1] P(I(I(x,y),I(z,I(x,I(N(y),u))))). given clause #85: (wt=13) 528 [hyper,1,3.1,455.1] P(I(I(I(x,I(N(x),y)),z),I(u,z))). given clause #86: (wt=17) 30 [hyper,1,7.1,3.1] P(I(I(N(I(x,y)),I(x,y)),I(I(y,z),I(x,z)))). given clause #87: (wt=13) 538 [hyper,1,16.1,456.1] P(I(I(x,I(N(y),y)),I(z,I(x,y)))). given clause #88: (wt=8) 1315 [hyper,1,85.1,538.1] P(I(x,I(y,I(z,x)))). given clause #89: (wt=8) 1341 [hyper,1,538.1,1315.1] P(I(x,I(y,I(z,y)))). -------- PROOF -------- ----> UNIT CONFLICT at 0.09 sec ----> 1424 [binary,1423.1,2.1] $F. Length of proof is 19. Level of proof is 12. ---------------- PROOF ---------------- 1 [] -P(I(x,y))| -P(x)|P(y). 2 [] -P(I(I(I(SK1,SK2),SK3),I(SK2,SK3))). 3 [] P(I(I(x,y),I(I(y,z),I(x,z)))). 4 [] P(I(I(N(x),x),x)). 5 [] P(I(x,I(N(x),y))). 6 [hyper,1,3.1,3.1] P(I(I(I(I(x,y),I(z,y)),u),I(I(z,x),u))). 7 [hyper,1,3.1,4.1] P(I(I(x,y),I(I(N(x),x),y))). 9 [hyper,1,3.1,5.1] P(I(I(I(N(x),y),z),I(x,z))). 16 [hyper,1,6.1,6.1] P(I(I(x,I(y,z)),I(I(u,y),I(x,I(u,z))))). 30 [hyper,1,7.1,3.1] P(I(I(N(I(x,y)),I(x,y)),I(I(y,z),I(x,z)))). 35 [hyper,1,6.1,9.1] P(I(I(x,N(y)),I(y,I(x,z)))). 40 [hyper,1,9.1,4.1] P(I(x,x)). 42 [hyper,1,5.1,40.1] P(I(N(I(x,x)),y)). 67 [hyper,1,9.1,35.1] P(I(x,I(y,I(N(x),z)))). 72 [hyper,1,35.1,42.1] P(I(x,I(N(I(y,y)),z))). 85 [hyper,1,3.1,67.1] P(I(I(I(x,I(N(y),z)),u),I(y,u))). 99 [hyper,1,3.1,72.1] P(I(I(I(N(I(x,x)),y),z),I(u,z))). 370 [hyper,1,99.1,4.1] P(I(x,I(y,y))). 412 [hyper,1,16.1,370.1] P(I(I(x,y),I(z,I(x,y)))). 456 [hyper,1,412.1,4.1] P(I(x,I(I(N(y),y),y))). 538 [hyper,1,16.1,456.1] P(I(I(x,I(N(y),y)),I(z,I(x,y)))). 1315 [hyper,1,85.1,538.1] P(I(x,I(y,I(z,x)))). 1341 [hyper,1,538.1,1315.1] P(I(x,I(y,I(z,y)))). 1423 [hyper,1,30.1,1341.1] P(I(I(I(x,y),z),I(y,z))). 1424 [binary,1423.1,2.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (or (not (P (I V1 V2))) (or (not (P V1)) (P V2))) NIL) (2 (input) (P (I (I V3 V4) (I (I V4 V5) (I V3 V5)))) NIL) (3 (input) (P (I (I (N V6) V6) V6)) NIL) (4 (input) (P (I V7 (I (N V7) V8))) NIL) (5 (input) (not (P (I (I (I (SK1) (SK2)) (SK3)) (I (SK2) (SK3))))) NIL) (6 (instantiate 1 ((V1 . v0)(V2 . v1))) (or (not (P (I v0 v1))) (or (not (P v0)) (P v1))) (1)) (7 (instantiate 5 ()) (not (P (I (I (I (SK1) (SK2)) (SK3)) (I (SK2) (SK3))))) (2)) (8 (instantiate 2 ((V3 . v0)(V4 . v1)(V5 . v2))) (P (I (I v0 v1) (I (I v1 v2) (I v0 v2)))) (3)) (9 (instantiate 3 ((V6 . v0))) (P (I (I (N v0) v0) v0)) (4)) (10 (instantiate 4 ((V7 . v0)(V8 . v1))) (P (I v0 (I (N v0) v1))) (5)) (11 (instantiate 6 ((v0 . (I v64 v65))(v1 . (I (I v65 v66) (I v64 v66))))) (or (not (P (I (I v64 v65) (I (I v65 v66) (I v64 v66))))) (or (not (P (I v64 v65))) (P (I (I v65 v66) (I v64 v66))))) NIL) (12 (instantiate 8 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I v64 v65) (I (I v65 v66) (I v64 v66)))) NIL) (13 (resolve 11 (1) 12 ()) (or (not (P (I v64 v65))) (P (I (I v65 v66) (I v64 v66)))) NIL) (14 (instantiate 13 ((v64 . v0)(v65 . v1)(v66 . v2))) (or (not (P (I v0 v1))) (P (I (I v1 v2) (I v0 v2)))) NIL) (15 (instantiate 14 ((v0 . (I v64 v65))(v1 . (I (I v65 v66) (I v64 v66))))) (or (not (P (I (I v64 v65) (I (I v65 v66) (I v64 v66))))) (P (I (I (I (I v65 v66) (I v64 v66)) v2) (I (I v64 v65) v2)))) NIL) (16 (instantiate 8 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I v64 v65) (I (I v65 v66) (I v64 v66)))) NIL) (17 (resolve 15 (1) 16 ()) (P (I (I (I (I v65 v66) (I v64 v66)) v2) (I (I v64 v65) v2))) NIL) (18 (instantiate 17 ((v2 . v3)(v64 . v2)(v65 . v0)(v66 . v1))) (P (I (I (I (I v0 v1) (I v2 v1)) v3) (I (I v2 v0) v3))) (6)) (19 (instantiate 6 ((v0 . (I v64 v65))(v1 . (I (I v65 v66) (I v64 v66))))) (or (not (P (I (I v64 v65) (I (I v65 v66) (I v64 v66))))) (or (not (P (I v64 v65))) (P (I (I v65 v66) (I v64 v66))))) NIL) (20 (instantiate 8 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I v64 v65) (I (I v65 v66) (I v64 v66)))) NIL) (21 (resolve 19 (1) 20 ()) (or (not (P (I v64 v65))) (P (I (I v65 v66) (I v64 v66)))) NIL) (22 (instantiate 21 ((v64 . v0)(v65 . v1)(v66 . v2))) (or (not (P (I v0 v1))) (P (I (I v1 v2) (I v0 v2)))) NIL) (23 (instantiate 22 ((v0 . (I (N v64) v64))(v1 . v64))) (or (not (P (I (I (N v64) v64) v64))) (P (I (I v64 v2) (I (I (N v64) v64) v2)))) NIL) (24 (instantiate 9 ((v0 . v64))) (P (I (I (N v64) v64) v64)) NIL) (25 (resolve 23 (1) 24 ()) (P (I (I v64 v2) (I (I (N v64) v64) v2))) NIL) (26 (instantiate 25 ((v2 . v1)(v64 . v0))) (P (I (I v0 v1) (I (I (N v0) v0) v1))) (7)) (27 (instantiate 6 ((v0 . (I v64 v65))(v1 . (I (I v65 v66) (I v64 v66))))) (or (not (P (I (I v64 v65) (I (I v65 v66) (I v64 v66))))) (or (not (P (I v64 v65))) (P (I (I v65 v66) (I v64 v66))))) NIL) (28 (instantiate 8 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I v64 v65) (I (I v65 v66) (I v64 v66)))) NIL) (29 (resolve 27 (1) 28 ()) (or (not (P (I v64 v65))) (P (I (I v65 v66) (I v64 v66)))) NIL) (30 (instantiate 29 ((v64 . v0)(v65 . v1)(v66 . v2))) (or (not (P (I v0 v1))) (P (I (I v1 v2) (I v0 v2)))) NIL) (31 (instantiate 30 ((v0 . v64)(v1 . (I (N v64) v65)))) (or (not (P (I v64 (I (N v64) v65)))) (P (I (I (I (N v64) v65) v2) (I v64 v2)))) NIL) (32 (instantiate 10 ((v0 . v64)(v1 . v65))) (P (I v64 (I (N v64) v65))) NIL) (33 (resolve 31 (1) 32 ()) (P (I (I (I (N v64) v65) v2) (I v64 v2))) NIL) (34 (instantiate 33 ((v64 . v0)(v65 . v1))) (P (I (I (I (N v0) v1) v2) (I v0 v2))) (9)) (35 (instantiate 6 ((v0 . (I (I (I v64 v65) (I v66 v65)) v67))(v1 . (I (I v66 v64) v67)))) (or (not (P (I (I (I (I v64 v65) (I v66 v65)) v67) (I (I v66 v64) v67)))) (or (not (P (I (I (I v64 v65) (I v66 v65)) v67))) (P (I (I v66 v64) v67)))) NIL) (36 (instantiate 18 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . v67))) (P (I (I (I (I v64 v65) (I v66 v65)) v67) (I (I v66 v64) v67))) NIL) (37 (resolve 35 (1) 36 ()) (or (not (P (I (I (I v64 v65) (I v66 v65)) v67))) (P (I (I v66 v64) v67))) NIL) (38 (instantiate 37 ((v64 . v0)(v65 . v1)(v66 . v2)(v67 . v3))) (or (not (P (I (I (I v0 v1) (I v2 v1)) v3))) (P (I (I v2 v0) v3))) NIL) (39 (instantiate 38 ((v0 . (I v64 v65))(v1 . (I v66 v65))(v3 . (I (I v66 v64) (I v2 (I v66 v65)))))) (or (not (P (I (I (I (I v64 v65) (I v66 v65)) (I v2 (I v66 v65))) (I (I v66 v64) (I v2 (I v66 v65)))))) (P (I (I v2 (I v64 v65)) (I (I v66 v64) (I v2 (I v66 v65)))))) NIL) (40 (instantiate 18 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . (I v2 (I v66 v65))))) (P (I (I (I (I v64 v65) (I v66 v65)) (I v2 (I v66 v65))) (I (I v66 v64) (I v2 (I v66 v65))))) NIL) (41 (resolve 39 (1) 40 ()) (P (I (I v2 (I v64 v65)) (I (I v66 v64) (I v2 (I v66 v65))))) NIL) (42 (instantiate 41 ((v2 . v0)(v64 . v1)(v65 . v2)(v66 . v3))) (P (I (I v0 (I v1 v2)) (I (I v3 v1) (I v0 (I v3 v2))))) (16)) (43 (instantiate 6 ((v0 . (I v64 v65))(v1 . (I (I (N v64) v64) v65)))) (or (not (P (I (I v64 v65) (I (I (N v64) v64) v65)))) (or (not (P (I v64 v65))) (P (I (I (N v64) v64) v65)))) NIL) (44 (instantiate 26 ((v0 . v64)(v1 . v65))) (P (I (I v64 v65) (I (I (N v64) v64) v65))) NIL) (45 (resolve 43 (1) 44 ()) (or (not (P (I v64 v65))) (P (I (I (N v64) v64) v65))) NIL) (46 (instantiate 45 ((v64 . v0)(v65 . v1))) (or (not (P (I v0 v1))) (P (I (I (N v0) v0) v1))) NIL) (47 (instantiate 46 ((v0 . (I v64 v65))(v1 . (I (I v65 v66) (I v64 v66))))) (or (not (P (I (I v64 v65) (I (I v65 v66) (I v64 v66))))) (P (I (I (N (I v64 v65)) (I v64 v65)) (I (I v65 v66) (I v64 v66))))) NIL) (48 (instantiate 8 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I v64 v65) (I (I v65 v66) (I v64 v66)))) NIL) (49 (resolve 47 (1) 48 ()) (P (I (I (N (I v64 v65)) (I v64 v65)) (I (I v65 v66) (I v64 v66)))) NIL) (50 (instantiate 49 ((v64 . v0)(v65 . v1)(v66 . v2))) (P (I (I (N (I v0 v1)) (I v0 v1)) (I (I v1 v2) (I v0 v2)))) (30)) (51 (instantiate 6 ((v0 . (I (I (I v64 v65) (I v66 v65)) v67))(v1 . 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(I v65 v67)))) (or (not (P (I (I (I v64 (I (N v65) v66)) v67) (I v65 v67)))) (or (not (P (I (I v64 (I (N v65) v66)) v67))) (P (I v65 v67)))) NIL) (140 (instantiate 98 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . v67))) (P (I (I (I v64 (I (N v65) v66)) v67) (I v65 v67))) NIL) (141 (resolve 139 (1) 140 ()) (or (not (P (I (I v64 (I (N v65) v66)) v67))) (P (I v65 v67))) NIL) (142 (instantiate 141 ((v64 . v0)(v65 . v1)(v66 . v2)(v67 . v3))) (or (not (P (I (I v0 (I (N v1) v2)) v3))) (P (I v1 v3))) NIL) (143 (instantiate 142 ((v0 . v64)(v1 . v65)(v2 . v65)(v3 . (I v66 (I v64 v65))))) (or (not (P (I (I v64 (I (N v65) v65)) (I v66 (I v64 v65))))) (P (I v65 (I v66 (I v64 v65))))) NIL) (144 (instantiate 138 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I v64 (I (N v65) v65)) (I v66 (I v64 v65)))) NIL) (145 (resolve 143 (1) 144 ()) (P (I v65 (I v66 (I v64 v65)))) NIL) (146 (instantiate 145 ((v64 . v2)(v65 . v0)(v66 . v1))) (P (I v0 (I v1 (I v2 v0)))) (1315)) (147 (instantiate 6 ((v0 . 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(I (I v65 v66) (I v64 v66))))) (or (not (P (I (I (N (I v64 v65)) (I v64 v65)) (I (I v65 v66) (I v64 v66))))) (or (not (P (I (N (I v64 v65)) (I v64 v65)))) (P (I (I v65 v66) (I v64 v66))))) NIL) (156 (instantiate 50 ((v0 . v64)(v1 . v65)(v2 . v66))) (P (I (I (N (I v64 v65)) (I v64 v65)) (I (I v65 v66) (I v64 v66)))) NIL) (157 (resolve 155 (1) 156 ()) (or (not (P (I (N (I v64 v65)) (I v64 v65)))) (P (I (I v65 v66) (I v64 v66)))) NIL) (158 (instantiate 157 ((v64 . v0)(v65 . v1)(v66 . v2))) (or (not (P (I (N (I v0 v1)) (I v0 v1)))) (P (I (I v1 v2) (I v0 v2)))) NIL) (159 (instantiate 158 ((v0 . v65)(v1 . (I v66 v65)))) (or (not (P (I (N (I v65 (I v66 v65))) (I v65 (I v66 v65))))) (P (I (I (I v66 v65) v2) (I v65 v2)))) NIL) (160 (instantiate 154 ((v0 . (N (I v65 (I v66 v65))))(v1 . v65)(v2 . v66))) (P (I (N (I v65 (I v66 v65))) (I v65 (I v66 v65)))) NIL) (161 (resolve 159 (1) 160 ()) (P (I (I (I v66 v65) v2) (I v65 v2))) NIL) (162 (instantiate 161 ((v65 . v1)(v66 . v0))) (P (I (I (I v0 v1) v2) (I v1 v2))) (1423)) (163 (instantiate 162 ((v0 . (SK1))(v1 . (SK2))(v2 . (SK3)))) (P (I (I (I (SK1) (SK2)) (SK3)) (I (SK2) (SK3)))) NIL) (164 (resolve 7 () 163 ()) false (1424)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 89 clauses generated 4909 clauses kept 1423 clauses forward subsumed 3491 clauses back subsumed 27 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.09 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8560 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/t1.out0100664000076400007640000006430610103522211015701 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:05 2004 The command was "../../bin/otter". The process ID is 8600. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(build_proof_object_2). dependent: set(order_history). clear(sigint_interact). assign(max_seconds,10). initial_proof_object(junk). ( (1 (input) (or (not (WOLF V1)) (ANIMAL V1)) NIL) (2 (input) (or (not (FOX V2)) (ANIMAL V2)) NIL) (3 (input) (or (not (BIRD V3)) (ANIMAL V3)) NIL) (4 (input) (or (not (SNAIL V4)) (ANIMAL V4)) NIL) (5 (input) (or (not (GRAIN V5)) (PLANT V5)) NIL) (6 (input) (WOLF (SK1)) NIL) (7 (input) (FOX (SK2)) NIL) (8 (input) (BIRD (SK3)) NIL) (9 (input) (SNAIL (SK4)) NIL) (10 (input) (GRAIN (SK5)) NIL) (11 (input) (or (not (SNAIL V11)) (or (not (BIRD V12)) (SMALLER V11 V12))) NIL) (12 (input) (or (not (BIRD V13)) (or (not (FOX V14)) (SMALLER V13 V14))) NIL) (13 (input) (or (not (FOX V15)) (or (not (WOLF V16)) (SMALLER V15 V16))) NIL) (14 (input) (or (not (SNAIL V17)) (PLANT (SK6 V17))) NIL) (15 (input) (or (not (SNAIL V17)) (EATS V17 (SK6 V17))) NIL) (16 (input) (or (not (WOLF V19)) (or (not (FOX V20)) (not (EATS V19 V20)))) NIL) (17 (input) (or (not (WOLF V21)) (or (not (GRAIN V22)) (not (EATS V21 V22)))) NIL) (18 (input) (or (not (BIRD V23)) (or (not (SNAIL V24)) (not (EATS V23 V24)))) NIL) (19 (input) (or (not (ANIMAL V25)) (or (not (PLANT V26)) (or (EATS V25 V26) (or (not (ANIMAL V27)) (or (not (SMALLER V27 V25)) (or (not (PLANT V28)) (or (not (EATS V27 V28)) (EATS V25 V27)))))))) NIL) (20 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (GRAIN (SK7 V29 V30))))) NIL) (21 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (not (EATS V30 (SK7 V29 V30)))))) NIL) ) 0 [] -WOLF(x)|ANIMAL(x). 0 [] -FOX(x)|ANIMAL(x). 0 [] -BIRD(x)|ANIMAL(x). 0 [] -SNAIL(x)|ANIMAL(x). 0 [] -GRAIN(x)|PLANT(x). 0 [] WOLF(SK1). 0 [] FOX(SK2). 0 [] BIRD(SK3). 0 [] SNAIL(SK4). 0 [] GRAIN(SK5). 0 [] -SNAIL(x)| -BIRD(y)|SMALLER(x,y). 0 [] -BIRD(x)| -FOX(y)|SMALLER(x,y). 0 [] -FOX(x)| -WOLF(y)|SMALLER(x,y). 0 [] -SNAIL(x)|PLANT(SK6(x)). 0 [] -SNAIL(x)|EATS(x,SK6(x)). 0 [] -WOLF(x)| -FOX(y)| -EATS(x,y). 0 [] -WOLF(x)| -GRAIN(y)| -EATS(x,y). 0 [] -BIRD(x)| -SNAIL(y)| -EATS(x,y). 0 [] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -PLANT(u)| -EATS(z,u)|EATS(x,z). 0 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)|GRAIN(SK7(x,y)). 0 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)| -EATS(y,SK7(x,y)). end_of_list. SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=8. This is a non-Horn set without equality. The strategy will be ordered hyper_res, unit deletion, and factoring, with satellites in sos and with nuclei in usable. dependent: set(hyper_res). dependent: set(factor). dependent: set(unit_deletion). ------------> process usable: ** KEPT (pick-wt=4): 1 [] -WOLF(x)|ANIMAL(x). ** KEPT (pick-wt=4): 2 [] -FOX(x)|ANIMAL(x). ** KEPT (pick-wt=4): 3 [] -BIRD(x)|ANIMAL(x). ** KEPT (pick-wt=4): 4 [] -SNAIL(x)|ANIMAL(x). ** KEPT (pick-wt=4): 5 [] -GRAIN(x)|PLANT(x). ** KEPT (pick-wt=7): 6 [] -SNAIL(x)| -BIRD(y)|SMALLER(x,y). ** KEPT (pick-wt=7): 7 [] -BIRD(x)| -FOX(y)|SMALLER(x,y). ** KEPT (pick-wt=7): 8 [] -FOX(x)| -WOLF(y)|SMALLER(x,y). ** KEPT (pick-wt=5): 9 [] -SNAIL(x)|PLANT(SK6(x)). ** KEPT (pick-wt=6): 10 [] -SNAIL(x)|EATS(x,SK6(x)). ** KEPT (pick-wt=7): 11 [] -WOLF(x)| -FOX(y)| -EATS(x,y). ** KEPT (pick-wt=7): 12 [] -WOLF(x)| -GRAIN(y)| -EATS(x,y). ** KEPT (pick-wt=7): 13 [] -BIRD(x)| -SNAIL(y)| -EATS(x,y). ** KEPT (pick-wt=20): 14 [] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -PLANT(u)| -EATS(z,u)|EATS(x,z). ** KEPT (pick-wt=11): 15 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)|GRAIN(SK7(x,y)). ** KEPT (pick-wt=12): 16 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)| -EATS(y,SK7(x,y)). ------------> process sos: ** KEPT (pick-wt=2): 24 [] WOLF(SK1). ** KEPT (pick-wt=2): 25 [] FOX(SK2). ** KEPT (pick-wt=2): 26 [] BIRD(SK3). ** KEPT (pick-wt=2): 27 [] SNAIL(SK4). ** KEPT (pick-wt=2): 28 [] GRAIN(SK5). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 24 [] WOLF(SK1). given clause #2: (wt=2) 25 [] FOX(SK2). given clause #3: (wt=2) 26 [] BIRD(SK3). given clause #4: (wt=2) 27 [] SNAIL(SK4). given clause #5: (wt=2) 28 [] GRAIN(SK5). given clause #6: (wt=2) 29 [hyper,1,24.1] ANIMAL(SK1). given clause #7: (wt=2) 31 [hyper,2,25.1] ANIMAL(SK2). given clause #8: (wt=2) 33 [hyper,3,26.1] ANIMAL(SK3). given clause #9: (wt=2) 37 [hyper,4,27.1] ANIMAL(SK4). given clause #10: (wt=2) 38 [hyper,5,28.1] PLANT(SK5). given clause #11: (wt=3) 30 [hyper,8,25.1,24.1] SMALLER(SK2,SK1). given clause #12: (wt=3) 32 [hyper,7,26.1,25.1] SMALLER(SK3,SK2). given clause #13: (wt=3) 35 [hyper,9,27.1] PLANT(SK6(SK4)). given clause #14: (wt=3) 36 [hyper,6,27.1,26.1] SMALLER(SK4,SK3). given clause #15: (wt=4) 34 [hyper,10,27.1] EATS(SK4,SK6(SK4)). given clause #16: (wt=7) 39 [hyper,18,33.1,35.1,37.1,36.1,34.1] EATS(SK3,SK6(SK4))|EATS(SK3,SK4). given clause #17: (wt=4) 44 [hyper,13,26.1,27.1,39.2] EATS(SK3,SK6(SK4)). given clause #18: (wt=6) 40 [hyper,14,33.1,38.1,37.1,36.1,35.1,34.1] EATS(SK3,SK5)|EATS(SK3,SK4). given clause #19: (wt=3) 48 [hyper,13,26.1,27.1,40.2] EATS(SK3,SK5). given clause #20: (wt=6) 46 [hyper,14,31.1,38.1,33.1,32.1,35.1,44.1] EATS(SK2,SK5)|EATS(SK2,SK3). given clause #21: (wt=7) 45 [hyper,18,31.1,35.1,33.1,32.1,44.1] EATS(SK2,SK6(SK4))|EATS(SK2,SK3). given clause #22: (wt=7) 51 [hyper,15,31.1,33.1,46.2] EATS(SK2,SK5)|GRAIN(SK7(SK2,SK3)). given clause #23: (wt=7) 53 [hyper,5,51.2] EATS(SK2,SK5)|PLANT(SK7(SK2,SK3)). given clause #24: (wt=8) 52 [hyper,15,31.1,33.1,45.2] EATS(SK2,SK6(SK4))|GRAIN(SK7(SK2,SK3)). given clause #25: (wt=8) 55 [hyper,5,52.2] EATS(SK2,SK6(SK4))|PLANT(SK7(SK2,SK3)). given clause #26: (wt=9) 49 [hyper,18,29.1,38.1,31.1,30.1,46.1] EATS(SK2,SK3)|EATS(SK1,SK5)|EATS(SK1,SK2). given clause #27: (wt=6) 58 [hyper,12,24.1,28.1,49.2] EATS(SK2,SK3)|EATS(SK1,SK2). given clause #28: (wt=3) 63 [hyper,11,24.1,25.1,58.2] EATS(SK2,SK3). given clause #29: (wt=4) 64 [hyper,15,31.1,33.1,63.1] GRAIN(SK7(SK2,SK3)). given clause #30: (wt=4) 65 [hyper,5,64.1] PLANT(SK7(SK2,SK3)). given clause #31: (wt=8) 66 [hyper,14,33.1,65.1,37.1,36.1,35.1,34.1] EATS(SK3,SK7(SK2,SK3))|EATS(SK3,SK4). given clause #32: (wt=3) 67 [hyper,16,31.1,33.1,63.1,66.1] EATS(SK3,SK4). -------- PROOF -------- -----> EMPTY CLAUSE at 0.01 sec ----> 71 [hyper,13,26.1,27.1,67.1] $F. Length of proof is 21. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -WOLF(x)|ANIMAL(x). 2 [] -FOX(x)|ANIMAL(x). 3 [] -BIRD(x)|ANIMAL(x). 4 [] -SNAIL(x)|ANIMAL(x). 5 [] -GRAIN(x)|PLANT(x). 6 [] -SNAIL(x)| -BIRD(y)|SMALLER(x,y). 7 [] -BIRD(x)| -FOX(y)|SMALLER(x,y). 8 [] -FOX(x)| -WOLF(y)|SMALLER(x,y). 9 [] -SNAIL(x)|PLANT(SK6(x)). 10 [] -SNAIL(x)|EATS(x,SK6(x)). 11 [] -WOLF(x)| -FOX(y)| -EATS(x,y). 12 [] -WOLF(x)| -GRAIN(y)| -EATS(x,y). 13 [] -BIRD(x)| -SNAIL(y)| -EATS(x,y). 14 [] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -PLANT(u)| -EATS(z,u)|EATS(x,z). 15 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)|GRAIN(SK7(x,y)). 16 [] -ANIMAL(x)| -ANIMAL(y)| -EATS(x,y)| -EATS(y,SK7(x,y)). 18 [factor,14.2.6] -ANIMAL(x)| -PLANT(y)|EATS(x,y)| -ANIMAL(z)| -SMALLER(z,x)| -EATS(z,y)|EATS(x,z). 24 [] WOLF(SK1). 25 [] FOX(SK2). 26 [] BIRD(SK3). 27 [] SNAIL(SK4). 28 [] GRAIN(SK5). 29 [hyper,1,24.1] ANIMAL(SK1). 30 [hyper,8,25.1,24.1] SMALLER(SK2,SK1). 31 [hyper,2,25.1] ANIMAL(SK2). 32 [hyper,7,26.1,25.1] SMALLER(SK3,SK2). 33 [hyper,3,26.1] ANIMAL(SK3). 34 [hyper,10,27.1] EATS(SK4,SK6(SK4)). 35 [hyper,9,27.1] PLANT(SK6(SK4)). 36 [hyper,6,27.1,26.1] SMALLER(SK4,SK3). 37 [hyper,4,27.1] ANIMAL(SK4). 38 [hyper,5,28.1] PLANT(SK5). 39 [hyper,18,33.1,35.1,37.1,36.1,34.1] EATS(SK3,SK6(SK4))|EATS(SK3,SK4). 44 [hyper,13,26.1,27.1,39.2] EATS(SK3,SK6(SK4)). 46 [hyper,14,31.1,38.1,33.1,32.1,35.1,44.1] EATS(SK2,SK5)|EATS(SK2,SK3). 49 [hyper,18,29.1,38.1,31.1,30.1,46.1] EATS(SK2,SK3)|EATS(SK1,SK5)|EATS(SK1,SK2). 58 [hyper,12,24.1,28.1,49.2] EATS(SK2,SK3)|EATS(SK1,SK2). 63 [hyper,11,24.1,25.1,58.2] EATS(SK2,SK3). 64 [hyper,15,31.1,33.1,63.1] GRAIN(SK7(SK2,SK3)). 65 [hyper,5,64.1] PLANT(SK7(SK2,SK3)). 66 [hyper,14,33.1,65.1,37.1,36.1,35.1,34.1] EATS(SK3,SK7(SK2,SK3))|EATS(SK3,SK4). 67 [hyper,16,31.1,33.1,63.1,66.1] EATS(SK3,SK4). 71 [hyper,13,26.1,27.1,67.1] $F. ------------ end of proof ------------- ;; BEGINNING OF PROOF OBJECT ( (1 (input) (or (not (WOLF V1)) (ANIMAL V1)) NIL) (2 (input) (or (not (FOX V2)) (ANIMAL V2)) NIL) (3 (input) (or (not (BIRD V3)) (ANIMAL V3)) NIL) (4 (input) (or (not (SNAIL V4)) (ANIMAL V4)) NIL) (5 (input) (or (not (GRAIN V5)) (PLANT V5)) NIL) (6 (input) (WOLF (SK1)) NIL) (7 (input) (FOX (SK2)) NIL) (8 (input) (BIRD (SK3)) NIL) (9 (input) (SNAIL (SK4)) NIL) (10 (input) (GRAIN (SK5)) NIL) (11 (input) (or (not (SNAIL V11)) (or (not (BIRD V12)) (SMALLER V11 V12))) NIL) (12 (input) (or (not (BIRD V13)) (or (not (FOX V14)) (SMALLER V13 V14))) NIL) (13 (input) (or (not (FOX V15)) (or (not (WOLF V16)) (SMALLER V15 V16))) NIL) (14 (input) (or (not (SNAIL V17)) (PLANT (SK6 V17))) NIL) (15 (input) (or (not (SNAIL V17)) (EATS V17 (SK6 V17))) NIL) (16 (input) (or (not (WOLF V19)) (or (not (FOX V20)) (not (EATS V19 V20)))) NIL) (17 (input) (or (not (WOLF V21)) (or (not (GRAIN V22)) (not (EATS V21 V22)))) NIL) (18 (input) (or (not (BIRD V23)) (or (not (SNAIL V24)) (not (EATS V23 V24)))) NIL) (19 (input) (or (not (ANIMAL V25)) (or (not (PLANT V26)) (or (EATS V25 V26) (or (not (ANIMAL V27)) (or (not (SMALLER V27 V25)) (or (not (PLANT V28)) (or (not (EATS V27 V28)) (EATS V25 V27)))))))) NIL) (20 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (GRAIN (SK7 V29 V30))))) NIL) (21 (input) (or (not (ANIMAL V29)) (or (not (ANIMAL V30)) (or (not (EATS V29 V30)) (not (EATS V30 (SK7 V29 V30)))))) NIL) (22 (instantiate 1 ((V1 . v0))) (or (not (WOLF v0)) (ANIMAL v0)) (1)) (23 (instantiate 2 ((V2 . v0))) (or (not (FOX v0)) (ANIMAL v0)) (2)) (24 (instantiate 3 ((V3 . v0))) (or (not (BIRD v0)) (ANIMAL v0)) (3)) (25 (instantiate 4 ((V4 . v0))) (or (not (SNAIL v0)) (ANIMAL v0)) (4)) (26 (instantiate 5 ((V5 . v0))) (or (not (GRAIN v0)) (PLANT v0)) (5)) (27 (instantiate 11 ((V11 . v0)(V12 . v1))) (or (not (SNAIL v0)) (or (not (BIRD v1)) (SMALLER v0 v1))) (6)) (28 (instantiate 12 ((V13 . v0)(V14 . v1))) (or (not (BIRD v0)) (or (not (FOX v1)) (SMALLER v0 v1))) (7)) (29 (instantiate 13 ((V15 . v0)(V16 . v1))) (or (not (FOX v0)) (or (not (WOLF v1)) (SMALLER v0 v1))) (8)) (30 (instantiate 14 ((V17 . v0))) (or (not (SNAIL v0)) (PLANT (SK6 v0))) (9)) (31 (instantiate 15 ((V17 . v0))) (or (not (SNAIL v0)) (EATS v0 (SK6 v0))) (10)) (32 (instantiate 16 ((V19 . v0)(V20 . v1))) (or (not (WOLF v0)) (or (not (FOX v1)) (not (EATS v0 v1)))) (11)) (33 (instantiate 17 ((V21 . v0)(V22 . v1))) (or (not (WOLF v0)) (or (not (GRAIN v1)) (not (EATS v0 v1)))) (12)) (34 (instantiate 18 ((V23 . v0)(V24 . v1))) (or (not (BIRD v0)) (or (not (SNAIL v1)) (not (EATS v0 v1)))) (13)) (35 (instantiate 19 ((V25 . v0)(V26 . v1)(V27 . v2)(V28 . v3))) (or (not (ANIMAL v0)) (or (not (PLANT v1)) (or (EATS v0 v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS v0 v2)))))))) (14)) (36 (instantiate 20 ((V29 . v0)(V30 . v1))) (or (not (ANIMAL v0)) (or (not (ANIMAL v1)) (or (not (EATS v0 v1)) (GRAIN (SK7 v0 v1))))) (15)) (37 (instantiate 21 ((V29 . v0)(V30 . v1))) (or (not (ANIMAL v0)) (or (not (ANIMAL v1)) (or (not (EATS v0 v1)) (not (EATS v1 (SK7 v0 v1)))))) (16)) (38 (instantiate 35 ((v1 . v3))) (or (not (ANIMAL v0)) (or (not (PLANT v3)) (or (EATS v0 v3) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (PLANT v3)) (or (not (EATS v2 v3)) (EATS v0 v2)))))))) NIL) (39 (propositional 38) (or (not (ANIMAL v0)) (or (not (PLANT v3)) (or (EATS v0 v3) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (EATS v2 v3)) (EATS v0 v2))))))) NIL) (40 (instantiate 39 ((v3 . v1))) (or (not (ANIMAL v0)) (or (not (PLANT v1)) (or (EATS v0 v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 v0)) (or (not (EATS v2 v1)) (EATS v0 v2))))))) (18)) (41 (instantiate 6 ()) (WOLF (SK1)) (24)) (42 (instantiate 7 ()) (FOX (SK2)) (25)) (43 (instantiate 8 ()) (BIRD (SK3)) (26)) (44 (instantiate 9 ()) (SNAIL (SK4)) (27)) (45 (instantiate 10 ()) (GRAIN (SK5)) (28)) (46 (instantiate 22 ((v0 . (SK1)))) (or (not (WOLF (SK1))) (ANIMAL (SK1))) NIL) (47 (resolve 46 (1) 41 ()) (ANIMAL (SK1)) (29)) (48 (instantiate 29 ((v0 . (SK2)))) (or (not (FOX (SK2))) (or (not (WOLF v1)) (SMALLER (SK2) v1))) NIL) (49 (resolve 48 (1) 42 ()) (or (not (WOLF v1)) (SMALLER (SK2) v1)) NIL) (50 (instantiate 49 ((v1 . v0))) (or (not (WOLF v0)) (SMALLER (SK2) v0)) NIL) (51 (instantiate 50 ((v0 . (SK1)))) (or (not (WOLF (SK1))) (SMALLER (SK2) (SK1))) NIL) (52 (resolve 51 (1) 41 ()) (SMALLER (SK2) (SK1)) (30)) (53 (instantiate 23 ((v0 . (SK2)))) (or (not (FOX (SK2))) (ANIMAL (SK2))) NIL) (54 (resolve 53 (1) 42 ()) (ANIMAL (SK2)) (31)) (55 (instantiate 28 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (or (not (FOX v1)) (SMALLER (SK3) v1))) NIL) (56 (resolve 55 (1) 43 ()) (or (not (FOX v1)) (SMALLER (SK3) v1)) NIL) (57 (instantiate 56 ((v1 . v0))) (or (not (FOX v0)) (SMALLER (SK3) v0)) NIL) (58 (instantiate 57 ((v0 . (SK2)))) (or (not (FOX (SK2))) (SMALLER (SK3) (SK2))) NIL) (59 (resolve 58 (1) 42 ()) (SMALLER (SK3) (SK2)) (32)) (60 (instantiate 24 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (ANIMAL (SK3))) NIL) (61 (resolve 60 (1) 43 ()) (ANIMAL (SK3)) (33)) (62 (instantiate 31 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (EATS (SK4) (SK6 (SK4)))) NIL) (63 (resolve 62 (1) 44 ()) (EATS (SK4) (SK6 (SK4))) (34)) (64 (instantiate 30 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (PLANT (SK6 (SK4)))) NIL) (65 (resolve 64 (1) 44 ()) (PLANT (SK6 (SK4))) (35)) (66 (instantiate 27 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (or (not (BIRD v1)) (SMALLER (SK4) v1))) NIL) (67 (resolve 66 (1) 44 ()) (or (not (BIRD v1)) (SMALLER (SK4) v1)) NIL) (68 (instantiate 67 ((v1 . v0))) (or (not (BIRD v0)) (SMALLER (SK4) v0)) NIL) (69 (instantiate 68 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (SMALLER (SK4) (SK3))) NIL) (70 (resolve 69 (1) 43 ()) (SMALLER (SK4) (SK3)) (36)) (71 (instantiate 25 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (ANIMAL (SK4))) NIL) (72 (resolve 71 (1) 44 ()) (ANIMAL (SK4)) (37)) (73 (instantiate 26 ((v0 . (SK5)))) (or (not (GRAIN (SK5))) (PLANT (SK5))) NIL) (74 (resolve 73 (1) 45 ()) (PLANT (SK5)) (38)) (75 (instantiate 40 ((v0 . (SK3)))) (or (not (ANIMAL (SK3))) (or (not (PLANT v1)) (or (EATS (SK3) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK3))) (or (not (EATS v2 v1)) (EATS (SK3) v2))))))) NIL) (76 (resolve 75 (1) 61 ()) (or (not (PLANT v1)) (or (EATS (SK3) v1) (or (not (ANIMAL v2)) (or (not (SMALLER v2 (SK3))) (or (not (EATS v2 v1)) (EATS (SK3) v2)))))) NIL) (77 (instantiate 76 ((v1 . v0)(v2 . v1))) (or (not (PLANT v0)) (or (EATS (SK3) v0) (or (not (ANIMAL v1)) (or (not (SMALLER v1 (SK3))) (or (not (EATS v1 v0)) (EATS (SK3) v1)))))) NIL) (78 (instantiate 77 ((v0 . 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(SK6 (SK4))))) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (PLANT (SK6 (SK4)))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4))))) NIL) (145 (resolve 144 (2 1) 65 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (or (not (EATS (SK4) (SK6 (SK4)))) (EATS (SK3) (SK4)))) NIL) (146 (resolve 145 (2 1) 63 ()) (or (EATS (SK3) (SK7 (SK2) (SK3))) (EATS (SK3) (SK4))) (66)) (147 (instantiate 37 ((v0 . (SK2)))) (or (not (ANIMAL (SK2))) (or (not (ANIMAL v1)) (or (not (EATS (SK2) v1)) (not (EATS v1 (SK7 (SK2) v1)))))) NIL) (148 (resolve 147 (1) 54 ()) (or (not (ANIMAL v1)) (or (not (EATS (SK2) v1)) (not (EATS v1 (SK7 (SK2) v1))))) NIL) (149 (instantiate 148 ((v1 . v0))) (or (not (ANIMAL v0)) (or (not (EATS (SK2) v0)) (not (EATS v0 (SK7 (SK2) v0))))) NIL) (150 (instantiate 149 ((v0 . (SK3)))) (or (not (ANIMAL (SK3))) (or (not (EATS (SK2) (SK3))) (not (EATS (SK3) (SK7 (SK2) (SK3)))))) NIL) (151 (resolve 150 (1) 61 ()) (or (not (EATS (SK2) (SK3))) (not (EATS (SK3) (SK7 (SK2) (SK3))))) NIL) (152 (resolve 151 (1) 125 ()) (not (EATS (SK3) (SK7 (SK2) (SK3)))) NIL) (153 (resolve 152 () 146 (1)) (EATS (SK3) (SK4)) (67)) (154 (instantiate 34 ((v0 . (SK3)))) (or (not (BIRD (SK3))) (or (not (SNAIL v1)) (not (EATS (SK3) v1)))) NIL) (155 (resolve 154 (1) 43 ()) (or (not (SNAIL v1)) (not (EATS (SK3) v1))) NIL) (156 (instantiate 155 ((v1 . v0))) (or (not (SNAIL v0)) (not (EATS (SK3) v0))) NIL) (157 (instantiate 156 ((v0 . (SK4)))) (or (not (SNAIL (SK4))) (not (EATS (SK3) (SK4)))) NIL) (158 (resolve 157 (1) 44 ()) (not (EATS (SK3) (SK4))) NIL) (159 (resolve 158 () 153 ()) false (71)) Search stopped by max_proofs option. ) ;; END OF PROOF OBJECT Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 32 clauses generated 83 clauses kept 70 clauses forward subsumed 29 clauses back subsumed 24 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8600 finished Mon Aug 2 15:31:05 2004 otter-3.3f/examples/ivy/group-comm.in0100644000076400007640000000062106747655711017264 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (= (F (E) V1) V1)) (2 (INPUT) (= (F (G V2) V2) (E))) (3 (INPUT) (= (F (F V3 V4) V5) (F V3 (F V4 V5)))) (4 (INPUT) (= (H V6 V7) (F V6 (F V7 (F (G V6) (G V7)))))) (5 (INPUT) (= (F V8 (F V8 V8)) (E))) (6 (INPUT) (= V9 V9)) (7 (INPUT) (NOT (= (H (H (SK1) (SK2)) (SK2)) (E))))) otter-3.3f/examples/ivy/comb-sk-w.in0100644000076400007640000000052306747655710016776 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (= V1 V1)) (2 (INPUT) (= (A (A (A (S) V2) V3) V4) (A (A V2 V4) (A V3 V4)))) (3 (INPUT) (= (A (A (K) V5) V6) V5)) (4 (INPUT) (NOT (= (A (A V7 (SK1 V7)) (SK2 V7)) (A (A (SK1 V7) (SK2 V7)) (SK2 V7)))))) otter-3.3f/examples/ivy/group-x2-refute.in0100644000076400007640000000052106747655711020151 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (= (F (E) V1) V1)) (2 (INPUT) (= (F (G V2) V2) (E))) (3 (INPUT) (= (F (F V3 V4) V5) (F V3 (F V4 V5)))) (4 (INPUT) (= (F V6 V6) (E))) (5 (INPUT) (= V7 V7)) (6 (INPUT) (NOT (= (F (SK1) (SK2)) (F (SK2) (SK1)))))) otter-3.3f/examples/ivy/group-x2.in0100644000076400007640000000052106747655711016661 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (= (F (E) V1) V1)) (2 (INPUT) (= (F (G V2) V2) (E))) (3 (INPUT) (= (F (F V3 V4) V5) (F V3 (F V4 V5)))) (4 (INPUT) (= (F V6 V6) (E))) (5 (INPUT) (= V7 V7)) (6 (INPUT) (NOT (= (F (SK1) (SK2)) (F (SK2) (SK1)))))) otter-3.3f/examples/ivy/index.html0100644000076400007640000000245207714267401016636 0ustar mccunemccune /home/mccune/otter-3.3/examples/ivy

/home/mccune/otter-3.3/examples/ivy

These are examples of Otter inputs constructed by Ivy.

otter < cd-cn19.in > cd-cn19.out

otter < comb-sk-w.in > comb-sk-w.out

otter < group-comm.in > group-comm.out

otter < group-x2.in > group-x2.out

otter < group-x2-refute.in > group-x2-refute.out

otter < lifsch.in > lifsch.out

otter < p-and-not-p.in > p-and-not-p.out

otter < steam.in > steam.out

otter < t1.in > t1.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/ivy/README0100644000076400007640000000006707313706260015515 0ustar mccunemccuneThese are examples of Otter inputs constructed by Ivy. otter-3.3f/examples/ivy/cd-cn19.in0100644000076400007640000000057006747655710016337 0ustar mccunemccuneset(auto).set(build_proof_object_2).clear(sigint_interact).assign(max_seconds, 10).initial_proof_object(junk). ((1 (INPUT) (OR (NOT (P (I V1 V2))) (OR (NOT (P V1)) (P V2)))) (2 (INPUT) (P (I (I V3 V4) (I (I V4 V5) (I V3 V5))))) (3 (INPUT) (P (I (I (N V6) V6) V6))) (4 (INPUT) (P (I V7 (I (N V7) V8)))) (5 (INPUT) (NOT (P (I (I (I (SK1) (SK2)) (SK3)) (I (SK2) (SK3))))))) otter-3.3f/examples/ivy/t1.in0100644000076400007640000000313606747656660015533 0ustar mccunemccuneset(auto). set(build_proof_object_2). clear(sigint_interact). assign(max_seconds, 10). initial_proof_object(junk). ((1 (INPUT) (OR (NOT (WOLF V1)) (ANIMAL V1))) (2 (INPUT) (OR (NOT (FOX V2)) (ANIMAL V2))) (3 (INPUT) (OR (NOT (BIRD V3)) (ANIMAL V3))) (4 (INPUT) (OR (NOT (SNAIL V4)) (ANIMAL V4))) (5 (INPUT) (OR (NOT (GRAIN V5)) (PLANT V5))) (6 (INPUT) (WOLF (SK1))) (7 (INPUT) (FOX (SK2))) (8 (INPUT) (BIRD (SK3))) (9 (INPUT) (SNAIL (SK4))) (10 (INPUT) (GRAIN (SK5))) (11 (INPUT) (OR (NOT (SNAIL V11)) (OR (NOT (BIRD V12)) (SMALLER V11 V12)))) (12 (INPUT) (OR (NOT (BIRD V13)) (OR (NOT (FOX V14)) (SMALLER V13 V14)))) (13 (INPUT) (OR (NOT (FOX V15)) (OR (NOT (WOLF V16)) (SMALLER V15 V16)))) (14 (INPUT) (OR (NOT (SNAIL V17)) (PLANT (SK6 V17)))) (15 (INPUT) (OR (NOT (SNAIL V17)) (EATS V17 (SK6 V17)))) (16 (INPUT) (OR (NOT (WOLF V19)) (OR (NOT (FOX V20)) (NOT (EATS V19 V20))))) (17 (INPUT) (OR (NOT (WOLF V21)) (OR (NOT (GRAIN V22)) (NOT (EATS V21 V22))))) (18 (INPUT) (OR (NOT (BIRD V23)) (OR (NOT (SNAIL V24)) (NOT (EATS V23 V24))))) (19 (INPUT) (OR (NOT (ANIMAL V25)) (OR (NOT (PLANT V26)) (OR (EATS V25 V26) (OR (NOT (ANIMAL V27)) (OR (NOT (SMALLER V27 V25)) (OR (NOT (PLANT V28)) (OR (NOT (EATS V27 V28)) (EATS V25 V27))))))))) (20 (INPUT) (OR (NOT (ANIMAL V29)) (OR (NOT (ANIMAL V30)) (OR (NOT (EATS V29 V30)) (GRAIN (SK7 V29 V30)))))) (21 (INPUT) (OR (NOT (ANIMAL V29)) (OR (NOT (ANIMAL V30)) (OR (NOT (EATS V29 V30)) (NOT (EATS V30 (SK7 V29 V30)))))))) otter-3.3f/examples/index.html0100644000076400007640000000221207714267401016021 0ustar mccunemccune /home/mccune/otter-3.3/examples

/home/mccune/otter-3.3/examples

  • auto . These problems are easy for Otter. All use the autonomous mode.
  • fringe . These problems illustrate some of Otter's esoteric features: hints, rewriting, tricks with orderings, algebraic geometry.
  • ivy . These are examples of Otter inputs constructed by Ivy.
  • kalman . Contributed by John Kalman.
  • misc . Miscellaneous easy problems.
  • program . Examples of programming Otter.
  • split . These problems were used to test Otter's experimental splitting rule.
  • wos . These problems were contributed by Larry Wos in 1994. Most illustrate the resonance strategy.

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/README0100644000076400007640000000217207264416354014714 0ustar mccunemccuneThe subdirectories contain some example input files for Otter 3.0.x Most of them run within a few seconds and require little memory. auto - examples (mostly from earlier releases) that run in Otter's autonomous mode. misc - other examples (mostly from earlier releases). kalman - some examples contributed by John Kalman (kalman@mat.aukuni.ac.nz). program - some examples of "programming" otter. WARNING: two_inv.in takes a few minutes. wos - some examples contributed by Larry Wos (wos@mcs.anl.gov) fringe - examples demonstrating some of the esoteric features. split - examples demonstrating the new splitting rule in 3.0.5. ivy - examples as used by the Ivy system (new in 3.0.6). The C shell script Run_group will run all of the examples in a subdirectory and compare the results to the results on my computer. Run it, for example, like this (a few seconds) Run_group kalman Also, you can run all of the examples like this (a few minutes) Run_all Of course, you can also run the examples individually, for example cd program ../../source/otter < two_inv.in > two_inv.out & otter-3.3f/examples/program/0040755000076400007640000000000010103530360015460 5ustar mccunemccuneotter-3.3f/examples/program/mission.in0100644000076400007640000000366505515270207017514 0ustar mccunemccune% % Missionaries and Cannibals Puzzle -- % % There are 3 missionaries, 3 cannibals, and a boat on the west bank of % a river. All wish to cross, but the boat holds at most 2 people. % If the missionaries ever outnumber the cannibals on either bank of the % river or in the boat, the outnumbered cannibals will be converted. % Can they all safely cross the river? If so, how? % (The boat cannot cross empty.) % % state(X,Y,Z) means that X missionaries, Y cannibals, and the boat % are on the Z side of the river. % set(hyper_res). set(prolog_style_variables). op(900, xfx, ||). op(900, xfx, &&). make_evaluable(_-_, $DIFF(_,_)). make_evaluable(_+_, $SUM(_,_)). make_evaluable(_<_, $LT(_,_)). make_evaluable(_<=_, $LE(_,_)). make_evaluable(_>_, $GT(_,_)). make_evaluable(_>=_, $GE(_,_)). make_evaluable(_==_, $EQ(_,_)). make_evaluable(_&&_, $AND(_,_)). make_evaluable(_||_, $OR(_,_)). list(usable). % MBS - missionaries on same side as the boat % CBS - cannibals on same side as the boat % BP - position of boat (either west or east) % M - missionaries to cross % C - cannibals to cross -state(MBS,CBS,BP) % If we have an achievable state, | -pick(M) % missionaries to cross | -pick(C) % cannibals to cross | -(M<=MBS) | -(C<=CBS) | -(M+C>0) % if number in boat > 0, | -(M+C<=2) % if number in boat <= 2, | -(C>=M||C==0) % if no conversions in the boat, % if no conversions after the boat leaves current side, | -(CBS-C>=MBS-M || CBS-C==0) % if no conversions when the boat arrives at the other side, | -((3-CBS)+C >= (3-MBS)+M || (3-CBS)+C==0) % then a crossing can occur | state((3-MBS)+M, (3-CBS)+C, otherside(BP)). % The following give the number of each that can cross. pick(0). pick(1). pick(2). -state(3,3,east). % goal state end_of_list. list(sos). state(3,3,west). % initial state end_of_list. list(demodulators). otherside(west) = east. otherside(east) = west. end_of_list. otter-3.3f/examples/program/jugs.out0100664000076400007640000000711610103522224017165 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:16 2004 The command was "../../bin/otter". The process ID is 8985. make_evaluable(_+_,$SUM(_,_)). make_evaluable(_-_,$DIFF(_,_)). make_evaluable(_<=_,$LE(_,_)). make_evaluable(_>_,$GT(_,_)). set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] -j(x,y)|j(3,y). 0 [] -j(x,y)|j(0,y). 0 [] -j(x,y)|j(x,4). 0 [] -j(x,y)|j(x,0). 0 [] -j(x,y)| -(x+y<=4)|j(0,y+x). 0 [] -j(x,y)| -(x+y>4)|j(x- (4-y),4). 0 [] -j(x,y)| -(x+y<=3)|j(x+y,0). 0 [] -j(x,y)| -(x+y>3)|j(3,y- (3-x)). 0 [] j(0,0). 0 [] -j(x,2). end_of_list. SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3. This is a Horn set without equality. The strategy will be hyperresolution, with satellites in sos and nuclei in usable. dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=6): 1 [] -j(x,y)|j(3,y). ** KEPT (pick-wt=6): 2 [] -j(x,y)|j(0,y). ** KEPT (pick-wt=6): 3 [] -j(x,y)|j(x,4). ** KEPT (pick-wt=6): 4 [] -j(x,y)|j(x,0). ** KEPT (pick-wt=13): 5 [] -j(x,y)| -(x+y<=4)|j(0,y+x). ** KEPT (pick-wt=15): 6 [] -j(x,y)| -(x+y>4)|j(x- (4-y),4). ** KEPT (pick-wt=13): 7 [] -j(x,y)| -(x+y<=3)|j(x+y,0). ** KEPT (pick-wt=15): 8 [] -j(x,y)| -(x+y>3)|j(3,y- (3-x)). ** KEPT (pick-wt=3): 9 [] -j(x,2). ------------> process sos: ** KEPT (pick-wt=3): 10 [] j(0,0). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 10 [] j(0,0). given clause #2: (wt=3) 11 [hyper,10,3] j(0,4). given clause #3: (wt=3) 12 [hyper,10,1] j(3,0). given clause #4: (wt=3) 13 [hyper,11,8,eval,demod] j(3,1). given clause #5: (wt=3) 14 [hyper,11,1] j(3,4). given clause #6: (wt=3) 15 [hyper,12,5,eval,demod] j(0,3). given clause #7: (wt=3) 16 [hyper,13,2] j(0,1). given clause #8: (wt=3) 17 [hyper,15,1] j(3,3). given clause #9: (wt=3) 18 [hyper,16,7,eval,demod] j(1,0). given clause #10: (wt=3) 19 [hyper,17,6,eval,demod] j(2,4). given clause #11: (wt=3) 20 [hyper,18,3] j(1,4). -------- PROOF -------- ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,9.1] $F. Length of proof is 6. Level of proof is 6. ---------------- PROOF ---------------- 2 [] -j(x,y)|j(0,y). 3 [] -j(x,y)|j(x,4). 7 [] -j(x,y)| -(x+y<=3)|j(x+y,0). 8 [] -j(x,y)| -(x+y>3)|j(3,y- (3-x)). 9 [] -j(x,2). 10 [] j(0,0). 11 [hyper,10,3] j(0,4). 13 [hyper,11,8,eval,demod] j(3,1). 16 [hyper,13,2] j(0,1). 18 [hyper,16,7,eval,demod] j(1,0). 20 [hyper,18,3] j(1,4). 22 [hyper,20,8,eval,demod] j(3,2). 23 [binary,22.1,9.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 11 clauses generated 61 clauses kept 22 clauses forward subsumed 49 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8985 finished Mon Aug 2 15:31:16 2004 otter-3.3f/examples/program/queens.in0100644000076400007640000000315105501211621017307 0ustar mccunemccune% The 8-queens problem. Place 8 queens on a chessboard such that % none can capture any other. % % Get all solutions (don't worry about isomorphic solutions). % % board([8,5,1]) means that queens are on the first 3 rows: % (row 1, col 1), (row 2, col 5), (row 3, col 8). % % 1 2 3 4 5 6 7 8 % 1 |x| | | | | | | | % 2 | | | | |x| | | | % 3 | | | | | | | |x| % 4 | | | | | | | | | % 5 | | | | | | | | | % 6 | | | | | | | | | % 7 | | | | | | | | | % 8 | | | | | | | | | % % For other board sizes/number of queens, change 'pick' property and % the denial in the passive list. % make_evaluable(_-_, $DIFF(_,_)). make_evaluable(_+_, $SUM(_,_)). make_evaluable(_==_, $EQ(_,_)). set(hyper_res). set(prolog_style_variables). assign(max_proofs,-1). % get all solutions set(sos_stack). % depth-first search clear(print_kept). clear(demod_history). list(usable). -board(B) | -pick(New_col) | % check that new queen is consistent with all preceding rows. -$TRUE(ok(B, 1, New_col)) | board([New_col|B]). pick(1). pick(2). pick(3). pick(4). pick(5). pick(6). pick(7). pick(8). end_of_list. list(sos). board([]). end_of_list. list(passive). -board([X1,X2,X3,X4,X5,X6,X7,X8]) | $Ans([X1,X2,X3,X4,X5,X6,X7,X8]). % -board([X1,X2,X3,X4,X5]) | $Ans([X1,X2,X3,X4,X5]). end_of_list. list(demodulators). ok([], X, Y) = $T. ok([H|T], Rows_back, New_col) = $IF(H == New_col, $F, $IF(H-Rows_back == New_col, $F, $IF(H+Rows_back == New_col, $F, ok(T, Rows_back+1, New_col)))). end_of_list. otter-3.3f/examples/program/jugs.in0100644000076400007640000000214305470212343016766 0ustar mccunemccune% We have a 3-gallon jug and a 4-gallon jug, both empty, and a well. % Our goal is to have exactly 2 gallons in the 4-gallon jug. We % can fill a jug from the well, empty a jug onto the ground, and % carefully pour water from one jug into the other. % % j(m, n) is the state in which the 3-gallon jug contains m gallons, % and the 4-gallon jug contains n gallons. make_evaluable(_+_, $SUM(_,_)). make_evaluable(_-_, $DIFF(_,_)). make_evaluable(_<=_, $LE(_,_)). make_evaluable(_>_, $GT(_,_)). set(auto). list(usable). -j(x, y) | j(3, y). % fill the 3-gallon jug -j(x, y) | j(0, y). % empty the 3-gallon jug -j(x, y) | j(x, 4). % fill the 4-gallon jug -j(x, y) | j(x, 0). % empty the 4-gallon jug -j(x, y) | -(x+y <= 4) | j(0, y+x). % empty the small jug into the big jug -j(x, y) | -(x+y > 4) | j(x - (4-y), 4). % small -> big, until full -j(x, y) | -(x+y <= 3) | j(x+y, 0). % empty the big jug into the small jug -j(x, y) | -(x+y > 3) | j(3, y - (3-x)). % big -> small, until full j(0, 0). % initial state --- both jugs empty -j(x, 2). % goal state --- 4-gallon jug containing 2 gallons end_of_list. otter-3.3f/examples/program/two_inv.in0100644000076400007640000000615407705555445017531 0ustar mccunemccune% The 2-inverter puzzle. % % The problem is to build a combinational circuit with 3 inputs % and 3 outputs, such that the outputs negate the inputs; we can % use as many AND and OR gates as we wish, but at most 2 NOT gates. % % The clause P(function, inversion_list) represents a wire, whose % state is a function of the inputs, and which depends on negated % wires listed in inversion_list. % % The initial clauses are % P(00001111, v). % input 1 % P(00110011, v). % input 2 % P(01010101, v). % input 3 % which represent the three input wires. The goal clause is % -P(11110000, v) | -P(11001100, v) | -P(10101010, v). % That is, the three output functions with unifiable inversion lists. % % The inversion lists are tricky: each has a variable as its tail, which % means that two lists unify iff on is an initial sublist of the other. % Two wires can be input to an OR or AND gate if their inversion lists % are unifiable. (Note this means that the second NOT gate must depend % on the first.) % % For example, P(01000110,[11111000,11001110|x]) means that we % can acheive the function 01000110 with a circuit in which 11111000 and % 11001110 are inverted. % % The following clause is placed on the passive list to subsume % circuits with 3 or more NOT gates. % P(x, [y1,y2,y3|y4]). % % If a proof is found, the corresponding circuit can be constructed by % going through the proof; each step represents a gate, and the parent % lists show how to connect the wires. % % The original formulation is by Steve Winker and is documented in % "Automated Reasoning: Introduction and Applications" by Wos et al. % This formulation does not use the "reversion" heuristic of Winker's % formulation. % % This takes about 40 minutes and about 6 megabytes on McCune's 486. % set(hyper_res). clear(back_sub). clear(demod_history). clear(print_kept). clear(print_given). assign(max_mem, 9000). assign(min_bit_width, 8). list(usable). % Rules for building circuits. -P(x, v) | -P(y, v) | P($BIT_AND(x,y), v). -P(x, v) | -P(y, v) | P($BIT_OR(x,y), v). -P(x, v) | P($BIT_AND(11111111,$BIT_NOT(x)), append_inversion(v,x)). end_of_list. list(sos). P(00001111, v). % input 1 P(00110011, v). % input 2 P(01010101, v). % input 3 end_of_list. list(usable). % Denial of the goal. -P(11110000, v) | -P(11001100, v) | -P(10101010, v). end_of_list. list(demodulators). % The following pair of demodulators inserts an element y just before the % tail-variable. append_inversion([x1|x2],y) = [x1|append_inversion(x2,y)]. $VAR(x) -> append_inversion(x,y) = [y|x]. end_of_list. list(passive). % The following clause subsumes functions obtained with 3 (or more) inversions. P(x, [y1,y2,y3|y4]). end_of_list. % The following list of weight templates gives first priority to the % goal functions, regardless of the inversion list. Recall that with % a multiliteral denial, all of the goals must be selected as given % clauses before a proof is found by hyper. Without these templates, % the three goals can sit on sos for a long time, delaying a proof. weight_list(pick_given). weight(P(11110000, $(1)), -50). weight(P(11001100, $(1)), -50). weight(P(10101010, $(1)), -50). end_of_list. otter-3.3f/examples/program/two_inv.out0100664000076400007640000000775410103522330017710 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:17 2004 The command was "../../bin/otter". The process ID is 9000. set(hyper_res). clear(back_sub). clear(demod_history). clear(print_kept). clear(print_given). assign(max_mem,9000). assign(min_bit_width,8). list(usable). 1 [] -P(x,v)| -P(y,v)|P($BIT_AND(x,y),v). 2 [] -P(x,v)| -P(y,v)|P($BIT_OR(x,y),v). 3 [] -P(x,v)|P($BIT_AND(11111111,$BIT_NOT(x)),append_inversion(v,x)). end_of_list. list(sos). 4 [] P(00001111,v). 5 [] P(00110011,v). 6 [] P(01010101,v). end_of_list. list(usable). 7 [] -P(11110000,v)| -P(11001100,v)| -P(10101010,v). end_of_list. list(demodulators). 8 [] append_inversion([x1|x2],y)=[x1|append_inversion(x2,y)]. 9 [] $VAR(x)->append_inversion(x,y)=[y|x]. end_of_list. list(passive). 10 [] P(x,[y1,y2,y3|y4]). end_of_list. weight_list(pick_given). weight(P(11110000,$(1)),-50). weight(P(11001100,$(1)),-50). weight(P(10101010,$(1)),-50). end_of_list. ======= end of input processing ======= =========== start of search =========== -- HEY mccune, WE HAVE A PROOF!! -- -----> EMPTY CLAUSE at 67.17 sec ----> 20227 [hyper,20222,7,20203,20178] $F. Length of proof is 26. Level of proof is 9. ---------------- PROOF ---------------- 1 [] -P(x,v)| -P(y,v)|P($BIT_AND(x,y),v). 2 [] -P(x,v)| -P(y,v)|P($BIT_OR(x,y),v). 3 [] -P(x,v)|P($BIT_AND(11111111,$BIT_NOT(x)),append_inversion(v,x)). 4 [] P(00001111,v). 5 [] P(00110011,v). 6 [] P(01010101,v). 7 [] -P(11110000,v)| -P(11001100,v)| -P(10101010,v). 16 [hyper,5,2,4,demod] P(00111111,x). 18 [hyper,5,1,4,demod] P(00000011,x). 26 [hyper,6,2,5,demod] P(01110111,x). 27 [hyper,6,2,4,demod] P(01011111,x). 30 [hyper,6,1,5,demod] P(00010001,x). 31 [hyper,6,1,4,demod] P(00000101,x). 40 [hyper,16,2,6,demod] P(01111111,x). 42 [hyper,16,1,6,demod] P(00010101,x). 47 [hyper,18,1,6,demod] P(00000001,x). 66 [hyper,42,2,18,demod] P(00010111,x). 73 [hyper,66,3,demod] P(11101000,[00010111|x]). 334 [hyper,73,2,47,demod] P(11101001,[00010111|x]). 336 [hyper,73,2,31,demod] P(11101101,[00010111|x]). 337 [hyper,73,2,30,demod] P(11111001,[00010111|x]). 338 [hyper,73,2,18,demod] P(11101011,[00010111|x]). 344 [hyper,73,1,27,demod] P(01001000,[00010111|x]). 345 [hyper,73,1,26,demod] P(01100000,[00010111|x]). 346 [hyper,73,1,16,demod] P(00101000,[00010111|x]). 754 [hyper,334,1,40,demod] P(01101001,[00010111|x]). 991 [hyper,754,3,demod] P(10010110,[00010111,01101001|x]). 8477 [hyper,991,2,346,demod] P(10111110,[00010111,01101001|x]). 8478 [hyper,991,2,345,demod] P(11110110,[00010111,01101001|x]). 8479 [hyper,991,2,344,demod] P(11011110,[00010111,01101001|x]). 20178 [hyper,8477,1,338,demod] P(10101010,[00010111,01101001|x]). 20203 [hyper,8478,1,337,demod] P(11110000,[00010111,01101001|x]). 20222 [hyper,8479,1,336,demod] P(11001100,[00010111,01101001|x]). 20227 [hyper,20222,7,20203,20178] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 8642 clauses generated 2069334 hyper_res generated 2069334 demod & eval rewrites 2103338 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 2049117 (subsumed by sos) 314773 unit deletions 0 factor simplifications 0 clauses kept 20216 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 0 usable size 8646 sos size 11577 demodulators size 2 passive size 1 hot size 0 Kbytes malloced 6835 ----------- times (seconds) ----------- user CPU time 67.17 (0 hr, 1 min, 7 sec) system CPU time 0.06 (0 hr, 0 min, 0 sec) wall-clock time 67 (0 hr, 1 min, 7 sec) That finishes the proof of the theorem. Process 9000 finished Mon Aug 2 15:32:24 2004 otter-3.3f/examples/program/eval.out0100664000076400007640000000645310103522224017147 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:16 2004 The command was "../../bin/otter". The process ID is 8980. set(rewriter). dependent: set(demod_inf). dependent: assign(max_levels, 1). dependent: set(sos_queue). dependent: clear(for_sub). dependent: clear(back_sub). dependent: assign(stats_level, 0). clear(demod_history). set(prolog_style_variables). make_evaluable(_-_,$DIFF(_,_)). make_evaluable(_<_,$LT(_,_)). make_evaluable(_*_,$PROD(_,_)). make_evaluable(_==_,$EQ(_,_)). make_evaluable(_&_,$AND(_,_)). op(700,xfx,@<). op(700,xfx,@<=). op(700,xfx,@>). op(700,xfx,@>=). make_evaluable(_@<_,$LLT(_,_)). make_evaluable(_@<=_,$LLE(_,_)). make_evaluable(_@>_,$LGT(_,_)). make_evaluable(_@>=_,$LGE(_,_)). lex([a,b,c,d,e,f,g]). list(demodulators). 1 [] factorial(N)=$IF(N==0,1,N*factorial(N-1)). 2 [] gcd(X,Y)=$IF(X==0,Y,$IF(Y==0,X,$IF(XX,[H|gt_list(X,T)],gt_list(X,T)). end_of_list. list(sos). 22 [] p(factorial(8)). 23 [] p(gcd(13004,5176)). 24 [] p(member(d,[a,b,c])). 25 [] p(subset([b,d],[a,b,c,d])). 26 [] p(intersect([b,d],[a,b,c,d])). 27 [] p(union([b,e],[a,b,c,d])). 28 [] p(reverse([a,b,c,d,e,f,g])). 29 [] p(quick_sort([c,a,b,f,c,c,e,d,b])). 30 [] p($FSUM("1.4e-3","3.222")). end_of_list. ======= end of input processing ======= =========== start of search =========== Starting on level 1, last kept clause of level 0 is 30. Starting on level 1, last kept clause of level 0 is 30. given clause #1: (wt=3) 22 [] p(factorial(8)). ** KEPT (pick-wt=2): 31 [22,demod] p(40320). given clause #2: (wt=4) 23 [] p(gcd(13004,5176)). ** KEPT (pick-wt=2): 32 [23,demod] p(4). given clause #3: (wt=10) 24 [] p(member(d,[a,b,c])). ** KEPT (pick-wt=2): 33 [24,demod] p($F). given clause #4: (wt=16) 25 [] p(subset([b,d],[a,b,c,d])). ** KEPT (pick-wt=2): 34 [25,demod] p($T). given clause #5: (wt=16) 26 [] p(intersect([b,d],[a,b,c,d])). ** KEPT (pick-wt=6): 35 [26,demod] p([b,d]). given clause #6: (wt=16) 27 [] p(union([b,e],[a,b,c,d])). ** KEPT (pick-wt=12): 36 [27,demod] p([e,a,b,c,d]). given clause #7: (wt=17) 28 [] p(reverse([a,b,c,d,e,f,g])). ** KEPT (pick-wt=16): 37 [28,demod] p([g,f,e,d,c,b,a]). given clause #8: (wt=21) 29 [] p(quick_sort([c,a,b,f,c,c,e,d,b])). ** KEPT (pick-wt=20): 38 [29,demod] p([a,b,b,c,c,c,d,e,f]). given clause #9: (wt=4) 30 [] p($FSUM("1.4e-3","3.222")). Search stopped by max_levels option. ** KEPT (pick-wt=2): 39 [30,demod] p("3.223400000000"). Search stopped by max_levels option. ============ end of search ============ Process 8980 finished Mon Aug 2 15:31:16 2004 otter-3.3f/examples/program/mission.out0100664000076400007640000001440410103522224017674 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:16 2004 The command was "../../bin/otter". The process ID is 8990. set(hyper_res). set(prolog_style_variables). op(900,xfx,||). op(900,xfx,&&). make_evaluable(_-_,$DIFF(_,_)). make_evaluable(_+_,$SUM(_,_)). make_evaluable(_<_,$LT(_,_)). make_evaluable(_<=_,$LE(_,_)). make_evaluable(_>_,$GT(_,_)). make_evaluable(_>=_,$GE(_,_)). make_evaluable(_==_,$EQ(_,_)). make_evaluable(_&&_,$AND(_,_)). make_evaluable(_||_,$OR(_,_)). list(usable). 1 [] -state(MBS,CBS,BP)| -pick(M)| -pick(C)| -(M<=MBS)| -(C<=CBS)| -(M+C>0)| -(M+C<=2)| -(C>=M||C==0)| -(CBS-C>=MBS-M||CBS-C==0)| -((3-CBS)+C>= (3-MBS)+M|| (3-CBS)+C==0)|state((3-MBS)+M,(3-CBS)+C,otherside(BP)). 2 [] pick(0). 3 [] pick(1). 4 [] pick(2). 5 [] -state(3,3,east). end_of_list. list(sos). 6 [] state(3,3,west). end_of_list. list(demodulators). 7 [] otherside(west)=east. 8 [] otherside(east)=west. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=4) 6 [] state(3,3,west). ** KEPT (pick-wt=4): 9 [hyper,6,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,0,east). ** KEPT (pick-wt=4): 10 [hyper,6,1,3,3,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,1,east). ** KEPT (pick-wt=4): 11 [hyper,6,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,0,east). given clause #2: (wt=4) 9 [hyper,6,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,0,east). ** KEPT (pick-wt=4): 12 [hyper,9,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,3,west). given clause #3: (wt=4) 10 [hyper,6,1,3,3,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,1,east). given clause #4: (wt=4) 11 [hyper,6,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,0,east). given clause #5: (wt=4) 12 [hyper,9,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,3,west). ** KEPT (pick-wt=4): 13 [hyper,12,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(3,0,east). given clause #6: (wt=4) 13 [hyper,12,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(3,0,east). ** KEPT (pick-wt=4): 14 [hyper,13,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(1,3,west). given clause #7: (wt=4) 14 [hyper,13,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(1,3,west). ** KEPT (pick-wt=4): 15 [hyper,14,1,2,4,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,2,east). given clause #8: (wt=4) 15 [hyper,14,1,2,4,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,2,east). ** KEPT (pick-wt=4): 16 [hyper,15,1,3,3,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,2,west). given clause #9: (wt=4) 16 [hyper,15,1,3,3,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,2,west). ** KEPT (pick-wt=4): 17 [hyper,16,1,2,4,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,3,east). given clause #10: (wt=4) 17 [hyper,16,1,2,4,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,3,east). ** KEPT (pick-wt=4): 18 [hyper,17,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(3,0,west). given clause #11: (wt=4) 18 [hyper,17,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(3,0,west). ** KEPT (pick-wt=4): 19 [hyper,18,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,3,east). given clause #12: (wt=4) 19 [hyper,18,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,3,east). ** KEPT (pick-wt=4): 20 [hyper,19,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,0,west). ** KEPT (pick-wt=4): 21 [hyper,19,1,2,3,eval,eval,eval,eval,eval,eval,eval,demod,8] state(1,1,west). given clause #13: (wt=4) 20 [hyper,19,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,0,west). -------- PROOF -------- ** KEPT (pick-wt=4): 22 [hyper,20,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(3,3,east). ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,5.1] $F. Length of proof is 11. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -state(MBS,CBS,BP)| -pick(M)| -pick(C)| -(M<=MBS)| -(C<=CBS)| -(M+C>0)| -(M+C<=2)| -(C>=M||C==0)| -(CBS-C>=MBS-M||CBS-C==0)| -((3-CBS)+C>= (3-MBS)+M|| (3-CBS)+C==0)|state((3-MBS)+M,(3-CBS)+C,otherside(BP)). 2 [] pick(0). 3 [] pick(1). 4 [] pick(2). 5 [] -state(3,3,east). 6 [] state(3,3,west). 7 [] otherside(west)=east. 8 [] otherside(east)=west. 9 [hyper,6,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,0,east). 12 [hyper,9,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,3,west). 13 [hyper,12,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(3,0,east). 14 [hyper,13,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(1,3,west). 15 [hyper,14,1,2,4,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,2,east). 16 [hyper,15,1,3,3,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,2,west). 17 [hyper,16,1,2,4,eval,eval,eval,eval,eval,eval,eval,demod,7] state(1,3,east). 18 [hyper,17,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(3,0,west). 19 [hyper,18,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(2,3,east). 20 [hyper,19,1,3,2,eval,eval,eval,eval,eval,eval,eval,demod,8] state(2,0,west). 22 [hyper,20,1,4,2,eval,eval,eval,eval,eval,eval,eval,demod,7] state(3,3,east). 23 [binary,22.1,5.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 13 clauses generated 27 hyper_res generated 27 demod & eval rewrites 135 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 13 (subsumed by sos) 1 unit deletions 0 factor simplifications 0 clauses kept 14 new demodulators 0 empty clauses 1 clauses back demodulated 0 clauses back subsumed 0 usable size 18 sos size 2 demodulators size 2 passive size 0 hot size 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8990 finished Mon Aug 2 15:31:16 2004 otter-3.3f/examples/program/queens.out0100664000076400007640000074133110103522225017522 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:16 2004 The command was "../../bin/otter". The process ID is 8995. make_evaluable(_-_,$DIFF(_,_)). make_evaluable(_+_,$SUM(_,_)). make_evaluable(_==_,$EQ(_,_)). set(hyper_res). set(prolog_style_variables). assign(max_proofs,-1). set(sos_stack). clear(print_kept). clear(demod_history). list(usable). 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). end_of_list. list(sos). 10 [] board([]). end_of_list. list(passive). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). end_of_list. list(demodulators). 12 [] ok([],X,Y)=$T. 13 [] ok([H|T],Rows_back,New_col)=$IF(H==New_col,$F,$IF(H-Rows_back==New_col,$F,$IF(H+Rows_back==New_col,$F,ok(T,Rows_back+1,New_col)))). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 10 [] board([]). given clause #2: (wt=4) 21 [hyper,10,1,2,eval] board([1]). given clause #3: (wt=6) 27 [hyper,21,1,4,eval] board([3,1]). given clause #4: (wt=8) 31 [hyper,27,1,6,eval] board([5,3,1]). given clause #5: (wt=10) 34 [hyper,31,1,3,eval] board([2,5,3,1]). given clause #6: (wt=12) 36 [hyper,34,1,5,eval] board([4,2,5,3,1]). given clause #7: (wt=12) 35 [hyper,34,1,9,eval] board([8,2,5,3,1]). given clause #8: (wt=10) 33 [hyper,31,1,8,eval] board([7,5,3,1]). given clause #9: (wt=12) 38 [hyper,33,1,3,eval] board([2,7,5,3,1]). given clause #10: (wt=14) 39 [hyper,38,1,5,eval] board([4,2,7,5,3,1]). given clause #11: (wt=16) 40 [hyper,39,1,7,eval] board([6,4,2,7,5,3,1]). given clause #12: (wt=12) 37 [hyper,33,1,5,eval] board([4,7,5,3,1]). given clause #13: (wt=10) 32 [hyper,31,1,9,eval] board([8,5,3,1]). given clause #14: (wt=12) 42 [hyper,32,1,3,eval] board([2,8,5,3,1]). given clause #15: (wt=14) 43 [hyper,42,1,5,eval] board([4,2,8,5,3,1]). given clause #16: (wt=16) 44 [hyper,43,1,7,eval] board([6,4,2,8,5,3,1]). given clause #17: (wt=12) 41 [hyper,32,1,5,eval] board([4,8,5,3,1]). given clause #18: (wt=8) 30 [hyper,27,1,7,eval] board([6,3,1]). given clause #19: (wt=10) 46 [hyper,30,1,3,eval] board([2,6,3,1]). given clause #20: (wt=12) 47 [hyper,46,1,8,eval] board([7,2,6,3,1]). given clause #21: (wt=14) 48 [hyper,47,1,6,eval] board([5,7,2,6,3,1]). given clause #22: (wt=10) 45 [hyper,30,1,9,eval] board([8,6,3,1]). given clause #23: (wt=12) 49 [hyper,45,1,3,eval] board([2,8,6,3,1]). given clause #24: (wt=14) 51 [hyper,49,1,5,eval] board([4,2,8,6,3,1]). given clause #25: (wt=14) 50 [hyper,49,1,6,eval] board([5,2,8,6,3,1]). given clause #26: (wt=8) 29 [hyper,27,1,8,eval] board([7,3,1]). given clause #27: (wt=10) 52 [hyper,29,1,3,eval] board([2,7,3,1]). given clause #28: (wt=12) 54 [hyper,52,1,5,eval] board([4,2,7,3,1]). given clause #29: (wt=14) 55 [hyper,54,1,9,eval] board([8,4,2,7,3,1]). given clause #30: (wt=12) 53 [hyper,52,1,9,eval] board([8,2,7,3,1]). given clause #31: (wt=14) 56 [hyper,53,1,6,eval] board([5,8,2,7,3,1]). given clause #32: (wt=8) 28 [hyper,27,1,9,eval] board([8,3,1]). given clause #33: (wt=10) 58 [hyper,28,1,3,eval] board([2,8,3,1]). given clause #34: (wt=12) 60 [hyper,58,1,5,eval] board([4,2,8,3,1]). given clause #35: (wt=12) 59 [hyper,58,1,8,eval] board([7,2,8,3,1]). given clause #36: (wt=10) 57 [hyper,28,1,7,eval] board([6,8,3,1]). given clause #37: (wt=12) 62 [hyper,57,1,3,eval] board([2,6,8,3,1]). given clause #38: (wt=12) 61 [hyper,57,1,5,eval] board([4,6,8,3,1]). given clause #39: (wt=14) 63 [hyper,61,1,3,eval] board([2,4,6,8,3,1]). given clause #40: (wt=16) 64 [hyper,63,1,6,eval] board([5,2,4,6,8,3,1]). given clause #41: (wt=6) 26 [hyper,21,1,5,eval] board([4,1]). given clause #42: (wt=8) 68 [hyper,26,1,3,eval] board([2,4,1]). given clause #43: (wt=10) 71 [hyper,68,1,6,eval] board([5,2,4,1]). given clause #44: (wt=12) 73 [hyper,71,1,4,eval] board([3,5,2,4,1]). given clause #45: (wt=12) 72 [hyper,71,1,9,eval] board([8,5,2,4,1]). given clause #46: (wt=10) 70 [hyper,68,1,8,eval] board([7,2,4,1]). given clause #47: (wt=12) 74 [hyper,70,1,4,eval] board([3,7,2,4,1]). given clause #48: (wt=10) 69 [hyper,68,1,9,eval] board([8,2,4,1]). given clause #49: (wt=12) 76 [hyper,69,1,4,eval] board([3,8,2,4,1]). given clause #50: (wt=14) 77 [hyper,76,1,8,eval] board([7,3,8,2,4,1]). given clause #51: (wt=12) 75 [hyper,69,1,7,eval] board([6,8,2,4,1]). given clause #52: (wt=14) 78 [hyper,75,1,4,eval] board([3,6,8,2,4,1]). given clause #53: (wt=8) 67 [hyper,26,1,7,eval] board([6,4,1]). given clause #54: (wt=10) 80 [hyper,67,1,4,eval] board([3,6,4,1]). given clause #55: (wt=10) 79 [hyper,67,1,9,eval] board([8,6,4,1]). given clause #56: (wt=12) 82 [hyper,79,1,3,eval] board([2,8,6,4,1]). given clause #57: (wt=14) 84 [hyper,82,1,6,eval] board([5,2,8,6,4,1]). given clause #58: (wt=16) 85 [hyper,84,1,4,eval] board([3,5,2,8,6,4,1]). given clause #59: (wt=14) 83 [hyper,82,1,8,eval] board([7,2,8,6,4,1]). given clause #60: (wt=16) 86 [hyper,83,1,4,eval] board([3,7,2,8,6,4,1]). given clause #61: (wt=12) 81 [hyper,79,1,4,eval] board([3,8,6,4,1]). given clause #62: (wt=14) 88 [hyper,81,1,6,eval] board([5,3,8,6,4,1]). given clause #63: (wt=14) 87 [hyper,81,1,8,eval] board([7,3,8,6,4,1]). given clause #64: (wt=8) 66 [hyper,26,1,8,eval] board([7,4,1]). given clause #65: (wt=10) 90 [hyper,66,1,4,eval] board([3,7,4,1]). given clause #66: (wt=12) 92 [hyper,90,1,7,eval] board([6,3,7,4,1]). given clause #67: (wt=14) 93 [hyper,92,1,3,eval] board([2,6,3,7,4,1]). given clause #68: (wt=16) 94 [hyper,93,1,6,eval] board([5,2,6,3,7,4,1]). given clause #69: (wt=12) 91 [hyper,90,1,9,eval] board([8,3,7,4,1]). given clause #70: (wt=14) 95 [hyper,91,1,3,eval] board([2,8,3,7,4,1]). given clause #71: (wt=16) 96 [hyper,95,1,6,eval] board([5,2,8,3,7,4,1]). given clause #72: (wt=10) 89 [hyper,66,1,6,eval] board([5,7,4,1]). given clause #73: (wt=12) 99 [hyper,89,1,3,eval] board([2,5,7,4,1]). given clause #74: (wt=12) 98 [hyper,89,1,4,eval] board([3,5,7,4,1]). given clause #75: (wt=12) 97 [hyper,89,1,9,eval] board([8,5,7,4,1]). given clause #76: (wt=14) 100 [hyper,97,1,3,eval] board([2,8,5,7,4,1]). given clause #77: (wt=8) 65 [hyper,26,1,9,eval] board([8,4,1]). given clause #78: (wt=10) 102 [hyper,65,1,4,eval] board([3,8,4,1]). given clause #79: (wt=10) 101 [hyper,65,1,6,eval] board([5,8,4,1]). given clause #80: (wt=12) 104 [hyper,101,1,3,eval] board([2,5,8,4,1]). given clause #81: (wt=12) 103 [hyper,101,1,4,eval] board([3,5,8,4,1]). given clause #82: (wt=6) 25 [hyper,21,1,6,eval] board([5,1]). given clause #83: (wt=8) 107 [hyper,25,1,3,eval] board([2,5,1]). given clause #84: (wt=10) 109 [hyper,107,1,7,eval] board([6,2,5,1]). given clause #85: (wt=12) 110 [hyper,109,1,4,eval] board([3,6,2,5,1]). given clause #86: (wt=14) 111 [hyper,110,1,8,eval] board([7,3,6,2,5,1]). given clause #87: (wt=16) 112 [hyper,111,1,5,eval] board([4,7,3,6,2,5,1]). given clause #88: (wt=10) 108 [hyper,107,1,9,eval] board([8,2,5,1]). given clause #89: (wt=12) 114 [hyper,108,1,4,eval] board([3,8,2,5,1]). given clause #90: (wt=14) 115 [hyper,114,1,8,eval] board([7,3,8,2,5,1]). given clause #91: (wt=16) 116 [hyper,115,1,5,eval] board([4,7,3,8,2,5,1]). given clause #92: (wt=12) 113 [hyper,108,1,7,eval] board([6,8,2,5,1]). given clause #93: (wt=14) 118 [hyper,113,1,4,eval] board([3,6,8,2,5,1]). given clause #94: (wt=14) 117 [hyper,113,1,5,eval] board([4,6,8,2,5,1]). given clause #95: (wt=8) 106 [hyper,25,1,8,eval] board([7,5,1]). given clause #96: (wt=10) 119 [hyper,106,1,3,eval] board([2,7,5,1]). given clause #97: (wt=12) 121 [hyper,119,1,5,eval] board([4,2,7,5,1]). given clause #98: (wt=14) 122 [hyper,121,1,9,eval] board([8,4,2,7,5,1]). given clause #99: (wt=12) 120 [hyper,119,1,7,eval] board([6,2,7,5,1]). given clause #100: (wt=14) 124 [hyper,120,1,4,eval] board([3,6,2,7,5,1]). given clause #101: (wt=14) 123 [hyper,120,1,9,eval] board([8,6,2,7,5,1]). given clause #102: (wt=8) 105 [hyper,25,1,9,eval] board([8,5,1]). given clause #103: (wt=10) 126 [hyper,105,1,3,eval] board([2,8,5,1]). given clause #104: (wt=12) 128 [hyper,126,1,5,eval] board([4,2,8,5,1]). given clause #105: (wt=14) 129 [hyper,128,1,8,eval] board([7,4,2,8,5,1]). given clause #106: (wt=16) 130 [hyper,129,1,4,eval] board([3,7,4,2,8,5,1]). given clause #107: (wt=12) 127 [hyper,126,1,8,eval] board([7,2,8,5,1]). given clause #108: (wt=14) 131 [hyper,127,1,4,eval] board([3,7,2,8,5,1]). given clause #109: (wt=16) 132 [hyper,131,1,7,eval] board([6,3,7,2,8,5,1]). given clause #110: (wt=10) 125 [hyper,105,1,7,eval] board([6,8,5,1]). given clause #111: (wt=12) 134 [hyper,125,1,4,eval] board([3,6,8,5,1]). given clause #112: (wt=14) 135 [hyper,134,1,8,eval] board([7,3,6,8,5,1]). given clause #113: (wt=16) 136 [hyper,135,1,3,eval] board([2,7,3,6,8,5,1]). -------- PROOF -------- 138 [binary,137.1,11.1] $Ans([4,2,7,3,6,8,5,1]). ----> UNIT CONFLICT at 0.04 sec ----> 138 [binary,137.1,11.1] $Ans([4,2,7,3,6,8,5,1]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 21 [hyper,10,1,2,eval] board([1]). 25 [hyper,21,1,6,eval] board([5,1]). 105 [hyper,25,1,9,eval] board([8,5,1]). 125 [hyper,105,1,7,eval] board([6,8,5,1]). 134 [hyper,125,1,4,eval] board([3,6,8,5,1]). 135 [hyper,134,1,8,eval] board([7,3,6,8,5,1]). 136 [hyper,135,1,3,eval] board([2,7,3,6,8,5,1]). 137 [hyper,136,1,5,eval] board([4,2,7,3,6,8,5,1]). 138 [binary,137.1,11.1] $Ans([4,2,7,3,6,8,5,1]). ------------ end of proof ------------- given clause #114: (wt=18) 137 [hyper,136,1,5,eval] board([4,2,7,3,6,8,5,1]). given clause #115: (wt=12) 133 [hyper,125,1,5,eval] board([4,6,8,5,1]). given clause #116: (wt=14) 140 [hyper,133,1,3,eval] board([2,4,6,8,5,1]). given clause #117: (wt=14) 139 [hyper,133,1,8,eval] board([7,4,6,8,5,1]). given clause #118: (wt=6) 24 [hyper,21,1,7,eval] board([6,1]). given clause #119: (wt=8) 143 [hyper,24,1,3,eval] board([2,6,1]). given clause #120: (wt=10) 145 [hyper,143,1,6,eval] board([5,2,6,1]). given clause #121: (wt=12) 147 [hyper,145,1,8,eval] board([7,5,2,6,1]). given clause #122: (wt=14) 148 [hyper,147,1,5,eval] board([4,7,5,2,6,1]). given clause #123: (wt=12) 146 [hyper,145,1,9,eval] board([8,5,2,6,1]). given clause #124: (wt=14) 149 [hyper,146,1,5,eval] board([4,8,5,2,6,1]). given clause #125: (wt=10) 144 [hyper,143,1,8,eval] board([7,2,6,1]). given clause #126: (wt=8) 142 [hyper,24,1,5,eval] board([4,6,1]). given clause #127: (wt=10) 151 [hyper,142,1,3,eval] board([2,4,6,1]). given clause #128: (wt=12) 153 [hyper,151,1,8,eval] board([7,2,4,6,1]). given clause #129: (wt=14) 155 [hyper,153,1,4,eval] board([3,7,2,4,6,1]). given clause #130: (wt=14) 154 [hyper,153,1,6,eval] board([5,7,2,4,6,1]). given clause #131: (wt=16) 156 [hyper,154,1,4,eval] board([3,5,7,2,4,6,1]). given clause #132: (wt=12) 152 [hyper,151,1,9,eval] board([8,2,4,6,1]). given clause #133: (wt=14) 158 [hyper,152,1,4,eval] board([3,8,2,4,6,1]). given clause #134: (wt=14) 157 [hyper,152,1,6,eval] board([5,8,2,4,6,1]). given clause #135: (wt=16) 159 [hyper,157,1,4,eval] board([3,5,8,2,4,6,1]). given clause #136: (wt=10) 150 [hyper,142,1,8,eval] board([7,4,6,1]). given clause #137: (wt=8) 141 [hyper,24,1,9,eval] board([8,6,1]). given clause #138: (wt=10) 162 [hyper,141,1,3,eval] board([2,8,6,1]). given clause #139: (wt=12) 164 [hyper,162,1,5,eval] board([4,2,8,6,1]). given clause #140: (wt=14) 165 [hyper,164,1,8,eval] board([7,4,2,8,6,1]). given clause #141: (wt=16) 166 [hyper,165,1,4,eval] board([3,7,4,2,8,6,1]). given clause #142: (wt=12) 163 [hyper,162,1,8,eval] board([7,2,8,6,1]). given clause #143: (wt=14) 167 [hyper,163,1,4,eval] board([3,7,2,8,6,1]). given clause #144: (wt=10) 161 [hyper,141,1,4,eval] board([3,8,6,1]). given clause #145: (wt=12) 168 [hyper,161,1,8,eval] board([7,3,8,6,1]). given clause #146: (wt=14) 169 [hyper,168,1,5,eval] board([4,7,3,8,6,1]). given clause #147: (wt=16) 170 [hyper,169,1,3,eval] board([2,4,7,3,8,6,1]). -------- PROOF -------- 172 [binary,171.1,11.1] $Ans([5,2,4,7,3,8,6,1]). ----> UNIT CONFLICT at 0.05 sec ----> 172 [binary,171.1,11.1] $Ans([5,2,4,7,3,8,6,1]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 21 [hyper,10,1,2,eval] board([1]). 24 [hyper,21,1,7,eval] board([6,1]). 141 [hyper,24,1,9,eval] board([8,6,1]). 161 [hyper,141,1,4,eval] board([3,8,6,1]). 168 [hyper,161,1,8,eval] board([7,3,8,6,1]). 169 [hyper,168,1,5,eval] board([4,7,3,8,6,1]). 170 [hyper,169,1,3,eval] board([2,4,7,3,8,6,1]). 171 [hyper,170,1,6,eval] board([5,2,4,7,3,8,6,1]). 172 [binary,171.1,11.1] $Ans([5,2,4,7,3,8,6,1]). ------------ end of proof ------------- given clause #148: (wt=18) 171 [hyper,170,1,6,eval] board([5,2,4,7,3,8,6,1]). given clause #149: (wt=10) 160 [hyper,141,1,6,eval] board([5,8,6,1]). given clause #150: (wt=12) 174 [hyper,160,1,3,eval] board([2,5,8,6,1]). given clause #151: (wt=14) 175 [hyper,174,1,5,eval] board([4,2,5,8,6,1]). given clause #152: (wt=12) 173 [hyper,160,1,8,eval] board([7,5,8,6,1]). given clause #153: (wt=14) 176 [hyper,173,1,5,eval] board([4,7,5,8,6,1]). given clause #154: (wt=6) 23 [hyper,21,1,8,eval] board([7,1]). given clause #155: (wt=8) 179 [hyper,23,1,3,eval] board([2,7,1]). given clause #156: (wt=10) 181 [hyper,179,1,7,eval] board([6,2,7,1]). given clause #157: (wt=12) 183 [hyper,181,1,4,eval] board([3,6,2,7,1]). given clause #158: (wt=12) 182 [hyper,181,1,9,eval] board([8,6,2,7,1]). given clause #159: (wt=10) 180 [hyper,179,1,9,eval] board([8,2,7,1]). given clause #160: (wt=12) 185 [hyper,180,1,4,eval] board([3,8,2,7,1]). given clause #161: (wt=12) 184 [hyper,180,1,7,eval] board([6,8,2,7,1]). given clause #162: (wt=14) 186 [hyper,184,1,5,eval] board([4,6,8,2,7,1]). given clause #163: (wt=8) 178 [hyper,23,1,5,eval] board([4,7,1]). given clause #164: (wt=10) 189 [hyper,178,1,3,eval] board([2,4,7,1]). given clause #165: (wt=12) 190 [hyper,189,1,9,eval] board([8,2,4,7,1]). given clause #166: (wt=14) 191 [hyper,190,1,6,eval] board([5,8,2,4,7,1]). given clause #167: (wt=16) 192 [hyper,191,1,4,eval] board([3,5,8,2,4,7,1]). given clause #168: (wt=10) 188 [hyper,178,1,7,eval] board([6,4,7,1]). given clause #169: (wt=12) 194 [hyper,188,1,4,eval] board([3,6,4,7,1]). given clause #170: (wt=14) 195 [hyper,194,1,6,eval] board([5,3,6,4,7,1]). given clause #171: (wt=12) 193 [hyper,188,1,9,eval] board([8,6,4,7,1]). given clause #172: (wt=14) 197 [hyper,193,1,3,eval] board([2,8,6,4,7,1]). given clause #173: (wt=16) 198 [hyper,197,1,6,eval] board([5,2,8,6,4,7,1]). -------- PROOF -------- 200 [binary,199.1,11.1] $Ans([3,5,2,8,6,4,7,1]). ----> UNIT CONFLICT at 0.06 sec ----> 200 [binary,199.1,11.1] $Ans([3,5,2,8,6,4,7,1]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 21 [hyper,10,1,2,eval] board([1]). 23 [hyper,21,1,8,eval] board([7,1]). 178 [hyper,23,1,5,eval] board([4,7,1]). 188 [hyper,178,1,7,eval] board([6,4,7,1]). 193 [hyper,188,1,9,eval] board([8,6,4,7,1]). 197 [hyper,193,1,3,eval] board([2,8,6,4,7,1]). 198 [hyper,197,1,6,eval] board([5,2,8,6,4,7,1]). 199 [hyper,198,1,4,eval] board([3,5,2,8,6,4,7,1]). 200 [binary,199.1,11.1] $Ans([3,5,2,8,6,4,7,1]). ------------ end of proof ------------- given clause #174: (wt=18) 199 [hyper,198,1,4,eval] board([3,5,2,8,6,4,7,1]). given clause #175: (wt=14) 196 [hyper,193,1,6,eval] board([5,8,6,4,7,1]). given clause #176: (wt=10) 187 [hyper,178,1,9,eval] board([8,4,7,1]). given clause #177: (wt=12) 201 [hyper,187,1,4,eval] board([3,8,4,7,1]). given clause #178: (wt=14) 202 [hyper,201,1,6,eval] board([5,3,8,4,7,1]). given clause #179: (wt=8) 177 [hyper,23,1,6,eval] board([5,7,1]). given clause #180: (wt=10) 205 [hyper,177,1,3,eval] board([2,5,7,1]). given clause #181: (wt=12) 207 [hyper,205,1,7,eval] board([6,2,5,7,1]). given clause #182: (wt=12) 206 [hyper,205,1,9,eval] board([8,2,5,7,1]). given clause #183: (wt=10) 204 [hyper,177,1,4,eval] board([3,5,7,1]). given clause #184: (wt=12) 209 [hyper,204,1,7,eval] board([6,3,5,7,1]). given clause #185: (wt=14) 210 [hyper,209,1,5,eval] board([4,6,3,5,7,1]). given clause #186: (wt=12) 208 [hyper,204,1,9,eval] board([8,3,5,7,1]). given clause #187: (wt=14) 211 [hyper,208,1,5,eval] board([4,8,3,5,7,1]). given clause #188: (wt=10) 203 [hyper,177,1,9,eval] board([8,5,7,1]). given clause #189: (wt=12) 213 [hyper,203,1,3,eval] board([2,8,5,7,1]). given clause #190: (wt=14) 214 [hyper,213,1,5,eval] board([4,2,8,5,7,1]). given clause #191: (wt=16) 215 [hyper,214,1,7,eval] board([6,4,2,8,5,7,1]). -------- PROOF -------- 217 [binary,216.1,11.1] $Ans([3,6,4,2,8,5,7,1]). ----> UNIT CONFLICT at 0.07 sec ----> 217 [binary,216.1,11.1] $Ans([3,6,4,2,8,5,7,1]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 21 [hyper,10,1,2,eval] board([1]). 23 [hyper,21,1,8,eval] board([7,1]). 177 [hyper,23,1,6,eval] board([5,7,1]). 203 [hyper,177,1,9,eval] board([8,5,7,1]). 213 [hyper,203,1,3,eval] board([2,8,5,7,1]). 214 [hyper,213,1,5,eval] board([4,2,8,5,7,1]). 215 [hyper,214,1,7,eval] board([6,4,2,8,5,7,1]). 216 [hyper,215,1,4,eval] board([3,6,4,2,8,5,7,1]). 217 [binary,216.1,11.1] $Ans([3,6,4,2,8,5,7,1]). ------------ end of proof ------------- given clause #192: (wt=18) 216 [hyper,215,1,4,eval] board([3,6,4,2,8,5,7,1]). given clause #193: (wt=12) 212 [hyper,203,1,7,eval] board([6,8,5,7,1]). given clause #194: (wt=14) 218 [hyper,212,1,5,eval] board([4,6,8,5,7,1]). given clause #195: (wt=6) 22 [hyper,21,1,9,eval] board([8,1]). given clause #196: (wt=8) 222 [hyper,22,1,3,eval] board([2,8,1]). given clause #197: (wt=10) 224 [hyper,222,1,6,eval] board([5,2,8,1]). given clause #198: (wt=12) 226 [hyper,224,1,4,eval] board([3,5,2,8,1]). given clause #199: (wt=12) 225 [hyper,224,1,8,eval] board([7,5,2,8,1]). given clause #200: (wt=10) 223 [hyper,222,1,8,eval] board([7,2,8,1]). given clause #201: (wt=12) 227 [hyper,223,1,4,eval] board([3,7,2,8,1]). given clause #202: (wt=8) 221 [hyper,22,1,5,eval] board([4,8,1]). given clause #203: (wt=10) 229 [hyper,221,1,3,eval] board([2,4,8,1]). given clause #204: (wt=12) 230 [hyper,229,1,8,eval] board([7,2,4,8,1]). given clause #205: (wt=14) 232 [hyper,230,1,4,eval] board([3,7,2,4,8,1]). given clause #206: (wt=16) 233 [hyper,232,1,7,eval] board([6,3,7,2,4,8,1]). given clause #207: (wt=14) 231 [hyper,230,1,6,eval] board([5,7,2,4,8,1]). given clause #208: (wt=10) 228 [hyper,221,1,8,eval] board([7,4,8,1]). given clause #209: (wt=12) 234 [hyper,228,1,4,eval] board([3,7,4,8,1]). given clause #210: (wt=8) 220 [hyper,22,1,6,eval] board([5,8,1]). given clause #211: (wt=10) 237 [hyper,220,1,3,eval] board([2,5,8,1]). given clause #212: (wt=12) 239 [hyper,237,1,5,eval] board([4,2,5,8,1]). given clause #213: (wt=14) 240 [hyper,239,1,8,eval] board([7,4,2,5,8,1]). given clause #214: (wt=12) 238 [hyper,237,1,7,eval] board([6,2,5,8,1]). given clause #215: (wt=14) 241 [hyper,238,1,4,eval] board([3,6,2,5,8,1]). given clause #216: (wt=10) 236 [hyper,220,1,4,eval] board([3,5,8,1]). given clause #217: (wt=12) 242 [hyper,236,1,7,eval] board([6,3,5,8,1]). given clause #218: (wt=10) 235 [hyper,220,1,8,eval] board([7,5,8,1]). given clause #219: (wt=12) 244 [hyper,235,1,3,eval] board([2,7,5,8,1]). given clause #220: (wt=12) 243 [hyper,235,1,5,eval] board([4,7,5,8,1]). given clause #221: (wt=8) 219 [hyper,22,1,7,eval] board([6,8,1]). given clause #222: (wt=10) 246 [hyper,219,1,3,eval] board([2,6,8,1]). given clause #223: (wt=12) 247 [hyper,246,1,8,eval] board([7,2,6,8,1]). given clause #224: (wt=14) 248 [hyper,247,1,6,eval] board([5,7,2,6,8,1]). given clause #225: (wt=10) 245 [hyper,219,1,4,eval] board([3,6,8,1]). given clause #226: (wt=12) 249 [hyper,245,1,8,eval] board([7,3,6,8,1]). given clause #227: (wt=14) 250 [hyper,249,1,3,eval] board([2,7,3,6,8,1]). given clause #228: (wt=16) 251 [hyper,250,1,5,eval] board([4,2,7,3,6,8,1]). given clause #229: (wt=4) 20 [hyper,10,1,3,eval] board([2]). given clause #230: (wt=6) 256 [hyper,20,1,5,eval] board([4,2]). given clause #231: (wt=8) 260 [hyper,256,1,2,eval] board([1,4,2]). given clause #232: (wt=10) 263 [hyper,260,1,4,eval] board([3,1,4,2]). given clause #233: (wt=12) 265 [hyper,263,1,6,eval] board([5,3,1,4,2]). given clause #234: (wt=12) 264 [hyper,263,1,9,eval] board([8,3,1,4,2]). given clause #235: (wt=14) 266 [hyper,264,1,7,eval] board([6,8,3,1,4,2]). given clause #236: (wt=10) 262 [hyper,260,1,8,eval] board([7,1,4,2]). given clause #237: (wt=12) 267 [hyper,262,1,6,eval] board([5,7,1,4,2]). given clause #238: (wt=14) 268 [hyper,267,1,4,eval] board([3,5,7,1,4,2]). given clause #239: (wt=16) 269 [hyper,268,1,7,eval] board([6,3,5,7,1,4,2]). given clause #240: (wt=10) 261 [hyper,260,1,9,eval] board([8,1,4,2]). given clause #241: (wt=12) 270 [hyper,261,1,6,eval] board([5,8,1,4,2]). given clause #242: (wt=14) 271 [hyper,270,1,4,eval] board([3,5,8,1,4,2]). given clause #243: (wt=16) 272 [hyper,271,1,7,eval] board([6,3,5,8,1,4,2]). given clause #244: (wt=8) 259 [hyper,256,1,7,eval] board([6,4,2]). given clause #245: (wt=10) 275 [hyper,259,1,2,eval] board([1,6,4,2]). given clause #246: (wt=12) 277 [hyper,275,1,4,eval] board([3,1,6,4,2]). given clause #247: (wt=14) 278 [hyper,277,1,6,eval] board([5,3,1,6,4,2]). given clause #248: (wt=16) 279 [hyper,278,1,8,eval] board([7,5,3,1,6,4,2]). given clause #249: (wt=12) 276 [hyper,275,1,6,eval] board([5,1,6,4,2]). given clause #250: (wt=10) 274 [hyper,259,1,4,eval] board([3,6,4,2]). given clause #251: (wt=12) 280 [hyper,274,1,6,eval] board([5,3,6,4,2]). given clause #252: (wt=10) 273 [hyper,259,1,9,eval] board([8,6,4,2]). given clause #253: (wt=12) 282 [hyper,273,1,4,eval] board([3,8,6,4,2]). given clause #254: (wt=14) 284 [hyper,282,1,2,eval] board([1,3,8,6,4,2]). given clause #255: (wt=16) 285 [hyper,284,1,8,eval] board([7,1,3,8,6,4,2]). -------- PROOF -------- 287 [binary,286.1,11.1] $Ans([5,7,1,3,8,6,4,2]). ----> UNIT CONFLICT at 0.09 sec ----> 287 [binary,286.1,11.1] $Ans([5,7,1,3,8,6,4,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 256 [hyper,20,1,5,eval] board([4,2]). 259 [hyper,256,1,7,eval] board([6,4,2]). 273 [hyper,259,1,9,eval] board([8,6,4,2]). 282 [hyper,273,1,4,eval] board([3,8,6,4,2]). 284 [hyper,282,1,2,eval] board([1,3,8,6,4,2]). 285 [hyper,284,1,8,eval] board([7,1,3,8,6,4,2]). 286 [hyper,285,1,6,eval] board([5,7,1,3,8,6,4,2]). 287 [binary,286.1,11.1] $Ans([5,7,1,3,8,6,4,2]). ------------ end of proof ------------- given clause #256: (wt=18) 286 [hyper,285,1,6,eval] board([5,7,1,3,8,6,4,2]). given clause #257: (wt=14) 283 [hyper,282,1,6,eval] board([5,3,8,6,4,2]). given clause #258: (wt=16) 288 [hyper,283,1,8,eval] board([7,5,3,8,6,4,2]). given clause #259: (wt=12) 281 [hyper,273,1,6,eval] board([5,8,6,4,2]). given clause #260: (wt=14) 289 [hyper,281,1,2,eval] board([1,5,8,6,4,2]). given clause #261: (wt=8) 258 [hyper,256,1,8,eval] board([7,4,2]). given clause #262: (wt=10) 291 [hyper,258,1,2,eval] board([1,7,4,2]). given clause #263: (wt=12) 293 [hyper,291,1,4,eval] board([3,1,7,4,2]). given clause #264: (wt=14) 295 [hyper,293,1,6,eval] board([5,3,1,7,4,2]). given clause #265: (wt=14) 294 [hyper,293,1,7,eval] board([6,3,1,7,4,2]). given clause #266: (wt=12) 292 [hyper,291,1,9,eval] board([8,1,7,4,2]). given clause #267: (wt=14) 297 [hyper,292,1,6,eval] board([5,8,1,7,4,2]). given clause #268: (wt=14) 296 [hyper,292,1,7,eval] board([6,8,1,7,4,2]). given clause #269: (wt=10) 290 [hyper,258,1,4,eval] board([3,7,4,2]). given clause #270: (wt=12) 298 [hyper,290,1,9,eval] board([8,3,7,4,2]). given clause #271: (wt=14) 299 [hyper,298,1,7,eval] board([6,8,3,7,4,2]). given clause #272: (wt=16) 300 [hyper,299,1,2,eval] board([1,6,8,3,7,4,2]). given clause #273: (wt=8) 257 [hyper,256,1,9,eval] board([8,4,2]). given clause #274: (wt=10) 302 [hyper,257,1,2,eval] board([1,8,4,2]). given clause #275: (wt=12) 304 [hyper,302,1,4,eval] board([3,1,8,4,2]). given clause #276: (wt=14) 305 [hyper,304,1,7,eval] board([6,3,1,8,4,2]). given clause #277: (wt=12) 303 [hyper,302,1,6,eval] board([5,1,8,4,2]). given clause #278: (wt=10) 301 [hyper,257,1,4,eval] board([3,8,4,2]). given clause #279: (wt=12) 306 [hyper,301,1,6,eval] board([5,3,8,4,2]). given clause #280: (wt=6) 255 [hyper,20,1,6,eval] board([5,2]). given clause #281: (wt=8) 310 [hyper,255,1,2,eval] board([1,5,2]). given clause #282: (wt=10) 313 [hyper,310,1,5,eval] board([4,1,5,2]). given clause #283: (wt=12) 314 [hyper,313,1,8,eval] board([7,4,1,5,2]). given clause #284: (wt=14) 315 [hyper,314,1,4,eval] board([3,7,4,1,5,2]). given clause #285: (wt=16) 316 [hyper,315,1,7,eval] board([6,3,7,4,1,5,2]). given clause #286: (wt=10) 312 [hyper,310,1,7,eval] board([6,1,5,2]). given clause #287: (wt=12) 317 [hyper,312,1,5,eval] board([4,6,1,5,2]). given clause #288: (wt=10) 311 [hyper,310,1,9,eval] board([8,1,5,2]). given clause #289: (wt=12) 318 [hyper,311,1,5,eval] board([4,8,1,5,2]). given clause #290: (wt=8) 309 [hyper,255,1,4,eval] board([3,5,2]). given clause #291: (wt=10) 321 [hyper,309,1,2,eval] board([1,3,5,2]). given clause #292: (wt=12) 323 [hyper,321,1,5,eval] board([4,1,3,5,2]). given clause #293: (wt=14) 324 [hyper,323,1,9,eval] board([8,4,1,3,5,2]). given clause #294: (wt=12) 322 [hyper,321,1,8,eval] board([7,1,3,5,2]). given clause #295: (wt=14) 325 [hyper,322,1,5,eval] board([4,7,1,3,5,2]). given clause #296: (wt=16) 326 [hyper,325,1,7,eval] board([6,4,7,1,3,5,2]). given clause #297: (wt=10) 320 [hyper,309,1,7,eval] board([6,3,5,2]). given clause #298: (wt=12) 327 [hyper,320,1,5,eval] board([4,6,3,5,2]). given clause #299: (wt=10) 319 [hyper,309,1,9,eval] board([8,3,5,2]). given clause #300: (wt=12) 328 [hyper,319,1,5,eval] board([4,8,3,5,2]). given clause #301: (wt=8) 308 [hyper,255,1,8,eval] board([7,5,2]). given clause #302: (wt=10) 330 [hyper,308,1,2,eval] board([1,7,5,2]). given clause #303: (wt=12) 332 [hyper,330,1,4,eval] board([3,1,7,5,2]). given clause #304: (wt=14) 334 [hyper,332,1,7,eval] board([6,3,1,7,5,2]). given clause #305: (wt=14) 333 [hyper,332,1,9,eval] board([8,3,1,7,5,2]). given clause #306: (wt=16) 335 [hyper,333,1,7,eval] board([6,8,3,1,7,5,2]). -------- PROOF -------- 337 [binary,336.1,11.1] $Ans([4,6,8,3,1,7,5,2]). ----> UNIT CONFLICT at 0.11 sec ----> 337 [binary,336.1,11.1] $Ans([4,6,8,3,1,7,5,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 255 [hyper,20,1,6,eval] board([5,2]). 308 [hyper,255,1,8,eval] board([7,5,2]). 330 [hyper,308,1,2,eval] board([1,7,5,2]). 332 [hyper,330,1,4,eval] board([3,1,7,5,2]). 333 [hyper,332,1,9,eval] board([8,3,1,7,5,2]). 335 [hyper,333,1,7,eval] board([6,8,3,1,7,5,2]). 336 [hyper,335,1,5,eval] board([4,6,8,3,1,7,5,2]). 337 [binary,336.1,11.1] $Ans([4,6,8,3,1,7,5,2]). ------------ end of proof ------------- given clause #307: (wt=18) 336 [hyper,335,1,5,eval] board([4,6,8,3,1,7,5,2]). given clause #308: (wt=12) 331 [hyper,330,1,5,eval] board([4,1,7,5,2]). given clause #309: (wt=14) 339 [hyper,331,1,7,eval] board([6,4,1,7,5,2]). given clause #310: (wt=14) 338 [hyper,331,1,9,eval] board([8,4,1,7,5,2]). given clause #311: (wt=10) 329 [hyper,308,1,5,eval] board([4,7,5,2]). given clause #312: (wt=12) 340 [hyper,329,1,2,eval] board([1,4,7,5,2]). given clause #313: (wt=14) 342 [hyper,340,1,4,eval] board([3,1,4,7,5,2]). given clause #314: (wt=16) 343 [hyper,342,1,7,eval] board([6,3,1,4,7,5,2]). given clause #315: (wt=14) 341 [hyper,340,1,9,eval] board([8,1,4,7,5,2]). given clause #316: (wt=16) 344 [hyper,341,1,7,eval] board([6,8,1,4,7,5,2]). -------- PROOF -------- 346 [binary,345.1,11.1] $Ans([3,6,8,1,4,7,5,2]). ----> UNIT CONFLICT at 0.12 sec ----> 346 [binary,345.1,11.1] $Ans([3,6,8,1,4,7,5,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 255 [hyper,20,1,6,eval] board([5,2]). 308 [hyper,255,1,8,eval] board([7,5,2]). 329 [hyper,308,1,5,eval] board([4,7,5,2]). 340 [hyper,329,1,2,eval] board([1,4,7,5,2]). 341 [hyper,340,1,9,eval] board([8,1,4,7,5,2]). 344 [hyper,341,1,7,eval] board([6,8,1,4,7,5,2]). 345 [hyper,344,1,4,eval] board([3,6,8,1,4,7,5,2]). 346 [binary,345.1,11.1] $Ans([3,6,8,1,4,7,5,2]). ------------ end of proof ------------- given clause #317: (wt=18) 345 [hyper,344,1,4,eval] board([3,6,8,1,4,7,5,2]). given clause #318: (wt=8) 307 [hyper,255,1,9,eval] board([8,5,2]). given clause #319: (wt=10) 349 [hyper,307,1,2,eval] board([1,8,5,2]). given clause #320: (wt=12) 352 [hyper,349,1,4,eval] board([3,1,8,5,2]). given clause #321: (wt=14) 353 [hyper,352,1,7,eval] board([6,3,1,8,5,2]). given clause #322: (wt=12) 351 [hyper,349,1,5,eval] board([4,1,8,5,2]). given clause #323: (wt=14) 354 [hyper,351,1,7,eval] board([6,4,1,8,5,2]). given clause #324: (wt=16) 355 [hyper,354,1,4,eval] board([3,6,4,1,8,5,2]). given clause #325: (wt=12) 350 [hyper,349,1,8,eval] board([7,1,8,5,2]). given clause #326: (wt=14) 356 [hyper,350,1,5,eval] board([4,7,1,8,5,2]). given clause #327: (wt=16) 357 [hyper,356,1,7,eval] board([6,4,7,1,8,5,2]). given clause #328: (wt=10) 348 [hyper,307,1,5,eval] board([4,8,5,2]). given clause #329: (wt=12) 359 [hyper,348,1,2,eval] board([1,4,8,5,2]). given clause #330: (wt=14) 360 [hyper,359,1,4,eval] board([3,1,4,8,5,2]). given clause #331: (wt=16) 361 [hyper,360,1,7,eval] board([6,3,1,4,8,5,2]). given clause #332: (wt=12) 358 [hyper,348,1,8,eval] board([7,4,8,5,2]). given clause #333: (wt=14) 362 [hyper,358,1,4,eval] board([3,7,4,8,5,2]). given clause #334: (wt=16) 363 [hyper,362,1,7,eval] board([6,3,7,4,8,5,2]). given clause #335: (wt=10) 347 [hyper,307,1,7,eval] board([6,8,5,2]). given clause #336: (wt=12) 366 [hyper,347,1,2,eval] board([1,6,8,5,2]). given clause #337: (wt=14) 367 [hyper,366,1,4,eval] board([3,1,6,8,5,2]). given clause #338: (wt=16) 368 [hyper,367,1,8,eval] board([7,3,1,6,8,5,2]). given clause #339: (wt=12) 365 [hyper,347,1,4,eval] board([3,6,8,5,2]). given clause #340: (wt=12) 364 [hyper,347,1,5,eval] board([4,6,8,5,2]). given clause #341: (wt=6) 254 [hyper,20,1,7,eval] board([6,2]). given clause #342: (wt=8) 371 [hyper,254,1,2,eval] board([1,6,2]). given clause #343: (wt=10) 373 [hyper,371,1,4,eval] board([3,1,6,2]). given clause #344: (wt=12) 376 [hyper,373,1,6,eval] board([5,3,1,6,2]). given clause #345: (wt=14) 377 [hyper,376,1,9,eval] board([8,5,3,1,6,2]). given clause #346: (wt=16) 378 [hyper,377,1,5,eval] board([4,8,5,3,1,6,2]). given clause #347: (wt=12) 375 [hyper,373,1,8,eval] board([7,3,1,6,2]). given clause #348: (wt=12) 374 [hyper,373,1,9,eval] board([8,3,1,6,2]). given clause #349: (wt=10) 372 [hyper,371,1,8,eval] board([7,1,6,2]). given clause #350: (wt=12) 380 [hyper,372,1,5,eval] board([4,7,1,6,2]). given clause #351: (wt=14) 381 [hyper,380,1,9,eval] board([8,4,7,1,6,2]). given clause #352: (wt=16) 382 [hyper,381,1,4,eval] board([3,8,4,7,1,6,2]). -------- PROOF -------- 384 [binary,383.1,11.1] $Ans([5,3,8,4,7,1,6,2]). ----> UNIT CONFLICT at 0.13 sec ----> 384 [binary,383.1,11.1] $Ans([5,3,8,4,7,1,6,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 254 [hyper,20,1,7,eval] board([6,2]). 371 [hyper,254,1,2,eval] board([1,6,2]). 372 [hyper,371,1,8,eval] board([7,1,6,2]). 380 [hyper,372,1,5,eval] board([4,7,1,6,2]). 381 [hyper,380,1,9,eval] board([8,4,7,1,6,2]). 382 [hyper,381,1,4,eval] board([3,8,4,7,1,6,2]). 383 [hyper,382,1,6,eval] board([5,3,8,4,7,1,6,2]). 384 [binary,383.1,11.1] $Ans([5,3,8,4,7,1,6,2]). ------------ end of proof ------------- given clause #353: (wt=18) 383 [hyper,382,1,6,eval] board([5,3,8,4,7,1,6,2]). given clause #354: (wt=12) 379 [hyper,372,1,6,eval] board([5,7,1,6,2]). given clause #355: (wt=14) 386 [hyper,379,1,4,eval] board([3,5,7,1,6,2]). given clause #356: (wt=14) 385 [hyper,379,1,9,eval] board([8,5,7,1,6,2]). given clause #357: (wt=8) 370 [hyper,254,1,4,eval] board([3,6,2]). given clause #358: (wt=10) 388 [hyper,370,1,2,eval] board([1,3,6,2]). given clause #359: (wt=12) 391 [hyper,388,1,5,eval] board([4,1,3,6,2]). given clause #360: (wt=14) 392 [hyper,391,1,9,eval] board([8,4,1,3,6,2]). given clause #361: (wt=16) 393 [hyper,392,1,6,eval] board([5,8,4,1,3,6,2]). given clause #362: (wt=12) 390 [hyper,388,1,8,eval] board([7,1,3,6,2]). given clause #363: (wt=14) 395 [hyper,390,1,5,eval] board([4,7,1,3,6,2]). given clause #364: (wt=14) 394 [hyper,390,1,6,eval] board([5,7,1,3,6,2]). given clause #365: (wt=12) 389 [hyper,388,1,9,eval] board([8,1,3,6,2]). given clause #366: (wt=14) 397 [hyper,389,1,5,eval] board([4,8,1,3,6,2]). given clause #367: (wt=14) 396 [hyper,389,1,6,eval] board([5,8,1,3,6,2]). given clause #368: (wt=10) 387 [hyper,370,1,8,eval] board([7,3,6,2]). given clause #369: (wt=12) 398 [hyper,387,1,5,eval] board([4,7,3,6,2]). given clause #370: (wt=14) 400 [hyper,398,1,2,eval] board([1,4,7,3,6,2]). given clause #371: (wt=16) 401 [hyper,400,1,6,eval] board([5,1,4,7,3,6,2]). given clause #372: (wt=14) 399 [hyper,398,1,9,eval] board([8,4,7,3,6,2]). given clause #373: (wt=16) 402 [hyper,399,1,6,eval] board([5,8,4,7,3,6,2]). given clause #374: (wt=8) 369 [hyper,254,1,9,eval] board([8,6,2]). given clause #375: (wt=10) 404 [hyper,369,1,2,eval] board([1,8,6,2]). given clause #376: (wt=12) 407 [hyper,404,1,5,eval] board([4,1,8,6,2]). given clause #377: (wt=12) 406 [hyper,404,1,6,eval] board([5,1,8,6,2]). given clause #378: (wt=12) 405 [hyper,404,1,8,eval] board([7,1,8,6,2]). given clause #379: (wt=14) 408 [hyper,405,1,5,eval] board([4,7,1,8,6,2]). given clause #380: (wt=10) 403 [hyper,369,1,4,eval] board([3,8,6,2]). given clause #381: (wt=12) 411 [hyper,403,1,2,eval] board([1,3,8,6,2]). given clause #382: (wt=14) 412 [hyper,411,1,5,eval] board([4,1,3,8,6,2]). given clause #383: (wt=16) 413 [hyper,412,1,8,eval] board([7,4,1,3,8,6,2]). -------- PROOF -------- 415 [binary,414.1,11.1] $Ans([5,7,4,1,3,8,6,2]). ----> UNIT CONFLICT at 0.14 sec ----> 415 [binary,414.1,11.1] $Ans([5,7,4,1,3,8,6,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 254 [hyper,20,1,7,eval] board([6,2]). 369 [hyper,254,1,9,eval] board([8,6,2]). 403 [hyper,369,1,4,eval] board([3,8,6,2]). 411 [hyper,403,1,2,eval] board([1,3,8,6,2]). 412 [hyper,411,1,5,eval] board([4,1,3,8,6,2]). 413 [hyper,412,1,8,eval] board([7,4,1,3,8,6,2]). 414 [hyper,413,1,6,eval] board([5,7,4,1,3,8,6,2]). 415 [binary,414.1,11.1] $Ans([5,7,4,1,3,8,6,2]). ------------ end of proof ------------- given clause #384: (wt=18) 414 [hyper,413,1,6,eval] board([5,7,4,1,3,8,6,2]). given clause #385: (wt=12) 410 [hyper,403,1,6,eval] board([5,3,8,6,2]). given clause #386: (wt=12) 409 [hyper,403,1,8,eval] board([7,3,8,6,2]). given clause #387: (wt=14) 416 [hyper,409,1,5,eval] board([4,7,3,8,6,2]). given clause #388: (wt=6) 253 [hyper,20,1,8,eval] board([7,2]). given clause #389: (wt=8) 419 [hyper,253,1,2,eval] board([1,7,2]). given clause #390: (wt=10) 423 [hyper,419,1,4,eval] board([3,1,7,2]). given clause #391: (wt=12) 425 [hyper,423,1,6,eval] board([5,3,1,7,2]). given clause #392: (wt=14) 426 [hyper,425,1,9,eval] board([8,5,3,1,7,2]). given clause #393: (wt=16) 427 [hyper,426,1,5,eval] board([4,8,5,3,1,7,2]). given clause #394: (wt=12) 424 [hyper,423,1,9,eval] board([8,3,1,7,2]). given clause #395: (wt=14) 428 [hyper,424,1,7,eval] board([6,8,3,1,7,2]). given clause #396: (wt=16) 429 [hyper,428,1,5,eval] board([4,6,8,3,1,7,2]). given clause #397: (wt=10) 422 [hyper,419,1,5,eval] board([4,1,7,2]). given clause #398: (wt=12) 430 [hyper,422,1,9,eval] board([8,4,1,7,2]). given clause #399: (wt=14) 431 [hyper,430,1,6,eval] board([5,8,4,1,7,2]). given clause #400: (wt=16) 432 [hyper,431,1,4,eval] board([3,5,8,4,1,7,2]). given clause #401: (wt=10) 421 [hyper,419,1,7,eval] board([6,1,7,2]). given clause #402: (wt=12) 433 [hyper,421,1,9,eval] board([8,6,1,7,2]). given clause #403: (wt=14) 434 [hyper,433,1,6,eval] board([5,8,6,1,7,2]). given clause #404: (wt=10) 420 [hyper,419,1,9,eval] board([8,1,7,2]). given clause #405: (wt=12) 435 [hyper,420,1,6,eval] board([5,8,1,7,2]). given clause #406: (wt=8) 418 [hyper,253,1,4,eval] board([3,7,2]). given clause #407: (wt=10) 438 [hyper,418,1,2,eval] board([1,3,7,2]). given clause #408: (wt=12) 439 [hyper,438,1,9,eval] board([8,1,3,7,2]). given clause #409: (wt=14) 441 [hyper,439,1,5,eval] board([4,8,1,3,7,2]). given clause #410: (wt=14) 440 [hyper,439,1,6,eval] board([5,8,1,3,7,2]). given clause #411: (wt=10) 437 [hyper,418,1,7,eval] board([6,3,7,2]). given clause #412: (wt=12) 442 [hyper,437,1,9,eval] board([8,6,3,7,2]). given clause #413: (wt=14) 444 [hyper,442,1,2,eval] board([1,8,6,3,7,2]). given clause #414: (wt=16) 446 [hyper,444,1,5,eval] board([4,1,8,6,3,7,2]). given clause #415: (wt=16) 445 [hyper,444,1,6,eval] board([5,1,8,6,3,7,2]). given clause #416: (wt=14) 443 [hyper,442,1,6,eval] board([5,8,6,3,7,2]). given clause #417: (wt=16) 447 [hyper,443,1,2,eval] board([1,5,8,6,3,7,2]). -------- PROOF -------- 449 [binary,448.1,11.1] $Ans([4,1,5,8,6,3,7,2]). ----> UNIT CONFLICT at 0.15 sec ----> 449 [binary,448.1,11.1] $Ans([4,1,5,8,6,3,7,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 253 [hyper,20,1,8,eval] board([7,2]). 418 [hyper,253,1,4,eval] board([3,7,2]). 437 [hyper,418,1,7,eval] board([6,3,7,2]). 442 [hyper,437,1,9,eval] board([8,6,3,7,2]). 443 [hyper,442,1,6,eval] board([5,8,6,3,7,2]). 447 [hyper,443,1,2,eval] board([1,5,8,6,3,7,2]). 448 [hyper,447,1,5,eval] board([4,1,5,8,6,3,7,2]). 449 [binary,448.1,11.1] $Ans([4,1,5,8,6,3,7,2]). ------------ end of proof ------------- given clause #418: (wt=18) 448 [hyper,447,1,5,eval] board([4,1,5,8,6,3,7,2]). given clause #419: (wt=10) 436 [hyper,418,1,9,eval] board([8,3,7,2]). given clause #420: (wt=8) 417 [hyper,253,1,6,eval] board([5,7,2]). given clause #421: (wt=10) 452 [hyper,417,1,2,eval] board([1,5,7,2]). given clause #422: (wt=12) 453 [hyper,452,1,9,eval] board([8,1,5,7,2]). given clause #423: (wt=14) 455 [hyper,453,1,5,eval] board([4,8,1,5,7,2]). given clause #424: (wt=14) 454 [hyper,453,1,7,eval] board([6,8,1,5,7,2]). given clause #425: (wt=16) 456 [hyper,454,1,4,eval] board([3,6,8,1,5,7,2]). given clause #426: (wt=10) 451 [hyper,417,1,4,eval] board([3,5,7,2]). given clause #427: (wt=12) 458 [hyper,451,1,2,eval] board([1,3,5,7,2]). given clause #428: (wt=14) 460 [hyper,458,1,5,eval] board([4,1,3,5,7,2]). given clause #429: (wt=14) 459 [hyper,458,1,7,eval] board([6,1,3,5,7,2]). given clause #430: (wt=16) 461 [hyper,459,1,5,eval] board([4,6,1,3,5,7,2]). given clause #431: (wt=12) 457 [hyper,451,1,9,eval] board([8,3,5,7,2]). given clause #432: (wt=14) 463 [hyper,457,1,5,eval] board([4,8,3,5,7,2]). given clause #433: (wt=14) 462 [hyper,457,1,7,eval] board([6,8,3,5,7,2]). given clause #434: (wt=16) 464 [hyper,462,1,5,eval] board([4,6,8,3,5,7,2]). given clause #435: (wt=10) 450 [hyper,417,1,9,eval] board([8,5,7,2]). given clause #436: (wt=12) 465 [hyper,450,1,2,eval] board([1,8,5,7,2]). given clause #437: (wt=14) 466 [hyper,465,1,5,eval] board([4,1,8,5,7,2]). given clause #438: (wt=16) 467 [hyper,466,1,7,eval] board([6,4,1,8,5,7,2]). -------- PROOF -------- 469 [binary,468.1,11.1] $Ans([3,6,4,1,8,5,7,2]). ----> UNIT CONFLICT at 0.16 sec ----> 469 [binary,468.1,11.1] $Ans([3,6,4,1,8,5,7,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 253 [hyper,20,1,8,eval] board([7,2]). 417 [hyper,253,1,6,eval] board([5,7,2]). 450 [hyper,417,1,9,eval] board([8,5,7,2]). 465 [hyper,450,1,2,eval] board([1,8,5,7,2]). 466 [hyper,465,1,5,eval] board([4,1,8,5,7,2]). 467 [hyper,466,1,7,eval] board([6,4,1,8,5,7,2]). 468 [hyper,467,1,4,eval] board([3,6,4,1,8,5,7,2]). 469 [binary,468.1,11.1] $Ans([3,6,4,1,8,5,7,2]). ------------ end of proof ------------- given clause #439: (wt=18) 468 [hyper,467,1,4,eval] board([3,6,4,1,8,5,7,2]). given clause #440: (wt=6) 252 [hyper,20,1,9,eval] board([8,2]). given clause #441: (wt=8) 473 [hyper,252,1,2,eval] board([1,8,2]). given clause #442: (wt=10) 476 [hyper,473,1,4,eval] board([3,1,8,2]). given clause #443: (wt=12) 477 [hyper,476,1,8,eval] board([7,3,1,8,2]). given clause #444: (wt=10) 475 [hyper,473,1,5,eval] board([4,1,8,2]). given clause #445: (wt=12) 478 [hyper,475,1,8,eval] board([7,4,1,8,2]). given clause #446: (wt=14) 480 [hyper,478,1,4,eval] board([3,7,4,1,8,2]). given clause #447: (wt=16) 481 [hyper,480,1,7,eval] board([6,3,7,4,1,8,2]). given clause #448: (wt=14) 479 [hyper,478,1,6,eval] board([5,7,4,1,8,2]). given clause #449: (wt=10) 474 [hyper,473,1,8,eval] board([7,1,8,2]). given clause #450: (wt=12) 482 [hyper,474,1,5,eval] board([4,7,1,8,2]). given clause #451: (wt=14) 483 [hyper,482,1,7,eval] board([6,4,7,1,8,2]). given clause #452: (wt=8) 472 [hyper,252,1,4,eval] board([3,8,2]). given clause #453: (wt=10) 485 [hyper,472,1,2,eval] board([1,3,8,2]). given clause #454: (wt=12) 487 [hyper,485,1,5,eval] board([4,1,3,8,2]). given clause #455: (wt=12) 486 [hyper,485,1,8,eval] board([7,1,3,8,2]). given clause #456: (wt=14) 488 [hyper,486,1,6,eval] board([5,7,1,3,8,2]). given clause #457: (wt=10) 484 [hyper,472,1,8,eval] board([7,3,8,2]). given clause #458: (wt=12) 489 [hyper,484,1,5,eval] board([4,7,3,8,2]). given clause #459: (wt=14) 490 [hyper,489,1,2,eval] board([1,4,7,3,8,2]). given clause #460: (wt=16) 491 [hyper,490,1,6,eval] board([5,1,4,7,3,8,2]). given clause #461: (wt=8) 471 [hyper,252,1,6,eval] board([5,8,2]). given clause #462: (wt=10) 494 [hyper,471,1,2,eval] board([1,5,8,2]). given clause #463: (wt=12) 495 [hyper,494,1,5,eval] board([4,1,5,8,2]). given clause #464: (wt=14) 496 [hyper,495,1,7,eval] board([6,4,1,5,8,2]). given clause #465: (wt=10) 493 [hyper,471,1,4,eval] board([3,5,8,2]). given clause #466: (wt=12) 497 [hyper,493,1,2,eval] board([1,3,5,8,2]). given clause #467: (wt=14) 498 [hyper,497,1,7,eval] board([6,1,3,5,8,2]). given clause #468: (wt=16) 499 [hyper,498,1,5,eval] board([4,6,1,3,5,8,2]). given clause #469: (wt=10) 492 [hyper,471,1,8,eval] board([7,5,8,2]). given clause #470: (wt=12) 501 [hyper,492,1,2,eval] board([1,7,5,8,2]). given clause #471: (wt=14) 503 [hyper,501,1,4,eval] board([3,1,7,5,8,2]). given clause #472: (wt=16) 504 [hyper,503,1,7,eval] board([6,3,1,7,5,8,2]). given clause #473: (wt=14) 502 [hyper,501,1,7,eval] board([6,1,7,5,8,2]). given clause #474: (wt=12) 500 [hyper,492,1,5,eval] board([4,7,5,8,2]). given clause #475: (wt=14) 506 [hyper,500,1,2,eval] board([1,4,7,5,8,2]). given clause #476: (wt=14) 505 [hyper,500,1,7,eval] board([6,4,7,5,8,2]). given clause #477: (wt=8) 470 [hyper,252,1,7,eval] board([6,8,2]). given clause #478: (wt=10) 509 [hyper,470,1,2,eval] board([1,6,8,2]). given clause #479: (wt=12) 511 [hyper,509,1,4,eval] board([3,1,6,8,2]). given clause #480: (wt=14) 512 [hyper,511,1,6,eval] board([5,3,1,6,8,2]). given clause #481: (wt=16) 513 [hyper,512,1,8,eval] board([7,5,3,1,6,8,2]). -------- PROOF -------- 515 [binary,514.1,11.1] $Ans([4,7,5,3,1,6,8,2]). ----> UNIT CONFLICT at 0.17 sec ----> 515 [binary,514.1,11.1] $Ans([4,7,5,3,1,6,8,2]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 20 [hyper,10,1,3,eval] board([2]). 252 [hyper,20,1,9,eval] board([8,2]). 470 [hyper,252,1,7,eval] board([6,8,2]). 509 [hyper,470,1,2,eval] board([1,6,8,2]). 511 [hyper,509,1,4,eval] board([3,1,6,8,2]). 512 [hyper,511,1,6,eval] board([5,3,1,6,8,2]). 513 [hyper,512,1,8,eval] board([7,5,3,1,6,8,2]). 514 [hyper,513,1,5,eval] board([4,7,5,3,1,6,8,2]). 515 [binary,514.1,11.1] $Ans([4,7,5,3,1,6,8,2]). ------------ end of proof ------------- given clause #482: (wt=18) 514 [hyper,513,1,5,eval] board([4,7,5,3,1,6,8,2]). given clause #483: (wt=12) 510 [hyper,509,1,8,eval] board([7,1,6,8,2]). given clause #484: (wt=14) 516 [hyper,510,1,6,eval] board([5,7,1,6,8,2]). given clause #485: (wt=10) 508 [hyper,470,1,4,eval] board([3,6,8,2]). given clause #486: (wt=12) 518 [hyper,508,1,2,eval] board([1,3,6,8,2]). given clause #487: (wt=12) 517 [hyper,508,1,8,eval] board([7,3,6,8,2]). given clause #488: (wt=10) 507 [hyper,470,1,5,eval] board([4,6,8,2]). given clause #489: (wt=12) 520 [hyper,507,1,2,eval] board([1,4,6,8,2]). given clause #490: (wt=14) 521 [hyper,520,1,6,eval] board([5,1,4,6,8,2]). given clause #491: (wt=12) 519 [hyper,507,1,8,eval] board([7,4,6,8,2]). given clause #492: (wt=14) 523 [hyper,519,1,2,eval] board([1,7,4,6,8,2]). given clause #493: (wt=14) 522 [hyper,519,1,6,eval] board([5,7,4,6,8,2]). given clause #494: (wt=4) 19 [hyper,10,1,4,eval] board([3]). given clause #495: (wt=6) 528 [hyper,19,1,2,eval] board([1,3]). given clause #496: (wt=8) 532 [hyper,528,1,5,eval] board([4,1,3]). given clause #497: (wt=10) 535 [hyper,532,1,3,eval] board([2,4,1,3]). given clause #498: (wt=12) 537 [hyper,535,1,6,eval] board([5,2,4,1,3]). given clause #499: (wt=12) 536 [hyper,535,1,9,eval] board([8,2,4,1,3]). given clause #500: (wt=14) 538 [hyper,536,1,7,eval] board([6,8,2,4,1,3]). given clause #501: (wt=10) 534 [hyper,532,1,8,eval] board([7,4,1,3]). given clause #502: (wt=12) 539 [hyper,534,1,6,eval] board([5,7,4,1,3]). given clause #503: (wt=14) 540 [hyper,539,1,3,eval] board([2,5,7,4,1,3]). given clause #504: (wt=10) 533 [hyper,532,1,9,eval] board([8,4,1,3]). given clause #505: (wt=12) 541 [hyper,533,1,6,eval] board([5,8,4,1,3]). given clause #506: (wt=14) 542 [hyper,541,1,3,eval] board([2,5,8,4,1,3]). given clause #507: (wt=8) 531 [hyper,528,1,7,eval] board([6,1,3]). given clause #508: (wt=10) 545 [hyper,531,1,3,eval] board([2,6,1,3]). given clause #509: (wt=12) 546 [hyper,545,1,6,eval] board([5,2,6,1,3]). given clause #510: (wt=14) 547 [hyper,546,1,8,eval] board([7,5,2,6,1,3]). given clause #511: (wt=16) 548 [hyper,547,1,5,eval] board([4,7,5,2,6,1,3]). given clause #512: (wt=10) 544 [hyper,531,1,5,eval] board([4,6,1,3]). given clause #513: (wt=12) 549 [hyper,544,1,3,eval] board([2,4,6,1,3]). given clause #514: (wt=14) 550 [hyper,549,1,8,eval] board([7,2,4,6,1,3]). given clause #515: (wt=16) 551 [hyper,550,1,6,eval] board([5,7,2,4,6,1,3]). given clause #516: (wt=10) 543 [hyper,531,1,9,eval] board([8,6,1,3]). given clause #517: (wt=12) 553 [hyper,543,1,3,eval] board([2,8,6,1,3]). given clause #518: (wt=14) 555 [hyper,553,1,5,eval] board([4,2,8,6,1,3]). given clause #519: (wt=16) 556 [hyper,555,1,8,eval] board([7,4,2,8,6,1,3]). given clause #520: (wt=14) 554 [hyper,553,1,8,eval] board([7,2,8,6,1,3]). given clause #521: (wt=12) 552 [hyper,543,1,6,eval] board([5,8,6,1,3]). given clause #522: (wt=14) 558 [hyper,552,1,3,eval] board([2,5,8,6,1,3]). given clause #523: (wt=16) 559 [hyper,558,1,5,eval] board([4,2,5,8,6,1,3]). given clause #524: (wt=14) 557 [hyper,552,1,8,eval] board([7,5,8,6,1,3]). given clause #525: (wt=16) 560 [hyper,557,1,5,eval] board([4,7,5,8,6,1,3]). given clause #526: (wt=8) 530 [hyper,528,1,8,eval] board([7,1,3]). given clause #527: (wt=10) 563 [hyper,530,1,3,eval] board([2,7,1,3]). given clause #528: (wt=12) 565 [hyper,563,1,7,eval] board([6,2,7,1,3]). given clause #529: (wt=12) 564 [hyper,563,1,9,eval] board([8,2,7,1,3]). given clause #530: (wt=14) 566 [hyper,564,1,7,eval] board([6,8,2,7,1,3]). given clause #531: (wt=16) 567 [hyper,566,1,5,eval] board([4,6,8,2,7,1,3]). given clause #532: (wt=10) 562 [hyper,530,1,5,eval] board([4,7,1,3]). given clause #533: (wt=12) 570 [hyper,562,1,3,eval] board([2,4,7,1,3]). given clause #534: (wt=12) 569 [hyper,562,1,7,eval] board([6,4,7,1,3]). given clause #535: (wt=12) 568 [hyper,562,1,9,eval] board([8,4,7,1,3]). given clause #536: (wt=10) 561 [hyper,530,1,6,eval] board([5,7,1,3]). given clause #537: (wt=12) 572 [hyper,561,1,3,eval] board([2,5,7,1,3]). given clause #538: (wt=14) 573 [hyper,572,1,7,eval] board([6,2,5,7,1,3]). given clause #539: (wt=12) 571 [hyper,561,1,9,eval] board([8,5,7,1,3]). given clause #540: (wt=14) 575 [hyper,571,1,3,eval] board([2,8,5,7,1,3]). given clause #541: (wt=16) 576 [hyper,575,1,5,eval] board([4,2,8,5,7,1,3]). -------- PROOF -------- 578 [binary,577.1,11.1] $Ans([6,4,2,8,5,7,1,3]). ----> UNIT CONFLICT at 0.20 sec ----> 578 [binary,577.1,11.1] $Ans([6,4,2,8,5,7,1,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 528 [hyper,19,1,2,eval] board([1,3]). 530 [hyper,528,1,8,eval] board([7,1,3]). 561 [hyper,530,1,6,eval] board([5,7,1,3]). 571 [hyper,561,1,9,eval] board([8,5,7,1,3]). 575 [hyper,571,1,3,eval] board([2,8,5,7,1,3]). 576 [hyper,575,1,5,eval] board([4,2,8,5,7,1,3]). 577 [hyper,576,1,7,eval] board([6,4,2,8,5,7,1,3]). 578 [binary,577.1,11.1] $Ans([6,4,2,8,5,7,1,3]). ------------ end of proof ------------- given clause #542: (wt=18) 577 [hyper,576,1,7,eval] board([6,4,2,8,5,7,1,3]). given clause #543: (wt=14) 574 [hyper,571,1,7,eval] board([6,8,5,7,1,3]). given clause #544: (wt=16) 579 [hyper,574,1,5,eval] board([4,6,8,5,7,1,3]). given clause #545: (wt=8) 529 [hyper,528,1,9,eval] board([8,1,3]). given clause #546: (wt=10) 582 [hyper,529,1,3,eval] board([2,8,1,3]). given clause #547: (wt=12) 583 [hyper,582,1,6,eval] board([5,2,8,1,3]). given clause #548: (wt=14) 584 [hyper,583,1,8,eval] board([7,5,2,8,1,3]). given clause #549: (wt=10) 581 [hyper,529,1,5,eval] board([4,8,1,3]). given clause #550: (wt=12) 585 [hyper,581,1,3,eval] board([2,4,8,1,3]). given clause #551: (wt=14) 586 [hyper,585,1,8,eval] board([7,2,4,8,1,3]). given clause #552: (wt=16) 587 [hyper,586,1,6,eval] board([5,7,2,4,8,1,3]). given clause #553: (wt=10) 580 [hyper,529,1,6,eval] board([5,8,1,3]). given clause #554: (wt=12) 588 [hyper,580,1,3,eval] board([2,5,8,1,3]). given clause #555: (wt=14) 590 [hyper,588,1,5,eval] board([4,2,5,8,1,3]). given clause #556: (wt=16) 591 [hyper,590,1,8,eval] board([7,4,2,5,8,1,3]). given clause #557: (wt=14) 589 [hyper,588,1,7,eval] board([6,2,5,8,1,3]). given clause #558: (wt=6) 527 [hyper,19,1,6,eval] board([5,3]). given clause #559: (wt=8) 594 [hyper,527,1,3,eval] board([2,5,3]). given clause #560: (wt=10) 596 [hyper,594,1,5,eval] board([4,2,5,3]). given clause #561: (wt=12) 598 [hyper,596,1,2,eval] board([1,4,2,5,3]). given clause #562: (wt=14) 599 [hyper,598,1,8,eval] board([7,1,4,2,5,3]). given clause #563: (wt=12) 597 [hyper,596,1,7,eval] board([6,4,2,5,3]). given clause #564: (wt=10) 595 [hyper,594,1,9,eval] board([8,2,5,3]). given clause #565: (wt=12) 601 [hyper,595,1,2,eval] board([1,8,2,5,3]). given clause #566: (wt=14) 603 [hyper,601,1,5,eval] board([4,1,8,2,5,3]). given clause #567: (wt=16) 604 [hyper,603,1,8,eval] board([7,4,1,8,2,5,3]). given clause #568: (wt=14) 602 [hyper,601,1,8,eval] board([7,1,8,2,5,3]). given clause #569: (wt=16) 605 [hyper,602,1,5,eval] board([4,7,1,8,2,5,3]). -------- PROOF -------- 607 [binary,606.1,11.1] $Ans([6,4,7,1,8,2,5,3]). ----> UNIT CONFLICT at 0.21 sec ----> 607 [binary,606.1,11.1] $Ans([6,4,7,1,8,2,5,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 527 [hyper,19,1,6,eval] board([5,3]). 594 [hyper,527,1,3,eval] board([2,5,3]). 595 [hyper,594,1,9,eval] board([8,2,5,3]). 601 [hyper,595,1,2,eval] board([1,8,2,5,3]). 602 [hyper,601,1,8,eval] board([7,1,8,2,5,3]). 605 [hyper,602,1,5,eval] board([4,7,1,8,2,5,3]). 606 [hyper,605,1,7,eval] board([6,4,7,1,8,2,5,3]). 607 [binary,606.1,11.1] $Ans([6,4,7,1,8,2,5,3]). ------------ end of proof ------------- given clause #570: (wt=18) 606 [hyper,605,1,7,eval] board([6,4,7,1,8,2,5,3]). given clause #571: (wt=12) 600 [hyper,595,1,7,eval] board([6,8,2,5,3]). given clause #572: (wt=14) 608 [hyper,600,1,5,eval] board([4,6,8,2,5,3]). given clause #573: (wt=16) 610 [hyper,608,1,2,eval] board([1,4,6,8,2,5,3]). given clause #574: (wt=16) 609 [hyper,608,1,8,eval] board([7,4,6,8,2,5,3]). -------- PROOF -------- 612 [binary,611.1,11.1] $Ans([1,7,4,6,8,2,5,3]). ----> UNIT CONFLICT at 0.21 sec ----> 612 [binary,611.1,11.1] $Ans([1,7,4,6,8,2,5,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 527 [hyper,19,1,6,eval] board([5,3]). 594 [hyper,527,1,3,eval] board([2,5,3]). 595 [hyper,594,1,9,eval] board([8,2,5,3]). 600 [hyper,595,1,7,eval] board([6,8,2,5,3]). 608 [hyper,600,1,5,eval] board([4,6,8,2,5,3]). 609 [hyper,608,1,8,eval] board([7,4,6,8,2,5,3]). 611 [hyper,609,1,2,eval] board([1,7,4,6,8,2,5,3]). 612 [binary,611.1,11.1] $Ans([1,7,4,6,8,2,5,3]). ------------ end of proof ------------- given clause #575: (wt=18) 611 [hyper,609,1,2,eval] board([1,7,4,6,8,2,5,3]). given clause #576: (wt=8) 593 [hyper,527,1,8,eval] board([7,5,3]). given clause #577: (wt=10) 615 [hyper,593,1,2,eval] board([1,7,5,3]). given clause #578: (wt=12) 617 [hyper,615,1,5,eval] board([4,1,7,5,3]). given clause #579: (wt=14) 619 [hyper,617,1,3,eval] board([2,4,1,7,5,3]). given clause #580: (wt=16) 620 [hyper,619,1,9,eval] board([8,2,4,1,7,5,3]). -------- PROOF -------- 622 [binary,621.1,11.1] $Ans([6,8,2,4,1,7,5,3]). ----> UNIT CONFLICT at 0.21 sec ----> 622 [binary,621.1,11.1] $Ans([6,8,2,4,1,7,5,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 527 [hyper,19,1,6,eval] board([5,3]). 593 [hyper,527,1,8,eval] board([7,5,3]). 615 [hyper,593,1,2,eval] board([1,7,5,3]). 617 [hyper,615,1,5,eval] board([4,1,7,5,3]). 619 [hyper,617,1,3,eval] board([2,4,1,7,5,3]). 620 [hyper,619,1,9,eval] board([8,2,4,1,7,5,3]). 621 [hyper,620,1,7,eval] board([6,8,2,4,1,7,5,3]). 622 [binary,621.1,11.1] $Ans([6,8,2,4,1,7,5,3]). ------------ end of proof ------------- given clause #581: (wt=18) 621 [hyper,620,1,7,eval] board([6,8,2,4,1,7,5,3]). given clause #582: (wt=14) 618 [hyper,617,1,7,eval] board([6,4,1,7,5,3]). given clause #583: (wt=16) 623 [hyper,618,1,9,eval] board([8,6,4,1,7,5,3]). given clause #584: (wt=12) 616 [hyper,615,1,7,eval] board([6,1,7,5,3]). given clause #585: (wt=14) 624 [hyper,616,1,3,eval] board([2,6,1,7,5,3]). given clause #586: (wt=10) 614 [hyper,593,1,3,eval] board([2,7,5,3]). given clause #587: (wt=12) 626 [hyper,614,1,5,eval] board([4,2,7,5,3]). given clause #588: (wt=14) 627 [hyper,626,1,7,eval] board([6,4,2,7,5,3]). given clause #589: (wt=16) 629 [hyper,627,1,2,eval] board([1,6,4,2,7,5,3]). given clause #590: (wt=16) 628 [hyper,627,1,9,eval] board([8,6,4,2,7,5,3]). given clause #591: (wt=12) 625 [hyper,614,1,7,eval] board([6,2,7,5,3]). given clause #592: (wt=10) 613 [hyper,593,1,5,eval] board([4,7,5,3]). given clause #593: (wt=12) 631 [hyper,613,1,2,eval] board([1,4,7,5,3]). given clause #594: (wt=12) 630 [hyper,613,1,7,eval] board([6,4,7,5,3]). given clause #595: (wt=8) 592 [hyper,527,1,9,eval] board([8,5,3]). given clause #596: (wt=10) 634 [hyper,592,1,2,eval] board([1,8,5,3]). given clause #597: (wt=12) 635 [hyper,634,1,5,eval] board([4,1,8,5,3]). given clause #598: (wt=14) 638 [hyper,635,1,3,eval] board([2,4,1,8,5,3]). given clause #599: (wt=16) 639 [hyper,638,1,8,eval] board([7,2,4,1,8,5,3]). given clause #600: (wt=14) 637 [hyper,635,1,7,eval] board([6,4,1,8,5,3]). given clause #601: (wt=14) 636 [hyper,635,1,8,eval] board([7,4,1,8,5,3]). given clause #602: (wt=10) 633 [hyper,592,1,3,eval] board([2,8,5,3]). given clause #603: (wt=12) 640 [hyper,633,1,5,eval] board([4,2,8,5,3]). given clause #604: (wt=14) 642 [hyper,640,1,7,eval] board([6,4,2,8,5,3]). given clause #605: (wt=16) 643 [hyper,642,1,2,eval] board([1,6,4,2,8,5,3]). given clause #606: (wt=14) 641 [hyper,640,1,8,eval] board([7,4,2,8,5,3]). given clause #607: (wt=16) 644 [hyper,641,1,2,eval] board([1,7,4,2,8,5,3]). given clause #608: (wt=10) 632 [hyper,592,1,5,eval] board([4,8,5,3]). given clause #609: (wt=12) 645 [hyper,632,1,2,eval] board([1,4,8,5,3]). given clause #610: (wt=14) 646 [hyper,645,1,8,eval] board([7,1,4,8,5,3]). given clause #611: (wt=16) 647 [hyper,646,1,3,eval] board([2,7,1,4,8,5,3]). -------- PROOF -------- 649 [binary,648.1,11.1] $Ans([6,2,7,1,4,8,5,3]). ----> UNIT CONFLICT at 0.23 sec ----> 649 [binary,648.1,11.1] $Ans([6,2,7,1,4,8,5,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 527 [hyper,19,1,6,eval] board([5,3]). 592 [hyper,527,1,9,eval] board([8,5,3]). 632 [hyper,592,1,5,eval] board([4,8,5,3]). 645 [hyper,632,1,2,eval] board([1,4,8,5,3]). 646 [hyper,645,1,8,eval] board([7,1,4,8,5,3]). 647 [hyper,646,1,3,eval] board([2,7,1,4,8,5,3]). 648 [hyper,647,1,7,eval] board([6,2,7,1,4,8,5,3]). 649 [binary,648.1,11.1] $Ans([6,2,7,1,4,8,5,3]). ------------ end of proof ------------- given clause #612: (wt=18) 648 [hyper,647,1,7,eval] board([6,2,7,1,4,8,5,3]). given clause #613: (wt=6) 526 [hyper,19,1,7,eval] board([6,3]). given clause #614: (wt=8) 652 [hyper,526,1,3,eval] board([2,6,3]). given clause #615: (wt=10) 654 [hyper,652,1,6,eval] board([5,2,6,3]). given clause #616: (wt=12) 656 [hyper,654,1,2,eval] board([1,5,2,6,3]). given clause #617: (wt=14) 657 [hyper,656,1,5,eval] board([4,1,5,2,6,3]). given clause #618: (wt=16) 658 [hyper,657,1,8,eval] board([7,4,1,5,2,6,3]). given clause #619: (wt=12) 655 [hyper,654,1,9,eval] board([8,5,2,6,3]). given clause #620: (wt=14) 660 [hyper,655,1,2,eval] board([1,8,5,2,6,3]). given clause #621: (wt=16) 662 [hyper,660,1,5,eval] board([4,1,8,5,2,6,3]). given clause #622: (wt=16) 661 [hyper,660,1,8,eval] board([7,1,8,5,2,6,3]). -------- PROOF -------- 664 [binary,663.1,11.1] $Ans([4,7,1,8,5,2,6,3]). ----> UNIT CONFLICT at 0.23 sec ----> 664 [binary,663.1,11.1] $Ans([4,7,1,8,5,2,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 652 [hyper,526,1,3,eval] board([2,6,3]). 654 [hyper,652,1,6,eval] board([5,2,6,3]). 655 [hyper,654,1,9,eval] board([8,5,2,6,3]). 660 [hyper,655,1,2,eval] board([1,8,5,2,6,3]). 661 [hyper,660,1,8,eval] board([7,1,8,5,2,6,3]). 663 [hyper,661,1,5,eval] board([4,7,1,8,5,2,6,3]). 664 [binary,663.1,11.1] $Ans([4,7,1,8,5,2,6,3]). ------------ end of proof ------------- given clause #623: (wt=18) 663 [hyper,661,1,5,eval] board([4,7,1,8,5,2,6,3]). given clause #624: (wt=14) 659 [hyper,655,1,5,eval] board([4,8,5,2,6,3]). given clause #625: (wt=16) 665 [hyper,659,1,8,eval] board([7,4,8,5,2,6,3]). given clause #626: (wt=10) 653 [hyper,652,1,8,eval] board([7,2,6,3]). given clause #627: (wt=12) 667 [hyper,653,1,2,eval] board([1,7,2,6,3]). given clause #628: (wt=14) 668 [hyper,667,1,5,eval] board([4,1,7,2,6,3]). given clause #629: (wt=16) 669 [hyper,668,1,9,eval] board([8,4,1,7,2,6,3]). -------- PROOF -------- 671 [binary,670.1,11.1] $Ans([5,8,4,1,7,2,6,3]). ----> UNIT CONFLICT at 0.23 sec ----> 671 [binary,670.1,11.1] $Ans([5,8,4,1,7,2,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 652 [hyper,526,1,3,eval] board([2,6,3]). 653 [hyper,652,1,8,eval] board([7,2,6,3]). 667 [hyper,653,1,2,eval] board([1,7,2,6,3]). 668 [hyper,667,1,5,eval] board([4,1,7,2,6,3]). 669 [hyper,668,1,9,eval] board([8,4,1,7,2,6,3]). 670 [hyper,669,1,6,eval] board([5,8,4,1,7,2,6,3]). 671 [binary,670.1,11.1] $Ans([5,8,4,1,7,2,6,3]). ------------ end of proof ------------- given clause #630: (wt=18) 670 [hyper,669,1,6,eval] board([5,8,4,1,7,2,6,3]). given clause #631: (wt=12) 666 [hyper,653,1,6,eval] board([5,7,2,6,3]). given clause #632: (wt=14) 672 [hyper,666,1,2,eval] board([1,5,7,2,6,3]). given clause #633: (wt=16) 673 [hyper,672,1,9,eval] board([8,1,5,7,2,6,3]). -------- PROOF -------- 675 [binary,674.1,11.1] $Ans([4,8,1,5,7,2,6,3]). ----> UNIT CONFLICT at 0.23 sec ----> 675 [binary,674.1,11.1] $Ans([4,8,1,5,7,2,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 652 [hyper,526,1,3,eval] board([2,6,3]). 653 [hyper,652,1,8,eval] board([7,2,6,3]). 666 [hyper,653,1,6,eval] board([5,7,2,6,3]). 672 [hyper,666,1,2,eval] board([1,5,7,2,6,3]). 673 [hyper,672,1,9,eval] board([8,1,5,7,2,6,3]). 674 [hyper,673,1,5,eval] board([4,8,1,5,7,2,6,3]). 675 [binary,674.1,11.1] $Ans([4,8,1,5,7,2,6,3]). ------------ end of proof ------------- given clause #634: (wt=18) 674 [hyper,673,1,5,eval] board([4,8,1,5,7,2,6,3]). given clause #635: (wt=8) 651 [hyper,526,1,5,eval] board([4,6,3]). given clause #636: (wt=10) 678 [hyper,651,1,2,eval] board([1,4,6,3]). given clause #637: (wt=12) 680 [hyper,678,1,6,eval] board([5,1,4,6,3]). given clause #638: (wt=12) 679 [hyper,678,1,9,eval] board([8,1,4,6,3]). given clause #639: (wt=14) 681 [hyper,679,1,6,eval] board([5,8,1,4,6,3]). given clause #640: (wt=16) 683 [hyper,681,1,3,eval] board([2,5,8,1,4,6,3]). given clause #641: (wt=16) 682 [hyper,681,1,8,eval] board([7,5,8,1,4,6,3]). -------- PROOF -------- 685 [binary,684.1,11.1] $Ans([2,7,5,8,1,4,6,3]). ----> UNIT CONFLICT at 0.24 sec ----> 685 [binary,684.1,11.1] $Ans([2,7,5,8,1,4,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 651 [hyper,526,1,5,eval] board([4,6,3]). 678 [hyper,651,1,2,eval] board([1,4,6,3]). 679 [hyper,678,1,9,eval] board([8,1,4,6,3]). 681 [hyper,679,1,6,eval] board([5,8,1,4,6,3]). 682 [hyper,681,1,8,eval] board([7,5,8,1,4,6,3]). 684 [hyper,682,1,3,eval] board([2,7,5,8,1,4,6,3]). 685 [binary,684.1,11.1] $Ans([2,7,5,8,1,4,6,3]). ------------ end of proof ------------- given clause #642: (wt=18) 684 [hyper,682,1,3,eval] board([2,7,5,8,1,4,6,3]). given clause #643: (wt=10) 677 [hyper,651,1,3,eval] board([2,4,6,3]). given clause #644: (wt=12) 687 [hyper,677,1,6,eval] board([5,2,4,6,3]). given clause #645: (wt=12) 686 [hyper,677,1,9,eval] board([8,2,4,6,3]). given clause #646: (wt=14) 688 [hyper,686,1,6,eval] board([5,8,2,4,6,3]). given clause #647: (wt=16) 689 [hyper,688,1,8,eval] board([7,5,8,2,4,6,3]). -------- PROOF -------- 691 [binary,690.1,11.1] $Ans([1,7,5,8,2,4,6,3]). ----> UNIT CONFLICT at 0.24 sec ----> 691 [binary,690.1,11.1] $Ans([1,7,5,8,2,4,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 651 [hyper,526,1,5,eval] board([4,6,3]). 677 [hyper,651,1,3,eval] board([2,4,6,3]). 686 [hyper,677,1,9,eval] board([8,2,4,6,3]). 688 [hyper,686,1,6,eval] board([5,8,2,4,6,3]). 689 [hyper,688,1,8,eval] board([7,5,8,2,4,6,3]). 690 [hyper,689,1,2,eval] board([1,7,5,8,2,4,6,3]). 691 [binary,690.1,11.1] $Ans([1,7,5,8,2,4,6,3]). ------------ end of proof ------------- given clause #648: (wt=18) 690 [hyper,689,1,2,eval] board([1,7,5,8,2,4,6,3]). given clause #649: (wt=10) 676 [hyper,651,1,8,eval] board([7,4,6,3]). given clause #650: (wt=12) 693 [hyper,676,1,2,eval] board([1,7,4,6,3]). given clause #651: (wt=12) 692 [hyper,676,1,6,eval] board([5,7,4,6,3]). given clause #652: (wt=8) 650 [hyper,526,1,9,eval] board([8,6,3]). given clause #653: (wt=10) 696 [hyper,650,1,2,eval] board([1,8,6,3]). given clause #654: (wt=12) 698 [hyper,696,1,5,eval] board([4,1,8,6,3]). given clause #655: (wt=14) 699 [hyper,698,1,8,eval] board([7,4,1,8,6,3]). given clause #656: (wt=16) 700 [hyper,699,1,6,eval] board([5,7,4,1,8,6,3]). -------- PROOF -------- 702 [binary,701.1,11.1] $Ans([2,5,7,4,1,8,6,3]). ----> UNIT CONFLICT at 0.24 sec ----> 702 [binary,701.1,11.1] $Ans([2,5,7,4,1,8,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 650 [hyper,526,1,9,eval] board([8,6,3]). 696 [hyper,650,1,2,eval] board([1,8,6,3]). 698 [hyper,696,1,5,eval] board([4,1,8,6,3]). 699 [hyper,698,1,8,eval] board([7,4,1,8,6,3]). 700 [hyper,699,1,6,eval] board([5,7,4,1,8,6,3]). 701 [hyper,700,1,3,eval] board([2,5,7,4,1,8,6,3]). 702 [binary,701.1,11.1] $Ans([2,5,7,4,1,8,6,3]). ------------ end of proof ------------- given clause #657: (wt=18) 701 [hyper,700,1,3,eval] board([2,5,7,4,1,8,6,3]). given clause #658: (wt=12) 697 [hyper,696,1,6,eval] board([5,1,8,6,3]). given clause #659: (wt=14) 703 [hyper,697,1,8,eval] board([7,5,1,8,6,3]). given clause #660: (wt=16) 704 [hyper,703,1,3,eval] board([2,7,5,1,8,6,3]). -------- PROOF -------- 706 [binary,705.1,11.1] $Ans([4,2,7,5,1,8,6,3]). ----> UNIT CONFLICT at 0.25 sec ----> 706 [binary,705.1,11.1] $Ans([4,2,7,5,1,8,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 650 [hyper,526,1,9,eval] board([8,6,3]). 696 [hyper,650,1,2,eval] board([1,8,6,3]). 697 [hyper,696,1,6,eval] board([5,1,8,6,3]). 703 [hyper,697,1,8,eval] board([7,5,1,8,6,3]). 704 [hyper,703,1,3,eval] board([2,7,5,1,8,6,3]). 705 [hyper,704,1,5,eval] board([4,2,7,5,1,8,6,3]). 706 [binary,705.1,11.1] $Ans([4,2,7,5,1,8,6,3]). ------------ end of proof ------------- given clause #661: (wt=18) 705 [hyper,704,1,5,eval] board([4,2,7,5,1,8,6,3]). given clause #662: (wt=10) 695 [hyper,650,1,3,eval] board([2,8,6,3]). given clause #663: (wt=12) 708 [hyper,695,1,5,eval] board([4,2,8,6,3]). given clause #664: (wt=14) 710 [hyper,708,1,2,eval] board([1,4,2,8,6,3]). given clause #665: (wt=16) 711 [hyper,710,1,8,eval] board([7,1,4,2,8,6,3]). -------- PROOF -------- 713 [binary,712.1,11.1] $Ans([5,7,1,4,2,8,6,3]). ----> UNIT CONFLICT at 0.25 sec ----> 713 [binary,712.1,11.1] $Ans([5,7,1,4,2,8,6,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 526 [hyper,19,1,7,eval] board([6,3]). 650 [hyper,526,1,9,eval] board([8,6,3]). 695 [hyper,650,1,3,eval] board([2,8,6,3]). 708 [hyper,695,1,5,eval] board([4,2,8,6,3]). 710 [hyper,708,1,2,eval] board([1,4,2,8,6,3]). 711 [hyper,710,1,8,eval] board([7,1,4,2,8,6,3]). 712 [hyper,711,1,6,eval] board([5,7,1,4,2,8,6,3]). 713 [binary,712.1,11.1] $Ans([5,7,1,4,2,8,6,3]). ------------ end of proof ------------- given clause #666: (wt=18) 712 [hyper,711,1,6,eval] board([5,7,1,4,2,8,6,3]). given clause #667: (wt=14) 709 [hyper,708,1,8,eval] board([7,4,2,8,6,3]). given clause #668: (wt=12) 707 [hyper,695,1,6,eval] board([5,2,8,6,3]). given clause #669: (wt=14) 715 [hyper,707,1,2,eval] board([1,5,2,8,6,3]). given clause #670: (wt=14) 714 [hyper,707,1,8,eval] board([7,5,2,8,6,3]). given clause #671: (wt=10) 694 [hyper,650,1,6,eval] board([5,8,6,3]). given clause #672: (wt=12) 717 [hyper,694,1,2,eval] board([1,5,8,6,3]). given clause #673: (wt=14) 718 [hyper,717,1,5,eval] board([4,1,5,8,6,3]). given clause #674: (wt=16) 719 [hyper,718,1,8,eval] board([7,4,1,5,8,6,3]). given clause #675: (wt=12) 716 [hyper,694,1,3,eval] board([2,5,8,6,3]). given clause #676: (wt=14) 720 [hyper,716,1,5,eval] board([4,2,5,8,6,3]). given clause #677: (wt=16) 721 [hyper,720,1,8,eval] board([7,4,2,5,8,6,3]). given clause #678: (wt=6) 525 [hyper,19,1,8,eval] board([7,3]). given clause #679: (wt=8) 723 [hyper,525,1,3,eval] board([2,7,3]). given clause #680: (wt=10) 725 [hyper,723,1,5,eval] board([4,2,7,3]). given clause #681: (wt=12) 728 [hyper,725,1,2,eval] board([1,4,2,7,3]). given clause #682: (wt=12) 727 [hyper,725,1,7,eval] board([6,4,2,7,3]). given clause #683: (wt=14) 729 [hyper,727,1,2,eval] board([1,6,4,2,7,3]). given clause #684: (wt=16) 730 [hyper,729,1,6,eval] board([5,1,6,4,2,7,3]). given clause #685: (wt=12) 726 [hyper,725,1,9,eval] board([8,4,2,7,3]). given clause #686: (wt=14) 731 [hyper,726,1,2,eval] board([1,8,4,2,7,3]). given clause #687: (wt=16) 732 [hyper,731,1,6,eval] board([5,1,8,4,2,7,3]). given clause #688: (wt=10) 724 [hyper,723,1,9,eval] board([8,2,7,3]). given clause #689: (wt=12) 735 [hyper,724,1,2,eval] board([1,8,2,7,3]). given clause #690: (wt=14) 736 [hyper,735,1,5,eval] board([4,1,8,2,7,3]). given clause #691: (wt=12) 734 [hyper,724,1,6,eval] board([5,8,2,7,3]). given clause #692: (wt=14) 737 [hyper,734,1,2,eval] board([1,5,8,2,7,3]). given clause #693: (wt=16) 738 [hyper,737,1,5,eval] board([4,1,5,8,2,7,3]). -------- PROOF -------- 740 [binary,739.1,11.1] $Ans([6,4,1,5,8,2,7,3]). ----> UNIT CONFLICT at 0.26 sec ----> 740 [binary,739.1,11.1] $Ans([6,4,1,5,8,2,7,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 525 [hyper,19,1,8,eval] board([7,3]). 723 [hyper,525,1,3,eval] board([2,7,3]). 724 [hyper,723,1,9,eval] board([8,2,7,3]). 734 [hyper,724,1,6,eval] board([5,8,2,7,3]). 737 [hyper,734,1,2,eval] board([1,5,8,2,7,3]). 738 [hyper,737,1,5,eval] board([4,1,5,8,2,7,3]). 739 [hyper,738,1,7,eval] board([6,4,1,5,8,2,7,3]). 740 [binary,739.1,11.1] $Ans([6,4,1,5,8,2,7,3]). ------------ end of proof ------------- given clause #694: (wt=18) 739 [hyper,738,1,7,eval] board([6,4,1,5,8,2,7,3]). given clause #695: (wt=12) 733 [hyper,724,1,7,eval] board([6,8,2,7,3]). given clause #696: (wt=14) 742 [hyper,733,1,2,eval] board([1,6,8,2,7,3]). given clause #697: (wt=14) 741 [hyper,733,1,5,eval] board([4,6,8,2,7,3]). given clause #698: (wt=16) 743 [hyper,741,1,2,eval] board([1,4,6,8,2,7,3]). -------- PROOF -------- 745 [binary,744.1,11.1] $Ans([5,1,4,6,8,2,7,3]). ----> UNIT CONFLICT at 0.26 sec ----> 745 [binary,744.1,11.1] $Ans([5,1,4,6,8,2,7,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 525 [hyper,19,1,8,eval] board([7,3]). 723 [hyper,525,1,3,eval] board([2,7,3]). 724 [hyper,723,1,9,eval] board([8,2,7,3]). 733 [hyper,724,1,7,eval] board([6,8,2,7,3]). 741 [hyper,733,1,5,eval] board([4,6,8,2,7,3]). 743 [hyper,741,1,2,eval] board([1,4,6,8,2,7,3]). 744 [hyper,743,1,6,eval] board([5,1,4,6,8,2,7,3]). 745 [binary,744.1,11.1] $Ans([5,1,4,6,8,2,7,3]). ------------ end of proof ------------- given clause #699: (wt=18) 744 [hyper,743,1,6,eval] board([5,1,4,6,8,2,7,3]). given clause #700: (wt=8) 722 [hyper,525,1,5,eval] board([4,7,3]). given clause #701: (wt=10) 748 [hyper,722,1,2,eval] board([1,4,7,3]). given clause #702: (wt=12) 750 [hyper,748,1,6,eval] board([5,1,4,7,3]). given clause #703: (wt=14) 751 [hyper,750,1,3,eval] board([2,5,1,4,7,3]). given clause #704: (wt=16) 752 [hyper,751,1,7,eval] board([6,2,5,1,4,7,3]). given clause #705: (wt=12) 749 [hyper,748,1,9,eval] board([8,1,4,7,3]). given clause #706: (wt=14) 755 [hyper,749,1,3,eval] board([2,8,1,4,7,3]). given clause #707: (wt=16) 756 [hyper,755,1,6,eval] board([5,2,8,1,4,7,3]). given clause #708: (wt=14) 754 [hyper,749,1,6,eval] board([5,8,1,4,7,3]). given clause #709: (wt=14) 753 [hyper,749,1,7,eval] board([6,8,1,4,7,3]). given clause #710: (wt=10) 747 [hyper,722,1,3,eval] board([2,4,7,3]). given clause #711: (wt=12) 758 [hyper,747,1,6,eval] board([5,2,4,7,3]). given clause #712: (wt=12) 757 [hyper,747,1,9,eval] board([8,2,4,7,3]). given clause #713: (wt=14) 760 [hyper,757,1,6,eval] board([5,8,2,4,7,3]). given clause #714: (wt=16) 761 [hyper,760,1,2,eval] board([1,5,8,2,4,7,3]). given clause #715: (wt=14) 759 [hyper,757,1,7,eval] board([6,8,2,4,7,3]). given clause #716: (wt=16) 762 [hyper,759,1,2,eval] board([1,6,8,2,4,7,3]). given clause #717: (wt=10) 746 [hyper,722,1,9,eval] board([8,4,7,3]). given clause #718: (wt=12) 764 [hyper,746,1,2,eval] board([1,8,4,7,3]). given clause #719: (wt=14) 765 [hyper,764,1,6,eval] board([5,1,8,4,7,3]). given clause #720: (wt=12) 763 [hyper,746,1,6,eval] board([5,8,4,7,3]). given clause #721: (wt=14) 766 [hyper,763,1,3,eval] board([2,5,8,4,7,3]). given clause #722: (wt=16) 767 [hyper,766,1,7,eval] board([6,2,5,8,4,7,3]). given clause #723: (wt=6) 524 [hyper,19,1,9,eval] board([8,3]). given clause #724: (wt=8) 770 [hyper,524,1,3,eval] board([2,8,3]). given clause #725: (wt=10) 773 [hyper,770,1,5,eval] board([4,2,8,3]). given clause #726: (wt=12) 775 [hyper,773,1,2,eval] board([1,4,2,8,3]). given clause #727: (wt=14) 776 [hyper,775,1,8,eval] board([7,1,4,2,8,3]). given clause #728: (wt=16) 777 [hyper,776,1,6,eval] board([5,7,1,4,2,8,3]). given clause #729: (wt=12) 774 [hyper,773,1,7,eval] board([6,4,2,8,3]). given clause #730: (wt=14) 778 [hyper,774,1,2,eval] board([1,6,4,2,8,3]). given clause #731: (wt=16) 779 [hyper,778,1,6,eval] board([5,1,6,4,2,8,3]). given clause #732: (wt=10) 772 [hyper,770,1,6,eval] board([5,2,8,3]). given clause #733: (wt=12) 780 [hyper,772,1,2,eval] board([1,5,2,8,3]). given clause #734: (wt=14) 781 [hyper,780,1,7,eval] board([6,1,5,2,8,3]). given clause #735: (wt=16) 782 [hyper,781,1,5,eval] board([4,6,1,5,2,8,3]). given clause #736: (wt=10) 771 [hyper,770,1,8,eval] board([7,2,8,3]). given clause #737: (wt=12) 783 [hyper,771,1,2,eval] board([1,7,2,8,3]). given clause #738: (wt=14) 784 [hyper,783,1,7,eval] board([6,1,7,2,8,3]). given clause #739: (wt=8) 769 [hyper,524,1,5,eval] board([4,8,3]). given clause #740: (wt=10) 787 [hyper,769,1,2,eval] board([1,4,8,3]). given clause #741: (wt=10) 786 [hyper,769,1,3,eval] board([2,4,8,3]). given clause #742: (wt=10) 785 [hyper,769,1,8,eval] board([7,4,8,3]). given clause #743: (wt=12) 788 [hyper,785,1,2,eval] board([1,7,4,8,3]). given clause #744: (wt=14) 789 [hyper,788,1,7,eval] board([6,1,7,4,8,3]). given clause #745: (wt=16) 790 [hyper,789,1,3,eval] board([2,6,1,7,4,8,3]). -------- PROOF -------- 792 [binary,791.1,11.1] $Ans([5,2,6,1,7,4,8,3]). ----> UNIT CONFLICT at 0.28 sec ----> 792 [binary,791.1,11.1] $Ans([5,2,6,1,7,4,8,3]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 19 [hyper,10,1,4,eval] board([3]). 524 [hyper,19,1,9,eval] board([8,3]). 769 [hyper,524,1,5,eval] board([4,8,3]). 785 [hyper,769,1,8,eval] board([7,4,8,3]). 788 [hyper,785,1,2,eval] board([1,7,4,8,3]). 789 [hyper,788,1,7,eval] board([6,1,7,4,8,3]). 790 [hyper,789,1,3,eval] board([2,6,1,7,4,8,3]). 791 [hyper,790,1,6,eval] board([5,2,6,1,7,4,8,3]). 792 [binary,791.1,11.1] $Ans([5,2,6,1,7,4,8,3]). ------------ end of proof ------------- given clause #746: (wt=18) 791 [hyper,790,1,6,eval] board([5,2,6,1,7,4,8,3]). given clause #747: (wt=8) 768 [hyper,524,1,7,eval] board([6,8,3]). given clause #748: (wt=10) 795 [hyper,768,1,2,eval] board([1,6,8,3]). given clause #749: (wt=10) 794 [hyper,768,1,3,eval] board([2,6,8,3]). given clause #750: (wt=10) 793 [hyper,768,1,5,eval] board([4,6,8,3]). given clause #751: (wt=12) 797 [hyper,793,1,2,eval] board([1,4,6,8,3]). given clause #752: (wt=14) 799 [hyper,797,1,6,eval] board([5,1,4,6,8,3]). given clause #753: (wt=14) 798 [hyper,797,1,8,eval] board([7,1,4,6,8,3]). given clause #754: (wt=16) 800 [hyper,798,1,6,eval] board([5,7,1,4,6,8,3]). given clause #755: (wt=12) 796 [hyper,793,1,3,eval] board([2,4,6,8,3]). given clause #756: (wt=14) 802 [hyper,796,1,6,eval] board([5,2,4,6,8,3]). given clause #757: (wt=14) 801 [hyper,796,1,8,eval] board([7,2,4,6,8,3]). given clause #758: (wt=16) 803 [hyper,801,1,6,eval] board([5,7,2,4,6,8,3]). given clause #759: (wt=4) 18 [hyper,10,1,5,eval] board([4]). given clause #760: (wt=6) 808 [hyper,18,1,2,eval] board([1,4]). given clause #761: (wt=8) 812 [hyper,808,1,4,eval] board([3,1,4]). given clause #762: (wt=10) 815 [hyper,812,1,6,eval] board([5,3,1,4]). given clause #763: (wt=12) 817 [hyper,815,1,3,eval] board([2,5,3,1,4]). given clause #764: (wt=14) 818 [hyper,817,1,9,eval] board([8,2,5,3,1,4]). given clause #765: (wt=12) 816 [hyper,815,1,8,eval] board([7,5,3,1,4]). given clause #766: (wt=14) 819 [hyper,816,1,3,eval] board([2,7,5,3,1,4]). given clause #767: (wt=10) 814 [hyper,812,1,7,eval] board([6,3,1,4]). given clause #768: (wt=12) 820 [hyper,814,1,3,eval] board([2,6,3,1,4]). given clause #769: (wt=14) 821 [hyper,820,1,8,eval] board([7,2,6,3,1,4]). given clause #770: (wt=16) 822 [hyper,821,1,6,eval] board([5,7,2,6,3,1,4]). given clause #771: (wt=10) 813 [hyper,812,1,9,eval] board([8,3,1,4]). given clause #772: (wt=12) 824 [hyper,813,1,3,eval] board([2,8,3,1,4]). given clause #773: (wt=14) 825 [hyper,824,1,8,eval] board([7,2,8,3,1,4]). given clause #774: (wt=12) 823 [hyper,813,1,7,eval] board([6,8,3,1,4]). given clause #775: (wt=14) 826 [hyper,823,1,3,eval] board([2,6,8,3,1,4]). given clause #776: (wt=8) 811 [hyper,808,1,6,eval] board([5,1,4]). given clause #777: (wt=10) 828 [hyper,811,1,3,eval] board([2,5,1,4]). given clause #778: (wt=12) 829 [hyper,828,1,7,eval] board([6,2,5,1,4]). given clause #779: (wt=14) 830 [hyper,829,1,4,eval] board([3,6,2,5,1,4]). given clause #780: (wt=16) 831 [hyper,830,1,8,eval] board([7,3,6,2,5,1,4]). given clause #781: (wt=10) 827 [hyper,811,1,9,eval] board([8,5,1,4]). given clause #782: (wt=12) 833 [hyper,827,1,3,eval] board([2,8,5,1,4]). given clause #783: (wt=14) 834 [hyper,833,1,8,eval] board([7,2,8,5,1,4]). given clause #784: (wt=16) 835 [hyper,834,1,4,eval] board([3,7,2,8,5,1,4]). -------- PROOF -------- 837 [binary,836.1,11.1] $Ans([6,3,7,2,8,5,1,4]). ----> UNIT CONFLICT at 0.29 sec ----> 837 [binary,836.1,11.1] $Ans([6,3,7,2,8,5,1,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 808 [hyper,18,1,2,eval] board([1,4]). 811 [hyper,808,1,6,eval] board([5,1,4]). 827 [hyper,811,1,9,eval] board([8,5,1,4]). 833 [hyper,827,1,3,eval] board([2,8,5,1,4]). 834 [hyper,833,1,8,eval] board([7,2,8,5,1,4]). 835 [hyper,834,1,4,eval] board([3,7,2,8,5,1,4]). 836 [hyper,835,1,7,eval] board([6,3,7,2,8,5,1,4]). 837 [binary,836.1,11.1] $Ans([6,3,7,2,8,5,1,4]). ------------ end of proof ------------- given clause #785: (wt=18) 836 [hyper,835,1,7,eval] board([6,3,7,2,8,5,1,4]). given clause #786: (wt=12) 832 [hyper,827,1,7,eval] board([6,8,5,1,4]). given clause #787: (wt=14) 838 [hyper,832,1,4,eval] board([3,6,8,5,1,4]). given clause #788: (wt=16) 839 [hyper,838,1,8,eval] board([7,3,6,8,5,1,4]). -------- PROOF -------- 841 [binary,840.1,11.1] $Ans([2,7,3,6,8,5,1,4]). ----> UNIT CONFLICT at 0.29 sec ----> 841 [binary,840.1,11.1] $Ans([2,7,3,6,8,5,1,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 808 [hyper,18,1,2,eval] board([1,4]). 811 [hyper,808,1,6,eval] board([5,1,4]). 827 [hyper,811,1,9,eval] board([8,5,1,4]). 832 [hyper,827,1,7,eval] board([6,8,5,1,4]). 838 [hyper,832,1,4,eval] board([3,6,8,5,1,4]). 839 [hyper,838,1,8,eval] board([7,3,6,8,5,1,4]). 840 [hyper,839,1,3,eval] board([2,7,3,6,8,5,1,4]). 841 [binary,840.1,11.1] $Ans([2,7,3,6,8,5,1,4]). ------------ end of proof ------------- given clause #789: (wt=18) 840 [hyper,839,1,3,eval] board([2,7,3,6,8,5,1,4]). given clause #790: (wt=8) 810 [hyper,808,1,8,eval] board([7,1,4]). given clause #791: (wt=10) 843 [hyper,810,1,3,eval] board([2,7,1,4]). given clause #792: (wt=12) 844 [hyper,843,1,7,eval] board([6,2,7,1,4]). given clause #793: (wt=14) 846 [hyper,844,1,4,eval] board([3,6,2,7,1,4]). given clause #794: (wt=14) 845 [hyper,844,1,9,eval] board([8,6,2,7,1,4]). given clause #795: (wt=10) 842 [hyper,810,1,6,eval] board([5,7,1,4]). given clause #796: (wt=12) 848 [hyper,842,1,3,eval] board([2,5,7,1,4]). given clause #797: (wt=14) 850 [hyper,848,1,7,eval] board([6,2,5,7,1,4]). given clause #798: (wt=14) 849 [hyper,848,1,9,eval] board([8,2,5,7,1,4]). given clause #799: (wt=12) 847 [hyper,842,1,4,eval] board([3,5,7,1,4]). given clause #800: (wt=14) 852 [hyper,847,1,7,eval] board([6,3,5,7,1,4]). given clause #801: (wt=14) 851 [hyper,847,1,9,eval] board([8,3,5,7,1,4]). given clause #802: (wt=8) 809 [hyper,808,1,9,eval] board([8,1,4]). given clause #803: (wt=10) 855 [hyper,809,1,3,eval] board([2,8,1,4]). given clause #804: (wt=12) 857 [hyper,855,1,6,eval] board([5,2,8,1,4]). given clause #805: (wt=14) 859 [hyper,857,1,4,eval] board([3,5,2,8,1,4]). given clause #806: (wt=14) 858 [hyper,857,1,8,eval] board([7,5,2,8,1,4]). given clause #807: (wt=12) 856 [hyper,855,1,8,eval] board([7,2,8,1,4]). given clause #808: (wt=14) 860 [hyper,856,1,4,eval] board([3,7,2,8,1,4]). given clause #809: (wt=10) 854 [hyper,809,1,6,eval] board([5,8,1,4]). given clause #810: (wt=12) 863 [hyper,854,1,3,eval] board([2,5,8,1,4]). given clause #811: (wt=14) 864 [hyper,863,1,7,eval] board([6,2,5,8,1,4]). given clause #812: (wt=16) 865 [hyper,864,1,4,eval] board([3,6,2,5,8,1,4]). given clause #813: (wt=12) 862 [hyper,854,1,4,eval] board([3,5,8,1,4]). given clause #814: (wt=14) 866 [hyper,862,1,7,eval] board([6,3,5,8,1,4]). given clause #815: (wt=12) 861 [hyper,854,1,8,eval] board([7,5,8,1,4]). given clause #816: (wt=14) 867 [hyper,861,1,3,eval] board([2,7,5,8,1,4]). given clause #817: (wt=10) 853 [hyper,809,1,7,eval] board([6,8,1,4]). given clause #818: (wt=12) 869 [hyper,853,1,3,eval] board([2,6,8,1,4]). given clause #819: (wt=14) 870 [hyper,869,1,8,eval] board([7,2,6,8,1,4]). given clause #820: (wt=16) 871 [hyper,870,1,6,eval] board([5,7,2,6,8,1,4]). given clause #821: (wt=12) 868 [hyper,853,1,4,eval] board([3,6,8,1,4]). given clause #822: (wt=14) 872 [hyper,868,1,8,eval] board([7,3,6,8,1,4]). given clause #823: (wt=16) 873 [hyper,872,1,3,eval] board([2,7,3,6,8,1,4]). given clause #824: (wt=6) 807 [hyper,18,1,3,eval] board([2,4]). given clause #825: (wt=8) 876 [hyper,807,1,6,eval] board([5,2,4]). given clause #826: (wt=10) 878 [hyper,876,1,4,eval] board([3,5,2,4]). given clause #827: (wt=12) 880 [hyper,878,1,2,eval] board([1,3,5,2,4]). given clause #828: (wt=14) 881 [hyper,880,1,8,eval] board([7,1,3,5,2,4]). given clause #829: (wt=12) 879 [hyper,878,1,7,eval] board([6,3,5,2,4]). given clause #830: (wt=10) 877 [hyper,876,1,9,eval] board([8,5,2,4]). given clause #831: (wt=12) 883 [hyper,877,1,2,eval] board([1,8,5,2,4]). given clause #832: (wt=14) 885 [hyper,883,1,4,eval] board([3,1,8,5,2,4]). given clause #833: (wt=16) 886 [hyper,885,1,7,eval] board([6,3,1,8,5,2,4]). given clause #834: (wt=14) 884 [hyper,883,1,8,eval] board([7,1,8,5,2,4]). given clause #835: (wt=12) 882 [hyper,877,1,7,eval] board([6,8,5,2,4]). given clause #836: (wt=14) 888 [hyper,882,1,2,eval] board([1,6,8,5,2,4]). given clause #837: (wt=16) 889 [hyper,888,1,4,eval] board([3,1,6,8,5,2,4]). -------- PROOF -------- 891 [binary,890.1,11.1] $Ans([7,3,1,6,8,5,2,4]). ----> UNIT CONFLICT at 0.31 sec ----> 891 [binary,890.1,11.1] $Ans([7,3,1,6,8,5,2,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 807 [hyper,18,1,3,eval] board([2,4]). 876 [hyper,807,1,6,eval] board([5,2,4]). 877 [hyper,876,1,9,eval] board([8,5,2,4]). 882 [hyper,877,1,7,eval] board([6,8,5,2,4]). 888 [hyper,882,1,2,eval] board([1,6,8,5,2,4]). 889 [hyper,888,1,4,eval] board([3,1,6,8,5,2,4]). 890 [hyper,889,1,8,eval] board([7,3,1,6,8,5,2,4]). 891 [binary,890.1,11.1] $Ans([7,3,1,6,8,5,2,4]). ------------ end of proof ------------- given clause #838: (wt=18) 890 [hyper,889,1,8,eval] board([7,3,1,6,8,5,2,4]). given clause #839: (wt=14) 887 [hyper,882,1,4,eval] board([3,6,8,5,2,4]). given clause #840: (wt=8) 875 [hyper,807,1,8,eval] board([7,2,4]). given clause #841: (wt=10) 893 [hyper,875,1,4,eval] board([3,7,2,4]). given clause #842: (wt=12) 895 [hyper,893,1,2,eval] board([1,3,7,2,4]). given clause #843: (wt=14) 896 [hyper,895,1,9,eval] board([8,1,3,7,2,4]). given clause #844: (wt=16) 897 [hyper,896,1,6,eval] board([5,8,1,3,7,2,4]). given clause #845: (wt=12) 894 [hyper,893,1,7,eval] board([6,3,7,2,4]). given clause #846: (wt=14) 898 [hyper,894,1,9,eval] board([8,6,3,7,2,4]). given clause #847: (wt=16) 900 [hyper,898,1,2,eval] board([1,8,6,3,7,2,4]). -------- PROOF -------- 902 [binary,901.1,11.1] $Ans([5,1,8,6,3,7,2,4]). ----> UNIT CONFLICT at 0.32 sec ----> 902 [binary,901.1,11.1] $Ans([5,1,8,6,3,7,2,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 807 [hyper,18,1,3,eval] board([2,4]). 875 [hyper,807,1,8,eval] board([7,2,4]). 893 [hyper,875,1,4,eval] board([3,7,2,4]). 894 [hyper,893,1,7,eval] board([6,3,7,2,4]). 898 [hyper,894,1,9,eval] board([8,6,3,7,2,4]). 900 [hyper,898,1,2,eval] board([1,8,6,3,7,2,4]). 901 [hyper,900,1,6,eval] board([5,1,8,6,3,7,2,4]). 902 [binary,901.1,11.1] $Ans([5,1,8,6,3,7,2,4]). ------------ end of proof ------------- given clause #848: (wt=18) 901 [hyper,900,1,6,eval] board([5,1,8,6,3,7,2,4]). given clause #849: (wt=16) 899 [hyper,898,1,6,eval] board([5,8,6,3,7,2,4]). -------- PROOF -------- 904 [binary,903.1,11.1] $Ans([1,5,8,6,3,7,2,4]). ----> UNIT CONFLICT at 0.32 sec ----> 904 [binary,903.1,11.1] $Ans([1,5,8,6,3,7,2,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 807 [hyper,18,1,3,eval] board([2,4]). 875 [hyper,807,1,8,eval] board([7,2,4]). 893 [hyper,875,1,4,eval] board([3,7,2,4]). 894 [hyper,893,1,7,eval] board([6,3,7,2,4]). 898 [hyper,894,1,9,eval] board([8,6,3,7,2,4]). 899 [hyper,898,1,6,eval] board([5,8,6,3,7,2,4]). 903 [hyper,899,1,2,eval] board([1,5,8,6,3,7,2,4]). 904 [binary,903.1,11.1] $Ans([1,5,8,6,3,7,2,4]). ------------ end of proof ------------- given clause #850: (wt=18) 903 [hyper,899,1,2,eval] board([1,5,8,6,3,7,2,4]). given clause #851: (wt=10) 892 [hyper,875,1,6,eval] board([5,7,2,4]). given clause #852: (wt=12) 906 [hyper,892,1,2,eval] board([1,5,7,2,4]). given clause #853: (wt=14) 907 [hyper,906,1,9,eval] board([8,1,5,7,2,4]). given clause #854: (wt=16) 908 [hyper,907,1,7,eval] board([6,8,1,5,7,2,4]). -------- PROOF -------- 910 [binary,909.1,11.1] $Ans([3,6,8,1,5,7,2,4]). ----> UNIT CONFLICT at 0.32 sec ----> 910 [binary,909.1,11.1] $Ans([3,6,8,1,5,7,2,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 807 [hyper,18,1,3,eval] board([2,4]). 875 [hyper,807,1,8,eval] board([7,2,4]). 892 [hyper,875,1,6,eval] board([5,7,2,4]). 906 [hyper,892,1,2,eval] board([1,5,7,2,4]). 907 [hyper,906,1,9,eval] board([8,1,5,7,2,4]). 908 [hyper,907,1,7,eval] board([6,8,1,5,7,2,4]). 909 [hyper,908,1,4,eval] board([3,6,8,1,5,7,2,4]). 910 [binary,909.1,11.1] $Ans([3,6,8,1,5,7,2,4]). ------------ end of proof ------------- given clause #855: (wt=18) 909 [hyper,908,1,4,eval] board([3,6,8,1,5,7,2,4]). given clause #856: (wt=12) 905 [hyper,892,1,4,eval] board([3,5,7,2,4]). given clause #857: (wt=14) 912 [hyper,905,1,2,eval] board([1,3,5,7,2,4]). given clause #858: (wt=16) 913 [hyper,912,1,7,eval] board([6,1,3,5,7,2,4]). given clause #859: (wt=14) 911 [hyper,905,1,9,eval] board([8,3,5,7,2,4]). given clause #860: (wt=16) 914 [hyper,911,1,7,eval] board([6,8,3,5,7,2,4]). given clause #861: (wt=8) 874 [hyper,807,1,9,eval] board([8,2,4]). given clause #862: (wt=10) 917 [hyper,874,1,4,eval] board([3,8,2,4]). given clause #863: (wt=12) 919 [hyper,917,1,2,eval] board([1,3,8,2,4]). given clause #864: (wt=14) 920 [hyper,919,1,8,eval] board([7,1,3,8,2,4]). given clause #865: (wt=16) 921 [hyper,920,1,6,eval] board([5,7,1,3,8,2,4]). given clause #866: (wt=12) 918 [hyper,917,1,8,eval] board([7,3,8,2,4]). given clause #867: (wt=10) 916 [hyper,874,1,6,eval] board([5,8,2,4]). given clause #868: (wt=12) 924 [hyper,916,1,2,eval] board([1,5,8,2,4]). given clause #869: (wt=12) 923 [hyper,916,1,4,eval] board([3,5,8,2,4]). given clause #870: (wt=14) 925 [hyper,923,1,2,eval] board([1,3,5,8,2,4]). given clause #871: (wt=16) 926 [hyper,925,1,7,eval] board([6,1,3,5,8,2,4]). given clause #872: (wt=12) 922 [hyper,916,1,8,eval] board([7,5,8,2,4]). given clause #873: (wt=14) 927 [hyper,922,1,2,eval] board([1,7,5,8,2,4]). given clause #874: (wt=16) 929 [hyper,927,1,4,eval] board([3,1,7,5,8,2,4]). -------- PROOF -------- 931 [binary,930.1,11.1] $Ans([6,3,1,7,5,8,2,4]). ----> UNIT CONFLICT at 0.33 sec ----> 931 [binary,930.1,11.1] $Ans([6,3,1,7,5,8,2,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 807 [hyper,18,1,3,eval] board([2,4]). 874 [hyper,807,1,9,eval] board([8,2,4]). 916 [hyper,874,1,6,eval] board([5,8,2,4]). 922 [hyper,916,1,8,eval] board([7,5,8,2,4]). 927 [hyper,922,1,2,eval] board([1,7,5,8,2,4]). 929 [hyper,927,1,4,eval] board([3,1,7,5,8,2,4]). 930 [hyper,929,1,7,eval] board([6,3,1,7,5,8,2,4]). 931 [binary,930.1,11.1] $Ans([6,3,1,7,5,8,2,4]). ------------ end of proof ------------- given clause #875: (wt=18) 930 [hyper,929,1,7,eval] board([6,3,1,7,5,8,2,4]). given clause #876: (wt=16) 928 [hyper,927,1,7,eval] board([6,1,7,5,8,2,4]). given clause #877: (wt=10) 915 [hyper,874,1,7,eval] board([6,8,2,4]). given clause #878: (wt=12) 933 [hyper,915,1,2,eval] board([1,6,8,2,4]). given clause #879: (wt=14) 935 [hyper,933,1,4,eval] board([3,1,6,8,2,4]). given clause #880: (wt=16) 936 [hyper,935,1,6,eval] board([5,3,1,6,8,2,4]). -------- PROOF -------- 938 [binary,937.1,11.1] $Ans([7,5,3,1,6,8,2,4]). ----> UNIT CONFLICT at 0.33 sec ----> 938 [binary,937.1,11.1] $Ans([7,5,3,1,6,8,2,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 807 [hyper,18,1,3,eval] board([2,4]). 874 [hyper,807,1,9,eval] board([8,2,4]). 915 [hyper,874,1,7,eval] board([6,8,2,4]). 933 [hyper,915,1,2,eval] board([1,6,8,2,4]). 935 [hyper,933,1,4,eval] board([3,1,6,8,2,4]). 936 [hyper,935,1,6,eval] board([5,3,1,6,8,2,4]). 937 [hyper,936,1,8,eval] board([7,5,3,1,6,8,2,4]). 938 [binary,937.1,11.1] $Ans([7,5,3,1,6,8,2,4]). ------------ end of proof ------------- given clause #881: (wt=18) 937 [hyper,936,1,8,eval] board([7,5,3,1,6,8,2,4]). given clause #882: (wt=14) 934 [hyper,933,1,8,eval] board([7,1,6,8,2,4]). given clause #883: (wt=16) 939 [hyper,934,1,6,eval] board([5,7,1,6,8,2,4]). given clause #884: (wt=12) 932 [hyper,915,1,4,eval] board([3,6,8,2,4]). given clause #885: (wt=14) 941 [hyper,932,1,2,eval] board([1,3,6,8,2,4]). given clause #886: (wt=14) 940 [hyper,932,1,8,eval] board([7,3,6,8,2,4]). given clause #887: (wt=6) 806 [hyper,18,1,7,eval] board([6,4]). given clause #888: (wt=8) 944 [hyper,806,1,2,eval] board([1,6,4]). given clause #889: (wt=10) 946 [hyper,944,1,4,eval] board([3,1,6,4]). given clause #890: (wt=12) 948 [hyper,946,1,6,eval] board([5,3,1,6,4]). given clause #891: (wt=14) 950 [hyper,948,1,8,eval] board([7,5,3,1,6,4]). given clause #892: (wt=16) 951 [hyper,950,1,3,eval] board([2,7,5,3,1,6,4]). given clause #893: (wt=14) 949 [hyper,948,1,9,eval] board([8,5,3,1,6,4]). given clause #894: (wt=16) 952 [hyper,949,1,3,eval] board([2,8,5,3,1,6,4]). given clause #895: (wt=12) 947 [hyper,946,1,8,eval] board([7,3,1,6,4]). given clause #896: (wt=10) 945 [hyper,944,1,6,eval] board([5,1,6,4]). given clause #897: (wt=12) 954 [hyper,945,1,3,eval] board([2,5,1,6,4]). given clause #898: (wt=14) 955 [hyper,954,1,9,eval] board([8,2,5,1,6,4]). given clause #899: (wt=16) 956 [hyper,955,1,4,eval] board([3,8,2,5,1,6,4]). -------- PROOF -------- 958 [binary,957.1,11.1] $Ans([7,3,8,2,5,1,6,4]). ----> UNIT CONFLICT at 0.34 sec ----> 958 [binary,957.1,11.1] $Ans([7,3,8,2,5,1,6,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 806 [hyper,18,1,7,eval] board([6,4]). 944 [hyper,806,1,2,eval] board([1,6,4]). 945 [hyper,944,1,6,eval] board([5,1,6,4]). 954 [hyper,945,1,3,eval] board([2,5,1,6,4]). 955 [hyper,954,1,9,eval] board([8,2,5,1,6,4]). 956 [hyper,955,1,4,eval] board([3,8,2,5,1,6,4]). 957 [hyper,956,1,8,eval] board([7,3,8,2,5,1,6,4]). 958 [binary,957.1,11.1] $Ans([7,3,8,2,5,1,6,4]). ------------ end of proof ------------- given clause #900: (wt=18) 957 [hyper,956,1,8,eval] board([7,3,8,2,5,1,6,4]). given clause #901: (wt=12) 953 [hyper,945,1,8,eval] board([7,5,1,6,4]). given clause #902: (wt=8) 943 [hyper,806,1,4,eval] board([3,6,4]). given clause #903: (wt=10) 959 [hyper,943,1,6,eval] board([5,3,6,4]). given clause #904: (wt=12) 961 [hyper,959,1,3,eval] board([2,5,3,6,4]). given clause #905: (wt=14) 962 [hyper,961,1,9,eval] board([8,2,5,3,6,4]). given clause #906: (wt=12) 960 [hyper,959,1,8,eval] board([7,5,3,6,4]). given clause #907: (wt=14) 963 [hyper,960,1,2,eval] board([1,7,5,3,6,4]). given clause #908: (wt=8) 942 [hyper,806,1,9,eval] board([8,6,4]). given clause #909: (wt=10) 966 [hyper,942,1,3,eval] board([2,8,6,4]). given clause #910: (wt=12) 968 [hyper,966,1,6,eval] board([5,2,8,6,4]). given clause #911: (wt=14) 971 [hyper,968,1,2,eval] board([1,5,2,8,6,4]). given clause #912: (wt=14) 970 [hyper,968,1,4,eval] board([3,5,2,8,6,4]). given clause #913: (wt=14) 969 [hyper,968,1,8,eval] board([7,5,2,8,6,4]). given clause #914: (wt=12) 967 [hyper,966,1,8,eval] board([7,2,8,6,4]). given clause #915: (wt=14) 973 [hyper,967,1,2,eval] board([1,7,2,8,6,4]). given clause #916: (wt=16) 974 [hyper,973,1,4,eval] board([3,1,7,2,8,6,4]). -------- PROOF -------- 976 [binary,975.1,11.1] $Ans([5,3,1,7,2,8,6,4]). ----> UNIT CONFLICT at 0.35 sec ----> 976 [binary,975.1,11.1] $Ans([5,3,1,7,2,8,6,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 806 [hyper,18,1,7,eval] board([6,4]). 942 [hyper,806,1,9,eval] board([8,6,4]). 966 [hyper,942,1,3,eval] board([2,8,6,4]). 967 [hyper,966,1,8,eval] board([7,2,8,6,4]). 973 [hyper,967,1,2,eval] board([1,7,2,8,6,4]). 974 [hyper,973,1,4,eval] board([3,1,7,2,8,6,4]). 975 [hyper,974,1,6,eval] board([5,3,1,7,2,8,6,4]). 976 [binary,975.1,11.1] $Ans([5,3,1,7,2,8,6,4]). ------------ end of proof ------------- given clause #917: (wt=18) 975 [hyper,974,1,6,eval] board([5,3,1,7,2,8,6,4]). given clause #918: (wt=14) 972 [hyper,967,1,4,eval] board([3,7,2,8,6,4]). given clause #919: (wt=10) 965 [hyper,942,1,4,eval] board([3,8,6,4]). given clause #920: (wt=12) 979 [hyper,965,1,2,eval] board([1,3,8,6,4]). given clause #921: (wt=14) 980 [hyper,979,1,8,eval] board([7,1,3,8,6,4]). given clause #922: (wt=16) 982 [hyper,980,1,3,eval] board([2,7,1,3,8,6,4]). given clause #923: (wt=16) 981 [hyper,980,1,6,eval] board([5,7,1,3,8,6,4]). -------- PROOF -------- 984 [binary,983.1,11.1] $Ans([2,5,7,1,3,8,6,4]). ----> UNIT CONFLICT at 0.35 sec ----> 984 [binary,983.1,11.1] $Ans([2,5,7,1,3,8,6,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 806 [hyper,18,1,7,eval] board([6,4]). 942 [hyper,806,1,9,eval] board([8,6,4]). 965 [hyper,942,1,4,eval] board([3,8,6,4]). 979 [hyper,965,1,2,eval] board([1,3,8,6,4]). 980 [hyper,979,1,8,eval] board([7,1,3,8,6,4]). 981 [hyper,980,1,6,eval] board([5,7,1,3,8,6,4]). 983 [hyper,981,1,3,eval] board([2,5,7,1,3,8,6,4]). 984 [binary,983.1,11.1] $Ans([2,5,7,1,3,8,6,4]). ------------ end of proof ------------- given clause #924: (wt=18) 983 [hyper,981,1,3,eval] board([2,5,7,1,3,8,6,4]). given clause #925: (wt=12) 978 [hyper,965,1,6,eval] board([5,3,8,6,4]). given clause #926: (wt=14) 985 [hyper,978,1,8,eval] board([7,5,3,8,6,4]). given clause #927: (wt=16) 986 [hyper,985,1,3,eval] board([2,7,5,3,8,6,4]). given clause #928: (wt=12) 977 [hyper,965,1,8,eval] board([7,3,8,6,4]). given clause #929: (wt=10) 964 [hyper,942,1,6,eval] board([5,8,6,4]). given clause #930: (wt=12) 989 [hyper,964,1,2,eval] board([1,5,8,6,4]). given clause #931: (wt=12) 988 [hyper,964,1,3,eval] board([2,5,8,6,4]). given clause #932: (wt=12) 987 [hyper,964,1,8,eval] board([7,5,8,6,4]). given clause #933: (wt=14) 990 [hyper,987,1,2,eval] board([1,7,5,8,6,4]). given clause #934: (wt=16) 991 [hyper,990,1,4,eval] board([3,1,7,5,8,6,4]). given clause #935: (wt=6) 805 [hyper,18,1,8,eval] board([7,4]). given clause #936: (wt=8) 994 [hyper,805,1,2,eval] board([1,7,4]). given clause #937: (wt=10) 997 [hyper,994,1,4,eval] board([3,1,7,4]). given clause #938: (wt=12) 999 [hyper,997,1,6,eval] board([5,3,1,7,4]). given clause #939: (wt=14) 1001 [hyper,999,1,3,eval] board([2,5,3,1,7,4]). given clause #940: (wt=16) 1002 [hyper,1001,1,9,eval] board([8,2,5,3,1,7,4]). given clause #941: (wt=14) 1000 [hyper,999,1,9,eval] board([8,5,3,1,7,4]). given clause #942: (wt=12) 998 [hyper,997,1,7,eval] board([6,3,1,7,4]). given clause #943: (wt=14) 1004 [hyper,998,1,3,eval] board([2,6,3,1,7,4]). given clause #944: (wt=14) 1003 [hyper,998,1,9,eval] board([8,6,3,1,7,4]). given clause #945: (wt=10) 996 [hyper,994,1,7,eval] board([6,1,7,4]). given clause #946: (wt=12) 1005 [hyper,996,1,3,eval] board([2,6,1,7,4]). given clause #947: (wt=14) 1006 [hyper,1005,1,6,eval] board([5,2,6,1,7,4]). given clause #948: (wt=16) 1007 [hyper,1006,1,9,eval] board([8,5,2,6,1,7,4]). given clause #949: (wt=10) 995 [hyper,994,1,9,eval] board([8,1,7,4]). given clause #950: (wt=12) 1010 [hyper,995,1,3,eval] board([2,8,1,7,4]). given clause #951: (wt=14) 1011 [hyper,1010,1,6,eval] board([5,2,8,1,7,4]). given clause #952: (wt=16) 1012 [hyper,1011,1,4,eval] board([3,5,2,8,1,7,4]). given clause #953: (wt=12) 1009 [hyper,995,1,6,eval] board([5,8,1,7,4]). given clause #954: (wt=14) 1013 [hyper,1009,1,3,eval] board([2,5,8,1,7,4]). given clause #955: (wt=16) 1014 [hyper,1013,1,7,eval] board([6,2,5,8,1,7,4]). -------- PROOF -------- 1016 [binary,1015.1,11.1] $Ans([3,6,2,5,8,1,7,4]). ----> UNIT CONFLICT at 0.36 sec ----> 1016 [binary,1015.1,11.1] $Ans([3,6,2,5,8,1,7,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 805 [hyper,18,1,8,eval] board([7,4]). 994 [hyper,805,1,2,eval] board([1,7,4]). 995 [hyper,994,1,9,eval] board([8,1,7,4]). 1009 [hyper,995,1,6,eval] board([5,8,1,7,4]). 1013 [hyper,1009,1,3,eval] board([2,5,8,1,7,4]). 1014 [hyper,1013,1,7,eval] board([6,2,5,8,1,7,4]). 1015 [hyper,1014,1,4,eval] board([3,6,2,5,8,1,7,4]). 1016 [binary,1015.1,11.1] $Ans([3,6,2,5,8,1,7,4]). ------------ end of proof ------------- given clause #956: (wt=18) 1015 [hyper,1014,1,4,eval] board([3,6,2,5,8,1,7,4]). given clause #957: (wt=12) 1008 [hyper,995,1,7,eval] board([6,8,1,7,4]). given clause #958: (wt=14) 1017 [hyper,1008,1,3,eval] board([2,6,8,1,7,4]). given clause #959: (wt=8) 993 [hyper,805,1,4,eval] board([3,7,4]). given clause #960: (wt=10) 1019 [hyper,993,1,7,eval] board([6,3,7,4]). given clause #961: (wt=12) 1020 [hyper,1019,1,3,eval] board([2,6,3,7,4]). given clause #962: (wt=14) 1021 [hyper,1020,1,6,eval] board([5,2,6,3,7,4]). given clause #963: (wt=16) 1023 [hyper,1021,1,2,eval] board([1,5,2,6,3,7,4]). given clause #964: (wt=16) 1022 [hyper,1021,1,9,eval] board([8,5,2,6,3,7,4]). given clause #965: (wt=10) 1018 [hyper,993,1,9,eval] board([8,3,7,4]). given clause #966: (wt=12) 1025 [hyper,1018,1,3,eval] board([2,8,3,7,4]). given clause #967: (wt=14) 1026 [hyper,1025,1,6,eval] board([5,2,8,3,7,4]). given clause #968: (wt=16) 1027 [hyper,1026,1,2,eval] board([1,5,2,8,3,7,4]). -------- PROOF -------- 1029 [binary,1028.1,11.1] $Ans([6,1,5,2,8,3,7,4]). ----> UNIT CONFLICT at 0.37 sec ----> 1029 [binary,1028.1,11.1] $Ans([6,1,5,2,8,3,7,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 805 [hyper,18,1,8,eval] board([7,4]). 993 [hyper,805,1,4,eval] board([3,7,4]). 1018 [hyper,993,1,9,eval] board([8,3,7,4]). 1025 [hyper,1018,1,3,eval] board([2,8,3,7,4]). 1026 [hyper,1025,1,6,eval] board([5,2,8,3,7,4]). 1027 [hyper,1026,1,2,eval] board([1,5,2,8,3,7,4]). 1028 [hyper,1027,1,7,eval] board([6,1,5,2,8,3,7,4]). 1029 [binary,1028.1,11.1] $Ans([6,1,5,2,8,3,7,4]). ------------ end of proof ------------- given clause #969: (wt=18) 1028 [hyper,1027,1,7,eval] board([6,1,5,2,8,3,7,4]). given clause #970: (wt=12) 1024 [hyper,1018,1,7,eval] board([6,8,3,7,4]). given clause #971: (wt=14) 1031 [hyper,1024,1,2,eval] board([1,6,8,3,7,4]). given clause #972: (wt=14) 1030 [hyper,1024,1,3,eval] board([2,6,8,3,7,4]). given clause #973: (wt=8) 992 [hyper,805,1,6,eval] board([5,7,4]). given clause #974: (wt=10) 1034 [hyper,992,1,3,eval] board([2,5,7,4]). given clause #975: (wt=12) 1035 [hyper,1034,1,7,eval] board([6,2,5,7,4]). given clause #976: (wt=14) 1036 [hyper,1035,1,2,eval] board([1,6,2,5,7,4]). given clause #977: (wt=16) 1037 [hyper,1036,1,4,eval] board([3,1,6,2,5,7,4]). -------- PROOF -------- 1039 [binary,1038.1,11.1] $Ans([8,3,1,6,2,5,7,4]). ----> UNIT CONFLICT at 0.37 sec ----> 1039 [binary,1038.1,11.1] $Ans([8,3,1,6,2,5,7,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 805 [hyper,18,1,8,eval] board([7,4]). 992 [hyper,805,1,6,eval] board([5,7,4]). 1034 [hyper,992,1,3,eval] board([2,5,7,4]). 1035 [hyper,1034,1,7,eval] board([6,2,5,7,4]). 1036 [hyper,1035,1,2,eval] board([1,6,2,5,7,4]). 1037 [hyper,1036,1,4,eval] board([3,1,6,2,5,7,4]). 1038 [hyper,1037,1,9,eval] board([8,3,1,6,2,5,7,4]). 1039 [binary,1038.1,11.1] $Ans([8,3,1,6,2,5,7,4]). ------------ end of proof ------------- given clause #978: (wt=18) 1038 [hyper,1037,1,9,eval] board([8,3,1,6,2,5,7,4]). given clause #979: (wt=10) 1033 [hyper,992,1,4,eval] board([3,5,7,4]). given clause #980: (wt=12) 1041 [hyper,1033,1,2,eval] board([1,3,5,7,4]). given clause #981: (wt=14) 1042 [hyper,1041,1,7,eval] board([6,1,3,5,7,4]). given clause #982: (wt=16) 1043 [hyper,1042,1,9,eval] board([8,6,1,3,5,7,4]). -------- PROOF -------- 1045 [binary,1044.1,11.1] $Ans([2,8,6,1,3,5,7,4]). ----> UNIT CONFLICT at 0.38 sec ----> 1045 [binary,1044.1,11.1] $Ans([2,8,6,1,3,5,7,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 805 [hyper,18,1,8,eval] board([7,4]). 992 [hyper,805,1,6,eval] board([5,7,4]). 1033 [hyper,992,1,4,eval] board([3,5,7,4]). 1041 [hyper,1033,1,2,eval] board([1,3,5,7,4]). 1042 [hyper,1041,1,7,eval] board([6,1,3,5,7,4]). 1043 [hyper,1042,1,9,eval] board([8,6,1,3,5,7,4]). 1044 [hyper,1043,1,3,eval] board([2,8,6,1,3,5,7,4]). 1045 [binary,1044.1,11.1] $Ans([2,8,6,1,3,5,7,4]). ------------ end of proof ------------- given clause #983: (wt=18) 1044 [hyper,1043,1,3,eval] board([2,8,6,1,3,5,7,4]). given clause #984: (wt=12) 1040 [hyper,1033,1,7,eval] board([6,3,5,7,4]). given clause #985: (wt=10) 1032 [hyper,992,1,9,eval] board([8,5,7,4]). given clause #986: (wt=12) 1048 [hyper,1032,1,2,eval] board([1,8,5,7,4]). given clause #987: (wt=12) 1047 [hyper,1032,1,3,eval] board([2,8,5,7,4]). given clause #988: (wt=12) 1046 [hyper,1032,1,7,eval] board([6,8,5,7,4]). given clause #989: (wt=14) 1049 [hyper,1046,1,2,eval] board([1,6,8,5,7,4]). given clause #990: (wt=16) 1050 [hyper,1049,1,4,eval] board([3,1,6,8,5,7,4]). given clause #991: (wt=6) 804 [hyper,18,1,9,eval] board([8,4]). given clause #992: (wt=8) 1053 [hyper,804,1,2,eval] board([1,8,4]). given clause #993: (wt=10) 1055 [hyper,1053,1,4,eval] board([3,1,8,4]). given clause #994: (wt=12) 1057 [hyper,1055,1,7,eval] board([6,3,1,8,4]). given clause #995: (wt=14) 1058 [hyper,1057,1,3,eval] board([2,6,3,1,8,4]). given clause #996: (wt=16) 1059 [hyper,1058,1,8,eval] board([7,2,6,3,1,8,4]). -------- PROOF -------- 1061 [binary,1060.1,11.1] $Ans([5,7,2,6,3,1,8,4]). ----> UNIT CONFLICT at 0.38 sec ----> 1061 [binary,1060.1,11.1] $Ans([5,7,2,6,3,1,8,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 804 [hyper,18,1,9,eval] board([8,4]). 1053 [hyper,804,1,2,eval] board([1,8,4]). 1055 [hyper,1053,1,4,eval] board([3,1,8,4]). 1057 [hyper,1055,1,7,eval] board([6,3,1,8,4]). 1058 [hyper,1057,1,3,eval] board([2,6,3,1,8,4]). 1059 [hyper,1058,1,8,eval] board([7,2,6,3,1,8,4]). 1060 [hyper,1059,1,6,eval] board([5,7,2,6,3,1,8,4]). 1061 [binary,1060.1,11.1] $Ans([5,7,2,6,3,1,8,4]). ------------ end of proof ------------- given clause #997: (wt=18) 1060 [hyper,1059,1,6,eval] board([5,7,2,6,3,1,8,4]). given clause #998: (wt=12) 1056 [hyper,1055,1,8,eval] board([7,3,1,8,4]). given clause #999: (wt=14) 1062 [hyper,1056,1,3,eval] board([2,7,3,1,8,4]). given clause #1000: (wt=10) 1054 [hyper,1053,1,6,eval] board([5,1,8,4]). given clause #1001: (wt=12) 1064 [hyper,1054,1,3,eval] board([2,5,1,8,4]). given clause #1002: (wt=14) 1065 [hyper,1064,1,7,eval] board([6,2,5,1,8,4]). given clause #1003: (wt=12) 1063 [hyper,1054,1,8,eval] board([7,5,1,8,4]). given clause #1004: (wt=14) 1066 [hyper,1063,1,3,eval] board([2,7,5,1,8,4]). given clause #1005: (wt=16) 1067 [hyper,1066,1,7,eval] board([6,2,7,5,1,8,4]). -------- PROOF -------- 1069 [binary,1068.1,11.1] $Ans([3,6,2,7,5,1,8,4]). ----> UNIT CONFLICT at 0.38 sec ----> 1069 [binary,1068.1,11.1] $Ans([3,6,2,7,5,1,8,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 804 [hyper,18,1,9,eval] board([8,4]). 1053 [hyper,804,1,2,eval] board([1,8,4]). 1054 [hyper,1053,1,6,eval] board([5,1,8,4]). 1063 [hyper,1054,1,8,eval] board([7,5,1,8,4]). 1066 [hyper,1063,1,3,eval] board([2,7,5,1,8,4]). 1067 [hyper,1066,1,7,eval] board([6,2,7,5,1,8,4]). 1068 [hyper,1067,1,4,eval] board([3,6,2,7,5,1,8,4]). 1069 [binary,1068.1,11.1] $Ans([3,6,2,7,5,1,8,4]). ------------ end of proof ------------- given clause #1006: (wt=18) 1068 [hyper,1067,1,4,eval] board([3,6,2,7,5,1,8,4]). given clause #1007: (wt=8) 1052 [hyper,804,1,4,eval] board([3,8,4]). given clause #1008: (wt=10) 1070 [hyper,1052,1,6,eval] board([5,3,8,4]). given clause #1009: (wt=12) 1072 [hyper,1070,1,3,eval] board([2,5,3,8,4]). given clause #1010: (wt=12) 1071 [hyper,1070,1,8,eval] board([7,5,3,8,4]). given clause #1011: (wt=14) 1074 [hyper,1071,1,2,eval] board([1,7,5,3,8,4]). given clause #1012: (wt=16) 1075 [hyper,1074,1,7,eval] board([6,1,7,5,3,8,4]). given clause #1013: (wt=14) 1073 [hyper,1071,1,3,eval] board([2,7,5,3,8,4]). given clause #1014: (wt=16) 1076 [hyper,1073,1,7,eval] board([6,2,7,5,3,8,4]). given clause #1015: (wt=8) 1051 [hyper,804,1,6,eval] board([5,8,4]). given clause #1016: (wt=10) 1078 [hyper,1051,1,3,eval] board([2,5,8,4]). given clause #1017: (wt=12) 1079 [hyper,1078,1,7,eval] board([6,2,5,8,4]). given clause #1018: (wt=14) 1081 [hyper,1079,1,2,eval] board([1,6,2,5,8,4]). given clause #1019: (wt=16) 1082 [hyper,1081,1,8,eval] board([7,1,6,2,5,8,4]). given clause #1020: (wt=14) 1080 [hyper,1079,1,4,eval] board([3,6,2,5,8,4]). given clause #1021: (wt=16) 1083 [hyper,1080,1,8,eval] board([7,3,6,2,5,8,4]). given clause #1022: (wt=10) 1077 [hyper,1051,1,4,eval] board([3,5,8,4]). given clause #1023: (wt=12) 1085 [hyper,1077,1,2,eval] board([1,3,5,8,4]). given clause #1024: (wt=14) 1087 [hyper,1085,1,7,eval] board([6,1,3,5,8,4]). given clause #1025: (wt=16) 1088 [hyper,1087,1,3,eval] board([2,6,1,3,5,8,4]). given clause #1026: (wt=14) 1086 [hyper,1085,1,8,eval] board([7,1,3,5,8,4]). given clause #1027: (wt=16) 1089 [hyper,1086,1,3,eval] board([2,7,1,3,5,8,4]). -------- PROOF -------- 1091 [binary,1090.1,11.1] $Ans([6,2,7,1,3,5,8,4]). ----> UNIT CONFLICT at 0.39 sec ----> 1091 [binary,1090.1,11.1] $Ans([6,2,7,1,3,5,8,4]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 18 [hyper,10,1,5,eval] board([4]). 804 [hyper,18,1,9,eval] board([8,4]). 1051 [hyper,804,1,6,eval] board([5,8,4]). 1077 [hyper,1051,1,4,eval] board([3,5,8,4]). 1085 [hyper,1077,1,2,eval] board([1,3,5,8,4]). 1086 [hyper,1085,1,8,eval] board([7,1,3,5,8,4]). 1089 [hyper,1086,1,3,eval] board([2,7,1,3,5,8,4]). 1090 [hyper,1089,1,7,eval] board([6,2,7,1,3,5,8,4]). 1091 [binary,1090.1,11.1] $Ans([6,2,7,1,3,5,8,4]). ------------ end of proof ------------- given clause #1028: (wt=18) 1090 [hyper,1089,1,7,eval] board([6,2,7,1,3,5,8,4]). given clause #1029: (wt=12) 1084 [hyper,1077,1,7,eval] board([6,3,5,8,4]). given clause #1030: (wt=4) 17 [hyper,10,1,6,eval] board([5]). given clause #1031: (wt=6) 1096 [hyper,17,1,2,eval] board([1,5]). given clause #1032: (wt=8) 1099 [hyper,1096,1,5,eval] board([4,1,5]). given clause #1033: (wt=10) 1101 [hyper,1099,1,7,eval] board([6,4,1,5]). given clause #1034: (wt=12) 1103 [hyper,1101,1,4,eval] board([3,6,4,1,5]). given clause #1035: (wt=12) 1102 [hyper,1101,1,9,eval] board([8,6,4,1,5]). given clause #1036: (wt=14) 1105 [hyper,1102,1,3,eval] board([2,8,6,4,1,5]). given clause #1037: (wt=16) 1106 [hyper,1105,1,8,eval] board([7,2,8,6,4,1,5]). -------- PROOF -------- 1108 [binary,1107.1,11.1] $Ans([3,7,2,8,6,4,1,5]). ----> UNIT CONFLICT at 0.40 sec ----> 1108 [binary,1107.1,11.1] $Ans([3,7,2,8,6,4,1,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1096 [hyper,17,1,2,eval] board([1,5]). 1099 [hyper,1096,1,5,eval] board([4,1,5]). 1101 [hyper,1099,1,7,eval] board([6,4,1,5]). 1102 [hyper,1101,1,9,eval] board([8,6,4,1,5]). 1105 [hyper,1102,1,3,eval] board([2,8,6,4,1,5]). 1106 [hyper,1105,1,8,eval] board([7,2,8,6,4,1,5]). 1107 [hyper,1106,1,4,eval] board([3,7,2,8,6,4,1,5]). 1108 [binary,1107.1,11.1] $Ans([3,7,2,8,6,4,1,5]). ------------ end of proof ------------- given clause #1038: (wt=18) 1107 [hyper,1106,1,4,eval] board([3,7,2,8,6,4,1,5]). given clause #1039: (wt=14) 1104 [hyper,1102,1,4,eval] board([3,8,6,4,1,5]). given clause #1040: (wt=16) 1109 [hyper,1104,1,8,eval] board([7,3,8,6,4,1,5]). given clause #1041: (wt=10) 1100 [hyper,1099,1,8,eval] board([7,4,1,5]). given clause #1042: (wt=12) 1110 [hyper,1100,1,4,eval] board([3,7,4,1,5]). given clause #1043: (wt=14) 1112 [hyper,1110,1,7,eval] board([6,3,7,4,1,5]). given clause #1044: (wt=16) 1113 [hyper,1112,1,3,eval] board([2,6,3,7,4,1,5]). given clause #1045: (wt=14) 1111 [hyper,1110,1,9,eval] board([8,3,7,4,1,5]). given clause #1046: (wt=16) 1114 [hyper,1111,1,3,eval] board([2,8,3,7,4,1,5]). given clause #1047: (wt=8) 1098 [hyper,1096,1,7,eval] board([6,1,5]). given clause #1048: (wt=10) 1115 [hyper,1098,1,5,eval] board([4,6,1,5]). given clause #1049: (wt=12) 1117 [hyper,1115,1,3,eval] board([2,4,6,1,5]). given clause #1050: (wt=14) 1119 [hyper,1117,1,8,eval] board([7,2,4,6,1,5]). given clause #1051: (wt=16) 1120 [hyper,1119,1,4,eval] board([3,7,2,4,6,1,5]). given clause #1052: (wt=14) 1118 [hyper,1117,1,9,eval] board([8,2,4,6,1,5]). given clause #1053: (wt=16) 1121 [hyper,1118,1,4,eval] board([3,8,2,4,6,1,5]). given clause #1054: (wt=12) 1116 [hyper,1115,1,8,eval] board([7,4,6,1,5]). given clause #1055: (wt=8) 1097 [hyper,1096,1,9,eval] board([8,1,5]). given clause #1056: (wt=10) 1123 [hyper,1097,1,5,eval] board([4,8,1,5]). given clause #1057: (wt=12) 1125 [hyper,1123,1,3,eval] board([2,4,8,1,5]). given clause #1058: (wt=14) 1126 [hyper,1125,1,8,eval] board([7,2,4,8,1,5]). given clause #1059: (wt=16) 1127 [hyper,1126,1,4,eval] board([3,7,2,4,8,1,5]). -------- PROOF -------- 1129 [binary,1128.1,11.1] $Ans([6,3,7,2,4,8,1,5]). ----> UNIT CONFLICT at 0.40 sec ----> 1129 [binary,1128.1,11.1] $Ans([6,3,7,2,4,8,1,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1096 [hyper,17,1,2,eval] board([1,5]). 1097 [hyper,1096,1,9,eval] board([8,1,5]). 1123 [hyper,1097,1,5,eval] board([4,8,1,5]). 1125 [hyper,1123,1,3,eval] board([2,4,8,1,5]). 1126 [hyper,1125,1,8,eval] board([7,2,4,8,1,5]). 1127 [hyper,1126,1,4,eval] board([3,7,2,4,8,1,5]). 1128 [hyper,1127,1,7,eval] board([6,3,7,2,4,8,1,5]). 1129 [binary,1128.1,11.1] $Ans([6,3,7,2,4,8,1,5]). ------------ end of proof ------------- given clause #1060: (wt=18) 1128 [hyper,1127,1,7,eval] board([6,3,7,2,4,8,1,5]). given clause #1061: (wt=12) 1124 [hyper,1123,1,8,eval] board([7,4,8,1,5]). given clause #1062: (wt=14) 1130 [hyper,1124,1,4,eval] board([3,7,4,8,1,5]). given clause #1063: (wt=10) 1122 [hyper,1097,1,7,eval] board([6,8,1,5]). given clause #1064: (wt=12) 1132 [hyper,1122,1,3,eval] board([2,6,8,1,5]). given clause #1065: (wt=14) 1133 [hyper,1132,1,8,eval] board([7,2,6,8,1,5]). given clause #1066: (wt=12) 1131 [hyper,1122,1,4,eval] board([3,6,8,1,5]). given clause #1067: (wt=14) 1134 [hyper,1131,1,8,eval] board([7,3,6,8,1,5]). given clause #1068: (wt=16) 1135 [hyper,1134,1,3,eval] board([2,7,3,6,8,1,5]). -------- PROOF -------- 1137 [binary,1136.1,11.1] $Ans([4,2,7,3,6,8,1,5]). ----> UNIT CONFLICT at 0.41 sec ----> 1137 [binary,1136.1,11.1] $Ans([4,2,7,3,6,8,1,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1096 [hyper,17,1,2,eval] board([1,5]). 1097 [hyper,1096,1,9,eval] board([8,1,5]). 1122 [hyper,1097,1,7,eval] board([6,8,1,5]). 1131 [hyper,1122,1,4,eval] board([3,6,8,1,5]). 1134 [hyper,1131,1,8,eval] board([7,3,6,8,1,5]). 1135 [hyper,1134,1,3,eval] board([2,7,3,6,8,1,5]). 1136 [hyper,1135,1,5,eval] board([4,2,7,3,6,8,1,5]). 1137 [binary,1136.1,11.1] $Ans([4,2,7,3,6,8,1,5]). ------------ end of proof ------------- given clause #1069: (wt=18) 1136 [hyper,1135,1,5,eval] board([4,2,7,3,6,8,1,5]). given clause #1070: (wt=6) 1095 [hyper,17,1,3,eval] board([2,5]). given clause #1071: (wt=8) 1140 [hyper,1095,1,5,eval] board([4,2,5]). given clause #1072: (wt=10) 1143 [hyper,1140,1,2,eval] board([1,4,2,5]). given clause #1073: (wt=12) 1146 [hyper,1143,1,4,eval] board([3,1,4,2,5]). given clause #1074: (wt=14) 1147 [hyper,1146,1,9,eval] board([8,3,1,4,2,5]). given clause #1075: (wt=16) 1148 [hyper,1147,1,7,eval] board([6,8,3,1,4,2,5]). given clause #1076: (wt=12) 1145 [hyper,1143,1,8,eval] board([7,1,4,2,5]). given clause #1077: (wt=12) 1144 [hyper,1143,1,9,eval] board([8,1,4,2,5]). given clause #1078: (wt=10) 1142 [hyper,1140,1,7,eval] board([6,4,2,5]). given clause #1079: (wt=12) 1150 [hyper,1142,1,4,eval] board([3,6,4,2,5]). given clause #1080: (wt=12) 1149 [hyper,1142,1,9,eval] board([8,6,4,2,5]). given clause #1081: (wt=14) 1151 [hyper,1149,1,4,eval] board([3,8,6,4,2,5]). given clause #1082: (wt=16) 1152 [hyper,1151,1,2,eval] board([1,3,8,6,4,2,5]). -------- PROOF -------- 1154 [binary,1153.1,11.1] $Ans([7,1,3,8,6,4,2,5]). ----> UNIT CONFLICT at 0.41 sec ----> 1154 [binary,1153.1,11.1] $Ans([7,1,3,8,6,4,2,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1095 [hyper,17,1,3,eval] board([2,5]). 1140 [hyper,1095,1,5,eval] board([4,2,5]). 1142 [hyper,1140,1,7,eval] board([6,4,2,5]). 1149 [hyper,1142,1,9,eval] board([8,6,4,2,5]). 1151 [hyper,1149,1,4,eval] board([3,8,6,4,2,5]). 1152 [hyper,1151,1,2,eval] board([1,3,8,6,4,2,5]). 1153 [hyper,1152,1,8,eval] board([7,1,3,8,6,4,2,5]). 1154 [binary,1153.1,11.1] $Ans([7,1,3,8,6,4,2,5]). ------------ end of proof ------------- given clause #1083: (wt=18) 1153 [hyper,1152,1,8,eval] board([7,1,3,8,6,4,2,5]). given clause #1084: (wt=10) 1141 [hyper,1140,1,8,eval] board([7,4,2,5]). given clause #1085: (wt=12) 1155 [hyper,1141,1,4,eval] board([3,7,4,2,5]). given clause #1086: (wt=14) 1156 [hyper,1155,1,9,eval] board([8,3,7,4,2,5]). given clause #1087: (wt=16) 1157 [hyper,1156,1,7,eval] board([6,8,3,7,4,2,5]). -------- PROOF -------- 1159 [binary,1158.1,11.1] $Ans([1,6,8,3,7,4,2,5]). ----> UNIT CONFLICT at 0.41 sec ----> 1159 [binary,1158.1,11.1] $Ans([1,6,8,3,7,4,2,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1095 [hyper,17,1,3,eval] board([2,5]). 1140 [hyper,1095,1,5,eval] board([4,2,5]). 1141 [hyper,1140,1,8,eval] board([7,4,2,5]). 1155 [hyper,1141,1,4,eval] board([3,7,4,2,5]). 1156 [hyper,1155,1,9,eval] board([8,3,7,4,2,5]). 1157 [hyper,1156,1,7,eval] board([6,8,3,7,4,2,5]). 1158 [hyper,1157,1,2,eval] board([1,6,8,3,7,4,2,5]). 1159 [binary,1158.1,11.1] $Ans([1,6,8,3,7,4,2,5]). ------------ end of proof ------------- given clause #1088: (wt=18) 1158 [hyper,1157,1,2,eval] board([1,6,8,3,7,4,2,5]). given clause #1089: (wt=8) 1139 [hyper,1095,1,7,eval] board([6,2,5]). given clause #1090: (wt=10) 1161 [hyper,1139,1,2,eval] board([1,6,2,5]). given clause #1091: (wt=12) 1163 [hyper,1161,1,4,eval] board([3,1,6,2,5]). given clause #1092: (wt=14) 1165 [hyper,1163,1,8,eval] board([7,3,1,6,2,5]). given clause #1093: (wt=14) 1164 [hyper,1163,1,9,eval] board([8,3,1,6,2,5]). given clause #1094: (wt=12) 1162 [hyper,1161,1,8,eval] board([7,1,6,2,5]). given clause #1095: (wt=14) 1166 [hyper,1162,1,5,eval] board([4,7,1,6,2,5]). given clause #1096: (wt=16) 1167 [hyper,1166,1,9,eval] board([8,4,7,1,6,2,5]). -------- PROOF -------- 1169 [binary,1168.1,11.1] $Ans([3,8,4,7,1,6,2,5]). ----> UNIT CONFLICT at 0.42 sec ----> 1169 [binary,1168.1,11.1] $Ans([3,8,4,7,1,6,2,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1095 [hyper,17,1,3,eval] board([2,5]). 1139 [hyper,1095,1,7,eval] board([6,2,5]). 1161 [hyper,1139,1,2,eval] board([1,6,2,5]). 1162 [hyper,1161,1,8,eval] board([7,1,6,2,5]). 1166 [hyper,1162,1,5,eval] board([4,7,1,6,2,5]). 1167 [hyper,1166,1,9,eval] board([8,4,7,1,6,2,5]). 1168 [hyper,1167,1,4,eval] board([3,8,4,7,1,6,2,5]). 1169 [binary,1168.1,11.1] $Ans([3,8,4,7,1,6,2,5]). ------------ end of proof ------------- given clause #1097: (wt=18) 1168 [hyper,1167,1,4,eval] board([3,8,4,7,1,6,2,5]). given clause #1098: (wt=10) 1160 [hyper,1139,1,4,eval] board([3,6,2,5]). given clause #1099: (wt=12) 1170 [hyper,1160,1,8,eval] board([7,3,6,2,5]). given clause #1100: (wt=14) 1171 [hyper,1170,1,5,eval] board([4,7,3,6,2,5]). given clause #1101: (wt=16) 1173 [hyper,1171,1,2,eval] board([1,4,7,3,6,2,5]). given clause #1102: (wt=16) 1172 [hyper,1171,1,9,eval] board([8,4,7,3,6,2,5]). given clause #1103: (wt=8) 1138 [hyper,1095,1,9,eval] board([8,2,5]). given clause #1104: (wt=10) 1176 [hyper,1138,1,2,eval] board([1,8,2,5]). given clause #1105: (wt=12) 1179 [hyper,1176,1,4,eval] board([3,1,8,2,5]). given clause #1106: (wt=14) 1180 [hyper,1179,1,8,eval] board([7,3,1,8,2,5]). given clause #1107: (wt=12) 1178 [hyper,1176,1,5,eval] board([4,1,8,2,5]). given clause #1108: (wt=14) 1181 [hyper,1178,1,8,eval] board([7,4,1,8,2,5]). given clause #1109: (wt=16) 1182 [hyper,1181,1,4,eval] board([3,7,4,1,8,2,5]). -------- PROOF -------- 1184 [binary,1183.1,11.1] $Ans([6,3,7,4,1,8,2,5]). ----> UNIT CONFLICT at 0.42 sec ----> 1184 [binary,1183.1,11.1] $Ans([6,3,7,4,1,8,2,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1095 [hyper,17,1,3,eval] board([2,5]). 1138 [hyper,1095,1,9,eval] board([8,2,5]). 1176 [hyper,1138,1,2,eval] board([1,8,2,5]). 1178 [hyper,1176,1,5,eval] board([4,1,8,2,5]). 1181 [hyper,1178,1,8,eval] board([7,4,1,8,2,5]). 1182 [hyper,1181,1,4,eval] board([3,7,4,1,8,2,5]). 1183 [hyper,1182,1,7,eval] board([6,3,7,4,1,8,2,5]). 1184 [binary,1183.1,11.1] $Ans([6,3,7,4,1,8,2,5]). ------------ end of proof ------------- given clause #1110: (wt=18) 1183 [hyper,1182,1,7,eval] board([6,3,7,4,1,8,2,5]). given clause #1111: (wt=12) 1177 [hyper,1176,1,8,eval] board([7,1,8,2,5]). given clause #1112: (wt=14) 1185 [hyper,1177,1,5,eval] board([4,7,1,8,2,5]). given clause #1113: (wt=16) 1186 [hyper,1185,1,7,eval] board([6,4,7,1,8,2,5]). given clause #1114: (wt=10) 1175 [hyper,1138,1,4,eval] board([3,8,2,5]). given clause #1115: (wt=12) 1187 [hyper,1175,1,8,eval] board([7,3,8,2,5]). given clause #1116: (wt=14) 1188 [hyper,1187,1,5,eval] board([4,7,3,8,2,5]). given clause #1117: (wt=16) 1189 [hyper,1188,1,2,eval] board([1,4,7,3,8,2,5]). given clause #1118: (wt=10) 1174 [hyper,1138,1,7,eval] board([6,8,2,5]). given clause #1119: (wt=12) 1191 [hyper,1174,1,4,eval] board([3,6,8,2,5]). given clause #1120: (wt=14) 1193 [hyper,1191,1,2,eval] board([1,3,6,8,2,5]). given clause #1121: (wt=14) 1192 [hyper,1191,1,8,eval] board([7,3,6,8,2,5]). given clause #1122: (wt=12) 1190 [hyper,1174,1,5,eval] board([4,6,8,2,5]). given clause #1123: (wt=14) 1195 [hyper,1190,1,2,eval] board([1,4,6,8,2,5]). given clause #1124: (wt=14) 1194 [hyper,1190,1,8,eval] board([7,4,6,8,2,5]). given clause #1125: (wt=16) 1196 [hyper,1194,1,2,eval] board([1,7,4,6,8,2,5]). given clause #1126: (wt=6) 1094 [hyper,17,1,4,eval] board([3,5]). given clause #1127: (wt=8) 1199 [hyper,1094,1,2,eval] board([1,3,5]). given clause #1128: (wt=10) 1202 [hyper,1199,1,5,eval] board([4,1,3,5]). given clause #1129: (wt=12) 1205 [hyper,1202,1,3,eval] board([2,4,1,3,5]). given clause #1130: (wt=14) 1206 [hyper,1205,1,9,eval] board([8,2,4,1,3,5]). given clause #1131: (wt=16) 1207 [hyper,1206,1,7,eval] board([6,8,2,4,1,3,5]). given clause #1132: (wt=12) 1204 [hyper,1202,1,8,eval] board([7,4,1,3,5]). given clause #1133: (wt=12) 1203 [hyper,1202,1,9,eval] board([8,4,1,3,5]). given clause #1134: (wt=10) 1201 [hyper,1199,1,7,eval] board([6,1,3,5]). given clause #1135: (wt=12) 1210 [hyper,1201,1,3,eval] board([2,6,1,3,5]). given clause #1136: (wt=12) 1209 [hyper,1201,1,5,eval] board([4,6,1,3,5]). given clause #1137: (wt=14) 1211 [hyper,1209,1,3,eval] board([2,4,6,1,3,5]). given clause #1138: (wt=16) 1212 [hyper,1211,1,8,eval] board([7,2,4,6,1,3,5]). given clause #1139: (wt=12) 1208 [hyper,1201,1,9,eval] board([8,6,1,3,5]). given clause #1140: (wt=14) 1213 [hyper,1208,1,3,eval] board([2,8,6,1,3,5]). given clause #1141: (wt=16) 1215 [hyper,1213,1,5,eval] board([4,2,8,6,1,3,5]). -------- PROOF -------- 1217 [binary,1216.1,11.1] $Ans([7,4,2,8,6,1,3,5]). ----> UNIT CONFLICT at 0.43 sec ----> 1217 [binary,1216.1,11.1] $Ans([7,4,2,8,6,1,3,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1094 [hyper,17,1,4,eval] board([3,5]). 1199 [hyper,1094,1,2,eval] board([1,3,5]). 1201 [hyper,1199,1,7,eval] board([6,1,3,5]). 1208 [hyper,1201,1,9,eval] board([8,6,1,3,5]). 1213 [hyper,1208,1,3,eval] board([2,8,6,1,3,5]). 1215 [hyper,1213,1,5,eval] board([4,2,8,6,1,3,5]). 1216 [hyper,1215,1,8,eval] board([7,4,2,8,6,1,3,5]). 1217 [binary,1216.1,11.1] $Ans([7,4,2,8,6,1,3,5]). ------------ end of proof ------------- given clause #1142: (wt=18) 1216 [hyper,1215,1,8,eval] board([7,4,2,8,6,1,3,5]). given clause #1143: (wt=16) 1214 [hyper,1213,1,8,eval] board([7,2,8,6,1,3,5]). given clause #1144: (wt=10) 1200 [hyper,1199,1,8,eval] board([7,1,3,5]). given clause #1145: (wt=12) 1219 [hyper,1200,1,3,eval] board([2,7,1,3,5]). given clause #1146: (wt=14) 1221 [hyper,1219,1,7,eval] board([6,2,7,1,3,5]). given clause #1147: (wt=14) 1220 [hyper,1219,1,9,eval] board([8,2,7,1,3,5]). given clause #1148: (wt=16) 1222 [hyper,1220,1,7,eval] board([6,8,2,7,1,3,5]). -------- PROOF -------- 1224 [binary,1223.1,11.1] $Ans([4,6,8,2,7,1,3,5]). ----> UNIT CONFLICT at 0.44 sec ----> 1224 [binary,1223.1,11.1] $Ans([4,6,8,2,7,1,3,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1094 [hyper,17,1,4,eval] board([3,5]). 1199 [hyper,1094,1,2,eval] board([1,3,5]). 1200 [hyper,1199,1,8,eval] board([7,1,3,5]). 1219 [hyper,1200,1,3,eval] board([2,7,1,3,5]). 1220 [hyper,1219,1,9,eval] board([8,2,7,1,3,5]). 1222 [hyper,1220,1,7,eval] board([6,8,2,7,1,3,5]). 1223 [hyper,1222,1,5,eval] board([4,6,8,2,7,1,3,5]). 1224 [binary,1223.1,11.1] $Ans([4,6,8,2,7,1,3,5]). ------------ end of proof ------------- given clause #1149: (wt=18) 1223 [hyper,1222,1,5,eval] board([4,6,8,2,7,1,3,5]). given clause #1150: (wt=12) 1218 [hyper,1200,1,5,eval] board([4,7,1,3,5]). given clause #1151: (wt=14) 1227 [hyper,1218,1,3,eval] board([2,4,7,1,3,5]). given clause #1152: (wt=14) 1226 [hyper,1218,1,7,eval] board([6,4,7,1,3,5]). given clause #1153: (wt=14) 1225 [hyper,1218,1,9,eval] board([8,4,7,1,3,5]). given clause #1154: (wt=8) 1198 [hyper,1094,1,7,eval] board([6,3,5]). given clause #1155: (wt=10) 1228 [hyper,1198,1,5,eval] board([4,6,3,5]). given clause #1156: (wt=12) 1230 [hyper,1228,1,3,eval] board([2,4,6,3,5]). given clause #1157: (wt=14) 1231 [hyper,1230,1,9,eval] board([8,2,4,6,3,5]). given clause #1158: (wt=12) 1229 [hyper,1228,1,8,eval] board([7,4,6,3,5]). given clause #1159: (wt=14) 1232 [hyper,1229,1,2,eval] board([1,7,4,6,3,5]). given clause #1160: (wt=8) 1197 [hyper,1094,1,9,eval] board([8,3,5]). given clause #1161: (wt=10) 1234 [hyper,1197,1,5,eval] board([4,8,3,5]). given clause #1162: (wt=12) 1236 [hyper,1234,1,3,eval] board([2,4,8,3,5]). given clause #1163: (wt=12) 1235 [hyper,1234,1,8,eval] board([7,4,8,3,5]). given clause #1164: (wt=14) 1237 [hyper,1235,1,2,eval] board([1,7,4,8,3,5]). given clause #1165: (wt=16) 1238 [hyper,1237,1,7,eval] board([6,1,7,4,8,3,5]). -------- PROOF -------- 1240 [binary,1239.1,11.1] $Ans([2,6,1,7,4,8,3,5]). ----> UNIT CONFLICT at 0.45 sec ----> 1240 [binary,1239.1,11.1] $Ans([2,6,1,7,4,8,3,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1094 [hyper,17,1,4,eval] board([3,5]). 1197 [hyper,1094,1,9,eval] board([8,3,5]). 1234 [hyper,1197,1,5,eval] board([4,8,3,5]). 1235 [hyper,1234,1,8,eval] board([7,4,8,3,5]). 1237 [hyper,1235,1,2,eval] board([1,7,4,8,3,5]). 1238 [hyper,1237,1,7,eval] board([6,1,7,4,8,3,5]). 1239 [hyper,1238,1,3,eval] board([2,6,1,7,4,8,3,5]). 1240 [binary,1239.1,11.1] $Ans([2,6,1,7,4,8,3,5]). ------------ end of proof ------------- given clause #1166: (wt=18) 1239 [hyper,1238,1,3,eval] board([2,6,1,7,4,8,3,5]). given clause #1167: (wt=10) 1233 [hyper,1197,1,7,eval] board([6,8,3,5]). given clause #1168: (wt=12) 1242 [hyper,1233,1,3,eval] board([2,6,8,3,5]). given clause #1169: (wt=12) 1241 [hyper,1233,1,5,eval] board([4,6,8,3,5]). given clause #1170: (wt=14) 1244 [hyper,1241,1,2,eval] board([1,4,6,8,3,5]). given clause #1171: (wt=16) 1245 [hyper,1244,1,8,eval] board([7,1,4,6,8,3,5]). given clause #1172: (wt=14) 1243 [hyper,1241,1,3,eval] board([2,4,6,8,3,5]). given clause #1173: (wt=16) 1246 [hyper,1243,1,8,eval] board([7,2,4,6,8,3,5]). given clause #1174: (wt=6) 1093 [hyper,17,1,8,eval] board([7,5]). given clause #1175: (wt=8) 1249 [hyper,1093,1,2,eval] board([1,7,5]). given clause #1176: (wt=10) 1252 [hyper,1249,1,4,eval] board([3,1,7,5]). given clause #1177: (wt=12) 1254 [hyper,1252,1,7,eval] board([6,3,1,7,5]). given clause #1178: (wt=14) 1256 [hyper,1254,1,3,eval] board([2,6,3,1,7,5]). given clause #1179: (wt=14) 1255 [hyper,1254,1,9,eval] board([8,6,3,1,7,5]). given clause #1180: (wt=12) 1253 [hyper,1252,1,9,eval] board([8,3,1,7,5]). given clause #1181: (wt=14) 1258 [hyper,1253,1,3,eval] board([2,8,3,1,7,5]). given clause #1182: (wt=16) 1259 [hyper,1258,1,5,eval] board([4,2,8,3,1,7,5]). given clause #1183: (wt=14) 1257 [hyper,1253,1,7,eval] board([6,8,3,1,7,5]). given clause #1184: (wt=16) 1260 [hyper,1257,1,5,eval] board([4,6,8,3,1,7,5]). -------- PROOF -------- 1262 [binary,1261.1,11.1] $Ans([2,4,6,8,3,1,7,5]). ----> UNIT CONFLICT at 0.45 sec ----> 1262 [binary,1261.1,11.1] $Ans([2,4,6,8,3,1,7,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1093 [hyper,17,1,8,eval] board([7,5]). 1249 [hyper,1093,1,2,eval] board([1,7,5]). 1252 [hyper,1249,1,4,eval] board([3,1,7,5]). 1253 [hyper,1252,1,9,eval] board([8,3,1,7,5]). 1257 [hyper,1253,1,7,eval] board([6,8,3,1,7,5]). 1260 [hyper,1257,1,5,eval] board([4,6,8,3,1,7,5]). 1261 [hyper,1260,1,3,eval] board([2,4,6,8,3,1,7,5]). 1262 [binary,1261.1,11.1] $Ans([2,4,6,8,3,1,7,5]). ------------ end of proof ------------- given clause #1185: (wt=18) 1261 [hyper,1260,1,3,eval] board([2,4,6,8,3,1,7,5]). given clause #1186: (wt=10) 1251 [hyper,1249,1,5,eval] board([4,1,7,5]). given clause #1187: (wt=12) 1265 [hyper,1251,1,3,eval] board([2,4,1,7,5]). given clause #1188: (wt=14) 1266 [hyper,1265,1,9,eval] board([8,2,4,1,7,5]). given clause #1189: (wt=16) 1268 [hyper,1266,1,4,eval] board([3,8,2,4,1,7,5]). given clause #1190: (wt=16) 1267 [hyper,1266,1,7,eval] board([6,8,2,4,1,7,5]). -------- PROOF -------- 1270 [binary,1269.1,11.1] $Ans([3,6,8,2,4,1,7,5]). ----> UNIT CONFLICT at 0.46 sec ----> 1270 [binary,1269.1,11.1] $Ans([3,6,8,2,4,1,7,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1093 [hyper,17,1,8,eval] board([7,5]). 1249 [hyper,1093,1,2,eval] board([1,7,5]). 1251 [hyper,1249,1,5,eval] board([4,1,7,5]). 1265 [hyper,1251,1,3,eval] board([2,4,1,7,5]). 1266 [hyper,1265,1,9,eval] board([8,2,4,1,7,5]). 1267 [hyper,1266,1,7,eval] board([6,8,2,4,1,7,5]). 1269 [hyper,1267,1,4,eval] board([3,6,8,2,4,1,7,5]). 1270 [binary,1269.1,11.1] $Ans([3,6,8,2,4,1,7,5]). ------------ end of proof ------------- given clause #1191: (wt=18) 1269 [hyper,1267,1,4,eval] board([3,6,8,2,4,1,7,5]). given clause #1192: (wt=12) 1264 [hyper,1251,1,7,eval] board([6,4,1,7,5]). given clause #1193: (wt=14) 1271 [hyper,1264,1,9,eval] board([8,6,4,1,7,5]). given clause #1194: (wt=16) 1272 [hyper,1271,1,4,eval] board([3,8,6,4,1,7,5]). given clause #1195: (wt=12) 1263 [hyper,1251,1,9,eval] board([8,4,1,7,5]). given clause #1196: (wt=10) 1250 [hyper,1249,1,7,eval] board([6,1,7,5]). given clause #1197: (wt=12) 1274 [hyper,1250,1,3,eval] board([2,6,1,7,5]). given clause #1198: (wt=12) 1273 [hyper,1250,1,9,eval] board([8,6,1,7,5]). given clause #1199: (wt=14) 1275 [hyper,1273,1,3,eval] board([2,8,6,1,7,5]). given clause #1200: (wt=16) 1276 [hyper,1275,1,5,eval] board([4,2,8,6,1,7,5]). given clause #1201: (wt=8) 1248 [hyper,1093,1,3,eval] board([2,7,5]). given clause #1202: (wt=10) 1278 [hyper,1248,1,5,eval] board([4,2,7,5]). given clause #1203: (wt=12) 1280 [hyper,1278,1,7,eval] board([6,4,2,7,5]). given clause #1204: (wt=14) 1282 [hyper,1280,1,2,eval] board([1,6,4,2,7,5]). given clause #1205: (wt=16) 1283 [hyper,1282,1,4,eval] board([3,1,6,4,2,7,5]). given clause #1206: (wt=14) 1281 [hyper,1280,1,9,eval] board([8,6,4,2,7,5]). given clause #1207: (wt=16) 1284 [hyper,1281,1,4,eval] board([3,8,6,4,2,7,5]). given clause #1208: (wt=12) 1279 [hyper,1278,1,9,eval] board([8,4,2,7,5]). given clause #1209: (wt=14) 1285 [hyper,1279,1,2,eval] board([1,8,4,2,7,5]). given clause #1210: (wt=16) 1286 [hyper,1285,1,4,eval] board([3,1,8,4,2,7,5]). -------- PROOF -------- 1288 [binary,1287.1,11.1] $Ans([6,3,1,8,4,2,7,5]). ----> UNIT CONFLICT at 0.46 sec ----> 1288 [binary,1287.1,11.1] $Ans([6,3,1,8,4,2,7,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1093 [hyper,17,1,8,eval] board([7,5]). 1248 [hyper,1093,1,3,eval] board([2,7,5]). 1278 [hyper,1248,1,5,eval] board([4,2,7,5]). 1279 [hyper,1278,1,9,eval] board([8,4,2,7,5]). 1285 [hyper,1279,1,2,eval] board([1,8,4,2,7,5]). 1286 [hyper,1285,1,4,eval] board([3,1,8,4,2,7,5]). 1287 [hyper,1286,1,7,eval] board([6,3,1,8,4,2,7,5]). 1288 [binary,1287.1,11.1] $Ans([6,3,1,8,4,2,7,5]). ------------ end of proof ------------- given clause #1211: (wt=18) 1287 [hyper,1286,1,7,eval] board([6,3,1,8,4,2,7,5]). given clause #1212: (wt=10) 1277 [hyper,1248,1,7,eval] board([6,2,7,5]). given clause #1213: (wt=12) 1290 [hyper,1277,1,4,eval] board([3,6,2,7,5]). given clause #1214: (wt=14) 1291 [hyper,1290,1,2,eval] board([1,3,6,2,7,5]). given clause #1215: (wt=16) 1293 [hyper,1291,1,5,eval] board([4,1,3,6,2,7,5]). -------- PROOF -------- 1295 [binary,1294.1,11.1] $Ans([8,4,1,3,6,2,7,5]). ----> UNIT CONFLICT at 0.47 sec ----> 1295 [binary,1294.1,11.1] $Ans([8,4,1,3,6,2,7,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1093 [hyper,17,1,8,eval] board([7,5]). 1248 [hyper,1093,1,3,eval] board([2,7,5]). 1277 [hyper,1248,1,7,eval] board([6,2,7,5]). 1290 [hyper,1277,1,4,eval] board([3,6,2,7,5]). 1291 [hyper,1290,1,2,eval] board([1,3,6,2,7,5]). 1293 [hyper,1291,1,5,eval] board([4,1,3,6,2,7,5]). 1294 [hyper,1293,1,9,eval] board([8,4,1,3,6,2,7,5]). 1295 [binary,1294.1,11.1] $Ans([8,4,1,3,6,2,7,5]). ------------ end of proof ------------- given clause #1216: (wt=18) 1294 [hyper,1293,1,9,eval] board([8,4,1,3,6,2,7,5]). given clause #1217: (wt=16) 1292 [hyper,1291,1,9,eval] board([8,1,3,6,2,7,5]). -------- PROOF -------- 1297 [binary,1296.1,11.1] $Ans([4,8,1,3,6,2,7,5]). ----> UNIT CONFLICT at 0.47 sec ----> 1297 [binary,1296.1,11.1] $Ans([4,8,1,3,6,2,7,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1093 [hyper,17,1,8,eval] board([7,5]). 1248 [hyper,1093,1,3,eval] board([2,7,5]). 1277 [hyper,1248,1,7,eval] board([6,2,7,5]). 1290 [hyper,1277,1,4,eval] board([3,6,2,7,5]). 1291 [hyper,1290,1,2,eval] board([1,3,6,2,7,5]). 1292 [hyper,1291,1,9,eval] board([8,1,3,6,2,7,5]). 1296 [hyper,1292,1,5,eval] board([4,8,1,3,6,2,7,5]). 1297 [binary,1296.1,11.1] $Ans([4,8,1,3,6,2,7,5]). ------------ end of proof ------------- given clause #1218: (wt=18) 1296 [hyper,1292,1,5,eval] board([4,8,1,3,6,2,7,5]). given clause #1219: (wt=12) 1289 [hyper,1277,1,9,eval] board([8,6,2,7,5]). given clause #1220: (wt=14) 1298 [hyper,1289,1,2,eval] board([1,8,6,2,7,5]). given clause #1221: (wt=16) 1299 [hyper,1298,1,5,eval] board([4,1,8,6,2,7,5]). given clause #1222: (wt=8) 1247 [hyper,1093,1,5,eval] board([4,7,5]). given clause #1223: (wt=10) 1301 [hyper,1247,1,2,eval] board([1,4,7,5]). given clause #1224: (wt=12) 1303 [hyper,1301,1,4,eval] board([3,1,4,7,5]). given clause #1225: (wt=14) 1305 [hyper,1303,1,7,eval] board([6,3,1,4,7,5]). given clause #1226: (wt=14) 1304 [hyper,1303,1,9,eval] board([8,3,1,4,7,5]). given clause #1227: (wt=16) 1306 [hyper,1304,1,7,eval] board([6,8,3,1,4,7,5]). -------- PROOF -------- 1308 [binary,1307.1,11.1] $Ans([2,6,8,3,1,4,7,5]). ----> UNIT CONFLICT at 0.47 sec ----> 1308 [binary,1307.1,11.1] $Ans([2,6,8,3,1,4,7,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1093 [hyper,17,1,8,eval] board([7,5]). 1247 [hyper,1093,1,5,eval] board([4,7,5]). 1301 [hyper,1247,1,2,eval] board([1,4,7,5]). 1303 [hyper,1301,1,4,eval] board([3,1,4,7,5]). 1304 [hyper,1303,1,9,eval] board([8,3,1,4,7,5]). 1306 [hyper,1304,1,7,eval] board([6,8,3,1,4,7,5]). 1307 [hyper,1306,1,3,eval] board([2,6,8,3,1,4,7,5]). 1308 [binary,1307.1,11.1] $Ans([2,6,8,3,1,4,7,5]). ------------ end of proof ------------- given clause #1228: (wt=18) 1307 [hyper,1306,1,3,eval] board([2,6,8,3,1,4,7,5]). given clause #1229: (wt=12) 1302 [hyper,1301,1,9,eval] board([8,1,4,7,5]). given clause #1230: (wt=14) 1310 [hyper,1302,1,3,eval] board([2,8,1,4,7,5]). given clause #1231: (wt=14) 1309 [hyper,1302,1,7,eval] board([6,8,1,4,7,5]). given clause #1232: (wt=16) 1311 [hyper,1309,1,4,eval] board([3,6,8,1,4,7,5]). given clause #1233: (wt=10) 1300 [hyper,1247,1,7,eval] board([6,4,7,5]). given clause #1234: (wt=12) 1313 [hyper,1300,1,4,eval] board([3,6,4,7,5]). given clause #1235: (wt=12) 1312 [hyper,1300,1,9,eval] board([8,6,4,7,5]). given clause #1236: (wt=14) 1314 [hyper,1312,1,3,eval] board([2,8,6,4,7,5]). given clause #1237: (wt=6) 1092 [hyper,17,1,9,eval] board([8,5]). given clause #1238: (wt=8) 1318 [hyper,1092,1,2,eval] board([1,8,5]). given clause #1239: (wt=10) 1321 [hyper,1318,1,4,eval] board([3,1,8,5]). given clause #1240: (wt=12) 1323 [hyper,1321,1,7,eval] board([6,3,1,8,5]). given clause #1241: (wt=14) 1324 [hyper,1323,1,3,eval] board([2,6,3,1,8,5]). given clause #1242: (wt=16) 1325 [hyper,1324,1,8,eval] board([7,2,6,3,1,8,5]). given clause #1243: (wt=12) 1322 [hyper,1321,1,8,eval] board([7,3,1,8,5]). given clause #1244: (wt=14) 1326 [hyper,1322,1,3,eval] board([2,7,3,1,8,5]). given clause #1245: (wt=16) 1327 [hyper,1326,1,5,eval] board([4,2,7,3,1,8,5]). given clause #1246: (wt=10) 1320 [hyper,1318,1,5,eval] board([4,1,8,5]). given clause #1247: (wt=12) 1330 [hyper,1320,1,3,eval] board([2,4,1,8,5]). given clause #1248: (wt=14) 1331 [hyper,1330,1,8,eval] board([7,2,4,1,8,5]). given clause #1249: (wt=12) 1329 [hyper,1320,1,7,eval] board([6,4,1,8,5]). given clause #1250: (wt=14) 1332 [hyper,1329,1,4,eval] board([3,6,4,1,8,5]). given clause #1251: (wt=12) 1328 [hyper,1320,1,8,eval] board([7,4,1,8,5]). given clause #1252: (wt=14) 1333 [hyper,1328,1,4,eval] board([3,7,4,1,8,5]). given clause #1253: (wt=16) 1334 [hyper,1333,1,7,eval] board([6,3,7,4,1,8,5]). given clause #1254: (wt=10) 1319 [hyper,1318,1,8,eval] board([7,1,8,5]). given clause #1255: (wt=12) 1336 [hyper,1319,1,3,eval] board([2,7,1,8,5]). given clause #1256: (wt=14) 1337 [hyper,1336,1,7,eval] board([6,2,7,1,8,5]). given clause #1257: (wt=12) 1335 [hyper,1319,1,5,eval] board([4,7,1,8,5]). given clause #1258: (wt=14) 1339 [hyper,1335,1,3,eval] board([2,4,7,1,8,5]). given clause #1259: (wt=14) 1338 [hyper,1335,1,7,eval] board([6,4,7,1,8,5]). given clause #1260: (wt=8) 1317 [hyper,1092,1,3,eval] board([2,8,5]). given clause #1261: (wt=10) 1341 [hyper,1317,1,5,eval] board([4,2,8,5]). given clause #1262: (wt=12) 1343 [hyper,1341,1,7,eval] board([6,4,2,8,5]). given clause #1263: (wt=14) 1345 [hyper,1343,1,2,eval] board([1,6,4,2,8,5]). given clause #1264: (wt=14) 1344 [hyper,1343,1,4,eval] board([3,6,4,2,8,5]). given clause #1265: (wt=12) 1342 [hyper,1341,1,8,eval] board([7,4,2,8,5]). given clause #1266: (wt=14) 1347 [hyper,1342,1,2,eval] board([1,7,4,2,8,5]). given clause #1267: (wt=14) 1346 [hyper,1342,1,4,eval] board([3,7,4,2,8,5]). given clause #1268: (wt=10) 1340 [hyper,1317,1,8,eval] board([7,2,8,5]). given clause #1269: (wt=12) 1348 [hyper,1340,1,4,eval] board([3,7,2,8,5]). given clause #1270: (wt=14) 1350 [hyper,1348,1,2,eval] board([1,3,7,2,8,5]). given clause #1271: (wt=14) 1349 [hyper,1348,1,7,eval] board([6,3,7,2,8,5]). given clause #1272: (wt=8) 1316 [hyper,1092,1,5,eval] board([4,8,5]). given clause #1273: (wt=10) 1352 [hyper,1316,1,2,eval] board([1,4,8,5]). given clause #1274: (wt=12) 1354 [hyper,1352,1,4,eval] board([3,1,4,8,5]). given clause #1275: (wt=14) 1355 [hyper,1354,1,7,eval] board([6,3,1,4,8,5]). given clause #1276: (wt=16) 1356 [hyper,1355,1,3,eval] board([2,6,3,1,4,8,5]). -------- PROOF -------- 1358 [binary,1357.1,11.1] $Ans([7,2,6,3,1,4,8,5]). ----> UNIT CONFLICT at 0.49 sec ----> 1358 [binary,1357.1,11.1] $Ans([7,2,6,3,1,4,8,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1092 [hyper,17,1,9,eval] board([8,5]). 1316 [hyper,1092,1,5,eval] board([4,8,5]). 1352 [hyper,1316,1,2,eval] board([1,4,8,5]). 1354 [hyper,1352,1,4,eval] board([3,1,4,8,5]). 1355 [hyper,1354,1,7,eval] board([6,3,1,4,8,5]). 1356 [hyper,1355,1,3,eval] board([2,6,3,1,4,8,5]). 1357 [hyper,1356,1,8,eval] board([7,2,6,3,1,4,8,5]). 1358 [binary,1357.1,11.1] $Ans([7,2,6,3,1,4,8,5]). ------------ end of proof ------------- given clause #1277: (wt=18) 1357 [hyper,1356,1,8,eval] board([7,2,6,3,1,4,8,5]). given clause #1278: (wt=12) 1353 [hyper,1352,1,8,eval] board([7,1,4,8,5]). given clause #1279: (wt=14) 1359 [hyper,1353,1,3,eval] board([2,7,1,4,8,5]). given clause #1280: (wt=16) 1360 [hyper,1359,1,7,eval] board([6,2,7,1,4,8,5]). -------- PROOF -------- 1362 [binary,1361.1,11.1] $Ans([3,6,2,7,1,4,8,5]). ----> UNIT CONFLICT at 0.49 sec ----> 1362 [binary,1361.1,11.1] $Ans([3,6,2,7,1,4,8,5]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 17 [hyper,10,1,6,eval] board([5]). 1092 [hyper,17,1,9,eval] board([8,5]). 1316 [hyper,1092,1,5,eval] board([4,8,5]). 1352 [hyper,1316,1,2,eval] board([1,4,8,5]). 1353 [hyper,1352,1,8,eval] board([7,1,4,8,5]). 1359 [hyper,1353,1,3,eval] board([2,7,1,4,8,5]). 1360 [hyper,1359,1,7,eval] board([6,2,7,1,4,8,5]). 1361 [hyper,1360,1,4,eval] board([3,6,2,7,1,4,8,5]). 1362 [binary,1361.1,11.1] $Ans([3,6,2,7,1,4,8,5]). ------------ end of proof ------------- given clause #1281: (wt=18) 1361 [hyper,1360,1,4,eval] board([3,6,2,7,1,4,8,5]). given clause #1282: (wt=10) 1351 [hyper,1316,1,8,eval] board([7,4,8,5]). given clause #1283: (wt=12) 1363 [hyper,1351,1,4,eval] board([3,7,4,8,5]). given clause #1284: (wt=14) 1364 [hyper,1363,1,7,eval] board([6,3,7,4,8,5]). given clause #1285: (wt=16) 1365 [hyper,1364,1,3,eval] board([2,6,3,7,4,8,5]). given clause #1286: (wt=8) 1315 [hyper,1092,1,7,eval] board([6,8,5]). given clause #1287: (wt=10) 1368 [hyper,1315,1,2,eval] board([1,6,8,5]). given clause #1288: (wt=12) 1370 [hyper,1368,1,4,eval] board([3,1,6,8,5]). given clause #1289: (wt=14) 1371 [hyper,1370,1,8,eval] board([7,3,1,6,8,5]). given clause #1290: (wt=12) 1369 [hyper,1368,1,8,eval] board([7,1,6,8,5]). given clause #1291: (wt=14) 1372 [hyper,1369,1,3,eval] board([2,7,1,6,8,5]). given clause #1292: (wt=10) 1367 [hyper,1315,1,4,eval] board([3,6,8,5]). given clause #1293: (wt=12) 1373 [hyper,1367,1,8,eval] board([7,3,6,8,5]). given clause #1294: (wt=14) 1374 [hyper,1373,1,3,eval] board([2,7,3,6,8,5]). given clause #1295: (wt=16) 1375 [hyper,1374,1,5,eval] board([4,2,7,3,6,8,5]). given clause #1296: (wt=10) 1366 [hyper,1315,1,5,eval] board([4,6,8,5]). given clause #1297: (wt=12) 1377 [hyper,1366,1,3,eval] board([2,4,6,8,5]). given clause #1298: (wt=14) 1378 [hyper,1377,1,8,eval] board([7,2,4,6,8,5]). given clause #1299: (wt=12) 1376 [hyper,1366,1,8,eval] board([7,4,6,8,5]). given clause #1300: (wt=14) 1379 [hyper,1376,1,2,eval] board([1,7,4,6,8,5]). given clause #1301: (wt=4) 16 [hyper,10,1,7,eval] board([6]). given clause #1302: (wt=6) 1384 [hyper,16,1,2,eval] board([1,6]). given clause #1303: (wt=8) 1387 [hyper,1384,1,4,eval] board([3,1,6]). given clause #1304: (wt=10) 1390 [hyper,1387,1,6,eval] board([5,3,1,6]). given clause #1305: (wt=12) 1392 [hyper,1390,1,8,eval] board([7,5,3,1,6]). given clause #1306: (wt=14) 1394 [hyper,1392,1,3,eval] board([2,7,5,3,1,6]). given clause #1307: (wt=16) 1395 [hyper,1394,1,5,eval] board([4,2,7,5,3,1,6]). given clause #1308: (wt=14) 1393 [hyper,1392,1,5,eval] board([4,7,5,3,1,6]). given clause #1309: (wt=12) 1391 [hyper,1390,1,9,eval] board([8,5,3,1,6]). given clause #1310: (wt=14) 1397 [hyper,1391,1,3,eval] board([2,8,5,3,1,6]). given clause #1311: (wt=16) 1398 [hyper,1397,1,5,eval] board([4,2,8,5,3,1,6]). given clause #1312: (wt=14) 1396 [hyper,1391,1,5,eval] board([4,8,5,3,1,6]). given clause #1313: (wt=10) 1389 [hyper,1387,1,8,eval] board([7,3,1,6]). given clause #1314: (wt=10) 1388 [hyper,1387,1,9,eval] board([8,3,1,6]). given clause #1315: (wt=8) 1386 [hyper,1384,1,6,eval] board([5,1,6]). given clause #1316: (wt=10) 1401 [hyper,1386,1,3,eval] board([2,5,1,6]). given clause #1317: (wt=12) 1402 [hyper,1401,1,9,eval] board([8,2,5,1,6]). given clause #1318: (wt=14) 1403 [hyper,1402,1,4,eval] board([3,8,2,5,1,6]). given clause #1319: (wt=16) 1404 [hyper,1403,1,8,eval] board([7,3,8,2,5,1,6]). -------- PROOF -------- 1406 [binary,1405.1,11.1] $Ans([4,7,3,8,2,5,1,6]). ----> UNIT CONFLICT at 0.51 sec ----> 1406 [binary,1405.1,11.1] $Ans([4,7,3,8,2,5,1,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1384 [hyper,16,1,2,eval] board([1,6]). 1386 [hyper,1384,1,6,eval] board([5,1,6]). 1401 [hyper,1386,1,3,eval] board([2,5,1,6]). 1402 [hyper,1401,1,9,eval] board([8,2,5,1,6]). 1403 [hyper,1402,1,4,eval] board([3,8,2,5,1,6]). 1404 [hyper,1403,1,8,eval] board([7,3,8,2,5,1,6]). 1405 [hyper,1404,1,5,eval] board([4,7,3,8,2,5,1,6]). 1406 [binary,1405.1,11.1] $Ans([4,7,3,8,2,5,1,6]). ------------ end of proof ------------- given clause #1320: (wt=18) 1405 [hyper,1404,1,5,eval] board([4,7,3,8,2,5,1,6]). given clause #1321: (wt=10) 1400 [hyper,1386,1,8,eval] board([7,5,1,6]). given clause #1322: (wt=10) 1399 [hyper,1386,1,9,eval] board([8,5,1,6]). given clause #1323: (wt=8) 1385 [hyper,1384,1,8,eval] board([7,1,6]). given clause #1324: (wt=10) 1409 [hyper,1385,1,3,eval] board([2,7,1,6]). given clause #1325: (wt=12) 1410 [hyper,1409,1,9,eval] board([8,2,7,1,6]). given clause #1326: (wt=14) 1411 [hyper,1410,1,4,eval] board([3,8,2,7,1,6]). given clause #1327: (wt=10) 1408 [hyper,1385,1,5,eval] board([4,7,1,6]). given clause #1328: (wt=12) 1412 [hyper,1408,1,9,eval] board([8,4,7,1,6]). given clause #1329: (wt=14) 1413 [hyper,1412,1,4,eval] board([3,8,4,7,1,6]). given clause #1330: (wt=16) 1414 [hyper,1413,1,6,eval] board([5,3,8,4,7,1,6]). given clause #1331: (wt=10) 1407 [hyper,1385,1,6,eval] board([5,7,1,6]). given clause #1332: (wt=12) 1416 [hyper,1407,1,4,eval] board([3,5,7,1,6]). given clause #1333: (wt=14) 1417 [hyper,1416,1,9,eval] board([8,3,5,7,1,6]). given clause #1334: (wt=16) 1418 [hyper,1417,1,5,eval] board([4,8,3,5,7,1,6]). given clause #1335: (wt=12) 1415 [hyper,1407,1,9,eval] board([8,5,7,1,6]). given clause #1336: (wt=14) 1419 [hyper,1415,1,3,eval] board([2,8,5,7,1,6]). given clause #1337: (wt=16) 1420 [hyper,1419,1,5,eval] board([4,2,8,5,7,1,6]). given clause #1338: (wt=6) 1383 [hyper,16,1,3,eval] board([2,6]). given clause #1339: (wt=8) 1422 [hyper,1383,1,6,eval] board([5,2,6]). given clause #1340: (wt=10) 1425 [hyper,1422,1,2,eval] board([1,5,2,6]). given clause #1341: (wt=12) 1427 [hyper,1425,1,5,eval] board([4,1,5,2,6]). given clause #1342: (wt=14) 1428 [hyper,1427,1,8,eval] board([7,4,1,5,2,6]). given clause #1343: (wt=16) 1429 [hyper,1428,1,4,eval] board([3,7,4,1,5,2,6]). given clause #1344: (wt=12) 1426 [hyper,1425,1,9,eval] board([8,1,5,2,6]). given clause #1345: (wt=14) 1430 [hyper,1426,1,5,eval] board([4,8,1,5,2,6]). given clause #1346: (wt=10) 1424 [hyper,1422,1,8,eval] board([7,5,2,6]). given clause #1347: (wt=12) 1432 [hyper,1424,1,2,eval] board([1,7,5,2,6]). given clause #1348: (wt=14) 1434 [hyper,1432,1,4,eval] board([3,1,7,5,2,6]). given clause #1349: (wt=16) 1435 [hyper,1434,1,9,eval] board([8,3,1,7,5,2,6]). given clause #1350: (wt=14) 1433 [hyper,1432,1,5,eval] board([4,1,7,5,2,6]). given clause #1351: (wt=16) 1436 [hyper,1433,1,9,eval] board([8,4,1,7,5,2,6]). given clause #1352: (wt=12) 1431 [hyper,1424,1,5,eval] board([4,7,5,2,6]). given clause #1353: (wt=10) 1423 [hyper,1422,1,9,eval] board([8,5,2,6]). given clause #1354: (wt=12) 1438 [hyper,1423,1,2,eval] board([1,8,5,2,6]). given clause #1355: (wt=14) 1441 [hyper,1438,1,4,eval] board([3,1,8,5,2,6]). given clause #1356: (wt=14) 1440 [hyper,1438,1,5,eval] board([4,1,8,5,2,6]). given clause #1357: (wt=14) 1439 [hyper,1438,1,8,eval] board([7,1,8,5,2,6]). given clause #1358: (wt=16) 1442 [hyper,1439,1,5,eval] board([4,7,1,8,5,2,6]). given clause #1359: (wt=12) 1437 [hyper,1423,1,5,eval] board([4,8,5,2,6]). given clause #1360: (wt=14) 1443 [hyper,1437,1,8,eval] board([7,4,8,5,2,6]). given clause #1361: (wt=16) 1444 [hyper,1443,1,4,eval] board([3,7,4,8,5,2,6]). given clause #1362: (wt=8) 1421 [hyper,1383,1,8,eval] board([7,2,6]). given clause #1363: (wt=10) 1446 [hyper,1421,1,2,eval] board([1,7,2,6]). given clause #1364: (wt=12) 1449 [hyper,1446,1,4,eval] board([3,1,7,2,6]). given clause #1365: (wt=14) 1451 [hyper,1449,1,6,eval] board([5,3,1,7,2,6]). given clause #1366: (wt=16) 1452 [hyper,1451,1,9,eval] board([8,5,3,1,7,2,6]). -------- PROOF -------- 1454 [binary,1453.1,11.1] $Ans([4,8,5,3,1,7,2,6]). ----> UNIT CONFLICT at 0.52 sec ----> 1454 [binary,1453.1,11.1] $Ans([4,8,5,3,1,7,2,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1383 [hyper,16,1,3,eval] board([2,6]). 1421 [hyper,1383,1,8,eval] board([7,2,6]). 1446 [hyper,1421,1,2,eval] board([1,7,2,6]). 1449 [hyper,1446,1,4,eval] board([3,1,7,2,6]). 1451 [hyper,1449,1,6,eval] board([5,3,1,7,2,6]). 1452 [hyper,1451,1,9,eval] board([8,5,3,1,7,2,6]). 1453 [hyper,1452,1,5,eval] board([4,8,5,3,1,7,2,6]). 1454 [binary,1453.1,11.1] $Ans([4,8,5,3,1,7,2,6]). ------------ end of proof ------------- given clause #1367: (wt=18) 1453 [hyper,1452,1,5,eval] board([4,8,5,3,1,7,2,6]). given clause #1368: (wt=14) 1450 [hyper,1449,1,9,eval] board([8,3,1,7,2,6]). given clause #1369: (wt=12) 1448 [hyper,1446,1,5,eval] board([4,1,7,2,6]). given clause #1370: (wt=14) 1455 [hyper,1448,1,9,eval] board([8,4,1,7,2,6]). given clause #1371: (wt=16) 1456 [hyper,1455,1,6,eval] board([5,8,4,1,7,2,6]). -------- PROOF -------- 1458 [binary,1457.1,11.1] $Ans([3,5,8,4,1,7,2,6]). ----> UNIT CONFLICT at 0.53 sec ----> 1458 [binary,1457.1,11.1] $Ans([3,5,8,4,1,7,2,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1383 [hyper,16,1,3,eval] board([2,6]). 1421 [hyper,1383,1,8,eval] board([7,2,6]). 1446 [hyper,1421,1,2,eval] board([1,7,2,6]). 1448 [hyper,1446,1,5,eval] board([4,1,7,2,6]). 1455 [hyper,1448,1,9,eval] board([8,4,1,7,2,6]). 1456 [hyper,1455,1,6,eval] board([5,8,4,1,7,2,6]). 1457 [hyper,1456,1,4,eval] board([3,5,8,4,1,7,2,6]). 1458 [binary,1457.1,11.1] $Ans([3,5,8,4,1,7,2,6]). ------------ end of proof ------------- given clause #1372: (wt=18) 1457 [hyper,1456,1,4,eval] board([3,5,8,4,1,7,2,6]). given clause #1373: (wt=12) 1447 [hyper,1446,1,9,eval] board([8,1,7,2,6]). given clause #1374: (wt=14) 1459 [hyper,1447,1,6,eval] board([5,8,1,7,2,6]). given clause #1375: (wt=10) 1445 [hyper,1421,1,6,eval] board([5,7,2,6]). given clause #1376: (wt=12) 1462 [hyper,1445,1,2,eval] board([1,5,7,2,6]). given clause #1377: (wt=14) 1463 [hyper,1462,1,9,eval] board([8,1,5,7,2,6]). given clause #1378: (wt=16) 1464 [hyper,1463,1,5,eval] board([4,8,1,5,7,2,6]). given clause #1379: (wt=12) 1461 [hyper,1445,1,4,eval] board([3,5,7,2,6]). given clause #1380: (wt=14) 1465 [hyper,1461,1,9,eval] board([8,3,5,7,2,6]). given clause #1381: (wt=16) 1466 [hyper,1465,1,5,eval] board([4,8,3,5,7,2,6]). given clause #1382: (wt=12) 1460 [hyper,1445,1,9,eval] board([8,5,7,2,6]). given clause #1383: (wt=6) 1382 [hyper,16,1,4,eval] board([3,6]). given clause #1384: (wt=8) 1469 [hyper,1382,1,2,eval] board([1,3,6]). given clause #1385: (wt=10) 1472 [hyper,1469,1,5,eval] board([4,1,3,6]). given clause #1386: (wt=12) 1474 [hyper,1472,1,8,eval] board([7,4,1,3,6]). given clause #1387: (wt=14) 1475 [hyper,1474,1,6,eval] board([5,7,4,1,3,6]). given clause #1388: (wt=16) 1476 [hyper,1475,1,3,eval] board([2,5,7,4,1,3,6]). given clause #1389: (wt=12) 1473 [hyper,1472,1,9,eval] board([8,4,1,3,6]). given clause #1390: (wt=14) 1477 [hyper,1473,1,6,eval] board([5,8,4,1,3,6]). given clause #1391: (wt=16) 1478 [hyper,1477,1,3,eval] board([2,5,8,4,1,3,6]). given clause #1392: (wt=10) 1471 [hyper,1469,1,8,eval] board([7,1,3,6]). given clause #1393: (wt=12) 1480 [hyper,1471,1,5,eval] board([4,7,1,3,6]). given clause #1394: (wt=14) 1482 [hyper,1480,1,3,eval] board([2,4,7,1,3,6]). given clause #1395: (wt=14) 1481 [hyper,1480,1,9,eval] board([8,4,7,1,3,6]). given clause #1396: (wt=12) 1479 [hyper,1471,1,6,eval] board([5,7,1,3,6]). given clause #1397: (wt=14) 1484 [hyper,1479,1,3,eval] board([2,5,7,1,3,6]). given clause #1398: (wt=14) 1483 [hyper,1479,1,9,eval] board([8,5,7,1,3,6]). given clause #1399: (wt=16) 1485 [hyper,1483,1,3,eval] board([2,8,5,7,1,3,6]). -------- PROOF -------- 1487 [binary,1486.1,11.1] $Ans([4,2,8,5,7,1,3,6]). ----> UNIT CONFLICT at 0.54 sec ----> 1487 [binary,1486.1,11.1] $Ans([4,2,8,5,7,1,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1469 [hyper,1382,1,2,eval] board([1,3,6]). 1471 [hyper,1469,1,8,eval] board([7,1,3,6]). 1479 [hyper,1471,1,6,eval] board([5,7,1,3,6]). 1483 [hyper,1479,1,9,eval] board([8,5,7,1,3,6]). 1485 [hyper,1483,1,3,eval] board([2,8,5,7,1,3,6]). 1486 [hyper,1485,1,5,eval] board([4,2,8,5,7,1,3,6]). 1487 [binary,1486.1,11.1] $Ans([4,2,8,5,7,1,3,6]). ------------ end of proof ------------- given clause #1400: (wt=18) 1486 [hyper,1485,1,5,eval] board([4,2,8,5,7,1,3,6]). given clause #1401: (wt=10) 1470 [hyper,1469,1,9,eval] board([8,1,3,6]). given clause #1402: (wt=12) 1489 [hyper,1470,1,5,eval] board([4,8,1,3,6]). given clause #1403: (wt=14) 1490 [hyper,1489,1,3,eval] board([2,4,8,1,3,6]). given clause #1404: (wt=16) 1491 [hyper,1490,1,8,eval] board([7,2,4,8,1,3,6]). -------- PROOF -------- 1493 [binary,1492.1,11.1] $Ans([5,7,2,4,8,1,3,6]). ----> UNIT CONFLICT at 0.54 sec ----> 1493 [binary,1492.1,11.1] $Ans([5,7,2,4,8,1,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1469 [hyper,1382,1,2,eval] board([1,3,6]). 1470 [hyper,1469,1,9,eval] board([8,1,3,6]). 1489 [hyper,1470,1,5,eval] board([4,8,1,3,6]). 1490 [hyper,1489,1,3,eval] board([2,4,8,1,3,6]). 1491 [hyper,1490,1,8,eval] board([7,2,4,8,1,3,6]). 1492 [hyper,1491,1,6,eval] board([5,7,2,4,8,1,3,6]). 1493 [binary,1492.1,11.1] $Ans([5,7,2,4,8,1,3,6]). ------------ end of proof ------------- given clause #1405: (wt=18) 1492 [hyper,1491,1,6,eval] board([5,7,2,4,8,1,3,6]). given clause #1406: (wt=12) 1488 [hyper,1470,1,6,eval] board([5,8,1,3,6]). given clause #1407: (wt=14) 1494 [hyper,1488,1,3,eval] board([2,5,8,1,3,6]). given clause #1408: (wt=16) 1495 [hyper,1494,1,5,eval] board([4,2,5,8,1,3,6]). -------- PROOF -------- 1497 [binary,1496.1,11.1] $Ans([7,4,2,5,8,1,3,6]). ----> UNIT CONFLICT at 0.54 sec ----> 1497 [binary,1496.1,11.1] $Ans([7,4,2,5,8,1,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1469 [hyper,1382,1,2,eval] board([1,3,6]). 1470 [hyper,1469,1,9,eval] board([8,1,3,6]). 1488 [hyper,1470,1,6,eval] board([5,8,1,3,6]). 1494 [hyper,1488,1,3,eval] board([2,5,8,1,3,6]). 1495 [hyper,1494,1,5,eval] board([4,2,5,8,1,3,6]). 1496 [hyper,1495,1,8,eval] board([7,4,2,5,8,1,3,6]). 1497 [binary,1496.1,11.1] $Ans([7,4,2,5,8,1,3,6]). ------------ end of proof ------------- given clause #1409: (wt=18) 1496 [hyper,1495,1,8,eval] board([7,4,2,5,8,1,3,6]). given clause #1410: (wt=8) 1468 [hyper,1382,1,6,eval] board([5,3,6]). given clause #1411: (wt=10) 1500 [hyper,1468,1,3,eval] board([2,5,3,6]). given clause #1412: (wt=12) 1502 [hyper,1500,1,5,eval] board([4,2,5,3,6]). given clause #1413: (wt=12) 1501 [hyper,1500,1,9,eval] board([8,2,5,3,6]). given clause #1414: (wt=10) 1499 [hyper,1468,1,8,eval] board([7,5,3,6]). given clause #1415: (wt=12) 1504 [hyper,1499,1,2,eval] board([1,7,5,3,6]). given clause #1416: (wt=14) 1505 [hyper,1504,1,5,eval] board([4,1,7,5,3,6]). given clause #1417: (wt=16) 1506 [hyper,1505,1,3,eval] board([2,4,1,7,5,3,6]). -------- PROOF -------- 1508 [binary,1507.1,11.1] $Ans([8,2,4,1,7,5,3,6]). ----> UNIT CONFLICT at 0.55 sec ----> 1508 [binary,1507.1,11.1] $Ans([8,2,4,1,7,5,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1468 [hyper,1382,1,6,eval] board([5,3,6]). 1499 [hyper,1468,1,8,eval] board([7,5,3,6]). 1504 [hyper,1499,1,2,eval] board([1,7,5,3,6]). 1505 [hyper,1504,1,5,eval] board([4,1,7,5,3,6]). 1506 [hyper,1505,1,3,eval] board([2,4,1,7,5,3,6]). 1507 [hyper,1506,1,9,eval] board([8,2,4,1,7,5,3,6]). 1508 [binary,1507.1,11.1] $Ans([8,2,4,1,7,5,3,6]). ------------ end of proof ------------- given clause #1418: (wt=18) 1507 [hyper,1506,1,9,eval] board([8,2,4,1,7,5,3,6]). given clause #1419: (wt=12) 1503 [hyper,1499,1,5,eval] board([4,7,5,3,6]). given clause #1420: (wt=10) 1498 [hyper,1468,1,9,eval] board([8,5,3,6]). given clause #1421: (wt=12) 1510 [hyper,1498,1,2,eval] board([1,8,5,3,6]). given clause #1422: (wt=14) 1511 [hyper,1510,1,5,eval] board([4,1,8,5,3,6]). given clause #1423: (wt=16) 1513 [hyper,1511,1,3,eval] board([2,4,1,8,5,3,6]). -------- PROOF -------- 1515 [binary,1514.1,11.1] $Ans([7,2,4,1,8,5,3,6]). ----> UNIT CONFLICT at 0.55 sec ----> 1515 [binary,1514.1,11.1] $Ans([7,2,4,1,8,5,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1468 [hyper,1382,1,6,eval] board([5,3,6]). 1498 [hyper,1468,1,9,eval] board([8,5,3,6]). 1510 [hyper,1498,1,2,eval] board([1,8,5,3,6]). 1511 [hyper,1510,1,5,eval] board([4,1,8,5,3,6]). 1513 [hyper,1511,1,3,eval] board([2,4,1,8,5,3,6]). 1514 [hyper,1513,1,8,eval] board([7,2,4,1,8,5,3,6]). 1515 [binary,1514.1,11.1] $Ans([7,2,4,1,8,5,3,6]). ------------ end of proof ------------- given clause #1424: (wt=18) 1514 [hyper,1513,1,8,eval] board([7,2,4,1,8,5,3,6]). given clause #1425: (wt=16) 1512 [hyper,1511,1,8,eval] board([7,4,1,8,5,3,6]). given clause #1426: (wt=12) 1509 [hyper,1498,1,5,eval] board([4,8,5,3,6]). given clause #1427: (wt=8) 1467 [hyper,1382,1,8,eval] board([7,3,6]). given clause #1428: (wt=10) 1517 [hyper,1467,1,3,eval] board([2,7,3,6]). given clause #1429: (wt=12) 1519 [hyper,1517,1,5,eval] board([4,2,7,3,6]). given clause #1430: (wt=14) 1520 [hyper,1519,1,9,eval] board([8,4,2,7,3,6]). given clause #1431: (wt=16) 1521 [hyper,1520,1,2,eval] board([1,8,4,2,7,3,6]). -------- PROOF -------- 1523 [binary,1522.1,11.1] $Ans([5,1,8,4,2,7,3,6]). ----> UNIT CONFLICT at 0.55 sec ----> 1523 [binary,1522.1,11.1] $Ans([5,1,8,4,2,7,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1467 [hyper,1382,1,8,eval] board([7,3,6]). 1517 [hyper,1467,1,3,eval] board([2,7,3,6]). 1519 [hyper,1517,1,5,eval] board([4,2,7,3,6]). 1520 [hyper,1519,1,9,eval] board([8,4,2,7,3,6]). 1521 [hyper,1520,1,2,eval] board([1,8,4,2,7,3,6]). 1522 [hyper,1521,1,6,eval] board([5,1,8,4,2,7,3,6]). 1523 [binary,1522.1,11.1] $Ans([5,1,8,4,2,7,3,6]). ------------ end of proof ------------- given clause #1432: (wt=18) 1522 [hyper,1521,1,6,eval] board([5,1,8,4,2,7,3,6]). given clause #1433: (wt=12) 1518 [hyper,1517,1,9,eval] board([8,2,7,3,6]). given clause #1434: (wt=14) 1524 [hyper,1518,1,6,eval] board([5,8,2,7,3,6]). given clause #1435: (wt=16) 1525 [hyper,1524,1,2,eval] board([1,5,8,2,7,3,6]). -------- PROOF -------- 1527 [binary,1526.1,11.1] $Ans([4,1,5,8,2,7,3,6]). ----> UNIT CONFLICT at 0.55 sec ----> 1527 [binary,1526.1,11.1] $Ans([4,1,5,8,2,7,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1467 [hyper,1382,1,8,eval] board([7,3,6]). 1517 [hyper,1467,1,3,eval] board([2,7,3,6]). 1518 [hyper,1517,1,9,eval] board([8,2,7,3,6]). 1524 [hyper,1518,1,6,eval] board([5,8,2,7,3,6]). 1525 [hyper,1524,1,2,eval] board([1,5,8,2,7,3,6]). 1526 [hyper,1525,1,5,eval] board([4,1,5,8,2,7,3,6]). 1527 [binary,1526.1,11.1] $Ans([4,1,5,8,2,7,3,6]). ------------ end of proof ------------- given clause #1436: (wt=18) 1526 [hyper,1525,1,5,eval] board([4,1,5,8,2,7,3,6]). given clause #1437: (wt=10) 1516 [hyper,1467,1,5,eval] board([4,7,3,6]). given clause #1438: (wt=12) 1529 [hyper,1516,1,2,eval] board([1,4,7,3,6]). given clause #1439: (wt=14) 1531 [hyper,1529,1,6,eval] board([5,1,4,7,3,6]). given clause #1440: (wt=16) 1532 [hyper,1531,1,3,eval] board([2,5,1,4,7,3,6]). given clause #1441: (wt=14) 1530 [hyper,1529,1,9,eval] board([8,1,4,7,3,6]). given clause #1442: (wt=16) 1534 [hyper,1530,1,3,eval] board([2,8,1,4,7,3,6]). -------- PROOF -------- 1536 [binary,1535.1,11.1] $Ans([5,2,8,1,4,7,3,6]). ----> UNIT CONFLICT at 0.56 sec ----> 1536 [binary,1535.1,11.1] $Ans([5,2,8,1,4,7,3,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1382 [hyper,16,1,4,eval] board([3,6]). 1467 [hyper,1382,1,8,eval] board([7,3,6]). 1516 [hyper,1467,1,5,eval] board([4,7,3,6]). 1529 [hyper,1516,1,2,eval] board([1,4,7,3,6]). 1530 [hyper,1529,1,9,eval] board([8,1,4,7,3,6]). 1534 [hyper,1530,1,3,eval] board([2,8,1,4,7,3,6]). 1535 [hyper,1534,1,6,eval] board([5,2,8,1,4,7,3,6]). 1536 [binary,1535.1,11.1] $Ans([5,2,8,1,4,7,3,6]). ------------ end of proof ------------- given clause #1443: (wt=18) 1535 [hyper,1534,1,6,eval] board([5,2,8,1,4,7,3,6]). given clause #1444: (wt=16) 1533 [hyper,1530,1,6,eval] board([5,8,1,4,7,3,6]). given clause #1445: (wt=12) 1528 [hyper,1516,1,9,eval] board([8,4,7,3,6]). given clause #1446: (wt=14) 1537 [hyper,1528,1,6,eval] board([5,8,4,7,3,6]). given clause #1447: (wt=16) 1538 [hyper,1537,1,3,eval] board([2,5,8,4,7,3,6]). given clause #1448: (wt=6) 1381 [hyper,16,1,5,eval] board([4,6]). given clause #1449: (wt=8) 1541 [hyper,1381,1,2,eval] board([1,4,6]). given clause #1450: (wt=10) 1544 [hyper,1541,1,6,eval] board([5,1,4,6]). given clause #1451: (wt=12) 1545 [hyper,1544,1,9,eval] board([8,5,1,4,6]). given clause #1452: (wt=14) 1546 [hyper,1545,1,3,eval] board([2,8,5,1,4,6]). given clause #1453: (wt=16) 1547 [hyper,1546,1,8,eval] board([7,2,8,5,1,4,6]). -------- PROOF -------- 1549 [binary,1548.1,11.1] $Ans([3,7,2,8,5,1,4,6]). ----> UNIT CONFLICT at 0.56 sec ----> 1549 [binary,1548.1,11.1] $Ans([3,7,2,8,5,1,4,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1381 [hyper,16,1,5,eval] board([4,6]). 1541 [hyper,1381,1,2,eval] board([1,4,6]). 1544 [hyper,1541,1,6,eval] board([5,1,4,6]). 1545 [hyper,1544,1,9,eval] board([8,5,1,4,6]). 1546 [hyper,1545,1,3,eval] board([2,8,5,1,4,6]). 1547 [hyper,1546,1,8,eval] board([7,2,8,5,1,4,6]). 1548 [hyper,1547,1,4,eval] board([3,7,2,8,5,1,4,6]). 1549 [binary,1548.1,11.1] $Ans([3,7,2,8,5,1,4,6]). ------------ end of proof ------------- given clause #1454: (wt=18) 1548 [hyper,1547,1,4,eval] board([3,7,2,8,5,1,4,6]). given clause #1455: (wt=10) 1543 [hyper,1541,1,8,eval] board([7,1,4,6]). given clause #1456: (wt=12) 1550 [hyper,1543,1,6,eval] board([5,7,1,4,6]). given clause #1457: (wt=14) 1552 [hyper,1550,1,3,eval] board([2,5,7,1,4,6]). given clause #1458: (wt=16) 1553 [hyper,1552,1,9,eval] board([8,2,5,7,1,4,6]). given clause #1459: (wt=14) 1551 [hyper,1550,1,4,eval] board([3,5,7,1,4,6]). given clause #1460: (wt=16) 1554 [hyper,1551,1,9,eval] board([8,3,5,7,1,4,6]). given clause #1461: (wt=10) 1542 [hyper,1541,1,9,eval] board([8,1,4,6]). given clause #1462: (wt=12) 1555 [hyper,1542,1,6,eval] board([5,8,1,4,6]). given clause #1463: (wt=14) 1558 [hyper,1555,1,3,eval] board([2,5,8,1,4,6]). given clause #1464: (wt=14) 1557 [hyper,1555,1,4,eval] board([3,5,8,1,4,6]). given clause #1465: (wt=14) 1556 [hyper,1555,1,8,eval] board([7,5,8,1,4,6]). given clause #1466: (wt=16) 1559 [hyper,1556,1,3,eval] board([2,7,5,8,1,4,6]). given clause #1467: (wt=8) 1540 [hyper,1381,1,3,eval] board([2,4,6]). given clause #1468: (wt=10) 1562 [hyper,1540,1,6,eval] board([5,2,4,6]). given clause #1469: (wt=12) 1564 [hyper,1562,1,4,eval] board([3,5,2,4,6]). given clause #1470: (wt=12) 1563 [hyper,1562,1,9,eval] board([8,5,2,4,6]). given clause #1471: (wt=10) 1561 [hyper,1540,1,8,eval] board([7,2,4,6]). given clause #1472: (wt=12) 1566 [hyper,1561,1,4,eval] board([3,7,2,4,6]). given clause #1473: (wt=12) 1565 [hyper,1561,1,6,eval] board([5,7,2,4,6]). given clause #1474: (wt=14) 1567 [hyper,1565,1,4,eval] board([3,5,7,2,4,6]). given clause #1475: (wt=16) 1569 [hyper,1567,1,2,eval] board([1,3,5,7,2,4,6]). given clause #1476: (wt=16) 1568 [hyper,1567,1,9,eval] board([8,3,5,7,2,4,6]). given clause #1477: (wt=10) 1560 [hyper,1540,1,9,eval] board([8,2,4,6]). given clause #1478: (wt=12) 1571 [hyper,1560,1,4,eval] board([3,8,2,4,6]). given clause #1479: (wt=14) 1572 [hyper,1571,1,8,eval] board([7,3,8,2,4,6]). given clause #1480: (wt=12) 1570 [hyper,1560,1,6,eval] board([5,8,2,4,6]). given clause #1481: (wt=14) 1574 [hyper,1570,1,4,eval] board([3,5,8,2,4,6]). given clause #1482: (wt=16) 1575 [hyper,1574,1,2,eval] board([1,3,5,8,2,4,6]). given clause #1483: (wt=14) 1573 [hyper,1570,1,8,eval] board([7,5,8,2,4,6]). given clause #1484: (wt=16) 1576 [hyper,1573,1,2,eval] board([1,7,5,8,2,4,6]). -------- PROOF -------- 1578 [binary,1577.1,11.1] $Ans([3,1,7,5,8,2,4,6]). ----> UNIT CONFLICT at 0.57 sec ----> 1578 [binary,1577.1,11.1] $Ans([3,1,7,5,8,2,4,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1381 [hyper,16,1,5,eval] board([4,6]). 1540 [hyper,1381,1,3,eval] board([2,4,6]). 1560 [hyper,1540,1,9,eval] board([8,2,4,6]). 1570 [hyper,1560,1,6,eval] board([5,8,2,4,6]). 1573 [hyper,1570,1,8,eval] board([7,5,8,2,4,6]). 1576 [hyper,1573,1,2,eval] board([1,7,5,8,2,4,6]). 1577 [hyper,1576,1,4,eval] board([3,1,7,5,8,2,4,6]). 1578 [binary,1577.1,11.1] $Ans([3,1,7,5,8,2,4,6]). ------------ end of proof ------------- given clause #1485: (wt=18) 1577 [hyper,1576,1,4,eval] board([3,1,7,5,8,2,4,6]). given clause #1486: (wt=8) 1539 [hyper,1381,1,8,eval] board([7,4,6]). given clause #1487: (wt=10) 1580 [hyper,1539,1,2,eval] board([1,7,4,6]). given clause #1488: (wt=12) 1582 [hyper,1580,1,4,eval] board([3,1,7,4,6]). given clause #1489: (wt=14) 1583 [hyper,1582,1,6,eval] board([5,3,1,7,4,6]). given clause #1490: (wt=16) 1585 [hyper,1583,1,3,eval] board([2,5,3,1,7,4,6]). -------- PROOF -------- 1587 [binary,1586.1,11.1] $Ans([8,2,5,3,1,7,4,6]). ----> UNIT CONFLICT at 0.57 sec ----> 1587 [binary,1586.1,11.1] $Ans([8,2,5,3,1,7,4,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1381 [hyper,16,1,5,eval] board([4,6]). 1539 [hyper,1381,1,8,eval] board([7,4,6]). 1580 [hyper,1539,1,2,eval] board([1,7,4,6]). 1582 [hyper,1580,1,4,eval] board([3,1,7,4,6]). 1583 [hyper,1582,1,6,eval] board([5,3,1,7,4,6]). 1585 [hyper,1583,1,3,eval] board([2,5,3,1,7,4,6]). 1586 [hyper,1585,1,9,eval] board([8,2,5,3,1,7,4,6]). 1587 [binary,1586.1,11.1] $Ans([8,2,5,3,1,7,4,6]). ------------ end of proof ------------- given clause #1491: (wt=18) 1586 [hyper,1585,1,9,eval] board([8,2,5,3,1,7,4,6]). given clause #1492: (wt=16) 1584 [hyper,1583,1,9,eval] board([8,5,3,1,7,4,6]). given clause #1493: (wt=12) 1581 [hyper,1580,1,9,eval] board([8,1,7,4,6]). given clause #1494: (wt=14) 1589 [hyper,1581,1,3,eval] board([2,8,1,7,4,6]). given clause #1495: (wt=16) 1590 [hyper,1589,1,6,eval] board([5,2,8,1,7,4,6]). -------- PROOF -------- 1592 [binary,1591.1,11.1] $Ans([3,5,2,8,1,7,4,6]). ----> UNIT CONFLICT at 0.57 sec ----> 1592 [binary,1591.1,11.1] $Ans([3,5,2,8,1,7,4,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1381 [hyper,16,1,5,eval] board([4,6]). 1539 [hyper,1381,1,8,eval] board([7,4,6]). 1580 [hyper,1539,1,2,eval] board([1,7,4,6]). 1581 [hyper,1580,1,9,eval] board([8,1,7,4,6]). 1589 [hyper,1581,1,3,eval] board([2,8,1,7,4,6]). 1590 [hyper,1589,1,6,eval] board([5,2,8,1,7,4,6]). 1591 [hyper,1590,1,4,eval] board([3,5,2,8,1,7,4,6]). 1592 [binary,1591.1,11.1] $Ans([3,5,2,8,1,7,4,6]). ------------ end of proof ------------- given clause #1496: (wt=18) 1591 [hyper,1590,1,4,eval] board([3,5,2,8,1,7,4,6]). given clause #1497: (wt=14) 1588 [hyper,1581,1,6,eval] board([5,8,1,7,4,6]). given clause #1498: (wt=16) 1593 [hyper,1588,1,3,eval] board([2,5,8,1,7,4,6]). given clause #1499: (wt=10) 1579 [hyper,1539,1,6,eval] board([5,7,4,6]). given clause #1500: (wt=12) 1595 [hyper,1579,1,4,eval] board([3,5,7,4,6]). given clause #1501: (wt=12) 1594 [hyper,1579,1,9,eval] board([8,5,7,4,6]). given clause #1502: (wt=14) 1596 [hyper,1594,1,3,eval] board([2,8,5,7,4,6]). given clause #1503: (wt=6) 1380 [hyper,16,1,9,eval] board([8,6]). given clause #1504: (wt=8) 1600 [hyper,1380,1,2,eval] board([1,8,6]). given clause #1505: (wt=10) 1603 [hyper,1600,1,5,eval] board([4,1,8,6]). given clause #1506: (wt=12) 1604 [hyper,1603,1,8,eval] board([7,4,1,8,6]). given clause #1507: (wt=14) 1606 [hyper,1604,1,4,eval] board([3,7,4,1,8,6]). given clause #1508: (wt=14) 1605 [hyper,1604,1,6,eval] board([5,7,4,1,8,6]). given clause #1509: (wt=16) 1607 [hyper,1605,1,3,eval] board([2,5,7,4,1,8,6]). given clause #1510: (wt=10) 1602 [hyper,1600,1,6,eval] board([5,1,8,6]). given clause #1511: (wt=12) 1608 [hyper,1602,1,8,eval] board([7,5,1,8,6]). given clause #1512: (wt=14) 1609 [hyper,1608,1,3,eval] board([2,7,5,1,8,6]). given clause #1513: (wt=16) 1610 [hyper,1609,1,5,eval] board([4,2,7,5,1,8,6]). given clause #1514: (wt=10) 1601 [hyper,1600,1,8,eval] board([7,1,8,6]). given clause #1515: (wt=12) 1611 [hyper,1601,1,5,eval] board([4,7,1,8,6]). given clause #1516: (wt=14) 1612 [hyper,1611,1,3,eval] board([2,4,7,1,8,6]). given clause #1517: (wt=8) 1599 [hyper,1380,1,3,eval] board([2,8,6]). given clause #1518: (wt=10) 1615 [hyper,1599,1,5,eval] board([4,2,8,6]). given clause #1519: (wt=12) 1617 [hyper,1615,1,2,eval] board([1,4,2,8,6]). given clause #1520: (wt=14) 1619 [hyper,1617,1,4,eval] board([3,1,4,2,8,6]). given clause #1521: (wt=16) 1620 [hyper,1619,1,6,eval] board([5,3,1,4,2,8,6]). given clause #1522: (wt=14) 1618 [hyper,1617,1,8,eval] board([7,1,4,2,8,6]). given clause #1523: (wt=16) 1621 [hyper,1618,1,6,eval] board([5,7,1,4,2,8,6]). -------- PROOF -------- 1623 [binary,1622.1,11.1] $Ans([3,5,7,1,4,2,8,6]). ----> UNIT CONFLICT at 0.59 sec ----> 1623 [binary,1622.1,11.1] $Ans([3,5,7,1,4,2,8,6]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 16 [hyper,10,1,7,eval] board([6]). 1380 [hyper,16,1,9,eval] board([8,6]). 1599 [hyper,1380,1,3,eval] board([2,8,6]). 1615 [hyper,1599,1,5,eval] board([4,2,8,6]). 1617 [hyper,1615,1,2,eval] board([1,4,2,8,6]). 1618 [hyper,1617,1,8,eval] board([7,1,4,2,8,6]). 1621 [hyper,1618,1,6,eval] board([5,7,1,4,2,8,6]). 1622 [hyper,1621,1,4,eval] board([3,5,7,1,4,2,8,6]). 1623 [binary,1622.1,11.1] $Ans([3,5,7,1,4,2,8,6]). ------------ end of proof ------------- given clause #1524: (wt=18) 1622 [hyper,1621,1,4,eval] board([3,5,7,1,4,2,8,6]). given clause #1525: (wt=12) 1616 [hyper,1615,1,8,eval] board([7,4,2,8,6]). given clause #1526: (wt=14) 1624 [hyper,1616,1,4,eval] board([3,7,4,2,8,6]). given clause #1527: (wt=10) 1614 [hyper,1599,1,6,eval] board([5,2,8,6]). given clause #1528: (wt=12) 1627 [hyper,1614,1,2,eval] board([1,5,2,8,6]). given clause #1529: (wt=12) 1626 [hyper,1614,1,4,eval] board([3,5,2,8,6]). given clause #1530: (wt=12) 1625 [hyper,1614,1,8,eval] board([7,5,2,8,6]). given clause #1531: (wt=10) 1613 [hyper,1599,1,8,eval] board([7,2,8,6]). given clause #1532: (wt=12) 1629 [hyper,1613,1,2,eval] board([1,7,2,8,6]). given clause #1533: (wt=14) 1630 [hyper,1629,1,4,eval] board([3,1,7,2,8,6]). given clause #1534: (wt=16) 1631 [hyper,1630,1,6,eval] board([5,3,1,7,2,8,6]). given clause #1535: (wt=12) 1628 [hyper,1613,1,4,eval] board([3,7,2,8,6]). given clause #1536: (wt=8) 1598 [hyper,1380,1,4,eval] board([3,8,6]). given clause #1537: (wt=10) 1634 [hyper,1598,1,2,eval] board([1,3,8,6]). given clause #1538: (wt=12) 1636 [hyper,1634,1,5,eval] board([4,1,3,8,6]). given clause #1539: (wt=14) 1638 [hyper,1636,1,3,eval] board([2,4,1,3,8,6]). given clause #1540: (wt=16) 1639 [hyper,1638,1,6,eval] board([5,2,4,1,3,8,6]). given clause #1541: (wt=14) 1637 [hyper,1636,1,8,eval] board([7,4,1,3,8,6]). given clause #1542: (wt=16) 1640 [hyper,1637,1,6,eval] board([5,7,4,1,3,8,6]). given clause #1543: (wt=12) 1635 [hyper,1634,1,8,eval] board([7,1,3,8,6]). given clause #1544: (wt=14) 1642 [hyper,1635,1,3,eval] board([2,7,1,3,8,6]). given clause #1545: (wt=14) 1641 [hyper,1635,1,6,eval] board([5,7,1,3,8,6]). given clause #1546: (wt=16) 1643 [hyper,1641,1,3,eval] board([2,5,7,1,3,8,6]). given clause #1547: (wt=10) 1633 [hyper,1598,1,6,eval] board([5,3,8,6]). given clause #1548: (wt=12) 1644 [hyper,1633,1,8,eval] board([7,5,3,8,6]). given clause #1549: (wt=14) 1645 [hyper,1644,1,3,eval] board([2,7,5,3,8,6]). given clause #1550: (wt=16) 1646 [hyper,1645,1,5,eval] board([4,2,7,5,3,8,6]). given clause #1551: (wt=10) 1632 [hyper,1598,1,8,eval] board([7,3,8,6]). given clause #1552: (wt=12) 1647 [hyper,1632,1,5,eval] board([4,7,3,8,6]). given clause #1553: (wt=14) 1648 [hyper,1647,1,3,eval] board([2,4,7,3,8,6]). given clause #1554: (wt=16) 1649 [hyper,1648,1,6,eval] board([5,2,4,7,3,8,6]). given clause #1555: (wt=8) 1597 [hyper,1380,1,6,eval] board([5,8,6]). given clause #1556: (wt=10) 1652 [hyper,1597,1,2,eval] board([1,5,8,6]). given clause #1557: (wt=12) 1653 [hyper,1652,1,5,eval] board([4,1,5,8,6]). given clause #1558: (wt=14) 1654 [hyper,1653,1,8,eval] board([7,4,1,5,8,6]). given clause #1559: (wt=10) 1651 [hyper,1597,1,3,eval] board([2,5,8,6]). given clause #1560: (wt=12) 1655 [hyper,1651,1,5,eval] board([4,2,5,8,6]). given clause #1561: (wt=14) 1656 [hyper,1655,1,8,eval] board([7,4,2,5,8,6]). given clause #1562: (wt=10) 1650 [hyper,1597,1,8,eval] board([7,5,8,6]). given clause #1563: (wt=12) 1658 [hyper,1650,1,2,eval] board([1,7,5,8,6]). given clause #1564: (wt=14) 1659 [hyper,1658,1,4,eval] board([3,1,7,5,8,6]). given clause #1565: (wt=12) 1657 [hyper,1650,1,5,eval] board([4,7,5,8,6]). given clause #1566: (wt=4) 15 [hyper,10,1,8,eval] board([7]). given clause #1567: (wt=6) 1664 [hyper,15,1,2,eval] board([1,7]). given clause #1568: (wt=8) 1668 [hyper,1664,1,4,eval] board([3,1,7]). given clause #1569: (wt=10) 1671 [hyper,1668,1,6,eval] board([5,3,1,7]). given clause #1570: (wt=12) 1673 [hyper,1671,1,3,eval] board([2,5,3,1,7]). given clause #1571: (wt=14) 1675 [hyper,1673,1,5,eval] board([4,2,5,3,1,7]). given clause #1572: (wt=14) 1674 [hyper,1673,1,9,eval] board([8,2,5,3,1,7]). given clause #1573: (wt=12) 1672 [hyper,1671,1,9,eval] board([8,5,3,1,7]). given clause #1574: (wt=14) 1676 [hyper,1672,1,5,eval] board([4,8,5,3,1,7]). given clause #1575: (wt=10) 1670 [hyper,1668,1,7,eval] board([6,3,1,7]). given clause #1576: (wt=12) 1678 [hyper,1670,1,3,eval] board([2,6,3,1,7]). given clause #1577: (wt=12) 1677 [hyper,1670,1,9,eval] board([8,6,3,1,7]). given clause #1578: (wt=10) 1669 [hyper,1668,1,9,eval] board([8,3,1,7]). given clause #1579: (wt=12) 1680 [hyper,1669,1,3,eval] board([2,8,3,1,7]). given clause #1580: (wt=14) 1681 [hyper,1680,1,5,eval] board([4,2,8,3,1,7]). given clause #1581: (wt=12) 1679 [hyper,1669,1,7,eval] board([6,8,3,1,7]). given clause #1582: (wt=14) 1682 [hyper,1679,1,5,eval] board([4,6,8,3,1,7]). given clause #1583: (wt=16) 1683 [hyper,1682,1,3,eval] board([2,4,6,8,3,1,7]). -------- PROOF -------- 1685 [binary,1684.1,11.1] $Ans([5,2,4,6,8,3,1,7]). ----> UNIT CONFLICT at 0.61 sec ----> 1685 [binary,1684.1,11.1] $Ans([5,2,4,6,8,3,1,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1664 [hyper,15,1,2,eval] board([1,7]). 1668 [hyper,1664,1,4,eval] board([3,1,7]). 1669 [hyper,1668,1,9,eval] board([8,3,1,7]). 1679 [hyper,1669,1,7,eval] board([6,8,3,1,7]). 1682 [hyper,1679,1,5,eval] board([4,6,8,3,1,7]). 1683 [hyper,1682,1,3,eval] board([2,4,6,8,3,1,7]). 1684 [hyper,1683,1,6,eval] board([5,2,4,6,8,3,1,7]). 1685 [binary,1684.1,11.1] $Ans([5,2,4,6,8,3,1,7]). ------------ end of proof ------------- given clause #1584: (wt=18) 1684 [hyper,1683,1,6,eval] board([5,2,4,6,8,3,1,7]). given clause #1585: (wt=8) 1667 [hyper,1664,1,5,eval] board([4,1,7]). given clause #1586: (wt=10) 1688 [hyper,1667,1,3,eval] board([2,4,1,7]). given clause #1587: (wt=12) 1690 [hyper,1688,1,6,eval] board([5,2,4,1,7]). given clause #1588: (wt=14) 1692 [hyper,1690,1,4,eval] board([3,5,2,4,1,7]). given clause #1589: (wt=14) 1691 [hyper,1690,1,9,eval] board([8,5,2,4,1,7]). given clause #1590: (wt=12) 1689 [hyper,1688,1,9,eval] board([8,2,4,1,7]). given clause #1591: (wt=14) 1694 [hyper,1689,1,4,eval] board([3,8,2,4,1,7]). given clause #1592: (wt=14) 1693 [hyper,1689,1,7,eval] board([6,8,2,4,1,7]). given clause #1593: (wt=16) 1695 [hyper,1693,1,4,eval] board([3,6,8,2,4,1,7]). given clause #1594: (wt=10) 1687 [hyper,1667,1,7,eval] board([6,4,1,7]). given clause #1595: (wt=12) 1696 [hyper,1687,1,9,eval] board([8,6,4,1,7]). given clause #1596: (wt=14) 1697 [hyper,1696,1,4,eval] board([3,8,6,4,1,7]). given clause #1597: (wt=16) 1698 [hyper,1697,1,6,eval] board([5,3,8,6,4,1,7]). given clause #1598: (wt=10) 1686 [hyper,1667,1,9,eval] board([8,4,1,7]). given clause #1599: (wt=12) 1699 [hyper,1686,1,6,eval] board([5,8,4,1,7]). given clause #1600: (wt=14) 1700 [hyper,1699,1,4,eval] board([3,5,8,4,1,7]). given clause #1601: (wt=8) 1666 [hyper,1664,1,7,eval] board([6,1,7]). given clause #1602: (wt=10) 1702 [hyper,1666,1,3,eval] board([2,6,1,7]). given clause #1603: (wt=12) 1703 [hyper,1702,1,6,eval] board([5,2,6,1,7]). given clause #1604: (wt=14) 1704 [hyper,1703,1,9,eval] board([8,5,2,6,1,7]). given clause #1605: (wt=16) 1705 [hyper,1704,1,5,eval] board([4,8,5,2,6,1,7]). given clause #1606: (wt=10) 1701 [hyper,1666,1,9,eval] board([8,6,1,7]). given clause #1607: (wt=12) 1707 [hyper,1701,1,3,eval] board([2,8,6,1,7]). given clause #1608: (wt=14) 1708 [hyper,1707,1,5,eval] board([4,2,8,6,1,7]). given clause #1609: (wt=12) 1706 [hyper,1701,1,6,eval] board([5,8,6,1,7]). given clause #1610: (wt=8) 1665 [hyper,1664,1,9,eval] board([8,1,7]). given clause #1611: (wt=10) 1711 [hyper,1665,1,3,eval] board([2,8,1,7]). given clause #1612: (wt=12) 1712 [hyper,1711,1,6,eval] board([5,2,8,1,7]). given clause #1613: (wt=14) 1713 [hyper,1712,1,4,eval] board([3,5,2,8,1,7]). given clause #1614: (wt=10) 1710 [hyper,1665,1,6,eval] board([5,8,1,7]). given clause #1615: (wt=12) 1714 [hyper,1710,1,3,eval] board([2,5,8,1,7]). given clause #1616: (wt=14) 1716 [hyper,1714,1,5,eval] board([4,2,5,8,1,7]). given clause #1617: (wt=14) 1715 [hyper,1714,1,7,eval] board([6,2,5,8,1,7]). given clause #1618: (wt=16) 1717 [hyper,1715,1,4,eval] board([3,6,2,5,8,1,7]). given clause #1619: (wt=10) 1709 [hyper,1665,1,7,eval] board([6,8,1,7]). given clause #1620: (wt=12) 1718 [hyper,1709,1,3,eval] board([2,6,8,1,7]). given clause #1621: (wt=6) 1663 [hyper,15,1,3,eval] board([2,7]). given clause #1622: (wt=8) 1721 [hyper,1663,1,5,eval] board([4,2,7]). given clause #1623: (wt=10) 1724 [hyper,1721,1,2,eval] board([1,4,2,7]). given clause #1624: (wt=12) 1725 [hyper,1724,1,9,eval] board([8,1,4,2,7]). given clause #1625: (wt=14) 1726 [hyper,1725,1,6,eval] board([5,8,1,4,2,7]). given clause #1626: (wt=16) 1727 [hyper,1726,1,4,eval] board([3,5,8,1,4,2,7]). -------- PROOF -------- 1729 [binary,1728.1,11.1] $Ans([6,3,5,8,1,4,2,7]). ----> UNIT CONFLICT at 0.62 sec ----> 1729 [binary,1728.1,11.1] $Ans([6,3,5,8,1,4,2,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1663 [hyper,15,1,3,eval] board([2,7]). 1721 [hyper,1663,1,5,eval] board([4,2,7]). 1724 [hyper,1721,1,2,eval] board([1,4,2,7]). 1725 [hyper,1724,1,9,eval] board([8,1,4,2,7]). 1726 [hyper,1725,1,6,eval] board([5,8,1,4,2,7]). 1727 [hyper,1726,1,4,eval] board([3,5,8,1,4,2,7]). 1728 [hyper,1727,1,7,eval] board([6,3,5,8,1,4,2,7]). 1729 [binary,1728.1,11.1] $Ans([6,3,5,8,1,4,2,7]). ------------ end of proof ------------- given clause #1627: (wt=18) 1728 [hyper,1727,1,7,eval] board([6,3,5,8,1,4,2,7]). given clause #1628: (wt=10) 1723 [hyper,1721,1,7,eval] board([6,4,2,7]). given clause #1629: (wt=12) 1731 [hyper,1723,1,2,eval] board([1,6,4,2,7]). given clause #1630: (wt=14) 1733 [hyper,1731,1,4,eval] board([3,1,6,4,2,7]). given clause #1631: (wt=16) 1734 [hyper,1733,1,6,eval] board([5,3,1,6,4,2,7]). given clause #1632: (wt=14) 1732 [hyper,1731,1,6,eval] board([5,1,6,4,2,7]). given clause #1633: (wt=12) 1730 [hyper,1723,1,9,eval] board([8,6,4,2,7]). given clause #1634: (wt=14) 1736 [hyper,1730,1,4,eval] board([3,8,6,4,2,7]). given clause #1635: (wt=16) 1737 [hyper,1736,1,6,eval] board([5,3,8,6,4,2,7]). given clause #1636: (wt=14) 1735 [hyper,1730,1,6,eval] board([5,8,6,4,2,7]). given clause #1637: (wt=10) 1722 [hyper,1721,1,9,eval] board([8,4,2,7]). given clause #1638: (wt=12) 1738 [hyper,1722,1,2,eval] board([1,8,4,2,7]). given clause #1639: (wt=14) 1740 [hyper,1738,1,4,eval] board([3,1,8,4,2,7]). given clause #1640: (wt=16) 1741 [hyper,1740,1,7,eval] board([6,3,1,8,4,2,7]). given clause #1641: (wt=14) 1739 [hyper,1738,1,6,eval] board([5,1,8,4,2,7]). given clause #1642: (wt=8) 1720 [hyper,1663,1,7,eval] board([6,2,7]). given clause #1643: (wt=10) 1744 [hyper,1720,1,2,eval] board([1,6,2,7]). given clause #1644: (wt=10) 1743 [hyper,1720,1,4,eval] board([3,6,2,7]). given clause #1645: (wt=12) 1745 [hyper,1743,1,2,eval] board([1,3,6,2,7]). given clause #1646: (wt=14) 1747 [hyper,1745,1,5,eval] board([4,1,3,6,2,7]). given clause #1647: (wt=16) 1748 [hyper,1747,1,9,eval] board([8,4,1,3,6,2,7]). -------- PROOF -------- 1750 [binary,1749.1,11.1] $Ans([5,8,4,1,3,6,2,7]). ----> UNIT CONFLICT at 0.63 sec ----> 1750 [binary,1749.1,11.1] $Ans([5,8,4,1,3,6,2,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1663 [hyper,15,1,3,eval] board([2,7]). 1720 [hyper,1663,1,7,eval] board([6,2,7]). 1743 [hyper,1720,1,4,eval] board([3,6,2,7]). 1745 [hyper,1743,1,2,eval] board([1,3,6,2,7]). 1747 [hyper,1745,1,5,eval] board([4,1,3,6,2,7]). 1748 [hyper,1747,1,9,eval] board([8,4,1,3,6,2,7]). 1749 [hyper,1748,1,6,eval] board([5,8,4,1,3,6,2,7]). 1750 [binary,1749.1,11.1] $Ans([5,8,4,1,3,6,2,7]). ------------ end of proof ------------- given clause #1648: (wt=18) 1749 [hyper,1748,1,6,eval] board([5,8,4,1,3,6,2,7]). given clause #1649: (wt=14) 1746 [hyper,1745,1,9,eval] board([8,1,3,6,2,7]). given clause #1650: (wt=16) 1752 [hyper,1746,1,5,eval] board([4,8,1,3,6,2,7]). given clause #1651: (wt=16) 1751 [hyper,1746,1,6,eval] board([5,8,1,3,6,2,7]). given clause #1652: (wt=10) 1742 [hyper,1720,1,9,eval] board([8,6,2,7]). given clause #1653: (wt=12) 1753 [hyper,1742,1,2,eval] board([1,8,6,2,7]). given clause #1654: (wt=14) 1755 [hyper,1753,1,5,eval] board([4,1,8,6,2,7]). given clause #1655: (wt=14) 1754 [hyper,1753,1,6,eval] board([5,1,8,6,2,7]). given clause #1656: (wt=8) 1719 [hyper,1663,1,9,eval] board([8,2,7]). given clause #1657: (wt=10) 1759 [hyper,1719,1,2,eval] board([1,8,2,7]). given clause #1658: (wt=12) 1760 [hyper,1759,1,5,eval] board([4,1,8,2,7]). given clause #1659: (wt=10) 1758 [hyper,1719,1,4,eval] board([3,8,2,7]). given clause #1660: (wt=12) 1761 [hyper,1758,1,2,eval] board([1,3,8,2,7]). given clause #1661: (wt=14) 1762 [hyper,1761,1,5,eval] board([4,1,3,8,2,7]). given clause #1662: (wt=10) 1757 [hyper,1719,1,6,eval] board([5,8,2,7]). given clause #1663: (wt=12) 1763 [hyper,1757,1,2,eval] board([1,5,8,2,7]). given clause #1664: (wt=14) 1764 [hyper,1763,1,5,eval] board([4,1,5,8,2,7]). given clause #1665: (wt=16) 1765 [hyper,1764,1,7,eval] board([6,4,1,5,8,2,7]). given clause #1666: (wt=10) 1756 [hyper,1719,1,7,eval] board([6,8,2,7]). given clause #1667: (wt=12) 1767 [hyper,1756,1,2,eval] board([1,6,8,2,7]). given clause #1668: (wt=14) 1768 [hyper,1767,1,4,eval] board([3,1,6,8,2,7]). given clause #1669: (wt=16) 1769 [hyper,1768,1,6,eval] board([5,3,1,6,8,2,7]). given clause #1670: (wt=12) 1766 [hyper,1756,1,5,eval] board([4,6,8,2,7]). given clause #1671: (wt=14) 1770 [hyper,1766,1,2,eval] board([1,4,6,8,2,7]). given clause #1672: (wt=16) 1771 [hyper,1770,1,6,eval] board([5,1,4,6,8,2,7]). given clause #1673: (wt=6) 1662 [hyper,15,1,4,eval] board([3,7]). given clause #1674: (wt=8) 1774 [hyper,1662,1,2,eval] board([1,3,7]). given clause #1675: (wt=10) 1776 [hyper,1774,1,7,eval] board([6,1,3,7]). given clause #1676: (wt=12) 1779 [hyper,1776,1,3,eval] board([2,6,1,3,7]). given clause #1677: (wt=14) 1780 [hyper,1779,1,6,eval] board([5,2,6,1,3,7]). given clause #1678: (wt=12) 1778 [hyper,1776,1,5,eval] board([4,6,1,3,7]). given clause #1679: (wt=12) 1777 [hyper,1776,1,9,eval] board([8,6,1,3,7]). given clause #1680: (wt=14) 1781 [hyper,1777,1,6,eval] board([5,8,6,1,3,7]). given clause #1681: (wt=16) 1782 [hyper,1781,1,3,eval] board([2,5,8,6,1,3,7]). -------- PROOF -------- 1784 [binary,1783.1,11.1] $Ans([4,2,5,8,6,1,3,7]). ----> UNIT CONFLICT at 0.65 sec ----> 1784 [binary,1783.1,11.1] $Ans([4,2,5,8,6,1,3,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1662 [hyper,15,1,4,eval] board([3,7]). 1774 [hyper,1662,1,2,eval] board([1,3,7]). 1776 [hyper,1774,1,7,eval] board([6,1,3,7]). 1777 [hyper,1776,1,9,eval] board([8,6,1,3,7]). 1781 [hyper,1777,1,6,eval] board([5,8,6,1,3,7]). 1782 [hyper,1781,1,3,eval] board([2,5,8,6,1,3,7]). 1783 [hyper,1782,1,5,eval] board([4,2,5,8,6,1,3,7]). 1784 [binary,1783.1,11.1] $Ans([4,2,5,8,6,1,3,7]). ------------ end of proof ------------- given clause #1682: (wt=18) 1783 [hyper,1782,1,5,eval] board([4,2,5,8,6,1,3,7]). given clause #1683: (wt=10) 1775 [hyper,1774,1,9,eval] board([8,1,3,7]). given clause #1684: (wt=12) 1787 [hyper,1775,1,3,eval] board([2,8,1,3,7]). given clause #1685: (wt=14) 1788 [hyper,1787,1,6,eval] board([5,2,8,1,3,7]). given clause #1686: (wt=12) 1786 [hyper,1775,1,5,eval] board([4,8,1,3,7]). given clause #1687: (wt=12) 1785 [hyper,1775,1,6,eval] board([5,8,1,3,7]). given clause #1688: (wt=8) 1773 [hyper,1662,1,7,eval] board([6,3,7]). given clause #1689: (wt=10) 1790 [hyper,1773,1,3,eval] board([2,6,3,7]). given clause #1690: (wt=12) 1791 [hyper,1790,1,6,eval] board([5,2,6,3,7]). given clause #1691: (wt=14) 1793 [hyper,1791,1,2,eval] board([1,5,2,6,3,7]). given clause #1692: (wt=16) 1794 [hyper,1793,1,5,eval] board([4,1,5,2,6,3,7]). given clause #1693: (wt=14) 1792 [hyper,1791,1,9,eval] board([8,5,2,6,3,7]). given clause #1694: (wt=16) 1795 [hyper,1792,1,5,eval] board([4,8,5,2,6,3,7]). given clause #1695: (wt=10) 1789 [hyper,1773,1,9,eval] board([8,6,3,7]). given clause #1696: (wt=12) 1798 [hyper,1789,1,2,eval] board([1,8,6,3,7]). given clause #1697: (wt=14) 1800 [hyper,1798,1,5,eval] board([4,1,8,6,3,7]). given clause #1698: (wt=14) 1799 [hyper,1798,1,6,eval] board([5,1,8,6,3,7]). given clause #1699: (wt=12) 1797 [hyper,1789,1,3,eval] board([2,8,6,3,7]). given clause #1700: (wt=14) 1802 [hyper,1797,1,5,eval] board([4,2,8,6,3,7]). given clause #1701: (wt=14) 1801 [hyper,1797,1,6,eval] board([5,2,8,6,3,7]). given clause #1702: (wt=12) 1796 [hyper,1789,1,6,eval] board([5,8,6,3,7]). given clause #1703: (wt=14) 1803 [hyper,1796,1,2,eval] board([1,5,8,6,3,7]). given clause #1704: (wt=16) 1804 [hyper,1803,1,5,eval] board([4,1,5,8,6,3,7]). given clause #1705: (wt=8) 1772 [hyper,1662,1,9,eval] board([8,3,7]). given clause #1706: (wt=10) 1806 [hyper,1772,1,3,eval] board([2,8,3,7]). given clause #1707: (wt=12) 1808 [hyper,1806,1,5,eval] board([4,2,8,3,7]). given clause #1708: (wt=14) 1810 [hyper,1808,1,2,eval] board([1,4,2,8,3,7]). given clause #1709: (wt=14) 1809 [hyper,1808,1,7,eval] board([6,4,2,8,3,7]). given clause #1710: (wt=12) 1807 [hyper,1806,1,6,eval] board([5,2,8,3,7]). given clause #1711: (wt=14) 1811 [hyper,1807,1,2,eval] board([1,5,2,8,3,7]). given clause #1712: (wt=16) 1812 [hyper,1811,1,7,eval] board([6,1,5,2,8,3,7]). -------- PROOF -------- 1814 [binary,1813.1,11.1] $Ans([4,6,1,5,2,8,3,7]). ----> UNIT CONFLICT at 0.66 sec ----> 1814 [binary,1813.1,11.1] $Ans([4,6,1,5,2,8,3,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1662 [hyper,15,1,4,eval] board([3,7]). 1772 [hyper,1662,1,9,eval] board([8,3,7]). 1806 [hyper,1772,1,3,eval] board([2,8,3,7]). 1807 [hyper,1806,1,6,eval] board([5,2,8,3,7]). 1811 [hyper,1807,1,2,eval] board([1,5,2,8,3,7]). 1812 [hyper,1811,1,7,eval] board([6,1,5,2,8,3,7]). 1813 [hyper,1812,1,5,eval] board([4,6,1,5,2,8,3,7]). 1814 [binary,1813.1,11.1] $Ans([4,6,1,5,2,8,3,7]). ------------ end of proof ------------- given clause #1713: (wt=18) 1813 [hyper,1812,1,5,eval] board([4,6,1,5,2,8,3,7]). given clause #1714: (wt=10) 1805 [hyper,1772,1,7,eval] board([6,8,3,7]). given clause #1715: (wt=12) 1817 [hyper,1805,1,2,eval] board([1,6,8,3,7]). given clause #1716: (wt=12) 1816 [hyper,1805,1,3,eval] board([2,6,8,3,7]). given clause #1717: (wt=12) 1815 [hyper,1805,1,5,eval] board([4,6,8,3,7]). given clause #1718: (wt=14) 1818 [hyper,1815,1,2,eval] board([1,4,6,8,3,7]). given clause #1719: (wt=16) 1819 [hyper,1818,1,6,eval] board([5,1,4,6,8,3,7]). given clause #1720: (wt=6) 1661 [hyper,15,1,5,eval] board([4,7]). given clause #1721: (wt=8) 1823 [hyper,1661,1,2,eval] board([1,4,7]). given clause #1722: (wt=10) 1826 [hyper,1823,1,4,eval] board([3,1,4,7]). given clause #1723: (wt=12) 1829 [hyper,1826,1,6,eval] board([5,3,1,4,7]). given clause #1724: (wt=12) 1828 [hyper,1826,1,7,eval] board([6,3,1,4,7]). given clause #1725: (wt=12) 1827 [hyper,1826,1,9,eval] board([8,3,1,4,7]). given clause #1726: (wt=14) 1830 [hyper,1827,1,7,eval] board([6,8,3,1,4,7]). given clause #1727: (wt=16) 1831 [hyper,1830,1,3,eval] board([2,6,8,3,1,4,7]). given clause #1728: (wt=10) 1825 [hyper,1823,1,6,eval] board([5,1,4,7]). given clause #1729: (wt=12) 1833 [hyper,1825,1,3,eval] board([2,5,1,4,7]). given clause #1730: (wt=14) 1834 [hyper,1833,1,7,eval] board([6,2,5,1,4,7]). given clause #1731: (wt=16) 1835 [hyper,1834,1,4,eval] board([3,6,2,5,1,4,7]). given clause #1732: (wt=12) 1832 [hyper,1825,1,9,eval] board([8,5,1,4,7]). given clause #1733: (wt=14) 1836 [hyper,1832,1,7,eval] board([6,8,5,1,4,7]). given clause #1734: (wt=16) 1837 [hyper,1836,1,4,eval] board([3,6,8,5,1,4,7]). given clause #1735: (wt=10) 1824 [hyper,1823,1,9,eval] board([8,1,4,7]). given clause #1736: (wt=12) 1840 [hyper,1824,1,3,eval] board([2,8,1,4,7]). given clause #1737: (wt=14) 1841 [hyper,1840,1,6,eval] board([5,2,8,1,4,7]). given clause #1738: (wt=16) 1842 [hyper,1841,1,4,eval] board([3,5,2,8,1,4,7]). given clause #1739: (wt=12) 1839 [hyper,1824,1,6,eval] board([5,8,1,4,7]). given clause #1740: (wt=14) 1843 [hyper,1839,1,4,eval] board([3,5,8,1,4,7]). given clause #1741: (wt=16) 1844 [hyper,1843,1,7,eval] board([6,3,5,8,1,4,7]). given clause #1742: (wt=12) 1838 [hyper,1824,1,7,eval] board([6,8,1,4,7]). given clause #1743: (wt=14) 1845 [hyper,1838,1,4,eval] board([3,6,8,1,4,7]). given clause #1744: (wt=8) 1822 [hyper,1661,1,3,eval] board([2,4,7]). given clause #1745: (wt=10) 1847 [hyper,1822,1,6,eval] board([5,2,4,7]). given clause #1746: (wt=12) 1848 [hyper,1847,1,9,eval] board([8,5,2,4,7]). given clause #1747: (wt=14) 1850 [hyper,1848,1,2,eval] board([1,8,5,2,4,7]). given clause #1748: (wt=16) 1851 [hyper,1850,1,4,eval] board([3,1,8,5,2,4,7]). -------- PROOF -------- 1853 [binary,1852.1,11.1] $Ans([6,3,1,8,5,2,4,7]). ----> UNIT CONFLICT at 0.67 sec ----> 1853 [binary,1852.1,11.1] $Ans([6,3,1,8,5,2,4,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1661 [hyper,15,1,5,eval] board([4,7]). 1822 [hyper,1661,1,3,eval] board([2,4,7]). 1847 [hyper,1822,1,6,eval] board([5,2,4,7]). 1848 [hyper,1847,1,9,eval] board([8,5,2,4,7]). 1850 [hyper,1848,1,2,eval] board([1,8,5,2,4,7]). 1851 [hyper,1850,1,4,eval] board([3,1,8,5,2,4,7]). 1852 [hyper,1851,1,7,eval] board([6,3,1,8,5,2,4,7]). 1853 [binary,1852.1,11.1] $Ans([6,3,1,8,5,2,4,7]). ------------ end of proof ------------- given clause #1749: (wt=18) 1852 [hyper,1851,1,7,eval] board([6,3,1,8,5,2,4,7]). given clause #1750: (wt=14) 1849 [hyper,1848,1,7,eval] board([6,8,5,2,4,7]). given clause #1751: (wt=16) 1854 [hyper,1849,1,4,eval] board([3,6,8,5,2,4,7]). given clause #1752: (wt=10) 1846 [hyper,1822,1,9,eval] board([8,2,4,7]). given clause #1753: (wt=12) 1856 [hyper,1846,1,6,eval] board([5,8,2,4,7]). given clause #1754: (wt=14) 1858 [hyper,1856,1,2,eval] board([1,5,8,2,4,7]). given clause #1755: (wt=14) 1857 [hyper,1856,1,4,eval] board([3,5,8,2,4,7]). given clause #1756: (wt=12) 1855 [hyper,1846,1,7,eval] board([6,8,2,4,7]). given clause #1757: (wt=14) 1860 [hyper,1855,1,2,eval] board([1,6,8,2,4,7]). given clause #1758: (wt=16) 1861 [hyper,1860,1,4,eval] board([3,1,6,8,2,4,7]). -------- PROOF -------- 1863 [binary,1862.1,11.1] $Ans([5,3,1,6,8,2,4,7]). ----> UNIT CONFLICT at 0.68 sec ----> 1863 [binary,1862.1,11.1] $Ans([5,3,1,6,8,2,4,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1661 [hyper,15,1,5,eval] board([4,7]). 1822 [hyper,1661,1,3,eval] board([2,4,7]). 1846 [hyper,1822,1,9,eval] board([8,2,4,7]). 1855 [hyper,1846,1,7,eval] board([6,8,2,4,7]). 1860 [hyper,1855,1,2,eval] board([1,6,8,2,4,7]). 1861 [hyper,1860,1,4,eval] board([3,1,6,8,2,4,7]). 1862 [hyper,1861,1,6,eval] board([5,3,1,6,8,2,4,7]). 1863 [binary,1862.1,11.1] $Ans([5,3,1,6,8,2,4,7]). ------------ end of proof ------------- given clause #1759: (wt=18) 1862 [hyper,1861,1,6,eval] board([5,3,1,6,8,2,4,7]). given clause #1760: (wt=14) 1859 [hyper,1855,1,4,eval] board([3,6,8,2,4,7]). given clause #1761: (wt=8) 1821 [hyper,1661,1,7,eval] board([6,4,7]). given clause #1762: (wt=10) 1866 [hyper,1821,1,2,eval] board([1,6,4,7]). given clause #1763: (wt=12) 1867 [hyper,1866,1,6,eval] board([5,1,6,4,7]). given clause #1764: (wt=10) 1865 [hyper,1821,1,4,eval] board([3,6,4,7]). given clause #1765: (wt=12) 1868 [hyper,1865,1,6,eval] board([5,3,6,4,7]). given clause #1766: (wt=10) 1864 [hyper,1821,1,9,eval] board([8,6,4,7]). given clause #1767: (wt=12) 1870 [hyper,1864,1,3,eval] board([2,8,6,4,7]). given clause #1768: (wt=14) 1871 [hyper,1870,1,6,eval] board([5,2,8,6,4,7]). given clause #1769: (wt=16) 1872 [hyper,1871,1,4,eval] board([3,5,2,8,6,4,7]). given clause #1770: (wt=12) 1869 [hyper,1864,1,6,eval] board([5,8,6,4,7]). given clause #1771: (wt=14) 1873 [hyper,1869,1,2,eval] board([1,5,8,6,4,7]). given clause #1772: (wt=8) 1820 [hyper,1661,1,9,eval] board([8,4,7]). given clause #1773: (wt=10) 1876 [hyper,1820,1,2,eval] board([1,8,4,7]). given clause #1774: (wt=12) 1877 [hyper,1876,1,6,eval] board([5,1,8,4,7]). given clause #1775: (wt=10) 1875 [hyper,1820,1,4,eval] board([3,8,4,7]). given clause #1776: (wt=12) 1878 [hyper,1875,1,6,eval] board([5,3,8,4,7]). given clause #1777: (wt=10) 1874 [hyper,1820,1,6,eval] board([5,8,4,7]). given clause #1778: (wt=12) 1879 [hyper,1874,1,3,eval] board([2,5,8,4,7]). given clause #1779: (wt=14) 1880 [hyper,1879,1,7,eval] board([6,2,5,8,4,7]). given clause #1780: (wt=16) 1881 [hyper,1880,1,4,eval] board([3,6,2,5,8,4,7]). given clause #1781: (wt=6) 1660 [hyper,15,1,6,eval] board([5,7]). given clause #1782: (wt=8) 1885 [hyper,1660,1,2,eval] board([1,5,7]). given clause #1783: (wt=10) 1887 [hyper,1885,1,7,eval] board([6,1,5,7]). given clause #1784: (wt=12) 1888 [hyper,1887,1,5,eval] board([4,6,1,5,7]). given clause #1785: (wt=10) 1886 [hyper,1885,1,9,eval] board([8,1,5,7]). given clause #1786: (wt=12) 1890 [hyper,1886,1,5,eval] board([4,8,1,5,7]). given clause #1787: (wt=12) 1889 [hyper,1886,1,7,eval] board([6,8,1,5,7]). given clause #1788: (wt=14) 1891 [hyper,1889,1,4,eval] board([3,6,8,1,5,7]). given clause #1789: (wt=8) 1884 [hyper,1660,1,3,eval] board([2,5,7]). given clause #1790: (wt=10) 1893 [hyper,1884,1,7,eval] board([6,2,5,7]). given clause #1791: (wt=12) 1894 [hyper,1893,1,2,eval] board([1,6,2,5,7]). given clause #1792: (wt=14) 1895 [hyper,1894,1,4,eval] board([3,1,6,2,5,7]). given clause #1793: (wt=16) 1896 [hyper,1895,1,9,eval] board([8,3,1,6,2,5,7]). given clause #1794: (wt=10) 1892 [hyper,1884,1,9,eval] board([8,2,5,7]). given clause #1795: (wt=12) 1898 [hyper,1892,1,2,eval] board([1,8,2,5,7]). given clause #1796: (wt=14) 1900 [hyper,1898,1,4,eval] board([3,1,8,2,5,7]). given clause #1797: (wt=14) 1899 [hyper,1898,1,5,eval] board([4,1,8,2,5,7]). given clause #1798: (wt=12) 1897 [hyper,1892,1,7,eval] board([6,8,2,5,7]). given clause #1799: (wt=14) 1902 [hyper,1897,1,4,eval] board([3,6,8,2,5,7]). given clause #1800: (wt=14) 1901 [hyper,1897,1,5,eval] board([4,6,8,2,5,7]). given clause #1801: (wt=8) 1883 [hyper,1660,1,4,eval] board([3,5,7]). given clause #1802: (wt=10) 1905 [hyper,1883,1,2,eval] board([1,3,5,7]). given clause #1803: (wt=12) 1907 [hyper,1905,1,5,eval] board([4,1,3,5,7]). given clause #1804: (wt=14) 1908 [hyper,1907,1,9,eval] board([8,4,1,3,5,7]). given clause #1805: (wt=12) 1906 [hyper,1905,1,7,eval] board([6,1,3,5,7]). given clause #1806: (wt=14) 1910 [hyper,1906,1,5,eval] board([4,6,1,3,5,7]). given clause #1807: (wt=16) 1911 [hyper,1910,1,3,eval] board([2,4,6,1,3,5,7]). given clause #1808: (wt=14) 1909 [hyper,1906,1,9,eval] board([8,6,1,3,5,7]). given clause #1809: (wt=16) 1912 [hyper,1909,1,3,eval] board([2,8,6,1,3,5,7]). -------- PROOF -------- 1914 [binary,1913.1,11.1] $Ans([4,2,8,6,1,3,5,7]). ----> UNIT CONFLICT at 0.70 sec ----> 1914 [binary,1913.1,11.1] $Ans([4,2,8,6,1,3,5,7]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 15 [hyper,10,1,8,eval] board([7]). 1660 [hyper,15,1,6,eval] board([5,7]). 1883 [hyper,1660,1,4,eval] board([3,5,7]). 1905 [hyper,1883,1,2,eval] board([1,3,5,7]). 1906 [hyper,1905,1,7,eval] board([6,1,3,5,7]). 1909 [hyper,1906,1,9,eval] board([8,6,1,3,5,7]). 1912 [hyper,1909,1,3,eval] board([2,8,6,1,3,5,7]). 1913 [hyper,1912,1,5,eval] board([4,2,8,6,1,3,5,7]). 1914 [binary,1913.1,11.1] $Ans([4,2,8,6,1,3,5,7]). ------------ end of proof ------------- given clause #1810: (wt=18) 1913 [hyper,1912,1,5,eval] board([4,2,8,6,1,3,5,7]). given clause #1811: (wt=10) 1904 [hyper,1883,1,7,eval] board([6,3,5,7]). given clause #1812: (wt=12) 1915 [hyper,1904,1,5,eval] board([4,6,3,5,7]). given clause #1813: (wt=10) 1903 [hyper,1883,1,9,eval] board([8,3,5,7]). given clause #1814: (wt=12) 1917 [hyper,1903,1,5,eval] board([4,8,3,5,7]). given clause #1815: (wt=12) 1916 [hyper,1903,1,7,eval] board([6,8,3,5,7]). given clause #1816: (wt=14) 1918 [hyper,1916,1,5,eval] board([4,6,8,3,5,7]). given clause #1817: (wt=16) 1919 [hyper,1918,1,3,eval] board([2,4,6,8,3,5,7]). given clause #1818: (wt=8) 1882 [hyper,1660,1,9,eval] board([8,5,7]). given clause #1819: (wt=10) 1922 [hyper,1882,1,2,eval] board([1,8,5,7]). given clause #1820: (wt=12) 1923 [hyper,1922,1,5,eval] board([4,1,8,5,7]). given clause #1821: (wt=14) 1924 [hyper,1923,1,7,eval] board([6,4,1,8,5,7]). given clause #1822: (wt=16) 1925 [hyper,1924,1,4,eval] board([3,6,4,1,8,5,7]). given clause #1823: (wt=10) 1921 [hyper,1882,1,3,eval] board([2,8,5,7]). given clause #1824: (wt=12) 1926 [hyper,1921,1,5,eval] board([4,2,8,5,7]). given clause #1825: (wt=14) 1927 [hyper,1926,1,7,eval] board([6,4,2,8,5,7]). given clause #1826: (wt=16) 1928 [hyper,1927,1,4,eval] board([3,6,4,2,8,5,7]). given clause #1827: (wt=10) 1920 [hyper,1882,1,7,eval] board([6,8,5,7]). given clause #1828: (wt=12) 1930 [hyper,1920,1,2,eval] board([1,6,8,5,7]). given clause #1829: (wt=14) 1931 [hyper,1930,1,4,eval] board([3,1,6,8,5,7]). given clause #1830: (wt=12) 1929 [hyper,1920,1,5,eval] board([4,6,8,5,7]). given clause #1831: (wt=4) 14 [hyper,10,1,9,eval] board([8]). given clause #1832: (wt=6) 1937 [hyper,14,1,2,eval] board([1,8]). given clause #1833: (wt=8) 1941 [hyper,1937,1,4,eval] board([3,1,8]). given clause #1834: (wt=10) 1943 [hyper,1941,1,7,eval] board([6,3,1,8]). given clause #1835: (wt=12) 1944 [hyper,1943,1,3,eval] board([2,6,3,1,8]). given clause #1836: (wt=14) 1945 [hyper,1944,1,8,eval] board([7,2,6,3,1,8]). given clause #1837: (wt=16) 1946 [hyper,1945,1,6,eval] board([5,7,2,6,3,1,8]). given clause #1838: (wt=10) 1942 [hyper,1941,1,8,eval] board([7,3,1,8]). given clause #1839: (wt=12) 1947 [hyper,1942,1,3,eval] board([2,7,3,1,8]). given clause #1840: (wt=14) 1948 [hyper,1947,1,5,eval] board([4,2,7,3,1,8]). given clause #1841: (wt=8) 1940 [hyper,1937,1,5,eval] board([4,1,8]). given clause #1842: (wt=10) 1951 [hyper,1940,1,3,eval] board([2,4,1,8]). given clause #1843: (wt=12) 1953 [hyper,1951,1,6,eval] board([5,2,4,1,8]). given clause #1844: (wt=12) 1952 [hyper,1951,1,8,eval] board([7,2,4,1,8]). given clause #1845: (wt=10) 1950 [hyper,1940,1,7,eval] board([6,4,1,8]). given clause #1846: (wt=12) 1954 [hyper,1950,1,4,eval] board([3,6,4,1,8]). given clause #1847: (wt=10) 1949 [hyper,1940,1,8,eval] board([7,4,1,8]). given clause #1848: (wt=12) 1956 [hyper,1949,1,4,eval] board([3,7,4,1,8]). given clause #1849: (wt=14) 1957 [hyper,1956,1,7,eval] board([6,3,7,4,1,8]). given clause #1850: (wt=12) 1955 [hyper,1949,1,6,eval] board([5,7,4,1,8]). given clause #1851: (wt=14) 1958 [hyper,1955,1,3,eval] board([2,5,7,4,1,8]). given clause #1852: (wt=8) 1939 [hyper,1937,1,6,eval] board([5,1,8]). given clause #1853: (wt=10) 1960 [hyper,1939,1,3,eval] board([2,5,1,8]). given clause #1854: (wt=12) 1961 [hyper,1960,1,7,eval] board([6,2,5,1,8]). given clause #1855: (wt=10) 1959 [hyper,1939,1,8,eval] board([7,5,1,8]). given clause #1856: (wt=12) 1962 [hyper,1959,1,3,eval] board([2,7,5,1,8]). given clause #1857: (wt=14) 1964 [hyper,1962,1,5,eval] board([4,2,7,5,1,8]). given clause #1858: (wt=14) 1963 [hyper,1962,1,7,eval] board([6,2,7,5,1,8]). given clause #1859: (wt=16) 1965 [hyper,1963,1,4,eval] board([3,6,2,7,5,1,8]). given clause #1860: (wt=8) 1938 [hyper,1937,1,8,eval] board([7,1,8]). given clause #1861: (wt=10) 1967 [hyper,1938,1,3,eval] board([2,7,1,8]). given clause #1862: (wt=12) 1968 [hyper,1967,1,7,eval] board([6,2,7,1,8]). given clause #1863: (wt=10) 1966 [hyper,1938,1,5,eval] board([4,7,1,8]). given clause #1864: (wt=12) 1970 [hyper,1966,1,3,eval] board([2,4,7,1,8]). given clause #1865: (wt=12) 1969 [hyper,1966,1,7,eval] board([6,4,7,1,8]). given clause #1866: (wt=6) 1936 [hyper,14,1,3,eval] board([2,8]). given clause #1867: (wt=8) 1973 [hyper,1936,1,5,eval] board([4,2,8]). given clause #1868: (wt=10) 1976 [hyper,1973,1,2,eval] board([1,4,2,8]). given clause #1869: (wt=12) 1978 [hyper,1976,1,4,eval] board([3,1,4,2,8]). given clause #1870: (wt=14) 1979 [hyper,1978,1,6,eval] board([5,3,1,4,2,8]). given clause #1871: (wt=12) 1977 [hyper,1976,1,8,eval] board([7,1,4,2,8]). given clause #1872: (wt=14) 1980 [hyper,1977,1,6,eval] board([5,7,1,4,2,8]). given clause #1873: (wt=16) 1981 [hyper,1980,1,4,eval] board([3,5,7,1,4,2,8]). -------- PROOF -------- 1983 [binary,1982.1,11.1] $Ans([6,3,5,7,1,4,2,8]). ----> UNIT CONFLICT at 0.72 sec ----> 1983 [binary,1982.1,11.1] $Ans([6,3,5,7,1,4,2,8]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 14 [hyper,10,1,9,eval] board([8]). 1936 [hyper,14,1,3,eval] board([2,8]). 1973 [hyper,1936,1,5,eval] board([4,2,8]). 1976 [hyper,1973,1,2,eval] board([1,4,2,8]). 1977 [hyper,1976,1,8,eval] board([7,1,4,2,8]). 1980 [hyper,1977,1,6,eval] board([5,7,1,4,2,8]). 1981 [hyper,1980,1,4,eval] board([3,5,7,1,4,2,8]). 1982 [hyper,1981,1,7,eval] board([6,3,5,7,1,4,2,8]). 1983 [binary,1982.1,11.1] $Ans([6,3,5,7,1,4,2,8]). ------------ end of proof ------------- given clause #1874: (wt=18) 1982 [hyper,1981,1,7,eval] board([6,3,5,7,1,4,2,8]). given clause #1875: (wt=10) 1975 [hyper,1973,1,7,eval] board([6,4,2,8]). given clause #1876: (wt=12) 1985 [hyper,1975,1,2,eval] board([1,6,4,2,8]). given clause #1877: (wt=14) 1986 [hyper,1985,1,6,eval] board([5,1,6,4,2,8]). given clause #1878: (wt=12) 1984 [hyper,1975,1,4,eval] board([3,6,4,2,8]). given clause #1879: (wt=14) 1987 [hyper,1984,1,6,eval] board([5,3,6,4,2,8]). given clause #1880: (wt=10) 1974 [hyper,1973,1,8,eval] board([7,4,2,8]). given clause #1881: (wt=12) 1989 [hyper,1974,1,2,eval] board([1,7,4,2,8]). given clause #1882: (wt=12) 1988 [hyper,1974,1,4,eval] board([3,7,4,2,8]). given clause #1883: (wt=8) 1972 [hyper,1936,1,6,eval] board([5,2,8]). given clause #1884: (wt=10) 1992 [hyper,1972,1,2,eval] board([1,5,2,8]). given clause #1885: (wt=12) 1993 [hyper,1992,1,7,eval] board([6,1,5,2,8]). given clause #1886: (wt=14) 1994 [hyper,1993,1,5,eval] board([4,6,1,5,2,8]). given clause #1887: (wt=10) 1991 [hyper,1972,1,4,eval] board([3,5,2,8]). given clause #1888: (wt=12) 1996 [hyper,1991,1,2,eval] board([1,3,5,2,8]). given clause #1889: (wt=14) 1998 [hyper,1996,1,5,eval] board([4,1,3,5,2,8]). given clause #1890: (wt=14) 1997 [hyper,1996,1,8,eval] board([7,1,3,5,2,8]). given clause #1891: (wt=16) 1999 [hyper,1997,1,5,eval] board([4,7,1,3,5,2,8]). -------- PROOF -------- 2001 [binary,2000.1,11.1] $Ans([6,4,7,1,3,5,2,8]). ----> UNIT CONFLICT at 0.73 sec ----> 2001 [binary,2000.1,11.1] $Ans([6,4,7,1,3,5,2,8]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 14 [hyper,10,1,9,eval] board([8]). 1936 [hyper,14,1,3,eval] board([2,8]). 1972 [hyper,1936,1,6,eval] board([5,2,8]). 1991 [hyper,1972,1,4,eval] board([3,5,2,8]). 1996 [hyper,1991,1,2,eval] board([1,3,5,2,8]). 1997 [hyper,1996,1,8,eval] board([7,1,3,5,2,8]). 1999 [hyper,1997,1,5,eval] board([4,7,1,3,5,2,8]). 2000 [hyper,1999,1,7,eval] board([6,4,7,1,3,5,2,8]). 2001 [binary,2000.1,11.1] $Ans([6,4,7,1,3,5,2,8]). ------------ end of proof ------------- given clause #1892: (wt=18) 2000 [hyper,1999,1,7,eval] board([6,4,7,1,3,5,2,8]). given clause #1893: (wt=12) 1995 [hyper,1991,1,7,eval] board([6,3,5,2,8]). given clause #1894: (wt=14) 2002 [hyper,1995,1,5,eval] board([4,6,3,5,2,8]). given clause #1895: (wt=10) 1990 [hyper,1972,1,8,eval] board([7,5,2,8]). given clause #1896: (wt=12) 2003 [hyper,1990,1,2,eval] board([1,7,5,2,8]). given clause #1897: (wt=14) 2004 [hyper,2003,1,5,eval] board([4,1,7,5,2,8]). given clause #1898: (wt=16) 2005 [hyper,2004,1,7,eval] board([6,4,1,7,5,2,8]). given clause #1899: (wt=8) 1971 [hyper,1936,1,8,eval] board([7,2,8]). given clause #1900: (wt=10) 2007 [hyper,1971,1,2,eval] board([1,7,2,8]). given clause #1901: (wt=12) 2009 [hyper,2007,1,4,eval] board([3,1,7,2,8]). given clause #1902: (wt=14) 2010 [hyper,2009,1,6,eval] board([5,3,1,7,2,8]). given clause #1903: (wt=12) 2008 [hyper,2007,1,7,eval] board([6,1,7,2,8]). given clause #1904: (wt=10) 2006 [hyper,1971,1,4,eval] board([3,7,2,8]). given clause #1905: (wt=12) 2012 [hyper,2006,1,2,eval] board([1,3,7,2,8]). given clause #1906: (wt=12) 2011 [hyper,2006,1,7,eval] board([6,3,7,2,8]). given clause #1907: (wt=6) 1935 [hyper,14,1,4,eval] board([3,8]). given clause #1908: (wt=8) 2015 [hyper,1935,1,2,eval] board([1,3,8]). given clause #1909: (wt=10) 2018 [hyper,2015,1,5,eval] board([4,1,3,8]). given clause #1910: (wt=12) 2020 [hyper,2018,1,3,eval] board([2,4,1,3,8]). given clause #1911: (wt=14) 2021 [hyper,2020,1,6,eval] board([5,2,4,1,3,8]). given clause #1912: (wt=12) 2019 [hyper,2018,1,8,eval] board([7,4,1,3,8]). given clause #1913: (wt=14) 2022 [hyper,2019,1,6,eval] board([5,7,4,1,3,8]). given clause #1914: (wt=10) 2017 [hyper,2015,1,7,eval] board([6,1,3,8]). given clause #1915: (wt=12) 2023 [hyper,2017,1,3,eval] board([2,6,1,3,8]). given clause #1916: (wt=14) 2024 [hyper,2023,1,6,eval] board([5,2,6,1,3,8]). given clause #1917: (wt=16) 2025 [hyper,2024,1,8,eval] board([7,5,2,6,1,3,8]). -------- PROOF -------- 2027 [binary,2026.1,11.1] $Ans([4,7,5,2,6,1,3,8]). ----> UNIT CONFLICT at 0.74 sec ----> 2027 [binary,2026.1,11.1] $Ans([4,7,5,2,6,1,3,8]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 14 [hyper,10,1,9,eval] board([8]). 1935 [hyper,14,1,4,eval] board([3,8]). 2015 [hyper,1935,1,2,eval] board([1,3,8]). 2017 [hyper,2015,1,7,eval] board([6,1,3,8]). 2023 [hyper,2017,1,3,eval] board([2,6,1,3,8]). 2024 [hyper,2023,1,6,eval] board([5,2,6,1,3,8]). 2025 [hyper,2024,1,8,eval] board([7,5,2,6,1,3,8]). 2026 [hyper,2025,1,5,eval] board([4,7,5,2,6,1,3,8]). 2027 [binary,2026.1,11.1] $Ans([4,7,5,2,6,1,3,8]). ------------ end of proof ------------- given clause #1918: (wt=18) 2026 [hyper,2025,1,5,eval] board([4,7,5,2,6,1,3,8]). given clause #1919: (wt=10) 2016 [hyper,2015,1,8,eval] board([7,1,3,8]). given clause #1920: (wt=12) 2029 [hyper,2016,1,3,eval] board([2,7,1,3,8]). given clause #1921: (wt=14) 2030 [hyper,2029,1,7,eval] board([6,2,7,1,3,8]). given clause #1922: (wt=12) 2028 [hyper,2016,1,6,eval] board([5,7,1,3,8]). given clause #1923: (wt=14) 2031 [hyper,2028,1,3,eval] board([2,5,7,1,3,8]). given clause #1924: (wt=16) 2032 [hyper,2031,1,7,eval] board([6,2,5,7,1,3,8]). given clause #1925: (wt=8) 2014 [hyper,1935,1,6,eval] board([5,3,8]). given clause #1926: (wt=10) 2034 [hyper,2014,1,3,eval] board([2,5,3,8]). given clause #1927: (wt=10) 2033 [hyper,2014,1,8,eval] board([7,5,3,8]). given clause #1928: (wt=12) 2036 [hyper,2033,1,2,eval] board([1,7,5,3,8]). given clause #1929: (wt=14) 2038 [hyper,2036,1,5,eval] board([4,1,7,5,3,8]). given clause #1930: (wt=16) 2039 [hyper,2038,1,7,eval] board([6,4,1,7,5,3,8]). given clause #1931: (wt=14) 2037 [hyper,2036,1,7,eval] board([6,1,7,5,3,8]). given clause #1932: (wt=12) 2035 [hyper,2033,1,3,eval] board([2,7,5,3,8]). given clause #1933: (wt=14) 2041 [hyper,2035,1,5,eval] board([4,2,7,5,3,8]). given clause #1934: (wt=16) 2042 [hyper,2041,1,7,eval] board([6,4,2,7,5,3,8]). given clause #1935: (wt=14) 2040 [hyper,2035,1,7,eval] board([6,2,7,5,3,8]). given clause #1936: (wt=8) 2013 [hyper,1935,1,8,eval] board([7,3,8]). given clause #1937: (wt=10) 2044 [hyper,2013,1,3,eval] board([2,7,3,8]). given clause #1938: (wt=10) 2043 [hyper,2013,1,5,eval] board([4,7,3,8]). given clause #1939: (wt=12) 2046 [hyper,2043,1,2,eval] board([1,4,7,3,8]). given clause #1940: (wt=14) 2047 [hyper,2046,1,6,eval] board([5,1,4,7,3,8]). given clause #1941: (wt=12) 2045 [hyper,2043,1,3,eval] board([2,4,7,3,8]). given clause #1942: (wt=14) 2048 [hyper,2045,1,6,eval] board([5,2,4,7,3,8]). given clause #1943: (wt=6) 1934 [hyper,14,1,5,eval] board([4,8]). given clause #1944: (wt=8) 2051 [hyper,1934,1,2,eval] board([1,4,8]). given clause #1945: (wt=10) 2053 [hyper,2051,1,4,eval] board([3,1,4,8]). given clause #1946: (wt=12) 2055 [hyper,2053,1,6,eval] board([5,3,1,4,8]). given clause #1947: (wt=14) 2057 [hyper,2055,1,3,eval] board([2,5,3,1,4,8]). given clause #1948: (wt=14) 2056 [hyper,2055,1,8,eval] board([7,5,3,1,4,8]). given clause #1949: (wt=12) 2054 [hyper,2053,1,7,eval] board([6,3,1,4,8]). given clause #1950: (wt=14) 2058 [hyper,2054,1,3,eval] board([2,6,3,1,4,8]). given clause #1951: (wt=16) 2059 [hyper,2058,1,8,eval] board([7,2,6,3,1,4,8]). -------- PROOF -------- 2061 [binary,2060.1,11.1] $Ans([5,7,2,6,3,1,4,8]). ----> UNIT CONFLICT at 0.75 sec ----> 2061 [binary,2060.1,11.1] $Ans([5,7,2,6,3,1,4,8]). Length of proof is 8. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -board(B)| -pick(New_col)| -$TRUE(ok(B,1,New_col))|board([New_col|B]). 2 [] pick(1). 3 [] pick(2). 4 [] pick(3). 5 [] pick(4). 6 [] pick(5). 7 [] pick(6). 8 [] pick(7). 9 [] pick(8). 10 [] board([]). 11 [] -board([X1,X2,X3,X4,X5,X6,X7,X8])|$Ans([X1,X2,X3,X4,X5,X6,X7,X8]). 14 [hyper,10,1,9,eval] board([8]). 1934 [hyper,14,1,5,eval] board([4,8]). 2051 [hyper,1934,1,2,eval] board([1,4,8]). 2053 [hyper,2051,1,4,eval] board([3,1,4,8]). 2054 [hyper,2053,1,7,eval] board([6,3,1,4,8]). 2058 [hyper,2054,1,3,eval] board([2,6,3,1,4,8]). 2059 [hyper,2058,1,8,eval] board([7,2,6,3,1,4,8]). 2060 [hyper,2059,1,6,eval] board([5,7,2,6,3,1,4,8]). 2061 [binary,2060.1,11.1] $Ans([5,7,2,6,3,1,4,8]). ------------ end of proof ------------- given clause #1952: (wt=18) 2060 [hyper,2059,1,6,eval] board([5,7,2,6,3,1,4,8]). given clause #1953: (wt=10) 2052 [hyper,2051,1,8,eval] board([7,1,4,8]). given clause #1954: (wt=12) 2063 [hyper,2052,1,3,eval] board([2,7,1,4,8]). given clause #1955: (wt=14) 2064 [hyper,2063,1,7,eval] board([6,2,7,1,4,8]). given clause #1956: (wt=16) 2065 [hyper,2064,1,4,eval] board([3,6,2,7,1,4,8]). given clause #1957: (wt=12) 2062 [hyper,2052,1,6,eval] board([5,7,1,4,8]). given clause #1958: (wt=14) 2066 [hyper,2062,1,3,eval] board([2,5,7,1,4,8]). given clause #1959: (wt=16) 2067 [hyper,2066,1,7,eval] board([6,2,5,7,1,4,8]). given clause #1960: (wt=8) 2050 [hyper,1934,1,3,eval] board([2,4,8]). given clause #1961: (wt=10) 2068 [hyper,2050,1,8,eval] board([7,2,4,8]). given clause #1962: (wt=12) 2070 [hyper,2068,1,4,eval] board([3,7,2,4,8]). given clause #1963: (wt=14) 2072 [hyper,2070,1,2,eval] board([1,3,7,2,4,8]). given clause #1964: (wt=14) 2071 [hyper,2070,1,7,eval] board([6,3,7,2,4,8]). given clause #1965: (wt=12) 2069 [hyper,2068,1,6,eval] board([5,7,2,4,8]). given clause #1966: (wt=14) 2073 [hyper,2069,1,2,eval] board([1,5,7,2,4,8]). given clause #1967: (wt=8) 2049 [hyper,1934,1,8,eval] board([7,4,8]). given clause #1968: (wt=10) 2075 [hyper,2049,1,2,eval] board([1,7,4,8]). given clause #1969: (wt=12) 2077 [hyper,2075,1,4,eval] board([3,1,7,4,8]). given clause #1970: (wt=14) 2079 [hyper,2077,1,6,eval] board([5,3,1,7,4,8]). given clause #1971: (wt=14) 2078 [hyper,2077,1,7,eval] board([6,3,1,7,4,8]). given clause #1972: (wt=12) 2076 [hyper,2075,1,7,eval] board([6,1,7,4,8]). given clause #1973: (wt=14) 2080 [hyper,2076,1,3,eval] board([2,6,1,7,4,8]). given clause #1974: (wt=16) 2081 [hyper,2080,1,6,eval] board([5,2,6,1,7,4,8]). given clause #1975: (wt=10) 2074 [hyper,2049,1,4,eval] board([3,7,4,8]). given clause #1976: (wt=12) 2082 [hyper,2074,1,7,eval] board([6,3,7,4,8]). given clause #1977: (wt=14) 2083 [hyper,2082,1,3,eval] board([2,6,3,7,4,8]). given clause #1978: (wt=16) 2084 [hyper,2083,1,6,eval] board([5,2,6,3,7,4,8]). given clause #1979: (wt=6) 1933 [hyper,14,1,6,eval] board([5,8]). given clause #1980: (wt=8) 2088 [hyper,1933,1,2,eval] board([1,5,8]). given clause #1981: (wt=10) 2090 [hyper,2088,1,5,eval] board([4,1,5,8]). given clause #1982: (wt=12) 2092 [hyper,2090,1,7,eval] board([6,4,1,5,8]). given clause #1983: (wt=12) 2091 [hyper,2090,1,8,eval] board([7,4,1,5,8]). given clause #1984: (wt=10) 2089 [hyper,2088,1,7,eval] board([6,1,5,8]). given clause #1985: (wt=8) 2087 [hyper,1933,1,3,eval] board([2,5,8]). given clause #1986: (wt=10) 2094 [hyper,2087,1,5,eval] board([4,2,5,8]). given clause #1987: (wt=12) 2097 [hyper,2094,1,2,eval] board([1,4,2,5,8]). given clause #1988: (wt=14) 2098 [hyper,2097,1,8,eval] board([7,1,4,2,5,8]). given clause #1989: (wt=12) 2096 [hyper,2094,1,7,eval] board([6,4,2,5,8]). given clause #1990: (wt=12) 2095 [hyper,2094,1,8,eval] board([7,4,2,5,8]). given clause #1991: (wt=10) 2093 [hyper,2087,1,7,eval] board([6,2,5,8]). given clause #1992: (wt=12) 2100 [hyper,2093,1,2,eval] board([1,6,2,5,8]). given clause #1993: (wt=14) 2101 [hyper,2100,1,8,eval] board([7,1,6,2,5,8]). given clause #1994: (wt=16) 2102 [hyper,2101,1,5,eval] board([4,7,1,6,2,5,8]). given clause #1995: (wt=12) 2099 [hyper,2093,1,4,eval] board([3,6,2,5,8]). given clause #1996: (wt=14) 2103 [hyper,2099,1,8,eval] board([7,3,6,2,5,8]). given clause #1997: (wt=16) 2104 [hyper,2103,1,5,eval] board([4,7,3,6,2,5,8]). given clause #1998: (wt=8) 2086 [hyper,1933,1,4,eval] board([3,5,8]). given clause #1999: (wt=10) 2106 [hyper,2086,1,2,eval] board([1,3,5,8]). given clause #2000: (wt=12) 2108 [hyper,2106,1,7,eval] board([6,1,3,5,8]). given clause #2001: (wt=14) 2110 [hyper,2108,1,3,eval] board([2,6,1,3,5,8]). given clause #2002: (wt=14) 2109 [hyper,2108,1,5,eval] board([4,6,1,3,5,8]). given clause #2003: (wt=12) 2107 [hyper,2106,1,8,eval] board([7,1,3,5,8]). given clause #2004: (wt=14) 2112 [hyper,2107,1,3,eval] board([2,7,1,3,5,8]). given clause #2005: (wt=16) 2113 [hyper,2112,1,7,eval] board([6,2,7,1,3,5,8]). given clause #2006: (wt=14) 2111 [hyper,2107,1,5,eval] board([4,7,1,3,5,8]). given clause #2007: (wt=16) 2114 [hyper,2111,1,7,eval] board([6,4,7,1,3,5,8]). given clause #2008: (wt=10) 2105 [hyper,2086,1,7,eval] board([6,3,5,8]). given clause #2009: (wt=8) 2085 [hyper,1933,1,8,eval] board([7,5,8]). given clause #2010: (wt=10) 2117 [hyper,2085,1,2,eval] board([1,7,5,8]). given clause #2011: (wt=12) 2119 [hyper,2117,1,4,eval] board([3,1,7,5,8]). given clause #2012: (wt=14) 2120 [hyper,2119,1,7,eval] board([6,3,1,7,5,8]). given clause #2013: (wt=12) 2118 [hyper,2117,1,7,eval] board([6,1,7,5,8]). given clause #2014: (wt=14) 2121 [hyper,2118,1,3,eval] board([2,6,1,7,5,8]). given clause #2015: (wt=10) 2116 [hyper,2085,1,3,eval] board([2,7,5,8]). given clause #2016: (wt=12) 2122 [hyper,2116,1,7,eval] board([6,2,7,5,8]). given clause #2017: (wt=10) 2115 [hyper,2085,1,5,eval] board([4,7,5,8]). given clause #2018: (wt=12) 2124 [hyper,2115,1,2,eval] board([1,4,7,5,8]). given clause #2019: (wt=12) 2123 [hyper,2115,1,7,eval] board([6,4,7,5,8]). given clause #2020: (wt=6) 1932 [hyper,14,1,7,eval] board([6,8]). given clause #2021: (wt=8) 2128 [hyper,1932,1,2,eval] board([1,6,8]). given clause #2022: (wt=10) 2130 [hyper,2128,1,4,eval] board([3,1,6,8]). given clause #2023: (wt=12) 2132 [hyper,2130,1,6,eval] board([5,3,1,6,8]). given clause #2024: (wt=14) 2133 [hyper,2132,1,8,eval] board([7,5,3,1,6,8]). given clause #2025: (wt=16) 2134 [hyper,2133,1,5,eval] board([4,7,5,3,1,6,8]). given clause #2026: (wt=12) 2131 [hyper,2130,1,8,eval] board([7,3,1,6,8]). given clause #2027: (wt=10) 2129 [hyper,2128,1,8,eval] board([7,1,6,8]). given clause #2028: (wt=12) 2136 [hyper,2129,1,3,eval] board([2,7,1,6,8]). given clause #2029: (wt=12) 2135 [hyper,2129,1,6,eval] board([5,7,1,6,8]). given clause #2030: (wt=8) 2127 [hyper,1932,1,3,eval] board([2,6,8]). given clause #2031: (wt=10) 2137 [hyper,2127,1,8,eval] board([7,2,6,8]). given clause #2032: (wt=12) 2139 [hyper,2137,1,2,eval] board([1,7,2,6,8]). given clause #2033: (wt=14) 2140 [hyper,2139,1,5,eval] board([4,1,7,2,6,8]). given clause #2034: (wt=12) 2138 [hyper,2137,1,6,eval] board([5,7,2,6,8]). given clause #2035: (wt=14) 2141 [hyper,2138,1,2,eval] board([1,5,7,2,6,8]). given clause #2036: (wt=8) 2126 [hyper,1932,1,4,eval] board([3,6,8]). given clause #2037: (wt=10) 2143 [hyper,2126,1,2,eval] board([1,3,6,8]). given clause #2038: (wt=12) 2144 [hyper,2143,1,8,eval] board([7,1,3,6,8]). given clause #2039: (wt=14) 2146 [hyper,2144,1,5,eval] board([4,7,1,3,6,8]). given clause #2040: (wt=14) 2145 [hyper,2144,1,6,eval] board([5,7,1,3,6,8]). given clause #2041: (wt=10) 2142 [hyper,2126,1,8,eval] board([7,3,6,8]). given clause #2042: (wt=12) 2147 [hyper,2142,1,3,eval] board([2,7,3,6,8]). given clause #2043: (wt=14) 2148 [hyper,2147,1,5,eval] board([4,2,7,3,6,8]). given clause #2044: (wt=8) 2125 [hyper,1932,1,5,eval] board([4,6,8]). given clause #2045: (wt=10) 2151 [hyper,2125,1,2,eval] board([1,4,6,8]). given clause #2046: (wt=12) 2153 [hyper,2151,1,6,eval] board([5,1,4,6,8]). given clause #2047: (wt=12) 2152 [hyper,2151,1,8,eval] board([7,1,4,6,8]). given clause #2048: (wt=14) 2154 [hyper,2152,1,6,eval] board([5,7,1,4,6,8]). given clause #2049: (wt=16) 2155 [hyper,2154,1,4,eval] board([3,5,7,1,4,6,8]). given clause #2050: (wt=10) 2150 [hyper,2125,1,3,eval] board([2,4,6,8]). given clause #2051: (wt=12) 2157 [hyper,2150,1,6,eval] board([5,2,4,6,8]). given clause #2052: (wt=12) 2156 [hyper,2150,1,8,eval] board([7,2,4,6,8]). given clause #2053: (wt=14) 2158 [hyper,2156,1,6,eval] board([5,7,2,4,6,8]). given clause #2054: (wt=16) 2159 [hyper,2158,1,4,eval] board([3,5,7,2,4,6,8]). given clause #2055: (wt=10) 2149 [hyper,2125,1,8,eval] board([7,4,6,8]). given clause #2056: (wt=12) 2161 [hyper,2149,1,2,eval] board([1,7,4,6,8]). given clause #2057: (wt=12) 2160 [hyper,2149,1,6,eval] board([5,7,4,6,8]). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ -------------- statistics ------------- clauses given 2057 clauses generated 2056 hyper_res generated 2056 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 0 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 2056 new demodulators 0 empty clauses 92 clauses back demodulated 0 clauses back subsumed 0 usable size 2066 sos size 0 demodulators size 2 passive size 1 hot size 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.79 (0 hr, 0 min, 0 sec) system CPU time 0.03 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) That finishes the proof of the theorem. Process 8995 finished Mon Aug 2 15:31:17 2004 otter-3.3f/examples/program/index.html0100644000076400007640000000152207714267401017473 0ustar mccunemccune /home/mccune/otter-3.3/examples/program

/home/mccune/otter-3.3/examples/program

Examples of programming Otter.

otter < eval.in > eval.out

otter < jugs.in > jugs.out

otter < mission.in > mission.out

otter < queens.in > queens.out

otter < two_inv.in > two_inv.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/program/README0100644000076400007640000000003707313710603016346 0ustar mccunemccuneExamples of programming Otter. otter-3.3f/examples/program/eval.in0100644000076400007640000000470007705345457016766 0ustar mccunemccune% % This test file demonstrates the use of demodulation as an % equational programming language, including built-in ($) functions. % set(rewriter). % meta-flag: demodulate clauses in sos. clear(demod_history). set(prolog_style_variables). % The following use pre-declared infix functors make_evaluable(_-_, $DIFF(_,_)). make_evaluable(_<_, $LT(_,_)). make_evaluable(_*_, $PROD(_,_)). make_evaluable(_==_, $EQ(_,_)). make_evaluable(_&_, $AND(_,_)). % Declare infix functors for lexical comparison % and make them evaluable. op(700, xfx, @<). op(700, xfx, @<=). op(700, xfx, @>). op(700, xfx, @>=). make_evaluable(_@<_, $LLT(_,_)). make_evaluable(_@<=_, $LLE(_,_)). make_evaluable(_@>_, $LGT(_,_)). make_evaluable(_@>=_, $LGE(_,_)). lex([a,b,c,d,e,f,g]). % order for quicksort function below list(demodulators). factorial(N) = % factorial for nonnegative integers $IF(N==0, 1, N*factorial(N-1)). gcd(X,Y) = % gcd for nonnegative integers $IF(X==0, Y, $IF(Y==0, X, $IF(X X, [H|gt_list(X,T)], gt_list(X,T)). end_of_list. list(sos). p(factorial(8)). p(gcd(13004,5176)). p(member(d,[a,b,c])). p(subset([b,d],[a,b,c,d])). p(intersect([b,d],[a,b,c,d])). p(union([b,e],[a,b,c,d])). p(reverse([a,b,c,d,e,f,g])). p(quick_sort([c,a,b,f,c,c,e,d,b])). p($FSUM("1.4e-3", "3.222")). end_of_list. otter-3.3f/examples/Run_all0100755000076400007640000000066307714271140015351 0ustar mccunemccune#!/bin/csh if (-e Run_all.out) /bin/mv Run_all.out Run_all.out.$$ echo "Sending output to Run_all.out ..." foreach i (auto misc kalman wos ivy split fringe program) echo "Running $i examples ..." ./Run_group $i >> Run_all.out end echo "Done. The output files are in */*.out[0-9]*" echo "" grep "times as fast as" Run_all.out echo "" awk '/Running/ {p = $2} /There is a problem/ {print "Error running " p}' Run_all.out echo "" otter-3.3f/examples/Run_all.out0100644000076400007640000001456210103526654016156 0ustar mccunemccuneRunning auto/cn19.in ... Okay, it seems to have run correctly. Running auto/comm.in ... Okay, it seems to have run correctly. Running auto/ec_yq.in ... Okay, it seems to have run correctly. Running auto/group.in ... Okay, it seems to have run correctly. Running auto/lifsch.in ... Okay, it seems to have run correctly. Running auto/mv25.in ... Okay, it seems to have run correctly. Running auto/pigeon.in ... Okay, it seems to have run correctly. Running auto/ring_x2.in ... Okay, it seems to have run correctly. Running auto/robbins.in ... Okay, it seems to have run correctly. Running auto/salt.in ... Okay, it seems to have run correctly. Running auto/sam.in ... Okay, it seems to have run correctly. Running auto/steam.in ... Okay, it seems to have run correctly. Running auto/tba_gg.in ... Okay, it seems to have run correctly. Running auto/wang1.in ... Okay, it seems to have run correctly. Running auto/w_sk.in ... Okay, it seems to have run correctly. Running auto/x2_quant.in ... Okay, it seems to have run correctly. Running auto/z11.in ... Okay, it seems to have run correctly. timenew=1.27, timeold=0.73. The new (out24641) times are about 0.574803 times as fast as the old (out) times. The output files have been left in auto/*.out24641. Running misc/andrews.in ... Okay, it seems to have run correctly. Running misc/cn.in ... Okay, it seems to have run correctly. Running misc/dem_alu.in ... Okay, it seems to have run correctly. Running misc/ec.in ... Okay, it seems to have run correctly. Running misc/kb_bench.in ... Okay, it seems to have run correctly. Running misc/mv.in ... Okay, it seems to have run correctly. Running misc/sax1.in ... Okay, it seems to have run correctly. Running misc/sax2.in ... Okay, it seems to have run correctly. Running misc/stage1.in ... Okay, it seems to have run correctly. Running misc/stage2.in ... Okay, it seems to have run correctly. Running misc/str_bws.in ... Okay, it seems to have run correctly. timenew=1.11, timeold=0.68. The new (out24734) times are about 0.612613 times as fast as the old (out) times. The output files have been left in misc/*.out24734. Running kalman/ex_1.in ... Okay, it seems to have run correctly. Running kalman/ex_2.in ... Okay, it seems to have run correctly. Running kalman/ex_3.in ... Okay, it seems to have run correctly. Running kalman/ex_4.in ... Okay, it seems to have run correctly. Running kalman/i1.in ... Okay, it seems to have run correctly. Running kalman/i2.in ... Okay, it seems to have run correctly. Running kalman/i3.in ... Okay, it seems to have run correctly. Running kalman/i4.in ... Okay, it seems to have run correctly. timenew=1.34, timeold=0.8. The new (out24797) times are about 0.597015 times as fast as the old (out) times. The output files have been left in kalman/*.out24797. Running wos/cursory.in ... Okay, it seems to have run correctly. Running wos/grp_exp3.in ... Okay, it seems to have run correctly. Running wos/grp_exp4.in ... Okay, it seems to have run correctly. Running wos/manyval.in ... Okay, it seems to have run correctly. Running wos/rigorous.in ... Okay, it seems to have run correctly. Running wos/rob_occ.in ... Okay, it seems to have run correctly. Running wos/twoval.in ... Okay, it seems to have run correctly. timenew=37.93, timeold=25.28. The new (out24845) times are about 0.666491 times as fast as the old (out) times. The output files have been left in wos/*.out24845. Running ivy/cd-cn19.in ... Okay, it seems to have run correctly. Running ivy/comb-sk-w.in ... Okay, it seems to have run correctly. Running ivy/group-comm.in ... Okay, it seems to have run correctly. Running ivy/group-x2.in ... Okay, it seems to have run correctly. Running ivy/group-x2-refute.in ... Okay, it seems to have run correctly. Running ivy/lifsch.in ... Okay, it seems to have run correctly. Running ivy/p-and-not-p.in ... Okay, it seems to have run correctly. Running ivy/steam.in ... Okay, it seems to have run correctly. Running ivy/t1.in ... Okay, it seems to have run correctly. timenew=0.63, timeold=0.31. The new (out24894) times are about 0.492063 times as fast as the old (out) times. The output files have been left in ivy/*.out24894. Running split/GEO010-2.in ... Okay, it seems to have run correctly. Running split/GEO036-2.in ... Okay, it seems to have run correctly. Running split/group2.in ... Okay, it seems to have run correctly. Running split/GRP025-1.in ... Okay, it seems to have run correctly. Running split/noncomm-group.in ... Okay, it seems to have run correctly. Running split/pair.in ... Okay, it seems to have run correctly. Running split/pigeon5.in ... Okay, it seems to have run correctly. Running split/power.in ... Okay, it seems to have run correctly. Running split/wang3.in ... Okay, it seems to have run correctly. Running split/zebra2.in ... Okay, it seems to have run correctly. Running split/zebra4.in ... Okay, it seems to have run correctly. The output files have been left in split/*.out24947. Running fringe/bring.in ... Okay, it seems to have run correctly. Running fringe/ec_yql.in ... Okay, it seems to have run correctly. Running fringe/gl4.in ... Okay, it seems to have run correctly. Running fringe/gl8.in ... Okay, it seems to have run correctly. Running fringe/if.in ... Okay, it seems to have run correctly. Running fringe/lexical1.in ... Okay, it seems to have run correctly. Running fringe/lexical2.in ... Okay, it seems to have run correctly. Running fringe/lexical3.in ... Okay, it seems to have run correctly. Running fringe/luka5h.in ... Okay, it seems to have run correctly. Running fringe/mfl_13.in ... Okay, it seems to have run correctly. Running fringe/olsax_hints.in ... Okay, it seems to have run correctly. Running fringe/rob_ocd.in ... Okay, it seems to have run correctly. Running fringe/x3tricks.in ... Okay, it seems to have run correctly. timenew=3.09, timeold=2. The new (out25196) times are about 0.647249 times as fast as the old (out) times. The output files have been left in fringe/*.out25196. Running program/eval.in ... Okay, it seems to have run correctly. Running program/jugs.in ... Okay, it seems to have run correctly. Running program/mission.in ... Okay, it seems to have run correctly. Running program/queens.in ... Okay, it seems to have run correctly. Running program/two_inv.in ... Okay, it seems to have run correctly. timenew=100.15, timeold=68.05. The new (out25269) times are about 0.679481 times as fast as the old (out) times. The output files have been left in program/*.out25269. otter-3.3f/examples/kalman/0040755000076400007640000000000010103530360015254 5ustar mccunemccuneotter-3.3f/examples/kalman/i4.in0100644000076400007640000001224105501171472016130 0ustar mccunemccune% From John Kalman % % (4) The input file %i4 below, which includes several % illustrations of list processing using Otter. % % % A railroad DEF has two sidings DBA and FCA connected at A. % It is understood that D, E are respectively to the left of E, F; % D, B are respectively to the left of B, A; and A, C are respectively % to the left of C, F. % The portion of the rails at A which is common to the two sidings is % long enough to permit a single wagon, like P or Q, to run in or out of it, % but is too short to contain the whole of an engine, like R. Hence, if an % engine turns up one siding, such as DBA, it must come back the same way. % Initially, P is at B, Q is at C, and R is at E. The problem is to use % the engine R to interchange the wagons P and Q. % [W.W.R. Ball and H.S.M. Coxeter, Mathematical Recreations and Essays, % Univ. of Toronto Press, 12th ed., 1974, page 116.] set(hyper_res). assign(stats_level,1). assign(max_given,2000). list(usable). % H(u,xA,xB,xC,xD,xE,xF), where u is a position and xA, xB, ... are lists, % means that it is possible to attain the configuration where the engine is % at position u and xA, xB, ... list the vehicles (engine, wagons) at positions % A, B, ... . % In describing the allowable moves, we first consider the case where % (u,v) is a pair of adjacent positions each distinct from A, v is to % the right of u (thus (u,v) is (C,F) or (D,B) or (D,E) or (E,F)), and % the engine is at position u. % If (u,v) is such a pair of positions, K1(u,v,y,z,x1,x2,x3,x4) means % that it is possible to attain the configuration where y and z list the % vehicles at positions u and v, and x1, x2, x3, x4 list the vehicles at % the remaining four positions. % The following clauses transform H-representations of attainable % configurations to K1-representations: -H(C,xA,xB,xC,xD,xE,xF) | K1(C,F,xC,xF,xA,xB,xD,xE). -H(D,xA,xB,xC,xD,xE,xF) | K1(D,B,xD,xB,xA,xC,xE,xF). -H(D,xA,xB,xC,xD,xE,xF) | K1(D,E,xD,xE,xA,xB,xC,xF). -H(E,xA,xB,xC,xD,xE,xF) | K1(E,F,xE,xF,xA,xB,xC,xD). % Given a pair of adjacent positions (u,v) as above and an attainable % configuration K1(u,v, ... ), the next three clauses describe all % allowable moves in which the engine goes from position u to position v. % In these clauses, K2(u,v,y,z,x1,x2,x3,x4) means that, after the move, % y and z are the lists of vehicles at position u and v; u, v, x1, x2, x3, x4 % are as before the move. % Move whole list at position u to position v (if [R] or [R,y0] or % [R,y0,y00] was the list at position u, this is the only allowable % move that takes R to position v): -K1(u,v,y,z,x1,x2,x3,x4) | K2(u,v,[],app(y,z),x1,x2,x3,x4). % For [y0|y1] at position u, where R is a member of y1, move y1 % to position v (if [y0,R] or [y0,R,y00] was the list at position u, % this is the only remaining allowable move that takes R to position v): -K1(u,v,[y0|y1],z,x1,x2,x3,x4) | -$TRUE(member(R,y1)) | K2(u,v,[y0],app(y1,z),x1,x2,x3,x4). % For [y0,y00,R] at position u, move R to position v: -K1(u,v,[y0,y00,R],[],x1,x2,x3,x4) | K2(u,v,[y0,y00],[R],x1,x2,x3,x4). % The following clauses transform K2-representations of attainable % configurations to H-representations: -K2(C,F,xC,xF,xA,xB,xD,xE) | H(F,xA,xB,xC,xD,xE,xF). -K2(D,B,xD,xB,xA,xC,xE,xF) | H(B,xA,xB,xC,xD,xE,xF). -K2(D,E,xD,xE,xA,xB,xC,xF) | H(E,xA,xB,xC,xD,xE,xF). -K2(E,F,xE,xF,xA,xB,xC,xD) | H(F,xA,xB,xC,xD,xE,xF). % The case where (u,v) is a pair of adjacent positions each distinct % from A, v is to the left of u (thus (u,v) is (B,D) or (E,D) or (F,C) or % (F,E)), and the engine is at position u, may be reduced to the previous case % with the help of the 'reverse' function. % Clauses to transform H-representations to K1-representations: -H(B,xA,xB,xC,xD,xE,xF) | K1(B,D,rev(xB),rev(xD),xA,xC,xE,xF). -H(E,xA,xB,xC,xD,xE,xF) | K1(E,D,rev(xE),rev(xD),xA,xB,xC,xF). -H(F,xA,xB,xC,xD,xE,xF) | K1(F,C,rev(xF),rev(xC),xA,xB,xD,xE). -H(F,xA,xB,xC,xD,xE,xF) | K1(F,E,rev(xF),rev(xE),xA,xB,xC,xD). % Clauses to transform K2-representations to H-representations: -K2(B,D,xB,xD,xA,xC,xE,xF) | H(D,xA,rev(xB),xC,rev(xD),xE,xF). -K2(E,D,xE,xD,xA,xB,xC,xF) | H(D,xA,xB,xC,rev(xD),rev(xE),xF). -K2(F,C,xF,xC,xA,xB,xD,xE) | H(C,xA,xB,rev(xC),xD,xE,rev(xF)). -K2(F,E,xF,xE,xA,xB,xC,xD) | H(E,xA,xB,xC,xD,rev(xE),rev(xF)). % Allowable moves between the position B (containing R) and A. -H(B,[],[R,u],xC,xD,xE,xF) | H(B,[u],[R],xC,xD,xE,xF). -H(B,[],[R,u,v],xC,xD,xE,xF) | H(B,[v],[R,u],xC,xD,xE,xF). -H(B,[],[u,R,v],xC,xD,xE,xF) | H(B,[v],[u,R],xC,xD,xE,xF). -H(B,[u],xB,xC,xD,xE,xF) | H(B,[],app(xB,[u]),xC,xD,xE,xF). % Allowable moves between the position C (containing R) and A. -H(C,[],xB,[y0|y1],xD,xE,xF) | -$TRUE(member(R,y1)) | H(C,[y0],xB,y1,xD,xE,xF). -H(C,[y0],xB,y1,xD,xE,xF) | H(C,[],xB,[y0|y1],xD,xE,xF). end_of_list. list(sos). H(E,[],[P],[Q],[],[R],[]). end_of_list. list(passive). -H(E,[],[Q],[P],[],[R],[]). end_of_list. list(demodulators). (member(x,[]) = $F). (member(x,[u|v]) = $IF($ID(x,u),$T,member(x,v))). (rev(x) = rev2(x,[])). (rev2([],x) = x). (rev2([y1|y2],z) = rev2(y2,[y1|z])). (app([u|v],y) = [u|app(v,y)]). (app([],y) = y). end_of_list. otter-3.3f/examples/kalman/ex_1.out0100664000076400007640000001406410103522156016651 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:37 2004 The command was "../../bin/otter". The process ID is 8439. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). set(sos_queue). assign(max_mem,5000). assign(stats_level,1). list(usable). 0 [] x=x. 0 [] x+y=y+x. 0 [] x*y=y*x. 0 [] (x+y)+z=x+y+z. 0 [] (x*y)*z=x*y*z. 0 [] x+x*y=x. 0 [] x* (x+y)=x. end_of_list. list(sos). 0 [] x+y*z= (x+y)* (x+z). 0 [] a* (b+c)!=a*b+a*c. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=7): 2 [] x+y=y+x. ** KEPT (pick-wt=7): 3 [] x*y=y*x. ** KEPT (pick-wt=11): 4 [] (x+y)+z=x+y+z. ---> New Demodulator: 5 [new_demod,4] (x+y)+z=x+y+z. ** KEPT (pick-wt=11): 6 [] (x*y)*z=x*y*z. ---> New Demodulator: 7 [new_demod,6] (x*y)*z=x*y*z. ** KEPT (pick-wt=7): 8 [] x+x*y=x. ---> New Demodulator: 9 [new_demod,8] x+x*y=x. ** KEPT (pick-wt=7): 10 [] x* (x+y)=x. ---> New Demodulator: 11 [new_demod,10] x* (x+y)=x. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x+y=y+x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x*y=y*x. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. ------------> process sos: ** KEPT (pick-wt=13): 12 [] x+y*z= (x+y)* (x+z). ---> New Demodulator: 13 [new_demod,12] x+y*z= (x+y)* (x+z). ** KEPT (pick-wt=17): 15 [copy,14,demod,13,flip.1] (a*b+a)* (a*b+c)!=a* (b+c). >>>> Starting back demodulation with 13. >> back demodulating 8 with 13. >>>> Starting back demodulation with 17. ======= end of input processing ======= =========== start of search =========== Starting on level 1, last kept clause of level 0 is 17. Starting on level 1, last kept clause of level 0 is 17. given clause #1: (wt=13) 12 [] x+y*z= (x+y)* (x+z). given clause #2: (wt=17) 15 [copy,14,demod,13,flip.1] (a*b+a)* (a*b+c)!=a* (b+c). given clause #3: (wt=9) 16 [back_demod,8,demod,13] (x+x)* (x+y)=x. Starting on level 2, last kept clause of level 1 is 44. Starting on level 2, last kept clause of level 1 is 44. given clause #4: (wt=13) 18 [para_into,12.1.1.2,10.1.1,flip.1] (x+y)* (x+y+z)=x+y. given clause #5: (wt=13) 20 [para_into,12.1.1,2.1.1] x*y+z= (z+x)* (z+y). given clause #6: (wt=13) 21 [copy,20,flip.1] (x+y)* (x+z)=y*z+x. given clause #7: (wt=17) 24 [para_from,12.1.1,4.1.1.1] (x+y)* (x+z)+u=x+y*z+u. given clause #8: (wt=17) 26 [para_into,15.1.1.1.1,3.1.1] (b*a+a)* (a*b+c)!=a* (b+c). given clause #9: (wt=13) 27 [para_into,15.1.1.1,2.1.1,demod,13,17] a* (a*b+c)!=a* (b+c). given clause #10: (wt=17) 28 [para_into,15.1.1.2.1,3.1.1] (a*b+a)* (b*a+c)!=a* (b+c). given clause #11: (wt=19) 29 [para_into,15.1.1.2,2.1.1,demod,13] (a*b+a)* (c+a)* (c+b)!=a* (b+c). given clause #12: (wt=17) 30 [para_into,15.1.1,3.1.1] (a*b+c)* (a*b+a)!=a* (b+c). given clause #13: (wt=21) 31 [para_into,16.1.1.1,12.1.1,demod,7] (x*y+x)* (x*y+y)* (x*y+z)=x*y. given clause #14: (wt=17) 33 [para_into,16.1.1.1,4.1.1,demod,5] (x+y+x+y)* (x+y+z)=x+y. Starting on level 3, last kept clause of level 2 is 209. Starting on level 3, last kept clause of level 2 is 209. given clause #15: (wt=23) 45 [para_into,18.1.1.1,12.1.1,demod,7,13] (x+y)* (x+z)* (x+y*z+u)= (x+y)* (x+z). given clause #16: (wt=19) 47 [para_into,18.1.1.1,4.1.1,demod,5,5] (x+y+z)* (x+y+z+u)=x+y+z. given clause #17: (wt=13) 49 [para_into,18.1.1.1,2.1.1] (x+y)* (y+x+z)=y+x. given clause #18: (wt=13) 53 [para_into,18.1.1.2.2,2.1.1] (x+y)* (x+z+y)=x+y. given clause #19: (wt=13) 55 [para_into,18.1.1.2,2.1.1,demod,5] (x+y)* (y+z+x)=x+y. given clause #20: (wt=5) 57 [para_into,18.1.1,16.1.1,flip.1] x+x=x. given clause #21: (wt=13) 59 [para_into,18.1.1,3.1.1] (x+y+z)* (x+y)=x+y. given clause #22: (wt=11) 61 [back_demod,43,demod,58] x* (x+y)*z=x*z. -------- PROOF -------- ----> UNIT CONFLICT at 0.03 sec ----> 399 [binary,397.1,376.1] $F. Length of proof is 13. Level of proof is 4. ---------------- PROOF ---------------- 2 [] x+y=y+x. 6 [] (x*y)*z=x*y*z. 8 [] x+x*y=x. 11,10 [] x* (x+y)=x. 13,12 [] x+y*z= (x+y)* (x+z). 14 [] a* (b+c)!=a*b+a*c. 15 [copy,14,demod,13,flip.1] (a*b+a)* (a*b+c)!=a* (b+c). 16 [back_demod,8,demod,13] (x+x)* (x+y)=x. 18 [para_into,12.1.1.2,10.1.1,flip.1] (x+y)* (x+y+z)=x+y. 20 [para_into,12.1.1,2.1.1] x*y+z= (z+x)* (z+y). 21 [copy,20,flip.1] (x+y)* (x+z)=y*z+x. 29 [para_into,15.1.1.2,2.1.1,demod,13] (a*b+a)* (c+a)* (c+b)!=a* (b+c). 43 [para_from,16.1.1,6.1.1.1,flip.1] (x+x)* (x+y)*z=x*z. 58,57 [para_into,18.1.1,16.1.1,flip.1] x+x=x. 61 [back_demod,43,demod,58] x* (x+y)*z=x*z. 129 [para_into,29.1.1.2.2,2.1.1] (a*b+a)* (c+a)* (b+c)!=a* (b+c). 357,356 [para_from,57.1.1,21.1.1.1,demod,11,flip.1] x*y+x=x. 376 [back_demod,129,demod,357] a* (c+a)* (b+c)!=a* (b+c). 397 [para_into,61.1.1.2.1,2.1.1] x* (y+x)*z=x*z. 399 [binary,397.1,376.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 22 clauses generated 476 clauses kept 231 clauses forward subsumed 363 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) That finishes the proof of the theorem. Process 8439 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/i1.in0100644000076400007640000000107205501171471016124 0ustar mccunemccune% From John Kalman: % % (1) The input file %i1 below. This is Example 4.27 on page 83 % of my latest notes. It illustrates that looping is possible when % for_sub is clear, and would be possible if backward subsumption were done % before forward subsumption. set(hyper_res). clear(for_sub). % switch off forward subsumption set(print_lists_at_end). assign(max_given,15). % stop after 15 given clauses assign(stats_level,1). % changed from 0 to 1 by McCune list(usable). -P(x) | P(x). end_of_list. list(sos). P(a). end_of_list. otter-3.3f/examples/kalman/ex_4.in0100644000076400007640000000122306011405561016445 0ustar mccunemccune% 4. A group where all commutators lie in the center satisfies the % equation h(x,y*z) = h(x,y)*h(x,z). This example illustrates the % lex command and the pick_given_ratio parameter. % % Contributed by John Kalman (kalman@math.auckland.ac.nz) set(knuth_bendix). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). op(350,xf,^). assign(pick_given_ratio,8). assign(stats_level,1). lex([a,b,c,e,_^ ,h(_,_),_*_]). list(usable). x=x. (x*y)*z=x*y*z. e*x=x. x^ *x=e. end_of_list. list(sos). h(x,y)= x*y*x^ *y^. h(x,y)*z = z*h(x,y). h(a,b*c)!=h(a,b)*h(a,c). end_of_list. otter-3.3f/examples/kalman/ex_3.out0100664000076400007640000004066110103522156016655 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8449. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(pick_given_ratio,10). assign(max_proofs,2). assign(stats_level,1). list(usable). 0 [] x=x. 0 [] x+y=y+x. 0 [] x*y=y*x. 0 [] (x+y)+z=x+y+z. 0 [] (x*y)*z=x*y*z. 0 [] x+x*y=x. 0 [] x* (x+y)=x. end_of_list. list(sos). 0 [] x*y+y*z+z*x= (x+y)* (y+z)* (z+x). 0 [] a+b*c!= (a+b)* (a+c). 0 [] d* (e+f)!=d*e+d*f. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=7): 2 [] x+y=y+x. ** KEPT (pick-wt=7): 3 [] x*y=y*x. ** KEPT (pick-wt=11): 4 [] (x+y)+z=x+y+z. ---> New Demodulator: 5 [new_demod,4] (x+y)+z=x+y+z. ** KEPT (pick-wt=11): 6 [] (x*y)*z=x*y*z. ---> New Demodulator: 7 [new_demod,6] (x*y)*z=x*y*z. ** KEPT (pick-wt=7): 8 [] x+x*y=x. ---> New Demodulator: 9 [new_demod,8] x+x*y=x. ** KEPT (pick-wt=7): 10 [] x* (x+y)=x. ---> New Demodulator: 11 [new_demod,10] x* (x+y)=x. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x+y=y+x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x*y=y*x. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. ------------> process sos: ** KEPT (pick-wt=23): 12 [] x*y+y*z+z*x= (x+y)* (y+z)* (z+x). ---> New Demodulator: 13 [new_demod,12] x*y+y*z+z*x= (x+y)* (y+z)* (z+x). ** KEPT (pick-wt=13): 14 [] a+b*c!= (a+b)* (a+c). ** KEPT (pick-wt=13): 16 [copy,15,flip.1] d*e+d*f!=d* (e+f). >>>> Starting back demodulation with 13. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=23) 12 [] x*y+y*z+z*x= (x+y)* (y+z)* (z+x). given clause #2: (wt=13) 14 [] a+b*c!= (a+b)* (a+c). given clause #3: (wt=13) 16 [copy,15,flip.1] d*e+d*f!=d* (e+f). given clause #4: (wt=13) 43 [para_into,14.1.1.2,3.1.1] a+c*b!= (a+b)* (a+c). given clause #5: (wt=13) 44 [para_into,14.1.1,2.1.1] b*c+a!= (a+b)* (a+c). given clause #6: (wt=13) 45 [para_into,16.1.1.1,3.1.1] e*d+d*f!=d* (e+f). given clause #7: (wt=13) 46 [para_into,16.1.1.2,3.1.1] d*e+f*d!=d* (e+f). given clause #8: (wt=13) 47 [para_into,16.1.1,2.1.1] d*f+d*e!=d* (e+f). given clause #9: (wt=13) 48 [para_into,43.1.1,2.1.1] c*b+a!= (a+b)* (a+c). given clause #10: (wt=13) 49 [para_into,45.1.1.2,3.1.1] e*d+f*d!=d* (e+f). given clause #11: (wt=13) 50 [para_into,45.1.1,2.1.1] d*f+e*d!=d* (e+f). given clause #12: (wt=27) 17 [para_into,12.1.1.1,10.1.1,demod,5] x+ (x+y)*z+z*x= (x+x+y)* (x+y+z)* (z+x). given clause #13: (wt=13) 51 [para_into,46.1.1,2.1.1] f*d+d*e!=d* (e+f). given clause #14: (wt=13) 52 [para_into,49.1.1,2.1.1] f*d+e*d!=d* (e+f). given clause #15: (wt=19) 39 [para_from,12.1.1,10.1.1.2,demod,7] x*y* (x+y)* (y+z)* (z+x)=x*y. given clause #16: (wt=19) 77 [para_from,17.1.1,10.1.1.2] x* (x+x+y)* (x+y+z)* (z+x)=x. given clause #17: (wt=5) 188 [para_from,77.1.1,8.1.1.2] x+x=x. given clause #18: (wt=5) 217 [para_from,188.1.1,10.1.1.2] x*x=x. given clause #19: (wt=9) 219 [para_from,188.1.1,4.1.1.1,flip.1] x+x+y=x+y. given clause #20: (wt=9) 321 [para_from,217.1.1,6.1.1.1,flip.1] x*x*y=x*y. given clause #21: (wt=9) 349 [para_into,219.1.1.2,2.1.1] x+y+x=x+y. given clause #22: (wt=9) 379 [para_into,321.1.1.2,3.1.1] x*y*x=x*y. given clause #23: (wt=31) 19 [para_into,12.1.1.1,6.1.1] x*y*z+z*u+u*x*y= (x*y+z)* (z+u)* (u+x*y). given clause #24: (wt=11) 319 [para_from,217.1.1,12.1.1.2.1,demod,9,189,11] x*y+y= (x+y)*y. given clause #25: (wt=11) 371 [back_demod,199,demod,350,350,322,322] (x+y)* (y+x)=x+y. given clause #26: (wt=7) 501 [para_into,371.1.1.1,8.1.1,demod,480,380,9] x* (y+x)=x. given clause #27: (wt=7) 539 [para_into,501.1.1,3.1.1] (x+y)*y=y. given clause #28: (wt=7) 541 [back_demod,529,demod,540,480,540,flip.1] (x+y)*x=x. given clause #29: (wt=7) 547 [back_demod,505,demod,540,542,flip.1] x+y*x=x. given clause #30: (wt=7) 555 [back_demod,479,demod,540] x*y+x=x. given clause #31: (wt=7) 569 [back_demod,319,demod,540] x*y+y=y. given clause #32: (wt=9) 535 [para_into,501.1.1.2,4.1.1] x* (y+z+x)=x. given clause #33: (wt=9) 561 [back_demod,441,demod,540] x*y*z+z=z. given clause #34: (wt=23) 21 [para_into,12.1.1.1,3.1.1] x*y+x*z+z*y= (y+x)* (x+z)* (z+y). given clause #35: (wt=9) 663 [back_demod,622,demod,657] x* (y+x+z)=x. given clause #36: (wt=9) 675 [para_into,539.1.1.1,4.1.1] (x+y+z)*z=z. given clause #37: (wt=9) 751 [para_into,547.1.1.2,6.1.1] x+y*z*x=x. given clause #38: (wt=9) 811 [para_into,561.1.1.1.2,3.1.1] x*y*z+y=y. given clause #39: (wt=9) 961 [para_into,663.1.1,3.1.1] (x+y+z)*y=y. given clause #40: (wt=9) 1032 [para_into,751.1.1.2.2,3.1.1] x+y*x*z=x. given clause #41: (wt=11) 549 [back_demod,499,demod,540,flip.1] x*y+y+z=y+z. given clause #42: (wt=11) 612 [para_from,501.1.1,6.1.1.1,flip.1] x* (y+x)*z=x*z. given clause #43: (wt=11) 656 [back_demod,99,demod,613,613] x*y* (z+x)=x*y. given clause #44: (wt=11) 693 [para_from,539.1.1,6.1.1.1,flip.1] (x+y)*y*z=y*z. given clause #45: (wt=31) 24 [para_into,12.1.1.2.1,6.1.1] x*y*z+y*z*u+u*x= (x+y*z)* (y*z+u)* (u+x). given clause #46: (wt=11) 742 [para_from,541.1.1,6.1.1.1,flip.1] (x+y)*x*z=x*z. given clause #47: (wt=11) 755 [para_from,547.1.1,4.1.1.1,flip.1] x+y*x+z=x+z. -------- PROOF -------- ----> UNIT CONFLICT at 0.17 sec ----> 1493 [binary,1491.1,43.1] $F. Length of proof is 55. Level of proof is 14. ---------------- PROOF ---------------- 2 [] x+y=y+x. 3 [] x*y=y*x. 5,4 [] (x+y)+z=x+y+z. 6 [] (x*y)*z=x*y*z. 9,8 [] x+x*y=x. 11,10 [] x* (x+y)=x. 12 [] x*y+y*z+z*x= (x+y)* (y+z)* (z+x). 14 [] a+b*c!= (a+b)* (a+c). 17 [para_into,12.1.1.1,10.1.1,demod,5] x+ (x+y)*z+z*x= (x+x+y)* (x+y+z)* (z+x). 21 [para_into,12.1.1.1,3.1.1] x*y+x*z+z*y= (y+x)* (x+z)* (z+y). 29,28 [para_into,12.1.1.2.2,10.1.1,demod,5] (x+y)*z+z*x+x= (x+y+z)* (z+x)* (x+x+y). 43 [para_into,14.1.1.2,3.1.1] a+c*b!= (a+b)* (a+c). 60 [para_into,17.1.1.2.1.1,2.1.1] x+ (y+x)*z+z*x= (x+x+y)* (x+y+z)* (z+x). 62 [para_into,17.1.1.2.1,10.1.1,demod,5,5,5,5,5,5] x+x+y+ (x+y+z)*x= (x+x+y)* (x+y+x+y+z)* (x+y+z+x). 71 [para_into,17.1.1.2,2.1.1] x+y*x+ (x+z)*y= (x+x+z)* (x+z+y)* (y+x). 72 [para_into,17.1.1,2.1.1,demod,5,29] (x+y+z)* (z+x)* (x+x+y)= (x+x+y)* (x+y+z)* (z+x). 74 [copy,62,flip.1] (x+x+y)* (x+y+x+y+z)* (x+y+z+x)=x+x+y+ (x+y+z)*x. 75 [copy,71,flip.1] (x+x+y)* (x+y+z)* (z+x)=x+z*x+ (x+y)*z. 76 [copy,72,flip.1] (x+x+y)* (x+y+z)* (z+x)= (x+y+z)* (z+x)* (x+x+y). 77 [para_from,17.1.1,10.1.1.2] x* (x+x+y)* (x+y+z)* (z+x)=x. 189,188 [para_from,77.1.1,8.1.1.2] x+x=x. 198,197 [para_into,188.1.1,4.1.1] x+y+x+y=x+y. 199 [para_from,188.1.1,77.1.1.2.2.1,demod,5,5,198] (x+y)* (x+y+x)* (x+y)* (y+x+y)=x+y. 218,217 [para_from,188.1.1,10.1.1.2] x*x=x. 220,219 [para_from,188.1.1,4.1.1.1,flip.1] x+x+y=x+y. 292,291 [back_demod,76,demod,220,220,flip.1] (x+y+z)* (z+x)* (x+y)= (x+y)* (x+y+z)* (z+x). 293 [back_demod,75,demod,220] (x+y)* (x+y+z)* (z+x)=x+z*x+ (x+y)*z. 294 [back_demod,74,demod,220,220] (x+y)* (x+y+x+y+z)* (x+y+z+x)=x+y+ (x+y+z)*x. 305 [back_demod,60,demod,220] x+ (y+x)*z+z*x= (x+y)* (x+y+z)* (z+x). 310 [back_demod,28,demod,220,292] (x+y)*z+z*x+x= (x+y)* (x+y+z)* (z+x). 317 [para_from,217.1.1,12.1.1.2.2,demod,189] x*y+y*x+x= (x+y)* (y+x)*x. 320,319 [para_from,217.1.1,12.1.1.2.1,demod,9,189,11] x*y+y= (x+y)*y. 322,321 [para_from,217.1.1,6.1.1.1,flip.1] x*x*y=x*y. 323 [back_demod,317,demod,320] x*y+ (y+x)*x= (x+y)* (y+x)*x. 325 [back_demod,310,demod,320] (x+y)*z+ (z+x)*x= (x+y)* (x+y+z)* (z+x). 348,347 [para_into,219.1.1.2,4.1.1,demod,5,5] x+y+x+y+z=x+y+z. 350,349 [para_into,219.1.1.2,2.1.1] x+y+x=x+y. 358 [back_demod,294,demod,348] (x+y)* (x+y+z)* (x+y+z+x)=x+y+ (x+y+z)*x. 371 [back_demod,199,demod,350,350,322,322] (x+y)* (y+x)=x+y. 380,379 [para_into,321.1.1.2,3.1.1] x*y*x=x*y. 392,391 [para_into,349.1.1.2,4.1.1] x+y+z+x=x+y+z. 393 [back_demod,358,demod,392,218,flip.1] x+y+ (x+y+z)*x= (x+y)* (x+y+z). 480,479 [para_into,319.1.1.1,3.1.1] x*y+x= (y+x)*x. 501 [para_into,371.1.1.1,8.1.1,demod,480,380,9] x* (y+x)=x. 505 [para_into,371.1.1.2,319.1.1] (x+y*x)* (y+x)*x=x+y*x. 524,523 [para_from,371.1.1,6.1.1.1,flip.1] (x+y)* (y+x)*z= (x+y)*z. 529 [back_demod,323,demod,524] x*y+ (y+x)*x= (x+y)*x. 540,539 [para_into,501.1.1,3.1.1] (x+y)*y=y. 542,541 [back_demod,529,demod,540,480,540,flip.1] (x+y)*x=x. 547 [back_demod,505,demod,540,542,flip.1] x+y*x=x. 568,567 [back_demod,325,demod,540] (x+y)*z+x= (x+y)* (x+y+z)* (z+x). 578,577 [back_demod,393,demod,542,350,flip.1] (x+y)* (x+y+z)=x+y. 694,693 [para_from,539.1.1,6.1.1.1,flip.1] (x+y)*y*z=y*z. 751 [para_into,547.1.1.2,6.1.1] x+y*z*x=x. 756,755 [para_from,547.1.1,4.1.1.1,flip.1] x+y*x+z=x+z. 758 [back_demod,293,demod,756] (x+y)* (x+y+z)* (z+x)=x+ (x+y)*z. 838,837 [para_into,21.1.1.2.1,541.1.1,demod,9,568,5,350,694] (x+y)* (x+y+z)* (z+x)= (x+y)* (x+z). 875,874 [back_demod,758,demod,838,flip.1] x+ (x+y)*z= (x+y)* (x+z). 890 [back_demod,305,demod,838] x+ (y+x)*z+z*x= (x+y)* (x+z). 1029,1028 [para_into,751.1.1.2.2,10.1.1,demod,5] x+y+z*x=x+y. 1041,1040 [back_demod,890,demod,1029] x+ (y+x)*z= (x+y)* (x+z). 1485,1484 [para_into,755.1.1.2.1,3.1.1] x+x*y+z=x+z. 1491 [para_into,755.1.1.2,12.1.1,demod,1041,875,578,1485,flip.1] x+y*z= (x+z)* (x+y). 1493 [binary,1491.1,43.1] $F. ------------ end of proof ------------- -------- PROOF -------- ----> UNIT CONFLICT at 0.18 sec ----> 1552 [binary,1551.1,1408.1] $F. Length of proof is 90. Level of proof is 20. ---------------- PROOF ---------------- 2 [] x+y=y+x. 3 [] x*y=y*x. 5,4 [] (x+y)+z=x+y+z. 7,6 [] (x*y)*z=x*y*z. 9,8 [] x+x*y=x. 11,10 [] x* (x+y)=x. 12 [] x*y+y*z+z*x= (x+y)* (y+z)* (z+x). 15 [] d* (e+f)!=d*e+d*f. 16 [copy,15,flip.1] d*e+d*f!=d* (e+f). 17 [para_into,12.1.1.1,10.1.1,demod,5] x+ (x+y)*z+z*x= (x+x+y)* (x+y+z)* (z+x). 19 [para_into,12.1.1.1,6.1.1] x*y*z+z*u+u*x*y= (x*y+z)* (z+u)* (u+x*y). 21 [para_into,12.1.1.1,3.1.1] x*y+x*z+z*y= (y+x)* (x+z)* (z+y). 24 [para_into,12.1.1.2.1,6.1.1] x*y*z+y*z*u+u*x= (x+y*z)* (y*z+u)* (u+x). 29,28 [para_into,12.1.1.2.2,10.1.1,demod,5] (x+y)*z+z*x+x= (x+y+z)* (z+x)* (x+x+y). 39 [para_from,12.1.1,10.1.1.2,demod,7] x*y* (x+y)* (y+z)* (z+x)=x*y. 47 [para_into,16.1.1,2.1.1] d*f+d*e!=d* (e+f). 60 [para_into,17.1.1.2.1.1,2.1.1] x+ (y+x)*z+z*x= (x+x+y)* (x+y+z)* (z+x). 62 [para_into,17.1.1.2.1,10.1.1,demod,5,5,5,5,5,5] x+x+y+ (x+y+z)*x= (x+x+y)* (x+y+x+y+z)* (x+y+z+x). 71 [para_into,17.1.1.2,2.1.1] x+y*x+ (x+z)*y= (x+x+z)* (x+z+y)* (y+x). 72 [para_into,17.1.1,2.1.1,demod,5,29] (x+y+z)* (z+x)* (x+x+y)= (x+x+y)* (x+y+z)* (z+x). 74 [copy,62,flip.1] (x+x+y)* (x+y+x+y+z)* (x+y+z+x)=x+x+y+ (x+y+z)*x. 75 [copy,71,flip.1] (x+x+y)* (x+y+z)* (z+x)=x+z*x+ (x+y)*z. 76 [copy,72,flip.1] (x+x+y)* (x+y+z)* (z+x)= (x+y+z)* (z+x)* (x+x+y). 77 [para_from,17.1.1,10.1.1.2] x* (x+x+y)* (x+y+z)* (z+x)=x. 99 [para_into,39.1.1.2.2.2.1,2.1.1] x*y* (x+y)* (z+y)* (z+x)=x*y. 189,188 [para_from,77.1.1,8.1.1.2] x+x=x. 198,197 [para_into,188.1.1,4.1.1] x+y+x+y=x+y. 199 [para_from,188.1.1,77.1.1.2.2.1,demod,5,5,198] (x+y)* (x+y+x)* (x+y)* (y+x+y)=x+y. 218,217 [para_from,188.1.1,10.1.1.2] x*x=x. 220,219 [para_from,188.1.1,4.1.1.1,flip.1] x+x+y=x+y. 292,291 [back_demod,76,demod,220,220,flip.1] (x+y+z)* (z+x)* (x+y)= (x+y)* (x+y+z)* (z+x). 293 [back_demod,75,demod,220] (x+y)* (x+y+z)* (z+x)=x+z*x+ (x+y)*z. 294 [back_demod,74,demod,220,220] (x+y)* (x+y+x+y+z)* (x+y+z+x)=x+y+ (x+y+z)*x. 305 [back_demod,60,demod,220] x+ (y+x)*z+z*x= (x+y)* (x+y+z)* (z+x). 310 [back_demod,28,demod,220,292] (x+y)*z+z*x+x= (x+y)* (x+y+z)* (z+x). 317 [para_from,217.1.1,12.1.1.2.2,demod,189] x*y+y*x+x= (x+y)* (y+x)*x. 320,319 [para_from,217.1.1,12.1.1.2.1,demod,9,189,11] x*y+y= (x+y)*y. 322,321 [para_from,217.1.1,6.1.1.1,flip.1] x*x*y=x*y. 323 [back_demod,317,demod,320] x*y+ (y+x)*x= (x+y)* (y+x)*x. 325 [back_demod,310,demod,320] (x+y)*z+ (z+x)*x= (x+y)* (x+y+z)* (z+x). 348,347 [para_into,219.1.1.2,4.1.1,demod,5,5] x+y+x+y+z=x+y+z. 350,349 [para_into,219.1.1.2,2.1.1] x+y+x=x+y. 358 [back_demod,294,demod,348] (x+y)* (x+y+z)* (x+y+z+x)=x+y+ (x+y+z)*x. 371 [back_demod,199,demod,350,350,322,322] (x+y)* (y+x)=x+y. 380,379 [para_into,321.1.1.2,3.1.1] x*y*x=x*y. 387 [para_from,321.1.1,12.1.1.1,demod,7,9] x*y+x*y*z+z*x=x* (x*y+z)* (z+x). 392,391 [para_into,349.1.1.2,4.1.1] x+y+z+x=x+y+z. 393 [back_demod,358,demod,392,218,flip.1] x+y+ (x+y+z)*x= (x+y)* (x+y+z). 406,405 [para_into,379.1.1.2,6.1.1] x*y*z*x=x*y*z. 410 [para_from,379.1.1,12.1.1.1,demod,7] x*y+y*x*z+z*x= (x+y*x)* (y*x+z)* (z+x). 435 [para_into,19.1.1.1,379.1.1] x*y+x*z+z*x*y= (x*y+x)* (x+z)* (z+x*y). 441 [para_into,19.1.1.2.1,217.1.1,demod,9,189,11] x*y*z+z= (x*y+z)*z. 480,479 [para_into,319.1.1.1,3.1.1] x*y+x= (y+x)*x. 486 [back_demod,435,demod,480,7] x*y+x*z+z*x*y= (y+x)*x* (x+z)* (z+x*y). 501 [para_into,371.1.1.1,8.1.1,demod,480,380,9] x* (y+x)=x. 505 [para_into,371.1.1.2,319.1.1] (x+y*x)* (y+x)*x=x+y*x. 524,523 [para_from,371.1.1,6.1.1.1,flip.1] (x+y)* (y+x)*z= (x+y)*z. 529 [back_demod,323,demod,524] x*y+ (y+x)*x= (x+y)*x. 540,539 [para_into,501.1.1,3.1.1] (x+y)*y=y. 542,541 [back_demod,529,demod,540,480,540,flip.1] (x+y)*x=x. 548,547 [back_demod,505,demod,540,542,flip.1] x+y*x=x. 561 [back_demod,441,demod,540] x*y*z+z=z. 568,567 [back_demod,325,demod,540] (x+y)*z+x= (x+y)* (x+y+z)* (z+x). 578,577 [back_demod,393,demod,542,350,flip.1] (x+y)* (x+y+z)=x+y. 584 [back_demod,410,demod,548] x*y+y*x*z+z*x=x* (y*x+z)* (z+x). 613,612 [para_from,501.1.1,6.1.1.1,flip.1] x* (y+x)*z=x*z. 657,656 [back_demod,99,demod,613,613] x*y* (z+x)=x*y. 665 [back_demod,584,demod,657] x*y+y*x*z+z*x=x* (y*x+z). 669 [back_demod,387,demod,657] x*y+x*y*z+z*x=x* (x*y+z). 694,693 [para_from,539.1.1,6.1.1.1,flip.1] (x+y)*y*z=y*z. 715,714 [back_demod,486,demod,694] x*y+x*z+z*x*y=x* (x+z)* (z+x*y). 752,751 [para_into,547.1.1.2,6.1.1] x+y*z*x=x. 756,755 [para_from,547.1.1,4.1.1.1,flip.1] x+y*x+z=x+z. 758 [back_demod,293,demod,756] (x+y)* (x+y+z)* (z+x)=x+ (x+y)*z. 806,805 [para_into,561.1.1.1.2,379.1.1] x*y*z+z*y=z*y. 812,811 [para_into,561.1.1.1.2,3.1.1] x*y*z+y=y. 821 [back_demod,665,demod,806] x*y+z*x=x* (y*x+z). 824 [copy,821,flip.1] x* (y*x+z)=x*y+z*x. 838,837 [para_into,21.1.1.2.1,541.1.1,demod,9,568,5,350,694] (x+y)* (x+y+z)* (z+x)= (x+y)* (x+z). 842,841 [para_into,21.1.1.2.1,379.1.1,demod,7,715,548,694,flip.1] x* (y*x+z)=x* (x+y)* (y+x*z). 875,874 [back_demod,758,demod,838,flip.1] x+ (x+y)*z= (x+y)* (x+z). 890 [back_demod,305,demod,838] x+ (y+x)*z+z*x= (x+y)* (x+z). 909,908 [back_demod,824,demod,842,flip.1] x*y+z*x=x* (x+y)* (y+x*z). 931 [back_demod,669,demod,909] x*y+x* (x+y*z)* (y*z+x*z)=x* (x*y+z). 1029,1028 [para_into,751.1.1.2.2,10.1.1,demod,5] x+y+z*x=x+y. 1041,1040 [back_demod,890,demod,1029] x+ (y+x)*z= (x+y)* (x+z). 1049 [back_demod,714,demod,1029] x*y+x*z=x* (x+z)* (z+x*y). 1146,1145 [para_into,612.1.1.2.1,2.1.1] x* (x+y)*z=x*z. 1155 [back_demod,1049,demod,1146] x*y+x*z=x* (z+x*y). 1165 [back_demod,931,demod,1146] x*y+x* (y*z+x*z)=x* (x*y+z). 1173,1172 [back_demod,908,demod,1146] x*y+z*x=x* (y+x*z). 1368,1367 [para_into,24.1.1.2,811.1.1,demod,406,1173,752,812,11] x* (y*z+x*z)=x*z. 1391,1390 [back_demod,1165,demod,1368] x*y+x*z=x* (x*y+z). 1402 [back_demod,1155,demod,1391] x* (x*y+z)=x* (z+x*y). 1408 [back_demod,47,demod,1391] d* (d*f+e)!=d* (e+f). 1485,1484 [para_into,755.1.1.2.1,3.1.1] x+x*y+z=x+z. 1492,1491 [para_into,755.1.1.2,12.1.1,demod,1041,875,578,1485,flip.1] x+y*z= (x+z)* (x+y). 1551 [back_demod,1402,demod,1492,657] x* (x*y+z)=x* (z+y). 1552 [binary,1551.1,1408.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 47 clauses generated 1459 clauses kept 903 clauses forward subsumed 1263 clauses back subsumed 5 Kbytes malloced 5859 ----------- times (seconds) ----------- user CPU time 0.18 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8449 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/ex_2.out0100664000076400007640000001154710103522156016655 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8444. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(pick_given_ratio,1). assign(max_mem,5000). assign(stats_level,1). lex([a,b,c,_+_,_*_]). list(usable). 0 [] x=x. 0 [] x+y=y+x. 0 [] x*y=y*x. 0 [] (x+y)+z=x+y+z. 0 [] (x*y)*z=x*y*z. 0 [] x+x*y=x. 0 [] x* (x+y)=x. end_of_list. list(sos). 0 [] x+y*z= (x+y)* (x+z). 0 [] a* (b+c)!=a*b+a*c. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=7): 2 [] x+y=y+x. ** KEPT (pick-wt=7): 3 [] x*y=y*x. ** KEPT (pick-wt=11): 4 [] (x+y)+z=x+y+z. ---> New Demodulator: 5 [new_demod,4] (x+y)+z=x+y+z. ** KEPT (pick-wt=11): 6 [] (x*y)*z=x*y*z. ---> New Demodulator: 7 [new_demod,6] (x*y)*z=x*y*z. ** KEPT (pick-wt=7): 8 [] x+x*y=x. ---> New Demodulator: 9 [new_demod,8] x+x*y=x. ** KEPT (pick-wt=7): 10 [] x* (x+y)=x. ---> New Demodulator: 11 [new_demod,10] x* (x+y)=x. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x+y=y+x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x*y=y*x. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. ------------> process sos: ** KEPT (pick-wt=13): 13 [copy,12,flip.1] (x+y)* (x+z)=x+y*z. ---> New Demodulator: 14 [new_demod,13] (x+y)* (x+z)=x+y*z. ** KEPT (pick-wt=13): 15 [] a* (b+c)!=a*b+a*c. >>>> Starting back demodulation with 14. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=13) 13 [copy,12,flip.1] (x+y)* (x+z)=x+y*z. given clause #2: (wt=11) 21 [para_into,13.1.1,3.1.1,demod,14] x+y*z=x+z*y. given clause #3: (wt=13) 15 [] a* (b+c)!=a*b+a*c. given clause #4: (wt=7) 31 [para_into,21.1.1,8.1.1,flip.1] x+y*x=x. given clause #5: (wt=13) 16 [para_into,13.1.1.1,2.1.1] (x+y)* (y+z)=y+x*z. given clause #6: (wt=5) 55 [para_from,31.1.1,10.1.1.2] x*x=x. given clause #7: (wt=13) 19 [para_into,13.1.1.2,2.1.1] (x+y)* (z+x)=x+y*z. given clause #8: (wt=5) 79 [para_from,55.1.1,31.1.1.2] x+x=x. given clause #9: (wt=17) 25 [para_from,13.1.1,6.1.1.1] (x+y*z)*u= (x+y)* (x+z)*u. given clause #10: (wt=7) 49 [para_into,31.1.1,2.1.1] x*y+y=y. given clause #11: (wt=15) 27 [para_into,21.1.1.2,13.1.1,demod,14] x+y+z*u=x+y+u*z. given clause #12: (wt=7) 83 [para_into,19.1.1.1,31.1.1,demod,7,54] x* (y+x)=x. given clause #13: (wt=15) 30 [para_into,21.1.1.2,6.1.1] x+y*z*u=x+u*y*z. given clause #14: (wt=7) 146 [para_into,49.1.1.1,3.1.1] x*y+x=x. given clause #15: (wt=11) 33 [para_into,21.1.1,2.1.1] x*y+z=z+y*x. -------- PROOF -------- ----> UNIT CONFLICT at 0.01 sec ----> 280 [binary,279.1,194.1] $F. Length of proof is 13. Level of proof is 7. ---------------- PROOF ---------------- 2 [] x+y=y+x. 3 [] x*y=y*x. 6 [] (x*y)*z=x*y*z. 8 [] x+x*y=x. 12 [] x+y*z= (x+y)* (x+z). 14,13 [copy,12,flip.1] (x+y)* (x+z)=x+y*z. 15 [] a* (b+c)!=a*b+a*c. 16 [para_into,13.1.1.1,2.1.1] (x+y)* (y+z)=y+x*z. 21 [para_into,13.1.1,3.1.1,demod,14] x+y*z=x+z*y. 26,25 [para_from,13.1.1,6.1.1.1] (x+y*z)*u= (x+y)* (x+z)*u. 31 [para_into,21.1.1,8.1.1,flip.1] x+y*x=x. 33 [para_into,21.1.1,2.1.1] x*y+z=z+y*x. 40 [para_into,15.1.1,3.1.1] (b+c)*a!=a*b+a*c. 46,45 [para_into,31.1.1.2,6.1.1] x+y*z*x=x. 49 [para_into,31.1.1,2.1.1] x*y+y=y. 68,67 [para_into,16.1.1.2,31.1.1,demod,46] (x+y)*y=y. 153,152 [para_from,49.1.1,16.1.1.2,demod,26,68] (x+y)*z=y*z+x*z. 194 [back_demod,40,demod,153] c*a+b*a!=a*b+a*c. 279 [para_into,33.1.1,21.1.1] x*y+z*u=u*z+y*x. 280 [binary,279.1,194.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 15 clauses generated 287 clauses kept 179 clauses forward subsumed 267 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8444 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/i3.out0100664000076400007640000056523210103522156016340 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8469. set(hyper_res). set(print_lists_at_end). assign(stats_level,1). list(usable). 1 [] K(0). 2 [] K(1). 3 [] L(0). 4 [] L(1). 5 [] L(2). 6 [] L(3). 7 [] L(4). 8 [] L(5). 9 [] L(6). 10 [] L(7). 11 [] D(0). 12 [] D(1). 13 [] D(2). 14 [] D(3). 15 [] D(4). 16 [] D(5). 17 [] D(6). 18 [] D(7). 19 [] D(8). 20 [] D(9). end_of_list. list(sos). 21 [] -K(u)| -D(x)| -D(y)|CS(u,x,y,$MOD($SUM($SUM(u,x),y),10),$DIV($SUM($SUM(u,x),y),10)). 22 [] -L(u)| -D(x)| -D(y)|CP(u,x,y,$MOD($SUM(u,$PROD(x,y)),10),$DIV($SUM(u,$PROD(x,y)),10)). 23 [] -CP(0,xd,xb,y1,x1)| -CP(x1,xd,xa,y2,y3)| -CP(0,xc,xb,z1,x2)| -CP(x2,xc,xa,z2,z3)| -$LT(xa,xc)| -CS(0,y1,0,xh,x3)| -CS(x3,y2,z1,xg,x4)| -CS(x4,y3,z2,xf,x5)| -CS(x5,0,z3,xe,0)|S(xa,xb,xc,xd,xe,xf,xg,xh). end_of_list. list(passive). 24 [] S(0,xb,xc,xd,xe,xf,xg,xh). 25 [] S(xa,xb,0,xd,xe,xf,xg,xh). 26 [] S(xa,xb,xc,xd,0,xf,xg,xh). 27 [] S(x1,x1,x3,x4,x5,x6,x7,x8). 28 [] S(x1,x2,x1,x4,x5,x6,x7,x8). 29 [] S(x1,x2,x3,x1,x5,x6,x7,x8). 30 [] S(x1,x2,x3,x4,x1,x6,x7,x8). 31 [] S(x1,x2,x3,x4,x5,x1,x7,x8). 32 [] S(x1,x2,x3,x4,x5,x6,x1,x8). 33 [] S(x1,x2,x3,x4,x5,x6,x7,x1). 34 [] S(x1,x2,x2,x4,x5,x6,x7,x8). 35 [] S(x1,x2,x3,x2,x5,x6,x7,x8). 36 [] S(x1,x2,x3,x4,x2,x6,x7,x8). 37 [] S(x1,x2,x3,x4,x5,x2,x7,x8). 38 [] S(x1,x2,x3,x4,x5,x6,x2,x8). 39 [] S(x1,x2,x3,x4,x5,x6,x7,x2). 40 [] S(x1,x2,x3,x3,x5,x6,x7,x8). 41 [] S(x1,x2,x3,x4,x3,x6,x7,x8). 42 [] S(x1,x2,x3,x4,x5,x3,x7,x8). 43 [] S(x1,x2,x3,x4,x5,x6,x3,x8). 44 [] S(x1,x2,x3,x4,x5,x6,x7,x3). 45 [] S(x1,x2,x3,x4,x4,x6,x7,x8). 46 [] S(x1,x2,x3,x4,x5,x4,x7,x8). 47 [] S(x1,x2,x3,x4,x5,x6,x4,x8). 48 [] S(x1,x2,x3,x4,x5,x6,x7,x4). 49 [] S(x1,x2,x3,x4,x5,x5,x7,x8). 50 [] S(x1,x2,x3,x4,x5,x6,x5,x8). 51 [] S(x1,x2,x3,x4,x5,x6,x7,x5). 52 [] S(x1,x2,x3,x4,x5,x6,x6,x8). 53 [] S(x1,x2,x3,x4,x5,x6,x7,x6). 54 [] S(x1,x2,x3,x4,x5,x6,x7,x7). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=24) 21 [] -K(u)| -D(x)| -D(y)|CS(u,x,y,$MOD($SUM($SUM(u,x),y),10),$DIV($SUM($SUM(u,x),y),10)). ** KEPT (pick-wt=6): 55 [hyper,21,2,20,20,demod] CS(1,9,9,9,1). ** KEPT (pick-wt=6): 56 [hyper,21,2,20,19,demod] CS(1,9,8,8,1). ** KEPT (pick-wt=6): 57 [hyper,21,2,20,18,demod] CS(1,9,7,7,1). ** KEPT (pick-wt=6): 58 [hyper,21,2,20,17,demod] CS(1,9,6,6,1). ** KEPT (pick-wt=6): 59 [hyper,21,2,20,16,demod] CS(1,9,5,5,1). ** KEPT (pick-wt=6): 60 [hyper,21,2,20,15,demod] CS(1,9,4,4,1). ** KEPT (pick-wt=6): 61 [hyper,21,2,20,14,demod] CS(1,9,3,3,1). ** KEPT (pick-wt=6): 62 [hyper,21,2,20,13,demod] CS(1,9,2,2,1). ** KEPT (pick-wt=6): 63 [hyper,21,2,20,12,demod] CS(1,9,1,1,1). ** KEPT (pick-wt=6): 64 [hyper,21,2,20,11,demod] CS(1,9,0,0,1). ** KEPT (pick-wt=6): 65 [hyper,21,2,19,20,demod] CS(1,8,9,8,1). ** KEPT (pick-wt=6): 66 [hyper,21,2,19,19,demod] CS(1,8,8,7,1). ** KEPT (pick-wt=6): 67 [hyper,21,2,19,18,demod] CS(1,8,7,6,1). ** KEPT (pick-wt=6): 68 [hyper,21,2,19,17,demod] CS(1,8,6,5,1). ** KEPT (pick-wt=6): 69 [hyper,21,2,19,16,demod] CS(1,8,5,4,1). ** KEPT (pick-wt=6): 70 [hyper,21,2,19,15,demod] CS(1,8,4,3,1). ** KEPT (pick-wt=6): 71 [hyper,21,2,19,14,demod] CS(1,8,3,2,1). ** KEPT (pick-wt=6): 72 [hyper,21,2,19,13,demod] CS(1,8,2,1,1). ** KEPT (pick-wt=6): 73 [hyper,21,2,19,12,demod] CS(1,8,1,0,1). ** KEPT (pick-wt=6): 74 [hyper,21,2,19,11,demod] CS(1,8,0,9,0). ** KEPT (pick-wt=6): 75 [hyper,21,2,18,20,demod] CS(1,7,9,7,1). ** KEPT (pick-wt=6): 76 [hyper,21,2,18,19,demod] CS(1,7,8,6,1). ** KEPT (pick-wt=6): 77 [hyper,21,2,18,18,demod] CS(1,7,7,5,1). ** KEPT (pick-wt=6): 78 [hyper,21,2,18,17,demod] CS(1,7,6,4,1). ** KEPT (pick-wt=6): 79 [hyper,21,2,18,16,demod] CS(1,7,5,3,1). ** KEPT (pick-wt=6): 80 [hyper,21,2,18,15,demod] CS(1,7,4,2,1). ** KEPT (pick-wt=6): 81 [hyper,21,2,18,14,demod] CS(1,7,3,1,1). ** KEPT (pick-wt=6): 82 [hyper,21,2,18,13,demod] CS(1,7,2,0,1). ** KEPT (pick-wt=6): 83 [hyper,21,2,18,12,demod] CS(1,7,1,9,0). ** KEPT (pick-wt=6): 84 [hyper,21,2,18,11,demod] CS(1,7,0,8,0). ** KEPT (pick-wt=6): 85 [hyper,21,2,17,20,demod] CS(1,6,9,6,1). ** KEPT (pick-wt=6): 86 [hyper,21,2,17,19,demod] CS(1,6,8,5,1). ** KEPT (pick-wt=6): 87 [hyper,21,2,17,18,demod] CS(1,6,7,4,1). ** KEPT (pick-wt=6): 88 [hyper,21,2,17,17,demod] CS(1,6,6,3,1). ** KEPT (pick-wt=6): 89 [hyper,21,2,17,16,demod] CS(1,6,5,2,1). ** KEPT (pick-wt=6): 90 [hyper,21,2,17,15,demod] CS(1,6,4,1,1). ** KEPT (pick-wt=6): 91 [hyper,21,2,17,14,demod] CS(1,6,3,0,1). ** KEPT (pick-wt=6): 92 [hyper,21,2,17,13,demod] CS(1,6,2,9,0). ** KEPT (pick-wt=6): 93 [hyper,21,2,17,12,demod] CS(1,6,1,8,0). ** KEPT (pick-wt=6): 94 [hyper,21,2,17,11,demod] CS(1,6,0,7,0). ** KEPT (pick-wt=6): 95 [hyper,21,2,16,20,demod] CS(1,5,9,5,1). ** KEPT (pick-wt=6): 96 [hyper,21,2,16,19,demod] CS(1,5,8,4,1). ** KEPT (pick-wt=6): 97 [hyper,21,2,16,18,demod] CS(1,5,7,3,1). ** KEPT (pick-wt=6): 98 [hyper,21,2,16,17,demod] CS(1,5,6,2,1). ** KEPT (pick-wt=6): 99 [hyper,21,2,16,16,demod] CS(1,5,5,1,1). ** KEPT (pick-wt=6): 100 [hyper,21,2,16,15,demod] CS(1,5,4,0,1). ** KEPT (pick-wt=6): 101 [hyper,21,2,16,14,demod] CS(1,5,3,9,0). ** KEPT (pick-wt=6): 102 [hyper,21,2,16,13,demod] CS(1,5,2,8,0). ** KEPT (pick-wt=6): 103 [hyper,21,2,16,12,demod] CS(1,5,1,7,0). ** KEPT (pick-wt=6): 104 [hyper,21,2,16,11,demod] CS(1,5,0,6,0). ** KEPT (pick-wt=6): 105 [hyper,21,2,15,20,demod] CS(1,4,9,4,1). ** KEPT (pick-wt=6): 106 [hyper,21,2,15,19,demod] CS(1,4,8,3,1). ** KEPT (pick-wt=6): 107 [hyper,21,2,15,18,demod] CS(1,4,7,2,1). ** KEPT (pick-wt=6): 108 [hyper,21,2,15,17,demod] CS(1,4,6,1,1). ** KEPT (pick-wt=6): 109 [hyper,21,2,15,16,demod] CS(1,4,5,0,1). ** KEPT (pick-wt=6): 110 [hyper,21,2,15,15,demod] CS(1,4,4,9,0). ** KEPT (pick-wt=6): 111 [hyper,21,2,15,14,demod] CS(1,4,3,8,0). ** KEPT (pick-wt=6): 112 [hyper,21,2,15,13,demod] CS(1,4,2,7,0). ** KEPT (pick-wt=6): 113 [hyper,21,2,15,12,demod] CS(1,4,1,6,0). ** KEPT (pick-wt=6): 114 [hyper,21,2,15,11,demod] CS(1,4,0,5,0). ** KEPT (pick-wt=6): 115 [hyper,21,2,14,20,demod] CS(1,3,9,3,1). ** KEPT (pick-wt=6): 116 [hyper,21,2,14,19,demod] CS(1,3,8,2,1). ** KEPT (pick-wt=6): 117 [hyper,21,2,14,18,demod] CS(1,3,7,1,1). ** KEPT (pick-wt=6): 118 [hyper,21,2,14,17,demod] CS(1,3,6,0,1). ** KEPT (pick-wt=6): 119 [hyper,21,2,14,16,demod] CS(1,3,5,9,0). ** KEPT (pick-wt=6): 120 [hyper,21,2,14,15,demod] CS(1,3,4,8,0). ** KEPT (pick-wt=6): 121 [hyper,21,2,14,14,demod] CS(1,3,3,7,0). ** KEPT (pick-wt=6): 122 [hyper,21,2,14,13,demod] CS(1,3,2,6,0). ** KEPT (pick-wt=6): 123 [hyper,21,2,14,12,demod] CS(1,3,1,5,0). ** KEPT (pick-wt=6): 124 [hyper,21,2,14,11,demod] CS(1,3,0,4,0). ** KEPT (pick-wt=6): 125 [hyper,21,2,13,20,demod] CS(1,2,9,2,1). ** KEPT (pick-wt=6): 126 [hyper,21,2,13,19,demod] CS(1,2,8,1,1). ** KEPT (pick-wt=6): 127 [hyper,21,2,13,18,demod] CS(1,2,7,0,1). ** KEPT (pick-wt=6): 128 [hyper,21,2,13,17,demod] CS(1,2,6,9,0). ** KEPT (pick-wt=6): 129 [hyper,21,2,13,16,demod] CS(1,2,5,8,0). ** KEPT (pick-wt=6): 130 [hyper,21,2,13,15,demod] CS(1,2,4,7,0). ** KEPT (pick-wt=6): 131 [hyper,21,2,13,14,demod] CS(1,2,3,6,0). ** KEPT (pick-wt=6): 132 [hyper,21,2,13,13,demod] CS(1,2,2,5,0). ** KEPT (pick-wt=6): 133 [hyper,21,2,13,12,demod] CS(1,2,1,4,0). ** KEPT (pick-wt=6): 134 [hyper,21,2,13,11,demod] CS(1,2,0,3,0). ** KEPT (pick-wt=6): 135 [hyper,21,2,12,20,demod] CS(1,1,9,1,1). ** KEPT (pick-wt=6): 136 [hyper,21,2,12,19,demod] CS(1,1,8,0,1). ** KEPT (pick-wt=6): 137 [hyper,21,2,12,18,demod] CS(1,1,7,9,0). ** KEPT (pick-wt=6): 138 [hyper,21,2,12,17,demod] CS(1,1,6,8,0). ** KEPT (pick-wt=6): 139 [hyper,21,2,12,16,demod] CS(1,1,5,7,0). ** KEPT (pick-wt=6): 140 [hyper,21,2,12,15,demod] CS(1,1,4,6,0). ** KEPT (pick-wt=6): 141 [hyper,21,2,12,14,demod] CS(1,1,3,5,0). ** KEPT (pick-wt=6): 142 [hyper,21,2,12,13,demod] CS(1,1,2,4,0). ** KEPT (pick-wt=6): 143 [hyper,21,2,12,12,demod] CS(1,1,1,3,0). ** KEPT (pick-wt=6): 144 [hyper,21,2,12,11,demod] CS(1,1,0,2,0). ** KEPT (pick-wt=6): 145 [hyper,21,2,11,20,demod] CS(1,0,9,0,1). ** KEPT (pick-wt=6): 146 [hyper,21,2,11,19,demod] CS(1,0,8,9,0). ** KEPT (pick-wt=6): 147 [hyper,21,2,11,18,demod] CS(1,0,7,8,0). ** KEPT (pick-wt=6): 148 [hyper,21,2,11,17,demod] CS(1,0,6,7,0). ** KEPT (pick-wt=6): 149 [hyper,21,2,11,16,demod] CS(1,0,5,6,0). ** KEPT (pick-wt=6): 150 [hyper,21,2,11,15,demod] CS(1,0,4,5,0). ** KEPT (pick-wt=6): 151 [hyper,21,2,11,14,demod] CS(1,0,3,4,0). ** KEPT (pick-wt=6): 152 [hyper,21,2,11,13,demod] CS(1,0,2,3,0). ** KEPT (pick-wt=6): 153 [hyper,21,2,11,12,demod] CS(1,0,1,2,0). ** KEPT (pick-wt=6): 154 [hyper,21,2,11,11,demod] CS(1,0,0,1,0). ** KEPT (pick-wt=6): 155 [hyper,21,1,20,20,demod] CS(0,9,9,8,1). ** KEPT (pick-wt=6): 156 [hyper,21,1,20,19,demod] CS(0,9,8,7,1). ** KEPT (pick-wt=6): 157 [hyper,21,1,20,18,demod] CS(0,9,7,6,1). ** KEPT (pick-wt=6): 158 [hyper,21,1,20,17,demod] CS(0,9,6,5,1). ** KEPT (pick-wt=6): 159 [hyper,21,1,20,16,demod] CS(0,9,5,4,1). ** KEPT (pick-wt=6): 160 [hyper,21,1,20,15,demod] CS(0,9,4,3,1). ** KEPT (pick-wt=6): 161 [hyper,21,1,20,14,demod] CS(0,9,3,2,1). ** KEPT (pick-wt=6): 162 [hyper,21,1,20,13,demod] CS(0,9,2,1,1). ** KEPT (pick-wt=6): 163 [hyper,21,1,20,12,demod] CS(0,9,1,0,1). ** KEPT (pick-wt=6): 164 [hyper,21,1,20,11,demod] CS(0,9,0,9,0). ** KEPT (pick-wt=6): 165 [hyper,21,1,19,20,demod] CS(0,8,9,7,1). ** KEPT (pick-wt=6): 166 [hyper,21,1,19,19,demod] CS(0,8,8,6,1). ** KEPT (pick-wt=6): 167 [hyper,21,1,19,18,demod] CS(0,8,7,5,1). ** KEPT (pick-wt=6): 168 [hyper,21,1,19,17,demod] CS(0,8,6,4,1). ** KEPT (pick-wt=6): 169 [hyper,21,1,19,16,demod] CS(0,8,5,3,1). ** KEPT (pick-wt=6): 170 [hyper,21,1,19,15,demod] CS(0,8,4,2,1). ** KEPT (pick-wt=6): 171 [hyper,21,1,19,14,demod] CS(0,8,3,1,1). ** KEPT (pick-wt=6): 172 [hyper,21,1,19,13,demod] CS(0,8,2,0,1). ** KEPT (pick-wt=6): 173 [hyper,21,1,19,12,demod] CS(0,8,1,9,0). ** KEPT (pick-wt=6): 174 [hyper,21,1,19,11,demod] CS(0,8,0,8,0). ** KEPT (pick-wt=6): 175 [hyper,21,1,18,20,demod] CS(0,7,9,6,1). ** KEPT (pick-wt=6): 176 [hyper,21,1,18,19,demod] CS(0,7,8,5,1). ** KEPT (pick-wt=6): 177 [hyper,21,1,18,18,demod] CS(0,7,7,4,1). ** KEPT (pick-wt=6): 178 [hyper,21,1,18,17,demod] CS(0,7,6,3,1). ** KEPT (pick-wt=6): 179 [hyper,21,1,18,16,demod] CS(0,7,5,2,1). ** KEPT (pick-wt=6): 180 [hyper,21,1,18,15,demod] CS(0,7,4,1,1). ** KEPT (pick-wt=6): 181 [hyper,21,1,18,14,demod] CS(0,7,3,0,1). ** KEPT (pick-wt=6): 182 [hyper,21,1,18,13,demod] CS(0,7,2,9,0). ** KEPT (pick-wt=6): 183 [hyper,21,1,18,12,demod] CS(0,7,1,8,0). ** KEPT (pick-wt=6): 184 [hyper,21,1,18,11,demod] CS(0,7,0,7,0). ** KEPT (pick-wt=6): 185 [hyper,21,1,17,20,demod] CS(0,6,9,5,1). ** KEPT (pick-wt=6): 186 [hyper,21,1,17,19,demod] CS(0,6,8,4,1). ** KEPT (pick-wt=6): 187 [hyper,21,1,17,18,demod] CS(0,6,7,3,1). ** KEPT (pick-wt=6): 188 [hyper,21,1,17,17,demod] CS(0,6,6,2,1). ** KEPT (pick-wt=6): 189 [hyper,21,1,17,16,demod] CS(0,6,5,1,1). ** KEPT (pick-wt=6): 190 [hyper,21,1,17,15,demod] CS(0,6,4,0,1). ** KEPT (pick-wt=6): 191 [hyper,21,1,17,14,demod] CS(0,6,3,9,0). ** KEPT (pick-wt=6): 192 [hyper,21,1,17,13,demod] CS(0,6,2,8,0). ** KEPT (pick-wt=6): 193 [hyper,21,1,17,12,demod] CS(0,6,1,7,0). ** KEPT (pick-wt=6): 194 [hyper,21,1,17,11,demod] CS(0,6,0,6,0). ** KEPT (pick-wt=6): 195 [hyper,21,1,16,20,demod] CS(0,5,9,4,1). ** KEPT (pick-wt=6): 196 [hyper,21,1,16,19,demod] CS(0,5,8,3,1). ** KEPT (pick-wt=6): 197 [hyper,21,1,16,18,demod] CS(0,5,7,2,1). ** KEPT (pick-wt=6): 198 [hyper,21,1,16,17,demod] CS(0,5,6,1,1). ** KEPT (pick-wt=6): 199 [hyper,21,1,16,16,demod] CS(0,5,5,0,1). ** KEPT (pick-wt=6): 200 [hyper,21,1,16,15,demod] CS(0,5,4,9,0). ** KEPT (pick-wt=6): 201 [hyper,21,1,16,14,demod] CS(0,5,3,8,0). ** KEPT (pick-wt=6): 202 [hyper,21,1,16,13,demod] CS(0,5,2,7,0). ** KEPT (pick-wt=6): 203 [hyper,21,1,16,12,demod] CS(0,5,1,6,0). ** KEPT (pick-wt=6): 204 [hyper,21,1,16,11,demod] CS(0,5,0,5,0). ** KEPT (pick-wt=6): 205 [hyper,21,1,15,20,demod] CS(0,4,9,3,1). ** KEPT (pick-wt=6): 206 [hyper,21,1,15,19,demod] CS(0,4,8,2,1). ** KEPT (pick-wt=6): 207 [hyper,21,1,15,18,demod] CS(0,4,7,1,1). ** KEPT (pick-wt=6): 208 [hyper,21,1,15,17,demod] CS(0,4,6,0,1). ** KEPT (pick-wt=6): 209 [hyper,21,1,15,16,demod] CS(0,4,5,9,0). ** KEPT (pick-wt=6): 210 [hyper,21,1,15,15,demod] CS(0,4,4,8,0). ** KEPT (pick-wt=6): 211 [hyper,21,1,15,14,demod] CS(0,4,3,7,0). ** KEPT (pick-wt=6): 212 [hyper,21,1,15,13,demod] CS(0,4,2,6,0). ** KEPT (pick-wt=6): 213 [hyper,21,1,15,12,demod] CS(0,4,1,5,0). ** KEPT (pick-wt=6): 214 [hyper,21,1,15,11,demod] CS(0,4,0,4,0). ** KEPT (pick-wt=6): 215 [hyper,21,1,14,20,demod] CS(0,3,9,2,1). ** KEPT (pick-wt=6): 216 [hyper,21,1,14,19,demod] CS(0,3,8,1,1). ** KEPT (pick-wt=6): 217 [hyper,21,1,14,18,demod] CS(0,3,7,0,1). ** KEPT (pick-wt=6): 218 [hyper,21,1,14,17,demod] CS(0,3,6,9,0). ** KEPT (pick-wt=6): 219 [hyper,21,1,14,16,demod] CS(0,3,5,8,0). ** KEPT (pick-wt=6): 220 [hyper,21,1,14,15,demod] CS(0,3,4,7,0). ** KEPT (pick-wt=6): 221 [hyper,21,1,14,14,demod] CS(0,3,3,6,0). ** KEPT (pick-wt=6): 222 [hyper,21,1,14,13,demod] CS(0,3,2,5,0). ** KEPT (pick-wt=6): 223 [hyper,21,1,14,12,demod] CS(0,3,1,4,0). ** KEPT (pick-wt=6): 224 [hyper,21,1,14,11,demod] CS(0,3,0,3,0). ** KEPT (pick-wt=6): 225 [hyper,21,1,13,20,demod] CS(0,2,9,1,1). ** KEPT (pick-wt=6): 226 [hyper,21,1,13,19,demod] CS(0,2,8,0,1). ** KEPT (pick-wt=6): 227 [hyper,21,1,13,18,demod] CS(0,2,7,9,0). ** KEPT (pick-wt=6): 228 [hyper,21,1,13,17,demod] CS(0,2,6,8,0). ** KEPT (pick-wt=6): 229 [hyper,21,1,13,16,demod] CS(0,2,5,7,0). ** KEPT (pick-wt=6): 230 [hyper,21,1,13,15,demod] CS(0,2,4,6,0). ** KEPT (pick-wt=6): 231 [hyper,21,1,13,14,demod] CS(0,2,3,5,0). ** KEPT (pick-wt=6): 232 [hyper,21,1,13,13,demod] CS(0,2,2,4,0). ** KEPT (pick-wt=6): 233 [hyper,21,1,13,12,demod] CS(0,2,1,3,0). ** KEPT (pick-wt=6): 234 [hyper,21,1,13,11,demod] CS(0,2,0,2,0). ** KEPT (pick-wt=6): 235 [hyper,21,1,12,20,demod] CS(0,1,9,0,1). ** KEPT (pick-wt=6): 236 [hyper,21,1,12,19,demod] CS(0,1,8,9,0). ** KEPT (pick-wt=6): 237 [hyper,21,1,12,18,demod] CS(0,1,7,8,0). ** KEPT (pick-wt=6): 238 [hyper,21,1,12,17,demod] CS(0,1,6,7,0). ** KEPT (pick-wt=6): 239 [hyper,21,1,12,16,demod] CS(0,1,5,6,0). ** KEPT (pick-wt=6): 240 [hyper,21,1,12,15,demod] CS(0,1,4,5,0). ** KEPT (pick-wt=6): 241 [hyper,21,1,12,14,demod] CS(0,1,3,4,0). ** KEPT (pick-wt=6): 242 [hyper,21,1,12,13,demod] CS(0,1,2,3,0). ** KEPT (pick-wt=6): 243 [hyper,21,1,12,12,demod] CS(0,1,1,2,0). ** KEPT (pick-wt=6): 244 [hyper,21,1,12,11,demod] CS(0,1,0,1,0). ** KEPT (pick-wt=6): 245 [hyper,21,1,11,20,demod] CS(0,0,9,9,0). ** KEPT (pick-wt=6): 246 [hyper,21,1,11,19,demod] CS(0,0,8,8,0). ** KEPT (pick-wt=6): 247 [hyper,21,1,11,18,demod] CS(0,0,7,7,0). ** KEPT (pick-wt=6): 248 [hyper,21,1,11,17,demod] CS(0,0,6,6,0). ** KEPT (pick-wt=6): 249 [hyper,21,1,11,16,demod] CS(0,0,5,5,0). ** KEPT (pick-wt=6): 250 [hyper,21,1,11,15,demod] CS(0,0,4,4,0). ** KEPT (pick-wt=6): 251 [hyper,21,1,11,14,demod] CS(0,0,3,3,0). ** KEPT (pick-wt=6): 252 [hyper,21,1,11,13,demod] CS(0,0,2,2,0). ** KEPT (pick-wt=6): 253 [hyper,21,1,11,12,demod] CS(0,0,1,1,0). ** KEPT (pick-wt=6): 254 [hyper,21,1,11,11,demod] CS(0,0,0,0,0). given clause #2: (wt=6) 55 [hyper,21,2,20,20,demod] CS(1,9,9,9,1). given clause #3: (wt=6) 56 [hyper,21,2,20,19,demod] CS(1,9,8,8,1). given clause #4: (wt=6) 57 [hyper,21,2,20,18,demod] CS(1,9,7,7,1). given clause #5: (wt=6) 58 [hyper,21,2,20,17,demod] CS(1,9,6,6,1). given clause #6: (wt=6) 59 [hyper,21,2,20,16,demod] CS(1,9,5,5,1). given clause #7: (wt=6) 60 [hyper,21,2,20,15,demod] CS(1,9,4,4,1). given clause #8: (wt=6) 61 [hyper,21,2,20,14,demod] CS(1,9,3,3,1). given clause #9: (wt=6) 62 [hyper,21,2,20,13,demod] CS(1,9,2,2,1). given clause #10: (wt=6) 63 [hyper,21,2,20,12,demod] CS(1,9,1,1,1). given clause #11: (wt=6) 64 [hyper,21,2,20,11,demod] CS(1,9,0,0,1). given clause #12: (wt=6) 65 [hyper,21,2,19,20,demod] CS(1,8,9,8,1). given clause #13: (wt=6) 66 [hyper,21,2,19,19,demod] CS(1,8,8,7,1). given clause #14: (wt=6) 67 [hyper,21,2,19,18,demod] CS(1,8,7,6,1). given clause #15: (wt=6) 68 [hyper,21,2,19,17,demod] CS(1,8,6,5,1). given clause #16: (wt=6) 69 [hyper,21,2,19,16,demod] CS(1,8,5,4,1). given clause #17: (wt=6) 70 [hyper,21,2,19,15,demod] CS(1,8,4,3,1). given clause #18: (wt=6) 71 [hyper,21,2,19,14,demod] CS(1,8,3,2,1). given clause #19: (wt=6) 72 [hyper,21,2,19,13,demod] CS(1,8,2,1,1). given clause #20: (wt=6) 73 [hyper,21,2,19,12,demod] CS(1,8,1,0,1). given clause #21: (wt=6) 74 [hyper,21,2,19,11,demod] CS(1,8,0,9,0). given clause #22: (wt=6) 75 [hyper,21,2,18,20,demod] CS(1,7,9,7,1). given clause #23: (wt=6) 76 [hyper,21,2,18,19,demod] CS(1,7,8,6,1). given clause #24: (wt=6) 77 [hyper,21,2,18,18,demod] CS(1,7,7,5,1). given clause #25: (wt=6) 78 [hyper,21,2,18,17,demod] CS(1,7,6,4,1). given clause #26: (wt=6) 79 [hyper,21,2,18,16,demod] CS(1,7,5,3,1). given clause #27: (wt=6) 80 [hyper,21,2,18,15,demod] CS(1,7,4,2,1). given clause #28: (wt=6) 81 [hyper,21,2,18,14,demod] CS(1,7,3,1,1). given clause #29: (wt=6) 82 [hyper,21,2,18,13,demod] CS(1,7,2,0,1). given clause #30: (wt=6) 83 [hyper,21,2,18,12,demod] CS(1,7,1,9,0). given clause #31: (wt=6) 84 [hyper,21,2,18,11,demod] CS(1,7,0,8,0). given clause #32: (wt=6) 85 [hyper,21,2,17,20,demod] CS(1,6,9,6,1). given clause #33: (wt=6) 86 [hyper,21,2,17,19,demod] CS(1,6,8,5,1). given clause #34: (wt=6) 87 [hyper,21,2,17,18,demod] CS(1,6,7,4,1). given clause #35: (wt=6) 88 [hyper,21,2,17,17,demod] CS(1,6,6,3,1). given clause #36: (wt=6) 89 [hyper,21,2,17,16,demod] CS(1,6,5,2,1). given clause #37: (wt=6) 90 [hyper,21,2,17,15,demod] CS(1,6,4,1,1). given clause #38: (wt=6) 91 [hyper,21,2,17,14,demod] CS(1,6,3,0,1). given clause #39: (wt=6) 92 [hyper,21,2,17,13,demod] CS(1,6,2,9,0). given clause #40: (wt=6) 93 [hyper,21,2,17,12,demod] CS(1,6,1,8,0). given clause #41: (wt=6) 94 [hyper,21,2,17,11,demod] CS(1,6,0,7,0). given clause #42: (wt=6) 95 [hyper,21,2,16,20,demod] CS(1,5,9,5,1). given clause #43: (wt=6) 96 [hyper,21,2,16,19,demod] CS(1,5,8,4,1). given clause #44: (wt=6) 97 [hyper,21,2,16,18,demod] CS(1,5,7,3,1). given clause #45: (wt=6) 98 [hyper,21,2,16,17,demod] CS(1,5,6,2,1). given clause #46: (wt=6) 99 [hyper,21,2,16,16,demod] CS(1,5,5,1,1). given clause #47: (wt=6) 100 [hyper,21,2,16,15,demod] CS(1,5,4,0,1). given clause #48: (wt=6) 101 [hyper,21,2,16,14,demod] CS(1,5,3,9,0). given clause #49: (wt=6) 102 [hyper,21,2,16,13,demod] CS(1,5,2,8,0). given clause #50: (wt=6) 103 [hyper,21,2,16,12,demod] CS(1,5,1,7,0). given clause #51: (wt=6) 104 [hyper,21,2,16,11,demod] CS(1,5,0,6,0). given clause #52: (wt=6) 105 [hyper,21,2,15,20,demod] CS(1,4,9,4,1). given clause #53: (wt=6) 106 [hyper,21,2,15,19,demod] CS(1,4,8,3,1). given clause #54: (wt=6) 107 [hyper,21,2,15,18,demod] CS(1,4,7,2,1). given clause #55: (wt=6) 108 [hyper,21,2,15,17,demod] CS(1,4,6,1,1). given clause #56: (wt=6) 109 [hyper,21,2,15,16,demod] CS(1,4,5,0,1). given clause #57: (wt=6) 110 [hyper,21,2,15,15,demod] CS(1,4,4,9,0). given clause #58: (wt=6) 111 [hyper,21,2,15,14,demod] CS(1,4,3,8,0). given clause #59: (wt=6) 112 [hyper,21,2,15,13,demod] CS(1,4,2,7,0). given clause #60: (wt=6) 113 [hyper,21,2,15,12,demod] CS(1,4,1,6,0). given clause #61: (wt=6) 114 [hyper,21,2,15,11,demod] CS(1,4,0,5,0). given clause #62: (wt=6) 115 [hyper,21,2,14,20,demod] CS(1,3,9,3,1). given clause #63: (wt=6) 116 [hyper,21,2,14,19,demod] CS(1,3,8,2,1). given clause #64: (wt=6) 117 [hyper,21,2,14,18,demod] CS(1,3,7,1,1). given clause #65: (wt=6) 118 [hyper,21,2,14,17,demod] CS(1,3,6,0,1). given clause #66: (wt=6) 119 [hyper,21,2,14,16,demod] CS(1,3,5,9,0). given clause #67: (wt=6) 120 [hyper,21,2,14,15,demod] CS(1,3,4,8,0). given clause #68: (wt=6) 121 [hyper,21,2,14,14,demod] CS(1,3,3,7,0). given clause #69: (wt=6) 122 [hyper,21,2,14,13,demod] CS(1,3,2,6,0). given clause #70: (wt=6) 123 [hyper,21,2,14,12,demod] CS(1,3,1,5,0). given clause #71: (wt=6) 124 [hyper,21,2,14,11,demod] CS(1,3,0,4,0). given clause #72: (wt=6) 125 [hyper,21,2,13,20,demod] CS(1,2,9,2,1). given clause #73: (wt=6) 126 [hyper,21,2,13,19,demod] CS(1,2,8,1,1). given clause #74: (wt=6) 127 [hyper,21,2,13,18,demod] CS(1,2,7,0,1). given clause #75: (wt=6) 128 [hyper,21,2,13,17,demod] CS(1,2,6,9,0). given clause #76: (wt=6) 129 [hyper,21,2,13,16,demod] CS(1,2,5,8,0). given clause #77: (wt=6) 130 [hyper,21,2,13,15,demod] CS(1,2,4,7,0). given clause #78: (wt=6) 131 [hyper,21,2,13,14,demod] CS(1,2,3,6,0). given clause #79: (wt=6) 132 [hyper,21,2,13,13,demod] CS(1,2,2,5,0). given clause #80: (wt=6) 133 [hyper,21,2,13,12,demod] CS(1,2,1,4,0). given clause #81: (wt=6) 134 [hyper,21,2,13,11,demod] CS(1,2,0,3,0). given clause #82: (wt=6) 135 [hyper,21,2,12,20,demod] CS(1,1,9,1,1). given clause #83: (wt=6) 136 [hyper,21,2,12,19,demod] CS(1,1,8,0,1). given clause #84: (wt=6) 137 [hyper,21,2,12,18,demod] CS(1,1,7,9,0). given clause #85: (wt=6) 138 [hyper,21,2,12,17,demod] CS(1,1,6,8,0). given clause #86: (wt=6) 139 [hyper,21,2,12,16,demod] CS(1,1,5,7,0). given clause #87: (wt=6) 140 [hyper,21,2,12,15,demod] CS(1,1,4,6,0). given clause #88: (wt=6) 141 [hyper,21,2,12,14,demod] CS(1,1,3,5,0). given clause #89: (wt=6) 142 [hyper,21,2,12,13,demod] CS(1,1,2,4,0). given clause #90: (wt=6) 143 [hyper,21,2,12,12,demod] CS(1,1,1,3,0). given clause #91: (wt=6) 144 [hyper,21,2,12,11,demod] CS(1,1,0,2,0). given clause #92: (wt=6) 145 [hyper,21,2,11,20,demod] CS(1,0,9,0,1). given clause #93: (wt=6) 146 [hyper,21,2,11,19,demod] CS(1,0,8,9,0). given clause #94: (wt=6) 147 [hyper,21,2,11,18,demod] CS(1,0,7,8,0). given clause #95: (wt=6) 148 [hyper,21,2,11,17,demod] CS(1,0,6,7,0). given clause #96: (wt=6) 149 [hyper,21,2,11,16,demod] CS(1,0,5,6,0). given clause #97: (wt=6) 150 [hyper,21,2,11,15,demod] CS(1,0,4,5,0). given clause #98: (wt=6) 151 [hyper,21,2,11,14,demod] CS(1,0,3,4,0). given clause #99: (wt=6) 152 [hyper,21,2,11,13,demod] CS(1,0,2,3,0). given clause #100: (wt=6) 153 [hyper,21,2,11,12,demod] CS(1,0,1,2,0). given clause #101: (wt=6) 154 [hyper,21,2,11,11,demod] CS(1,0,0,1,0). given clause #102: (wt=6) 155 [hyper,21,1,20,20,demod] CS(0,9,9,8,1). given clause #103: (wt=6) 156 [hyper,21,1,20,19,demod] CS(0,9,8,7,1). given clause #104: (wt=6) 157 [hyper,21,1,20,18,demod] CS(0,9,7,6,1). given clause #105: (wt=6) 158 [hyper,21,1,20,17,demod] CS(0,9,6,5,1). given clause #106: (wt=6) 159 [hyper,21,1,20,16,demod] CS(0,9,5,4,1). given clause #107: (wt=6) 160 [hyper,21,1,20,15,demod] CS(0,9,4,3,1). given clause #108: (wt=6) 161 [hyper,21,1,20,14,demod] CS(0,9,3,2,1). given clause #109: (wt=6) 162 [hyper,21,1,20,13,demod] CS(0,9,2,1,1). given clause #110: (wt=6) 163 [hyper,21,1,20,12,demod] CS(0,9,1,0,1). given clause #111: (wt=6) 164 [hyper,21,1,20,11,demod] CS(0,9,0,9,0). given clause #112: (wt=6) 165 [hyper,21,1,19,20,demod] CS(0,8,9,7,1). given clause #113: (wt=6) 166 [hyper,21,1,19,19,demod] CS(0,8,8,6,1). given clause #114: (wt=6) 167 [hyper,21,1,19,18,demod] CS(0,8,7,5,1). given clause #115: (wt=6) 168 [hyper,21,1,19,17,demod] CS(0,8,6,4,1). given clause #116: (wt=6) 169 [hyper,21,1,19,16,demod] CS(0,8,5,3,1). given clause #117: (wt=6) 170 [hyper,21,1,19,15,demod] CS(0,8,4,2,1). given clause #118: (wt=6) 171 [hyper,21,1,19,14,demod] CS(0,8,3,1,1). given clause #119: (wt=6) 172 [hyper,21,1,19,13,demod] CS(0,8,2,0,1). given clause #120: (wt=6) 173 [hyper,21,1,19,12,demod] CS(0,8,1,9,0). given clause #121: (wt=6) 174 [hyper,21,1,19,11,demod] CS(0,8,0,8,0). given clause #122: (wt=6) 175 [hyper,21,1,18,20,demod] CS(0,7,9,6,1). given clause #123: (wt=6) 176 [hyper,21,1,18,19,demod] CS(0,7,8,5,1). given clause #124: (wt=6) 177 [hyper,21,1,18,18,demod] CS(0,7,7,4,1). given clause #125: (wt=6) 178 [hyper,21,1,18,17,demod] CS(0,7,6,3,1). given clause #126: (wt=6) 179 [hyper,21,1,18,16,demod] CS(0,7,5,2,1). given clause #127: (wt=6) 180 [hyper,21,1,18,15,demod] CS(0,7,4,1,1). given clause #128: (wt=6) 181 [hyper,21,1,18,14,demod] CS(0,7,3,0,1). given clause #129: (wt=6) 182 [hyper,21,1,18,13,demod] CS(0,7,2,9,0). given clause #130: (wt=6) 183 [hyper,21,1,18,12,demod] CS(0,7,1,8,0). given clause #131: (wt=6) 184 [hyper,21,1,18,11,demod] CS(0,7,0,7,0). given clause #132: (wt=6) 185 [hyper,21,1,17,20,demod] CS(0,6,9,5,1). given clause #133: (wt=6) 186 [hyper,21,1,17,19,demod] CS(0,6,8,4,1). given clause #134: (wt=6) 187 [hyper,21,1,17,18,demod] CS(0,6,7,3,1). given clause #135: (wt=6) 188 [hyper,21,1,17,17,demod] CS(0,6,6,2,1). given clause #136: (wt=6) 189 [hyper,21,1,17,16,demod] CS(0,6,5,1,1). given clause #137: (wt=6) 190 [hyper,21,1,17,15,demod] CS(0,6,4,0,1). given clause #138: (wt=6) 191 [hyper,21,1,17,14,demod] CS(0,6,3,9,0). given clause #139: (wt=6) 192 [hyper,21,1,17,13,demod] CS(0,6,2,8,0). given clause #140: (wt=6) 193 [hyper,21,1,17,12,demod] CS(0,6,1,7,0). given clause #141: (wt=6) 194 [hyper,21,1,17,11,demod] CS(0,6,0,6,0). given clause #142: (wt=6) 195 [hyper,21,1,16,20,demod] CS(0,5,9,4,1). given clause #143: (wt=6) 196 [hyper,21,1,16,19,demod] CS(0,5,8,3,1). given clause #144: (wt=6) 197 [hyper,21,1,16,18,demod] CS(0,5,7,2,1). given clause #145: (wt=6) 198 [hyper,21,1,16,17,demod] CS(0,5,6,1,1). given clause #146: (wt=6) 199 [hyper,21,1,16,16,demod] CS(0,5,5,0,1). given clause #147: (wt=6) 200 [hyper,21,1,16,15,demod] CS(0,5,4,9,0). given clause #148: (wt=6) 201 [hyper,21,1,16,14,demod] CS(0,5,3,8,0). given clause #149: (wt=6) 202 [hyper,21,1,16,13,demod] CS(0,5,2,7,0). given clause #150: (wt=6) 203 [hyper,21,1,16,12,demod] CS(0,5,1,6,0). given clause #151: (wt=6) 204 [hyper,21,1,16,11,demod] CS(0,5,0,5,0). given clause #152: (wt=6) 205 [hyper,21,1,15,20,demod] CS(0,4,9,3,1). given clause #153: (wt=6) 206 [hyper,21,1,15,19,demod] CS(0,4,8,2,1). given clause #154: (wt=6) 207 [hyper,21,1,15,18,demod] CS(0,4,7,1,1). given clause #155: (wt=6) 208 [hyper,21,1,15,17,demod] CS(0,4,6,0,1). given clause #156: (wt=6) 209 [hyper,21,1,15,16,demod] CS(0,4,5,9,0). given clause #157: (wt=6) 210 [hyper,21,1,15,15,demod] CS(0,4,4,8,0). given clause #158: (wt=6) 211 [hyper,21,1,15,14,demod] CS(0,4,3,7,0). given clause #159: (wt=6) 212 [hyper,21,1,15,13,demod] CS(0,4,2,6,0). given clause #160: (wt=6) 213 [hyper,21,1,15,12,demod] CS(0,4,1,5,0). given clause #161: (wt=6) 214 [hyper,21,1,15,11,demod] CS(0,4,0,4,0). given clause #162: (wt=6) 215 [hyper,21,1,14,20,demod] CS(0,3,9,2,1). given clause #163: (wt=6) 216 [hyper,21,1,14,19,demod] CS(0,3,8,1,1). given clause #164: (wt=6) 217 [hyper,21,1,14,18,demod] CS(0,3,7,0,1). given clause #165: (wt=6) 218 [hyper,21,1,14,17,demod] CS(0,3,6,9,0). given clause #166: (wt=6) 219 [hyper,21,1,14,16,demod] CS(0,3,5,8,0). given clause #167: (wt=6) 220 [hyper,21,1,14,15,demod] CS(0,3,4,7,0). given clause #168: (wt=6) 221 [hyper,21,1,14,14,demod] CS(0,3,3,6,0). given clause #169: (wt=6) 222 [hyper,21,1,14,13,demod] CS(0,3,2,5,0). given clause #170: (wt=6) 223 [hyper,21,1,14,12,demod] CS(0,3,1,4,0). given clause #171: (wt=6) 224 [hyper,21,1,14,11,demod] CS(0,3,0,3,0). given clause #172: (wt=6) 225 [hyper,21,1,13,20,demod] CS(0,2,9,1,1). given clause #173: (wt=6) 226 [hyper,21,1,13,19,demod] CS(0,2,8,0,1). given clause #174: (wt=6) 227 [hyper,21,1,13,18,demod] CS(0,2,7,9,0). given clause #175: (wt=6) 228 [hyper,21,1,13,17,demod] CS(0,2,6,8,0). given clause #176: (wt=6) 229 [hyper,21,1,13,16,demod] CS(0,2,5,7,0). given clause #177: (wt=6) 230 [hyper,21,1,13,15,demod] CS(0,2,4,6,0). given clause #178: (wt=6) 231 [hyper,21,1,13,14,demod] CS(0,2,3,5,0). given clause #179: (wt=6) 232 [hyper,21,1,13,13,demod] CS(0,2,2,4,0). given clause #180: (wt=6) 233 [hyper,21,1,13,12,demod] CS(0,2,1,3,0). given clause #181: (wt=6) 234 [hyper,21,1,13,11,demod] CS(0,2,0,2,0). given clause #182: (wt=6) 235 [hyper,21,1,12,20,demod] CS(0,1,9,0,1). given clause #183: (wt=6) 236 [hyper,21,1,12,19,demod] CS(0,1,8,9,0). given clause #184: (wt=6) 237 [hyper,21,1,12,18,demod] CS(0,1,7,8,0). given clause #185: (wt=6) 238 [hyper,21,1,12,17,demod] CS(0,1,6,7,0). given clause #186: (wt=6) 239 [hyper,21,1,12,16,demod] CS(0,1,5,6,0). given clause #187: (wt=6) 240 [hyper,21,1,12,15,demod] CS(0,1,4,5,0). given clause #188: (wt=6) 241 [hyper,21,1,12,14,demod] CS(0,1,3,4,0). given clause #189: (wt=6) 242 [hyper,21,1,12,13,demod] CS(0,1,2,3,0). given clause #190: (wt=6) 243 [hyper,21,1,12,12,demod] CS(0,1,1,2,0). given clause #191: (wt=6) 244 [hyper,21,1,12,11,demod] CS(0,1,0,1,0). given clause #192: (wt=6) 245 [hyper,21,1,11,20,demod] CS(0,0,9,9,0). given clause #193: (wt=6) 246 [hyper,21,1,11,19,demod] CS(0,0,8,8,0). given clause #194: (wt=6) 247 [hyper,21,1,11,18,demod] CS(0,0,7,7,0). given clause #195: (wt=6) 248 [hyper,21,1,11,17,demod] CS(0,0,6,6,0). given clause #196: (wt=6) 249 [hyper,21,1,11,16,demod] CS(0,0,5,5,0). given clause #197: (wt=6) 250 [hyper,21,1,11,15,demod] CS(0,0,4,4,0). given clause #198: (wt=6) 251 [hyper,21,1,11,14,demod] CS(0,0,3,3,0). given clause #199: (wt=6) 252 [hyper,21,1,11,13,demod] CS(0,0,2,2,0). given clause #200: (wt=6) 253 [hyper,21,1,11,12,demod] CS(0,0,1,1,0). given clause #201: (wt=6) 254 [hyper,21,1,11,11,demod] CS(0,0,0,0,0). given clause #202: (wt=24) 22 [] -L(u)| -D(x)| -D(y)|CP(u,x,y,$MOD($SUM(u,$PROD(x,y)),10),$DIV($SUM(u,$PROD(x,y)),10)). ** KEPT (pick-wt=6): 255 [hyper,22,10,20,20,demod] CP(7,9,9,8,8). ** KEPT (pick-wt=6): 256 [hyper,22,10,20,19,demod] CP(7,9,8,9,7). ** KEPT (pick-wt=6): 257 [hyper,22,10,20,18,demod] CP(7,9,7,0,7). ** KEPT (pick-wt=6): 258 [hyper,22,10,20,17,demod] CP(7,9,6,1,6). ** KEPT (pick-wt=6): 259 [hyper,22,10,20,16,demod] CP(7,9,5,2,5). ** KEPT (pick-wt=6): 260 [hyper,22,10,20,15,demod] CP(7,9,4,3,4). ** KEPT (pick-wt=6): 261 [hyper,22,10,20,14,demod] CP(7,9,3,4,3). ** KEPT (pick-wt=6): 262 [hyper,22,10,20,13,demod] CP(7,9,2,5,2). ** KEPT (pick-wt=6): 263 [hyper,22,10,20,12,demod] CP(7,9,1,6,1). ** KEPT (pick-wt=6): 264 [hyper,22,10,20,11,demod] CP(7,9,0,7,0). ** KEPT (pick-wt=6): 265 [hyper,22,10,19,20,demod] CP(7,8,9,9,7). ** KEPT (pick-wt=6): 266 [hyper,22,10,19,19,demod] CP(7,8,8,1,7). ** KEPT (pick-wt=6): 267 [hyper,22,10,19,18,demod] CP(7,8,7,3,6). ** KEPT (pick-wt=6): 268 [hyper,22,10,19,17,demod] CP(7,8,6,5,5). ** KEPT (pick-wt=6): 269 [hyper,22,10,19,16,demod] CP(7,8,5,7,4). ** KEPT (pick-wt=6): 270 [hyper,22,10,19,15,demod] CP(7,8,4,9,3). ** KEPT (pick-wt=6): 271 [hyper,22,10,19,14,demod] CP(7,8,3,1,3). ** KEPT (pick-wt=6): 272 [hyper,22,10,19,13,demod] CP(7,8,2,3,2). ** KEPT (pick-wt=6): 273 [hyper,22,10,19,12,demod] CP(7,8,1,5,1). ** KEPT (pick-wt=6): 274 [hyper,22,10,19,11,demod] CP(7,8,0,7,0). ** KEPT (pick-wt=6): 275 [hyper,22,10,18,20,demod] CP(7,7,9,0,7). ** KEPT (pick-wt=6): 276 [hyper,22,10,18,19,demod] CP(7,7,8,3,6). ** KEPT (pick-wt=6): 277 [hyper,22,10,18,18,demod] CP(7,7,7,6,5). ** KEPT (pick-wt=6): 278 [hyper,22,10,18,17,demod] CP(7,7,6,9,4). ** KEPT (pick-wt=6): 279 [hyper,22,10,18,16,demod] CP(7,7,5,2,4). ** KEPT (pick-wt=6): 280 [hyper,22,10,18,15,demod] CP(7,7,4,5,3). ** KEPT (pick-wt=6): 281 [hyper,22,10,18,14,demod] CP(7,7,3,8,2). ** KEPT (pick-wt=6): 282 [hyper,22,10,18,13,demod] CP(7,7,2,1,2). ** KEPT (pick-wt=6): 283 [hyper,22,10,18,12,demod] CP(7,7,1,4,1). ** KEPT (pick-wt=6): 284 [hyper,22,10,18,11,demod] CP(7,7,0,7,0). ** KEPT (pick-wt=6): 285 [hyper,22,10,17,20,demod] CP(7,6,9,1,6). ** KEPT (pick-wt=6): 286 [hyper,22,10,17,19,demod] CP(7,6,8,5,5). ** KEPT (pick-wt=6): 287 [hyper,22,10,17,18,demod] CP(7,6,7,9,4). ** KEPT (pick-wt=6): 288 [hyper,22,10,17,17,demod] CP(7,6,6,3,4). ** KEPT (pick-wt=6): 289 [hyper,22,10,17,16,demod] CP(7,6,5,7,3). ** KEPT (pick-wt=6): 290 [hyper,22,10,17,15,demod] CP(7,6,4,1,3). ** KEPT (pick-wt=6): 291 [hyper,22,10,17,14,demod] CP(7,6,3,5,2). ** KEPT (pick-wt=6): 292 [hyper,22,10,17,13,demod] CP(7,6,2,9,1). ** KEPT (pick-wt=6): 293 [hyper,22,10,17,12,demod] CP(7,6,1,3,1). ** KEPT (pick-wt=6): 294 [hyper,22,10,17,11,demod] CP(7,6,0,7,0). ** KEPT (pick-wt=6): 295 [hyper,22,10,16,20,demod] CP(7,5,9,2,5). ** KEPT (pick-wt=6): 296 [hyper,22,10,16,19,demod] CP(7,5,8,7,4). ** KEPT (pick-wt=6): 297 [hyper,22,10,16,18,demod] CP(7,5,7,2,4). ** KEPT (pick-wt=6): 298 [hyper,22,10,16,17,demod] CP(7,5,6,7,3). ** KEPT (pick-wt=6): 299 [hyper,22,10,16,16,demod] CP(7,5,5,2,3). ** KEPT (pick-wt=6): 300 [hyper,22,10,16,15,demod] CP(7,5,4,7,2). ** KEPT (pick-wt=6): 301 [hyper,22,10,16,14,demod] CP(7,5,3,2,2). ** KEPT (pick-wt=6): 302 [hyper,22,10,16,13,demod] CP(7,5,2,7,1). ** KEPT (pick-wt=6): 303 [hyper,22,10,16,12,demod] CP(7,5,1,2,1). ** KEPT (pick-wt=6): 304 [hyper,22,10,16,11,demod] CP(7,5,0,7,0). ** KEPT (pick-wt=6): 305 [hyper,22,10,15,20,demod] CP(7,4,9,3,4). ** KEPT (pick-wt=6): 306 [hyper,22,10,15,19,demod] CP(7,4,8,9,3). ** KEPT (pick-wt=6): 307 [hyper,22,10,15,18,demod] CP(7,4,7,5,3). ** KEPT (pick-wt=6): 308 [hyper,22,10,15,17,demod] CP(7,4,6,1,3). ** KEPT (pick-wt=6): 309 [hyper,22,10,15,16,demod] CP(7,4,5,7,2). ** KEPT (pick-wt=6): 310 [hyper,22,10,15,15,demod] CP(7,4,4,3,2). ** KEPT (pick-wt=6): 311 [hyper,22,10,15,14,demod] CP(7,4,3,9,1). ** KEPT (pick-wt=6): 312 [hyper,22,10,15,13,demod] CP(7,4,2,5,1). ** KEPT (pick-wt=6): 313 [hyper,22,10,15,12,demod] CP(7,4,1,1,1). ** KEPT (pick-wt=6): 314 [hyper,22,10,15,11,demod] CP(7,4,0,7,0). ** KEPT (pick-wt=6): 315 [hyper,22,10,14,20,demod] CP(7,3,9,4,3). ** KEPT (pick-wt=6): 316 [hyper,22,10,14,19,demod] CP(7,3,8,1,3). ** KEPT (pick-wt=6): 317 [hyper,22,10,14,18,demod] CP(7,3,7,8,2). ** KEPT (pick-wt=6): 318 [hyper,22,10,14,17,demod] CP(7,3,6,5,2). ** KEPT (pick-wt=6): 319 [hyper,22,10,14,16,demod] CP(7,3,5,2,2). ** KEPT (pick-wt=6): 320 [hyper,22,10,14,15,demod] CP(7,3,4,9,1). ** KEPT (pick-wt=6): 321 [hyper,22,10,14,14,demod] CP(7,3,3,6,1). ** KEPT (pick-wt=6): 322 [hyper,22,10,14,13,demod] CP(7,3,2,3,1). ** KEPT (pick-wt=6): 323 [hyper,22,10,14,12,demod] CP(7,3,1,0,1). ** KEPT (pick-wt=6): 324 [hyper,22,10,14,11,demod] CP(7,3,0,7,0). ** KEPT (pick-wt=6): 325 [hyper,22,10,13,20,demod] CP(7,2,9,5,2). ** KEPT (pick-wt=6): 326 [hyper,22,10,13,19,demod] CP(7,2,8,3,2). ** KEPT (pick-wt=6): 327 [hyper,22,10,13,18,demod] CP(7,2,7,1,2). ** KEPT (pick-wt=6): 328 [hyper,22,10,13,17,demod] CP(7,2,6,9,1). ** KEPT (pick-wt=6): 329 [hyper,22,10,13,16,demod] CP(7,2,5,7,1). ** KEPT (pick-wt=6): 330 [hyper,22,10,13,15,demod] CP(7,2,4,5,1). ** KEPT (pick-wt=6): 331 [hyper,22,10,13,14,demod] CP(7,2,3,3,1). ** KEPT (pick-wt=6): 332 [hyper,22,10,13,13,demod] CP(7,2,2,1,1). ** KEPT (pick-wt=6): 333 [hyper,22,10,13,12,demod] CP(7,2,1,9,0). ** KEPT (pick-wt=6): 334 [hyper,22,10,13,11,demod] CP(7,2,0,7,0). ** KEPT (pick-wt=6): 335 [hyper,22,10,12,20,demod] CP(7,1,9,6,1). ** KEPT (pick-wt=6): 336 [hyper,22,10,12,19,demod] CP(7,1,8,5,1). ** KEPT (pick-wt=6): 337 [hyper,22,10,12,18,demod] CP(7,1,7,4,1). ** KEPT (pick-wt=6): 338 [hyper,22,10,12,17,demod] CP(7,1,6,3,1). ** KEPT (pick-wt=6): 339 [hyper,22,10,12,16,demod] CP(7,1,5,2,1). ** KEPT (pick-wt=6): 340 [hyper,22,10,12,15,demod] CP(7,1,4,1,1). ** KEPT (pick-wt=6): 341 [hyper,22,10,12,14,demod] CP(7,1,3,0,1). ** KEPT (pick-wt=6): 342 [hyper,22,10,12,13,demod] CP(7,1,2,9,0). ** KEPT (pick-wt=6): 343 [hyper,22,10,12,12,demod] CP(7,1,1,8,0). ** KEPT (pick-wt=6): 344 [hyper,22,10,12,11,demod] CP(7,1,0,7,0). ** KEPT (pick-wt=6): 345 [hyper,22,10,11,20,demod] CP(7,0,9,7,0). ** KEPT (pick-wt=6): 346 [hyper,22,10,11,19,demod] CP(7,0,8,7,0). ** KEPT (pick-wt=6): 347 [hyper,22,10,11,18,demod] CP(7,0,7,7,0). ** KEPT (pick-wt=6): 348 [hyper,22,10,11,17,demod] CP(7,0,6,7,0). ** KEPT (pick-wt=6): 349 [hyper,22,10,11,16,demod] CP(7,0,5,7,0). ** KEPT (pick-wt=6): 350 [hyper,22,10,11,15,demod] CP(7,0,4,7,0). ** KEPT (pick-wt=6): 351 [hyper,22,10,11,14,demod] CP(7,0,3,7,0). ** KEPT (pick-wt=6): 352 [hyper,22,10,11,13,demod] CP(7,0,2,7,0). ** KEPT (pick-wt=6): 353 [hyper,22,10,11,12,demod] CP(7,0,1,7,0). ** KEPT (pick-wt=6): 354 [hyper,22,10,11,11,demod] CP(7,0,0,7,0). ** KEPT (pick-wt=6): 355 [hyper,22,9,20,20,demod] CP(6,9,9,7,8). ** KEPT (pick-wt=6): 356 [hyper,22,9,20,19,demod] CP(6,9,8,8,7). ** KEPT (pick-wt=6): 357 [hyper,22,9,20,18,demod] CP(6,9,7,9,6). ** KEPT (pick-wt=6): 358 [hyper,22,9,20,17,demod] CP(6,9,6,0,6). ** KEPT (pick-wt=6): 359 [hyper,22,9,20,16,demod] CP(6,9,5,1,5). ** KEPT (pick-wt=6): 360 [hyper,22,9,20,15,demod] CP(6,9,4,2,4). ** KEPT (pick-wt=6): 361 [hyper,22,9,20,14,demod] CP(6,9,3,3,3). ** KEPT (pick-wt=6): 362 [hyper,22,9,20,13,demod] CP(6,9,2,4,2). ** KEPT (pick-wt=6): 363 [hyper,22,9,20,12,demod] CP(6,9,1,5,1). ** KEPT (pick-wt=6): 364 [hyper,22,9,20,11,demod] CP(6,9,0,6,0). ** KEPT (pick-wt=6): 365 [hyper,22,9,19,20,demod] CP(6,8,9,8,7). ** KEPT (pick-wt=6): 366 [hyper,22,9,19,19,demod] CP(6,8,8,0,7). ** KEPT (pick-wt=6): 367 [hyper,22,9,19,18,demod] CP(6,8,7,2,6). ** KEPT (pick-wt=6): 368 [hyper,22,9,19,17,demod] CP(6,8,6,4,5). ** KEPT (pick-wt=6): 369 [hyper,22,9,19,16,demod] CP(6,8,5,6,4). ** KEPT (pick-wt=6): 370 [hyper,22,9,19,15,demod] CP(6,8,4,8,3). ** KEPT (pick-wt=6): 371 [hyper,22,9,19,14,demod] CP(6,8,3,0,3). ** KEPT (pick-wt=6): 372 [hyper,22,9,19,13,demod] CP(6,8,2,2,2). ** KEPT (pick-wt=6): 373 [hyper,22,9,19,12,demod] CP(6,8,1,4,1). ** KEPT (pick-wt=6): 374 [hyper,22,9,19,11,demod] CP(6,8,0,6,0). ** KEPT (pick-wt=6): 375 [hyper,22,9,18,20,demod] CP(6,7,9,9,6). ** KEPT (pick-wt=6): 376 [hyper,22,9,18,19,demod] CP(6,7,8,2,6). ** KEPT (pick-wt=6): 377 [hyper,22,9,18,18,demod] CP(6,7,7,5,5). ** KEPT (pick-wt=6): 378 [hyper,22,9,18,17,demod] CP(6,7,6,8,4). ** KEPT (pick-wt=6): 379 [hyper,22,9,18,16,demod] CP(6,7,5,1,4). ** KEPT (pick-wt=6): 380 [hyper,22,9,18,15,demod] CP(6,7,4,4,3). ** KEPT (pick-wt=6): 381 [hyper,22,9,18,14,demod] CP(6,7,3,7,2). ** KEPT (pick-wt=6): 382 [hyper,22,9,18,13,demod] CP(6,7,2,0,2). ** KEPT (pick-wt=6): 383 [hyper,22,9,18,12,demod] CP(6,7,1,3,1). ** KEPT (pick-wt=6): 384 [hyper,22,9,18,11,demod] CP(6,7,0,6,0). ** KEPT (pick-wt=6): 385 [hyper,22,9,17,20,demod] CP(6,6,9,0,6). ** KEPT (pick-wt=6): 386 [hyper,22,9,17,19,demod] CP(6,6,8,4,5). ** KEPT (pick-wt=6): 387 [hyper,22,9,17,18,demod] CP(6,6,7,8,4). ** KEPT (pick-wt=6): 388 [hyper,22,9,17,17,demod] CP(6,6,6,2,4). ** KEPT (pick-wt=6): 389 [hyper,22,9,17,16,demod] CP(6,6,5,6,3). ** KEPT (pick-wt=6): 390 [hyper,22,9,17,15,demod] CP(6,6,4,0,3). ** KEPT (pick-wt=6): 391 [hyper,22,9,17,14,demod] CP(6,6,3,4,2). ** KEPT (pick-wt=6): 392 [hyper,22,9,17,13,demod] CP(6,6,2,8,1). ** KEPT (pick-wt=6): 393 [hyper,22,9,17,12,demod] CP(6,6,1,2,1). ** KEPT (pick-wt=6): 394 [hyper,22,9,17,11,demod] CP(6,6,0,6,0). ** KEPT (pick-wt=6): 395 [hyper,22,9,16,20,demod] CP(6,5,9,1,5). ** KEPT (pick-wt=6): 396 [hyper,22,9,16,19,demod] CP(6,5,8,6,4). ** KEPT (pick-wt=6): 397 [hyper,22,9,16,18,demod] CP(6,5,7,1,4). ** KEPT (pick-wt=6): 398 [hyper,22,9,16,17,demod] CP(6,5,6,6,3). ** KEPT (pick-wt=6): 399 [hyper,22,9,16,16,demod] CP(6,5,5,1,3). ** KEPT (pick-wt=6): 400 [hyper,22,9,16,15,demod] CP(6,5,4,6,2). ** KEPT (pick-wt=6): 401 [hyper,22,9,16,14,demod] CP(6,5,3,1,2). ** KEPT (pick-wt=6): 402 [hyper,22,9,16,13,demod] CP(6,5,2,6,1). ** KEPT (pick-wt=6): 403 [hyper,22,9,16,12,demod] CP(6,5,1,1,1). ** KEPT (pick-wt=6): 404 [hyper,22,9,16,11,demod] CP(6,5,0,6,0). ** KEPT (pick-wt=6): 405 [hyper,22,9,15,20,demod] CP(6,4,9,2,4). ** KEPT (pick-wt=6): 406 [hyper,22,9,15,19,demod] CP(6,4,8,8,3). ** KEPT (pick-wt=6): 407 [hyper,22,9,15,18,demod] CP(6,4,7,4,3). ** KEPT (pick-wt=6): 408 [hyper,22,9,15,17,demod] CP(6,4,6,0,3). ** KEPT (pick-wt=6): 409 [hyper,22,9,15,16,demod] CP(6,4,5,6,2). ** KEPT (pick-wt=6): 410 [hyper,22,9,15,15,demod] CP(6,4,4,2,2). ** KEPT (pick-wt=6): 411 [hyper,22,9,15,14,demod] CP(6,4,3,8,1). ** KEPT (pick-wt=6): 412 [hyper,22,9,15,13,demod] CP(6,4,2,4,1). ** KEPT (pick-wt=6): 413 [hyper,22,9,15,12,demod] CP(6,4,1,0,1). ** KEPT (pick-wt=6): 414 [hyper,22,9,15,11,demod] CP(6,4,0,6,0). ** KEPT (pick-wt=6): 415 [hyper,22,9,14,20,demod] CP(6,3,9,3,3). ** KEPT (pick-wt=6): 416 [hyper,22,9,14,19,demod] CP(6,3,8,0,3). ** KEPT (pick-wt=6): 417 [hyper,22,9,14,18,demod] CP(6,3,7,7,2). ** KEPT (pick-wt=6): 418 [hyper,22,9,14,17,demod] CP(6,3,6,4,2). ** KEPT (pick-wt=6): 419 [hyper,22,9,14,16,demod] CP(6,3,5,1,2). ** KEPT (pick-wt=6): 420 [hyper,22,9,14,15,demod] CP(6,3,4,8,1). ** KEPT (pick-wt=6): 421 [hyper,22,9,14,14,demod] CP(6,3,3,5,1). ** KEPT (pick-wt=6): 422 [hyper,22,9,14,13,demod] CP(6,3,2,2,1). ** KEPT (pick-wt=6): 423 [hyper,22,9,14,12,demod] CP(6,3,1,9,0). ** KEPT (pick-wt=6): 424 [hyper,22,9,14,11,demod] CP(6,3,0,6,0). ** KEPT (pick-wt=6): 425 [hyper,22,9,13,20,demod] CP(6,2,9,4,2). ** KEPT (pick-wt=6): 426 [hyper,22,9,13,19,demod] CP(6,2,8,2,2). ** KEPT (pick-wt=6): 427 [hyper,22,9,13,18,demod] CP(6,2,7,0,2). ** KEPT (pick-wt=6): 428 [hyper,22,9,13,17,demod] CP(6,2,6,8,1). ** KEPT (pick-wt=6): 429 [hyper,22,9,13,16,demod] CP(6,2,5,6,1). ** KEPT (pick-wt=6): 430 [hyper,22,9,13,15,demod] CP(6,2,4,4,1). ** KEPT (pick-wt=6): 431 [hyper,22,9,13,14,demod] CP(6,2,3,2,1). ** KEPT (pick-wt=6): 432 [hyper,22,9,13,13,demod] CP(6,2,2,0,1). ** KEPT (pick-wt=6): 433 [hyper,22,9,13,12,demod] CP(6,2,1,8,0). ** KEPT (pick-wt=6): 434 [hyper,22,9,13,11,demod] CP(6,2,0,6,0). ** KEPT (pick-wt=6): 435 [hyper,22,9,12,20,demod] CP(6,1,9,5,1). ** KEPT (pick-wt=6): 436 [hyper,22,9,12,19,demod] CP(6,1,8,4,1). ** KEPT (pick-wt=6): 437 [hyper,22,9,12,18,demod] CP(6,1,7,3,1). ** KEPT (pick-wt=6): 438 [hyper,22,9,12,17,demod] CP(6,1,6,2,1). ** KEPT (pick-wt=6): 439 [hyper,22,9,12,16,demod] CP(6,1,5,1,1). ** KEPT (pick-wt=6): 440 [hyper,22,9,12,15,demod] CP(6,1,4,0,1). ** KEPT (pick-wt=6): 441 [hyper,22,9,12,14,demod] CP(6,1,3,9,0). ** KEPT (pick-wt=6): 442 [hyper,22,9,12,13,demod] CP(6,1,2,8,0). ** KEPT (pick-wt=6): 443 [hyper,22,9,12,12,demod] CP(6,1,1,7,0). ** KEPT (pick-wt=6): 444 [hyper,22,9,12,11,demod] CP(6,1,0,6,0). ** KEPT (pick-wt=6): 445 [hyper,22,9,11,20,demod] CP(6,0,9,6,0). ** KEPT (pick-wt=6): 446 [hyper,22,9,11,19,demod] CP(6,0,8,6,0). ** KEPT (pick-wt=6): 447 [hyper,22,9,11,18,demod] CP(6,0,7,6,0). ** KEPT (pick-wt=6): 448 [hyper,22,9,11,17,demod] CP(6,0,6,6,0). ** KEPT (pick-wt=6): 449 [hyper,22,9,11,16,demod] CP(6,0,5,6,0). ** KEPT (pick-wt=6): 450 [hyper,22,9,11,15,demod] CP(6,0,4,6,0). ** KEPT (pick-wt=6): 451 [hyper,22,9,11,14,demod] CP(6,0,3,6,0). ** KEPT (pick-wt=6): 452 [hyper,22,9,11,13,demod] CP(6,0,2,6,0). ** KEPT (pick-wt=6): 453 [hyper,22,9,11,12,demod] CP(6,0,1,6,0). ** KEPT (pick-wt=6): 454 [hyper,22,9,11,11,demod] CP(6,0,0,6,0). ** KEPT (pick-wt=6): 455 [hyper,22,8,20,20,demod] CP(5,9,9,6,8). ** KEPT (pick-wt=6): 456 [hyper,22,8,20,19,demod] CP(5,9,8,7,7). ** KEPT (pick-wt=6): 457 [hyper,22,8,20,18,demod] CP(5,9,7,8,6). ** KEPT (pick-wt=6): 458 [hyper,22,8,20,17,demod] CP(5,9,6,9,5). ** KEPT (pick-wt=6): 459 [hyper,22,8,20,16,demod] CP(5,9,5,0,5). ** KEPT (pick-wt=6): 460 [hyper,22,8,20,15,demod] CP(5,9,4,1,4). ** KEPT (pick-wt=6): 461 [hyper,22,8,20,14,demod] CP(5,9,3,2,3). ** KEPT (pick-wt=6): 462 [hyper,22,8,20,13,demod] CP(5,9,2,3,2). ** KEPT (pick-wt=6): 463 [hyper,22,8,20,12,demod] CP(5,9,1,4,1). ** KEPT (pick-wt=6): 464 [hyper,22,8,20,11,demod] CP(5,9,0,5,0). ** KEPT (pick-wt=6): 465 [hyper,22,8,19,20,demod] CP(5,8,9,7,7). ** KEPT (pick-wt=6): 466 [hyper,22,8,19,19,demod] CP(5,8,8,9,6). ** KEPT (pick-wt=6): 467 [hyper,22,8,19,18,demod] CP(5,8,7,1,6). ** KEPT (pick-wt=6): 468 [hyper,22,8,19,17,demod] CP(5,8,6,3,5). ** KEPT (pick-wt=6): 469 [hyper,22,8,19,16,demod] CP(5,8,5,5,4). ** KEPT (pick-wt=6): 470 [hyper,22,8,19,15,demod] CP(5,8,4,7,3). ** KEPT (pick-wt=6): 471 [hyper,22,8,19,14,demod] CP(5,8,3,9,2). ** KEPT (pick-wt=6): 472 [hyper,22,8,19,13,demod] CP(5,8,2,1,2). ** KEPT (pick-wt=6): 473 [hyper,22,8,19,12,demod] CP(5,8,1,3,1). ** KEPT (pick-wt=6): 474 [hyper,22,8,19,11,demod] CP(5,8,0,5,0). ** KEPT (pick-wt=6): 475 [hyper,22,8,18,20,demod] CP(5,7,9,8,6). ** KEPT (pick-wt=6): 476 [hyper,22,8,18,19,demod] CP(5,7,8,1,6). ** KEPT (pick-wt=6): 477 [hyper,22,8,18,18,demod] CP(5,7,7,4,5). ** KEPT (pick-wt=6): 478 [hyper,22,8,18,17,demod] CP(5,7,6,7,4). ** KEPT (pick-wt=6): 479 [hyper,22,8,18,16,demod] CP(5,7,5,0,4). ** KEPT (pick-wt=6): 480 [hyper,22,8,18,15,demod] CP(5,7,4,3,3). ** KEPT (pick-wt=6): 481 [hyper,22,8,18,14,demod] CP(5,7,3,6,2). ** KEPT (pick-wt=6): 482 [hyper,22,8,18,13,demod] CP(5,7,2,9,1). ** KEPT (pick-wt=6): 483 [hyper,22,8,18,12,demod] CP(5,7,1,2,1). ** KEPT (pick-wt=6): 484 [hyper,22,8,18,11,demod] CP(5,7,0,5,0). ** KEPT (pick-wt=6): 485 [hyper,22,8,17,20,demod] CP(5,6,9,9,5). ** KEPT (pick-wt=6): 486 [hyper,22,8,17,19,demod] CP(5,6,8,3,5). ** KEPT (pick-wt=6): 487 [hyper,22,8,17,18,demod] CP(5,6,7,7,4). ** KEPT (pick-wt=6): 488 [hyper,22,8,17,17,demod] CP(5,6,6,1,4). ** KEPT (pick-wt=6): 489 [hyper,22,8,17,16,demod] CP(5,6,5,5,3). ** KEPT (pick-wt=6): 490 [hyper,22,8,17,15,demod] CP(5,6,4,9,2). ** KEPT (pick-wt=6): 491 [hyper,22,8,17,14,demod] CP(5,6,3,3,2). ** KEPT (pick-wt=6): 492 [hyper,22,8,17,13,demod] CP(5,6,2,7,1). ** KEPT (pick-wt=6): 493 [hyper,22,8,17,12,demod] CP(5,6,1,1,1). ** KEPT (pick-wt=6): 494 [hyper,22,8,17,11,demod] CP(5,6,0,5,0). ** KEPT (pick-wt=6): 495 [hyper,22,8,16,20,demod] CP(5,5,9,0,5). ** KEPT (pick-wt=6): 496 [hyper,22,8,16,19,demod] CP(5,5,8,5,4). ** KEPT (pick-wt=6): 497 [hyper,22,8,16,18,demod] CP(5,5,7,0,4). ** KEPT (pick-wt=6): 498 [hyper,22,8,16,17,demod] CP(5,5,6,5,3). ** KEPT (pick-wt=6): 499 [hyper,22,8,16,16,demod] CP(5,5,5,0,3). ** KEPT (pick-wt=6): 500 [hyper,22,8,16,15,demod] CP(5,5,4,5,2). ** KEPT (pick-wt=6): 501 [hyper,22,8,16,14,demod] CP(5,5,3,0,2). ** KEPT (pick-wt=6): 502 [hyper,22,8,16,13,demod] CP(5,5,2,5,1). ** KEPT (pick-wt=6): 503 [hyper,22,8,16,12,demod] CP(5,5,1,0,1). ** KEPT (pick-wt=6): 504 [hyper,22,8,16,11,demod] CP(5,5,0,5,0). ** KEPT (pick-wt=6): 505 [hyper,22,8,15,20,demod] CP(5,4,9,1,4). ** KEPT (pick-wt=6): 506 [hyper,22,8,15,19,demod] CP(5,4,8,7,3). ** KEPT (pick-wt=6): 507 [hyper,22,8,15,18,demod] CP(5,4,7,3,3). ** KEPT (pick-wt=6): 508 [hyper,22,8,15,17,demod] CP(5,4,6,9,2). ** KEPT (pick-wt=6): 509 [hyper,22,8,15,16,demod] CP(5,4,5,5,2). ** KEPT (pick-wt=6): 510 [hyper,22,8,15,15,demod] CP(5,4,4,1,2). ** KEPT (pick-wt=6): 511 [hyper,22,8,15,14,demod] CP(5,4,3,7,1). ** KEPT (pick-wt=6): 512 [hyper,22,8,15,13,demod] CP(5,4,2,3,1). ** KEPT (pick-wt=6): 513 [hyper,22,8,15,12,demod] CP(5,4,1,9,0). ** KEPT (pick-wt=6): 514 [hyper,22,8,15,11,demod] CP(5,4,0,5,0). ** KEPT (pick-wt=6): 515 [hyper,22,8,14,20,demod] CP(5,3,9,2,3). ** KEPT (pick-wt=6): 516 [hyper,22,8,14,19,demod] CP(5,3,8,9,2). ** KEPT (pick-wt=6): 517 [hyper,22,8,14,18,demod] CP(5,3,7,6,2). ** KEPT (pick-wt=6): 518 [hyper,22,8,14,17,demod] CP(5,3,6,3,2). ** KEPT (pick-wt=6): 519 [hyper,22,8,14,16,demod] CP(5,3,5,0,2). ** KEPT (pick-wt=6): 520 [hyper,22,8,14,15,demod] CP(5,3,4,7,1). ** KEPT (pick-wt=6): 521 [hyper,22,8,14,14,demod] CP(5,3,3,4,1). ** KEPT (pick-wt=6): 522 [hyper,22,8,14,13,demod] CP(5,3,2,1,1). ** KEPT (pick-wt=6): 523 [hyper,22,8,14,12,demod] CP(5,3,1,8,0). ** KEPT (pick-wt=6): 524 [hyper,22,8,14,11,demod] CP(5,3,0,5,0). ** KEPT (pick-wt=6): 525 [hyper,22,8,13,20,demod] CP(5,2,9,3,2). ** KEPT (pick-wt=6): 526 [hyper,22,8,13,19,demod] CP(5,2,8,1,2). ** KEPT (pick-wt=6): 527 [hyper,22,8,13,18,demod] CP(5,2,7,9,1). ** KEPT (pick-wt=6): 528 [hyper,22,8,13,17,demod] CP(5,2,6,7,1). ** KEPT (pick-wt=6): 529 [hyper,22,8,13,16,demod] CP(5,2,5,5,1). ** KEPT (pick-wt=6): 530 [hyper,22,8,13,15,demod] CP(5,2,4,3,1). ** KEPT (pick-wt=6): 531 [hyper,22,8,13,14,demod] CP(5,2,3,1,1). ** KEPT (pick-wt=6): 532 [hyper,22,8,13,13,demod] CP(5,2,2,9,0). ** KEPT (pick-wt=6): 533 [hyper,22,8,13,12,demod] CP(5,2,1,7,0). ** KEPT (pick-wt=6): 534 [hyper,22,8,13,11,demod] CP(5,2,0,5,0). ** KEPT (pick-wt=6): 535 [hyper,22,8,12,20,demod] CP(5,1,9,4,1). ** KEPT (pick-wt=6): 536 [hyper,22,8,12,19,demod] CP(5,1,8,3,1). ** KEPT (pick-wt=6): 537 [hyper,22,8,12,18,demod] CP(5,1,7,2,1). ** KEPT (pick-wt=6): 538 [hyper,22,8,12,17,demod] CP(5,1,6,1,1). ** KEPT (pick-wt=6): 539 [hyper,22,8,12,16,demod] CP(5,1,5,0,1). ** KEPT (pick-wt=6): 540 [hyper,22,8,12,15,demod] CP(5,1,4,9,0). ** KEPT (pick-wt=6): 541 [hyper,22,8,12,14,demod] CP(5,1,3,8,0). ** KEPT (pick-wt=6): 542 [hyper,22,8,12,13,demod] CP(5,1,2,7,0). ** KEPT (pick-wt=6): 543 [hyper,22,8,12,12,demod] CP(5,1,1,6,0). ** KEPT (pick-wt=6): 544 [hyper,22,8,12,11,demod] CP(5,1,0,5,0). ** KEPT (pick-wt=6): 545 [hyper,22,8,11,20,demod] CP(5,0,9,5,0). ** KEPT (pick-wt=6): 546 [hyper,22,8,11,19,demod] CP(5,0,8,5,0). ** KEPT (pick-wt=6): 547 [hyper,22,8,11,18,demod] CP(5,0,7,5,0). ** KEPT (pick-wt=6): 548 [hyper,22,8,11,17,demod] CP(5,0,6,5,0). ** KEPT (pick-wt=6): 549 [hyper,22,8,11,16,demod] CP(5,0,5,5,0). ** KEPT (pick-wt=6): 550 [hyper,22,8,11,15,demod] CP(5,0,4,5,0). ** KEPT (pick-wt=6): 551 [hyper,22,8,11,14,demod] CP(5,0,3,5,0). ** KEPT (pick-wt=6): 552 [hyper,22,8,11,13,demod] CP(5,0,2,5,0). ** KEPT (pick-wt=6): 553 [hyper,22,8,11,12,demod] CP(5,0,1,5,0). ** KEPT (pick-wt=6): 554 [hyper,22,8,11,11,demod] CP(5,0,0,5,0). ** KEPT (pick-wt=6): 555 [hyper,22,7,20,20,demod] CP(4,9,9,5,8). ** KEPT (pick-wt=6): 556 [hyper,22,7,20,19,demod] CP(4,9,8,6,7). ** KEPT (pick-wt=6): 557 [hyper,22,7,20,18,demod] CP(4,9,7,7,6). ** KEPT (pick-wt=6): 558 [hyper,22,7,20,17,demod] CP(4,9,6,8,5). ** KEPT (pick-wt=6): 559 [hyper,22,7,20,16,demod] CP(4,9,5,9,4). ** KEPT (pick-wt=6): 560 [hyper,22,7,20,15,demod] CP(4,9,4,0,4). ** KEPT (pick-wt=6): 561 [hyper,22,7,20,14,demod] CP(4,9,3,1,3). ** KEPT (pick-wt=6): 562 [hyper,22,7,20,13,demod] CP(4,9,2,2,2). ** KEPT (pick-wt=6): 563 [hyper,22,7,20,12,demod] CP(4,9,1,3,1). ** KEPT (pick-wt=6): 564 [hyper,22,7,20,11,demod] CP(4,9,0,4,0). ** KEPT (pick-wt=6): 565 [hyper,22,7,19,20,demod] CP(4,8,9,6,7). ** KEPT (pick-wt=6): 566 [hyper,22,7,19,19,demod] CP(4,8,8,8,6). ** KEPT (pick-wt=6): 567 [hyper,22,7,19,18,demod] CP(4,8,7,0,6). ** KEPT (pick-wt=6): 568 [hyper,22,7,19,17,demod] CP(4,8,6,2,5). ** KEPT (pick-wt=6): 569 [hyper,22,7,19,16,demod] CP(4,8,5,4,4). ** KEPT (pick-wt=6): 570 [hyper,22,7,19,15,demod] CP(4,8,4,6,3). ** KEPT (pick-wt=6): 571 [hyper,22,7,19,14,demod] CP(4,8,3,8,2). ** KEPT (pick-wt=6): 572 [hyper,22,7,19,13,demod] CP(4,8,2,0,2). ** KEPT (pick-wt=6): 573 [hyper,22,7,19,12,demod] CP(4,8,1,2,1). ** KEPT (pick-wt=6): 574 [hyper,22,7,19,11,demod] CP(4,8,0,4,0). ** KEPT (pick-wt=6): 575 [hyper,22,7,18,20,demod] CP(4,7,9,7,6). ** KEPT (pick-wt=6): 576 [hyper,22,7,18,19,demod] CP(4,7,8,0,6). ** KEPT (pick-wt=6): 577 [hyper,22,7,18,18,demod] CP(4,7,7,3,5). ** KEPT (pick-wt=6): 578 [hyper,22,7,18,17,demod] CP(4,7,6,6,4). ** KEPT (pick-wt=6): 579 [hyper,22,7,18,16,demod] CP(4,7,5,9,3). ** KEPT (pick-wt=6): 580 [hyper,22,7,18,15,demod] CP(4,7,4,2,3). ** KEPT (pick-wt=6): 581 [hyper,22,7,18,14,demod] CP(4,7,3,5,2). ** KEPT (pick-wt=6): 582 [hyper,22,7,18,13,demod] CP(4,7,2,8,1). ** KEPT (pick-wt=6): 583 [hyper,22,7,18,12,demod] CP(4,7,1,1,1). ** KEPT (pick-wt=6): 584 [hyper,22,7,18,11,demod] CP(4,7,0,4,0). ** KEPT (pick-wt=6): 585 [hyper,22,7,17,20,demod] CP(4,6,9,8,5). ** KEPT (pick-wt=6): 586 [hyper,22,7,17,19,demod] CP(4,6,8,2,5). ** KEPT (pick-wt=6): 587 [hyper,22,7,17,18,demod] CP(4,6,7,6,4). ** KEPT (pick-wt=6): 588 [hyper,22,7,17,17,demod] CP(4,6,6,0,4). ** KEPT (pick-wt=6): 589 [hyper,22,7,17,16,demod] CP(4,6,5,4,3). ** KEPT (pick-wt=6): 590 [hyper,22,7,17,15,demod] CP(4,6,4,8,2). ** KEPT (pick-wt=6): 591 [hyper,22,7,17,14,demod] CP(4,6,3,2,2). ** KEPT (pick-wt=6): 592 [hyper,22,7,17,13,demod] CP(4,6,2,6,1). ** KEPT (pick-wt=6): 593 [hyper,22,7,17,12,demod] CP(4,6,1,0,1). ** KEPT (pick-wt=6): 594 [hyper,22,7,17,11,demod] CP(4,6,0,4,0). ** KEPT (pick-wt=6): 595 [hyper,22,7,16,20,demod] CP(4,5,9,9,4). ** KEPT (pick-wt=6): 596 [hyper,22,7,16,19,demod] CP(4,5,8,4,4). ** KEPT (pick-wt=6): 597 [hyper,22,7,16,18,demod] CP(4,5,7,9,3). ** KEPT (pick-wt=6): 598 [hyper,22,7,16,17,demod] CP(4,5,6,4,3). ** KEPT (pick-wt=6): 599 [hyper,22,7,16,16,demod] CP(4,5,5,9,2). ** KEPT (pick-wt=6): 600 [hyper,22,7,16,15,demod] CP(4,5,4,4,2). ** KEPT (pick-wt=6): 601 [hyper,22,7,16,14,demod] CP(4,5,3,9,1). ** KEPT (pick-wt=6): 602 [hyper,22,7,16,13,demod] CP(4,5,2,4,1). ** KEPT (pick-wt=6): 603 [hyper,22,7,16,12,demod] CP(4,5,1,9,0). ** KEPT (pick-wt=6): 604 [hyper,22,7,16,11,demod] CP(4,5,0,4,0). ** KEPT (pick-wt=6): 605 [hyper,22,7,15,20,demod] CP(4,4,9,0,4). ** KEPT (pick-wt=6): 606 [hyper,22,7,15,19,demod] CP(4,4,8,6,3). ** KEPT (pick-wt=6): 607 [hyper,22,7,15,18,demod] CP(4,4,7,2,3). ** KEPT (pick-wt=6): 608 [hyper,22,7,15,17,demod] CP(4,4,6,8,2). ** KEPT (pick-wt=6): 609 [hyper,22,7,15,16,demod] CP(4,4,5,4,2). ** KEPT (pick-wt=6): 610 [hyper,22,7,15,15,demod] CP(4,4,4,0,2). ** KEPT (pick-wt=6): 611 [hyper,22,7,15,14,demod] CP(4,4,3,6,1). ** KEPT (pick-wt=6): 612 [hyper,22,7,15,13,demod] CP(4,4,2,2,1). ** KEPT (pick-wt=6): 613 [hyper,22,7,15,12,demod] CP(4,4,1,8,0). ** KEPT (pick-wt=6): 614 [hyper,22,7,15,11,demod] CP(4,4,0,4,0). ** KEPT (pick-wt=6): 615 [hyper,22,7,14,20,demod] CP(4,3,9,1,3). ** KEPT (pick-wt=6): 616 [hyper,22,7,14,19,demod] CP(4,3,8,8,2). ** KEPT (pick-wt=6): 617 [hyper,22,7,14,18,demod] CP(4,3,7,5,2). ** KEPT (pick-wt=6): 618 [hyper,22,7,14,17,demod] CP(4,3,6,2,2). ** KEPT (pick-wt=6): 619 [hyper,22,7,14,16,demod] CP(4,3,5,9,1). ** KEPT (pick-wt=6): 620 [hyper,22,7,14,15,demod] CP(4,3,4,6,1). ** KEPT (pick-wt=6): 621 [hyper,22,7,14,14,demod] CP(4,3,3,3,1). ** KEPT (pick-wt=6): 622 [hyper,22,7,14,13,demod] CP(4,3,2,0,1). ** KEPT (pick-wt=6): 623 [hyper,22,7,14,12,demod] CP(4,3,1,7,0). ** KEPT (pick-wt=6): 624 [hyper,22,7,14,11,demod] CP(4,3,0,4,0). ** KEPT (pick-wt=6): 625 [hyper,22,7,13,20,demod] CP(4,2,9,2,2). ** KEPT (pick-wt=6): 626 [hyper,22,7,13,19,demod] CP(4,2,8,0,2). ** KEPT (pick-wt=6): 627 [hyper,22,7,13,18,demod] CP(4,2,7,8,1). ** KEPT (pick-wt=6): 628 [hyper,22,7,13,17,demod] CP(4,2,6,6,1). ** KEPT (pick-wt=6): 629 [hyper,22,7,13,16,demod] CP(4,2,5,4,1). ** KEPT (pick-wt=6): 630 [hyper,22,7,13,15,demod] CP(4,2,4,2,1). ** KEPT (pick-wt=6): 631 [hyper,22,7,13,14,demod] CP(4,2,3,0,1). ** KEPT (pick-wt=6): 632 [hyper,22,7,13,13,demod] CP(4,2,2,8,0). ** KEPT (pick-wt=6): 633 [hyper,22,7,13,12,demod] CP(4,2,1,6,0). ** KEPT (pick-wt=6): 634 [hyper,22,7,13,11,demod] CP(4,2,0,4,0). ** KEPT (pick-wt=6): 635 [hyper,22,7,12,20,demod] CP(4,1,9,3,1). ** KEPT (pick-wt=6): 636 [hyper,22,7,12,19,demod] CP(4,1,8,2,1). ** KEPT (pick-wt=6): 637 [hyper,22,7,12,18,demod] CP(4,1,7,1,1). ** KEPT (pick-wt=6): 638 [hyper,22,7,12,17,demod] CP(4,1,6,0,1). ** KEPT (pick-wt=6): 639 [hyper,22,7,12,16,demod] CP(4,1,5,9,0). ** KEPT (pick-wt=6): 640 [hyper,22,7,12,15,demod] CP(4,1,4,8,0). ** KEPT (pick-wt=6): 641 [hyper,22,7,12,14,demod] CP(4,1,3,7,0). ** KEPT (pick-wt=6): 642 [hyper,22,7,12,13,demod] CP(4,1,2,6,0). ** KEPT (pick-wt=6): 643 [hyper,22,7,12,12,demod] CP(4,1,1,5,0). ** KEPT (pick-wt=6): 644 [hyper,22,7,12,11,demod] CP(4,1,0,4,0). ** KEPT (pick-wt=6): 645 [hyper,22,7,11,20,demod] CP(4,0,9,4,0). ** KEPT (pick-wt=6): 646 [hyper,22,7,11,19,demod] CP(4,0,8,4,0). ** KEPT (pick-wt=6): 647 [hyper,22,7,11,18,demod] CP(4,0,7,4,0). ** KEPT (pick-wt=6): 648 [hyper,22,7,11,17,demod] CP(4,0,6,4,0). ** KEPT (pick-wt=6): 649 [hyper,22,7,11,16,demod] CP(4,0,5,4,0). ** KEPT (pick-wt=6): 650 [hyper,22,7,11,15,demod] CP(4,0,4,4,0). ** KEPT (pick-wt=6): 651 [hyper,22,7,11,14,demod] CP(4,0,3,4,0). ** KEPT (pick-wt=6): 652 [hyper,22,7,11,13,demod] CP(4,0,2,4,0). ** KEPT (pick-wt=6): 653 [hyper,22,7,11,12,demod] CP(4,0,1,4,0). ** KEPT (pick-wt=6): 654 [hyper,22,7,11,11,demod] CP(4,0,0,4,0). ** KEPT (pick-wt=6): 655 [hyper,22,6,20,20,demod] CP(3,9,9,4,8). ** KEPT (pick-wt=6): 656 [hyper,22,6,20,19,demod] CP(3,9,8,5,7). ** KEPT (pick-wt=6): 657 [hyper,22,6,20,18,demod] CP(3,9,7,6,6). ** KEPT (pick-wt=6): 658 [hyper,22,6,20,17,demod] CP(3,9,6,7,5). ** KEPT (pick-wt=6): 659 [hyper,22,6,20,16,demod] CP(3,9,5,8,4). ** KEPT (pick-wt=6): 660 [hyper,22,6,20,15,demod] CP(3,9,4,9,3). ** KEPT (pick-wt=6): 661 [hyper,22,6,20,14,demod] CP(3,9,3,0,3). ** KEPT (pick-wt=6): 662 [hyper,22,6,20,13,demod] CP(3,9,2,1,2). ** KEPT (pick-wt=6): 663 [hyper,22,6,20,12,demod] CP(3,9,1,2,1). ** KEPT (pick-wt=6): 664 [hyper,22,6,20,11,demod] CP(3,9,0,3,0). ** KEPT (pick-wt=6): 665 [hyper,22,6,19,20,demod] CP(3,8,9,5,7). ** KEPT (pick-wt=6): 666 [hyper,22,6,19,19,demod] CP(3,8,8,7,6). ** KEPT (pick-wt=6): 667 [hyper,22,6,19,18,demod] CP(3,8,7,9,5). ** KEPT (pick-wt=6): 668 [hyper,22,6,19,17,demod] CP(3,8,6,1,5). ** KEPT (pick-wt=6): 669 [hyper,22,6,19,16,demod] CP(3,8,5,3,4). ** KEPT (pick-wt=6): 670 [hyper,22,6,19,15,demod] CP(3,8,4,5,3). ** KEPT (pick-wt=6): 671 [hyper,22,6,19,14,demod] CP(3,8,3,7,2). ** KEPT (pick-wt=6): 672 [hyper,22,6,19,13,demod] CP(3,8,2,9,1). ** KEPT (pick-wt=6): 673 [hyper,22,6,19,12,demod] CP(3,8,1,1,1). ** KEPT (pick-wt=6): 674 [hyper,22,6,19,11,demod] CP(3,8,0,3,0). ** KEPT (pick-wt=6): 675 [hyper,22,6,18,20,demod] CP(3,7,9,6,6). ** KEPT (pick-wt=6): 676 [hyper,22,6,18,19,demod] CP(3,7,8,9,5). ** KEPT (pick-wt=6): 677 [hyper,22,6,18,18,demod] CP(3,7,7,2,5). ** KEPT (pick-wt=6): 678 [hyper,22,6,18,17,demod] CP(3,7,6,5,4). ** KEPT (pick-wt=6): 679 [hyper,22,6,18,16,demod] CP(3,7,5,8,3). ** KEPT (pick-wt=6): 680 [hyper,22,6,18,15,demod] CP(3,7,4,1,3). ** KEPT (pick-wt=6): 681 [hyper,22,6,18,14,demod] CP(3,7,3,4,2). ** KEPT (pick-wt=6): 682 [hyper,22,6,18,13,demod] CP(3,7,2,7,1). ** KEPT (pick-wt=6): 683 [hyper,22,6,18,12,demod] CP(3,7,1,0,1). ** KEPT (pick-wt=6): 684 [hyper,22,6,18,11,demod] CP(3,7,0,3,0). ** KEPT (pick-wt=6): 685 [hyper,22,6,17,20,demod] CP(3,6,9,7,5). ** KEPT (pick-wt=6): 686 [hyper,22,6,17,19,demod] CP(3,6,8,1,5). ** KEPT (pick-wt=6): 687 [hyper,22,6,17,18,demod] CP(3,6,7,5,4). ** KEPT (pick-wt=6): 688 [hyper,22,6,17,17,demod] CP(3,6,6,9,3). ** KEPT (pick-wt=6): 689 [hyper,22,6,17,16,demod] CP(3,6,5,3,3). ** KEPT (pick-wt=6): 690 [hyper,22,6,17,15,demod] CP(3,6,4,7,2). ** KEPT (pick-wt=6): 691 [hyper,22,6,17,14,demod] CP(3,6,3,1,2). ** KEPT (pick-wt=6): 692 [hyper,22,6,17,13,demod] CP(3,6,2,5,1). ** KEPT (pick-wt=6): 693 [hyper,22,6,17,12,demod] CP(3,6,1,9,0). ** KEPT (pick-wt=6): 694 [hyper,22,6,17,11,demod] CP(3,6,0,3,0). ** KEPT (pick-wt=6): 695 [hyper,22,6,16,20,demod] CP(3,5,9,8,4). ** KEPT (pick-wt=6): 696 [hyper,22,6,16,19,demod] CP(3,5,8,3,4). ** KEPT (pick-wt=6): 697 [hyper,22,6,16,18,demod] CP(3,5,7,8,3). ** KEPT (pick-wt=6): 698 [hyper,22,6,16,17,demod] CP(3,5,6,3,3). ** KEPT (pick-wt=6): 699 [hyper,22,6,16,16,demod] CP(3,5,5,8,2). ** KEPT (pick-wt=6): 700 [hyper,22,6,16,15,demod] CP(3,5,4,3,2). ** KEPT (pick-wt=6): 701 [hyper,22,6,16,14,demod] CP(3,5,3,8,1). ** KEPT (pick-wt=6): 702 [hyper,22,6,16,13,demod] CP(3,5,2,3,1). ** KEPT (pick-wt=6): 703 [hyper,22,6,16,12,demod] CP(3,5,1,8,0). ** KEPT (pick-wt=6): 704 [hyper,22,6,16,11,demod] CP(3,5,0,3,0). ** KEPT (pick-wt=6): 705 [hyper,22,6,15,20,demod] CP(3,4,9,9,3). ** KEPT (pick-wt=6): 706 [hyper,22,6,15,19,demod] CP(3,4,8,5,3). ** KEPT (pick-wt=6): 707 [hyper,22,6,15,18,demod] CP(3,4,7,1,3). ** KEPT (pick-wt=6): 708 [hyper,22,6,15,17,demod] CP(3,4,6,7,2). ** KEPT (pick-wt=6): 709 [hyper,22,6,15,16,demod] CP(3,4,5,3,2). ** KEPT (pick-wt=6): 710 [hyper,22,6,15,15,demod] CP(3,4,4,9,1). ** KEPT (pick-wt=6): 711 [hyper,22,6,15,14,demod] CP(3,4,3,5,1). ** KEPT (pick-wt=6): 712 [hyper,22,6,15,13,demod] CP(3,4,2,1,1). ** KEPT (pick-wt=6): 713 [hyper,22,6,15,12,demod] CP(3,4,1,7,0). ** KEPT (pick-wt=6): 714 [hyper,22,6,15,11,demod] CP(3,4,0,3,0). ** KEPT (pick-wt=6): 715 [hyper,22,6,14,20,demod] CP(3,3,9,0,3). ** KEPT (pick-wt=6): 716 [hyper,22,6,14,19,demod] CP(3,3,8,7,2). ** KEPT (pick-wt=6): 717 [hyper,22,6,14,18,demod] CP(3,3,7,4,2). ** KEPT (pick-wt=6): 718 [hyper,22,6,14,17,demod] CP(3,3,6,1,2). ** KEPT (pick-wt=6): 719 [hyper,22,6,14,16,demod] CP(3,3,5,8,1). ** KEPT (pick-wt=6): 720 [hyper,22,6,14,15,demod] CP(3,3,4,5,1). ** KEPT (pick-wt=6): 721 [hyper,22,6,14,14,demod] CP(3,3,3,2,1). ** KEPT (pick-wt=6): 722 [hyper,22,6,14,13,demod] CP(3,3,2,9,0). ** KEPT (pick-wt=6): 723 [hyper,22,6,14,12,demod] CP(3,3,1,6,0). ** KEPT (pick-wt=6): 724 [hyper,22,6,14,11,demod] CP(3,3,0,3,0). ** KEPT (pick-wt=6): 725 [hyper,22,6,13,20,demod] CP(3,2,9,1,2). ** KEPT (pick-wt=6): 726 [hyper,22,6,13,19,demod] CP(3,2,8,9,1). ** KEPT (pick-wt=6): 727 [hyper,22,6,13,18,demod] CP(3,2,7,7,1). ** KEPT (pick-wt=6): 728 [hyper,22,6,13,17,demod] CP(3,2,6,5,1). ** KEPT (pick-wt=6): 729 [hyper,22,6,13,16,demod] CP(3,2,5,3,1). ** KEPT (pick-wt=6): 730 [hyper,22,6,13,15,demod] CP(3,2,4,1,1). ** KEPT (pick-wt=6): 731 [hyper,22,6,13,14,demod] CP(3,2,3,9,0). ** KEPT (pick-wt=6): 732 [hyper,22,6,13,13,demod] CP(3,2,2,7,0). ** KEPT (pick-wt=6): 733 [hyper,22,6,13,12,demod] CP(3,2,1,5,0). ** KEPT (pick-wt=6): 734 [hyper,22,6,13,11,demod] CP(3,2,0,3,0). ** KEPT (pick-wt=6): 735 [hyper,22,6,12,20,demod] CP(3,1,9,2,1). ** KEPT (pick-wt=6): 736 [hyper,22,6,12,19,demod] CP(3,1,8,1,1). ** KEPT (pick-wt=6): 737 [hyper,22,6,12,18,demod] CP(3,1,7,0,1). ** KEPT (pick-wt=6): 738 [hyper,22,6,12,17,demod] CP(3,1,6,9,0). ** KEPT (pick-wt=6): 739 [hyper,22,6,12,16,demod] CP(3,1,5,8,0). ** KEPT (pick-wt=6): 740 [hyper,22,6,12,15,demod] CP(3,1,4,7,0). ** KEPT (pick-wt=6): 741 [hyper,22,6,12,14,demod] CP(3,1,3,6,0). ** KEPT (pick-wt=6): 742 [hyper,22,6,12,13,demod] CP(3,1,2,5,0). ** KEPT (pick-wt=6): 743 [hyper,22,6,12,12,demod] CP(3,1,1,4,0). ** KEPT (pick-wt=6): 744 [hyper,22,6,12,11,demod] CP(3,1,0,3,0). ** KEPT (pick-wt=6): 745 [hyper,22,6,11,20,demod] CP(3,0,9,3,0). ** KEPT (pick-wt=6): 746 [hyper,22,6,11,19,demod] CP(3,0,8,3,0). ** KEPT (pick-wt=6): 747 [hyper,22,6,11,18,demod] CP(3,0,7,3,0). ** KEPT (pick-wt=6): 748 [hyper,22,6,11,17,demod] CP(3,0,6,3,0). ** KEPT (pick-wt=6): 749 [hyper,22,6,11,16,demod] CP(3,0,5,3,0). ** KEPT (pick-wt=6): 750 [hyper,22,6,11,15,demod] CP(3,0,4,3,0). ** KEPT (pick-wt=6): 751 [hyper,22,6,11,14,demod] CP(3,0,3,3,0). ** KEPT (pick-wt=6): 752 [hyper,22,6,11,13,demod] CP(3,0,2,3,0). ** KEPT (pick-wt=6): 753 [hyper,22,6,11,12,demod] CP(3,0,1,3,0). ** KEPT (pick-wt=6): 754 [hyper,22,6,11,11,demod] CP(3,0,0,3,0). ** KEPT (pick-wt=6): 755 [hyper,22,5,20,20,demod] CP(2,9,9,3,8). ** KEPT (pick-wt=6): 756 [hyper,22,5,20,19,demod] CP(2,9,8,4,7). ** KEPT (pick-wt=6): 757 [hyper,22,5,20,18,demod] CP(2,9,7,5,6). ** KEPT (pick-wt=6): 758 [hyper,22,5,20,17,demod] CP(2,9,6,6,5). ** KEPT (pick-wt=6): 759 [hyper,22,5,20,16,demod] CP(2,9,5,7,4). ** KEPT (pick-wt=6): 760 [hyper,22,5,20,15,demod] CP(2,9,4,8,3). ** KEPT (pick-wt=6): 761 [hyper,22,5,20,14,demod] CP(2,9,3,9,2). ** KEPT (pick-wt=6): 762 [hyper,22,5,20,13,demod] CP(2,9,2,0,2). ** KEPT (pick-wt=6): 763 [hyper,22,5,20,12,demod] CP(2,9,1,1,1). ** KEPT (pick-wt=6): 764 [hyper,22,5,20,11,demod] CP(2,9,0,2,0). ** KEPT (pick-wt=6): 765 [hyper,22,5,19,20,demod] CP(2,8,9,4,7). ** KEPT (pick-wt=6): 766 [hyper,22,5,19,19,demod] CP(2,8,8,6,6). ** KEPT (pick-wt=6): 767 [hyper,22,5,19,18,demod] CP(2,8,7,8,5). ** KEPT (pick-wt=6): 768 [hyper,22,5,19,17,demod] CP(2,8,6,0,5). ** KEPT (pick-wt=6): 769 [hyper,22,5,19,16,demod] CP(2,8,5,2,4). ** KEPT (pick-wt=6): 770 [hyper,22,5,19,15,demod] CP(2,8,4,4,3). ** KEPT (pick-wt=6): 771 [hyper,22,5,19,14,demod] CP(2,8,3,6,2). ** KEPT (pick-wt=6): 772 [hyper,22,5,19,13,demod] CP(2,8,2,8,1). ** KEPT (pick-wt=6): 773 [hyper,22,5,19,12,demod] CP(2,8,1,0,1). ** KEPT (pick-wt=6): 774 [hyper,22,5,19,11,demod] CP(2,8,0,2,0). ** KEPT (pick-wt=6): 775 [hyper,22,5,18,20,demod] CP(2,7,9,5,6). ** KEPT (pick-wt=6): 776 [hyper,22,5,18,19,demod] CP(2,7,8,8,5). ** KEPT (pick-wt=6): 777 [hyper,22,5,18,18,demod] CP(2,7,7,1,5). ** KEPT (pick-wt=6): 778 [hyper,22,5,18,17,demod] CP(2,7,6,4,4). ** KEPT (pick-wt=6): 779 [hyper,22,5,18,16,demod] CP(2,7,5,7,3). ** KEPT (pick-wt=6): 780 [hyper,22,5,18,15,demod] CP(2,7,4,0,3). ** KEPT (pick-wt=6): 781 [hyper,22,5,18,14,demod] CP(2,7,3,3,2). ** KEPT (pick-wt=6): 782 [hyper,22,5,18,13,demod] CP(2,7,2,6,1). ** KEPT (pick-wt=6): 783 [hyper,22,5,18,12,demod] CP(2,7,1,9,0). ** KEPT (pick-wt=6): 784 [hyper,22,5,18,11,demod] CP(2,7,0,2,0). ** KEPT (pick-wt=6): 785 [hyper,22,5,17,20,demod] CP(2,6,9,6,5). ** KEPT (pick-wt=6): 786 [hyper,22,5,17,19,demod] CP(2,6,8,0,5). ** KEPT (pick-wt=6): 787 [hyper,22,5,17,18,demod] CP(2,6,7,4,4). ** KEPT (pick-wt=6): 788 [hyper,22,5,17,17,demod] CP(2,6,6,8,3). ** KEPT (pick-wt=6): 789 [hyper,22,5,17,16,demod] CP(2,6,5,2,3). ** KEPT (pick-wt=6): 790 [hyper,22,5,17,15,demod] CP(2,6,4,6,2). ** KEPT (pick-wt=6): 791 [hyper,22,5,17,14,demod] CP(2,6,3,0,2). ** KEPT (pick-wt=6): 792 [hyper,22,5,17,13,demod] CP(2,6,2,4,1). ** KEPT (pick-wt=6): 793 [hyper,22,5,17,12,demod] CP(2,6,1,8,0). ** KEPT (pick-wt=6): 794 [hyper,22,5,17,11,demod] CP(2,6,0,2,0). ** KEPT (pick-wt=6): 795 [hyper,22,5,16,20,demod] CP(2,5,9,7,4). ** KEPT (pick-wt=6): 796 [hyper,22,5,16,19,demod] CP(2,5,8,2,4). ** KEPT (pick-wt=6): 797 [hyper,22,5,16,18,demod] CP(2,5,7,7,3). ** KEPT (pick-wt=6): 798 [hyper,22,5,16,17,demod] CP(2,5,6,2,3). ** KEPT (pick-wt=6): 799 [hyper,22,5,16,16,demod] CP(2,5,5,7,2). ** KEPT (pick-wt=6): 800 [hyper,22,5,16,15,demod] CP(2,5,4,2,2). ** KEPT (pick-wt=6): 801 [hyper,22,5,16,14,demod] CP(2,5,3,7,1). ** KEPT (pick-wt=6): 802 [hyper,22,5,16,13,demod] CP(2,5,2,2,1). ** KEPT (pick-wt=6): 803 [hyper,22,5,16,12,demod] CP(2,5,1,7,0). ** KEPT (pick-wt=6): 804 [hyper,22,5,16,11,demod] CP(2,5,0,2,0). ** KEPT (pick-wt=6): 805 [hyper,22,5,15,20,demod] CP(2,4,9,8,3). ** KEPT (pick-wt=6): 806 [hyper,22,5,15,19,demod] CP(2,4,8,4,3). ** KEPT (pick-wt=6): 807 [hyper,22,5,15,18,demod] CP(2,4,7,0,3). ** KEPT (pick-wt=6): 808 [hyper,22,5,15,17,demod] CP(2,4,6,6,2). ** KEPT (pick-wt=6): 809 [hyper,22,5,15,16,demod] CP(2,4,5,2,2). ** KEPT (pick-wt=6): 810 [hyper,22,5,15,15,demod] CP(2,4,4,8,1). ** KEPT (pick-wt=6): 811 [hyper,22,5,15,14,demod] CP(2,4,3,4,1). ** KEPT (pick-wt=6): 812 [hyper,22,5,15,13,demod] CP(2,4,2,0,1). ** KEPT (pick-wt=6): 813 [hyper,22,5,15,12,demod] CP(2,4,1,6,0). ** KEPT (pick-wt=6): 814 [hyper,22,5,15,11,demod] CP(2,4,0,2,0). ** KEPT (pick-wt=6): 815 [hyper,22,5,14,20,demod] CP(2,3,9,9,2). ** KEPT (pick-wt=6): 816 [hyper,22,5,14,19,demod] CP(2,3,8,6,2). ** KEPT (pick-wt=6): 817 [hyper,22,5,14,18,demod] CP(2,3,7,3,2). ** KEPT (pick-wt=6): 818 [hyper,22,5,14,17,demod] CP(2,3,6,0,2). ** KEPT (pick-wt=6): 819 [hyper,22,5,14,16,demod] CP(2,3,5,7,1). ** KEPT (pick-wt=6): 820 [hyper,22,5,14,15,demod] CP(2,3,4,4,1). ** KEPT (pick-wt=6): 821 [hyper,22,5,14,14,demod] CP(2,3,3,1,1). ** KEPT (pick-wt=6): 822 [hyper,22,5,14,13,demod] CP(2,3,2,8,0). ** KEPT (pick-wt=6): 823 [hyper,22,5,14,12,demod] CP(2,3,1,5,0). ** KEPT (pick-wt=6): 824 [hyper,22,5,14,11,demod] CP(2,3,0,2,0). ** KEPT (pick-wt=6): 825 [hyper,22,5,13,20,demod] CP(2,2,9,0,2). ** KEPT (pick-wt=6): 826 [hyper,22,5,13,19,demod] CP(2,2,8,8,1). ** KEPT (pick-wt=6): 827 [hyper,22,5,13,18,demod] CP(2,2,7,6,1). ** KEPT (pick-wt=6): 828 [hyper,22,5,13,17,demod] CP(2,2,6,4,1). ** KEPT (pick-wt=6): 829 [hyper,22,5,13,16,demod] CP(2,2,5,2,1). ** KEPT (pick-wt=6): 830 [hyper,22,5,13,15,demod] CP(2,2,4,0,1). ** KEPT (pick-wt=6): 831 [hyper,22,5,13,14,demod] CP(2,2,3,8,0). ** KEPT (pick-wt=6): 832 [hyper,22,5,13,13,demod] CP(2,2,2,6,0). ** KEPT (pick-wt=6): 833 [hyper,22,5,13,12,demod] CP(2,2,1,4,0). ** KEPT (pick-wt=6): 834 [hyper,22,5,13,11,demod] CP(2,2,0,2,0). ** KEPT (pick-wt=6): 835 [hyper,22,5,12,20,demod] CP(2,1,9,1,1). ** KEPT (pick-wt=6): 836 [hyper,22,5,12,19,demod] CP(2,1,8,0,1). ** KEPT (pick-wt=6): 837 [hyper,22,5,12,18,demod] CP(2,1,7,9,0). ** KEPT (pick-wt=6): 838 [hyper,22,5,12,17,demod] CP(2,1,6,8,0). ** KEPT (pick-wt=6): 839 [hyper,22,5,12,16,demod] CP(2,1,5,7,0). ** KEPT (pick-wt=6): 840 [hyper,22,5,12,15,demod] CP(2,1,4,6,0). ** KEPT (pick-wt=6): 841 [hyper,22,5,12,14,demod] CP(2,1,3,5,0). ** KEPT (pick-wt=6): 842 [hyper,22,5,12,13,demod] CP(2,1,2,4,0). ** KEPT (pick-wt=6): 843 [hyper,22,5,12,12,demod] CP(2,1,1,3,0). ** KEPT (pick-wt=6): 844 [hyper,22,5,12,11,demod] CP(2,1,0,2,0). ** KEPT (pick-wt=6): 845 [hyper,22,5,11,20,demod] CP(2,0,9,2,0). ** KEPT (pick-wt=6): 846 [hyper,22,5,11,19,demod] CP(2,0,8,2,0). ** KEPT (pick-wt=6): 847 [hyper,22,5,11,18,demod] CP(2,0,7,2,0). ** KEPT (pick-wt=6): 848 [hyper,22,5,11,17,demod] CP(2,0,6,2,0). ** KEPT (pick-wt=6): 849 [hyper,22,5,11,16,demod] CP(2,0,5,2,0). ** KEPT (pick-wt=6): 850 [hyper,22,5,11,15,demod] CP(2,0,4,2,0). ** KEPT (pick-wt=6): 851 [hyper,22,5,11,14,demod] CP(2,0,3,2,0). ** KEPT (pick-wt=6): 852 [hyper,22,5,11,13,demod] CP(2,0,2,2,0). ** KEPT (pick-wt=6): 853 [hyper,22,5,11,12,demod] CP(2,0,1,2,0). ** KEPT (pick-wt=6): 854 [hyper,22,5,11,11,demod] CP(2,0,0,2,0). ** KEPT (pick-wt=6): 855 [hyper,22,4,20,20,demod] CP(1,9,9,2,8). ** KEPT (pick-wt=6): 856 [hyper,22,4,20,19,demod] CP(1,9,8,3,7). ** KEPT (pick-wt=6): 857 [hyper,22,4,20,18,demod] CP(1,9,7,4,6). ** KEPT (pick-wt=6): 858 [hyper,22,4,20,17,demod] CP(1,9,6,5,5). ** KEPT (pick-wt=6): 859 [hyper,22,4,20,16,demod] CP(1,9,5,6,4). ** KEPT (pick-wt=6): 860 [hyper,22,4,20,15,demod] CP(1,9,4,7,3). ** KEPT (pick-wt=6): 861 [hyper,22,4,20,14,demod] CP(1,9,3,8,2). ** KEPT (pick-wt=6): 862 [hyper,22,4,20,13,demod] CP(1,9,2,9,1). ** KEPT (pick-wt=6): 863 [hyper,22,4,20,12,demod] CP(1,9,1,0,1). ** KEPT (pick-wt=6): 864 [hyper,22,4,20,11,demod] CP(1,9,0,1,0). ** KEPT (pick-wt=6): 865 [hyper,22,4,19,20,demod] CP(1,8,9,3,7). ** KEPT (pick-wt=6): 866 [hyper,22,4,19,19,demod] CP(1,8,8,5,6). ** KEPT (pick-wt=6): 867 [hyper,22,4,19,18,demod] CP(1,8,7,7,5). ** KEPT (pick-wt=6): 868 [hyper,22,4,19,17,demod] CP(1,8,6,9,4). ** KEPT (pick-wt=6): 869 [hyper,22,4,19,16,demod] CP(1,8,5,1,4). ** KEPT (pick-wt=6): 870 [hyper,22,4,19,15,demod] CP(1,8,4,3,3). ** KEPT (pick-wt=6): 871 [hyper,22,4,19,14,demod] CP(1,8,3,5,2). ** KEPT (pick-wt=6): 872 [hyper,22,4,19,13,demod] CP(1,8,2,7,1). ** KEPT (pick-wt=6): 873 [hyper,22,4,19,12,demod] CP(1,8,1,9,0). ** KEPT (pick-wt=6): 874 [hyper,22,4,19,11,demod] CP(1,8,0,1,0). ** KEPT (pick-wt=6): 875 [hyper,22,4,18,20,demod] CP(1,7,9,4,6). ** KEPT (pick-wt=6): 876 [hyper,22,4,18,19,demod] CP(1,7,8,7,5). ** KEPT (pick-wt=6): 877 [hyper,22,4,18,18,demod] CP(1,7,7,0,5). ** KEPT (pick-wt=6): 878 [hyper,22,4,18,17,demod] CP(1,7,6,3,4). ** KEPT (pick-wt=6): 879 [hyper,22,4,18,16,demod] CP(1,7,5,6,3). ** KEPT (pick-wt=6): 880 [hyper,22,4,18,15,demod] CP(1,7,4,9,2). ** KEPT (pick-wt=6): 881 [hyper,22,4,18,14,demod] CP(1,7,3,2,2). ** KEPT (pick-wt=6): 882 [hyper,22,4,18,13,demod] CP(1,7,2,5,1). ** KEPT (pick-wt=6): 883 [hyper,22,4,18,12,demod] CP(1,7,1,8,0). ** KEPT (pick-wt=6): 884 [hyper,22,4,18,11,demod] CP(1,7,0,1,0). ** KEPT (pick-wt=6): 885 [hyper,22,4,17,20,demod] CP(1,6,9,5,5). ** KEPT (pick-wt=6): 886 [hyper,22,4,17,19,demod] CP(1,6,8,9,4). ** KEPT (pick-wt=6): 887 [hyper,22,4,17,18,demod] CP(1,6,7,3,4). ** KEPT (pick-wt=6): 888 [hyper,22,4,17,17,demod] CP(1,6,6,7,3). ** KEPT (pick-wt=6): 889 [hyper,22,4,17,16,demod] CP(1,6,5,1,3). ** KEPT (pick-wt=6): 890 [hyper,22,4,17,15,demod] CP(1,6,4,5,2). ** KEPT (pick-wt=6): 891 [hyper,22,4,17,14,demod] CP(1,6,3,9,1). ** KEPT (pick-wt=6): 892 [hyper,22,4,17,13,demod] CP(1,6,2,3,1). ** KEPT (pick-wt=6): 893 [hyper,22,4,17,12,demod] CP(1,6,1,7,0). ** KEPT (pick-wt=6): 894 [hyper,22,4,17,11,demod] CP(1,6,0,1,0). ** KEPT (pick-wt=6): 895 [hyper,22,4,16,20,demod] CP(1,5,9,6,4). ** KEPT (pick-wt=6): 896 [hyper,22,4,16,19,demod] CP(1,5,8,1,4). ** KEPT (pick-wt=6): 897 [hyper,22,4,16,18,demod] CP(1,5,7,6,3). ** KEPT (pick-wt=6): 898 [hyper,22,4,16,17,demod] CP(1,5,6,1,3). ** KEPT (pick-wt=6): 899 [hyper,22,4,16,16,demod] CP(1,5,5,6,2). ** KEPT (pick-wt=6): 900 [hyper,22,4,16,15,demod] CP(1,5,4,1,2). ** KEPT (pick-wt=6): 901 [hyper,22,4,16,14,demod] CP(1,5,3,6,1). ** KEPT (pick-wt=6): 902 [hyper,22,4,16,13,demod] CP(1,5,2,1,1). ** KEPT (pick-wt=6): 903 [hyper,22,4,16,12,demod] CP(1,5,1,6,0). ** KEPT (pick-wt=6): 904 [hyper,22,4,16,11,demod] CP(1,5,0,1,0). ** KEPT (pick-wt=6): 905 [hyper,22,4,15,20,demod] CP(1,4,9,7,3). ** KEPT (pick-wt=6): 906 [hyper,22,4,15,19,demod] CP(1,4,8,3,3). ** KEPT (pick-wt=6): 907 [hyper,22,4,15,18,demod] CP(1,4,7,9,2). ** KEPT (pick-wt=6): 908 [hyper,22,4,15,17,demod] CP(1,4,6,5,2). ** KEPT (pick-wt=6): 909 [hyper,22,4,15,16,demod] CP(1,4,5,1,2). ** KEPT (pick-wt=6): 910 [hyper,22,4,15,15,demod] CP(1,4,4,7,1). ** KEPT (pick-wt=6): 911 [hyper,22,4,15,14,demod] CP(1,4,3,3,1). ** KEPT (pick-wt=6): 912 [hyper,22,4,15,13,demod] CP(1,4,2,9,0). ** KEPT (pick-wt=6): 913 [hyper,22,4,15,12,demod] CP(1,4,1,5,0). ** KEPT (pick-wt=6): 914 [hyper,22,4,15,11,demod] CP(1,4,0,1,0). ** KEPT (pick-wt=6): 915 [hyper,22,4,14,20,demod] CP(1,3,9,8,2). ** KEPT (pick-wt=6): 916 [hyper,22,4,14,19,demod] CP(1,3,8,5,2). ** KEPT (pick-wt=6): 917 [hyper,22,4,14,18,demod] CP(1,3,7,2,2). ** KEPT (pick-wt=6): 918 [hyper,22,4,14,17,demod] CP(1,3,6,9,1). ** KEPT (pick-wt=6): 919 [hyper,22,4,14,16,demod] CP(1,3,5,6,1). ** KEPT (pick-wt=6): 920 [hyper,22,4,14,15,demod] CP(1,3,4,3,1). ** KEPT (pick-wt=6): 921 [hyper,22,4,14,14,demod] CP(1,3,3,0,1). ** KEPT (pick-wt=6): 922 [hyper,22,4,14,13,demod] CP(1,3,2,7,0). ** KEPT (pick-wt=6): 923 [hyper,22,4,14,12,demod] CP(1,3,1,4,0). ** KEPT (pick-wt=6): 924 [hyper,22,4,14,11,demod] CP(1,3,0,1,0). ** KEPT (pick-wt=6): 925 [hyper,22,4,13,20,demod] CP(1,2,9,9,1). ** KEPT (pick-wt=6): 926 [hyper,22,4,13,19,demod] CP(1,2,8,7,1). ** KEPT (pick-wt=6): 927 [hyper,22,4,13,18,demod] CP(1,2,7,5,1). ** KEPT (pick-wt=6): 928 [hyper,22,4,13,17,demod] CP(1,2,6,3,1). ** KEPT (pick-wt=6): 929 [hyper,22,4,13,16,demod] CP(1,2,5,1,1). ** KEPT (pick-wt=6): 930 [hyper,22,4,13,15,demod] CP(1,2,4,9,0). ** KEPT (pick-wt=6): 931 [hyper,22,4,13,14,demod] CP(1,2,3,7,0). ** KEPT (pick-wt=6): 932 [hyper,22,4,13,13,demod] CP(1,2,2,5,0). ** KEPT (pick-wt=6): 933 [hyper,22,4,13,12,demod] CP(1,2,1,3,0). ** KEPT (pick-wt=6): 934 [hyper,22,4,13,11,demod] CP(1,2,0,1,0). ** KEPT (pick-wt=6): 935 [hyper,22,4,12,20,demod] CP(1,1,9,0,1). ** KEPT (pick-wt=6): 936 [hyper,22,4,12,19,demod] CP(1,1,8,9,0). ** KEPT (pick-wt=6): 937 [hyper,22,4,12,18,demod] CP(1,1,7,8,0). ** KEPT (pick-wt=6): 938 [hyper,22,4,12,17,demod] CP(1,1,6,7,0). ** KEPT (pick-wt=6): 939 [hyper,22,4,12,16,demod] CP(1,1,5,6,0). ** KEPT (pick-wt=6): 940 [hyper,22,4,12,15,demod] CP(1,1,4,5,0). ** KEPT (pick-wt=6): 941 [hyper,22,4,12,14,demod] CP(1,1,3,4,0). ** KEPT (pick-wt=6): 942 [hyper,22,4,12,13,demod] CP(1,1,2,3,0). ** KEPT (pick-wt=6): 943 [hyper,22,4,12,12,demod] CP(1,1,1,2,0). ** KEPT (pick-wt=6): 944 [hyper,22,4,12,11,demod] CP(1,1,0,1,0). ** KEPT (pick-wt=6): 945 [hyper,22,4,11,20,demod] CP(1,0,9,1,0). ** KEPT (pick-wt=6): 946 [hyper,22,4,11,19,demod] CP(1,0,8,1,0). ** KEPT (pick-wt=6): 947 [hyper,22,4,11,18,demod] CP(1,0,7,1,0). ** KEPT (pick-wt=6): 948 [hyper,22,4,11,17,demod] CP(1,0,6,1,0). ** KEPT (pick-wt=6): 949 [hyper,22,4,11,16,demod] CP(1,0,5,1,0). ** KEPT (pick-wt=6): 950 [hyper,22,4,11,15,demod] CP(1,0,4,1,0). ** KEPT (pick-wt=6): 951 [hyper,22,4,11,14,demod] CP(1,0,3,1,0). ** KEPT (pick-wt=6): 952 [hyper,22,4,11,13,demod] CP(1,0,2,1,0). ** KEPT (pick-wt=6): 953 [hyper,22,4,11,12,demod] CP(1,0,1,1,0). ** KEPT (pick-wt=6): 954 [hyper,22,4,11,11,demod] CP(1,0,0,1,0). ** KEPT (pick-wt=6): 955 [hyper,22,3,20,20,demod] CP(0,9,9,1,8). ** KEPT (pick-wt=6): 956 [hyper,22,3,20,19,demod] CP(0,9,8,2,7). ** KEPT (pick-wt=6): 957 [hyper,22,3,20,18,demod] CP(0,9,7,3,6). ** KEPT (pick-wt=6): 958 [hyper,22,3,20,17,demod] CP(0,9,6,4,5). ** KEPT (pick-wt=6): 959 [hyper,22,3,20,16,demod] CP(0,9,5,5,4). ** KEPT (pick-wt=6): 960 [hyper,22,3,20,15,demod] CP(0,9,4,6,3). ** KEPT (pick-wt=6): 961 [hyper,22,3,20,14,demod] CP(0,9,3,7,2). ** KEPT (pick-wt=6): 962 [hyper,22,3,20,13,demod] CP(0,9,2,8,1). ** KEPT (pick-wt=6): 963 [hyper,22,3,20,12,demod] CP(0,9,1,9,0). ** KEPT (pick-wt=6): 964 [hyper,22,3,20,11,demod] CP(0,9,0,0,0). ** KEPT (pick-wt=6): 965 [hyper,22,3,19,20,demod] CP(0,8,9,2,7). ** KEPT (pick-wt=6): 966 [hyper,22,3,19,19,demod] CP(0,8,8,4,6). ** KEPT (pick-wt=6): 967 [hyper,22,3,19,18,demod] CP(0,8,7,6,5). ** KEPT (pick-wt=6): 968 [hyper,22,3,19,17,demod] CP(0,8,6,8,4). ** KEPT (pick-wt=6): 969 [hyper,22,3,19,16,demod] CP(0,8,5,0,4). ** KEPT (pick-wt=6): 970 [hyper,22,3,19,15,demod] CP(0,8,4,2,3). ** KEPT (pick-wt=6): 971 [hyper,22,3,19,14,demod] CP(0,8,3,4,2). ** KEPT (pick-wt=6): 972 [hyper,22,3,19,13,demod] CP(0,8,2,6,1). ** KEPT (pick-wt=6): 973 [hyper,22,3,19,12,demod] CP(0,8,1,8,0). ** KEPT (pick-wt=6): 974 [hyper,22,3,19,11,demod] CP(0,8,0,0,0). ** KEPT (pick-wt=6): 975 [hyper,22,3,18,20,demod] CP(0,7,9,3,6). ** KEPT (pick-wt=6): 976 [hyper,22,3,18,19,demod] CP(0,7,8,6,5). ** KEPT (pick-wt=6): 977 [hyper,22,3,18,18,demod] CP(0,7,7,9,4). ** KEPT (pick-wt=6): 978 [hyper,22,3,18,17,demod] CP(0,7,6,2,4). ** KEPT (pick-wt=6): 979 [hyper,22,3,18,16,demod] CP(0,7,5,5,3). ** KEPT (pick-wt=6): 980 [hyper,22,3,18,15,demod] CP(0,7,4,8,2). ** KEPT (pick-wt=6): 981 [hyper,22,3,18,14,demod] CP(0,7,3,1,2). ** KEPT (pick-wt=6): 982 [hyper,22,3,18,13,demod] CP(0,7,2,4,1). ** KEPT (pick-wt=6): 983 [hyper,22,3,18,12,demod] CP(0,7,1,7,0). ** KEPT (pick-wt=6): 984 [hyper,22,3,18,11,demod] CP(0,7,0,0,0). ** KEPT (pick-wt=6): 985 [hyper,22,3,17,20,demod] CP(0,6,9,4,5). ** KEPT (pick-wt=6): 986 [hyper,22,3,17,19,demod] CP(0,6,8,8,4). ** KEPT (pick-wt=6): 987 [hyper,22,3,17,18,demod] CP(0,6,7,2,4). ** KEPT (pick-wt=6): 988 [hyper,22,3,17,17,demod] CP(0,6,6,6,3). ** KEPT (pick-wt=6): 989 [hyper,22,3,17,16,demod] CP(0,6,5,0,3). ** KEPT (pick-wt=6): 990 [hyper,22,3,17,15,demod] CP(0,6,4,4,2). ** KEPT (pick-wt=6): 991 [hyper,22,3,17,14,demod] CP(0,6,3,8,1). ** KEPT (pick-wt=6): 992 [hyper,22,3,17,13,demod] CP(0,6,2,2,1). ** KEPT (pick-wt=6): 993 [hyper,22,3,17,12,demod] CP(0,6,1,6,0). ** KEPT (pick-wt=6): 994 [hyper,22,3,17,11,demod] CP(0,6,0,0,0). ** KEPT (pick-wt=6): 995 [hyper,22,3,16,20,demod] CP(0,5,9,5,4). ** KEPT (pick-wt=6): 996 [hyper,22,3,16,19,demod] CP(0,5,8,0,4). ** KEPT (pick-wt=6): 997 [hyper,22,3,16,18,demod] CP(0,5,7,5,3). ** KEPT (pick-wt=6): 998 [hyper,22,3,16,17,demod] CP(0,5,6,0,3). ** KEPT (pick-wt=6): 999 [hyper,22,3,16,16,demod] CP(0,5,5,5,2). ** KEPT (pick-wt=6): 1000 [hyper,22,3,16,15,demod] CP(0,5,4,0,2). ** KEPT (pick-wt=6): 1001 [hyper,22,3,16,14,demod] CP(0,5,3,5,1). ** KEPT (pick-wt=6): 1002 [hyper,22,3,16,13,demod] CP(0,5,2,0,1). ** KEPT (pick-wt=6): 1003 [hyper,22,3,16,12,demod] CP(0,5,1,5,0). ** KEPT (pick-wt=6): 1004 [hyper,22,3,16,11,demod] CP(0,5,0,0,0). ** KEPT (pick-wt=6): 1005 [hyper,22,3,15,20,demod] CP(0,4,9,6,3). ** KEPT (pick-wt=6): 1006 [hyper,22,3,15,19,demod] CP(0,4,8,2,3). ** KEPT (pick-wt=6): 1007 [hyper,22,3,15,18,demod] CP(0,4,7,8,2). ** KEPT (pick-wt=6): 1008 [hyper,22,3,15,17,demod] CP(0,4,6,4,2). ** KEPT (pick-wt=6): 1009 [hyper,22,3,15,16,demod] CP(0,4,5,0,2). ** KEPT (pick-wt=6): 1010 [hyper,22,3,15,15,demod] CP(0,4,4,6,1). ** KEPT (pick-wt=6): 1011 [hyper,22,3,15,14,demod] CP(0,4,3,2,1). ** KEPT (pick-wt=6): 1012 [hyper,22,3,15,13,demod] CP(0,4,2,8,0). ** KEPT (pick-wt=6): 1013 [hyper,22,3,15,12,demod] CP(0,4,1,4,0). ** KEPT (pick-wt=6): 1014 [hyper,22,3,15,11,demod] CP(0,4,0,0,0). ** KEPT (pick-wt=6): 1015 [hyper,22,3,14,20,demod] CP(0,3,9,7,2). ** KEPT (pick-wt=6): 1016 [hyper,22,3,14,19,demod] CP(0,3,8,4,2). ** KEPT (pick-wt=6): 1017 [hyper,22,3,14,18,demod] CP(0,3,7,1,2). ** KEPT (pick-wt=6): 1018 [hyper,22,3,14,17,demod] CP(0,3,6,8,1). ** KEPT (pick-wt=6): 1019 [hyper,22,3,14,16,demod] CP(0,3,5,5,1). ** KEPT (pick-wt=6): 1020 [hyper,22,3,14,15,demod] CP(0,3,4,2,1). ** KEPT (pick-wt=6): 1021 [hyper,22,3,14,14,demod] CP(0,3,3,9,0). ** KEPT (pick-wt=6): 1022 [hyper,22,3,14,13,demod] CP(0,3,2,6,0). ** KEPT (pick-wt=6): 1023 [hyper,22,3,14,12,demod] CP(0,3,1,3,0). ** KEPT (pick-wt=6): 1024 [hyper,22,3,14,11,demod] CP(0,3,0,0,0). ** KEPT (pick-wt=6): 1025 [hyper,22,3,13,20,demod] CP(0,2,9,8,1). ** KEPT (pick-wt=6): 1026 [hyper,22,3,13,19,demod] CP(0,2,8,6,1). ** KEPT (pick-wt=6): 1027 [hyper,22,3,13,18,demod] CP(0,2,7,4,1). ** KEPT (pick-wt=6): 1028 [hyper,22,3,13,17,demod] CP(0,2,6,2,1). ** KEPT (pick-wt=6): 1029 [hyper,22,3,13,16,demod] CP(0,2,5,0,1). ** KEPT (pick-wt=6): 1030 [hyper,22,3,13,15,demod] CP(0,2,4,8,0). ** KEPT (pick-wt=6): 1031 [hyper,22,3,13,14,demod] CP(0,2,3,6,0). ** KEPT (pick-wt=6): 1032 [hyper,22,3,13,13,demod] CP(0,2,2,4,0). ** KEPT (pick-wt=6): 1033 [hyper,22,3,13,12,demod] CP(0,2,1,2,0). ** KEPT (pick-wt=6): 1034 [hyper,22,3,13,11,demod] CP(0,2,0,0,0). ** KEPT (pick-wt=6): 1035 [hyper,22,3,12,20,demod] CP(0,1,9,9,0). ** KEPT (pick-wt=6): 1036 [hyper,22,3,12,19,demod] CP(0,1,8,8,0). ** KEPT (pick-wt=6): 1037 [hyper,22,3,12,18,demod] CP(0,1,7,7,0). ** KEPT (pick-wt=6): 1038 [hyper,22,3,12,17,demod] CP(0,1,6,6,0). ** KEPT (pick-wt=6): 1039 [hyper,22,3,12,16,demod] CP(0,1,5,5,0). ** KEPT (pick-wt=6): 1040 [hyper,22,3,12,15,demod] CP(0,1,4,4,0). ** KEPT (pick-wt=6): 1041 [hyper,22,3,12,14,demod] CP(0,1,3,3,0). ** KEPT (pick-wt=6): 1042 [hyper,22,3,12,13,demod] CP(0,1,2,2,0). ** KEPT (pick-wt=6): 1043 [hyper,22,3,12,12,demod] CP(0,1,1,1,0). ** KEPT (pick-wt=6): 1044 [hyper,22,3,12,11,demod] CP(0,1,0,0,0). ** KEPT (pick-wt=6): 1045 [hyper,22,3,11,20,demod] CP(0,0,9,0,0). ** KEPT (pick-wt=6): 1046 [hyper,22,3,11,19,demod] CP(0,0,8,0,0). ** KEPT (pick-wt=6): 1047 [hyper,22,3,11,18,demod] CP(0,0,7,0,0). ** KEPT (pick-wt=6): 1048 [hyper,22,3,11,17,demod] CP(0,0,6,0,0). ** KEPT (pick-wt=6): 1049 [hyper,22,3,11,16,demod] CP(0,0,5,0,0). ** KEPT (pick-wt=6): 1050 [hyper,22,3,11,15,demod] CP(0,0,4,0,0). ** KEPT (pick-wt=6): 1051 [hyper,22,3,11,14,demod] CP(0,0,3,0,0). ** KEPT (pick-wt=6): 1052 [hyper,22,3,11,13,demod] CP(0,0,2,0,0). ** KEPT (pick-wt=6): 1053 [hyper,22,3,11,12,demod] CP(0,0,1,0,0). ** KEPT (pick-wt=6): 1054 [hyper,22,3,11,11,demod] CP(0,0,0,0,0). given clause #203: (wt=6) 255 [hyper,22,10,20,20,demod] CP(7,9,9,8,8). given clause #204: (wt=6) 256 [hyper,22,10,20,19,demod] CP(7,9,8,9,7). given clause #205: (wt=6) 257 [hyper,22,10,20,18,demod] CP(7,9,7,0,7). given clause #206: (wt=6) 258 [hyper,22,10,20,17,demod] CP(7,9,6,1,6). given clause #207: (wt=6) 259 [hyper,22,10,20,16,demod] CP(7,9,5,2,5). given clause #208: (wt=6) 260 [hyper,22,10,20,15,demod] CP(7,9,4,3,4). given clause #209: (wt=6) 261 [hyper,22,10,20,14,demod] CP(7,9,3,4,3). given clause #210: (wt=6) 262 [hyper,22,10,20,13,demod] CP(7,9,2,5,2). given clause #211: (wt=6) 263 [hyper,22,10,20,12,demod] CP(7,9,1,6,1). given clause #212: (wt=6) 264 [hyper,22,10,20,11,demod] CP(7,9,0,7,0). given clause #213: (wt=6) 265 [hyper,22,10,19,20,demod] CP(7,8,9,9,7). given clause #214: (wt=6) 266 [hyper,22,10,19,19,demod] CP(7,8,8,1,7). given clause #215: (wt=6) 267 [hyper,22,10,19,18,demod] CP(7,8,7,3,6). given clause #216: (wt=6) 268 [hyper,22,10,19,17,demod] CP(7,8,6,5,5). given clause #217: (wt=6) 269 [hyper,22,10,19,16,demod] CP(7,8,5,7,4). given clause #218: (wt=6) 270 [hyper,22,10,19,15,demod] CP(7,8,4,9,3). given clause #219: (wt=6) 271 [hyper,22,10,19,14,demod] CP(7,8,3,1,3). given clause #220: (wt=6) 272 [hyper,22,10,19,13,demod] CP(7,8,2,3,2). given clause #221: (wt=6) 273 [hyper,22,10,19,12,demod] CP(7,8,1,5,1). given clause #222: (wt=6) 274 [hyper,22,10,19,11,demod] CP(7,8,0,7,0). given clause #223: (wt=6) 275 [hyper,22,10,18,20,demod] CP(7,7,9,0,7). given clause #224: (wt=6) 276 [hyper,22,10,18,19,demod] CP(7,7,8,3,6). given clause #225: (wt=6) 277 [hyper,22,10,18,18,demod] CP(7,7,7,6,5). given clause #226: (wt=6) 278 [hyper,22,10,18,17,demod] CP(7,7,6,9,4). given clause #227: (wt=6) 279 [hyper,22,10,18,16,demod] CP(7,7,5,2,4). given clause #228: (wt=6) 280 [hyper,22,10,18,15,demod] CP(7,7,4,5,3). given clause #229: (wt=6) 281 [hyper,22,10,18,14,demod] CP(7,7,3,8,2). given clause #230: (wt=6) 282 [hyper,22,10,18,13,demod] CP(7,7,2,1,2). given clause #231: (wt=6) 283 [hyper,22,10,18,12,demod] CP(7,7,1,4,1). given clause #232: (wt=6) 284 [hyper,22,10,18,11,demod] CP(7,7,0,7,0). given clause #233: (wt=6) 285 [hyper,22,10,17,20,demod] CP(7,6,9,1,6). given clause #234: (wt=6) 286 [hyper,22,10,17,19,demod] CP(7,6,8,5,5). given clause #235: (wt=6) 287 [hyper,22,10,17,18,demod] CP(7,6,7,9,4). given clause #236: (wt=6) 288 [hyper,22,10,17,17,demod] CP(7,6,6,3,4). given clause #237: (wt=6) 289 [hyper,22,10,17,16,demod] CP(7,6,5,7,3). given clause #238: (wt=6) 290 [hyper,22,10,17,15,demod] CP(7,6,4,1,3). given clause #239: (wt=6) 291 [hyper,22,10,17,14,demod] CP(7,6,3,5,2). given clause #240: (wt=6) 292 [hyper,22,10,17,13,demod] CP(7,6,2,9,1). given clause #241: (wt=6) 293 [hyper,22,10,17,12,demod] CP(7,6,1,3,1). given clause #242: (wt=6) 294 [hyper,22,10,17,11,demod] CP(7,6,0,7,0). given clause #243: (wt=6) 295 [hyper,22,10,16,20,demod] CP(7,5,9,2,5). given clause #244: (wt=6) 296 [hyper,22,10,16,19,demod] CP(7,5,8,7,4). given clause #245: (wt=6) 297 [hyper,22,10,16,18,demod] CP(7,5,7,2,4). given clause #246: (wt=6) 298 [hyper,22,10,16,17,demod] CP(7,5,6,7,3). given clause #247: (wt=6) 299 [hyper,22,10,16,16,demod] CP(7,5,5,2,3). given clause #248: (wt=6) 300 [hyper,22,10,16,15,demod] CP(7,5,4,7,2). given clause #249: (wt=6) 301 [hyper,22,10,16,14,demod] CP(7,5,3,2,2). given clause #250: (wt=6) 302 [hyper,22,10,16,13,demod] CP(7,5,2,7,1). given clause #251: (wt=6) 303 [hyper,22,10,16,12,demod] CP(7,5,1,2,1). given clause #252: (wt=6) 304 [hyper,22,10,16,11,demod] CP(7,5,0,7,0). given clause #253: (wt=6) 305 [hyper,22,10,15,20,demod] CP(7,4,9,3,4). given clause #254: (wt=6) 306 [hyper,22,10,15,19,demod] CP(7,4,8,9,3). given clause #255: (wt=6) 307 [hyper,22,10,15,18,demod] CP(7,4,7,5,3). given clause #256: (wt=6) 308 [hyper,22,10,15,17,demod] CP(7,4,6,1,3). given clause #257: (wt=6) 309 [hyper,22,10,15,16,demod] CP(7,4,5,7,2). given clause #258: (wt=6) 310 [hyper,22,10,15,15,demod] CP(7,4,4,3,2). given clause #259: (wt=6) 311 [hyper,22,10,15,14,demod] CP(7,4,3,9,1). given clause #260: (wt=6) 312 [hyper,22,10,15,13,demod] CP(7,4,2,5,1). given clause #261: (wt=6) 313 [hyper,22,10,15,12,demod] CP(7,4,1,1,1). given clause #262: (wt=6) 314 [hyper,22,10,15,11,demod] CP(7,4,0,7,0). given clause #263: (wt=6) 315 [hyper,22,10,14,20,demod] CP(7,3,9,4,3). given clause #264: (wt=6) 316 [hyper,22,10,14,19,demod] CP(7,3,8,1,3). given clause #265: (wt=6) 317 [hyper,22,10,14,18,demod] CP(7,3,7,8,2). given clause #266: (wt=6) 318 [hyper,22,10,14,17,demod] CP(7,3,6,5,2). given clause #267: (wt=6) 319 [hyper,22,10,14,16,demod] CP(7,3,5,2,2). given clause #268: (wt=6) 320 [hyper,22,10,14,15,demod] CP(7,3,4,9,1). given clause #269: (wt=6) 321 [hyper,22,10,14,14,demod] CP(7,3,3,6,1). given clause #270: (wt=6) 322 [hyper,22,10,14,13,demod] CP(7,3,2,3,1). given clause #271: (wt=6) 323 [hyper,22,10,14,12,demod] CP(7,3,1,0,1). given clause #272: (wt=6) 324 [hyper,22,10,14,11,demod] CP(7,3,0,7,0). given clause #273: (wt=6) 325 [hyper,22,10,13,20,demod] CP(7,2,9,5,2). given clause #274: (wt=6) 326 [hyper,22,10,13,19,demod] CP(7,2,8,3,2). given clause #275: (wt=6) 327 [hyper,22,10,13,18,demod] CP(7,2,7,1,2). given clause #276: (wt=6) 328 [hyper,22,10,13,17,demod] CP(7,2,6,9,1). given clause #277: (wt=6) 329 [hyper,22,10,13,16,demod] CP(7,2,5,7,1). given clause #278: (wt=6) 330 [hyper,22,10,13,15,demod] CP(7,2,4,5,1). given clause #279: (wt=6) 331 [hyper,22,10,13,14,demod] CP(7,2,3,3,1). given clause #280: (wt=6) 332 [hyper,22,10,13,13,demod] CP(7,2,2,1,1). given clause #281: (wt=6) 333 [hyper,22,10,13,12,demod] CP(7,2,1,9,0). given clause #282: (wt=6) 334 [hyper,22,10,13,11,demod] CP(7,2,0,7,0). given clause #283: (wt=6) 335 [hyper,22,10,12,20,demod] CP(7,1,9,6,1). given clause #284: (wt=6) 336 [hyper,22,10,12,19,demod] CP(7,1,8,5,1). given clause #285: (wt=6) 337 [hyper,22,10,12,18,demod] CP(7,1,7,4,1). given clause #286: (wt=6) 338 [hyper,22,10,12,17,demod] CP(7,1,6,3,1). given clause #287: (wt=6) 339 [hyper,22,10,12,16,demod] CP(7,1,5,2,1). given clause #288: (wt=6) 340 [hyper,22,10,12,15,demod] CP(7,1,4,1,1). given clause #289: (wt=6) 341 [hyper,22,10,12,14,demod] CP(7,1,3,0,1). given clause #290: (wt=6) 342 [hyper,22,10,12,13,demod] CP(7,1,2,9,0). given clause #291: (wt=6) 343 [hyper,22,10,12,12,demod] CP(7,1,1,8,0). given clause #292: (wt=6) 344 [hyper,22,10,12,11,demod] CP(7,1,0,7,0). given clause #293: (wt=6) 345 [hyper,22,10,11,20,demod] CP(7,0,9,7,0). given clause #294: (wt=6) 346 [hyper,22,10,11,19,demod] CP(7,0,8,7,0). given clause #295: (wt=6) 347 [hyper,22,10,11,18,demod] CP(7,0,7,7,0). given clause #296: (wt=6) 348 [hyper,22,10,11,17,demod] CP(7,0,6,7,0). given clause #297: (wt=6) 349 [hyper,22,10,11,16,demod] CP(7,0,5,7,0). given clause #298: (wt=6) 350 [hyper,22,10,11,15,demod] CP(7,0,4,7,0). given clause #299: (wt=6) 351 [hyper,22,10,11,14,demod] CP(7,0,3,7,0). given clause #300: (wt=6) 352 [hyper,22,10,11,13,demod] CP(7,0,2,7,0). given clause #301: (wt=6) 353 [hyper,22,10,11,12,demod] CP(7,0,1,7,0). given clause #302: (wt=6) 354 [hyper,22,10,11,11,demod] CP(7,0,0,7,0). given clause #303: (wt=6) 355 [hyper,22,9,20,20,demod] CP(6,9,9,7,8). given clause #304: (wt=6) 356 [hyper,22,9,20,19,demod] CP(6,9,8,8,7). given clause #305: (wt=6) 357 [hyper,22,9,20,18,demod] CP(6,9,7,9,6). given clause #306: (wt=6) 358 [hyper,22,9,20,17,demod] CP(6,9,6,0,6). given clause #307: (wt=6) 359 [hyper,22,9,20,16,demod] CP(6,9,5,1,5). given clause #308: (wt=6) 360 [hyper,22,9,20,15,demod] CP(6,9,4,2,4). given clause #309: (wt=6) 361 [hyper,22,9,20,14,demod] CP(6,9,3,3,3). given clause #310: (wt=6) 362 [hyper,22,9,20,13,demod] CP(6,9,2,4,2). given clause #311: (wt=6) 363 [hyper,22,9,20,12,demod] CP(6,9,1,5,1). given clause #312: (wt=6) 364 [hyper,22,9,20,11,demod] CP(6,9,0,6,0). given clause #313: (wt=6) 365 [hyper,22,9,19,20,demod] CP(6,8,9,8,7). given clause #314: (wt=6) 366 [hyper,22,9,19,19,demod] CP(6,8,8,0,7). given clause #315: (wt=6) 367 [hyper,22,9,19,18,demod] CP(6,8,7,2,6). given clause #316: (wt=6) 368 [hyper,22,9,19,17,demod] CP(6,8,6,4,5). given clause #317: (wt=6) 369 [hyper,22,9,19,16,demod] CP(6,8,5,6,4). given clause #318: (wt=6) 370 [hyper,22,9,19,15,demod] CP(6,8,4,8,3). given clause #319: (wt=6) 371 [hyper,22,9,19,14,demod] CP(6,8,3,0,3). given clause #320: (wt=6) 372 [hyper,22,9,19,13,demod] CP(6,8,2,2,2). given clause #321: (wt=6) 373 [hyper,22,9,19,12,demod] CP(6,8,1,4,1). given clause #322: (wt=6) 374 [hyper,22,9,19,11,demod] CP(6,8,0,6,0). given clause #323: (wt=6) 375 [hyper,22,9,18,20,demod] CP(6,7,9,9,6). given clause #324: (wt=6) 376 [hyper,22,9,18,19,demod] CP(6,7,8,2,6). given clause #325: (wt=6) 377 [hyper,22,9,18,18,demod] CP(6,7,7,5,5). given clause #326: (wt=6) 378 [hyper,22,9,18,17,demod] CP(6,7,6,8,4). given clause #327: (wt=6) 379 [hyper,22,9,18,16,demod] CP(6,7,5,1,4). given clause #328: (wt=6) 380 [hyper,22,9,18,15,demod] CP(6,7,4,4,3). given clause #329: (wt=6) 381 [hyper,22,9,18,14,demod] CP(6,7,3,7,2). given clause #330: (wt=6) 382 [hyper,22,9,18,13,demod] CP(6,7,2,0,2). given clause #331: (wt=6) 383 [hyper,22,9,18,12,demod] CP(6,7,1,3,1). given clause #332: (wt=6) 384 [hyper,22,9,18,11,demod] CP(6,7,0,6,0). given clause #333: (wt=6) 385 [hyper,22,9,17,20,demod] CP(6,6,9,0,6). given clause #334: (wt=6) 386 [hyper,22,9,17,19,demod] CP(6,6,8,4,5). given clause #335: (wt=6) 387 [hyper,22,9,17,18,demod] CP(6,6,7,8,4). given clause #336: (wt=6) 388 [hyper,22,9,17,17,demod] CP(6,6,6,2,4). given clause #337: (wt=6) 389 [hyper,22,9,17,16,demod] CP(6,6,5,6,3). given clause #338: (wt=6) 390 [hyper,22,9,17,15,demod] CP(6,6,4,0,3). given clause #339: (wt=6) 391 [hyper,22,9,17,14,demod] CP(6,6,3,4,2). given clause #340: (wt=6) 392 [hyper,22,9,17,13,demod] CP(6,6,2,8,1). given clause #341: (wt=6) 393 [hyper,22,9,17,12,demod] CP(6,6,1,2,1). given clause #342: (wt=6) 394 [hyper,22,9,17,11,demod] CP(6,6,0,6,0). given clause #343: (wt=6) 395 [hyper,22,9,16,20,demod] CP(6,5,9,1,5). given clause #344: (wt=6) 396 [hyper,22,9,16,19,demod] CP(6,5,8,6,4). given clause #345: (wt=6) 397 [hyper,22,9,16,18,demod] CP(6,5,7,1,4). given clause #346: (wt=6) 398 [hyper,22,9,16,17,demod] CP(6,5,6,6,3). given clause #347: (wt=6) 399 [hyper,22,9,16,16,demod] CP(6,5,5,1,3). given clause #348: (wt=6) 400 [hyper,22,9,16,15,demod] CP(6,5,4,6,2). given clause #349: (wt=6) 401 [hyper,22,9,16,14,demod] CP(6,5,3,1,2). given clause #350: (wt=6) 402 [hyper,22,9,16,13,demod] CP(6,5,2,6,1). given clause #351: (wt=6) 403 [hyper,22,9,16,12,demod] CP(6,5,1,1,1). given clause #352: (wt=6) 404 [hyper,22,9,16,11,demod] CP(6,5,0,6,0). given clause #353: (wt=6) 405 [hyper,22,9,15,20,demod] CP(6,4,9,2,4). given clause #354: (wt=6) 406 [hyper,22,9,15,19,demod] CP(6,4,8,8,3). given clause #355: (wt=6) 407 [hyper,22,9,15,18,demod] CP(6,4,7,4,3). given clause #356: (wt=6) 408 [hyper,22,9,15,17,demod] CP(6,4,6,0,3). given clause #357: (wt=6) 409 [hyper,22,9,15,16,demod] CP(6,4,5,6,2). given clause #358: (wt=6) 410 [hyper,22,9,15,15,demod] CP(6,4,4,2,2). given clause #359: (wt=6) 411 [hyper,22,9,15,14,demod] CP(6,4,3,8,1). given clause #360: (wt=6) 412 [hyper,22,9,15,13,demod] CP(6,4,2,4,1). given clause #361: (wt=6) 413 [hyper,22,9,15,12,demod] CP(6,4,1,0,1). given clause #362: (wt=6) 414 [hyper,22,9,15,11,demod] CP(6,4,0,6,0). given clause #363: (wt=6) 415 [hyper,22,9,14,20,demod] CP(6,3,9,3,3). given clause #364: (wt=6) 416 [hyper,22,9,14,19,demod] CP(6,3,8,0,3). given clause #365: (wt=6) 417 [hyper,22,9,14,18,demod] CP(6,3,7,7,2). given clause #366: (wt=6) 418 [hyper,22,9,14,17,demod] CP(6,3,6,4,2). given clause #367: (wt=6) 419 [hyper,22,9,14,16,demod] CP(6,3,5,1,2). given clause #368: (wt=6) 420 [hyper,22,9,14,15,demod] CP(6,3,4,8,1). given clause #369: (wt=6) 421 [hyper,22,9,14,14,demod] CP(6,3,3,5,1). given clause #370: (wt=6) 422 [hyper,22,9,14,13,demod] CP(6,3,2,2,1). given clause #371: (wt=6) 423 [hyper,22,9,14,12,demod] CP(6,3,1,9,0). given clause #372: (wt=6) 424 [hyper,22,9,14,11,demod] CP(6,3,0,6,0). given clause #373: (wt=6) 425 [hyper,22,9,13,20,demod] CP(6,2,9,4,2). given clause #374: (wt=6) 426 [hyper,22,9,13,19,demod] CP(6,2,8,2,2). given clause #375: (wt=6) 427 [hyper,22,9,13,18,demod] CP(6,2,7,0,2). given clause #376: (wt=6) 428 [hyper,22,9,13,17,demod] CP(6,2,6,8,1). given clause #377: (wt=6) 429 [hyper,22,9,13,16,demod] CP(6,2,5,6,1). given clause #378: (wt=6) 430 [hyper,22,9,13,15,demod] CP(6,2,4,4,1). given clause #379: (wt=6) 431 [hyper,22,9,13,14,demod] CP(6,2,3,2,1). given clause #380: (wt=6) 432 [hyper,22,9,13,13,demod] CP(6,2,2,0,1). given clause #381: (wt=6) 433 [hyper,22,9,13,12,demod] CP(6,2,1,8,0). given clause #382: (wt=6) 434 [hyper,22,9,13,11,demod] CP(6,2,0,6,0). given clause #383: (wt=6) 435 [hyper,22,9,12,20,demod] CP(6,1,9,5,1). given clause #384: (wt=6) 436 [hyper,22,9,12,19,demod] CP(6,1,8,4,1). given clause #385: (wt=6) 437 [hyper,22,9,12,18,demod] CP(6,1,7,3,1). given clause #386: (wt=6) 438 [hyper,22,9,12,17,demod] CP(6,1,6,2,1). given clause #387: (wt=6) 439 [hyper,22,9,12,16,demod] CP(6,1,5,1,1). given clause #388: (wt=6) 440 [hyper,22,9,12,15,demod] CP(6,1,4,0,1). given clause #389: (wt=6) 441 [hyper,22,9,12,14,demod] CP(6,1,3,9,0). given clause #390: (wt=6) 442 [hyper,22,9,12,13,demod] CP(6,1,2,8,0). given clause #391: (wt=6) 443 [hyper,22,9,12,12,demod] CP(6,1,1,7,0). given clause #392: (wt=6) 444 [hyper,22,9,12,11,demod] CP(6,1,0,6,0). given clause #393: (wt=6) 445 [hyper,22,9,11,20,demod] CP(6,0,9,6,0). given clause #394: (wt=6) 446 [hyper,22,9,11,19,demod] CP(6,0,8,6,0). given clause #395: (wt=6) 447 [hyper,22,9,11,18,demod] CP(6,0,7,6,0). given clause #396: (wt=6) 448 [hyper,22,9,11,17,demod] CP(6,0,6,6,0). given clause #397: (wt=6) 449 [hyper,22,9,11,16,demod] CP(6,0,5,6,0). given clause #398: (wt=6) 450 [hyper,22,9,11,15,demod] CP(6,0,4,6,0). given clause #399: (wt=6) 451 [hyper,22,9,11,14,demod] CP(6,0,3,6,0). given clause #400: (wt=6) 452 [hyper,22,9,11,13,demod] CP(6,0,2,6,0). given clause #401: (wt=6) 453 [hyper,22,9,11,12,demod] CP(6,0,1,6,0). given clause #402: (wt=6) 454 [hyper,22,9,11,11,demod] CP(6,0,0,6,0). given clause #403: (wt=6) 455 [hyper,22,8,20,20,demod] CP(5,9,9,6,8). given clause #404: (wt=6) 456 [hyper,22,8,20,19,demod] CP(5,9,8,7,7). given clause #405: (wt=6) 457 [hyper,22,8,20,18,demod] CP(5,9,7,8,6). given clause #406: (wt=6) 458 [hyper,22,8,20,17,demod] CP(5,9,6,9,5). given clause #407: (wt=6) 459 [hyper,22,8,20,16,demod] CP(5,9,5,0,5). given clause #408: (wt=6) 460 [hyper,22,8,20,15,demod] CP(5,9,4,1,4). given clause #409: (wt=6) 461 [hyper,22,8,20,14,demod] CP(5,9,3,2,3). given clause #410: (wt=6) 462 [hyper,22,8,20,13,demod] CP(5,9,2,3,2). given clause #411: (wt=6) 463 [hyper,22,8,20,12,demod] CP(5,9,1,4,1). given clause #412: (wt=6) 464 [hyper,22,8,20,11,demod] CP(5,9,0,5,0). given clause #413: (wt=6) 465 [hyper,22,8,19,20,demod] CP(5,8,9,7,7). given clause #414: (wt=6) 466 [hyper,22,8,19,19,demod] CP(5,8,8,9,6). given clause #415: (wt=6) 467 [hyper,22,8,19,18,demod] CP(5,8,7,1,6). given clause #416: (wt=6) 468 [hyper,22,8,19,17,demod] CP(5,8,6,3,5). given clause #417: (wt=6) 469 [hyper,22,8,19,16,demod] CP(5,8,5,5,4). given clause #418: (wt=6) 470 [hyper,22,8,19,15,demod] CP(5,8,4,7,3). given clause #419: (wt=6) 471 [hyper,22,8,19,14,demod] CP(5,8,3,9,2). given clause #420: (wt=6) 472 [hyper,22,8,19,13,demod] CP(5,8,2,1,2). given clause #421: (wt=6) 473 [hyper,22,8,19,12,demod] CP(5,8,1,3,1). given clause #422: (wt=6) 474 [hyper,22,8,19,11,demod] CP(5,8,0,5,0). given clause #423: (wt=6) 475 [hyper,22,8,18,20,demod] CP(5,7,9,8,6). given clause #424: (wt=6) 476 [hyper,22,8,18,19,demod] CP(5,7,8,1,6). given clause #425: (wt=6) 477 [hyper,22,8,18,18,demod] CP(5,7,7,4,5). given clause #426: (wt=6) 478 [hyper,22,8,18,17,demod] CP(5,7,6,7,4). given clause #427: (wt=6) 479 [hyper,22,8,18,16,demod] CP(5,7,5,0,4). given clause #428: (wt=6) 480 [hyper,22,8,18,15,demod] CP(5,7,4,3,3). given clause #429: (wt=6) 481 [hyper,22,8,18,14,demod] CP(5,7,3,6,2). given clause #430: (wt=6) 482 [hyper,22,8,18,13,demod] CP(5,7,2,9,1). given clause #431: (wt=6) 483 [hyper,22,8,18,12,demod] CP(5,7,1,2,1). given clause #432: (wt=6) 484 [hyper,22,8,18,11,demod] CP(5,7,0,5,0). given clause #433: (wt=6) 485 [hyper,22,8,17,20,demod] CP(5,6,9,9,5). given clause #434: (wt=6) 486 [hyper,22,8,17,19,demod] CP(5,6,8,3,5). given clause #435: (wt=6) 487 [hyper,22,8,17,18,demod] CP(5,6,7,7,4). given clause #436: (wt=6) 488 [hyper,22,8,17,17,demod] CP(5,6,6,1,4). given clause #437: (wt=6) 489 [hyper,22,8,17,16,demod] CP(5,6,5,5,3). given clause #438: (wt=6) 490 [hyper,22,8,17,15,demod] CP(5,6,4,9,2). given clause #439: (wt=6) 491 [hyper,22,8,17,14,demod] CP(5,6,3,3,2). given clause #440: (wt=6) 492 [hyper,22,8,17,13,demod] CP(5,6,2,7,1). given clause #441: (wt=6) 493 [hyper,22,8,17,12,demod] CP(5,6,1,1,1). given clause #442: (wt=6) 494 [hyper,22,8,17,11,demod] CP(5,6,0,5,0). given clause #443: (wt=6) 495 [hyper,22,8,16,20,demod] CP(5,5,9,0,5). given clause #444: (wt=6) 496 [hyper,22,8,16,19,demod] CP(5,5,8,5,4). given clause #445: (wt=6) 497 [hyper,22,8,16,18,demod] CP(5,5,7,0,4). given clause #446: (wt=6) 498 [hyper,22,8,16,17,demod] CP(5,5,6,5,3). given clause #447: (wt=6) 499 [hyper,22,8,16,16,demod] CP(5,5,5,0,3). given clause #448: (wt=6) 500 [hyper,22,8,16,15,demod] CP(5,5,4,5,2). given clause #449: (wt=6) 501 [hyper,22,8,16,14,demod] CP(5,5,3,0,2). given clause #450: (wt=6) 502 [hyper,22,8,16,13,demod] CP(5,5,2,5,1). given clause #451: (wt=6) 503 [hyper,22,8,16,12,demod] CP(5,5,1,0,1). given clause #452: (wt=6) 504 [hyper,22,8,16,11,demod] CP(5,5,0,5,0). given clause #453: (wt=6) 505 [hyper,22,8,15,20,demod] CP(5,4,9,1,4). given clause #454: (wt=6) 506 [hyper,22,8,15,19,demod] CP(5,4,8,7,3). given clause #455: (wt=6) 507 [hyper,22,8,15,18,demod] CP(5,4,7,3,3). given clause #456: (wt=6) 508 [hyper,22,8,15,17,demod] CP(5,4,6,9,2). given clause #457: (wt=6) 509 [hyper,22,8,15,16,demod] CP(5,4,5,5,2). given clause #458: (wt=6) 510 [hyper,22,8,15,15,demod] CP(5,4,4,1,2). given clause #459: (wt=6) 511 [hyper,22,8,15,14,demod] CP(5,4,3,7,1). given clause #460: (wt=6) 512 [hyper,22,8,15,13,demod] CP(5,4,2,3,1). given clause #461: (wt=6) 513 [hyper,22,8,15,12,demod] CP(5,4,1,9,0). given clause #462: (wt=6) 514 [hyper,22,8,15,11,demod] CP(5,4,0,5,0). given clause #463: (wt=6) 515 [hyper,22,8,14,20,demod] CP(5,3,9,2,3). given clause #464: (wt=6) 516 [hyper,22,8,14,19,demod] CP(5,3,8,9,2). given clause #465: (wt=6) 517 [hyper,22,8,14,18,demod] CP(5,3,7,6,2). given clause #466: (wt=6) 518 [hyper,22,8,14,17,demod] CP(5,3,6,3,2). given clause #467: (wt=6) 519 [hyper,22,8,14,16,demod] CP(5,3,5,0,2). given clause #468: (wt=6) 520 [hyper,22,8,14,15,demod] CP(5,3,4,7,1). given clause #469: (wt=6) 521 [hyper,22,8,14,14,demod] CP(5,3,3,4,1). given clause #470: (wt=6) 522 [hyper,22,8,14,13,demod] CP(5,3,2,1,1). given clause #471: (wt=6) 523 [hyper,22,8,14,12,demod] CP(5,3,1,8,0). given clause #472: (wt=6) 524 [hyper,22,8,14,11,demod] CP(5,3,0,5,0). given clause #473: (wt=6) 525 [hyper,22,8,13,20,demod] CP(5,2,9,3,2). given clause #474: (wt=6) 526 [hyper,22,8,13,19,demod] CP(5,2,8,1,2). given clause #475: (wt=6) 527 [hyper,22,8,13,18,demod] CP(5,2,7,9,1). given clause #476: (wt=6) 528 [hyper,22,8,13,17,demod] CP(5,2,6,7,1). given clause #477: (wt=6) 529 [hyper,22,8,13,16,demod] CP(5,2,5,5,1). given clause #478: (wt=6) 530 [hyper,22,8,13,15,demod] CP(5,2,4,3,1). given clause #479: (wt=6) 531 [hyper,22,8,13,14,demod] CP(5,2,3,1,1). given clause #480: (wt=6) 532 [hyper,22,8,13,13,demod] CP(5,2,2,9,0). given clause #481: (wt=6) 533 [hyper,22,8,13,12,demod] CP(5,2,1,7,0). given clause #482: (wt=6) 534 [hyper,22,8,13,11,demod] CP(5,2,0,5,0). given clause #483: (wt=6) 535 [hyper,22,8,12,20,demod] CP(5,1,9,4,1). given clause #484: (wt=6) 536 [hyper,22,8,12,19,demod] CP(5,1,8,3,1). given clause #485: (wt=6) 537 [hyper,22,8,12,18,demod] CP(5,1,7,2,1). given clause #486: (wt=6) 538 [hyper,22,8,12,17,demod] CP(5,1,6,1,1). given clause #487: (wt=6) 539 [hyper,22,8,12,16,demod] CP(5,1,5,0,1). given clause #488: (wt=6) 540 [hyper,22,8,12,15,demod] CP(5,1,4,9,0). given clause #489: (wt=6) 541 [hyper,22,8,12,14,demod] CP(5,1,3,8,0). given clause #490: (wt=6) 542 [hyper,22,8,12,13,demod] CP(5,1,2,7,0). given clause #491: (wt=6) 543 [hyper,22,8,12,12,demod] CP(5,1,1,6,0). given clause #492: (wt=6) 544 [hyper,22,8,12,11,demod] CP(5,1,0,5,0). given clause #493: (wt=6) 545 [hyper,22,8,11,20,demod] CP(5,0,9,5,0). given clause #494: (wt=6) 546 [hyper,22,8,11,19,demod] CP(5,0,8,5,0). given clause #495: (wt=6) 547 [hyper,22,8,11,18,demod] CP(5,0,7,5,0). given clause #496: (wt=6) 548 [hyper,22,8,11,17,demod] CP(5,0,6,5,0). given clause #497: (wt=6) 549 [hyper,22,8,11,16,demod] CP(5,0,5,5,0). given clause #498: (wt=6) 550 [hyper,22,8,11,15,demod] CP(5,0,4,5,0). given clause #499: (wt=6) 551 [hyper,22,8,11,14,demod] CP(5,0,3,5,0). given clause #500: (wt=6) 552 [hyper,22,8,11,13,demod] CP(5,0,2,5,0). given clause #501: (wt=6) 553 [hyper,22,8,11,12,demod] CP(5,0,1,5,0). given clause #502: (wt=6) 554 [hyper,22,8,11,11,demod] CP(5,0,0,5,0). given clause #503: (wt=6) 555 [hyper,22,7,20,20,demod] CP(4,9,9,5,8). given clause #504: (wt=6) 556 [hyper,22,7,20,19,demod] CP(4,9,8,6,7). given clause #505: (wt=6) 557 [hyper,22,7,20,18,demod] CP(4,9,7,7,6). given clause #506: (wt=6) 558 [hyper,22,7,20,17,demod] CP(4,9,6,8,5). given clause #507: (wt=6) 559 [hyper,22,7,20,16,demod] CP(4,9,5,9,4). given clause #508: (wt=6) 560 [hyper,22,7,20,15,demod] CP(4,9,4,0,4). given clause #509: (wt=6) 561 [hyper,22,7,20,14,demod] CP(4,9,3,1,3). given clause #510: (wt=6) 562 [hyper,22,7,20,13,demod] CP(4,9,2,2,2). given clause #511: (wt=6) 563 [hyper,22,7,20,12,demod] CP(4,9,1,3,1). given clause #512: (wt=6) 564 [hyper,22,7,20,11,demod] CP(4,9,0,4,0). given clause #513: (wt=6) 565 [hyper,22,7,19,20,demod] CP(4,8,9,6,7). given clause #514: (wt=6) 566 [hyper,22,7,19,19,demod] CP(4,8,8,8,6). given clause #515: (wt=6) 567 [hyper,22,7,19,18,demod] CP(4,8,7,0,6). given clause #516: (wt=6) 568 [hyper,22,7,19,17,demod] CP(4,8,6,2,5). given clause #517: (wt=6) 569 [hyper,22,7,19,16,demod] CP(4,8,5,4,4). given clause #518: (wt=6) 570 [hyper,22,7,19,15,demod] CP(4,8,4,6,3). given clause #519: (wt=6) 571 [hyper,22,7,19,14,demod] CP(4,8,3,8,2). given clause #520: (wt=6) 572 [hyper,22,7,19,13,demod] CP(4,8,2,0,2). given clause #521: (wt=6) 573 [hyper,22,7,19,12,demod] CP(4,8,1,2,1). given clause #522: (wt=6) 574 [hyper,22,7,19,11,demod] CP(4,8,0,4,0). given clause #523: (wt=6) 575 [hyper,22,7,18,20,demod] CP(4,7,9,7,6). given clause #524: (wt=6) 576 [hyper,22,7,18,19,demod] CP(4,7,8,0,6). given clause #525: (wt=6) 577 [hyper,22,7,18,18,demod] CP(4,7,7,3,5). given clause #526: (wt=6) 578 [hyper,22,7,18,17,demod] CP(4,7,6,6,4). given clause #527: (wt=6) 579 [hyper,22,7,18,16,demod] CP(4,7,5,9,3). given clause #528: (wt=6) 580 [hyper,22,7,18,15,demod] CP(4,7,4,2,3). given clause #529: (wt=6) 581 [hyper,22,7,18,14,demod] CP(4,7,3,5,2). given clause #530: (wt=6) 582 [hyper,22,7,18,13,demod] CP(4,7,2,8,1). given clause #531: (wt=6) 583 [hyper,22,7,18,12,demod] CP(4,7,1,1,1). given clause #532: (wt=6) 584 [hyper,22,7,18,11,demod] CP(4,7,0,4,0). given clause #533: (wt=6) 585 [hyper,22,7,17,20,demod] CP(4,6,9,8,5). given clause #534: (wt=6) 586 [hyper,22,7,17,19,demod] CP(4,6,8,2,5). given clause #535: (wt=6) 587 [hyper,22,7,17,18,demod] CP(4,6,7,6,4). given clause #536: (wt=6) 588 [hyper,22,7,17,17,demod] CP(4,6,6,0,4). given clause #537: (wt=6) 589 [hyper,22,7,17,16,demod] CP(4,6,5,4,3). given clause #538: (wt=6) 590 [hyper,22,7,17,15,demod] CP(4,6,4,8,2). given clause #539: (wt=6) 591 [hyper,22,7,17,14,demod] CP(4,6,3,2,2). given clause #540: (wt=6) 592 [hyper,22,7,17,13,demod] CP(4,6,2,6,1). given clause #541: (wt=6) 593 [hyper,22,7,17,12,demod] CP(4,6,1,0,1). given clause #542: (wt=6) 594 [hyper,22,7,17,11,demod] CP(4,6,0,4,0). given clause #543: (wt=6) 595 [hyper,22,7,16,20,demod] CP(4,5,9,9,4). given clause #544: (wt=6) 596 [hyper,22,7,16,19,demod] CP(4,5,8,4,4). given clause #545: (wt=6) 597 [hyper,22,7,16,18,demod] CP(4,5,7,9,3). given clause #546: (wt=6) 598 [hyper,22,7,16,17,demod] CP(4,5,6,4,3). given clause #547: (wt=6) 599 [hyper,22,7,16,16,demod] CP(4,5,5,9,2). given clause #548: (wt=6) 600 [hyper,22,7,16,15,demod] CP(4,5,4,4,2). given clause #549: (wt=6) 601 [hyper,22,7,16,14,demod] CP(4,5,3,9,1). given clause #550: (wt=6) 602 [hyper,22,7,16,13,demod] CP(4,5,2,4,1). given clause #551: (wt=6) 603 [hyper,22,7,16,12,demod] CP(4,5,1,9,0). given clause #552: (wt=6) 604 [hyper,22,7,16,11,demod] CP(4,5,0,4,0). given clause #553: (wt=6) 605 [hyper,22,7,15,20,demod] CP(4,4,9,0,4). given clause #554: (wt=6) 606 [hyper,22,7,15,19,demod] CP(4,4,8,6,3). given clause #555: (wt=6) 607 [hyper,22,7,15,18,demod] CP(4,4,7,2,3). given clause #556: (wt=6) 608 [hyper,22,7,15,17,demod] CP(4,4,6,8,2). given clause #557: (wt=6) 609 [hyper,22,7,15,16,demod] CP(4,4,5,4,2). given clause #558: (wt=6) 610 [hyper,22,7,15,15,demod] CP(4,4,4,0,2). given clause #559: (wt=6) 611 [hyper,22,7,15,14,demod] CP(4,4,3,6,1). given clause #560: (wt=6) 612 [hyper,22,7,15,13,demod] CP(4,4,2,2,1). given clause #561: (wt=6) 613 [hyper,22,7,15,12,demod] CP(4,4,1,8,0). given clause #562: (wt=6) 614 [hyper,22,7,15,11,demod] CP(4,4,0,4,0). given clause #563: (wt=6) 615 [hyper,22,7,14,20,demod] CP(4,3,9,1,3). given clause #564: (wt=6) 616 [hyper,22,7,14,19,demod] CP(4,3,8,8,2). given clause #565: (wt=6) 617 [hyper,22,7,14,18,demod] CP(4,3,7,5,2). given clause #566: (wt=6) 618 [hyper,22,7,14,17,demod] CP(4,3,6,2,2). given clause #567: (wt=6) 619 [hyper,22,7,14,16,demod] CP(4,3,5,9,1). given clause #568: (wt=6) 620 [hyper,22,7,14,15,demod] CP(4,3,4,6,1). given clause #569: (wt=6) 621 [hyper,22,7,14,14,demod] CP(4,3,3,3,1). given clause #570: (wt=6) 622 [hyper,22,7,14,13,demod] CP(4,3,2,0,1). given clause #571: (wt=6) 623 [hyper,22,7,14,12,demod] CP(4,3,1,7,0). given clause #572: (wt=6) 624 [hyper,22,7,14,11,demod] CP(4,3,0,4,0). given clause #573: (wt=6) 625 [hyper,22,7,13,20,demod] CP(4,2,9,2,2). given clause #574: (wt=6) 626 [hyper,22,7,13,19,demod] CP(4,2,8,0,2). given clause #575: (wt=6) 627 [hyper,22,7,13,18,demod] CP(4,2,7,8,1). given clause #576: (wt=6) 628 [hyper,22,7,13,17,demod] CP(4,2,6,6,1). given clause #577: (wt=6) 629 [hyper,22,7,13,16,demod] CP(4,2,5,4,1). given clause #578: (wt=6) 630 [hyper,22,7,13,15,demod] CP(4,2,4,2,1). given clause #579: (wt=6) 631 [hyper,22,7,13,14,demod] CP(4,2,3,0,1). given clause #580: (wt=6) 632 [hyper,22,7,13,13,demod] CP(4,2,2,8,0). given clause #581: (wt=6) 633 [hyper,22,7,13,12,demod] CP(4,2,1,6,0). given clause #582: (wt=6) 634 [hyper,22,7,13,11,demod] CP(4,2,0,4,0). given clause #583: (wt=6) 635 [hyper,22,7,12,20,demod] CP(4,1,9,3,1). given clause #584: (wt=6) 636 [hyper,22,7,12,19,demod] CP(4,1,8,2,1). given clause #585: (wt=6) 637 [hyper,22,7,12,18,demod] CP(4,1,7,1,1). given clause #586: (wt=6) 638 [hyper,22,7,12,17,demod] CP(4,1,6,0,1). given clause #587: (wt=6) 639 [hyper,22,7,12,16,demod] CP(4,1,5,9,0). given clause #588: (wt=6) 640 [hyper,22,7,12,15,demod] CP(4,1,4,8,0). given clause #589: (wt=6) 641 [hyper,22,7,12,14,demod] CP(4,1,3,7,0). given clause #590: (wt=6) 642 [hyper,22,7,12,13,demod] CP(4,1,2,6,0). given clause #591: (wt=6) 643 [hyper,22,7,12,12,demod] CP(4,1,1,5,0). given clause #592: (wt=6) 644 [hyper,22,7,12,11,demod] CP(4,1,0,4,0). given clause #593: (wt=6) 645 [hyper,22,7,11,20,demod] CP(4,0,9,4,0). given clause #594: (wt=6) 646 [hyper,22,7,11,19,demod] CP(4,0,8,4,0). given clause #595: (wt=6) 647 [hyper,22,7,11,18,demod] CP(4,0,7,4,0). given clause #596: (wt=6) 648 [hyper,22,7,11,17,demod] CP(4,0,6,4,0). given clause #597: (wt=6) 649 [hyper,22,7,11,16,demod] CP(4,0,5,4,0). given clause #598: (wt=6) 650 [hyper,22,7,11,15,demod] CP(4,0,4,4,0). given clause #599: (wt=6) 651 [hyper,22,7,11,14,demod] CP(4,0,3,4,0). given clause #600: (wt=6) 652 [hyper,22,7,11,13,demod] CP(4,0,2,4,0). given clause #601: (wt=6) 653 [hyper,22,7,11,12,demod] CP(4,0,1,4,0). given clause #602: (wt=6) 654 [hyper,22,7,11,11,demod] CP(4,0,0,4,0). given clause #603: (wt=6) 655 [hyper,22,6,20,20,demod] CP(3,9,9,4,8). given clause #604: (wt=6) 656 [hyper,22,6,20,19,demod] CP(3,9,8,5,7). given clause #605: (wt=6) 657 [hyper,22,6,20,18,demod] CP(3,9,7,6,6). given clause #606: (wt=6) 658 [hyper,22,6,20,17,demod] CP(3,9,6,7,5). given clause #607: (wt=6) 659 [hyper,22,6,20,16,demod] CP(3,9,5,8,4). given clause #608: (wt=6) 660 [hyper,22,6,20,15,demod] CP(3,9,4,9,3). given clause #609: (wt=6) 661 [hyper,22,6,20,14,demod] CP(3,9,3,0,3). given clause #610: (wt=6) 662 [hyper,22,6,20,13,demod] CP(3,9,2,1,2). given clause #611: (wt=6) 663 [hyper,22,6,20,12,demod] CP(3,9,1,2,1). given clause #612: (wt=6) 664 [hyper,22,6,20,11,demod] CP(3,9,0,3,0). given clause #613: (wt=6) 665 [hyper,22,6,19,20,demod] CP(3,8,9,5,7). given clause #614: (wt=6) 666 [hyper,22,6,19,19,demod] CP(3,8,8,7,6). given clause #615: (wt=6) 667 [hyper,22,6,19,18,demod] CP(3,8,7,9,5). given clause #616: (wt=6) 668 [hyper,22,6,19,17,demod] CP(3,8,6,1,5). given clause #617: (wt=6) 669 [hyper,22,6,19,16,demod] CP(3,8,5,3,4). given clause #618: (wt=6) 670 [hyper,22,6,19,15,demod] CP(3,8,4,5,3). given clause #619: (wt=6) 671 [hyper,22,6,19,14,demod] CP(3,8,3,7,2). given clause #620: (wt=6) 672 [hyper,22,6,19,13,demod] CP(3,8,2,9,1). given clause #621: (wt=6) 673 [hyper,22,6,19,12,demod] CP(3,8,1,1,1). given clause #622: (wt=6) 674 [hyper,22,6,19,11,demod] CP(3,8,0,3,0). given clause #623: (wt=6) 675 [hyper,22,6,18,20,demod] CP(3,7,9,6,6). given clause #624: (wt=6) 676 [hyper,22,6,18,19,demod] CP(3,7,8,9,5). given clause #625: (wt=6) 677 [hyper,22,6,18,18,demod] CP(3,7,7,2,5). given clause #626: (wt=6) 678 [hyper,22,6,18,17,demod] CP(3,7,6,5,4). given clause #627: (wt=6) 679 [hyper,22,6,18,16,demod] CP(3,7,5,8,3). given clause #628: (wt=6) 680 [hyper,22,6,18,15,demod] CP(3,7,4,1,3). given clause #629: (wt=6) 681 [hyper,22,6,18,14,demod] CP(3,7,3,4,2). given clause #630: (wt=6) 682 [hyper,22,6,18,13,demod] CP(3,7,2,7,1). given clause #631: (wt=6) 683 [hyper,22,6,18,12,demod] CP(3,7,1,0,1). given clause #632: (wt=6) 684 [hyper,22,6,18,11,demod] CP(3,7,0,3,0). given clause #633: (wt=6) 685 [hyper,22,6,17,20,demod] CP(3,6,9,7,5). given clause #634: (wt=6) 686 [hyper,22,6,17,19,demod] CP(3,6,8,1,5). given clause #635: (wt=6) 687 [hyper,22,6,17,18,demod] CP(3,6,7,5,4). given clause #636: (wt=6) 688 [hyper,22,6,17,17,demod] CP(3,6,6,9,3). given clause #637: (wt=6) 689 [hyper,22,6,17,16,demod] CP(3,6,5,3,3). given clause #638: (wt=6) 690 [hyper,22,6,17,15,demod] CP(3,6,4,7,2). given clause #639: (wt=6) 691 [hyper,22,6,17,14,demod] CP(3,6,3,1,2). given clause #640: (wt=6) 692 [hyper,22,6,17,13,demod] CP(3,6,2,5,1). given clause #641: (wt=6) 693 [hyper,22,6,17,12,demod] CP(3,6,1,9,0). given clause #642: (wt=6) 694 [hyper,22,6,17,11,demod] CP(3,6,0,3,0). given clause #643: (wt=6) 695 [hyper,22,6,16,20,demod] CP(3,5,9,8,4). given clause #644: (wt=6) 696 [hyper,22,6,16,19,demod] CP(3,5,8,3,4). given clause #645: (wt=6) 697 [hyper,22,6,16,18,demod] CP(3,5,7,8,3). given clause #646: (wt=6) 698 [hyper,22,6,16,17,demod] CP(3,5,6,3,3). given clause #647: (wt=6) 699 [hyper,22,6,16,16,demod] CP(3,5,5,8,2). given clause #648: (wt=6) 700 [hyper,22,6,16,15,demod] CP(3,5,4,3,2). given clause #649: (wt=6) 701 [hyper,22,6,16,14,demod] CP(3,5,3,8,1). given clause #650: (wt=6) 702 [hyper,22,6,16,13,demod] CP(3,5,2,3,1). given clause #651: (wt=6) 703 [hyper,22,6,16,12,demod] CP(3,5,1,8,0). given clause #652: (wt=6) 704 [hyper,22,6,16,11,demod] CP(3,5,0,3,0). given clause #653: (wt=6) 705 [hyper,22,6,15,20,demod] CP(3,4,9,9,3). given clause #654: (wt=6) 706 [hyper,22,6,15,19,demod] CP(3,4,8,5,3). given clause #655: (wt=6) 707 [hyper,22,6,15,18,demod] CP(3,4,7,1,3). given clause #656: (wt=6) 708 [hyper,22,6,15,17,demod] CP(3,4,6,7,2). given clause #657: (wt=6) 709 [hyper,22,6,15,16,demod] CP(3,4,5,3,2). given clause #658: (wt=6) 710 [hyper,22,6,15,15,demod] CP(3,4,4,9,1). given clause #659: (wt=6) 711 [hyper,22,6,15,14,demod] CP(3,4,3,5,1). given clause #660: (wt=6) 712 [hyper,22,6,15,13,demod] CP(3,4,2,1,1). given clause #661: (wt=6) 713 [hyper,22,6,15,12,demod] CP(3,4,1,7,0). given clause #662: (wt=6) 714 [hyper,22,6,15,11,demod] CP(3,4,0,3,0). given clause #663: (wt=6) 715 [hyper,22,6,14,20,demod] CP(3,3,9,0,3). given clause #664: (wt=6) 716 [hyper,22,6,14,19,demod] CP(3,3,8,7,2). given clause #665: (wt=6) 717 [hyper,22,6,14,18,demod] CP(3,3,7,4,2). given clause #666: (wt=6) 718 [hyper,22,6,14,17,demod] CP(3,3,6,1,2). given clause #667: (wt=6) 719 [hyper,22,6,14,16,demod] CP(3,3,5,8,1). given clause #668: (wt=6) 720 [hyper,22,6,14,15,demod] CP(3,3,4,5,1). given clause #669: (wt=6) 721 [hyper,22,6,14,14,demod] CP(3,3,3,2,1). given clause #670: (wt=6) 722 [hyper,22,6,14,13,demod] CP(3,3,2,9,0). given clause #671: (wt=6) 723 [hyper,22,6,14,12,demod] CP(3,3,1,6,0). given clause #672: (wt=6) 724 [hyper,22,6,14,11,demod] CP(3,3,0,3,0). given clause #673: (wt=6) 725 [hyper,22,6,13,20,demod] CP(3,2,9,1,2). given clause #674: (wt=6) 726 [hyper,22,6,13,19,demod] CP(3,2,8,9,1). given clause #675: (wt=6) 727 [hyper,22,6,13,18,demod] CP(3,2,7,7,1). given clause #676: (wt=6) 728 [hyper,22,6,13,17,demod] CP(3,2,6,5,1). given clause #677: (wt=6) 729 [hyper,22,6,13,16,demod] CP(3,2,5,3,1). given clause #678: (wt=6) 730 [hyper,22,6,13,15,demod] CP(3,2,4,1,1). given clause #679: (wt=6) 731 [hyper,22,6,13,14,demod] CP(3,2,3,9,0). given clause #680: (wt=6) 732 [hyper,22,6,13,13,demod] CP(3,2,2,7,0). given clause #681: (wt=6) 733 [hyper,22,6,13,12,demod] CP(3,2,1,5,0). given clause #682: (wt=6) 734 [hyper,22,6,13,11,demod] CP(3,2,0,3,0). given clause #683: (wt=6) 735 [hyper,22,6,12,20,demod] CP(3,1,9,2,1). given clause #684: (wt=6) 736 [hyper,22,6,12,19,demod] CP(3,1,8,1,1). given clause #685: (wt=6) 737 [hyper,22,6,12,18,demod] CP(3,1,7,0,1). given clause #686: (wt=6) 738 [hyper,22,6,12,17,demod] CP(3,1,6,9,0). given clause #687: (wt=6) 739 [hyper,22,6,12,16,demod] CP(3,1,5,8,0). given clause #688: (wt=6) 740 [hyper,22,6,12,15,demod] CP(3,1,4,7,0). given clause #689: (wt=6) 741 [hyper,22,6,12,14,demod] CP(3,1,3,6,0). given clause #690: (wt=6) 742 [hyper,22,6,12,13,demod] CP(3,1,2,5,0). given clause #691: (wt=6) 743 [hyper,22,6,12,12,demod] CP(3,1,1,4,0). given clause #692: (wt=6) 744 [hyper,22,6,12,11,demod] CP(3,1,0,3,0). given clause #693: (wt=6) 745 [hyper,22,6,11,20,demod] CP(3,0,9,3,0). given clause #694: (wt=6) 746 [hyper,22,6,11,19,demod] CP(3,0,8,3,0). given clause #695: (wt=6) 747 [hyper,22,6,11,18,demod] CP(3,0,7,3,0). given clause #696: (wt=6) 748 [hyper,22,6,11,17,demod] CP(3,0,6,3,0). given clause #697: (wt=6) 749 [hyper,22,6,11,16,demod] CP(3,0,5,3,0). given clause #698: (wt=6) 750 [hyper,22,6,11,15,demod] CP(3,0,4,3,0). given clause #699: (wt=6) 751 [hyper,22,6,11,14,demod] CP(3,0,3,3,0). given clause #700: (wt=6) 752 [hyper,22,6,11,13,demod] CP(3,0,2,3,0). given clause #701: (wt=6) 753 [hyper,22,6,11,12,demod] CP(3,0,1,3,0). given clause #702: (wt=6) 754 [hyper,22,6,11,11,demod] CP(3,0,0,3,0). given clause #703: (wt=6) 755 [hyper,22,5,20,20,demod] CP(2,9,9,3,8). given clause #704: (wt=6) 756 [hyper,22,5,20,19,demod] CP(2,9,8,4,7). given clause #705: (wt=6) 757 [hyper,22,5,20,18,demod] CP(2,9,7,5,6). given clause #706: (wt=6) 758 [hyper,22,5,20,17,demod] CP(2,9,6,6,5). given clause #707: (wt=6) 759 [hyper,22,5,20,16,demod] CP(2,9,5,7,4). given clause #708: (wt=6) 760 [hyper,22,5,20,15,demod] CP(2,9,4,8,3). given clause #709: (wt=6) 761 [hyper,22,5,20,14,demod] CP(2,9,3,9,2). given clause #710: (wt=6) 762 [hyper,22,5,20,13,demod] CP(2,9,2,0,2). given clause #711: (wt=6) 763 [hyper,22,5,20,12,demod] CP(2,9,1,1,1). given clause #712: (wt=6) 764 [hyper,22,5,20,11,demod] CP(2,9,0,2,0). given clause #713: (wt=6) 765 [hyper,22,5,19,20,demod] CP(2,8,9,4,7). given clause #714: (wt=6) 766 [hyper,22,5,19,19,demod] CP(2,8,8,6,6). given clause #715: (wt=6) 767 [hyper,22,5,19,18,demod] CP(2,8,7,8,5). given clause #716: (wt=6) 768 [hyper,22,5,19,17,demod] CP(2,8,6,0,5). given clause #717: (wt=6) 769 [hyper,22,5,19,16,demod] CP(2,8,5,2,4). given clause #718: (wt=6) 770 [hyper,22,5,19,15,demod] CP(2,8,4,4,3). given clause #719: (wt=6) 771 [hyper,22,5,19,14,demod] CP(2,8,3,6,2). given clause #720: (wt=6) 772 [hyper,22,5,19,13,demod] CP(2,8,2,8,1). given clause #721: (wt=6) 773 [hyper,22,5,19,12,demod] CP(2,8,1,0,1). given clause #722: (wt=6) 774 [hyper,22,5,19,11,demod] CP(2,8,0,2,0). given clause #723: (wt=6) 775 [hyper,22,5,18,20,demod] CP(2,7,9,5,6). given clause #724: (wt=6) 776 [hyper,22,5,18,19,demod] CP(2,7,8,8,5). given clause #725: (wt=6) 777 [hyper,22,5,18,18,demod] CP(2,7,7,1,5). given clause #726: (wt=6) 778 [hyper,22,5,18,17,demod] CP(2,7,6,4,4). given clause #727: (wt=6) 779 [hyper,22,5,18,16,demod] CP(2,7,5,7,3). given clause #728: (wt=6) 780 [hyper,22,5,18,15,demod] CP(2,7,4,0,3). given clause #729: (wt=6) 781 [hyper,22,5,18,14,demod] CP(2,7,3,3,2). given clause #730: (wt=6) 782 [hyper,22,5,18,13,demod] CP(2,7,2,6,1). given clause #731: (wt=6) 783 [hyper,22,5,18,12,demod] CP(2,7,1,9,0). given clause #732: (wt=6) 784 [hyper,22,5,18,11,demod] CP(2,7,0,2,0). given clause #733: (wt=6) 785 [hyper,22,5,17,20,demod] CP(2,6,9,6,5). given clause #734: (wt=6) 786 [hyper,22,5,17,19,demod] CP(2,6,8,0,5). given clause #735: (wt=6) 787 [hyper,22,5,17,18,demod] CP(2,6,7,4,4). given clause #736: (wt=6) 788 [hyper,22,5,17,17,demod] CP(2,6,6,8,3). given clause #737: (wt=6) 789 [hyper,22,5,17,16,demod] CP(2,6,5,2,3). given clause #738: (wt=6) 790 [hyper,22,5,17,15,demod] CP(2,6,4,6,2). given clause #739: (wt=6) 791 [hyper,22,5,17,14,demod] CP(2,6,3,0,2). given clause #740: (wt=6) 792 [hyper,22,5,17,13,demod] CP(2,6,2,4,1). given clause #741: (wt=6) 793 [hyper,22,5,17,12,demod] CP(2,6,1,8,0). given clause #742: (wt=6) 794 [hyper,22,5,17,11,demod] CP(2,6,0,2,0). given clause #743: (wt=6) 795 [hyper,22,5,16,20,demod] CP(2,5,9,7,4). given clause #744: (wt=6) 796 [hyper,22,5,16,19,demod] CP(2,5,8,2,4). given clause #745: (wt=6) 797 [hyper,22,5,16,18,demod] CP(2,5,7,7,3). given clause #746: (wt=6) 798 [hyper,22,5,16,17,demod] CP(2,5,6,2,3). given clause #747: (wt=6) 799 [hyper,22,5,16,16,demod] CP(2,5,5,7,2). given clause #748: (wt=6) 800 [hyper,22,5,16,15,demod] CP(2,5,4,2,2). given clause #749: (wt=6) 801 [hyper,22,5,16,14,demod] CP(2,5,3,7,1). given clause #750: (wt=6) 802 [hyper,22,5,16,13,demod] CP(2,5,2,2,1). given clause #751: (wt=6) 803 [hyper,22,5,16,12,demod] CP(2,5,1,7,0). given clause #752: (wt=6) 804 [hyper,22,5,16,11,demod] CP(2,5,0,2,0). given clause #753: (wt=6) 805 [hyper,22,5,15,20,demod] CP(2,4,9,8,3). given clause #754: (wt=6) 806 [hyper,22,5,15,19,demod] CP(2,4,8,4,3). given clause #755: (wt=6) 807 [hyper,22,5,15,18,demod] CP(2,4,7,0,3). given clause #756: (wt=6) 808 [hyper,22,5,15,17,demod] CP(2,4,6,6,2). given clause #757: (wt=6) 809 [hyper,22,5,15,16,demod] CP(2,4,5,2,2). given clause #758: (wt=6) 810 [hyper,22,5,15,15,demod] CP(2,4,4,8,1). given clause #759: (wt=6) 811 [hyper,22,5,15,14,demod] CP(2,4,3,4,1). given clause #760: (wt=6) 812 [hyper,22,5,15,13,demod] CP(2,4,2,0,1). given clause #761: (wt=6) 813 [hyper,22,5,15,12,demod] CP(2,4,1,6,0). given clause #762: (wt=6) 814 [hyper,22,5,15,11,demod] CP(2,4,0,2,0). given clause #763: (wt=6) 815 [hyper,22,5,14,20,demod] CP(2,3,9,9,2). given clause #764: (wt=6) 816 [hyper,22,5,14,19,demod] CP(2,3,8,6,2). given clause #765: (wt=6) 817 [hyper,22,5,14,18,demod] CP(2,3,7,3,2). given clause #766: (wt=6) 818 [hyper,22,5,14,17,demod] CP(2,3,6,0,2). given clause #767: (wt=6) 819 [hyper,22,5,14,16,demod] CP(2,3,5,7,1). given clause #768: (wt=6) 820 [hyper,22,5,14,15,demod] CP(2,3,4,4,1). given clause #769: (wt=6) 821 [hyper,22,5,14,14,demod] CP(2,3,3,1,1). given clause #770: (wt=6) 822 [hyper,22,5,14,13,demod] CP(2,3,2,8,0). given clause #771: (wt=6) 823 [hyper,22,5,14,12,demod] CP(2,3,1,5,0). given clause #772: (wt=6) 824 [hyper,22,5,14,11,demod] CP(2,3,0,2,0). given clause #773: (wt=6) 825 [hyper,22,5,13,20,demod] CP(2,2,9,0,2). given clause #774: (wt=6) 826 [hyper,22,5,13,19,demod] CP(2,2,8,8,1). given clause #775: (wt=6) 827 [hyper,22,5,13,18,demod] CP(2,2,7,6,1). given clause #776: (wt=6) 828 [hyper,22,5,13,17,demod] CP(2,2,6,4,1). given clause #777: (wt=6) 829 [hyper,22,5,13,16,demod] CP(2,2,5,2,1). given clause #778: (wt=6) 830 [hyper,22,5,13,15,demod] CP(2,2,4,0,1). given clause #779: (wt=6) 831 [hyper,22,5,13,14,demod] CP(2,2,3,8,0). given clause #780: (wt=6) 832 [hyper,22,5,13,13,demod] CP(2,2,2,6,0). given clause #781: (wt=6) 833 [hyper,22,5,13,12,demod] CP(2,2,1,4,0). given clause #782: (wt=6) 834 [hyper,22,5,13,11,demod] CP(2,2,0,2,0). given clause #783: (wt=6) 835 [hyper,22,5,12,20,demod] CP(2,1,9,1,1). given clause #784: (wt=6) 836 [hyper,22,5,12,19,demod] CP(2,1,8,0,1). given clause #785: (wt=6) 837 [hyper,22,5,12,18,demod] CP(2,1,7,9,0). given clause #786: (wt=6) 838 [hyper,22,5,12,17,demod] CP(2,1,6,8,0). given clause #787: (wt=6) 839 [hyper,22,5,12,16,demod] CP(2,1,5,7,0). given clause #788: (wt=6) 840 [hyper,22,5,12,15,demod] CP(2,1,4,6,0). given clause #789: (wt=6) 841 [hyper,22,5,12,14,demod] CP(2,1,3,5,0). given clause #790: (wt=6) 842 [hyper,22,5,12,13,demod] CP(2,1,2,4,0). given clause #791: (wt=6) 843 [hyper,22,5,12,12,demod] CP(2,1,1,3,0). given clause #792: (wt=6) 844 [hyper,22,5,12,11,demod] CP(2,1,0,2,0). given clause #793: (wt=6) 845 [hyper,22,5,11,20,demod] CP(2,0,9,2,0). given clause #794: (wt=6) 846 [hyper,22,5,11,19,demod] CP(2,0,8,2,0). given clause #795: (wt=6) 847 [hyper,22,5,11,18,demod] CP(2,0,7,2,0). given clause #796: (wt=6) 848 [hyper,22,5,11,17,demod] CP(2,0,6,2,0). given clause #797: (wt=6) 849 [hyper,22,5,11,16,demod] CP(2,0,5,2,0). given clause #798: (wt=6) 850 [hyper,22,5,11,15,demod] CP(2,0,4,2,0). given clause #799: (wt=6) 851 [hyper,22,5,11,14,demod] CP(2,0,3,2,0). given clause #800: (wt=6) 852 [hyper,22,5,11,13,demod] CP(2,0,2,2,0). given clause #801: (wt=6) 853 [hyper,22,5,11,12,demod] CP(2,0,1,2,0). given clause #802: (wt=6) 854 [hyper,22,5,11,11,demod] CP(2,0,0,2,0). given clause #803: (wt=6) 855 [hyper,22,4,20,20,demod] CP(1,9,9,2,8). given clause #804: (wt=6) 856 [hyper,22,4,20,19,demod] CP(1,9,8,3,7). given clause #805: (wt=6) 857 [hyper,22,4,20,18,demod] CP(1,9,7,4,6). given clause #806: (wt=6) 858 [hyper,22,4,20,17,demod] CP(1,9,6,5,5). given clause #807: (wt=6) 859 [hyper,22,4,20,16,demod] CP(1,9,5,6,4). given clause #808: (wt=6) 860 [hyper,22,4,20,15,demod] CP(1,9,4,7,3). given clause #809: (wt=6) 861 [hyper,22,4,20,14,demod] CP(1,9,3,8,2). given clause #810: (wt=6) 862 [hyper,22,4,20,13,demod] CP(1,9,2,9,1). given clause #811: (wt=6) 863 [hyper,22,4,20,12,demod] CP(1,9,1,0,1). given clause #812: (wt=6) 864 [hyper,22,4,20,11,demod] CP(1,9,0,1,0). given clause #813: (wt=6) 865 [hyper,22,4,19,20,demod] CP(1,8,9,3,7). given clause #814: (wt=6) 866 [hyper,22,4,19,19,demod] CP(1,8,8,5,6). given clause #815: (wt=6) 867 [hyper,22,4,19,18,demod] CP(1,8,7,7,5). given clause #816: (wt=6) 868 [hyper,22,4,19,17,demod] CP(1,8,6,9,4). given clause #817: (wt=6) 869 [hyper,22,4,19,16,demod] CP(1,8,5,1,4). given clause #818: (wt=6) 870 [hyper,22,4,19,15,demod] CP(1,8,4,3,3). given clause #819: (wt=6) 871 [hyper,22,4,19,14,demod] CP(1,8,3,5,2). given clause #820: (wt=6) 872 [hyper,22,4,19,13,demod] CP(1,8,2,7,1). given clause #821: (wt=6) 873 [hyper,22,4,19,12,demod] CP(1,8,1,9,0). given clause #822: (wt=6) 874 [hyper,22,4,19,11,demod] CP(1,8,0,1,0). given clause #823: (wt=6) 875 [hyper,22,4,18,20,demod] CP(1,7,9,4,6). given clause #824: (wt=6) 876 [hyper,22,4,18,19,demod] CP(1,7,8,7,5). given clause #825: (wt=6) 877 [hyper,22,4,18,18,demod] CP(1,7,7,0,5). given clause #826: (wt=6) 878 [hyper,22,4,18,17,demod] CP(1,7,6,3,4). given clause #827: (wt=6) 879 [hyper,22,4,18,16,demod] CP(1,7,5,6,3). given clause #828: (wt=6) 880 [hyper,22,4,18,15,demod] CP(1,7,4,9,2). given clause #829: (wt=6) 881 [hyper,22,4,18,14,demod] CP(1,7,3,2,2). given clause #830: (wt=6) 882 [hyper,22,4,18,13,demod] CP(1,7,2,5,1). given clause #831: (wt=6) 883 [hyper,22,4,18,12,demod] CP(1,7,1,8,0). given clause #832: (wt=6) 884 [hyper,22,4,18,11,demod] CP(1,7,0,1,0). given clause #833: (wt=6) 885 [hyper,22,4,17,20,demod] CP(1,6,9,5,5). given clause #834: (wt=6) 886 [hyper,22,4,17,19,demod] CP(1,6,8,9,4). given clause #835: (wt=6) 887 [hyper,22,4,17,18,demod] CP(1,6,7,3,4). given clause #836: (wt=6) 888 [hyper,22,4,17,17,demod] CP(1,6,6,7,3). given clause #837: (wt=6) 889 [hyper,22,4,17,16,demod] CP(1,6,5,1,3). given clause #838: (wt=6) 890 [hyper,22,4,17,15,demod] CP(1,6,4,5,2). given clause #839: (wt=6) 891 [hyper,22,4,17,14,demod] CP(1,6,3,9,1). given clause #840: (wt=6) 892 [hyper,22,4,17,13,demod] CP(1,6,2,3,1). given clause #841: (wt=6) 893 [hyper,22,4,17,12,demod] CP(1,6,1,7,0). given clause #842: (wt=6) 894 [hyper,22,4,17,11,demod] CP(1,6,0,1,0). given clause #843: (wt=6) 895 [hyper,22,4,16,20,demod] CP(1,5,9,6,4). given clause #844: (wt=6) 896 [hyper,22,4,16,19,demod] CP(1,5,8,1,4). given clause #845: (wt=6) 897 [hyper,22,4,16,18,demod] CP(1,5,7,6,3). given clause #846: (wt=6) 898 [hyper,22,4,16,17,demod] CP(1,5,6,1,3). given clause #847: (wt=6) 899 [hyper,22,4,16,16,demod] CP(1,5,5,6,2). given clause #848: (wt=6) 900 [hyper,22,4,16,15,demod] CP(1,5,4,1,2). given clause #849: (wt=6) 901 [hyper,22,4,16,14,demod] CP(1,5,3,6,1). given clause #850: (wt=6) 902 [hyper,22,4,16,13,demod] CP(1,5,2,1,1). given clause #851: (wt=6) 903 [hyper,22,4,16,12,demod] CP(1,5,1,6,0). given clause #852: (wt=6) 904 [hyper,22,4,16,11,demod] CP(1,5,0,1,0). given clause #853: (wt=6) 905 [hyper,22,4,15,20,demod] CP(1,4,9,7,3). given clause #854: (wt=6) 906 [hyper,22,4,15,19,demod] CP(1,4,8,3,3). given clause #855: (wt=6) 907 [hyper,22,4,15,18,demod] CP(1,4,7,9,2). given clause #856: (wt=6) 908 [hyper,22,4,15,17,demod] CP(1,4,6,5,2). given clause #857: (wt=6) 909 [hyper,22,4,15,16,demod] CP(1,4,5,1,2). given clause #858: (wt=6) 910 [hyper,22,4,15,15,demod] CP(1,4,4,7,1). given clause #859: (wt=6) 911 [hyper,22,4,15,14,demod] CP(1,4,3,3,1). given clause #860: (wt=6) 912 [hyper,22,4,15,13,demod] CP(1,4,2,9,0). given clause #861: (wt=6) 913 [hyper,22,4,15,12,demod] CP(1,4,1,5,0). given clause #862: (wt=6) 914 [hyper,22,4,15,11,demod] CP(1,4,0,1,0). given clause #863: (wt=6) 915 [hyper,22,4,14,20,demod] CP(1,3,9,8,2). given clause #864: (wt=6) 916 [hyper,22,4,14,19,demod] CP(1,3,8,5,2). given clause #865: (wt=6) 917 [hyper,22,4,14,18,demod] CP(1,3,7,2,2). given clause #866: (wt=6) 918 [hyper,22,4,14,17,demod] CP(1,3,6,9,1). given clause #867: (wt=6) 919 [hyper,22,4,14,16,demod] CP(1,3,5,6,1). given clause #868: (wt=6) 920 [hyper,22,4,14,15,demod] CP(1,3,4,3,1). given clause #869: (wt=6) 921 [hyper,22,4,14,14,demod] CP(1,3,3,0,1). given clause #870: (wt=6) 922 [hyper,22,4,14,13,demod] CP(1,3,2,7,0). given clause #871: (wt=6) 923 [hyper,22,4,14,12,demod] CP(1,3,1,4,0). given clause #872: (wt=6) 924 [hyper,22,4,14,11,demod] CP(1,3,0,1,0). given clause #873: (wt=6) 925 [hyper,22,4,13,20,demod] CP(1,2,9,9,1). given clause #874: (wt=6) 926 [hyper,22,4,13,19,demod] CP(1,2,8,7,1). given clause #875: (wt=6) 927 [hyper,22,4,13,18,demod] CP(1,2,7,5,1). given clause #876: (wt=6) 928 [hyper,22,4,13,17,demod] CP(1,2,6,3,1). given clause #877: (wt=6) 929 [hyper,22,4,13,16,demod] CP(1,2,5,1,1). given clause #878: (wt=6) 930 [hyper,22,4,13,15,demod] CP(1,2,4,9,0). given clause #879: (wt=6) 931 [hyper,22,4,13,14,demod] CP(1,2,3,7,0). given clause #880: (wt=6) 932 [hyper,22,4,13,13,demod] CP(1,2,2,5,0). given clause #881: (wt=6) 933 [hyper,22,4,13,12,demod] CP(1,2,1,3,0). given clause #882: (wt=6) 934 [hyper,22,4,13,11,demod] CP(1,2,0,1,0). given clause #883: (wt=6) 935 [hyper,22,4,12,20,demod] CP(1,1,9,0,1). given clause #884: (wt=6) 936 [hyper,22,4,12,19,demod] CP(1,1,8,9,0). given clause #885: (wt=6) 937 [hyper,22,4,12,18,demod] CP(1,1,7,8,0). given clause #886: (wt=6) 938 [hyper,22,4,12,17,demod] CP(1,1,6,7,0). given clause #887: (wt=6) 939 [hyper,22,4,12,16,demod] CP(1,1,5,6,0). given clause #888: (wt=6) 940 [hyper,22,4,12,15,demod] CP(1,1,4,5,0). given clause #889: (wt=6) 941 [hyper,22,4,12,14,demod] CP(1,1,3,4,0). given clause #890: (wt=6) 942 [hyper,22,4,12,13,demod] CP(1,1,2,3,0). given clause #891: (wt=6) 943 [hyper,22,4,12,12,demod] CP(1,1,1,2,0). given clause #892: (wt=6) 944 [hyper,22,4,12,11,demod] CP(1,1,0,1,0). given clause #893: (wt=6) 945 [hyper,22,4,11,20,demod] CP(1,0,9,1,0). given clause #894: (wt=6) 946 [hyper,22,4,11,19,demod] CP(1,0,8,1,0). given clause #895: (wt=6) 947 [hyper,22,4,11,18,demod] CP(1,0,7,1,0). given clause #896: (wt=6) 948 [hyper,22,4,11,17,demod] CP(1,0,6,1,0). given clause #897: (wt=6) 949 [hyper,22,4,11,16,demod] CP(1,0,5,1,0). given clause #898: (wt=6) 950 [hyper,22,4,11,15,demod] CP(1,0,4,1,0). given clause #899: (wt=6) 951 [hyper,22,4,11,14,demod] CP(1,0,3,1,0). given clause #900: (wt=6) 952 [hyper,22,4,11,13,demod] CP(1,0,2,1,0). given clause #901: (wt=6) 953 [hyper,22,4,11,12,demod] CP(1,0,1,1,0). given clause #902: (wt=6) 954 [hyper,22,4,11,11,demod] CP(1,0,0,1,0). given clause #903: (wt=6) 955 [hyper,22,3,20,20,demod] CP(0,9,9,1,8). given clause #904: (wt=6) 956 [hyper,22,3,20,19,demod] CP(0,9,8,2,7). given clause #905: (wt=6) 957 [hyper,22,3,20,18,demod] CP(0,9,7,3,6). given clause #906: (wt=6) 958 [hyper,22,3,20,17,demod] CP(0,9,6,4,5). given clause #907: (wt=6) 959 [hyper,22,3,20,16,demod] CP(0,9,5,5,4). given clause #908: (wt=6) 960 [hyper,22,3,20,15,demod] CP(0,9,4,6,3). given clause #909: (wt=6) 961 [hyper,22,3,20,14,demod] CP(0,9,3,7,2). given clause #910: (wt=6) 962 [hyper,22,3,20,13,demod] CP(0,9,2,8,1). given clause #911: (wt=6) 963 [hyper,22,3,20,12,demod] CP(0,9,1,9,0). given clause #912: (wt=6) 964 [hyper,22,3,20,11,demod] CP(0,9,0,0,0). given clause #913: (wt=6) 965 [hyper,22,3,19,20,demod] CP(0,8,9,2,7). given clause #914: (wt=6) 966 [hyper,22,3,19,19,demod] CP(0,8,8,4,6). given clause #915: (wt=6) 967 [hyper,22,3,19,18,demod] CP(0,8,7,6,5). given clause #916: (wt=6) 968 [hyper,22,3,19,17,demod] CP(0,8,6,8,4). given clause #917: (wt=6) 969 [hyper,22,3,19,16,demod] CP(0,8,5,0,4). given clause #918: (wt=6) 970 [hyper,22,3,19,15,demod] CP(0,8,4,2,3). given clause #919: (wt=6) 971 [hyper,22,3,19,14,demod] CP(0,8,3,4,2). given clause #920: (wt=6) 972 [hyper,22,3,19,13,demod] CP(0,8,2,6,1). given clause #921: (wt=6) 973 [hyper,22,3,19,12,demod] CP(0,8,1,8,0). given clause #922: (wt=6) 974 [hyper,22,3,19,11,demod] CP(0,8,0,0,0). given clause #923: (wt=6) 975 [hyper,22,3,18,20,demod] CP(0,7,9,3,6). given clause #924: (wt=6) 976 [hyper,22,3,18,19,demod] CP(0,7,8,6,5). given clause #925: (wt=6) 977 [hyper,22,3,18,18,demod] CP(0,7,7,9,4). given clause #926: (wt=6) 978 [hyper,22,3,18,17,demod] CP(0,7,6,2,4). given clause #927: (wt=6) 979 [hyper,22,3,18,16,demod] CP(0,7,5,5,3). given clause #928: (wt=6) 980 [hyper,22,3,18,15,demod] CP(0,7,4,8,2). given clause #929: (wt=6) 981 [hyper,22,3,18,14,demod] CP(0,7,3,1,2). given clause #930: (wt=6) 982 [hyper,22,3,18,13,demod] CP(0,7,2,4,1). given clause #931: (wt=6) 983 [hyper,22,3,18,12,demod] CP(0,7,1,7,0). given clause #932: (wt=6) 984 [hyper,22,3,18,11,demod] CP(0,7,0,0,0). given clause #933: (wt=6) 985 [hyper,22,3,17,20,demod] CP(0,6,9,4,5). given clause #934: (wt=6) 986 [hyper,22,3,17,19,demod] CP(0,6,8,8,4). given clause #935: (wt=6) 987 [hyper,22,3,17,18,demod] CP(0,6,7,2,4). given clause #936: (wt=6) 988 [hyper,22,3,17,17,demod] CP(0,6,6,6,3). given clause #937: (wt=6) 989 [hyper,22,3,17,16,demod] CP(0,6,5,0,3). given clause #938: (wt=6) 990 [hyper,22,3,17,15,demod] CP(0,6,4,4,2). given clause #939: (wt=6) 991 [hyper,22,3,17,14,demod] CP(0,6,3,8,1). given clause #940: (wt=6) 992 [hyper,22,3,17,13,demod] CP(0,6,2,2,1). given clause #941: (wt=6) 993 [hyper,22,3,17,12,demod] CP(0,6,1,6,0). given clause #942: (wt=6) 994 [hyper,22,3,17,11,demod] CP(0,6,0,0,0). given clause #943: (wt=6) 995 [hyper,22,3,16,20,demod] CP(0,5,9,5,4). given clause #944: (wt=6) 996 [hyper,22,3,16,19,demod] CP(0,5,8,0,4). given clause #945: (wt=6) 997 [hyper,22,3,16,18,demod] CP(0,5,7,5,3). given clause #946: (wt=6) 998 [hyper,22,3,16,17,demod] CP(0,5,6,0,3). given clause #947: (wt=6) 999 [hyper,22,3,16,16,demod] CP(0,5,5,5,2). given clause #948: (wt=6) 1000 [hyper,22,3,16,15,demod] CP(0,5,4,0,2). given clause #949: (wt=6) 1001 [hyper,22,3,16,14,demod] CP(0,5,3,5,1). given clause #950: (wt=6) 1002 [hyper,22,3,16,13,demod] CP(0,5,2,0,1). given clause #951: (wt=6) 1003 [hyper,22,3,16,12,demod] CP(0,5,1,5,0). given clause #952: (wt=6) 1004 [hyper,22,3,16,11,demod] CP(0,5,0,0,0). given clause #953: (wt=6) 1005 [hyper,22,3,15,20,demod] CP(0,4,9,6,3). given clause #954: (wt=6) 1006 [hyper,22,3,15,19,demod] CP(0,4,8,2,3). given clause #955: (wt=6) 1007 [hyper,22,3,15,18,demod] CP(0,4,7,8,2). given clause #956: (wt=6) 1008 [hyper,22,3,15,17,demod] CP(0,4,6,4,2). given clause #957: (wt=6) 1009 [hyper,22,3,15,16,demod] CP(0,4,5,0,2). given clause #958: (wt=6) 1010 [hyper,22,3,15,15,demod] CP(0,4,4,6,1). given clause #959: (wt=6) 1011 [hyper,22,3,15,14,demod] CP(0,4,3,2,1). given clause #960: (wt=6) 1012 [hyper,22,3,15,13,demod] CP(0,4,2,8,0). given clause #961: (wt=6) 1013 [hyper,22,3,15,12,demod] CP(0,4,1,4,0). given clause #962: (wt=6) 1014 [hyper,22,3,15,11,demod] CP(0,4,0,0,0). given clause #963: (wt=6) 1015 [hyper,22,3,14,20,demod] CP(0,3,9,7,2). given clause #964: (wt=6) 1016 [hyper,22,3,14,19,demod] CP(0,3,8,4,2). given clause #965: (wt=6) 1017 [hyper,22,3,14,18,demod] CP(0,3,7,1,2). given clause #966: (wt=6) 1018 [hyper,22,3,14,17,demod] CP(0,3,6,8,1). given clause #967: (wt=6) 1019 [hyper,22,3,14,16,demod] CP(0,3,5,5,1). given clause #968: (wt=6) 1020 [hyper,22,3,14,15,demod] CP(0,3,4,2,1). given clause #969: (wt=6) 1021 [hyper,22,3,14,14,demod] CP(0,3,3,9,0). given clause #970: (wt=6) 1022 [hyper,22,3,14,13,demod] CP(0,3,2,6,0). given clause #971: (wt=6) 1023 [hyper,22,3,14,12,demod] CP(0,3,1,3,0). given clause #972: (wt=6) 1024 [hyper,22,3,14,11,demod] CP(0,3,0,0,0). given clause #973: (wt=6) 1025 [hyper,22,3,13,20,demod] CP(0,2,9,8,1). given clause #974: (wt=6) 1026 [hyper,22,3,13,19,demod] CP(0,2,8,6,1). given clause #975: (wt=6) 1027 [hyper,22,3,13,18,demod] CP(0,2,7,4,1). given clause #976: (wt=6) 1028 [hyper,22,3,13,17,demod] CP(0,2,6,2,1). given clause #977: (wt=6) 1029 [hyper,22,3,13,16,demod] CP(0,2,5,0,1). given clause #978: (wt=6) 1030 [hyper,22,3,13,15,demod] CP(0,2,4,8,0). given clause #979: (wt=6) 1031 [hyper,22,3,13,14,demod] CP(0,2,3,6,0). given clause #980: (wt=6) 1032 [hyper,22,3,13,13,demod] CP(0,2,2,4,0). given clause #981: (wt=6) 1033 [hyper,22,3,13,12,demod] CP(0,2,1,2,0). given clause #982: (wt=6) 1034 [hyper,22,3,13,11,demod] CP(0,2,0,0,0). given clause #983: (wt=6) 1035 [hyper,22,3,12,20,demod] CP(0,1,9,9,0). given clause #984: (wt=6) 1036 [hyper,22,3,12,19,demod] CP(0,1,8,8,0). given clause #985: (wt=6) 1037 [hyper,22,3,12,18,demod] CP(0,1,7,7,0). given clause #986: (wt=6) 1038 [hyper,22,3,12,17,demod] CP(0,1,6,6,0). given clause #987: (wt=6) 1039 [hyper,22,3,12,16,demod] CP(0,1,5,5,0). given clause #988: (wt=6) 1040 [hyper,22,3,12,15,demod] CP(0,1,4,4,0). given clause #989: (wt=6) 1041 [hyper,22,3,12,14,demod] CP(0,1,3,3,0). given clause #990: (wt=6) 1042 [hyper,22,3,12,13,demod] CP(0,1,2,2,0). given clause #991: (wt=6) 1043 [hyper,22,3,12,12,demod] CP(0,1,1,1,0). given clause #992: (wt=6) 1044 [hyper,22,3,12,11,demod] CP(0,1,0,0,0). given clause #993: (wt=6) 1045 [hyper,22,3,11,20,demod] CP(0,0,9,0,0). given clause #994: (wt=6) 1046 [hyper,22,3,11,19,demod] CP(0,0,8,0,0). given clause #995: (wt=6) 1047 [hyper,22,3,11,18,demod] CP(0,0,7,0,0). given clause #996: (wt=6) 1048 [hyper,22,3,11,17,demod] CP(0,0,6,0,0). given clause #997: (wt=6) 1049 [hyper,22,3,11,16,demod] CP(0,0,5,0,0). given clause #998: (wt=6) 1050 [hyper,22,3,11,15,demod] CP(0,0,4,0,0). given clause #999: (wt=6) 1051 [hyper,22,3,11,14,demod] CP(0,0,3,0,0). given clause #1000: (wt=6) 1052 [hyper,22,3,11,13,demod] CP(0,0,2,0,0). given clause #1001: (wt=6) 1053 [hyper,22,3,11,12,demod] CP(0,0,1,0,0). given clause #1002: (wt=6) 1054 [hyper,22,3,11,11,demod] CP(0,0,0,0,0). given clause #1003: (wt=60) 23 [] -CP(0,xd,xb,y1,x1)| -CP(x1,xd,xa,y2,y3)| -CP(0,xc,xb,z1,x2)| -CP(x2,xc,xa,z2,z3)| -$LT(xa,xc)| -CS(0,y1,0,xh,x3)| -CS(x3,y2,z1,xg,x4)| -CS(x4,y3,z2,xf,x5)| -CS(x5,0,z3,xe,0)|S(xa,xb,xc,xd,xe,xf,xg,xh). ** KEPT (pick-wt=9): 1055 [hyper,23,1031,1029,961,759,eval,194,247,237,250] S(5,3,9,2,4,8,7,6). ** KEPT (pick-wt=9): 1056 [hyper,23,1030,1031,1000,801,eval,174,194,247,253] S(3,4,5,2,1,7,6,8). ** KEPT (pick-wt=9): 1057 [hyper,23,1029,930,969,570,eval,254,164,248,251] S(4,5,8,2,3,6,9,0). ** KEPT (pick-wt=9): 1058 [hyper,23,1026,931,1006,711,eval,194,182,249,253] S(3,8,4,2,1,5,9,6). ** KEPT (pick-wt=9): 1059 [hyper,23,1026,931,996,601,eval,194,184,245,253] S(3,8,5,2,1,9,7,6). ** KEPT (pick-wt=9): 1060 [hyper,23,1006,709,986,589,eval,234,216,130,251] S(5,8,6,4,3,7,1,2). ** KEPT (pick-wt=9): 1061 [hyper,23,1006,708,976,478,eval,234,178,127,150] S(6,8,7,4,5,0,3,2). ** KEPT (pick-wt=9): 1062 [hyper,23,1005,711,995,601,eval,194,199,135,153] S(3,9,5,4,2,1,0,6). ** KEPT (pick-wt=9): 1063 [hyper,23,1002,897,962,857,eval,254,186,120,248] S(7,2,9,5,6,8,4,0). ** KEPT (pick-wt=9): 1064 [hyper,23,1000,797,970,667,eval,254,182,215,149] S(7,4,8,5,6,2,9,0). ** KEPT (pick-wt=9): 1065 [hyper,23,998,700,968,570,eval,254,216,128,251] S(4,6,8,5,3,9,1,0). ** KEPT (pick-wt=9): 1066 [hyper,23,996,601,986,591,eval,254,156,142,252] S(3,8,6,5,2,4,7,0). ** KEPT (pick-wt=9): 1067 [hyper,23,996,600,986,590,eval,254,206,126,152] S(4,8,6,5,3,1,2,0). ** KEPT (pick-wt=9): 1068 [hyper,23,991,892,1011,912,eval,174,222,235,154] S(2,3,4,6,1,0,5,8). ** KEPT (pick-wt=9): 1069 [hyper,23,991,889,981,779,eval,174,243,217,151] S(5,3,7,6,4,0,2,8). ** KEPT (pick-wt=9): 1070 [hyper,23,987,589,967,469,eval,234,208,119,250] S(5,7,8,6,4,9,0,2). ** KEPT (pick-wt=9): 1071 [hyper,23,985,491,995,601,eval,214,219,225,153] S(3,9,5,6,2,1,8,4). ** KEPT (pick-wt=9): 1072 [hyper,23,982,878,972,868,eval,214,218,205,150] S(6,2,8,7,5,3,9,4). ** KEPT (pick-wt=9): 1073 [hyper,23,980,782,1000,802,eval,174,194,242,253] S(2,4,5,7,1,3,6,8). ** KEPT (pick-wt=9): 1074 [hyper,23,970,671,1000,801,eval,234,184,227,253] S(3,4,5,8,1,9,7,2). ** KEPT (pick-wt=9): 1075 [hyper,23,967,471,997,701,eval,194,159,126,153] S(3,7,5,8,2,1,4,6). ** KEPT (pick-wt=9): 1076 [hyper,23,965,269,985,489,eval,234,180,109,151] S(5,9,6,8,4,0,1,2). ** KEPT (pick-wt=9): 1077 [hyper,23,965,269,975,379,eval,234,181,113,250] S(5,9,7,8,4,6,0,2). ** KEPT (pick-wt=9): 1078 [hyper,23,962,861,1012,1011,eval,174,166,132,253] S(3,2,4,9,1,5,6,8). ** KEPT (pick-wt=9): 1079 [hyper,23,962,859,982,879,eval,174,190,108,151] S(5,2,7,9,4,1,0,8). ** KEPT (pick-wt=9): 1080 [hyper,23,961,762,991,892,eval,184,246,231,253] S(2,3,6,9,1,5,8,7). given clause #1004: (wt=9) 1055 [hyper,23,1031,1029,961,759,eval,194,247,237,250] S(5,3,9,2,4,8,7,6). given clause #1005: (wt=9) 1056 [hyper,23,1030,1031,1000,801,eval,174,194,247,253] S(3,4,5,2,1,7,6,8). given clause #1006: (wt=9) 1057 [hyper,23,1029,930,969,570,eval,254,164,248,251] S(4,5,8,2,3,6,9,0). given clause #1007: (wt=9) 1058 [hyper,23,1026,931,1006,711,eval,194,182,249,253] S(3,8,4,2,1,5,9,6). given clause #1008: (wt=9) 1059 [hyper,23,1026,931,996,601,eval,194,184,245,253] S(3,8,5,2,1,9,7,6). given clause #1009: (wt=9) 1060 [hyper,23,1006,709,986,589,eval,234,216,130,251] S(5,8,6,4,3,7,1,2). given clause #1010: (wt=9) 1061 [hyper,23,1006,708,976,478,eval,234,178,127,150] S(6,8,7,4,5,0,3,2). given clause #1011: (wt=9) 1062 [hyper,23,1005,711,995,601,eval,194,199,135,153] S(3,9,5,4,2,1,0,6). given clause #1012: (wt=9) 1063 [hyper,23,1002,897,962,857,eval,254,186,120,248] S(7,2,9,5,6,8,4,0). given clause #1013: (wt=9) 1064 [hyper,23,1000,797,970,667,eval,254,182,215,149] S(7,4,8,5,6,2,9,0). given clause #1014: (wt=9) 1065 [hyper,23,998,700,968,570,eval,254,216,128,251] S(4,6,8,5,3,9,1,0). given clause #1015: (wt=9) 1066 [hyper,23,996,601,986,591,eval,254,156,142,252] S(3,8,6,5,2,4,7,0). given clause #1016: (wt=9) 1067 [hyper,23,996,600,986,590,eval,254,206,126,152] S(4,8,6,5,3,1,2,0). given clause #1017: (wt=9) 1068 [hyper,23,991,892,1011,912,eval,174,222,235,154] S(2,3,4,6,1,0,5,8). given clause #1018: (wt=9) 1069 [hyper,23,991,889,981,779,eval,174,243,217,151] S(5,3,7,6,4,0,2,8). given clause #1019: (wt=9) 1070 [hyper,23,987,589,967,469,eval,234,208,119,250] S(5,7,8,6,4,9,0,2). given clause #1020: (wt=9) 1071 [hyper,23,985,491,995,601,eval,214,219,225,153] S(3,9,5,6,2,1,8,4). given clause #1021: (wt=9) 1072 [hyper,23,982,878,972,868,eval,214,218,205,150] S(6,2,8,7,5,3,9,4). given clause #1022: (wt=9) 1073 [hyper,23,980,782,1000,802,eval,174,194,242,253] S(2,4,5,7,1,3,6,8). given clause #1023: (wt=9) 1074 [hyper,23,970,671,1000,801,eval,234,184,227,253] S(3,4,5,8,1,9,7,2). given clause #1024: (wt=9) 1075 [hyper,23,967,471,997,701,eval,194,159,126,153] S(3,7,5,8,2,1,4,6). given clause #1025: (wt=9) 1076 [hyper,23,965,269,985,489,eval,234,180,109,151] S(5,9,6,8,4,0,1,2). given clause #1026: (wt=9) 1077 [hyper,23,965,269,975,379,eval,234,181,113,250] S(5,9,7,8,4,6,0,2). given clause #1027: (wt=9) 1078 [hyper,23,962,861,1012,1011,eval,174,166,132,253] S(3,2,4,9,1,5,6,8). given clause #1028: (wt=9) 1079 [hyper,23,962,859,982,879,eval,174,190,108,151] S(5,2,7,9,4,1,0,8). given clause #1029: (wt=9) 1080 [hyper,23,961,762,991,892,eval,184,246,231,253] S(2,3,6,9,1,5,8,7). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ list(usable). 1 [] K(0). 2 [] K(1). 3 [] L(0). 4 [] L(1). 5 [] L(2). 6 [] L(3). 7 [] L(4). 8 [] L(5). 9 [] L(6). 10 [] L(7). 11 [] D(0). 12 [] D(1). 13 [] D(2). 14 [] D(3). 15 [] D(4). 16 [] D(5). 17 [] D(6). 18 [] D(7). 19 [] D(8). 20 [] D(9). 21 [] -K(u)| -D(x)| -D(y)|CS(u,x,y,$MOD($SUM($SUM(u,x),y),10),$DIV($SUM($SUM(u,x),y),10)). 55 [hyper,21,2,20,20,demod] CS(1,9,9,9,1). 56 [hyper,21,2,20,19,demod] CS(1,9,8,8,1). 57 [hyper,21,2,20,18,demod] CS(1,9,7,7,1). 58 [hyper,21,2,20,17,demod] CS(1,9,6,6,1). 59 [hyper,21,2,20,16,demod] CS(1,9,5,5,1). 60 [hyper,21,2,20,15,demod] CS(1,9,4,4,1). 61 [hyper,21,2,20,14,demod] CS(1,9,3,3,1). 62 [hyper,21,2,20,13,demod] CS(1,9,2,2,1). 63 [hyper,21,2,20,12,demod] CS(1,9,1,1,1). 64 [hyper,21,2,20,11,demod] CS(1,9,0,0,1). 65 [hyper,21,2,19,20,demod] CS(1,8,9,8,1). 66 [hyper,21,2,19,19,demod] CS(1,8,8,7,1). 67 [hyper,21,2,19,18,demod] CS(1,8,7,6,1). 68 [hyper,21,2,19,17,demod] CS(1,8,6,5,1). 69 [hyper,21,2,19,16,demod] CS(1,8,5,4,1). 70 [hyper,21,2,19,15,demod] CS(1,8,4,3,1). 71 [hyper,21,2,19,14,demod] CS(1,8,3,2,1). 72 [hyper,21,2,19,13,demod] CS(1,8,2,1,1). 73 [hyper,21,2,19,12,demod] CS(1,8,1,0,1). 74 [hyper,21,2,19,11,demod] CS(1,8,0,9,0). 75 [hyper,21,2,18,20,demod] CS(1,7,9,7,1). 76 [hyper,21,2,18,19,demod] CS(1,7,8,6,1). 77 [hyper,21,2,18,18,demod] CS(1,7,7,5,1). 78 [hyper,21,2,18,17,demod] CS(1,7,6,4,1). 79 [hyper,21,2,18,16,demod] CS(1,7,5,3,1). 80 [hyper,21,2,18,15,demod] CS(1,7,4,2,1). 81 [hyper,21,2,18,14,demod] CS(1,7,3,1,1). 82 [hyper,21,2,18,13,demod] CS(1,7,2,0,1). 83 [hyper,21,2,18,12,demod] CS(1,7,1,9,0). 84 [hyper,21,2,18,11,demod] CS(1,7,0,8,0). 85 [hyper,21,2,17,20,demod] CS(1,6,9,6,1). 86 [hyper,21,2,17,19,demod] CS(1,6,8,5,1). 87 [hyper,21,2,17,18,demod] CS(1,6,7,4,1). 88 [hyper,21,2,17,17,demod] CS(1,6,6,3,1). 89 [hyper,21,2,17,16,demod] CS(1,6,5,2,1). 90 [hyper,21,2,17,15,demod] CS(1,6,4,1,1). 91 [hyper,21,2,17,14,demod] CS(1,6,3,0,1). 92 [hyper,21,2,17,13,demod] CS(1,6,2,9,0). 93 [hyper,21,2,17,12,demod] CS(1,6,1,8,0). 94 [hyper,21,2,17,11,demod] CS(1,6,0,7,0). 95 [hyper,21,2,16,20,demod] CS(1,5,9,5,1). 96 [hyper,21,2,16,19,demod] CS(1,5,8,4,1). 97 [hyper,21,2,16,18,demod] CS(1,5,7,3,1). 98 [hyper,21,2,16,17,demod] CS(1,5,6,2,1). 99 [hyper,21,2,16,16,demod] CS(1,5,5,1,1). 100 [hyper,21,2,16,15,demod] CS(1,5,4,0,1). 101 [hyper,21,2,16,14,demod] CS(1,5,3,9,0). 102 [hyper,21,2,16,13,demod] CS(1,5,2,8,0). 103 [hyper,21,2,16,12,demod] CS(1,5,1,7,0). 104 [hyper,21,2,16,11,demod] CS(1,5,0,6,0). 105 [hyper,21,2,15,20,demod] CS(1,4,9,4,1). 106 [hyper,21,2,15,19,demod] CS(1,4,8,3,1). 107 [hyper,21,2,15,18,demod] CS(1,4,7,2,1). 108 [hyper,21,2,15,17,demod] CS(1,4,6,1,1). 109 [hyper,21,2,15,16,demod] CS(1,4,5,0,1). 110 [hyper,21,2,15,15,demod] CS(1,4,4,9,0). 111 [hyper,21,2,15,14,demod] CS(1,4,3,8,0). 112 [hyper,21,2,15,13,demod] CS(1,4,2,7,0). 113 [hyper,21,2,15,12,demod] CS(1,4,1,6,0). 114 [hyper,21,2,15,11,demod] CS(1,4,0,5,0). 115 [hyper,21,2,14,20,demod] CS(1,3,9,3,1). 116 [hyper,21,2,14,19,demod] CS(1,3,8,2,1). 117 [hyper,21,2,14,18,demod] CS(1,3,7,1,1). 118 [hyper,21,2,14,17,demod] CS(1,3,6,0,1). 119 [hyper,21,2,14,16,demod] CS(1,3,5,9,0). 120 [hyper,21,2,14,15,demod] CS(1,3,4,8,0). 121 [hyper,21,2,14,14,demod] CS(1,3,3,7,0). 122 [hyper,21,2,14,13,demod] CS(1,3,2,6,0). 123 [hyper,21,2,14,12,demod] CS(1,3,1,5,0). 124 [hyper,21,2,14,11,demod] CS(1,3,0,4,0). 125 [hyper,21,2,13,20,demod] CS(1,2,9,2,1). 126 [hyper,21,2,13,19,demod] CS(1,2,8,1,1). 127 [hyper,21,2,13,18,demod] CS(1,2,7,0,1). 128 [hyper,21,2,13,17,demod] CS(1,2,6,9,0). 129 [hyper,21,2,13,16,demod] CS(1,2,5,8,0). 130 [hyper,21,2,13,15,demod] CS(1,2,4,7,0). 131 [hyper,21,2,13,14,demod] CS(1,2,3,6,0). 132 [hyper,21,2,13,13,demod] CS(1,2,2,5,0). 133 [hyper,21,2,13,12,demod] CS(1,2,1,4,0). 134 [hyper,21,2,13,11,demod] CS(1,2,0,3,0). 135 [hyper,21,2,12,20,demod] CS(1,1,9,1,1). 136 [hyper,21,2,12,19,demod] CS(1,1,8,0,1). 137 [hyper,21,2,12,18,demod] CS(1,1,7,9,0). 138 [hyper,21,2,12,17,demod] CS(1,1,6,8,0). 139 [hyper,21,2,12,16,demod] CS(1,1,5,7,0). 140 [hyper,21,2,12,15,demod] CS(1,1,4,6,0). 141 [hyper,21,2,12,14,demod] CS(1,1,3,5,0). 142 [hyper,21,2,12,13,demod] CS(1,1,2,4,0). 143 [hyper,21,2,12,12,demod] CS(1,1,1,3,0). 144 [hyper,21,2,12,11,demod] CS(1,1,0,2,0). 145 [hyper,21,2,11,20,demod] CS(1,0,9,0,1). 146 [hyper,21,2,11,19,demod] CS(1,0,8,9,0). 147 [hyper,21,2,11,18,demod] CS(1,0,7,8,0). 148 [hyper,21,2,11,17,demod] CS(1,0,6,7,0). 149 [hyper,21,2,11,16,demod] CS(1,0,5,6,0). 150 [hyper,21,2,11,15,demod] CS(1,0,4,5,0). 151 [hyper,21,2,11,14,demod] CS(1,0,3,4,0). 152 [hyper,21,2,11,13,demod] CS(1,0,2,3,0). 153 [hyper,21,2,11,12,demod] CS(1,0,1,2,0). 154 [hyper,21,2,11,11,demod] CS(1,0,0,1,0). 155 [hyper,21,1,20,20,demod] CS(0,9,9,8,1). 156 [hyper,21,1,20,19,demod] CS(0,9,8,7,1). 157 [hyper,21,1,20,18,demod] CS(0,9,7,6,1). 158 [hyper,21,1,20,17,demod] CS(0,9,6,5,1). 159 [hyper,21,1,20,16,demod] CS(0,9,5,4,1). 160 [hyper,21,1,20,15,demod] CS(0,9,4,3,1). 161 [hyper,21,1,20,14,demod] CS(0,9,3,2,1). 162 [hyper,21,1,20,13,demod] CS(0,9,2,1,1). 163 [hyper,21,1,20,12,demod] CS(0,9,1,0,1). 164 [hyper,21,1,20,11,demod] CS(0,9,0,9,0). 165 [hyper,21,1,19,20,demod] CS(0,8,9,7,1). 166 [hyper,21,1,19,19,demod] CS(0,8,8,6,1). 167 [hyper,21,1,19,18,demod] CS(0,8,7,5,1). 168 [hyper,21,1,19,17,demod] CS(0,8,6,4,1). 169 [hyper,21,1,19,16,demod] CS(0,8,5,3,1). 170 [hyper,21,1,19,15,demod] CS(0,8,4,2,1). 171 [hyper,21,1,19,14,demod] CS(0,8,3,1,1). 172 [hyper,21,1,19,13,demod] CS(0,8,2,0,1). 173 [hyper,21,1,19,12,demod] CS(0,8,1,9,0). 174 [hyper,21,1,19,11,demod] CS(0,8,0,8,0). 175 [hyper,21,1,18,20,demod] CS(0,7,9,6,1). 176 [hyper,21,1,18,19,demod] CS(0,7,8,5,1). 177 [hyper,21,1,18,18,demod] CS(0,7,7,4,1). 178 [hyper,21,1,18,17,demod] CS(0,7,6,3,1). 179 [hyper,21,1,18,16,demod] CS(0,7,5,2,1). 180 [hyper,21,1,18,15,demod] CS(0,7,4,1,1). 181 [hyper,21,1,18,14,demod] CS(0,7,3,0,1). 182 [hyper,21,1,18,13,demod] CS(0,7,2,9,0). 183 [hyper,21,1,18,12,demod] CS(0,7,1,8,0). 184 [hyper,21,1,18,11,demod] CS(0,7,0,7,0). 185 [hyper,21,1,17,20,demod] CS(0,6,9,5,1). 186 [hyper,21,1,17,19,demod] CS(0,6,8,4,1). 187 [hyper,21,1,17,18,demod] CS(0,6,7,3,1). 188 [hyper,21,1,17,17,demod] CS(0,6,6,2,1). 189 [hyper,21,1,17,16,demod] CS(0,6,5,1,1). 190 [hyper,21,1,17,15,demod] CS(0,6,4,0,1). 191 [hyper,21,1,17,14,demod] CS(0,6,3,9,0). 192 [hyper,21,1,17,13,demod] CS(0,6,2,8,0). 193 [hyper,21,1,17,12,demod] CS(0,6,1,7,0). 194 [hyper,21,1,17,11,demod] CS(0,6,0,6,0). 195 [hyper,21,1,16,20,demod] CS(0,5,9,4,1). 196 [hyper,21,1,16,19,demod] CS(0,5,8,3,1). 197 [hyper,21,1,16,18,demod] CS(0,5,7,2,1). 198 [hyper,21,1,16,17,demod] CS(0,5,6,1,1). 199 [hyper,21,1,16,16,demod] CS(0,5,5,0,1). 200 [hyper,21,1,16,15,demod] CS(0,5,4,9,0). 201 [hyper,21,1,16,14,demod] CS(0,5,3,8,0). 202 [hyper,21,1,16,13,demod] CS(0,5,2,7,0). 203 [hyper,21,1,16,12,demod] CS(0,5,1,6,0). 204 [hyper,21,1,16,11,demod] CS(0,5,0,5,0). 205 [hyper,21,1,15,20,demod] CS(0,4,9,3,1). 206 [hyper,21,1,15,19,demod] CS(0,4,8,2,1). 207 [hyper,21,1,15,18,demod] CS(0,4,7,1,1). 208 [hyper,21,1,15,17,demod] CS(0,4,6,0,1). 209 [hyper,21,1,15,16,demod] CS(0,4,5,9,0). 210 [hyper,21,1,15,15,demod] CS(0,4,4,8,0). 211 [hyper,21,1,15,14,demod] CS(0,4,3,7,0). 212 [hyper,21,1,15,13,demod] CS(0,4,2,6,0). 213 [hyper,21,1,15,12,demod] CS(0,4,1,5,0). 214 [hyper,21,1,15,11,demod] CS(0,4,0,4,0). 215 [hyper,21,1,14,20,demod] CS(0,3,9,2,1). 216 [hyper,21,1,14,19,demod] CS(0,3,8,1,1). 217 [hyper,21,1,14,18,demod] CS(0,3,7,0,1). 218 [hyper,21,1,14,17,demod] CS(0,3,6,9,0). 219 [hyper,21,1,14,16,demod] CS(0,3,5,8,0). 220 [hyper,21,1,14,15,demod] CS(0,3,4,7,0). 221 [hyper,21,1,14,14,demod] CS(0,3,3,6,0). 222 [hyper,21,1,14,13,demod] CS(0,3,2,5,0). 223 [hyper,21,1,14,12,demod] CS(0,3,1,4,0). 224 [hyper,21,1,14,11,demod] CS(0,3,0,3,0). 225 [hyper,21,1,13,20,demod] CS(0,2,9,1,1). 226 [hyper,21,1,13,19,demod] CS(0,2,8,0,1). 227 [hyper,21,1,13,18,demod] CS(0,2,7,9,0). 228 [hyper,21,1,13,17,demod] CS(0,2,6,8,0). 229 [hyper,21,1,13,16,demod] CS(0,2,5,7,0). 230 [hyper,21,1,13,15,demod] CS(0,2,4,6,0). 231 [hyper,21,1,13,14,demod] CS(0,2,3,5,0). 232 [hyper,21,1,13,13,demod] CS(0,2,2,4,0). 233 [hyper,21,1,13,12,demod] CS(0,2,1,3,0). 234 [hyper,21,1,13,11,demod] CS(0,2,0,2,0). 235 [hyper,21,1,12,20,demod] CS(0,1,9,0,1). 236 [hyper,21,1,12,19,demod] CS(0,1,8,9,0). 237 [hyper,21,1,12,18,demod] CS(0,1,7,8,0). 238 [hyper,21,1,12,17,demod] CS(0,1,6,7,0). 239 [hyper,21,1,12,16,demod] CS(0,1,5,6,0). 240 [hyper,21,1,12,15,demod] CS(0,1,4,5,0). 241 [hyper,21,1,12,14,demod] CS(0,1,3,4,0). 242 [hyper,21,1,12,13,demod] CS(0,1,2,3,0). 243 [hyper,21,1,12,12,demod] CS(0,1,1,2,0). 244 [hyper,21,1,12,11,demod] CS(0,1,0,1,0). 245 [hyper,21,1,11,20,demod] CS(0,0,9,9,0). 246 [hyper,21,1,11,19,demod] CS(0,0,8,8,0). 247 [hyper,21,1,11,18,demod] CS(0,0,7,7,0). 248 [hyper,21,1,11,17,demod] CS(0,0,6,6,0). 249 [hyper,21,1,11,16,demod] CS(0,0,5,5,0). 250 [hyper,21,1,11,15,demod] CS(0,0,4,4,0). 251 [hyper,21,1,11,14,demod] CS(0,0,3,3,0). 252 [hyper,21,1,11,13,demod] CS(0,0,2,2,0). 253 [hyper,21,1,11,12,demod] CS(0,0,1,1,0). 254 [hyper,21,1,11,11,demod] CS(0,0,0,0,0). 22 [] -L(u)| -D(x)| -D(y)|CP(u,x,y,$MOD($SUM(u,$PROD(x,y)),10),$DIV($SUM(u,$PROD(x,y)),10)). 255 [hyper,22,10,20,20,demod] CP(7,9,9,8,8). 256 [hyper,22,10,20,19,demod] CP(7,9,8,9,7). 257 [hyper,22,10,20,18,demod] CP(7,9,7,0,7). 258 [hyper,22,10,20,17,demod] CP(7,9,6,1,6). 259 [hyper,22,10,20,16,demod] CP(7,9,5,2,5). 260 [hyper,22,10,20,15,demod] CP(7,9,4,3,4). 261 [hyper,22,10,20,14,demod] CP(7,9,3,4,3). 262 [hyper,22,10,20,13,demod] CP(7,9,2,5,2). 263 [hyper,22,10,20,12,demod] CP(7,9,1,6,1). 264 [hyper,22,10,20,11,demod] CP(7,9,0,7,0). 265 [hyper,22,10,19,20,demod] CP(7,8,9,9,7). 266 [hyper,22,10,19,19,demod] CP(7,8,8,1,7). 267 [hyper,22,10,19,18,demod] CP(7,8,7,3,6). 268 [hyper,22,10,19,17,demod] CP(7,8,6,5,5). 269 [hyper,22,10,19,16,demod] CP(7,8,5,7,4). 270 [hyper,22,10,19,15,demod] CP(7,8,4,9,3). 271 [hyper,22,10,19,14,demod] CP(7,8,3,1,3). 272 [hyper,22,10,19,13,demod] CP(7,8,2,3,2). 273 [hyper,22,10,19,12,demod] CP(7,8,1,5,1). 274 [hyper,22,10,19,11,demod] CP(7,8,0,7,0). 275 [hyper,22,10,18,20,demod] CP(7,7,9,0,7). 276 [hyper,22,10,18,19,demod] CP(7,7,8,3,6). 277 [hyper,22,10,18,18,demod] CP(7,7,7,6,5). 278 [hyper,22,10,18,17,demod] CP(7,7,6,9,4). 279 [hyper,22,10,18,16,demod] CP(7,7,5,2,4). 280 [hyper,22,10,18,15,demod] CP(7,7,4,5,3). 281 [hyper,22,10,18,14,demod] CP(7,7,3,8,2). 282 [hyper,22,10,18,13,demod] CP(7,7,2,1,2). 283 [hyper,22,10,18,12,demod] CP(7,7,1,4,1). 284 [hyper,22,10,18,11,demod] CP(7,7,0,7,0). 285 [hyper,22,10,17,20,demod] CP(7,6,9,1,6). 286 [hyper,22,10,17,19,demod] CP(7,6,8,5,5). 287 [hyper,22,10,17,18,demod] CP(7,6,7,9,4). 288 [hyper,22,10,17,17,demod] CP(7,6,6,3,4). 289 [hyper,22,10,17,16,demod] CP(7,6,5,7,3). 290 [hyper,22,10,17,15,demod] CP(7,6,4,1,3). 291 [hyper,22,10,17,14,demod] CP(7,6,3,5,2). 292 [hyper,22,10,17,13,demod] CP(7,6,2,9,1). 293 [hyper,22,10,17,12,demod] CP(7,6,1,3,1). 294 [hyper,22,10,17,11,demod] CP(7,6,0,7,0). 295 [hyper,22,10,16,20,demod] CP(7,5,9,2,5). 296 [hyper,22,10,16,19,demod] CP(7,5,8,7,4). 297 [hyper,22,10,16,18,demod] CP(7,5,7,2,4). 298 [hyper,22,10,16,17,demod] CP(7,5,6,7,3). 299 [hyper,22,10,16,16,demod] CP(7,5,5,2,3). 300 [hyper,22,10,16,15,demod] CP(7,5,4,7,2). 301 [hyper,22,10,16,14,demod] CP(7,5,3,2,2). 302 [hyper,22,10,16,13,demod] CP(7,5,2,7,1). 303 [hyper,22,10,16,12,demod] CP(7,5,1,2,1). 304 [hyper,22,10,16,11,demod] CP(7,5,0,7,0). 305 [hyper,22,10,15,20,demod] CP(7,4,9,3,4). 306 [hyper,22,10,15,19,demod] CP(7,4,8,9,3). 307 [hyper,22,10,15,18,demod] CP(7,4,7,5,3). 308 [hyper,22,10,15,17,demod] CP(7,4,6,1,3). 309 [hyper,22,10,15,16,demod] CP(7,4,5,7,2). 310 [hyper,22,10,15,15,demod] CP(7,4,4,3,2). 311 [hyper,22,10,15,14,demod] CP(7,4,3,9,1). 312 [hyper,22,10,15,13,demod] CP(7,4,2,5,1). 313 [hyper,22,10,15,12,demod] CP(7,4,1,1,1). 314 [hyper,22,10,15,11,demod] CP(7,4,0,7,0). 315 [hyper,22,10,14,20,demod] CP(7,3,9,4,3). 316 [hyper,22,10,14,19,demod] CP(7,3,8,1,3). 317 [hyper,22,10,14,18,demod] CP(7,3,7,8,2). 318 [hyper,22,10,14,17,demod] CP(7,3,6,5,2). 319 [hyper,22,10,14,16,demod] CP(7,3,5,2,2). 320 [hyper,22,10,14,15,demod] CP(7,3,4,9,1). 321 [hyper,22,10,14,14,demod] CP(7,3,3,6,1). 322 [hyper,22,10,14,13,demod] CP(7,3,2,3,1). 323 [hyper,22,10,14,12,demod] CP(7,3,1,0,1). 324 [hyper,22,10,14,11,demod] CP(7,3,0,7,0). 325 [hyper,22,10,13,20,demod] CP(7,2,9,5,2). 326 [hyper,22,10,13,19,demod] CP(7,2,8,3,2). 327 [hyper,22,10,13,18,demod] CP(7,2,7,1,2). 328 [hyper,22,10,13,17,demod] CP(7,2,6,9,1). 329 [hyper,22,10,13,16,demod] CP(7,2,5,7,1). 330 [hyper,22,10,13,15,demod] CP(7,2,4,5,1). 331 [hyper,22,10,13,14,demod] CP(7,2,3,3,1). 332 [hyper,22,10,13,13,demod] CP(7,2,2,1,1). 333 [hyper,22,10,13,12,demod] CP(7,2,1,9,0). 334 [hyper,22,10,13,11,demod] CP(7,2,0,7,0). 335 [hyper,22,10,12,20,demod] CP(7,1,9,6,1). 336 [hyper,22,10,12,19,demod] CP(7,1,8,5,1). 337 [hyper,22,10,12,18,demod] CP(7,1,7,4,1). 338 [hyper,22,10,12,17,demod] CP(7,1,6,3,1). 339 [hyper,22,10,12,16,demod] CP(7,1,5,2,1). 340 [hyper,22,10,12,15,demod] CP(7,1,4,1,1). 341 [hyper,22,10,12,14,demod] CP(7,1,3,0,1). 342 [hyper,22,10,12,13,demod] CP(7,1,2,9,0). 343 [hyper,22,10,12,12,demod] CP(7,1,1,8,0). 344 [hyper,22,10,12,11,demod] CP(7,1,0,7,0). 345 [hyper,22,10,11,20,demod] CP(7,0,9,7,0). 346 [hyper,22,10,11,19,demod] CP(7,0,8,7,0). 347 [hyper,22,10,11,18,demod] CP(7,0,7,7,0). 348 [hyper,22,10,11,17,demod] CP(7,0,6,7,0). 349 [hyper,22,10,11,16,demod] CP(7,0,5,7,0). 350 [hyper,22,10,11,15,demod] CP(7,0,4,7,0). 351 [hyper,22,10,11,14,demod] CP(7,0,3,7,0). 352 [hyper,22,10,11,13,demod] CP(7,0,2,7,0). 353 [hyper,22,10,11,12,demod] CP(7,0,1,7,0). 354 [hyper,22,10,11,11,demod] CP(7,0,0,7,0). 355 [hyper,22,9,20,20,demod] CP(6,9,9,7,8). 356 [hyper,22,9,20,19,demod] CP(6,9,8,8,7). 357 [hyper,22,9,20,18,demod] CP(6,9,7,9,6). 358 [hyper,22,9,20,17,demod] CP(6,9,6,0,6). 359 [hyper,22,9,20,16,demod] CP(6,9,5,1,5). 360 [hyper,22,9,20,15,demod] CP(6,9,4,2,4). 361 [hyper,22,9,20,14,demod] CP(6,9,3,3,3). 362 [hyper,22,9,20,13,demod] CP(6,9,2,4,2). 363 [hyper,22,9,20,12,demod] CP(6,9,1,5,1). 364 [hyper,22,9,20,11,demod] CP(6,9,0,6,0). 365 [hyper,22,9,19,20,demod] CP(6,8,9,8,7). 366 [hyper,22,9,19,19,demod] CP(6,8,8,0,7). 367 [hyper,22,9,19,18,demod] CP(6,8,7,2,6). 368 [hyper,22,9,19,17,demod] CP(6,8,6,4,5). 369 [hyper,22,9,19,16,demod] CP(6,8,5,6,4). 370 [hyper,22,9,19,15,demod] CP(6,8,4,8,3). 371 [hyper,22,9,19,14,demod] CP(6,8,3,0,3). 372 [hyper,22,9,19,13,demod] CP(6,8,2,2,2). 373 [hyper,22,9,19,12,demod] CP(6,8,1,4,1). 374 [hyper,22,9,19,11,demod] CP(6,8,0,6,0). 375 [hyper,22,9,18,20,demod] CP(6,7,9,9,6). 376 [hyper,22,9,18,19,demod] CP(6,7,8,2,6). 377 [hyper,22,9,18,18,demod] CP(6,7,7,5,5). 378 [hyper,22,9,18,17,demod] CP(6,7,6,8,4). 379 [hyper,22,9,18,16,demod] CP(6,7,5,1,4). 380 [hyper,22,9,18,15,demod] CP(6,7,4,4,3). 381 [hyper,22,9,18,14,demod] CP(6,7,3,7,2). 382 [hyper,22,9,18,13,demod] CP(6,7,2,0,2). 383 [hyper,22,9,18,12,demod] CP(6,7,1,3,1). 384 [hyper,22,9,18,11,demod] CP(6,7,0,6,0). 385 [hyper,22,9,17,20,demod] CP(6,6,9,0,6). 386 [hyper,22,9,17,19,demod] CP(6,6,8,4,5). 387 [hyper,22,9,17,18,demod] CP(6,6,7,8,4). 388 [hyper,22,9,17,17,demod] CP(6,6,6,2,4). 389 [hyper,22,9,17,16,demod] CP(6,6,5,6,3). 390 [hyper,22,9,17,15,demod] CP(6,6,4,0,3). 391 [hyper,22,9,17,14,demod] CP(6,6,3,4,2). 392 [hyper,22,9,17,13,demod] CP(6,6,2,8,1). 393 [hyper,22,9,17,12,demod] CP(6,6,1,2,1). 394 [hyper,22,9,17,11,demod] CP(6,6,0,6,0). 395 [hyper,22,9,16,20,demod] CP(6,5,9,1,5). 396 [hyper,22,9,16,19,demod] CP(6,5,8,6,4). 397 [hyper,22,9,16,18,demod] CP(6,5,7,1,4). 398 [hyper,22,9,16,17,demod] CP(6,5,6,6,3). 399 [hyper,22,9,16,16,demod] CP(6,5,5,1,3). 400 [hyper,22,9,16,15,demod] CP(6,5,4,6,2). 401 [hyper,22,9,16,14,demod] CP(6,5,3,1,2). 402 [hyper,22,9,16,13,demod] CP(6,5,2,6,1). 403 [hyper,22,9,16,12,demod] CP(6,5,1,1,1). 404 [hyper,22,9,16,11,demod] CP(6,5,0,6,0). 405 [hyper,22,9,15,20,demod] CP(6,4,9,2,4). 406 [hyper,22,9,15,19,demod] CP(6,4,8,8,3). 407 [hyper,22,9,15,18,demod] CP(6,4,7,4,3). 408 [hyper,22,9,15,17,demod] CP(6,4,6,0,3). 409 [hyper,22,9,15,16,demod] CP(6,4,5,6,2). 410 [hyper,22,9,15,15,demod] CP(6,4,4,2,2). 411 [hyper,22,9,15,14,demod] CP(6,4,3,8,1). 412 [hyper,22,9,15,13,demod] CP(6,4,2,4,1). 413 [hyper,22,9,15,12,demod] CP(6,4,1,0,1). 414 [hyper,22,9,15,11,demod] CP(6,4,0,6,0). 415 [hyper,22,9,14,20,demod] CP(6,3,9,3,3). 416 [hyper,22,9,14,19,demod] CP(6,3,8,0,3). 417 [hyper,22,9,14,18,demod] CP(6,3,7,7,2). 418 [hyper,22,9,14,17,demod] CP(6,3,6,4,2). 419 [hyper,22,9,14,16,demod] CP(6,3,5,1,2). 420 [hyper,22,9,14,15,demod] CP(6,3,4,8,1). 421 [hyper,22,9,14,14,demod] CP(6,3,3,5,1). 422 [hyper,22,9,14,13,demod] CP(6,3,2,2,1). 423 [hyper,22,9,14,12,demod] CP(6,3,1,9,0). 424 [hyper,22,9,14,11,demod] CP(6,3,0,6,0). 425 [hyper,22,9,13,20,demod] CP(6,2,9,4,2). 426 [hyper,22,9,13,19,demod] CP(6,2,8,2,2). 427 [hyper,22,9,13,18,demod] CP(6,2,7,0,2). 428 [hyper,22,9,13,17,demod] CP(6,2,6,8,1). 429 [hyper,22,9,13,16,demod] CP(6,2,5,6,1). 430 [hyper,22,9,13,15,demod] CP(6,2,4,4,1). 431 [hyper,22,9,13,14,demod] CP(6,2,3,2,1). 432 [hyper,22,9,13,13,demod] CP(6,2,2,0,1). 433 [hyper,22,9,13,12,demod] CP(6,2,1,8,0). 434 [hyper,22,9,13,11,demod] CP(6,2,0,6,0). 435 [hyper,22,9,12,20,demod] CP(6,1,9,5,1). 436 [hyper,22,9,12,19,demod] CP(6,1,8,4,1). 437 [hyper,22,9,12,18,demod] CP(6,1,7,3,1). 438 [hyper,22,9,12,17,demod] CP(6,1,6,2,1). 439 [hyper,22,9,12,16,demod] CP(6,1,5,1,1). 440 [hyper,22,9,12,15,demod] CP(6,1,4,0,1). 441 [hyper,22,9,12,14,demod] CP(6,1,3,9,0). 442 [hyper,22,9,12,13,demod] CP(6,1,2,8,0). 443 [hyper,22,9,12,12,demod] CP(6,1,1,7,0). 444 [hyper,22,9,12,11,demod] CP(6,1,0,6,0). 445 [hyper,22,9,11,20,demod] CP(6,0,9,6,0). 446 [hyper,22,9,11,19,demod] CP(6,0,8,6,0). 447 [hyper,22,9,11,18,demod] CP(6,0,7,6,0). 448 [hyper,22,9,11,17,demod] CP(6,0,6,6,0). 449 [hyper,22,9,11,16,demod] CP(6,0,5,6,0). 450 [hyper,22,9,11,15,demod] CP(6,0,4,6,0). 451 [hyper,22,9,11,14,demod] CP(6,0,3,6,0). 452 [hyper,22,9,11,13,demod] CP(6,0,2,6,0). 453 [hyper,22,9,11,12,demod] CP(6,0,1,6,0). 454 [hyper,22,9,11,11,demod] CP(6,0,0,6,0). 455 [hyper,22,8,20,20,demod] CP(5,9,9,6,8). 456 [hyper,22,8,20,19,demod] CP(5,9,8,7,7). 457 [hyper,22,8,20,18,demod] CP(5,9,7,8,6). 458 [hyper,22,8,20,17,demod] CP(5,9,6,9,5). 459 [hyper,22,8,20,16,demod] CP(5,9,5,0,5). 460 [hyper,22,8,20,15,demod] CP(5,9,4,1,4). 461 [hyper,22,8,20,14,demod] CP(5,9,3,2,3). 462 [hyper,22,8,20,13,demod] CP(5,9,2,3,2). 463 [hyper,22,8,20,12,demod] CP(5,9,1,4,1). 464 [hyper,22,8,20,11,demod] CP(5,9,0,5,0). 465 [hyper,22,8,19,20,demod] CP(5,8,9,7,7). 466 [hyper,22,8,19,19,demod] CP(5,8,8,9,6). 467 [hyper,22,8,19,18,demod] CP(5,8,7,1,6). 468 [hyper,22,8,19,17,demod] CP(5,8,6,3,5). 469 [hyper,22,8,19,16,demod] CP(5,8,5,5,4). 470 [hyper,22,8,19,15,demod] CP(5,8,4,7,3). 471 [hyper,22,8,19,14,demod] CP(5,8,3,9,2). 472 [hyper,22,8,19,13,demod] CP(5,8,2,1,2). 473 [hyper,22,8,19,12,demod] CP(5,8,1,3,1). 474 [hyper,22,8,19,11,demod] CP(5,8,0,5,0). 475 [hyper,22,8,18,20,demod] CP(5,7,9,8,6). 476 [hyper,22,8,18,19,demod] CP(5,7,8,1,6). 477 [hyper,22,8,18,18,demod] CP(5,7,7,4,5). 478 [hyper,22,8,18,17,demod] CP(5,7,6,7,4). 479 [hyper,22,8,18,16,demod] CP(5,7,5,0,4). 480 [hyper,22,8,18,15,demod] CP(5,7,4,3,3). 481 [hyper,22,8,18,14,demod] CP(5,7,3,6,2). 482 [hyper,22,8,18,13,demod] CP(5,7,2,9,1). 483 [hyper,22,8,18,12,demod] CP(5,7,1,2,1). 484 [hyper,22,8,18,11,demod] CP(5,7,0,5,0). 485 [hyper,22,8,17,20,demod] CP(5,6,9,9,5). 486 [hyper,22,8,17,19,demod] CP(5,6,8,3,5). 487 [hyper,22,8,17,18,demod] CP(5,6,7,7,4). 488 [hyper,22,8,17,17,demod] CP(5,6,6,1,4). 489 [hyper,22,8,17,16,demod] CP(5,6,5,5,3). 490 [hyper,22,8,17,15,demod] CP(5,6,4,9,2). 491 [hyper,22,8,17,14,demod] CP(5,6,3,3,2). 492 [hyper,22,8,17,13,demod] CP(5,6,2,7,1). 493 [hyper,22,8,17,12,demod] CP(5,6,1,1,1). 494 [hyper,22,8,17,11,demod] CP(5,6,0,5,0). 495 [hyper,22,8,16,20,demod] CP(5,5,9,0,5). 496 [hyper,22,8,16,19,demod] CP(5,5,8,5,4). 497 [hyper,22,8,16,18,demod] CP(5,5,7,0,4). 498 [hyper,22,8,16,17,demod] CP(5,5,6,5,3). 499 [hyper,22,8,16,16,demod] CP(5,5,5,0,3). 500 [hyper,22,8,16,15,demod] CP(5,5,4,5,2). 501 [hyper,22,8,16,14,demod] CP(5,5,3,0,2). 502 [hyper,22,8,16,13,demod] CP(5,5,2,5,1). 503 [hyper,22,8,16,12,demod] CP(5,5,1,0,1). 504 [hyper,22,8,16,11,demod] CP(5,5,0,5,0). 505 [hyper,22,8,15,20,demod] CP(5,4,9,1,4). 506 [hyper,22,8,15,19,demod] CP(5,4,8,7,3). 507 [hyper,22,8,15,18,demod] CP(5,4,7,3,3). 508 [hyper,22,8,15,17,demod] CP(5,4,6,9,2). 509 [hyper,22,8,15,16,demod] CP(5,4,5,5,2). 510 [hyper,22,8,15,15,demod] CP(5,4,4,1,2). 511 [hyper,22,8,15,14,demod] CP(5,4,3,7,1). 512 [hyper,22,8,15,13,demod] CP(5,4,2,3,1). 513 [hyper,22,8,15,12,demod] CP(5,4,1,9,0). 514 [hyper,22,8,15,11,demod] CP(5,4,0,5,0). 515 [hyper,22,8,14,20,demod] CP(5,3,9,2,3). 516 [hyper,22,8,14,19,demod] CP(5,3,8,9,2). 517 [hyper,22,8,14,18,demod] CP(5,3,7,6,2). 518 [hyper,22,8,14,17,demod] CP(5,3,6,3,2). 519 [hyper,22,8,14,16,demod] CP(5,3,5,0,2). 520 [hyper,22,8,14,15,demod] CP(5,3,4,7,1). 521 [hyper,22,8,14,14,demod] CP(5,3,3,4,1). 522 [hyper,22,8,14,13,demod] CP(5,3,2,1,1). 523 [hyper,22,8,14,12,demod] CP(5,3,1,8,0). 524 [hyper,22,8,14,11,demod] CP(5,3,0,5,0). 525 [hyper,22,8,13,20,demod] CP(5,2,9,3,2). 526 [hyper,22,8,13,19,demod] CP(5,2,8,1,2). 527 [hyper,22,8,13,18,demod] CP(5,2,7,9,1). 528 [hyper,22,8,13,17,demod] CP(5,2,6,7,1). 529 [hyper,22,8,13,16,demod] CP(5,2,5,5,1). 530 [hyper,22,8,13,15,demod] CP(5,2,4,3,1). 531 [hyper,22,8,13,14,demod] CP(5,2,3,1,1). 532 [hyper,22,8,13,13,demod] CP(5,2,2,9,0). 533 [hyper,22,8,13,12,demod] CP(5,2,1,7,0). 534 [hyper,22,8,13,11,demod] CP(5,2,0,5,0). 535 [hyper,22,8,12,20,demod] CP(5,1,9,4,1). 536 [hyper,22,8,12,19,demod] CP(5,1,8,3,1). 537 [hyper,22,8,12,18,demod] CP(5,1,7,2,1). 538 [hyper,22,8,12,17,demod] CP(5,1,6,1,1). 539 [hyper,22,8,12,16,demod] CP(5,1,5,0,1). 540 [hyper,22,8,12,15,demod] CP(5,1,4,9,0). 541 [hyper,22,8,12,14,demod] CP(5,1,3,8,0). 542 [hyper,22,8,12,13,demod] CP(5,1,2,7,0). 543 [hyper,22,8,12,12,demod] CP(5,1,1,6,0). 544 [hyper,22,8,12,11,demod] CP(5,1,0,5,0). 545 [hyper,22,8,11,20,demod] CP(5,0,9,5,0). 546 [hyper,22,8,11,19,demod] CP(5,0,8,5,0). 547 [hyper,22,8,11,18,demod] CP(5,0,7,5,0). 548 [hyper,22,8,11,17,demod] CP(5,0,6,5,0). 549 [hyper,22,8,11,16,demod] CP(5,0,5,5,0). 550 [hyper,22,8,11,15,demod] CP(5,0,4,5,0). 551 [hyper,22,8,11,14,demod] CP(5,0,3,5,0). 552 [hyper,22,8,11,13,demod] CP(5,0,2,5,0). 553 [hyper,22,8,11,12,demod] CP(5,0,1,5,0). 554 [hyper,22,8,11,11,demod] CP(5,0,0,5,0). 555 [hyper,22,7,20,20,demod] CP(4,9,9,5,8). 556 [hyper,22,7,20,19,demod] CP(4,9,8,6,7). 557 [hyper,22,7,20,18,demod] CP(4,9,7,7,6). 558 [hyper,22,7,20,17,demod] CP(4,9,6,8,5). 559 [hyper,22,7,20,16,demod] CP(4,9,5,9,4). 560 [hyper,22,7,20,15,demod] CP(4,9,4,0,4). 561 [hyper,22,7,20,14,demod] CP(4,9,3,1,3). 562 [hyper,22,7,20,13,demod] CP(4,9,2,2,2). 563 [hyper,22,7,20,12,demod] CP(4,9,1,3,1). 564 [hyper,22,7,20,11,demod] CP(4,9,0,4,0). 565 [hyper,22,7,19,20,demod] CP(4,8,9,6,7). 566 [hyper,22,7,19,19,demod] CP(4,8,8,8,6). 567 [hyper,22,7,19,18,demod] CP(4,8,7,0,6). 568 [hyper,22,7,19,17,demod] CP(4,8,6,2,5). 569 [hyper,22,7,19,16,demod] CP(4,8,5,4,4). 570 [hyper,22,7,19,15,demod] CP(4,8,4,6,3). 571 [hyper,22,7,19,14,demod] CP(4,8,3,8,2). 572 [hyper,22,7,19,13,demod] CP(4,8,2,0,2). 573 [hyper,22,7,19,12,demod] CP(4,8,1,2,1). 574 [hyper,22,7,19,11,demod] CP(4,8,0,4,0). 575 [hyper,22,7,18,20,demod] CP(4,7,9,7,6). 576 [hyper,22,7,18,19,demod] CP(4,7,8,0,6). 577 [hyper,22,7,18,18,demod] CP(4,7,7,3,5). 578 [hyper,22,7,18,17,demod] CP(4,7,6,6,4). 579 [hyper,22,7,18,16,demod] CP(4,7,5,9,3). 580 [hyper,22,7,18,15,demod] CP(4,7,4,2,3). 581 [hyper,22,7,18,14,demod] CP(4,7,3,5,2). 582 [hyper,22,7,18,13,demod] CP(4,7,2,8,1). 583 [hyper,22,7,18,12,demod] CP(4,7,1,1,1). 584 [hyper,22,7,18,11,demod] CP(4,7,0,4,0). 585 [hyper,22,7,17,20,demod] CP(4,6,9,8,5). 586 [hyper,22,7,17,19,demod] CP(4,6,8,2,5). 587 [hyper,22,7,17,18,demod] CP(4,6,7,6,4). 588 [hyper,22,7,17,17,demod] CP(4,6,6,0,4). 589 [hyper,22,7,17,16,demod] CP(4,6,5,4,3). 590 [hyper,22,7,17,15,demod] CP(4,6,4,8,2). 591 [hyper,22,7,17,14,demod] CP(4,6,3,2,2). 592 [hyper,22,7,17,13,demod] CP(4,6,2,6,1). 593 [hyper,22,7,17,12,demod] CP(4,6,1,0,1). 594 [hyper,22,7,17,11,demod] CP(4,6,0,4,0). 595 [hyper,22,7,16,20,demod] CP(4,5,9,9,4). 596 [hyper,22,7,16,19,demod] CP(4,5,8,4,4). 597 [hyper,22,7,16,18,demod] CP(4,5,7,9,3). 598 [hyper,22,7,16,17,demod] CP(4,5,6,4,3). 599 [hyper,22,7,16,16,demod] CP(4,5,5,9,2). 600 [hyper,22,7,16,15,demod] CP(4,5,4,4,2). 601 [hyper,22,7,16,14,demod] CP(4,5,3,9,1). 602 [hyper,22,7,16,13,demod] CP(4,5,2,4,1). 603 [hyper,22,7,16,12,demod] CP(4,5,1,9,0). 604 [hyper,22,7,16,11,demod] CP(4,5,0,4,0). 605 [hyper,22,7,15,20,demod] CP(4,4,9,0,4). 606 [hyper,22,7,15,19,demod] CP(4,4,8,6,3). 607 [hyper,22,7,15,18,demod] CP(4,4,7,2,3). 608 [hyper,22,7,15,17,demod] CP(4,4,6,8,2). 609 [hyper,22,7,15,16,demod] CP(4,4,5,4,2). 610 [hyper,22,7,15,15,demod] CP(4,4,4,0,2). 611 [hyper,22,7,15,14,demod] CP(4,4,3,6,1). 612 [hyper,22,7,15,13,demod] CP(4,4,2,2,1). 613 [hyper,22,7,15,12,demod] CP(4,4,1,8,0). 614 [hyper,22,7,15,11,demod] CP(4,4,0,4,0). 615 [hyper,22,7,14,20,demod] CP(4,3,9,1,3). 616 [hyper,22,7,14,19,demod] CP(4,3,8,8,2). 617 [hyper,22,7,14,18,demod] CP(4,3,7,5,2). 618 [hyper,22,7,14,17,demod] CP(4,3,6,2,2). 619 [hyper,22,7,14,16,demod] CP(4,3,5,9,1). 620 [hyper,22,7,14,15,demod] CP(4,3,4,6,1). 621 [hyper,22,7,14,14,demod] CP(4,3,3,3,1). 622 [hyper,22,7,14,13,demod] CP(4,3,2,0,1). 623 [hyper,22,7,14,12,demod] CP(4,3,1,7,0). 624 [hyper,22,7,14,11,demod] CP(4,3,0,4,0). 625 [hyper,22,7,13,20,demod] CP(4,2,9,2,2). 626 [hyper,22,7,13,19,demod] CP(4,2,8,0,2). 627 [hyper,22,7,13,18,demod] CP(4,2,7,8,1). 628 [hyper,22,7,13,17,demod] CP(4,2,6,6,1). 629 [hyper,22,7,13,16,demod] CP(4,2,5,4,1). 630 [hyper,22,7,13,15,demod] CP(4,2,4,2,1). 631 [hyper,22,7,13,14,demod] CP(4,2,3,0,1). 632 [hyper,22,7,13,13,demod] CP(4,2,2,8,0). 633 [hyper,22,7,13,12,demod] CP(4,2,1,6,0). 634 [hyper,22,7,13,11,demod] CP(4,2,0,4,0). 635 [hyper,22,7,12,20,demod] CP(4,1,9,3,1). 636 [hyper,22,7,12,19,demod] CP(4,1,8,2,1). 637 [hyper,22,7,12,18,demod] CP(4,1,7,1,1). 638 [hyper,22,7,12,17,demod] CP(4,1,6,0,1). 639 [hyper,22,7,12,16,demod] CP(4,1,5,9,0). 640 [hyper,22,7,12,15,demod] CP(4,1,4,8,0). 641 [hyper,22,7,12,14,demod] CP(4,1,3,7,0). 642 [hyper,22,7,12,13,demod] CP(4,1,2,6,0). 643 [hyper,22,7,12,12,demod] CP(4,1,1,5,0). 644 [hyper,22,7,12,11,demod] CP(4,1,0,4,0). 645 [hyper,22,7,11,20,demod] CP(4,0,9,4,0). 646 [hyper,22,7,11,19,demod] CP(4,0,8,4,0). 647 [hyper,22,7,11,18,demod] CP(4,0,7,4,0). 648 [hyper,22,7,11,17,demod] CP(4,0,6,4,0). 649 [hyper,22,7,11,16,demod] CP(4,0,5,4,0). 650 [hyper,22,7,11,15,demod] CP(4,0,4,4,0). 651 [hyper,22,7,11,14,demod] CP(4,0,3,4,0). 652 [hyper,22,7,11,13,demod] CP(4,0,2,4,0). 653 [hyper,22,7,11,12,demod] CP(4,0,1,4,0). 654 [hyper,22,7,11,11,demod] CP(4,0,0,4,0). 655 [hyper,22,6,20,20,demod] CP(3,9,9,4,8). 656 [hyper,22,6,20,19,demod] CP(3,9,8,5,7). 657 [hyper,22,6,20,18,demod] CP(3,9,7,6,6). 658 [hyper,22,6,20,17,demod] CP(3,9,6,7,5). 659 [hyper,22,6,20,16,demod] CP(3,9,5,8,4). 660 [hyper,22,6,20,15,demod] CP(3,9,4,9,3). 661 [hyper,22,6,20,14,demod] CP(3,9,3,0,3). 662 [hyper,22,6,20,13,demod] CP(3,9,2,1,2). 663 [hyper,22,6,20,12,demod] CP(3,9,1,2,1). 664 [hyper,22,6,20,11,demod] CP(3,9,0,3,0). 665 [hyper,22,6,19,20,demod] CP(3,8,9,5,7). 666 [hyper,22,6,19,19,demod] CP(3,8,8,7,6). 667 [hyper,22,6,19,18,demod] CP(3,8,7,9,5). 668 [hyper,22,6,19,17,demod] CP(3,8,6,1,5). 669 [hyper,22,6,19,16,demod] CP(3,8,5,3,4). 670 [hyper,22,6,19,15,demod] CP(3,8,4,5,3). 671 [hyper,22,6,19,14,demod] CP(3,8,3,7,2). 672 [hyper,22,6,19,13,demod] CP(3,8,2,9,1). 673 [hyper,22,6,19,12,demod] CP(3,8,1,1,1). 674 [hyper,22,6,19,11,demod] CP(3,8,0,3,0). 675 [hyper,22,6,18,20,demod] CP(3,7,9,6,6). 676 [hyper,22,6,18,19,demod] CP(3,7,8,9,5). 677 [hyper,22,6,18,18,demod] CP(3,7,7,2,5). 678 [hyper,22,6,18,17,demod] CP(3,7,6,5,4). 679 [hyper,22,6,18,16,demod] CP(3,7,5,8,3). 680 [hyper,22,6,18,15,demod] CP(3,7,4,1,3). 681 [hyper,22,6,18,14,demod] CP(3,7,3,4,2). 682 [hyper,22,6,18,13,demod] CP(3,7,2,7,1). 683 [hyper,22,6,18,12,demod] CP(3,7,1,0,1). 684 [hyper,22,6,18,11,demod] CP(3,7,0,3,0). 685 [hyper,22,6,17,20,demod] CP(3,6,9,7,5). 686 [hyper,22,6,17,19,demod] CP(3,6,8,1,5). 687 [hyper,22,6,17,18,demod] CP(3,6,7,5,4). 688 [hyper,22,6,17,17,demod] CP(3,6,6,9,3). 689 [hyper,22,6,17,16,demod] CP(3,6,5,3,3). 690 [hyper,22,6,17,15,demod] CP(3,6,4,7,2). 691 [hyper,22,6,17,14,demod] CP(3,6,3,1,2). 692 [hyper,22,6,17,13,demod] CP(3,6,2,5,1). 693 [hyper,22,6,17,12,demod] CP(3,6,1,9,0). 694 [hyper,22,6,17,11,demod] CP(3,6,0,3,0). 695 [hyper,22,6,16,20,demod] CP(3,5,9,8,4). 696 [hyper,22,6,16,19,demod] CP(3,5,8,3,4). 697 [hyper,22,6,16,18,demod] CP(3,5,7,8,3). 698 [hyper,22,6,16,17,demod] CP(3,5,6,3,3). 699 [hyper,22,6,16,16,demod] CP(3,5,5,8,2). 700 [hyper,22,6,16,15,demod] CP(3,5,4,3,2). 701 [hyper,22,6,16,14,demod] CP(3,5,3,8,1). 702 [hyper,22,6,16,13,demod] CP(3,5,2,3,1). 703 [hyper,22,6,16,12,demod] CP(3,5,1,8,0). 704 [hyper,22,6,16,11,demod] CP(3,5,0,3,0). 705 [hyper,22,6,15,20,demod] CP(3,4,9,9,3). 706 [hyper,22,6,15,19,demod] CP(3,4,8,5,3). 707 [hyper,22,6,15,18,demod] CP(3,4,7,1,3). 708 [hyper,22,6,15,17,demod] CP(3,4,6,7,2). 709 [hyper,22,6,15,16,demod] CP(3,4,5,3,2). 710 [hyper,22,6,15,15,demod] CP(3,4,4,9,1). 711 [hyper,22,6,15,14,demod] CP(3,4,3,5,1). 712 [hyper,22,6,15,13,demod] CP(3,4,2,1,1). 713 [hyper,22,6,15,12,demod] CP(3,4,1,7,0). 714 [hyper,22,6,15,11,demod] CP(3,4,0,3,0). 715 [hyper,22,6,14,20,demod] CP(3,3,9,0,3). 716 [hyper,22,6,14,19,demod] CP(3,3,8,7,2). 717 [hyper,22,6,14,18,demod] CP(3,3,7,4,2). 718 [hyper,22,6,14,17,demod] CP(3,3,6,1,2). 719 [hyper,22,6,14,16,demod] CP(3,3,5,8,1). 720 [hyper,22,6,14,15,demod] CP(3,3,4,5,1). 721 [hyper,22,6,14,14,demod] CP(3,3,3,2,1). 722 [hyper,22,6,14,13,demod] CP(3,3,2,9,0). 723 [hyper,22,6,14,12,demod] CP(3,3,1,6,0). 724 [hyper,22,6,14,11,demod] CP(3,3,0,3,0). 725 [hyper,22,6,13,20,demod] CP(3,2,9,1,2). 726 [hyper,22,6,13,19,demod] CP(3,2,8,9,1). 727 [hyper,22,6,13,18,demod] CP(3,2,7,7,1). 728 [hyper,22,6,13,17,demod] CP(3,2,6,5,1). 729 [hyper,22,6,13,16,demod] CP(3,2,5,3,1). 730 [hyper,22,6,13,15,demod] CP(3,2,4,1,1). 731 [hyper,22,6,13,14,demod] CP(3,2,3,9,0). 732 [hyper,22,6,13,13,demod] CP(3,2,2,7,0). 733 [hyper,22,6,13,12,demod] CP(3,2,1,5,0). 734 [hyper,22,6,13,11,demod] CP(3,2,0,3,0). 735 [hyper,22,6,12,20,demod] CP(3,1,9,2,1). 736 [hyper,22,6,12,19,demod] CP(3,1,8,1,1). 737 [hyper,22,6,12,18,demod] CP(3,1,7,0,1). 738 [hyper,22,6,12,17,demod] CP(3,1,6,9,0). 739 [hyper,22,6,12,16,demod] CP(3,1,5,8,0). 740 [hyper,22,6,12,15,demod] CP(3,1,4,7,0). 741 [hyper,22,6,12,14,demod] CP(3,1,3,6,0). 742 [hyper,22,6,12,13,demod] CP(3,1,2,5,0). 743 [hyper,22,6,12,12,demod] CP(3,1,1,4,0). 744 [hyper,22,6,12,11,demod] CP(3,1,0,3,0). 745 [hyper,22,6,11,20,demod] CP(3,0,9,3,0). 746 [hyper,22,6,11,19,demod] CP(3,0,8,3,0). 747 [hyper,22,6,11,18,demod] CP(3,0,7,3,0). 748 [hyper,22,6,11,17,demod] CP(3,0,6,3,0). 749 [hyper,22,6,11,16,demod] CP(3,0,5,3,0). 750 [hyper,22,6,11,15,demod] CP(3,0,4,3,0). 751 [hyper,22,6,11,14,demod] CP(3,0,3,3,0). 752 [hyper,22,6,11,13,demod] CP(3,0,2,3,0). 753 [hyper,22,6,11,12,demod] CP(3,0,1,3,0). 754 [hyper,22,6,11,11,demod] CP(3,0,0,3,0). 755 [hyper,22,5,20,20,demod] CP(2,9,9,3,8). 756 [hyper,22,5,20,19,demod] CP(2,9,8,4,7). 757 [hyper,22,5,20,18,demod] CP(2,9,7,5,6). 758 [hyper,22,5,20,17,demod] CP(2,9,6,6,5). 759 [hyper,22,5,20,16,demod] CP(2,9,5,7,4). 760 [hyper,22,5,20,15,demod] CP(2,9,4,8,3). 761 [hyper,22,5,20,14,demod] CP(2,9,3,9,2). 762 [hyper,22,5,20,13,demod] CP(2,9,2,0,2). 763 [hyper,22,5,20,12,demod] CP(2,9,1,1,1). 764 [hyper,22,5,20,11,demod] CP(2,9,0,2,0). 765 [hyper,22,5,19,20,demod] CP(2,8,9,4,7). 766 [hyper,22,5,19,19,demod] CP(2,8,8,6,6). 767 [hyper,22,5,19,18,demod] CP(2,8,7,8,5). 768 [hyper,22,5,19,17,demod] CP(2,8,6,0,5). 769 [hyper,22,5,19,16,demod] CP(2,8,5,2,4). 770 [hyper,22,5,19,15,demod] CP(2,8,4,4,3). 771 [hyper,22,5,19,14,demod] CP(2,8,3,6,2). 772 [hyper,22,5,19,13,demod] CP(2,8,2,8,1). 773 [hyper,22,5,19,12,demod] CP(2,8,1,0,1). 774 [hyper,22,5,19,11,demod] CP(2,8,0,2,0). 775 [hyper,22,5,18,20,demod] CP(2,7,9,5,6). 776 [hyper,22,5,18,19,demod] CP(2,7,8,8,5). 777 [hyper,22,5,18,18,demod] CP(2,7,7,1,5). 778 [hyper,22,5,18,17,demod] CP(2,7,6,4,4). 779 [hyper,22,5,18,16,demod] CP(2,7,5,7,3). 780 [hyper,22,5,18,15,demod] CP(2,7,4,0,3). 781 [hyper,22,5,18,14,demod] CP(2,7,3,3,2). 782 [hyper,22,5,18,13,demod] CP(2,7,2,6,1). 783 [hyper,22,5,18,12,demod] CP(2,7,1,9,0). 784 [hyper,22,5,18,11,demod] CP(2,7,0,2,0). 785 [hyper,22,5,17,20,demod] CP(2,6,9,6,5). 786 [hyper,22,5,17,19,demod] CP(2,6,8,0,5). 787 [hyper,22,5,17,18,demod] CP(2,6,7,4,4). 788 [hyper,22,5,17,17,demod] CP(2,6,6,8,3). 789 [hyper,22,5,17,16,demod] CP(2,6,5,2,3). 790 [hyper,22,5,17,15,demod] CP(2,6,4,6,2). 791 [hyper,22,5,17,14,demod] CP(2,6,3,0,2). 792 [hyper,22,5,17,13,demod] CP(2,6,2,4,1). 793 [hyper,22,5,17,12,demod] CP(2,6,1,8,0). 794 [hyper,22,5,17,11,demod] CP(2,6,0,2,0). 795 [hyper,22,5,16,20,demod] CP(2,5,9,7,4). 796 [hyper,22,5,16,19,demod] CP(2,5,8,2,4). 797 [hyper,22,5,16,18,demod] CP(2,5,7,7,3). 798 [hyper,22,5,16,17,demod] CP(2,5,6,2,3). 799 [hyper,22,5,16,16,demod] CP(2,5,5,7,2). 800 [hyper,22,5,16,15,demod] CP(2,5,4,2,2). 801 [hyper,22,5,16,14,demod] CP(2,5,3,7,1). 802 [hyper,22,5,16,13,demod] CP(2,5,2,2,1). 803 [hyper,22,5,16,12,demod] CP(2,5,1,7,0). 804 [hyper,22,5,16,11,demod] CP(2,5,0,2,0). 805 [hyper,22,5,15,20,demod] CP(2,4,9,8,3). 806 [hyper,22,5,15,19,demod] CP(2,4,8,4,3). 807 [hyper,22,5,15,18,demod] CP(2,4,7,0,3). 808 [hyper,22,5,15,17,demod] CP(2,4,6,6,2). 809 [hyper,22,5,15,16,demod] CP(2,4,5,2,2). 810 [hyper,22,5,15,15,demod] CP(2,4,4,8,1). 811 [hyper,22,5,15,14,demod] CP(2,4,3,4,1). 812 [hyper,22,5,15,13,demod] CP(2,4,2,0,1). 813 [hyper,22,5,15,12,demod] CP(2,4,1,6,0). 814 [hyper,22,5,15,11,demod] CP(2,4,0,2,0). 815 [hyper,22,5,14,20,demod] CP(2,3,9,9,2). 816 [hyper,22,5,14,19,demod] CP(2,3,8,6,2). 817 [hyper,22,5,14,18,demod] CP(2,3,7,3,2). 818 [hyper,22,5,14,17,demod] CP(2,3,6,0,2). 819 [hyper,22,5,14,16,demod] CP(2,3,5,7,1). 820 [hyper,22,5,14,15,demod] CP(2,3,4,4,1). 821 [hyper,22,5,14,14,demod] CP(2,3,3,1,1). 822 [hyper,22,5,14,13,demod] CP(2,3,2,8,0). 823 [hyper,22,5,14,12,demod] CP(2,3,1,5,0). 824 [hyper,22,5,14,11,demod] CP(2,3,0,2,0). 825 [hyper,22,5,13,20,demod] CP(2,2,9,0,2). 826 [hyper,22,5,13,19,demod] CP(2,2,8,8,1). 827 [hyper,22,5,13,18,demod] CP(2,2,7,6,1). 828 [hyper,22,5,13,17,demod] CP(2,2,6,4,1). 829 [hyper,22,5,13,16,demod] CP(2,2,5,2,1). 830 [hyper,22,5,13,15,demod] CP(2,2,4,0,1). 831 [hyper,22,5,13,14,demod] CP(2,2,3,8,0). 832 [hyper,22,5,13,13,demod] CP(2,2,2,6,0). 833 [hyper,22,5,13,12,demod] CP(2,2,1,4,0). 834 [hyper,22,5,13,11,demod] CP(2,2,0,2,0). 835 [hyper,22,5,12,20,demod] CP(2,1,9,1,1). 836 [hyper,22,5,12,19,demod] CP(2,1,8,0,1). 837 [hyper,22,5,12,18,demod] CP(2,1,7,9,0). 838 [hyper,22,5,12,17,demod] CP(2,1,6,8,0). 839 [hyper,22,5,12,16,demod] CP(2,1,5,7,0). 840 [hyper,22,5,12,15,demod] CP(2,1,4,6,0). 841 [hyper,22,5,12,14,demod] CP(2,1,3,5,0). 842 [hyper,22,5,12,13,demod] CP(2,1,2,4,0). 843 [hyper,22,5,12,12,demod] CP(2,1,1,3,0). 844 [hyper,22,5,12,11,demod] CP(2,1,0,2,0). 845 [hyper,22,5,11,20,demod] CP(2,0,9,2,0). 846 [hyper,22,5,11,19,demod] CP(2,0,8,2,0). 847 [hyper,22,5,11,18,demod] CP(2,0,7,2,0). 848 [hyper,22,5,11,17,demod] CP(2,0,6,2,0). 849 [hyper,22,5,11,16,demod] CP(2,0,5,2,0). 850 [hyper,22,5,11,15,demod] CP(2,0,4,2,0). 851 [hyper,22,5,11,14,demod] CP(2,0,3,2,0). 852 [hyper,22,5,11,13,demod] CP(2,0,2,2,0). 853 [hyper,22,5,11,12,demod] CP(2,0,1,2,0). 854 [hyper,22,5,11,11,demod] CP(2,0,0,2,0). 855 [hyper,22,4,20,20,demod] CP(1,9,9,2,8). 856 [hyper,22,4,20,19,demod] CP(1,9,8,3,7). 857 [hyper,22,4,20,18,demod] CP(1,9,7,4,6). 858 [hyper,22,4,20,17,demod] CP(1,9,6,5,5). 859 [hyper,22,4,20,16,demod] CP(1,9,5,6,4). 860 [hyper,22,4,20,15,demod] CP(1,9,4,7,3). 861 [hyper,22,4,20,14,demod] CP(1,9,3,8,2). 862 [hyper,22,4,20,13,demod] CP(1,9,2,9,1). 863 [hyper,22,4,20,12,demod] CP(1,9,1,0,1). 864 [hyper,22,4,20,11,demod] CP(1,9,0,1,0). 865 [hyper,22,4,19,20,demod] CP(1,8,9,3,7). 866 [hyper,22,4,19,19,demod] CP(1,8,8,5,6). 867 [hyper,22,4,19,18,demod] CP(1,8,7,7,5). 868 [hyper,22,4,19,17,demod] CP(1,8,6,9,4). 869 [hyper,22,4,19,16,demod] CP(1,8,5,1,4). 870 [hyper,22,4,19,15,demod] CP(1,8,4,3,3). 871 [hyper,22,4,19,14,demod] CP(1,8,3,5,2). 872 [hyper,22,4,19,13,demod] CP(1,8,2,7,1). 873 [hyper,22,4,19,12,demod] CP(1,8,1,9,0). 874 [hyper,22,4,19,11,demod] CP(1,8,0,1,0). 875 [hyper,22,4,18,20,demod] CP(1,7,9,4,6). 876 [hyper,22,4,18,19,demod] CP(1,7,8,7,5). 877 [hyper,22,4,18,18,demod] CP(1,7,7,0,5). 878 [hyper,22,4,18,17,demod] CP(1,7,6,3,4). 879 [hyper,22,4,18,16,demod] CP(1,7,5,6,3). 880 [hyper,22,4,18,15,demod] CP(1,7,4,9,2). 881 [hyper,22,4,18,14,demod] CP(1,7,3,2,2). 882 [hyper,22,4,18,13,demod] CP(1,7,2,5,1). 883 [hyper,22,4,18,12,demod] CP(1,7,1,8,0). 884 [hyper,22,4,18,11,demod] CP(1,7,0,1,0). 885 [hyper,22,4,17,20,demod] CP(1,6,9,5,5). 886 [hyper,22,4,17,19,demod] CP(1,6,8,9,4). 887 [hyper,22,4,17,18,demod] CP(1,6,7,3,4). 888 [hyper,22,4,17,17,demod] CP(1,6,6,7,3). 889 [hyper,22,4,17,16,demod] CP(1,6,5,1,3). 890 [hyper,22,4,17,15,demod] CP(1,6,4,5,2). 891 [hyper,22,4,17,14,demod] CP(1,6,3,9,1). 892 [hyper,22,4,17,13,demod] CP(1,6,2,3,1). 893 [hyper,22,4,17,12,demod] CP(1,6,1,7,0). 894 [hyper,22,4,17,11,demod] CP(1,6,0,1,0). 895 [hyper,22,4,16,20,demod] CP(1,5,9,6,4). 896 [hyper,22,4,16,19,demod] CP(1,5,8,1,4). 897 [hyper,22,4,16,18,demod] CP(1,5,7,6,3). 898 [hyper,22,4,16,17,demod] CP(1,5,6,1,3). 899 [hyper,22,4,16,16,demod] CP(1,5,5,6,2). 900 [hyper,22,4,16,15,demod] CP(1,5,4,1,2). 901 [hyper,22,4,16,14,demod] CP(1,5,3,6,1). 902 [hyper,22,4,16,13,demod] CP(1,5,2,1,1). 903 [hyper,22,4,16,12,demod] CP(1,5,1,6,0). 904 [hyper,22,4,16,11,demod] CP(1,5,0,1,0). 905 [hyper,22,4,15,20,demod] CP(1,4,9,7,3). 906 [hyper,22,4,15,19,demod] CP(1,4,8,3,3). 907 [hyper,22,4,15,18,demod] CP(1,4,7,9,2). 908 [hyper,22,4,15,17,demod] CP(1,4,6,5,2). 909 [hyper,22,4,15,16,demod] CP(1,4,5,1,2). 910 [hyper,22,4,15,15,demod] CP(1,4,4,7,1). 911 [hyper,22,4,15,14,demod] CP(1,4,3,3,1). 912 [hyper,22,4,15,13,demod] CP(1,4,2,9,0). 913 [hyper,22,4,15,12,demod] CP(1,4,1,5,0). 914 [hyper,22,4,15,11,demod] CP(1,4,0,1,0). 915 [hyper,22,4,14,20,demod] CP(1,3,9,8,2). 916 [hyper,22,4,14,19,demod] CP(1,3,8,5,2). 917 [hyper,22,4,14,18,demod] CP(1,3,7,2,2). 918 [hyper,22,4,14,17,demod] CP(1,3,6,9,1). 919 [hyper,22,4,14,16,demod] CP(1,3,5,6,1). 920 [hyper,22,4,14,15,demod] CP(1,3,4,3,1). 921 [hyper,22,4,14,14,demod] CP(1,3,3,0,1). 922 [hyper,22,4,14,13,demod] CP(1,3,2,7,0). 923 [hyper,22,4,14,12,demod] CP(1,3,1,4,0). 924 [hyper,22,4,14,11,demod] CP(1,3,0,1,0). 925 [hyper,22,4,13,20,demod] CP(1,2,9,9,1). 926 [hyper,22,4,13,19,demod] CP(1,2,8,7,1). 927 [hyper,22,4,13,18,demod] CP(1,2,7,5,1). 928 [hyper,22,4,13,17,demod] CP(1,2,6,3,1). 929 [hyper,22,4,13,16,demod] CP(1,2,5,1,1). 930 [hyper,22,4,13,15,demod] CP(1,2,4,9,0). 931 [hyper,22,4,13,14,demod] CP(1,2,3,7,0). 932 [hyper,22,4,13,13,demod] CP(1,2,2,5,0). 933 [hyper,22,4,13,12,demod] CP(1,2,1,3,0). 934 [hyper,22,4,13,11,demod] CP(1,2,0,1,0). 935 [hyper,22,4,12,20,demod] CP(1,1,9,0,1). 936 [hyper,22,4,12,19,demod] CP(1,1,8,9,0). 937 [hyper,22,4,12,18,demod] CP(1,1,7,8,0). 938 [hyper,22,4,12,17,demod] CP(1,1,6,7,0). 939 [hyper,22,4,12,16,demod] CP(1,1,5,6,0). 940 [hyper,22,4,12,15,demod] CP(1,1,4,5,0). 941 [hyper,22,4,12,14,demod] CP(1,1,3,4,0). 942 [hyper,22,4,12,13,demod] CP(1,1,2,3,0). 943 [hyper,22,4,12,12,demod] CP(1,1,1,2,0). 944 [hyper,22,4,12,11,demod] CP(1,1,0,1,0). 945 [hyper,22,4,11,20,demod] CP(1,0,9,1,0). 946 [hyper,22,4,11,19,demod] CP(1,0,8,1,0). 947 [hyper,22,4,11,18,demod] CP(1,0,7,1,0). 948 [hyper,22,4,11,17,demod] CP(1,0,6,1,0). 949 [hyper,22,4,11,16,demod] CP(1,0,5,1,0). 950 [hyper,22,4,11,15,demod] CP(1,0,4,1,0). 951 [hyper,22,4,11,14,demod] CP(1,0,3,1,0). 952 [hyper,22,4,11,13,demod] CP(1,0,2,1,0). 953 [hyper,22,4,11,12,demod] CP(1,0,1,1,0). 954 [hyper,22,4,11,11,demod] CP(1,0,0,1,0). 955 [hyper,22,3,20,20,demod] CP(0,9,9,1,8). 956 [hyper,22,3,20,19,demod] CP(0,9,8,2,7). 957 [hyper,22,3,20,18,demod] CP(0,9,7,3,6). 958 [hyper,22,3,20,17,demod] CP(0,9,6,4,5). 959 [hyper,22,3,20,16,demod] CP(0,9,5,5,4). 960 [hyper,22,3,20,15,demod] CP(0,9,4,6,3). 961 [hyper,22,3,20,14,demod] CP(0,9,3,7,2). 962 [hyper,22,3,20,13,demod] CP(0,9,2,8,1). 963 [hyper,22,3,20,12,demod] CP(0,9,1,9,0). 964 [hyper,22,3,20,11,demod] CP(0,9,0,0,0). 965 [hyper,22,3,19,20,demod] CP(0,8,9,2,7). 966 [hyper,22,3,19,19,demod] CP(0,8,8,4,6). 967 [hyper,22,3,19,18,demod] CP(0,8,7,6,5). 968 [hyper,22,3,19,17,demod] CP(0,8,6,8,4). 969 [hyper,22,3,19,16,demod] CP(0,8,5,0,4). 970 [hyper,22,3,19,15,demod] CP(0,8,4,2,3). 971 [hyper,22,3,19,14,demod] CP(0,8,3,4,2). 972 [hyper,22,3,19,13,demod] CP(0,8,2,6,1). 973 [hyper,22,3,19,12,demod] CP(0,8,1,8,0). 974 [hyper,22,3,19,11,demod] CP(0,8,0,0,0). 975 [hyper,22,3,18,20,demod] CP(0,7,9,3,6). 976 [hyper,22,3,18,19,demod] CP(0,7,8,6,5). 977 [hyper,22,3,18,18,demod] CP(0,7,7,9,4). 978 [hyper,22,3,18,17,demod] CP(0,7,6,2,4). 979 [hyper,22,3,18,16,demod] CP(0,7,5,5,3). 980 [hyper,22,3,18,15,demod] CP(0,7,4,8,2). 981 [hyper,22,3,18,14,demod] CP(0,7,3,1,2). 982 [hyper,22,3,18,13,demod] CP(0,7,2,4,1). 983 [hyper,22,3,18,12,demod] CP(0,7,1,7,0). 984 [hyper,22,3,18,11,demod] CP(0,7,0,0,0). 985 [hyper,22,3,17,20,demod] CP(0,6,9,4,5). 986 [hyper,22,3,17,19,demod] CP(0,6,8,8,4). 987 [hyper,22,3,17,18,demod] CP(0,6,7,2,4). 988 [hyper,22,3,17,17,demod] CP(0,6,6,6,3). 989 [hyper,22,3,17,16,demod] CP(0,6,5,0,3). 990 [hyper,22,3,17,15,demod] CP(0,6,4,4,2). 991 [hyper,22,3,17,14,demod] CP(0,6,3,8,1). 992 [hyper,22,3,17,13,demod] CP(0,6,2,2,1). 993 [hyper,22,3,17,12,demod] CP(0,6,1,6,0). 994 [hyper,22,3,17,11,demod] CP(0,6,0,0,0). 995 [hyper,22,3,16,20,demod] CP(0,5,9,5,4). 996 [hyper,22,3,16,19,demod] CP(0,5,8,0,4). 997 [hyper,22,3,16,18,demod] CP(0,5,7,5,3). 998 [hyper,22,3,16,17,demod] CP(0,5,6,0,3). 999 [hyper,22,3,16,16,demod] CP(0,5,5,5,2). 1000 [hyper,22,3,16,15,demod] CP(0,5,4,0,2). 1001 [hyper,22,3,16,14,demod] CP(0,5,3,5,1). 1002 [hyper,22,3,16,13,demod] CP(0,5,2,0,1). 1003 [hyper,22,3,16,12,demod] CP(0,5,1,5,0). 1004 [hyper,22,3,16,11,demod] CP(0,5,0,0,0). 1005 [hyper,22,3,15,20,demod] CP(0,4,9,6,3). 1006 [hyper,22,3,15,19,demod] CP(0,4,8,2,3). 1007 [hyper,22,3,15,18,demod] CP(0,4,7,8,2). 1008 [hyper,22,3,15,17,demod] CP(0,4,6,4,2). 1009 [hyper,22,3,15,16,demod] CP(0,4,5,0,2). 1010 [hyper,22,3,15,15,demod] CP(0,4,4,6,1). 1011 [hyper,22,3,15,14,demod] CP(0,4,3,2,1). 1012 [hyper,22,3,15,13,demod] CP(0,4,2,8,0). 1013 [hyper,22,3,15,12,demod] CP(0,4,1,4,0). 1014 [hyper,22,3,15,11,demod] CP(0,4,0,0,0). 1015 [hyper,22,3,14,20,demod] CP(0,3,9,7,2). 1016 [hyper,22,3,14,19,demod] CP(0,3,8,4,2). 1017 [hyper,22,3,14,18,demod] CP(0,3,7,1,2). 1018 [hyper,22,3,14,17,demod] CP(0,3,6,8,1). 1019 [hyper,22,3,14,16,demod] CP(0,3,5,5,1). 1020 [hyper,22,3,14,15,demod] CP(0,3,4,2,1). 1021 [hyper,22,3,14,14,demod] CP(0,3,3,9,0). 1022 [hyper,22,3,14,13,demod] CP(0,3,2,6,0). 1023 [hyper,22,3,14,12,demod] CP(0,3,1,3,0). 1024 [hyper,22,3,14,11,demod] CP(0,3,0,0,0). 1025 [hyper,22,3,13,20,demod] CP(0,2,9,8,1). 1026 [hyper,22,3,13,19,demod] CP(0,2,8,6,1). 1027 [hyper,22,3,13,18,demod] CP(0,2,7,4,1). 1028 [hyper,22,3,13,17,demod] CP(0,2,6,2,1). 1029 [hyper,22,3,13,16,demod] CP(0,2,5,0,1). 1030 [hyper,22,3,13,15,demod] CP(0,2,4,8,0). 1031 [hyper,22,3,13,14,demod] CP(0,2,3,6,0). 1032 [hyper,22,3,13,13,demod] CP(0,2,2,4,0). 1033 [hyper,22,3,13,12,demod] CP(0,2,1,2,0). 1034 [hyper,22,3,13,11,demod] CP(0,2,0,0,0). 1035 [hyper,22,3,12,20,demod] CP(0,1,9,9,0). 1036 [hyper,22,3,12,19,demod] CP(0,1,8,8,0). 1037 [hyper,22,3,12,18,demod] CP(0,1,7,7,0). 1038 [hyper,22,3,12,17,demod] CP(0,1,6,6,0). 1039 [hyper,22,3,12,16,demod] CP(0,1,5,5,0). 1040 [hyper,22,3,12,15,demod] CP(0,1,4,4,0). 1041 [hyper,22,3,12,14,demod] CP(0,1,3,3,0). 1042 [hyper,22,3,12,13,demod] CP(0,1,2,2,0). 1043 [hyper,22,3,12,12,demod] CP(0,1,1,1,0). 1044 [hyper,22,3,12,11,demod] CP(0,1,0,0,0). 1045 [hyper,22,3,11,20,demod] CP(0,0,9,0,0). 1046 [hyper,22,3,11,19,demod] CP(0,0,8,0,0). 1047 [hyper,22,3,11,18,demod] CP(0,0,7,0,0). 1048 [hyper,22,3,11,17,demod] CP(0,0,6,0,0). 1049 [hyper,22,3,11,16,demod] CP(0,0,5,0,0). 1050 [hyper,22,3,11,15,demod] CP(0,0,4,0,0). 1051 [hyper,22,3,11,14,demod] CP(0,0,3,0,0). 1052 [hyper,22,3,11,13,demod] CP(0,0,2,0,0). 1053 [hyper,22,3,11,12,demod] CP(0,0,1,0,0). 1054 [hyper,22,3,11,11,demod] CP(0,0,0,0,0). 23 [] -CP(0,xd,xb,y1,x1)| -CP(x1,xd,xa,y2,y3)| -CP(0,xc,xb,z1,x2)| -CP(x2,xc,xa,z2,z3)| -$LT(xa,xc)| -CS(0,y1,0,xh,x3)| -CS(x3,y2,z1,xg,x4)| -CS(x4,y3,z2,xf,x5)| -CS(x5,0,z3,xe,0)|S(xa,xb,xc,xd,xe,xf,xg,xh). 1055 [hyper,23,1031,1029,961,759,eval,194,247,237,250] S(5,3,9,2,4,8,7,6). 1056 [hyper,23,1030,1031,1000,801,eval,174,194,247,253] S(3,4,5,2,1,7,6,8). 1057 [hyper,23,1029,930,969,570,eval,254,164,248,251] S(4,5,8,2,3,6,9,0). 1058 [hyper,23,1026,931,1006,711,eval,194,182,249,253] S(3,8,4,2,1,5,9,6). 1059 [hyper,23,1026,931,996,601,eval,194,184,245,253] S(3,8,5,2,1,9,7,6). 1060 [hyper,23,1006,709,986,589,eval,234,216,130,251] S(5,8,6,4,3,7,1,2). 1061 [hyper,23,1006,708,976,478,eval,234,178,127,150] S(6,8,7,4,5,0,3,2). 1062 [hyper,23,1005,711,995,601,eval,194,199,135,153] S(3,9,5,4,2,1,0,6). 1063 [hyper,23,1002,897,962,857,eval,254,186,120,248] S(7,2,9,5,6,8,4,0). 1064 [hyper,23,1000,797,970,667,eval,254,182,215,149] S(7,4,8,5,6,2,9,0). 1065 [hyper,23,998,700,968,570,eval,254,216,128,251] S(4,6,8,5,3,9,1,0). 1066 [hyper,23,996,601,986,591,eval,254,156,142,252] S(3,8,6,5,2,4,7,0). 1067 [hyper,23,996,600,986,590,eval,254,206,126,152] S(4,8,6,5,3,1,2,0). 1068 [hyper,23,991,892,1011,912,eval,174,222,235,154] S(2,3,4,6,1,0,5,8). 1069 [hyper,23,991,889,981,779,eval,174,243,217,151] S(5,3,7,6,4,0,2,8). 1070 [hyper,23,987,589,967,469,eval,234,208,119,250] S(5,7,8,6,4,9,0,2). 1071 [hyper,23,985,491,995,601,eval,214,219,225,153] S(3,9,5,6,2,1,8,4). 1072 [hyper,23,982,878,972,868,eval,214,218,205,150] S(6,2,8,7,5,3,9,4). 1073 [hyper,23,980,782,1000,802,eval,174,194,242,253] S(2,4,5,7,1,3,6,8). 1074 [hyper,23,970,671,1000,801,eval,234,184,227,253] S(3,4,5,8,1,9,7,2). 1075 [hyper,23,967,471,997,701,eval,194,159,126,153] S(3,7,5,8,2,1,4,6). 1076 [hyper,23,965,269,985,489,eval,234,180,109,151] S(5,9,6,8,4,0,1,2). 1077 [hyper,23,965,269,975,379,eval,234,181,113,250] S(5,9,7,8,4,6,0,2). 1078 [hyper,23,962,861,1012,1011,eval,174,166,132,253] S(3,2,4,9,1,5,6,8). 1079 [hyper,23,962,859,982,879,eval,174,190,108,151] S(5,2,7,9,4,1,0,8). 1080 [hyper,23,961,762,991,892,eval,184,246,231,253] S(2,3,6,9,1,5,8,7). end_of_list. list(sos). end_of_list. list(demodulators). end_of_list. -------------- statistics ------------- clauses given 1029 clauses generated 5374 clauses kept 1026 clauses forward subsumed 4348 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.38 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8469 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/ex_2.in0100644000076400007640000000121306011405564016445 0ustar mccunemccune% 2. This file produces a second proof of the result of ex_1. % Example ex_2 illustrates the lex command and the pick_given_ratio % parameter. % % Contributed by John Kalman (kalman@math.auckland.ac.nz) set(knuth_bendix). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(pick_given_ratio,1). assign(max_mem,5000). assign(stats_level,1). lex([a,b,c,_+_,_*_]). list(usable). x=x. x+y=y+x. x*y=y*x. (x+y)+z=x+y+z. (x*y)*z=x*y*z. x+ (x*y)=x. x* (x+y)=x. end_of_list. list(sos). x+ (y*z)= (x+y)* (x+z). a* (b+c)!= (a*b)+ (a*c). end_of_list. otter-3.3f/examples/kalman/ex_4.out0100664000076400007640000002161010103522156016647 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8454. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). op(350,xf,^). assign(pick_given_ratio,8). assign(stats_level,1). lex([a,b,c,e,_^ ,h(_,_),_*_]). list(usable). 0 [] x=x. 0 [] (x*y)*z=x*y*z. 0 [] e*x=x. 0 [] x^ *x=e. end_of_list. list(sos). 0 [] h(x,y)=x*y*x^ *y^ . 0 [] h(x,y)*z=z*h(x,y). 0 [] h(a,b*c)!=h(a,b)*h(a,c). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=11): 2 [] (x*y)*z=x*y*z. ---> New Demodulator: 3 [new_demod,2] (x*y)*z=x*y*z. ** KEPT (pick-wt=5): 4 [] e*x=x. ---> New Demodulator: 5 [new_demod,4] e*x=x. ** KEPT (pick-wt=6): 6 [] x^ *x=e. ---> New Demodulator: 7 [new_demod,6] x^ *x=e. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back demodulation with 3. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. ------------> process sos: ** KEPT (pick-wt=13): 9 [copy,8,flip.1] x*y*x^ *y^ =h(x,y). ---> New Demodulator: 10 [new_demod,9] x*y*x^ *y^ =h(x,y). ** KEPT (pick-wt=11): 11 [] h(x,y)*z=z*h(x,y). ** KEPT (pick-wt=13): 13 [copy,12,flip.1] h(a,b)*h(a,c)!=h(a,b*c). >>>> Starting back demodulation with 10. ** KEPT (pick-wt=11): 14 [copy,11,flip.1] x*h(y,z)=h(y,z)*x. Following clause subsumed by 11 during input processing: 0 [copy,14,flip.1] h(x,y)*z=z*h(x,y). ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=13) 9 [copy,8,flip.1] x*y*x^ *y^ =h(x,y). given clause #2: (wt=11) 15 [para_into,9.1.1.2.2,6.1.1] x^ *x*e=h(x^ ,x). given clause #3: (wt=6) 32 [para_into,15.1.1.2,4.1.1,demod,7,flip.1] h(e^ ,e)=e. given clause #4: (wt=11) 17 [para_into,9.1.1.2,4.1.1] x*x^ *e^ =h(x,e). given clause #5: (wt=9) 38 [para_into,17.1.1,4.1.1] e^ *e^ =h(e,e). given clause #6: (wt=11) 21 [para_into,9.1.1,4.1.1] x*e^ *x^ =h(e,x). given clause #7: (wt=12) 30 [para_into,15.1.1.2,6.1.1] (e^ )^ *e=h((e^ )^ ,e^ ). given clause #8: (wt=14) 46 [para_from,30.1.1,2.1.1.1,demod,26,37,5] (e^ )^ *e^ *x= (e^ )^ *x. given clause #9: (wt=9) 48 [para_into,46.1.1.2,38.1.1,demod,7] (e^ )^ *h(e,e)=e. given clause #10: (wt=19) 19 [para_into,9.1.1.2,2.1.1] x*y*z*x^ * (y*z)^ =h(x,y*z). given clause #11: (wt=4) 70 [back_demod,38,demod,67,65] e^ =e. given clause #12: (wt=5) 64 [back_demod,48,demod,57] h(e,e)=e. given clause #13: (wt=8) 74 [back_demod,60,demod,71] x*x^ =h(e,x). given clause #14: (wt=10) 78 [back_demod,17,demod,71] x*x^ *e=h(x,e). given clause #15: (wt=14) 72 [back_demod,42,demod,71,5] x*y* (x*y)^ =h(e,x*y). given clause #16: (wt=6) 112 [para_into,72.1.1.2.2.1,6.1.1,demod,71,16,7,65] h(x^ ,x)=e. given clause #17: (wt=8) 120 [back_demod,15,demod,113] x^ *x*e=e. given clause #18: (wt=8) 126 [para_from,120.1.1,2.1.1.1,demod,5,3,5,flip.1] x^ *x*y=y. given clause #19: (wt=19) 23 [para_into,9.1.1,2.1.1] x*y*z* (x*y)^ *z^ =h(x*y,z). given clause #20: (wt=5) 137 [para_into,126.1.1.2,6.1.1,demod,129] x*e=x. given clause #21: (wt=7) 148 [back_demod,78,demod,138,75] h(e,x)=h(x,e). given clause #22: (wt=7) 151 [copy,148,flip.1] h(x,e)=h(e,x). given clause #23: (wt=9) 128 [para_into,126.1.1.2,126.1.1] (x^ )^ *y=x*y. given clause #24: (wt=5) 188 [para_into,128.1.1,137.1.1,demod,138] (x^ )^ =x. given clause #25: (wt=5) 192 [para_into,128.1.1,6.1.1,demod,75,flip.1] h(e,x)=e. given clause #26: (wt=5) 196 [back_demod,154,demod,189,75,193,189,flip.1] h(x,x)=e. given clause #27: (wt=5) 205 [back_demod,96,demod,193,71,138,191,75,193,193,flip.1] h(x,e)=e. given clause #28: (wt=17) 25 [para_from,9.1.1,2.1.1.1,demod,3,3] h(x,y)*z=x*y*x^ *y^ *z. given clause #29: (wt=6) 207 [back_demod,94,demod,193,138,75,193,flip.1] h(x,x^ )=e. given clause #30: (wt=6) 219 [back_demod,74,demod,193] x*x^ =e. given clause #31: (wt=8) 190 [para_into,128.1.1,126.1.1,flip.1] x*x^ *y=y. given clause #32: (wt=9) 199 [back_demod,122,demod,193,138,75,193,flip.1] h(x,x^ *x^ )=e. given clause #33: (wt=8) 244 [para_into,199.1.1.2.1,188.1.1,demod,189] h(x^ ,x*x)=e. given clause #34: (wt=9) 209 [back_demod,143,demod,193,138] x* (y*x)^ =y^ . given clause #35: (wt=9) 250 [para_into,209.1.1.2.1,209.1.1,demod,189] (x*y)^ *x=y^ . given clause #36: (wt=10) 262 [para_from,209.1.1,190.1.1.2] x*y^ = (y*x^ )^ . given clause #37: (wt=17) 27 [back_demod,14,demod,26] x*h(y,z)=y*z*y^ *z^ *x. given clause #38: (wt=8) 298 [para_from,262.1.1,244.1.1.2,demod,189,189] h(x,(x*x)^ )=e. given clause #39: (wt=9) 308 [back_demod,221,demod,303] h(x,y*x)=h(x,y). given clause #40: (wt=10) 263 [para_from,209.1.1,19.1.1.2.2.2,demod,10,flip.1] h(x,y*x^ )=h(x,y). given clause #41: (wt=10) 267 [para_from,209.1.1,126.1.1.2] x^ *y^ = (y*x)^ . given clause #42: (wt=8) 370 [back_demod,325,demod,369,369,369,189,369,189,324] h(x,y)=h(y,x)^ . given clause #43: (wt=8) 390 [copy,370,flip.1] h(x,y)^ =h(y,x). given clause #44: (wt=7) 423 [para_from,390.1.1,9.1.1.2.2.1,demod,26,320,26,420,flip.1] h(h(x,y),z)=e. given clause #45: (wt=7) 440 [para_from,423.1.1,390.1.1.1,demod,71,flip.1] h(x,h(y,z))=e. given clause #46: (wt=19) 28 [back_demod,13,demod,26] a*b*a^ *b^ *h(a,c)!=h(a,b*c). given clause #47: (wt=8) 434 [para_into,423.1.1.1,370.1.1] h(h(x,y)^ ,z)=e. given clause #48: (wt=8) 458 [para_into,440.1.1.2,370.1.1] h(x,h(y,z)^ )=e. given clause #49: (wt=10) 270 [copy,262,flip.1] (x*y^ )^ =y*x^ . given clause #50: (wt=10) 271 [copy,267,flip.1] (x*y)^ =y^ *x^ . -------- PROOF -------- ----> UNIT CONFLICT at 0.03 sec ----> 492 [binary,490.1,463.1] $F. Length of proof is 37. Level of proof is 18. ---------------- PROOF ---------------- 3,2 [] (x*y)*z=x*y*z. 5,4 [] e*x=x. 7,6 [] x^ *x=e. 8 [] h(x,y)=x*y*x^ *y^ . 9 [copy,8,flip.1] x*y*x^ *y^ =h(x,y). 11 [] h(x,y)*z=z*h(x,y). 12 [] h(a,b*c)!=h(a,b)*h(a,c). 13 [copy,12,flip.1] h(a,b)*h(a,c)!=h(a,b*c). 14 [copy,11,flip.1] x*h(y,z)=h(y,z)*x. 16,15 [para_into,9.1.1.2.2,6.1.1] x^ *x*e=h(x^ ,x). 17 [para_into,9.1.1.2,4.1.1] x*x^ *e^ =h(x,e). 19 [para_into,9.1.1.2,2.1.1] x*y*z*x^ * (y*z)^ =h(x,y*z). 21 [para_into,9.1.1,4.1.1] x*e^ *x^ =h(e,x). 26,25 [para_from,9.1.1,2.1.1.1,demod,3,3] h(x,y)*z=x*y*x^ *y^ *z. 27 [back_demod,14,demod,26] x*h(y,z)=y*z*y^ *z^ *x. 28 [back_demod,13,demod,26] a*b*a^ *b^ *h(a,c)!=h(a,b*c). 30 [para_into,15.1.1.2,6.1.1] (e^ )^ *e=h((e^ )^ ,e^ ). 37,36 [para_from,15.1.1,2.1.1.1,demod,26,3,5] x^ *x* (x^ )^ *x^ *y=x^ *x*y. 38 [para_into,17.1.1,4.1.1] e^ *e^ =h(e,e). 42 [para_into,21.1.1,2.1.1] x*y*e^ * (x*y)^ =h(e,x*y). 47,46 [para_from,30.1.1,2.1.1.1,demod,26,37,5] (e^ )^ *e^ *x= (e^ )^ *x. 48 [para_into,46.1.1.2,38.1.1,demod,7] (e^ )^ *h(e,e)=e. 52 [para_into,46.1.1.2,9.1.1,flip.1] (e^ )^ *x* (e^ )^ *x^ = (e^ )^ *h(e^ ,x). 57,56 [para_from,48.1.1,2.1.1.1,demod,5,26,5,5,47,47,flip.1] (e^ )^ *x=x. 60 [back_demod,52,demod,57,57,57] x*x^ =h(e^ ,x). 65,64 [back_demod,48,demod,57] h(e,e)=e. 67,66 [back_demod,46,demod,57,57] e^ *x=x. 71,70 [back_demod,38,demod,67,65] e^ =e. 72 [back_demod,42,demod,71,5] x*y* (x*y)^ =h(e,x*y). 75,74 [back_demod,60,demod,71] x*x^ =h(e,x). 113,112 [para_into,72.1.1.2.2.1,6.1.1,demod,71,16,7,65] h(x^ ,x)=e. 120 [back_demod,15,demod,113] x^ *x*e=e. 127,126 [para_from,120.1.1,2.1.1.1,demod,5,3,5,flip.1] x^ *x*y=y. 129,128 [para_into,126.1.1.2,126.1.1] (x^ )^ *y=x*y. 134 [para_into,126.1.1.2,72.1.1] x^ *h(e,x*y)=y* (x*y)^ . 138,137 [para_into,126.1.1.2,6.1.1,demod,129] x*e=x. 143 [copy,134,flip.1] x* (y*x)^ =y^ *h(e,y*x). 193,192 [para_into,128.1.1,6.1.1,demod,75,flip.1] h(e,x)=e. 209 [back_demod,143,demod,193,138] x* (y*x)^ =y^ . 267 [para_from,209.1.1,126.1.1.2] x^ *y^ = (y*x)^ . 271 [copy,267,flip.1] (x*y)^ =y^ *x^ . 463 [para_into,28.1.1.2.2.2,27.1.1,demod,127] a*b*c*a^ *c^ *b^ !=h(a,b*c). 490 [para_from,271.1.1,19.1.1.2.2.2.2] x*y*z*x^ *z^ *y^ =h(x,y*z). 492 [binary,490.1,463.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 50 clauses generated 740 clauses kept 282 clauses forward subsumed 674 clauses back subsumed 2 Kbytes malloced 2929 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8454 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/ex_3.in0100644000076400007640000000155306011405515016451 0ustar mccunemccune% 3. If a lattice with join operation + and meet operation * % satisfies the equation (x*y)+(y*z)+(z*x) = (x+y)*(y+z)*(z+x) % then it satisfies both the equations in ex_1. In this example % the inclusion of the two negative unit clauses together, and % the particular choice of the pick_given_ratio parameter, % turn out to be very helpful. % % Contributed by John Kalman (kalman@math.auckland.ac.nz) % set(knuth_bendix). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(pick_given_ratio,10). assign(max_proofs,2). assign(stats_level,1). list(usable). x=x. x+y=y+x. x*y=y*x. (x+y)+z=x+y+z. (x*y)*z=x*y*z. x+ (x*y)=x. x* (x+y)=x. end_of_list. list(sos). (x*y)+ (y*z)+ (z*x)= (x+y) * (y+z) * (z+x). a+ (b*c)!= (a+b)* (a+c). d* (e+f)!= (d*e)+ (d*f). end_of_list. otter-3.3f/examples/kalman/ex_1.in0100644000076400007640000000131306011405156016442 0ustar mccunemccune% 1. If a lattice with join operation + and meet operation * % satisfies the equation x+(y*z) = (x+y)*(x+z) then it satisfies % the equation x*(y+z) = (x*y)+(x*z). This example illustrates % the sos_queue flag. % % Contributed by John Kalman (kalman@math.auckland.ac.nz) set(knuth_bendix). clear(print_kept). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). set(sos_queue). % assign(pick_given_ratio,1). assign(max_mem,5000). assign(stats_level,1). list(usable). x=x. x+y=y+x. x*y=y*x. (x+y)+z=x+y+z. (x*y)*z=x*y*z. x+ (x*y)=x. x* (x+y)=x. end_of_list. list(sos). x+ (y*z)= (x+y)* (x+z). a* (b+c)!= (a*b)+ (a*c). end_of_list. otter-3.3f/examples/kalman/i4.out0100664000076400007640000061456210103522156016342 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8474. set(hyper_res). assign(stats_level,1). assign(max_given,2000). list(usable). 1 [] -H(C,xA,xB,xC,xD,xE,xF)|K1(C,F,xC,xF,xA,xB,xD,xE). 2 [] -H(D,xA,xB,xC,xD,xE,xF)|K1(D,B,xD,xB,xA,xC,xE,xF). 3 [] -H(D,xA,xB,xC,xD,xE,xF)|K1(D,E,xD,xE,xA,xB,xC,xF). 4 [] -H(E,xA,xB,xC,xD,xE,xF)|K1(E,F,xE,xF,xA,xB,xC,xD). 5 [] -K1(u,v,y,z,x1,x2,x3,x4)|K2(u,v,[],app(y,z),x1,x2,x3,x4). 6 [] -K1(u,v,[y0|y1],z,x1,x2,x3,x4)| -$TRUE(member(R,y1))|K2(u,v,[y0],app(y1,z),x1,x2,x3,x4). 7 [] -K1(u,v,[y0,y00,R],[],x1,x2,x3,x4)|K2(u,v,[y0,y00],[R],x1,x2,x3,x4). 8 [] -K2(C,F,xC,xF,xA,xB,xD,xE)|H(F,xA,xB,xC,xD,xE,xF). 9 [] -K2(D,B,xD,xB,xA,xC,xE,xF)|H(B,xA,xB,xC,xD,xE,xF). 10 [] -K2(D,E,xD,xE,xA,xB,xC,xF)|H(E,xA,xB,xC,xD,xE,xF). 11 [] -K2(E,F,xE,xF,xA,xB,xC,xD)|H(F,xA,xB,xC,xD,xE,xF). 12 [] -H(B,xA,xB,xC,xD,xE,xF)|K1(B,D,rev(xB),rev(xD),xA,xC,xE,xF). 13 [] -H(E,xA,xB,xC,xD,xE,xF)|K1(E,D,rev(xE),rev(xD),xA,xB,xC,xF). 14 [] -H(F,xA,xB,xC,xD,xE,xF)|K1(F,C,rev(xF),rev(xC),xA,xB,xD,xE). 15 [] -H(F,xA,xB,xC,xD,xE,xF)|K1(F,E,rev(xF),rev(xE),xA,xB,xC,xD). 16 [] -K2(B,D,xB,xD,xA,xC,xE,xF)|H(D,xA,rev(xB),xC,rev(xD),xE,xF). 17 [] -K2(E,D,xE,xD,xA,xB,xC,xF)|H(D,xA,xB,xC,rev(xD),rev(xE),xF). 18 [] -K2(F,C,xF,xC,xA,xB,xD,xE)|H(C,xA,xB,rev(xC),xD,xE,rev(xF)). 19 [] -K2(F,E,xF,xE,xA,xB,xC,xD)|H(E,xA,xB,xC,xD,rev(xE),rev(xF)). 20 [] -H(B,[],[R,u],xC,xD,xE,xF)|H(B,[u],[R],xC,xD,xE,xF). 21 [] -H(B,[],[R,u,v],xC,xD,xE,xF)|H(B,[v],[R,u],xC,xD,xE,xF). 22 [] -H(B,[],[u,R,v],xC,xD,xE,xF)|H(B,[v],[u,R],xC,xD,xE,xF). 23 [] -H(B,[u],xB,xC,xD,xE,xF)|H(B,[],app(xB,[u]),xC,xD,xE,xF). 24 [] -H(C,[],xB,[y0|y1],xD,xE,xF)| -$TRUE(member(R,y1))|H(C,[y0],xB,y1,xD,xE,xF). 25 [] -H(C,[y0],xB,y1,xD,xE,xF)|H(C,[],xB,[y0|y1],xD,xE,xF). end_of_list. list(sos). 26 [] H(E,[],[P],[Q],[],[R],[]). end_of_list. list(passive). 27 [] -H(E,[],[Q],[P],[],[R],[]). end_of_list. list(demodulators). 28 [] member(x,[])=$F. 29 [] member(x,[u|v])=$IF($ID(x,u),$T,member(x,v)). 30 [] rev(x)=rev2(x,[]). 31 [] rev2([],x)=x. 32 [] rev2([y1|y2],z)=rev2(y2,[y1|z]). 33 [] app([u|v],y)=[u|app(v,y)]. 34 [] app([],y)=y. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=14) 26 [] H(E,[],[P],[Q],[],[R],[]). ** KEPT (pick-wt=15): 35 [hyper,26,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 36 [hyper,26,4] K1(E,F,[R],[],[],[P],[Q],[]). given clause #2: (wt=15) 35 [hyper,26,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 37 [hyper,35,5,demod,33,34] K2(E,D,[],[R],[],[P],[Q],[]). given clause #3: (wt=15) 36 [hyper,26,4] K1(E,F,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 38 [hyper,36,5,demod,33,34] K2(E,F,[],[R],[],[P],[Q],[]). given clause #4: (wt=15) 37 [hyper,35,5,demod,33,34] K2(E,D,[],[R],[],[P],[Q],[]). ** KEPT (pick-wt=14): 39 [hyper,37,17,demod,30,32,31,30,31] H(D,[],[P],[Q],[R],[],[]). given clause #5: (wt=14) 39 [hyper,37,17,demod,30,32,31,30,31] H(D,[],[P],[Q],[R],[],[]). ** KEPT (pick-wt=15): 40 [hyper,39,3] K1(D,E,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 41 [hyper,39,2] K1(D,B,[R],[P],[],[Q],[],[]). given clause #6: (wt=15) 38 [hyper,36,5,demod,33,34] K2(E,F,[],[R],[],[P],[Q],[]). ** KEPT (pick-wt=14): 42 [hyper,38,11] H(F,[],[P],[Q],[],[],[R]). given clause #7: (wt=14) 42 [hyper,38,11] H(F,[],[P],[Q],[],[],[R]). ** KEPT (pick-wt=15): 43 [hyper,42,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 44 [hyper,42,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[],[P],[],[]). given clause #8: (wt=15) 40 [hyper,39,3] K1(D,E,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 45 [hyper,40,5,demod,33,34] K2(D,E,[],[R],[],[P],[Q],[]). given clause #9: (wt=15) 41 [hyper,39,2] K1(D,B,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 46 [hyper,41,5,demod,33,34] K2(D,B,[],[R,P],[],[Q],[],[]). given clause #10: (wt=15) 43 [hyper,42,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 47 [hyper,43,5,demod,33,34] K2(F,E,[],[R],[],[P],[Q],[]). given clause #11: (wt=15) 44 [hyper,42,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 48 [hyper,44,5,demod,33,34] K2(F,C,[],[R,Q],[],[P],[],[]). given clause #12: (wt=15) 45 [hyper,40,5,demod,33,34] K2(D,E,[],[R],[],[P],[Q],[]). given clause #13: (wt=15) 46 [hyper,41,5,demod,33,34] K2(D,B,[],[R,P],[],[Q],[],[]). ** KEPT (pick-wt=14): 49 [hyper,46,9] H(B,[],[R,P],[Q],[],[],[]). given clause #14: (wt=14) 49 [hyper,46,9] H(B,[],[R,P],[Q],[],[],[]). ** KEPT (pick-wt=14): 50 [hyper,49,20] H(B,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 51 [hyper,49,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[Q],[],[]). given clause #15: (wt=14) 50 [hyper,49,20] H(B,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 52 [hyper,50,12,demod,30,32,31,30,31] K1(B,D,[R],[],[P],[Q],[],[]). given clause #16: (wt=15) 47 [hyper,43,5,demod,33,34] K2(F,E,[],[R],[],[P],[Q],[]). given clause #17: (wt=15) 48 [hyper,44,5,demod,33,34] K2(F,C,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=14): 53 [hyper,48,18,demod,30,32,32,31,30,31] H(C,[],[P],[Q,R],[],[],[]). given clause #18: (wt=14) 53 [hyper,48,18,demod,30,32,32,31,30,31] H(C,[],[P],[Q,R],[],[],[]). ** KEPT (pick-wt=14): 54 [hyper,53,24,eval] H(C,[Q],[P],[R],[],[],[]). ** KEPT (pick-wt=15): 55 [hyper,53,1] K1(C,F,[Q,R],[],[],[P],[],[]). given clause #19: (wt=14) 54 [hyper,53,24,eval] H(C,[Q],[P],[R],[],[],[]). ** KEPT (pick-wt=15): 56 [hyper,54,1] K1(C,F,[R],[],[Q],[P],[],[]). given clause #20: (wt=15) 51 [hyper,49,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 57 [hyper,51,6,eval,demod,33,34] K2(B,D,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 58 [hyper,51,5,demod,33,33,34] K2(B,D,[],[P,R],[],[Q],[],[]). given clause #21: (wt=15) 52 [hyper,50,12,demod,30,32,31,30,31] K1(B,D,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 59 [hyper,52,5,demod,33,34] K2(B,D,[],[R],[P],[Q],[],[]). given clause #22: (wt=15) 55 [hyper,53,1] K1(C,F,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 60 [hyper,55,6,eval,demod,33,34] K2(C,F,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 61 [hyper,55,5,demod,33,33,34] K2(C,F,[],[Q,R],[],[P],[],[]). given clause #23: (wt=15) 56 [hyper,54,1] K1(C,F,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 62 [hyper,56,5,demod,33,34] K2(C,F,[],[R],[Q],[P],[],[]). given clause #24: (wt=15) 57 [hyper,51,6,eval,demod,33,34] K2(B,D,[P],[R],[],[Q],[],[]). given clause #25: (wt=15) 58 [hyper,51,5,demod,33,33,34] K2(B,D,[],[P,R],[],[Q],[],[]). ** KEPT (pick-wt=14): 63 [hyper,58,16,demod,30,31,30,32,32,31] H(D,[],[],[Q],[R,P],[],[]). given clause #26: (wt=14) 63 [hyper,58,16,demod,30,31,30,32,32,31] H(D,[],[],[Q],[R,P],[],[]). ** KEPT (pick-wt=15): 64 [hyper,63,3] K1(D,E,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 65 [hyper,63,2] K1(D,B,[R,P],[],[],[Q],[],[]). given clause #27: (wt=15) 59 [hyper,52,5,demod,33,34] K2(B,D,[],[R],[P],[Q],[],[]). ** KEPT (pick-wt=14): 66 [hyper,59,16,demod,30,31,30,32,31] H(D,[P],[],[Q],[R],[],[]). given clause #28: (wt=14) 66 [hyper,59,16,demod,30,31,30,32,31] H(D,[P],[],[Q],[R],[],[]). ** KEPT (pick-wt=15): 67 [hyper,66,3] K1(D,E,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 68 [hyper,66,2] K1(D,B,[R],[],[P],[Q],[],[]). given clause #29: (wt=15) 60 [hyper,55,6,eval,demod,33,34] K2(C,F,[Q],[R],[],[P],[],[]). given clause #30: (wt=15) 61 [hyper,55,5,demod,33,33,34] K2(C,F,[],[Q,R],[],[P],[],[]). ** KEPT (pick-wt=14): 69 [hyper,61,8] H(F,[],[P],[],[],[],[Q,R]). given clause #31: (wt=14) 69 [hyper,61,8] H(F,[],[P],[],[],[],[Q,R]). ** KEPT (pick-wt=15): 70 [hyper,69,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 71 [hyper,69,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[],[P],[],[]). given clause #32: (wt=15) 62 [hyper,56,5,demod,33,34] K2(C,F,[],[R],[Q],[P],[],[]). ** KEPT (pick-wt=14): 72 [hyper,62,8] H(F,[Q],[P],[],[],[],[R]). given clause #33: (wt=14) 72 [hyper,62,8] H(F,[Q],[P],[],[],[],[R]). ** KEPT (pick-wt=15): 73 [hyper,72,15,demod,30,32,31,30,31] K1(F,E,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 74 [hyper,72,14,demod,30,32,31,30,31] K1(F,C,[R],[],[Q],[P],[],[]). given clause #34: (wt=15) 64 [hyper,63,3] K1(D,E,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 75 [hyper,64,5,demod,33,33,34] K2(D,E,[],[R,P],[],[],[Q],[]). given clause #35: (wt=15) 65 [hyper,63,2] K1(D,B,[R,P],[],[],[Q],[],[]). given clause #36: (wt=15) 67 [hyper,66,3] K1(D,E,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 76 [hyper,67,5,demod,33,34] K2(D,E,[],[R],[P],[],[Q],[]). given clause #37: (wt=15) 68 [hyper,66,2] K1(D,B,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 77 [hyper,68,5,demod,33,34] K2(D,B,[],[R],[P],[Q],[],[]). given clause #38: (wt=15) 70 [hyper,69,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 78 [hyper,70,5,demod,33,33,34] K2(F,E,[],[R,Q],[],[P],[],[]). given clause #39: (wt=15) 71 [hyper,69,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[],[P],[],[]). given clause #40: (wt=15) 73 [hyper,72,15,demod,30,32,31,30,31] K1(F,E,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 79 [hyper,73,5,demod,33,34] K2(F,E,[],[R],[Q],[P],[],[]). given clause #41: (wt=15) 74 [hyper,72,14,demod,30,32,31,30,31] K1(F,C,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 80 [hyper,74,5,demod,33,34] K2(F,C,[],[R],[Q],[P],[],[]). given clause #42: (wt=15) 75 [hyper,64,5,demod,33,33,34] K2(D,E,[],[R,P],[],[],[Q],[]). ** KEPT (pick-wt=14): 81 [hyper,75,10] H(E,[],[],[Q],[],[R,P],[]). given clause #43: (wt=14) 81 [hyper,75,10] H(E,[],[],[Q],[],[R,P],[]). ** KEPT (pick-wt=15): 82 [hyper,81,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 83 [hyper,81,4] K1(E,F,[R,P],[],[],[],[Q],[]). given clause #44: (wt=15) 76 [hyper,67,5,demod,33,34] K2(D,E,[],[R],[P],[],[Q],[]). ** KEPT (pick-wt=14): 84 [hyper,76,10] H(E,[P],[],[Q],[],[R],[]). given clause #45: (wt=14) 84 [hyper,76,10] H(E,[P],[],[Q],[],[R],[]). ** KEPT (pick-wt=15): 85 [hyper,84,13,demod,30,32,31,30,31] K1(E,D,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 86 [hyper,84,4] K1(E,F,[R],[],[P],[],[Q],[]). given clause #46: (wt=15) 77 [hyper,68,5,demod,33,34] K2(D,B,[],[R],[P],[Q],[],[]). given clause #47: (wt=15) 78 [hyper,70,5,demod,33,33,34] K2(F,E,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=14): 87 [hyper,78,19,demod,30,32,32,31,30,31] H(E,[],[P],[],[],[Q,R],[]). given clause #48: (wt=14) 87 [hyper,78,19,demod,30,32,32,31,30,31] H(E,[],[P],[],[],[Q,R],[]). ** KEPT (pick-wt=15): 88 [hyper,87,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 89 [hyper,87,4] K1(E,F,[Q,R],[],[],[P],[],[]). given clause #49: (wt=15) 79 [hyper,73,5,demod,33,34] K2(F,E,[],[R],[Q],[P],[],[]). ** KEPT (pick-wt=14): 90 [hyper,79,19,demod,30,32,31,30,31] H(E,[Q],[P],[],[],[R],[]). given clause #50: (wt=14) 90 [hyper,79,19,demod,30,32,31,30,31] H(E,[Q],[P],[],[],[R],[]). ** KEPT (pick-wt=15): 91 [hyper,90,13,demod,30,32,31,30,31] K1(E,D,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 92 [hyper,90,4] K1(E,F,[R],[],[Q],[P],[],[]). given clause #51: (wt=15) 80 [hyper,74,5,demod,33,34] K2(F,C,[],[R],[Q],[P],[],[]). given clause #52: (wt=15) 82 [hyper,81,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 93 [hyper,82,6,eval,demod,33,34] K2(E,D,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 94 [hyper,82,5,demod,33,33,34] K2(E,D,[],[P,R],[],[],[Q],[]). given clause #53: (wt=15) 83 [hyper,81,4] K1(E,F,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 95 [hyper,83,5,demod,33,33,34] K2(E,F,[],[R,P],[],[],[Q],[]). given clause #54: (wt=15) 85 [hyper,84,13,demod,30,32,31,30,31] K1(E,D,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 96 [hyper,85,5,demod,33,34] K2(E,D,[],[R],[P],[],[Q],[]). given clause #55: (wt=15) 86 [hyper,84,4] K1(E,F,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 97 [hyper,86,5,demod,33,34] K2(E,F,[],[R],[P],[],[Q],[]). given clause #56: (wt=15) 88 [hyper,87,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 98 [hyper,88,5,demod,33,33,34] K2(E,D,[],[R,Q],[],[P],[],[]). given clause #57: (wt=15) 89 [hyper,87,4] K1(E,F,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 99 [hyper,89,6,eval,demod,33,34] K2(E,F,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 100 [hyper,89,5,demod,33,33,34] K2(E,F,[],[Q,R],[],[P],[],[]). given clause #58: (wt=15) 91 [hyper,90,13,demod,30,32,31,30,31] K1(E,D,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 101 [hyper,91,5,demod,33,34] K2(E,D,[],[R],[Q],[P],[],[]). given clause #59: (wt=15) 92 [hyper,90,4] K1(E,F,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 102 [hyper,92,5,demod,33,34] K2(E,F,[],[R],[Q],[P],[],[]). given clause #60: (wt=15) 93 [hyper,82,6,eval,demod,33,34] K2(E,D,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=14): 103 [hyper,93,17,demod,30,32,31,30,32,31] H(D,[],[],[Q],[R],[P],[]). given clause #61: (wt=14) 103 [hyper,93,17,demod,30,32,31,30,32,31] H(D,[],[],[Q],[R],[P],[]). ** KEPT (pick-wt=15): 104 [hyper,103,3] K1(D,E,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 105 [hyper,103,2] K1(D,B,[R],[],[],[Q],[P],[]). given clause #62: (wt=15) 94 [hyper,82,5,demod,33,33,34] K2(E,D,[],[P,R],[],[],[Q],[]). given clause #63: (wt=15) 95 [hyper,83,5,demod,33,33,34] K2(E,F,[],[R,P],[],[],[Q],[]). ** KEPT (pick-wt=14): 106 [hyper,95,11] H(F,[],[],[Q],[],[],[R,P]). given clause #64: (wt=14) 106 [hyper,95,11] H(F,[],[],[Q],[],[],[R,P]). ** KEPT (pick-wt=15): 107 [hyper,106,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 108 [hyper,106,14,demod,30,32,32,31,30,32,31] K1(F,C,[P,R],[Q],[],[],[],[]). given clause #65: (wt=15) 96 [hyper,85,5,demod,33,34] K2(E,D,[],[R],[P],[],[Q],[]). given clause #66: (wt=15) 97 [hyper,86,5,demod,33,34] K2(E,F,[],[R],[P],[],[Q],[]). ** KEPT (pick-wt=14): 109 [hyper,97,11] H(F,[P],[],[Q],[],[],[R]). given clause #67: (wt=14) 109 [hyper,97,11] H(F,[P],[],[Q],[],[],[R]). ** KEPT (pick-wt=15): 110 [hyper,109,15,demod,30,32,31,30,31] K1(F,E,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 111 [hyper,109,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[P],[],[],[]). given clause #68: (wt=15) 98 [hyper,88,5,demod,33,33,34] K2(E,D,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=14): 112 [hyper,98,17,demod,30,32,32,31,30,31] H(D,[],[P],[],[Q,R],[],[]). given clause #69: (wt=14) 112 [hyper,98,17,demod,30,32,32,31,30,31] H(D,[],[P],[],[Q,R],[],[]). ** KEPT (pick-wt=15): 113 [hyper,112,3] K1(D,E,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 114 [hyper,112,2] K1(D,B,[Q,R],[P],[],[],[],[]). given clause #70: (wt=15) 99 [hyper,89,6,eval,demod,33,34] K2(E,F,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 115 [hyper,99,11] H(F,[],[P],[],[],[Q],[R]). given clause #71: (wt=14) 115 [hyper,99,11] H(F,[],[P],[],[],[Q],[R]). ** KEPT (pick-wt=15): 116 [hyper,115,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 117 [hyper,115,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[P],[],[Q]). given clause #72: (wt=15) 100 [hyper,89,5,demod,33,33,34] K2(E,F,[],[Q,R],[],[P],[],[]). given clause #73: (wt=15) 101 [hyper,91,5,demod,33,34] K2(E,D,[],[R],[Q],[P],[],[]). ** KEPT (pick-wt=14): 118 [hyper,101,17,demod,30,32,31,30,31] H(D,[Q],[P],[],[R],[],[]). given clause #74: (wt=14) 118 [hyper,101,17,demod,30,32,31,30,31] H(D,[Q],[P],[],[R],[],[]). ** KEPT (pick-wt=15): 119 [hyper,118,3] K1(D,E,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 120 [hyper,118,2] K1(D,B,[R],[P],[Q],[],[],[]). given clause #75: (wt=15) 102 [hyper,92,5,demod,33,34] K2(E,F,[],[R],[Q],[P],[],[]). given clause #76: (wt=15) 104 [hyper,103,3] K1(D,E,[R],[P],[],[],[Q],[]). given clause #77: (wt=15) 105 [hyper,103,2] K1(D,B,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 121 [hyper,105,5,demod,33,34] K2(D,B,[],[R],[],[Q],[P],[]). given clause #78: (wt=15) 107 [hyper,106,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 122 [hyper,107,6,eval,demod,33,34] K2(F,E,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 123 [hyper,107,5,demod,33,33,34] K2(F,E,[],[P,R],[],[],[Q],[]). given clause #79: (wt=15) 108 [hyper,106,14,demod,30,32,32,31,30,32,31] K1(F,C,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 124 [hyper,108,6,eval,demod,33,34] K2(F,C,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 125 [hyper,108,5,demod,33,33,34] K2(F,C,[],[P,R,Q],[],[],[],[]). given clause #80: (wt=15) 110 [hyper,109,15,demod,30,32,31,30,31] K1(F,E,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 126 [hyper,110,5,demod,33,34] K2(F,E,[],[R],[P],[],[Q],[]). given clause #81: (wt=15) 111 [hyper,109,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 127 [hyper,111,5,demod,33,34] K2(F,C,[],[R,Q],[P],[],[],[]). given clause #82: (wt=15) 113 [hyper,112,3] K1(D,E,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 128 [hyper,113,6,eval,demod,33,34] K2(D,E,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 129 [hyper,113,5,demod,33,33,34] K2(D,E,[],[Q,R],[],[P],[],[]). given clause #83: (wt=15) 114 [hyper,112,2] K1(D,B,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 130 [hyper,114,6,eval,demod,33,34] K2(D,B,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 131 [hyper,114,5,demod,33,33,34] K2(D,B,[],[Q,R,P],[],[],[],[]). given clause #84: (wt=15) 116 [hyper,115,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[],[P],[],[]). given clause #85: (wt=15) 117 [hyper,115,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 132 [hyper,117,5,demod,33,34] K2(F,C,[],[R],[],[P],[],[Q]). given clause #86: (wt=15) 119 [hyper,118,3] K1(D,E,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 133 [hyper,119,5,demod,33,34] K2(D,E,[],[R],[Q],[P],[],[]). given clause #87: (wt=15) 120 [hyper,118,2] K1(D,B,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 134 [hyper,120,5,demod,33,34] K2(D,B,[],[R,P],[Q],[],[],[]). given clause #88: (wt=15) 121 [hyper,105,5,demod,33,34] K2(D,B,[],[R],[],[Q],[P],[]). ** KEPT (pick-wt=14): 135 [hyper,121,9] H(B,[],[R],[Q],[],[P],[]). given clause #89: (wt=14) 135 [hyper,121,9] H(B,[],[R],[Q],[],[P],[]). ** KEPT (pick-wt=15): 136 [hyper,135,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[Q],[P],[]). given clause #90: (wt=15) 122 [hyper,107,6,eval,demod,33,34] K2(F,E,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=14): 137 [hyper,122,19,demod,30,32,31,30,32,31] H(E,[],[],[Q],[],[R],[P]). given clause #91: (wt=14) 137 [hyper,122,19,demod,30,32,31,30,32,31] H(E,[],[],[Q],[],[R],[P]). ** KEPT (pick-wt=15): 138 [hyper,137,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 139 [hyper,137,4] K1(E,F,[R],[P],[],[],[Q],[]). given clause #92: (wt=15) 123 [hyper,107,5,demod,33,33,34] K2(F,E,[],[P,R],[],[],[Q],[]). given clause #93: (wt=15) 124 [hyper,108,6,eval,demod,33,34] K2(F,C,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 140 [hyper,124,18,demod,30,32,32,31,30,32,31] H(C,[],[],[Q,R],[],[],[P]). given clause #94: (wt=14) 140 [hyper,124,18,demod,30,32,32,31,30,32,31] H(C,[],[],[Q,R],[],[],[P]). ** KEPT (pick-wt=14): 141 [hyper,140,24,eval] H(C,[Q],[],[R],[],[],[P]). ** KEPT (pick-wt=15): 142 [hyper,140,1] K1(C,F,[Q,R],[P],[],[],[],[]). given clause #95: (wt=14) 141 [hyper,140,24,eval] H(C,[Q],[],[R],[],[],[P]). ** KEPT (pick-wt=15): 143 [hyper,141,1] K1(C,F,[R],[P],[Q],[],[],[]). given clause #96: (wt=15) 125 [hyper,108,5,demod,33,33,34] K2(F,C,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 144 [hyper,125,18,demod,30,32,32,32,31,30,31] H(C,[],[],[Q,R,P],[],[],[]). given clause #97: (wt=14) 144 [hyper,125,18,demod,30,32,32,32,31,30,31] H(C,[],[],[Q,R,P],[],[],[]). ** KEPT (pick-wt=14): 145 [hyper,144,24,eval] H(C,[Q],[],[R,P],[],[],[]). ** KEPT (pick-wt=15): 146 [hyper,144,1] K1(C,F,[Q,R,P],[],[],[],[],[]). given clause #98: (wt=14) 145 [hyper,144,24,eval] H(C,[Q],[],[R,P],[],[],[]). ** KEPT (pick-wt=15): 147 [hyper,145,1] K1(C,F,[R,P],[],[Q],[],[],[]). given clause #99: (wt=15) 126 [hyper,110,5,demod,33,34] K2(F,E,[],[R],[P],[],[Q],[]). given clause #100: (wt=15) 127 [hyper,111,5,demod,33,34] K2(F,C,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=14): 148 [hyper,127,18,demod,30,32,32,31,30,31] H(C,[P],[],[Q,R],[],[],[]). given clause #101: (wt=14) 148 [hyper,127,18,demod,30,32,32,31,30,31] H(C,[P],[],[Q,R],[],[],[]). ** KEPT (pick-wt=14): 149 [hyper,148,25] H(C,[],[],[P,Q,R],[],[],[]). ** KEPT (pick-wt=15): 150 [hyper,148,1] K1(C,F,[Q,R],[],[P],[],[],[]). given clause #102: (wt=14) 149 [hyper,148,25] H(C,[],[],[P,Q,R],[],[],[]). ** KEPT (pick-wt=15): 151 [hyper,149,1] K1(C,F,[P,Q,R],[],[],[],[],[]). given clause #103: (wt=15) 128 [hyper,113,6,eval,demod,33,34] K2(D,E,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 152 [hyper,128,10] H(E,[],[P],[],[Q],[R],[]). given clause #104: (wt=14) 152 [hyper,128,10] H(E,[],[P],[],[Q],[R],[]). ** KEPT (pick-wt=15): 153 [hyper,152,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 154 [hyper,152,4] K1(E,F,[R],[],[],[P],[],[Q]). given clause #105: (wt=15) 129 [hyper,113,5,demod,33,33,34] K2(D,E,[],[Q,R],[],[P],[],[]). given clause #106: (wt=15) 130 [hyper,114,6,eval,demod,33,34] K2(D,B,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 155 [hyper,130,9] H(B,[],[R,P],[],[Q],[],[]). given clause #107: (wt=14) 155 [hyper,130,9] H(B,[],[R,P],[],[Q],[],[]). ** KEPT (pick-wt=14): 156 [hyper,155,20] H(B,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 157 [hyper,155,12,demod,30,32,32,31,30,32,31] K1(B,D,[P,R],[Q],[],[],[],[]). given clause #108: (wt=14) 156 [hyper,155,20] H(B,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 158 [hyper,156,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[P],[],[],[]). given clause #109: (wt=15) 131 [hyper,114,5,demod,33,33,34] K2(D,B,[],[Q,R,P],[],[],[],[]). ** KEPT (pick-wt=14): 159 [hyper,131,9] H(B,[],[Q,R,P],[],[],[],[]). given clause #110: (wt=14) 159 [hyper,131,9] H(B,[],[Q,R,P],[],[],[],[]). ** KEPT (pick-wt=14): 160 [hyper,159,22] H(B,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 161 [hyper,159,12,demod,30,32,32,32,31,30,31] K1(B,D,[P,R,Q],[],[],[],[],[]). given clause #111: (wt=14) 160 [hyper,159,22] H(B,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 162 [hyper,160,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[P],[],[],[]). given clause #112: (wt=15) 132 [hyper,117,5,demod,33,34] K2(F,C,[],[R],[],[P],[],[Q]). ** KEPT (pick-wt=14): 163 [hyper,132,18,demod,30,32,31,30,31] H(C,[],[P],[R],[],[Q],[]). given clause #113: (wt=14) 163 [hyper,132,18,demod,30,32,31,30,31] H(C,[],[P],[R],[],[Q],[]). ** KEPT (pick-wt=15): 164 [hyper,163,1] K1(C,F,[R],[],[],[P],[],[Q]). given clause #114: (wt=15) 133 [hyper,119,5,demod,33,34] K2(D,E,[],[R],[Q],[P],[],[]). given clause #115: (wt=15) 134 [hyper,120,5,demod,33,34] K2(D,B,[],[R,P],[Q],[],[],[]). ** KEPT (pick-wt=14): 165 [hyper,134,9] H(B,[Q],[R,P],[],[],[],[]). given clause #116: (wt=14) 165 [hyper,134,9] H(B,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 166 [hyper,165,23,demod,33,33,34] H(B,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 167 [hyper,165,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[Q],[],[],[]). given clause #117: (wt=14) 166 [hyper,165,23,demod,33,33,34] H(B,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 168 [hyper,166,12,demod,30,32,32,32,31,30,31] K1(B,D,[Q,P,R],[],[],[],[],[]). given clause #118: (wt=15) 136 [hyper,135,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 169 [hyper,136,5,demod,33,34] K2(B,D,[],[R],[],[Q],[P],[]). given clause #119: (wt=15) 138 [hyper,137,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 170 [hyper,138,5,demod,33,34] K2(E,D,[],[R],[],[],[Q],[P]). given clause #120: (wt=15) 139 [hyper,137,4] K1(E,F,[R],[P],[],[],[Q],[]). given clause #121: (wt=15) 142 [hyper,140,1] K1(C,F,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 171 [hyper,142,6,eval,demod,33,34] K2(C,F,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 172 [hyper,142,5,demod,33,33,34] K2(C,F,[],[Q,R,P],[],[],[],[]). given clause #122: (wt=15) 143 [hyper,141,1] K1(C,F,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 173 [hyper,143,5,demod,33,34] K2(C,F,[],[R,P],[Q],[],[],[]). given clause #123: (wt=15) 146 [hyper,144,1] K1(C,F,[Q,R,P],[],[],[],[],[]). given clause #124: (wt=15) 147 [hyper,145,1] K1(C,F,[R,P],[],[Q],[],[],[]). given clause #125: (wt=15) 150 [hyper,148,1] K1(C,F,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 174 [hyper,150,6,eval,demod,33,34] K2(C,F,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 175 [hyper,150,5,demod,33,33,34] K2(C,F,[],[Q,R],[P],[],[],[]). given clause #126: (wt=15) 151 [hyper,149,1] K1(C,F,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 176 [hyper,151,7] K2(C,F,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 177 [hyper,151,6,eval,demod,33,33,34] K2(C,F,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 178 [hyper,151,5,demod,33,33,33,34] K2(C,F,[],[P,Q,R],[],[],[],[]). given clause #127: (wt=15) 153 [hyper,152,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[],[P],[],[]). given clause #128: (wt=15) 154 [hyper,152,4] K1(E,F,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 179 [hyper,154,5,demod,33,34] K2(E,F,[],[R],[],[P],[],[Q]). given clause #129: (wt=15) 157 [hyper,155,12,demod,30,32,32,31,30,32,31] K1(B,D,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 180 [hyper,157,6,eval,demod,33,34] K2(B,D,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 181 [hyper,157,5,demod,33,33,34] K2(B,D,[],[P,R,Q],[],[],[],[]). given clause #130: (wt=15) 158 [hyper,156,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 182 [hyper,158,5,demod,33,34] K2(B,D,[],[R,Q],[P],[],[],[]). given clause #131: (wt=15) 161 [hyper,159,12,demod,30,32,32,32,31,30,31] K1(B,D,[P,R,Q],[],[],[],[],[]). given clause #132: (wt=15) 162 [hyper,160,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[P],[],[],[]). given clause #133: (wt=15) 164 [hyper,163,1] K1(C,F,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 183 [hyper,164,5,demod,33,34] K2(C,F,[],[R],[],[P],[],[Q]). given clause #134: (wt=15) 167 [hyper,165,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 184 [hyper,167,6,eval,demod,33,34] K2(B,D,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 185 [hyper,167,5,demod,33,33,34] K2(B,D,[],[P,R],[Q],[],[],[]). given clause #135: (wt=15) 168 [hyper,166,12,demod,30,32,32,32,31,30,31] K1(B,D,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 186 [hyper,168,7] K2(B,D,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 187 [hyper,168,6,eval,demod,33,33,34] K2(B,D,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 188 [hyper,168,5,demod,33,33,33,34] K2(B,D,[],[Q,P,R],[],[],[],[]). given clause #136: (wt=15) 169 [hyper,136,5,demod,33,34] K2(B,D,[],[R],[],[Q],[P],[]). given clause #137: (wt=15) 170 [hyper,138,5,demod,33,34] K2(E,D,[],[R],[],[],[Q],[P]). ** KEPT (pick-wt=14): 189 [hyper,170,17,demod,30,32,31,30,31] H(D,[],[],[Q],[R],[],[P]). given clause #138: (wt=14) 189 [hyper,170,17,demod,30,32,31,30,31] H(D,[],[],[Q],[R],[],[P]). ** KEPT (pick-wt=15): 190 [hyper,189,3] K1(D,E,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 191 [hyper,189,2] K1(D,B,[R],[],[],[Q],[],[P]). given clause #139: (wt=15) 171 [hyper,142,6,eval,demod,33,34] K2(C,F,[Q],[R,P],[],[],[],[]). given clause #140: (wt=15) 172 [hyper,142,5,demod,33,33,34] K2(C,F,[],[Q,R,P],[],[],[],[]). ** KEPT (pick-wt=14): 192 [hyper,172,8] H(F,[],[],[],[],[],[Q,R,P]). given clause #141: (wt=14) 192 [hyper,172,8] H(F,[],[],[],[],[],[Q,R,P]). ** KEPT (pick-wt=15): 193 [hyper,192,15,demod,30,32,32,32,31,30,31] K1(F,E,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 194 [hyper,192,14,demod,30,32,32,32,31,30,31] K1(F,C,[P,R,Q],[],[],[],[],[]). given clause #142: (wt=15) 173 [hyper,143,5,demod,33,34] K2(C,F,[],[R,P],[Q],[],[],[]). ** KEPT (pick-wt=14): 195 [hyper,173,8] H(F,[Q],[],[],[],[],[R,P]). given clause #143: (wt=14) 195 [hyper,173,8] H(F,[Q],[],[],[],[],[R,P]). ** KEPT (pick-wt=15): 196 [hyper,195,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 197 [hyper,195,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[Q],[],[],[]). given clause #144: (wt=15) 174 [hyper,150,6,eval,demod,33,34] K2(C,F,[Q],[R],[P],[],[],[]). given clause #145: (wt=15) 175 [hyper,150,5,demod,33,33,34] K2(C,F,[],[Q,R],[P],[],[],[]). ** KEPT (pick-wt=14): 198 [hyper,175,8] H(F,[P],[],[],[],[],[Q,R]). given clause #146: (wt=14) 198 [hyper,175,8] H(F,[P],[],[],[],[],[Q,R]). ** KEPT (pick-wt=15): 199 [hyper,198,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 200 [hyper,198,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[P],[],[],[]). given clause #147: (wt=15) 176 [hyper,151,7] K2(C,F,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 201 [hyper,176,8] H(F,[],[],[P,Q],[],[],[R]). given clause #148: (wt=14) 201 [hyper,176,8] H(F,[],[],[P,Q],[],[],[R]). ** KEPT (pick-wt=15): 202 [hyper,201,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 203 [hyper,201,14,demod,30,32,31,30,32,32,31] K1(F,C,[R],[Q,P],[],[],[],[]). given clause #149: (wt=15) 177 [hyper,151,6,eval,demod,33,33,34] K2(C,F,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 204 [hyper,177,8] H(F,[],[],[P],[],[],[Q,R]). given clause #150: (wt=14) 204 [hyper,177,8] H(F,[],[],[P],[],[],[Q,R]). ** KEPT (pick-wt=15): 205 [hyper,204,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[],[],[P],[]). ** KEPT (pick-wt=15): 206 [hyper,204,14,demod,30,32,32,31,30,32,31] K1(F,C,[R,Q],[P],[],[],[],[]). given clause #151: (wt=15) 178 [hyper,151,5,demod,33,33,33,34] K2(C,F,[],[P,Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 207 [hyper,178,8] H(F,[],[],[],[],[],[P,Q,R]). given clause #152: (wt=14) 207 [hyper,178,8] H(F,[],[],[],[],[],[P,Q,R]). ** KEPT (pick-wt=15): 208 [hyper,207,15,demod,30,32,32,32,31,30,31] K1(F,E,[R,Q,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 209 [hyper,207,14,demod,30,32,32,32,31,30,31] K1(F,C,[R,Q,P],[],[],[],[],[]). given clause #153: (wt=15) 179 [hyper,154,5,demod,33,34] K2(E,F,[],[R],[],[P],[],[Q]). ** KEPT (pick-wt=14): 210 [hyper,179,11] H(F,[],[P],[],[Q],[],[R]). given clause #154: (wt=14) 210 [hyper,179,11] H(F,[],[P],[],[Q],[],[R]). ** KEPT (pick-wt=15): 211 [hyper,210,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 212 [hyper,210,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[P],[Q],[]). given clause #155: (wt=15) 180 [hyper,157,6,eval,demod,33,34] K2(B,D,[P],[R,Q],[],[],[],[]). given clause #156: (wt=15) 181 [hyper,157,5,demod,33,33,34] K2(B,D,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 213 [hyper,181,16,demod,30,31,30,32,32,32,31] H(D,[],[],[],[Q,R,P],[],[]). given clause #157: (wt=14) 213 [hyper,181,16,demod,30,31,30,32,32,32,31] H(D,[],[],[],[Q,R,P],[],[]). ** KEPT (pick-wt=15): 214 [hyper,213,3] K1(D,E,[Q,R,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 215 [hyper,213,2] K1(D,B,[Q,R,P],[],[],[],[],[]). given clause #158: (wt=15) 182 [hyper,158,5,demod,33,34] K2(B,D,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=14): 216 [hyper,182,16,demod,30,31,30,32,32,31] H(D,[P],[],[],[Q,R],[],[]). given clause #159: (wt=14) 216 [hyper,182,16,demod,30,31,30,32,32,31] H(D,[P],[],[],[Q,R],[],[]). ** KEPT (pick-wt=15): 217 [hyper,216,3] K1(D,E,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 218 [hyper,216,2] K1(D,B,[Q,R],[],[P],[],[],[]). given clause #160: (wt=15) 183 [hyper,164,5,demod,33,34] K2(C,F,[],[R],[],[P],[],[Q]). given clause #161: (wt=15) 184 [hyper,167,6,eval,demod,33,34] K2(B,D,[P],[R],[Q],[],[],[]). given clause #162: (wt=15) 185 [hyper,167,5,demod,33,33,34] K2(B,D,[],[P,R],[Q],[],[],[]). ** KEPT (pick-wt=14): 219 [hyper,185,16,demod,30,31,30,32,32,31] H(D,[Q],[],[],[R,P],[],[]). given clause #163: (wt=14) 219 [hyper,185,16,demod,30,31,30,32,32,31] H(D,[Q],[],[],[R,P],[],[]). ** KEPT (pick-wt=15): 220 [hyper,219,3] K1(D,E,[R,P],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 221 [hyper,219,2] K1(D,B,[R,P],[],[Q],[],[],[]). given clause #164: (wt=15) 186 [hyper,168,7] K2(B,D,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 222 [hyper,186,16,demod,30,32,32,31,30,32,31] H(D,[],[P,Q],[],[R],[],[]). given clause #165: (wt=14) 222 [hyper,186,16,demod,30,32,32,31,30,32,31] H(D,[],[P,Q],[],[R],[],[]). ** KEPT (pick-wt=15): 223 [hyper,222,3] K1(D,E,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 224 [hyper,222,2] K1(D,B,[R],[P,Q],[],[],[],[]). given clause #166: (wt=15) 187 [hyper,168,6,eval,demod,33,33,34] K2(B,D,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=14): 225 [hyper,187,16,demod,30,32,31,30,32,32,31] H(D,[],[Q],[],[R,P],[],[]). given clause #167: (wt=14) 225 [hyper,187,16,demod,30,32,31,30,32,32,31] H(D,[],[Q],[],[R,P],[],[]). ** KEPT (pick-wt=15): 226 [hyper,225,3] K1(D,E,[R,P],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 227 [hyper,225,2] K1(D,B,[R,P],[Q],[],[],[],[]). given clause #168: (wt=15) 188 [hyper,168,5,demod,33,33,33,34] K2(B,D,[],[Q,P,R],[],[],[],[]). ** KEPT (pick-wt=14): 228 [hyper,188,16,demod,30,31,30,32,32,32,31] H(D,[],[],[],[R,P,Q],[],[]). given clause #169: (wt=14) 228 [hyper,188,16,demod,30,31,30,32,32,32,31] H(D,[],[],[],[R,P,Q],[],[]). ** KEPT (pick-wt=15): 229 [hyper,228,3] K1(D,E,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 230 [hyper,228,2] K1(D,B,[R,P,Q],[],[],[],[],[]). given clause #170: (wt=15) 190 [hyper,189,3] K1(D,E,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 231 [hyper,190,5,demod,33,34] K2(D,E,[],[R],[],[],[Q],[P]). given clause #171: (wt=15) 191 [hyper,189,2] K1(D,B,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 232 [hyper,191,5,demod,33,34] K2(D,B,[],[R],[],[Q],[],[P]). given clause #172: (wt=15) 193 [hyper,192,15,demod,30,32,32,32,31,30,31] K1(F,E,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 233 [hyper,193,6,eval,demod,33,33,34] K2(F,E,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 234 [hyper,193,5,demod,33,33,33,34] K2(F,E,[],[P,R,Q],[],[],[],[]). given clause #173: (wt=15) 194 [hyper,192,14,demod,30,32,32,32,31,30,31] K1(F,C,[P,R,Q],[],[],[],[],[]). given clause #174: (wt=15) 196 [hyper,195,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 235 [hyper,196,6,eval,demod,33,34] K2(F,E,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 236 [hyper,196,5,demod,33,33,34] K2(F,E,[],[P,R],[Q],[],[],[]). given clause #175: (wt=15) 197 [hyper,195,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 237 [hyper,197,6,eval,demod,33,34] K2(F,C,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 238 [hyper,197,5,demod,33,33,34] K2(F,C,[],[P,R],[Q],[],[],[]). given clause #176: (wt=15) 199 [hyper,198,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 239 [hyper,199,5,demod,33,33,34] K2(F,E,[],[R,Q],[P],[],[],[]). given clause #177: (wt=15) 200 [hyper,198,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[P],[],[],[]). given clause #178: (wt=15) 202 [hyper,201,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 240 [hyper,202,5,demod,33,34] K2(F,E,[],[R],[],[],[P,Q],[]). given clause #179: (wt=15) 203 [hyper,201,14,demod,30,32,31,30,32,32,31] K1(F,C,[R],[Q,P],[],[],[],[]). ** KEPT (pick-wt=15): 241 [hyper,203,5,demod,33,34] K2(F,C,[],[R,Q,P],[],[],[],[]). given clause #180: (wt=15) 205 [hyper,204,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[],[],[P],[]). ** KEPT (pick-wt=15): 242 [hyper,205,5,demod,33,33,34] K2(F,E,[],[R,Q],[],[],[P],[]). given clause #181: (wt=15) 206 [hyper,204,14,demod,30,32,32,31,30,32,31] K1(F,C,[R,Q],[P],[],[],[],[]). given clause #182: (wt=15) 208 [hyper,207,15,demod,30,32,32,32,31,30,31] K1(F,E,[R,Q,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 243 [hyper,208,5,demod,33,33,33,34] K2(F,E,[],[R,Q,P],[],[],[],[]). given clause #183: (wt=15) 209 [hyper,207,14,demod,30,32,32,32,31,30,31] K1(F,C,[R,Q,P],[],[],[],[],[]). given clause #184: (wt=15) 211 [hyper,210,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 244 [hyper,211,5,demod,33,34] K2(F,E,[],[R],[],[P],[],[Q]). given clause #185: (wt=15) 212 [hyper,210,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 245 [hyper,212,5,demod,33,34] K2(F,C,[],[R],[],[P],[Q],[]). given clause #186: (wt=15) 214 [hyper,213,3] K1(D,E,[Q,R,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 246 [hyper,214,6,eval,demod,33,33,34] K2(D,E,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 247 [hyper,214,5,demod,33,33,33,34] K2(D,E,[],[Q,R,P],[],[],[],[]). given clause #187: (wt=15) 215 [hyper,213,2] K1(D,B,[Q,R,P],[],[],[],[],[]). given clause #188: (wt=15) 217 [hyper,216,3] K1(D,E,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 248 [hyper,217,6,eval,demod,33,34] K2(D,E,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 249 [hyper,217,5,demod,33,33,34] K2(D,E,[],[Q,R],[P],[],[],[]). given clause #189: (wt=15) 218 [hyper,216,2] K1(D,B,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 250 [hyper,218,6,eval,demod,33,34] K2(D,B,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 251 [hyper,218,5,demod,33,33,34] K2(D,B,[],[Q,R],[P],[],[],[]). given clause #190: (wt=15) 220 [hyper,219,3] K1(D,E,[R,P],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 252 [hyper,220,5,demod,33,33,34] K2(D,E,[],[R,P],[Q],[],[],[]). given clause #191: (wt=15) 221 [hyper,219,2] K1(D,B,[R,P],[],[Q],[],[],[]). given clause #192: (wt=15) 223 [hyper,222,3] K1(D,E,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 253 [hyper,223,5,demod,33,34] K2(D,E,[],[R],[],[P,Q],[],[]). given clause #193: (wt=15) 224 [hyper,222,2] K1(D,B,[R],[P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 254 [hyper,224,5,demod,33,34] K2(D,B,[],[R,P,Q],[],[],[],[]). given clause #194: (wt=15) 226 [hyper,225,3] K1(D,E,[R,P],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 255 [hyper,226,5,demod,33,33,34] K2(D,E,[],[R,P],[],[Q],[],[]). given clause #195: (wt=15) 227 [hyper,225,2] K1(D,B,[R,P],[Q],[],[],[],[]). given clause #196: (wt=15) 229 [hyper,228,3] K1(D,E,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 256 [hyper,229,5,demod,33,33,33,34] K2(D,E,[],[R,P,Q],[],[],[],[]). given clause #197: (wt=15) 230 [hyper,228,2] K1(D,B,[R,P,Q],[],[],[],[],[]). given clause #198: (wt=15) 231 [hyper,190,5,demod,33,34] K2(D,E,[],[R],[],[],[Q],[P]). given clause #199: (wt=15) 232 [hyper,191,5,demod,33,34] K2(D,B,[],[R],[],[Q],[],[P]). ** KEPT (pick-wt=14): 257 [hyper,232,9] H(B,[],[R],[Q],[],[],[P]). given clause #200: (wt=14) 257 [hyper,232,9] H(B,[],[R],[Q],[],[],[P]). ** KEPT (pick-wt=15): 258 [hyper,257,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[Q],[],[P]). given clause #201: (wt=15) 233 [hyper,193,6,eval,demod,33,33,34] K2(F,E,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 259 [hyper,233,19,demod,30,32,32,31,30,32,31] H(E,[],[],[],[],[Q,R],[P]). given clause #202: (wt=14) 259 [hyper,233,19,demod,30,32,32,31,30,32,31] H(E,[],[],[],[],[Q,R],[P]). ** KEPT (pick-wt=15): 260 [hyper,259,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 261 [hyper,259,4] K1(E,F,[Q,R],[P],[],[],[],[]). given clause #203: (wt=15) 234 [hyper,193,5,demod,33,33,33,34] K2(F,E,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 262 [hyper,234,19,demod,30,32,32,32,31,30,31] H(E,[],[],[],[],[Q,R,P],[]). given clause #204: (wt=14) 262 [hyper,234,19,demod,30,32,32,32,31,30,31] H(E,[],[],[],[],[Q,R,P],[]). ** KEPT (pick-wt=15): 263 [hyper,262,13,demod,30,32,32,32,31,30,31] K1(E,D,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 264 [hyper,262,4] K1(E,F,[Q,R,P],[],[],[],[],[]). given clause #205: (wt=15) 235 [hyper,196,6,eval,demod,33,34] K2(F,E,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=14): 265 [hyper,235,19,demod,30,32,31,30,32,31] H(E,[Q],[],[],[],[R],[P]). given clause #206: (wt=14) 265 [hyper,235,19,demod,30,32,31,30,32,31] H(E,[Q],[],[],[],[R],[P]). ** KEPT (pick-wt=15): 266 [hyper,265,13,demod,30,32,31,30,31] K1(E,D,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 267 [hyper,265,4] K1(E,F,[R],[P],[Q],[],[],[]). given clause #207: (wt=15) 236 [hyper,196,5,demod,33,33,34] K2(F,E,[],[P,R],[Q],[],[],[]). ** KEPT (pick-wt=14): 268 [hyper,236,19,demod,30,32,32,31,30,31] H(E,[Q],[],[],[],[R,P],[]). given clause #208: (wt=14) 268 [hyper,236,19,demod,30,32,32,31,30,31] H(E,[Q],[],[],[],[R,P],[]). ** KEPT (pick-wt=15): 269 [hyper,268,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 270 [hyper,268,4] K1(E,F,[R,P],[],[Q],[],[],[]). given clause #209: (wt=15) 237 [hyper,197,6,eval,demod,33,34] K2(F,C,[P],[R],[Q],[],[],[]). given clause #210: (wt=15) 238 [hyper,197,5,demod,33,33,34] K2(F,C,[],[P,R],[Q],[],[],[]). given clause #211: (wt=15) 239 [hyper,199,5,demod,33,33,34] K2(F,E,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=14): 271 [hyper,239,19,demod,30,32,32,31,30,31] H(E,[P],[],[],[],[Q,R],[]). given clause #212: (wt=14) 271 [hyper,239,19,demod,30,32,32,31,30,31] H(E,[P],[],[],[],[Q,R],[]). ** KEPT (pick-wt=15): 272 [hyper,271,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 273 [hyper,271,4] K1(E,F,[Q,R],[],[P],[],[],[]). given clause #213: (wt=15) 240 [hyper,202,5,demod,33,34] K2(F,E,[],[R],[],[],[P,Q],[]). ** KEPT (pick-wt=14): 274 [hyper,240,19,demod,30,32,31,30,31] H(E,[],[],[P,Q],[],[R],[]). given clause #214: (wt=14) 274 [hyper,240,19,demod,30,32,31,30,31] H(E,[],[],[P,Q],[],[R],[]). ** KEPT (pick-wt=15): 275 [hyper,274,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 276 [hyper,274,4] K1(E,F,[R],[],[],[],[P,Q],[]). given clause #215: (wt=15) 241 [hyper,203,5,demod,33,34] K2(F,C,[],[R,Q,P],[],[],[],[]). given clause #216: (wt=15) 242 [hyper,205,5,demod,33,33,34] K2(F,E,[],[R,Q],[],[],[P],[]). ** KEPT (pick-wt=14): 277 [hyper,242,19,demod,30,32,32,31,30,31] H(E,[],[],[P],[],[Q,R],[]). given clause #217: (wt=14) 277 [hyper,242,19,demod,30,32,32,31,30,31] H(E,[],[],[P],[],[Q,R],[]). ** KEPT (pick-wt=15): 278 [hyper,277,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[],[],[P],[]). ** KEPT (pick-wt=15): 279 [hyper,277,4] K1(E,F,[Q,R],[],[],[],[P],[]). given clause #218: (wt=15) 243 [hyper,208,5,demod,33,33,33,34] K2(F,E,[],[R,Q,P],[],[],[],[]). ** KEPT (pick-wt=14): 280 [hyper,243,19,demod,30,32,32,32,31,30,31] H(E,[],[],[],[],[P,Q,R],[]). given clause #219: (wt=14) 280 [hyper,243,19,demod,30,32,32,32,31,30,31] H(E,[],[],[],[],[P,Q,R],[]). ** KEPT (pick-wt=15): 281 [hyper,280,13,demod,30,32,32,32,31,30,31] K1(E,D,[R,Q,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 282 [hyper,280,4] K1(E,F,[P,Q,R],[],[],[],[],[]). given clause #220: (wt=15) 244 [hyper,211,5,demod,33,34] K2(F,E,[],[R],[],[P],[],[Q]). given clause #221: (wt=15) 245 [hyper,212,5,demod,33,34] K2(F,C,[],[R],[],[P],[Q],[]). ** KEPT (pick-wt=14): 283 [hyper,245,18,demod,30,32,31,30,31] H(C,[],[P],[R],[Q],[],[]). given clause #222: (wt=14) 283 [hyper,245,18,demod,30,32,31,30,31] H(C,[],[P],[R],[Q],[],[]). ** KEPT (pick-wt=15): 284 [hyper,283,1] K1(C,F,[R],[],[],[P],[Q],[]). given clause #223: (wt=15) 246 [hyper,214,6,eval,demod,33,33,34] K2(D,E,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 285 [hyper,246,10] H(E,[],[],[],[Q],[R,P],[]). given clause #224: (wt=14) 285 [hyper,246,10] H(E,[],[],[],[Q],[R,P],[]). ** KEPT (pick-wt=15): 286 [hyper,285,13,demod,30,32,32,31,30,32,31] K1(E,D,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 287 [hyper,285,4] K1(E,F,[R,P],[],[],[],[],[Q]). given clause #225: (wt=15) 247 [hyper,214,5,demod,33,33,33,34] K2(D,E,[],[Q,R,P],[],[],[],[]). given clause #226: (wt=15) 248 [hyper,217,6,eval,demod,33,34] K2(D,E,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=14): 288 [hyper,248,10] H(E,[P],[],[],[Q],[R],[]). given clause #227: (wt=14) 288 [hyper,248,10] H(E,[P],[],[],[Q],[R],[]). ** KEPT (pick-wt=15): 289 [hyper,288,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 290 [hyper,288,4] K1(E,F,[R],[],[P],[],[],[Q]). given clause #228: (wt=15) 249 [hyper,217,5,demod,33,33,34] K2(D,E,[],[Q,R],[P],[],[],[]). given clause #229: (wt=15) 250 [hyper,218,6,eval,demod,33,34] K2(D,B,[Q],[R],[P],[],[],[]). given clause #230: (wt=15) 251 [hyper,218,5,demod,33,33,34] K2(D,B,[],[Q,R],[P],[],[],[]). given clause #231: (wt=15) 252 [hyper,220,5,demod,33,33,34] K2(D,E,[],[R,P],[Q],[],[],[]). given clause #232: (wt=15) 253 [hyper,223,5,demod,33,34] K2(D,E,[],[R],[],[P,Q],[],[]). ** KEPT (pick-wt=14): 291 [hyper,253,10] H(E,[],[P,Q],[],[],[R],[]). given clause #233: (wt=14) 291 [hyper,253,10] H(E,[],[P,Q],[],[],[R],[]). ** KEPT (pick-wt=15): 292 [hyper,291,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 293 [hyper,291,4] K1(E,F,[R],[],[],[P,Q],[],[]). given clause #234: (wt=15) 254 [hyper,224,5,demod,33,34] K2(D,B,[],[R,P,Q],[],[],[],[]). given clause #235: (wt=15) 255 [hyper,226,5,demod,33,33,34] K2(D,E,[],[R,P],[],[Q],[],[]). ** KEPT (pick-wt=14): 294 [hyper,255,10] H(E,[],[Q],[],[],[R,P],[]). given clause #236: (wt=14) 294 [hyper,255,10] H(E,[],[Q],[],[],[R,P],[]). ** KEPT (pick-wt=15): 295 [hyper,294,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 296 [hyper,294,4] K1(E,F,[R,P],[],[],[Q],[],[]). given clause #237: (wt=15) 256 [hyper,229,5,demod,33,33,33,34] K2(D,E,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=14): 297 [hyper,256,10] H(E,[],[],[],[],[R,P,Q],[]). given clause #238: (wt=14) 297 [hyper,256,10] H(E,[],[],[],[],[R,P,Q],[]). ** KEPT (pick-wt=15): 298 [hyper,297,13,demod,30,32,32,32,31,30,31] K1(E,D,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 299 [hyper,297,4] K1(E,F,[R,P,Q],[],[],[],[],[]). given clause #239: (wt=15) 258 [hyper,257,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 300 [hyper,258,5,demod,33,34] K2(B,D,[],[R],[],[Q],[],[P]). given clause #240: (wt=15) 260 [hyper,259,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 301 [hyper,260,5,demod,33,33,34] K2(E,D,[],[R,Q],[],[],[],[P]). given clause #241: (wt=15) 261 [hyper,259,4] K1(E,F,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 302 [hyper,261,6,eval,demod,33,34] K2(E,F,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 303 [hyper,261,5,demod,33,33,34] K2(E,F,[],[Q,R,P],[],[],[],[]). given clause #242: (wt=15) 263 [hyper,262,13,demod,30,32,32,32,31,30,31] K1(E,D,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 304 [hyper,263,6,eval,demod,33,33,34] K2(E,D,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 305 [hyper,263,5,demod,33,33,33,34] K2(E,D,[],[P,R,Q],[],[],[],[]). given clause #243: (wt=15) 264 [hyper,262,4] K1(E,F,[Q,R,P],[],[],[],[],[]). given clause #244: (wt=15) 266 [hyper,265,13,demod,30,32,31,30,31] K1(E,D,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 306 [hyper,266,5,demod,33,34] K2(E,D,[],[R],[Q],[],[],[P]). given clause #245: (wt=15) 267 [hyper,265,4] K1(E,F,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 307 [hyper,267,5,demod,33,34] K2(E,F,[],[R,P],[Q],[],[],[]). given clause #246: (wt=15) 269 [hyper,268,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 308 [hyper,269,6,eval,demod,33,34] K2(E,D,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 309 [hyper,269,5,demod,33,33,34] K2(E,D,[],[P,R],[Q],[],[],[]). given clause #247: (wt=15) 270 [hyper,268,4] K1(E,F,[R,P],[],[Q],[],[],[]). given clause #248: (wt=15) 272 [hyper,271,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 310 [hyper,272,5,demod,33,33,34] K2(E,D,[],[R,Q],[P],[],[],[]). given clause #249: (wt=15) 273 [hyper,271,4] K1(E,F,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 311 [hyper,273,6,eval,demod,33,34] K2(E,F,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 312 [hyper,273,5,demod,33,33,34] K2(E,F,[],[Q,R],[P],[],[],[]). given clause #250: (wt=15) 275 [hyper,274,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 313 [hyper,275,5,demod,33,34] K2(E,D,[],[R],[],[],[P,Q],[]). given clause #251: (wt=15) 276 [hyper,274,4] K1(E,F,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 314 [hyper,276,5,demod,33,34] K2(E,F,[],[R],[],[],[P,Q],[]). given clause #252: (wt=15) 278 [hyper,277,13,demod,30,32,32,31,30,31] K1(E,D,[R,Q],[],[],[],[P],[]). ** KEPT (pick-wt=15): 315 [hyper,278,5,demod,33,33,34] K2(E,D,[],[R,Q],[],[],[P],[]). given clause #253: (wt=15) 279 [hyper,277,4] K1(E,F,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 316 [hyper,279,6,eval,demod,33,34] K2(E,F,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 317 [hyper,279,5,demod,33,33,34] K2(E,F,[],[Q,R],[],[],[P],[]). given clause #254: (wt=15) 281 [hyper,280,13,demod,30,32,32,32,31,30,31] K1(E,D,[R,Q,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 318 [hyper,281,5,demod,33,33,33,34] K2(E,D,[],[R,Q,P],[],[],[],[]). given clause #255: (wt=15) 282 [hyper,280,4] K1(E,F,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 319 [hyper,282,7] K2(E,F,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 320 [hyper,282,6,eval,demod,33,33,34] K2(E,F,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 321 [hyper,282,5,demod,33,33,33,34] K2(E,F,[],[P,Q,R],[],[],[],[]). given clause #256: (wt=15) 284 [hyper,283,1] K1(C,F,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 322 [hyper,284,5,demod,33,34] K2(C,F,[],[R],[],[P],[Q],[]). given clause #257: (wt=15) 286 [hyper,285,13,demod,30,32,32,31,30,32,31] K1(E,D,[P,R],[Q],[],[],[],[]). given clause #258: (wt=15) 287 [hyper,285,4] K1(E,F,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 323 [hyper,287,5,demod,33,33,34] K2(E,F,[],[R,P],[],[],[],[Q]). given clause #259: (wt=15) 289 [hyper,288,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[P],[],[],[]). given clause #260: (wt=15) 290 [hyper,288,4] K1(E,F,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 324 [hyper,290,5,demod,33,34] K2(E,F,[],[R],[P],[],[],[Q]). given clause #261: (wt=15) 292 [hyper,291,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 325 [hyper,292,5,demod,33,34] K2(E,D,[],[R],[],[P,Q],[],[]). given clause #262: (wt=15) 293 [hyper,291,4] K1(E,F,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 326 [hyper,293,5,demod,33,34] K2(E,F,[],[R],[],[P,Q],[],[]). given clause #263: (wt=15) 295 [hyper,294,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 327 [hyper,295,6,eval,demod,33,34] K2(E,D,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 328 [hyper,295,5,demod,33,33,34] K2(E,D,[],[P,R],[],[Q],[],[]). given clause #264: (wt=15) 296 [hyper,294,4] K1(E,F,[R,P],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 329 [hyper,296,5,demod,33,33,34] K2(E,F,[],[R,P],[],[Q],[],[]). given clause #265: (wt=15) 298 [hyper,297,13,demod,30,32,32,32,31,30,31] K1(E,D,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 330 [hyper,298,7] K2(E,D,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 331 [hyper,298,6,eval,demod,33,33,34] K2(E,D,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 332 [hyper,298,5,demod,33,33,33,34] K2(E,D,[],[Q,P,R],[],[],[],[]). given clause #266: (wt=15) 299 [hyper,297,4] K1(E,F,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 333 [hyper,299,5,demod,33,33,33,34] K2(E,F,[],[R,P,Q],[],[],[],[]). given clause #267: (wt=15) 300 [hyper,258,5,demod,33,34] K2(B,D,[],[R],[],[Q],[],[P]). given clause #268: (wt=15) 301 [hyper,260,5,demod,33,33,34] K2(E,D,[],[R,Q],[],[],[],[P]). ** KEPT (pick-wt=14): 334 [hyper,301,17,demod,30,32,32,31,30,31] H(D,[],[],[],[Q,R],[],[P]). given clause #269: (wt=14) 334 [hyper,301,17,demod,30,32,32,31,30,31] H(D,[],[],[],[Q,R],[],[P]). ** KEPT (pick-wt=15): 335 [hyper,334,3] K1(D,E,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 336 [hyper,334,2] K1(D,B,[Q,R],[],[],[],[],[P]). given clause #270: (wt=15) 302 [hyper,261,6,eval,demod,33,34] K2(E,F,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 337 [hyper,302,11] H(F,[],[],[],[],[Q],[R,P]). given clause #271: (wt=14) 337 [hyper,302,11] H(F,[],[],[],[],[Q],[R,P]). ** KEPT (pick-wt=15): 338 [hyper,337,15,demod,30,32,32,31,30,32,31] K1(F,E,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 339 [hyper,337,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[],[],[],[Q]). given clause #272: (wt=15) 303 [hyper,261,5,demod,33,33,34] K2(E,F,[],[Q,R,P],[],[],[],[]). given clause #273: (wt=15) 304 [hyper,263,6,eval,demod,33,33,34] K2(E,D,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 340 [hyper,304,17,demod,30,32,32,31,30,32,31] H(D,[],[],[],[Q,R],[P],[]). given clause #274: (wt=14) 340 [hyper,304,17,demod,30,32,32,31,30,32,31] H(D,[],[],[],[Q,R],[P],[]). ** KEPT (pick-wt=15): 341 [hyper,340,3] K1(D,E,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 342 [hyper,340,2] K1(D,B,[Q,R],[],[],[],[P],[]). given clause #275: (wt=15) 305 [hyper,263,5,demod,33,33,33,34] K2(E,D,[],[P,R,Q],[],[],[],[]). given clause #276: (wt=15) 306 [hyper,266,5,demod,33,34] K2(E,D,[],[R],[Q],[],[],[P]). ** KEPT (pick-wt=14): 343 [hyper,306,17,demod,30,32,31,30,31] H(D,[Q],[],[],[R],[],[P]). given clause #277: (wt=14) 343 [hyper,306,17,demod,30,32,31,30,31] H(D,[Q],[],[],[R],[],[P]). ** KEPT (pick-wt=15): 344 [hyper,343,3] K1(D,E,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 345 [hyper,343,2] K1(D,B,[R],[],[Q],[],[],[P]). given clause #278: (wt=15) 307 [hyper,267,5,demod,33,34] K2(E,F,[],[R,P],[Q],[],[],[]). given clause #279: (wt=15) 308 [hyper,269,6,eval,demod,33,34] K2(E,D,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=14): 346 [hyper,308,17,demod,30,32,31,30,32,31] H(D,[Q],[],[],[R],[P],[]). given clause #280: (wt=14) 346 [hyper,308,17,demod,30,32,31,30,32,31] H(D,[Q],[],[],[R],[P],[]). ** KEPT (pick-wt=15): 347 [hyper,346,3] K1(D,E,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 348 [hyper,346,2] K1(D,B,[R],[],[Q],[],[P],[]). given clause #281: (wt=15) 309 [hyper,269,5,demod,33,33,34] K2(E,D,[],[P,R],[Q],[],[],[]). given clause #282: (wt=15) 310 [hyper,272,5,demod,33,33,34] K2(E,D,[],[R,Q],[P],[],[],[]). given clause #283: (wt=15) 311 [hyper,273,6,eval,demod,33,34] K2(E,F,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=14): 349 [hyper,311,11] H(F,[P],[],[],[],[Q],[R]). given clause #284: (wt=14) 349 [hyper,311,11] H(F,[P],[],[],[],[Q],[R]). ** KEPT (pick-wt=15): 350 [hyper,349,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 351 [hyper,349,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[],[],[Q]). given clause #285: (wt=15) 312 [hyper,273,5,demod,33,33,34] K2(E,F,[],[Q,R],[P],[],[],[]). given clause #286: (wt=15) 313 [hyper,275,5,demod,33,34] K2(E,D,[],[R],[],[],[P,Q],[]). ** KEPT (pick-wt=14): 352 [hyper,313,17,demod,30,32,31,30,31] H(D,[],[],[P,Q],[R],[],[]). given clause #287: (wt=14) 352 [hyper,313,17,demod,30,32,31,30,31] H(D,[],[],[P,Q],[R],[],[]). ** KEPT (pick-wt=15): 353 [hyper,352,3] K1(D,E,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 354 [hyper,352,2] K1(D,B,[R],[],[],[P,Q],[],[]). given clause #288: (wt=15) 314 [hyper,276,5,demod,33,34] K2(E,F,[],[R],[],[],[P,Q],[]). given clause #289: (wt=15) 315 [hyper,278,5,demod,33,33,34] K2(E,D,[],[R,Q],[],[],[P],[]). ** KEPT (pick-wt=14): 355 [hyper,315,17,demod,30,32,32,31,30,31] H(D,[],[],[P],[Q,R],[],[]). given clause #290: (wt=14) 355 [hyper,315,17,demod,30,32,32,31,30,31] H(D,[],[],[P],[Q,R],[],[]). ** KEPT (pick-wt=15): 356 [hyper,355,3] K1(D,E,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 357 [hyper,355,2] K1(D,B,[Q,R],[],[],[P],[],[]). given clause #291: (wt=15) 316 [hyper,279,6,eval,demod,33,34] K2(E,F,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 358 [hyper,316,11] H(F,[],[],[P],[],[Q],[R]). given clause #292: (wt=14) 358 [hyper,316,11] H(F,[],[],[P],[],[Q],[R]). ** KEPT (pick-wt=15): 359 [hyper,358,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 360 [hyper,358,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[],[],[],[Q]). given clause #293: (wt=15) 317 [hyper,279,5,demod,33,33,34] K2(E,F,[],[Q,R],[],[],[P],[]). given clause #294: (wt=15) 318 [hyper,281,5,demod,33,33,33,34] K2(E,D,[],[R,Q,P],[],[],[],[]). ** KEPT (pick-wt=14): 361 [hyper,318,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[P,Q,R],[],[]). given clause #295: (wt=14) 361 [hyper,318,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[P,Q,R],[],[]). ** KEPT (pick-wt=15): 362 [hyper,361,3] K1(D,E,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 363 [hyper,361,2] K1(D,B,[P,Q,R],[],[],[],[],[]). given clause #296: (wt=15) 319 [hyper,282,7] K2(E,F,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 364 [hyper,319,11] H(F,[],[],[],[],[P,Q],[R]). given clause #297: (wt=14) 364 [hyper,319,11] H(F,[],[],[],[],[P,Q],[R]). ** KEPT (pick-wt=15): 365 [hyper,364,15,demod,30,32,31,30,32,32,31] K1(F,E,[R],[Q,P],[],[],[],[]). ** KEPT (pick-wt=15): 366 [hyper,364,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[],[P,Q]). given clause #298: (wt=15) 320 [hyper,282,6,eval,demod,33,33,34] K2(E,F,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 367 [hyper,320,11] H(F,[],[],[],[],[P],[Q,R]). given clause #299: (wt=14) 367 [hyper,320,11] H(F,[],[],[],[],[P],[Q,R]). ** KEPT (pick-wt=15): 368 [hyper,367,15,demod,30,32,32,31,30,32,31] K1(F,E,[R,Q],[P],[],[],[],[]). ** KEPT (pick-wt=15): 369 [hyper,367,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[],[],[],[P]). given clause #300: (wt=15) 321 [hyper,282,5,demod,33,33,33,34] K2(E,F,[],[P,Q,R],[],[],[],[]). given clause #301: (wt=15) 322 [hyper,284,5,demod,33,34] K2(C,F,[],[R],[],[P],[Q],[]). given clause #302: (wt=15) 323 [hyper,287,5,demod,33,33,34] K2(E,F,[],[R,P],[],[],[],[Q]). ** KEPT (pick-wt=14): 370 [hyper,323,11] H(F,[],[],[],[Q],[],[R,P]). given clause #303: (wt=14) 370 [hyper,323,11] H(F,[],[],[],[Q],[],[R,P]). ** KEPT (pick-wt=15): 371 [hyper,370,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 372 [hyper,370,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[],[],[Q],[]). given clause #304: (wt=15) 324 [hyper,290,5,demod,33,34] K2(E,F,[],[R],[P],[],[],[Q]). ** KEPT (pick-wt=14): 373 [hyper,324,11] H(F,[P],[],[],[Q],[],[R]). given clause #305: (wt=14) 373 [hyper,324,11] H(F,[P],[],[],[Q],[],[R]). ** KEPT (pick-wt=15): 374 [hyper,373,15,demod,30,32,31,30,31] K1(F,E,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 375 [hyper,373,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[],[Q],[]). given clause #306: (wt=15) 325 [hyper,292,5,demod,33,34] K2(E,D,[],[R],[],[P,Q],[],[]). given clause #307: (wt=15) 326 [hyper,293,5,demod,33,34] K2(E,F,[],[R],[],[P,Q],[],[]). ** KEPT (pick-wt=14): 376 [hyper,326,11] H(F,[],[P,Q],[],[],[],[R]). given clause #308: (wt=14) 376 [hyper,326,11] H(F,[],[P,Q],[],[],[],[R]). ** KEPT (pick-wt=15): 377 [hyper,376,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 378 [hyper,376,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[P,Q],[],[]). given clause #309: (wt=15) 327 [hyper,295,6,eval,demod,33,34] K2(E,D,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 379 [hyper,327,17,demod,30,32,31,30,32,31] H(D,[],[Q],[],[R],[P],[]). given clause #310: (wt=14) 379 [hyper,327,17,demod,30,32,31,30,32,31] H(D,[],[Q],[],[R],[P],[]). ** KEPT (pick-wt=15): 380 [hyper,379,3] K1(D,E,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 381 [hyper,379,2] K1(D,B,[R],[Q],[],[],[P],[]). given clause #311: (wt=15) 328 [hyper,295,5,demod,33,33,34] K2(E,D,[],[P,R],[],[Q],[],[]). given clause #312: (wt=15) 329 [hyper,296,5,demod,33,33,34] K2(E,F,[],[R,P],[],[Q],[],[]). ** KEPT (pick-wt=14): 382 [hyper,329,11] H(F,[],[Q],[],[],[],[R,P]). given clause #313: (wt=14) 382 [hyper,329,11] H(F,[],[Q],[],[],[],[R,P]). ** KEPT (pick-wt=15): 383 [hyper,382,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 384 [hyper,382,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[],[Q],[],[]). given clause #314: (wt=15) 330 [hyper,298,7] K2(E,D,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 385 [hyper,330,17,demod,30,32,31,30,32,32,31] H(D,[],[],[],[R],[P,Q],[]). given clause #315: (wt=14) 385 [hyper,330,17,demod,30,32,31,30,32,32,31] H(D,[],[],[],[R],[P,Q],[]). ** KEPT (pick-wt=15): 386 [hyper,385,3] K1(D,E,[R],[P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 387 [hyper,385,2] K1(D,B,[R],[],[],[],[P,Q],[]). given clause #316: (wt=15) 331 [hyper,298,6,eval,demod,33,33,34] K2(E,D,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=14): 388 [hyper,331,17,demod,30,32,32,31,30,32,31] H(D,[],[],[],[R,P],[Q],[]). given clause #317: (wt=14) 388 [hyper,331,17,demod,30,32,32,31,30,32,31] H(D,[],[],[],[R,P],[Q],[]). ** KEPT (pick-wt=15): 389 [hyper,388,3] K1(D,E,[R,P],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 390 [hyper,388,2] K1(D,B,[R,P],[],[],[],[Q],[]). given clause #318: (wt=15) 332 [hyper,298,5,demod,33,33,33,34] K2(E,D,[],[Q,P,R],[],[],[],[]). given clause #319: (wt=15) 333 [hyper,299,5,demod,33,33,33,34] K2(E,F,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=14): 391 [hyper,333,11] H(F,[],[],[],[],[],[R,P,Q]). given clause #320: (wt=14) 391 [hyper,333,11] H(F,[],[],[],[],[],[R,P,Q]). ** KEPT (pick-wt=15): 392 [hyper,391,15,demod,30,32,32,32,31,30,31] K1(F,E,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 393 [hyper,391,14,demod,30,32,32,32,31,30,31] K1(F,C,[Q,P,R],[],[],[],[],[]). given clause #321: (wt=15) 335 [hyper,334,3] K1(D,E,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 394 [hyper,335,6,eval,demod,33,34] K2(D,E,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 395 [hyper,335,5,demod,33,33,34] K2(D,E,[],[Q,R],[],[],[],[P]). given clause #322: (wt=15) 336 [hyper,334,2] K1(D,B,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 396 [hyper,336,6,eval,demod,33,34] K2(D,B,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 397 [hyper,336,5,demod,33,33,34] K2(D,B,[],[Q,R],[],[],[],[P]). given clause #323: (wt=15) 338 [hyper,337,15,demod,30,32,32,31,30,32,31] K1(F,E,[P,R],[Q],[],[],[],[]). given clause #324: (wt=15) 339 [hyper,337,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 398 [hyper,339,6,eval,demod,33,34] K2(F,C,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 399 [hyper,339,5,demod,33,33,34] K2(F,C,[],[P,R],[],[],[],[Q]). given clause #325: (wt=15) 341 [hyper,340,3] K1(D,E,[Q,R],[P],[],[],[],[]). given clause #326: (wt=15) 342 [hyper,340,2] K1(D,B,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 400 [hyper,342,6,eval,demod,33,34] K2(D,B,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 401 [hyper,342,5,demod,33,33,34] K2(D,B,[],[Q,R],[],[],[P],[]). given clause #327: (wt=15) 344 [hyper,343,3] K1(D,E,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 402 [hyper,344,5,demod,33,34] K2(D,E,[],[R],[Q],[],[],[P]). given clause #328: (wt=15) 345 [hyper,343,2] K1(D,B,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 403 [hyper,345,5,demod,33,34] K2(D,B,[],[R],[Q],[],[],[P]). given clause #329: (wt=15) 347 [hyper,346,3] K1(D,E,[R],[P],[Q],[],[],[]). given clause #330: (wt=15) 348 [hyper,346,2] K1(D,B,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 404 [hyper,348,5,demod,33,34] K2(D,B,[],[R],[Q],[],[P],[]). given clause #331: (wt=15) 350 [hyper,349,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[P],[],[],[]). given clause #332: (wt=15) 351 [hyper,349,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 405 [hyper,351,5,demod,33,34] K2(F,C,[],[R],[P],[],[],[Q]). given clause #333: (wt=15) 353 [hyper,352,3] K1(D,E,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 406 [hyper,353,5,demod,33,34] K2(D,E,[],[R],[],[],[P,Q],[]). given clause #334: (wt=15) 354 [hyper,352,2] K1(D,B,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 407 [hyper,354,5,demod,33,34] K2(D,B,[],[R],[],[P,Q],[],[]). given clause #335: (wt=15) 356 [hyper,355,3] K1(D,E,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 408 [hyper,356,6,eval,demod,33,34] K2(D,E,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 409 [hyper,356,5,demod,33,33,34] K2(D,E,[],[Q,R],[],[],[P],[]). given clause #336: (wt=15) 357 [hyper,355,2] K1(D,B,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 410 [hyper,357,6,eval,demod,33,34] K2(D,B,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 411 [hyper,357,5,demod,33,33,34] K2(D,B,[],[Q,R],[],[P],[],[]). given clause #337: (wt=15) 359 [hyper,358,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[],[],[P],[]). given clause #338: (wt=15) 360 [hyper,358,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 412 [hyper,360,5,demod,33,34] K2(F,C,[],[R,P],[],[],[],[Q]). given clause #339: (wt=15) 362 [hyper,361,3] K1(D,E,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 413 [hyper,362,7] K2(D,E,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 414 [hyper,362,6,eval,demod,33,33,34] K2(D,E,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 415 [hyper,362,5,demod,33,33,33,34] K2(D,E,[],[P,Q,R],[],[],[],[]). given clause #340: (wt=15) 363 [hyper,361,2] K1(D,B,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 416 [hyper,363,7] K2(D,B,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 417 [hyper,363,6,eval,demod,33,33,34] K2(D,B,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 418 [hyper,363,5,demod,33,33,33,34] K2(D,B,[],[P,Q,R],[],[],[],[]). given clause #341: (wt=15) 365 [hyper,364,15,demod,30,32,31,30,32,32,31] K1(F,E,[R],[Q,P],[],[],[],[]). given clause #342: (wt=15) 366 [hyper,364,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 419 [hyper,366,5,demod,33,34] K2(F,C,[],[R],[],[],[],[P,Q]). given clause #343: (wt=15) 368 [hyper,367,15,demod,30,32,32,31,30,32,31] K1(F,E,[R,Q],[P],[],[],[],[]). given clause #344: (wt=15) 369 [hyper,367,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 420 [hyper,369,5,demod,33,33,34] K2(F,C,[],[R,Q],[],[],[],[P]). given clause #345: (wt=15) 371 [hyper,370,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 421 [hyper,371,6,eval,demod,33,34] K2(F,E,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 422 [hyper,371,5,demod,33,33,34] K2(F,E,[],[P,R],[],[],[],[Q]). given clause #346: (wt=15) 372 [hyper,370,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 423 [hyper,372,6,eval,demod,33,34] K2(F,C,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 424 [hyper,372,5,demod,33,33,34] K2(F,C,[],[P,R],[],[],[Q],[]). given clause #347: (wt=15) 374 [hyper,373,15,demod,30,32,31,30,31] K1(F,E,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 425 [hyper,374,5,demod,33,34] K2(F,E,[],[R],[P],[],[],[Q]). given clause #348: (wt=15) 375 [hyper,373,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 426 [hyper,375,5,demod,33,34] K2(F,C,[],[R],[P],[],[Q],[]). given clause #349: (wt=15) 377 [hyper,376,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 427 [hyper,377,5,demod,33,34] K2(F,E,[],[R],[],[P,Q],[],[]). given clause #350: (wt=15) 378 [hyper,376,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 428 [hyper,378,5,demod,33,34] K2(F,C,[],[R],[],[P,Q],[],[]). given clause #351: (wt=15) 380 [hyper,379,3] K1(D,E,[R],[P],[],[Q],[],[]). given clause #352: (wt=15) 381 [hyper,379,2] K1(D,B,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 429 [hyper,381,5,demod,33,34] K2(D,B,[],[R,Q],[],[],[P],[]). given clause #353: (wt=15) 383 [hyper,382,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 430 [hyper,383,6,eval,demod,33,34] K2(F,E,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 431 [hyper,383,5,demod,33,33,34] K2(F,E,[],[P,R],[],[Q],[],[]). given clause #354: (wt=15) 384 [hyper,382,14,demod,30,32,32,31,30,31] K1(F,C,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 432 [hyper,384,6,eval,demod,33,34] K2(F,C,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 433 [hyper,384,5,demod,33,33,34] K2(F,C,[],[P,R],[],[Q],[],[]). given clause #355: (wt=15) 386 [hyper,385,3] K1(D,E,[R],[P,Q],[],[],[],[]). given clause #356: (wt=15) 387 [hyper,385,2] K1(D,B,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 434 [hyper,387,5,demod,33,34] K2(D,B,[],[R],[],[],[P,Q],[]). given clause #357: (wt=15) 389 [hyper,388,3] K1(D,E,[R,P],[Q],[],[],[],[]). given clause #358: (wt=15) 390 [hyper,388,2] K1(D,B,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 435 [hyper,390,5,demod,33,33,34] K2(D,B,[],[R,P],[],[],[Q],[]). given clause #359: (wt=15) 392 [hyper,391,15,demod,30,32,32,32,31,30,31] K1(F,E,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 436 [hyper,392,7] K2(F,E,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 437 [hyper,392,6,eval,demod,33,33,34] K2(F,E,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 438 [hyper,392,5,demod,33,33,33,34] K2(F,E,[],[Q,P,R],[],[],[],[]). given clause #360: (wt=15) 393 [hyper,391,14,demod,30,32,32,32,31,30,31] K1(F,C,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 439 [hyper,393,7] K2(F,C,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 440 [hyper,393,6,eval,demod,33,33,34] K2(F,C,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 441 [hyper,393,5,demod,33,33,33,34] K2(F,C,[],[Q,P,R],[],[],[],[]). given clause #361: (wt=15) 394 [hyper,335,6,eval,demod,33,34] K2(D,E,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 442 [hyper,394,10] H(E,[],[],[],[Q],[R],[P]). given clause #362: (wt=14) 442 [hyper,394,10] H(E,[],[],[],[Q],[R],[P]). ** KEPT (pick-wt=15): 443 [hyper,442,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 444 [hyper,442,4] K1(E,F,[R],[P],[],[],[],[Q]). given clause #363: (wt=15) 395 [hyper,335,5,demod,33,33,34] K2(D,E,[],[Q,R],[],[],[],[P]). given clause #364: (wt=15) 396 [hyper,336,6,eval,demod,33,34] K2(D,B,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 445 [hyper,396,9] H(B,[],[R],[],[Q],[],[P]). given clause #365: (wt=14) 445 [hyper,396,9] H(B,[],[R],[],[Q],[],[P]). ** KEPT (pick-wt=15): 446 [hyper,445,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[],[],[],[P]). given clause #366: (wt=15) 397 [hyper,336,5,demod,33,33,34] K2(D,B,[],[Q,R],[],[],[],[P]). ** KEPT (pick-wt=14): 447 [hyper,397,9] H(B,[],[Q,R],[],[],[],[P]). given clause #367: (wt=14) 447 [hyper,397,9] H(B,[],[Q,R],[],[],[],[P]). ** KEPT (pick-wt=15): 448 [hyper,447,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[],[],[],[P]). given clause #368: (wt=15) 398 [hyper,339,6,eval,demod,33,34] K2(F,C,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=14): 449 [hyper,398,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[],[Q],[P]). given clause #369: (wt=14) 449 [hyper,398,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[],[Q],[P]). ** KEPT (pick-wt=15): 450 [hyper,449,1] K1(C,F,[R],[P],[],[],[],[Q]). given clause #370: (wt=15) 399 [hyper,339,5,demod,33,33,34] K2(F,C,[],[P,R],[],[],[],[Q]). ** KEPT (pick-wt=14): 451 [hyper,399,18,demod,30,32,32,31,30,31] H(C,[],[],[R,P],[],[Q],[]). given clause #371: (wt=14) 451 [hyper,399,18,demod,30,32,32,31,30,31] H(C,[],[],[R,P],[],[Q],[]). ** KEPT (pick-wt=15): 452 [hyper,451,1] K1(C,F,[R,P],[],[],[],[],[Q]). given clause #372: (wt=15) 400 [hyper,342,6,eval,demod,33,34] K2(D,B,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 453 [hyper,400,9] H(B,[],[R],[],[Q],[P],[]). given clause #373: (wt=14) 453 [hyper,400,9] H(B,[],[R],[],[Q],[P],[]). ** KEPT (pick-wt=15): 454 [hyper,453,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[],[],[P],[]). given clause #374: (wt=15) 401 [hyper,342,5,demod,33,33,34] K2(D,B,[],[Q,R],[],[],[P],[]). ** KEPT (pick-wt=14): 455 [hyper,401,9] H(B,[],[Q,R],[],[],[P],[]). given clause #375: (wt=14) 455 [hyper,401,9] H(B,[],[Q,R],[],[],[P],[]). ** KEPT (pick-wt=15): 456 [hyper,455,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[],[],[P],[]). given clause #376: (wt=15) 402 [hyper,344,5,demod,33,34] K2(D,E,[],[R],[Q],[],[],[P]). given clause #377: (wt=15) 403 [hyper,345,5,demod,33,34] K2(D,B,[],[R],[Q],[],[],[P]). ** KEPT (pick-wt=14): 457 [hyper,403,9] H(B,[Q],[R],[],[],[],[P]). given clause #378: (wt=14) 457 [hyper,403,9] H(B,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 458 [hyper,457,23,demod,33,34] H(B,[],[R,Q],[],[],[],[P]). ** KEPT (pick-wt=15): 459 [hyper,457,12,demod,30,32,31,30,31] K1(B,D,[R],[],[Q],[],[],[P]). given clause #379: (wt=14) 458 [hyper,457,23,demod,33,34] H(B,[],[R,Q],[],[],[],[P]). ** KEPT (pick-wt=15): 460 [hyper,458,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[],[],[P]). given clause #380: (wt=15) 404 [hyper,348,5,demod,33,34] K2(D,B,[],[R],[Q],[],[P],[]). ** KEPT (pick-wt=14): 461 [hyper,404,9] H(B,[Q],[R],[],[],[P],[]). given clause #381: (wt=14) 461 [hyper,404,9] H(B,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 462 [hyper,461,23,demod,33,34] H(B,[],[R,Q],[],[],[P],[]). ** KEPT (pick-wt=15): 463 [hyper,461,12,demod,30,32,31,30,31] K1(B,D,[R],[],[Q],[],[P],[]). given clause #382: (wt=14) 462 [hyper,461,23,demod,33,34] H(B,[],[R,Q],[],[],[P],[]). ** KEPT (pick-wt=15): 464 [hyper,462,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[],[P],[]). given clause #383: (wt=15) 405 [hyper,351,5,demod,33,34] K2(F,C,[],[R],[P],[],[],[Q]). ** KEPT (pick-wt=14): 465 [hyper,405,18,demod,30,32,31,30,31] H(C,[P],[],[R],[],[Q],[]). given clause #384: (wt=14) 465 [hyper,405,18,demod,30,32,31,30,31] H(C,[P],[],[R],[],[Q],[]). ** KEPT (pick-wt=14): 466 [hyper,465,25] H(C,[],[],[P,R],[],[Q],[]). ** KEPT (pick-wt=15): 467 [hyper,465,1] K1(C,F,[R],[],[P],[],[],[Q]). given clause #385: (wt=14) 466 [hyper,465,25] H(C,[],[],[P,R],[],[Q],[]). ** KEPT (pick-wt=15): 468 [hyper,466,1] K1(C,F,[P,R],[],[],[],[],[Q]). given clause #386: (wt=15) 406 [hyper,353,5,demod,33,34] K2(D,E,[],[R],[],[],[P,Q],[]). given clause #387: (wt=15) 407 [hyper,354,5,demod,33,34] K2(D,B,[],[R],[],[P,Q],[],[]). ** KEPT (pick-wt=14): 469 [hyper,407,9] H(B,[],[R],[P,Q],[],[],[]). given clause #388: (wt=14) 469 [hyper,407,9] H(B,[],[R],[P,Q],[],[],[]). ** KEPT (pick-wt=15): 470 [hyper,469,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[P,Q],[],[]). given clause #389: (wt=15) 408 [hyper,356,6,eval,demod,33,34] K2(D,E,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 471 [hyper,408,10] H(E,[],[],[P],[Q],[R],[]). given clause #390: (wt=14) 471 [hyper,408,10] H(E,[],[],[P],[Q],[R],[]). ** KEPT (pick-wt=15): 472 [hyper,471,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 473 [hyper,471,4] K1(E,F,[R],[],[],[],[P],[Q]). given clause #391: (wt=15) 409 [hyper,356,5,demod,33,33,34] K2(D,E,[],[Q,R],[],[],[P],[]). given clause #392: (wt=15) 410 [hyper,357,6,eval,demod,33,34] K2(D,B,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 474 [hyper,410,9] H(B,[],[R],[P],[Q],[],[]). given clause #393: (wt=14) 474 [hyper,410,9] H(B,[],[R],[P],[Q],[],[]). ** KEPT (pick-wt=15): 475 [hyper,474,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[],[P],[],[]). given clause #394: (wt=15) 411 [hyper,357,5,demod,33,33,34] K2(D,B,[],[Q,R],[],[P],[],[]). ** KEPT (pick-wt=14): 476 [hyper,411,9] H(B,[],[Q,R],[P],[],[],[]). given clause #395: (wt=14) 476 [hyper,411,9] H(B,[],[Q,R],[P],[],[],[]). ** KEPT (pick-wt=15): 477 [hyper,476,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[],[P],[],[]). given clause #396: (wt=15) 412 [hyper,360,5,demod,33,34] K2(F,C,[],[R,P],[],[],[],[Q]). given clause #397: (wt=15) 413 [hyper,362,7] K2(D,E,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 478 [hyper,413,10] H(E,[],[],[],[P,Q],[R],[]). given clause #398: (wt=14) 478 [hyper,413,10] H(E,[],[],[],[P,Q],[R],[]). ** KEPT (pick-wt=15): 479 [hyper,478,13,demod,30,32,31,30,32,32,31] K1(E,D,[R],[Q,P],[],[],[],[]). ** KEPT (pick-wt=15): 480 [hyper,478,4] K1(E,F,[R],[],[],[],[],[P,Q]). given clause #399: (wt=15) 414 [hyper,362,6,eval,demod,33,33,34] K2(D,E,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 481 [hyper,414,10] H(E,[],[],[],[P],[Q,R],[]). given clause #400: (wt=14) 481 [hyper,414,10] H(E,[],[],[],[P],[Q,R],[]). ** KEPT (pick-wt=15): 482 [hyper,481,13,demod,30,32,32,31,30,32,31] K1(E,D,[R,Q],[P],[],[],[],[]). ** KEPT (pick-wt=15): 483 [hyper,481,4] K1(E,F,[Q,R],[],[],[],[],[P]). given clause #401: (wt=15) 415 [hyper,362,5,demod,33,33,33,34] K2(D,E,[],[P,Q,R],[],[],[],[]). given clause #402: (wt=15) 416 [hyper,363,7] K2(D,B,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 484 [hyper,416,9] H(B,[],[R],[],[P,Q],[],[]). given clause #403: (wt=14) 484 [hyper,416,9] H(B,[],[R],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 485 [hyper,484,12,demod,30,32,31,30,32,32,31] K1(B,D,[R],[Q,P],[],[],[],[]). given clause #404: (wt=15) 417 [hyper,363,6,eval,demod,33,33,34] K2(D,B,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 486 [hyper,417,9] H(B,[],[Q,R],[],[P],[],[]). given clause #405: (wt=14) 486 [hyper,417,9] H(B,[],[Q,R],[],[P],[],[]). ** KEPT (pick-wt=15): 487 [hyper,486,12,demod,30,32,32,31,30,32,31] K1(B,D,[R,Q],[P],[],[],[],[]). given clause #406: (wt=15) 418 [hyper,363,5,demod,33,33,33,34] K2(D,B,[],[P,Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 488 [hyper,418,9] H(B,[],[P,Q,R],[],[],[],[]). given clause #407: (wt=14) 488 [hyper,418,9] H(B,[],[P,Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 489 [hyper,488,12,demod,30,32,32,32,31,30,31] K1(B,D,[R,Q,P],[],[],[],[],[]). given clause #408: (wt=15) 419 [hyper,366,5,demod,33,34] K2(F,C,[],[R],[],[],[],[P,Q]). ** KEPT (pick-wt=14): 490 [hyper,419,18,demod,30,32,31,30,31] H(C,[],[],[R],[],[P,Q],[]). given clause #409: (wt=14) 490 [hyper,419,18,demod,30,32,31,30,31] H(C,[],[],[R],[],[P,Q],[]). ** KEPT (pick-wt=15): 491 [hyper,490,1] K1(C,F,[R],[],[],[],[],[P,Q]). given clause #410: (wt=15) 420 [hyper,369,5,demod,33,33,34] K2(F,C,[],[R,Q],[],[],[],[P]). ** KEPT (pick-wt=14): 492 [hyper,420,18,demod,30,32,32,31,30,31] H(C,[],[],[Q,R],[],[P],[]). given clause #411: (wt=14) 492 [hyper,420,18,demod,30,32,32,31,30,31] H(C,[],[],[Q,R],[],[P],[]). ** KEPT (pick-wt=14): 493 [hyper,492,24,eval] H(C,[Q],[],[R],[],[P],[]). ** KEPT (pick-wt=15): 494 [hyper,492,1] K1(C,F,[Q,R],[],[],[],[],[P]). given clause #412: (wt=14) 493 [hyper,492,24,eval] H(C,[Q],[],[R],[],[P],[]). ** KEPT (pick-wt=15): 495 [hyper,493,1] K1(C,F,[R],[],[Q],[],[],[P]). given clause #413: (wt=15) 421 [hyper,371,6,eval,demod,33,34] K2(F,E,[P],[R],[],[],[],[Q]). given clause #414: (wt=15) 422 [hyper,371,5,demod,33,33,34] K2(F,E,[],[P,R],[],[],[],[Q]). given clause #415: (wt=15) 423 [hyper,372,6,eval,demod,33,34] K2(F,C,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=14): 496 [hyper,423,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[Q],[],[P]). given clause #416: (wt=14) 496 [hyper,423,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[Q],[],[P]). ** KEPT (pick-wt=15): 497 [hyper,496,1] K1(C,F,[R],[P],[],[],[Q],[]). given clause #417: (wt=15) 424 [hyper,372,5,demod,33,33,34] K2(F,C,[],[P,R],[],[],[Q],[]). ** KEPT (pick-wt=14): 498 [hyper,424,18,demod,30,32,32,31,30,31] H(C,[],[],[R,P],[Q],[],[]). given clause #418: (wt=14) 498 [hyper,424,18,demod,30,32,32,31,30,31] H(C,[],[],[R,P],[Q],[],[]). ** KEPT (pick-wt=15): 499 [hyper,498,1] K1(C,F,[R,P],[],[],[],[Q],[]). given clause #419: (wt=15) 425 [hyper,374,5,demod,33,34] K2(F,E,[],[R],[P],[],[],[Q]). given clause #420: (wt=15) 426 [hyper,375,5,demod,33,34] K2(F,C,[],[R],[P],[],[Q],[]). ** KEPT (pick-wt=14): 500 [hyper,426,18,demod,30,32,31,30,31] H(C,[P],[],[R],[Q],[],[]). given clause #421: (wt=14) 500 [hyper,426,18,demod,30,32,31,30,31] H(C,[P],[],[R],[Q],[],[]). ** KEPT (pick-wt=14): 501 [hyper,500,25] H(C,[],[],[P,R],[Q],[],[]). ** KEPT (pick-wt=15): 502 [hyper,500,1] K1(C,F,[R],[],[P],[],[Q],[]). given clause #422: (wt=14) 501 [hyper,500,25] H(C,[],[],[P,R],[Q],[],[]). ** KEPT (pick-wt=15): 503 [hyper,501,1] K1(C,F,[P,R],[],[],[],[Q],[]). given clause #423: (wt=15) 427 [hyper,377,5,demod,33,34] K2(F,E,[],[R],[],[P,Q],[],[]). given clause #424: (wt=15) 428 [hyper,378,5,demod,33,34] K2(F,C,[],[R],[],[P,Q],[],[]). ** KEPT (pick-wt=14): 504 [hyper,428,18,demod,30,32,31,30,31] H(C,[],[P,Q],[R],[],[],[]). given clause #425: (wt=14) 504 [hyper,428,18,demod,30,32,31,30,31] H(C,[],[P,Q],[R],[],[],[]). ** KEPT (pick-wt=15): 505 [hyper,504,1] K1(C,F,[R],[],[],[P,Q],[],[]). given clause #426: (wt=15) 429 [hyper,381,5,demod,33,34] K2(D,B,[],[R,Q],[],[],[P],[]). given clause #427: (wt=15) 430 [hyper,383,6,eval,demod,33,34] K2(F,E,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 506 [hyper,430,19,demod,30,32,31,30,32,31] H(E,[],[Q],[],[],[R],[P]). given clause #428: (wt=14) 506 [hyper,430,19,demod,30,32,31,30,32,31] H(E,[],[Q],[],[],[R],[P]). ** KEPT (pick-wt=15): 507 [hyper,506,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 508 [hyper,506,4] K1(E,F,[R],[P],[],[Q],[],[]). given clause #429: (wt=15) 431 [hyper,383,5,demod,33,33,34] K2(F,E,[],[P,R],[],[Q],[],[]). given clause #430: (wt=15) 432 [hyper,384,6,eval,demod,33,34] K2(F,C,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 509 [hyper,432,18,demod,30,32,31,30,32,31] H(C,[],[Q],[R],[],[],[P]). given clause #431: (wt=14) 509 [hyper,432,18,demod,30,32,31,30,32,31] H(C,[],[Q],[R],[],[],[P]). ** KEPT (pick-wt=15): 510 [hyper,509,1] K1(C,F,[R],[P],[],[Q],[],[]). given clause #432: (wt=15) 433 [hyper,384,5,demod,33,33,34] K2(F,C,[],[P,R],[],[Q],[],[]). ** KEPT (pick-wt=14): 511 [hyper,433,18,demod,30,32,32,31,30,31] H(C,[],[Q],[R,P],[],[],[]). given clause #433: (wt=14) 511 [hyper,433,18,demod,30,32,32,31,30,31] H(C,[],[Q],[R,P],[],[],[]). ** KEPT (pick-wt=15): 512 [hyper,511,1] K1(C,F,[R,P],[],[],[Q],[],[]). given clause #434: (wt=15) 434 [hyper,387,5,demod,33,34] K2(D,B,[],[R],[],[],[P,Q],[]). ** KEPT (pick-wt=14): 513 [hyper,434,9] H(B,[],[R],[],[],[P,Q],[]). given clause #435: (wt=14) 513 [hyper,434,9] H(B,[],[R],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 514 [hyper,513,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[P,Q],[]). given clause #436: (wt=15) 435 [hyper,390,5,demod,33,33,34] K2(D,B,[],[R,P],[],[],[Q],[]). ** KEPT (pick-wt=14): 515 [hyper,435,9] H(B,[],[R,P],[],[],[Q],[]). given clause #437: (wt=14) 515 [hyper,435,9] H(B,[],[R,P],[],[],[Q],[]). ** KEPT (pick-wt=14): 516 [hyper,515,20] H(B,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 517 [hyper,515,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[],[Q],[]). given clause #438: (wt=14) 516 [hyper,515,20] H(B,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 518 [hyper,516,12,demod,30,32,31,30,31] K1(B,D,[R],[],[P],[],[Q],[]). given clause #439: (wt=15) 436 [hyper,392,7] K2(F,E,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 519 [hyper,436,19,demod,30,32,31,30,32,32,31] H(E,[],[],[],[],[R],[P,Q]). given clause #440: (wt=14) 519 [hyper,436,19,demod,30,32,31,30,32,32,31] H(E,[],[],[],[],[R],[P,Q]). ** KEPT (pick-wt=15): 520 [hyper,519,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 521 [hyper,519,4] K1(E,F,[R],[P,Q],[],[],[],[]). given clause #441: (wt=15) 437 [hyper,392,6,eval,demod,33,33,34] K2(F,E,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=14): 522 [hyper,437,19,demod,30,32,32,31,30,32,31] H(E,[],[],[],[],[R,P],[Q]). given clause #442: (wt=14) 522 [hyper,437,19,demod,30,32,32,31,30,32,31] H(E,[],[],[],[],[R,P],[Q]). ** KEPT (pick-wt=15): 523 [hyper,522,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 524 [hyper,522,4] K1(E,F,[R,P],[Q],[],[],[],[]). given clause #443: (wt=15) 438 [hyper,392,5,demod,33,33,33,34] K2(F,E,[],[Q,P,R],[],[],[],[]). given clause #444: (wt=15) 439 [hyper,393,7] K2(F,C,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 525 [hyper,439,18,demod,30,32,31,30,32,32,31] H(C,[],[],[R],[],[],[P,Q]). given clause #445: (wt=14) 525 [hyper,439,18,demod,30,32,31,30,32,32,31] H(C,[],[],[R],[],[],[P,Q]). ** KEPT (pick-wt=15): 526 [hyper,525,1] K1(C,F,[R],[P,Q],[],[],[],[]). given clause #446: (wt=15) 440 [hyper,393,6,eval,demod,33,33,34] K2(F,C,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=14): 527 [hyper,440,18,demod,30,32,32,31,30,32,31] H(C,[],[],[R,P],[],[],[Q]). given clause #447: (wt=14) 527 [hyper,440,18,demod,30,32,32,31,30,32,31] H(C,[],[],[R,P],[],[],[Q]). ** KEPT (pick-wt=15): 528 [hyper,527,1] K1(C,F,[R,P],[Q],[],[],[],[]). given clause #448: (wt=15) 441 [hyper,393,5,demod,33,33,33,34] K2(F,C,[],[Q,P,R],[],[],[],[]). ** KEPT (pick-wt=14): 529 [hyper,441,18,demod,30,32,32,32,31,30,31] H(C,[],[],[R,P,Q],[],[],[]). given clause #449: (wt=14) 529 [hyper,441,18,demod,30,32,32,32,31,30,31] H(C,[],[],[R,P,Q],[],[],[]). ** KEPT (pick-wt=15): 530 [hyper,529,1] K1(C,F,[R,P,Q],[],[],[],[],[]). given clause #450: (wt=15) 443 [hyper,442,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[],[],[],[P]). given clause #451: (wt=15) 444 [hyper,442,4] K1(E,F,[R],[P],[],[],[],[Q]). given clause #452: (wt=15) 446 [hyper,445,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 531 [hyper,446,5,demod,33,34] K2(B,D,[],[R,Q],[],[],[],[P]). given clause #453: (wt=15) 448 [hyper,447,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[],[],[],[P]). given clause #454: (wt=15) 450 [hyper,449,1] K1(C,F,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 532 [hyper,450,5,demod,33,34] K2(C,F,[],[R,P],[],[],[],[Q]). given clause #455: (wt=15) 452 [hyper,451,1] K1(C,F,[R,P],[],[],[],[],[Q]). given clause #456: (wt=15) 454 [hyper,453,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 533 [hyper,454,5,demod,33,34] K2(B,D,[],[R,Q],[],[],[P],[]). given clause #457: (wt=15) 456 [hyper,455,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[],[],[P],[]). given clause #458: (wt=15) 459 [hyper,457,12,demod,30,32,31,30,31] K1(B,D,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 534 [hyper,459,5,demod,33,34] K2(B,D,[],[R],[Q],[],[],[P]). given clause #459: (wt=15) 460 [hyper,458,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 535 [hyper,460,6,eval,demod,33,34] K2(B,D,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 536 [hyper,460,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[],[],[P]). given clause #460: (wt=15) 463 [hyper,461,12,demod,30,32,31,30,31] K1(B,D,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 537 [hyper,463,5,demod,33,34] K2(B,D,[],[R],[Q],[],[P],[]). given clause #461: (wt=15) 464 [hyper,462,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 538 [hyper,464,6,eval,demod,33,34] K2(B,D,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 539 [hyper,464,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[],[P],[]). given clause #462: (wt=15) 467 [hyper,465,1] K1(C,F,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 540 [hyper,467,5,demod,33,34] K2(C,F,[],[R],[P],[],[],[Q]). given clause #463: (wt=15) 468 [hyper,466,1] K1(C,F,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 541 [hyper,468,6,eval,demod,33,34] K2(C,F,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 542 [hyper,468,5,demod,33,33,34] K2(C,F,[],[P,R],[],[],[],[Q]). given clause #464: (wt=15) 470 [hyper,469,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 543 [hyper,470,5,demod,33,34] K2(B,D,[],[R],[],[P,Q],[],[]). given clause #465: (wt=15) 472 [hyper,471,13,demod,30,32,31,30,32,31] K1(E,D,[R],[Q],[],[],[P],[]). given clause #466: (wt=15) 473 [hyper,471,4] K1(E,F,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 544 [hyper,473,5,demod,33,34] K2(E,F,[],[R],[],[],[P],[Q]). given clause #467: (wt=15) 475 [hyper,474,12,demod,30,32,31,30,32,31] K1(B,D,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 545 [hyper,475,5,demod,33,34] K2(B,D,[],[R,Q],[],[P],[],[]). given clause #468: (wt=15) 477 [hyper,476,12,demod,30,32,32,31,30,31] K1(B,D,[R,Q],[],[],[P],[],[]). given clause #469: (wt=15) 479 [hyper,478,13,demod,30,32,31,30,32,32,31] K1(E,D,[R],[Q,P],[],[],[],[]). given clause #470: (wt=15) 480 [hyper,478,4] K1(E,F,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 546 [hyper,480,5,demod,33,34] K2(E,F,[],[R],[],[],[],[P,Q]). given clause #471: (wt=15) 482 [hyper,481,13,demod,30,32,32,31,30,32,31] K1(E,D,[R,Q],[P],[],[],[],[]). given clause #472: (wt=15) 483 [hyper,481,4] K1(E,F,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 547 [hyper,483,6,eval,demod,33,34] K2(E,F,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 548 [hyper,483,5,demod,33,33,34] K2(E,F,[],[Q,R],[],[],[],[P]). given clause #473: (wt=15) 485 [hyper,484,12,demod,30,32,31,30,32,32,31] K1(B,D,[R],[Q,P],[],[],[],[]). ** KEPT (pick-wt=15): 549 [hyper,485,5,demod,33,34] K2(B,D,[],[R,Q,P],[],[],[],[]). given clause #474: (wt=15) 487 [hyper,486,12,demod,30,32,32,31,30,32,31] K1(B,D,[R,Q],[P],[],[],[],[]). given clause #475: (wt=15) 489 [hyper,488,12,demod,30,32,32,32,31,30,31] K1(B,D,[R,Q,P],[],[],[],[],[]). given clause #476: (wt=15) 491 [hyper,490,1] K1(C,F,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 550 [hyper,491,5,demod,33,34] K2(C,F,[],[R],[],[],[],[P,Q]). given clause #477: (wt=15) 494 [hyper,492,1] K1(C,F,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 551 [hyper,494,6,eval,demod,33,34] K2(C,F,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 552 [hyper,494,5,demod,33,33,34] K2(C,F,[],[Q,R],[],[],[],[P]). given clause #478: (wt=15) 495 [hyper,493,1] K1(C,F,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 553 [hyper,495,5,demod,33,34] K2(C,F,[],[R],[Q],[],[],[P]). given clause #479: (wt=15) 497 [hyper,496,1] K1(C,F,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 554 [hyper,497,5,demod,33,34] K2(C,F,[],[R,P],[],[],[Q],[]). given clause #480: (wt=15) 499 [hyper,498,1] K1(C,F,[R,P],[],[],[],[Q],[]). given clause #481: (wt=15) 502 [hyper,500,1] K1(C,F,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 555 [hyper,502,5,demod,33,34] K2(C,F,[],[R],[P],[],[Q],[]). given clause #482: (wt=15) 503 [hyper,501,1] K1(C,F,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 556 [hyper,503,6,eval,demod,33,34] K2(C,F,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 557 [hyper,503,5,demod,33,33,34] K2(C,F,[],[P,R],[],[],[Q],[]). given clause #483: (wt=15) 505 [hyper,504,1] K1(C,F,[R],[],[],[P,Q],[],[]). ** KEPT (pick-wt=15): 558 [hyper,505,5,demod,33,34] K2(C,F,[],[R],[],[P,Q],[],[]). given clause #484: (wt=15) 507 [hyper,506,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 559 [hyper,507,5,demod,33,34] K2(E,D,[],[R],[],[Q],[],[P]). given clause #485: (wt=15) 508 [hyper,506,4] K1(E,F,[R],[P],[],[Q],[],[]). given clause #486: (wt=15) 510 [hyper,509,1] K1(C,F,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 560 [hyper,510,5,demod,33,34] K2(C,F,[],[R,P],[],[Q],[],[]). given clause #487: (wt=15) 512 [hyper,511,1] K1(C,F,[R,P],[],[],[Q],[],[]). given clause #488: (wt=15) 514 [hyper,513,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 561 [hyper,514,5,demod,33,34] K2(B,D,[],[R],[],[],[P,Q],[]). given clause #489: (wt=15) 517 [hyper,515,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 562 [hyper,517,6,eval,demod,33,34] K2(B,D,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 563 [hyper,517,5,demod,33,33,34] K2(B,D,[],[P,R],[],[],[Q],[]). given clause #490: (wt=15) 518 [hyper,516,12,demod,30,32,31,30,31] K1(B,D,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 564 [hyper,518,5,demod,33,34] K2(B,D,[],[R],[P],[],[Q],[]). given clause #491: (wt=15) 520 [hyper,519,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 565 [hyper,520,5,demod,33,34] K2(E,D,[],[R],[],[],[],[P,Q]). given clause #492: (wt=15) 521 [hyper,519,4] K1(E,F,[R],[P,Q],[],[],[],[]). given clause #493: (wt=15) 523 [hyper,522,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 566 [hyper,523,6,eval,demod,33,34] K2(E,D,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 567 [hyper,523,5,demod,33,33,34] K2(E,D,[],[P,R],[],[],[],[Q]). given clause #494: (wt=15) 524 [hyper,522,4] K1(E,F,[R,P],[Q],[],[],[],[]). given clause #495: (wt=15) 526 [hyper,525,1] K1(C,F,[R],[P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 568 [hyper,526,5,demod,33,34] K2(C,F,[],[R,P,Q],[],[],[],[]). given clause #496: (wt=15) 528 [hyper,527,1] K1(C,F,[R,P],[Q],[],[],[],[]). given clause #497: (wt=15) 530 [hyper,529,1] K1(C,F,[R,P,Q],[],[],[],[],[]). given clause #498: (wt=15) 531 [hyper,446,5,demod,33,34] K2(B,D,[],[R,Q],[],[],[],[P]). given clause #499: (wt=15) 532 [hyper,450,5,demod,33,34] K2(C,F,[],[R,P],[],[],[],[Q]). given clause #500: (wt=15) 533 [hyper,454,5,demod,33,34] K2(B,D,[],[R,Q],[],[],[P],[]). given clause #501: (wt=15) 534 [hyper,459,5,demod,33,34] K2(B,D,[],[R],[Q],[],[],[P]). given clause #502: (wt=15) 535 [hyper,460,6,eval,demod,33,34] K2(B,D,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 569 [hyper,535,16,demod,30,32,31,30,32,31] H(D,[],[Q],[],[R],[],[P]). given clause #503: (wt=14) 569 [hyper,535,16,demod,30,32,31,30,32,31] H(D,[],[Q],[],[R],[],[P]). ** KEPT (pick-wt=15): 570 [hyper,569,3] K1(D,E,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 571 [hyper,569,2] K1(D,B,[R],[Q],[],[],[],[P]). given clause #504: (wt=15) 536 [hyper,460,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[],[],[P]). ** KEPT (pick-wt=14): 572 [hyper,536,16,demod,30,31,30,32,32,31] H(D,[],[],[],[R,Q],[],[P]). given clause #505: (wt=14) 572 [hyper,536,16,demod,30,31,30,32,32,31] H(D,[],[],[],[R,Q],[],[P]). ** KEPT (pick-wt=15): 573 [hyper,572,3] K1(D,E,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 574 [hyper,572,2] K1(D,B,[R,Q],[],[],[],[],[P]). given clause #506: (wt=15) 537 [hyper,463,5,demod,33,34] K2(B,D,[],[R],[Q],[],[P],[]). given clause #507: (wt=15) 538 [hyper,464,6,eval,demod,33,34] K2(B,D,[Q],[R],[],[],[P],[]). given clause #508: (wt=15) 539 [hyper,464,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[],[P],[]). ** KEPT (pick-wt=14): 575 [hyper,539,16,demod,30,31,30,32,32,31] H(D,[],[],[],[R,Q],[P],[]). given clause #509: (wt=14) 575 [hyper,539,16,demod,30,31,30,32,32,31] H(D,[],[],[],[R,Q],[P],[]). ** KEPT (pick-wt=15): 576 [hyper,575,3] K1(D,E,[R,Q],[P],[],[],[],[]). ** KEPT (pick-wt=15): 577 [hyper,575,2] K1(D,B,[R,Q],[],[],[],[P],[]). given clause #510: (wt=15) 540 [hyper,467,5,demod,33,34] K2(C,F,[],[R],[P],[],[],[Q]). given clause #511: (wt=15) 541 [hyper,468,6,eval,demod,33,34] K2(C,F,[P],[R],[],[],[],[Q]). given clause #512: (wt=15) 542 [hyper,468,5,demod,33,33,34] K2(C,F,[],[P,R],[],[],[],[Q]). ** KEPT (pick-wt=14): 578 [hyper,542,8] H(F,[],[],[],[],[Q],[P,R]). given clause #513: (wt=14) 578 [hyper,542,8] H(F,[],[],[],[],[Q],[P,R]). ** KEPT (pick-wt=15): 579 [hyper,578,15,demod,30,32,32,31,30,32,31] K1(F,E,[R,P],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 580 [hyper,578,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[],[],[],[Q]). given clause #514: (wt=15) 543 [hyper,470,5,demod,33,34] K2(B,D,[],[R],[],[P,Q],[],[]). given clause #515: (wt=15) 544 [hyper,473,5,demod,33,34] K2(E,F,[],[R],[],[],[P],[Q]). ** KEPT (pick-wt=14): 581 [hyper,544,11] H(F,[],[],[P],[Q],[],[R]). given clause #516: (wt=14) 581 [hyper,544,11] H(F,[],[],[P],[Q],[],[R]). ** KEPT (pick-wt=15): 582 [hyper,581,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 583 [hyper,581,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[],[],[Q],[]). given clause #517: (wt=15) 545 [hyper,475,5,demod,33,34] K2(B,D,[],[R,Q],[],[P],[],[]). given clause #518: (wt=15) 546 [hyper,480,5,demod,33,34] K2(E,F,[],[R],[],[],[],[P,Q]). ** KEPT (pick-wt=14): 584 [hyper,546,11] H(F,[],[],[],[P,Q],[],[R]). given clause #519: (wt=14) 584 [hyper,546,11] H(F,[],[],[],[P,Q],[],[R]). ** KEPT (pick-wt=15): 585 [hyper,584,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 586 [hyper,584,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[P,Q],[]). given clause #520: (wt=15) 547 [hyper,483,6,eval,demod,33,34] K2(E,F,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 587 [hyper,547,11] H(F,[],[],[],[P],[Q],[R]). given clause #521: (wt=14) 587 [hyper,547,11] H(F,[],[],[],[P],[Q],[R]). ** KEPT (pick-wt=15): 588 [hyper,587,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 589 [hyper,587,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[P],[Q]). given clause #522: (wt=15) 548 [hyper,483,5,demod,33,33,34] K2(E,F,[],[Q,R],[],[],[],[P]). ** KEPT (pick-wt=14): 590 [hyper,548,11] H(F,[],[],[],[P],[],[Q,R]). given clause #523: (wt=14) 590 [hyper,548,11] H(F,[],[],[],[P],[],[Q,R]). ** KEPT (pick-wt=15): 591 [hyper,590,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 592 [hyper,590,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[],[],[P],[]). given clause #524: (wt=15) 549 [hyper,485,5,demod,33,34] K2(B,D,[],[R,Q,P],[],[],[],[]). given clause #525: (wt=15) 550 [hyper,491,5,demod,33,34] K2(C,F,[],[R],[],[],[],[P,Q]). given clause #526: (wt=15) 551 [hyper,494,6,eval,demod,33,34] K2(C,F,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 593 [hyper,551,8] H(F,[],[],[Q],[],[P],[R]). given clause #527: (wt=14) 593 [hyper,551,8] H(F,[],[],[Q],[],[P],[R]). ** KEPT (pick-wt=15): 594 [hyper,593,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 595 [hyper,593,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[],[],[],[P]). given clause #528: (wt=15) 552 [hyper,494,5,demod,33,33,34] K2(C,F,[],[Q,R],[],[],[],[P]). given clause #529: (wt=15) 553 [hyper,495,5,demod,33,34] K2(C,F,[],[R],[Q],[],[],[P]). ** KEPT (pick-wt=14): 596 [hyper,553,8] H(F,[Q],[],[],[],[P],[R]). given clause #530: (wt=14) 596 [hyper,553,8] H(F,[Q],[],[],[],[P],[R]). ** KEPT (pick-wt=15): 597 [hyper,596,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 598 [hyper,596,14,demod,30,32,31,30,31] K1(F,C,[R],[],[Q],[],[],[P]). given clause #531: (wt=15) 554 [hyper,497,5,demod,33,34] K2(C,F,[],[R,P],[],[],[Q],[]). given clause #532: (wt=15) 555 [hyper,502,5,demod,33,34] K2(C,F,[],[R],[P],[],[Q],[]). given clause #533: (wt=15) 556 [hyper,503,6,eval,demod,33,34] K2(C,F,[P],[R],[],[],[Q],[]). given clause #534: (wt=15) 557 [hyper,503,5,demod,33,33,34] K2(C,F,[],[P,R],[],[],[Q],[]). ** KEPT (pick-wt=14): 599 [hyper,557,8] H(F,[],[],[],[Q],[],[P,R]). given clause #535: (wt=14) 599 [hyper,557,8] H(F,[],[],[],[Q],[],[P,R]). ** KEPT (pick-wt=15): 600 [hyper,599,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 601 [hyper,599,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[],[],[Q],[]). given clause #536: (wt=15) 558 [hyper,505,5,demod,33,34] K2(C,F,[],[R],[],[P,Q],[],[]). given clause #537: (wt=15) 559 [hyper,507,5,demod,33,34] K2(E,D,[],[R],[],[Q],[],[P]). given clause #538: (wt=15) 560 [hyper,510,5,demod,33,34] K2(C,F,[],[R,P],[],[Q],[],[]). given clause #539: (wt=15) 561 [hyper,514,5,demod,33,34] K2(B,D,[],[R],[],[],[P,Q],[]). given clause #540: (wt=15) 562 [hyper,517,6,eval,demod,33,34] K2(B,D,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=14): 602 [hyper,562,16,demod,30,32,31,30,32,31] H(D,[],[P],[],[R],[Q],[]). given clause #541: (wt=14) 602 [hyper,562,16,demod,30,32,31,30,32,31] H(D,[],[P],[],[R],[Q],[]). ** KEPT (pick-wt=15): 603 [hyper,602,3] K1(D,E,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 604 [hyper,602,2] K1(D,B,[R],[P],[],[],[Q],[]). given clause #542: (wt=15) 563 [hyper,517,5,demod,33,33,34] K2(B,D,[],[P,R],[],[],[Q],[]). given clause #543: (wt=15) 564 [hyper,518,5,demod,33,34] K2(B,D,[],[R],[P],[],[Q],[]). ** KEPT (pick-wt=14): 605 [hyper,564,16,demod,30,31,30,32,31] H(D,[P],[],[],[R],[Q],[]). given clause #544: (wt=14) 605 [hyper,564,16,demod,30,31,30,32,31] H(D,[P],[],[],[R],[Q],[]). ** KEPT (pick-wt=15): 606 [hyper,605,3] K1(D,E,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 607 [hyper,605,2] K1(D,B,[R],[],[P],[],[Q],[]). given clause #545: (wt=15) 565 [hyper,520,5,demod,33,34] K2(E,D,[],[R],[],[],[],[P,Q]). ** KEPT (pick-wt=14): 608 [hyper,565,17,demod,30,32,31,30,31] H(D,[],[],[],[R],[],[P,Q]). given clause #546: (wt=14) 608 [hyper,565,17,demod,30,32,31,30,31] H(D,[],[],[],[R],[],[P,Q]). ** KEPT (pick-wt=15): 609 [hyper,608,3] K1(D,E,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 610 [hyper,608,2] K1(D,B,[R],[],[],[],[],[P,Q]). given clause #547: (wt=15) 566 [hyper,523,6,eval,demod,33,34] K2(E,D,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=14): 611 [hyper,566,17,demod,30,32,31,30,32,31] H(D,[],[],[],[R],[P],[Q]). given clause #548: (wt=14) 611 [hyper,566,17,demod,30,32,31,30,32,31] H(D,[],[],[],[R],[P],[Q]). ** KEPT (pick-wt=15): 612 [hyper,611,3] K1(D,E,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 613 [hyper,611,2] K1(D,B,[R],[],[],[],[P],[Q]). given clause #549: (wt=15) 567 [hyper,523,5,demod,33,33,34] K2(E,D,[],[P,R],[],[],[],[Q]). ** KEPT (pick-wt=14): 614 [hyper,567,17,demod,30,32,32,31,30,31] H(D,[],[],[],[R,P],[],[Q]). given clause #550: (wt=14) 614 [hyper,567,17,demod,30,32,32,31,30,31] H(D,[],[],[],[R,P],[],[Q]). ** KEPT (pick-wt=15): 615 [hyper,614,3] K1(D,E,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 616 [hyper,614,2] K1(D,B,[R,P],[],[],[],[],[Q]). given clause #551: (wt=15) 568 [hyper,526,5,demod,33,34] K2(C,F,[],[R,P,Q],[],[],[],[]). given clause #552: (wt=15) 570 [hyper,569,3] K1(D,E,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 617 [hyper,570,5,demod,33,34] K2(D,E,[],[R],[],[Q],[],[P]). given clause #553: (wt=15) 571 [hyper,569,2] K1(D,B,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 618 [hyper,571,5,demod,33,34] K2(D,B,[],[R,Q],[],[],[],[P]). given clause #554: (wt=15) 573 [hyper,572,3] K1(D,E,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 619 [hyper,573,5,demod,33,33,34] K2(D,E,[],[R,Q],[],[],[],[P]). given clause #555: (wt=15) 574 [hyper,572,2] K1(D,B,[R,Q],[],[],[],[],[P]). given clause #556: (wt=15) 576 [hyper,575,3] K1(D,E,[R,Q],[P],[],[],[],[]). ** KEPT (pick-wt=15): 620 [hyper,576,5,demod,33,33,34] K2(D,E,[],[R,Q,P],[],[],[],[]). given clause #557: (wt=15) 577 [hyper,575,2] K1(D,B,[R,Q],[],[],[],[P],[]). given clause #558: (wt=15) 579 [hyper,578,15,demod,30,32,32,31,30,32,31] K1(F,E,[R,P],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 621 [hyper,579,5,demod,33,33,34] K2(F,E,[],[R,P,Q],[],[],[],[]). given clause #559: (wt=15) 580 [hyper,578,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[],[],[],[Q]). given clause #560: (wt=15) 582 [hyper,581,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 622 [hyper,582,5,demod,33,34] K2(F,E,[],[R],[],[],[P],[Q]). given clause #561: (wt=15) 583 [hyper,581,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 623 [hyper,583,5,demod,33,34] K2(F,C,[],[R,P],[],[],[Q],[]). given clause #562: (wt=15) 585 [hyper,584,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 624 [hyper,585,5,demod,33,34] K2(F,E,[],[R],[],[],[],[P,Q]). given clause #563: (wt=15) 586 [hyper,584,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 625 [hyper,586,5,demod,33,34] K2(F,C,[],[R],[],[],[P,Q],[]). given clause #564: (wt=15) 588 [hyper,587,15,demod,30,32,31,30,32,31] K1(F,E,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 626 [hyper,588,5,demod,33,34] K2(F,E,[],[R,Q],[],[],[],[P]). given clause #565: (wt=15) 589 [hyper,587,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 627 [hyper,589,5,demod,33,34] K2(F,C,[],[R],[],[],[P],[Q]). given clause #566: (wt=15) 591 [hyper,590,15,demod,30,32,32,31,30,31] K1(F,E,[R,Q],[],[],[],[],[P]). given clause #567: (wt=15) 592 [hyper,590,14,demod,30,32,32,31,30,31] K1(F,C,[R,Q],[],[],[],[P],[]). ** KEPT (pick-wt=15): 628 [hyper,592,5,demod,33,33,34] K2(F,C,[],[R,Q],[],[],[P],[]). given clause #568: (wt=15) 594 [hyper,593,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 629 [hyper,594,5,demod,33,34] K2(F,E,[],[R,P],[],[],[Q],[]). given clause #569: (wt=15) 595 [hyper,593,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[],[],[],[P]). given clause #570: (wt=15) 597 [hyper,596,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 630 [hyper,597,5,demod,33,34] K2(F,E,[],[R,P],[Q],[],[],[]). given clause #571: (wt=15) 598 [hyper,596,14,demod,30,32,31,30,31] K1(F,C,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 631 [hyper,598,5,demod,33,34] K2(F,C,[],[R],[Q],[],[],[P]). given clause #572: (wt=15) 600 [hyper,599,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 632 [hyper,600,5,demod,33,33,34] K2(F,E,[],[R,P],[],[],[],[Q]). given clause #573: (wt=15) 601 [hyper,599,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[],[],[Q],[]). given clause #574: (wt=15) 603 [hyper,602,3] K1(D,E,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 633 [hyper,603,5,demod,33,34] K2(D,E,[],[R,Q],[],[P],[],[]). given clause #575: (wt=15) 604 [hyper,602,2] K1(D,B,[R],[P],[],[],[Q],[]). given clause #576: (wt=15) 606 [hyper,605,3] K1(D,E,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 634 [hyper,606,5,demod,33,34] K2(D,E,[],[R,Q],[P],[],[],[]). given clause #577: (wt=15) 607 [hyper,605,2] K1(D,B,[R],[],[P],[],[Q],[]). ** KEPT (pick-wt=15): 635 [hyper,607,5,demod,33,34] K2(D,B,[],[R],[P],[],[Q],[]). given clause #578: (wt=15) 609 [hyper,608,3] K1(D,E,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 636 [hyper,609,5,demod,33,34] K2(D,E,[],[R],[],[],[],[P,Q]). given clause #579: (wt=15) 610 [hyper,608,2] K1(D,B,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 637 [hyper,610,5,demod,33,34] K2(D,B,[],[R],[],[],[],[P,Q]). given clause #580: (wt=15) 612 [hyper,611,3] K1(D,E,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 638 [hyper,612,5,demod,33,34] K2(D,E,[],[R,P],[],[],[],[Q]). given clause #581: (wt=15) 613 [hyper,611,2] K1(D,B,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 639 [hyper,613,5,demod,33,34] K2(D,B,[],[R],[],[],[P],[Q]). given clause #582: (wt=15) 615 [hyper,614,3] K1(D,E,[R,P],[],[],[],[],[Q]). given clause #583: (wt=15) 616 [hyper,614,2] K1(D,B,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 640 [hyper,616,5,demod,33,33,34] K2(D,B,[],[R,P],[],[],[],[Q]). given clause #584: (wt=15) 617 [hyper,570,5,demod,33,34] K2(D,E,[],[R],[],[Q],[],[P]). given clause #585: (wt=15) 618 [hyper,571,5,demod,33,34] K2(D,B,[],[R,Q],[],[],[],[P]). given clause #586: (wt=15) 619 [hyper,573,5,demod,33,33,34] K2(D,E,[],[R,Q],[],[],[],[P]). ** KEPT (pick-wt=14): 641 [hyper,619,10] H(E,[],[],[],[],[R,Q],[P]). given clause #587: (wt=14) 641 [hyper,619,10] H(E,[],[],[],[],[R,Q],[P]). ** KEPT (pick-wt=15): 642 [hyper,641,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 643 [hyper,641,4] K1(E,F,[R,Q],[P],[],[],[],[]). given clause #588: (wt=15) 620 [hyper,576,5,demod,33,33,34] K2(D,E,[],[R,Q,P],[],[],[],[]). ** KEPT (pick-wt=14): 644 [hyper,620,10] H(E,[],[],[],[],[R,Q,P],[]). given clause #589: (wt=14) 644 [hyper,620,10] H(E,[],[],[],[],[R,Q,P],[]). ** KEPT (pick-wt=15): 645 [hyper,644,13,demod,30,32,32,32,31,30,31] K1(E,D,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 646 [hyper,644,4] K1(E,F,[R,Q,P],[],[],[],[],[]). given clause #590: (wt=15) 621 [hyper,579,5,demod,33,33,34] K2(F,E,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=14): 647 [hyper,621,19,demod,30,32,32,32,31,30,31] H(E,[],[],[],[],[Q,P,R],[]). given clause #591: (wt=14) 647 [hyper,621,19,demod,30,32,32,32,31,30,31] H(E,[],[],[],[],[Q,P,R],[]). ** KEPT (pick-wt=15): 648 [hyper,647,13,demod,30,32,32,32,31,30,31] K1(E,D,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 649 [hyper,647,4] K1(E,F,[Q,P,R],[],[],[],[],[]). given clause #592: (wt=15) 622 [hyper,582,5,demod,33,34] K2(F,E,[],[R],[],[],[P],[Q]). given clause #593: (wt=15) 623 [hyper,583,5,demod,33,34] K2(F,C,[],[R,P],[],[],[Q],[]). given clause #594: (wt=15) 624 [hyper,585,5,demod,33,34] K2(F,E,[],[R],[],[],[],[P,Q]). given clause #595: (wt=15) 625 [hyper,586,5,demod,33,34] K2(F,C,[],[R],[],[],[P,Q],[]). ** KEPT (pick-wt=14): 650 [hyper,625,18,demod,30,32,31,30,31] H(C,[],[],[R],[P,Q],[],[]). given clause #596: (wt=14) 650 [hyper,625,18,demod,30,32,31,30,31] H(C,[],[],[R],[P,Q],[],[]). ** KEPT (pick-wt=15): 651 [hyper,650,1] K1(C,F,[R],[],[],[],[P,Q],[]). given clause #597: (wt=15) 626 [hyper,588,5,demod,33,34] K2(F,E,[],[R,Q],[],[],[],[P]). given clause #598: (wt=15) 627 [hyper,589,5,demod,33,34] K2(F,C,[],[R],[],[],[P],[Q]). ** KEPT (pick-wt=14): 652 [hyper,627,18,demod,30,32,31,30,31] H(C,[],[],[R],[P],[Q],[]). given clause #599: (wt=14) 652 [hyper,627,18,demod,30,32,31,30,31] H(C,[],[],[R],[P],[Q],[]). ** KEPT (pick-wt=15): 653 [hyper,652,1] K1(C,F,[R],[],[],[],[P],[Q]). given clause #600: (wt=15) 628 [hyper,592,5,demod,33,33,34] K2(F,C,[],[R,Q],[],[],[P],[]). ** KEPT (pick-wt=14): 654 [hyper,628,18,demod,30,32,32,31,30,31] H(C,[],[],[Q,R],[P],[],[]). given clause #601: (wt=14) 654 [hyper,628,18,demod,30,32,32,31,30,31] H(C,[],[],[Q,R],[P],[],[]). ** KEPT (pick-wt=14): 655 [hyper,654,24,eval] H(C,[Q],[],[R],[P],[],[]). ** KEPT (pick-wt=15): 656 [hyper,654,1] K1(C,F,[Q,R],[],[],[],[P],[]). given clause #602: (wt=14) 655 [hyper,654,24,eval] H(C,[Q],[],[R],[P],[],[]). ** KEPT (pick-wt=15): 657 [hyper,655,1] K1(C,F,[R],[],[Q],[],[P],[]). given clause #603: (wt=15) 629 [hyper,594,5,demod,33,34] K2(F,E,[],[R,P],[],[],[Q],[]). ** KEPT (pick-wt=14): 658 [hyper,629,19,demod,30,32,32,31,30,31] H(E,[],[],[Q],[],[P,R],[]). given clause #604: (wt=14) 658 [hyper,629,19,demod,30,32,32,31,30,31] H(E,[],[],[Q],[],[P,R],[]). ** KEPT (pick-wt=15): 659 [hyper,658,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 660 [hyper,658,4] K1(E,F,[P,R],[],[],[],[Q],[]). given clause #605: (wt=15) 630 [hyper,597,5,demod,33,34] K2(F,E,[],[R,P],[Q],[],[],[]). ** KEPT (pick-wt=14): 661 [hyper,630,19,demod,30,32,32,31,30,31] H(E,[Q],[],[],[],[P,R],[]). given clause #606: (wt=14) 661 [hyper,630,19,demod,30,32,32,31,30,31] H(E,[Q],[],[],[],[P,R],[]). ** KEPT (pick-wt=15): 662 [hyper,661,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 663 [hyper,661,4] K1(E,F,[P,R],[],[Q],[],[],[]). given clause #607: (wt=15) 631 [hyper,598,5,demod,33,34] K2(F,C,[],[R],[Q],[],[],[P]). given clause #608: (wt=15) 632 [hyper,600,5,demod,33,33,34] K2(F,E,[],[R,P],[],[],[],[Q]). ** KEPT (pick-wt=14): 664 [hyper,632,19,demod,30,32,32,31,30,31] H(E,[],[],[],[Q],[P,R],[]). given clause #609: (wt=14) 664 [hyper,632,19,demod,30,32,32,31,30,31] H(E,[],[],[],[Q],[P,R],[]). ** KEPT (pick-wt=15): 665 [hyper,664,13,demod,30,32,32,31,30,32,31] K1(E,D,[R,P],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 666 [hyper,664,4] K1(E,F,[P,R],[],[],[],[],[Q]). given clause #610: (wt=15) 633 [hyper,603,5,demod,33,34] K2(D,E,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=14): 667 [hyper,633,10] H(E,[],[P],[],[],[R,Q],[]). given clause #611: (wt=14) 667 [hyper,633,10] H(E,[],[P],[],[],[R,Q],[]). ** KEPT (pick-wt=15): 668 [hyper,667,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 669 [hyper,667,4] K1(E,F,[R,Q],[],[],[P],[],[]). given clause #612: (wt=15) 634 [hyper,606,5,demod,33,34] K2(D,E,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=14): 670 [hyper,634,10] H(E,[P],[],[],[],[R,Q],[]). given clause #613: (wt=14) 670 [hyper,634,10] H(E,[P],[],[],[],[R,Q],[]). ** KEPT (pick-wt=15): 671 [hyper,670,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 672 [hyper,670,4] K1(E,F,[R,Q],[],[P],[],[],[]). given clause #614: (wt=15) 635 [hyper,607,5,demod,33,34] K2(D,B,[],[R],[P],[],[Q],[]). given clause #615: (wt=15) 636 [hyper,609,5,demod,33,34] K2(D,E,[],[R],[],[],[],[P,Q]). given clause #616: (wt=15) 637 [hyper,610,5,demod,33,34] K2(D,B,[],[R],[],[],[],[P,Q]). ** KEPT (pick-wt=14): 673 [hyper,637,9] H(B,[],[R],[],[],[],[P,Q]). given clause #617: (wt=14) 673 [hyper,637,9] H(B,[],[R],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 674 [hyper,673,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[],[P,Q]). given clause #618: (wt=15) 638 [hyper,612,5,demod,33,34] K2(D,E,[],[R,P],[],[],[],[Q]). given clause #619: (wt=15) 639 [hyper,613,5,demod,33,34] K2(D,B,[],[R],[],[],[P],[Q]). ** KEPT (pick-wt=14): 675 [hyper,639,9] H(B,[],[R],[],[],[P],[Q]). given clause #620: (wt=14) 675 [hyper,639,9] H(B,[],[R],[],[],[P],[Q]). ** KEPT (pick-wt=15): 676 [hyper,675,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[P],[Q]). given clause #621: (wt=15) 640 [hyper,616,5,demod,33,33,34] K2(D,B,[],[R,P],[],[],[],[Q]). ** KEPT (pick-wt=14): 677 [hyper,640,9] H(B,[],[R,P],[],[],[],[Q]). given clause #622: (wt=14) 677 [hyper,640,9] H(B,[],[R,P],[],[],[],[Q]). ** KEPT (pick-wt=14): 678 [hyper,677,20] H(B,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 679 [hyper,677,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[],[],[Q]). given clause #623: (wt=14) 678 [hyper,677,20] H(B,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 680 [hyper,678,12,demod,30,32,31,30,31] K1(B,D,[R],[],[P],[],[],[Q]). given clause #624: (wt=15) 642 [hyper,641,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 681 [hyper,642,6,eval,demod,33,34] K2(E,D,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 682 [hyper,642,5,demod,33,33,34] K2(E,D,[],[Q,R],[],[],[],[P]). given clause #625: (wt=15) 643 [hyper,641,4] K1(E,F,[R,Q],[P],[],[],[],[]). ** KEPT (pick-wt=15): 683 [hyper,643,5,demod,33,33,34] K2(E,F,[],[R,Q,P],[],[],[],[]). given clause #626: (wt=15) 645 [hyper,644,13,demod,30,32,32,32,31,30,31] K1(E,D,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 684 [hyper,645,7] K2(E,D,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 685 [hyper,645,6,eval,demod,33,33,34] K2(E,D,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 686 [hyper,645,5,demod,33,33,33,34] K2(E,D,[],[P,Q,R],[],[],[],[]). given clause #627: (wt=15) 646 [hyper,644,4] K1(E,F,[R,Q,P],[],[],[],[],[]). given clause #628: (wt=15) 648 [hyper,647,13,demod,30,32,32,32,31,30,31] K1(E,D,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 687 [hyper,648,5,demod,33,33,33,34] K2(E,D,[],[R,P,Q],[],[],[],[]). given clause #629: (wt=15) 649 [hyper,647,4] K1(E,F,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 688 [hyper,649,7] K2(E,F,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 689 [hyper,649,6,eval,demod,33,33,34] K2(E,F,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 690 [hyper,649,5,demod,33,33,33,34] K2(E,F,[],[Q,P,R],[],[],[],[]). given clause #630: (wt=15) 651 [hyper,650,1] K1(C,F,[R],[],[],[],[P,Q],[]). ** KEPT (pick-wt=15): 691 [hyper,651,5,demod,33,34] K2(C,F,[],[R],[],[],[P,Q],[]). given clause #631: (wt=15) 653 [hyper,652,1] K1(C,F,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 692 [hyper,653,5,demod,33,34] K2(C,F,[],[R],[],[],[P],[Q]). given clause #632: (wt=15) 656 [hyper,654,1] K1(C,F,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 693 [hyper,656,6,eval,demod,33,34] K2(C,F,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 694 [hyper,656,5,demod,33,33,34] K2(C,F,[],[Q,R],[],[],[P],[]). given clause #633: (wt=15) 657 [hyper,655,1] K1(C,F,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 695 [hyper,657,5,demod,33,34] K2(C,F,[],[R],[Q],[],[P],[]). given clause #634: (wt=15) 659 [hyper,658,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 696 [hyper,659,5,demod,33,33,34] K2(E,D,[],[R,P],[],[],[Q],[]). given clause #635: (wt=15) 660 [hyper,658,4] K1(E,F,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 697 [hyper,660,6,eval,demod,33,34] K2(E,F,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 698 [hyper,660,5,demod,33,33,34] K2(E,F,[],[P,R],[],[],[Q],[]). given clause #636: (wt=15) 662 [hyper,661,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 699 [hyper,662,5,demod,33,33,34] K2(E,D,[],[R,P],[Q],[],[],[]). given clause #637: (wt=15) 663 [hyper,661,4] K1(E,F,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 700 [hyper,663,6,eval,demod,33,34] K2(E,F,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 701 [hyper,663,5,demod,33,33,34] K2(E,F,[],[P,R],[Q],[],[],[]). given clause #638: (wt=15) 665 [hyper,664,13,demod,30,32,32,31,30,32,31] K1(E,D,[R,P],[Q],[],[],[],[]). given clause #639: (wt=15) 666 [hyper,664,4] K1(E,F,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 702 [hyper,666,6,eval,demod,33,34] K2(E,F,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 703 [hyper,666,5,demod,33,33,34] K2(E,F,[],[P,R],[],[],[],[Q]). given clause #640: (wt=15) 668 [hyper,667,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 704 [hyper,668,6,eval,demod,33,34] K2(E,D,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 705 [hyper,668,5,demod,33,33,34] K2(E,D,[],[Q,R],[],[P],[],[]). given clause #641: (wt=15) 669 [hyper,667,4] K1(E,F,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 706 [hyper,669,5,demod,33,33,34] K2(E,F,[],[R,Q],[],[P],[],[]). given clause #642: (wt=15) 671 [hyper,670,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 707 [hyper,671,6,eval,demod,33,34] K2(E,D,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 708 [hyper,671,5,demod,33,33,34] K2(E,D,[],[Q,R],[P],[],[],[]). given clause #643: (wt=15) 672 [hyper,670,4] K1(E,F,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 709 [hyper,672,5,demod,33,33,34] K2(E,F,[],[R,Q],[P],[],[],[]). given clause #644: (wt=15) 674 [hyper,673,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[],[P,Q]). ** KEPT (pick-wt=15): 710 [hyper,674,5,demod,33,34] K2(B,D,[],[R],[],[],[],[P,Q]). given clause #645: (wt=15) 676 [hyper,675,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 711 [hyper,676,5,demod,33,34] K2(B,D,[],[R],[],[],[P],[Q]). given clause #646: (wt=15) 679 [hyper,677,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 712 [hyper,679,6,eval,demod,33,34] K2(B,D,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 713 [hyper,679,5,demod,33,33,34] K2(B,D,[],[P,R],[],[],[],[Q]). given clause #647: (wt=15) 680 [hyper,678,12,demod,30,32,31,30,31] K1(B,D,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 714 [hyper,680,5,demod,33,34] K2(B,D,[],[R],[P],[],[],[Q]). given clause #648: (wt=15) 681 [hyper,642,6,eval,demod,33,34] K2(E,D,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 715 [hyper,681,17,demod,30,32,31,30,32,31] H(D,[],[],[],[R],[Q],[P]). given clause #649: (wt=14) 715 [hyper,681,17,demod,30,32,31,30,32,31] H(D,[],[],[],[R],[Q],[P]). ** KEPT (pick-wt=15): 716 [hyper,715,3] K1(D,E,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 717 [hyper,715,2] K1(D,B,[R],[],[],[],[Q],[P]). given clause #650: (wt=15) 682 [hyper,642,5,demod,33,33,34] K2(E,D,[],[Q,R],[],[],[],[P]). given clause #651: (wt=15) 683 [hyper,643,5,demod,33,33,34] K2(E,F,[],[R,Q,P],[],[],[],[]). ** KEPT (pick-wt=14): 718 [hyper,683,11] H(F,[],[],[],[],[],[R,Q,P]). given clause #652: (wt=14) 718 [hyper,683,11] H(F,[],[],[],[],[],[R,Q,P]). ** KEPT (pick-wt=15): 719 [hyper,718,15,demod,30,32,32,32,31,30,31] K1(F,E,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 720 [hyper,718,14,demod,30,32,32,32,31,30,31] K1(F,C,[P,Q,R],[],[],[],[],[]). given clause #653: (wt=15) 684 [hyper,645,7] K2(E,D,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 721 [hyper,684,17,demod,30,32,31,30,32,32,31] H(D,[],[],[],[R],[Q,P],[]). given clause #654: (wt=14) 721 [hyper,684,17,demod,30,32,31,30,32,32,31] H(D,[],[],[],[R],[Q,P],[]). ** KEPT (pick-wt=15): 722 [hyper,721,3] K1(D,E,[R],[Q,P],[],[],[],[]). ** KEPT (pick-wt=15): 723 [hyper,721,2] K1(D,B,[R],[],[],[],[Q,P],[]). given clause #655: (wt=15) 685 [hyper,645,6,eval,demod,33,33,34] K2(E,D,[P],[Q,R],[],[],[],[]). given clause #656: (wt=15) 686 [hyper,645,5,demod,33,33,33,34] K2(E,D,[],[P,Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 724 [hyper,686,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[R,Q,P],[],[]). given clause #657: (wt=14) 724 [hyper,686,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[R,Q,P],[],[]). ** KEPT (pick-wt=15): 725 [hyper,724,3] K1(D,E,[R,Q,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 726 [hyper,724,2] K1(D,B,[R,Q,P],[],[],[],[],[]). given clause #658: (wt=15) 687 [hyper,648,5,demod,33,33,33,34] K2(E,D,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=14): 727 [hyper,687,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[Q,P,R],[],[]). given clause #659: (wt=14) 727 [hyper,687,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[Q,P,R],[],[]). ** KEPT (pick-wt=15): 728 [hyper,727,3] K1(D,E,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 729 [hyper,727,2] K1(D,B,[Q,P,R],[],[],[],[],[]). given clause #660: (wt=15) 688 [hyper,649,7] K2(E,F,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 730 [hyper,688,11] H(F,[],[],[],[],[Q,P],[R]). given clause #661: (wt=14) 730 [hyper,688,11] H(F,[],[],[],[],[Q,P],[R]). ** KEPT (pick-wt=15): 731 [hyper,730,15,demod,30,32,31,30,32,32,31] K1(F,E,[R],[P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 732 [hyper,730,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[],[Q,P]). given clause #662: (wt=15) 689 [hyper,649,6,eval,demod,33,33,34] K2(E,F,[Q],[P,R],[],[],[],[]). given clause #663: (wt=15) 690 [hyper,649,5,demod,33,33,33,34] K2(E,F,[],[Q,P,R],[],[],[],[]). ** KEPT (pick-wt=14): 733 [hyper,690,11] H(F,[],[],[],[],[],[Q,P,R]). given clause #664: (wt=14) 733 [hyper,690,11] H(F,[],[],[],[],[],[Q,P,R]). ** KEPT (pick-wt=15): 734 [hyper,733,15,demod,30,32,32,32,31,30,31] K1(F,E,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 735 [hyper,733,14,demod,30,32,32,32,31,30,31] K1(F,C,[R,P,Q],[],[],[],[],[]). given clause #665: (wt=15) 691 [hyper,651,5,demod,33,34] K2(C,F,[],[R],[],[],[P,Q],[]). given clause #666: (wt=15) 692 [hyper,653,5,demod,33,34] K2(C,F,[],[R],[],[],[P],[Q]). given clause #667: (wt=15) 693 [hyper,656,6,eval,demod,33,34] K2(C,F,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 736 [hyper,693,8] H(F,[],[],[Q],[P],[],[R]). given clause #668: (wt=14) 736 [hyper,693,8] H(F,[],[],[Q],[P],[],[R]). ** KEPT (pick-wt=15): 737 [hyper,736,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 738 [hyper,736,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[],[],[P],[]). given clause #669: (wt=15) 694 [hyper,656,5,demod,33,33,34] K2(C,F,[],[Q,R],[],[],[P],[]). given clause #670: (wt=15) 695 [hyper,657,5,demod,33,34] K2(C,F,[],[R],[Q],[],[P],[]). ** KEPT (pick-wt=14): 739 [hyper,695,8] H(F,[Q],[],[],[P],[],[R]). given clause #671: (wt=14) 739 [hyper,695,8] H(F,[Q],[],[],[P],[],[R]). ** KEPT (pick-wt=15): 740 [hyper,739,15,demod,30,32,31,30,31] K1(F,E,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 741 [hyper,739,14,demod,30,32,31,30,31] K1(F,C,[R],[],[Q],[],[P],[]). given clause #672: (wt=15) 696 [hyper,659,5,demod,33,33,34] K2(E,D,[],[R,P],[],[],[Q],[]). ** KEPT (pick-wt=14): 742 [hyper,696,17,demod,30,32,32,31,30,31] H(D,[],[],[Q],[P,R],[],[]). given clause #673: (wt=14) 742 [hyper,696,17,demod,30,32,32,31,30,31] H(D,[],[],[Q],[P,R],[],[]). ** KEPT (pick-wt=15): 743 [hyper,742,3] K1(D,E,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 744 [hyper,742,2] K1(D,B,[P,R],[],[],[Q],[],[]). given clause #674: (wt=15) 697 [hyper,660,6,eval,demod,33,34] K2(E,F,[P],[R],[],[],[Q],[]). given clause #675: (wt=15) 698 [hyper,660,5,demod,33,33,34] K2(E,F,[],[P,R],[],[],[Q],[]). ** KEPT (pick-wt=14): 745 [hyper,698,11] H(F,[],[],[Q],[],[],[P,R]). given clause #676: (wt=14) 745 [hyper,698,11] H(F,[],[],[Q],[],[],[P,R]). ** KEPT (pick-wt=15): 746 [hyper,745,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 747 [hyper,745,14,demod,30,32,32,31,30,32,31] K1(F,C,[R,P],[Q],[],[],[],[]). given clause #677: (wt=15) 699 [hyper,662,5,demod,33,33,34] K2(E,D,[],[R,P],[Q],[],[],[]). ** KEPT (pick-wt=14): 748 [hyper,699,17,demod,30,32,32,31,30,31] H(D,[Q],[],[],[P,R],[],[]). given clause #678: (wt=14) 748 [hyper,699,17,demod,30,32,32,31,30,31] H(D,[Q],[],[],[P,R],[],[]). ** KEPT (pick-wt=15): 749 [hyper,748,3] K1(D,E,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 750 [hyper,748,2] K1(D,B,[P,R],[],[Q],[],[],[]). given clause #679: (wt=15) 700 [hyper,663,6,eval,demod,33,34] K2(E,F,[P],[R],[Q],[],[],[]). given clause #680: (wt=15) 701 [hyper,663,5,demod,33,33,34] K2(E,F,[],[P,R],[Q],[],[],[]). ** KEPT (pick-wt=14): 751 [hyper,701,11] H(F,[Q],[],[],[],[],[P,R]). given clause #681: (wt=14) 751 [hyper,701,11] H(F,[Q],[],[],[],[],[P,R]). ** KEPT (pick-wt=15): 752 [hyper,751,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 753 [hyper,751,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[Q],[],[],[]). given clause #682: (wt=15) 702 [hyper,666,6,eval,demod,33,34] K2(E,F,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=14): 754 [hyper,702,11] H(F,[],[],[],[Q],[P],[R]). given clause #683: (wt=14) 754 [hyper,702,11] H(F,[],[],[],[Q],[P],[R]). ** KEPT (pick-wt=15): 755 [hyper,754,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 756 [hyper,754,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[Q],[P]). given clause #684: (wt=15) 703 [hyper,666,5,demod,33,33,34] K2(E,F,[],[P,R],[],[],[],[Q]). given clause #685: (wt=15) 704 [hyper,668,6,eval,demod,33,34] K2(E,D,[Q],[R],[],[P],[],[]). given clause #686: (wt=15) 705 [hyper,668,5,demod,33,33,34] K2(E,D,[],[Q,R],[],[P],[],[]). ** KEPT (pick-wt=14): 757 [hyper,705,17,demod,30,32,32,31,30,31] H(D,[],[P],[],[R,Q],[],[]). given clause #687: (wt=14) 757 [hyper,705,17,demod,30,32,32,31,30,31] H(D,[],[P],[],[R,Q],[],[]). ** KEPT (pick-wt=15): 758 [hyper,757,3] K1(D,E,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 759 [hyper,757,2] K1(D,B,[R,Q],[P],[],[],[],[]). given clause #688: (wt=15) 706 [hyper,669,5,demod,33,33,34] K2(E,F,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=14): 760 [hyper,706,11] H(F,[],[P],[],[],[],[R,Q]). given clause #689: (wt=14) 760 [hyper,706,11] H(F,[],[P],[],[],[],[R,Q]). ** KEPT (pick-wt=15): 761 [hyper,760,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 762 [hyper,760,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[],[P],[],[]). given clause #690: (wt=15) 707 [hyper,671,6,eval,demod,33,34] K2(E,D,[Q],[R],[P],[],[],[]). given clause #691: (wt=15) 708 [hyper,671,5,demod,33,33,34] K2(E,D,[],[Q,R],[P],[],[],[]). ** KEPT (pick-wt=14): 763 [hyper,708,17,demod,30,32,32,31,30,31] H(D,[P],[],[],[R,Q],[],[]). given clause #692: (wt=14) 763 [hyper,708,17,demod,30,32,32,31,30,31] H(D,[P],[],[],[R,Q],[],[]). ** KEPT (pick-wt=15): 764 [hyper,763,3] K1(D,E,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 765 [hyper,763,2] K1(D,B,[R,Q],[],[P],[],[],[]). given clause #693: (wt=15) 709 [hyper,672,5,demod,33,33,34] K2(E,F,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=14): 766 [hyper,709,11] H(F,[P],[],[],[],[],[R,Q]). given clause #694: (wt=14) 766 [hyper,709,11] H(F,[P],[],[],[],[],[R,Q]). ** KEPT (pick-wt=15): 767 [hyper,766,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 768 [hyper,766,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[P],[],[],[]). given clause #695: (wt=15) 710 [hyper,674,5,demod,33,34] K2(B,D,[],[R],[],[],[],[P,Q]). given clause #696: (wt=15) 711 [hyper,676,5,demod,33,34] K2(B,D,[],[R],[],[],[P],[Q]). given clause #697: (wt=15) 712 [hyper,679,6,eval,demod,33,34] K2(B,D,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=14): 769 [hyper,712,16,demod,30,32,31,30,32,31] H(D,[],[P],[],[R],[],[Q]). given clause #698: (wt=14) 769 [hyper,712,16,demod,30,32,31,30,32,31] H(D,[],[P],[],[R],[],[Q]). ** KEPT (pick-wt=15): 770 [hyper,769,3] K1(D,E,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 771 [hyper,769,2] K1(D,B,[R],[P],[],[],[],[Q]). given clause #699: (wt=15) 713 [hyper,679,5,demod,33,33,34] K2(B,D,[],[P,R],[],[],[],[Q]). given clause #700: (wt=15) 714 [hyper,680,5,demod,33,34] K2(B,D,[],[R],[P],[],[],[Q]). ** KEPT (pick-wt=14): 772 [hyper,714,16,demod,30,31,30,32,31] H(D,[P],[],[],[R],[],[Q]). given clause #701: (wt=14) 772 [hyper,714,16,demod,30,31,30,32,31] H(D,[P],[],[],[R],[],[Q]). ** KEPT (pick-wt=15): 773 [hyper,772,3] K1(D,E,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 774 [hyper,772,2] K1(D,B,[R],[],[P],[],[],[Q]). given clause #702: (wt=15) 716 [hyper,715,3] K1(D,E,[R],[Q],[],[],[],[P]). given clause #703: (wt=15) 717 [hyper,715,2] K1(D,B,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 775 [hyper,717,5,demod,33,34] K2(D,B,[],[R],[],[],[Q],[P]). given clause #704: (wt=15) 719 [hyper,718,15,demod,30,32,32,32,31,30,31] K1(F,E,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 776 [hyper,719,7] K2(F,E,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 777 [hyper,719,6,eval,demod,33,33,34] K2(F,E,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 778 [hyper,719,5,demod,33,33,33,34] K2(F,E,[],[P,Q,R],[],[],[],[]). given clause #705: (wt=15) 720 [hyper,718,14,demod,30,32,32,32,31,30,31] K1(F,C,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 779 [hyper,720,7] K2(F,C,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 780 [hyper,720,6,eval,demod,33,33,34] K2(F,C,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 781 [hyper,720,5,demod,33,33,33,34] K2(F,C,[],[P,Q,R],[],[],[],[]). given clause #706: (wt=15) 722 [hyper,721,3] K1(D,E,[R],[Q,P],[],[],[],[]). given clause #707: (wt=15) 723 [hyper,721,2] K1(D,B,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 782 [hyper,723,5,demod,33,34] K2(D,B,[],[R],[],[],[Q,P],[]). given clause #708: (wt=15) 725 [hyper,724,3] K1(D,E,[R,Q,P],[],[],[],[],[]). given clause #709: (wt=15) 726 [hyper,724,2] K1(D,B,[R,Q,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 783 [hyper,726,5,demod,33,33,33,34] K2(D,B,[],[R,Q,P],[],[],[],[]). given clause #710: (wt=15) 728 [hyper,727,3] K1(D,E,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 784 [hyper,728,7] K2(D,E,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 785 [hyper,728,6,eval,demod,33,33,34] K2(D,E,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 786 [hyper,728,5,demod,33,33,33,34] K2(D,E,[],[Q,P,R],[],[],[],[]). given clause #711: (wt=15) 729 [hyper,727,2] K1(D,B,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 787 [hyper,729,7] K2(D,B,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 788 [hyper,729,6,eval,demod,33,33,34] K2(D,B,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 789 [hyper,729,5,demod,33,33,33,34] K2(D,B,[],[Q,P,R],[],[],[],[]). given clause #712: (wt=15) 731 [hyper,730,15,demod,30,32,31,30,32,32,31] K1(F,E,[R],[P,Q],[],[],[],[]). given clause #713: (wt=15) 732 [hyper,730,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 790 [hyper,732,5,demod,33,34] K2(F,C,[],[R],[],[],[],[Q,P]). given clause #714: (wt=15) 734 [hyper,733,15,demod,30,32,32,32,31,30,31] K1(F,E,[R,P,Q],[],[],[],[],[]). given clause #715: (wt=15) 735 [hyper,733,14,demod,30,32,32,32,31,30,31] K1(F,C,[R,P,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 791 [hyper,735,5,demod,33,33,33,34] K2(F,C,[],[R,P,Q],[],[],[],[]). given clause #716: (wt=15) 737 [hyper,736,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 792 [hyper,737,5,demod,33,34] K2(F,E,[],[R],[],[],[Q],[P]). given clause #717: (wt=15) 738 [hyper,736,14,demod,30,32,31,30,32,31] K1(F,C,[R],[Q],[],[],[P],[]). given clause #718: (wt=15) 740 [hyper,739,15,demod,30,32,31,30,31] K1(F,E,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 793 [hyper,740,5,demod,33,34] K2(F,E,[],[R],[Q],[],[],[P]). given clause #719: (wt=15) 741 [hyper,739,14,demod,30,32,31,30,31] K1(F,C,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 794 [hyper,741,5,demod,33,34] K2(F,C,[],[R],[Q],[],[P],[]). given clause #720: (wt=15) 743 [hyper,742,3] K1(D,E,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 795 [hyper,743,6,eval,demod,33,34] K2(D,E,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 796 [hyper,743,5,demod,33,33,34] K2(D,E,[],[P,R],[],[],[Q],[]). given clause #721: (wt=15) 744 [hyper,742,2] K1(D,B,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 797 [hyper,744,6,eval,demod,33,34] K2(D,B,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 798 [hyper,744,5,demod,33,33,34] K2(D,B,[],[P,R],[],[Q],[],[]). given clause #722: (wt=15) 746 [hyper,745,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[],[],[Q],[]). given clause #723: (wt=15) 747 [hyper,745,14,demod,30,32,32,31,30,32,31] K1(F,C,[R,P],[Q],[],[],[],[]). given clause #724: (wt=15) 749 [hyper,748,3] K1(D,E,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 799 [hyper,749,6,eval,demod,33,34] K2(D,E,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 800 [hyper,749,5,demod,33,33,34] K2(D,E,[],[P,R],[Q],[],[],[]). given clause #725: (wt=15) 750 [hyper,748,2] K1(D,B,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 801 [hyper,750,6,eval,demod,33,34] K2(D,B,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 802 [hyper,750,5,demod,33,33,34] K2(D,B,[],[P,R],[Q],[],[],[]). given clause #726: (wt=15) 752 [hyper,751,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[Q],[],[],[]). given clause #727: (wt=15) 753 [hyper,751,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 803 [hyper,753,5,demod,33,33,34] K2(F,C,[],[R,P],[Q],[],[],[]). given clause #728: (wt=15) 755 [hyper,754,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[],[],[],[Q]). given clause #729: (wt=15) 756 [hyper,754,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 804 [hyper,756,5,demod,33,34] K2(F,C,[],[R],[],[],[Q],[P]). given clause #730: (wt=15) 758 [hyper,757,3] K1(D,E,[R,Q],[],[],[P],[],[]). given clause #731: (wt=15) 759 [hyper,757,2] K1(D,B,[R,Q],[P],[],[],[],[]). given clause #732: (wt=15) 761 [hyper,760,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 805 [hyper,761,6,eval,demod,33,34] K2(F,E,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 806 [hyper,761,5,demod,33,33,34] K2(F,E,[],[Q,R],[],[P],[],[]). given clause #733: (wt=15) 762 [hyper,760,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 807 [hyper,762,6,eval,demod,33,34] K2(F,C,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 808 [hyper,762,5,demod,33,33,34] K2(F,C,[],[Q,R],[],[P],[],[]). given clause #734: (wt=15) 764 [hyper,763,3] K1(D,E,[R,Q],[],[P],[],[],[]). given clause #735: (wt=15) 765 [hyper,763,2] K1(D,B,[R,Q],[],[P],[],[],[]). ** KEPT (pick-wt=15): 809 [hyper,765,5,demod,33,33,34] K2(D,B,[],[R,Q],[P],[],[],[]). given clause #736: (wt=15) 767 [hyper,766,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 810 [hyper,767,6,eval,demod,33,34] K2(F,E,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 811 [hyper,767,5,demod,33,33,34] K2(F,E,[],[Q,R],[P],[],[],[]). given clause #737: (wt=15) 768 [hyper,766,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 812 [hyper,768,6,eval,demod,33,34] K2(F,C,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 813 [hyper,768,5,demod,33,33,34] K2(F,C,[],[Q,R],[P],[],[],[]). given clause #738: (wt=15) 770 [hyper,769,3] K1(D,E,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 814 [hyper,770,5,demod,33,34] K2(D,E,[],[R],[],[P],[],[Q]). given clause #739: (wt=15) 771 [hyper,769,2] K1(D,B,[R],[P],[],[],[],[Q]). given clause #740: (wt=15) 773 [hyper,772,3] K1(D,E,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 815 [hyper,773,5,demod,33,34] K2(D,E,[],[R],[P],[],[],[Q]). given clause #741: (wt=15) 774 [hyper,772,2] K1(D,B,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 816 [hyper,774,5,demod,33,34] K2(D,B,[],[R],[P],[],[],[Q]). given clause #742: (wt=15) 775 [hyper,717,5,demod,33,34] K2(D,B,[],[R],[],[],[Q],[P]). ** KEPT (pick-wt=14): 817 [hyper,775,9] H(B,[],[R],[],[],[Q],[P]). given clause #743: (wt=14) 817 [hyper,775,9] H(B,[],[R],[],[],[Q],[P]). ** KEPT (pick-wt=15): 818 [hyper,817,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[Q],[P]). given clause #744: (wt=15) 776 [hyper,719,7] K2(F,E,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 819 [hyper,776,19,demod,30,32,31,30,32,32,31] H(E,[],[],[],[],[R],[Q,P]). given clause #745: (wt=14) 819 [hyper,776,19,demod,30,32,31,30,32,32,31] H(E,[],[],[],[],[R],[Q,P]). ** KEPT (pick-wt=15): 820 [hyper,819,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 821 [hyper,819,4] K1(E,F,[R],[Q,P],[],[],[],[]). given clause #746: (wt=15) 777 [hyper,719,6,eval,demod,33,33,34] K2(F,E,[P],[Q,R],[],[],[],[]). given clause #747: (wt=15) 778 [hyper,719,5,demod,33,33,33,34] K2(F,E,[],[P,Q,R],[],[],[],[]). given clause #748: (wt=15) 779 [hyper,720,7] K2(F,C,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 822 [hyper,779,18,demod,30,32,31,30,32,32,31] H(C,[],[],[R],[],[],[Q,P]). given clause #749: (wt=14) 822 [hyper,779,18,demod,30,32,31,30,32,32,31] H(C,[],[],[R],[],[],[Q,P]). ** KEPT (pick-wt=15): 823 [hyper,822,1] K1(C,F,[R],[Q,P],[],[],[],[]). given clause #750: (wt=15) 780 [hyper,720,6,eval,demod,33,33,34] K2(F,C,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 824 [hyper,780,18,demod,30,32,32,31,30,32,31] H(C,[],[],[R,Q],[],[],[P]). given clause #751: (wt=14) 824 [hyper,780,18,demod,30,32,32,31,30,32,31] H(C,[],[],[R,Q],[],[],[P]). ** KEPT (pick-wt=15): 825 [hyper,824,1] K1(C,F,[R,Q],[P],[],[],[],[]). given clause #752: (wt=15) 781 [hyper,720,5,demod,33,33,33,34] K2(F,C,[],[P,Q,R],[],[],[],[]). ** KEPT (pick-wt=14): 826 [hyper,781,18,demod,30,32,32,32,31,30,31] H(C,[],[],[R,Q,P],[],[],[]). given clause #753: (wt=14) 826 [hyper,781,18,demod,30,32,32,32,31,30,31] H(C,[],[],[R,Q,P],[],[],[]). ** KEPT (pick-wt=15): 827 [hyper,826,1] K1(C,F,[R,Q,P],[],[],[],[],[]). given clause #754: (wt=15) 782 [hyper,723,5,demod,33,34] K2(D,B,[],[R],[],[],[Q,P],[]). ** KEPT (pick-wt=14): 828 [hyper,782,9] H(B,[],[R],[],[],[Q,P],[]). given clause #755: (wt=14) 828 [hyper,782,9] H(B,[],[R],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 829 [hyper,828,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[Q,P],[]). given clause #756: (wt=15) 783 [hyper,726,5,demod,33,33,33,34] K2(D,B,[],[R,Q,P],[],[],[],[]). ** KEPT (pick-wt=14): 830 [hyper,783,9] H(B,[],[R,Q,P],[],[],[],[]). given clause #757: (wt=14) 830 [hyper,783,9] H(B,[],[R,Q,P],[],[],[],[]). ** KEPT (pick-wt=14): 831 [hyper,830,21] H(B,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 832 [hyper,830,12,demod,30,32,32,32,31,30,31] K1(B,D,[P,Q,R],[],[],[],[],[]). given clause #758: (wt=14) 831 [hyper,830,21] H(B,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 833 [hyper,831,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[P],[],[],[]). given clause #759: (wt=15) 784 [hyper,728,7] K2(D,E,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 834 [hyper,784,10] H(E,[],[],[],[Q,P],[R],[]). given clause #760: (wt=14) 834 [hyper,784,10] H(E,[],[],[],[Q,P],[R],[]). ** KEPT (pick-wt=15): 835 [hyper,834,13,demod,30,32,31,30,32,32,31] K1(E,D,[R],[P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 836 [hyper,834,4] K1(E,F,[R],[],[],[],[],[Q,P]). given clause #761: (wt=15) 785 [hyper,728,6,eval,demod,33,33,34] K2(D,E,[Q],[P,R],[],[],[],[]). given clause #762: (wt=15) 786 [hyper,728,5,demod,33,33,33,34] K2(D,E,[],[Q,P,R],[],[],[],[]). given clause #763: (wt=15) 787 [hyper,729,7] K2(D,B,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 837 [hyper,787,9] H(B,[],[R],[],[Q,P],[],[]). given clause #764: (wt=14) 837 [hyper,787,9] H(B,[],[R],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 838 [hyper,837,12,demod,30,32,31,30,32,32,31] K1(B,D,[R],[P,Q],[],[],[],[]). given clause #765: (wt=15) 788 [hyper,729,6,eval,demod,33,33,34] K2(D,B,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=14): 839 [hyper,788,9] H(B,[],[P,R],[],[Q],[],[]). given clause #766: (wt=14) 839 [hyper,788,9] H(B,[],[P,R],[],[Q],[],[]). ** KEPT (pick-wt=15): 840 [hyper,839,12,demod,30,32,32,31,30,32,31] K1(B,D,[R,P],[Q],[],[],[],[]). given clause #767: (wt=15) 789 [hyper,729,5,demod,33,33,33,34] K2(D,B,[],[Q,P,R],[],[],[],[]). ** KEPT (pick-wt=14): 841 [hyper,789,9] H(B,[],[Q,P,R],[],[],[],[]). given clause #768: (wt=14) 841 [hyper,789,9] H(B,[],[Q,P,R],[],[],[],[]). ** KEPT (pick-wt=15): 842 [hyper,841,12,demod,30,32,32,32,31,30,31] K1(B,D,[R,P,Q],[],[],[],[],[]). given clause #769: (wt=15) 790 [hyper,732,5,demod,33,34] K2(F,C,[],[R],[],[],[],[Q,P]). ** KEPT (pick-wt=14): 843 [hyper,790,18,demod,30,32,31,30,31] H(C,[],[],[R],[],[Q,P],[]). given clause #770: (wt=14) 843 [hyper,790,18,demod,30,32,31,30,31] H(C,[],[],[R],[],[Q,P],[]). ** KEPT (pick-wt=15): 844 [hyper,843,1] K1(C,F,[R],[],[],[],[],[Q,P]). given clause #771: (wt=15) 791 [hyper,735,5,demod,33,33,33,34] K2(F,C,[],[R,P,Q],[],[],[],[]). ** KEPT (pick-wt=14): 845 [hyper,791,18,demod,30,32,32,32,31,30,31] H(C,[],[],[Q,P,R],[],[],[]). given clause #772: (wt=14) 845 [hyper,791,18,demod,30,32,32,32,31,30,31] H(C,[],[],[Q,P,R],[],[],[]). ** KEPT (pick-wt=14): 846 [hyper,845,24,eval] H(C,[Q],[],[P,R],[],[],[]). ** KEPT (pick-wt=15): 847 [hyper,845,1] K1(C,F,[Q,P,R],[],[],[],[],[]). given clause #773: (wt=14) 846 [hyper,845,24,eval] H(C,[Q],[],[P,R],[],[],[]). ** KEPT (pick-wt=15): 848 [hyper,846,1] K1(C,F,[P,R],[],[Q],[],[],[]). given clause #774: (wt=15) 792 [hyper,737,5,demod,33,34] K2(F,E,[],[R],[],[],[Q],[P]). ** KEPT (pick-wt=14): 849 [hyper,792,19,demod,30,32,31,30,31] H(E,[],[],[Q],[P],[R],[]). given clause #775: (wt=14) 849 [hyper,792,19,demod,30,32,31,30,31] H(E,[],[],[Q],[P],[R],[]). ** KEPT (pick-wt=15): 850 [hyper,849,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 851 [hyper,849,4] K1(E,F,[R],[],[],[],[Q],[P]). given clause #776: (wt=15) 793 [hyper,740,5,demod,33,34] K2(F,E,[],[R],[Q],[],[],[P]). ** KEPT (pick-wt=14): 852 [hyper,793,19,demod,30,32,31,30,31] H(E,[Q],[],[],[P],[R],[]). given clause #777: (wt=14) 852 [hyper,793,19,demod,30,32,31,30,31] H(E,[Q],[],[],[P],[R],[]). ** KEPT (pick-wt=15): 853 [hyper,852,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 854 [hyper,852,4] K1(E,F,[R],[],[Q],[],[],[P]). given clause #778: (wt=15) 794 [hyper,741,5,demod,33,34] K2(F,C,[],[R],[Q],[],[P],[]). given clause #779: (wt=15) 795 [hyper,743,6,eval,demod,33,34] K2(D,E,[P],[R],[],[],[Q],[]). given clause #780: (wt=15) 796 [hyper,743,5,demod,33,33,34] K2(D,E,[],[P,R],[],[],[Q],[]). given clause #781: (wt=15) 797 [hyper,744,6,eval,demod,33,34] K2(D,B,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 855 [hyper,797,9] H(B,[],[R],[Q],[P],[],[]). given clause #782: (wt=14) 855 [hyper,797,9] H(B,[],[R],[Q],[P],[],[]). ** KEPT (pick-wt=15): 856 [hyper,855,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[],[Q],[],[]). given clause #783: (wt=15) 798 [hyper,744,5,demod,33,33,34] K2(D,B,[],[P,R],[],[Q],[],[]). ** KEPT (pick-wt=14): 857 [hyper,798,9] H(B,[],[P,R],[Q],[],[],[]). given clause #784: (wt=14) 857 [hyper,798,9] H(B,[],[P,R],[Q],[],[],[]). ** KEPT (pick-wt=15): 858 [hyper,857,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[],[Q],[],[]). given clause #785: (wt=15) 799 [hyper,749,6,eval,demod,33,34] K2(D,E,[P],[R],[Q],[],[],[]). given clause #786: (wt=15) 800 [hyper,749,5,demod,33,33,34] K2(D,E,[],[P,R],[Q],[],[],[]). given clause #787: (wt=15) 801 [hyper,750,6,eval,demod,33,34] K2(D,B,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=14): 859 [hyper,801,9] H(B,[Q],[R],[],[P],[],[]). given clause #788: (wt=14) 859 [hyper,801,9] H(B,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 860 [hyper,859,23,demod,33,34] H(B,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=15): 861 [hyper,859,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[Q],[],[],[]). given clause #789: (wt=14) 860 [hyper,859,23,demod,33,34] H(B,[],[R,Q],[],[P],[],[]). ** KEPT (pick-wt=15): 862 [hyper,860,12,demod,30,32,32,31,30,32,31] K1(B,D,[Q,R],[P],[],[],[],[]). given clause #790: (wt=15) 802 [hyper,750,5,demod,33,33,34] K2(D,B,[],[P,R],[Q],[],[],[]). ** KEPT (pick-wt=14): 863 [hyper,802,9] H(B,[Q],[P,R],[],[],[],[]). given clause #791: (wt=14) 863 [hyper,802,9] H(B,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=14): 864 [hyper,863,23,demod,33,33,34] H(B,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 865 [hyper,863,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[Q],[],[],[]). given clause #792: (wt=14) 864 [hyper,863,23,demod,33,33,34] H(B,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 866 [hyper,864,12,demod,30,32,32,32,31,30,31] K1(B,D,[Q,R,P],[],[],[],[],[]). given clause #793: (wt=15) 803 [hyper,753,5,demod,33,33,34] K2(F,C,[],[R,P],[Q],[],[],[]). given clause #794: (wt=15) 804 [hyper,756,5,demod,33,34] K2(F,C,[],[R],[],[],[Q],[P]). ** KEPT (pick-wt=14): 867 [hyper,804,18,demod,30,32,31,30,31] H(C,[],[],[R],[Q],[P],[]). given clause #795: (wt=14) 867 [hyper,804,18,demod,30,32,31,30,31] H(C,[],[],[R],[Q],[P],[]). ** KEPT (pick-wt=15): 868 [hyper,867,1] K1(C,F,[R],[],[],[],[Q],[P]). given clause #796: (wt=15) 805 [hyper,761,6,eval,demod,33,34] K2(F,E,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 869 [hyper,805,19,demod,30,32,31,30,32,31] H(E,[],[P],[],[],[R],[Q]). given clause #797: (wt=14) 869 [hyper,805,19,demod,30,32,31,30,32,31] H(E,[],[P],[],[],[R],[Q]). ** KEPT (pick-wt=15): 870 [hyper,869,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 871 [hyper,869,4] K1(E,F,[R],[Q],[],[P],[],[]). given clause #798: (wt=15) 806 [hyper,761,5,demod,33,33,34] K2(F,E,[],[Q,R],[],[P],[],[]). given clause #799: (wt=15) 807 [hyper,762,6,eval,demod,33,34] K2(F,C,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 872 [hyper,807,18,demod,30,32,31,30,32,31] H(C,[],[P],[R],[],[],[Q]). given clause #800: (wt=14) 872 [hyper,807,18,demod,30,32,31,30,32,31] H(C,[],[P],[R],[],[],[Q]). ** KEPT (pick-wt=15): 873 [hyper,872,1] K1(C,F,[R],[Q],[],[P],[],[]). given clause #801: (wt=15) 808 [hyper,762,5,demod,33,33,34] K2(F,C,[],[Q,R],[],[P],[],[]). ** KEPT (pick-wt=14): 874 [hyper,808,18,demod,30,32,32,31,30,31] H(C,[],[P],[R,Q],[],[],[]). given clause #802: (wt=14) 874 [hyper,808,18,demod,30,32,32,31,30,31] H(C,[],[P],[R,Q],[],[],[]). ** KEPT (pick-wt=15): 875 [hyper,874,1] K1(C,F,[R,Q],[],[],[P],[],[]). given clause #803: (wt=15) 809 [hyper,765,5,demod,33,33,34] K2(D,B,[],[R,Q],[P],[],[],[]). given clause #804: (wt=15) 810 [hyper,767,6,eval,demod,33,34] K2(F,E,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=14): 876 [hyper,810,19,demod,30,32,31,30,32,31] H(E,[P],[],[],[],[R],[Q]). given clause #805: (wt=14) 876 [hyper,810,19,demod,30,32,31,30,32,31] H(E,[P],[],[],[],[R],[Q]). ** KEPT (pick-wt=15): 877 [hyper,876,13,demod,30,32,31,30,31] K1(E,D,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 878 [hyper,876,4] K1(E,F,[R],[Q],[P],[],[],[]). given clause #806: (wt=15) 811 [hyper,767,5,demod,33,33,34] K2(F,E,[],[Q,R],[P],[],[],[]). given clause #807: (wt=15) 812 [hyper,768,6,eval,demod,33,34] K2(F,C,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=14): 879 [hyper,812,18,demod,30,32,31,30,32,31] H(C,[P],[],[R],[],[],[Q]). given clause #808: (wt=14) 879 [hyper,812,18,demod,30,32,31,30,32,31] H(C,[P],[],[R],[],[],[Q]). ** KEPT (pick-wt=14): 880 [hyper,879,25] H(C,[],[],[P,R],[],[],[Q]). ** KEPT (pick-wt=15): 881 [hyper,879,1] K1(C,F,[R],[Q],[P],[],[],[]). given clause #809: (wt=14) 880 [hyper,879,25] H(C,[],[],[P,R],[],[],[Q]). ** KEPT (pick-wt=15): 882 [hyper,880,1] K1(C,F,[P,R],[Q],[],[],[],[]). given clause #810: (wt=15) 813 [hyper,768,5,demod,33,33,34] K2(F,C,[],[Q,R],[P],[],[],[]). ** KEPT (pick-wt=14): 883 [hyper,813,18,demod,30,32,32,31,30,31] H(C,[P],[],[R,Q],[],[],[]). given clause #811: (wt=14) 883 [hyper,813,18,demod,30,32,32,31,30,31] H(C,[P],[],[R,Q],[],[],[]). ** KEPT (pick-wt=14): 884 [hyper,883,25] H(C,[],[],[P,R,Q],[],[],[]). ** KEPT (pick-wt=15): 885 [hyper,883,1] K1(C,F,[R,Q],[],[P],[],[],[]). given clause #812: (wt=14) 884 [hyper,883,25] H(C,[],[],[P,R,Q],[],[],[]). ** KEPT (pick-wt=15): 886 [hyper,884,1] K1(C,F,[P,R,Q],[],[],[],[],[]). given clause #813: (wt=15) 814 [hyper,770,5,demod,33,34] K2(D,E,[],[R],[],[P],[],[Q]). given clause #814: (wt=15) 815 [hyper,773,5,demod,33,34] K2(D,E,[],[R],[P],[],[],[Q]). given clause #815: (wt=15) 816 [hyper,774,5,demod,33,34] K2(D,B,[],[R],[P],[],[],[Q]). given clause #816: (wt=15) 818 [hyper,817,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 887 [hyper,818,5,demod,33,34] K2(B,D,[],[R],[],[],[Q],[P]). given clause #817: (wt=15) 820 [hyper,819,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 888 [hyper,820,5,demod,33,34] K2(E,D,[],[R],[],[],[],[Q,P]). given clause #818: (wt=15) 821 [hyper,819,4] K1(E,F,[R],[Q,P],[],[],[],[]). given clause #819: (wt=15) 823 [hyper,822,1] K1(C,F,[R],[Q,P],[],[],[],[]). ** KEPT (pick-wt=15): 889 [hyper,823,5,demod,33,34] K2(C,F,[],[R,Q,P],[],[],[],[]). given clause #820: (wt=15) 825 [hyper,824,1] K1(C,F,[R,Q],[P],[],[],[],[]). given clause #821: (wt=15) 827 [hyper,826,1] K1(C,F,[R,Q,P],[],[],[],[],[]). given clause #822: (wt=15) 829 [hyper,828,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 890 [hyper,829,5,demod,33,34] K2(B,D,[],[R],[],[],[Q,P],[]). given clause #823: (wt=15) 832 [hyper,830,12,demod,30,32,32,32,31,30,31] K1(B,D,[P,Q,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 891 [hyper,832,7] K2(B,D,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=15): 892 [hyper,832,6,eval,demod,33,33,34] K2(B,D,[P],[Q,R],[],[],[],[]). ** KEPT (pick-wt=15): 893 [hyper,832,5,demod,33,33,33,34] K2(B,D,[],[P,Q,R],[],[],[],[]). given clause #824: (wt=15) 833 [hyper,831,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[P],[],[],[]). ** KEPT (pick-wt=15): 894 [hyper,833,6,eval,demod,33,34] K2(B,D,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=15): 895 [hyper,833,5,demod,33,33,34] K2(B,D,[],[Q,R],[P],[],[],[]). given clause #825: (wt=15) 835 [hyper,834,13,demod,30,32,31,30,32,32,31] K1(E,D,[R],[P,Q],[],[],[],[]). given clause #826: (wt=15) 836 [hyper,834,4] K1(E,F,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 896 [hyper,836,5,demod,33,34] K2(E,F,[],[R],[],[],[],[Q,P]). given clause #827: (wt=15) 838 [hyper,837,12,demod,30,32,31,30,32,32,31] K1(B,D,[R],[P,Q],[],[],[],[]). ** KEPT (pick-wt=15): 897 [hyper,838,5,demod,33,34] K2(B,D,[],[R,P,Q],[],[],[],[]). given clause #828: (wt=15) 840 [hyper,839,12,demod,30,32,32,31,30,32,31] K1(B,D,[R,P],[Q],[],[],[],[]). given clause #829: (wt=15) 842 [hyper,841,12,demod,30,32,32,32,31,30,31] K1(B,D,[R,P,Q],[],[],[],[],[]). given clause #830: (wt=15) 844 [hyper,843,1] K1(C,F,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 898 [hyper,844,5,demod,33,34] K2(C,F,[],[R],[],[],[],[Q,P]). given clause #831: (wt=15) 847 [hyper,845,1] K1(C,F,[Q,P,R],[],[],[],[],[]). ** KEPT (pick-wt=15): 899 [hyper,847,7] K2(C,F,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=15): 900 [hyper,847,6,eval,demod,33,33,34] K2(C,F,[Q],[P,R],[],[],[],[]). ** KEPT (pick-wt=15): 901 [hyper,847,5,demod,33,33,33,34] K2(C,F,[],[Q,P,R],[],[],[],[]). given clause #832: (wt=15) 848 [hyper,846,1] K1(C,F,[P,R],[],[Q],[],[],[]). ** KEPT (pick-wt=15): 902 [hyper,848,6,eval,demod,33,34] K2(C,F,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=15): 903 [hyper,848,5,demod,33,33,34] K2(C,F,[],[P,R],[Q],[],[],[]). given clause #833: (wt=15) 850 [hyper,849,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[],[],[Q],[]). given clause #834: (wt=15) 851 [hyper,849,4] K1(E,F,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 904 [hyper,851,5,demod,33,34] K2(E,F,[],[R],[],[],[Q],[P]). given clause #835: (wt=15) 853 [hyper,852,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[Q],[],[],[]). given clause #836: (wt=15) 854 [hyper,852,4] K1(E,F,[R],[],[Q],[],[],[P]). ** KEPT (pick-wt=15): 905 [hyper,854,5,demod,33,34] K2(E,F,[],[R],[Q],[],[],[P]). given clause #837: (wt=15) 856 [hyper,855,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 906 [hyper,856,5,demod,33,34] K2(B,D,[],[R,P],[],[Q],[],[]). given clause #838: (wt=15) 858 [hyper,857,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[],[Q],[],[]). given clause #839: (wt=15) 861 [hyper,859,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[Q],[],[],[]). ** KEPT (pick-wt=15): 907 [hyper,861,5,demod,33,34] K2(B,D,[],[R,P],[Q],[],[],[]). given clause #840: (wt=15) 862 [hyper,860,12,demod,30,32,32,31,30,32,31] K1(B,D,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 908 [hyper,862,6,eval,demod,33,34] K2(B,D,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 909 [hyper,862,5,demod,33,33,34] K2(B,D,[],[Q,R,P],[],[],[],[]). given clause #841: (wt=15) 865 [hyper,863,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[Q],[],[],[]). given clause #842: (wt=15) 866 [hyper,864,12,demod,30,32,32,32,31,30,31] K1(B,D,[Q,R,P],[],[],[],[],[]). given clause #843: (wt=15) 868 [hyper,867,1] K1(C,F,[R],[],[],[],[Q],[P]). ** KEPT (pick-wt=15): 910 [hyper,868,5,demod,33,34] K2(C,F,[],[R],[],[],[Q],[P]). given clause #844: (wt=15) 870 [hyper,869,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 911 [hyper,870,5,demod,33,34] K2(E,D,[],[R],[],[P],[],[Q]). given clause #845: (wt=15) 871 [hyper,869,4] K1(E,F,[R],[Q],[],[P],[],[]). given clause #846: (wt=15) 873 [hyper,872,1] K1(C,F,[R],[Q],[],[P],[],[]). ** KEPT (pick-wt=15): 912 [hyper,873,5,demod,33,34] K2(C,F,[],[R,Q],[],[P],[],[]). given clause #847: (wt=15) 875 [hyper,874,1] K1(C,F,[R,Q],[],[],[P],[],[]). given clause #848: (wt=15) 877 [hyper,876,13,demod,30,32,31,30,31] K1(E,D,[R],[],[P],[],[],[Q]). ** KEPT (pick-wt=15): 913 [hyper,877,5,demod,33,34] K2(E,D,[],[R],[P],[],[],[Q]). given clause #849: (wt=15) 878 [hyper,876,4] K1(E,F,[R],[Q],[P],[],[],[]). given clause #850: (wt=15) 881 [hyper,879,1] K1(C,F,[R],[Q],[P],[],[],[]). ** KEPT (pick-wt=15): 914 [hyper,881,5,demod,33,34] K2(C,F,[],[R,Q],[P],[],[],[]). given clause #851: (wt=15) 882 [hyper,880,1] K1(C,F,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 915 [hyper,882,6,eval,demod,33,34] K2(C,F,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 916 [hyper,882,5,demod,33,33,34] K2(C,F,[],[P,R,Q],[],[],[],[]). given clause #852: (wt=15) 885 [hyper,883,1] K1(C,F,[R,Q],[],[P],[],[],[]). given clause #853: (wt=15) 886 [hyper,884,1] K1(C,F,[P,R,Q],[],[],[],[],[]). given clause #854: (wt=15) 887 [hyper,818,5,demod,33,34] K2(B,D,[],[R],[],[],[Q],[P]). given clause #855: (wt=15) 888 [hyper,820,5,demod,33,34] K2(E,D,[],[R],[],[],[],[Q,P]). ** KEPT (pick-wt=14): 917 [hyper,888,17,demod,30,32,31,30,31] H(D,[],[],[],[R],[],[Q,P]). given clause #856: (wt=14) 917 [hyper,888,17,demod,30,32,31,30,31] H(D,[],[],[],[R],[],[Q,P]). ** KEPT (pick-wt=15): 918 [hyper,917,3] K1(D,E,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 919 [hyper,917,2] K1(D,B,[R],[],[],[],[],[Q,P]). given clause #857: (wt=15) 889 [hyper,823,5,demod,33,34] K2(C,F,[],[R,Q,P],[],[],[],[]). given clause #858: (wt=15) 890 [hyper,829,5,demod,33,34] K2(B,D,[],[R],[],[],[Q,P],[]). given clause #859: (wt=15) 891 [hyper,832,7] K2(B,D,[P,Q],[R],[],[],[],[]). ** KEPT (pick-wt=14): 920 [hyper,891,16,demod,30,32,32,31,30,32,31] H(D,[],[Q,P],[],[R],[],[]). given clause #860: (wt=14) 920 [hyper,891,16,demod,30,32,32,31,30,32,31] H(D,[],[Q,P],[],[R],[],[]). ** KEPT (pick-wt=15): 921 [hyper,920,3] K1(D,E,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 922 [hyper,920,2] K1(D,B,[R],[Q,P],[],[],[],[]). given clause #861: (wt=15) 892 [hyper,832,6,eval,demod,33,33,34] K2(B,D,[P],[Q,R],[],[],[],[]). given clause #862: (wt=15) 893 [hyper,832,5,demod,33,33,33,34] K2(B,D,[],[P,Q,R],[],[],[],[]). given clause #863: (wt=15) 894 [hyper,833,6,eval,demod,33,34] K2(B,D,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=14): 923 [hyper,894,16,demod,30,32,31,30,32,31] H(D,[P],[Q],[],[R],[],[]). given clause #864: (wt=14) 923 [hyper,894,16,demod,30,32,31,30,32,31] H(D,[P],[Q],[],[R],[],[]). ** KEPT (pick-wt=15): 924 [hyper,923,3] K1(D,E,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 925 [hyper,923,2] K1(D,B,[R],[Q],[P],[],[],[]). given clause #865: (wt=15) 895 [hyper,833,5,demod,33,33,34] K2(B,D,[],[Q,R],[P],[],[],[]). given clause #866: (wt=15) 896 [hyper,836,5,demod,33,34] K2(E,F,[],[R],[],[],[],[Q,P]). ** KEPT (pick-wt=14): 926 [hyper,896,11] H(F,[],[],[],[Q,P],[],[R]). given clause #867: (wt=14) 926 [hyper,896,11] H(F,[],[],[],[Q,P],[],[R]). ** KEPT (pick-wt=15): 927 [hyper,926,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 928 [hyper,926,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[Q,P],[]). given clause #868: (wt=15) 897 [hyper,838,5,demod,33,34] K2(B,D,[],[R,P,Q],[],[],[],[]). given clause #869: (wt=15) 898 [hyper,844,5,demod,33,34] K2(C,F,[],[R],[],[],[],[Q,P]). given clause #870: (wt=15) 899 [hyper,847,7] K2(C,F,[Q,P],[R],[],[],[],[]). ** KEPT (pick-wt=14): 929 [hyper,899,8] H(F,[],[],[Q,P],[],[],[R]). given clause #871: (wt=14) 929 [hyper,899,8] H(F,[],[],[Q,P],[],[],[R]). ** KEPT (pick-wt=15): 930 [hyper,929,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 931 [hyper,929,14,demod,30,32,31,30,32,32,31] K1(F,C,[R],[P,Q],[],[],[],[]). given clause #872: (wt=15) 900 [hyper,847,6,eval,demod,33,33,34] K2(C,F,[Q],[P,R],[],[],[],[]). given clause #873: (wt=15) 901 [hyper,847,5,demod,33,33,33,34] K2(C,F,[],[Q,P,R],[],[],[],[]). given clause #874: (wt=15) 902 [hyper,848,6,eval,demod,33,34] K2(C,F,[P],[R],[Q],[],[],[]). ** KEPT (pick-wt=14): 932 [hyper,902,8] H(F,[Q],[],[P],[],[],[R]). given clause #875: (wt=14) 932 [hyper,902,8] H(F,[Q],[],[P],[],[],[R]). ** KEPT (pick-wt=15): 933 [hyper,932,15,demod,30,32,31,30,31] K1(F,E,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 934 [hyper,932,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[Q],[],[],[]). given clause #876: (wt=15) 903 [hyper,848,5,demod,33,33,34] K2(C,F,[],[P,R],[Q],[],[],[]). given clause #877: (wt=15) 904 [hyper,851,5,demod,33,34] K2(E,F,[],[R],[],[],[Q],[P]). given clause #878: (wt=15) 905 [hyper,854,5,demod,33,34] K2(E,F,[],[R],[Q],[],[],[P]). given clause #879: (wt=15) 906 [hyper,856,5,demod,33,34] K2(B,D,[],[R,P],[],[Q],[],[]). given clause #880: (wt=15) 907 [hyper,861,5,demod,33,34] K2(B,D,[],[R,P],[Q],[],[],[]). given clause #881: (wt=15) 908 [hyper,862,6,eval,demod,33,34] K2(B,D,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 935 [hyper,908,16,demod,30,32,31,30,32,32,31] H(D,[],[Q],[],[P,R],[],[]). given clause #882: (wt=14) 935 [hyper,908,16,demod,30,32,31,30,32,32,31] H(D,[],[Q],[],[P,R],[],[]). ** KEPT (pick-wt=15): 936 [hyper,935,3] K1(D,E,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 937 [hyper,935,2] K1(D,B,[P,R],[Q],[],[],[],[]). given clause #883: (wt=15) 909 [hyper,862,5,demod,33,33,34] K2(B,D,[],[Q,R,P],[],[],[],[]). ** KEPT (pick-wt=14): 938 [hyper,909,16,demod,30,31,30,32,32,32,31] H(D,[],[],[],[P,R,Q],[],[]). given clause #884: (wt=14) 938 [hyper,909,16,demod,30,31,30,32,32,32,31] H(D,[],[],[],[P,R,Q],[],[]). ** KEPT (pick-wt=15): 939 [hyper,938,3] K1(D,E,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 940 [hyper,938,2] K1(D,B,[P,R,Q],[],[],[],[],[]). given clause #885: (wt=15) 910 [hyper,868,5,demod,33,34] K2(C,F,[],[R],[],[],[Q],[P]). given clause #886: (wt=15) 911 [hyper,870,5,demod,33,34] K2(E,D,[],[R],[],[P],[],[Q]). given clause #887: (wt=15) 912 [hyper,873,5,demod,33,34] K2(C,F,[],[R,Q],[],[P],[],[]). given clause #888: (wt=15) 913 [hyper,877,5,demod,33,34] K2(E,D,[],[R],[P],[],[],[Q]). given clause #889: (wt=15) 914 [hyper,881,5,demod,33,34] K2(C,F,[],[R,Q],[P],[],[],[]). given clause #890: (wt=15) 915 [hyper,882,6,eval,demod,33,34] K2(C,F,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 941 [hyper,915,8] H(F,[],[],[P],[],[],[R,Q]). given clause #891: (wt=14) 941 [hyper,915,8] H(F,[],[],[P],[],[],[R,Q]). ** KEPT (pick-wt=15): 942 [hyper,941,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 943 [hyper,941,14,demod,30,32,32,31,30,32,31] K1(F,C,[Q,R],[P],[],[],[],[]). given clause #892: (wt=15) 916 [hyper,882,5,demod,33,33,34] K2(C,F,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 944 [hyper,916,8] H(F,[],[],[],[],[],[P,R,Q]). given clause #893: (wt=14) 944 [hyper,916,8] H(F,[],[],[],[],[],[P,R,Q]). ** KEPT (pick-wt=15): 945 [hyper,944,15,demod,30,32,32,32,31,30,31] K1(F,E,[Q,R,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 946 [hyper,944,14,demod,30,32,32,32,31,30,31] K1(F,C,[Q,R,P],[],[],[],[],[]). given clause #894: (wt=15) 918 [hyper,917,3] K1(D,E,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 947 [hyper,918,5,demod,33,34] K2(D,E,[],[R],[],[],[],[Q,P]). given clause #895: (wt=15) 919 [hyper,917,2] K1(D,B,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 948 [hyper,919,5,demod,33,34] K2(D,B,[],[R],[],[],[],[Q,P]). given clause #896: (wt=15) 921 [hyper,920,3] K1(D,E,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 949 [hyper,921,5,demod,33,34] K2(D,E,[],[R],[],[Q,P],[],[]). given clause #897: (wt=15) 922 [hyper,920,2] K1(D,B,[R],[Q,P],[],[],[],[]). given clause #898: (wt=15) 924 [hyper,923,3] K1(D,E,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 950 [hyper,924,5,demod,33,34] K2(D,E,[],[R],[P],[Q],[],[]). given clause #899: (wt=15) 925 [hyper,923,2] K1(D,B,[R],[Q],[P],[],[],[]). given clause #900: (wt=15) 927 [hyper,926,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 951 [hyper,927,5,demod,33,34] K2(F,E,[],[R],[],[],[],[Q,P]). given clause #901: (wt=15) 928 [hyper,926,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 952 [hyper,928,5,demod,33,34] K2(F,C,[],[R],[],[],[Q,P],[]). given clause #902: (wt=15) 930 [hyper,929,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 953 [hyper,930,5,demod,33,34] K2(F,E,[],[R],[],[],[Q,P],[]). given clause #903: (wt=15) 931 [hyper,929,14,demod,30,32,31,30,32,32,31] K1(F,C,[R],[P,Q],[],[],[],[]). given clause #904: (wt=15) 933 [hyper,932,15,demod,30,32,31,30,31] K1(F,E,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 954 [hyper,933,5,demod,33,34] K2(F,E,[],[R],[Q],[],[P],[]). given clause #905: (wt=15) 934 [hyper,932,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[Q],[],[],[]). given clause #906: (wt=15) 936 [hyper,935,3] K1(D,E,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 955 [hyper,936,6,eval,demod,33,34] K2(D,E,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 956 [hyper,936,5,demod,33,33,34] K2(D,E,[],[P,R],[],[Q],[],[]). given clause #907: (wt=15) 937 [hyper,935,2] K1(D,B,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 957 [hyper,937,6,eval,demod,33,34] K2(D,B,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 958 [hyper,937,5,demod,33,33,34] K2(D,B,[],[P,R,Q],[],[],[],[]). given clause #908: (wt=15) 939 [hyper,938,3] K1(D,E,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 959 [hyper,939,6,eval,demod,33,33,34] K2(D,E,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 960 [hyper,939,5,demod,33,33,33,34] K2(D,E,[],[P,R,Q],[],[],[],[]). given clause #909: (wt=15) 940 [hyper,938,2] K1(D,B,[P,R,Q],[],[],[],[],[]). given clause #910: (wt=15) 942 [hyper,941,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 961 [hyper,942,6,eval,demod,33,34] K2(F,E,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 962 [hyper,942,5,demod,33,33,34] K2(F,E,[],[Q,R],[],[],[P],[]). given clause #911: (wt=15) 943 [hyper,941,14,demod,30,32,32,31,30,32,31] K1(F,C,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 963 [hyper,943,6,eval,demod,33,34] K2(F,C,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 964 [hyper,943,5,demod,33,33,34] K2(F,C,[],[Q,R,P],[],[],[],[]). given clause #912: (wt=15) 945 [hyper,944,15,demod,30,32,32,32,31,30,31] K1(F,E,[Q,R,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 965 [hyper,945,6,eval,demod,33,33,34] K2(F,E,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 966 [hyper,945,5,demod,33,33,33,34] K2(F,E,[],[Q,R,P],[],[],[],[]). given clause #913: (wt=15) 946 [hyper,944,14,demod,30,32,32,32,31,30,31] K1(F,C,[Q,R,P],[],[],[],[],[]). given clause #914: (wt=15) 947 [hyper,918,5,demod,33,34] K2(D,E,[],[R],[],[],[],[Q,P]). given clause #915: (wt=15) 948 [hyper,919,5,demod,33,34] K2(D,B,[],[R],[],[],[],[Q,P]). ** KEPT (pick-wt=14): 967 [hyper,948,9] H(B,[],[R],[],[],[],[Q,P]). given clause #916: (wt=14) 967 [hyper,948,9] H(B,[],[R],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 968 [hyper,967,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[],[Q,P]). given clause #917: (wt=15) 949 [hyper,921,5,demod,33,34] K2(D,E,[],[R],[],[Q,P],[],[]). ** KEPT (pick-wt=14): 969 [hyper,949,10] H(E,[],[Q,P],[],[],[R],[]). given clause #918: (wt=14) 969 [hyper,949,10] H(E,[],[Q,P],[],[],[R],[]). ** KEPT (pick-wt=15): 970 [hyper,969,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 971 [hyper,969,4] K1(E,F,[R],[],[],[Q,P],[],[]). given clause #919: (wt=15) 950 [hyper,924,5,demod,33,34] K2(D,E,[],[R],[P],[Q],[],[]). ** KEPT (pick-wt=14): 972 [hyper,950,10] H(E,[P],[Q],[],[],[R],[]). given clause #920: (wt=14) 972 [hyper,950,10] H(E,[P],[Q],[],[],[R],[]). ** KEPT (pick-wt=15): 973 [hyper,972,13,demod,30,32,31,30,31] K1(E,D,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 974 [hyper,972,4] K1(E,F,[R],[],[P],[Q],[],[]). given clause #921: (wt=15) 951 [hyper,927,5,demod,33,34] K2(F,E,[],[R],[],[],[],[Q,P]). given clause #922: (wt=15) 952 [hyper,928,5,demod,33,34] K2(F,C,[],[R],[],[],[Q,P],[]). ** KEPT (pick-wt=14): 975 [hyper,952,18,demod,30,32,31,30,31] H(C,[],[],[R],[Q,P],[],[]). given clause #923: (wt=14) 975 [hyper,952,18,demod,30,32,31,30,31] H(C,[],[],[R],[Q,P],[],[]). ** KEPT (pick-wt=15): 976 [hyper,975,1] K1(C,F,[R],[],[],[],[Q,P],[]). given clause #924: (wt=15) 953 [hyper,930,5,demod,33,34] K2(F,E,[],[R],[],[],[Q,P],[]). ** KEPT (pick-wt=14): 977 [hyper,953,19,demod,30,32,31,30,31] H(E,[],[],[Q,P],[],[R],[]). given clause #925: (wt=14) 977 [hyper,953,19,demod,30,32,31,30,31] H(E,[],[],[Q,P],[],[R],[]). ** KEPT (pick-wt=15): 978 [hyper,977,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 979 [hyper,977,4] K1(E,F,[R],[],[],[],[Q,P],[]). given clause #926: (wt=15) 954 [hyper,933,5,demod,33,34] K2(F,E,[],[R],[Q],[],[P],[]). ** KEPT (pick-wt=14): 980 [hyper,954,19,demod,30,32,31,30,31] H(E,[Q],[],[P],[],[R],[]). given clause #927: (wt=14) 980 [hyper,954,19,demod,30,32,31,30,31] H(E,[Q],[],[P],[],[R],[]). ** KEPT (pick-wt=15): 981 [hyper,980,13,demod,30,32,31,30,31] K1(E,D,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 982 [hyper,980,4] K1(E,F,[R],[],[Q],[],[P],[]). given clause #928: (wt=15) 955 [hyper,936,6,eval,demod,33,34] K2(D,E,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 983 [hyper,955,10] H(E,[],[Q],[],[P],[R],[]). given clause #929: (wt=14) 983 [hyper,955,10] H(E,[],[Q],[],[P],[R],[]). ** KEPT (pick-wt=15): 984 [hyper,983,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 985 [hyper,983,4] K1(E,F,[R],[],[],[Q],[],[P]). given clause #930: (wt=15) 956 [hyper,936,5,demod,33,33,34] K2(D,E,[],[P,R],[],[Q],[],[]). ** KEPT (pick-wt=14): 986 [hyper,956,10] H(E,[],[Q],[],[],[P,R],[]). given clause #931: (wt=14) 986 [hyper,956,10] H(E,[],[Q],[],[],[P,R],[]). ** KEPT (pick-wt=15): 987 [hyper,986,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 988 [hyper,986,4] K1(E,F,[P,R],[],[],[Q],[],[]). given clause #932: (wt=15) 957 [hyper,937,6,eval,demod,33,34] K2(D,B,[P],[R,Q],[],[],[],[]). given clause #933: (wt=15) 958 [hyper,937,5,demod,33,33,34] K2(D,B,[],[P,R,Q],[],[],[],[]). given clause #934: (wt=15) 959 [hyper,939,6,eval,demod,33,33,34] K2(D,E,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 989 [hyper,959,10] H(E,[],[],[],[P],[R,Q],[]). given clause #935: (wt=14) 989 [hyper,959,10] H(E,[],[],[],[P],[R,Q],[]). ** KEPT (pick-wt=15): 990 [hyper,989,13,demod,30,32,32,31,30,32,31] K1(E,D,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 991 [hyper,989,4] K1(E,F,[R,Q],[],[],[],[],[P]). given clause #936: (wt=15) 960 [hyper,939,5,demod,33,33,33,34] K2(D,E,[],[P,R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 992 [hyper,960,10] H(E,[],[],[],[],[P,R,Q],[]). given clause #937: (wt=14) 992 [hyper,960,10] H(E,[],[],[],[],[P,R,Q],[]). ** KEPT (pick-wt=15): 993 [hyper,992,13,demod,30,32,32,32,31,30,31] K1(E,D,[Q,R,P],[],[],[],[],[]). ** KEPT (pick-wt=15): 994 [hyper,992,4] K1(E,F,[P,R,Q],[],[],[],[],[]). given clause #938: (wt=15) 961 [hyper,942,6,eval,demod,33,34] K2(F,E,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 995 [hyper,961,19,demod,30,32,31,30,32,31] H(E,[],[],[P],[],[R],[Q]). given clause #939: (wt=14) 995 [hyper,961,19,demod,30,32,31,30,32,31] H(E,[],[],[P],[],[R],[Q]). ** KEPT (pick-wt=15): 996 [hyper,995,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 997 [hyper,995,4] K1(E,F,[R],[Q],[],[],[P],[]). given clause #940: (wt=15) 962 [hyper,942,5,demod,33,33,34] K2(F,E,[],[Q,R],[],[],[P],[]). ** KEPT (pick-wt=14): 998 [hyper,962,19,demod,30,32,32,31,30,31] H(E,[],[],[P],[],[R,Q],[]). given clause #941: (wt=14) 998 [hyper,962,19,demod,30,32,32,31,30,31] H(E,[],[],[P],[],[R,Q],[]). ** KEPT (pick-wt=15): 999 [hyper,998,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 1000 [hyper,998,4] K1(E,F,[R,Q],[],[],[],[P],[]). given clause #942: (wt=15) 963 [hyper,943,6,eval,demod,33,34] K2(F,C,[Q],[R,P],[],[],[],[]). given clause #943: (wt=15) 964 [hyper,943,5,demod,33,33,34] K2(F,C,[],[Q,R,P],[],[],[],[]). given clause #944: (wt=15) 965 [hyper,945,6,eval,demod,33,33,34] K2(F,E,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 1001 [hyper,965,19,demod,30,32,32,31,30,32,31] H(E,[],[],[],[],[P,R],[Q]). given clause #945: (wt=14) 1001 [hyper,965,19,demod,30,32,32,31,30,32,31] H(E,[],[],[],[],[P,R],[Q]). ** KEPT (pick-wt=15): 1002 [hyper,1001,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 1003 [hyper,1001,4] K1(E,F,[P,R],[Q],[],[],[],[]). given clause #946: (wt=15) 966 [hyper,945,5,demod,33,33,33,34] K2(F,E,[],[Q,R,P],[],[],[],[]). given clause #947: (wt=15) 968 [hyper,967,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[],[],[Q,P]). ** KEPT (pick-wt=15): 1004 [hyper,968,5,demod,33,34] K2(B,D,[],[R],[],[],[],[Q,P]). given clause #948: (wt=15) 970 [hyper,969,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1005 [hyper,970,5,demod,33,34] K2(E,D,[],[R],[],[Q,P],[],[]). given clause #949: (wt=15) 971 [hyper,969,4] K1(E,F,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1006 [hyper,971,5,demod,33,34] K2(E,F,[],[R],[],[Q,P],[],[]). given clause #950: (wt=15) 973 [hyper,972,13,demod,30,32,31,30,31] K1(E,D,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 1007 [hyper,973,5,demod,33,34] K2(E,D,[],[R],[P],[Q],[],[]). given clause #951: (wt=15) 974 [hyper,972,4] K1(E,F,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 1008 [hyper,974,5,demod,33,34] K2(E,F,[],[R],[P],[Q],[],[]). given clause #952: (wt=15) 976 [hyper,975,1] K1(C,F,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 1009 [hyper,976,5,demod,33,34] K2(C,F,[],[R],[],[],[Q,P],[]). given clause #953: (wt=15) 978 [hyper,977,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 1010 [hyper,978,5,demod,33,34] K2(E,D,[],[R],[],[],[Q,P],[]). given clause #954: (wt=15) 979 [hyper,977,4] K1(E,F,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 1011 [hyper,979,5,demod,33,34] K2(E,F,[],[R],[],[],[Q,P],[]). given clause #955: (wt=15) 981 [hyper,980,13,demod,30,32,31,30,31] K1(E,D,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 1012 [hyper,981,5,demod,33,34] K2(E,D,[],[R],[Q],[],[P],[]). given clause #956: (wt=15) 982 [hyper,980,4] K1(E,F,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 1013 [hyper,982,5,demod,33,34] K2(E,F,[],[R],[Q],[],[P],[]). given clause #957: (wt=15) 984 [hyper,983,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 1014 [hyper,984,5,demod,33,34] K2(E,D,[],[R,P],[],[Q],[],[]). given clause #958: (wt=15) 985 [hyper,983,4] K1(E,F,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 1015 [hyper,985,5,demod,33,34] K2(E,F,[],[R],[],[Q],[],[P]). given clause #959: (wt=15) 987 [hyper,986,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[],[Q],[],[]). given clause #960: (wt=15) 988 [hyper,986,4] K1(E,F,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 1016 [hyper,988,6,eval,demod,33,34] K2(E,F,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 1017 [hyper,988,5,demod,33,33,34] K2(E,F,[],[P,R],[],[Q],[],[]). given clause #961: (wt=15) 990 [hyper,989,13,demod,30,32,32,31,30,32,31] K1(E,D,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 1018 [hyper,990,6,eval,demod,33,34] K2(E,D,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=15): 1019 [hyper,990,5,demod,33,33,34] K2(E,D,[],[Q,R,P],[],[],[],[]). given clause #962: (wt=15) 991 [hyper,989,4] K1(E,F,[R,Q],[],[],[],[],[P]). ** KEPT (pick-wt=15): 1020 [hyper,991,5,demod,33,33,34] K2(E,F,[],[R,Q],[],[],[],[P]). given clause #963: (wt=15) 993 [hyper,992,13,demod,30,32,32,32,31,30,31] K1(E,D,[Q,R,P],[],[],[],[],[]). given clause #964: (wt=15) 994 [hyper,992,4] K1(E,F,[P,R,Q],[],[],[],[],[]). ** KEPT (pick-wt=15): 1021 [hyper,994,6,eval,demod,33,33,34] K2(E,F,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=15): 1022 [hyper,994,5,demod,33,33,33,34] K2(E,F,[],[P,R,Q],[],[],[],[]). given clause #965: (wt=15) 996 [hyper,995,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 1023 [hyper,996,5,demod,33,34] K2(E,D,[],[R],[],[],[P],[Q]). given clause #966: (wt=15) 997 [hyper,995,4] K1(E,F,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 1024 [hyper,997,5,demod,33,34] K2(E,F,[],[R,Q],[],[],[P],[]). given clause #967: (wt=15) 999 [hyper,998,13,demod,30,32,32,31,30,31] K1(E,D,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 1025 [hyper,999,6,eval,demod,33,34] K2(E,D,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 1026 [hyper,999,5,demod,33,33,34] K2(E,D,[],[Q,R],[],[],[P],[]). given clause #968: (wt=15) 1000 [hyper,998,4] K1(E,F,[R,Q],[],[],[],[P],[]). given clause #969: (wt=15) 1002 [hyper,1001,13,demod,30,32,32,31,30,31] K1(E,D,[R,P],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 1027 [hyper,1002,5,demod,33,33,34] K2(E,D,[],[R,P],[],[],[],[Q]). given clause #970: (wt=15) 1003 [hyper,1001,4] K1(E,F,[P,R],[Q],[],[],[],[]). given clause #971: (wt=15) 1004 [hyper,968,5,demod,33,34] K2(B,D,[],[R],[],[],[],[Q,P]). given clause #972: (wt=15) 1005 [hyper,970,5,demod,33,34] K2(E,D,[],[R],[],[Q,P],[],[]). given clause #973: (wt=15) 1006 [hyper,971,5,demod,33,34] K2(E,F,[],[R],[],[Q,P],[],[]). ** KEPT (pick-wt=14): 1028 [hyper,1006,11] H(F,[],[Q,P],[],[],[],[R]). given clause #974: (wt=14) 1028 [hyper,1006,11] H(F,[],[Q,P],[],[],[],[R]). ** KEPT (pick-wt=15): 1029 [hyper,1028,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1030 [hyper,1028,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[Q,P],[],[]). given clause #975: (wt=15) 1007 [hyper,973,5,demod,33,34] K2(E,D,[],[R],[P],[Q],[],[]). given clause #976: (wt=15) 1008 [hyper,974,5,demod,33,34] K2(E,F,[],[R],[P],[Q],[],[]). ** KEPT (pick-wt=14): 1031 [hyper,1008,11] H(F,[P],[Q],[],[],[],[R]). given clause #977: (wt=14) 1031 [hyper,1008,11] H(F,[P],[Q],[],[],[],[R]). ** KEPT (pick-wt=15): 1032 [hyper,1031,15,demod,30,32,31,30,31] K1(F,E,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 1033 [hyper,1031,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[Q],[],[]). given clause #978: (wt=15) 1009 [hyper,976,5,demod,33,34] K2(C,F,[],[R],[],[],[Q,P],[]). given clause #979: (wt=15) 1010 [hyper,978,5,demod,33,34] K2(E,D,[],[R],[],[],[Q,P],[]). ** KEPT (pick-wt=14): 1034 [hyper,1010,17,demod,30,32,31,30,31] H(D,[],[],[Q,P],[R],[],[]). given clause #980: (wt=14) 1034 [hyper,1010,17,demod,30,32,31,30,31] H(D,[],[],[Q,P],[R],[],[]). ** KEPT (pick-wt=15): 1035 [hyper,1034,3] K1(D,E,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 1036 [hyper,1034,2] K1(D,B,[R],[],[],[Q,P],[],[]). given clause #981: (wt=15) 1011 [hyper,979,5,demod,33,34] K2(E,F,[],[R],[],[],[Q,P],[]). given clause #982: (wt=15) 1012 [hyper,981,5,demod,33,34] K2(E,D,[],[R],[Q],[],[P],[]). ** KEPT (pick-wt=14): 1037 [hyper,1012,17,demod,30,32,31,30,31] H(D,[Q],[],[P],[R],[],[]). given clause #983: (wt=14) 1037 [hyper,1012,17,demod,30,32,31,30,31] H(D,[Q],[],[P],[R],[],[]). ** KEPT (pick-wt=15): 1038 [hyper,1037,3] K1(D,E,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 1039 [hyper,1037,2] K1(D,B,[R],[],[Q],[P],[],[]). given clause #984: (wt=15) 1013 [hyper,982,5,demod,33,34] K2(E,F,[],[R],[Q],[],[P],[]). given clause #985: (wt=15) 1014 [hyper,984,5,demod,33,34] K2(E,D,[],[R,P],[],[Q],[],[]). given clause #986: (wt=15) 1015 [hyper,985,5,demod,33,34] K2(E,F,[],[R],[],[Q],[],[P]). ** KEPT (pick-wt=14): 1040 [hyper,1015,11] H(F,[],[Q],[],[P],[],[R]). given clause #987: (wt=14) 1040 [hyper,1015,11] H(F,[],[Q],[],[P],[],[R]). ** KEPT (pick-wt=15): 1041 [hyper,1040,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 1042 [hyper,1040,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[Q],[P],[]). given clause #988: (wt=15) 1016 [hyper,988,6,eval,demod,33,34] K2(E,F,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 1043 [hyper,1016,11] H(F,[],[Q],[],[],[P],[R]). given clause #989: (wt=14) 1043 [hyper,1016,11] H(F,[],[Q],[],[],[P],[R]). ** KEPT (pick-wt=15): 1044 [hyper,1043,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 1045 [hyper,1043,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[Q],[],[P]). given clause #990: (wt=15) 1017 [hyper,988,5,demod,33,33,34] K2(E,F,[],[P,R],[],[Q],[],[]). ** KEPT (pick-wt=14): 1046 [hyper,1017,11] H(F,[],[Q],[],[],[],[P,R]). given clause #991: (wt=14) 1046 [hyper,1017,11] H(F,[],[Q],[],[],[],[P,R]). ** KEPT (pick-wt=15): 1047 [hyper,1046,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 1048 [hyper,1046,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[],[Q],[],[]). given clause #992: (wt=15) 1018 [hyper,990,6,eval,demod,33,34] K2(E,D,[Q],[R,P],[],[],[],[]). ** KEPT (pick-wt=14): 1049 [hyper,1018,17,demod,30,32,32,31,30,32,31] H(D,[],[],[],[P,R],[Q],[]). given clause #993: (wt=14) 1049 [hyper,1018,17,demod,30,32,32,31,30,32,31] H(D,[],[],[],[P,R],[Q],[]). ** KEPT (pick-wt=15): 1050 [hyper,1049,3] K1(D,E,[P,R],[Q],[],[],[],[]). ** KEPT (pick-wt=15): 1051 [hyper,1049,2] K1(D,B,[P,R],[],[],[],[Q],[]). given clause #994: (wt=15) 1019 [hyper,990,5,demod,33,33,34] K2(E,D,[],[Q,R,P],[],[],[],[]). given clause #995: (wt=15) 1020 [hyper,991,5,demod,33,33,34] K2(E,F,[],[R,Q],[],[],[],[P]). ** KEPT (pick-wt=14): 1052 [hyper,1020,11] H(F,[],[],[],[P],[],[R,Q]). given clause #996: (wt=14) 1052 [hyper,1020,11] H(F,[],[],[],[P],[],[R,Q]). ** KEPT (pick-wt=15): 1053 [hyper,1052,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 1054 [hyper,1052,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[],[],[P],[]). given clause #997: (wt=15) 1021 [hyper,994,6,eval,demod,33,33,34] K2(E,F,[P],[R,Q],[],[],[],[]). ** KEPT (pick-wt=14): 1055 [hyper,1021,11] H(F,[],[],[],[],[P],[R,Q]). given clause #998: (wt=14) 1055 [hyper,1021,11] H(F,[],[],[],[],[P],[R,Q]). ** KEPT (pick-wt=15): 1056 [hyper,1055,15,demod,30,32,32,31,30,32,31] K1(F,E,[Q,R],[P],[],[],[],[]). ** KEPT (pick-wt=15): 1057 [hyper,1055,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[],[],[],[P]). given clause #999: (wt=15) 1022 [hyper,994,5,demod,33,33,33,34] K2(E,F,[],[P,R,Q],[],[],[],[]). given clause #1000: (wt=15) 1023 [hyper,996,5,demod,33,34] K2(E,D,[],[R],[],[],[P],[Q]). ** KEPT (pick-wt=14): 1058 [hyper,1023,17,demod,30,32,31,30,31] H(D,[],[],[P],[R],[],[Q]). given clause #1001: (wt=14) 1058 [hyper,1023,17,demod,30,32,31,30,31] H(D,[],[],[P],[R],[],[Q]). ** KEPT (pick-wt=15): 1059 [hyper,1058,3] K1(D,E,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 1060 [hyper,1058,2] K1(D,B,[R],[],[],[P],[],[Q]). given clause #1002: (wt=15) 1024 [hyper,997,5,demod,33,34] K2(E,F,[],[R,Q],[],[],[P],[]). given clause #1003: (wt=15) 1025 [hyper,999,6,eval,demod,33,34] K2(E,D,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 1061 [hyper,1025,17,demod,30,32,31,30,32,31] H(D,[],[],[P],[R],[Q],[]). given clause #1004: (wt=14) 1061 [hyper,1025,17,demod,30,32,31,30,32,31] H(D,[],[],[P],[R],[Q],[]). ** KEPT (pick-wt=15): 1062 [hyper,1061,3] K1(D,E,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 1063 [hyper,1061,2] K1(D,B,[R],[],[],[P],[Q],[]). given clause #1005: (wt=15) 1026 [hyper,999,5,demod,33,33,34] K2(E,D,[],[Q,R],[],[],[P],[]). ** KEPT (pick-wt=14): 1064 [hyper,1026,17,demod,30,32,32,31,30,31] H(D,[],[],[P],[R,Q],[],[]). given clause #1006: (wt=14) 1064 [hyper,1026,17,demod,30,32,32,31,30,31] H(D,[],[],[P],[R,Q],[],[]). ** KEPT (pick-wt=15): 1065 [hyper,1064,3] K1(D,E,[R,Q],[],[],[],[P],[]). ** KEPT (pick-wt=15): 1066 [hyper,1064,2] K1(D,B,[R,Q],[],[],[P],[],[]). given clause #1007: (wt=15) 1027 [hyper,1002,5,demod,33,33,34] K2(E,D,[],[R,P],[],[],[],[Q]). ** KEPT (pick-wt=14): 1067 [hyper,1027,17,demod,30,32,32,31,30,31] H(D,[],[],[],[P,R],[],[Q]). given clause #1008: (wt=14) 1067 [hyper,1027,17,demod,30,32,32,31,30,31] H(D,[],[],[],[P,R],[],[Q]). ** KEPT (pick-wt=15): 1068 [hyper,1067,3] K1(D,E,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 1069 [hyper,1067,2] K1(D,B,[P,R],[],[],[],[],[Q]). given clause #1009: (wt=15) 1029 [hyper,1028,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1070 [hyper,1029,5,demod,33,34] K2(F,E,[],[R],[],[Q,P],[],[]). given clause #1010: (wt=15) 1030 [hyper,1028,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1071 [hyper,1030,5,demod,33,34] K2(F,C,[],[R],[],[Q,P],[],[]). given clause #1011: (wt=15) 1032 [hyper,1031,15,demod,30,32,31,30,31] K1(F,E,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 1072 [hyper,1032,5,demod,33,34] K2(F,E,[],[R],[P],[Q],[],[]). given clause #1012: (wt=15) 1033 [hyper,1031,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 1073 [hyper,1033,5,demod,33,34] K2(F,C,[],[R],[P],[Q],[],[]). given clause #1013: (wt=15) 1035 [hyper,1034,3] K1(D,E,[R],[],[],[],[Q,P],[]). ** KEPT (pick-wt=15): 1074 [hyper,1035,5,demod,33,34] K2(D,E,[],[R],[],[],[Q,P],[]). given clause #1014: (wt=15) 1036 [hyper,1034,2] K1(D,B,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1075 [hyper,1036,5,demod,33,34] K2(D,B,[],[R],[],[Q,P],[],[]). given clause #1015: (wt=15) 1038 [hyper,1037,3] K1(D,E,[R],[],[Q],[],[P],[]). ** KEPT (pick-wt=15): 1076 [hyper,1038,5,demod,33,34] K2(D,E,[],[R],[Q],[],[P],[]). given clause #1016: (wt=15) 1039 [hyper,1037,2] K1(D,B,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 1077 [hyper,1039,5,demod,33,34] K2(D,B,[],[R],[Q],[P],[],[]). given clause #1017: (wt=15) 1041 [hyper,1040,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 1078 [hyper,1041,5,demod,33,34] K2(F,E,[],[R],[],[Q],[],[P]). given clause #1018: (wt=15) 1042 [hyper,1040,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 1079 [hyper,1042,5,demod,33,34] K2(F,C,[],[R],[],[Q],[P],[]). given clause #1019: (wt=15) 1044 [hyper,1043,15,demod,30,32,31,30,32,31] K1(F,E,[R],[P],[],[Q],[],[]). ** KEPT (pick-wt=15): 1080 [hyper,1044,5,demod,33,34] K2(F,E,[],[R,P],[],[Q],[],[]). given clause #1020: (wt=15) 1045 [hyper,1043,14,demod,30,32,31,30,31] K1(F,C,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 1081 [hyper,1045,5,demod,33,34] K2(F,C,[],[R],[],[Q],[],[P]). given clause #1021: (wt=15) 1047 [hyper,1046,15,demod,30,32,32,31,30,31] K1(F,E,[R,P],[],[],[Q],[],[]). given clause #1022: (wt=15) 1048 [hyper,1046,14,demod,30,32,32,31,30,31] K1(F,C,[R,P],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 1082 [hyper,1048,5,demod,33,33,34] K2(F,C,[],[R,P],[],[Q],[],[]). given clause #1023: (wt=15) 1050 [hyper,1049,3] K1(D,E,[P,R],[Q],[],[],[],[]). given clause #1024: (wt=15) 1051 [hyper,1049,2] K1(D,B,[P,R],[],[],[],[Q],[]). ** KEPT (pick-wt=15): 1083 [hyper,1051,6,eval,demod,33,34] K2(D,B,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=15): 1084 [hyper,1051,5,demod,33,33,34] K2(D,B,[],[P,R],[],[],[Q],[]). given clause #1025: (wt=15) 1053 [hyper,1052,15,demod,30,32,32,31,30,31] K1(F,E,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 1085 [hyper,1053,6,eval,demod,33,34] K2(F,E,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 1086 [hyper,1053,5,demod,33,33,34] K2(F,E,[],[Q,R],[],[],[],[P]). given clause #1026: (wt=15) 1054 [hyper,1052,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[],[],[P],[]). ** KEPT (pick-wt=15): 1087 [hyper,1054,6,eval,demod,33,34] K2(F,C,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=15): 1088 [hyper,1054,5,demod,33,33,34] K2(F,C,[],[Q,R],[],[],[P],[]). given clause #1027: (wt=15) 1056 [hyper,1055,15,demod,30,32,32,31,30,32,31] K1(F,E,[Q,R],[P],[],[],[],[]). given clause #1028: (wt=15) 1057 [hyper,1055,14,demod,30,32,32,31,30,31] K1(F,C,[Q,R],[],[],[],[],[P]). ** KEPT (pick-wt=15): 1089 [hyper,1057,6,eval,demod,33,34] K2(F,C,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=15): 1090 [hyper,1057,5,demod,33,33,34] K2(F,C,[],[Q,R],[],[],[],[P]). given clause #1029: (wt=15) 1059 [hyper,1058,3] K1(D,E,[R],[],[],[],[P],[Q]). ** KEPT (pick-wt=15): 1091 [hyper,1059,5,demod,33,34] K2(D,E,[],[R],[],[],[P],[Q]). given clause #1030: (wt=15) 1060 [hyper,1058,2] K1(D,B,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 1092 [hyper,1060,5,demod,33,34] K2(D,B,[],[R],[],[P],[],[Q]). given clause #1031: (wt=15) 1062 [hyper,1061,3] K1(D,E,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 1093 [hyper,1062,5,demod,33,34] K2(D,E,[],[R,Q],[],[],[P],[]). given clause #1032: (wt=15) 1063 [hyper,1061,2] K1(D,B,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 1094 [hyper,1063,5,demod,33,34] K2(D,B,[],[R],[],[P],[Q],[]). given clause #1033: (wt=15) 1065 [hyper,1064,3] K1(D,E,[R,Q],[],[],[],[P],[]). given clause #1034: (wt=15) 1066 [hyper,1064,2] K1(D,B,[R,Q],[],[],[P],[],[]). ** KEPT (pick-wt=15): 1095 [hyper,1066,5,demod,33,33,34] K2(D,B,[],[R,Q],[],[P],[],[]). given clause #1035: (wt=15) 1068 [hyper,1067,3] K1(D,E,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 1096 [hyper,1068,6,eval,demod,33,34] K2(D,E,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 1097 [hyper,1068,5,demod,33,33,34] K2(D,E,[],[P,R],[],[],[],[Q]). given clause #1036: (wt=15) 1069 [hyper,1067,2] K1(D,B,[P,R],[],[],[],[],[Q]). ** KEPT (pick-wt=15): 1098 [hyper,1069,6,eval,demod,33,34] K2(D,B,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=15): 1099 [hyper,1069,5,demod,33,33,34] K2(D,B,[],[P,R],[],[],[],[Q]). given clause #1037: (wt=15) 1070 [hyper,1029,5,demod,33,34] K2(F,E,[],[R],[],[Q,P],[],[]). given clause #1038: (wt=15) 1071 [hyper,1030,5,demod,33,34] K2(F,C,[],[R],[],[Q,P],[],[]). ** KEPT (pick-wt=14): 1100 [hyper,1071,18,demod,30,32,31,30,31] H(C,[],[Q,P],[R],[],[],[]). given clause #1039: (wt=14) 1100 [hyper,1071,18,demod,30,32,31,30,31] H(C,[],[Q,P],[R],[],[],[]). ** KEPT (pick-wt=15): 1101 [hyper,1100,1] K1(C,F,[R],[],[],[Q,P],[],[]). given clause #1040: (wt=15) 1072 [hyper,1032,5,demod,33,34] K2(F,E,[],[R],[P],[Q],[],[]). given clause #1041: (wt=15) 1073 [hyper,1033,5,demod,33,34] K2(F,C,[],[R],[P],[Q],[],[]). ** KEPT (pick-wt=14): 1102 [hyper,1073,18,demod,30,32,31,30,31] H(C,[P],[Q],[R],[],[],[]). given clause #1042: (wt=14) 1102 [hyper,1073,18,demod,30,32,31,30,31] H(C,[P],[Q],[R],[],[],[]). ** KEPT (pick-wt=14): 1103 [hyper,1102,25] H(C,[],[Q],[P,R],[],[],[]). ** KEPT (pick-wt=15): 1104 [hyper,1102,1] K1(C,F,[R],[],[P],[Q],[],[]). given clause #1043: (wt=14) 1103 [hyper,1102,25] H(C,[],[Q],[P,R],[],[],[]). ** KEPT (pick-wt=15): 1105 [hyper,1103,1] K1(C,F,[P,R],[],[],[Q],[],[]). given clause #1044: (wt=15) 1074 [hyper,1035,5,demod,33,34] K2(D,E,[],[R],[],[],[Q,P],[]). given clause #1045: (wt=15) 1075 [hyper,1036,5,demod,33,34] K2(D,B,[],[R],[],[Q,P],[],[]). ** KEPT (pick-wt=14): 1106 [hyper,1075,9] H(B,[],[R],[Q,P],[],[],[]). given clause #1046: (wt=14) 1106 [hyper,1075,9] H(B,[],[R],[Q,P],[],[],[]). ** KEPT (pick-wt=15): 1107 [hyper,1106,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[Q,P],[],[]). given clause #1047: (wt=15) 1076 [hyper,1038,5,demod,33,34] K2(D,E,[],[R],[Q],[],[P],[]). given clause #1048: (wt=15) 1077 [hyper,1039,5,demod,33,34] K2(D,B,[],[R],[Q],[P],[],[]). ** KEPT (pick-wt=14): 1108 [hyper,1077,9] H(B,[Q],[R],[P],[],[],[]). given clause #1049: (wt=14) 1108 [hyper,1077,9] H(B,[Q],[R],[P],[],[],[]). ** KEPT (pick-wt=14): 1109 [hyper,1108,23,demod,33,34] H(B,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=15): 1110 [hyper,1108,12,demod,30,32,31,30,31] K1(B,D,[R],[],[Q],[P],[],[]). given clause #1050: (wt=14) 1109 [hyper,1108,23,demod,33,34] H(B,[],[R,Q],[P],[],[],[]). ** KEPT (pick-wt=15): 1111 [hyper,1109,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[P],[],[]). given clause #1051: (wt=15) 1078 [hyper,1041,5,demod,33,34] K2(F,E,[],[R],[],[Q],[],[P]). given clause #1052: (wt=15) 1079 [hyper,1042,5,demod,33,34] K2(F,C,[],[R],[],[Q],[P],[]). ** KEPT (pick-wt=14): 1112 [hyper,1079,18,demod,30,32,31,30,31] H(C,[],[Q],[R],[P],[],[]). given clause #1053: (wt=14) 1112 [hyper,1079,18,demod,30,32,31,30,31] H(C,[],[Q],[R],[P],[],[]). ** KEPT (pick-wt=15): 1113 [hyper,1112,1] K1(C,F,[R],[],[],[Q],[P],[]). given clause #1054: (wt=15) 1080 [hyper,1044,5,demod,33,34] K2(F,E,[],[R,P],[],[Q],[],[]). given clause #1055: (wt=15) 1081 [hyper,1045,5,demod,33,34] K2(F,C,[],[R],[],[Q],[],[P]). ** KEPT (pick-wt=14): 1114 [hyper,1081,18,demod,30,32,31,30,31] H(C,[],[Q],[R],[],[P],[]). given clause #1056: (wt=14) 1114 [hyper,1081,18,demod,30,32,31,30,31] H(C,[],[Q],[R],[],[P],[]). ** KEPT (pick-wt=15): 1115 [hyper,1114,1] K1(C,F,[R],[],[],[Q],[],[P]). given clause #1057: (wt=15) 1082 [hyper,1048,5,demod,33,33,34] K2(F,C,[],[R,P],[],[Q],[],[]). given clause #1058: (wt=15) 1083 [hyper,1051,6,eval,demod,33,34] K2(D,B,[P],[R],[],[],[Q],[]). ** KEPT (pick-wt=14): 1116 [hyper,1083,9] H(B,[],[R],[],[P],[Q],[]). given clause #1059: (wt=14) 1116 [hyper,1083,9] H(B,[],[R],[],[P],[Q],[]). ** KEPT (pick-wt=15): 1117 [hyper,1116,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[],[],[Q],[]). given clause #1060: (wt=15) 1084 [hyper,1051,5,demod,33,33,34] K2(D,B,[],[P,R],[],[],[Q],[]). ** KEPT (pick-wt=14): 1118 [hyper,1084,9] H(B,[],[P,R],[],[],[Q],[]). given clause #1061: (wt=14) 1118 [hyper,1084,9] H(B,[],[P,R],[],[],[Q],[]). ** KEPT (pick-wt=15): 1119 [hyper,1118,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[],[],[Q],[]). given clause #1062: (wt=15) 1085 [hyper,1053,6,eval,demod,33,34] K2(F,E,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 1120 [hyper,1085,19,demod,30,32,31,30,32,31] H(E,[],[],[],[P],[R],[Q]). given clause #1063: (wt=14) 1120 [hyper,1085,19,demod,30,32,31,30,32,31] H(E,[],[],[],[P],[R],[Q]). ** KEPT (pick-wt=15): 1121 [hyper,1120,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 1122 [hyper,1120,4] K1(E,F,[R],[Q],[],[],[],[P]). given clause #1064: (wt=15) 1086 [hyper,1053,5,demod,33,33,34] K2(F,E,[],[Q,R],[],[],[],[P]). given clause #1065: (wt=15) 1087 [hyper,1054,6,eval,demod,33,34] K2(F,C,[Q],[R],[],[],[P],[]). ** KEPT (pick-wt=14): 1123 [hyper,1087,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[P],[],[Q]). given clause #1066: (wt=14) 1123 [hyper,1087,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[P],[],[Q]). ** KEPT (pick-wt=15): 1124 [hyper,1123,1] K1(C,F,[R],[Q],[],[],[P],[]). given clause #1067: (wt=15) 1088 [hyper,1054,5,demod,33,33,34] K2(F,C,[],[Q,R],[],[],[P],[]). ** KEPT (pick-wt=14): 1125 [hyper,1088,18,demod,30,32,32,31,30,31] H(C,[],[],[R,Q],[P],[],[]). given clause #1068: (wt=14) 1125 [hyper,1088,18,demod,30,32,32,31,30,31] H(C,[],[],[R,Q],[P],[],[]). ** KEPT (pick-wt=15): 1126 [hyper,1125,1] K1(C,F,[R,Q],[],[],[],[P],[]). given clause #1069: (wt=15) 1089 [hyper,1057,6,eval,demod,33,34] K2(F,C,[Q],[R],[],[],[],[P]). ** KEPT (pick-wt=14): 1127 [hyper,1089,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[],[P],[Q]). given clause #1070: (wt=14) 1127 [hyper,1089,18,demod,30,32,31,30,32,31] H(C,[],[],[R],[],[P],[Q]). ** KEPT (pick-wt=15): 1128 [hyper,1127,1] K1(C,F,[R],[Q],[],[],[],[P]). given clause #1071: (wt=15) 1090 [hyper,1057,5,demod,33,33,34] K2(F,C,[],[Q,R],[],[],[],[P]). ** KEPT (pick-wt=14): 1129 [hyper,1090,18,demod,30,32,32,31,30,31] H(C,[],[],[R,Q],[],[P],[]). given clause #1072: (wt=14) 1129 [hyper,1090,18,demod,30,32,32,31,30,31] H(C,[],[],[R,Q],[],[P],[]). ** KEPT (pick-wt=15): 1130 [hyper,1129,1] K1(C,F,[R,Q],[],[],[],[],[P]). given clause #1073: (wt=15) 1091 [hyper,1059,5,demod,33,34] K2(D,E,[],[R],[],[],[P],[Q]). given clause #1074: (wt=15) 1092 [hyper,1060,5,demod,33,34] K2(D,B,[],[R],[],[P],[],[Q]). ** KEPT (pick-wt=14): 1131 [hyper,1092,9] H(B,[],[R],[P],[],[],[Q]). given clause #1075: (wt=14) 1131 [hyper,1092,9] H(B,[],[R],[P],[],[],[Q]). ** KEPT (pick-wt=15): 1132 [hyper,1131,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[P],[],[Q]). given clause #1076: (wt=15) 1093 [hyper,1062,5,demod,33,34] K2(D,E,[],[R,Q],[],[],[P],[]). given clause #1077: (wt=15) 1094 [hyper,1063,5,demod,33,34] K2(D,B,[],[R],[],[P],[Q],[]). ** KEPT (pick-wt=14): 1133 [hyper,1094,9] H(B,[],[R],[P],[],[Q],[]). given clause #1078: (wt=14) 1133 [hyper,1094,9] H(B,[],[R],[P],[],[Q],[]). ** KEPT (pick-wt=15): 1134 [hyper,1133,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[P],[Q],[]). given clause #1079: (wt=15) 1095 [hyper,1066,5,demod,33,33,34] K2(D,B,[],[R,Q],[],[P],[],[]). given clause #1080: (wt=15) 1096 [hyper,1068,6,eval,demod,33,34] K2(D,E,[P],[R],[],[],[],[Q]). given clause #1081: (wt=15) 1097 [hyper,1068,5,demod,33,33,34] K2(D,E,[],[P,R],[],[],[],[Q]). given clause #1082: (wt=15) 1098 [hyper,1069,6,eval,demod,33,34] K2(D,B,[P],[R],[],[],[],[Q]). ** KEPT (pick-wt=14): 1135 [hyper,1098,9] H(B,[],[R],[],[P],[],[Q]). given clause #1083: (wt=14) 1135 [hyper,1098,9] H(B,[],[R],[],[P],[],[Q]). ** KEPT (pick-wt=15): 1136 [hyper,1135,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[],[],[],[Q]). given clause #1084: (wt=15) 1099 [hyper,1069,5,demod,33,33,34] K2(D,B,[],[P,R],[],[],[],[Q]). ** KEPT (pick-wt=14): 1137 [hyper,1099,9] H(B,[],[P,R],[],[],[],[Q]). given clause #1085: (wt=14) 1137 [hyper,1099,9] H(B,[],[P,R],[],[],[],[Q]). ** KEPT (pick-wt=15): 1138 [hyper,1137,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[],[],[],[Q]). given clause #1086: (wt=15) 1101 [hyper,1100,1] K1(C,F,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1139 [hyper,1101,5,demod,33,34] K2(C,F,[],[R],[],[Q,P],[],[]). given clause #1087: (wt=15) 1104 [hyper,1102,1] K1(C,F,[R],[],[P],[Q],[],[]). ** KEPT (pick-wt=15): 1140 [hyper,1104,5,demod,33,34] K2(C,F,[],[R],[P],[Q],[],[]). given clause #1088: (wt=15) 1105 [hyper,1103,1] K1(C,F,[P,R],[],[],[Q],[],[]). ** KEPT (pick-wt=15): 1141 [hyper,1105,6,eval,demod,33,34] K2(C,F,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=15): 1142 [hyper,1105,5,demod,33,33,34] K2(C,F,[],[P,R],[],[Q],[],[]). given clause #1089: (wt=15) 1107 [hyper,1106,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[Q,P],[],[]). ** KEPT (pick-wt=15): 1143 [hyper,1107,5,demod,33,34] K2(B,D,[],[R],[],[Q,P],[],[]). given clause #1090: (wt=15) 1110 [hyper,1108,12,demod,30,32,31,30,31] K1(B,D,[R],[],[Q],[P],[],[]). ** KEPT (pick-wt=15): 1144 [hyper,1110,5,demod,33,34] K2(B,D,[],[R],[Q],[P],[],[]). given clause #1091: (wt=15) 1111 [hyper,1109,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[P],[],[]). ** KEPT (pick-wt=15): 1145 [hyper,1111,6,eval,demod,33,34] K2(B,D,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=15): 1146 [hyper,1111,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[P],[],[]). given clause #1092: (wt=15) 1113 [hyper,1112,1] K1(C,F,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 1147 [hyper,1113,5,demod,33,34] K2(C,F,[],[R],[],[Q],[P],[]). given clause #1093: (wt=15) 1115 [hyper,1114,1] K1(C,F,[R],[],[],[Q],[],[P]). ** KEPT (pick-wt=15): 1148 [hyper,1115,5,demod,33,34] K2(C,F,[],[R],[],[Q],[],[P]). given clause #1094: (wt=15) 1117 [hyper,1116,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[],[],[Q],[]). ** KEPT (pick-wt=15): 1149 [hyper,1117,5,demod,33,34] K2(B,D,[],[R,P],[],[],[Q],[]). given clause #1095: (wt=15) 1119 [hyper,1118,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[],[],[Q],[]). given clause #1096: (wt=15) 1121 [hyper,1120,13,demod,30,32,31,30,32,31] K1(E,D,[R],[P],[],[],[],[Q]). given clause #1097: (wt=15) 1122 [hyper,1120,4] K1(E,F,[R],[Q],[],[],[],[P]). given clause #1098: (wt=15) 1124 [hyper,1123,1] K1(C,F,[R],[Q],[],[],[P],[]). ** KEPT (pick-wt=15): 1150 [hyper,1124,5,demod,33,34] K2(C,F,[],[R,Q],[],[],[P],[]). given clause #1099: (wt=15) 1126 [hyper,1125,1] K1(C,F,[R,Q],[],[],[],[P],[]). given clause #1100: (wt=15) 1128 [hyper,1127,1] K1(C,F,[R],[Q],[],[],[],[P]). ** KEPT (pick-wt=15): 1151 [hyper,1128,5,demod,33,34] K2(C,F,[],[R,Q],[],[],[],[P]). given clause #1101: (wt=15) 1130 [hyper,1129,1] K1(C,F,[R,Q],[],[],[],[],[P]). given clause #1102: (wt=15) 1132 [hyper,1131,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[P],[],[Q]). ** KEPT (pick-wt=15): 1152 [hyper,1132,5,demod,33,34] K2(B,D,[],[R],[],[P],[],[Q]). given clause #1103: (wt=15) 1134 [hyper,1133,12,demod,30,32,31,30,31] K1(B,D,[R],[],[],[P],[Q],[]). ** KEPT (pick-wt=15): 1153 [hyper,1134,5,demod,33,34] K2(B,D,[],[R],[],[P],[Q],[]). given clause #1104: (wt=15) 1136 [hyper,1135,12,demod,30,32,31,30,32,31] K1(B,D,[R],[P],[],[],[],[Q]). ** KEPT (pick-wt=15): 1154 [hyper,1136,5,demod,33,34] K2(B,D,[],[R,P],[],[],[],[Q]). given clause #1105: (wt=15) 1138 [hyper,1137,12,demod,30,32,32,31,30,31] K1(B,D,[R,P],[],[],[],[],[Q]). given clause #1106: (wt=15) 1139 [hyper,1101,5,demod,33,34] K2(C,F,[],[R],[],[Q,P],[],[]). given clause #1107: (wt=15) 1140 [hyper,1104,5,demod,33,34] K2(C,F,[],[R],[P],[Q],[],[]). given clause #1108: (wt=15) 1141 [hyper,1105,6,eval,demod,33,34] K2(C,F,[P],[R],[],[Q],[],[]). ** KEPT (pick-wt=14): 1155 [hyper,1141,8] H(F,[],[Q],[P],[],[],[R]). given clause #1109: (wt=14) 1155 [hyper,1141,8] H(F,[],[Q],[P],[],[],[R]). ** KEPT (pick-wt=15): 1156 [hyper,1155,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 1157 [hyper,1155,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[],[Q],[],[]). given clause #1110: (wt=15) 1142 [hyper,1105,5,demod,33,33,34] K2(C,F,[],[P,R],[],[Q],[],[]). given clause #1111: (wt=15) 1143 [hyper,1107,5,demod,33,34] K2(B,D,[],[R],[],[Q,P],[],[]). given clause #1112: (wt=15) 1144 [hyper,1110,5,demod,33,34] K2(B,D,[],[R],[Q],[P],[],[]). given clause #1113: (wt=15) 1145 [hyper,1111,6,eval,demod,33,34] K2(B,D,[Q],[R],[],[P],[],[]). ** KEPT (pick-wt=14): 1158 [hyper,1145,16,demod,30,32,31,30,32,31] H(D,[],[Q],[P],[R],[],[]). given clause #1114: (wt=14) 1158 [hyper,1145,16,demod,30,32,31,30,32,31] H(D,[],[Q],[P],[R],[],[]). ** KEPT (pick-wt=15): 1159 [hyper,1158,3] K1(D,E,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 1160 [hyper,1158,2] K1(D,B,[R],[Q],[],[P],[],[]). given clause #1115: (wt=15) 1146 [hyper,1111,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[P],[],[]). given clause #1116: (wt=15) 1147 [hyper,1113,5,demod,33,34] K2(C,F,[],[R],[],[Q],[P],[]). given clause #1117: (wt=15) 1148 [hyper,1115,5,demod,33,34] K2(C,F,[],[R],[],[Q],[],[P]). given clause #1118: (wt=15) 1149 [hyper,1117,5,demod,33,34] K2(B,D,[],[R,P],[],[],[Q],[]). given clause #1119: (wt=15) 1150 [hyper,1124,5,demod,33,34] K2(C,F,[],[R,Q],[],[],[P],[]). given clause #1120: (wt=15) 1151 [hyper,1128,5,demod,33,34] K2(C,F,[],[R,Q],[],[],[],[P]). given clause #1121: (wt=15) 1152 [hyper,1132,5,demod,33,34] K2(B,D,[],[R],[],[P],[],[Q]). given clause #1122: (wt=15) 1153 [hyper,1134,5,demod,33,34] K2(B,D,[],[R],[],[P],[Q],[]). given clause #1123: (wt=15) 1154 [hyper,1136,5,demod,33,34] K2(B,D,[],[R,P],[],[],[],[Q]). given clause #1124: (wt=15) 1156 [hyper,1155,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 1161 [hyper,1156,5,demod,33,34] K2(F,E,[],[R],[],[Q],[P],[]). given clause #1125: (wt=15) 1157 [hyper,1155,14,demod,30,32,31,30,32,31] K1(F,C,[R],[P],[],[Q],[],[]). given clause #1126: (wt=15) 1159 [hyper,1158,3] K1(D,E,[R],[],[],[Q],[P],[]). ** KEPT (pick-wt=15): 1162 [hyper,1159,5,demod,33,34] K2(D,E,[],[R],[],[Q],[P],[]). given clause #1127: (wt=15) 1160 [hyper,1158,2] K1(D,B,[R],[Q],[],[P],[],[]). given clause #1128: (wt=15) 1161 [hyper,1156,5,demod,33,34] K2(F,E,[],[R],[],[Q],[P],[]). -------- PROOF -------- ** KEPT (pick-wt=14): 1163 [hyper,1161,19,demod,30,32,31,30,31] H(E,[],[Q],[P],[],[R],[]). ----> UNIT CONFLICT at 0.11 sec ----> 1164 [binary,1163.1,27.1] $F. Length of proof is 64. Level of proof is 64. ---------------- PROOF ---------------- 1 [] -H(C,xA,xB,xC,xD,xE,xF)|K1(C,F,xC,xF,xA,xB,xD,xE). 2 [] -H(D,xA,xB,xC,xD,xE,xF)|K1(D,B,xD,xB,xA,xC,xE,xF). 3 [] -H(D,xA,xB,xC,xD,xE,xF)|K1(D,E,xD,xE,xA,xB,xC,xF). 4 [] -H(E,xA,xB,xC,xD,xE,xF)|K1(E,F,xE,xF,xA,xB,xC,xD). 5 [] -K1(u,v,y,z,x1,x2,x3,x4)|K2(u,v,[],app(y,z),x1,x2,x3,x4). 6 [] -K1(u,v,[y0|y1],z,x1,x2,x3,x4)| -$TRUE(member(R,y1))|K2(u,v,[y0],app(y1,z),x1,x2,x3,x4). 8 [] -K2(C,F,xC,xF,xA,xB,xD,xE)|H(F,xA,xB,xC,xD,xE,xF). 9 [] -K2(D,B,xD,xB,xA,xC,xE,xF)|H(B,xA,xB,xC,xD,xE,xF). 10 [] -K2(D,E,xD,xE,xA,xB,xC,xF)|H(E,xA,xB,xC,xD,xE,xF). 11 [] -K2(E,F,xE,xF,xA,xB,xC,xD)|H(F,xA,xB,xC,xD,xE,xF). 12 [] -H(B,xA,xB,xC,xD,xE,xF)|K1(B,D,rev(xB),rev(xD),xA,xC,xE,xF). 13 [] -H(E,xA,xB,xC,xD,xE,xF)|K1(E,D,rev(xE),rev(xD),xA,xB,xC,xF). 14 [] -H(F,xA,xB,xC,xD,xE,xF)|K1(F,C,rev(xF),rev(xC),xA,xB,xD,xE). 15 [] -H(F,xA,xB,xC,xD,xE,xF)|K1(F,E,rev(xF),rev(xE),xA,xB,xC,xD). 16 [] -K2(B,D,xB,xD,xA,xC,xE,xF)|H(D,xA,rev(xB),xC,rev(xD),xE,xF). 17 [] -K2(E,D,xE,xD,xA,xB,xC,xF)|H(D,xA,xB,xC,rev(xD),rev(xE),xF). 18 [] -K2(F,C,xF,xC,xA,xB,xD,xE)|H(C,xA,xB,rev(xC),xD,xE,rev(xF)). 19 [] -K2(F,E,xF,xE,xA,xB,xC,xD)|H(E,xA,xB,xC,xD,rev(xE),rev(xF)). 21 [] -H(B,[],[R,u,v],xC,xD,xE,xF)|H(B,[v],[R,u],xC,xD,xE,xF). 23 [] -H(B,[u],xB,xC,xD,xE,xF)|H(B,[],app(xB,[u]),xC,xD,xE,xF). 24 [] -H(C,[],xB,[y0|y1],xD,xE,xF)| -$TRUE(member(R,y1))|H(C,[y0],xB,y1,xD,xE,xF). 25 [] -H(C,[y0],xB,y1,xD,xE,xF)|H(C,[],xB,[y0|y1],xD,xE,xF). 26 [] H(E,[],[P],[Q],[],[R],[]). 27 [] -H(E,[],[Q],[P],[],[R],[]). 30 [] rev(x)=rev2(x,[]). 31 [] rev2([],x)=x. 32 [] rev2([y1|y2],z)=rev2(y2,[y1|z]). 33 [] app([u|v],y)=[u|app(v,y)]. 34 [] app([],y)=y. 35 [hyper,26,13,demod,30,32,31,30,31] K1(E,D,[R],[],[],[P],[Q],[]). 37 [hyper,35,5,demod,33,34] K2(E,D,[],[R],[],[P],[Q],[]). 39 [hyper,37,17,demod,30,32,31,30,31] H(D,[],[P],[Q],[R],[],[]). 41 [hyper,39,2] K1(D,B,[R],[P],[],[Q],[],[]). 46 [hyper,41,5,demod,33,34] K2(D,B,[],[R,P],[],[Q],[],[]). 49 [hyper,46,9] H(B,[],[R,P],[Q],[],[],[]). 51 [hyper,49,12,demod,30,32,32,31,30,31] K1(B,D,[P,R],[],[],[Q],[],[]). 58 [hyper,51,5,demod,33,33,34] K2(B,D,[],[P,R],[],[Q],[],[]). 63 [hyper,58,16,demod,30,31,30,32,32,31] H(D,[],[],[Q],[R,P],[],[]). 64 [hyper,63,3] K1(D,E,[R,P],[],[],[],[Q],[]). 75 [hyper,64,5,demod,33,33,34] K2(D,E,[],[R,P],[],[],[Q],[]). 81 [hyper,75,10] H(E,[],[],[Q],[],[R,P],[]). 83 [hyper,81,4] K1(E,F,[R,P],[],[],[],[Q],[]). 95 [hyper,83,5,demod,33,33,34] K2(E,F,[],[R,P],[],[],[Q],[]). 106 [hyper,95,11] H(F,[],[],[Q],[],[],[R,P]). 108 [hyper,106,14,demod,30,32,32,31,30,32,31] K1(F,C,[P,R],[Q],[],[],[],[]). 124 [hyper,108,6,eval,demod,33,34] K2(F,C,[P],[R,Q],[],[],[],[]). 140 [hyper,124,18,demod,30,32,32,31,30,32,31] H(C,[],[],[Q,R],[],[],[P]). 141 [hyper,140,24,eval] H(C,[Q],[],[R],[],[],[P]). 143 [hyper,141,1] K1(C,F,[R],[P],[Q],[],[],[]). 173 [hyper,143,5,demod,33,34] K2(C,F,[],[R,P],[Q],[],[],[]). 195 [hyper,173,8] H(F,[Q],[],[],[],[],[R,P]). 196 [hyper,195,15,demod,30,32,32,31,30,31] K1(F,E,[P,R],[],[Q],[],[],[]). 236 [hyper,196,5,demod,33,33,34] K2(F,E,[],[P,R],[Q],[],[],[]). 268 [hyper,236,19,demod,30,32,32,31,30,31] H(E,[Q],[],[],[],[R,P],[]). 269 [hyper,268,13,demod,30,32,32,31,30,31] K1(E,D,[P,R],[],[Q],[],[],[]). 308 [hyper,269,6,eval,demod,33,34] K2(E,D,[P],[R],[Q],[],[],[]). 346 [hyper,308,17,demod,30,32,31,30,32,31] H(D,[Q],[],[],[R],[P],[]). 348 [hyper,346,2] K1(D,B,[R],[],[Q],[],[P],[]). 404 [hyper,348,5,demod,33,34] K2(D,B,[],[R],[Q],[],[P],[]). 461 [hyper,404,9] H(B,[Q],[R],[],[],[P],[]). 462 [hyper,461,23,demod,33,34] H(B,[],[R,Q],[],[],[P],[]). 464 [hyper,462,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[],[],[P],[]). 539 [hyper,464,5,demod,33,33,34] K2(B,D,[],[Q,R],[],[],[P],[]). 575 [hyper,539,16,demod,30,31,30,32,32,31] H(D,[],[],[],[R,Q],[P],[]). 576 [hyper,575,3] K1(D,E,[R,Q],[P],[],[],[],[]). 620 [hyper,576,5,demod,33,33,34] K2(D,E,[],[R,Q,P],[],[],[],[]). 644 [hyper,620,10] H(E,[],[],[],[],[R,Q,P],[]). 645 [hyper,644,13,demod,30,32,32,32,31,30,31] K1(E,D,[P,Q,R],[],[],[],[],[]). 686 [hyper,645,5,demod,33,33,33,34] K2(E,D,[],[P,Q,R],[],[],[],[]). 724 [hyper,686,17,demod,30,32,32,32,31,30,31] H(D,[],[],[],[R,Q,P],[],[]). 726 [hyper,724,2] K1(D,B,[R,Q,P],[],[],[],[],[]). 783 [hyper,726,5,demod,33,33,33,34] K2(D,B,[],[R,Q,P],[],[],[],[]). 830 [hyper,783,9] H(B,[],[R,Q,P],[],[],[],[]). 831 [hyper,830,21] H(B,[P],[R,Q],[],[],[],[]). 833 [hyper,831,12,demod,30,32,32,31,30,31] K1(B,D,[Q,R],[],[P],[],[],[]). 894 [hyper,833,6,eval,demod,33,34] K2(B,D,[Q],[R],[P],[],[],[]). 923 [hyper,894,16,demod,30,32,31,30,32,31] H(D,[P],[Q],[],[R],[],[]). 924 [hyper,923,3] K1(D,E,[R],[],[P],[Q],[],[]). 950 [hyper,924,5,demod,33,34] K2(D,E,[],[R],[P],[Q],[],[]). 972 [hyper,950,10] H(E,[P],[Q],[],[],[R],[]). 974 [hyper,972,4] K1(E,F,[R],[],[P],[Q],[],[]). 1008 [hyper,974,5,demod,33,34] K2(E,F,[],[R],[P],[Q],[],[]). 1031 [hyper,1008,11] H(F,[P],[Q],[],[],[],[R]). 1033 [hyper,1031,14,demod,30,32,31,30,31] K1(F,C,[R],[],[P],[Q],[],[]). 1073 [hyper,1033,5,demod,33,34] K2(F,C,[],[R],[P],[Q],[],[]). 1102 [hyper,1073,18,demod,30,32,31,30,31] H(C,[P],[Q],[R],[],[],[]). 1103 [hyper,1102,25] H(C,[],[Q],[P,R],[],[],[]). 1105 [hyper,1103,1] K1(C,F,[P,R],[],[],[Q],[],[]). 1141 [hyper,1105,6,eval,demod,33,34] K2(C,F,[P],[R],[],[Q],[],[]). 1155 [hyper,1141,8] H(F,[],[Q],[P],[],[],[R]). 1156 [hyper,1155,15,demod,30,32,31,30,31] K1(F,E,[R],[],[],[Q],[P],[]). 1161 [hyper,1156,5,demod,33,34] K2(F,E,[],[R],[],[Q],[P],[]). 1163 [hyper,1161,19,demod,30,32,31,30,31] H(E,[],[Q],[P],[],[R],[]). 1164 [binary,1163.1,27.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 1128 clauses generated 1465 clauses kept 1129 clauses forward subsumed 336 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.11 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) That finishes the proof of the theorem. Process 8474 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/i3.in0100644000076400007640000001157505501171471016137 0ustar mccunemccune% From John Kalman % % (3) The input file %i3 below, due to Mark Waddell and me, for % solving the cryptarithmetic puzzle ab x cd = efgh, where a, b, c, d, % e, f, g, and h are distinct digits. % We wish to find all 8-tuples (a,b,c,d,e,f,g,h) of distinct digits % such that the product % % a b % % c d % _______ % % e f g h % _______ % % is valid. For example, since 72 x 95 = 6840, (7,2,9,5,6,8,4,0) % is one such 8-tuple. % It is understood that a, c, and e are non-zero. % Since multiplication is commutative, we may as well assume that a < c; % for example, we do not need to find the 8-tuple (9,5,7,2,6,8,4,0) % as well as the 8-tuple (7,2,9,5,6,8,4,0). % % The computation of the above product may be represented as follows: % % a b % % c d % ___________ % % y3 y2 y1 % % z3 z2 z1 % ___________ % % e f g h % ___________ % % We use the predicate CS(u,x,y,z,v) to express that % % x % % y % _ % % z % _ % % is a possible column in the addition of an integer in which x % occurs as a digit to an integer in which y occurs as a digit; % u is the carryover from the previous column and v is the carryover % to the next column. % For example, CS(0,6,8,4,1) and CS(1,3,4,8,0) are true, and occur % in the computation of the product 72 x 95. % Note that, in such an addition, u is 0 or 1, and v is 0 or 1. % % We use the predicate CP(u,x,y,z,v) to express that % % ... y ... % % x % ___________ % % ... z ... % ___________ % % is a possible step in the multiplication of an integer in which % y occurs as a digit by the one-digit integer x; u is the carryover % from the previous step and v is the carryover to the next step. % For example, CP(1,5,7,6,3) is true, and represents a step in % the multiplication 72 x 95. % Note that, in such a multiplication, u and v are at most 8 (since % 9 x 9 = 81), or, if x and y are required to be distinct, at most 7 % (since 9 x 8 = 72). [In fact, there is not much gain to be made from % using the fact that carryovers of 9 and 8 are impossible. Experimental % runs took 39.34 secs with L(0) to L(7), and 42.48 secs using arbitrary % digits.] set(hyper_res). set(print_lists_at_end). assign(stats_level,1). % Output a few important statistics list(usable). K(0). % Sum carryover (at most 1) K(1). L(0). % Product carryover (at most 7 for distinct digits) L(1). L(2). L(3). L(4). L(5). L(6). L(7). D(0). % Digits D(1). D(2). D(3). D(4). D(5). D(6). D(7). D(8). D(9). end_of_list. list(sos). -K(u) | -D(x) | -D(y) | CS(u,x,y,$MOD($SUM($SUM(u,x),y),10),$DIV($SUM($SUM(u,x),y),10)). -L(u) | -D(x) | -D(y) | CP(u,x,y,$MOD($SUM(u,$PROD(x,y)),10),$DIV($SUM(u,$PROD(x,y)),10)). -CP(0,xd,xb,y1,x1) | -CP(x1,xd,xa,y2,y3) | -CP(0,xc,xb,z1,x2) | -CP(x2,xc,xa,z2,z3) | -$LT(xa,xc) | -CS(0,y1,0,xh,x3) | -CS(x3,y2,z1,xg,x4) | -CS(x4,y3,z2,xf,x5) | -CS(x5,0,z3,xe,0) | S(xa,xb,xc,xd,xe,xf,xg,xh). end_of_list. list(passive). % The following three clauses subsume "solutions" with a = 0, c = 0, or e = 0 S(0,xb,xc,xd,xe,xf,xg,xh). S(xa,xb,0,xd,xe,xf,xg,xh). S(xa,xb,xc,xd,0,xf,xg,xh). % The following 28 clauses subsume "solutions" in which distinct % letters are represented by the same digit S(x1,x1,x3,x4,x5,x6,x7,x8). S(x1,x2,x1,x4,x5,x6,x7,x8). S(x1,x2,x3,x1,x5,x6,x7,x8). S(x1,x2,x3,x4,x1,x6,x7,x8). S(x1,x2,x3,x4,x5,x1,x7,x8). S(x1,x2,x3,x4,x5,x6,x1,x8). S(x1,x2,x3,x4,x5,x6,x7,x1). S(x1,x2,x2,x4,x5,x6,x7,x8). S(x1,x2,x3,x2,x5,x6,x7,x8). S(x1,x2,x3,x4,x2,x6,x7,x8). S(x1,x2,x3,x4,x5,x2,x7,x8). S(x1,x2,x3,x4,x5,x6,x2,x8). S(x1,x2,x3,x4,x5,x6,x7,x2). S(x1,x2,x3,x3,x5,x6,x7,x8). S(x1,x2,x3,x4,x3,x6,x7,x8). S(x1,x2,x3,x4,x5,x3,x7,x8). S(x1,x2,x3,x4,x5,x6,x3,x8). S(x1,x2,x3,x4,x5,x6,x7,x3). S(x1,x2,x3,x4,x4,x6,x7,x8). S(x1,x2,x3,x4,x5,x4,x7,x8). S(x1,x2,x3,x4,x5,x6,x4,x8). S(x1,x2,x3,x4,x5,x6,x7,x4). S(x1,x2,x3,x4,x5,x5,x7,x8). S(x1,x2,x3,x4,x5,x6,x5,x8). S(x1,x2,x3,x4,x5,x6,x7,x5). S(x1,x2,x3,x4,x5,x6,x6,x8). S(x1,x2,x3,x4,x5,x6,x7,x6). S(x1,x2,x3,x4,x5,x6,x7,x7). end_of_list. otter-3.3f/examples/kalman/index.html0100644000076400007640000000201407714267401017264 0ustar mccunemccune /home/mccune/otter-3.3/examples/kalman

/home/mccune/otter-3.3/examples/kalman

Contributed by John Kalman.

otter < ex_1.in > ex_1.out

otter < ex_2.in > ex_2.out

otter < ex_3.in > ex_3.out

otter < ex_4.in > ex_4.out

otter < i1.in > i1.out

otter < i2.in > i2.out

otter < i3.in > i3.out

otter < i4.in > i4.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/kalman/i1.out0100664000076400007640000000536110103522156016326 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8459. set(hyper_res). clear(for_sub). set(print_lists_at_end). assign(max_given,15). assign(stats_level,1). list(usable). 1 [] -P(x)|P(x). end_of_list. list(sos). 2 [] P(a). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 2 [] P(a). ** KEPT (pick-wt=2): 3 [hyper,2,1] P(a). 3 back subsumes 2. given clause #2: (wt=2) 3 [hyper,2,1] P(a). ** KEPT (pick-wt=2): 4 [hyper,3,1] P(a). 4 back subsumes 3. given clause #3: (wt=2) 4 [hyper,3,1] P(a). ** KEPT (pick-wt=2): 5 [hyper,4,1] P(a). 5 back subsumes 4. given clause #4: (wt=2) 5 [hyper,4,1] P(a). ** KEPT (pick-wt=2): 6 [hyper,5,1] P(a). 6 back subsumes 5. given clause #5: (wt=2) 6 [hyper,5,1] P(a). ** KEPT (pick-wt=2): 7 [hyper,6,1] P(a). 7 back subsumes 6. given clause #6: (wt=2) 7 [hyper,6,1] P(a). ** KEPT (pick-wt=2): 8 [hyper,7,1] P(a). 8 back subsumes 7. given clause #7: (wt=2) 8 [hyper,7,1] P(a). ** KEPT (pick-wt=2): 9 [hyper,8,1] P(a). 9 back subsumes 8. given clause #8: (wt=2) 9 [hyper,8,1] P(a). ** KEPT (pick-wt=2): 10 [hyper,9,1] P(a). 10 back subsumes 9. given clause #9: (wt=2) 10 [hyper,9,1] P(a). ** KEPT (pick-wt=2): 11 [hyper,10,1] P(a). 11 back subsumes 10. given clause #10: (wt=2) 11 [hyper,10,1] P(a). ** KEPT (pick-wt=2): 12 [hyper,11,1] P(a). 12 back subsumes 11. given clause #11: (wt=2) 12 [hyper,11,1] P(a). ** KEPT (pick-wt=2): 13 [hyper,12,1] P(a). 13 back subsumes 12. given clause #12: (wt=2) 13 [hyper,12,1] P(a). ** KEPT (pick-wt=2): 14 [hyper,13,1] P(a). 14 back subsumes 13. given clause #13: (wt=2) 14 [hyper,13,1] P(a). ** KEPT (pick-wt=2): 15 [hyper,14,1] P(a). 15 back subsumes 14. given clause #14: (wt=2) 15 [hyper,14,1] P(a). ** KEPT (pick-wt=2): 16 [hyper,15,1] P(a). 16 back subsumes 15. given clause #15: (wt=2) 16 [hyper,15,1] P(a). Search stopped by max_given option. ** KEPT (pick-wt=2): 17 [hyper,16,1] P(a). 17 back subsumes 16. Search stopped by max_given option. ============ end of search ============ list(usable). 1 [] -P(x)|P(x). end_of_list. list(sos). 17 [hyper,16,1] P(a). end_of_list. list(demodulators). end_of_list. -------------- statistics ------------- clauses given 15 clauses generated 15 clauses kept 15 clauses forward subsumed 0 clauses back subsumed 15 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8459 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/kalman/README0100644000076400007640000000003407313711003016132 0ustar mccunemccuneContributed by John Kalman. otter-3.3f/examples/kalman/i2.in0100644000076400007640000000100005501171471016114 0ustar mccunemccune% From John Kalman % % (2) The input file %i2 below. This is Example 5.15 on page 97 % of my latest notes, and was suggested by Robert O'Callahan. It shows % how the inequality predicate on a finite set can be computed with % the help of the passive list. set(hyper_res). set(print_lists_at_end). assign(stats_level,1). % changed from 0 to 1 by McCune list(usable). P(A). P(B). P(C). P(D). end_of_list. list(sos). -P(x) | -P(y) | NE(x,y). end_of_list. list(passive). NE(x,x). end_of_list. otter-3.3f/examples/kalman/i2.out0100664000076400007640000000535510103522156016332 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:30:38 2004 The command was "../../bin/otter". The process ID is 8464. set(hyper_res). set(print_lists_at_end). assign(stats_level,1). list(usable). 1 [] P(A). 2 [] P(B). 3 [] P(C). 4 [] P(D). end_of_list. list(sos). 5 [] -P(x)| -P(y)|NE(x,y). end_of_list. list(passive). 6 [] NE(x,x). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=7) 5 [] -P(x)| -P(y)|NE(x,y). ** KEPT (pick-wt=3): 7 [hyper,5,4,3] NE(D,C). ** KEPT (pick-wt=3): 8 [hyper,5,4,2] NE(D,B). ** KEPT (pick-wt=3): 9 [hyper,5,4,1] NE(D,A). ** KEPT (pick-wt=3): 10 [hyper,5,3,4] NE(C,D). ** KEPT (pick-wt=3): 11 [hyper,5,3,2] NE(C,B). ** KEPT (pick-wt=3): 12 [hyper,5,3,1] NE(C,A). ** KEPT (pick-wt=3): 13 [hyper,5,2,4] NE(B,D). ** KEPT (pick-wt=3): 14 [hyper,5,2,3] NE(B,C). ** KEPT (pick-wt=3): 15 [hyper,5,2,1] NE(B,A). ** KEPT (pick-wt=3): 16 [hyper,5,1,4] NE(A,D). ** KEPT (pick-wt=3): 17 [hyper,5,1,3] NE(A,C). ** KEPT (pick-wt=3): 18 [hyper,5,1,2] NE(A,B). given clause #2: (wt=3) 7 [hyper,5,4,3] NE(D,C). given clause #3: (wt=3) 8 [hyper,5,4,2] NE(D,B). given clause #4: (wt=3) 9 [hyper,5,4,1] NE(D,A). given clause #5: (wt=3) 10 [hyper,5,3,4] NE(C,D). given clause #6: (wt=3) 11 [hyper,5,3,2] NE(C,B). given clause #7: (wt=3) 12 [hyper,5,3,1] NE(C,A). given clause #8: (wt=3) 13 [hyper,5,2,4] NE(B,D). given clause #9: (wt=3) 14 [hyper,5,2,3] NE(B,C). given clause #10: (wt=3) 15 [hyper,5,2,1] NE(B,A). given clause #11: (wt=3) 16 [hyper,5,1,4] NE(A,D). given clause #12: (wt=3) 17 [hyper,5,1,3] NE(A,C). given clause #13: (wt=3) 18 [hyper,5,1,2] NE(A,B). Search stopped because sos empty. Search stopped because sos empty. ============ end of search ============ list(usable). 1 [] P(A). 2 [] P(B). 3 [] P(C). 4 [] P(D). 5 [] -P(x)| -P(y)|NE(x,y). 7 [hyper,5,4,3] NE(D,C). 8 [hyper,5,4,2] NE(D,B). 9 [hyper,5,4,1] NE(D,A). 10 [hyper,5,3,4] NE(C,D). 11 [hyper,5,3,2] NE(C,B). 12 [hyper,5,3,1] NE(C,A). 13 [hyper,5,2,4] NE(B,D). 14 [hyper,5,2,3] NE(B,C). 15 [hyper,5,2,1] NE(B,A). 16 [hyper,5,1,4] NE(A,D). 17 [hyper,5,1,3] NE(A,C). 18 [hyper,5,1,2] NE(A,B). end_of_list. list(sos). end_of_list. list(demodulators). end_of_list. -------------- statistics ------------- clauses given 13 clauses generated 16 clauses kept 12 clauses forward subsumed 4 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8464 finished Mon Aug 2 15:30:38 2004 otter-3.3f/examples/split/0040755000076400007640000000000010103530360015144 5ustar mccunemccuneotter-3.3f/examples/split/GEO010-2.in0100644000076400007640000001033410041251466016474 0ustar mccunemccune%-------------------------------------------------------------------------- % File : GEO010-2 : TPTP v2.0.0. Released v1.0.0. % Domain : Geometry % Problem : Collinearity is invariant % Version : [Quaife, 1989] axioms. % English : For all points x, y, and z, if x, y, and z are collinear % in one order, they are collinear in any order. % Refs : McCharen J.D., Overbeek R.A., Wos L.A. (1976), Problems and % Experiments for and with Automated Theorem Proving Programs, % IEEE Transactions on Computers C-25(8), 773-782. % : Schwabbauser W., Szmielew W., and Tarski A. (1983), % Metamathematische Methoden in der Geometrie, Springer-Verlag, % Berlin, Germany. % : Quaife A. (1989), Automated Development of Tarski's Geometry, % Journal of Automated Reasoning 5(1), 97-118. % Source : [TPTP] % Names : % Status : unsatisfiable % Rating : 0.89 v2.0.0 % Syntax : Number of clauses : 25 ( 6 non-Horn; 8 unit; 21 RR) % Number of literals : 73 ( 8 equality) % Maximal clause size : 8 ( 2 average) % Number of predicates : 4 ( 0 propositional; 2-4 arity) % Number of functors : 11 ( 6 constant; 0-6 arity) % Number of variables : 84 ( 3 singleton) % Maximal term depth : 2 ( 1 average) % Comments : % : tptp2X: -fotter:hypothesis:[set(auto),set(tptp_eq)] -trm_equality:stfp GEO010-2.p %-------------------------------------------------------------------------- set(prolog_style_variables). set(auto2). set(tptp_eq). set(split_when_given). set(split_pos). assign(split_depth, 10). list(usable). % reflexivity, axiom. equal(A,A). % reflexivity_for_equidistance, axiom. equidistant(A,B,B,A). % transitivity_for_equidistance, axiom. -equidistant(A,B,C,D) | -equidistant(A,B,E,F) | equidistant(C,D,E,F). % identity_for_equidistance, axiom. -equidistant(A,B,C,C) | equal(A,B). % segment_construction1, axiom. between(A,B,extension(A,B,C,D)). % segment_construction2, axiom. equidistant(A,extension(B,A,C,D),C,D). % outer_five_segment, axiom. -equidistant(A,B,C,D) | -equidistant(B,E,D,F) | -equidistant(A,G,C,H) | -equidistant(B,G,D,H) | -between(A,B,E) | -between(C,D,F) | equal(A,B) | equidistant(E,G,F,H). % identity_for_betweeness, axiom. -between(A,B,A) | equal(A,B). % inner_pasch1, axiom. -between(A,B,C) | -between(D,E,C) | between(B,inner_pasch(A,B,C,E,D),D). % inner_pasch2, axiom. -between(A,B,C) | -between(D,E,C) | between(E,inner_pasch(A,B,C,E,D),A). % lower_dimension1, axiom. -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). % lower_dimension2, axiom. -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). % lower_dimension3, axiom. -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). % upper_dimension, axiom. -equidistant(A,B,A,C) | -equidistant(D,B,D,C) | -equidistant(E,B,E,C) | between(A,D,E) | between(D,E,A) | between(E,A,D) | equal(B,C). % euclid1, axiom. -between(A,B,C) | -between(D,B,E) | equal(A,B) | between(A,D,euclid1(A,D,B,E,C)). % euclid2, axiom. -between(A,B,C) | -between(D,B,E) | equal(A,B) | between(A,E,euclid2(A,D,B,E,C)). % euclid3, axiom. -between(A,B,C) | -between(D,B,E) | equal(A,B) | between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)). % continuity1, axiom. -equidistant(A,B,A,C) | -equidistant(A,D,A,E) | -between(A,B,D) | -between(B,F,D) | between(C,continuous(A,B,C,F,D,E),E). % continuity2, axiom. -equidistant(A,B,A,C) | -equidistant(A,D,A,E) | -between(A,B,D) | -between(B,F,D) | equidistant(A,F,A,continuous(A,B,C,F,D,E)). % colinearity1, axiom. -between(A,B,C) | colinear(A,B,C). % colinearity2, axiom. -between(A,B,C) | colinear(C,A,B). % colinearity3, axiom. -between(A,B,C) | colinear(B,C,A). % colinearity4, axiom. -colinear(A,B,C) | between(A,B,C) | between(B,C,A) | between(C,A,B). end_of_list. list(sos). % abc_colinear, hypothesis. colinear(a,b,c). % prove_colinear_in_all_orders, conjecture. -colinear(a,c,b) | -colinear(b,a,c) | -colinear(b,c,a) | -colinear(c,a,b) | -colinear(c,b,a). end_of_list. %-------------------------------------------------------------------------- otter-3.3f/examples/split/wang3.out0100664000076400007640000022355310103522217016727 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:10 2004 The command was "../../bin/otter". The process ID is 8782. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(split_when_given). dependent: set(back_unit_deletion). set(split_pos). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level,1). list(sos). 0 [] m!=b. 0 [] y=j| -p(y,j)|y=k. 0 [] k=j|p(k,j). end_of_list. list(usable). 0 [] y=m|p(y,m)|v1=m|v1=y| -p(y,v1)| -p(v1,y). 0 [] y=b| -p(y,b)|v=b|v=y| -p(y,v)| -p(v,y). 0 [] y=k|y=m|y=b| -p(y,k). 0 [] y=m| -p(y,m)|f(y)!=m. 0 [] y=m| -p(y,m)|f(y)!=y. 0 [] y=m| -p(y,m)|p(y,f(y)). 0 [] y=m| -p(y,m)|p(f(y),y). 0 [] y=b|p(y,b)|g(y)!=b. 0 [] y=b|p(y,b)|g(y)!=y. 0 [] y=b|p(y,b)|p(y,g(y)). 0 [] y=b|p(y,b)|p(g(y),y). 0 [] m=k|p(m,k). 0 [] b=k|p(b,k). 0 [] x=x. end_of_list. ------------> process usable: ** KEPT (pick-wt=18): 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). ** KEPT (pick-wt=18): 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). ** KEPT (pick-wt=12): 3 [] x=k|x=m|x=b| -p(x,k). ** KEPT (pick-wt=10): 4 [] x=m| -p(x,m)|f(x)!=m. ** KEPT (pick-wt=10): 5 [] x=m| -p(x,m)|f(x)!=x. ** KEPT (pick-wt=10): 6 [] x=m| -p(x,m)|p(x,f(x)). ** KEPT (pick-wt=10): 7 [] x=m| -p(x,m)|p(f(x),x). ** KEPT (pick-wt=10): 8 [] x=b|p(x,b)|g(x)!=b. ** KEPT (pick-wt=10): 9 [] x=b|p(x,b)|g(x)!=x. ** KEPT (pick-wt=10): 10 [] x=b|p(x,b)|p(x,g(x)). ** KEPT (pick-wt=10): 11 [] x=b|p(x,b)|p(g(x),x). ** KEPT (pick-wt=6): 12 [] m=k|p(m,k). ** KEPT (pick-wt=6): 14 [copy,13,flip.1] k=b|p(b,k). ** KEPT (pick-wt=3): 15 [] x=x. Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] x=x. >>>> Starting back unit deletion with 15. ------------> process sos: ** KEPT (pick-wt=3): 16 [] m!=b. ** KEPT (pick-wt=9): 17 [] x=j| -p(x,j)|x=k. ** KEPT (pick-wt=6): 18 [] k=j|p(k,j). >>>> Starting back unit deletion with 16. ======= end of input processing ======= =========== start of search =========== Splitting on clause 18 [] k=j|p(k,j). Case [1] (process 8783): Assumption: 26 [18,split.1] k=j. Splitting on clause 30 [back_demod,14,demod,27,27] j=b|p(b,j). --- refuted case [1.1] Case [1.1] (process 8784): Assumption: 93 [30,split.1.1] j=b. -----> EMPTY CLAUSE at 0.00 sec ----> 117 [back_demod,56,demod,94,94,unit_del,16,15] $F. Length of proof is 8. Level of proof is 3. Case [1.1] ---------------- PROOF ---------------- 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 15 [] x=x. 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 27,26 [18,split.1] k=j. 28 [back_demod,25,demod,27,27] j!=b|p(m,j). 29 [back_demod,17,demod,27,factor_simp] x=j| -p(x,j). 30 [back_demod,14,demod,27,27] j=b|p(b,j). 56 [binary,29.2,28.2] m=j|j!=b. 94,93 [30,split.1.1] j=b. 117 [back_demod,56,demod,94,94,unit_del,16,15] $F. ------------ end of proof ------------- ------- statistics (process 8784) ------- clauses given 6 clauses generated 206 clauses kept 113 clauses forward subsumed 136 clauses back subsumed 2 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8784 finished Mon Aug 2 15:31:10 2004 Refuted case [1.1]. --- refuted case [1.2] Case [1.2] (process 8785): Assumption: 94 [30,split.1.2] p(b,j). ----> UNIT CONFLICT at 0.00 sec ----> 112 [binary,110.1,93.1] $F. Length of proof is 7. Level of proof is 4. Case [1.2] ---------------- PROOF ---------------- 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 27,26 [18,split.1] k=j. 29 [back_demod,17,demod,27,factor_simp] x=j| -p(x,j). 30 [back_demod,14,demod,27,27] j=b|p(b,j). 93 [30,split_neg.1.2] j!=b. 94 [30,split.1.2] p(b,j). 110 [binary,94.1,29.2,flip.1] j=b. 112 [binary,110.1,93.1] $F. ------------ end of proof ------------- ------- statistics (process 8785) ------- clauses given 8 clauses generated 252 clauses kept 108 clauses forward subsumed 152 clauses back subsumed 36 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8785 finished Mon Aug 2 15:31:10 2004 Refuted case [1.2]. ------- statistics (process 8783) ------- clauses given 6 clauses generated 206 clauses kept 90 clauses forward subsumed 123 clauses back subsumed 2 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8783 finished Mon Aug 2 15:31:10 2004 Refuted case [1]. Case [2] (process 8786): Assumption: 27 [18,split.2] p(k,j). Splitting on clause 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). Case [2.1] (process 8787): Assumption: 129 [47,split.2.1] p(b,j). Splitting on clause 80 [binary,25.1,14.1] p(m,k)|p(b,k). Case [2.1.1] (process 8788): Assumption: 157 [80,split.2.1.1] p(m,k). Splitting on clause 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). Case [2.1.1.1] (process 8789): Assumption: 176 [161,split.2.1.1.1] p(m,b). Splitting on clause 188 [binary,17.2,129.1,flip.1,flip.2] j=b|k=b. Case [2.1.1.1.1] (process 8790): Assumption: 266 [188,split.2.1.1.1.1] j=b. 0 [back_unit_del,273.1,14.1] p(b,k). Splitting on clause 304 [back_demod,190,demod,267,267,267,289,267,267,289,unit_del,273,290] f(b)=b|f(b)=k. --- refuted case [2.1.1.1.1.1] Case [2.1.1.1.1.1] (process 8791): Assumption: 319 [304,split.2.1.1.1.1.1] f(b)=b. -----> EMPTY CLAUSE at 0.00 sec ----> 321 [back_demod,305,demod,320,320,unit_del,291,273] $F. Length of proof is 24. Level of proof is 9. Case [2.1.1.1.1.1] ---------------- PROOF ---------------- 5 [] x=m| -p(x,m)|f(x)!=x. 7 [] x=m| -p(x,m)|p(f(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 15 [] x=x. 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 129 [47,split.2.1] p(b,j). 157 [80,split.2.1.1] p(m,k). 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). 176 [161,split.2.1.1.1] p(m,b). 187 [binary,17.1,5.3,flip.3] -p(f(j),j)|f(j)=k|m=j| -p(j,m). 188 [binary,17.2,129.1,flip.1,flip.2] j=b|k=b. 190 [binary,17.2,7.3,flip.3] f(j)=j|f(j)=k|m=j| -p(j,m). 221 [para_from,17.1.1,129.1.1,unit_del,129,flip.2] p(j,j)|k=b. 223 [para_from,17.1.1,14.2.1,unit_del,129,factor_simp] k=b|p(j,k). 231 [para_from,17.1.1,16.1.1] j!=b| -p(m,j)|m=k. 252 [para_from,17.3.1,16.1.1] k!=b|m=j| -p(m,j). 267,266 [188,split.2.1.1.1.1] j=b. 273 [back_demod,252,demod,267,267,unit_del,16,176] k!=b. 289,288 [back_demod,231,demod,267,267,unit_del,15,176] m=k. 290 [back_demod,223,demod,267,unit_del,273] p(b,k). 291 [back_demod,221,demod,267,267,unit_del,273] p(b,b). 304 [back_demod,190,demod,267,267,267,289,267,267,289,unit_del,273,290] f(b)=b|f(b)=k. 305 [back_demod,187,demod,267,267,267,289,267,267,289,unit_del,273,290] -p(f(b),b)|f(b)=k. 320,319 [304,split.2.1.1.1.1.1] f(b)=b. 321 [back_demod,305,demod,320,320,unit_del,291,273] $F. ------------ end of proof ------------- ------- statistics (process 8791) ------- clauses given 22 clauses generated 754 clauses kept 316 clauses forward subsumed 615 clauses back subsumed 67 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8791 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1.1.1]. --- refuted case [2.1.1.1.1.2] Case [2.1.1.1.1.2] (process 8792): Assumption: 320 [304,split.2.1.1.1.1.2] f(b)=k. -----> EMPTY CLAUSE at 0.01 sec ----> 376 [binary,316.2,290.1,demod,321,unit_del,273,15] $F. Length of proof is 23. Level of proof is 9. Case [2.1.1.1.1.2] ---------------- PROOF ---------------- 4 [] x=m| -p(x,m)|f(x)!=m. 7 [] x=m| -p(x,m)|p(f(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 15 [] x=x. 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 129 [47,split.2.1] p(b,j). 157 [80,split.2.1.1] p(m,k). 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). 176 [161,split.2.1.1.1] p(m,b). 188 [binary,17.2,129.1,flip.1,flip.2] j=b|k=b. 190 [binary,17.2,7.3,flip.3] f(j)=j|f(j)=k|m=j| -p(j,m). 223 [para_from,17.1.1,14.2.1,unit_del,129,factor_simp] k=b|p(j,k). 231 [para_from,17.1.1,16.1.1] j!=b| -p(m,j)|m=k. 252 [para_from,17.3.1,16.1.1] k!=b|m=j| -p(m,j). 256 [para_from,17.3.1,4.2.2] x=m| -p(x,k)|f(x)!=m|m=j| -p(m,j). 267,266 [188,split.2.1.1.1.1] j=b. 269 [back_demod,256,demod,267,267,unit_del,16,176] x=m| -p(x,k)|f(x)!=m. 273 [back_demod,252,demod,267,267,unit_del,16,176] k!=b. 289,288 [back_demod,231,demod,267,267,unit_del,15,176] m=k. 290 [back_demod,223,demod,267,unit_del,273] p(b,k). 304 [back_demod,190,demod,267,267,267,289,267,267,289,unit_del,273,290] f(b)=b|f(b)=k. 316 [back_demod,269,demod,289,289] x=k| -p(x,k)|f(x)!=k. 321,320 [304,split.2.1.1.1.1.2] f(b)=k. 376 [binary,316.2,290.1,demod,321,unit_del,273,15] $F. ------------ end of proof ------------- ------- statistics (process 8792) ------- clauses given 29 clauses generated 1142 clauses kept 371 clauses forward subsumed 944 clauses back subsumed 67 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8792 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1.1.2]. ------- statistics (process 8790) ------- clauses given 22 clauses generated 754 clauses kept 315 clauses forward subsumed 615 clauses back subsumed 67 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8790 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1.1]. Case [2.1.1.1.2] (process 8793): Assumption: 267 [188,split.2.1.1.1.2] k=b. Splitting on clause 273 [back_unit_del,266.1,261.1,demod,268] p(j,b)|p(j,g(j)). --- refuted case [2.1.1.1.2.1] Case [2.1.1.1.2.1] (process 8794): Assumption: 427 [273,split.2.1.1.1.2.1] p(j,b). 0 [back_unit_del,427.1,308.2] m=j. 0 [back_unit_del,427.1,280.2] p(b,m). -----> EMPTY CLAUSE at 0.01 sec ----> 462 [binary,448.1,436.1,unit_del,441,438] $F. Length of proof is 33. Level of proof is 9. Case [2.1.1.1.2.1] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 7 [] x=m| -p(x,m)|p(f(x),x). 10 [] x=b|p(x,b)|p(x,g(x)). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 26 [18,split_neg.2] k!=j. 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 129 [47,split.2.1] p(b,j). 154 [para_into,129.1.2,1.3.1] p(b,m)|x=m|p(x,m)|j=x| -p(x,j)| -p(j,x). 156 [factor,154.1.3,unit_del,16,129] p(b,m)|j=b| -p(j,b). 157 [80,split.2.1.1] p(m,k). 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). 176 [161,split.2.1.1.1] p(m,b). 188 [binary,17.2,129.1,flip.1,flip.2] j=b|k=b. 201 [para_into,17.2.2,3.3.1,unit_del,26,flip.4] x=j| -p(x,b)|x=k|m=j| -p(j,k). 210 [factor,201.1.4,unit_del,176] m=j|m=k| -p(j,k). 246 [para_from,17.3.1,10.2.2,unit_del,129,flip.4] x=b|p(x,k)|p(x,g(x))|j=b. 261 [factor,246.1.4] j=b|p(j,k)|p(j,g(j)). 266 [188,split_neg.2.1.1.1.2] j!=b. 268,267 [188,split.2.1.1.1.2] k=b. 273 [back_unit_del,266.1,261.1,demod,268] p(j,b)|p(j,g(j)). 280 [back_unit_del,266.1,156.2] p(b,m)| -p(j,b). 308 [back_demod,210,demod,268,268,unit_del,16] m=j| -p(j,b). 328 [back_demod,3,demod,268,268,factor_simp] x=b|x=m| -p(x,b). 335 [binary,280.1,7.2,unit_del,16] -p(j,b)|p(f(b),b). 337 [binary,280.1,5.2,unit_del,16] -p(j,b)|f(b)!=b. 338 [binary,280.1,4.2,unit_del,16] -p(j,b)|f(b)!=m. 427 [273,split.2.1.1.1.2.1] p(j,b). 435 [back_unit_del,427.1,338.1] f(b)!=m. 436 [back_unit_del,427.1,337.1] f(b)!=b. 438 [back_unit_del,427.1,335.1] p(f(b),b). 440,439 [back_unit_del,427.1,308.2] m=j. 441 [back_demod,435,demod,440] f(b)!=j. 448 [back_demod,328,demod,440] x=b|x=j| -p(x,b). 462 [binary,448.1,436.1,unit_del,441,438] $F. ------------ end of proof ------------- ------- statistics (process 8794) ------- clauses given 32 clauses generated 1471 clauses kept 458 clauses forward subsumed 1156 clauses back subsumed 205 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8794 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1.2.1]. --- refuted case [2.1.1.1.2.2] Case [2.1.1.1.2.2] (process 8795): Assumption: 428 [273,split.2.1.1.1.2.2] p(j,g(j)). 0 [back_unit_del,427.1,299.1] -p(m,j). 0 [back_unit_del,427.1,272.1] g(j)!=j. 0 [back_unit_del,427.1,271.1] g(j)!=b. ----> UNIT CONFLICT at 0.00 sec ----> 479 [binary,477.1,475.1] $F. Length of proof is 23. Level of proof is 9. Case [2.1.1.1.2.2] ---------------- PROOF ---------------- 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 129 [47,split.2.1] p(b,j). 186 [binary,17.1,9.3] -p(g(j),j)|g(j)=k|j=b|p(j,b). 188 [binary,17.2,129.1,flip.1,flip.2] j=b|k=b. 245 [para_from,17.3.1,11.2.2,unit_del,129,flip.4] x=b|p(x,k)|p(g(x),x)|j=b. 246 [para_from,17.3.1,10.2.2,unit_del,129,flip.4] x=b|p(x,k)|p(x,g(x))|j=b. 248 [para_from,17.3.1,8.2.2,unit_del,129,flip.4] x=b|p(x,k)|g(x)!=b|j=b. 260 [factor,245.1.4] j=b|p(j,k)|p(g(j),j). 261 [factor,246.1.4] j=b|p(j,k)|p(j,g(j)). 263 [factor,248.1.4] j=b|p(j,k)|g(j)!=b. 266 [188,split_neg.2.1.1.1.2] j!=b. 268,267 [188,split.2.1.1.1.2] k=b. 271 [back_unit_del,266.1,263.1,demod,268] p(j,b)|g(j)!=b. 273 [back_unit_del,266.1,261.1,demod,268] p(j,b)|p(j,g(j)). 274 [back_unit_del,266.1,260.1,demod,268] p(j,b)|p(g(j),j). 279 [back_unit_del,266.1,186.3,demod,268] -p(g(j),j)|g(j)=b|p(j,b). 427 [273,split_neg.2.1.1.1.2.2] -p(j,b). 471 [back_unit_del,427.1,279.3] -p(g(j),j)|g(j)=b. 473 [back_unit_del,427.1,274.1] p(g(j),j). 475 [back_unit_del,427.1,271.1] g(j)!=b. 477 [back_unit_del,473.1,471.1] g(j)=b. 479 [binary,477.1,475.1] $F. ------------ end of proof ------------- ------- statistics (process 8795) ------- clauses given 24 clauses generated 1313 clauses kept 475 clauses forward subsumed 928 clauses back subsumed 201 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8795 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1.2.2]. ------- statistics (process 8793) ------- clauses given 24 clauses generated 1241 clauses kept 424 clauses forward subsumed 905 clauses back subsumed 122 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8793 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1.2]. ------- statistics (process 8789) ------- clauses given 14 clauses generated 622 clauses kept 264 clauses forward subsumed 347 clauses back subsumed 55 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8789 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.1]. Case [2.1.1.2] (process 8796): Assumption: 177 [161,split.2.1.1.2] p(b,k). Splitting on clause 182 [back_unit_del,176.1,163.1] p(k,b)|p(k,g(k)). Case [2.1.1.2.1] (process 8797): Assumption: 411 [182,split.2.1.1.2.1] p(k,b). Splitting on clause 414 [back_unit_del,411.1,208.3] p(b,m)|k=b. --- refuted case [2.1.1.2.1.1] Case [2.1.1.2.1.1] (process 8798): Assumption: 430 [414,split.2.1.1.2.1.1] p(b,m). -----> EMPTY CLAUSE at 0.13 sec ----> 906 [back_demod,882,demod,897,897,unit_del,432,434] $F. Length of proof is 39. Level of proof is 14. Case [2.1.1.2.1.1] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 20 [binary,16.1,10.1] p(m,b)|p(m,g(m)). 21 [binary,16.1,9.1] p(m,b)|g(m)!=m. 22 [binary,16.1,8.1] p(m,b)|g(m)!=b. 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 129 [47,split.2.1] p(b,j). 157 [80,split.2.1.1] p(m,k). 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). 163 [para_into,157.1.2,10.1.1] p(m,b)|p(k,b)|p(k,g(k)). 176 [161,split_neg.2.1.1.2] -p(m,b). 177 [161,split.2.1.1.2] p(b,k). 182 [back_unit_del,176.1,163.1] p(k,b)|p(k,g(k)). 184 [back_unit_del,176.1,22.1] g(m)!=b. 185 [back_unit_del,176.1,21.1] g(m)!=m. 186 [back_unit_del,176.1,20.1] p(m,g(m)). 187 [back_unit_del,176.1,19.1] p(g(m),m). 206 [para_into,177.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 208 [factor,206.1.3,unit_del,16,177] p(b,m)|k=b| -p(k,b). 226 [binary,186.1,2.6,unit_del,184,16,185,187] -p(g(m),b). 238 [para_into,226.1.2,7.1.1,unit_del,187] -p(b,m)|p(f(b),b). 239 [para_into,226.1.2,6.1.1,unit_del,187] -p(b,m)|p(b,f(b)). 240 [para_into,226.1.2,5.1.1,unit_del,187] -p(b,m)|f(b)!=b. 241 [para_into,226.1.2,4.1.1,unit_del,187] -p(b,m)|f(b)!=m. 411 [182,split.2.1.1.2.1] p(k,b). 414 [back_unit_del,411.1,208.3] p(b,m)|k=b. 430 [414,split.2.1.1.2.1.1] p(b,m). 431 [back_unit_del,430.1,241.1] f(b)!=m. 432 [back_unit_del,430.1,240.1] f(b)!=b. 433 [back_unit_del,430.1,239.1] p(b,f(b)). 434 [back_unit_del,430.1,238.1] p(f(b),b). 449 [binary,433.1,1.6,unit_del,431,16,432,434] p(f(b),m). 457 [binary,449.1,2.5,unit_del,432,434,16,431] -p(m,f(b)). 461 [para_into,457.1.2,3.1.1,unit_del,157,431,432] -p(f(b),k). 882 [para_from,17.3.1,457.1.2,unit_del,157] f(b)=j| -p(f(b),j). 897,896 [para_from,17.3.1,434.1.2,unit_del,461,129,flip.1] j=b. 906 [back_demod,882,demod,897,897,unit_del,432,434] $F. ------------ end of proof ------------- ------- statistics (process 8798) ------- clauses given 62 clauses generated 4523 clauses kept 902 clauses forward subsumed 3498 clauses back subsumed 350 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.13 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8798 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.2.1.1]. --- refuted case [2.1.1.2.1.2] Case [2.1.1.2.1.2] (process 8799): Assumption: 431 [414,split.2.1.1.2.1.2] k=b. ----> UNIT CONFLICT at 0.00 sec ----> 448 [binary,447.1,176.1] $F. Length of proof is 15. Level of proof is 10. Case [2.1.1.2.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 10 [] x=b|p(x,b)|p(x,g(x)). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 157 [80,split.2.1.1] p(m,k). 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). 163 [para_into,157.1.2,10.1.1] p(m,b)|p(k,b)|p(k,g(k)). 176 [161,split_neg.2.1.1.2] -p(m,b). 177 [161,split.2.1.1.2] p(b,k). 182 [back_unit_del,176.1,163.1] p(k,b)|p(k,g(k)). 206 [para_into,177.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 208 [factor,206.1.3,unit_del,16,177] p(b,m)|k=b| -p(k,b). 411 [182,split.2.1.1.2.1] p(k,b). 414 [back_unit_del,411.1,208.3] p(b,m)|k=b. 432,431 [414,split.2.1.1.2.1.2] k=b. 447 [back_demod,157,demod,432] p(m,b). 448 [binary,447.1,176.1] $F. ------------ end of proof ------------- ------- statistics (process 8799) ------- clauses given 36 clauses generated 2012 clauses kept 445 clauses forward subsumed 1527 clauses back subsumed 270 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8799 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.2.1.2]. ------- statistics (process 8797) ------- clauses given 36 clauses generated 2002 clauses kept 428 clauses forward subsumed 1506 clauses back subsumed 266 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8797 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.2.1]. --- refuted case [2.1.1.2.2] Case [2.1.1.2.2] (process 8800): Assumption: 412 [182,split.2.1.1.2.2] p(k,g(k)). 0 [back_unit_del,411.1,181.1] g(k)!=k. 0 [back_unit_del,411.1,180.1] g(k)!=b. ----> UNIT CONFLICT at 0.01 sec ----> 496 [binary,495.1,411.1] $F. Length of proof is 31. Level of proof is 13. Case [2.1.1.2.2] ---------------- PROOF ---------------- 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 157 [80,split.2.1.1] p(m,k). 161 [para_into,157.1.2,14.1.1] p(m,b)|p(b,k). 162 [para_into,157.1.2,11.1.1] p(m,b)|p(k,b)|p(g(k),k). 163 [para_into,157.1.2,10.1.1] p(m,b)|p(k,b)|p(k,g(k)). 164 [para_into,157.1.2,9.1.1] p(m,b)|p(k,b)|g(k)!=k. 165 [para_into,157.1.2,8.1.1] p(m,b)|p(k,b)|g(k)!=b. 176 [161,split_neg.2.1.1.2] -p(m,b). 180 [back_unit_del,176.1,165.1] p(k,b)|g(k)!=b. 181 [back_unit_del,176.1,164.1] p(k,b)|g(k)!=k. 182 [back_unit_del,176.1,163.1] p(k,b)|p(k,g(k)). 183 [back_unit_del,176.1,162.1] p(k,b)|p(g(k),k). 365 [binary,180.2,3.3] p(k,b)|g(k)=k|g(k)=m| -p(g(k),k). 406 [para_into,181.2.1,3.2.1] p(k,b)|m!=k|g(k)=k|g(k)=b| -p(g(k),k). 411 [182,split_neg.2.1.1.2.2] -p(k,b). 412 [182,split.2.1.1.2.2] p(k,g(k)). 417 [back_unit_del,411.1,406.1] m!=k|g(k)=k|g(k)=b| -p(g(k),k). 438 [back_unit_del,411.1,365.1] g(k)=k|g(k)=m| -p(g(k),k). 443 [back_unit_del,411.1,183.1] p(g(k),k). 444 [back_unit_del,411.1,181.1] g(k)!=k. 455,454 [back_unit_del,443.1,438.3,unit_del,444] g(k)=m. 456 [back_unit_del,444.1,417.2,demod,455,455,unit_del,16,157] m!=k. 457 [back_demod,412,demod,455] p(k,m). 487 [binary,457.1,7.2,unit_del,456] p(f(k),k). 488 [binary,457.1,6.2,unit_del,456] p(k,f(k)). 489 [binary,457.1,5.2,unit_del,456] f(k)!=k. 490 [binary,457.1,4.2,unit_del,456] f(k)!=m. 493,492 [binary,487.1,3.4,unit_del,489,490] f(k)=b. 495 [back_demod,488,demod,493] p(k,b). 496 [binary,495.1,411.1] $F. ------------ end of proof ------------- ------- statistics (process 8800) ------- clauses given 38 clauses generated 2152 clauses kept 492 clauses forward subsumed 1617 clauses back subsumed 305 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8800 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.2.2]. ------- statistics (process 8796) ------- clauses given 33 clauses generated 1896 clauses kept 409 clauses forward subsumed 1421 clauses back subsumed 140 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8796 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1.2]. ------- statistics (process 8788) ------- clauses given 11 clauses generated 386 clauses kept 174 clauses forward subsumed 210 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8788 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.1]. Case [2.1.2] (process 8801): Assumption: 158 [80,split.2.1.2] p(b,k). 0 [back_unit_del,157.1,25.2] k!=b. 0 [back_unit_del,157.1,12.2] m=k. Splitting on clause 169 [back_unit_del,157.1,82.1] p(k,b)|p(k,g(k)). --- refuted case [2.1.2.1] Case [2.1.2.1] (process 8802): Assumption: 215 [169,split.2.1.2.1] p(k,b). ----> UNIT CONFLICT at 0.04 sec ----> 391 [binary,389.1,382.1] $F. Length of proof is 30. Level of proof is 9. Case [2.1.2.1] ---------------- PROOF ---------------- 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 7 [] x=m| -p(x,m)|p(f(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 25 [para_into,16.1.1,12.1.1] k!=b|p(m,k). 26 [18,split_neg.2] k!=j. 27 [18,split.2] p(k,j). 30 [para_into,26.1.1,14.1.1,flip.1] j!=b|p(b,k). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 66 [para_into,27.1.2,7.1.1] p(k,m)| -p(j,m)|p(f(j),j). 68 [para_into,27.1.2,5.1.1] p(k,m)| -p(j,m)|f(j)!=j. 72 [para_into,27.1.2,3.1.1,flip.2] p(k,k)|m=j|j=b| -p(j,k). 80 [binary,25.1,14.1] p(m,k)|p(b,k). 116 [para_into,30.2.1,4.1.1] j!=b|p(m,k)| -p(b,m)|f(b)!=m. 129 [47,split.2.1] p(b,j). 157 [80,split_neg.2.1.2] -p(m,k). 158 [80,split.2.1.2] p(b,k). 161 [back_unit_del,157.1,116.2] j!=b| -p(b,m)|f(b)!=m. 171 [back_unit_del,157.1,25.2] k!=b. 173,172 [back_unit_del,157.1,12.2] m=k. 182 [back_demod,161,demod,173,173,unit_del,158] j!=b|f(b)!=k. 184 [back_demod,157,demod,173] -p(k,k). 192 [back_demod,72,demod,173,unit_del,184,26] j=b| -p(j,k). 195 [back_demod,68,demod,173,173,unit_del,184] -p(j,k)|f(j)!=j. 197 [back_demod,66,demod,173,173,unit_del,184] -p(j,k)|p(f(j),j). 243 [binary,182.1,192.1] f(b)!=k| -p(j,k). 297 [para_into,197.2.2,192.1.1,factor_simp] -p(j,k)|p(f(j),b). 340 [binary,17.1,195.2] -p(f(j),j)|f(j)=k| -p(j,k). 345,344 [binary,17.2,129.1,unit_del,171,flip.1] j=b. 348 [back_demod,340,demod,345,345,345,345,unit_del,158] -p(f(b),b)|f(b)=k. 370 [back_demod,297,demod,345,345,unit_del,158] p(f(b),b). 382 [back_demod,243,demod,345,unit_del,158] f(b)!=k. 389 [back_unit_del,370.1,348.1] f(b)=k. 391 [binary,389.1,382.1] $F. ------------ end of proof ------------- ------- statistics (process 8802) ------- clauses given 36 clauses generated 1338 clauses kept 386 clauses forward subsumed 1138 clauses back subsumed 101 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8802 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.2.1]. The Assumption for case [2.1.2.1] was not used; therefore we skip case: [2.1.2.2]. ------- statistics (process 8801) ------- clauses given 17 clauses generated 579 clauses kept 212 clauses forward subsumed 422 clauses back subsumed 69 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8801 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1.2]. ------- statistics (process 8787) ------- clauses given 9 clauses generated 335 clauses kept 155 clauses forward subsumed 180 clauses back subsumed 9 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8787 finished Mon Aug 2 15:31:10 2004 Refuted case [2.1]. Case [2.2] (process 8803): Assumption: 130 [47,split.2.2] p(b,k). Splitting on clause 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). Case [2.2.1] (process 8804): Assumption: 180 [19,split.2.2.1] p(m,b). Splitting on clause 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). Case [2.2.1.1] (process 8805): Assumption: 190 [182,split.2.2.1.1] p(k,b). Splitting on clause 191 [back_unit_del,190.1,179.3] p(b,m)|k=b. Case [2.2.1.1.1] (process 8806): Assumption: 203 [191,split.2.2.1.1.1] p(b,m). Splitting on clause 255 [para_into,234.1.2,12.1.1] p(f(b),k)|p(m,k). --- refuted case [2.2.1.1.1.1] Case [2.2.1.1.1.1] (process 8807): Assumption: 475 [255,split.2.2.1.1.1.1] p(f(b),k). ----> UNIT CONFLICT at 0.00 sec ----> 491 [binary,490.1,487.1] $F. Length of proof is 25. Level of proof is 12. Case [2.2.1.1.1.1] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 130 [47,split.2.2] p(b,k). 177 [para_into,130.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 179 [factor,177.1.3,unit_del,16,130] p(b,m)|k=b| -p(k,b). 180 [19,split.2.2.1] p(m,b). 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). 190 [182,split.2.2.1.1] p(k,b). 191 [back_unit_del,190.1,179.3] p(b,m)|k=b. 203 [191,split.2.2.1.1.1] p(b,m). 227 [binary,203.1,7.2,unit_del,16] p(f(b),b). 228 [binary,203.1,6.2,unit_del,16] p(b,f(b)). 229 [binary,203.1,5.2,unit_del,16] f(b)!=b. 230 [binary,203.1,4.2,unit_del,16] f(b)!=m. 234 [binary,227.1,1.5,unit_del,230,16,229,228] p(f(b),m). 248 [binary,230.1,2.4,unit_del,16,180,229,234] -p(m,f(b)). 250 [para_into,230.1.1,3.1.1,unit_del,230,229,flip.1] m!=k| -p(f(b),k). 255 [para_into,234.1.2,12.1.1] p(f(b),k)|p(m,k). 259 [para_into,248.1.2,3.1.1,unit_del,230,229] -p(m,k)| -p(f(b),k). 450 [binary,250.1,12.1] -p(f(b),k)|p(m,k). 475 [255,split.2.2.1.1.1.1] p(f(b),k). 487 [back_unit_del,475.1,450.1] p(m,k). 490 [back_unit_del,475.1,259.2] -p(m,k). 491 [binary,490.1,487.1] $F. ------------ end of proof ------------- ------- statistics (process 8807) ------- clauses given 34 clauses generated 1896 clauses kept 487 clauses forward subsumed 1348 clauses back subsumed 179 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8807 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1.1]. Case [2.2.1.1.1.2] (process 8808): Assumption: 476 [255,split.2.2.1.1.1.2] p(m,k). Splitting on clause 776 [para_into,773.1.2,11.1.1,unit_del,180] p(j,b)|p(g(j),j). Case [2.2.1.1.1.2.1] (process 8809): Assumption: 790 [776,split.2.2.1.1.1.2.1] p(j,b). Splitting on clause 192 [back_unit_del,190.1,162.4] m=k|p(k,m)|k=b. --- refuted case [2.2.1.1.1.2.1.1] Case [2.2.1.1.1.2.1.1] (process 8810): Assumption: 806 [192,split.2.2.1.1.1.2.1.1] m=k. ----> UNIT CONFLICT at 0.00 sec ----> 815 [binary,814.1,27.1] $F. Length of proof is 26. Level of proof is 13. Case [2.2.1.1.1.2.1.1] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 162 [binary,130.1,1.6,unit_del,16,flip.1,flip.3] m=k|p(k,m)|k=b| -p(k,b). 177 [para_into,130.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 179 [factor,177.1.3,unit_del,16,130] p(b,m)|k=b| -p(k,b). 180 [19,split.2.2.1] p(m,b). 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). 190 [182,split.2.2.1.1] p(k,b). 191 [back_unit_del,190.1,179.3] p(b,m)|k=b. 192 [back_unit_del,190.1,162.4] m=k|p(k,m)|k=b. 203 [191,split.2.2.1.1.1] p(b,m). 227 [binary,203.1,7.2,unit_del,16] p(f(b),b). 228 [binary,203.1,6.2,unit_del,16] p(b,f(b)). 229 [binary,203.1,5.2,unit_del,16] f(b)!=b. 230 [binary,203.1,4.2,unit_del,16] f(b)!=m. 234 [binary,227.1,1.5,unit_del,230,16,229,228] p(f(b),m). 255 [para_into,234.1.2,12.1.1] p(f(b),k)|p(m,k). 475 [255,split_neg.2.2.1.1.1.2] -p(f(b),k). 734 [para_from,17.1.1,203.1.2,unit_del,129] -p(m,j)|m=k. 773 [para_from,734.2.1,234.1.2,unit_del,475] -p(m,j). 807,806 [192,split.2.2.1.1.1.2.1.1] m=k. 814 [back_demod,773,demod,807] -p(k,j). 815 [binary,814.1,27.1] $F. ------------ end of proof ------------- ------- statistics (process 8810) ------- clauses given 58 clauses generated 4010 clauses kept 811 clauses forward subsumed 3101 clauses back subsumed 556 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8810 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1.2.1.1]. --- refuted case [2.2.1.1.1.2.1.2] Case [2.2.1.1.1.2.1.2] (process 8811): Assumption: 807 [192,split.2.2.1.1.1.2.1.2] p(k,m). -----> EMPTY CLAUSE at 0.00 sec ----> 825 [back_unit_del,807.1,617.1,demod,824,824,824,824,824,unit_del,229,229,227] $F. Length of proof is 28. Level of proof is 13. Case [2.2.1.1.1.2.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 130 [47,split.2.2] p(b,k). 162 [binary,130.1,1.6,unit_del,16,flip.1,flip.3] m=k|p(k,m)|k=b| -p(k,b). 177 [para_into,130.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 179 [factor,177.1.3,unit_del,16,130] p(b,m)|k=b| -p(k,b). 180 [19,split.2.2.1] p(m,b). 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). 190 [182,split.2.2.1.1] p(k,b). 191 [back_unit_del,190.1,179.3] p(b,m)|k=b. 192 [back_unit_del,190.1,162.4] m=k|p(k,m)|k=b. 203 [191,split.2.2.1.1.1] p(b,m). 227 [binary,203.1,7.2,unit_del,16] p(f(b),b). 228 [binary,203.1,6.2,unit_del,16] p(b,f(b)). 229 [binary,203.1,5.2,unit_del,16] f(b)!=b. 230 [binary,203.1,4.2,unit_del,16] f(b)!=m. 234 [binary,227.1,1.5,unit_del,230,16,229,228] p(f(b),m). 255 [para_into,234.1.2,12.1.1] p(f(b),k)|p(m,k). 475 [255,split_neg.2.2.1.1.1.2] -p(f(b),k). 476 [255,split.2.2.1.1.1.2] p(m,k). 477 [binary,476.1,2.6,unit_del,190,16] k=b|m=k| -p(k,m). 490 [para_into,475.1.2,4.1.1,unit_del,234] -p(k,m)|f(k)!=m. 617 [binary,490.2,3.2] -p(k,m)|f(k)=k|f(k)=b| -p(f(k),k). 806 [192,split_neg.2.2.1.1.1.2.1.2] m!=k. 807 [192,split.2.2.1.1.1.2.1.2] p(k,m). 824,823 [back_unit_del,806.1,477.2,unit_del,807] k=b. 825 [back_unit_del,807.1,617.1,demod,824,824,824,824,824,unit_del,229,229,227] $F. ------------ end of proof ------------- ------- statistics (process 8811) ------- clauses given 58 clauses generated 4040 clauses kept 821 clauses forward subsumed 3108 clauses back subsumed 558 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8811 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1.2.1.2]. --- refuted case [2.2.1.1.1.2.1.3] Case [2.2.1.1.1.2.1.3] (process 8812): Assumption: 808 [192,split.2.2.1.1.1.2.1.3] k=b. ----> UNIT CONFLICT at 0.00 sec ----> 812 [binary,811.1,203.1] $F. Length of proof is 17. Level of proof is 7. Case [2.2.1.1.1.2.1.3] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 130 [47,split.2.2] p(b,k). 162 [binary,130.1,1.6,unit_del,16,flip.1,flip.3] m=k|p(k,m)|k=b| -p(k,b). 177 [para_into,130.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 179 [factor,177.1.3,unit_del,16,130] p(b,m)|k=b| -p(k,b). 180 [19,split.2.2.1] p(m,b). 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). 190 [182,split.2.2.1.1] p(k,b). 191 [back_unit_del,190.1,179.3] p(b,m)|k=b. 192 [back_unit_del,190.1,162.4] m=k|p(k,m)|k=b. 203 [191,split.2.2.1.1.1] p(b,m). 807 [192,split_neg.2.2.1.1.1.2.1.3] -p(k,m). 809,808 [192,split.2.2.1.1.1.2.1.3] k=b. 811 [back_demod,807,demod,809] -p(b,m). 812 [binary,811.1,203.1] $F. ------------ end of proof ------------- ------- statistics (process 8812) ------- clauses given 58 clauses generated 4031 clauses kept 808 clauses forward subsumed 3115 clauses back subsumed 610 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8812 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1.2.1.3]. ------- statistics (process 8809) ------- clauses given 58 clauses generated 4010 clauses kept 803 clauses forward subsumed 3097 clauses back subsumed 556 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8809 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1.2.1]. The Assumption for case [2.2.1.1.1.2.1] was not used; therefore we skip case: [2.2.1.1.1.2.2]. ------- statistics (process 8808) ------- clauses given 54 clauses generated 3784 clauses kept 787 clauses forward subsumed 2887 clauses back subsumed 538 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.17 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8808 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1.2]. ------- statistics (process 8806) ------- clauses given 34 clauses generated 1881 clauses kept 472 clauses forward subsumed 1347 clauses back subsumed 179 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.07 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8806 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.1]. --- refuted case [2.2.1.1.2] Case [2.2.1.1.2] (process 8813): Assumption: 204 [191,split.2.2.1.1.2] k=b. ----> UNIT CONFLICT at 0.00 sec ----> 224 [binary,223.1,129.1] $F. Length of proof is 14. Level of proof is 8. Case [2.2.1.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 177 [para_into,130.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 179 [factor,177.1.3,unit_del,16,130] p(b,m)|k=b| -p(k,b). 180 [19,split.2.2.1] p(m,b). 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). 190 [182,split.2.2.1.1] p(k,b). 191 [back_unit_del,190.1,179.3] p(b,m)|k=b. 205,204 [191,split.2.2.1.1.2] k=b. 223 [back_demod,27,demod,205] p(b,j). 224 [binary,223.1,129.1] $F. ------------ end of proof ------------- ------- statistics (process 8813) ------- clauses given 14 clauses generated 495 clauses kept 221 clauses forward subsumed 327 clauses back subsumed 102 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8813 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1.2]. ------- statistics (process 8805) ------- clauses given 14 clauses generated 485 clauses kept 201 clauses forward subsumed 282 clauses back subsumed 79 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8805 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.1]. --- refuted case [2.2.1.2] Case [2.2.1.2] (process 8814): Assumption: 191 [182,split.2.2.1.2] p(m,k). ----> UNIT CONFLICT at 0.00 sec ----> 247 [binary,246.1,243.1] $F. Length of proof is 29. Level of proof is 9. Case [2.2.1.2] ---------------- PROOF ---------------- 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 48 [para_into,27.1.1,11.1.1] p(b,j)|p(k,b)|p(g(k),k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 50 [para_into,27.1.1,9.1.1] p(b,j)|p(k,b)|g(k)!=k. 51 [para_into,27.1.1,8.1.1] p(b,j)|p(k,b)|g(k)!=b. 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 133 [back_unit_del,129.1,51.1] p(k,b)|g(k)!=b. 134 [back_unit_del,129.1,50.1] p(k,b)|g(k)!=k. 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 136 [back_unit_del,129.1,48.1] p(k,b)|p(g(k),k). 180 [19,split.2.2.1] p(m,b). 182 [para_into,180.1.1,12.1.1] p(k,b)|p(m,k). 190 [182,split_neg.2.2.1.2] -p(k,b). 191 [182,split.2.2.1.2] p(m,k). 192 [back_unit_del,190.1,136.1] p(g(k),k). 193 [back_unit_del,190.1,135.1] p(k,g(k)). 194 [back_unit_del,190.1,134.1] g(k)!=k. 195 [back_unit_del,190.1,133.1] g(k)!=b. 218 [binary,191.1,2.5,unit_del,16,180,flip.2] k=b|m=k| -p(k,m). 222,221 [binary,192.1,3.4,unit_del,194,195] g(k)=m. 223 [back_demod,194,demod,222] m!=k. 224 [back_demod,193,demod,222] p(k,m). 227,226 [back_unit_del,223.1,218.2,unit_del,224] k=b. 243 [back_demod,190,demod,227] -p(b,b). 246 [back_demod,130,demod,227] p(b,b). 247 [binary,246.1,243.1] $F. ------------ end of proof ------------- ------- statistics (process 8814) ------- clauses given 15 clauses generated 563 clauses kept 242 clauses forward subsumed 345 clauses back subsumed 134 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8814 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1.2]. ------- statistics (process 8804) ------- clauses given 12 clauses generated 436 clauses kept 188 clauses forward subsumed 246 clauses back subsumed 63 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8804 finished Mon Aug 2 15:31:10 2004 Refuted case [2.2.1]. Case [2.2.2] (process 8815): Assumption: 181 [19,split.2.2.2] p(g(m),m). Splitting on clause 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). Case [2.2.2.1] (process 8816): Assumption: 435 [135,split.2.2.2.1] p(k,b). 0 [back_unit_del,435.1,185.1] p(m,k). Splitting on clause 438 [back_unit_del,435.1,273.1] p(b,m)|m=k. Case [2.2.2.1.1] (process 8817): Assumption: 465 [438,split.2.2.2.1.1] p(b,m). 0 [back_unit_del,1167.1,767.1] -p(j,k). Splitting on clause 1175 [back_unit_del,1167.1,823.1] p(j,b)|p(j,g(j)). Case [2.2.2.1.1.1] (process 8818): Assumption: 1214 [1175,split.2.2.2.1.1.1] p(j,b). Splitting on clause 437 [back_unit_del,435.1,274.1] p(m,m)|p(k,m)|k=b. Case [2.2.2.1.1.1.1] (process 8819): Assumption: 1242 [437,split.2.2.2.1.1.1.1] p(m,m). Splitting on clause 1253 [back_unit_del,1249.1,451.2] m=k|k=b. --- refuted case [2.2.2.1.1.1.1.1] Case [2.2.2.1.1.1.1.1] (process 8820): Assumption: 1255 [1253,split.2.2.2.1.1.1.1.1] m=k. ----> UNIT CONFLICT at 0.00 sec ----> 1263 [binary,1262.1,1261.1] $F. Length of proof is 64. Level of proof is 18. Case [2.2.2.1.1.1.1.1] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 20 [binary,16.1,10.1] p(m,b)|p(m,g(m)). 21 [binary,16.1,9.1] p(m,b)|g(m)!=m. 22 [binary,16.1,8.1] p(m,b)|g(m)!=b. 26 [18,split_neg.2] k!=j. 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 149 [para_into,129.1.2,7.1.1] -p(b,m)| -p(j,m)|p(f(j),j). 154 [para_into,129.1.2,3.2.1,unit_del,26] -p(b,m)|j=b| -p(j,k). 162 [binary,130.1,1.6,unit_del,16,flip.1,flip.3] m=k|p(k,m)|k=b| -p(k,b). 180 [19,split_neg.2.2.2] -p(m,b). 181 [19,split.2.2.2] p(g(m),m). 182 [back_unit_del,180.1,22.1] g(m)!=b. 183 [back_unit_del,180.1,21.1] g(m)!=m. 184 [back_unit_del,180.1,20.1] p(m,g(m)). 185 [para_into,180.1.1,12.1.1] -p(k,b)|p(m,k). 198 [binary,181.1,2.5,unit_del,182,16,183,184] -p(g(m),b). 229 [para_into,198.1.2,7.1.1,unit_del,181] -p(b,m)|p(f(b),b). 230 [para_into,198.1.2,6.1.1,unit_del,181] -p(b,m)|p(b,f(b)). 231 [para_into,198.1.2,5.1.1,unit_del,181] -p(b,m)|f(b)!=b. 232 [para_into,198.1.2,4.1.1,unit_del,181] -p(b,m)|f(b)!=m. 262 [binary,185.2,2.6,unit_del,16,factor_simp] -p(k,b)|k=b|m=k| -p(k,m). 270 [para_into,185.2.2,1.4.1,flip.5] -p(k,b)|p(m,x)|x=m|p(x,m)|m=k| -p(x,k)| -p(k,x). 272 [para_into,185.2.2,1.1.1] -p(k,b)|p(m,m)|p(k,m)|x=m|x=k| -p(k,x)| -p(x,k). 273 [factor,270.1.7,unit_del,180,16,130] -p(k,b)|p(b,m)|m=k. 274 [factor,272.1.6,unit_del,16,130,flip.4] -p(k,b)|p(m,m)|p(k,m)|k=b. 435 [135,split.2.2.2.1] p(k,b). 437 [back_unit_del,435.1,274.1] p(m,m)|p(k,m)|k=b. 438 [back_unit_del,435.1,273.1] p(b,m)|m=k. 447 [back_unit_del,435.1,262.1] k=b|m=k| -p(k,m). 449 [back_unit_del,435.1,185.1] p(m,k). 451 [back_unit_del,435.1,162.4] m=k|p(k,m)|k=b. 465 [438,split.2.2.2.1.1] p(b,m). 466 [back_unit_del,465.1,232.1] f(b)!=m. 467 [back_unit_del,465.1,231.1] f(b)!=b. 468 [back_unit_del,465.1,230.1] p(b,f(b)). 469 [back_unit_del,465.1,229.1] p(f(b),b). 472 [back_unit_del,465.1,154.1] j=b| -p(j,k). 476 [back_unit_del,465.1,149.1] -p(j,m)|p(f(j),j). 491 [binary,468.1,1.6,unit_del,466,16,467,469] p(f(b),m). 499 [binary,491.1,2.5,unit_del,467,469,16,466] -p(m,f(b)). 503 [para_into,499.1.2,3.1.1,unit_del,449,466,467] -p(f(b),k). 682 [para_into,476.1.1,472.1.1,unit_del,465] p(f(j),j)| -p(j,k). 767 [para_into,682.1.1.1,472.1.1,factor_simp] p(f(b),j)| -p(j,k). 823 [para_into,767.2.1,10.1.1,unit_del,130] p(f(b),j)|p(j,b)|p(j,g(j)). 1033 [para_from,17.1.1,468.1.2,unit_del,129] -p(f(b),j)|f(b)=k. 1087 [para_from,17.1.1,465.1.2,unit_del,129] -p(m,j)|m=k. 1149 [para_from,1087.2.1,491.1.2,unit_del,503] -p(m,j). 1167 [para_from,1033.2.1,499.1.2,unit_del,449] -p(f(b),j). 1175 [back_unit_del,1167.1,823.1] p(j,b)|p(j,g(j)). 1177 [back_unit_del,1167.1,767.1] -p(j,k). 1214 [1175,split.2.2.2.1.1.1] p(j,b). 1242 [437,split.2.2.2.1.1.1.1] p(m,m). 1246 [para_from,447.1.1,1177.1.2,unit_del,1214] m=k| -p(k,m). 1249 [para_from,1246.1.1,1149.1.1,unit_del,27] -p(k,m). 1253 [back_unit_del,1249.1,451.2] m=k|k=b. 1256,1255 [1253,split.2.2.2.1.1.1.1.1] m=k. 1261 [back_demod,1249,demod,1256] -p(k,k). 1262 [back_demod,1242,demod,1256,1256] p(k,k). 1263 [binary,1262.1,1261.1] $F. ------------ end of proof ------------- ------- statistics (process 8820) ------- clauses given 92 clauses generated 7392 clauses kept 1259 clauses forward subsumed 5909 clauses back subsumed 889 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8820 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.1.1.1]. --- refuted case [2.2.2.1.1.1.1.2] Case [2.2.2.1.1.1.1.2] (process 8821): Assumption: 1256 [1253,split.2.2.2.1.1.1.1.2] k=b. ----> UNIT CONFLICT at 0.00 sec ----> 1261 [binary,1260.1,465.1] $F. Length of proof is 59. Level of proof is 18. Case [2.2.2.1.1.1.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 20 [binary,16.1,10.1] p(m,b)|p(m,g(m)). 21 [binary,16.1,9.1] p(m,b)|g(m)!=m. 22 [binary,16.1,8.1] p(m,b)|g(m)!=b. 26 [18,split_neg.2] k!=j. 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 149 [para_into,129.1.2,7.1.1] -p(b,m)| -p(j,m)|p(f(j),j). 154 [para_into,129.1.2,3.2.1,unit_del,26] -p(b,m)|j=b| -p(j,k). 162 [binary,130.1,1.6,unit_del,16,flip.1,flip.3] m=k|p(k,m)|k=b| -p(k,b). 180 [19,split_neg.2.2.2] -p(m,b). 181 [19,split.2.2.2] p(g(m),m). 182 [back_unit_del,180.1,22.1] g(m)!=b. 183 [back_unit_del,180.1,21.1] g(m)!=m. 184 [back_unit_del,180.1,20.1] p(m,g(m)). 185 [para_into,180.1.1,12.1.1] -p(k,b)|p(m,k). 198 [binary,181.1,2.5,unit_del,182,16,183,184] -p(g(m),b). 229 [para_into,198.1.2,7.1.1,unit_del,181] -p(b,m)|p(f(b),b). 230 [para_into,198.1.2,6.1.1,unit_del,181] -p(b,m)|p(b,f(b)). 231 [para_into,198.1.2,5.1.1,unit_del,181] -p(b,m)|f(b)!=b. 232 [para_into,198.1.2,4.1.1,unit_del,181] -p(b,m)|f(b)!=m. 262 [binary,185.2,2.6,unit_del,16,factor_simp] -p(k,b)|k=b|m=k| -p(k,m). 270 [para_into,185.2.2,1.4.1,flip.5] -p(k,b)|p(m,x)|x=m|p(x,m)|m=k| -p(x,k)| -p(k,x). 273 [factor,270.1.7,unit_del,180,16,130] -p(k,b)|p(b,m)|m=k. 435 [135,split.2.2.2.1] p(k,b). 438 [back_unit_del,435.1,273.1] p(b,m)|m=k. 447 [back_unit_del,435.1,262.1] k=b|m=k| -p(k,m). 449 [back_unit_del,435.1,185.1] p(m,k). 451 [back_unit_del,435.1,162.4] m=k|p(k,m)|k=b. 465 [438,split.2.2.2.1.1] p(b,m). 466 [back_unit_del,465.1,232.1] f(b)!=m. 467 [back_unit_del,465.1,231.1] f(b)!=b. 468 [back_unit_del,465.1,230.1] p(b,f(b)). 469 [back_unit_del,465.1,229.1] p(f(b),b). 472 [back_unit_del,465.1,154.1] j=b| -p(j,k). 476 [back_unit_del,465.1,149.1] -p(j,m)|p(f(j),j). 491 [binary,468.1,1.6,unit_del,466,16,467,469] p(f(b),m). 499 [binary,491.1,2.5,unit_del,467,469,16,466] -p(m,f(b)). 503 [para_into,499.1.2,3.1.1,unit_del,449,466,467] -p(f(b),k). 682 [para_into,476.1.1,472.1.1,unit_del,465] p(f(j),j)| -p(j,k). 767 [para_into,682.1.1.1,472.1.1,factor_simp] p(f(b),j)| -p(j,k). 823 [para_into,767.2.1,10.1.1,unit_del,130] p(f(b),j)|p(j,b)|p(j,g(j)). 1033 [para_from,17.1.1,468.1.2,unit_del,129] -p(f(b),j)|f(b)=k. 1087 [para_from,17.1.1,465.1.2,unit_del,129] -p(m,j)|m=k. 1149 [para_from,1087.2.1,491.1.2,unit_del,503] -p(m,j). 1167 [para_from,1033.2.1,499.1.2,unit_del,449] -p(f(b),j). 1175 [back_unit_del,1167.1,823.1] p(j,b)|p(j,g(j)). 1177 [back_unit_del,1167.1,767.1] -p(j,k). 1214 [1175,split.2.2.2.1.1.1] p(j,b). 1246 [para_from,447.1.1,1177.1.2,unit_del,1214] m=k| -p(k,m). 1249 [para_from,1246.1.1,1149.1.1,unit_del,27] -p(k,m). 1253 [back_unit_del,1249.1,451.2] m=k|k=b. 1257,1256 [1253,split.2.2.2.1.1.1.1.2] k=b. 1260 [back_demod,1249,demod,1257] -p(b,m). 1261 [binary,1260.1,465.1] $F. ------------ end of proof ------------- ------- statistics (process 8821) ------- clauses given 92 clauses generated 7400 clauses kept 1257 clauses forward subsumed 5917 clauses back subsumed 892 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8821 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.1.1.2]. ------- statistics (process 8819) ------- clauses given 92 clauses generated 7392 clauses kept 1252 clauses forward subsumed 5909 clauses back subsumed 889 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8819 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.1.1]. --- refuted case [2.2.2.1.1.1.2] Case [2.2.2.1.1.1.2] (process 8822): Assumption: 1243 [437,split.2.2.2.1.1.1.2] p(k,m). 0 [back_unit_del,1243.1,458.1] f(k)!=m. 0 [back_unit_del,1243.1,457.1] f(k)!=k. 0 [back_unit_del,1243.1,456.1] p(k,f(k)). 0 [back_unit_del,1243.1,455.1] p(f(k),k). ----> UNIT CONFLICT at 0.02 sec ----> 1306 [binary,1305.1,1304.1] $F. Length of proof is 33. Level of proof is 12. Case [2.2.2.1.1.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 7 [] x=m| -p(x,m)|p(f(x),x). 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 180 [19,split_neg.2.2.2] -p(m,b). 185 [para_into,180.1.1,12.1.1] -p(k,b)|p(m,k). 262 [binary,185.2,2.6,unit_del,16,factor_simp] -p(k,b)|k=b|m=k| -p(k,m). 272 [para_into,185.2.2,1.1.1] -p(k,b)|p(m,m)|p(k,m)|x=m|x=k| -p(k,x)| -p(x,k). 274 [factor,272.1.6,unit_del,16,130,flip.4] -p(k,b)|p(m,m)|p(k,m)|k=b. 435 [135,split.2.2.2.1] p(k,b). 437 [back_unit_del,435.1,274.1] p(m,m)|p(k,m)|k=b. 447 [back_unit_del,435.1,262.1] k=b|m=k| -p(k,m). 455 [para_into,435.1.1,7.1.1,unit_del,180] -p(k,m)|p(f(k),k). 457 [para_into,435.1.1,5.1.1,unit_del,180] -p(k,m)|f(k)!=k. 458 [para_into,435.1.1,4.1.1,unit_del,180] -p(k,m)|f(k)!=m. 531 [binary,455.2,3.4] -p(k,m)|f(k)=k|f(k)=m|f(k)=b. 567 [para_into,457.2.1,3.3.1,flip.2] -p(k,m)|k!=b|f(k)=k|f(k)=m| -p(f(k),k). 1242 [437,split_neg.2.2.2.1.1.1.2] -p(m,m). 1243 [437,split.2.2.2.1.1.1.2] p(k,m). 1260 [back_unit_del,1243.1,567.1] k!=b|f(k)=k|f(k)=m| -p(f(k),k). 1284 [back_unit_del,1243.1,531.1] f(k)=k|f(k)=m|f(k)=b. 1285 [back_unit_del,1243.1,458.1] f(k)!=m. 1286 [back_unit_del,1243.1,457.1] f(k)!=k. 1289 [back_unit_del,1243.1,447.3] k=b|m=k. 1291,1290 [back_unit_del,1285.1,1284.2,unit_del,1286] f(k)=b. 1292 [back_unit_del,1286.1,1260.2,demod,1291,1291,unit_del,16,130] k!=b. 1295,1294 [back_unit_del,1292.1,1289.1] m=k. 1304 [back_demod,1243,demod,1295] p(k,k). 1305 [back_demod,1242,demod,1295,1295] -p(k,k). 1306 [binary,1305.1,1304.1] $F. ------------ end of proof ------------- ------- statistics (process 8822) ------- clauses given 87 clauses generated 7119 clauses kept 1301 clauses forward subsumed 5650 clauses back subsumed 878 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8822 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.1.2]. --- refuted case [2.2.2.1.1.1.3] Case [2.2.2.1.1.1.3] (process 8823): Assumption: 1244 [437,split.2.2.2.1.1.1.3] k=b. ----> UNIT CONFLICT at 0.00 sec ----> 1250 [binary,1249.1,465.1] $F. Length of proof is 21. Level of proof is 8. Case [2.2.2.1.1.1.3] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 180 [19,split_neg.2.2.2] -p(m,b). 185 [para_into,180.1.1,12.1.1] -p(k,b)|p(m,k). 270 [para_into,185.2.2,1.4.1,flip.5] -p(k,b)|p(m,x)|x=m|p(x,m)|m=k| -p(x,k)| -p(k,x). 272 [para_into,185.2.2,1.1.1] -p(k,b)|p(m,m)|p(k,m)|x=m|x=k| -p(k,x)| -p(x,k). 273 [factor,270.1.7,unit_del,180,16,130] -p(k,b)|p(b,m)|m=k. 274 [factor,272.1.6,unit_del,16,130,flip.4] -p(k,b)|p(m,m)|p(k,m)|k=b. 435 [135,split.2.2.2.1] p(k,b). 437 [back_unit_del,435.1,274.1] p(m,m)|p(k,m)|k=b. 438 [back_unit_del,435.1,273.1] p(b,m)|m=k. 465 [438,split.2.2.2.1.1] p(b,m). 1243 [437,split_neg.2.2.2.1.1.1.3] -p(k,m). 1245,1244 [437,split.2.2.2.1.1.1.3] k=b. 1249 [back_demod,1243,demod,1245] -p(b,m). 1250 [binary,1249.1,465.1] $F. ------------ end of proof ------------- ------- statistics (process 8823) ------- clauses given 87 clauses generated 7004 clauses kept 1246 clauses forward subsumed 5554 clauses back subsumed 860 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8823 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.1.3]. ------- statistics (process 8818) ------- clauses given 87 clauses generated 7000 clauses kept 1239 clauses forward subsumed 5553 clauses back subsumed 814 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8818 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.1]. --- refuted case [2.2.2.1.1.2] Case [2.2.2.1.1.2] (process 8824): Assumption: 1215 [1175,split.2.2.2.1.1.2] p(j,g(j)). 0 [back_unit_del,1214.1,1174.1] g(j)!=j. 0 [back_unit_del,1214.1,1173.1] g(j)!=b. ----> UNIT CONFLICT at 0.01 sec ----> 1274 [binary,1273.1,1177.1] $F. Length of proof is 57. Level of proof is 16. Case [2.2.2.1.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 2 [] x=b| -p(x,b)|y=b|y=x| -p(x,y)| -p(y,x). 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 17 [] x=j| -p(x,j)|x=k. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 20 [binary,16.1,10.1] p(m,b)|p(m,g(m)). 21 [binary,16.1,9.1] p(m,b)|g(m)!=m. 22 [binary,16.1,8.1] p(m,b)|g(m)!=b. 26 [18,split_neg.2] k!=j. 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 149 [para_into,129.1.2,7.1.1] -p(b,m)| -p(j,m)|p(f(j),j). 154 [para_into,129.1.2,3.2.1,unit_del,26] -p(b,m)|j=b| -p(j,k). 180 [19,split_neg.2.2.2] -p(m,b). 181 [19,split.2.2.2] p(g(m),m). 182 [back_unit_del,180.1,22.1] g(m)!=b. 183 [back_unit_del,180.1,21.1] g(m)!=m. 184 [back_unit_del,180.1,20.1] p(m,g(m)). 185 [para_into,180.1.1,12.1.1] -p(k,b)|p(m,k). 198 [binary,181.1,2.5,unit_del,182,16,183,184] -p(g(m),b). 229 [para_into,198.1.2,7.1.1,unit_del,181] -p(b,m)|p(f(b),b). 230 [para_into,198.1.2,6.1.1,unit_del,181] -p(b,m)|p(b,f(b)). 231 [para_into,198.1.2,5.1.1,unit_del,181] -p(b,m)|f(b)!=b. 232 [para_into,198.1.2,4.1.1,unit_del,181] -p(b,m)|f(b)!=m. 270 [para_into,185.2.2,1.4.1,flip.5] -p(k,b)|p(m,x)|x=m|p(x,m)|m=k| -p(x,k)| -p(k,x). 273 [factor,270.1.7,unit_del,180,16,130] -p(k,b)|p(b,m)|m=k. 435 [135,split.2.2.2.1] p(k,b). 438 [back_unit_del,435.1,273.1] p(b,m)|m=k. 449 [back_unit_del,435.1,185.1] p(m,k). 465 [438,split.2.2.2.1.1] p(b,m). 466 [back_unit_del,465.1,232.1] f(b)!=m. 467 [back_unit_del,465.1,231.1] f(b)!=b. 468 [back_unit_del,465.1,230.1] p(b,f(b)). 469 [back_unit_del,465.1,229.1] p(f(b),b). 472 [back_unit_del,465.1,154.1] j=b| -p(j,k). 476 [back_unit_del,465.1,149.1] -p(j,m)|p(f(j),j). 491 [binary,468.1,1.6,unit_del,466,16,467,469] p(f(b),m). 499 [binary,491.1,2.5,unit_del,467,469,16,466] -p(m,f(b)). 682 [para_into,476.1.1,472.1.1,unit_del,465] p(f(j),j)| -p(j,k). 767 [para_into,682.1.1.1,472.1.1,factor_simp] p(f(b),j)| -p(j,k). 822 [para_into,767.2.1,11.1.1,unit_del,130] p(f(b),j)|p(j,b)|p(g(j),j). 823 [para_into,767.2.1,10.1.1,unit_del,130] p(f(b),j)|p(j,b)|p(j,g(j)). 824 [para_into,767.2.1,9.1.1,unit_del,130] p(f(b),j)|p(j,b)|g(j)!=j. 1033 [para_from,17.1.1,468.1.2,unit_del,129] -p(f(b),j)|f(b)=k. 1167 [para_from,1033.2.1,499.1.2,unit_del,449] -p(f(b),j). 1174 [back_unit_del,1167.1,824.1] p(j,b)|g(j)!=j. 1175 [back_unit_del,1167.1,823.1] p(j,b)|p(j,g(j)). 1176 [back_unit_del,1167.1,822.1] p(j,b)|p(g(j),j). 1177 [back_unit_del,1167.1,767.1] -p(j,k). 1200 [binary,1174.2,17.1] p(j,b)| -p(g(j),j)|g(j)=k. 1214 [1175,split_neg.2.2.2.1.1.2] -p(j,b). 1215 [1175,split.2.2.2.1.1.2] p(j,g(j)). 1228 [back_unit_del,1214.1,1200.1] -p(g(j),j)|g(j)=k. 1241 [back_unit_del,1214.1,1176.1] p(g(j),j). 1248,1247 [back_unit_del,1241.1,1228.1] g(j)=k. 1273 [back_demod,1215,demod,1248] p(j,k). 1274 [binary,1273.1,1177.1] $F. ------------ end of proof ------------- ------- statistics (process 8824) ------- clauses given 83 clauses generated 6824 clauses kept 1270 clauses forward subsumed 5378 clauses back subsumed 779 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8824 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1.2]. ------- statistics (process 8817) ------- clauses given 83 clauses generated 6747 clauses kept 1211 clauses forward subsumed 5334 clauses back subsumed 726 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.36 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8817 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.1]. --- refuted case [2.2.2.1.2] Case [2.2.2.1.2] (process 8825): Assumption: 466 [438,split.2.2.2.1.2] m=k. ----> UNIT CONFLICT at 0.00 sec ----> 475 [binary,474.1,472.1] $F. Length of proof is 23. Level of proof is 9. Case [2.2.2.1.2] ---------------- PROOF ---------------- 1 [] x=m|p(x,m)|y=m|y=x| -p(x,y)| -p(y,x). 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 12 [] m=k|p(m,k). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 16 [] m!=b. 18 [] k=j|p(k,j). 19 [binary,16.1,11.1] p(m,b)|p(g(m),m). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 129 [47,split_neg.2.2] -p(b,j). 130 [47,split.2.2] p(b,k). 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 177 [para_into,130.1.2,1.3.1] p(b,m)|x=m|p(x,m)|k=x| -p(x,k)| -p(k,x). 179 [factor,177.1.3,unit_del,16,130] p(b,m)|k=b| -p(k,b). 180 [19,split_neg.2.2.2] -p(m,b). 185 [para_into,180.1.1,12.1.1] -p(k,b)|p(m,k). 270 [para_into,185.2.2,1.4.1,flip.5] -p(k,b)|p(m,x)|x=m|p(x,m)|m=k| -p(x,k)| -p(k,x). 273 [factor,270.1.7,unit_del,180,16,130] -p(k,b)|p(b,m)|m=k. 435 [135,split.2.2.2.1] p(k,b). 438 [back_unit_del,435.1,273.1] p(b,m)|m=k. 449 [back_unit_del,435.1,185.1] p(m,k). 450 [back_unit_del,435.1,179.3] p(b,m)|k=b. 465 [438,split_neg.2.2.2.1.2] -p(b,m). 467,466 [438,split.2.2.2.1.2] m=k. 469,468 [back_unit_del,465.1,450.1] k=b. 472 [back_demod,465,demod,467,469] -p(b,b). 474 [back_demod,449,demod,467,469,469] p(b,b). 475 [binary,474.1,472.1] $F. ------------ end of proof ------------- ------- statistics (process 8825) ------- clauses given 35 clauses generated 2080 clauses kept 471 clauses forward subsumed 1549 clauses back subsumed 313 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8825 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1.2]. ------- statistics (process 8816) ------- clauses given 35 clauses generated 2077 clauses kept 463 clauses forward subsumed 1541 clauses back subsumed 302 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8816 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.1]. --- refuted case [2.2.2.2] Case [2.2.2.2] (process 8826): Assumption: 436 [135,split.2.2.2.2] p(k,g(k)). 0 [back_unit_del,435.1,134.1] g(k)!=k. 0 [back_unit_del,435.1,133.1] g(k)!=b. 0 [back_unit_del,481.1,12.1] p(m,k). ----> UNIT CONFLICT at 0.01 sec ----> 528 [binary,527.1,435.1] $F. Length of proof is 27. Level of proof is 11. Case [2.2.2.2] ---------------- PROOF ---------------- 3 [] x=k|x=m|x=b| -p(x,k). 4 [] x=m| -p(x,m)|f(x)!=m. 5 [] x=m| -p(x,m)|f(x)!=x. 6 [] x=m| -p(x,m)|p(x,f(x)). 7 [] x=m| -p(x,m)|p(f(x),x). 8 [] x=b|p(x,b)|g(x)!=b. 9 [] x=b|p(x,b)|g(x)!=x. 10 [] x=b|p(x,b)|p(x,g(x)). 11 [] x=b|p(x,b)|p(g(x),x). 13 [] b=k|p(b,k). 14 [copy,13,flip.1] k=b|p(b,k). 18 [] k=j|p(k,j). 27 [18,split.2] p(k,j). 47 [para_into,27.1.1,14.1.1] p(b,j)|p(b,k). 48 [para_into,27.1.1,11.1.1] p(b,j)|p(k,b)|p(g(k),k). 49 [para_into,27.1.1,10.1.1] p(b,j)|p(k,b)|p(k,g(k)). 50 [para_into,27.1.1,9.1.1] p(b,j)|p(k,b)|g(k)!=k. 51 [para_into,27.1.1,8.1.1] p(b,j)|p(k,b)|g(k)!=b. 129 [47,split_neg.2.2] -p(b,j). 133 [back_unit_del,129.1,51.1] p(k,b)|g(k)!=b. 134 [back_unit_del,129.1,50.1] p(k,b)|g(k)!=k. 135 [back_unit_del,129.1,49.1] p(k,b)|p(k,g(k)). 136 [back_unit_del,129.1,48.1] p(k,b)|p(g(k),k). 388 [binary,133.2,3.3] p(k,b)|g(k)=k|g(k)=m| -p(g(k),k). 435 [135,split_neg.2.2.2.2] -p(k,b). 436 [135,split.2.2.2.2] p(k,g(k)). 462 [back_unit_del,435.1,388.1] g(k)=k|g(k)=m| -p(g(k),k). 467 [back_unit_del,435.1,136.1] p(g(k),k). 468 [back_unit_del,435.1,134.1] g(k)!=k. 479,478 [back_unit_del,467.1,462.3,unit_del,468] g(k)=m. 481 [back_demod,468,demod,479] m!=k. 483 [back_demod,436,demod,479] p(k,m). 519 [binary,483.1,7.2,unit_del,481] p(f(k),k). 520 [binary,483.1,6.2,unit_del,481] p(k,f(k)). 521 [binary,483.1,5.2,unit_del,481] f(k)!=k. 522 [binary,483.1,4.2,unit_del,481] f(k)!=m. 525,524 [binary,519.1,3.4,unit_del,521,522] f(k)=b. 527 [back_demod,520,demod,525] p(k,b). 528 [binary,527.1,435.1] $F. ------------ end of proof ------------- ------- statistics (process 8826) ------- clauses given 38 clauses generated 2252 clauses kept 524 clauses forward subsumed 1697 clauses back subsumed 320 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8826 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2.2]. ------- statistics (process 8815) ------- clauses given 32 clauses generated 1952 clauses kept 433 clauses forward subsumed 1448 clauses back subsumed 126 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8815 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2.2]. ------- statistics (process 8803) ------- clauses given 10 clauses generated 389 clauses kept 178 clauses forward subsumed 212 clauses back subsumed 59 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8803 finished Mon Aug 2 15:31:11 2004 Refuted case [2.2]. ------- statistics (process 8786) ------- clauses given 7 clauses generated 284 clauses kept 127 clauses forward subsumed 156 clauses back subsumed 1 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8786 finished Mon Aug 2 15:31:11 2004 Refuted case [2].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8782) ------- clauses given 2 clauses generated 40 clauses kept 24 clauses forward subsumed 29 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8782 finished Mon Aug 2 15:31:11 2004 otter-3.3f/examples/split/group2.in0100644000076400007640000000116706472067425016741 0ustar mccunemccune% A group with at most 2 elemets must be commutative. set(knuth_bendix). set(hyper_res). set(split_when_given). set(split_pos). assign(pick_given_ratio, 4). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level, 1). list(usable). x=x. end_of_list. list(sos). % group axioms e * x = x. x * e = x. i(x) * x = e. x * i(x) = e. (x * y) * z = x * (y * z). i(e) = e. i(i(x)) = x. i(x * y) = i(y) * i(x). i(x) * (x * y) = y. x * (i(x) * y) = y. % There are at most 2 elements x = a1 | x = a2. % Denial of commutativity. c * b != b * c. end_of_list. otter-3.3f/examples/split/power.out0100664000076400007640000002376010103522216017041 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:09 2004 The command was "../../bin/otter". The process ID is 8775. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(ur_res). set(order_eq). set(split_when_given). dependent: set(back_unit_deletion). set(split_pos). assign(pick_given_ratio,4). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level,1). list(usable). 1 [] -EL(z,inter(x,y))|EL(z,x). 2 [] -EL(z,inter(x,y))|EL(z,y). 3 [] EL(z,inter(x,y))| -EL(z,x)| -EL(z,y). 4 [] -SUBSET(x,y)| -EL(z,x)|EL(z,y). 5 [] SUBSET(x,y)|EL(f17(x,y),x). 6 [] SUBSET(x,y)| -EL(f17(x,y),y). 7 [] -EL(z,pset(x))|SUBSET(z,x). 8 [] EL(z,pset(x))| -SUBSET(z,x). 9 [] x=y| -SUBSET(x,y)| -SUBSET(y,x). 10 [] x!=y|SUBSET(x,y). 11 [] x=x. 12 [] SUBSET(x,x). 13 [] EL(x,pset(x)). 14 [] -SUBSET(u,inter(x,y))|SUBSET(u,x). 15 [] -SUBSET(u,inter(x,y))|SUBSET(u,y). 16 [] SUBSET(u,inter(x,y))| -SUBSET(u,x)| -SUBSET(u,y). end_of_list. list(sos). 17 [] pset(inter(A,B))!=inter(pset(A),pset(B)). end_of_list. ======= end of input processing ======= =========== start of search =========== Splitting on clause 126 [binary,25.1,5.1] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(pset(A),pset(B))). --- refuted case [1] Case [1] (process 8776): Assumption: 1869 [126,split.1] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). ----> UNIT CONFLICT at 0.08 sec ----> 2034 [binary,2033.1,1992.1] $F. Length of proof is 24. Level of proof is 11. Case [1] ---------------- PROOF ---------------- 1 [] -EL(z,inter(x,y))|EL(z,x). 2 [] -EL(z,inter(x,y))|EL(z,y). 3 [] EL(z,inter(x,y))| -EL(z,x)| -EL(z,y). 5 [] SUBSET(x,y)|EL(f17(x,y),x). 6 [] SUBSET(x,y)| -EL(f17(x,y),y). 7 [] -EL(z,pset(x))|SUBSET(z,x). 8 [] EL(z,pset(x))| -SUBSET(z,x). 9 [] x=y| -SUBSET(x,y)| -SUBSET(y,x). 14 [] -SUBSET(u,inter(x,y))|SUBSET(u,x). 15 [] -SUBSET(u,inter(x,y))|SUBSET(u,y). 16 [] SUBSET(u,inter(x,y))| -SUBSET(u,x)| -SUBSET(u,y). 17 [] pset(inter(A,B))!=inter(pset(A),pset(B)). 18 [binary,17.1,9.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -SUBSET(inter(pset(A),pset(B)),pset(inter(A,B))). 25 [binary,18.1,5.1] -SUBSET(inter(pset(A),pset(B)),pset(inter(A,B)))|EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 30 [binary,18.2,6.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(inter(A,B))). 31 [binary,18.2,5.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(pset(A),pset(B))). 126 [binary,25.1,5.1] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(pset(A),pset(B))). 159 [binary,30.2,8.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(A,B)). 192 [binary,31.2,2.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(B)). 193 [binary,31.2,1.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(A)). 264 [binary,192.2,7.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B). 272 [binary,264.1,6.1] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B)| -EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),inter(pset(A),pset(B))). 311 [binary,193.2,7.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A). 319 [binary,311.1,6.1] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A)| -EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),inter(pset(A),pset(B))). 1049 [binary,159.2,16.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A)| -SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B). 1869 [126,split.1] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 1870 [binary,1869.1,7.1] SUBSET(f17(pset(inter(A,B)),inter(pset(A),pset(B))),inter(A,B)). 1879 [binary,1870.1,15.1] SUBSET(f17(pset(inter(A,B)),inter(pset(A),pset(B))),B). 1880 [binary,1870.1,14.1] SUBSET(f17(pset(inter(A,B)),inter(pset(A),pset(B))),A). 1889 [binary,1879.1,8.2] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(B)). 1926 [binary,1880.1,8.2] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(A)). 1992 [ur,1926,3,1889] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),inter(pset(A),pset(B))). 2003 [back_unit_del,1992.1,319.2] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A). 2005 [back_unit_del,1992.1,272.2] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B). 2007 [back_unit_del,2003.1,1049.2,unit_del,2005] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B))). 2033 [binary,2007.1,6.1] -EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),inter(pset(A),pset(B))). 2034 [binary,2033.1,1992.1] $F. ------------ end of proof ------------- ------- statistics (process 8776) ------- clauses given 297 clauses generated 3120 clauses kept 2016 clauses forward subsumed 1103 clauses back subsumed 1797 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.08 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8776 finished Mon Aug 2 15:31:09 2004 Refuted case [1]. --- refuted case [2] Case [2] (process 8777): Assumption: 1870 [126,split.2] EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(pset(A),pset(B))). 0 [back_unit_del,1869.1,125.1] -EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(inter(A,B))). 0 [back_unit_del,1869.1,102.2] -SUBSET(inter(pset(A),pset(B)),inter(pset(inter(A,B)),v65472)). 0 [back_unit_del,1869.1,88.2] -SUBSET(inter(pset(A),pset(B)),inter(v65472,pset(inter(A,B)))). 0 [back_unit_del,1869.1,63.2] -EL(inter(pset(A),pset(B)),pset(pset(inter(A,B)))). 0 [back_unit_del,1869.1,25.2] -SUBSET(inter(pset(A),pset(B)),pset(inter(A,B))). ----> UNIT CONFLICT at 0.06 sec ----> 1912 [binary,1911.1,1869.1] $F. Length of proof is 18. Level of proof is 8. Case [2] ---------------- PROOF ---------------- 1 [] -EL(z,inter(x,y))|EL(z,x). 2 [] -EL(z,inter(x,y))|EL(z,y). 5 [] SUBSET(x,y)|EL(f17(x,y),x). 6 [] SUBSET(x,y)| -EL(f17(x,y),y). 7 [] -EL(z,pset(x))|SUBSET(z,x). 8 [] EL(z,pset(x))| -SUBSET(z,x). 9 [] x=y| -SUBSET(x,y)| -SUBSET(y,x). 16 [] SUBSET(u,inter(x,y))| -SUBSET(u,x)| -SUBSET(u,y). 17 [] pset(inter(A,B))!=inter(pset(A),pset(B)). 18 [binary,17.1,9.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -SUBSET(inter(pset(A),pset(B)),pset(inter(A,B))). 25 [binary,18.1,5.1] -SUBSET(inter(pset(A),pset(B)),pset(inter(A,B)))|EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 30 [binary,18.2,6.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(inter(A,B))). 31 [binary,18.2,5.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(pset(A),pset(B))). 126 [binary,25.1,5.1] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(pset(A),pset(B))). 159 [binary,30.2,8.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),inter(A,B)). 192 [binary,31.2,2.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(B)). 193 [binary,31.2,1.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|EL(f17(inter(pset(A),pset(B)),pset(inter(A,B))),pset(A)). 264 [binary,192.2,7.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B). 273 [binary,264.1,5.1] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B)|EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 311 [binary,193.2,7.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))|SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A). 320 [binary,311.1,5.1] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A)|EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 1049 [binary,159.2,16.1] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B)))| -SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A)| -SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B). 1869 [126,split_neg.2] -EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 1890 [back_unit_del,1869.1,320.2] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),A). 1892 [back_unit_del,1869.1,273.2] SUBSET(f17(inter(pset(A),pset(B)),pset(inter(A,B))),B). 1905 [back_unit_del,1890.1,1049.2,unit_del,1892] -SUBSET(pset(inter(A,B)),inter(pset(A),pset(B))). 1911 [binary,1905.1,5.1] EL(f17(pset(inter(A,B)),inter(pset(A),pset(B))),pset(inter(A,B))). 1912 [binary,1911.1,1869.1] $F. ------------ end of proof ------------- ------- statistics (process 8777) ------- clauses given 277 clauses generated 2897 clauses kept 1894 clauses forward subsumed 1004 clauses back subsumed 1698 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.06 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8777 finished Mon Aug 2 15:31:10 2004 Refuted case [2].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8775) ------- clauses given 276 clauses generated 2854 clauses kept 1851 clauses forward subsumed 1002 clauses back subsumed 29 Kbytes malloced 3906 ----------- times (seconds) ----------- user CPU time 0.29 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8775 finished Mon Aug 2 15:31:10 2004 otter-3.3f/examples/split/GEO036-2.out0100664000076400007640000004376210103522213016710 0ustar mccunemccune WARNING, with splitting, max_seconds is checked against the wall clock. ----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:07 2004 The command was "../../bin/otter". The process ID is 8636. set(prolog_style_variables). set(auto2). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 20000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(tptp_eq). set(split_when_given). dependent: set(back_unit_deletion). dependent: set(unit_deletion). set(split_pos). list(usable). 0 [] equal(A,A). 0 [] equidistant(A,B,B,A). 0 [] -equidistant(A,B,C,D)| -equidistant(A,B,E,F)|equidistant(C,D,E,F). 0 [] -equidistant(A,B,C,C)|equal(A,B). 0 [] between(A,B,extension(A,B,C,D)). 0 [] equidistant(A,extension(B,A,C,D),C,D). 0 [] -equidistant(A,B,C,D)| -equidistant(B,E,D,F)| -equidistant(A,G,C,H)| -equidistant(B,G,D,H)| -between(A,B,E)| -between(C,D,F)|equal(A,B)|equidistant(E,G,F,H). 0 [] -between(A,B,A)|equal(A,B). 0 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). 0 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). 0 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). 0 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). 0 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). 0 [] -equidistant(A,B,A,C)| -equidistant(D,B,D,C)| -equidistant(E,B,E,C)|between(A,D,E)|between(D,E,A)|between(E,A,D)|equal(B,C). 0 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,D,euclid1(A,D,B,E,C)). 0 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,E,euclid2(A,D,B,E,C)). 0 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)). 0 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|between(C,continuous(A,B,C,F,D,E),E). 0 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|equidistant(A,F,A,continuous(A,B,C,F,D,E)). end_of_list. list(sos). 0 [] equal(lower_dimension_point_1,lower_dimension_point_2)|equal(lower_dimension_point_2,lower_dimension_point_3)|equal(lower_dimension_point_1,lower_dimension_point_3). end_of_list. Every positive clause in sos is ground (or sos is empty); therefore we move all positive usable clauses to sos. Properties of input clauses: prop=0, horn=0, equality=1, symmetry=0, max_lits=8. Setting hyper_res, because there are nonunits. dependent: set(hyper_res). Setting ur_res, because this is a nonunit set containing either equality literals or non-Horn clauses. dependent: set(ur_res). Setting factor and unit_deletion, because there are non-Horn clauses. dependent: set(factor). Equality is present, so we set the knuth_bendix flag. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). As an incomplete heuristic, we paramodulate with units only. dependent: set(para_from_units_only). dependent: set(para_into_units_only). ------------> process usable: ** KEPT (pick-wt=15): 1 [] -equidistant(A,B,C,D)| -equidistant(A,B,E,F)|equidistant(C,D,E,F). ** KEPT (pick-wt=8): 2 [] -equidistant(A,B,C,C)|equal(A,B). ** KEPT (pick-wt=36): 3 [] -equidistant(A,B,C,D)| -equidistant(B,E,D,F)| -equidistant(A,G,C,H)| -equidistant(B,G,D,H)| -between(A,B,E)| -between(C,D,F)|equal(A,B)|equidistant(E,G,F,H). ** KEPT (pick-wt=7): 4 [] -between(A,B,A)|equal(A,B). ** KEPT (pick-wt=17): 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). ** KEPT (pick-wt=17): 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). ** KEPT (pick-wt=4): 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). ** KEPT (pick-wt=4): 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). ** KEPT (pick-wt=4): 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). ** KEPT (pick-wt=30): 10 [] -equidistant(A,B,A,C)| -equidistant(D,B,D,C)| -equidistant(E,B,E,C)|between(A,D,E)|between(D,E,A)|between(E,A,D)|equal(B,C). ** KEPT (pick-wt=20): 11 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,D,euclid1(A,D,B,E,C)). ** KEPT (pick-wt=20): 12 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,E,euclid2(A,D,B,E,C)). ** KEPT (pick-wt=25): 13 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)). ** KEPT (pick-wt=28): 14 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|between(C,continuous(A,B,C,F,D,E),E). ** KEPT (pick-wt=29): 15 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|equidistant(A,F,A,continuous(A,B,C,F,D,E)). >>>> Starting back unit deletion with 7. >>>> Starting back unit deletion with 8. >>>> Starting back unit deletion with 9. ------------> process sos: ** KEPT (pick-wt=9): 35 [copy,34,flip.1,flip.2,flip.3] equal(lower_dimension_point_2,lower_dimension_point_1)|equal(lower_dimension_point_3,lower_dimension_point_2)|equal(lower_dimension_point_3,lower_dimension_point_1). ** KEPT (pick-wt=3): 36 [] equal(A,A). ** KEPT (pick-wt=5): 37 [] equidistant(A,B,B,A). ** KEPT (pick-wt=8): 38 [] between(A,B,extension(A,B,C,D)). ** KEPT (pick-wt=9): 39 [] equidistant(A,extension(B,A,C,D),C,D). Following clause subsumed by 36 during input processing: 0 [copy,36,flip.1] equal(A,A). >>>> Starting back unit deletion with 36. 37 back subsumes 31. >>>> Starting back unit deletion with 37. 0 [back_unit_del,37.1,30.3] -equidistant(E2518,F2518,E2518,F2518)| -equidistant(F2518,G2518,F2518,G2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,F2518,G2518,F2518). ** KEPT (pick-wt=22): 40 [back_unit_del,37.1,30.3] -equidistant(A,B,A,B)| -equidistant(B,C,B,C)| -between(A,B,C)|equal(A,B)|equidistant(C,B,C,B). >>>> Starting back unit deletion with 38. >>>> Starting back unit deletion with 39. 40 back subsumes 30. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=9) 35 [copy,34,flip.1,flip.2,flip.3] equal(lower_dimension_point_2,lower_dimension_point_1)|equal(lower_dimension_point_3,lower_dimension_point_2)|equal(lower_dimension_point_3,lower_dimension_point_1). Splitting on clause 35 [copy,34,flip.1,flip.2,flip.3] equal(lower_dimension_point_2,lower_dimension_point_1)|equal(lower_dimension_point_3,lower_dimension_point_2)|equal(lower_dimension_point_3,lower_dimension_point_1). Case [1] (process 8637): Assumption: 41 [35,split.1] equal(lower_dimension_point_2,lower_dimension_point_1). given clause #2: (wt=3) 36 [] equal(A,A). given clause #3: (wt=3) 41 [35,split.1] equal(lower_dimension_point_2,lower_dimension_point_1). given clause #4: (wt=4) 43 [back_demod,9,demod,42] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1). given clause #5: (wt=4) 44 [back_demod,8,demod,42] -between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1). given clause #6: (wt=5) 37 [] equidistant(A,B,B,A). 0 [back_unit_del,46.1,19.2] -equidistant(E2518,F2518,E2518,F2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). 0 [back_unit_del,46.1,19.1] -equidistant(F2518,G2518,F2518,G2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). given clause #7: (wt=4) 45 [back_demod,7,demod,42] -between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3). given clause #8: (wt=5) 46 [hyper,37,16] equidistant(A,B,A,B). given clause #9: (wt=8) 38 [] between(A,B,extension(A,B,C,D)). given clause #10: (wt=9) 39 [] equidistant(A,extension(B,A,C,D),C,D). given clause #11: (wt=19) 48 [hyper,38,29,46,46] equidistant(A,A,A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C))). given clause #12: (wt=7) 62 [hyper,39,2,flip.1] equal(extension(A,B,C,C),B). --- refuted case [1] ----> UNIT CONFLICT at 0.03 sec ----> 77 [binary,76.1,43.1] $F. Length of proof is 5. Level of proof is 3. Case [1] ---------------- PROOF ---------------- 2 [] -equidistant(A,B,C,C)|equal(A,B). 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). 34 [] equal(lower_dimension_point_1,lower_dimension_point_2)|equal(lower_dimension_point_2,lower_dimension_point_3)|equal(lower_dimension_point_1,lower_dimension_point_3). 35 [copy,34,flip.1,flip.2,flip.3] equal(lower_dimension_point_2,lower_dimension_point_1)|equal(lower_dimension_point_3,lower_dimension_point_2)|equal(lower_dimension_point_3,lower_dimension_point_1). 38 [] between(A,B,extension(A,B,C,D)). 39 [] equidistant(A,extension(B,A,C,D),C,D). 42,41 [35,split.1] equal(lower_dimension_point_2,lower_dimension_point_1). 43 [back_demod,9,demod,42] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1). 62 [hyper,39,2,flip.1] equal(extension(A,B,C,C),B). 76 [para_from,62.1.1,38.1.3] between(A,B,B). 77 [binary,76.1,43.1] $F. ------------ end of proof ------------- ------- statistics (process 8637) ------- clauses given 12 clauses generated 321 clauses kept 73 clauses forward subsumed 263 clauses back subsumed 9 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8637 finished Mon Aug 2 15:31:07 2004 Refuted case [1]. Case [2] (process 8638): Assumption: 42 [35,split.2] equal(lower_dimension_point_3,lower_dimension_point_2). given clause #2: (wt=3) 36 [] equal(A,A). given clause #3: (wt=3) 41 [35,split_neg.2] -equal(lower_dimension_point_2,lower_dimension_point_1). given clause #4: (wt=3) 42 [35,split.2] equal(lower_dimension_point_3,lower_dimension_point_2). given clause #5: (wt=4) 44 [back_demod,9,demod,43] -between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_2). given clause #6: (wt=5) 37 [] equidistant(A,B,B,A). 0 [back_unit_del,48.1,19.2] -equidistant(E2518,F2518,E2518,F2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). 0 [back_unit_del,48.1,19.1] -equidistant(F2518,G2518,F2518,G2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). given clause #7: (wt=4) 45 [back_demod,8,demod,43] -between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1). given clause #8: (wt=4) 46 [back_demod,7,demod,43] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2). given clause #9: (wt=5) 47 [ur,41,2] -equidistant(lower_dimension_point_2,lower_dimension_point_1,A,A). given clause #10: (wt=5) 48 [hyper,37,16] equidistant(A,B,A,B). given clause #11: (wt=8) 38 [] between(A,B,extension(A,B,C,D)). given clause #12: (wt=5) 50 [ur,47,1,37] -equidistant(A,A,lower_dimension_point_2,lower_dimension_point_1). given clause #13: (wt=5) 51 [ur,47,1,37] -equidistant(lower_dimension_point_1,lower_dimension_point_2,A,A). given clause #14: (wt=5) 67 [ur,51,1,48] -equidistant(A,A,lower_dimension_point_1,lower_dimension_point_2). given clause #15: (wt=9) 39 [] equidistant(A,extension(B,A,C,D),C,D). given clause #16: (wt=19) 52 [hyper,38,29,48,48] equidistant(A,A,A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C))). given clause #17: (wt=7) 73 [hyper,39,2,flip.1] equal(extension(A,B,C,C),B). --- refuted case [2] ----> UNIT CONFLICT at 0.03 sec ----> 92 [binary,91.1,46.1] $F. Length of proof is 5. Level of proof is 3. Case [2] ---------------- PROOF ---------------- 2 [] -equidistant(A,B,C,C)|equal(A,B). 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). 34 [] equal(lower_dimension_point_1,lower_dimension_point_2)|equal(lower_dimension_point_2,lower_dimension_point_3)|equal(lower_dimension_point_1,lower_dimension_point_3). 35 [copy,34,flip.1,flip.2,flip.3] equal(lower_dimension_point_2,lower_dimension_point_1)|equal(lower_dimension_point_3,lower_dimension_point_2)|equal(lower_dimension_point_3,lower_dimension_point_1). 38 [] between(A,B,extension(A,B,C,D)). 39 [] equidistant(A,extension(B,A,C,D),C,D). 43,42 [35,split.2] equal(lower_dimension_point_3,lower_dimension_point_2). 46 [back_demod,7,demod,43] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2). 73 [hyper,39,2,flip.1] equal(extension(A,B,C,C),B). 91 [para_from,73.1.1,38.1.3] between(A,B,B). 92 [binary,91.1,46.1] $F. ------------ end of proof ------------- ------- statistics (process 8638) ------- clauses given 17 clauses generated 376 clauses kept 88 clauses forward subsumed 304 clauses back subsumed 13 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8638 finished Mon Aug 2 15:31:07 2004 Refuted case [2]. Case [3] (process 8639): Assumption: 43 [35,split.3] equal(lower_dimension_point_3,lower_dimension_point_1). given clause #2: (wt=3) 36 [] equal(A,A). given clause #3: (wt=3) 41 [35,split_neg.3] -equal(lower_dimension_point_2,lower_dimension_point_1). given clause #4: (wt=3) 43 [35,split.3] equal(lower_dimension_point_3,lower_dimension_point_1). given clause #5: (wt=4) 45 [back_demod,9,demod,44] -between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2). given clause #6: (wt=5) 37 [] equidistant(A,B,B,A). 0 [back_unit_del,50.1,19.2] -equidistant(E2518,F2518,E2518,F2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). 0 [back_unit_del,50.1,19.1] -equidistant(F2518,G2518,F2518,G2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). given clause #7: (wt=4) 46 [back_demod,8,demod,44] -between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1). given clause #8: (wt=4) 47 [back_demod,7,demod,44] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1). given clause #9: (wt=4) 48 [ur,41,4] -between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_2). given clause #10: (wt=5) 49 [ur,41,2] -equidistant(lower_dimension_point_2,lower_dimension_point_1,A,A). given clause #11: (wt=8) 38 [] between(A,B,extension(A,B,C,D)). given clause #12: (wt=5) 50 [hyper,37,16] equidistant(A,B,A,B). given clause #13: (wt=5) 52 [ur,49,1,37] -equidistant(A,A,lower_dimension_point_2,lower_dimension_point_1). given clause #14: (wt=5) 53 [ur,49,1,37] -equidistant(lower_dimension_point_1,lower_dimension_point_2,A,A). given clause #15: (wt=5) 69 [ur,53,1,50] -equidistant(A,A,lower_dimension_point_1,lower_dimension_point_2). given clause #16: (wt=9) 39 [] equidistant(A,extension(B,A,C,D),C,D). given clause #17: (wt=7) 75 [hyper,39,2,flip.1] equal(extension(A,B,C,C),B). --- refuted case [3] ----> UNIT CONFLICT at 0.03 sec ----> 86 [binary,85.1,46.1] $F. Length of proof is 5. Level of proof is 3. Case [3] ---------------- PROOF ---------------- 2 [] -equidistant(A,B,C,C)|equal(A,B). 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). 34 [] equal(lower_dimension_point_1,lower_dimension_point_2)|equal(lower_dimension_point_2,lower_dimension_point_3)|equal(lower_dimension_point_1,lower_dimension_point_3). 35 [copy,34,flip.1,flip.2,flip.3] equal(lower_dimension_point_2,lower_dimension_point_1)|equal(lower_dimension_point_3,lower_dimension_point_2)|equal(lower_dimension_point_3,lower_dimension_point_1). 38 [] between(A,B,extension(A,B,C,D)). 39 [] equidistant(A,extension(B,A,C,D),C,D). 44,43 [35,split.3] equal(lower_dimension_point_3,lower_dimension_point_1). 46 [back_demod,8,demod,44] -between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1). 75 [hyper,39,2,flip.1] equal(extension(A,B,C,C),B). 85 [para_from,75.1.1,38.1.3] between(A,B,B). 86 [binary,85.1,46.1] $F. ------------ end of proof ------------- ------- statistics (process 8639) ------- clauses given 17 clauses generated 343 clauses kept 82 clauses forward subsumed 279 clauses back subsumed 13 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8639 finished Mon Aug 2 15:31:07 2004 Refuted case [3].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8636) ------- clauses given 1 clauses generated 53 clauses kept 39 clauses forward subsumed 25 clauses back subsumed 2 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8636 finished Mon Aug 2 15:31:07 2004 otter-3.3f/examples/split/zebra4.out0100664000076400007640000026314210103522221017070 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:11 2004 The command was "../../bin/otter". The process ID is 8846. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(split_when_given). dependent: set(back_unit_deletion). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level,1). assign(max_distinct_vars,0). list(usable). 0 [] x=x. 0 [] x=1|x=2|x=3|x=4|x=5. end_of_list. formula_list(usable). all x y z u v (distinct5(x,y,z,u,v)<->x!=y&x!=z&x!=u&x!=v&y!=z&y!=u&y!=v&z!=u&z!=v&u!=v). all x y (successor(x,y)<->x=1&y=2|x=2&y=3|x=3&y=4|x=4&y=5). all x y (next_to(x,y)<->successor(x,y)|successor(y,x)). end_of_list. -------> usable clausifies to: list(usable). 0 [] -distinct5(x,y,z,u,v)|x!=y. 0 [] -distinct5(x,y,z,u,v)|x!=z. 0 [] -distinct5(x,y,z,u,v)|x!=u. 0 [] -distinct5(x,y,z,u,v)|x!=v. 0 [] -distinct5(x,y,z,u,v)|y!=z. 0 [] -distinct5(x,y,z,u,v)|y!=u. 0 [] -distinct5(x,y,z,u,v)|y!=v. 0 [] -distinct5(x,y,z,u,v)|z!=u. 0 [] -distinct5(x,y,z,u,v)|z!=v. 0 [] -distinct5(x,y,z,u,v)|u!=v. 0 [] distinct5(x,y,z,u,v)|x=y|x=z|x=u|x=v|y=z|y=u|y=v|z=u|z=v|u=v. 0 [] -successor(x,y)|x=1|x=2|x=3|x=4. 0 [] -successor(x,y)|x=1|x=2|x=3|y=5. 0 [] -successor(x,y)|x=1|x=2|y=4|x=4. 0 [] -successor(x,y)|x=1|x=2|y=4|y=5. 0 [] -successor(x,y)|x=1|y=3|x=3|x=4. 0 [] -successor(x,y)|x=1|y=3|x=3|y=5. 0 [] -successor(x,y)|x=1|y=3|y=4|x=4. 0 [] -successor(x,y)|x=1|y=3|y=4|y=5. 0 [] -successor(x,y)|y=2|x=2|x=3|x=4. 0 [] -successor(x,y)|y=2|x=2|x=3|y=5. 0 [] -successor(x,y)|y=2|x=2|y=4|x=4. 0 [] -successor(x,y)|y=2|x=2|y=4|y=5. 0 [] -successor(x,y)|y=2|y=3|x=3|x=4. 0 [] -successor(x,y)|y=2|y=3|x=3|y=5. 0 [] -successor(x,y)|y=2|y=3|y=4|x=4. 0 [] -successor(x,y)|y=2|y=3|y=4|y=5. 0 [] successor(x,y)|x!=1|y!=2. 0 [] successor(x,y)|x!=2|y!=3. 0 [] successor(x,y)|x!=3|y!=4. 0 [] successor(x,y)|x!=4|y!=5. 0 [] -next_to(x,y)|successor(x,y)|successor(y,x). 0 [] next_to(x,y)| -successor(x,y). 0 [] next_to(x,y)| -successor(y,x). end_of_list. list(sos). 0 [] distinct5(1,2,3,4,5). 0 [] distinct5(red,green,ivory,ayellow,blue). 0 [] distinct5(eng,aspan,aukra,norw,japan). 0 [] distinct5(dog,asnail,fox,horse,azebra). 0 [] distinct5(coffee,atea,milk,orange,apple). 0 [] distinct5(old,kool,chest,lucky,parli). 0 [] eng=red. 0 [] aspan=dog. 0 [] coffee=green. 0 [] aukra=atea. 0 [] old=asnail. 0 [] kool=ayellow. 0 [] milk=3. 0 [] norw=1. 0 [] lucky=orange. 0 [] japan=parli. 0 [] blue=2. 0 [] successor(ivory,green). 0 [] next_to(kool,horse). 0 [] next_to(chest,fox). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=15): 2 [] x=1|x=2|x=3|x=4|x=5. ** KEPT (pick-wt=9): 3 [] -distinct5(x,y,z,u,v)|x!=y. ** KEPT (pick-wt=9): 4 [] -distinct5(x,y,z,u,v)|x!=z. ** KEPT (pick-wt=9): 5 [] -distinct5(x,y,z,u,v)|x!=u. ** KEPT (pick-wt=9): 6 [] -distinct5(x,y,z,u,v)|x!=v. ** KEPT (pick-wt=9): 7 [] -distinct5(x,y,z,u,v)|y!=z. ** KEPT (pick-wt=9): 8 [] -distinct5(x,y,z,u,v)|y!=u. ** KEPT (pick-wt=9): 9 [] -distinct5(x,y,z,u,v)|y!=v. ** KEPT (pick-wt=9): 10 [] -distinct5(x,y,z,u,v)|z!=u. ** KEPT (pick-wt=9): 11 [] -distinct5(x,y,z,u,v)|z!=v. ** KEPT (pick-wt=9): 12 [] -distinct5(x,y,z,u,v)|u!=v. ** KEPT (pick-wt=36): 13 [] distinct5(x,y,z,u,v)|x=y|x=z|x=u|x=v|y=z|y=u|y=v|z=u|z=v|u=v. ** KEPT (pick-wt=15): 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. ** KEPT (pick-wt=15): 15 [] -successor(x,y)|x=1|x=2|x=3|y=5. ** KEPT (pick-wt=15): 16 [] -successor(x,y)|x=1|x=2|y=4|x=4. ** KEPT (pick-wt=15): 17 [] -successor(x,y)|x=1|x=2|y=4|y=5. ** KEPT (pick-wt=15): 18 [] -successor(x,y)|x=1|y=3|x=3|x=4. ** KEPT (pick-wt=15): 19 [] -successor(x,y)|x=1|y=3|x=3|y=5. ** KEPT (pick-wt=15): 20 [] -successor(x,y)|x=1|y=3|y=4|x=4. ** KEPT (pick-wt=15): 21 [] -successor(x,y)|x=1|y=3|y=4|y=5. ** KEPT (pick-wt=15): 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. ** KEPT (pick-wt=15): 23 [] -successor(x,y)|y=2|x=2|x=3|y=5. ** KEPT (pick-wt=15): 24 [] -successor(x,y)|y=2|x=2|y=4|x=4. ** KEPT (pick-wt=15): 25 [] -successor(x,y)|y=2|x=2|y=4|y=5. ** KEPT (pick-wt=15): 26 [] -successor(x,y)|y=2|y=3|x=3|x=4. ** KEPT (pick-wt=15): 27 [] -successor(x,y)|y=2|y=3|x=3|y=5. ** KEPT (pick-wt=15): 28 [] -successor(x,y)|y=2|y=3|y=4|x=4. ** KEPT (pick-wt=15): 29 [] -successor(x,y)|y=2|y=3|y=4|y=5. ** KEPT (pick-wt=9): 30 [] successor(x,y)|x!=1|y!=2. ** KEPT (pick-wt=9): 31 [] successor(x,y)|x!=2|y!=3. ** KEPT (pick-wt=9): 32 [] successor(x,y)|x!=3|y!=4. ** KEPT (pick-wt=9): 33 [] successor(x,y)|x!=4|y!=5. ** KEPT (pick-wt=9): 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). ** KEPT (pick-wt=6): 35 [] next_to(x,y)| -successor(x,y). ** KEPT (pick-wt=6): 36 [] next_to(x,y)| -successor(y,x). Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back unit deletion with 1. ------------> process sos: ** KEPT (pick-wt=6): 37 [] distinct5(1,2,3,4,5). ** KEPT (pick-wt=6): 38 [] distinct5(red,green,ivory,ayellow,blue). ** KEPT (pick-wt=6): 39 [] distinct5(eng,aspan,aukra,norw,japan). ** KEPT (pick-wt=6): 40 [] distinct5(dog,asnail,fox,horse,azebra). ** KEPT (pick-wt=6): 41 [] distinct5(coffee,atea,milk,orange,apple). ** KEPT (pick-wt=6): 42 [] distinct5(old,kool,chest,lucky,parli). ** KEPT (pick-wt=3): 44 [copy,43,flip.1] red=eng. ---> New Demodulator: 45 [new_demod,44] red=eng. ** KEPT (pick-wt=3): 47 [copy,46,flip.1] dog=aspan. ---> New Demodulator: 48 [new_demod,47] dog=aspan. ** KEPT (pick-wt=3): 50 [copy,49,flip.1] green=coffee. ---> New Demodulator: 51 [new_demod,50] green=coffee. ** KEPT (pick-wt=3): 52 [] aukra=atea. ---> New Demodulator: 53 [new_demod,52] aukra=atea. ** KEPT (pick-wt=3): 54 [] old=asnail. ---> New Demodulator: 55 [new_demod,54] old=asnail. ** KEPT (pick-wt=3): 56 [] kool=ayellow. ---> New Demodulator: 57 [new_demod,56] kool=ayellow. ** KEPT (pick-wt=3): 58 [] milk=3. ---> New Demodulator: 59 [new_demod,58] milk=3. ** KEPT (pick-wt=3): 60 [] norw=1. ---> New Demodulator: 61 [new_demod,60] norw=1. ** KEPT (pick-wt=3): 63 [copy,62,flip.1] orange=lucky. ---> New Demodulator: 64 [new_demod,63] orange=lucky. ** KEPT (pick-wt=3): 66 [copy,65,flip.1] parli=japan. ---> New Demodulator: 67 [new_demod,66] parli=japan. ** KEPT (pick-wt=3): 68 [] blue=2. ---> New Demodulator: 69 [new_demod,68] blue=2. ** KEPT (pick-wt=3): 71 [copy,70,demod,51] successor(ivory,coffee). ** KEPT (pick-wt=3): 73 [copy,72,demod,57] next_to(ayellow,horse). ** KEPT (pick-wt=3): 74 [] next_to(chest,fox). >>>> Starting back unit deletion with 37. >>>> Starting back unit deletion with 38. >>>> Starting back unit deletion with 39. >>>> Starting back unit deletion with 40. >>>> Starting back unit deletion with 41. >>>> Starting back unit deletion with 42. >>>> Starting back demodulation with 45. >> back demodulating 38 with 45. >>>> Starting back unit deletion with 44. >>>> Starting back demodulation with 48. >> back demodulating 40 with 48. >>>> Starting back unit deletion with 47. >>>> Starting back demodulation with 51. >>>> Starting back unit deletion with 50. >>>> Starting back demodulation with 53. >> back demodulating 39 with 53. >>>> Starting back unit deletion with 52. >>>> Starting back demodulation with 55. >> back demodulating 42 with 55. >>>> Starting back unit deletion with 54. >>>> Starting back demodulation with 57. >>>> Starting back unit deletion with 56. >>>> Starting back demodulation with 59. >> back demodulating 41 with 59. >>>> Starting back unit deletion with 58. >>>> Starting back demodulation with 61. >>>> Starting back unit deletion with 60. >>>> Starting back demodulation with 64. >>>> Starting back unit deletion with 63. >>>> Starting back demodulation with 67. >>>> Starting back unit deletion with 66. >>>> Starting back demodulation with 69. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 71. >>>> Starting back unit deletion with 73. >>>> Starting back unit deletion with 74. >>>> Starting back unit deletion with 75. >>>> Starting back unit deletion with 76. >>>> Starting back unit deletion with 77. >>>> Starting back unit deletion with 78. >>>> Starting back unit deletion with 79. ======= end of input processing ======= =========== start of search =========== Splitting on clause 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). Case [1] (process 8847): Assumption: 532 [106,split.1] successor(ayellow,horse). Splitting on clause 117 [binary,74.1,34.1] successor(chest,fox)|successor(fox,chest). Case [1.1] (process 8848): Assumption: 562 [117,split.1.1] successor(chest,fox). Splitting on clause 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. Case [1.1.1] (process 8849): Assumption: 596 [181,split.1.1.1] ivory=3. Splitting on clause 717 [back_unit_del,672.1,364.4,unit_del,691] aspan=3|aspan=4. --- refuted case [1.1.1.1] Case [1.1.1.1] (process 8850): Assumption: 859 [717,split.1.1.1.1] aspan=3. ----> UNIT CONFLICT at 0.00 sec ----> 894 [binary,892.1,886.1] $F. Length of proof is 128. Level of proof is 14. Case [1.1.1.1] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 24 [] -successor(x,y)|y=2|x=2|y=4|x=4. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 87 [binary,71.1,24.1] coffee=2|ivory=2|coffee=4|ivory=4. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 146 [binary,37.1,10.1,flip.1] 4!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 152 [binary,37.1,4.1,flip.1] 3!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 158 [binary,75.1,8.1] coffee!=ayellow. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 183 [back_unit_del,155.1,87.2,unit_del,157] coffee=4|ivory=4. 207 [para_into,156.1.1,2.3.1,unit_del,155,flip.1] ayellow!=3|ivory=1|ivory=4|ivory=5. 209 [para_into,158.1.1,2.4.1,unit_del,157,flip.1] ayellow!=4|coffee=1|coffee=3|coffee=5. 213 [para_into,161.1.1,2.5.1,unit_del,160,flip.1] ayellow!=5|eng=1|eng=3|eng=4. 218 [para_into,162.1.1,2.3.1,unit_del,155,flip.1] eng!=3|ivory=1|ivory=4|ivory=5. 220 [para_into,163.1.1,2.4.1,unit_del,160,flip.1] coffee!=4|eng=1|eng=3|eng=5. 227 [binary,76.1,8.1,flip.1] horse!=asnail. 232 [binary,76.1,3.1] aspan!=asnail. 281 [para_into,227.1.1,2.2.1,flip.1] asnail!=2|horse=1|horse=3|horse=4|horse=5. 305 [para_into,232.1.1,2.3.1,flip.1] asnail!=3|aspan=1|aspan=2|aspan=4|aspan=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 311 [binary,77.1,9.1,flip.1] japan!=aspan. 312 [binary,77.1,8.1] aspan!=1. 313 [binary,77.1,7.1,flip.1] atea!=aspan. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 316 [binary,77.1,4.1] eng!=atea. 317 [binary,77.1,3.1] eng!=aspan. 319 [back_unit_del,312.1,305.2] asnail!=3|aspan=2|aspan=4|aspan=5. 327 [back_unit_del,315.1,220.2] coffee!=4|eng=3|eng=5. 331 [back_unit_del,315.1,213.2] ayellow!=5|eng=3|eng=4. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 362 [para_into,311.1.1,2.3.1,unit_del,308,flip.1] aspan!=3|japan=2|japan=4|japan=5. 364 [binary,312.1,2.1] aspan=2|aspan=3|aspan=4|aspan=5. 368 [para_into,313.1.1,2.2.1,unit_del,310,flip.1] aspan!=2|atea=3|atea=4|atea=5. 372 [para_into,316.1.1,2.5.1,unit_del,315,160,flip.1] atea!=5|eng=3|eng=4. 375 [para_into,317.1.1,2.5.1,unit_del,315,160,flip.1] aspan!=5|eng=3|eng=4. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 384 [binary,78.1,6.1,flip.1] japan!=asnail. 385 [binary,78.1,5.1,flip.1] lucky!=asnail. 387 [binary,78.1,3.1,flip.1] ayellow!=asnail. 430 [para_into,382.1.1,2.1.1,flip.1] ayellow!=1|lucky=2|lucky=3|lucky=4|lucky=5. 436 [para_into,384.1.1,2.4.1,unit_del,308,flip.1] asnail!=4|japan=2|japan=3|japan=5. 439 [para_into,385.1.1,2.5.1,flip.1] asnail!=5|lucky=1|lucky=2|lucky=3|lucky=4. 452 [para_into,387.1.1,2.1.1,unit_del,154,flip.1] asnail!=1|ayellow=3|ayellow=4|ayellow=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 466 [back_unit_del,455.1,439.4] asnail!=5|lucky=1|lucky=2|lucky=4. 467 [back_unit_del,455.1,430.3] ayellow!=1|lucky=2|lucky=4|lucky=5. 481 [back_unit_del,458.1,368.2] aspan!=2|atea=4|atea=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 488 [back_unit_del,461.1,209.3] ayellow!=4|coffee=1|coffee=5. 531 [para_into,462.1.1,2.4.1,unit_del,157,461,flip.1] atea!=4|coffee=1|coffee=5. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 597,596 [181,split.1.1.1] ivory=3. 609 [back_demod,218,demod,597,597,597,unit_del,152,146,145] eng!=3. 610 [back_demod,207,demod,597,597,597,unit_del,152,146,145] ayellow!=3. 616,615 [back_demod,183,demod,597,unit_del,146] coffee=4. 624 [back_unit_del,609.1,375.2] aspan!=5|eng=4. 626 [back_unit_del,609.1,372.2] atea!=5|eng=4. 630 [back_unit_del,609.1,331.2] ayellow!=5|eng=4. 633,632 [back_unit_del,609.1,327.2,demod,616,unit_del,1] eng=5. 638 [back_unit_del,610.1,549.2] ayellow=1|ayellow=4. 640 [back_unit_del,610.1,541.2] horse=2|ayellow=4. 642 [back_unit_del,610.1,452.2] asnail!=1|ayellow=4|ayellow=5. 651 [back_demod,531,demod,616,616,unit_del,151,144] atea!=4. 665 [back_demod,488,demod,616,616,unit_del,151,144] ayellow!=4. 666 [back_demod,460,demod,616] lucky!=4. 669 [back_demod,630,demod,633,unit_del,144] ayellow!=5. 671 [back_demod,626,demod,633,unit_del,144] atea!=5. 672 [back_demod,624,demod,633,unit_del,144] aspan!=5. 684 [back_demod,314,demod,633] japan!=5. 690,689 [back_unit_del,651.1,484.2,unit_del,671] atea=2. 691 [back_unit_del,651.1,481.2,demod,690,unit_del,147] aspan!=2. 696 [back_unit_del,665.1,642.2,unit_del,669] asnail!=1. 698,697 [back_unit_del,665.1,640.2] horse=2. 700,699 [back_unit_del,665.1,638.2] ayellow=1. 714 [back_unit_del,666.1,466.4] asnail!=5|lucky=1|lucky=2. 717 [back_unit_del,672.1,364.4,unit_del,691] aspan=3|aspan=4. 721 [back_unit_del,672.1,319.4,unit_del,691] asnail!=3|aspan=4. 727 [back_unit_del,684.1,436.4] asnail!=4|japan=2|japan=3. 734 [back_unit_del,684.1,362.4] aspan!=3|japan=2|japan=4. 741 [back_demod,457,demod,690] lucky!=2. 742 [back_demod,309,demod,690] japan!=2. 753 [back_demod,281,demod,698,698,698,698,unit_del,153,149,148,147] asnail!=2. 773,772 [back_demod,467,demod,700,unit_del,1,741,666] lucky=5. 789 [back_unit_del,741.1,714.3,demod,773,unit_del,150] asnail!=5. 794 [back_unit_del,742.1,734.2] aspan!=3|japan=4. 797 [back_unit_del,742.1,727.2] asnail!=4|japan=3. 857 [binary,696.1,2.1,unit_del,753,789] asnail=3|asnail=4. 860,859 [717,split.1.1.1.1] aspan=3. 868,867 [back_demod,794,demod,860,unit_del,1] japan=4. 876 [back_demod,721,demod,860,unit_del,146] asnail!=3. 886 [back_demod,797,demod,868,unit_del,146] asnail!=4. 892 [back_unit_del,876.1,857.1] asnail=4. 894 [binary,892.1,886.1] $F. ------------ end of proof ------------- ------- statistics (process 8850) ------- clauses given 122 clauses generated 15057 clauses kept 857 clauses forward subsumed 932 clauses back subsumed 381 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8850 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.1.1]. --- refuted case [1.1.1.2] Case [1.1.1.2] (process 8851): Assumption: 860 [717,split.1.1.1.2] aspan=4. -----> EMPTY CLAUSE at 0.00 sec ----> 889 [back_demod,798,demod,884,872,unit_del,1,146] $F. Length of proof is 128. Level of proof is 14. Case [1.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 24 [] -successor(x,y)|y=2|x=2|y=4|x=4. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 87 [binary,71.1,24.1] coffee=2|ivory=2|coffee=4|ivory=4. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 146 [binary,37.1,10.1,flip.1] 4!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 152 [binary,37.1,4.1,flip.1] 3!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 158 [binary,75.1,8.1] coffee!=ayellow. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 183 [back_unit_del,155.1,87.2,unit_del,157] coffee=4|ivory=4. 207 [para_into,156.1.1,2.3.1,unit_del,155,flip.1] ayellow!=3|ivory=1|ivory=4|ivory=5. 209 [para_into,158.1.1,2.4.1,unit_del,157,flip.1] ayellow!=4|coffee=1|coffee=3|coffee=5. 213 [para_into,161.1.1,2.5.1,unit_del,160,flip.1] ayellow!=5|eng=1|eng=3|eng=4. 218 [para_into,162.1.1,2.3.1,unit_del,155,flip.1] eng!=3|ivory=1|ivory=4|ivory=5. 220 [para_into,163.1.1,2.4.1,unit_del,160,flip.1] coffee!=4|eng=1|eng=3|eng=5. 227 [binary,76.1,8.1,flip.1] horse!=asnail. 232 [binary,76.1,3.1] aspan!=asnail. 281 [para_into,227.1.1,2.2.1,flip.1] asnail!=2|horse=1|horse=3|horse=4|horse=5. 304 [para_into,232.1.1,2.4.1,flip.1] asnail!=4|aspan=1|aspan=2|aspan=3|aspan=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 311 [binary,77.1,9.1,flip.1] japan!=aspan. 312 [binary,77.1,8.1] aspan!=1. 313 [binary,77.1,7.1,flip.1] atea!=aspan. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 316 [binary,77.1,4.1] eng!=atea. 317 [binary,77.1,3.1] eng!=aspan. 320 [back_unit_del,312.1,304.2] asnail!=4|aspan=2|aspan=3|aspan=5. 327 [back_unit_del,315.1,220.2] coffee!=4|eng=3|eng=5. 331 [back_unit_del,315.1,213.2] ayellow!=5|eng=3|eng=4. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 361 [para_into,311.1.1,2.4.1,unit_del,308,flip.1] aspan!=4|japan=2|japan=3|japan=5. 364 [binary,312.1,2.1] aspan=2|aspan=3|aspan=4|aspan=5. 368 [para_into,313.1.1,2.2.1,unit_del,310,flip.1] aspan!=2|atea=3|atea=4|atea=5. 372 [para_into,316.1.1,2.5.1,unit_del,315,160,flip.1] atea!=5|eng=3|eng=4. 375 [para_into,317.1.1,2.5.1,unit_del,315,160,flip.1] aspan!=5|eng=3|eng=4. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 384 [binary,78.1,6.1,flip.1] japan!=asnail. 385 [binary,78.1,5.1,flip.1] lucky!=asnail. 387 [binary,78.1,3.1,flip.1] ayellow!=asnail. 430 [para_into,382.1.1,2.1.1,flip.1] ayellow!=1|lucky=2|lucky=3|lucky=4|lucky=5. 437 [para_into,384.1.1,2.3.1,unit_del,308,flip.1] asnail!=3|japan=2|japan=4|japan=5. 439 [para_into,385.1.1,2.5.1,flip.1] asnail!=5|lucky=1|lucky=2|lucky=3|lucky=4. 452 [para_into,387.1.1,2.1.1,unit_del,154,flip.1] asnail!=1|ayellow=3|ayellow=4|ayellow=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 466 [back_unit_del,455.1,439.4] asnail!=5|lucky=1|lucky=2|lucky=4. 467 [back_unit_del,455.1,430.3] ayellow!=1|lucky=2|lucky=4|lucky=5. 481 [back_unit_del,458.1,368.2] aspan!=2|atea=4|atea=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 488 [back_unit_del,461.1,209.3] ayellow!=4|coffee=1|coffee=5. 531 [para_into,462.1.1,2.4.1,unit_del,157,461,flip.1] atea!=4|coffee=1|coffee=5. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 597,596 [181,split.1.1.1] ivory=3. 609 [back_demod,218,demod,597,597,597,unit_del,152,146,145] eng!=3. 610 [back_demod,207,demod,597,597,597,unit_del,152,146,145] ayellow!=3. 616,615 [back_demod,183,demod,597,unit_del,146] coffee=4. 624 [back_unit_del,609.1,375.2] aspan!=5|eng=4. 626 [back_unit_del,609.1,372.2] atea!=5|eng=4. 630 [back_unit_del,609.1,331.2] ayellow!=5|eng=4. 633,632 [back_unit_del,609.1,327.2,demod,616,unit_del,1] eng=5. 638 [back_unit_del,610.1,549.2] ayellow=1|ayellow=4. 640 [back_unit_del,610.1,541.2] horse=2|ayellow=4. 642 [back_unit_del,610.1,452.2] asnail!=1|ayellow=4|ayellow=5. 651 [back_demod,531,demod,616,616,unit_del,151,144] atea!=4. 665 [back_demod,488,demod,616,616,unit_del,151,144] ayellow!=4. 666 [back_demod,460,demod,616] lucky!=4. 669 [back_demod,630,demod,633,unit_del,144] ayellow!=5. 671 [back_demod,626,demod,633,unit_del,144] atea!=5. 672 [back_demod,624,demod,633,unit_del,144] aspan!=5. 684 [back_demod,314,demod,633] japan!=5. 690,689 [back_unit_del,651.1,484.2,unit_del,671] atea=2. 691 [back_unit_del,651.1,481.2,demod,690,unit_del,147] aspan!=2. 696 [back_unit_del,665.1,642.2,unit_del,669] asnail!=1. 698,697 [back_unit_del,665.1,640.2] horse=2. 700,699 [back_unit_del,665.1,638.2] ayellow=1. 714 [back_unit_del,666.1,466.4] asnail!=5|lucky=1|lucky=2. 717 [back_unit_del,672.1,364.4,unit_del,691] aspan=3|aspan=4. 720 [back_unit_del,672.1,320.4,unit_del,691] asnail!=4|aspan=3. 726 [back_unit_del,684.1,437.4] asnail!=3|japan=2|japan=4. 735 [back_unit_del,684.1,361.4] aspan!=4|japan=2|japan=3. 741 [back_demod,457,demod,690] lucky!=2. 742 [back_demod,309,demod,690] japan!=2. 753 [back_demod,281,demod,698,698,698,698,unit_del,153,149,148,147] asnail!=2. 773,772 [back_demod,467,demod,700,unit_del,1,741,666] lucky=5. 789 [back_unit_del,741.1,714.3,demod,773,unit_del,150] asnail!=5. 793 [back_unit_del,742.1,735.2] aspan!=4|japan=3. 798 [back_unit_del,742.1,726.2] asnail!=3|japan=4. 857 [binary,696.1,2.1,unit_del,753,789] asnail=3|asnail=4. 859 [717,split_neg.1.1.1.2] aspan!=3. 861,860 [717,split.1.1.1.2] aspan=4. 863 [back_unit_del,859.1,720.2] asnail!=4. 872,871 [back_demod,793,demod,861,unit_del,1] japan=3. 884,883 [back_unit_del,863.1,857.2] asnail=3. 889 [back_demod,798,demod,884,872,unit_del,1,146] $F. ------------ end of proof ------------- ------- statistics (process 8851) ------- clauses given 122 clauses generated 15060 clauses kept 853 clauses forward subsumed 925 clauses back subsumed 385 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8851 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.1.2]. ------- statistics (process 8849) ------- clauses given 122 clauses generated 15055 clauses kept 827 clauses forward subsumed 905 clauses back subsumed 373 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.23 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8849 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.1]. Case [1.1.2] (process 8852): Assumption: 597 [181,split.1.1.2] ivory=4. Splitting on clause 678 [back_unit_del,625.1,521.3] apple!=2|atea=4. Case [1.1.2.1] (process 8853): Assumption: 851 [678,split.1.1.2.1] apple!=2. Splitting on clause 679 [back_unit_del,625.1,520.3] apple!=4|atea=2. Case [1.1.2.1.1] (process 8854): Assumption: 855 [679,split.1.1.2.1.1] apple!=4. Splitting on clause 680 [back_unit_del,625.1,484.3] atea=2|atea=4. --- refuted case [1.1.2.1.1.1] Case [1.1.2.1.1.1] (process 8855): Assumption: 863 [680,split.1.1.2.1.1.1] atea=2. -----> EMPTY CLAUSE at 0.01 sec ----> 946 [back_demod,911,demod,924,unit_del,936,149] $F. Length of proof is 137. Level of proof is 16. Case [1.1.2.1.1.1] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 23 [] -successor(x,y)|y=2|x=2|x=3|y=5. 26 [] -successor(x,y)|y=2|y=3|x=3|x=4. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 74 [] next_to(chest,fox). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 88 [binary,71.1,23.1] coffee=2|ivory=2|ivory=3|coffee=5. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 117 [binary,74.1,34.1] successor(chest,fox)|successor(fox,chest). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 158 [binary,75.1,8.1] coffee!=ayellow. 159 [binary,75.1,7.1,flip.1] ivory!=coffee. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 182 [back_unit_del,155.1,88.2,unit_del,157] ivory=3|coffee=5. 206 [para_into,156.1.1,2.4.1,unit_del,155,flip.1] ayellow!=4|ivory=1|ivory=3|ivory=5. 208 [para_into,158.1.1,2.5.1,unit_del,157,flip.1] ayellow!=5|coffee=1|coffee=3|coffee=4. 210 [para_into,159.1.1,2.4.1,unit_del,155,flip.1] coffee!=4|ivory=1|ivory=3|ivory=5. 215 [para_into,161.1.1,2.3.1,unit_del,160,flip.1] ayellow!=3|eng=1|eng=4|eng=5. 217 [para_into,162.1.1,2.4.1,unit_del,155,flip.1] eng!=4|ivory=1|ivory=3|ivory=5. 219 [para_into,163.1.1,2.5.1,unit_del,160,flip.1] coffee!=5|eng=1|eng=3|eng=4. 225 [binary,76.1,10.1,flip.1] horse!=fox. 227 [binary,76.1,8.1,flip.1] horse!=asnail. 228 [binary,76.1,7.1,flip.1] fox!=asnail. 271 [para_into,225.1.1,2.2.1,flip.1] fox!=2|horse=1|horse=3|horse=4|horse=5. 281 [para_into,227.1.1,2.2.1,flip.1] asnail!=2|horse=1|horse=3|horse=4|horse=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 328 [back_unit_del,315.1,219.2] coffee!=5|eng=3|eng=4. 329 [back_unit_del,315.1,215.2] ayellow!=3|eng=4|eng=5. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 378 [binary,78.1,12.1] lucky!=japan. 379 [binary,78.1,11.1,flip.1] japan!=chest. 380 [binary,78.1,10.1,flip.1] lucky!=chest. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 383 [binary,78.1,7.1,flip.1] chest!=ayellow. 384 [binary,78.1,6.1,flip.1] japan!=asnail. 385 [binary,78.1,5.1,flip.1] lucky!=asnail. 386 [binary,78.1,4.1,flip.1] chest!=asnail. 387 [binary,78.1,3.1,flip.1] ayellow!=asnail. 412 [para_into,378.1.1,2.4.1,flip.1] japan!=4|lucky=1|lucky=2|lucky=3|lucky=5. 415 [para_into,379.1.1,2.5.1,unit_del,308,flip.1] chest!=5|japan=2|japan=3|japan=4. 420 [para_into,380.1.1,2.4.1,flip.1] chest!=4|lucky=1|lucky=2|lucky=3|lucky=5. 435 [para_into,384.1.1,2.5.1,unit_del,308,flip.1] asnail!=5|japan=2|japan=3|japan=4. 440 [para_into,385.1.1,2.4.1,flip.1] asnail!=4|lucky=1|lucky=2|lucky=3|lucky=5. 446 [para_into,386.1.1,2.3.1,flip.1] asnail!=3|chest=1|chest=2|chest=4|chest=5. 452 [para_into,387.1.1,2.1.1,unit_del,154,flip.1] asnail!=1|ayellow=3|ayellow=4|ayellow=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 465 [back_unit_del,455.1,440.4] asnail!=4|lucky=1|lucky=2|lucky=5. 472 [back_unit_del,455.1,420.4] chest!=4|lucky=1|lucky=2|lucky=5. 475 [back_unit_del,455.1,412.4] japan!=4|lucky=1|lucky=2|lucky=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 489 [back_unit_del,461.1,208.3] ayellow!=5|coffee=1|coffee=4. 524 [para_into,457.1.1,2.2.1,unit_del,455,flip.1] atea!=2|lucky=1|lucky=4|lucky=5. 530 [para_into,462.1.1,2.5.1,unit_del,157,461,flip.1] atea!=5|coffee=1|coffee=4. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 562 [117,split.1.1] successor(chest,fox). 567 [binary,562.1,26.1] fox=2|fox=3|chest=3|chest=4. 596 [181,split_neg.1.1.2] ivory!=3. 598,597 [181,split.1.1.2] ivory=4. 599 [back_unit_del,596.1,217.3,demod,598,598,unit_del,151,144] eng!=4. 600 [back_unit_del,596.1,210.3,demod,598,598,unit_del,151,144] coffee!=4. 601 [back_unit_del,596.1,206.3,demod,598,598,unit_del,151,144] ayellow!=4. 604,603 [back_unit_del,596.1,182.1] coffee=5. 622 [back_unit_del,599.1,329.2] ayellow!=3|eng=5. 624,623 [back_unit_del,599.1,328.3,demod,604,unit_del,1] eng=3. 625 [back_unit_del,600.1,530.3,demod,604,unit_del,150] atea!=5. 628 [back_unit_del,600.1,489.3,demod,604,unit_del,150] ayellow!=5. 633 [back_unit_del,601.1,549.3] ayellow=1|ayellow=3. 635 [back_unit_del,601.1,541.3] horse=2|ayellow=3. 655 [back_demod,460,demod,604] lucky!=5. 658 [back_demod,622,demod,624,unit_del,145] ayellow!=3. 675 [back_demod,314,demod,624] japan!=3. 680 [back_unit_del,625.1,484.3] atea=2|atea=4. 688 [back_unit_del,628.1,452.4,unit_del,658,601] asnail!=1. 697 [back_unit_del,655.1,524.4] atea!=2|lucky=1|lucky=4. 705 [back_unit_del,655.1,475.4] japan!=4|lucky=1|lucky=2. 707 [back_unit_del,655.1,472.4] chest!=4|lucky=1|lucky=2. 711 [back_unit_del,655.1,465.4] asnail!=4|lucky=1|lucky=2. 714,713 [back_unit_del,658.1,635.2] horse=2. 716,715 [back_unit_del,658.1,633.2] ayellow=1. 731 [back_unit_del,675.1,435.3] asnail!=5|japan=2|japan=4. 734 [back_unit_del,675.1,415.3] chest!=5|japan=2|japan=4. 753 [back_demod,281,demod,714,714,714,714,unit_del,153,149,148,147] asnail!=2. 754 [back_demod,271,demod,714,714,714,714,unit_del,153,149,148,147] fox!=2. 781 [back_demod,383,demod,716] chest!=1. 782 [back_demod,382,demod,716] lucky!=1. 802 [back_unit_del,754.1,567.1] fox=3|chest=3|chest=4. 831 [back_unit_del,781.1,446.2] asnail!=3|chest=2|chest=4|chest=5. 838 [back_unit_del,782.1,711.2] asnail!=4|lucky=2. 840 [back_unit_del,782.1,707.2] chest!=4|lucky=2. 842 [back_unit_del,782.1,705.2] japan!=4|lucky=2. 846 [back_unit_del,782.1,697.2] atea!=2|lucky=4. 849 [binary,688.1,2.1,unit_del,753] asnail=3|asnail=4|asnail=5. 864,863 [680,split.1.1.2.1.1.1] atea=2. 869,868 [back_demod,846,demod,864,unit_del,1] lucky=4. 876 [back_demod,309,demod,864] japan!=2. 880 [back_demod,842,demod,869,unit_del,148] japan!=4. 881 [back_demod,840,demod,869,unit_del,148] chest!=4. 882 [back_demod,838,demod,869,unit_del,148] asnail!=4. 899 [back_unit_del,876.1,734.2,unit_del,880] chest!=5. 900 [back_unit_del,876.1,731.2,unit_del,880] asnail!=5. 911 [back_unit_del,881.1,802.3] fox=3|chest=3. 915,914 [back_unit_del,882.1,849.2,unit_del,900] asnail=3. 924,923 [back_unit_del,899.1,831.4,demod,915,unit_del,1,881] chest=2. 936 [back_demod,228,demod,915] fox!=3. 946 [back_demod,911,demod,924,unit_del,936,149] $F. ------------ end of proof ------------- ------- statistics (process 8855) ------- clauses given 123 clauses generated 15329 clauses kept 907 clauses forward subsumed 932 clauses back subsumed 448 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8855 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.2.1.1.1]. --- refuted case [1.1.2.1.1.2] Case [1.1.2.1.1.2] (process 8856): Assumption: 864 [680,split.1.1.2.1.1.2] atea=4. -----> EMPTY CLAUSE at 0.00 sec ----> 901 [back_unit_del,878.1,740.3,demod,882,unit_del,1,886] $F. Length of proof is 110. Level of proof is 13. Case [1.1.2.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 23 [] -successor(x,y)|y=2|x=2|x=3|y=5. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 88 [binary,71.1,23.1] coffee=2|ivory=2|ivory=3|coffee=5. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 159 [binary,75.1,7.1,flip.1] ivory!=coffee. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 182 [back_unit_del,155.1,88.2,unit_del,157] ivory=3|coffee=5. 206 [para_into,156.1.1,2.4.1,unit_del,155,flip.1] ayellow!=4|ivory=1|ivory=3|ivory=5. 210 [para_into,159.1.1,2.4.1,unit_del,155,flip.1] coffee!=4|ivory=1|ivory=3|ivory=5. 215 [para_into,161.1.1,2.3.1,unit_del,160,flip.1] ayellow!=3|eng=1|eng=4|eng=5. 217 [para_into,162.1.1,2.4.1,unit_del,155,flip.1] eng!=4|ivory=1|ivory=3|ivory=5. 219 [para_into,163.1.1,2.5.1,unit_del,160,flip.1] coffee!=5|eng=1|eng=3|eng=4. 230 [binary,76.1,5.1,flip.1] horse!=aspan. 296 [para_into,230.1.1,2.2.1,flip.1] aspan!=2|horse=1|horse=3|horse=4|horse=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 311 [binary,77.1,9.1,flip.1] japan!=aspan. 312 [binary,77.1,8.1] aspan!=1. 313 [binary,77.1,7.1,flip.1] atea!=aspan. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 317 [binary,77.1,3.1] eng!=aspan. 328 [back_unit_del,315.1,219.2] coffee!=5|eng=3|eng=4. 329 [back_unit_del,315.1,215.2] ayellow!=3|eng=4|eng=5. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 360 [para_into,311.1.1,2.5.1,unit_del,308,flip.1] aspan!=5|japan=2|japan=3|japan=4. 364 [binary,312.1,2.1] aspan=2|aspan=3|aspan=4|aspan=5. 366 [para_into,313.1.1,2.4.1,unit_del,310,flip.1] aspan!=4|atea=2|atea=3|atea=5. 377 [para_into,317.1.1,2.3.1,unit_del,315,160,flip.1] aspan!=3|eng=4|eng=5. 378 [binary,78.1,12.1] lucky!=japan. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 414 [para_into,378.1.1,2.2.1,flip.1] japan!=2|lucky=1|lucky=3|lucky=4|lucky=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 474 [back_unit_del,455.1,414.3] japan!=2|lucky=1|lucky=4|lucky=5. 482 [back_unit_del,458.1,366.3] aspan!=4|atea=2|atea=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 523 [para_into,457.1.1,2.4.1,unit_del,455,flip.1] atea!=4|lucky=1|lucky=2|lucky=5. 530 [para_into,462.1.1,2.5.1,unit_del,157,461,flip.1] atea!=5|coffee=1|coffee=4. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 596 [181,split_neg.1.1.2] ivory!=3. 598,597 [181,split.1.1.2] ivory=4. 599 [back_unit_del,596.1,217.3,demod,598,598,unit_del,151,144] eng!=4. 600 [back_unit_del,596.1,210.3,demod,598,598,unit_del,151,144] coffee!=4. 601 [back_unit_del,596.1,206.3,demod,598,598,unit_del,151,144] ayellow!=4. 604,603 [back_unit_del,596.1,182.1] coffee=5. 615 [back_unit_del,599.1,377.2] aspan!=3|eng=5. 622 [back_unit_del,599.1,329.2] ayellow!=3|eng=5. 624,623 [back_unit_del,599.1,328.3,demod,604,unit_del,1] eng=3. 625 [back_unit_del,600.1,530.3,demod,604,unit_del,150] atea!=5. 633 [back_unit_del,601.1,549.3] ayellow=1|ayellow=3. 635 [back_unit_del,601.1,541.3] horse=2|ayellow=3. 655 [back_demod,460,demod,604] lucky!=5. 658 [back_demod,622,demod,624,unit_del,145] ayellow!=3. 660 [back_demod,615,demod,624,unit_del,145] aspan!=3. 675 [back_demod,314,demod,624] japan!=3. 680 [back_unit_del,625.1,484.3] atea=2|atea=4. 681 [back_unit_del,625.1,482.3] aspan!=4|atea=2. 698 [back_unit_del,655.1,523.4] atea!=4|lucky=1|lucky=2. 706 [back_unit_del,655.1,474.4] japan!=2|lucky=1|lucky=4. 714,713 [back_unit_del,658.1,635.2] horse=2. 716,715 [back_unit_del,658.1,633.2] ayellow=1. 719 [back_unit_del,660.1,364.2] aspan=2|aspan=4|aspan=5. 740 [back_unit_del,675.1,360.3] aspan!=5|japan=2|japan=4. 752 [back_demod,296,demod,714,714,714,714,unit_del,153,149,148,147] aspan!=2. 782 [back_demod,382,demod,716] lucky!=1. 789 [back_unit_del,752.1,719.1] aspan=4|aspan=5. 841 [back_unit_del,782.1,706.2] japan!=2|lucky=4. 845 [back_unit_del,782.1,698.2] atea!=4|lucky=2. 863 [680,split_neg.1.1.2.1.1.2] atea!=2. 865,864 [680,split.1.1.2.1.1.2] atea=4. 867 [back_unit_del,863.1,681.2] aspan!=4. 872,871 [back_demod,845,demod,865,unit_del,1] lucky=2. 878 [back_demod,309,demod,865] japan!=4. 882,881 [back_unit_del,867.1,789.1] aspan=5. 886 [back_demod,841,demod,872,unit_del,148] japan!=2. 901 [back_unit_del,878.1,740.3,demod,882,unit_del,1,886] $F. ------------ end of proof ------------- ------- statistics (process 8856) ------- clauses given 123 clauses generated 15290 clauses kept 868 clauses forward subsumed 866 clauses back subsumed 414 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8856 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.2.1.1.2]. ------- statistics (process 8854) ------- clauses given 123 clauses generated 15281 clauses kept 835 clauses forward subsumed 837 clauses back subsumed 406 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8854 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.2.1.1]. The Assumption for case [1.1.2.1.1] was not used; therefore we skip case: [1.1.2.1.2]. ------- statistics (process 8853) ------- clauses given 121 clauses generated 15187 clauses kept 828 clauses forward subsumed 821 clauses back subsumed 404 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8853 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.2.1]. The Assumption for case [1.1.2.1] was not used; therefore we skip case: [1.1.2.2]. ------- statistics (process 8852) ------- clauses given 119 clauses generated 15078 clauses kept 824 clauses forward subsumed 815 clauses back subsumed 399 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.23 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8852 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1.2]. ------- statistics (process 8848) ------- clauses given 89 clauses generated 10717 clauses kept 577 clauses forward subsumed 337 clauses back subsumed 163 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8848 finished Mon Aug 2 15:31:12 2004 Refuted case [1.1]. Case [1.2] (process 8857): Assumption: 563 [117,split.1.2] successor(fox,chest). Splitting on clause 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. Case [1.2.1] (process 8858): Assumption: 611 [181,split.1.2.1] ivory=3. Splitting on clause 564 [binary,562.1,33.1] chest!=4|fox!=5. Case [1.2.1.1] (process 8859): Assumption: 869 [564,split.1.2.1.1] chest!=4. Splitting on clause 732 [back_unit_del,687.1,364.4,unit_del,706] aspan=3|aspan=4. --- refuted case [1.2.1.1.1] Case [1.2.1.1.1] (process 8860): Assumption: 900 [732,split.1.2.1.1.1] aspan=3. ----> UNIT CONFLICT at 0.00 sec ----> 926 [binary,924.1,920.1] $F. Length of proof is 128. Level of proof is 14. Case [1.2.1.1.1] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 24 [] -successor(x,y)|y=2|x=2|y=4|x=4. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 87 [binary,71.1,24.1] coffee=2|ivory=2|coffee=4|ivory=4. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 146 [binary,37.1,10.1,flip.1] 4!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 152 [binary,37.1,4.1,flip.1] 3!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 158 [binary,75.1,8.1] coffee!=ayellow. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 183 [back_unit_del,155.1,87.2,unit_del,157] coffee=4|ivory=4. 207 [para_into,156.1.1,2.3.1,unit_del,155,flip.1] ayellow!=3|ivory=1|ivory=4|ivory=5. 209 [para_into,158.1.1,2.4.1,unit_del,157,flip.1] ayellow!=4|coffee=1|coffee=3|coffee=5. 213 [para_into,161.1.1,2.5.1,unit_del,160,flip.1] ayellow!=5|eng=1|eng=3|eng=4. 218 [para_into,162.1.1,2.3.1,unit_del,155,flip.1] eng!=3|ivory=1|ivory=4|ivory=5. 220 [para_into,163.1.1,2.4.1,unit_del,160,flip.1] coffee!=4|eng=1|eng=3|eng=5. 227 [binary,76.1,8.1,flip.1] horse!=asnail. 232 [binary,76.1,3.1] aspan!=asnail. 281 [para_into,227.1.1,2.2.1,flip.1] asnail!=2|horse=1|horse=3|horse=4|horse=5. 305 [para_into,232.1.1,2.3.1,flip.1] asnail!=3|aspan=1|aspan=2|aspan=4|aspan=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 311 [binary,77.1,9.1,flip.1] japan!=aspan. 312 [binary,77.1,8.1] aspan!=1. 313 [binary,77.1,7.1,flip.1] atea!=aspan. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 316 [binary,77.1,4.1] eng!=atea. 317 [binary,77.1,3.1] eng!=aspan. 319 [back_unit_del,312.1,305.2] asnail!=3|aspan=2|aspan=4|aspan=5. 327 [back_unit_del,315.1,220.2] coffee!=4|eng=3|eng=5. 331 [back_unit_del,315.1,213.2] ayellow!=5|eng=3|eng=4. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 362 [para_into,311.1.1,2.3.1,unit_del,308,flip.1] aspan!=3|japan=2|japan=4|japan=5. 364 [binary,312.1,2.1] aspan=2|aspan=3|aspan=4|aspan=5. 368 [para_into,313.1.1,2.2.1,unit_del,310,flip.1] aspan!=2|atea=3|atea=4|atea=5. 372 [para_into,316.1.1,2.5.1,unit_del,315,160,flip.1] atea!=5|eng=3|eng=4. 375 [para_into,317.1.1,2.5.1,unit_del,315,160,flip.1] aspan!=5|eng=3|eng=4. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 384 [binary,78.1,6.1,flip.1] japan!=asnail. 385 [binary,78.1,5.1,flip.1] lucky!=asnail. 387 [binary,78.1,3.1,flip.1] ayellow!=asnail. 430 [para_into,382.1.1,2.1.1,flip.1] ayellow!=1|lucky=2|lucky=3|lucky=4|lucky=5. 436 [para_into,384.1.1,2.4.1,unit_del,308,flip.1] asnail!=4|japan=2|japan=3|japan=5. 439 [para_into,385.1.1,2.5.1,flip.1] asnail!=5|lucky=1|lucky=2|lucky=3|lucky=4. 452 [para_into,387.1.1,2.1.1,unit_del,154,flip.1] asnail!=1|ayellow=3|ayellow=4|ayellow=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 466 [back_unit_del,455.1,439.4] asnail!=5|lucky=1|lucky=2|lucky=4. 467 [back_unit_del,455.1,430.3] ayellow!=1|lucky=2|lucky=4|lucky=5. 481 [back_unit_del,458.1,368.2] aspan!=2|atea=4|atea=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 488 [back_unit_del,461.1,209.3] ayellow!=4|coffee=1|coffee=5. 531 [para_into,462.1.1,2.4.1,unit_del,157,461,flip.1] atea!=4|coffee=1|coffee=5. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 612,611 [181,split.1.2.1] ivory=3. 624 [back_demod,218,demod,612,612,612,unit_del,152,146,145] eng!=3. 625 [back_demod,207,demod,612,612,612,unit_del,152,146,145] ayellow!=3. 631,630 [back_demod,183,demod,612,unit_del,146] coffee=4. 639 [back_unit_del,624.1,375.2] aspan!=5|eng=4. 641 [back_unit_del,624.1,372.2] atea!=5|eng=4. 645 [back_unit_del,624.1,331.2] ayellow!=5|eng=4. 648,647 [back_unit_del,624.1,327.2,demod,631,unit_del,1] eng=5. 653 [back_unit_del,625.1,549.2] ayellow=1|ayellow=4. 655 [back_unit_del,625.1,541.2] horse=2|ayellow=4. 657 [back_unit_del,625.1,452.2] asnail!=1|ayellow=4|ayellow=5. 666 [back_demod,531,demod,631,631,unit_del,151,144] atea!=4. 680 [back_demod,488,demod,631,631,unit_del,151,144] ayellow!=4. 681 [back_demod,460,demod,631] lucky!=4. 684 [back_demod,645,demod,648,unit_del,144] ayellow!=5. 686 [back_demod,641,demod,648,unit_del,144] atea!=5. 687 [back_demod,639,demod,648,unit_del,144] aspan!=5. 699 [back_demod,314,demod,648] japan!=5. 705,704 [back_unit_del,666.1,484.2,unit_del,686] atea=2. 706 [back_unit_del,666.1,481.2,demod,705,unit_del,147] aspan!=2. 711 [back_unit_del,680.1,657.2,unit_del,684] asnail!=1. 713,712 [back_unit_del,680.1,655.2] horse=2. 715,714 [back_unit_del,680.1,653.2] ayellow=1. 729 [back_unit_del,681.1,466.4] asnail!=5|lucky=1|lucky=2. 732 [back_unit_del,687.1,364.4,unit_del,706] aspan=3|aspan=4. 736 [back_unit_del,687.1,319.4,unit_del,706] asnail!=3|aspan=4. 742 [back_unit_del,699.1,436.4] asnail!=4|japan=2|japan=3. 749 [back_unit_del,699.1,362.4] aspan!=3|japan=2|japan=4. 756 [back_demod,457,demod,705] lucky!=2. 757 [back_demod,309,demod,705] japan!=2. 768 [back_demod,281,demod,713,713,713,713,unit_del,153,149,148,147] asnail!=2. 788,787 [back_demod,467,demod,715,unit_del,1,756,681] lucky=5. 804 [back_unit_del,756.1,729.3,demod,788,unit_del,150] asnail!=5. 809 [back_unit_del,757.1,749.2] aspan!=3|japan=4. 812 [back_unit_del,757.1,742.2] asnail!=4|japan=3. 867 [binary,711.1,2.1,unit_del,768,804] asnail=3|asnail=4. 901,900 [732,split.1.2.1.1.1] aspan=3. 911,910 [back_demod,809,demod,901,unit_del,1] japan=4. 913 [back_demod,736,demod,901,unit_del,146] asnail!=3. 920 [back_demod,812,demod,911,unit_del,146] asnail!=4. 924 [back_unit_del,913.1,867.1] asnail=4. 926 [binary,924.1,920.1] $F. ------------ end of proof ------------- ------- statistics (process 8860) ------- clauses given 128 clauses generated 15693 clauses kept 887 clauses forward subsumed 1027 clauses back subsumed 406 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8860 finished Mon Aug 2 15:31:12 2004 Refuted case [1.2.1.1.1]. --- refuted case [1.2.1.1.2] Case [1.2.1.1.2] (process 8861): Assumption: 901 [732,split.1.2.1.1.2] aspan=4. -----> EMPTY CLAUSE at 0.00 sec ----> 922 [back_demod,813,demod,921,914,unit_del,1,146] $F. Length of proof is 128. Level of proof is 14. Case [1.2.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 24 [] -successor(x,y)|y=2|x=2|y=4|x=4. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 87 [binary,71.1,24.1] coffee=2|ivory=2|coffee=4|ivory=4. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 146 [binary,37.1,10.1,flip.1] 4!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 152 [binary,37.1,4.1,flip.1] 3!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 158 [binary,75.1,8.1] coffee!=ayellow. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 183 [back_unit_del,155.1,87.2,unit_del,157] coffee=4|ivory=4. 207 [para_into,156.1.1,2.3.1,unit_del,155,flip.1] ayellow!=3|ivory=1|ivory=4|ivory=5. 209 [para_into,158.1.1,2.4.1,unit_del,157,flip.1] ayellow!=4|coffee=1|coffee=3|coffee=5. 213 [para_into,161.1.1,2.5.1,unit_del,160,flip.1] ayellow!=5|eng=1|eng=3|eng=4. 218 [para_into,162.1.1,2.3.1,unit_del,155,flip.1] eng!=3|ivory=1|ivory=4|ivory=5. 220 [para_into,163.1.1,2.4.1,unit_del,160,flip.1] coffee!=4|eng=1|eng=3|eng=5. 227 [binary,76.1,8.1,flip.1] horse!=asnail. 232 [binary,76.1,3.1] aspan!=asnail. 281 [para_into,227.1.1,2.2.1,flip.1] asnail!=2|horse=1|horse=3|horse=4|horse=5. 304 [para_into,232.1.1,2.4.1,flip.1] asnail!=4|aspan=1|aspan=2|aspan=3|aspan=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 311 [binary,77.1,9.1,flip.1] japan!=aspan. 312 [binary,77.1,8.1] aspan!=1. 313 [binary,77.1,7.1,flip.1] atea!=aspan. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 316 [binary,77.1,4.1] eng!=atea. 317 [binary,77.1,3.1] eng!=aspan. 320 [back_unit_del,312.1,304.2] asnail!=4|aspan=2|aspan=3|aspan=5. 327 [back_unit_del,315.1,220.2] coffee!=4|eng=3|eng=5. 331 [back_unit_del,315.1,213.2] ayellow!=5|eng=3|eng=4. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 361 [para_into,311.1.1,2.4.1,unit_del,308,flip.1] aspan!=4|japan=2|japan=3|japan=5. 364 [binary,312.1,2.1] aspan=2|aspan=3|aspan=4|aspan=5. 368 [para_into,313.1.1,2.2.1,unit_del,310,flip.1] aspan!=2|atea=3|atea=4|atea=5. 372 [para_into,316.1.1,2.5.1,unit_del,315,160,flip.1] atea!=5|eng=3|eng=4. 375 [para_into,317.1.1,2.5.1,unit_del,315,160,flip.1] aspan!=5|eng=3|eng=4. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 384 [binary,78.1,6.1,flip.1] japan!=asnail. 385 [binary,78.1,5.1,flip.1] lucky!=asnail. 387 [binary,78.1,3.1,flip.1] ayellow!=asnail. 430 [para_into,382.1.1,2.1.1,flip.1] ayellow!=1|lucky=2|lucky=3|lucky=4|lucky=5. 437 [para_into,384.1.1,2.3.1,unit_del,308,flip.1] asnail!=3|japan=2|japan=4|japan=5. 439 [para_into,385.1.1,2.5.1,flip.1] asnail!=5|lucky=1|lucky=2|lucky=3|lucky=4. 452 [para_into,387.1.1,2.1.1,unit_del,154,flip.1] asnail!=1|ayellow=3|ayellow=4|ayellow=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 466 [back_unit_del,455.1,439.4] asnail!=5|lucky=1|lucky=2|lucky=4. 467 [back_unit_del,455.1,430.3] ayellow!=1|lucky=2|lucky=4|lucky=5. 481 [back_unit_del,458.1,368.2] aspan!=2|atea=4|atea=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 488 [back_unit_del,461.1,209.3] ayellow!=4|coffee=1|coffee=5. 531 [para_into,462.1.1,2.4.1,unit_del,157,461,flip.1] atea!=4|coffee=1|coffee=5. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 612,611 [181,split.1.2.1] ivory=3. 624 [back_demod,218,demod,612,612,612,unit_del,152,146,145] eng!=3. 625 [back_demod,207,demod,612,612,612,unit_del,152,146,145] ayellow!=3. 631,630 [back_demod,183,demod,612,unit_del,146] coffee=4. 639 [back_unit_del,624.1,375.2] aspan!=5|eng=4. 641 [back_unit_del,624.1,372.2] atea!=5|eng=4. 645 [back_unit_del,624.1,331.2] ayellow!=5|eng=4. 648,647 [back_unit_del,624.1,327.2,demod,631,unit_del,1] eng=5. 653 [back_unit_del,625.1,549.2] ayellow=1|ayellow=4. 655 [back_unit_del,625.1,541.2] horse=2|ayellow=4. 657 [back_unit_del,625.1,452.2] asnail!=1|ayellow=4|ayellow=5. 666 [back_demod,531,demod,631,631,unit_del,151,144] atea!=4. 680 [back_demod,488,demod,631,631,unit_del,151,144] ayellow!=4. 681 [back_demod,460,demod,631] lucky!=4. 684 [back_demod,645,demod,648,unit_del,144] ayellow!=5. 686 [back_demod,641,demod,648,unit_del,144] atea!=5. 687 [back_demod,639,demod,648,unit_del,144] aspan!=5. 699 [back_demod,314,demod,648] japan!=5. 705,704 [back_unit_del,666.1,484.2,unit_del,686] atea=2. 706 [back_unit_del,666.1,481.2,demod,705,unit_del,147] aspan!=2. 711 [back_unit_del,680.1,657.2,unit_del,684] asnail!=1. 713,712 [back_unit_del,680.1,655.2] horse=2. 715,714 [back_unit_del,680.1,653.2] ayellow=1. 729 [back_unit_del,681.1,466.4] asnail!=5|lucky=1|lucky=2. 732 [back_unit_del,687.1,364.4,unit_del,706] aspan=3|aspan=4. 735 [back_unit_del,687.1,320.4,unit_del,706] asnail!=4|aspan=3. 741 [back_unit_del,699.1,437.4] asnail!=3|japan=2|japan=4. 750 [back_unit_del,699.1,361.4] aspan!=4|japan=2|japan=3. 756 [back_demod,457,demod,705] lucky!=2. 757 [back_demod,309,demod,705] japan!=2. 768 [back_demod,281,demod,713,713,713,713,unit_del,153,149,148,147] asnail!=2. 788,787 [back_demod,467,demod,715,unit_del,1,756,681] lucky=5. 804 [back_unit_del,756.1,729.3,demod,788,unit_del,150] asnail!=5. 808 [back_unit_del,757.1,750.2] aspan!=4|japan=3. 813 [back_unit_del,757.1,741.2] asnail!=3|japan=4. 867 [binary,711.1,2.1,unit_del,768,804] asnail=3|asnail=4. 900 [732,split_neg.1.2.1.1.2] aspan!=3. 902,901 [732,split.1.2.1.1.2] aspan=4. 905 [back_unit_del,900.1,735.2] asnail!=4. 914,913 [back_demod,808,demod,902,unit_del,1] japan=3. 921,920 [back_unit_del,905.1,867.2] asnail=3. 922 [back_demod,813,demod,921,914,unit_del,1,146] $F. ------------ end of proof ------------- ------- statistics (process 8861) ------- clauses given 128 clauses generated 15696 clauses kept 884 clauses forward subsumed 1026 clauses back subsumed 409 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8861 finished Mon Aug 2 15:31:12 2004 Refuted case [1.2.1.1.2]. ------- statistics (process 8859) ------- clauses given 128 clauses generated 15691 clauses kept 866 clauses forward subsumed 1004 clauses back subsumed 404 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.07 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8859 finished Mon Aug 2 15:31:12 2004 Refuted case [1.2.1.1]. The Assumption for case [1.2.1.1] was not used; therefore we skip case: [1.2.1.2]. ------- statistics (process 8858) ------- clauses given 121 clauses generated 14422 clauses kept 837 clauses forward subsumed 854 clauses back subsumed 392 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.19 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8858 finished Mon Aug 2 15:31:12 2004 Refuted case [1.2.1]. Case [1.2.2] (process 8862): Assumption: 612 [181,split.1.2.2] ivory=4. Splitting on clause 564 [binary,562.1,33.1] chest!=4|fox!=5. Case [1.2.2.1] (process 8863): Assumption: 870 [564,split.1.2.2.1] chest!=4. Splitting on clause 565 [binary,562.1,32.1] chest!=3|fox!=4. Case [1.2.2.1.1] (process 8864): Assumption: 886 [565,split.1.2.2.1.1] chest!=3. Splitting on clause 566 [binary,562.1,31.1] chest!=2|fox!=3. Case [1.2.2.1.1.1] (process 8865): Assumption: 898 [566,split.1.2.2.1.1.1] chest!=2. Splitting on clause 693 [back_unit_del,640.1,521.3] apple!=2|atea=4. Case [1.2.2.1.1.1.1] (process 8866): Assumption: 966 [693,split.1.2.2.1.1.1.1] apple!=2. Splitting on clause 694 [back_unit_del,640.1,520.3] apple!=4|atea=2. Case [1.2.2.1.1.1.1.1] (process 8867): Assumption: 970 [694,split.1.2.2.1.1.1.1.1] apple!=4. Splitting on clause 695 [back_unit_del,640.1,484.3] atea=2|atea=4. --- refuted case [1.2.2.1.1.1.1.1.1] Case [1.2.2.1.1.1.1.1.1] (process 8868): Assumption: 978 [695,split.1.2.2.1.1.1.1.1.1] atea=2. -----> EMPTY CLAUSE at 0.00 sec ----> 994 [back_demod,861,demod,987,990,unit_del,1,148] $F. Length of proof is 107. Level of proof is 16. Case [1.2.2.1.1.1.1.1.1] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 23 [] -successor(x,y)|y=2|x=2|x=3|y=5. 25 [] -successor(x,y)|y=2|x=2|y=4|y=5. 31 [] successor(x,y)|x!=2|y!=3. 33 [] successor(x,y)|x!=4|y!=5. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 74 [] next_to(chest,fox). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 88 [binary,71.1,23.1] coffee=2|ivory=2|ivory=3|coffee=5. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 117 [binary,74.1,34.1] successor(chest,fox)|successor(fox,chest). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 159 [binary,75.1,7.1,flip.1] ivory!=coffee. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 182 [back_unit_del,155.1,88.2,unit_del,157] ivory=3|coffee=5. 206 [para_into,156.1.1,2.4.1,unit_del,155,flip.1] ayellow!=4|ivory=1|ivory=3|ivory=5. 210 [para_into,159.1.1,2.4.1,unit_del,155,flip.1] coffee!=4|ivory=1|ivory=3|ivory=5. 215 [para_into,161.1.1,2.3.1,unit_del,160,flip.1] ayellow!=3|eng=1|eng=4|eng=5. 217 [para_into,162.1.1,2.4.1,unit_del,155,flip.1] eng!=4|ivory=1|ivory=3|ivory=5. 219 [para_into,163.1.1,2.5.1,unit_del,160,flip.1] coffee!=5|eng=1|eng=3|eng=4. 225 [binary,76.1,10.1,flip.1] horse!=fox. 271 [para_into,225.1.1,2.2.1,flip.1] fox!=2|horse=1|horse=3|horse=4|horse=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 328 [back_unit_del,315.1,219.2] coffee!=5|eng=3|eng=4. 329 [back_unit_del,315.1,215.2] ayellow!=3|eng=4|eng=5. 358 [para_into,309.1.1,2.2.1,unit_del,308,flip.1] atea!=2|japan=3|japan=4|japan=5. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 378 [binary,78.1,12.1] lucky!=japan. 379 [binary,78.1,11.1,flip.1] japan!=chest. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 412 [para_into,378.1.1,2.4.1,flip.1] japan!=4|lucky=1|lucky=2|lucky=3|lucky=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 475 [back_unit_del,455.1,412.4] japan!=4|lucky=1|lucky=2|lucky=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 524 [para_into,457.1.1,2.2.1,unit_del,455,flip.1] atea!=2|lucky=1|lucky=4|lucky=5. 530 [para_into,462.1.1,2.5.1,unit_del,157,461,flip.1] atea!=5|coffee=1|coffee=4. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 562 [117,split_neg.1.2] -successor(chest,fox). 563 [117,split.1.2] successor(fox,chest). 564 [binary,562.1,33.1] chest!=4|fox!=5. 566 [binary,562.1,31.1] chest!=2|fox!=3. 583 [binary,563.1,25.1] chest=2|fox=2|chest=4|chest=5. 611 [181,split_neg.1.2.2] ivory!=3. 613,612 [181,split.1.2.2] ivory=4. 614 [back_unit_del,611.1,217.3,demod,613,613,unit_del,151,144] eng!=4. 615 [back_unit_del,611.1,210.3,demod,613,613,unit_del,151,144] coffee!=4. 616 [back_unit_del,611.1,206.3,demod,613,613,unit_del,151,144] ayellow!=4. 619,618 [back_unit_del,611.1,182.1] coffee=5. 637 [back_unit_del,614.1,329.2] ayellow!=3|eng=5. 639,638 [back_unit_del,614.1,328.3,demod,619,unit_del,1] eng=3. 640 [back_unit_del,615.1,530.3,demod,619,unit_del,150] atea!=5. 648 [back_unit_del,616.1,549.3] ayellow=1|ayellow=3. 650 [back_unit_del,616.1,541.3] horse=2|ayellow=3. 670 [back_demod,460,demod,619] lucky!=5. 673 [back_demod,637,demod,639,unit_del,145] ayellow!=3. 690 [back_demod,314,demod,639] japan!=3. 695 [back_unit_del,640.1,484.3] atea=2|atea=4. 712 [back_unit_del,670.1,524.4] atea!=2|lucky=1|lucky=4. 720 [back_unit_del,670.1,475.4] japan!=4|lucky=1|lucky=2. 729,728 [back_unit_del,673.1,650.2] horse=2. 731,730 [back_unit_del,673.1,648.2] ayellow=1. 756 [back_unit_del,690.1,358.2] atea!=2|japan=4|japan=5. 769 [back_demod,271,demod,729,729,729,729,unit_del,153,149,148,147] fox!=2. 797 [back_demod,382,demod,731] lucky!=1. 820 [back_unit_del,769.1,583.2] chest=2|chest=4|chest=5. 861 [back_unit_del,797.1,720.2] japan!=4|lucky=2. 865 [back_unit_del,797.1,712.2] atea!=2|lucky=4. 870 [564,split.1.2.2.1] chest!=4. 882 [back_unit_del,870.1,820.2] chest=2|chest=5. 898 [566,split.1.2.2.1.1.1] chest!=2. 908,907 [back_unit_del,898.1,882.1] chest=5. 935 [back_demod,379,demod,908] japan!=5. 947 [back_unit_del,935.1,756.3] atea!=2|japan=4. 979,978 [695,split.1.2.2.1.1.1.1.1.1] atea=2. 987,986 [back_demod,947,demod,979,unit_del,1] japan=4. 990,989 [back_demod,865,demod,979,unit_del,1] lucky=4. 994 [back_demod,861,demod,987,990,unit_del,1,148] $F. ------------ end of proof ------------- ------- statistics (process 8868) ------- clauses given 137 clauses generated 16218 clauses kept 955 clauses forward subsumed 985 clauses back subsumed 496 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8868 finished Mon Aug 2 15:31:13 2004 Refuted case [1.2.2.1.1.1.1.1.1]. --- refuted case [1.2.2.1.1.1.1.1.2] Case [1.2.2.1.1.1.1.1.2] (process 8869): Assumption: 979 [695,split.1.2.2.1.1.1.1.1.2] atea=4. -----> EMPTY CLAUSE at 0.00 sec ----> 993 [back_demod,860,demod,987,989,unit_del,1,148] $F. Length of proof is 107. Level of proof is 16. Case [1.2.2.1.1.1.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 23 [] -successor(x,y)|y=2|x=2|x=3|y=5. 25 [] -successor(x,y)|y=2|x=2|y=4|y=5. 31 [] successor(x,y)|x!=2|y!=3. 33 [] successor(x,y)|x!=4|y!=5. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 37 [] distinct5(1,2,3,4,5). 38 [] distinct5(red,green,ivory,ayellow,blue). 39 [] distinct5(eng,aspan,aukra,norw,japan). 40 [] distinct5(dog,asnail,fox,horse,azebra). 41 [] distinct5(coffee,atea,milk,orange,apple). 42 [] distinct5(old,kool,chest,lucky,parli). 43 [] eng=red. 45,44 [copy,43,flip.1] red=eng. 46 [] aspan=dog. 48,47 [copy,46,flip.1] dog=aspan. 49 [] coffee=green. 51,50 [copy,49,flip.1] green=coffee. 53,52 [] aukra=atea. 55,54 [] old=asnail. 57,56 [] kool=ayellow. 59,58 [] milk=3. 61,60 [] norw=1. 62 [] lucky=orange. 64,63 [copy,62,flip.1] orange=lucky. 65 [] japan=parli. 67,66 [copy,65,flip.1] parli=japan. 69,68 [] blue=2. 70 [] successor(ivory,green). 71 [copy,70,demod,51] successor(ivory,coffee). 72 [] next_to(kool,horse). 73 [copy,72,demod,57] next_to(ayellow,horse). 74 [] next_to(chest,fox). 75 [back_demod,38,demod,45,51,69] distinct5(eng,coffee,ivory,ayellow,2). 76 [back_demod,40,demod,48] distinct5(aspan,asnail,fox,horse,azebra). 77 [back_demod,39,demod,53,61] distinct5(eng,aspan,atea,1,japan). 78 [back_demod,42,demod,55,57,67] distinct5(asnail,ayellow,chest,lucky,japan). 79 [back_demod,41,demod,59,64] distinct5(coffee,atea,3,lucky,apple). 88 [binary,71.1,23.1] coffee=2|ivory=2|ivory=3|coffee=5. 89 [binary,71.1,22.1] coffee=2|ivory=2|ivory=3|ivory=4. 106 [binary,73.1,34.1] successor(ayellow,horse)|successor(horse,ayellow). 117 [binary,74.1,34.1] successor(chest,fox)|successor(fox,chest). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 154 [binary,75.1,12.1] ayellow!=2. 155 [binary,75.1,11.1] ivory!=2. 156 [binary,75.1,10.1] ivory!=ayellow. 157 [binary,75.1,9.1] coffee!=2. 159 [binary,75.1,7.1,flip.1] ivory!=coffee. 160 [binary,75.1,6.1] eng!=2. 161 [binary,75.1,5.1] eng!=ayellow. 162 [binary,75.1,4.1,flip.1] ivory!=eng. 163 [binary,75.1,3.1] eng!=coffee. 181 [back_unit_del,155.1,89.2,unit_del,157] ivory=3|ivory=4. 182 [back_unit_del,155.1,88.2,unit_del,157] ivory=3|coffee=5. 206 [para_into,156.1.1,2.4.1,unit_del,155,flip.1] ayellow!=4|ivory=1|ivory=3|ivory=5. 210 [para_into,159.1.1,2.4.1,unit_del,155,flip.1] coffee!=4|ivory=1|ivory=3|ivory=5. 215 [para_into,161.1.1,2.3.1,unit_del,160,flip.1] ayellow!=3|eng=1|eng=4|eng=5. 217 [para_into,162.1.1,2.4.1,unit_del,155,flip.1] eng!=4|ivory=1|ivory=3|ivory=5. 219 [para_into,163.1.1,2.5.1,unit_del,160,flip.1] coffee!=5|eng=1|eng=3|eng=4. 225 [binary,76.1,10.1,flip.1] horse!=fox. 271 [para_into,225.1.1,2.2.1,flip.1] fox!=2|horse=1|horse=3|horse=4|horse=5. 308 [binary,77.1,12.1,flip.1] japan!=1. 309 [binary,77.1,11.1,flip.1] japan!=atea. 310 [binary,77.1,10.1] atea!=1. 314 [binary,77.1,6.1,flip.1] japan!=eng. 315 [binary,77.1,5.1] eng!=1. 328 [back_unit_del,315.1,219.2] coffee!=5|eng=3|eng=4. 329 [back_unit_del,315.1,215.2] ayellow!=3|eng=4|eng=5. 356 [para_into,309.1.1,2.4.1,unit_del,308,flip.1] atea!=4|japan=2|japan=3|japan=5. 359 [binary,310.1,2.1] atea=2|atea=3|atea=4|atea=5. 378 [binary,78.1,12.1] lucky!=japan. 379 [binary,78.1,11.1,flip.1] japan!=chest. 382 [binary,78.1,8.1,flip.1] lucky!=ayellow. 414 [para_into,378.1.1,2.2.1,flip.1] japan!=2|lucky=1|lucky=3|lucky=4|lucky=5. 455 [binary,79.1,10.1,flip.1] lucky!=3. 457 [binary,79.1,8.1,flip.1] lucky!=atea. 458 [binary,79.1,7.1] atea!=3. 460 [binary,79.1,5.1,flip.1] lucky!=coffee. 461 [binary,79.1,4.1] coffee!=3. 462 [binary,79.1,3.1] coffee!=atea. 474 [back_unit_del,455.1,414.3] japan!=2|lucky=1|lucky=4|lucky=5. 484 [back_unit_del,458.1,359.2] atea=2|atea=4|atea=5. 523 [para_into,457.1.1,2.4.1,unit_del,455,flip.1] atea!=4|lucky=1|lucky=2|lucky=5. 530 [para_into,462.1.1,2.5.1,unit_del,157,461,flip.1] atea!=5|coffee=1|coffee=4. 532 [106,split.1] successor(ayellow,horse). 541 [binary,532.1,22.1,unit_del,154] horse=2|ayellow=3|ayellow=4. 549 [binary,532.1,14.1,unit_del,154] ayellow=1|ayellow=3|ayellow=4. 562 [117,split_neg.1.2] -successor(chest,fox). 563 [117,split.1.2] successor(fox,chest). 564 [binary,562.1,33.1] chest!=4|fox!=5. 566 [binary,562.1,31.1] chest!=2|fox!=3. 583 [binary,563.1,25.1] chest=2|fox=2|chest=4|chest=5. 611 [181,split_neg.1.2.2] ivory!=3. 613,612 [181,split.1.2.2] ivory=4. 614 [back_unit_del,611.1,217.3,demod,613,613,unit_del,151,144] eng!=4. 615 [back_unit_del,611.1,210.3,demod,613,613,unit_del,151,144] coffee!=4. 616 [back_unit_del,611.1,206.3,demod,613,613,unit_del,151,144] ayellow!=4. 619,618 [back_unit_del,611.1,182.1] coffee=5. 637 [back_unit_del,614.1,329.2] ayellow!=3|eng=5. 639,638 [back_unit_del,614.1,328.3,demod,619,unit_del,1] eng=3. 640 [back_unit_del,615.1,530.3,demod,619,unit_del,150] atea!=5. 648 [back_unit_del,616.1,549.3] ayellow=1|ayellow=3. 650 [back_unit_del,616.1,541.3] horse=2|ayellow=3. 670 [back_demod,460,demod,619] lucky!=5. 673 [back_demod,637,demod,639,unit_del,145] ayellow!=3. 690 [back_demod,314,demod,639] japan!=3. 695 [back_unit_del,640.1,484.3] atea=2|atea=4. 713 [back_unit_del,670.1,523.4] atea!=4|lucky=1|lucky=2. 721 [back_unit_del,670.1,474.4] japan!=2|lucky=1|lucky=4. 729,728 [back_unit_del,673.1,650.2] horse=2. 731,730 [back_unit_del,673.1,648.2] ayellow=1. 757 [back_unit_del,690.1,356.3] atea!=4|japan=2|japan=5. 769 [back_demod,271,demod,729,729,729,729,unit_del,153,149,148,147] fox!=2. 797 [back_demod,382,demod,731] lucky!=1. 820 [back_unit_del,769.1,583.2] chest=2|chest=4|chest=5. 860 [back_unit_del,797.1,721.2] japan!=2|lucky=4. 864 [back_unit_del,797.1,713.2] atea!=4|lucky=2. 870 [564,split.1.2.2.1] chest!=4. 882 [back_unit_del,870.1,820.2] chest=2|chest=5. 898 [566,split.1.2.2.1.1.1] chest!=2. 908,907 [back_unit_del,898.1,882.1] chest=5. 935 [back_demod,379,demod,908] japan!=5. 946 [back_unit_del,935.1,757.3] atea!=4|japan=2. 980,979 [695,split.1.2.2.1.1.1.1.1.2] atea=4. 987,986 [back_demod,946,demod,980,unit_del,1] japan=2. 989,988 [back_demod,864,demod,980,unit_del,1] lucky=2. 993 [back_demod,860,demod,987,989,unit_del,1,148] $F. ------------ end of proof ------------- ------- statistics (process 8869) ------- clauses given 137 clauses generated 16220 clauses kept 954 clauses forward subsumed 988 clauses back subsumed 498 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8869 finished Mon Aug 2 15:31:13 2004 Refuted case [1.2.2.1.1.1.1.1.2]. ------- statistics (process 8867) ------- clauses given 137 clauses generated 16218 clauses kept 943 clauses forward subsumed 966 clauses back subsumed 496 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8867 finished Mon Aug 2 15:31:13 2004 Refuted case [1.2.2.1.1.1.1.1]. The Assumption for case [1.2.2.1.1.1.1.1] was not used; therefore we skip case: [1.2.2.1.1.1.1.2]. ------- statistics (process 8866) ------- clauses given 135 clauses generated 16124 clauses kept 936 clauses forward subsumed 950 clauses back subsumed 494 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8866 finished Mon Aug 2 15:31:13 2004 Refuted case [1.2.2.1.1.1.1]. The Assumption for case [1.2.2.1.1.1.1] was not used; therefore we skip case: [1.2.2.1.1.1.2]. ------- statistics (process 8865) ------- clauses given 133 clauses generated 16015 clauses kept 932 clauses forward subsumed 944 clauses back subsumed 489 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.09 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8865 finished Mon Aug 2 15:31:13 2004 Refuted case [1.2.2.1.1.1]. Possible model detected on branch [1.2.2.1.1.2]. Case [1.2.2.1.1.2] (process 8870): Assumption: 900 [566,split.1.2.2.1.1.2] fox!=3. Possible model detected on branch [1.2.2.1.1.2]. Here are the clauses in Usable and SoS. It seems that no more inferences or splitting can be done. If the search strategy is complete, these clauses should lead to a model of the input. list(usable). 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 3 [] -distinct5(x,y,z,u,v)|x!=y. 4 [] -distinct5(x,y,z,u,v)|x!=z. 5 [] -distinct5(x,y,z,u,v)|x!=u. 6 [] -distinct5(x,y,z,u,v)|x!=v. 7 [] -distinct5(x,y,z,u,v)|y!=z. 8 [] -distinct5(x,y,z,u,v)|y!=u. 9 [] -distinct5(x,y,z,u,v)|y!=v. 10 [] -distinct5(x,y,z,u,v)|z!=u. 11 [] -distinct5(x,y,z,u,v)|z!=v. 12 [] -distinct5(x,y,z,u,v)|u!=v. 13 [] distinct5(x,y,z,u,v)|x=y|x=z|x=u|x=v|y=z|y=u|y=v|z=u|z=v|u=v. 14 [] -successor(x,y)|x=1|x=2|x=3|x=4. 15 [] -successor(x,y)|x=1|x=2|x=3|y=5. 16 [] -successor(x,y)|x=1|x=2|y=4|x=4. 17 [] -successor(x,y)|x=1|x=2|y=4|y=5. 18 [] -successor(x,y)|x=1|y=3|x=3|x=4. 19 [] -successor(x,y)|x=1|y=3|x=3|y=5. 20 [] -successor(x,y)|x=1|y=3|y=4|x=4. 21 [] -successor(x,y)|x=1|y=3|y=4|y=5. 22 [] -successor(x,y)|y=2|x=2|x=3|x=4. 23 [] -successor(x,y)|y=2|x=2|x=3|y=5. 24 [] -successor(x,y)|y=2|x=2|y=4|x=4. 25 [] -successor(x,y)|y=2|x=2|y=4|y=5. 26 [] -successor(x,y)|y=2|y=3|x=3|x=4. 27 [] -successor(x,y)|y=2|y=3|x=3|y=5. 28 [] -successor(x,y)|y=2|y=3|y=4|x=4. 29 [] -successor(x,y)|y=2|y=3|y=4|y=5. 30 [] successor(x,y)|x!=1|y!=2. 31 [] successor(x,y)|x!=2|y!=3. 32 [] successor(x,y)|x!=3|y!=4. 33 [] successor(x,y)|x!=4|y!=5. 34 [] -next_to(x,y)|successor(x,y)|successor(y,x). 35 [] next_to(x,y)| -successor(x,y). 36 [] next_to(x,y)| -successor(y,x). 58 [] milk=3. 60 [] norw=1. 68 [] blue=2. 37 [] distinct5(1,2,3,4,5). 144 [binary,37.1,12.1,flip.1] 5!=4. 145 [binary,37.1,11.1,flip.1] 5!=3. 146 [binary,37.1,10.1,flip.1] 4!=3. 147 [binary,37.1,9.1,flip.1] 5!=2. 148 [binary,37.1,8.1,flip.1] 4!=2. 149 [binary,37.1,7.1,flip.1] 3!=2. 150 [binary,37.1,6.1,flip.1] 5!=1. 151 [binary,37.1,5.1,flip.1] 4!=1. 152 [binary,37.1,4.1,flip.1] 3!=1. 153 [binary,37.1,3.1,flip.1] 2!=1. 612 [181,split.1.2.2] ivory=4. 618 [back_unit_del,611.1,182.1] coffee=5. 620 [back_unit_del,611.1,176.3,demod,619,613,613,unit_del,151,144] successor(4,5). 621 [back_unit_del,611.1,173.3,demod,619,613,613,unit_del,151,144] next_to(5,4). 622 [back_unit_del,611.1,170.3,demod,619,613,613,unit_del,151,144] next_to(4,5). 638 [back_unit_del,614.1,328.3,demod,619,unit_del,1] eng=3. 671 [back_demod,50,demod,619] green=5. 691 [back_demod,44,demod,639] red=3. 728 [back_unit_del,673.1,650.2] horse=2. 730 [back_unit_del,673.1,648.2] ayellow=1. 732 [back_unit_del,673.1,646.2,demod,729] successor(1,2). 733 [back_unit_del,673.1,644.2,demod,729] next_to(2,1). 766 [back_demod,708,demod,729] next_to(1,2). 798 [back_demod,56,demod,731] kool=1. 898 [566,split_neg.1.2.2.1.1.2] chest=2. 906 [back_demod,884,demod,899,unit_del,147] fox=1. 908 [back_demod,858,demod,899,unit_del,1] lucky=4. 911 [back_demod,821,demod,899,907,907,907,unit_del,152,151,150] -successor(2,1). 941 [back_demod,63,demod,909] orange=4. 953 [back_unit_del,932.1,695.2] atea=2. 957 [back_unit_del,933.1,698.3,unit_del,955] apple=1. 959 [back_unit_del,934.1,918.1] japan=5. 966 [back_unit_del,935.1,868.2,unit_del,947] asnail=3. 970 [back_unit_del,945.1,804.2] aspan=4. 973 [back_demod,52,demod,954] aukra=2. 975 [back_demod,66,demod,960] parli=5. 981 [back_demod,54,demod,967] old=3. 983 [back_demod,952,demod,971,unit_del,1,980] azebra=5. 985 [back_demod,47,demod,971] dog=4. 678 [back_demod,627,demod,639,unit_del,673,643] distinct5(3,5,4,1,2). 964 [back_unit_del,935.1,914.2,demod,960,unit_del,947] distinct5(3,1,2,4,5). 969 [back_unit_del,945.1,806.2,demod,954,960] distinct5(3,4,2,1,5). 972 [back_demod,940,demod,954,958,unit_del,153] distinct5(5,2,3,4,1). 987 [back_unit_del,980.1,979.2,demod,984,unit_del,144] distinct5(4,3,1,2,5). end_of_list. list(sos). end_of_list. ------- statistics (process 8870) ------- clauses given 141 clauses generated 17799 clauses kept 947 clauses forward subsumed 1158 clauses back subsumed 482 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.17 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8870 finished Mon Aug 2 15:31:13 2004 ------- statistics (process 8864) ------- clauses given 121 clauses generated 14267 clauses kept 871 clauses forward subsumed 721 clauses back subsumed 456 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8864 finished Mon Aug 2 15:31:13 2004 ------- statistics (process 8863) ------- clauses given 119 clauses generated 14150 clauses kept 859 clauses forward subsumed 715 clauses back subsumed 445 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8863 finished Mon Aug 2 15:31:13 2004 ------- statistics (process 8862) ------- clauses given 117 clauses generated 14029 clauses kept 843 clauses forward subsumed 709 clauses back subsumed 411 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.17 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8862 finished Mon Aug 2 15:31:13 2004 ------- statistics (process 8857) ------- clauses given 90 clauses generated 10881 clauses kept 592 clauses forward subsumed 339 clauses back subsumed 166 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8857 finished Mon Aug 2 15:31:13 2004 ------- statistics (process 8847) ------- clauses given 86 clauses generated 10382 clauses kept 543 clauses forward subsumed 331 clauses back subsumed 155 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8847 finished Mon Aug 2 15:31:13 2004 ------- statistics (process 8846) ------- clauses given 83 clauses generated 10047 clauses kept 513 clauses forward subsumed 321 clauses back subsumed 131 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.60 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 sec) Process 8846 finished Mon Aug 2 15:31:13 2004 otter-3.3f/examples/split/pigeon5.in0100644000076400007640000000170306471147021017053 0ustar mccunemccune% % Pigeon hole problem -- 5 pigeons into 4 holes. % set(binary_res) . set(split_when_given). set(split_pos). clear(print_kept). clear(print_back_sub). assign(stats_level, 1). list(sos) . % Every pigeon flies into a hole. p00 | p01 | p02 | p03 . p04 | p05 | p06 | p07 . p08 | p09 | p10 | p11 . p12 | p13 | p14 | p15 . p16 | p17 | p18 | p19 . % Each hole holds at most one piegeon. -p00 | -p04 . -p00 | -p08 . -p00 | -p12 . -p00 | -p16 . -p04 | -p08 . -p04 | -p12 . -p04 | -p16 . -p08 | -p12 . -p08 | -p16 . -p12 | -p16 . -p01 | -p05 . -p01 | -p09 . -p01 | -p13 . -p01 | -p17 . -p05 | -p09 . -p05 | -p13 . -p05 | -p17 . -p09 | -p13 . -p09 | -p17 . -p13 | -p17 . -p02 | -p06 . -p02 | -p10 . -p02 | -p14 . -p02 | -p18 . -p06 | -p10 . -p06 | -p14 . -p06 | -p18 . -p10 | -p14 . -p10 | -p18 . -p14 | -p18 . -p03 | -p07 . -p03 | -p11 . -p03 | -p15 . -p03 | -p19 . -p07 | -p11 . -p07 | -p15 . -p07 | -p19 . -p11 | -p15 . -p11 | -p19 . -p15 | -p19 . end_of_list . otter-3.3f/examples/split/GEO036-2.in0100644000076400007640000000722506767772044016535 0ustar mccunemccune%-------------------------------------------------------------------------- % File : GEO036-2 : TPTP v2.0.0. Released v1.0.0. % Domain : Geometry % Problem : The 3 axiom set points are distinct % Version : [Quaife, 1989] axioms. % English : % Refs : Schwabbauser W., Szmielew W., and Tarski A. (1983), % Metamathematische Methoden in der Geometrie, Springer-Verlag, % Berlin, Germany. % : Quaife A. (1989), Automated Development of Tarski's Geometry, % Journal of Automated Reasoning 5(1), 97-118. % Source : [TPTP] % Names : % Status : unsatisfiable % Rating : 0.33 v2.0.0 % Syntax : Number of clauses : 20 ( 6 non-Horn; 7 unit; 16 RR) % Number of literals : 60 ( 11 equality) % Maximal clause size : 8 ( 3 average) % Number of predicates : 3 ( 0 propositional; 2-4 arity) % Number of functors : 8 ( 3 constant; 0-6 arity) % Number of variables : 72 ( 3 singleton) % Maximal term depth : 2 ( 1 average) % Comments : % : tptp2X: -fotter:hypothesis:[set(auto),set(tptp_eq)] -trm_equality:stfp GEO036-2.p %-------------------------------------------------------------------------- set(prolog_style_variables). set(auto2). set(tptp_eq). set(split_when_given). set(split_pos). list(usable). % reflexivity, axiom. equal(A,A). % reflexivity_for_equidistance, axiom. equidistant(A,B,B,A). % transitivity_for_equidistance, axiom. -equidistant(A,B,C,D) | -equidistant(A,B,E,F) | equidistant(C,D,E,F). % identity_for_equidistance, axiom. -equidistant(A,B,C,C) | equal(A,B). % segment_construction1, axiom. between(A,B,extension(A,B,C,D)). % segment_construction2, axiom. equidistant(A,extension(B,A,C,D),C,D). % outer_five_segment, axiom. -equidistant(A,B,C,D) | -equidistant(B,E,D,F) | -equidistant(A,G,C,H) | -equidistant(B,G,D,H) | -between(A,B,E) | -between(C,D,F) | equal(A,B) | equidistant(E,G,F,H). % identity_for_betweeness, axiom. -between(A,B,A) | equal(A,B). % inner_pasch1, axiom. -between(A,B,C) | -between(D,E,C) | between(B,inner_pasch(A,B,C,E,D),D). % inner_pasch2, axiom. -between(A,B,C) | -between(D,E,C) | between(E,inner_pasch(A,B,C,E,D),A). % lower_dimension1, axiom. -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). % lower_dimension2, axiom. -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). % lower_dimension3, axiom. -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). % upper_dimension, axiom. -equidistant(A,B,A,C) | -equidistant(D,B,D,C) | -equidistant(E,B,E,C) | between(A,D,E) | between(D,E,A) | between(E,A,D) | equal(B,C). % euclid1, axiom. -between(A,B,C) | -between(D,B,E) | equal(A,B) | between(A,D,euclid1(A,D,B,E,C)). % euclid2, axiom. -between(A,B,C) | -between(D,B,E) | equal(A,B) | between(A,E,euclid2(A,D,B,E,C)). % euclid3, axiom. -between(A,B,C) | -between(D,B,E) | equal(A,B) | between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)). % continuity1, axiom. -equidistant(A,B,A,C) | -equidistant(A,D,A,E) | -between(A,B,D) | -between(B,F,D) | between(C,continuous(A,B,C,F,D,E),E). % continuity2, axiom. -equidistant(A,B,A,C) | -equidistant(A,D,A,E) | -between(A,B,D) | -between(B,F,D) | equidistant(A,F,A,continuous(A,B,C,F,D,E)). end_of_list. list(sos). % prove_axioms_points_are_distinct, conjecture. equal(lower_dimension_point_1,lower_dimension_point_2) | equal(lower_dimension_point_2,lower_dimension_point_3) | equal(lower_dimension_point_1,lower_dimension_point_3). end_of_list. %-------------------------------------------------------------------------- otter-3.3f/examples/split/wang3.in0100644000076400007640000000147306472064322016533 0ustar mccunemccune% This is the Wang 3 problem. set(knuth_bendix). set(binary_res). set(split_when_given). set(split_pos). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level, 1). list(sos). (m != b). (y = j) | -p(y,j) | (y = k). (k = j) | p(k,j). end_of_list. list(usable). (y = m) | p(y,m) | (v1 = m) | (v1 = y) | -p(y,v1) | -p(v1,y). (y = b) | -p(y,b) | (v = b) | (v = y) | -p(y,v) | -p(v,y). (y = k) | (y = m) | (y = b) | -p(y,k). (y = m) | -p(y,m) | (f(y) != m). (y = m) | -p(y,m) | (f(y) != y). (y = m) | -p(y,m) | p(y,f(y)). (y = m) | -p(y,m) | p(f(y),y). (y = b) | p(y,b) | (g(y) != b). (y = b) | p(y,b) | (g(y) != y). (y = b) | p(y,b) | p(y,g(y)). (y = b) | p(y,b) | p(g(y),y). (m = k) | p(m,k). (b = k) | p(b,k). (x = x). end_of_list. otter-3.3f/examples/split/zebra2.in0100644000076400007640000000531406510475161016677 0ustar mccunemccune% This is the zebra puzzle with Dale Myers' representation. % The set of clauses is satisfiable, and a model is an answer. set(binary_res). set(knuth_bendix). set(split_when_given). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level, 1). list(usable). x=x. % The domain consists of exactly 5 elements, named 1,2,3,4,5. % In the following clause, it is important that the variables % are on the left-hand sides of the equations, because ground % equations are oriented with the heavy side on the left, and % integers are lighter than the other constants. The lexicographic % ASCII ordering is used to compare symbols.) Don't worry about % any ground literals---Otter will flip the backward ones. x=1 | x=2 | x=3 | x=4 | x=5. 1!=2. 1!=3. 1!=4. 1!=5. 2!=3. 2!=4. 2!=5. 3!=4. 3!=5. 4!=5. % There are 5 different colors. red!=green. red!=ivory. red!=ayellow. red!=blue. green!=ivory. green!=ayellow. green!=blue. ivory!=ayellow. ivory!=blue. ayellow!=blue. % There are 5 different nationalities. eng!=aspan. eng!=aukra. eng!=norw. eng!=japan. aspan!=aukra. aspan!=norw. aspan!=japan. aukra!=norw. aukra!=japan. norw!=japan. % There are 5 different pets. dog!=asnail. dog!=fox. dog!=horse. dog!=azebra. asnail!=fox. asnail!=horse. asnail!=azebra. fox!=horse. fox!=azebra. horse!=azebra. % There are 5 different drinks. coffee!=atea. coffee!=milk. coffee!=orange. coffee!=apple. atea!=milk. atea!=orange. atea!=apple. milk!=orange. milk!=apple. orange!=apple. % There are 5 different smokes. old!=kool. old!=chest. old!=lucky. old!=parli. kool!=chest. kool!=lucky. kool!=parli. chest!=lucky. chest!=parli. lucky!=parli. end_of_list. list(sos). % Here are the clues. % Simple clues. eng=red. aspan=dog. coffee=green. aukra=atea. old=asnail. kool=ayellow. milk=3. norw=1. lucky=orange. japan=parli. blue=2. % Conditional clues. % ivory is to the left of green. ivory!=5. % missing from 3.0.5 version green!=1. % missing from 3.0.5 version ivory!=1 | green=2. ivory!=2 | green=3. ivory!=3 | green=4. ivory!=4 | green=5. ivory=1 | green!=2. ivory=2 | green!=3. ivory=3 | green!=4. ivory=4 | green!=5. % kool is next to horse. kool!=1 | horse=2. kool!=2 | horse=1 | horse=3. kool!=3 | horse=2 | horse=4. kool!=4 | horse=3 | horse=5. kool!=5 | horse=4. horse!=1 | kool=2. horse!=2 | kool=1 | kool=3. horse!=3 | kool=2 | kool=4. horse!=4 | kool=3 | kool=5. horse!=5 | kool=4. % chest is next to fox. chest!=1 | fox=2. chest!=2 | fox=1 | fox=3. chest!=3 | fox=2 | fox=4. chest!=4 | fox=3 | fox=5. chest!=5 | fox=4. fox!=1 | chest=2. fox!=2 | chest=1 | chest=3. fox!=3 | chest=2 | chest=4. fox!=4 | chest=3 | chest=5. fox!=5 | chest=4. end_of_list. otter-3.3f/examples/split/README.more0100644000076400007640000000161307313672013016776 0ustar mccunemccuneHere are some problems that we used to test the new splitting rule. GEO010-2.in from the TPTP GEO036-2.in from the TPTP GRP025-1.in from the TPTP group2.in A group with at most 2 elements is commutative. pair.in Ordered pair theorem in naive set theory. pigeon5.in Propositional pigeon hole problem (5 pigeons). power.in Powerset-intersection theorem in naive set theory. wang3.in Wang-3 problem. zebra2.in This is the zebra puzzle with Dale Myers' rep. (satisfiable). zebra4.in Like Z2, with a cleaner rep., but it takes longer (satisfiable). noncomm-group.in Find a noncommutative group of order 6. otter-3.3f/examples/split/noncomm-group.out0100664000076400007640000030126310103522214020500 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:08 2004 The command was "../../bin/otter". The process ID is 8662. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(split_when_given). dependent: set(back_unit_deletion). dependent: set(unit_deletion). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_proofs). assign(stats_level,1). list(usable). 0 [] x=x. end_of_list. list(sos). 0 [] 0!=1. 0 [] 0!=2. 0 [] 0!=3. 0 [] 0!=4. 0 [] 0!=5. 0 [] 1!=2. 0 [] 1!=3. 0 [] 1!=4. 0 [] 1!=5. 0 [] 2!=3. 0 [] 2!=4. 0 [] 2!=5. 0 [] 3!=4. 0 [] 3!=5. 0 [] 4!=5. 0 [] e=0. 0 [] f(1,2)!=f(2,1). 0 [] f(e,0)=0. 0 [] f(e,1)=1. 0 [] f(e,2)=2. 0 [] f(e,3)=3. 0 [] f(e,4)=4. 0 [] f(e,5)=5. 0 [] f(g(0),0)=e. 0 [] f(g(1),1)=e. 0 [] f(g(2),2)=e. 0 [] f(g(3),3)=e. 0 [] f(g(4),4)=e. 0 [] f(g(5),5)=e. 0 [] f(f(0,0),0)=f(0,f(0,0)). 0 [] f(f(1,1),1)=f(1,f(1,1)). 0 [] f(f(1,0),1)=f(1,f(0,1)). 0 [] f(f(0,1),1)=f(0,f(1,1)). 0 [] f(f(0,0),1)=f(0,f(0,1)). 0 [] f(f(1,1),0)=f(1,f(1,0)). 0 [] f(f(0,1),0)=f(0,f(1,0)). 0 [] f(f(1,0),0)=f(1,f(0,0)). 0 [] f(f(2,2),2)=f(2,f(2,2)). 0 [] f(f(2,1),2)=f(2,f(1,2)). 0 [] f(f(2,0),2)=f(2,f(0,2)). 0 [] f(f(1,2),2)=f(1,f(2,2)). 0 [] f(f(1,1),2)=f(1,f(1,2)). 0 [] f(f(1,0),2)=f(1,f(0,2)). 0 [] f(f(0,2),2)=f(0,f(2,2)). 0 [] f(f(0,1),2)=f(0,f(1,2)). 0 [] f(f(0,0),2)=f(0,f(0,2)). 0 [] f(f(2,2),1)=f(2,f(2,1)). 0 [] f(f(2,2),0)=f(2,f(2,0)). 0 [] f(f(1,2),1)=f(1,f(2,1)). 0 [] f(f(1,2),0)=f(1,f(2,0)). 0 [] f(f(0,2),1)=f(0,f(2,1)). 0 [] f(f(0,2),0)=f(0,f(2,0)). 0 [] f(f(2,1),1)=f(2,f(1,1)). 0 [] f(f(2,1),0)=f(2,f(1,0)). 0 [] f(f(2,0),1)=f(2,f(0,1)). 0 [] f(f(2,0),0)=f(2,f(0,0)). 0 [] f(f(3,3),3)=f(3,f(3,3)). 0 [] f(f(3,2),3)=f(3,f(2,3)). 0 [] f(f(3,1),3)=f(3,f(1,3)). 0 [] f(f(3,0),3)=f(3,f(0,3)). 0 [] f(f(2,3),3)=f(2,f(3,3)). 0 [] f(f(2,2),3)=f(2,f(2,3)). 0 [] f(f(2,1),3)=f(2,f(1,3)). 0 [] f(f(2,0),3)=f(2,f(0,3)). 0 [] f(f(1,3),3)=f(1,f(3,3)). 0 [] f(f(1,2),3)=f(1,f(2,3)). 0 [] f(f(1,1),3)=f(1,f(1,3)). 0 [] f(f(1,0),3)=f(1,f(0,3)). 0 [] f(f(0,3),3)=f(0,f(3,3)). 0 [] f(f(0,2),3)=f(0,f(2,3)). 0 [] f(f(0,1),3)=f(0,f(1,3)). 0 [] f(f(0,0),3)=f(0,f(0,3)). 0 [] f(f(3,3),2)=f(3,f(3,2)). 0 [] f(f(3,3),1)=f(3,f(3,1)). 0 [] f(f(3,3),0)=f(3,f(3,0)). 0 [] f(f(2,3),2)=f(2,f(3,2)). 0 [] f(f(2,3),1)=f(2,f(3,1)). 0 [] f(f(2,3),0)=f(2,f(3,0)). 0 [] f(f(1,3),2)=f(1,f(3,2)). 0 [] f(f(1,3),1)=f(1,f(3,1)). 0 [] f(f(1,3),0)=f(1,f(3,0)). 0 [] f(f(0,3),2)=f(0,f(3,2)). 0 [] f(f(0,3),1)=f(0,f(3,1)). 0 [] f(f(0,3),0)=f(0,f(3,0)). 0 [] f(f(3,2),2)=f(3,f(2,2)). 0 [] f(f(3,2),1)=f(3,f(2,1)). 0 [] f(f(3,2),0)=f(3,f(2,0)). 0 [] f(f(3,1),2)=f(3,f(1,2)). 0 [] f(f(3,1),1)=f(3,f(1,1)). 0 [] f(f(3,1),0)=f(3,f(1,0)). 0 [] f(f(3,0),2)=f(3,f(0,2)). 0 [] f(f(3,0),1)=f(3,f(0,1)). 0 [] f(f(3,0),0)=f(3,f(0,0)). 0 [] f(f(4,4),4)=f(4,f(4,4)). 0 [] f(f(4,3),4)=f(4,f(3,4)). 0 [] f(f(4,2),4)=f(4,f(2,4)). 0 [] f(f(4,1),4)=f(4,f(1,4)). 0 [] f(f(4,0),4)=f(4,f(0,4)). 0 [] f(f(3,4),4)=f(3,f(4,4)). 0 [] f(f(3,3),4)=f(3,f(3,4)). 0 [] f(f(3,2),4)=f(3,f(2,4)). 0 [] f(f(3,1),4)=f(3,f(1,4)). 0 [] f(f(3,0),4)=f(3,f(0,4)). 0 [] f(f(2,4),4)=f(2,f(4,4)). 0 [] f(f(2,3),4)=f(2,f(3,4)). 0 [] f(f(2,2),4)=f(2,f(2,4)). 0 [] f(f(2,1),4)=f(2,f(1,4)). 0 [] f(f(2,0),4)=f(2,f(0,4)). 0 [] f(f(1,4),4)=f(1,f(4,4)). 0 [] f(f(1,3),4)=f(1,f(3,4)). 0 [] f(f(1,2),4)=f(1,f(2,4)). 0 [] f(f(1,1),4)=f(1,f(1,4)). 0 [] f(f(1,0),4)=f(1,f(0,4)). 0 [] f(f(0,4),4)=f(0,f(4,4)). 0 [] f(f(0,3),4)=f(0,f(3,4)). 0 [] f(f(0,2),4)=f(0,f(2,4)). 0 [] f(f(0,1),4)=f(0,f(1,4)). 0 [] f(f(0,0),4)=f(0,f(0,4)). 0 [] f(f(4,4),3)=f(4,f(4,3)). 0 [] f(f(4,4),2)=f(4,f(4,2)). 0 [] f(f(4,4),1)=f(4,f(4,1)). 0 [] f(f(4,4),0)=f(4,f(4,0)). 0 [] f(f(3,4),3)=f(3,f(4,3)). 0 [] f(f(3,4),2)=f(3,f(4,2)). 0 [] f(f(3,4),1)=f(3,f(4,1)). 0 [] f(f(3,4),0)=f(3,f(4,0)). 0 [] f(f(2,4),3)=f(2,f(4,3)). 0 [] f(f(2,4),2)=f(2,f(4,2)). 0 [] f(f(2,4),1)=f(2,f(4,1)). 0 [] f(f(2,4),0)=f(2,f(4,0)). 0 [] f(f(1,4),3)=f(1,f(4,3)). 0 [] f(f(1,4),2)=f(1,f(4,2)). 0 [] f(f(1,4),1)=f(1,f(4,1)). 0 [] f(f(1,4),0)=f(1,f(4,0)). 0 [] f(f(0,4),3)=f(0,f(4,3)). 0 [] f(f(0,4),2)=f(0,f(4,2)). 0 [] f(f(0,4),1)=f(0,f(4,1)). 0 [] f(f(0,4),0)=f(0,f(4,0)). 0 [] f(f(4,3),3)=f(4,f(3,3)). 0 [] f(f(4,3),2)=f(4,f(3,2)). 0 [] f(f(4,3),1)=f(4,f(3,1)). 0 [] f(f(4,3),0)=f(4,f(3,0)). 0 [] f(f(4,2),3)=f(4,f(2,3)). 0 [] f(f(4,2),2)=f(4,f(2,2)). 0 [] f(f(4,2),1)=f(4,f(2,1)). 0 [] f(f(4,2),0)=f(4,f(2,0)). 0 [] f(f(4,1),3)=f(4,f(1,3)). 0 [] f(f(4,1),2)=f(4,f(1,2)). 0 [] f(f(4,1),1)=f(4,f(1,1)). 0 [] f(f(4,1),0)=f(4,f(1,0)). 0 [] f(f(4,0),3)=f(4,f(0,3)). 0 [] f(f(4,0),2)=f(4,f(0,2)). 0 [] f(f(4,0),1)=f(4,f(0,1)). 0 [] f(f(4,0),0)=f(4,f(0,0)). 0 [] f(f(5,5),5)=f(5,f(5,5)). 0 [] f(f(5,4),5)=f(5,f(4,5)). 0 [] f(f(5,3),5)=f(5,f(3,5)). 0 [] f(f(5,2),5)=f(5,f(2,5)). 0 [] f(f(5,1),5)=f(5,f(1,5)). 0 [] f(f(5,0),5)=f(5,f(0,5)). 0 [] f(f(4,5),5)=f(4,f(5,5)). 0 [] f(f(4,4),5)=f(4,f(4,5)). 0 [] f(f(4,3),5)=f(4,f(3,5)). 0 [] f(f(4,2),5)=f(4,f(2,5)). 0 [] f(f(4,1),5)=f(4,f(1,5)). 0 [] f(f(4,0),5)=f(4,f(0,5)). 0 [] f(f(3,5),5)=f(3,f(5,5)). 0 [] f(f(3,4),5)=f(3,f(4,5)). 0 [] f(f(3,3),5)=f(3,f(3,5)). 0 [] f(f(3,2),5)=f(3,f(2,5)). 0 [] f(f(3,1),5)=f(3,f(1,5)). 0 [] f(f(3,0),5)=f(3,f(0,5)). 0 [] f(f(2,5),5)=f(2,f(5,5)). 0 [] f(f(2,4),5)=f(2,f(4,5)). 0 [] f(f(2,3),5)=f(2,f(3,5)). 0 [] f(f(2,2),5)=f(2,f(2,5)). 0 [] f(f(2,1),5)=f(2,f(1,5)). 0 [] f(f(2,0),5)=f(2,f(0,5)). 0 [] f(f(1,5),5)=f(1,f(5,5)). 0 [] f(f(1,4),5)=f(1,f(4,5)). 0 [] f(f(1,3),5)=f(1,f(3,5)). 0 [] f(f(1,2),5)=f(1,f(2,5)). 0 [] f(f(1,1),5)=f(1,f(1,5)). 0 [] f(f(1,0),5)=f(1,f(0,5)). 0 [] f(f(0,5),5)=f(0,f(5,5)). 0 [] f(f(0,4),5)=f(0,f(4,5)). 0 [] f(f(0,3),5)=f(0,f(3,5)). 0 [] f(f(0,2),5)=f(0,f(2,5)). 0 [] f(f(0,1),5)=f(0,f(1,5)). 0 [] f(f(0,0),5)=f(0,f(0,5)). 0 [] f(f(5,5),4)=f(5,f(5,4)). 0 [] f(f(5,5),3)=f(5,f(5,3)). 0 [] f(f(5,5),2)=f(5,f(5,2)). 0 [] f(f(5,5),1)=f(5,f(5,1)). 0 [] f(f(5,5),0)=f(5,f(5,0)). 0 [] f(f(4,5),4)=f(4,f(5,4)). 0 [] f(f(4,5),3)=f(4,f(5,3)). 0 [] f(f(4,5),2)=f(4,f(5,2)). 0 [] f(f(4,5),1)=f(4,f(5,1)). 0 [] f(f(4,5),0)=f(4,f(5,0)). 0 [] f(f(3,5),4)=f(3,f(5,4)). 0 [] f(f(3,5),3)=f(3,f(5,3)). 0 [] f(f(3,5),2)=f(3,f(5,2)). 0 [] f(f(3,5),1)=f(3,f(5,1)). 0 [] f(f(3,5),0)=f(3,f(5,0)). 0 [] f(f(2,5),4)=f(2,f(5,4)). 0 [] f(f(2,5),3)=f(2,f(5,3)). 0 [] f(f(2,5),2)=f(2,f(5,2)). 0 [] f(f(2,5),1)=f(2,f(5,1)). 0 [] f(f(2,5),0)=f(2,f(5,0)). 0 [] f(f(1,5),4)=f(1,f(5,4)). 0 [] f(f(1,5),3)=f(1,f(5,3)). 0 [] f(f(1,5),2)=f(1,f(5,2)). 0 [] f(f(1,5),1)=f(1,f(5,1)). 0 [] f(f(1,5),0)=f(1,f(5,0)). 0 [] f(f(0,5),4)=f(0,f(5,4)). 0 [] f(f(0,5),3)=f(0,f(5,3)). 0 [] f(f(0,5),2)=f(0,f(5,2)). 0 [] f(f(0,5),1)=f(0,f(5,1)). 0 [] f(f(0,5),0)=f(0,f(5,0)). 0 [] f(f(5,4),4)=f(5,f(4,4)). 0 [] f(f(5,4),3)=f(5,f(4,3)). 0 [] f(f(5,4),2)=f(5,f(4,2)). 0 [] f(f(5,4),1)=f(5,f(4,1)). 0 [] f(f(5,4),0)=f(5,f(4,0)). 0 [] f(f(5,3),4)=f(5,f(3,4)). 0 [] f(f(5,3),3)=f(5,f(3,3)). 0 [] f(f(5,3),2)=f(5,f(3,2)). 0 [] f(f(5,3),1)=f(5,f(3,1)). 0 [] f(f(5,3),0)=f(5,f(3,0)). 0 [] f(f(5,2),4)=f(5,f(2,4)). 0 [] f(f(5,2),3)=f(5,f(2,3)). 0 [] f(f(5,2),2)=f(5,f(2,2)). 0 [] f(f(5,2),1)=f(5,f(2,1)). 0 [] f(f(5,2),0)=f(5,f(2,0)). 0 [] f(f(5,1),4)=f(5,f(1,4)). 0 [] f(f(5,1),3)=f(5,f(1,3)). 0 [] f(f(5,1),2)=f(5,f(1,2)). 0 [] f(f(5,1),1)=f(5,f(1,1)). 0 [] f(f(5,1),0)=f(5,f(1,0)). 0 [] f(f(5,0),4)=f(5,f(0,4)). 0 [] f(f(5,0),3)=f(5,f(0,3)). 0 [] f(f(5,0),2)=f(5,f(0,2)). 0 [] f(f(5,0),1)=f(5,f(0,1)). 0 [] f(f(5,0),0)=f(5,f(0,0)). 0 [] g(0)=0|g(0)=1|g(0)=2|g(0)=3|g(0)=4|g(0)=5. 0 [] g(1)=0|g(1)=1|g(1)=2|g(1)=3|g(1)=4|g(1)=5. 0 [] g(2)=0|g(2)=1|g(2)=2|g(2)=3|g(2)=4|g(2)=5. 0 [] g(3)=0|g(3)=1|g(3)=2|g(3)=3|g(3)=4|g(3)=5. 0 [] g(4)=0|g(4)=1|g(4)=2|g(4)=3|g(4)=4|g(4)=5. 0 [] g(5)=0|g(5)=1|g(5)=2|g(5)=3|g(5)=4|g(5)=5. 0 [] f(0,0)=0|f(0,0)=1|f(0,0)=2|f(0,0)=3|f(0,0)=4|f(0,0)=5. 0 [] f(1,1)=0|f(1,1)=1|f(1,1)=2|f(1,1)=3|f(1,1)=4|f(1,1)=5. 0 [] f(0,1)=0|f(0,1)=1|f(0,1)=2|f(0,1)=3|f(0,1)=4|f(0,1)=5. 0 [] f(1,0)=0|f(1,0)=1|f(1,0)=2|f(1,0)=3|f(1,0)=4|f(1,0)=5. 0 [] f(2,2)=0|f(2,2)=1|f(2,2)=2|f(2,2)=3|f(2,2)=4|f(2,2)=5. 0 [] f(1,2)=0|f(1,2)=1|f(1,2)=2|f(1,2)=3|f(1,2)=4|f(1,2)=5. 0 [] f(0,2)=0|f(0,2)=1|f(0,2)=2|f(0,2)=3|f(0,2)=4|f(0,2)=5. 0 [] f(2,1)=0|f(2,1)=1|f(2,1)=2|f(2,1)=3|f(2,1)=4|f(2,1)=5. 0 [] f(2,0)=0|f(2,0)=1|f(2,0)=2|f(2,0)=3|f(2,0)=4|f(2,0)=5. 0 [] f(3,3)=0|f(3,3)=1|f(3,3)=2|f(3,3)=3|f(3,3)=4|f(3,3)=5. 0 [] f(2,3)=0|f(2,3)=1|f(2,3)=2|f(2,3)=3|f(2,3)=4|f(2,3)=5. 0 [] f(1,3)=0|f(1,3)=1|f(1,3)=2|f(1,3)=3|f(1,3)=4|f(1,3)=5. 0 [] f(0,3)=0|f(0,3)=1|f(0,3)=2|f(0,3)=3|f(0,3)=4|f(0,3)=5. 0 [] f(3,2)=0|f(3,2)=1|f(3,2)=2|f(3,2)=3|f(3,2)=4|f(3,2)=5. 0 [] f(3,1)=0|f(3,1)=1|f(3,1)=2|f(3,1)=3|f(3,1)=4|f(3,1)=5. 0 [] f(3,0)=0|f(3,0)=1|f(3,0)=2|f(3,0)=3|f(3,0)=4|f(3,0)=5. 0 [] f(4,4)=0|f(4,4)=1|f(4,4)=2|f(4,4)=3|f(4,4)=4|f(4,4)=5. 0 [] f(3,4)=0|f(3,4)=1|f(3,4)=2|f(3,4)=3|f(3,4)=4|f(3,4)=5. 0 [] f(2,4)=0|f(2,4)=1|f(2,4)=2|f(2,4)=3|f(2,4)=4|f(2,4)=5. 0 [] f(1,4)=0|f(1,4)=1|f(1,4)=2|f(1,4)=3|f(1,4)=4|f(1,4)=5. 0 [] f(0,4)=0|f(0,4)=1|f(0,4)=2|f(0,4)=3|f(0,4)=4|f(0,4)=5. 0 [] f(4,3)=0|f(4,3)=1|f(4,3)=2|f(4,3)=3|f(4,3)=4|f(4,3)=5. 0 [] f(4,2)=0|f(4,2)=1|f(4,2)=2|f(4,2)=3|f(4,2)=4|f(4,2)=5. 0 [] f(4,1)=0|f(4,1)=1|f(4,1)=2|f(4,1)=3|f(4,1)=4|f(4,1)=5. 0 [] f(4,0)=0|f(4,0)=1|f(4,0)=2|f(4,0)=3|f(4,0)=4|f(4,0)=5. 0 [] f(5,5)=0|f(5,5)=1|f(5,5)=2|f(5,5)=3|f(5,5)=4|f(5,5)=5. 0 [] f(4,5)=0|f(4,5)=1|f(4,5)=2|f(4,5)=3|f(4,5)=4|f(4,5)=5. 0 [] f(3,5)=0|f(3,5)=1|f(3,5)=2|f(3,5)=3|f(3,5)=4|f(3,5)=5. 0 [] f(2,5)=0|f(2,5)=1|f(2,5)=2|f(2,5)=3|f(2,5)=4|f(2,5)=5. 0 [] f(1,5)=0|f(1,5)=1|f(1,5)=2|f(1,5)=3|f(1,5)=4|f(1,5)=5. 0 [] f(0,5)=0|f(0,5)=1|f(0,5)=2|f(0,5)=3|f(0,5)=4|f(0,5)=5. 0 [] f(5,4)=0|f(5,4)=1|f(5,4)=2|f(5,4)=3|f(5,4)=4|f(5,4)=5. 0 [] f(5,3)=0|f(5,3)=1|f(5,3)=2|f(5,3)=3|f(5,3)=4|f(5,3)=5. 0 [] f(5,2)=0|f(5,2)=1|f(5,2)=2|f(5,2)=3|f(5,2)=4|f(5,2)=5. 0 [] f(5,1)=0|f(5,1)=1|f(5,1)=2|f(5,1)=3|f(5,1)=4|f(5,1)=5. 0 [] f(5,0)=0|f(5,0)=1|f(5,0)=2|f(5,0)=3|f(5,0)=4|f(5,0)=5. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back unit deletion with 1. ------------> process sos: ** KEPT (pick-wt=3): 3 [copy,2,flip.1] 1!=0. ** KEPT (pick-wt=3): 5 [copy,4,flip.1] 2!=0. ** KEPT (pick-wt=3): 7 [copy,6,flip.1] 3!=0. ** KEPT (pick-wt=3): 9 [copy,8,flip.1] 4!=0. ** KEPT (pick-wt=3): 11 [copy,10,flip.1] 5!=0. ** KEPT (pick-wt=3): 13 [copy,12,flip.1] 2!=1. ** KEPT (pick-wt=3): 15 [copy,14,flip.1] 3!=1. ** KEPT (pick-wt=3): 17 [copy,16,flip.1] 4!=1. ** KEPT (pick-wt=3): 19 [copy,18,flip.1] 5!=1. ** KEPT (pick-wt=3): 21 [copy,20,flip.1] 3!=2. ** KEPT (pick-wt=3): 23 [copy,22,flip.1] 4!=2. ** KEPT (pick-wt=3): 25 [copy,24,flip.1] 5!=2. ** KEPT (pick-wt=3): 27 [copy,26,flip.1] 4!=3. ** KEPT (pick-wt=3): 29 [copy,28,flip.1] 5!=3. ** KEPT (pick-wt=3): 31 [copy,30,flip.1] 5!=4. ** KEPT (pick-wt=3): 32 [] e=0. ---> New Demodulator: 33 [new_demod,32] e=0. ** KEPT (pick-wt=7): 35 [copy,34,flip.1] f(2,1)!=f(1,2). ** KEPT (pick-wt=5): 37 [copy,36,demod,33] f(0,0)=0. ---> New Demodulator: 38 [new_demod,37] f(0,0)=0. ** KEPT (pick-wt=5): 40 [copy,39,demod,33] f(0,1)=1. ---> New Demodulator: 41 [new_demod,40] f(0,1)=1. ** KEPT (pick-wt=5): 43 [copy,42,demod,33] f(0,2)=2. ---> New Demodulator: 44 [new_demod,43] f(0,2)=2. ** KEPT (pick-wt=5): 46 [copy,45,demod,33] f(0,3)=3. ---> New Demodulator: 47 [new_demod,46] f(0,3)=3. ** KEPT (pick-wt=5): 49 [copy,48,demod,33] f(0,4)=4. ---> New Demodulator: 50 [new_demod,49] f(0,4)=4. ** KEPT (pick-wt=5): 52 [copy,51,demod,33] f(0,5)=5. ---> New Demodulator: 53 [new_demod,52] f(0,5)=5. ** KEPT (pick-wt=6): 55 [copy,54,demod,33] f(g(0),0)=0. ---> New Demodulator: 56 [new_demod,55] f(g(0),0)=0. ** KEPT (pick-wt=6): 58 [copy,57,demod,33] f(g(1),1)=0. ---> New Demodulator: 59 [new_demod,58] f(g(1),1)=0. ** KEPT (pick-wt=6): 61 [copy,60,demod,33] f(g(2),2)=0. ---> New Demodulator: 62 [new_demod,61] f(g(2),2)=0. ** KEPT (pick-wt=6): 64 [copy,63,demod,33] f(g(3),3)=0. ---> New Demodulator: 65 [new_demod,64] f(g(3),3)=0. ** KEPT (pick-wt=6): 67 [copy,66,demod,33] f(g(4),4)=0. ---> New Demodulator: 68 [new_demod,67] f(g(4),4)=0. ** KEPT (pick-wt=6): 70 [copy,69,demod,33] f(g(5),5)=0. ---> New Demodulator: 71 [new_demod,70] f(g(5),5)=0. Following clause subsumed by 1 during input processing: 0 [demod,38,38,38,38] 0=0. ** KEPT (pick-wt=11): 72 [] f(f(1,1),1)=f(1,f(1,1)). ---> New Demodulator: 73 [new_demod,72] f(f(1,1),1)=f(1,f(1,1)). ** KEPT (pick-wt=9): 75 [copy,74,demod,41] f(f(1,0),1)=f(1,1). ---> New Demodulator: 76 [new_demod,75] f(f(1,0),1)=f(1,1). ** KEPT (pick-wt=9): 78 [copy,77,demod,41,flip.1] f(0,f(1,1))=f(1,1). ---> New Demodulator: 79 [new_demod,78] f(0,f(1,1))=f(1,1). Following clause subsumed by 1 during input processing: 0 [demod,38,41,41,41] 1=1. ** KEPT (pick-wt=11): 80 [] f(f(1,1),0)=f(1,f(1,0)). ---> New Demodulator: 81 [new_demod,80] f(f(1,1),0)=f(1,f(1,0)). ** KEPT (pick-wt=9): 83 [copy,82,demod,41,flip.1] f(0,f(1,0))=f(1,0). ---> New Demodulator: 84 [new_demod,83] f(0,f(1,0))=f(1,0). ** KEPT (pick-wt=9): 86 [copy,85,demod,38] f(f(1,0),0)=f(1,0). ---> New Demodulator: 87 [new_demod,86] f(f(1,0),0)=f(1,0). ** KEPT (pick-wt=11): 88 [] f(f(2,2),2)=f(2,f(2,2)). ---> New Demodulator: 89 [new_demod,88] f(f(2,2),2)=f(2,f(2,2)). ** KEPT (pick-wt=11): 90 [] f(f(2,1),2)=f(2,f(1,2)). ---> New Demodulator: 91 [new_demod,90] f(f(2,1),2)=f(2,f(1,2)). ** KEPT (pick-wt=9): 93 [copy,92,demod,44] f(f(2,0),2)=f(2,2). ---> New Demodulator: 94 [new_demod,93] f(f(2,0),2)=f(2,2). ** KEPT (pick-wt=11): 95 [] f(f(1,2),2)=f(1,f(2,2)). ---> New Demodulator: 96 [new_demod,95] f(f(1,2),2)=f(1,f(2,2)). ** KEPT (pick-wt=11): 97 [] f(f(1,1),2)=f(1,f(1,2)). ---> New Demodulator: 98 [new_demod,97] f(f(1,1),2)=f(1,f(1,2)). ** KEPT (pick-wt=9): 100 [copy,99,demod,44] f(f(1,0),2)=f(1,2). ---> New Demodulator: 101 [new_demod,100] f(f(1,0),2)=f(1,2). ** KEPT (pick-wt=9): 103 [copy,102,demod,44,flip.1] f(0,f(2,2))=f(2,2). ---> New Demodulator: 104 [new_demod,103] f(0,f(2,2))=f(2,2). ** KEPT (pick-wt=9): 106 [copy,105,demod,41,flip.1] f(0,f(1,2))=f(1,2). ---> New Demodulator: 107 [new_demod,106] f(0,f(1,2))=f(1,2). Following clause subsumed by 1 during input processing: 0 [demod,38,44,44,44] 2=2. ** KEPT (pick-wt=11): 108 [] f(f(2,2),1)=f(2,f(2,1)). ---> New Demodulator: 109 [new_demod,108] f(f(2,2),1)=f(2,f(2,1)). ** KEPT (pick-wt=11): 110 [] f(f(2,2),0)=f(2,f(2,0)). ---> New Demodulator: 111 [new_demod,110] f(f(2,2),0)=f(2,f(2,0)). ** KEPT (pick-wt=11): 112 [] f(f(1,2),1)=f(1,f(2,1)). ---> New Demodulator: 113 [new_demod,112] f(f(1,2),1)=f(1,f(2,1)). ** KEPT (pick-wt=11): 114 [] f(f(1,2),0)=f(1,f(2,0)). ---> New Demodulator: 115 [new_demod,114] f(f(1,2),0)=f(1,f(2,0)). ** KEPT (pick-wt=9): 117 [copy,116,demod,44,flip.1] f(0,f(2,1))=f(2,1). ---> New Demodulator: 118 [new_demod,117] f(0,f(2,1))=f(2,1). ** KEPT (pick-wt=9): 120 [copy,119,demod,44,flip.1] f(0,f(2,0))=f(2,0). ---> New Demodulator: 121 [new_demod,120] f(0,f(2,0))=f(2,0). ** KEPT (pick-wt=11): 122 [] f(f(2,1),1)=f(2,f(1,1)). ---> New Demodulator: 123 [new_demod,122] f(f(2,1),1)=f(2,f(1,1)). ** KEPT (pick-wt=11): 124 [] f(f(2,1),0)=f(2,f(1,0)). ---> New Demodulator: 125 [new_demod,124] f(f(2,1),0)=f(2,f(1,0)). ** KEPT (pick-wt=9): 127 [copy,126,demod,41] f(f(2,0),1)=f(2,1). ---> New Demodulator: 128 [new_demod,127] f(f(2,0),1)=f(2,1). ** KEPT (pick-wt=9): 130 [copy,129,demod,38] f(f(2,0),0)=f(2,0). ---> New Demodulator: 131 [new_demod,130] f(f(2,0),0)=f(2,0). ** KEPT (pick-wt=11): 132 [] f(f(3,3),3)=f(3,f(3,3)). ---> New Demodulator: 133 [new_demod,132] f(f(3,3),3)=f(3,f(3,3)). ** KEPT (pick-wt=11): 134 [] f(f(3,2),3)=f(3,f(2,3)). ---> New Demodulator: 135 [new_demod,134] f(f(3,2),3)=f(3,f(2,3)). ** KEPT (pick-wt=11): 136 [] f(f(3,1),3)=f(3,f(1,3)). ---> New Demodulator: 137 [new_demod,136] f(f(3,1),3)=f(3,f(1,3)). ** KEPT (pick-wt=9): 139 [copy,138,demod,47] f(f(3,0),3)=f(3,3). ---> New Demodulator: 140 [new_demod,139] f(f(3,0),3)=f(3,3). ** KEPT (pick-wt=11): 141 [] f(f(2,3),3)=f(2,f(3,3)). ---> New Demodulator: 142 [new_demod,141] f(f(2,3),3)=f(2,f(3,3)). ** KEPT (pick-wt=11): 143 [] f(f(2,2),3)=f(2,f(2,3)). ---> New Demodulator: 144 [new_demod,143] f(f(2,2),3)=f(2,f(2,3)). ** KEPT (pick-wt=11): 145 [] f(f(2,1),3)=f(2,f(1,3)). ---> New Demodulator: 146 [new_demod,145] f(f(2,1),3)=f(2,f(1,3)). ** KEPT (pick-wt=9): 148 [copy,147,demod,47] f(f(2,0),3)=f(2,3). ---> New Demodulator: 149 [new_demod,148] f(f(2,0),3)=f(2,3). ** KEPT (pick-wt=11): 150 [] f(f(1,3),3)=f(1,f(3,3)). ---> New Demodulator: 151 [new_demod,150] f(f(1,3),3)=f(1,f(3,3)). ** KEPT (pick-wt=11): 152 [] f(f(1,2),3)=f(1,f(2,3)). ---> New Demodulator: 153 [new_demod,152] f(f(1,2),3)=f(1,f(2,3)). ** KEPT (pick-wt=11): 154 [] f(f(1,1),3)=f(1,f(1,3)). ---> New Demodulator: 155 [new_demod,154] f(f(1,1),3)=f(1,f(1,3)). ** KEPT (pick-wt=9): 157 [copy,156,demod,47] f(f(1,0),3)=f(1,3). ---> New Demodulator: 158 [new_demod,157] f(f(1,0),3)=f(1,3). ** KEPT (pick-wt=9): 160 [copy,159,demod,47,flip.1] f(0,f(3,3))=f(3,3). ---> New Demodulator: 161 [new_demod,160] f(0,f(3,3))=f(3,3). ** KEPT (pick-wt=9): 163 [copy,162,demod,44,flip.1] f(0,f(2,3))=f(2,3). ---> New Demodulator: 164 [new_demod,163] f(0,f(2,3))=f(2,3). ** KEPT (pick-wt=9): 166 [copy,165,demod,41,flip.1] f(0,f(1,3))=f(1,3). ---> New Demodulator: 167 [new_demod,166] f(0,f(1,3))=f(1,3). Following clause subsumed by 1 during input processing: 0 [demod,38,47,47,47] 3=3. ** KEPT (pick-wt=11): 168 [] f(f(3,3),2)=f(3,f(3,2)). ---> New Demodulator: 169 [new_demod,168] f(f(3,3),2)=f(3,f(3,2)). ** KEPT (pick-wt=11): 170 [] f(f(3,3),1)=f(3,f(3,1)). ---> New Demodulator: 171 [new_demod,170] f(f(3,3),1)=f(3,f(3,1)). ** KEPT (pick-wt=11): 172 [] f(f(3,3),0)=f(3,f(3,0)). ---> New Demodulator: 173 [new_demod,172] f(f(3,3),0)=f(3,f(3,0)). ** KEPT (pick-wt=11): 174 [] f(f(2,3),2)=f(2,f(3,2)). ---> New Demodulator: 175 [new_demod,174] f(f(2,3),2)=f(2,f(3,2)). ** KEPT (pick-wt=11): 176 [] f(f(2,3),1)=f(2,f(3,1)). ---> New Demodulator: 177 [new_demod,176] f(f(2,3),1)=f(2,f(3,1)). ** KEPT (pick-wt=11): 178 [] f(f(2,3),0)=f(2,f(3,0)). ---> New Demodulator: 179 [new_demod,178] f(f(2,3),0)=f(2,f(3,0)). ** KEPT (pick-wt=11): 180 [] f(f(1,3),2)=f(1,f(3,2)). ---> New Demodulator: 181 [new_demod,180] f(f(1,3),2)=f(1,f(3,2)). ** KEPT (pick-wt=11): 182 [] f(f(1,3),1)=f(1,f(3,1)). ---> New Demodulator: 183 [new_demod,182] f(f(1,3),1)=f(1,f(3,1)). ** KEPT (pick-wt=11): 184 [] f(f(1,3),0)=f(1,f(3,0)). ---> New Demodulator: 185 [new_demod,184] f(f(1,3),0)=f(1,f(3,0)). ** KEPT (pick-wt=9): 187 [copy,186,demod,47,flip.1] f(0,f(3,2))=f(3,2). ---> New Demodulator: 188 [new_demod,187] f(0,f(3,2))=f(3,2). ** KEPT (pick-wt=9): 190 [copy,189,demod,47,flip.1] f(0,f(3,1))=f(3,1). ---> New Demodulator: 191 [new_demod,190] f(0,f(3,1))=f(3,1). ** KEPT (pick-wt=9): 193 [copy,192,demod,47,flip.1] f(0,f(3,0))=f(3,0). ---> New Demodulator: 194 [new_demod,193] f(0,f(3,0))=f(3,0). ** KEPT (pick-wt=11): 195 [] f(f(3,2),2)=f(3,f(2,2)). ---> New Demodulator: 196 [new_demod,195] f(f(3,2),2)=f(3,f(2,2)). ** KEPT (pick-wt=11): 197 [] f(f(3,2),1)=f(3,f(2,1)). ---> New Demodulator: 198 [new_demod,197] f(f(3,2),1)=f(3,f(2,1)). ** KEPT (pick-wt=11): 199 [] f(f(3,2),0)=f(3,f(2,0)). ---> New Demodulator: 200 [new_demod,199] f(f(3,2),0)=f(3,f(2,0)). ** KEPT (pick-wt=11): 201 [] f(f(3,1),2)=f(3,f(1,2)). ---> New Demodulator: 202 [new_demod,201] f(f(3,1),2)=f(3,f(1,2)). ** KEPT (pick-wt=11): 203 [] f(f(3,1),1)=f(3,f(1,1)). ---> New Demodulator: 204 [new_demod,203] f(f(3,1),1)=f(3,f(1,1)). ** KEPT (pick-wt=11): 205 [] f(f(3,1),0)=f(3,f(1,0)). ---> New Demodulator: 206 [new_demod,205] f(f(3,1),0)=f(3,f(1,0)). ** KEPT (pick-wt=9): 208 [copy,207,demod,44] f(f(3,0),2)=f(3,2). ---> New Demodulator: 209 [new_demod,208] f(f(3,0),2)=f(3,2). ** KEPT (pick-wt=9): 211 [copy,210,demod,41] f(f(3,0),1)=f(3,1). ---> New Demodulator: 212 [new_demod,211] f(f(3,0),1)=f(3,1). ** KEPT (pick-wt=9): 214 [copy,213,demod,38] f(f(3,0),0)=f(3,0). ---> New Demodulator: 215 [new_demod,214] f(f(3,0),0)=f(3,0). ** KEPT (pick-wt=11): 216 [] f(f(4,4),4)=f(4,f(4,4)). ---> New Demodulator: 217 [new_demod,216] f(f(4,4),4)=f(4,f(4,4)). ** KEPT (pick-wt=11): 218 [] f(f(4,3),4)=f(4,f(3,4)). ---> New Demodulator: 219 [new_demod,218] f(f(4,3),4)=f(4,f(3,4)). ** KEPT (pick-wt=11): 220 [] f(f(4,2),4)=f(4,f(2,4)). ---> New Demodulator: 221 [new_demod,220] f(f(4,2),4)=f(4,f(2,4)). ** KEPT (pick-wt=11): 222 [] f(f(4,1),4)=f(4,f(1,4)). ---> New Demodulator: 223 [new_demod,222] f(f(4,1),4)=f(4,f(1,4)). ** KEPT (pick-wt=9): 225 [copy,224,demod,50] f(f(4,0),4)=f(4,4). ---> New Demodulator: 226 [new_demod,225] f(f(4,0),4)=f(4,4). ** KEPT (pick-wt=11): 227 [] f(f(3,4),4)=f(3,f(4,4)). ---> New Demodulator: 228 [new_demod,227] f(f(3,4),4)=f(3,f(4,4)). ** KEPT (pick-wt=11): 229 [] f(f(3,3),4)=f(3,f(3,4)). ---> New Demodulator: 230 [new_demod,229] f(f(3,3),4)=f(3,f(3,4)). ** KEPT (pick-wt=11): 231 [] f(f(3,2),4)=f(3,f(2,4)). ---> New Demodulator: 232 [new_demod,231] f(f(3,2),4)=f(3,f(2,4)). ** KEPT (pick-wt=11): 233 [] f(f(3,1),4)=f(3,f(1,4)). ---> New Demodulator: 234 [new_demod,233] f(f(3,1),4)=f(3,f(1,4)). ** KEPT (pick-wt=9): 236 [copy,235,demod,50] f(f(3,0),4)=f(3,4). ---> New Demodulator: 237 [new_demod,236] f(f(3,0),4)=f(3,4). ** KEPT (pick-wt=11): 238 [] f(f(2,4),4)=f(2,f(4,4)). ---> New Demodulator: 239 [new_demod,238] f(f(2,4),4)=f(2,f(4,4)). ** KEPT (pick-wt=11): 240 [] f(f(2,3),4)=f(2,f(3,4)). ---> New Demodulator: 241 [new_demod,240] f(f(2,3),4)=f(2,f(3,4)). ** KEPT (pick-wt=11): 242 [] f(f(2,2),4)=f(2,f(2,4)). ---> New Demodulator: 243 [new_demod,242] f(f(2,2),4)=f(2,f(2,4)). ** KEPT (pick-wt=11): 244 [] f(f(2,1),4)=f(2,f(1,4)). ---> New Demodulator: 245 [new_demod,244] f(f(2,1),4)=f(2,f(1,4)). ** KEPT (pick-wt=9): 247 [copy,246,demod,50] f(f(2,0),4)=f(2,4). ---> New Demodulator: 248 [new_demod,247] f(f(2,0),4)=f(2,4). ** KEPT (pick-wt=11): 249 [] f(f(1,4),4)=f(1,f(4,4)). ---> New Demodulator: 250 [new_demod,249] f(f(1,4),4)=f(1,f(4,4)). ** KEPT (pick-wt=11): 251 [] f(f(1,3),4)=f(1,f(3,4)). ---> New Demodulator: 252 [new_demod,251] f(f(1,3),4)=f(1,f(3,4)). ** KEPT (pick-wt=11): 253 [] f(f(1,2),4)=f(1,f(2,4)). ---> New Demodulator: 254 [new_demod,253] f(f(1,2),4)=f(1,f(2,4)). ** KEPT (pick-wt=11): 255 [] f(f(1,1),4)=f(1,f(1,4)). ---> New Demodulator: 256 [new_demod,255] f(f(1,1),4)=f(1,f(1,4)). ** KEPT (pick-wt=9): 258 [copy,257,demod,50] f(f(1,0),4)=f(1,4). ---> New Demodulator: 259 [new_demod,258] f(f(1,0),4)=f(1,4). ** KEPT (pick-wt=9): 261 [copy,260,demod,50,flip.1] f(0,f(4,4))=f(4,4). ---> New Demodulator: 262 [new_demod,261] f(0,f(4,4))=f(4,4). ** KEPT (pick-wt=9): 264 [copy,263,demod,47,flip.1] f(0,f(3,4))=f(3,4). ---> New Demodulator: 265 [new_demod,264] f(0,f(3,4))=f(3,4). ** KEPT (pick-wt=9): 267 [copy,266,demod,44,flip.1] f(0,f(2,4))=f(2,4). ---> New Demodulator: 268 [new_demod,267] f(0,f(2,4))=f(2,4). ** KEPT (pick-wt=9): 270 [copy,269,demod,41,flip.1] f(0,f(1,4))=f(1,4). ---> New Demodulator: 271 [new_demod,270] f(0,f(1,4))=f(1,4). Following clause subsumed by 1 during input processing: 0 [demod,38,50,50,50] 4=4. ** KEPT (pick-wt=11): 272 [] f(f(4,4),3)=f(4,f(4,3)). ---> New Demodulator: 273 [new_demod,272] f(f(4,4),3)=f(4,f(4,3)). ** KEPT (pick-wt=11): 274 [] f(f(4,4),2)=f(4,f(4,2)). ---> New Demodulator: 275 [new_demod,274] f(f(4,4),2)=f(4,f(4,2)). ** KEPT (pick-wt=11): 276 [] f(f(4,4),1)=f(4,f(4,1)). ---> New Demodulator: 277 [new_demod,276] f(f(4,4),1)=f(4,f(4,1)). ** KEPT (pick-wt=11): 278 [] f(f(4,4),0)=f(4,f(4,0)). ---> New Demodulator: 279 [new_demod,278] f(f(4,4),0)=f(4,f(4,0)). ** KEPT (pick-wt=11): 280 [] f(f(3,4),3)=f(3,f(4,3)). ---> New Demodulator: 281 [new_demod,280] f(f(3,4),3)=f(3,f(4,3)). ** KEPT (pick-wt=11): 282 [] f(f(3,4),2)=f(3,f(4,2)). ---> New Demodulator: 283 [new_demod,282] f(f(3,4),2)=f(3,f(4,2)). ** KEPT (pick-wt=11): 284 [] f(f(3,4),1)=f(3,f(4,1)). ---> New Demodulator: 285 [new_demod,284] f(f(3,4),1)=f(3,f(4,1)). ** KEPT (pick-wt=11): 286 [] f(f(3,4),0)=f(3,f(4,0)). ---> New Demodulator: 287 [new_demod,286] f(f(3,4),0)=f(3,f(4,0)). ** KEPT (pick-wt=11): 288 [] f(f(2,4),3)=f(2,f(4,3)). ---> New Demodulator: 289 [new_demod,288] f(f(2,4),3)=f(2,f(4,3)). ** KEPT (pick-wt=11): 290 [] f(f(2,4),2)=f(2,f(4,2)). ---> New Demodulator: 291 [new_demod,290] f(f(2,4),2)=f(2,f(4,2)). ** KEPT (pick-wt=11): 292 [] f(f(2,4),1)=f(2,f(4,1)). ---> New Demodulator: 293 [new_demod,292] f(f(2,4),1)=f(2,f(4,1)). ** KEPT (pick-wt=11): 294 [] f(f(2,4),0)=f(2,f(4,0)). ---> New Demodulator: 295 [new_demod,294] f(f(2,4),0)=f(2,f(4,0)). ** KEPT (pick-wt=11): 296 [] f(f(1,4),3)=f(1,f(4,3)). ---> New Demodulator: 297 [new_demod,296] f(f(1,4),3)=f(1,f(4,3)). ** KEPT (pick-wt=11): 298 [] f(f(1,4),2)=f(1,f(4,2)). ---> New Demodulator: 299 [new_demod,298] f(f(1,4),2)=f(1,f(4,2)). ** KEPT (pick-wt=11): 300 [] f(f(1,4),1)=f(1,f(4,1)). ---> New Demodulator: 301 [new_demod,300] f(f(1,4),1)=f(1,f(4,1)). ** KEPT (pick-wt=11): 302 [] f(f(1,4),0)=f(1,f(4,0)). ---> New Demodulator: 303 [new_demod,302] f(f(1,4),0)=f(1,f(4,0)). ** KEPT (pick-wt=9): 305 [copy,304,demod,50,flip.1] f(0,f(4,3))=f(4,3). ---> New Demodulator: 306 [new_demod,305] f(0,f(4,3))=f(4,3). ** KEPT (pick-wt=9): 308 [copy,307,demod,50,flip.1] f(0,f(4,2))=f(4,2). ---> New Demodulator: 309 [new_demod,308] f(0,f(4,2))=f(4,2). ** KEPT (pick-wt=9): 311 [copy,310,demod,50,flip.1] f(0,f(4,1))=f(4,1). ---> New Demodulator: 312 [new_demod,311] f(0,f(4,1))=f(4,1). ** KEPT (pick-wt=9): 314 [copy,313,demod,50,flip.1] f(0,f(4,0))=f(4,0). ---> New Demodulator: 315 [new_demod,314] f(0,f(4,0))=f(4,0). ** KEPT (pick-wt=11): 316 [] f(f(4,3),3)=f(4,f(3,3)). ---> New Demodulator: 317 [new_demod,316] f(f(4,3),3)=f(4,f(3,3)). ** KEPT (pick-wt=11): 318 [] f(f(4,3),2)=f(4,f(3,2)). ---> New Demodulator: 319 [new_demod,318] f(f(4,3),2)=f(4,f(3,2)). ** KEPT (pick-wt=11): 320 [] f(f(4,3),1)=f(4,f(3,1)). ---> New Demodulator: 321 [new_demod,320] f(f(4,3),1)=f(4,f(3,1)). ** KEPT (pick-wt=11): 322 [] f(f(4,3),0)=f(4,f(3,0)). ---> New Demodulator: 323 [new_demod,322] f(f(4,3),0)=f(4,f(3,0)). ** KEPT (pick-wt=11): 324 [] f(f(4,2),3)=f(4,f(2,3)). ---> New Demodulator: 325 [new_demod,324] f(f(4,2),3)=f(4,f(2,3)). ** KEPT (pick-wt=11): 326 [] f(f(4,2),2)=f(4,f(2,2)). ---> New Demodulator: 327 [new_demod,326] f(f(4,2),2)=f(4,f(2,2)). ** KEPT (pick-wt=11): 328 [] f(f(4,2),1)=f(4,f(2,1)). ---> New Demodulator: 329 [new_demod,328] f(f(4,2),1)=f(4,f(2,1)). ** KEPT (pick-wt=11): 330 [] f(f(4,2),0)=f(4,f(2,0)). ---> New Demodulator: 331 [new_demod,330] f(f(4,2),0)=f(4,f(2,0)). ** KEPT (pick-wt=11): 332 [] f(f(4,1),3)=f(4,f(1,3)). ---> New Demodulator: 333 [new_demod,332] f(f(4,1),3)=f(4,f(1,3)). ** KEPT (pick-wt=11): 334 [] f(f(4,1),2)=f(4,f(1,2)). ---> New Demodulator: 335 [new_demod,334] f(f(4,1),2)=f(4,f(1,2)). ** KEPT (pick-wt=11): 336 [] f(f(4,1),1)=f(4,f(1,1)). ---> New Demodulator: 337 [new_demod,336] f(f(4,1),1)=f(4,f(1,1)). ** KEPT (pick-wt=11): 338 [] f(f(4,1),0)=f(4,f(1,0)). ---> New Demodulator: 339 [new_demod,338] f(f(4,1),0)=f(4,f(1,0)). ** KEPT (pick-wt=9): 341 [copy,340,demod,47] f(f(4,0),3)=f(4,3). ---> New Demodulator: 342 [new_demod,341] f(f(4,0),3)=f(4,3). ** KEPT (pick-wt=9): 344 [copy,343,demod,44] f(f(4,0),2)=f(4,2). ---> New Demodulator: 345 [new_demod,344] f(f(4,0),2)=f(4,2). ** KEPT (pick-wt=9): 347 [copy,346,demod,41] f(f(4,0),1)=f(4,1). ---> New Demodulator: 348 [new_demod,347] f(f(4,0),1)=f(4,1). ** KEPT (pick-wt=9): 350 [copy,349,demod,38] f(f(4,0),0)=f(4,0). ---> New Demodulator: 351 [new_demod,350] f(f(4,0),0)=f(4,0). ** KEPT (pick-wt=11): 352 [] f(f(5,5),5)=f(5,f(5,5)). ---> New Demodulator: 353 [new_demod,352] f(f(5,5),5)=f(5,f(5,5)). ** KEPT (pick-wt=11): 354 [] f(f(5,4),5)=f(5,f(4,5)). ---> New Demodulator: 355 [new_demod,354] f(f(5,4),5)=f(5,f(4,5)). ** KEPT (pick-wt=11): 356 [] f(f(5,3),5)=f(5,f(3,5)). ---> New Demodulator: 357 [new_demod,356] f(f(5,3),5)=f(5,f(3,5)). ** KEPT (pick-wt=11): 358 [] f(f(5,2),5)=f(5,f(2,5)). ---> New Demodulator: 359 [new_demod,358] f(f(5,2),5)=f(5,f(2,5)). ** KEPT (pick-wt=11): 360 [] f(f(5,1),5)=f(5,f(1,5)). ---> New Demodulator: 361 [new_demod,360] f(f(5,1),5)=f(5,f(1,5)). ** KEPT (pick-wt=9): 363 [copy,362,demod,53] f(f(5,0),5)=f(5,5). ---> New Demodulator: 364 [new_demod,363] f(f(5,0),5)=f(5,5). ** KEPT (pick-wt=11): 365 [] f(f(4,5),5)=f(4,f(5,5)). ---> New Demodulator: 366 [new_demod,365] f(f(4,5),5)=f(4,f(5,5)). ** KEPT (pick-wt=11): 367 [] f(f(4,4),5)=f(4,f(4,5)). ---> New Demodulator: 368 [new_demod,367] f(f(4,4),5)=f(4,f(4,5)). ** KEPT (pick-wt=11): 369 [] f(f(4,3),5)=f(4,f(3,5)). ---> New Demodulator: 370 [new_demod,369] f(f(4,3),5)=f(4,f(3,5)). ** KEPT (pick-wt=11): 371 [] f(f(4,2),5)=f(4,f(2,5)). ---> New Demodulator: 372 [new_demod,371] f(f(4,2),5)=f(4,f(2,5)). ** KEPT (pick-wt=11): 373 [] f(f(4,1),5)=f(4,f(1,5)). ---> New Demodulator: 374 [new_demod,373] f(f(4,1),5)=f(4,f(1,5)). ** KEPT (pick-wt=9): 376 [copy,375,demod,53] f(f(4,0),5)=f(4,5). ---> New Demodulator: 377 [new_demod,376] f(f(4,0),5)=f(4,5). ** KEPT (pick-wt=11): 378 [] f(f(3,5),5)=f(3,f(5,5)). ---> New Demodulator: 379 [new_demod,378] f(f(3,5),5)=f(3,f(5,5)). ** KEPT (pick-wt=11): 380 [] f(f(3,4),5)=f(3,f(4,5)). ---> New Demodulator: 381 [new_demod,380] f(f(3,4),5)=f(3,f(4,5)). ** KEPT (pick-wt=11): 382 [] f(f(3,3),5)=f(3,f(3,5)). ---> New Demodulator: 383 [new_demod,382] f(f(3,3),5)=f(3,f(3,5)). ** KEPT (pick-wt=11): 384 [] f(f(3,2),5)=f(3,f(2,5)). ---> New Demodulator: 385 [new_demod,384] f(f(3,2),5)=f(3,f(2,5)). ** KEPT (pick-wt=11): 386 [] f(f(3,1),5)=f(3,f(1,5)). ---> New Demodulator: 387 [new_demod,386] f(f(3,1),5)=f(3,f(1,5)). ** KEPT (pick-wt=9): 389 [copy,388,demod,53] f(f(3,0),5)=f(3,5). ---> New Demodulator: 390 [new_demod,389] f(f(3,0),5)=f(3,5). ** KEPT (pick-wt=11): 391 [] f(f(2,5),5)=f(2,f(5,5)). ---> New Demodulator: 392 [new_demod,391] f(f(2,5),5)=f(2,f(5,5)). ** KEPT (pick-wt=11): 393 [] f(f(2,4),5)=f(2,f(4,5)). ---> New Demodulator: 394 [new_demod,393] f(f(2,4),5)=f(2,f(4,5)). ** KEPT (pick-wt=11): 395 [] f(f(2,3),5)=f(2,f(3,5)). ---> New Demodulator: 396 [new_demod,395] f(f(2,3),5)=f(2,f(3,5)). ** KEPT (pick-wt=11): 397 [] f(f(2,2),5)=f(2,f(2,5)). ---> New Demodulator: 398 [new_demod,397] f(f(2,2),5)=f(2,f(2,5)). ** KEPT (pick-wt=11): 399 [] f(f(2,1),5)=f(2,f(1,5)). ---> New Demodulator: 400 [new_demod,399] f(f(2,1),5)=f(2,f(1,5)). ** KEPT (pick-wt=9): 402 [copy,401,demod,53] f(f(2,0),5)=f(2,5). ---> New Demodulator: 403 [new_demod,402] f(f(2,0),5)=f(2,5). ** KEPT (pick-wt=11): 404 [] f(f(1,5),5)=f(1,f(5,5)). ---> New Demodulator: 405 [new_demod,404] f(f(1,5),5)=f(1,f(5,5)). ** KEPT (pick-wt=11): 406 [] f(f(1,4),5)=f(1,f(4,5)). ---> New Demodulator: 407 [new_demod,406] f(f(1,4),5)=f(1,f(4,5)). ** KEPT (pick-wt=11): 408 [] f(f(1,3),5)=f(1,f(3,5)). ---> New Demodulator: 409 [new_demod,408] f(f(1,3),5)=f(1,f(3,5)). ** KEPT (pick-wt=11): 410 [] f(f(1,2),5)=f(1,f(2,5)). ---> New Demodulator: 411 [new_demod,410] f(f(1,2),5)=f(1,f(2,5)). ** KEPT (pick-wt=11): 412 [] f(f(1,1),5)=f(1,f(1,5)). ---> New Demodulator: 413 [new_demod,412] f(f(1,1),5)=f(1,f(1,5)). ** KEPT (pick-wt=9): 415 [copy,414,demod,53] f(f(1,0),5)=f(1,5). ---> New Demodulator: 416 [new_demod,415] f(f(1,0),5)=f(1,5). ** KEPT (pick-wt=9): 418 [copy,417,demod,53,flip.1] f(0,f(5,5))=f(5,5). ---> New Demodulator: 419 [new_demod,418] f(0,f(5,5))=f(5,5). ** KEPT (pick-wt=9): 421 [copy,420,demod,50,flip.1] f(0,f(4,5))=f(4,5). ---> New Demodulator: 422 [new_demod,421] f(0,f(4,5))=f(4,5). ** KEPT (pick-wt=9): 424 [copy,423,demod,47,flip.1] f(0,f(3,5))=f(3,5). ---> New Demodulator: 425 [new_demod,424] f(0,f(3,5))=f(3,5). ** KEPT (pick-wt=9): 427 [copy,426,demod,44,flip.1] f(0,f(2,5))=f(2,5). ---> New Demodulator: 428 [new_demod,427] f(0,f(2,5))=f(2,5). ** KEPT (pick-wt=9): 430 [copy,429,demod,41,flip.1] f(0,f(1,5))=f(1,5). ---> New Demodulator: 431 [new_demod,430] f(0,f(1,5))=f(1,5). Following clause subsumed by 1 during input processing: 0 [demod,38,53,53,53] 5=5. ** KEPT (pick-wt=11): 432 [] f(f(5,5),4)=f(5,f(5,4)). ---> New Demodulator: 433 [new_demod,432] f(f(5,5),4)=f(5,f(5,4)). ** KEPT (pick-wt=11): 434 [] f(f(5,5),3)=f(5,f(5,3)). ---> New Demodulator: 435 [new_demod,434] f(f(5,5),3)=f(5,f(5,3)). ** KEPT (pick-wt=11): 436 [] f(f(5,5),2)=f(5,f(5,2)). ---> New Demodulator: 437 [new_demod,436] f(f(5,5),2)=f(5,f(5,2)). ** KEPT (pick-wt=11): 438 [] f(f(5,5),1)=f(5,f(5,1)). ---> New Demodulator: 439 [new_demod,438] f(f(5,5),1)=f(5,f(5,1)). ** KEPT (pick-wt=11): 440 [] f(f(5,5),0)=f(5,f(5,0)). ---> New Demodulator: 441 [new_demod,440] f(f(5,5),0)=f(5,f(5,0)). ** KEPT (pick-wt=11): 442 [] f(f(4,5),4)=f(4,f(5,4)). ---> New Demodulator: 443 [new_demod,442] f(f(4,5),4)=f(4,f(5,4)). ** KEPT (pick-wt=11): 444 [] f(f(4,5),3)=f(4,f(5,3)). ---> New Demodulator: 445 [new_demod,444] f(f(4,5),3)=f(4,f(5,3)). ** KEPT (pick-wt=11): 446 [] f(f(4,5),2)=f(4,f(5,2)). ---> New Demodulator: 447 [new_demod,446] f(f(4,5),2)=f(4,f(5,2)). ** KEPT (pick-wt=11): 448 [] f(f(4,5),1)=f(4,f(5,1)). ---> New Demodulator: 449 [new_demod,448] f(f(4,5),1)=f(4,f(5,1)). ** KEPT (pick-wt=11): 450 [] f(f(4,5),0)=f(4,f(5,0)). ---> New Demodulator: 451 [new_demod,450] f(f(4,5),0)=f(4,f(5,0)). ** KEPT (pick-wt=11): 452 [] f(f(3,5),4)=f(3,f(5,4)). ---> New Demodulator: 453 [new_demod,452] f(f(3,5),4)=f(3,f(5,4)). ** KEPT (pick-wt=11): 454 [] f(f(3,5),3)=f(3,f(5,3)). ---> New Demodulator: 455 [new_demod,454] f(f(3,5),3)=f(3,f(5,3)). ** KEPT (pick-wt=11): 456 [] f(f(3,5),2)=f(3,f(5,2)). ---> New Demodulator: 457 [new_demod,456] f(f(3,5),2)=f(3,f(5,2)). ** KEPT (pick-wt=11): 458 [] f(f(3,5),1)=f(3,f(5,1)). ---> New Demodulator: 459 [new_demod,458] f(f(3,5),1)=f(3,f(5,1)). ** KEPT (pick-wt=11): 460 [] f(f(3,5),0)=f(3,f(5,0)). ---> New Demodulator: 461 [new_demod,460] f(f(3,5),0)=f(3,f(5,0)). ** KEPT (pick-wt=11): 462 [] f(f(2,5),4)=f(2,f(5,4)). ---> New Demodulator: 463 [new_demod,462] f(f(2,5),4)=f(2,f(5,4)). ** KEPT (pick-wt=11): 464 [] f(f(2,5),3)=f(2,f(5,3)). ---> New Demodulator: 465 [new_demod,464] f(f(2,5),3)=f(2,f(5,3)). ** KEPT (pick-wt=11): 466 [] f(f(2,5),2)=f(2,f(5,2)). ---> New Demodulator: 467 [new_demod,466] f(f(2,5),2)=f(2,f(5,2)). ** KEPT (pick-wt=11): 468 [] f(f(2,5),1)=f(2,f(5,1)). ---> New Demodulator: 469 [new_demod,468] f(f(2,5),1)=f(2,f(5,1)). ** KEPT (pick-wt=11): 470 [] f(f(2,5),0)=f(2,f(5,0)). ---> New Demodulator: 471 [new_demod,470] f(f(2,5),0)=f(2,f(5,0)). ** KEPT (pick-wt=11): 472 [] f(f(1,5),4)=f(1,f(5,4)). ---> New Demodulator: 473 [new_demod,472] f(f(1,5),4)=f(1,f(5,4)). ** KEPT (pick-wt=11): 474 [] f(f(1,5),3)=f(1,f(5,3)). ---> New Demodulator: 475 [new_demod,474] f(f(1,5),3)=f(1,f(5,3)). ** KEPT (pick-wt=11): 476 [] f(f(1,5),2)=f(1,f(5,2)). ---> New Demodulator: 477 [new_demod,476] f(f(1,5),2)=f(1,f(5,2)). ** KEPT (pick-wt=11): 478 [] f(f(1,5),1)=f(1,f(5,1)). ---> New Demodulator: 479 [new_demod,478] f(f(1,5),1)=f(1,f(5,1)). ** KEPT (pick-wt=11): 480 [] f(f(1,5),0)=f(1,f(5,0)). ---> New Demodulator: 481 [new_demod,480] f(f(1,5),0)=f(1,f(5,0)). ** KEPT (pick-wt=9): 483 [copy,482,demod,53,flip.1] f(0,f(5,4))=f(5,4). ---> New Demodulator: 484 [new_demod,483] f(0,f(5,4))=f(5,4). ** KEPT (pick-wt=9): 486 [copy,485,demod,53,flip.1] f(0,f(5,3))=f(5,3). ---> New Demodulator: 487 [new_demod,486] f(0,f(5,3))=f(5,3). ** KEPT (pick-wt=9): 489 [copy,488,demod,53,flip.1] f(0,f(5,2))=f(5,2). ---> New Demodulator: 490 [new_demod,489] f(0,f(5,2))=f(5,2). ** KEPT (pick-wt=9): 492 [copy,491,demod,53,flip.1] f(0,f(5,1))=f(5,1). ---> New Demodulator: 493 [new_demod,492] f(0,f(5,1))=f(5,1). ** KEPT (pick-wt=9): 495 [copy,494,demod,53,flip.1] f(0,f(5,0))=f(5,0). ---> New Demodulator: 496 [new_demod,495] f(0,f(5,0))=f(5,0). ** KEPT (pick-wt=11): 497 [] f(f(5,4),4)=f(5,f(4,4)). ---> New Demodulator: 498 [new_demod,497] f(f(5,4),4)=f(5,f(4,4)). ** KEPT (pick-wt=11): 499 [] f(f(5,4),3)=f(5,f(4,3)). ---> New Demodulator: 500 [new_demod,499] f(f(5,4),3)=f(5,f(4,3)). ** KEPT (pick-wt=11): 501 [] f(f(5,4),2)=f(5,f(4,2)). ---> New Demodulator: 502 [new_demod,501] f(f(5,4),2)=f(5,f(4,2)). ** KEPT (pick-wt=11): 503 [] f(f(5,4),1)=f(5,f(4,1)). ---> New Demodulator: 504 [new_demod,503] f(f(5,4),1)=f(5,f(4,1)). ** KEPT (pick-wt=11): 505 [] f(f(5,4),0)=f(5,f(4,0)). ---> New Demodulator: 506 [new_demod,505] f(f(5,4),0)=f(5,f(4,0)). ** KEPT (pick-wt=11): 507 [] f(f(5,3),4)=f(5,f(3,4)). ---> New Demodulator: 508 [new_demod,507] f(f(5,3),4)=f(5,f(3,4)). ** KEPT (pick-wt=11): 509 [] f(f(5,3),3)=f(5,f(3,3)). ---> New Demodulator: 510 [new_demod,509] f(f(5,3),3)=f(5,f(3,3)). ** KEPT (pick-wt=11): 511 [] f(f(5,3),2)=f(5,f(3,2)). ---> New Demodulator: 512 [new_demod,511] f(f(5,3),2)=f(5,f(3,2)). ** KEPT (pick-wt=11): 513 [] f(f(5,3),1)=f(5,f(3,1)). ---> New Demodulator: 514 [new_demod,513] f(f(5,3),1)=f(5,f(3,1)). ** KEPT (pick-wt=11): 515 [] f(f(5,3),0)=f(5,f(3,0)). ---> New Demodulator: 516 [new_demod,515] f(f(5,3),0)=f(5,f(3,0)). ** KEPT (pick-wt=11): 517 [] f(f(5,2),4)=f(5,f(2,4)). ---> New Demodulator: 518 [new_demod,517] f(f(5,2),4)=f(5,f(2,4)). ** KEPT (pick-wt=11): 519 [] f(f(5,2),3)=f(5,f(2,3)). ---> New Demodulator: 520 [new_demod,519] f(f(5,2),3)=f(5,f(2,3)). ** KEPT (pick-wt=11): 521 [] f(f(5,2),2)=f(5,f(2,2)). ---> New Demodulator: 522 [new_demod,521] f(f(5,2),2)=f(5,f(2,2)). ** KEPT (pick-wt=11): 523 [] f(f(5,2),1)=f(5,f(2,1)). ---> New Demodulator: 524 [new_demod,523] f(f(5,2),1)=f(5,f(2,1)). ** KEPT (pick-wt=11): 525 [] f(f(5,2),0)=f(5,f(2,0)). ---> New Demodulator: 526 [new_demod,525] f(f(5,2),0)=f(5,f(2,0)). ** KEPT (pick-wt=11): 527 [] f(f(5,1),4)=f(5,f(1,4)). ---> New Demodulator: 528 [new_demod,527] f(f(5,1),4)=f(5,f(1,4)). ** KEPT (pick-wt=11): 529 [] f(f(5,1),3)=f(5,f(1,3)). ---> New Demodulator: 530 [new_demod,529] f(f(5,1),3)=f(5,f(1,3)). ** KEPT (pick-wt=11): 531 [] f(f(5,1),2)=f(5,f(1,2)). ---> New Demodulator: 532 [new_demod,531] f(f(5,1),2)=f(5,f(1,2)). ** KEPT (pick-wt=11): 533 [] f(f(5,1),1)=f(5,f(1,1)). ---> New Demodulator: 534 [new_demod,533] f(f(5,1),1)=f(5,f(1,1)). ** KEPT (pick-wt=11): 535 [] f(f(5,1),0)=f(5,f(1,0)). ---> New Demodulator: 536 [new_demod,535] f(f(5,1),0)=f(5,f(1,0)). ** KEPT (pick-wt=9): 538 [copy,537,demod,50] f(f(5,0),4)=f(5,4). ---> New Demodulator: 539 [new_demod,538] f(f(5,0),4)=f(5,4). ** KEPT (pick-wt=9): 541 [copy,540,demod,47] f(f(5,0),3)=f(5,3). ---> New Demodulator: 542 [new_demod,541] f(f(5,0),3)=f(5,3). ** KEPT (pick-wt=9): 544 [copy,543,demod,44] f(f(5,0),2)=f(5,2). ---> New Demodulator: 545 [new_demod,544] f(f(5,0),2)=f(5,2). ** KEPT (pick-wt=9): 547 [copy,546,demod,41] f(f(5,0),1)=f(5,1). ---> New Demodulator: 548 [new_demod,547] f(f(5,0),1)=f(5,1). ** KEPT (pick-wt=9): 550 [copy,549,demod,38] f(f(5,0),0)=f(5,0). ---> New Demodulator: 551 [new_demod,550] f(f(5,0),0)=f(5,0). ** KEPT (pick-wt=24): 552 [] g(0)=0|g(0)=1|g(0)=2|g(0)=3|g(0)=4|g(0)=5. ** KEPT (pick-wt=24): 553 [] g(1)=0|g(1)=1|g(1)=2|g(1)=3|g(1)=4|g(1)=5. ** KEPT (pick-wt=24): 554 [] g(2)=0|g(2)=1|g(2)=2|g(2)=3|g(2)=4|g(2)=5. ** KEPT (pick-wt=24): 555 [] g(3)=0|g(3)=1|g(3)=2|g(3)=3|g(3)=4|g(3)=5. ** KEPT (pick-wt=24): 556 [] g(4)=0|g(4)=1|g(4)=2|g(4)=3|g(4)=4|g(4)=5. ** KEPT (pick-wt=24): 557 [] g(5)=0|g(5)=1|g(5)=2|g(5)=3|g(5)=4|g(5)=5. Following clause subsumed by 1 during input processing: 0 [demod,38,38,38,38,38,38,unit_del,3,5,7,9,11] 0=0. ** KEPT (pick-wt=30): 558 [] f(1,1)=0|f(1,1)=1|f(1,1)=2|f(1,1)=3|f(1,1)=4|f(1,1)=5. Following clause subsumed by 1 during input processing: 0 [demod,41,41,41,41,41,41,unit_del,3,13,15,17,19] 1=1. ** KEPT (pick-wt=30): 559 [] f(1,0)=0|f(1,0)=1|f(1,0)=2|f(1,0)=3|f(1,0)=4|f(1,0)=5. ** KEPT (pick-wt=30): 560 [] f(2,2)=0|f(2,2)=1|f(2,2)=2|f(2,2)=3|f(2,2)=4|f(2,2)=5. ** KEPT (pick-wt=30): 561 [] f(1,2)=0|f(1,2)=1|f(1,2)=2|f(1,2)=3|f(1,2)=4|f(1,2)=5. Following clause subsumed by 1 during input processing: 0 [demod,44,44,44,44,44,44,unit_del,5,13,21,23,25] 2=2. ** KEPT (pick-wt=30): 562 [] f(2,1)=0|f(2,1)=1|f(2,1)=2|f(2,1)=3|f(2,1)=4|f(2,1)=5. ** KEPT (pick-wt=30): 563 [] f(2,0)=0|f(2,0)=1|f(2,0)=2|f(2,0)=3|f(2,0)=4|f(2,0)=5. ** KEPT (pick-wt=30): 564 [] f(3,3)=0|f(3,3)=1|f(3,3)=2|f(3,3)=3|f(3,3)=4|f(3,3)=5. ** KEPT (pick-wt=30): 565 [] f(2,3)=0|f(2,3)=1|f(2,3)=2|f(2,3)=3|f(2,3)=4|f(2,3)=5. ** KEPT (pick-wt=30): 566 [] f(1,3)=0|f(1,3)=1|f(1,3)=2|f(1,3)=3|f(1,3)=4|f(1,3)=5. Following clause subsumed by 1 during input processing: 0 [demod,47,47,47,47,47,47,unit_del,7,15,21,27,29] 3=3. ** KEPT (pick-wt=30): 567 [] f(3,2)=0|f(3,2)=1|f(3,2)=2|f(3,2)=3|f(3,2)=4|f(3,2)=5. ** KEPT (pick-wt=30): 568 [] f(3,1)=0|f(3,1)=1|f(3,1)=2|f(3,1)=3|f(3,1)=4|f(3,1)=5. ** KEPT (pick-wt=30): 569 [] f(3,0)=0|f(3,0)=1|f(3,0)=2|f(3,0)=3|f(3,0)=4|f(3,0)=5. ** KEPT (pick-wt=30): 570 [] f(4,4)=0|f(4,4)=1|f(4,4)=2|f(4,4)=3|f(4,4)=4|f(4,4)=5. ** KEPT (pick-wt=30): 571 [] f(3,4)=0|f(3,4)=1|f(3,4)=2|f(3,4)=3|f(3,4)=4|f(3,4)=5. ** KEPT (pick-wt=30): 572 [] f(2,4)=0|f(2,4)=1|f(2,4)=2|f(2,4)=3|f(2,4)=4|f(2,4)=5. ** KEPT (pick-wt=30): 573 [] f(1,4)=0|f(1,4)=1|f(1,4)=2|f(1,4)=3|f(1,4)=4|f(1,4)=5. Following clause subsumed by 1 during input processing: 0 [demod,50,50,50,50,50,50,unit_del,9,17,23,27,31] 4=4. ** KEPT (pick-wt=30): 574 [] f(4,3)=0|f(4,3)=1|f(4,3)=2|f(4,3)=3|f(4,3)=4|f(4,3)=5. ** KEPT (pick-wt=30): 575 [] f(4,2)=0|f(4,2)=1|f(4,2)=2|f(4,2)=3|f(4,2)=4|f(4,2)=5. ** KEPT (pick-wt=30): 576 [] f(4,1)=0|f(4,1)=1|f(4,1)=2|f(4,1)=3|f(4,1)=4|f(4,1)=5. ** KEPT (pick-wt=30): 577 [] f(4,0)=0|f(4,0)=1|f(4,0)=2|f(4,0)=3|f(4,0)=4|f(4,0)=5. ** KEPT (pick-wt=30): 578 [] f(5,5)=0|f(5,5)=1|f(5,5)=2|f(5,5)=3|f(5,5)=4|f(5,5)=5. ** KEPT (pick-wt=30): 579 [] f(4,5)=0|f(4,5)=1|f(4,5)=2|f(4,5)=3|f(4,5)=4|f(4,5)=5. ** KEPT (pick-wt=30): 580 [] f(3,5)=0|f(3,5)=1|f(3,5)=2|f(3,5)=3|f(3,5)=4|f(3,5)=5. ** KEPT (pick-wt=30): 581 [] f(2,5)=0|f(2,5)=1|f(2,5)=2|f(2,5)=3|f(2,5)=4|f(2,5)=5. ** KEPT (pick-wt=30): 582 [] f(1,5)=0|f(1,5)=1|f(1,5)=2|f(1,5)=3|f(1,5)=4|f(1,5)=5. Following clause subsumed by 1 during input processing: 0 [demod,53,53,53,53,53,53,unit_del,11,19,25,29,31] 5=5. ** KEPT (pick-wt=30): 583 [] f(5,4)=0|f(5,4)=1|f(5,4)=2|f(5,4)=3|f(5,4)=4|f(5,4)=5. ** KEPT (pick-wt=30): 584 [] f(5,3)=0|f(5,3)=1|f(5,3)=2|f(5,3)=3|f(5,3)=4|f(5,3)=5. ** KEPT (pick-wt=30): 585 [] f(5,2)=0|f(5,2)=1|f(5,2)=2|f(5,2)=3|f(5,2)=4|f(5,2)=5. ** KEPT (pick-wt=30): 586 [] f(5,1)=0|f(5,1)=1|f(5,1)=2|f(5,1)=3|f(5,1)=4|f(5,1)=5. ** KEPT (pick-wt=30): 587 [] f(5,0)=0|f(5,0)=1|f(5,0)=2|f(5,0)=3|f(5,0)=4|f(5,0)=5. >>>> Starting back unit deletion with 3. >>>> Starting back unit deletion with 5. >>>> Starting back unit deletion with 7. >>>> Starting back unit deletion with 9. >>>> Starting back unit deletion with 11. >>>> Starting back unit deletion with 13. >>>> Starting back unit deletion with 15. >>>> Starting back unit deletion with 17. >>>> Starting back unit deletion with 19. >>>> Starting back unit deletion with 21. >>>> Starting back unit deletion with 23. >>>> Starting back unit deletion with 25. >>>> Starting back unit deletion with 27. >>>> Starting back unit deletion with 29. >>>> Starting back unit deletion with 31. >>>> Starting back demodulation with 33. >>>> Starting back unit deletion with 32. >>>> Starting back unit deletion with 35. >>>> Starting back demodulation with 38. >>>> Starting back unit deletion with 37. >>>> Starting back demodulation with 41. >>>> Starting back unit deletion with 40. >>>> Starting back demodulation with 44. >>>> Starting back unit deletion with 43. >>>> Starting back demodulation with 47. >>>> Starting back unit deletion with 46. >>>> Starting back demodulation with 50. >>>> Starting back unit deletion with 49. >>>> Starting back demodulation with 53. >>>> Starting back unit deletion with 52. >>>> Starting back demodulation with 56. >>>> Starting back unit deletion with 55. >>>> Starting back demodulation with 59. >>>> Starting back unit deletion with 58. >>>> Starting back demodulation with 62. >>>> Starting back unit deletion with 61. >>>> Starting back demodulation with 65. >>>> Starting back unit deletion with 64. >>>> Starting back demodulation with 68. >>>> Starting back unit deletion with 67. >>>> Starting back demodulation with 71. >>>> Starting back unit deletion with 70. >>>> Starting back demodulation with 73. >>>> Starting back unit deletion with 72. >>>> Starting back demodulation with 76. >>>> Starting back unit deletion with 75. >>>> Starting back demodulation with 79. >>>> Starting back unit deletion with 78. >>>> Starting back demodulation with 81. >>>> Starting back unit deletion with 80. >>>> Starting back demodulation with 84. >>>> Starting back unit deletion with 83. >>>> Starting back demodulation with 87. >>>> Starting back unit deletion with 86. >>>> Starting back demodulation with 89. >>>> Starting back unit deletion with 88. >>>> Starting back demodulation with 91. >>>> Starting back unit deletion with 90. >>>> Starting back demodulation with 94. >>>> Starting back unit deletion with 93. >>>> Starting back demodulation with 96. >>>> Starting back unit deletion with 95. >>>> Starting back demodulation with 98. >>>> Starting back unit deletion with 97. >>>> Starting back demodulation with 101. >>>> Starting back unit deletion with 100. >>>> Starting back demodulation with 104. >>>> Starting back unit deletion with 103. >>>> Starting back demodulation with 107. >>>> Starting back unit deletion with 106. >>>> Starting back demodulation with 109. >>>> Starting back unit deletion with 108. >>>> Starting back demodulation with 111. >>>> Starting back unit deletion with 110. >>>> Starting back demodulation with 113. >>>> Starting back unit deletion with 112. >>>> Starting back demodulation with 115. >>>> Starting back unit deletion with 114. >>>> Starting back demodulation with 118. >>>> Starting back unit deletion with 117. >>>> Starting back demodulation with 121. >>>> Starting back unit deletion with 120. >>>> Starting back demodulation with 123. >>>> Starting back unit deletion with 122. >>>> Starting back demodulation with 125. >>>> Starting back unit deletion with 124. >>>> Starting back demodulation with 128. >>>> Starting back unit deletion with 127. >>>> Starting back demodulation with 131. >>>> Starting back unit deletion with 130. >>>> Starting back demodulation with 133. >>>> Starting back unit deletion with 132. >>>> Starting back demodulation with 135. >>>> Starting back unit deletion with 134. >>>> Starting back demodulation with 137. >>>> Starting back unit deletion with 136. >>>> Starting back demodulation with 140. >>>> Starting back unit deletion with 139. >>>> Starting back demodulation with 142. >>>> Starting back unit deletion with 141. >>>> Starting back demodulation with 144. >>>> Starting back unit deletion with 143. >>>> Starting back demodulation with 146. >>>> Starting back unit deletion with 145. >>>> Starting back demodulation with 149. >>>> Starting back unit deletion with 148. >>>> Starting back demodulation with 151. >>>> Starting back unit deletion with 150. >>>> Starting back demodulation with 153. >>>> Starting back unit deletion with 152. >>>> Starting back demodulation with 155. >>>> Starting back unit deletion with 154. >>>> Starting back demodulation with 158. >>>> Starting back unit deletion with 157. >>>> Starting back demodulation with 161. >>>> Starting back unit deletion with 160. >>>> Starting back demodulation with 164. >>>> Starting back unit deletion with 163. >>>> Starting back demodulation with 167. >>>> Starting back unit deletion with 166. >>>> Starting back demodulation with 169. >>>> Starting back unit deletion with 168. >>>> Starting back demodulation with 171. >>>> Starting back unit deletion with 170. >>>> Starting back demodulation with 173. >>>> Starting back unit deletion with 172. >>>> Starting back demodulation with 175. >>>> Starting back unit deletion with 174. >>>> Starting back demodulation with 177. >>>> Starting back unit deletion with 176. >>>> Starting back demodulation with 179. >>>> Starting back unit deletion with 178. >>>> Starting back demodulation with 181. >>>> Starting back unit deletion with 180. >>>> Starting back demodulation with 183. >>>> Starting back unit deletion with 182. >>>> Starting back demodulation with 185. >>>> Starting back unit deletion with 184. >>>> Starting back demodulation with 188. >>>> Starting back unit deletion with 187. >>>> Starting back demodulation with 191. >>>> Starting back unit deletion with 190. >>>> Starting back demodulation with 194. >>>> Starting back unit deletion with 193. >>>> Starting back demodulation with 196. >>>> Starting back unit deletion with 195. >>>> Starting back demodulation with 198. >>>> Starting back unit deletion with 197. >>>> Starting back demodulation with 200. >>>> Starting back unit deletion with 199. >>>> Starting back demodulation with 202. >>>> Starting back unit deletion with 201. >>>> Starting back demodulation with 204. >>>> Starting back unit deletion with 203. >>>> Starting back demodulation with 206. >>>> Starting back unit deletion with 205. >>>> Starting back demodulation with 209. >>>> Starting back unit deletion with 208. >>>> Starting back demodulation with 212. >>>> Starting back unit deletion with 211. >>>> Starting back demodulation with 215. >>>> Starting back unit deletion with 214. >>>> Starting back demodulation with 217. >>>> Starting back unit deletion with 216. >>>> Starting back demodulation with 219. >>>> Starting back unit deletion with 218. >>>> Starting back demodulation with 221. >>>> Starting back unit deletion with 220. >>>> Starting back demodulation with 223. >>>> Starting back unit deletion with 222. >>>> Starting back demodulation with 226. >>>> Starting back unit deletion with 225. >>>> Starting back demodulation with 228. >>>> Starting back unit deletion with 227. >>>> Starting back demodulation with 230. >>>> Starting back unit deletion with 229. >>>> Starting back demodulation with 232. >>>> Starting back unit deletion with 231. >>>> Starting back demodulation with 234. >>>> Starting back unit deletion with 233. >>>> Starting back demodulation with 237. >>>> Starting back unit deletion with 236. >>>> Starting back demodulation with 239. >>>> Starting back unit deletion with 238. >>>> Starting back demodulation with 241. >>>> Starting back unit deletion with 240. >>>> Starting back demodulation with 243. >>>> Starting back unit deletion with 242. >>>> Starting back demodulation with 245. >>>> Starting back unit deletion with 244. >>>> Starting back demodulation with 248. >>>> Starting back unit deletion with 247. >>>> Starting back demodulation with 250. >>>> Starting back unit deletion with 249. >>>> Starting back demodulation with 252. >>>> Starting back unit deletion with 251. >>>> Starting back demodulation with 254. >>>> Starting back unit deletion with 253. >>>> Starting back demodulation with 256. >>>> Starting back unit deletion with 255. >>>> Starting back demodulation with 259. >>>> Starting back unit deletion with 258. >>>> Starting back demodulation with 262. >>>> Starting back unit deletion with 261. >>>> Starting back demodulation with 265. >>>> Starting back unit deletion with 264. >>>> Starting back demodulation with 268. >>>> Starting back unit deletion with 267. >>>> Starting back demodulation with 271. >>>> Starting back unit deletion with 270. >>>> Starting back demodulation with 273. >>>> Starting back unit deletion with 272. >>>> Starting back demodulation with 275. >>>> Starting back unit deletion with 274. >>>> Starting back demodulation with 277. >>>> Starting back unit deletion with 276. >>>> Starting back demodulation with 279. >>>> Starting back unit deletion with 278. >>>> Starting back demodulation with 281. >>>> Starting back unit deletion with 280. >>>> Starting back demodulation with 283. >>>> Starting back unit deletion with 282. >>>> Starting back demodulation with 285. >>>> Starting back unit deletion with 284. >>>> Starting back demodulation with 287. >>>> Starting back unit deletion with 286. >>>> Starting back demodulation with 289. >>>> Starting back unit deletion with 288. >>>> Starting back demodulation with 291. >>>> Starting back unit deletion with 290. >>>> Starting back demodulation with 293. >>>> Starting back unit deletion with 292. >>>> Starting back demodulation with 295. >>>> Starting back unit deletion with 294. >>>> Starting back demodulation with 297. >>>> Starting back unit deletion with 296. >>>> Starting back demodulation with 299. >>>> Starting back unit deletion with 298. >>>> Starting back demodulation with 301. >>>> Starting back unit deletion with 300. >>>> Starting back demodulation with 303. >>>> Starting back unit deletion with 302. >>>> Starting back demodulation with 306. >>>> Starting back unit deletion with 305. >>>> Starting back demodulation with 309. >>>> Starting back unit deletion with 308. >>>> Starting back demodulation with 312. >>>> Starting back unit deletion with 311. >>>> Starting back demodulation with 315. >>>> Starting back unit deletion with 314. >>>> Starting back demodulation with 317. >>>> Starting back unit deletion with 316. >>>> Starting back demodulation with 319. >>>> Starting back unit deletion with 318. >>>> Starting back demodulation with 321. >>>> Starting back unit deletion with 320. >>>> Starting back demodulation with 323. >>>> Starting back unit deletion with 322. >>>> Starting back demodulation with 325. >>>> Starting back unit deletion with 324. >>>> Starting back demodulation with 327. >>>> Starting back unit deletion with 326. >>>> Starting back demodulation with 329. >>>> Starting back unit deletion with 328. >>>> Starting back demodulation with 331. >>>> Starting back unit deletion with 330. >>>> Starting back demodulation with 333. >>>> Starting back unit deletion with 332. >>>> Starting back demodulation with 335. >>>> Starting back unit deletion with 334. >>>> Starting back demodulation with 337. >>>> Starting back unit deletion with 336. >>>> Starting back demodulation with 339. >>>> Starting back unit deletion with 338. >>>> Starting back demodulation with 342. >>>> Starting back unit deletion with 341. >>>> Starting back demodulation with 345. >>>> Starting back unit deletion with 344. >>>> Starting back demodulation with 348. >>>> Starting back unit deletion with 347. >>>> Starting back demodulation with 351. >>>> Starting back unit deletion with 350. >>>> Starting back demodulation with 353. >>>> Starting back unit deletion with 352. >>>> Starting back demodulation with 355. >>>> Starting back unit deletion with 354. >>>> Starting back demodulation with 357. >>>> Starting back unit deletion with 356. >>>> Starting back demodulation with 359. >>>> Starting back unit deletion with 358. >>>> Starting back demodulation with 361. >>>> Starting back unit deletion with 360. >>>> Starting back demodulation with 364. >>>> Starting back unit deletion with 363. >>>> Starting back demodulation with 366. >>>> Starting back unit deletion with 365. >>>> Starting back demodulation with 368. >>>> Starting back unit deletion with 367. >>>> Starting back demodulation with 370. >>>> Starting back unit deletion with 369. >>>> Starting back demodulation with 372. >>>> Starting back unit deletion with 371. >>>> Starting back demodulation with 374. >>>> Starting back unit deletion with 373. >>>> Starting back demodulation with 377. >>>> Starting back unit deletion with 376. >>>> Starting back demodulation with 379. >>>> Starting back unit deletion with 378. >>>> Starting back demodulation with 381. >>>> Starting back unit deletion with 380. >>>> Starting back demodulation with 383. >>>> Starting back unit deletion with 382. >>>> Starting back demodulation with 385. >>>> Starting back unit deletion with 384. >>>> Starting back demodulation with 387. >>>> Starting back unit deletion with 386. >>>> Starting back demodulation with 390. >>>> Starting back unit deletion with 389. >>>> Starting back demodulation with 392. >>>> Starting back unit deletion with 391. >>>> Starting back demodulation with 394. >>>> Starting back unit deletion with 393. >>>> Starting back demodulation with 396. >>>> Starting back unit deletion with 395. >>>> Starting back demodulation with 398. >>>> Starting back unit deletion with 397. >>>> Starting back demodulation with 400. >>>> Starting back unit deletion with 399. >>>> Starting back demodulation with 403. >>>> Starting back unit deletion with 402. >>>> Starting back demodulation with 405. >>>> Starting back unit deletion with 404. >>>> Starting back demodulation with 407. >>>> Starting back unit deletion with 406. >>>> Starting back demodulation with 409. >>>> Starting back unit deletion with 408. >>>> Starting back demodulation with 411. >>>> Starting back unit deletion with 410. >>>> Starting back demodulation with 413. >>>> Starting back unit deletion with 412. >>>> Starting back demodulation with 416. >>>> Starting back unit deletion with 415. >>>> Starting back demodulation with 419. >>>> Starting back unit deletion with 418. >>>> Starting back demodulation with 422. >>>> Starting back unit deletion with 421. >>>> Starting back demodulation with 425. >>>> Starting back unit deletion with 424. >>>> Starting back demodulation with 428. >>>> Starting back unit deletion with 427. >>>> Starting back demodulation with 431. >>>> Starting back unit deletion with 430. >>>> Starting back demodulation with 433. >>>> Starting back unit deletion with 432. >>>> Starting back demodulation with 435. >>>> Starting back unit deletion with 434. >>>> Starting back demodulation with 437. >>>> Starting back unit deletion with 436. >>>> Starting back demodulation with 439. >>>> Starting back unit deletion with 438. >>>> Starting back demodulation with 441. >>>> Starting back unit deletion with 440. >>>> Starting back demodulation with 443. >>>> Starting back unit deletion with 442. >>>> Starting back demodulation with 445. >>>> Starting back unit deletion with 444. >>>> Starting back demodulation with 447. >>>> Starting back unit deletion with 446. >>>> Starting back demodulation with 449. >>>> Starting back unit deletion with 448. >>>> Starting back demodulation with 451. >>>> Starting back unit deletion with 450. >>>> Starting back demodulation with 453. >>>> Starting back unit deletion with 452. >>>> Starting back demodulation with 455. >>>> Starting back unit deletion with 454. >>>> Starting back demodulation with 457. >>>> Starting back unit deletion with 456. >>>> Starting back demodulation with 459. >>>> Starting back unit deletion with 458. >>>> Starting back demodulation with 461. >>>> Starting back unit deletion with 460. >>>> Starting back demodulation with 463. >>>> Starting back unit deletion with 462. >>>> Starting back demodulation with 465. >>>> Starting back unit deletion with 464. >>>> Starting back demodulation with 467. >>>> Starting back unit deletion with 466. >>>> Starting back demodulation with 469. >>>> Starting back unit deletion with 468. >>>> Starting back demodulation with 471. >>>> Starting back unit deletion with 470. >>>> Starting back demodulation with 473. >>>> Starting back unit deletion with 472. >>>> Starting back demodulation with 475. >>>> Starting back unit deletion with 474. >>>> Starting back demodulation with 477. >>>> Starting back unit deletion with 476. >>>> Starting back demodulation with 479. >>>> Starting back unit deletion with 478. >>>> Starting back demodulation with 481. >>>> Starting back unit deletion with 480. >>>> Starting back demodulation with 484. >>>> Starting back unit deletion with 483. >>>> Starting back demodulation with 487. >>>> Starting back unit deletion with 486. >>>> Starting back demodulation with 490. >>>> Starting back unit deletion with 489. >>>> Starting back demodulation with 493. >>>> Starting back unit deletion with 492. >>>> Starting back demodulation with 496. >>>> Starting back unit deletion with 495. >>>> Starting back demodulation with 498. >>>> Starting back unit deletion with 497. >>>> Starting back demodulation with 500. >>>> Starting back unit deletion with 499. >>>> Starting back demodulation with 502. >>>> Starting back unit deletion with 501. >>>> Starting back demodulation with 504. >>>> Starting back unit deletion with 503. >>>> Starting back demodulation with 506. >>>> Starting back unit deletion with 505. >>>> Starting back demodulation with 508. >>>> Starting back unit deletion with 507. >>>> Starting back demodulation with 510. >>>> Starting back unit deletion with 509. >>>> Starting back demodulation with 512. >>>> Starting back unit deletion with 511. >>>> Starting back demodulation with 514. >>>> Starting back unit deletion with 513. >>>> Starting back demodulation with 516. >>>> Starting back unit deletion with 515. >>>> Starting back demodulation with 518. >>>> Starting back unit deletion with 517. >>>> Starting back demodulation with 520. >>>> Starting back unit deletion with 519. >>>> Starting back demodulation with 522. >>>> Starting back unit deletion with 521. >>>> Starting back demodulation with 524. >>>> Starting back unit deletion with 523. >>>> Starting back demodulation with 526. >>>> Starting back unit deletion with 525. >>>> Starting back demodulation with 528. >>>> Starting back unit deletion with 527. >>>> Starting back demodulation with 530. >>>> Starting back unit deletion with 529. >>>> Starting back demodulation with 532. >>>> Starting back unit deletion with 531. >>>> Starting back demodulation with 534. >>>> Starting back unit deletion with 533. >>>> Starting back demodulation with 536. >>>> Starting back unit deletion with 535. >>>> Starting back demodulation with 539. >>>> Starting back unit deletion with 538. >>>> Starting back demodulation with 542. >>>> Starting back unit deletion with 541. >>>> Starting back demodulation with 545. >>>> Starting back unit deletion with 544. >>>> Starting back demodulation with 548. >>>> Starting back unit deletion with 547. >>>> Starting back demodulation with 551. >>>> Starting back unit deletion with 550. ======= end of input processing ======= =========== start of search =========== Splitting on clause 552 [] g(0)=0|g(0)=1|g(0)=2|g(0)=3|g(0)=4|g(0)=5. Case [1] (process 8663): Assumption: 588 [552,split.1] g(0)=0. Splitting on clause 553 [] g(1)=0|g(1)=1|g(1)=2|g(1)=3|g(1)=4|g(1)=5. Case [1.1] (process 8664): Assumption: 590 [553,split.1.1] g(1)=0. ----> UNIT CONFLICT at 0.00 sec ----> 594 [binary,592.1,3.1] $F. ------- statistics (process 8664) ------- clauses given 242 clauses generated 448 clauses kept 279 clauses forward subsumed 462 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8664 finished Mon Aug 2 15:31:08 2004 Refuted case [1.1]. Case [1.2] (process 8665): Assumption: 591 [553,split.1.2] g(1)=1. Splitting on clause 554 [] g(2)=0|g(2)=1|g(2)=2|g(2)=3|g(2)=4|g(2)=5. Case [1.2.1] (process 8666): Assumption: 625 [554,split.1.2.1] g(2)=0. ----> UNIT CONFLICT at 0.00 sec ----> 629 [binary,627.1,5.1] $F. ------- statistics (process 8666) ------- clauses given 258 clauses generated 478 clauses kept 297 clauses forward subsumed 504 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8666 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.1]. Case [1.2.2] (process 8667): Assumption: 626 [554,split.1.2.2] g(2)=1. ----> UNIT CONFLICT at 0.00 sec ----> 632 [binary,630.1,13.1] $F. ------- statistics (process 8667) ------- clauses given 258 clauses generated 478 clauses kept 299 clauses forward subsumed 505 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8667 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.2]. Case [1.2.3] (process 8668): Assumption: 627 [554,split.1.2.3] g(2)=2. Splitting on clause 555 [] g(3)=0|g(3)=1|g(3)=2|g(3)=3|g(3)=4|g(3)=5. Case [1.2.3.1] (process 8669): Assumption: 663 [555,split.1.2.3.1] g(3)=0. ----> UNIT CONFLICT at 0.00 sec ----> 667 [binary,665.1,7.1] $F. ------- statistics (process 8669) ------- clauses given 275 clauses generated 510 clauses kept 317 clauses forward subsumed 549 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8669 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.1]. Case [1.2.3.2] (process 8670): Assumption: 664 [555,split.1.2.3.2] g(3)=1. ----> UNIT CONFLICT at 0.00 sec ----> 670 [binary,668.1,15.1] $F. ------- statistics (process 8670) ------- clauses given 275 clauses generated 510 clauses kept 319 clauses forward subsumed 550 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8670 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.2]. Case [1.2.3.3] (process 8671): Assumption: 665 [555,split.1.2.3.3] g(3)=2. ----> UNIT CONFLICT at 0.00 sec ----> 671 [binary,669.1,21.1] $F. ------- statistics (process 8671) ------- clauses given 275 clauses generated 510 clauses kept 320 clauses forward subsumed 551 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8671 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.3]. Case [1.2.3.4] (process 8672): Assumption: 666 [555,split.1.2.3.4] g(3)=3. Splitting on clause 556 [] g(4)=0|g(4)=1|g(4)=2|g(4)=3|g(4)=4|g(4)=5. Case [1.2.3.4.1] (process 8673): Assumption: 704 [556,split.1.2.3.4.1] g(4)=0. ----> UNIT CONFLICT at 0.00 sec ----> 708 [binary,706.1,9.1] $F. ------- statistics (process 8673) ------- clauses given 293 clauses generated 544 clauses kept 339 clauses forward subsumed 597 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8673 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.1]. Case [1.2.3.4.2] (process 8674): Assumption: 705 [556,split.1.2.3.4.2] g(4)=1. ----> UNIT CONFLICT at 0.00 sec ----> 711 [binary,709.1,17.1] $F. ------- statistics (process 8674) ------- clauses given 293 clauses generated 544 clauses kept 341 clauses forward subsumed 598 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8674 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.2]. Case [1.2.3.4.3] (process 8675): Assumption: 706 [556,split.1.2.3.4.3] g(4)=2. ----> UNIT CONFLICT at 0.00 sec ----> 712 [binary,710.1,23.1] $F. ------- statistics (process 8675) ------- clauses given 293 clauses generated 544 clauses kept 342 clauses forward subsumed 599 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8675 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.3]. Case [1.2.3.4.4] (process 8676): Assumption: 707 [556,split.1.2.3.4.4] g(4)=3. ----> UNIT CONFLICT at 0.00 sec ----> 713 [binary,711.1,27.1] $F. ------- statistics (process 8676) ------- clauses given 293 clauses generated 544 clauses kept 343 clauses forward subsumed 600 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8676 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.4]. Case [1.2.3.4.5] (process 8677): Assumption: 708 [556,split.1.2.3.4.5] g(4)=4. Splitting on clause 557 [] g(5)=0|g(5)=1|g(5)=2|g(5)=3|g(5)=4|g(5)=5. Case [1.2.3.4.5.1] (process 8678): Assumption: 748 [557,split.1.2.3.4.5.1] g(5)=0. ----> UNIT CONFLICT at 0.00 sec ----> 752 [binary,750.1,11.1] $F. ------- statistics (process 8678) ------- clauses given 312 clauses generated 580 clauses kept 363 clauses forward subsumed 648 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8678 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.1]. Case [1.2.3.4.5.2] (process 8679): Assumption: 749 [557,split.1.2.3.4.5.2] g(5)=1. ----> UNIT CONFLICT at 0.00 sec ----> 755 [binary,753.1,19.1] $F. ------- statistics (process 8679) ------- clauses given 312 clauses generated 580 clauses kept 365 clauses forward subsumed 649 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8679 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.2]. Case [1.2.3.4.5.3] (process 8680): Assumption: 750 [557,split.1.2.3.4.5.3] g(5)=2. ----> UNIT CONFLICT at 0.00 sec ----> 756 [binary,754.1,25.1] $F. ------- statistics (process 8680) ------- clauses given 312 clauses generated 580 clauses kept 366 clauses forward subsumed 650 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8680 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.3]. Case [1.2.3.4.5.4] (process 8681): Assumption: 751 [557,split.1.2.3.4.5.4] g(5)=3. ----> UNIT CONFLICT at 0.00 sec ----> 757 [binary,755.1,29.1] $F. ------- statistics (process 8681) ------- clauses given 312 clauses generated 580 clauses kept 367 clauses forward subsumed 651 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8681 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.4]. Case [1.2.3.4.5.5] (process 8682): Assumption: 752 [557,split.1.2.3.4.5.5] g(5)=4. ----> UNIT CONFLICT at 0.00 sec ----> 758 [binary,756.1,31.1] $F. ------- statistics (process 8682) ------- clauses given 312 clauses generated 580 clauses kept 368 clauses forward subsumed 652 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8682 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.5]. Case [1.2.3.4.5.6] (process 8683): Assumption: 753 [557,split.1.2.3.4.5.6] g(5)=5. Splitting on clause 561 [] f(1,2)=0|f(1,2)=1|f(1,2)=2|f(1,2)=3|f(1,2)=4|f(1,2)=5. Case [1.2.3.4.5.6.1] (process 8684): Assumption: 795 [561,split.1.2.3.4.5.6.1] f(1,2)=0. ----> UNIT CONFLICT at 0.00 sec ----> 799 [binary,797.1,13.1] $F. ------- statistics (process 8684) ------- clauses given 332 clauses generated 618 clauses kept 389 clauses forward subsumed 703 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8684 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6.1]. Case [1.2.3.4.5.6.2] (process 8685): Assumption: 796 [561,split.1.2.3.4.5.6.2] f(1,2)=1. ----> UNIT CONFLICT at 0.00 sec ----> 800 [binary,798.1,5.1] $F. ------- statistics (process 8685) ------- clauses given 332 clauses generated 618 clauses kept 390 clauses forward subsumed 705 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8685 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6.2]. Case [1.2.3.4.5.6.3] (process 8686): Assumption: 797 [561,split.1.2.3.4.5.6.3] f(1,2)=2. ----> UNIT CONFLICT at 0.00 sec ----> 801 [binary,799.1,3.1] $F. ------- statistics (process 8686) ------- clauses given 332 clauses generated 618 clauses kept 391 clauses forward subsumed 705 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8686 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6.3]. Case [1.2.3.4.5.6.4] (process 8687): Assumption: 798 [561,split.1.2.3.4.5.6.4] f(1,2)=3. ----> UNIT CONFLICT at 0.00 sec ----> 849 [binary,847.1,820.1] $F. ------- statistics (process 8687) ------- clauses given 332 clauses generated 618 clauses kept 416 clauses forward subsumed 715 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8687 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6.4]. Case [1.2.3.4.5.6.5] (process 8688): Assumption: 799 [561,split.1.2.3.4.5.6.5] f(1,2)=4. ----> UNIT CONFLICT at 0.00 sec ----> 846 [binary,844.1,821.1] $F. ------- statistics (process 8688) ------- clauses given 332 clauses generated 618 clauses kept 415 clauses forward subsumed 716 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8688 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6.5]. Case [1.2.3.4.5.6.6] (process 8689): Assumption: 800 [561,split.1.2.3.4.5.6.6] f(1,2)=5. ----> UNIT CONFLICT at 0.00 sec ----> 843 [binary,841.1,822.1] $F. ------- statistics (process 8689) ------- clauses given 332 clauses generated 618 clauses kept 414 clauses forward subsumed 717 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8689 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6.6]. ------- statistics (process 8683) ------- clauses given 332 clauses generated 618 clauses kept 387 clauses forward subsumed 702 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8683 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5.6]. ------- statistics (process 8677) ------- clauses given 312 clauses generated 580 clauses kept 361 clauses forward subsumed 648 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8677 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.5]. Case [1.2.3.4.6] (process 8690): Assumption: 709 [556,split.1.2.3.4.6] g(4)=5. Splitting on clause 557 [] g(5)=0|g(5)=1|g(5)=2|g(5)=3|g(5)=4|g(5)=5. Case [1.2.3.4.6.1] (process 8691): Assumption: 737 [557,split.1.2.3.4.6.1] g(5)=0. ----> UNIT CONFLICT at 0.00 sec ----> 741 [binary,739.1,11.1] $F. ------- statistics (process 8691) ------- clauses given 308 clauses generated 572 clauses kept 358 clauses forward subsumed 632 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8691 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.1]. Case [1.2.3.4.6.2] (process 8692): Assumption: 738 [557,split.1.2.3.4.6.2] g(5)=1. ----> UNIT CONFLICT at 0.00 sec ----> 744 [binary,742.1,17.1] $F. ------- statistics (process 8692) ------- clauses given 308 clauses generated 572 clauses kept 360 clauses forward subsumed 633 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8692 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.2]. Case [1.2.3.4.6.3] (process 8693): Assumption: 739 [557,split.1.2.3.4.6.3] g(5)=2. ----> UNIT CONFLICT at 0.00 sec ----> 745 [binary,743.1,23.1] $F. ------- statistics (process 8693) ------- clauses given 308 clauses generated 572 clauses kept 361 clauses forward subsumed 634 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8693 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.3]. Case [1.2.3.4.6.4] (process 8694): Assumption: 740 [557,split.1.2.3.4.6.4] g(5)=3. ----> UNIT CONFLICT at 0.00 sec ----> 746 [binary,744.1,27.1] $F. ------- statistics (process 8694) ------- clauses given 308 clauses generated 572 clauses kept 362 clauses forward subsumed 635 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8694 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.4]. Case [1.2.3.4.6.5] (process 8695): Assumption: 741 [557,split.1.2.3.4.6.5] g(5)=4. Splitting on clause 561 [] f(1,2)=0|f(1,2)=1|f(1,2)=2|f(1,2)=3|f(1,2)=4|f(1,2)=5. Case [1.2.3.4.6.5.1] (process 8696): Assumption: 795 [561,split.1.2.3.4.6.5.1] f(1,2)=0. ----> UNIT CONFLICT at 0.00 sec ----> 799 [binary,797.1,13.1] $F. ------- statistics (process 8696) ------- clauses given 336 clauses generated 626 clauses kept 389 clauses forward subsumed 711 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8696 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.1]. Case [1.2.3.4.6.5.2] (process 8697): Assumption: 796 [561,split.1.2.3.4.6.5.2] f(1,2)=1. ----> UNIT CONFLICT at 0.00 sec ----> 800 [binary,798.1,5.1] $F. ------- statistics (process 8697) ------- clauses given 336 clauses generated 626 clauses kept 390 clauses forward subsumed 713 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8697 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.2]. Case [1.2.3.4.6.5.3] (process 8698): Assumption: 797 [561,split.1.2.3.4.6.5.3] f(1,2)=2. ----> UNIT CONFLICT at 0.00 sec ----> 801 [binary,799.1,3.1] $F. ------- statistics (process 8698) ------- clauses given 336 clauses generated 626 clauses kept 391 clauses forward subsumed 713 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8698 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.3]. Case [1.2.3.4.6.5.4] (process 8699): Assumption: 798 [561,split.1.2.3.4.6.5.4] f(1,2)=3. ----> UNIT CONFLICT at 0.00 sec ----> 849 [binary,847.1,820.1] $F. ------- statistics (process 8699) ------- clauses given 336 clauses generated 626 clauses kept 416 clauses forward subsumed 723 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8699 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.4]. Case [1.2.3.4.6.5.5] (process 8700): Assumption: 799 [561,split.1.2.3.4.6.5.5] f(1,2)=4. 913 back subsumes 562. Splitting on clause 565 [] f(2,3)=0|f(2,3)=1|f(2,3)=2|f(2,3)=3|f(2,3)=4|f(2,3)=5. Case [1.2.3.4.6.5.5.1] (process 8701): Assumption: 1010 [565,split.1.2.3.4.6.5.5.1] f(2,3)=0. ----> UNIT CONFLICT at 0.00 sec ----> 1028 [binary,1026.1,21.1] $F. ------- statistics (process 8701) ------- clauses given 413 clauses generated 779 clauses kept 509 clauses forward subsumed 919 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8701 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.1]. Case [1.2.3.4.6.5.5.2] (process 8702): Assumption: 1011 [565,split.1.2.3.4.6.5.5.2] f(2,3)=1. ----> UNIT CONFLICT at 0.00 sec ----> 1029 [binary,1027.1,29.1] $F. ------- statistics (process 8702) ------- clauses given 413 clauses generated 779 clauses kept 510 clauses forward subsumed 920 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8702 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.2]. Case [1.2.3.4.6.5.5.3] (process 8703): Assumption: 1012 [565,split.1.2.3.4.6.5.5.3] f(2,3)=2. ----> UNIT CONFLICT at 0.00 sec ----> 1030 [binary,1028.1,7.1] $F. ------- statistics (process 8703) ------- clauses given 413 clauses generated 779 clauses kept 511 clauses forward subsumed 921 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8703 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.3]. Case [1.2.3.4.6.5.5.4] (process 8704): Assumption: 1013 [565,split.1.2.3.4.6.5.5.4] f(2,3)=3. ----> UNIT CONFLICT at 0.00 sec ----> 1031 [binary,1029.1,17.1] $F. ------- statistics (process 8704) ------- clauses given 413 clauses generated 779 clauses kept 512 clauses forward subsumed 923 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8704 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.4]. Case [1.2.3.4.6.5.5.5] (process 8705): Assumption: 1014 [565,split.1.2.3.4.6.5.5.5] f(2,3)=4. Splitting on clause 566 [] f(1,3)=0|f(1,3)=1|f(1,3)=2|f(1,3)=3|f(1,3)=4|f(1,3)=5. Case [1.2.3.4.6.5.5.5.1] (process 8706): Assumption: 1104 [566,split.1.2.3.4.6.5.5.5.1] f(1,3)=0. ----> UNIT CONFLICT at 0.00 sec ----> 1112 [binary,1110.1,15.1] $F. ------- statistics (process 8706) ------- clauses given 441 clauses generated 833 clauses kept 553 clauses forward subsumed 1041 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8706 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.5.1]. Case [1.2.3.4.6.5.5.5.2] (process 8707): Assumption: 1105 [566,split.1.2.3.4.6.5.5.5.2] f(1,3)=1. ----> UNIT CONFLICT at 0.00 sec ----> 1117 [binary,1115.1,23.1] $F. ------- statistics (process 8707) ------- clauses given 441 clauses generated 833 clauses kept 556 clauses forward subsumed 1042 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8707 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.5.2]. Case [1.2.3.4.6.5.5.5.3] (process 8708): Assumption: 1106 [566,split.1.2.3.4.6.5.5.5.3] f(1,3)=2. ----> UNIT CONFLICT at 0.00 sec ----> 1114 [binary,1112.1,29.1] $F. ------- statistics (process 8708) ------- clauses given 441 clauses generated 833 clauses kept 555 clauses forward subsumed 1043 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8708 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.5.3]. Case [1.2.3.4.6.5.5.5.4] (process 8709): Assumption: 1107 [566,split.1.2.3.4.6.5.5.5.4] f(1,3)=3. ----> UNIT CONFLICT at 0.00 sec ----> 1115 [binary,1113.1,7.1] $F. ------- statistics (process 8709) ------- clauses given 441 clauses generated 833 clauses kept 556 clauses forward subsumed 1044 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8709 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.5.4]. Case [1.2.3.4.6.5.5.5.5] (process 8710): Assumption: 1108 [566,split.1.2.3.4.6.5.5.5.5] f(1,3)=4. ----> UNIT CONFLICT at 0.00 sec ----> 1116 [binary,1114.1,21.1] $F. ------- statistics (process 8710) ------- clauses given 441 clauses generated 833 clauses kept 557 clauses forward subsumed 1045 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8710 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2.3.4.6.5.5.5.5]. Possible model detected on branch [1.2.3.4.6.5.5.5.6]. Case [1.2.3.4.6.5.5.5.6] (process 8711): Assumption: 1109 [566,split.1.2.3.4.6.5.5.5.6] f(1,3)=5. Possible model detected on branch [1.2.3.4.6.5.5.5.6]. Here are the clauses in Usable and SoS. It seems that no more inferences or splitting can be done. If the search strategy is complete, these clauses should lead to a model of the input. list(usable). 1 [] x=x. 3 [copy,2,flip.1] 1!=0. 5 [copy,4,flip.1] 2!=0. 7 [copy,6,flip.1] 3!=0. 9 [copy,8,flip.1] 4!=0. 11 [copy,10,flip.1] 5!=0. 13 [copy,12,flip.1] 2!=1. 15 [copy,14,flip.1] 3!=1. 17 [copy,16,flip.1] 4!=1. 19 [copy,18,flip.1] 5!=1. 21 [copy,20,flip.1] 3!=2. 23 [copy,22,flip.1] 4!=2. 25 [copy,24,flip.1] 5!=2. 27 [copy,26,flip.1] 4!=3. 29 [copy,28,flip.1] 5!=3. 31 [copy,30,flip.1] 5!=4. 32 [] e=0. 37 [copy,36,demod,33] f(0,0)=0. 40 [copy,39,demod,33] f(0,1)=1. 43 [copy,42,demod,33] f(0,2)=2. 46 [copy,45,demod,33] f(0,3)=3. 49 [copy,48,demod,33] f(0,4)=4. 52 [copy,51,demod,33] f(0,5)=5. 588 [552,split.1] g(0)=0. 591 [553,split.1.2] g(1)=1. 593 [back_demod,58,demod,592] f(1,1)=0. 615 [back_demod,72,demod,594,41,594,flip.1] f(1,0)=1. 627 [554,split.1.2.3] g(2)=2. 629 [back_demod,61,demod,628] f(2,2)=0. 651 [back_demod,88,demod,630,44,630,flip.1] f(2,0)=2. 666 [555,split.1.2.3.4] g(3)=3. 668 [back_demod,64,demod,667] f(3,3)=0. 690 [back_demod,132,demod,669,47,669,flip.1] f(3,0)=3. 709 [556,split.1.2.3.4.6] g(4)=5. 711 [back_demod,67,demod,710] f(5,4)=0. 741 [557,split.1.2.3.4.6.5] g(5)=4. 743 [back_demod,70,demod,742] f(4,5)=0. 745 [back_demod,735,demod,744] f(5,0)=5. 747 [back_demod,731,demod,744,50,flip.1] f(4,0)=4. 799 [561,split.1.2.3.4.6.5.5] f(1,2)=4. 801 [back_demod,647,demod,800] f(4,2)=1. 803 [back_demod,609,demod,800] f(1,4)=2. 822 [back_demod,719,demod,802] f(5,1)=2. 838 [back_demod,755,demod,804] f(2,5)=1. 914 [back_demod,771,demod,823] f(2,1)=5. 1014 [565,split.1.2.3.4.6.5.5.5] f(2,3)=4. 1030 [back_demod,877,demod,1015,804,841] f(2,4)=3. 1032 [back_demod,815,demod,1015,804] f(4,3)=2. 1048 [back_demod,956,demod,1031] f(3,2)=5. 1068 [back_demod,840,demod,1031] f(5,2)=3. 1072 [back_demod,757,demod,1031] f(3,5)=2. 1109 [566,split.1.2.3.4.6.5.5.5.6] f(1,3)=5. 1115 [back_demod,1096,demod,1110,839] f(1,5)=3. 1117 [back_demod,1070,demod,1110] f(4,4)=5. 1119 [back_demod,1064,demod,1110,839] f(3,4)=1. 1121 [back_demod,962,demod,1110,839] f(5,3)=1. 1123 [back_demod,1052,demod,1116,1015] f(3,1)=4. 1125 [back_demod,958,demod,1116] f(4,1)=3. 1127 [back_demod,932,demod,1116,1015] f(5,5)=4. end_of_list. list(sos). end_of_list. ------- statistics (process 8711) ------- clauses given 449 clauses generated 849 clauses kept 564 clauses forward subsumed 1106 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8711 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8705) ------- clauses given 441 clauses generated 833 clauses kept 549 clauses forward subsumed 1041 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8705 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8700) ------- clauses given 413 clauses generated 779 clauses kept 500 clauses forward subsumed 915 clauses back subsumed 1 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8700 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8695) ------- clauses given 336 clauses generated 626 clauses kept 387 clauses forward subsumed 710 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8695 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8690) ------- clauses given 308 clauses generated 572 clauses kept 356 clauses forward subsumed 632 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8690 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8672) ------- clauses given 293 clauses generated 544 clauses kept 337 clauses forward subsumed 597 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8672 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8668) ------- clauses given 275 clauses generated 510 clauses kept 315 clauses forward subsumed 549 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8668 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8665) ------- clauses given 258 clauses generated 478 clauses kept 295 clauses forward subsumed 504 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8665 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8663) ------- clauses given 242 clauses generated 448 clauses kept 277 clauses forward subsumed 462 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8663 finished Mon Aug 2 15:31:08 2004 ------- statistics (process 8662) ------- clauses given 240 clauses generated 446 clauses kept 276 clauses forward subsumed 459 clauses back subsumed 0 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8662 finished Mon Aug 2 15:31:08 2004 otter-3.3f/examples/split/pigeon5.out0100664000076400007640000023066410103522215017255 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:09 2004 The command was "../../bin/otter". The process ID is 8730. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(split_when_given). dependent: set(back_unit_deletion). set(split_pos). clear(print_kept). clear(print_back_sub). assign(stats_level,1). list(sos). 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 10 [] -p04| -p08. 11 [] -p04| -p12. 12 [] -p04| -p16. 13 [] -p08| -p12. 14 [] -p08| -p16. 15 [] -p12| -p16. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 20 [] -p05| -p09. 21 [] -p05| -p13. 22 [] -p05| -p17. 23 [] -p09| -p13. 24 [] -p09| -p17. 25 [] -p13| -p17. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 30 [] -p06| -p10. 31 [] -p06| -p14. 32 [] -p06| -p18. 33 [] -p10| -p14. 34 [] -p10| -p18. 35 [] -p14| -p18. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 40 [] -p07| -p11. 41 [] -p07| -p15. 42 [] -p07| -p19. 43 [] -p11| -p15. 44 [] -p11| -p19. 45 [] -p15| -p19. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=2) 6 [] -p00| -p04. given clause #2: (wt=2) 7 [] -p00| -p08. given clause #3: (wt=2) 8 [] -p00| -p12. given clause #4: (wt=2) 9 [] -p00| -p16. given clause #5: (wt=2) 10 [] -p04| -p08. given clause #6: (wt=2) 11 [] -p04| -p12. given clause #7: (wt=2) 12 [] -p04| -p16. given clause #8: (wt=2) 13 [] -p08| -p12. given clause #9: (wt=2) 14 [] -p08| -p16. given clause #10: (wt=2) 15 [] -p12| -p16. given clause #11: (wt=2) 16 [] -p01| -p05. given clause #12: (wt=2) 17 [] -p01| -p09. given clause #13: (wt=2) 18 [] -p01| -p13. given clause #14: (wt=2) 19 [] -p01| -p17. given clause #15: (wt=2) 20 [] -p05| -p09. given clause #16: (wt=2) 21 [] -p05| -p13. given clause #17: (wt=2) 22 [] -p05| -p17. given clause #18: (wt=2) 23 [] -p09| -p13. given clause #19: (wt=2) 24 [] -p09| -p17. given clause #20: (wt=2) 25 [] -p13| -p17. given clause #21: (wt=2) 26 [] -p02| -p06. given clause #22: (wt=2) 27 [] -p02| -p10. given clause #23: (wt=2) 28 [] -p02| -p14. given clause #24: (wt=2) 29 [] -p02| -p18. given clause #25: (wt=2) 30 [] -p06| -p10. given clause #26: (wt=2) 31 [] -p06| -p14. given clause #27: (wt=2) 32 [] -p06| -p18. given clause #28: (wt=2) 33 [] -p10| -p14. given clause #29: (wt=2) 34 [] -p10| -p18. given clause #30: (wt=2) 35 [] -p14| -p18. given clause #31: (wt=2) 36 [] -p03| -p07. given clause #32: (wt=2) 37 [] -p03| -p11. given clause #33: (wt=2) 38 [] -p03| -p15. given clause #34: (wt=2) 39 [] -p03| -p19. given clause #35: (wt=2) 40 [] -p07| -p11. given clause #36: (wt=2) 41 [] -p07| -p15. given clause #37: (wt=2) 42 [] -p07| -p19. given clause #38: (wt=2) 43 [] -p11| -p15. given clause #39: (wt=2) 44 [] -p11| -p19. given clause #40: (wt=2) 45 [] -p15| -p19. given clause #41: (wt=4) 1 [] p00|p01|p02|p03. Splitting on clause 1 [] p00|p01|p02|p03. Case [1] (process 8731): Assumption: 46 [1,split.1] p00. >>>> Starting back unit deletion with 46. 0 [back_unit_del,46.1,9.1] -p16. 0 [back_unit_del,46.1,8.1] -p12. 0 [back_unit_del,46.1,7.1] -p08. 0 [back_unit_del,46.1,6.1] -p04. >>>> Starting back unit deletion with 47. >>>> Starting back unit deletion with 48. >>>> Starting back unit deletion with 49. >>>> Starting back unit deletion with 50. given clause #42: (wt=1) 46 [1,split.1] p00. given clause #43: (wt=3) 51 [back_unit_del,47.1,5.1] p17|p18|p19. Splitting on clause 51 [back_unit_del,47.1,5.1] p17|p18|p19. Case [1.1] (process 8732): Assumption: 55 [51,split.1.1] p17. >>>> Starting back unit deletion with 55. 0 [back_unit_del,55.1,25.2] -p13. 0 [back_unit_del,55.1,24.2] -p09. 0 [back_unit_del,55.1,22.2] -p05. 0 [back_unit_del,55.1,19.2] -p01. >>>> Starting back unit deletion with 56. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. given clause #44: (wt=1) 55 [51,split.1.1] p17. given clause #45: (wt=2) 60 [back_unit_del,56.1,52.1] p14|p15. Splitting on clause 60 [back_unit_del,56.1,52.1] p14|p15. --- refuted case [1.1.1] Case [1.1.1] (process 8733): Assumption: 63 [60,split.1.1.1] p14. >>>> Starting back unit deletion with 63. 0 [back_unit_del,63.1,35.1] -p18. 0 [back_unit_del,63.1,33.2] -p10. 0 [back_unit_del,63.1,31.2] -p06. 0 [back_unit_del,63.1,28.2] -p02. >>>> Starting back unit deletion with 64. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,44.1] -p19. 0 [back_unit_del,68.1,43.1] -p15. 0 [back_unit_del,68.1,40.2] -p07. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,69.1] $F. Length of proof is 22. Level of proof is 10. Case [1.1.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 22 [] -p05| -p17. 24 [] -p09| -p17. 25 [] -p13| -p17. 31 [] -p06| -p14. 33 [] -p10| -p14. 40 [] -p07| -p11. 46 [1,split.1] p00. 47 [back_unit_del,46.1,9.1] -p16. 48 [back_unit_del,46.1,8.1] -p12. 49 [back_unit_del,46.1,7.1] -p08. 50 [back_unit_del,46.1,6.1] -p04. 51 [back_unit_del,47.1,5.1] p17|p18|p19. 52 [back_unit_del,48.1,4.1] p13|p14|p15. 53 [back_unit_del,49.1,3.1] p09|p10|p11. 54 [back_unit_del,50.1,2.1] p05|p06|p07. 55 [51,split.1.1] p17. 56 [back_unit_del,55.1,25.2] -p13. 57 [back_unit_del,55.1,24.2] -p09. 58 [back_unit_del,55.1,22.2] -p05. 60 [back_unit_del,56.1,52.1] p14|p15. 61 [back_unit_del,57.1,53.1] p10|p11. 62 [back_unit_del,58.1,54.1] p06|p07. 63 [60,split.1.1.1] p14. 65 [back_unit_del,63.1,33.2] -p10. 66 [back_unit_del,63.1,31.2] -p06. 68 [back_unit_del,65.1,61.1] p11. 69 [back_unit_del,66.1,62.1] p07. 72 [back_unit_del,68.1,40.2] -p07. 73 [binary,72.1,69.1] $F. ------------ end of proof ------------- ------- statistics (process 8733) ------- clauses given 45 clauses generated 24 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8733 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.1]. --- refuted case [1.1.2] Case [1.1.2] (process 8734): Assumption: 64 [60,split.1.1.2] p15. >>>> Starting back unit deletion with 63. >>>> Starting back unit deletion with 64. 0 [back_unit_del,64.1,45.1] -p19. 0 [back_unit_del,64.1,43.2] -p11. 0 [back_unit_del,64.1,41.2] -p07. 0 [back_unit_del,64.1,38.2] -p03. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. 0 [back_unit_del,69.1,34.1] -p18. 0 [back_unit_del,69.1,30.2] -p06. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,70.1] $F. Length of proof is 22. Level of proof is 10. Case [1.1.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 22 [] -p05| -p17. 24 [] -p09| -p17. 25 [] -p13| -p17. 30 [] -p06| -p10. 41 [] -p07| -p15. 43 [] -p11| -p15. 46 [1,split.1] p00. 47 [back_unit_del,46.1,9.1] -p16. 48 [back_unit_del,46.1,8.1] -p12. 49 [back_unit_del,46.1,7.1] -p08. 50 [back_unit_del,46.1,6.1] -p04. 51 [back_unit_del,47.1,5.1] p17|p18|p19. 52 [back_unit_del,48.1,4.1] p13|p14|p15. 53 [back_unit_del,49.1,3.1] p09|p10|p11. 54 [back_unit_del,50.1,2.1] p05|p06|p07. 55 [51,split.1.1] p17. 56 [back_unit_del,55.1,25.2] -p13. 57 [back_unit_del,55.1,24.2] -p09. 58 [back_unit_del,55.1,22.2] -p05. 60 [back_unit_del,56.1,52.1] p14|p15. 61 [back_unit_del,57.1,53.1] p10|p11. 62 [back_unit_del,58.1,54.1] p06|p07. 64 [60,split.1.1.2] p15. 66 [back_unit_del,64.1,43.2] -p11. 67 [back_unit_del,64.1,41.2] -p07. 69 [back_unit_del,66.1,61.2] p10. 70 [back_unit_del,67.1,62.2] p06. 72 [back_unit_del,69.1,30.2] -p06. 73 [binary,72.1,70.1] $F. ------------ end of proof ------------- ------- statistics (process 8734) ------- clauses given 45 clauses generated 23 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 42 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8734 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.2]. ------- statistics (process 8732) ------- clauses given 45 clauses generated 15 clauses kept 17 clauses forward subsumed 0 clauses back subsumed 27 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8732 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1]. Case [1.2] (process 8735): Assumption: 56 [51,split.1.2] p18. >>>> Starting back unit deletion with 55. >>>> Starting back unit deletion with 56. 0 [back_unit_del,56.1,35.2] -p14. 0 [back_unit_del,56.1,34.2] -p10. 0 [back_unit_del,56.1,32.2] -p06. 0 [back_unit_del,56.1,29.2] -p02. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. given clause #44: (wt=1) 55 [51,split_neg.1.2] -p17. given clause #45: (wt=1) 56 [51,split.1.2] p18. given clause #46: (wt=2) 61 [back_unit_del,57.1,52.2] p13|p15. Splitting on clause 61 [back_unit_del,57.1,52.2] p13|p15. --- refuted case [1.2.1] Case [1.2.1] (process 8736): Assumption: 64 [61,split.1.2.1] p13. >>>> Starting back unit deletion with 64. 0 [back_unit_del,64.1,23.2] -p09. 0 [back_unit_del,64.1,21.2] -p05. 0 [back_unit_del,64.1,18.2] -p01. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,44.1] -p19. 0 [back_unit_del,68.1,43.1] -p15. 0 [back_unit_del,68.1,40.2] -p07. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,69.1] $F. Length of proof is 22. Level of proof is 10. Case [1.2.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 21 [] -p05| -p13. 23 [] -p09| -p13. 32 [] -p06| -p18. 34 [] -p10| -p18. 35 [] -p14| -p18. 40 [] -p07| -p11. 46 [1,split.1] p00. 47 [back_unit_del,46.1,9.1] -p16. 48 [back_unit_del,46.1,8.1] -p12. 49 [back_unit_del,46.1,7.1] -p08. 50 [back_unit_del,46.1,6.1] -p04. 51 [back_unit_del,47.1,5.1] p17|p18|p19. 52 [back_unit_del,48.1,4.1] p13|p14|p15. 53 [back_unit_del,49.1,3.1] p09|p10|p11. 54 [back_unit_del,50.1,2.1] p05|p06|p07. 56 [51,split.1.2] p18. 57 [back_unit_del,56.1,35.2] -p14. 58 [back_unit_del,56.1,34.2] -p10. 59 [back_unit_del,56.1,32.2] -p06. 61 [back_unit_del,57.1,52.2] p13|p15. 62 [back_unit_del,58.1,53.2] p09|p11. 63 [back_unit_del,59.1,54.2] p05|p07. 64 [61,split.1.2.1] p13. 65 [back_unit_del,64.1,23.2] -p09. 66 [back_unit_del,64.1,21.2] -p05. 68 [back_unit_del,65.1,62.1] p11. 69 [back_unit_del,66.1,63.1] p07. 72 [back_unit_del,68.1,40.2] -p07. 73 [binary,72.1,69.1] $F. ------------ end of proof ------------- ------- statistics (process 8736) ------- clauses given 46 clauses generated 23 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8736 finished Mon Aug 2 15:31:09 2004 Refuted case [1.2.1]. --- refuted case [1.2.2] Case [1.2.2] (process 8737): Assumption: 65 [61,split.1.2.2] p15. >>>> Starting back unit deletion with 64. >>>> Starting back unit deletion with 65. 0 [back_unit_del,65.1,45.1] -p19. 0 [back_unit_del,65.1,43.2] -p11. 0 [back_unit_del,65.1,41.2] -p07. 0 [back_unit_del,65.1,38.2] -p03. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. 0 [back_unit_del,70.1,20.2] -p05. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,71.1] $F. Length of proof is 22. Level of proof is 10. Case [1.2.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 20 [] -p05| -p09. 32 [] -p06| -p18. 34 [] -p10| -p18. 35 [] -p14| -p18. 41 [] -p07| -p15. 43 [] -p11| -p15. 46 [1,split.1] p00. 47 [back_unit_del,46.1,9.1] -p16. 48 [back_unit_del,46.1,8.1] -p12. 49 [back_unit_del,46.1,7.1] -p08. 50 [back_unit_del,46.1,6.1] -p04. 51 [back_unit_del,47.1,5.1] p17|p18|p19. 52 [back_unit_del,48.1,4.1] p13|p14|p15. 53 [back_unit_del,49.1,3.1] p09|p10|p11. 54 [back_unit_del,50.1,2.1] p05|p06|p07. 56 [51,split.1.2] p18. 57 [back_unit_del,56.1,35.2] -p14. 58 [back_unit_del,56.1,34.2] -p10. 59 [back_unit_del,56.1,32.2] -p06. 61 [back_unit_del,57.1,52.2] p13|p15. 62 [back_unit_del,58.1,53.2] p09|p11. 63 [back_unit_del,59.1,54.2] p05|p07. 65 [61,split.1.2.2] p15. 67 [back_unit_del,65.1,43.2] -p11. 68 [back_unit_del,65.1,41.2] -p07. 70 [back_unit_del,67.1,62.2] p09. 71 [back_unit_del,68.1,63.2] p05. 72 [back_unit_del,70.1,20.2] -p05. 73 [binary,72.1,71.1] $F. ------------ end of proof ------------- ------- statistics (process 8737) ------- clauses given 46 clauses generated 22 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 45 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8737 finished Mon Aug 2 15:31:09 2004 Refuted case [1.2.2]. ------- statistics (process 8735) ------- clauses given 46 clauses generated 15 clauses kept 18 clauses forward subsumed 0 clauses back subsumed 31 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8735 finished Mon Aug 2 15:31:09 2004 Refuted case [1.2]. Case [1.3] (process 8738): Assumption: 57 [51,split.1.3] p19. >>>> Starting back unit deletion with 55. >>>> Starting back unit deletion with 56. >>>> Starting back unit deletion with 57. 0 [back_unit_del,57.1,45.2] -p15. 0 [back_unit_del,57.1,44.2] -p11. 0 [back_unit_del,57.1,42.2] -p07. 0 [back_unit_del,57.1,39.2] -p03. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. given clause #44: (wt=1) 55 [51,split_neg.1.3] -p17. given clause #45: (wt=1) 56 [51,split_neg.1.3] -p18. given clause #46: (wt=1) 57 [51,split.1.3] p19. given clause #47: (wt=2) 62 [back_unit_del,58.1,52.3] p13|p14. Splitting on clause 62 [back_unit_del,58.1,52.3] p13|p14. --- refuted case [1.3.1] Case [1.3.1] (process 8739): Assumption: 65 [62,split.1.3.1] p13. >>>> Starting back unit deletion with 65. 0 [back_unit_del,65.1,23.2] -p09. 0 [back_unit_del,65.1,21.2] -p05. 0 [back_unit_del,65.1,18.2] -p01. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. 0 [back_unit_del,69.1,33.1] -p14. 0 [back_unit_del,69.1,30.2] -p06. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,70.1] $F. Length of proof is 22. Level of proof is 10. Case [1.3.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 21 [] -p05| -p13. 23 [] -p09| -p13. 30 [] -p06| -p10. 42 [] -p07| -p19. 44 [] -p11| -p19. 45 [] -p15| -p19. 46 [1,split.1] p00. 47 [back_unit_del,46.1,9.1] -p16. 48 [back_unit_del,46.1,8.1] -p12. 49 [back_unit_del,46.1,7.1] -p08. 50 [back_unit_del,46.1,6.1] -p04. 51 [back_unit_del,47.1,5.1] p17|p18|p19. 52 [back_unit_del,48.1,4.1] p13|p14|p15. 53 [back_unit_del,49.1,3.1] p09|p10|p11. 54 [back_unit_del,50.1,2.1] p05|p06|p07. 57 [51,split.1.3] p19. 58 [back_unit_del,57.1,45.2] -p15. 59 [back_unit_del,57.1,44.2] -p11. 60 [back_unit_del,57.1,42.2] -p07. 62 [back_unit_del,58.1,52.3] p13|p14. 63 [back_unit_del,59.1,53.3] p09|p10. 64 [back_unit_del,60.1,54.3] p05|p06. 65 [62,split.1.3.1] p13. 66 [back_unit_del,65.1,23.2] -p09. 67 [back_unit_del,65.1,21.2] -p05. 69 [back_unit_del,66.1,63.1] p10. 70 [back_unit_del,67.1,64.1] p06. 72 [back_unit_del,69.1,30.2] -p06. 73 [binary,72.1,70.1] $F. ------------ end of proof ------------- ------- statistics (process 8739) ------- clauses given 47 clauses generated 22 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 42 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8739 finished Mon Aug 2 15:31:09 2004 Refuted case [1.3.1]. --- refuted case [1.3.2] Case [1.3.2] (process 8740): Assumption: 66 [62,split.1.3.2] p14. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. 0 [back_unit_del,66.1,33.2] -p10. 0 [back_unit_del,66.1,31.2] -p06. 0 [back_unit_del,66.1,28.2] -p02. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. 0 [back_unit_del,70.1,20.2] -p05. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,71.1] $F. Length of proof is 22. Level of proof is 10. Case [1.3.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 6 [] -p00| -p04. 7 [] -p00| -p08. 8 [] -p00| -p12. 9 [] -p00| -p16. 20 [] -p05| -p09. 31 [] -p06| -p14. 33 [] -p10| -p14. 42 [] -p07| -p19. 44 [] -p11| -p19. 45 [] -p15| -p19. 46 [1,split.1] p00. 47 [back_unit_del,46.1,9.1] -p16. 48 [back_unit_del,46.1,8.1] -p12. 49 [back_unit_del,46.1,7.1] -p08. 50 [back_unit_del,46.1,6.1] -p04. 51 [back_unit_del,47.1,5.1] p17|p18|p19. 52 [back_unit_del,48.1,4.1] p13|p14|p15. 53 [back_unit_del,49.1,3.1] p09|p10|p11. 54 [back_unit_del,50.1,2.1] p05|p06|p07. 57 [51,split.1.3] p19. 58 [back_unit_del,57.1,45.2] -p15. 59 [back_unit_del,57.1,44.2] -p11. 60 [back_unit_del,57.1,42.2] -p07. 62 [back_unit_del,58.1,52.3] p13|p14. 63 [back_unit_del,59.1,53.3] p09|p10. 64 [back_unit_del,60.1,54.3] p05|p06. 66 [62,split.1.3.2] p14. 67 [back_unit_del,66.1,33.2] -p10. 68 [back_unit_del,66.1,31.2] -p06. 70 [back_unit_del,67.1,63.2] p09. 71 [back_unit_del,68.1,64.2] p05. 72 [back_unit_del,70.1,20.2] -p05. 73 [binary,72.1,71.1] $F. ------------ end of proof ------------- ------- statistics (process 8740) ------- clauses given 47 clauses generated 21 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 45 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8740 finished Mon Aug 2 15:31:09 2004 Refuted case [1.3.2]. ------- statistics (process 8738) ------- clauses given 47 clauses generated 15 clauses kept 19 clauses forward subsumed 0 clauses back subsumed 35 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8738 finished Mon Aug 2 15:31:09 2004 Refuted case [1.3]. ------- statistics (process 8731) ------- clauses given 43 clauses generated 8 clauses kept 9 clauses forward subsumed 0 clauses back subsumed 14 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8731 finished Mon Aug 2 15:31:09 2004 Refuted case [1]. Case [2] (process 8741): Assumption: 47 [1,split.2] p01. >>>> Starting back unit deletion with 46. >>>> Starting back unit deletion with 47. 0 [back_unit_del,47.1,19.1] -p17. 0 [back_unit_del,47.1,18.1] -p13. 0 [back_unit_del,47.1,17.1] -p09. 0 [back_unit_del,47.1,16.1] -p05. >>>> Starting back unit deletion with 48. >>>> Starting back unit deletion with 49. >>>> Starting back unit deletion with 50. >>>> Starting back unit deletion with 51. given clause #42: (wt=1) 46 [1,split_neg.2] -p00. given clause #43: (wt=1) 47 [1,split.2] p01. given clause #44: (wt=3) 52 [back_unit_del,48.1,5.2] p16|p18|p19. Splitting on clause 52 [back_unit_del,48.1,5.2] p16|p18|p19. Case [2.1] (process 8742): Assumption: 56 [52,split.2.1] p16. >>>> Starting back unit deletion with 56. 0 [back_unit_del,56.1,15.2] -p12. 0 [back_unit_del,56.1,14.2] -p08. 0 [back_unit_del,56.1,12.2] -p04. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. given clause #45: (wt=1) 56 [52,split.2.1] p16. given clause #46: (wt=2) 60 [back_unit_del,57.1,53.1] p14|p15. Splitting on clause 60 [back_unit_del,57.1,53.1] p14|p15. --- refuted case [2.1.1] Case [2.1.1] (process 8743): Assumption: 63 [60,split.2.1.1] p14. >>>> Starting back unit deletion with 63. 0 [back_unit_del,63.1,35.1] -p18. 0 [back_unit_del,63.1,33.2] -p10. 0 [back_unit_del,63.1,31.2] -p06. 0 [back_unit_del,63.1,28.2] -p02. >>>> Starting back unit deletion with 64. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,44.1] -p19. 0 [back_unit_del,68.1,43.1] -p15. 0 [back_unit_del,68.1,40.2] -p07. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,69.1] $F. Length of proof is 22. Level of proof is 10. Case [2.1.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 12 [] -p04| -p16. 14 [] -p08| -p16. 15 [] -p12| -p16. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 31 [] -p06| -p14. 33 [] -p10| -p14. 40 [] -p07| -p11. 47 [1,split.2] p01. 48 [back_unit_del,47.1,19.1] -p17. 49 [back_unit_del,47.1,18.1] -p13. 50 [back_unit_del,47.1,17.1] -p09. 51 [back_unit_del,47.1,16.1] -p05. 52 [back_unit_del,48.1,5.2] p16|p18|p19. 53 [back_unit_del,49.1,4.2] p12|p14|p15. 54 [back_unit_del,50.1,3.2] p08|p10|p11. 55 [back_unit_del,51.1,2.2] p04|p06|p07. 56 [52,split.2.1] p16. 57 [back_unit_del,56.1,15.2] -p12. 58 [back_unit_del,56.1,14.2] -p08. 59 [back_unit_del,56.1,12.2] -p04. 60 [back_unit_del,57.1,53.1] p14|p15. 61 [back_unit_del,58.1,54.1] p10|p11. 62 [back_unit_del,59.1,55.1] p06|p07. 63 [60,split.2.1.1] p14. 65 [back_unit_del,63.1,33.2] -p10. 66 [back_unit_del,63.1,31.2] -p06. 68 [back_unit_del,65.1,61.1] p11. 69 [back_unit_del,66.1,62.1] p07. 72 [back_unit_del,68.1,40.2] -p07. 73 [binary,72.1,69.1] $F. ------------ end of proof ------------- ------- statistics (process 8743) ------- clauses given 46 clauses generated 23 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8743 finished Mon Aug 2 15:31:09 2004 Refuted case [2.1.1]. --- refuted case [2.1.2] Case [2.1.2] (process 8744): Assumption: 64 [60,split.2.1.2] p15. >>>> Starting back unit deletion with 63. >>>> Starting back unit deletion with 64. 0 [back_unit_del,64.1,45.1] -p19. 0 [back_unit_del,64.1,43.2] -p11. 0 [back_unit_del,64.1,41.2] -p07. 0 [back_unit_del,64.1,38.2] -p03. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. 0 [back_unit_del,69.1,34.1] -p18. 0 [back_unit_del,69.1,30.2] -p06. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,70.1] $F. Length of proof is 22. Level of proof is 10. Case [2.1.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 12 [] -p04| -p16. 14 [] -p08| -p16. 15 [] -p12| -p16. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 30 [] -p06| -p10. 41 [] -p07| -p15. 43 [] -p11| -p15. 47 [1,split.2] p01. 48 [back_unit_del,47.1,19.1] -p17. 49 [back_unit_del,47.1,18.1] -p13. 50 [back_unit_del,47.1,17.1] -p09. 51 [back_unit_del,47.1,16.1] -p05. 52 [back_unit_del,48.1,5.2] p16|p18|p19. 53 [back_unit_del,49.1,4.2] p12|p14|p15. 54 [back_unit_del,50.1,3.2] p08|p10|p11. 55 [back_unit_del,51.1,2.2] p04|p06|p07. 56 [52,split.2.1] p16. 57 [back_unit_del,56.1,15.2] -p12. 58 [back_unit_del,56.1,14.2] -p08. 59 [back_unit_del,56.1,12.2] -p04. 60 [back_unit_del,57.1,53.1] p14|p15. 61 [back_unit_del,58.1,54.1] p10|p11. 62 [back_unit_del,59.1,55.1] p06|p07. 64 [60,split.2.1.2] p15. 66 [back_unit_del,64.1,43.2] -p11. 67 [back_unit_del,64.1,41.2] -p07. 69 [back_unit_del,66.1,61.2] p10. 70 [back_unit_del,67.1,62.2] p06. 72 [back_unit_del,69.1,30.2] -p06. 73 [binary,72.1,70.1] $F. ------------ end of proof ------------- ------- statistics (process 8744) ------- clauses given 46 clauses generated 22 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 42 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8744 finished Mon Aug 2 15:31:09 2004 Refuted case [2.1.2]. ------- statistics (process 8742) ------- clauses given 46 clauses generated 14 clauses kept 17 clauses forward subsumed 0 clauses back subsumed 27 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8742 finished Mon Aug 2 15:31:09 2004 Refuted case [2.1]. Case [2.2] (process 8745): Assumption: 57 [52,split.2.2] p18. >>>> Starting back unit deletion with 56. >>>> Starting back unit deletion with 57. 0 [back_unit_del,57.1,35.2] -p14. 0 [back_unit_del,57.1,34.2] -p10. 0 [back_unit_del,57.1,32.2] -p06. 0 [back_unit_del,57.1,29.2] -p02. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. given clause #45: (wt=1) 56 [52,split_neg.2.2] -p16. given clause #46: (wt=1) 57 [52,split.2.2] p18. given clause #47: (wt=2) 62 [back_unit_del,58.1,53.2] p12|p15. Splitting on clause 62 [back_unit_del,58.1,53.2] p12|p15. --- refuted case [2.2.1] Case [2.2.1] (process 8746): Assumption: 65 [62,split.2.2.1] p12. >>>> Starting back unit deletion with 65. 0 [back_unit_del,65.1,13.2] -p08. 0 [back_unit_del,65.1,11.2] -p04. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,44.1] -p19. 0 [back_unit_del,68.1,43.1] -p15. 0 [back_unit_del,68.1,40.2] -p07. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,69.1] $F. Length of proof is 22. Level of proof is 10. Case [2.2.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 11 [] -p04| -p12. 13 [] -p08| -p12. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 32 [] -p06| -p18. 34 [] -p10| -p18. 35 [] -p14| -p18. 40 [] -p07| -p11. 47 [1,split.2] p01. 48 [back_unit_del,47.1,19.1] -p17. 49 [back_unit_del,47.1,18.1] -p13. 50 [back_unit_del,47.1,17.1] -p09. 51 [back_unit_del,47.1,16.1] -p05. 52 [back_unit_del,48.1,5.2] p16|p18|p19. 53 [back_unit_del,49.1,4.2] p12|p14|p15. 54 [back_unit_del,50.1,3.2] p08|p10|p11. 55 [back_unit_del,51.1,2.2] p04|p06|p07. 57 [52,split.2.2] p18. 58 [back_unit_del,57.1,35.2] -p14. 59 [back_unit_del,57.1,34.2] -p10. 60 [back_unit_del,57.1,32.2] -p06. 62 [back_unit_del,58.1,53.2] p12|p15. 63 [back_unit_del,59.1,54.2] p08|p11. 64 [back_unit_del,60.1,55.2] p04|p07. 65 [62,split.2.2.1] p12. 66 [back_unit_del,65.1,13.2] -p08. 67 [back_unit_del,65.1,11.2] -p04. 68 [back_unit_del,66.1,63.1] p11. 69 [back_unit_del,67.1,64.1] p07. 72 [back_unit_del,68.1,40.2] -p07. 73 [binary,72.1,69.1] $F. ------------ end of proof ------------- ------- statistics (process 8746) ------- clauses given 47 clauses generated 22 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8746 finished Mon Aug 2 15:31:09 2004 Refuted case [2.2.1]. --- refuted case [2.2.2] Case [2.2.2] (process 8747): Assumption: 66 [62,split.2.2.2] p15. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. 0 [back_unit_del,66.1,45.1] -p19. 0 [back_unit_del,66.1,43.2] -p11. 0 [back_unit_del,66.1,41.2] -p07. 0 [back_unit_del,66.1,38.2] -p03. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 71. 0 [back_unit_del,71.1,10.2] -p04. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,72.1] $F. Length of proof is 22. Level of proof is 10. Case [2.2.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 10 [] -p04| -p08. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 32 [] -p06| -p18. 34 [] -p10| -p18. 35 [] -p14| -p18. 41 [] -p07| -p15. 43 [] -p11| -p15. 47 [1,split.2] p01. 48 [back_unit_del,47.1,19.1] -p17. 49 [back_unit_del,47.1,18.1] -p13. 50 [back_unit_del,47.1,17.1] -p09. 51 [back_unit_del,47.1,16.1] -p05. 52 [back_unit_del,48.1,5.2] p16|p18|p19. 53 [back_unit_del,49.1,4.2] p12|p14|p15. 54 [back_unit_del,50.1,3.2] p08|p10|p11. 55 [back_unit_del,51.1,2.2] p04|p06|p07. 57 [52,split.2.2] p18. 58 [back_unit_del,57.1,35.2] -p14. 59 [back_unit_del,57.1,34.2] -p10. 60 [back_unit_del,57.1,32.2] -p06. 62 [back_unit_del,58.1,53.2] p12|p15. 63 [back_unit_del,59.1,54.2] p08|p11. 64 [back_unit_del,60.1,55.2] p04|p07. 66 [62,split.2.2.2] p15. 68 [back_unit_del,66.1,43.2] -p11. 69 [back_unit_del,66.1,41.2] -p07. 71 [back_unit_del,68.1,63.2] p08. 72 [back_unit_del,69.1,64.2] p04. 73 [back_unit_del,71.1,10.2] -p04. 74 [binary,73.1,72.1] $F. ------------ end of proof ------------- ------- statistics (process 8747) ------- clauses given 47 clauses generated 22 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 47 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8747 finished Mon Aug 2 15:31:09 2004 Refuted case [2.2.2]. ------- statistics (process 8745) ------- clauses given 47 clauses generated 15 clauses kept 19 clauses forward subsumed 0 clauses back subsumed 34 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8745 finished Mon Aug 2 15:31:09 2004 Refuted case [2.2]. Case [2.3] (process 8748): Assumption: 58 [52,split.2.3] p19. >>>> Starting back unit deletion with 56. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 58. 0 [back_unit_del,58.1,45.2] -p15. 0 [back_unit_del,58.1,44.2] -p11. 0 [back_unit_del,58.1,42.2] -p07. 0 [back_unit_del,58.1,39.2] -p03. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. >>>> Starting back unit deletion with 62. given clause #45: (wt=1) 56 [52,split_neg.2.3] -p16. given clause #46: (wt=1) 57 [52,split_neg.2.3] -p18. given clause #47: (wt=1) 58 [52,split.2.3] p19. given clause #48: (wt=2) 63 [back_unit_del,59.1,53.3] p12|p14. Splitting on clause 63 [back_unit_del,59.1,53.3] p12|p14. --- refuted case [2.3.1] Case [2.3.1] (process 8749): Assumption: 66 [63,split.2.3.1] p12. >>>> Starting back unit deletion with 66. 0 [back_unit_del,66.1,13.2] -p08. 0 [back_unit_del,66.1,11.2] -p04. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. 0 [back_unit_del,69.1,33.1] -p14. 0 [back_unit_del,69.1,30.2] -p06. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,70.1] $F. Length of proof is 22. Level of proof is 10. Case [2.3.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 11 [] -p04| -p12. 13 [] -p08| -p12. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 30 [] -p06| -p10. 42 [] -p07| -p19. 44 [] -p11| -p19. 45 [] -p15| -p19. 47 [1,split.2] p01. 48 [back_unit_del,47.1,19.1] -p17. 49 [back_unit_del,47.1,18.1] -p13. 50 [back_unit_del,47.1,17.1] -p09. 51 [back_unit_del,47.1,16.1] -p05. 52 [back_unit_del,48.1,5.2] p16|p18|p19. 53 [back_unit_del,49.1,4.2] p12|p14|p15. 54 [back_unit_del,50.1,3.2] p08|p10|p11. 55 [back_unit_del,51.1,2.2] p04|p06|p07. 58 [52,split.2.3] p19. 59 [back_unit_del,58.1,45.2] -p15. 60 [back_unit_del,58.1,44.2] -p11. 61 [back_unit_del,58.1,42.2] -p07. 63 [back_unit_del,59.1,53.3] p12|p14. 64 [back_unit_del,60.1,54.3] p08|p10. 65 [back_unit_del,61.1,55.3] p04|p06. 66 [63,split.2.3.1] p12. 67 [back_unit_del,66.1,13.2] -p08. 68 [back_unit_del,66.1,11.2] -p04. 69 [back_unit_del,67.1,64.1] p10. 70 [back_unit_del,68.1,65.1] p06. 72 [back_unit_del,69.1,30.2] -p06. 73 [binary,72.1,70.1] $F. ------------ end of proof ------------- ------- statistics (process 8749) ------- clauses given 48 clauses generated 21 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 42 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8749 finished Mon Aug 2 15:31:09 2004 Refuted case [2.3.1]. --- refuted case [2.3.2] Case [2.3.2] (process 8750): Assumption: 67 [63,split.2.3.2] p14. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. 0 [back_unit_del,67.1,33.2] -p10. 0 [back_unit_del,67.1,31.2] -p06. 0 [back_unit_del,67.1,28.2] -p02. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 71. 0 [back_unit_del,71.1,10.2] -p04. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,72.1] $F. Length of proof is 22. Level of proof is 10. Case [2.3.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 10 [] -p04| -p08. 16 [] -p01| -p05. 17 [] -p01| -p09. 18 [] -p01| -p13. 19 [] -p01| -p17. 31 [] -p06| -p14. 33 [] -p10| -p14. 42 [] -p07| -p19. 44 [] -p11| -p19. 45 [] -p15| -p19. 47 [1,split.2] p01. 48 [back_unit_del,47.1,19.1] -p17. 49 [back_unit_del,47.1,18.1] -p13. 50 [back_unit_del,47.1,17.1] -p09. 51 [back_unit_del,47.1,16.1] -p05. 52 [back_unit_del,48.1,5.2] p16|p18|p19. 53 [back_unit_del,49.1,4.2] p12|p14|p15. 54 [back_unit_del,50.1,3.2] p08|p10|p11. 55 [back_unit_del,51.1,2.2] p04|p06|p07. 58 [52,split.2.3] p19. 59 [back_unit_del,58.1,45.2] -p15. 60 [back_unit_del,58.1,44.2] -p11. 61 [back_unit_del,58.1,42.2] -p07. 63 [back_unit_del,59.1,53.3] p12|p14. 64 [back_unit_del,60.1,54.3] p08|p10. 65 [back_unit_del,61.1,55.3] p04|p06. 67 [63,split.2.3.2] p14. 68 [back_unit_del,67.1,33.2] -p10. 69 [back_unit_del,67.1,31.2] -p06. 71 [back_unit_del,68.1,64.2] p08. 72 [back_unit_del,69.1,65.2] p04. 73 [back_unit_del,71.1,10.2] -p04. 74 [binary,73.1,72.1] $F. ------------ end of proof ------------- ------- statistics (process 8750) ------- clauses given 48 clauses generated 21 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 47 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8750 finished Mon Aug 2 15:31:09 2004 Refuted case [2.3.2]. ------- statistics (process 8748) ------- clauses given 48 clauses generated 15 clauses kept 20 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8748 finished Mon Aug 2 15:31:09 2004 Refuted case [2.3]. ------- statistics (process 8741) ------- clauses given 44 clauses generated 8 clauses kept 10 clauses forward subsumed 0 clauses back subsumed 18 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8741 finished Mon Aug 2 15:31:09 2004 Refuted case [2]. Case [3] (process 8751): Assumption: 48 [1,split.3] p02. >>>> Starting back unit deletion with 46. >>>> Starting back unit deletion with 47. >>>> Starting back unit deletion with 48. 0 [back_unit_del,48.1,29.1] -p18. 0 [back_unit_del,48.1,28.1] -p14. 0 [back_unit_del,48.1,27.1] -p10. 0 [back_unit_del,48.1,26.1] -p06. >>>> Starting back unit deletion with 49. >>>> Starting back unit deletion with 50. >>>> Starting back unit deletion with 51. >>>> Starting back unit deletion with 52. given clause #42: (wt=1) 46 [1,split_neg.3] -p00. given clause #43: (wt=1) 47 [1,split_neg.3] -p01. given clause #44: (wt=1) 48 [1,split.3] p02. given clause #45: (wt=3) 53 [back_unit_del,49.1,5.3] p16|p17|p19. Splitting on clause 53 [back_unit_del,49.1,5.3] p16|p17|p19. Case [3.1] (process 8752): Assumption: 57 [53,split.3.1] p16. >>>> Starting back unit deletion with 57. 0 [back_unit_del,57.1,15.2] -p12. 0 [back_unit_del,57.1,14.2] -p08. 0 [back_unit_del,57.1,12.2] -p04. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. given clause #46: (wt=1) 57 [53,split.3.1] p16. given clause #47: (wt=2) 61 [back_unit_del,58.1,54.1] p13|p15. Splitting on clause 61 [back_unit_del,58.1,54.1] p13|p15. --- refuted case [3.1.1] Case [3.1.1] (process 8753): Assumption: 64 [61,split.3.1.1] p13. >>>> Starting back unit deletion with 64. 0 [back_unit_del,64.1,25.1] -p17. 0 [back_unit_del,64.1,23.2] -p09. 0 [back_unit_del,64.1,21.2] -p05. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,44.1] -p19. 0 [back_unit_del,68.1,43.1] -p15. 0 [back_unit_del,68.1,40.2] -p07. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,69.1] $F. Length of proof is 22. Level of proof is 10. Case [3.1.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 12 [] -p04| -p16. 14 [] -p08| -p16. 15 [] -p12| -p16. 21 [] -p05| -p13. 23 [] -p09| -p13. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 40 [] -p07| -p11. 48 [1,split.3] p02. 49 [back_unit_del,48.1,29.1] -p18. 50 [back_unit_del,48.1,28.1] -p14. 51 [back_unit_del,48.1,27.1] -p10. 52 [back_unit_del,48.1,26.1] -p06. 53 [back_unit_del,49.1,5.3] p16|p17|p19. 54 [back_unit_del,50.1,4.3] p12|p13|p15. 55 [back_unit_del,51.1,3.3] p08|p09|p11. 56 [back_unit_del,52.1,2.3] p04|p05|p07. 57 [53,split.3.1] p16. 58 [back_unit_del,57.1,15.2] -p12. 59 [back_unit_del,57.1,14.2] -p08. 60 [back_unit_del,57.1,12.2] -p04. 61 [back_unit_del,58.1,54.1] p13|p15. 62 [back_unit_del,59.1,55.1] p09|p11. 63 [back_unit_del,60.1,56.1] p05|p07. 64 [61,split.3.1.1] p13. 66 [back_unit_del,64.1,23.2] -p09. 67 [back_unit_del,64.1,21.2] -p05. 68 [back_unit_del,66.1,62.1] p11. 69 [back_unit_del,67.1,63.1] p07. 72 [back_unit_del,68.1,40.2] -p07. 73 [binary,72.1,69.1] $F. ------------ end of proof ------------- ------- statistics (process 8753) ------- clauses given 47 clauses generated 22 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8753 finished Mon Aug 2 15:31:09 2004 Refuted case [3.1.1]. --- refuted case [3.1.2] Case [3.1.2] (process 8754): Assumption: 65 [61,split.3.1.2] p15. >>>> Starting back unit deletion with 64. >>>> Starting back unit deletion with 65. 0 [back_unit_del,65.1,45.1] -p19. 0 [back_unit_del,65.1,43.2] -p11. 0 [back_unit_del,65.1,41.2] -p07. 0 [back_unit_del,65.1,38.2] -p03. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. 0 [back_unit_del,70.1,24.1] -p17. 0 [back_unit_del,70.1,20.2] -p05. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,71.1] $F. Length of proof is 22. Level of proof is 10. Case [3.1.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 12 [] -p04| -p16. 14 [] -p08| -p16. 15 [] -p12| -p16. 20 [] -p05| -p09. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 41 [] -p07| -p15. 43 [] -p11| -p15. 48 [1,split.3] p02. 49 [back_unit_del,48.1,29.1] -p18. 50 [back_unit_del,48.1,28.1] -p14. 51 [back_unit_del,48.1,27.1] -p10. 52 [back_unit_del,48.1,26.1] -p06. 53 [back_unit_del,49.1,5.3] p16|p17|p19. 54 [back_unit_del,50.1,4.3] p12|p13|p15. 55 [back_unit_del,51.1,3.3] p08|p09|p11. 56 [back_unit_del,52.1,2.3] p04|p05|p07. 57 [53,split.3.1] p16. 58 [back_unit_del,57.1,15.2] -p12. 59 [back_unit_del,57.1,14.2] -p08. 60 [back_unit_del,57.1,12.2] -p04. 61 [back_unit_del,58.1,54.1] p13|p15. 62 [back_unit_del,59.1,55.1] p09|p11. 63 [back_unit_del,60.1,56.1] p05|p07. 65 [61,split.3.1.2] p15. 67 [back_unit_del,65.1,43.2] -p11. 68 [back_unit_del,65.1,41.2] -p07. 70 [back_unit_del,67.1,62.2] p09. 71 [back_unit_del,68.1,63.2] p05. 73 [back_unit_del,70.1,20.2] -p05. 74 [binary,73.1,71.1] $F. ------------ end of proof ------------- ------- statistics (process 8754) ------- clauses given 47 clauses generated 22 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 45 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8754 finished Mon Aug 2 15:31:09 2004 Refuted case [3.1.2]. ------- statistics (process 8752) ------- clauses given 47 clauses generated 14 clauses kept 18 clauses forward subsumed 0 clauses back subsumed 31 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8752 finished Mon Aug 2 15:31:09 2004 Refuted case [3.1]. Case [3.2] (process 8755): Assumption: 58 [53,split.3.2] p17. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 58. 0 [back_unit_del,58.1,25.2] -p13. 0 [back_unit_del,58.1,24.2] -p09. 0 [back_unit_del,58.1,22.2] -p05. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. given clause #46: (wt=1) 57 [53,split_neg.3.2] -p16. given clause #47: (wt=1) 58 [53,split.3.2] p17. given clause #48: (wt=2) 62 [back_unit_del,59.1,54.2] p12|p15. Splitting on clause 62 [back_unit_del,59.1,54.2] p12|p15. --- refuted case [3.2.1] Case [3.2.1] (process 8756): Assumption: 65 [62,split.3.2.1] p12. >>>> Starting back unit deletion with 65. 0 [back_unit_del,65.1,13.2] -p08. 0 [back_unit_del,65.1,11.2] -p04. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,44.1] -p19. 0 [back_unit_del,68.1,43.1] -p15. 0 [back_unit_del,68.1,40.2] -p07. ----> UNIT CONFLICT at 0.00 sec ----> 73 [binary,72.1,69.1] $F. Length of proof is 22. Level of proof is 10. Case [3.2.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 11 [] -p04| -p12. 13 [] -p08| -p12. 22 [] -p05| -p17. 24 [] -p09| -p17. 25 [] -p13| -p17. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 40 [] -p07| -p11. 48 [1,split.3] p02. 49 [back_unit_del,48.1,29.1] -p18. 50 [back_unit_del,48.1,28.1] -p14. 51 [back_unit_del,48.1,27.1] -p10. 52 [back_unit_del,48.1,26.1] -p06. 53 [back_unit_del,49.1,5.3] p16|p17|p19. 54 [back_unit_del,50.1,4.3] p12|p13|p15. 55 [back_unit_del,51.1,3.3] p08|p09|p11. 56 [back_unit_del,52.1,2.3] p04|p05|p07. 58 [53,split.3.2] p17. 59 [back_unit_del,58.1,25.2] -p13. 60 [back_unit_del,58.1,24.2] -p09. 61 [back_unit_del,58.1,22.2] -p05. 62 [back_unit_del,59.1,54.2] p12|p15. 63 [back_unit_del,60.1,55.2] p08|p11. 64 [back_unit_del,61.1,56.2] p04|p07. 65 [62,split.3.2.1] p12. 66 [back_unit_del,65.1,13.2] -p08. 67 [back_unit_del,65.1,11.2] -p04. 68 [back_unit_del,66.1,63.1] p11. 69 [back_unit_del,67.1,64.1] p07. 72 [back_unit_del,68.1,40.2] -p07. 73 [binary,72.1,69.1] $F. ------------ end of proof ------------- ------- statistics (process 8756) ------- clauses given 48 clauses generated 21 clauses kept 27 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8756 finished Mon Aug 2 15:31:09 2004 Refuted case [3.2.1]. --- refuted case [3.2.2] Case [3.2.2] (process 8757): Assumption: 66 [62,split.3.2.2] p15. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. 0 [back_unit_del,66.1,45.1] -p19. 0 [back_unit_del,66.1,43.2] -p11. 0 [back_unit_del,66.1,41.2] -p07. 0 [back_unit_del,66.1,38.2] -p03. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 71. 0 [back_unit_del,71.1,10.2] -p04. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,72.1] $F. Length of proof is 22. Level of proof is 10. Case [3.2.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 10 [] -p04| -p08. 22 [] -p05| -p17. 24 [] -p09| -p17. 25 [] -p13| -p17. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 41 [] -p07| -p15. 43 [] -p11| -p15. 48 [1,split.3] p02. 49 [back_unit_del,48.1,29.1] -p18. 50 [back_unit_del,48.1,28.1] -p14. 51 [back_unit_del,48.1,27.1] -p10. 52 [back_unit_del,48.1,26.1] -p06. 53 [back_unit_del,49.1,5.3] p16|p17|p19. 54 [back_unit_del,50.1,4.3] p12|p13|p15. 55 [back_unit_del,51.1,3.3] p08|p09|p11. 56 [back_unit_del,52.1,2.3] p04|p05|p07. 58 [53,split.3.2] p17. 59 [back_unit_del,58.1,25.2] -p13. 60 [back_unit_del,58.1,24.2] -p09. 61 [back_unit_del,58.1,22.2] -p05. 62 [back_unit_del,59.1,54.2] p12|p15. 63 [back_unit_del,60.1,55.2] p08|p11. 64 [back_unit_del,61.1,56.2] p04|p07. 66 [62,split.3.2.2] p15. 68 [back_unit_del,66.1,43.2] -p11. 69 [back_unit_del,66.1,41.2] -p07. 71 [back_unit_del,68.1,63.2] p08. 72 [back_unit_del,69.1,64.2] p04. 73 [back_unit_del,71.1,10.2] -p04. 74 [binary,73.1,72.1] $F. ------------ end of proof ------------- ------- statistics (process 8757) ------- clauses given 48 clauses generated 21 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 47 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8757 finished Mon Aug 2 15:31:09 2004 Refuted case [3.2.2]. ------- statistics (process 8755) ------- clauses given 48 clauses generated 14 clauses kept 19 clauses forward subsumed 0 clauses back subsumed 34 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8755 finished Mon Aug 2 15:31:09 2004 Refuted case [3.2]. Case [3.3] (process 8758): Assumption: 59 [53,split.3.3] p19. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. 0 [back_unit_del,59.1,45.2] -p15. 0 [back_unit_del,59.1,44.2] -p11. 0 [back_unit_del,59.1,42.2] -p07. 0 [back_unit_del,59.1,39.2] -p03. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. >>>> Starting back unit deletion with 62. >>>> Starting back unit deletion with 63. given clause #46: (wt=1) 57 [53,split_neg.3.3] -p16. given clause #47: (wt=1) 58 [53,split_neg.3.3] -p17. given clause #48: (wt=1) 59 [53,split.3.3] p19. given clause #49: (wt=2) 64 [back_unit_del,60.1,54.3] p12|p13. Splitting on clause 64 [back_unit_del,60.1,54.3] p12|p13. --- refuted case [3.3.1] Case [3.3.1] (process 8759): Assumption: 67 [64,split.3.3.1] p12. >>>> Starting back unit deletion with 67. 0 [back_unit_del,67.1,13.2] -p08. 0 [back_unit_del,67.1,11.2] -p04. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. 0 [back_unit_del,70.1,23.1] -p13. 0 [back_unit_del,70.1,20.2] -p05. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,71.1] $F. Length of proof is 22. Level of proof is 10. Case [3.3.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 11 [] -p04| -p12. 13 [] -p08| -p12. 20 [] -p05| -p09. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 42 [] -p07| -p19. 44 [] -p11| -p19. 45 [] -p15| -p19. 48 [1,split.3] p02. 49 [back_unit_del,48.1,29.1] -p18. 50 [back_unit_del,48.1,28.1] -p14. 51 [back_unit_del,48.1,27.1] -p10. 52 [back_unit_del,48.1,26.1] -p06. 53 [back_unit_del,49.1,5.3] p16|p17|p19. 54 [back_unit_del,50.1,4.3] p12|p13|p15. 55 [back_unit_del,51.1,3.3] p08|p09|p11. 56 [back_unit_del,52.1,2.3] p04|p05|p07. 59 [53,split.3.3] p19. 60 [back_unit_del,59.1,45.2] -p15. 61 [back_unit_del,59.1,44.2] -p11. 62 [back_unit_del,59.1,42.2] -p07. 64 [back_unit_del,60.1,54.3] p12|p13. 65 [back_unit_del,61.1,55.3] p08|p09. 66 [back_unit_del,62.1,56.3] p04|p05. 67 [64,split.3.3.1] p12. 68 [back_unit_del,67.1,13.2] -p08. 69 [back_unit_del,67.1,11.2] -p04. 70 [back_unit_del,68.1,65.1] p09. 71 [back_unit_del,69.1,66.1] p05. 73 [back_unit_del,70.1,20.2] -p05. 74 [binary,73.1,71.1] $F. ------------ end of proof ------------- ------- statistics (process 8759) ------- clauses given 49 clauses generated 21 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 45 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8759 finished Mon Aug 2 15:31:09 2004 Refuted case [3.3.1]. --- refuted case [3.3.2] Case [3.3.2] (process 8760): Assumption: 68 [64,split.3.3.2] p13. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,23.2] -p09. 0 [back_unit_del,68.1,21.2] -p05. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 71. 0 [back_unit_del,71.1,10.2] -p04. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,72.1] $F. Length of proof is 22. Level of proof is 10. Case [3.3.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 10 [] -p04| -p08. 21 [] -p05| -p13. 23 [] -p09| -p13. 26 [] -p02| -p06. 27 [] -p02| -p10. 28 [] -p02| -p14. 29 [] -p02| -p18. 42 [] -p07| -p19. 44 [] -p11| -p19. 45 [] -p15| -p19. 48 [1,split.3] p02. 49 [back_unit_del,48.1,29.1] -p18. 50 [back_unit_del,48.1,28.1] -p14. 51 [back_unit_del,48.1,27.1] -p10. 52 [back_unit_del,48.1,26.1] -p06. 53 [back_unit_del,49.1,5.3] p16|p17|p19. 54 [back_unit_del,50.1,4.3] p12|p13|p15. 55 [back_unit_del,51.1,3.3] p08|p09|p11. 56 [back_unit_del,52.1,2.3] p04|p05|p07. 59 [53,split.3.3] p19. 60 [back_unit_del,59.1,45.2] -p15. 61 [back_unit_del,59.1,44.2] -p11. 62 [back_unit_del,59.1,42.2] -p07. 64 [back_unit_del,60.1,54.3] p12|p13. 65 [back_unit_del,61.1,55.3] p08|p09. 66 [back_unit_del,62.1,56.3] p04|p05. 68 [64,split.3.3.2] p13. 69 [back_unit_del,68.1,23.2] -p09. 70 [back_unit_del,68.1,21.2] -p05. 71 [back_unit_del,69.1,65.2] p08. 72 [back_unit_del,70.1,66.2] p04. 73 [back_unit_del,71.1,10.2] -p04. 74 [binary,73.1,72.1] $F. ------------ end of proof ------------- ------- statistics (process 8760) ------- clauses given 49 clauses generated 20 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 47 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8760 finished Mon Aug 2 15:31:09 2004 Refuted case [3.3.2]. ------- statistics (process 8758) ------- clauses given 49 clauses generated 15 clauses kept 21 clauses forward subsumed 0 clauses back subsumed 41 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8758 finished Mon Aug 2 15:31:09 2004 Refuted case [3.3]. ------- statistics (process 8751) ------- clauses given 45 clauses generated 8 clauses kept 11 clauses forward subsumed 0 clauses back subsumed 22 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8751 finished Mon Aug 2 15:31:09 2004 Refuted case [3]. Case [4] (process 8761): Assumption: 49 [1,split.4] p03. >>>> Starting back unit deletion with 46. >>>> Starting back unit deletion with 47. >>>> Starting back unit deletion with 48. >>>> Starting back unit deletion with 49. 0 [back_unit_del,49.1,39.1] -p19. 0 [back_unit_del,49.1,38.1] -p15. 0 [back_unit_del,49.1,37.1] -p11. 0 [back_unit_del,49.1,36.1] -p07. >>>> Starting back unit deletion with 50. >>>> Starting back unit deletion with 51. >>>> Starting back unit deletion with 52. >>>> Starting back unit deletion with 53. given clause #42: (wt=1) 46 [1,split_neg.4] -p00. given clause #43: (wt=1) 47 [1,split_neg.4] -p01. given clause #44: (wt=1) 48 [1,split_neg.4] -p02. given clause #45: (wt=1) 49 [1,split.4] p03. given clause #46: (wt=3) 54 [back_unit_del,50.1,5.4] p16|p17|p18. Splitting on clause 54 [back_unit_del,50.1,5.4] p16|p17|p18. Case [4.1] (process 8762): Assumption: 58 [54,split.4.1] p16. >>>> Starting back unit deletion with 58. 0 [back_unit_del,58.1,15.2] -p12. 0 [back_unit_del,58.1,14.2] -p08. 0 [back_unit_del,58.1,12.2] -p04. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. given clause #47: (wt=1) 58 [54,split.4.1] p16. given clause #48: (wt=2) 62 [back_unit_del,59.1,55.1] p13|p14. Splitting on clause 62 [back_unit_del,59.1,55.1] p13|p14. --- refuted case [4.1.1] Case [4.1.1] (process 8763): Assumption: 65 [62,split.4.1.1] p13. >>>> Starting back unit deletion with 65. 0 [back_unit_del,65.1,25.1] -p17. 0 [back_unit_del,65.1,23.2] -p09. 0 [back_unit_del,65.1,21.2] -p05. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. 0 [back_unit_del,69.1,34.1] -p18. 0 [back_unit_del,69.1,33.1] -p14. 0 [back_unit_del,69.1,30.2] -p06. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,70.1] $F. Length of proof is 22. Level of proof is 10. Case [4.1.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 12 [] -p04| -p16. 14 [] -p08| -p16. 15 [] -p12| -p16. 21 [] -p05| -p13. 23 [] -p09| -p13. 30 [] -p06| -p10. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 49 [1,split.4] p03. 50 [back_unit_del,49.1,39.1] -p19. 51 [back_unit_del,49.1,38.1] -p15. 52 [back_unit_del,49.1,37.1] -p11. 53 [back_unit_del,49.1,36.1] -p07. 54 [back_unit_del,50.1,5.4] p16|p17|p18. 55 [back_unit_del,51.1,4.4] p12|p13|p14. 56 [back_unit_del,52.1,3.4] p08|p09|p10. 57 [back_unit_del,53.1,2.4] p04|p05|p06. 58 [54,split.4.1] p16. 59 [back_unit_del,58.1,15.2] -p12. 60 [back_unit_del,58.1,14.2] -p08. 61 [back_unit_del,58.1,12.2] -p04. 62 [back_unit_del,59.1,55.1] p13|p14. 63 [back_unit_del,60.1,56.1] p09|p10. 64 [back_unit_del,61.1,57.1] p05|p06. 65 [62,split.4.1.1] p13. 67 [back_unit_del,65.1,23.2] -p09. 68 [back_unit_del,65.1,21.2] -p05. 69 [back_unit_del,67.1,63.1] p10. 70 [back_unit_del,68.1,64.1] p06. 73 [back_unit_del,69.1,30.2] -p06. 74 [binary,73.1,70.1] $F. ------------ end of proof ------------- ------- statistics (process 8763) ------- clauses given 48 clauses generated 22 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 42 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8763 finished Mon Aug 2 15:31:09 2004 Refuted case [4.1.1]. --- refuted case [4.1.2] Case [4.1.2] (process 8764): Assumption: 66 [62,split.4.1.2] p14. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. 0 [back_unit_del,66.1,35.1] -p18. 0 [back_unit_del,66.1,33.2] -p10. 0 [back_unit_del,66.1,31.2] -p06. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. 0 [back_unit_del,70.1,24.1] -p17. 0 [back_unit_del,70.1,20.2] -p05. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,71.1] $F. Length of proof is 22. Level of proof is 10. Case [4.1.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 12 [] -p04| -p16. 14 [] -p08| -p16. 15 [] -p12| -p16. 20 [] -p05| -p09. 31 [] -p06| -p14. 33 [] -p10| -p14. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 49 [1,split.4] p03. 50 [back_unit_del,49.1,39.1] -p19. 51 [back_unit_del,49.1,38.1] -p15. 52 [back_unit_del,49.1,37.1] -p11. 53 [back_unit_del,49.1,36.1] -p07. 54 [back_unit_del,50.1,5.4] p16|p17|p18. 55 [back_unit_del,51.1,4.4] p12|p13|p14. 56 [back_unit_del,52.1,3.4] p08|p09|p10. 57 [back_unit_del,53.1,2.4] p04|p05|p06. 58 [54,split.4.1] p16. 59 [back_unit_del,58.1,15.2] -p12. 60 [back_unit_del,58.1,14.2] -p08. 61 [back_unit_del,58.1,12.2] -p04. 62 [back_unit_del,59.1,55.1] p13|p14. 63 [back_unit_del,60.1,56.1] p09|p10. 64 [back_unit_del,61.1,57.1] p05|p06. 66 [62,split.4.1.2] p14. 68 [back_unit_del,66.1,33.2] -p10. 69 [back_unit_del,66.1,31.2] -p06. 70 [back_unit_del,68.1,63.2] p09. 71 [back_unit_del,69.1,64.2] p05. 73 [back_unit_del,70.1,20.2] -p05. 74 [binary,73.1,71.1] $F. ------------ end of proof ------------- ------- statistics (process 8764) ------- clauses given 48 clauses generated 21 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 45 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8764 finished Mon Aug 2 15:31:09 2004 Refuted case [4.1.2]. ------- statistics (process 8762) ------- clauses given 48 clauses generated 14 clauses kept 19 clauses forward subsumed 0 clauses back subsumed 35 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8762 finished Mon Aug 2 15:31:09 2004 Refuted case [4.1]. Case [4.2] (process 8765): Assumption: 59 [54,split.4.2] p17. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. 0 [back_unit_del,59.1,25.2] -p13. 0 [back_unit_del,59.1,24.2] -p09. 0 [back_unit_del,59.1,22.2] -p05. >>>> Starting back unit deletion with 60. >>>> Starting back unit deletion with 61. >>>> Starting back unit deletion with 62. given clause #47: (wt=1) 58 [54,split_neg.4.2] -p16. given clause #48: (wt=1) 59 [54,split.4.2] p17. given clause #49: (wt=2) 63 [back_unit_del,60.1,55.2] p12|p14. Splitting on clause 63 [back_unit_del,60.1,55.2] p12|p14. --- refuted case [4.2.1] Case [4.2.1] (process 8766): Assumption: 66 [63,split.4.2.1] p12. >>>> Starting back unit deletion with 66. 0 [back_unit_del,66.1,13.2] -p08. 0 [back_unit_del,66.1,11.2] -p04. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. 0 [back_unit_del,69.1,34.1] -p18. 0 [back_unit_del,69.1,33.1] -p14. 0 [back_unit_del,69.1,30.2] -p06. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,70.1] $F. Length of proof is 22. Level of proof is 10. Case [4.2.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 11 [] -p04| -p12. 13 [] -p08| -p12. 22 [] -p05| -p17. 24 [] -p09| -p17. 25 [] -p13| -p17. 30 [] -p06| -p10. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 49 [1,split.4] p03. 50 [back_unit_del,49.1,39.1] -p19. 51 [back_unit_del,49.1,38.1] -p15. 52 [back_unit_del,49.1,37.1] -p11. 53 [back_unit_del,49.1,36.1] -p07. 54 [back_unit_del,50.1,5.4] p16|p17|p18. 55 [back_unit_del,51.1,4.4] p12|p13|p14. 56 [back_unit_del,52.1,3.4] p08|p09|p10. 57 [back_unit_del,53.1,2.4] p04|p05|p06. 59 [54,split.4.2] p17. 60 [back_unit_del,59.1,25.2] -p13. 61 [back_unit_del,59.1,24.2] -p09. 62 [back_unit_del,59.1,22.2] -p05. 63 [back_unit_del,60.1,55.2] p12|p14. 64 [back_unit_del,61.1,56.2] p08|p10. 65 [back_unit_del,62.1,57.2] p04|p06. 66 [63,split.4.2.1] p12. 67 [back_unit_del,66.1,13.2] -p08. 68 [back_unit_del,66.1,11.2] -p04. 69 [back_unit_del,67.1,64.1] p10. 70 [back_unit_del,68.1,65.1] p06. 73 [back_unit_del,69.1,30.2] -p06. 74 [binary,73.1,70.1] $F. ------------ end of proof ------------- ------- statistics (process 8766) ------- clauses given 49 clauses generated 21 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 42 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8766 finished Mon Aug 2 15:31:09 2004 Refuted case [4.2.1]. --- refuted case [4.2.2] Case [4.2.2] (process 8767): Assumption: 67 [63,split.4.2.2] p14. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. 0 [back_unit_del,67.1,35.1] -p18. 0 [back_unit_del,67.1,33.2] -p10. 0 [back_unit_del,67.1,31.2] -p06. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 71. 0 [back_unit_del,71.1,10.2] -p04. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,72.1] $F. Length of proof is 22. Level of proof is 10. Case [4.2.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 10 [] -p04| -p08. 22 [] -p05| -p17. 24 [] -p09| -p17. 25 [] -p13| -p17. 31 [] -p06| -p14. 33 [] -p10| -p14. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 49 [1,split.4] p03. 50 [back_unit_del,49.1,39.1] -p19. 51 [back_unit_del,49.1,38.1] -p15. 52 [back_unit_del,49.1,37.1] -p11. 53 [back_unit_del,49.1,36.1] -p07. 54 [back_unit_del,50.1,5.4] p16|p17|p18. 55 [back_unit_del,51.1,4.4] p12|p13|p14. 56 [back_unit_del,52.1,3.4] p08|p09|p10. 57 [back_unit_del,53.1,2.4] p04|p05|p06. 59 [54,split.4.2] p17. 60 [back_unit_del,59.1,25.2] -p13. 61 [back_unit_del,59.1,24.2] -p09. 62 [back_unit_del,59.1,22.2] -p05. 63 [back_unit_del,60.1,55.2] p12|p14. 64 [back_unit_del,61.1,56.2] p08|p10. 65 [back_unit_del,62.1,57.2] p04|p06. 67 [63,split.4.2.2] p14. 69 [back_unit_del,67.1,33.2] -p10. 70 [back_unit_del,67.1,31.2] -p06. 71 [back_unit_del,69.1,64.2] p08. 72 [back_unit_del,70.1,65.2] p04. 73 [back_unit_del,71.1,10.2] -p04. 74 [binary,73.1,72.1] $F. ------------ end of proof ------------- ------- statistics (process 8767) ------- clauses given 49 clauses generated 20 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 47 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8767 finished Mon Aug 2 15:31:09 2004 Refuted case [4.2.2]. ------- statistics (process 8765) ------- clauses given 49 clauses generated 14 clauses kept 20 clauses forward subsumed 0 clauses back subsumed 38 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8765 finished Mon Aug 2 15:31:09 2004 Refuted case [4.2]. Case [4.3] (process 8768): Assumption: 60 [54,split.4.3] p18. >>>> Starting back unit deletion with 58. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 60. 0 [back_unit_del,60.1,35.2] -p14. 0 [back_unit_del,60.1,34.2] -p10. 0 [back_unit_del,60.1,32.2] -p06. >>>> Starting back unit deletion with 61. >>>> Starting back unit deletion with 62. >>>> Starting back unit deletion with 63. given clause #47: (wt=1) 58 [54,split_neg.4.3] -p16. given clause #48: (wt=1) 59 [54,split_neg.4.3] -p17. given clause #49: (wt=1) 60 [54,split.4.3] p18. given clause #50: (wt=2) 64 [back_unit_del,61.1,55.3] p12|p13. Splitting on clause 64 [back_unit_del,61.1,55.3] p12|p13. --- refuted case [4.3.1] Case [4.3.1] (process 8769): Assumption: 67 [64,split.4.3.1] p12. >>>> Starting back unit deletion with 67. 0 [back_unit_del,67.1,13.2] -p08. 0 [back_unit_del,67.1,11.2] -p04. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. 0 [back_unit_del,70.1,23.1] -p13. 0 [back_unit_del,70.1,20.2] -p05. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,71.1] $F. Length of proof is 22. Level of proof is 10. Case [4.3.1] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 11 [] -p04| -p12. 13 [] -p08| -p12. 20 [] -p05| -p09. 32 [] -p06| -p18. 34 [] -p10| -p18. 35 [] -p14| -p18. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 49 [1,split.4] p03. 50 [back_unit_del,49.1,39.1] -p19. 51 [back_unit_del,49.1,38.1] -p15. 52 [back_unit_del,49.1,37.1] -p11. 53 [back_unit_del,49.1,36.1] -p07. 54 [back_unit_del,50.1,5.4] p16|p17|p18. 55 [back_unit_del,51.1,4.4] p12|p13|p14. 56 [back_unit_del,52.1,3.4] p08|p09|p10. 57 [back_unit_del,53.1,2.4] p04|p05|p06. 60 [54,split.4.3] p18. 61 [back_unit_del,60.1,35.2] -p14. 62 [back_unit_del,60.1,34.2] -p10. 63 [back_unit_del,60.1,32.2] -p06. 64 [back_unit_del,61.1,55.3] p12|p13. 65 [back_unit_del,62.1,56.3] p08|p09. 66 [back_unit_del,63.1,57.3] p04|p05. 67 [64,split.4.3.1] p12. 68 [back_unit_del,67.1,13.2] -p08. 69 [back_unit_del,67.1,11.2] -p04. 70 [back_unit_del,68.1,65.1] p09. 71 [back_unit_del,69.1,66.1] p05. 73 [back_unit_del,70.1,20.2] -p05. 74 [binary,73.1,71.1] $F. ------------ end of proof ------------- ------- statistics (process 8769) ------- clauses given 50 clauses generated 20 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 45 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8769 finished Mon Aug 2 15:31:09 2004 Refuted case [4.3.1]. --- refuted case [4.3.2] Case [4.3.2] (process 8770): Assumption: 68 [64,split.4.3.2] p13. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. 0 [back_unit_del,68.1,23.2] -p09. 0 [back_unit_del,68.1,21.2] -p05. >>>> Starting back unit deletion with 69. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 71. 0 [back_unit_del,71.1,10.2] -p04. ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,72.1] $F. Length of proof is 22. Level of proof is 10. Case [4.3.2] ---------------- PROOF ---------------- 1 [] p00|p01|p02|p03. 2 [] p04|p05|p06|p07. 3 [] p08|p09|p10|p11. 4 [] p12|p13|p14|p15. 5 [] p16|p17|p18|p19. 10 [] -p04| -p08. 21 [] -p05| -p13. 23 [] -p09| -p13. 32 [] -p06| -p18. 34 [] -p10| -p18. 35 [] -p14| -p18. 36 [] -p03| -p07. 37 [] -p03| -p11. 38 [] -p03| -p15. 39 [] -p03| -p19. 49 [1,split.4] p03. 50 [back_unit_del,49.1,39.1] -p19. 51 [back_unit_del,49.1,38.1] -p15. 52 [back_unit_del,49.1,37.1] -p11. 53 [back_unit_del,49.1,36.1] -p07. 54 [back_unit_del,50.1,5.4] p16|p17|p18. 55 [back_unit_del,51.1,4.4] p12|p13|p14. 56 [back_unit_del,52.1,3.4] p08|p09|p10. 57 [back_unit_del,53.1,2.4] p04|p05|p06. 60 [54,split.4.3] p18. 61 [back_unit_del,60.1,35.2] -p14. 62 [back_unit_del,60.1,34.2] -p10. 63 [back_unit_del,60.1,32.2] -p06. 64 [back_unit_del,61.1,55.3] p12|p13. 65 [back_unit_del,62.1,56.3] p08|p09. 66 [back_unit_del,63.1,57.3] p04|p05. 68 [64,split.4.3.2] p13. 69 [back_unit_del,68.1,23.2] -p09. 70 [back_unit_del,68.1,21.2] -p05. 71 [back_unit_del,69.1,65.2] p08. 72 [back_unit_del,70.1,66.2] p04. 73 [back_unit_del,71.1,10.2] -p04. 74 [binary,73.1,72.1] $F. ------------ end of proof ------------- ------- statistics (process 8770) ------- clauses given 50 clauses generated 19 clauses kept 28 clauses forward subsumed 0 clauses back subsumed 47 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8770 finished Mon Aug 2 15:31:09 2004 Refuted case [4.3.2]. ------- statistics (process 8768) ------- clauses given 50 clauses generated 14 clauses kept 21 clauses forward subsumed 0 clauses back subsumed 41 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8768 finished Mon Aug 2 15:31:09 2004 Refuted case [4.3]. ------- statistics (process 8761) ------- clauses given 46 clauses generated 8 clauses kept 12 clauses forward subsumed 0 clauses back subsumed 26 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8761 finished Mon Aug 2 15:31:09 2004 Refuted case [4].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8730) ------- clauses given 41 clauses generated 0 clauses kept 0 clauses forward subsumed 0 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8730 finished Mon Aug 2 15:31:09 2004 otter-3.3f/examples/split/power.in0100644000076400007640000000204606472070671016651 0ustar mccunemccune% Naive set theory % Powerset of intersection is intersection of powersets. set(binary_res). set(ur_res). set(order_eq). set(split_when_given). set(split_pos). assign(pick_given_ratio, 4). % assign(max_distinct_vars, 0). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level, 1). list(usable). % Definition of intersection. -EL(z,inter(x,y)) | EL(z,x). -EL(z,inter(x,y)) | EL(z,y). EL(z,inter(x,y)) | -EL(z,x) | -EL(z,y). % Definition of subset. -SUBSET(x,y) | -EL(z,x) | EL(z,y). SUBSET(x,y) | EL(f17(x,y),x). SUBSET(x,y) | -EL(f17(x,y),y). % Definition of powerset. -EL(z,pset(x)) | SUBSET(z,x). EL(z,pset(x)) | -SUBSET(z,x). % Definition of equality (x = y) | -SUBSET(x,y) | -SUBSET(y,x). (x != y) | SUBSET(x,y). % Lemmas x = x. SUBSET(x,x). EL(x,pset(x)). -SUBSET(u,inter(x,y)) | SUBSET(u,x). -SUBSET(u,inter(x,y)) | SUBSET(u,y). SUBSET(u,inter(x,y)) | -SUBSET(u,x) | -SUBSET(u,y). end_of_list. list(sos). pset(inter(A,B)) != inter(pset(A),pset(B)). end_of_list. otter-3.3f/examples/split/GRP025-1.out0100664000076400007640000005442510103522214016722 0ustar mccunemccune WARNING, with splitting, max_seconds is checked against the wall clock. ----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:08 2004 The command was "../../bin/otter". The process ID is 8651. set(prolog_style_variables). set(auto2). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 20000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(tptp_eq). set(split_when_given). dependent: set(back_unit_deletion). dependent: set(unit_deletion). set(split_pos). list(usable). 0 [] equal(A,A). 0 [] group_member(identity_for(A),A). 0 [] product(A,identity_for(A),B,B). 0 [] product(A,B,identity_for(A),B). 0 [] -group_member(A,B)|group_member(inverse(B,A),B). 0 [] product(A,inverse(A,B),B,identity_for(A)). 0 [] product(A,B,inverse(A,B),identity_for(A)). 0 [] -group_member(A,B)| -group_member(C,B)|product(B,A,C,multiply(B,A,C)). 0 [] -group_member(A,B)| -group_member(C,B)|group_member(multiply(B,A,C),B). 0 [] -product(A,B,C,D)| -product(A,B,C,E)|equal(E,D). 0 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,D,E,G)|product(A,B,F,G). 0 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,B,F,G)|product(A,D,E,G). end_of_list. list(sos). 0 [] group_member(a,g1). 0 [] group_member(b,g1). 0 [] group_member(c,g2). 0 [] group_member(d,g2). 0 [] -group_member(A,g1)|equal(A,a)|equal(A,b). 0 [] -group_member(A,g2)|equal(A,c)|equal(A,d). 0 [] product(g1,a,a,a). 0 [] product(g1,a,b,b). 0 [] product(g1,b,a,b). 0 [] product(g1,b,b,a). 0 [] product(g2,c,c,c). 0 [] product(g2,c,d,d). 0 [] product(g2,d,c,d). 0 [] product(g2,d,d,c). 0 [] equal(an_isomorphism(a),c). 0 [] equal(an_isomorphism(b),d). 0 [] group_member(d1,g1). 0 [] group_member(d2,g1). 0 [] group_member(d3,g1). 0 [] product(g1,d1,d2,d3). 0 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). end_of_list. Every positive clause in sos is ground (or sos is empty); therefore we move all positive usable clauses to sos. Properties of input clauses: prop=0, horn=0, equality=1, symmetry=0, max_lits=4. Setting hyper_res, because there are nonunits. dependent: set(hyper_res). Setting ur_res, because this is a nonunit set containing either equality literals or non-Horn clauses. dependent: set(ur_res). Setting factor and unit_deletion, because there are non-Horn clauses. dependent: set(factor). Equality is present, so we set the knuth_bendix flag. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). As an incomplete heuristic, we paramodulate with units only. dependent: set(para_from_units_only). dependent: set(para_into_units_only). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -group_member(A,B)|group_member(inverse(B,A),B). ** KEPT (pick-wt=14): 2 [] -group_member(A,B)| -group_member(C,B)|product(B,A,C,multiply(B,A,C)). ** KEPT (pick-wt=12): 3 [] -group_member(A,B)| -group_member(C,B)|group_member(multiply(B,A,C),B). ** KEPT (pick-wt=13): 4 [] -product(A,B,C,D)| -product(A,B,C,E)|equal(E,D). ** KEPT (pick-wt=20): 5 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,D,E,G)|product(A,B,F,G). ** KEPT (pick-wt=20): 6 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,B,F,G)|product(A,D,E,G). ------------> process sos: ** KEPT (pick-wt=3): 16 [] group_member(a,g1). ** KEPT (pick-wt=3): 17 [] group_member(b,g1). ** KEPT (pick-wt=3): 18 [] group_member(c,g2). ** KEPT (pick-wt=3): 19 [] group_member(d,g2). ** KEPT (pick-wt=9): 20 [] -group_member(A,g1)|equal(A,a)|equal(A,b). ** KEPT (pick-wt=9): 21 [] -group_member(A,g2)|equal(A,c)|equal(A,d). ** KEPT (pick-wt=5): 22 [] product(g1,a,a,a). ** KEPT (pick-wt=5): 23 [] product(g1,a,b,b). ** KEPT (pick-wt=5): 24 [] product(g1,b,a,b). ** KEPT (pick-wt=5): 25 [] product(g1,b,b,a). ** KEPT (pick-wt=5): 26 [] product(g2,c,c,c). ** KEPT (pick-wt=5): 27 [] product(g2,c,d,d). ** KEPT (pick-wt=5): 28 [] product(g2,d,c,d). ** KEPT (pick-wt=5): 29 [] product(g2,d,d,c). ** KEPT (pick-wt=4): 30 [] equal(an_isomorphism(a),c). ---> New Demodulator: 31 [new_demod,30] equal(an_isomorphism(a),c). ** KEPT (pick-wt=4): 32 [] equal(an_isomorphism(b),d). ---> New Demodulator: 33 [new_demod,32] equal(an_isomorphism(b),d). ** KEPT (pick-wt=3): 34 [] group_member(d1,g1). ** KEPT (pick-wt=3): 35 [] group_member(d2,g1). ** KEPT (pick-wt=3): 36 [] group_member(d3,g1). ** KEPT (pick-wt=5): 37 [] product(g1,d1,d2,d3). ** KEPT (pick-wt=8): 38 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). ** KEPT (pick-wt=3): 39 [] equal(A,A). ** KEPT (pick-wt=4): 40 [] group_member(identity_for(A),A). ** KEPT (pick-wt=6): 41 [] product(A,identity_for(A),B,B). ** KEPT (pick-wt=6): 42 [] product(A,B,identity_for(A),B). ** KEPT (pick-wt=8): 43 [] product(A,inverse(A,B),B,identity_for(A)). ** KEPT (pick-wt=8): 44 [] product(A,B,inverse(A,B),identity_for(A)). >>>> Starting back unit deletion with 16. >>>> Starting back unit deletion with 17. >>>> Starting back unit deletion with 18. >>>> Starting back unit deletion with 19. >>>> Starting back unit deletion with 22. >>>> Starting back unit deletion with 23. >>>> Starting back unit deletion with 24. >>>> Starting back unit deletion with 25. >>>> Starting back unit deletion with 26. >>>> Starting back unit deletion with 27. >>>> Starting back unit deletion with 28. >>>> Starting back unit deletion with 29. >>>> Starting back demodulation with 31. >>>> Starting back unit deletion with 30. >>>> Starting back demodulation with 33. >>>> Starting back unit deletion with 32. >>>> Starting back unit deletion with 34. >>>> Starting back unit deletion with 35. >>>> Starting back unit deletion with 36. >>>> Starting back unit deletion with 37. >>>> Starting back unit deletion with 38. Following clause subsumed by 39 during input processing: 0 [copy,39,flip.1] equal(A,A). 39 back subsumes 9. >>>> Starting back unit deletion with 39. >>>> Starting back unit deletion with 40. >>>> Starting back unit deletion with 41. >>>> Starting back unit deletion with 42. >>>> Starting back unit deletion with 43. >>>> Starting back unit deletion with 44. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 16 [] group_member(a,g1). given clause #2: (wt=3) 17 [] group_member(b,g1). given clause #3: (wt=3) 18 [] group_member(c,g2). given clause #4: (wt=3) 19 [] group_member(d,g2). given clause #5: (wt=3) 34 [] group_member(d1,g1). given clause #6: (wt=9) 20 [] -group_member(A,g1)|equal(A,a)|equal(A,b). given clause #7: (wt=3) 35 [] group_member(d2,g1). given clause #8: (wt=3) 36 [] group_member(d3,g1). given clause #9: (wt=3) 39 [] equal(A,A). given clause #10: (wt=4) 30 [] equal(an_isomorphism(a),c). given clause #11: (wt=9) 21 [] -group_member(A,g2)|equal(A,c)|equal(A,d). given clause #12: (wt=4) 32 [] equal(an_isomorphism(b),d). given clause #13: (wt=4) 40 [] group_member(identity_for(A),A). given clause #14: (wt=5) 22 [] product(g1,a,a,a). given clause #15: (wt=5) 23 [] product(g1,a,b,b). given clause #16: (wt=5) 24 [] product(g1,b,a,b). given clause #17: (wt=5) 25 [] product(g1,b,b,a). given clause #18: (wt=5) 26 [] product(g2,c,c,c). given clause #19: (wt=5) 27 [] product(g2,c,d,d). given clause #20: (wt=5) 28 [] product(g2,d,c,d). given clause #21: (wt=5) 29 [] product(g2,d,d,c). given clause #22: (wt=5) 37 [] product(g1,d1,d2,d3). given clause #23: (wt=5) 47 [hyper,16,1] group_member(inverse(g1,a),g1). given clause #24: (wt=5) 54 [hyper,17,1] group_member(inverse(g1,b),g1). given clause #25: (wt=5) 57 [hyper,18,1] group_member(inverse(g2,c),g2). given clause #26: (wt=8) 38 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). given clause #27: (wt=5) 64 [hyper,19,1] group_member(inverse(g2,d),g2). given clause #28: (wt=5) 75 [hyper,34,1] group_member(inverse(g1,d1),g1). given clause #29: (wt=5) 92 [hyper,35,1] group_member(inverse(g1,d2),g1). given clause #30: (wt=5) 112 [hyper,36,1] group_member(inverse(g1,d3),g1). given clause #31: (wt=6) 41 [] product(A,identity_for(A),B,B). given clause #32: (wt=6) 42 [] product(A,B,identity_for(A),B). given clause #33: (wt=6) 45 [hyper,16,8] group_member(multiply(g1,a,a),g1). given clause #34: (wt=6) 48 [hyper,17,8] group_member(multiply(g1,b,b),g1). given clause #35: (wt=6) 50 [hyper,17,3,16] group_member(multiply(g1,a,b),g1). given clause #36: (wt=8) 43 [] product(A,inverse(A,B),B,identity_for(A)). given clause #37: (wt=6) 51 [hyper,17,3,16] group_member(multiply(g1,b,a),g1). given clause #38: (wt=6) 55 [hyper,18,8] group_member(multiply(g2,c,c),g2). given clause #39: (wt=6) 58 [hyper,19,8] group_member(multiply(g2,d,d),g2). given clause #40: (wt=6) 60 [hyper,19,3,18] group_member(multiply(g2,c,d),g2). given clause #41: (wt=8) 44 [] product(A,B,inverse(A,B),identity_for(A)). given clause #42: (wt=6) 61 [hyper,19,3,18] group_member(multiply(g2,d,c),g2). given clause #43: (wt=6) 65 [hyper,34,8] group_member(multiply(g1,d1,d1),g1). given clause #44: (wt=6) 67 [hyper,34,3,17] group_member(multiply(g1,b,d1),g1). given clause #45: (wt=6) 68 [hyper,34,3,16] group_member(multiply(g1,a,d1),g1). given clause #46: (wt=8) 46 [hyper,16,7] product(g1,a,a,multiply(g1,a,a)). given clause #47: (wt=6) 69 [hyper,34,3,17] group_member(multiply(g1,d1,b),g1). given clause #48: (wt=6) 70 [hyper,34,3,16] group_member(multiply(g1,d1,a),g1). given clause #49: (wt=6) 76 [hyper,20,34] equal(d1,a)|equal(d1,b). Splitting on clause 76 [hyper,20,34] equal(d1,a)|equal(d1,b). Case [1] (process 8652): Assumption: 1098 [76,split.1] equal(d1,a). given clause #50: (wt=3) 1098 [76,split.1] equal(d1,a). given clause #51: (wt=8) 49 [hyper,17,7] product(g1,b,b,multiply(g1,b,b)). given clause #52: (wt=5) 1105 [back_demod,37,demod,1099] product(g1,a,d2,d3). given clause #53: (wt=5) 1121 [hyper,1105,12,22] product(g1,a,d3,d3). given clause #54: (wt=6) 77 [hyper,35,20] equal(d2,a)|equal(d2,b). Splitting on clause 77 [hyper,35,20] equal(d2,a)|equal(d2,b). Case [1.1] (process 8653): Assumption: 1124 [77,split.1.1] equal(d2,a). given clause #55: (wt=3) 1124 [77,split.1.1] equal(d2,a). given clause #56: (wt=8) 52 [hyper,17,2,16] product(g1,a,b,multiply(g1,a,b)). given clause #57: (wt=5) 1126 [back_demod,1105,demod,1125] product(g1,a,a,d3). --- refuted case [1.1] ----> UNIT CONFLICT at 0.00 sec ----> 1161 [binary,1160.1,529.1] $F. Length of proof is 12. Level of proof is 6. Case [1.1] ---------------- PROOF ---------------- 4 [] -product(A,B,C,D)| -product(A,B,C,E)|equal(E,D). 5 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,D,E,G)|product(A,B,F,G). 20 [] -group_member(A,g1)|equal(A,a)|equal(A,b). 22 [] product(g1,a,a,a). 26 [] product(g2,c,c,c). 31,30 [] equal(an_isomorphism(a),c). 34 [] group_member(d1,g1). 35 [] group_member(d2,g1). 37 [] product(g1,d1,d2,d3). 38 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). 41 [] product(A,identity_for(A),B,B). 43 [] product(A,inverse(A,B),B,identity_for(A)). 44 [] product(A,B,inverse(A,B),identity_for(A)). 76 [hyper,20,34] equal(d1,a)|equal(d1,b). 77 [hyper,35,20] equal(d2,a)|equal(d2,b). 529 [hyper,43,5,26,41] product(g2,inverse(g2,c),c,c). 694 [ur,44,5,41,38] -product(g2,inverse(g2,an_isomorphism(d1)),an_isomorphism(d3),an_isomorphism(d2)). 1099,1098 [76,split.1] equal(d1,a). 1100 [back_demod,694,demod,1099,31] -product(g2,inverse(g2,c),an_isomorphism(d3),an_isomorphism(d2)). 1105 [back_demod,37,demod,1099] product(g1,a,d2,d3). 1125,1124 [77,split.1.1] equal(d2,a). 1126 [back_demod,1105,demod,1125] product(g1,a,a,d3). 1131 [back_demod,1100,demod,1125,31] -product(g2,inverse(g2,c),an_isomorphism(d3),c). 1159,1158 [hyper,1126,4,22] equal(d3,a). 1160 [back_demod,1131,demod,1159,31] -product(g2,inverse(g2,c),c,c). 1161 [binary,1160.1,529.1] $F. ------------ end of proof ------------- ------- statistics (process 8653) ------- clauses given 57 clauses generated 3327 clauses kept 1151 clauses forward subsumed 2966 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8653 finished Mon Aug 2 15:31:08 2004 Refuted case [1.1]. Case [1.2] (process 8654): Assumption: 1125 [77,split.1.2] equal(d2,b). given clause #55: (wt=3) 1125 [77,split.1.2] equal(d2,b). given clause #56: (wt=8) 52 [hyper,17,2,16] product(g1,a,b,multiply(g1,a,b)). given clause #57: (wt=3) 1127 [back_demod,1124,demod,1126] -equal(b,a). given clause #58: (wt=5) 1128 [back_demod,1105,demod,1126] product(g1,a,b,d3). --- refuted case [1.2] ----> UNIT CONFLICT at 0.01 sec ----> 1170 [binary,1169.1,528.1] $F. Length of proof is 12. Level of proof is 6. Case [1.2] ---------------- PROOF ---------------- 4 [] -product(A,B,C,D)| -product(A,B,C,E)|equal(E,D). 5 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,D,E,G)|product(A,B,F,G). 20 [] -group_member(A,g1)|equal(A,a)|equal(A,b). 23 [] product(g1,a,b,b). 27 [] product(g2,c,d,d). 31,30 [] equal(an_isomorphism(a),c). 33,32 [] equal(an_isomorphism(b),d). 34 [] group_member(d1,g1). 35 [] group_member(d2,g1). 37 [] product(g1,d1,d2,d3). 38 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). 41 [] product(A,identity_for(A),B,B). 43 [] product(A,inverse(A,B),B,identity_for(A)). 44 [] product(A,B,inverse(A,B),identity_for(A)). 76 [hyper,20,34] equal(d1,a)|equal(d1,b). 77 [hyper,35,20] equal(d2,a)|equal(d2,b). 528 [hyper,43,5,27,41] product(g2,inverse(g2,c),d,d). 694 [ur,44,5,41,38] -product(g2,inverse(g2,an_isomorphism(d1)),an_isomorphism(d3),an_isomorphism(d2)). 1099,1098 [76,split.1] equal(d1,a). 1100 [back_demod,694,demod,1099,31] -product(g2,inverse(g2,c),an_isomorphism(d3),an_isomorphism(d2)). 1105 [back_demod,37,demod,1099] product(g1,a,d2,d3). 1126,1125 [77,split.1.2] equal(d2,b). 1128 [back_demod,1105,demod,1126] product(g1,a,b,d3). 1133 [back_demod,1100,demod,1126,33] -product(g2,inverse(g2,c),an_isomorphism(d3),d). 1168,1167 [hyper,1128,4,23] equal(d3,b). 1169 [back_demod,1133,demod,1168,33] -product(g2,inverse(g2,c),d,d). 1170 [binary,1169.1,528.1] $F. ------------ end of proof ------------- ------- statistics (process 8654) ------- clauses given 58 clauses generated 3326 clauses kept 1160 clauses forward subsumed 2957 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8654 finished Mon Aug 2 15:31:08 2004 Refuted case [1.2]. ------- statistics (process 8652) ------- clauses given 54 clauses generated 3244 clauses kept 1117 clauses forward subsumed 2763 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8652 finished Mon Aug 2 15:31:08 2004 Refuted case [1]. Case [2] (process 8655): Assumption: 1099 [76,split.2] equal(d1,b). given clause #50: (wt=3) 1099 [76,split.2] equal(d1,b). given clause #51: (wt=8) 49 [hyper,17,7] product(g1,b,b,multiply(g1,b,b)). given clause #52: (wt=3) 1101 [back_demod,1098,demod,1100] -equal(b,a). given clause #53: (wt=5) 1107 [back_demod,37,demod,1100] product(g1,b,d2,d3). given clause #54: (wt=5) 1125 [ur,1101,4,24] -product(g1,b,a,a). given clause #55: (wt=5) 1126 [ur,1101,4,23] -product(g1,a,b,a). given clause #56: (wt=8) 52 [hyper,17,2,16] product(g1,a,b,multiply(g1,a,b)). given clause #57: (wt=5) 1129 [ur,1101,4,25] -product(g1,b,b,b). given clause #58: (wt=5) 1130 [ur,1101,4,22] -product(g1,a,a,b). given clause #59: (wt=5) 1131 [hyper,1107,12,23] product(g1,a,d3,d3). given clause #60: (wt=6) 77 [hyper,35,20] equal(d2,a)|equal(d2,b). Splitting on clause 77 [hyper,35,20] equal(d2,a)|equal(d2,b). Case [2.1] (process 8656): Assumption: 1162 [77,split.2.1] equal(d2,a). given clause #61: (wt=8) 53 [hyper,17,2,16] product(g1,b,a,multiply(g1,b,a)). given clause #62: (wt=3) 1162 [77,split.2.1] equal(d2,a). given clause #63: (wt=5) 1164 [back_demod,1107,demod,1163] product(g1,b,a,d3). --- refuted case [2.1] ----> UNIT CONFLICT at 0.01 sec ----> 1198 [binary,1197.1,527.1] $F. Length of proof is 12. Level of proof is 6. Case [2.1] ---------------- PROOF ---------------- 4 [] -product(A,B,C,D)| -product(A,B,C,E)|equal(E,D). 5 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,D,E,G)|product(A,B,F,G). 20 [] -group_member(A,g1)|equal(A,a)|equal(A,b). 24 [] product(g1,b,a,b). 28 [] product(g2,d,c,d). 31,30 [] equal(an_isomorphism(a),c). 33,32 [] equal(an_isomorphism(b),d). 34 [] group_member(d1,g1). 35 [] group_member(d2,g1). 37 [] product(g1,d1,d2,d3). 38 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). 41 [] product(A,identity_for(A),B,B). 43 [] product(A,inverse(A,B),B,identity_for(A)). 44 [] product(A,B,inverse(A,B),identity_for(A)). 76 [hyper,20,34] equal(d1,a)|equal(d1,b). 77 [hyper,35,20] equal(d2,a)|equal(d2,b). 527 [hyper,43,5,28,41] product(g2,inverse(g2,d),d,c). 694 [ur,44,5,41,38] -product(g2,inverse(g2,an_isomorphism(d1)),an_isomorphism(d3),an_isomorphism(d2)). 1100,1099 [76,split.2] equal(d1,b). 1102 [back_demod,694,demod,1100,33] -product(g2,inverse(g2,d),an_isomorphism(d3),an_isomorphism(d2)). 1107 [back_demod,37,demod,1100] product(g1,b,d2,d3). 1163,1162 [77,split.2.1] equal(d2,a). 1164 [back_demod,1107,demod,1163] product(g1,b,a,d3). 1169 [back_demod,1102,demod,1163,31] -product(g2,inverse(g2,d),an_isomorphism(d3),c). 1196,1195 [hyper,1164,4,24] equal(d3,b). 1197 [back_demod,1169,demod,1196,33] -product(g2,inverse(g2,d),d,c). 1198 [binary,1197.1,527.1] $F. ------------ end of proof ------------- ------- statistics (process 8656) ------- clauses given 63 clauses generated 3509 clauses kept 1187 clauses forward subsumed 3160 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8656 finished Mon Aug 2 15:31:08 2004 Refuted case [2.1]. Case [2.2] (process 8657): Assumption: 1163 [77,split.2.2] equal(d2,b). given clause #61: (wt=8) 53 [hyper,17,2,16] product(g1,b,a,multiply(g1,b,a)). given clause #62: (wt=3) 1163 [77,split.2.2] equal(d2,b). given clause #63: (wt=5) 1165 [back_demod,1107,demod,1164] product(g1,b,b,d3). --- refuted case [2.2] ----> UNIT CONFLICT at 0.00 sec ----> 1199 [binary,1198.1,526.1] $F. Length of proof is 12. Level of proof is 6. Case [2.2] ---------------- PROOF ---------------- 4 [] -product(A,B,C,D)| -product(A,B,C,E)|equal(E,D). 5 [] -product(A,B,C,D)| -product(A,C,E,F)| -product(A,D,E,G)|product(A,B,F,G). 20 [] -group_member(A,g1)|equal(A,a)|equal(A,b). 25 [] product(g1,b,b,a). 29 [] product(g2,d,d,c). 31,30 [] equal(an_isomorphism(a),c). 33,32 [] equal(an_isomorphism(b),d). 34 [] group_member(d1,g1). 35 [] group_member(d2,g1). 37 [] product(g1,d1,d2,d3). 38 [] -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). 41 [] product(A,identity_for(A),B,B). 43 [] product(A,inverse(A,B),B,identity_for(A)). 44 [] product(A,B,inverse(A,B),identity_for(A)). 76 [hyper,20,34] equal(d1,a)|equal(d1,b). 77 [hyper,35,20] equal(d2,a)|equal(d2,b). 526 [hyper,43,5,29,41] product(g2,inverse(g2,d),c,d). 694 [ur,44,5,41,38] -product(g2,inverse(g2,an_isomorphism(d1)),an_isomorphism(d3),an_isomorphism(d2)). 1100,1099 [76,split.2] equal(d1,b). 1102 [back_demod,694,demod,1100,33] -product(g2,inverse(g2,d),an_isomorphism(d3),an_isomorphism(d2)). 1107 [back_demod,37,demod,1100] product(g1,b,d2,d3). 1164,1163 [77,split.2.2] equal(d2,b). 1165 [back_demod,1107,demod,1164] product(g1,b,b,d3). 1170 [back_demod,1102,demod,1164,33] -product(g2,inverse(g2,d),an_isomorphism(d3),d). 1197,1196 [hyper,1165,4,25] equal(d3,a). 1198 [back_demod,1170,demod,1197,31] -product(g2,inverse(g2,d),c,d). 1199 [binary,1198.1,526.1] $F. ------------ end of proof ------------- ------- statistics (process 8657) ------- clauses given 63 clauses generated 3508 clauses kept 1188 clauses forward subsumed 3160 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8657 finished Mon Aug 2 15:31:08 2004 Refuted case [2.2]. ------- statistics (process 8655) ------- clauses given 60 clauses generated 3436 clauses kept 1154 clauses forward subsumed 2979 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.02 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8655 finished Mon Aug 2 15:31:08 2004 Refuted case [2].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8651) ------- clauses given 49 clauses generated 3126 clauses kept 1093 clauses forward subsumed 2151 clauses back subsumed 2 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.07 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8651 finished Mon Aug 2 15:31:08 2004 otter-3.3f/examples/split/noncomm-group.in0100644000076400007640000002212607053062212020302 0ustar mccunemccune% This input file causes Otter to find a noncommutative group % of order 6. We start with a ground system for a group of % order 6 and state that two of the elements don't commute. % We apply splitting, which terminates because a branch cannot % be refuted. That branch gives us a model, that is, a % noncommutative group of order 6. % % This method of model search was developed as a possible % alternative to MACE. set(knuth_bendix). set(split_when_given). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_proofs). assign(stats_level, 1). list(usable). x = x. % Not necessary. If omitted, we derive and keep 0=0,1=1,2=2,... . end_of_list. list(sos). 0 != 1. % The six elements 0--5 are distinct. 0 != 2. 0 != 3. 0 != 4. 0 != 5. 1 != 2. 1 != 3. 1 != 4. 1 != 5. 2 != 3. 2 != 4. 2 != 5. 3 != 4. 3 != 5. 4 != 5. e = 0. % let 0 be the identity. f(1,2) != f(2,1). % 1 and 2 don't commute. f(e,0)=0. % instances of f(e,x) = x. f(e,1)=1. f(e,2)=2. f(e,3)=3. f(e,4)=4. f(e,5)=5. f(g(0),0)=e. % instances of f(g(x),x) = e. f(g(1),1)=e. f(g(2),2)=e. f(g(3),3)=e. f(g(4),4)=e. f(g(5),5)=e. f(f(0,0),0)=f(0,f(0,0)). % instances of associativity. f(f(1,1),1)=f(1,f(1,1)). f(f(1,0),1)=f(1,f(0,1)). f(f(0,1),1)=f(0,f(1,1)). f(f(0,0),1)=f(0,f(0,1)). f(f(1,1),0)=f(1,f(1,0)). f(f(0,1),0)=f(0,f(1,0)). f(f(1,0),0)=f(1,f(0,0)). f(f(2,2),2)=f(2,f(2,2)). f(f(2,1),2)=f(2,f(1,2)). f(f(2,0),2)=f(2,f(0,2)). f(f(1,2),2)=f(1,f(2,2)). f(f(1,1),2)=f(1,f(1,2)). f(f(1,0),2)=f(1,f(0,2)). f(f(0,2),2)=f(0,f(2,2)). f(f(0,1),2)=f(0,f(1,2)). f(f(0,0),2)=f(0,f(0,2)). f(f(2,2),1)=f(2,f(2,1)). f(f(2,2),0)=f(2,f(2,0)). f(f(1,2),1)=f(1,f(2,1)). f(f(1,2),0)=f(1,f(2,0)). f(f(0,2),1)=f(0,f(2,1)). f(f(0,2),0)=f(0,f(2,0)). f(f(2,1),1)=f(2,f(1,1)). f(f(2,1),0)=f(2,f(1,0)). f(f(2,0),1)=f(2,f(0,1)). f(f(2,0),0)=f(2,f(0,0)). f(f(3,3),3)=f(3,f(3,3)). f(f(3,2),3)=f(3,f(2,3)). f(f(3,1),3)=f(3,f(1,3)). f(f(3,0),3)=f(3,f(0,3)). f(f(2,3),3)=f(2,f(3,3)). f(f(2,2),3)=f(2,f(2,3)). f(f(2,1),3)=f(2,f(1,3)). f(f(2,0),3)=f(2,f(0,3)). f(f(1,3),3)=f(1,f(3,3)). f(f(1,2),3)=f(1,f(2,3)). f(f(1,1),3)=f(1,f(1,3)). f(f(1,0),3)=f(1,f(0,3)). f(f(0,3),3)=f(0,f(3,3)). f(f(0,2),3)=f(0,f(2,3)). f(f(0,1),3)=f(0,f(1,3)). f(f(0,0),3)=f(0,f(0,3)). f(f(3,3),2)=f(3,f(3,2)). f(f(3,3),1)=f(3,f(3,1)). f(f(3,3),0)=f(3,f(3,0)). f(f(2,3),2)=f(2,f(3,2)). f(f(2,3),1)=f(2,f(3,1)). f(f(2,3),0)=f(2,f(3,0)). f(f(1,3),2)=f(1,f(3,2)). f(f(1,3),1)=f(1,f(3,1)). f(f(1,3),0)=f(1,f(3,0)). f(f(0,3),2)=f(0,f(3,2)). f(f(0,3),1)=f(0,f(3,1)). f(f(0,3),0)=f(0,f(3,0)). f(f(3,2),2)=f(3,f(2,2)). f(f(3,2),1)=f(3,f(2,1)). f(f(3,2),0)=f(3,f(2,0)). f(f(3,1),2)=f(3,f(1,2)). f(f(3,1),1)=f(3,f(1,1)). f(f(3,1),0)=f(3,f(1,0)). f(f(3,0),2)=f(3,f(0,2)). f(f(3,0),1)=f(3,f(0,1)). f(f(3,0),0)=f(3,f(0,0)). f(f(4,4),4)=f(4,f(4,4)). f(f(4,3),4)=f(4,f(3,4)). f(f(4,2),4)=f(4,f(2,4)). f(f(4,1),4)=f(4,f(1,4)). f(f(4,0),4)=f(4,f(0,4)). f(f(3,4),4)=f(3,f(4,4)). f(f(3,3),4)=f(3,f(3,4)). f(f(3,2),4)=f(3,f(2,4)). f(f(3,1),4)=f(3,f(1,4)). f(f(3,0),4)=f(3,f(0,4)). f(f(2,4),4)=f(2,f(4,4)). f(f(2,3),4)=f(2,f(3,4)). f(f(2,2),4)=f(2,f(2,4)). f(f(2,1),4)=f(2,f(1,4)). f(f(2,0),4)=f(2,f(0,4)). f(f(1,4),4)=f(1,f(4,4)). f(f(1,3),4)=f(1,f(3,4)). f(f(1,2),4)=f(1,f(2,4)). f(f(1,1),4)=f(1,f(1,4)). f(f(1,0),4)=f(1,f(0,4)). f(f(0,4),4)=f(0,f(4,4)). f(f(0,3),4)=f(0,f(3,4)). f(f(0,2),4)=f(0,f(2,4)). f(f(0,1),4)=f(0,f(1,4)). f(f(0,0),4)=f(0,f(0,4)). f(f(4,4),3)=f(4,f(4,3)). f(f(4,4),2)=f(4,f(4,2)). f(f(4,4),1)=f(4,f(4,1)). f(f(4,4),0)=f(4,f(4,0)). f(f(3,4),3)=f(3,f(4,3)). f(f(3,4),2)=f(3,f(4,2)). f(f(3,4),1)=f(3,f(4,1)). f(f(3,4),0)=f(3,f(4,0)). f(f(2,4),3)=f(2,f(4,3)). f(f(2,4),2)=f(2,f(4,2)). f(f(2,4),1)=f(2,f(4,1)). f(f(2,4),0)=f(2,f(4,0)). f(f(1,4),3)=f(1,f(4,3)). f(f(1,4),2)=f(1,f(4,2)). f(f(1,4),1)=f(1,f(4,1)). f(f(1,4),0)=f(1,f(4,0)). f(f(0,4),3)=f(0,f(4,3)). f(f(0,4),2)=f(0,f(4,2)). f(f(0,4),1)=f(0,f(4,1)). f(f(0,4),0)=f(0,f(4,0)). f(f(4,3),3)=f(4,f(3,3)). f(f(4,3),2)=f(4,f(3,2)). f(f(4,3),1)=f(4,f(3,1)). f(f(4,3),0)=f(4,f(3,0)). f(f(4,2),3)=f(4,f(2,3)). f(f(4,2),2)=f(4,f(2,2)). f(f(4,2),1)=f(4,f(2,1)). f(f(4,2),0)=f(4,f(2,0)). f(f(4,1),3)=f(4,f(1,3)). f(f(4,1),2)=f(4,f(1,2)). f(f(4,1),1)=f(4,f(1,1)). f(f(4,1),0)=f(4,f(1,0)). f(f(4,0),3)=f(4,f(0,3)). f(f(4,0),2)=f(4,f(0,2)). f(f(4,0),1)=f(4,f(0,1)). f(f(4,0),0)=f(4,f(0,0)). f(f(5,5),5)=f(5,f(5,5)). f(f(5,4),5)=f(5,f(4,5)). f(f(5,3),5)=f(5,f(3,5)). f(f(5,2),5)=f(5,f(2,5)). f(f(5,1),5)=f(5,f(1,5)). f(f(5,0),5)=f(5,f(0,5)). f(f(4,5),5)=f(4,f(5,5)). f(f(4,4),5)=f(4,f(4,5)). f(f(4,3),5)=f(4,f(3,5)). f(f(4,2),5)=f(4,f(2,5)). f(f(4,1),5)=f(4,f(1,5)). f(f(4,0),5)=f(4,f(0,5)). f(f(3,5),5)=f(3,f(5,5)). f(f(3,4),5)=f(3,f(4,5)). f(f(3,3),5)=f(3,f(3,5)). f(f(3,2),5)=f(3,f(2,5)). f(f(3,1),5)=f(3,f(1,5)). f(f(3,0),5)=f(3,f(0,5)). f(f(2,5),5)=f(2,f(5,5)). f(f(2,4),5)=f(2,f(4,5)). f(f(2,3),5)=f(2,f(3,5)). f(f(2,2),5)=f(2,f(2,5)). f(f(2,1),5)=f(2,f(1,5)). f(f(2,0),5)=f(2,f(0,5)). f(f(1,5),5)=f(1,f(5,5)). f(f(1,4),5)=f(1,f(4,5)). f(f(1,3),5)=f(1,f(3,5)). f(f(1,2),5)=f(1,f(2,5)). f(f(1,1),5)=f(1,f(1,5)). f(f(1,0),5)=f(1,f(0,5)). f(f(0,5),5)=f(0,f(5,5)). f(f(0,4),5)=f(0,f(4,5)). f(f(0,3),5)=f(0,f(3,5)). f(f(0,2),5)=f(0,f(2,5)). f(f(0,1),5)=f(0,f(1,5)). f(f(0,0),5)=f(0,f(0,5)). f(f(5,5),4)=f(5,f(5,4)). f(f(5,5),3)=f(5,f(5,3)). f(f(5,5),2)=f(5,f(5,2)). f(f(5,5),1)=f(5,f(5,1)). f(f(5,5),0)=f(5,f(5,0)). f(f(4,5),4)=f(4,f(5,4)). f(f(4,5),3)=f(4,f(5,3)). f(f(4,5),2)=f(4,f(5,2)). f(f(4,5),1)=f(4,f(5,1)). f(f(4,5),0)=f(4,f(5,0)). f(f(3,5),4)=f(3,f(5,4)). f(f(3,5),3)=f(3,f(5,3)). f(f(3,5),2)=f(3,f(5,2)). f(f(3,5),1)=f(3,f(5,1)). f(f(3,5),0)=f(3,f(5,0)). f(f(2,5),4)=f(2,f(5,4)). f(f(2,5),3)=f(2,f(5,3)). f(f(2,5),2)=f(2,f(5,2)). f(f(2,5),1)=f(2,f(5,1)). f(f(2,5),0)=f(2,f(5,0)). f(f(1,5),4)=f(1,f(5,4)). f(f(1,5),3)=f(1,f(5,3)). f(f(1,5),2)=f(1,f(5,2)). f(f(1,5),1)=f(1,f(5,1)). f(f(1,5),0)=f(1,f(5,0)). f(f(0,5),4)=f(0,f(5,4)). f(f(0,5),3)=f(0,f(5,3)). f(f(0,5),2)=f(0,f(5,2)). f(f(0,5),1)=f(0,f(5,1)). f(f(0,5),0)=f(0,f(5,0)). f(f(5,4),4)=f(5,f(4,4)). f(f(5,4),3)=f(5,f(4,3)). f(f(5,4),2)=f(5,f(4,2)). f(f(5,4),1)=f(5,f(4,1)). f(f(5,4),0)=f(5,f(4,0)). f(f(5,3),4)=f(5,f(3,4)). f(f(5,3),3)=f(5,f(3,3)). f(f(5,3),2)=f(5,f(3,2)). f(f(5,3),1)=f(5,f(3,1)). f(f(5,3),0)=f(5,f(3,0)). f(f(5,2),4)=f(5,f(2,4)). f(f(5,2),3)=f(5,f(2,3)). f(f(5,2),2)=f(5,f(2,2)). f(f(5,2),1)=f(5,f(2,1)). f(f(5,2),0)=f(5,f(2,0)). f(f(5,1),4)=f(5,f(1,4)). f(f(5,1),3)=f(5,f(1,3)). f(f(5,1),2)=f(5,f(1,2)). f(f(5,1),1)=f(5,f(1,1)). f(f(5,1),0)=f(5,f(1,0)). f(f(5,0),4)=f(5,f(0,4)). f(f(5,0),3)=f(5,f(0,3)). f(f(5,0),2)=f(5,f(0,2)). f(f(5,0),1)=f(5,f(0,1)). f(f(5,0),0)=f(5,f(0,0)). % g is closed. g(0)=0 | g(0)=1 | g(0)=2 | g(0)=3 | g(0)=4 | g(0)=5. g(1)=0 | g(1)=1 | g(1)=2 | g(1)=3 | g(1)=4 | g(1)=5. g(2)=0 | g(2)=1 | g(2)=2 | g(2)=3 | g(2)=4 | g(2)=5. g(3)=0 | g(3)=1 | g(3)=2 | g(3)=3 | g(3)=4 | g(3)=5. g(4)=0 | g(4)=1 | g(4)=2 | g(4)=3 | g(4)=4 | g(4)=5. g(5)=0 | g(5)=1 | g(5)=2 | g(5)=3 | g(5)=4 | g(5)=5. % f is closed. f(0,0)=0 | f(0,0)=1 | f(0,0)=2 | f(0,0)=3 | f(0,0)=4 | f(0,0)=5. f(1,1)=0 | f(1,1)=1 | f(1,1)=2 | f(1,1)=3 | f(1,1)=4 | f(1,1)=5. f(0,1)=0 | f(0,1)=1 | f(0,1)=2 | f(0,1)=3 | f(0,1)=4 | f(0,1)=5. f(1,0)=0 | f(1,0)=1 | f(1,0)=2 | f(1,0)=3 | f(1,0)=4 | f(1,0)=5. f(2,2)=0 | f(2,2)=1 | f(2,2)=2 | f(2,2)=3 | f(2,2)=4 | f(2,2)=5. f(1,2)=0 | f(1,2)=1 | f(1,2)=2 | f(1,2)=3 | f(1,2)=4 | f(1,2)=5. f(0,2)=0 | f(0,2)=1 | f(0,2)=2 | f(0,2)=3 | f(0,2)=4 | f(0,2)=5. f(2,1)=0 | f(2,1)=1 | f(2,1)=2 | f(2,1)=3 | f(2,1)=4 | f(2,1)=5. f(2,0)=0 | f(2,0)=1 | f(2,0)=2 | f(2,0)=3 | f(2,0)=4 | f(2,0)=5. f(3,3)=0 | f(3,3)=1 | f(3,3)=2 | f(3,3)=3 | f(3,3)=4 | f(3,3)=5. f(2,3)=0 | f(2,3)=1 | f(2,3)=2 | f(2,3)=3 | f(2,3)=4 | f(2,3)=5. f(1,3)=0 | f(1,3)=1 | f(1,3)=2 | f(1,3)=3 | f(1,3)=4 | f(1,3)=5. f(0,3)=0 | f(0,3)=1 | f(0,3)=2 | f(0,3)=3 | f(0,3)=4 | f(0,3)=5. f(3,2)=0 | f(3,2)=1 | f(3,2)=2 | f(3,2)=3 | f(3,2)=4 | f(3,2)=5. f(3,1)=0 | f(3,1)=1 | f(3,1)=2 | f(3,1)=3 | f(3,1)=4 | f(3,1)=5. f(3,0)=0 | f(3,0)=1 | f(3,0)=2 | f(3,0)=3 | f(3,0)=4 | f(3,0)=5. f(4,4)=0 | f(4,4)=1 | f(4,4)=2 | f(4,4)=3 | f(4,4)=4 | f(4,4)=5. f(3,4)=0 | f(3,4)=1 | f(3,4)=2 | f(3,4)=3 | f(3,4)=4 | f(3,4)=5. f(2,4)=0 | f(2,4)=1 | f(2,4)=2 | f(2,4)=3 | f(2,4)=4 | f(2,4)=5. f(1,4)=0 | f(1,4)=1 | f(1,4)=2 | f(1,4)=3 | f(1,4)=4 | f(1,4)=5. f(0,4)=0 | f(0,4)=1 | f(0,4)=2 | f(0,4)=3 | f(0,4)=4 | f(0,4)=5. f(4,3)=0 | f(4,3)=1 | f(4,3)=2 | f(4,3)=3 | f(4,3)=4 | f(4,3)=5. f(4,2)=0 | f(4,2)=1 | f(4,2)=2 | f(4,2)=3 | f(4,2)=4 | f(4,2)=5. f(4,1)=0 | f(4,1)=1 | f(4,1)=2 | f(4,1)=3 | f(4,1)=4 | f(4,1)=5. f(4,0)=0 | f(4,0)=1 | f(4,0)=2 | f(4,0)=3 | f(4,0)=4 | f(4,0)=5. f(5,5)=0 | f(5,5)=1 | f(5,5)=2 | f(5,5)=3 | f(5,5)=4 | f(5,5)=5. f(4,5)=0 | f(4,5)=1 | f(4,5)=2 | f(4,5)=3 | f(4,5)=4 | f(4,5)=5. f(3,5)=0 | f(3,5)=1 | f(3,5)=2 | f(3,5)=3 | f(3,5)=4 | f(3,5)=5. f(2,5)=0 | f(2,5)=1 | f(2,5)=2 | f(2,5)=3 | f(2,5)=4 | f(2,5)=5. f(1,5)=0 | f(1,5)=1 | f(1,5)=2 | f(1,5)=3 | f(1,5)=4 | f(1,5)=5. f(0,5)=0 | f(0,5)=1 | f(0,5)=2 | f(0,5)=3 | f(0,5)=4 | f(0,5)=5. f(5,4)=0 | f(5,4)=1 | f(5,4)=2 | f(5,4)=3 | f(5,4)=4 | f(5,4)=5. f(5,3)=0 | f(5,3)=1 | f(5,3)=2 | f(5,3)=3 | f(5,3)=4 | f(5,3)=5. f(5,2)=0 | f(5,2)=1 | f(5,2)=2 | f(5,2)=3 | f(5,2)=4 | f(5,2)=5. f(5,1)=0 | f(5,1)=1 | f(5,1)=2 | f(5,1)=3 | f(5,1)=4 | f(5,1)=5. f(5,0)=0 | f(5,0)=1 | f(5,0)=2 | f(5,0)=3 | f(5,0)=4 | f(5,0)=5. end_of_list. otter-3.3f/examples/split/zebra4.in0100644000076400007640000000347206472071166016710 0ustar mccunemccune% This is the zebra puzzle with Dale Myers' representation, with % definitions added to make it more natural. Unfortunately, the % definitions make it run much slower. % The set of clauses is satisfiable, and a model is an answer. set(binary_res). set(knuth_bendix). set(split_when_given). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level, 1). assign(max_distinct_vars, 0). % Keep ground clauses only. list(usable). x=x. % The domain consists of at most 5 elements, named 1,2,3,4,5. % In the following clause, it is important that the variables % are on the left-hand sides of the equations, because ground % equations are oriented with the heavy side on the left, and % integers are lighter than the other constants. The lexicographic % ASCII ordering is used to compare symbols.) Don't worry about % any ground literals---Otter will flip the backward ones. x=1 | x=2 | x=3 | x=4 | x=5. end_of_list. formula_list(usable). % Definitions of distinct5, successor, and next_to. all x y z u v (distinct5(x,y,z,u,v) <-> (x!=y & x!=z & x!=u & x!=v & y!=z & y!=u & y!=v & z!=u & z!=v & u!=v)). all x y (successor(x,y) <-> (x=1 & y=2) | (x=2 & y=3) | (x=3 & y=4) | (x=4 & y=5) ). all x y (next_to(x,y) <-> successor(x,y) | successor(y,x)). end_of_list. list(sos). distinct5(1, 2, 3, 4, 5). distinct5(red, green, ivory, ayellow, blue). distinct5(eng, aspan, aukra, norw, japan). distinct5(dog, asnail, fox, horse, azebra). distinct5(coffee, atea, milk, orange, apple). distinct5(old, kool, chest, lucky, parli). % Here are the clues. eng=red. aspan=dog. coffee=green. aukra=atea. old=asnail. kool=ayellow. milk=3. norw=1. lucky=orange. japan=parli. blue=2. successor(ivory, green). next_to(kool, horse). next_to(chest, fox). end_of_list. otter-3.3f/examples/split/temp10100755000076400007640000000103207313463732016132 0ustar mccunemccune#!/bin/csh cat << END_OF_HEAD Examples in $PWD

Examples in $PWD

END_OF_HEAD if (-e README) then echo "Here is the README file." endif foreach i (*.in) echo "
    " $i:r foreach j ($i:r.*) echo "
  • $j" end echo "
" $i:r end cat << END_OF_TAIL

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. END_OF_TAIL otter-3.3f/examples/split/group2.out0100664000076400007640000002026710103522214017120 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:07 2004 The command was "../../bin/otter". The process ID is 8644. set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(hyper_res). set(split_when_given). dependent: set(back_unit_deletion). dependent: set(unit_deletion). set(split_pos). assign(pick_given_ratio,4). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level,1). list(usable). 0 [] x=x. end_of_list. list(sos). 0 [] e*x=x. 0 [] x*e=x. 0 [] i(x)*x=e. 0 [] x*i(x)=e. 0 [] (x*y)*z=x*y*z. 0 [] i(e)=e. 0 [] i(i(x))=x. 0 [] i(x*y)=i(y)*i(x). 0 [] i(x)*x*y=y. 0 [] x*i(x)*y=y. 0 [] x=a1|x=a2. 0 [] c*b!=b*c. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back unit deletion with 1. ------------> process sos: ** KEPT (pick-wt=5): 2 [] e*x=x. ---> New Demodulator: 3 [new_demod,2] e*x=x. ** KEPT (pick-wt=5): 4 [] x*e=x. ---> New Demodulator: 5 [new_demod,4] x*e=x. ** KEPT (pick-wt=6): 6 [] i(x)*x=e. ---> New Demodulator: 7 [new_demod,6] i(x)*x=e. ** KEPT (pick-wt=6): 8 [] x*i(x)=e. ---> New Demodulator: 9 [new_demod,8] x*i(x)=e. ** KEPT (pick-wt=11): 10 [] (x*y)*z=x*y*z. ---> New Demodulator: 11 [new_demod,10] (x*y)*z=x*y*z. ** KEPT (pick-wt=4): 12 [] i(e)=e. ---> New Demodulator: 13 [new_demod,12] i(e)=e. ** KEPT (pick-wt=5): 14 [] i(i(x))=x. ---> New Demodulator: 15 [new_demod,14] i(i(x))=x. ** KEPT (pick-wt=10): 16 [] i(x*y)=i(y)*i(x). ---> New Demodulator: 17 [new_demod,16] i(x*y)=i(y)*i(x). ** KEPT (pick-wt=8): 18 [] i(x)*x*y=y. ---> New Demodulator: 19 [new_demod,18] i(x)*x*y=y. ** KEPT (pick-wt=8): 20 [] x*i(x)*y=y. ---> New Demodulator: 21 [new_demod,20] x*i(x)*y=y. ** KEPT (pick-wt=6): 22 [] x=a1|x=a2. ** KEPT (pick-wt=7): 23 [] c*b!=b*c. >>>> Starting back demodulation with 3. >>>> Starting back unit deletion with 2. >>>> Starting back demodulation with 5. >>>> Starting back unit deletion with 4. >>>> Starting back demodulation with 7. >>>> Starting back unit deletion with 6. >>>> Starting back demodulation with 9. >>>> Starting back unit deletion with 8. >>>> Starting back demodulation with 11. >>>> Starting back unit deletion with 10. >>>> Starting back demodulation with 13. >>>> Starting back unit deletion with 12. >>>> Starting back demodulation with 15. >>>> Starting back unit deletion with 14. >>>> Starting back demodulation with 17. >>>> Starting back unit deletion with 16. >>>> Starting back demodulation with 19. >>>> Starting back unit deletion with 18. >>>> Starting back demodulation with 21. >>>> Starting back unit deletion with 20. >>>> Starting back unit deletion with 23. ======= end of input processing ======= =========== start of search =========== Splitting on clause 28 [para_from,22.1.1,12.1.1.1] i(a1)=e|e=a2. --- refuted case [1] Case [1] (process 8645): Assumption: 55 [28,split.1] i(a1)=e. ----> UNIT CONFLICT at 0.14 sec ----> 553 [binary,552.1,1.1] $F. Length of proof is 25. Level of proof is 12. Case [1] ---------------- PROOF ---------------- 1 [] x=x. 2 [] e*x=x. 4 [] x*e=x. 13,12 [] i(e)=e. 15,14 [] i(i(x))=x. 22 [] x=a1|x=a2. 23 [] c*b!=b*c. 24 [para_from,22.1.1,14.1.1,demod,15] a1=x|x=a2. 28 [para_from,22.1.1,12.1.1.1] i(a1)=e|e=a2. 31 [para_from,22.2.1,14.1.1,demod,15] a2=x|x=a1. 40 [para_into,31.1.1,31.1.1] x=y|y=a1|x=a1. 49 [para_into,23.1.1.1,31.2.1,flip.1,flip.2] b*c!=a1*b|c=a2. 51 [para_into,23.1.1.2,31.2.1,flip.2] c*a1!=b*c|b=a2. 55 [28,split.1] i(a1)=e. 61,60 [para_from,55.1.1,14.1.1.1,demod,13] e=a1. 80,79 [back_demod,4,demod,61] x*a1=x. 82,81 [back_demod,2,demod,61] a1*x=x. 84 [back_demod,51,demod,80,flip.1] b*c!=c|b=a2. 85 [back_demod,49,demod,82] b*c!=b|c=a2. 90 [para_into,79.1.1.2,24.1.1] x*y=x|y=a2. 92 [para_into,81.1.1.1,24.1.1] x*y=y|x=a2. 211,210 [para_into,84.1.1.1,31.2.1,demod,82,unit_del,1] b=a2. 228 [back_demod,85,demod,211,211] a2*c!=a2|c=a2. 233 [back_demod,23,demod,211,211] c*a2!=a2*c. 260 [hyper,40,233] a2*c=a1|c*a2=a1. 313 [para_from,90.2.1,233.1.1.1,flip.1] a2*c!=a2*a2|x*c=x. 364 [para_from,92.2.1,233.1.1.1,flip.1] a2*c!=a2*a2|c*x=x. 537,536 [hyper,228,90] c=a2. 542,541 [back_demod,364,demod,537,537,unit_del,1] a2*x=x. 545,544 [back_demod,313,demod,537,542,542,537,unit_del,1] x*a2=x. 548,547 [back_demod,260,demod,537,545,537,545] a2=a1. 552 [back_demod,233,demod,537,548,548,80,548,537,548,80] a1!=a1. 553 [binary,552.1,1.1] $F. ------------ end of proof ------------- ------- statistics (process 8645) ------- clauses given 48 clauses generated 2026 clauses kept 529 clauses forward subsumed 1590 clauses back subsumed 40 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.14 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8645 finished Mon Aug 2 15:31:08 2004 Refuted case [1]. --- refuted case [2] Case [2] (process 8646): Assumption: 56 [28,split.2] e=a2. -----> EMPTY CLAUSE at 0.16 sec ----> 572 [back_demod,567,demod,571,100,571,unit_del,1,1] $F. Length of proof is 28. Level of proof is 11. Case [2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] e*x=x. 4 [] x*e=x. 8 [] x*i(x)=e. 12 [] i(e)=e. 15,14 [] i(i(x))=x. 22 [] x=a1|x=a2. 23 [] c*b!=b*c. 24 [para_from,22.1.1,14.1.1,demod,15] a1=x|x=a2. 28 [para_from,22.1.1,12.1.1.1] i(a1)=e|e=a2. 31 [para_from,22.2.1,14.1.1,demod,15] a2=x|x=a1. 39 [para_from,24.2.1,14.1.1,demod,15] a2=x|a1=x. 50 [para_into,23.1.1.1,24.2.1,flip.1,flip.2] b*c!=a2*b|c=a1. 52 [para_into,23.1.1.2,24.2.1,flip.2] c*a2!=b*c|b=a1. 55 [28,split_neg.2] i(a1)!=e. 57,56 [28,split.2] e=a2. 58 [back_demod,55,demod,57] i(a1)!=a2. 68 [back_demod,8,demod,57] x*i(x)=a2. 73,72 [back_demod,4,demod,57] x*a2=x. 75,74 [back_demod,2,demod,57] a2*x=x. 78 [back_demod,52,demod,73,flip.1] b*c!=c|b=a1. 79 [back_demod,50,demod,75] b*c!=b|c=a1. 82,81 [hyper,58,24,flip.1] i(a1)=a1. 83 [back_demod,58,demod,82,flip.1] a2!=a1. 87 [para_into,83.1.1,39.1.1] x!=a1|a1=x. 90 [para_into,72.1.1.2,31.1.1] x*y=x|y=a1. 100,99 [para_into,68.1.1.2,81.1.1] a1*a1=a2. 113 [para_from,87.2.1,99.1.1.1] x*a1=a2|x!=a1. 114 [para_from,87.2.1,81.1.1.1] i(x)=a1|x!=a1. 187 [para_into,114.1.1,14.1.1] x=a1|i(x)!=a1. 192 [para_from,187.1.1,23.1.1.2] c*a1!=b*c|i(b)!=a1. 259,258 [para_into,78.1.1.1,24.2.1,demod,75,unit_del,1] b=a1. 270 [back_demod,192,demod,259,259,82,unit_del,1] c*a1!=a1*c. 284 [back_demod,79,demod,259,259] a1*c!=a1|c=a1. 567 [para_from,113.1.1,270.1.1,flip.1] a1*c!=a2|c!=a1. 571,570 [hyper,284,90] c=a1. 572 [back_demod,567,demod,571,100,571,unit_del,1,1] $F. ------------ end of proof ------------- ------- statistics (process 8646) ------- clauses given 54 clauses generated 2392 clauses kept 550 clauses forward subsumed 1907 clauses back subsumed 16 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.16 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8646 finished Mon Aug 2 15:31:08 2004 Refuted case [2].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8644) ------- clauses given 13 clauses generated 135 clauses kept 44 clauses forward subsumed 105 clauses back subsumed 0 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8644 finished Mon Aug 2 15:31:08 2004 otter-3.3f/examples/split/index.html0100644000076400007640000000272307714267401017163 0ustar mccunemccune /home/mccune/otter-3.3/examples/split

/home/mccune/otter-3.3/examples/split

These problems were used to test Otter's experimental splitting rule.

otter < GEO010-2.in > GEO010-2.out

otter < GEO036-2.in > GEO036-2.out

otter < group2.in > group2.out

otter < GRP025-1.in > GRP025-1.out

otter < noncomm-group.in > noncomm-group.out

otter < pair.in > pair.out

otter < pigeon5.in > pigeon5.out

otter < power.in > power.out

otter < wang3.in > wang3.out

otter < zebra2.in > zebra2.out

otter < zebra4.in > zebra4.out

These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory. otter-3.3f/examples/split/README0100644000076400007640000000010607313672052016034 0ustar mccunemccuneThese problems were used to test Otter's experimental splitting rule. otter-3.3f/examples/split/pair.out0100664000076400007640000004357110103522215016641 0ustar mccunemccune WARNING, with splitting, max_seconds is checked against the wall clock. ----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:08 2004 The command was "../../bin/otter". The process ID is 8716. set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(split_when_given). dependent: set(back_unit_deletion). WARNING: clear(print_kept) flag already clear. clear(print_kept). clear(print_given). WARNING: clear(print_new_demod) flag already clear. clear(print_new_demod). WARNING: clear(print_back_demod) flag already clear. clear(print_back_demod). WARNING: clear(print_back_sub) flag already clear. clear(print_back_sub). WARNING: assign(stats_level,1) already has that value. assign(stats_level,1). list(usable). 0 [] x=x. 0 [] z!=x|el(z,nop(x,y)). 0 [] z!=y|el(z,nop(x,y)). 0 [] -el(z,nop(x,y))|z=x|z=y. 0 [] op(x,y)=nop(nop(x,x),nop(x,y)). 0 [] op(A,B)=op(C,D). 0 [] A!=C|B!=D. end_of_list. SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3. This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). ------------> process usable: ** KEPT (pick-wt=8): 1 [] x!=y|el(x,nop(y,z)). ** KEPT (pick-wt=8): 2 [] x!=y|el(x,nop(z,y)). ** KEPT (pick-wt=11): 3 [] -el(x,nop(y,z))|x=y|x=z. ** KEPT (pick-wt=6): 5 [copy,4,flip.1,flip.2] C!=A|D!=B. ------------> process sos: ** KEPT (pick-wt=3): 7 [] x=x. ** KEPT (pick-wt=11): 8 [] op(x,y)=nop(nop(x,x),nop(x,y)). ---> New Demodulator: 9 [new_demod,8] op(x,y)=nop(nop(x,x),nop(x,y)). ** KEPT (pick-wt=15): 11 [copy,10,demod,9,9,flip.1] nop(nop(C,C),nop(C,D))=nop(nop(A,A),nop(A,B)). ---> New Demodulator: 12 [new_demod,11] nop(nop(C,C),nop(C,D))=nop(nop(A,A),nop(A,B)). Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] x=x. >>>> Starting back unit deletion with 7. >>>> Starting back demodulation with 9. >>>> Starting back unit deletion with 8. >>>> Starting back demodulation with 12. >>>> Starting back unit deletion with 11. ======= end of input processing ======= =========== start of search =========== Splitting on clause 190 [factor,185.1.3] nop(C,D)!=nop(B,B)|B!=A. Case [1] (process 8717): Assumption: 335 [190,split.1] nop(C,D)!=nop(B,B). Splitting on clause 215 [factor,210.1.3,flip.2] nop(D,C)!=nop(A,A)|B!=A. Case [1.1] (process 8718): Assumption: 359 [215,split.1.1] nop(D,C)!=nop(A,A). Splitting on clause 240 [factor,236.1.3] nop(D,C)!=nop(B,B)|B!=A. Case [1.1.1] (process 8719): Assumption: 470 [240,split.1.1.1] nop(D,C)!=nop(B,B). Splitting on clause 264 [factor,260.1.3,flip.2] nop(C,D)!=nop(A,A)|B!=A. Case [1.1.1.1] (process 8720): Assumption: 496 [264,split.1.1.1.1] nop(C,D)!=nop(A,A). Splitting on clause 749 [binary,674.1,3.1] C=A|C=B. --- refuted case [1.1.1.1.1] Case [1.1.1.1.1] (process 8721): Assumption: 895 [749,split.1.1.1.1.1] C=A. ----> UNIT CONFLICT at 0.12 sec ----> 1256 [binary,1255.1,7.1] $F. Length of proof is 31. Level of proof is 14. Case [1.1.1.1.1] ---------------- PROOF ---------------- 1 [] x!=y|el(x,nop(y,z)). 2 [] x!=y|el(x,nop(z,y)). 3 [] -el(x,nop(y,z))|x=y|x=z. 4 [] A!=C|B!=D. 5 [copy,4,flip.1,flip.2] C!=A|D!=B. 6 [factor,3.2.3] -el(x,nop(y,y))|x=y. 7 [] x=x. 9,8 [] op(x,y)=nop(nop(x,x),nop(x,y)). 10 [] op(A,B)=op(C,D). 11 [copy,10,demod,9,9,flip.1] nop(nop(C,C),nop(C,D))=nop(nop(A,A),nop(A,B)). 13 [binary,7.1,2.1] el(x,nop(y,x)). 14 [binary,7.1,1.1] el(x,nop(x,y)). 15 [para_into,13.1.2,6.2.1] el(x,y)| -el(nop(z,x),nop(y,y)). 16 [para_into,13.1.2,3.3.1] el(x,y)| -el(nop(z,x),nop(u,y))|nop(z,x)=u. 18 [para_into,14.1.2,6.2.1] el(x,y)| -el(nop(x,z),nop(y,y)). 19 [para_into,14.1.2,3.3.1] el(x,y)| -el(nop(x,z),nop(u,y))|nop(x,z)=u. 24 [binary,15.2,2.2] el(x,y)|nop(z,x)!=y. 32 [binary,24.1,6.1] nop(x,y)!=nop(z,z)|y=z. 46 [binary,18.2,2.2] el(x,y)|nop(x,z)!=y. 55 [binary,46.1,6.1] nop(x,y)!=nop(z,z)|x=z. 64 [binary,32.2,5.1] nop(x,C)!=nop(A,A)|D!=B. 95 [binary,55.2,5.1] nop(C,x)!=nop(A,A)|D!=B. 125 [binary,11.1,24.2] el(nop(C,D),nop(nop(A,A),nop(A,B))). 210 [para_into,64.2.1,55.2.1] nop(x,C)!=nop(A,A)|y!=B|nop(D,z)!=nop(y,y). 215 [factor,210.1.3,flip.2] nop(D,C)!=nop(A,A)|B!=A. 260 [para_into,95.2.1,32.2.1] nop(C,x)!=nop(A,A)|y!=B|nop(z,D)!=nop(y,y). 264 [factor,260.1.3,flip.2] nop(C,D)!=nop(A,A)|B!=A. 359 [215,split.1.1] nop(D,C)!=nop(A,A). 496 [264,split.1.1.1.1] nop(C,D)!=nop(A,A). 674 [binary,125.1,19.2,unit_del,496] el(C,nop(A,B)). 676 [binary,125.1,16.2,unit_del,496] el(D,nop(A,B)). 749 [binary,674.1,3.1] C=A|C=B. 773 [binary,676.1,3.1] D=A|D=B. 896,895 [749,split.1.1.1.1.1] C=A. 1058 [back_demod,359,demod,896] nop(D,A)!=nop(A,A). 1183 [back_demod,5,demod,896,unit_del,7] D!=B. 1189,1188 [back_unit_del,1183.1,773.2] D=A. 1255 [back_demod,1058,demod,1189] nop(A,A)!=nop(A,A). 1256 [binary,1255.1,7.1] $F. ------------ end of proof ------------- ------- statistics (process 8721) ------- clauses given 32 clauses generated 1135 clauses kept 1246 clauses forward subsumed 424 clauses back subsumed 107 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.12 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8721 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.1.1.1]. --- refuted case [1.1.1.1.2] Case [1.1.1.1.2] (process 8722): Assumption: 896 [749,split.1.1.1.1.2] C=B. ----> UNIT CONFLICT at 0.11 sec ----> 1188 [binary,1187.1,1014.1] $F. Length of proof is 32. Level of proof is 13. Case [1.1.1.1.2] ---------------- PROOF ---------------- 1 [] x!=y|el(x,nop(y,z)). 2 [] x!=y|el(x,nop(z,y)). 3 [] -el(x,nop(y,z))|x=y|x=z. 4 [] A!=C|B!=D. 5 [copy,4,flip.1,flip.2] C!=A|D!=B. 6 [factor,3.2.3] -el(x,nop(y,y))|x=y. 7 [] x=x. 9,8 [] op(x,y)=nop(nop(x,x),nop(x,y)). 10 [] op(A,B)=op(C,D). 11 [copy,10,demod,9,9,flip.1] nop(nop(C,C),nop(C,D))=nop(nop(A,A),nop(A,B)). 13 [binary,7.1,2.1] el(x,nop(y,x)). 14 [binary,7.1,1.1] el(x,nop(x,y)). 15 [para_into,13.1.2,6.2.1] el(x,y)| -el(nop(z,x),nop(y,y)). 18 [para_into,14.1.2,6.2.1] el(x,y)| -el(nop(x,z),nop(y,y)). 19 [para_into,14.1.2,3.3.1] el(x,y)| -el(nop(x,z),nop(u,y))|nop(x,z)=u. 24 [binary,15.2,2.2] el(x,y)|nop(z,x)!=y. 32 [binary,24.1,6.1] nop(x,y)!=nop(z,z)|y=z. 46 [binary,18.2,2.2] el(x,y)|nop(x,z)!=y. 55 [binary,46.1,6.1] nop(x,y)!=nop(z,z)|x=z. 63 [binary,32.2,5.2] nop(x,D)!=nop(B,B)|C!=A. 95 [binary,55.2,5.1] nop(C,x)!=nop(A,A)|D!=B. 124 [binary,11.1,46.2] el(nop(C,C),nop(nop(A,A),nop(A,B))). 125 [binary,11.1,24.2] el(nop(C,D),nop(nop(A,A),nop(A,B))). 185 [para_into,63.2.1,55.2.1] nop(x,D)!=nop(B,B)|y!=A|nop(C,z)!=nop(y,y). 190 [factor,185.1.3] nop(C,D)!=nop(B,B)|B!=A. 260 [para_into,95.2.1,32.2.1] nop(C,x)!=nop(A,A)|y!=B|nop(z,D)!=nop(y,y). 264 [factor,260.1.3,flip.2] nop(C,D)!=nop(A,A)|B!=A. 335 [190,split.1] nop(C,D)!=nop(B,B). 496 [264,split.1.1.1.1] nop(C,D)!=nop(A,A). 613 [binary,124.1,3.1] nop(C,C)=nop(A,A)|nop(C,C)=nop(A,B). 674 [binary,125.1,19.2,unit_del,496] el(C,nop(A,B)). 678,677 [binary,125.1,3.1,unit_del,496] nop(C,D)=nop(A,B). 720 [back_demod,335,demod,678,flip.1] nop(B,B)!=nop(A,B). 749 [binary,674.1,3.1] C=A|C=B. 895 [749,split_neg.1.1.1.1.2] C!=A. 897,896 [749,split.1.1.1.1.2] C=B. 898 [back_demod,895,demod,897] B!=A. 1014 [back_demod,613,demod,897,897,897,897,unit_del,720] nop(B,B)=nop(A,A). 1187 [binary,898.1,55.2] nop(B,x)!=nop(A,A). 1188 [binary,1187.1,1014.1] $F. ------------ end of proof ------------- ------- statistics (process 8722) ------- clauses given 34 clauses generated 1144 clauses kept 1177 clauses forward subsumed 472 clauses back subsumed 81 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.11 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8722 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.1.1.2]. ------- statistics (process 8720) ------- clauses given 32 clauses generated 1120 clauses kept 888 clauses forward subsumed 330 clauses back subsumed 5 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.15 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8720 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.1.1]. --- refuted case [1.1.1.2] Case [1.1.1.2] (process 8723): Assumption: 498 [264,split.1.1.1.2] B!=A. ----> UNIT CONFLICT at 0.06 sec ----> 708 [binary,707.1,7.1] $F. Length of proof is 25. Level of proof is 11. Case [1.1.1.2] ---------------- PROOF ---------------- 1 [] x!=y|el(x,nop(y,z)). 2 [] x!=y|el(x,nop(z,y)). 3 [] -el(x,nop(y,z))|x=y|x=z. 4 [] A!=C|B!=D. 5 [copy,4,flip.1,flip.2] C!=A|D!=B. 6 [factor,3.2.3] -el(x,nop(y,y))|x=y. 7 [] x=x. 13 [binary,7.1,2.1] el(x,nop(y,x)). 14 [binary,7.1,1.1] el(x,nop(x,y)). 15 [para_into,13.1.2,6.2.1] el(x,y)| -el(nop(z,x),nop(y,y)). 18 [para_into,14.1.2,6.2.1] el(x,y)| -el(nop(x,z),nop(y,y)). 19 [para_into,14.1.2,3.3.1] el(x,y)| -el(nop(x,z),nop(u,y))|nop(x,z)=u. 24 [binary,15.2,2.2] el(x,y)|nop(z,x)!=y. 32 [binary,24.1,6.1] nop(x,y)!=nop(z,z)|y=z. 46 [binary,18.2,2.2] el(x,y)|nop(x,z)!=y. 55 [binary,46.1,6.1] nop(x,y)!=nop(z,z)|x=z. 64 [binary,32.2,5.1] nop(x,C)!=nop(A,A)|D!=B. 95 [binary,55.2,5.1] nop(C,x)!=nop(A,A)|D!=B. 210 [para_into,64.2.1,55.2.1] nop(x,C)!=nop(A,A)|y!=B|nop(D,z)!=nop(y,y). 215 [factor,210.1.3,flip.2] nop(D,C)!=nop(A,A)|B!=A. 260 [para_into,95.2.1,32.2.1] nop(C,x)!=nop(A,A)|y!=B|nop(z,D)!=nop(y,y). 264 [factor,260.1.3,flip.2] nop(C,D)!=nop(A,A)|B!=A. 359 [215,split.1.1] nop(D,C)!=nop(A,A). 374 [para_into,359.1.1.2,6.2.1] nop(D,x)!=nop(A,A)| -el(C,nop(x,x)). 496 [264,split_neg.1.1.1.2] nop(C,D)=nop(A,A). 571 [binary,19.3,359.1] el(D,x)| -el(nop(D,C),nop(nop(A,A),x)). 668,667 [binary,496.1,55.1] C=A. 670,669 [binary,496.1,32.1] D=A. 676 [back_demod,571,demod,670,670,668,unit_del,14] el(A,x). 707 [back_demod,374,demod,670,668,unit_del,676] nop(A,x)!=nop(A,A). 708 [binary,707.1,7.1] $F. ------------ end of proof ------------- ------- statistics (process 8723) ------- clauses given 28 clauses generated 842 clauses kept 698 clauses forward subsumed 297 clauses back subsumed 52 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.07 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8723 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.1.2]. ------- statistics (process 8719) ------- clauses given 24 clauses generated 655 clauses kept 491 clauses forward subsumed 179 clauses back subsumed 4 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8719 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1.1]. The Assumption for case [1.1.1] was not used; therefore we skip case: [1.1.2]. ------- statistics (process 8718) ------- clauses given 22 clauses generated 631 clauses kept 465 clauses forward subsumed 178 clauses back subsumed 4 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8718 finished Mon Aug 2 15:31:09 2004 Refuted case [1.1]. --- refuted case [1.2] Case [1.2] (process 8724): Assumption: 361 [215,split.1.2] B!=A. ----> UNIT CONFLICT at 0.10 sec ----> 765 [binary,764.1,621.1] $F. Length of proof is 21. Level of proof is 10. Case [1.2] ---------------- PROOF ---------------- 1 [] x!=y|el(x,nop(y,z)). 2 [] x!=y|el(x,nop(z,y)). 3 [] -el(x,nop(y,z))|x=y|x=z. 4 [] A!=C|B!=D. 5 [copy,4,flip.1,flip.2] C!=A|D!=B. 6 [factor,3.2.3] -el(x,nop(y,y))|x=y. 7 [] x=x. 9,8 [] op(x,y)=nop(nop(x,x),nop(x,y)). 10 [] op(A,B)=op(C,D). 11 [copy,10,demod,9,9,flip.1] nop(nop(C,C),nop(C,D))=nop(nop(A,A),nop(A,B)). 13 [binary,7.1,2.1] el(x,nop(y,x)). 14 [binary,7.1,1.1] el(x,nop(x,y)). 15 [para_into,13.1.2,6.2.1] el(x,y)| -el(nop(z,x),nop(y,y)). 18 [para_into,14.1.2,6.2.1] el(x,y)| -el(nop(x,z),nop(y,y)). 24 [binary,15.2,2.2] el(x,y)|nop(z,x)!=y. 32 [binary,24.1,6.1] nop(x,y)!=nop(z,z)|y=z. 46 [binary,18.2,2.2] el(x,y)|nop(x,z)!=y. 55 [binary,46.1,6.1] nop(x,y)!=nop(z,z)|x=z. 64 [binary,32.2,5.1] nop(x,C)!=nop(A,A)|D!=B. 210 [para_into,64.2.1,55.2.1] nop(x,C)!=nop(A,A)|y!=B|nop(D,z)!=nop(y,y). 215 [factor,210.1.3,flip.2] nop(D,C)!=nop(A,A)|B!=A. 359 [215,split_neg.1.2] nop(D,C)=nop(A,A). 361 [215,split.1.2] B!=A. 363 [binary,361.1,32.2] nop(x,B)!=nop(A,A). 486,485 [binary,359.1,55.1] D=A. 488,487 [binary,359.1,32.1] C=A. 621 [back_demod,11,demod,488,488,488,486,flip.1] nop(nop(A,A),nop(A,B))=nop(nop(A,A),nop(A,A)). 764 [binary,363.1,32.2] nop(x,nop(y,B))!=nop(nop(A,A),nop(A,A)). 765 [binary,764.1,621.1] $F. ------------ end of proof ------------- ------- statistics (process 8724) ------- clauses given 28 clauses generated 842 clauses kept 756 clauses forward subsumed 312 clauses back subsumed 92 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.10 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8724 finished Mon Aug 2 15:31:09 2004 Refuted case [1.2]. ------- statistics (process 8717) ------- clauses given 19 clauses generated 476 clauses kept 354 clauses forward subsumed 132 clauses back subsumed 2 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8717 finished Mon Aug 2 15:31:09 2004 Refuted case [1]. --- refuted case [2] Case [2] (process 8725): Assumption: 337 [190,split.2] B!=A. ----> UNIT CONFLICT at 0.09 sec ----> 641 [binary,640.1,411.1] $F. Length of proof is 23. Level of proof is 12. Case [2] ---------------- PROOF ---------------- 1 [] x!=y|el(x,nop(y,z)). 2 [] x!=y|el(x,nop(z,y)). 3 [] -el(x,nop(y,z))|x=y|x=z. 4 [] A!=C|B!=D. 5 [copy,4,flip.1,flip.2] C!=A|D!=B. 6 [factor,3.2.3] -el(x,nop(y,y))|x=y. 7 [] x=x. 9,8 [] op(x,y)=nop(nop(x,x),nop(x,y)). 10 [] op(A,B)=op(C,D). 11 [copy,10,demod,9,9,flip.1] nop(nop(C,C),nop(C,D))=nop(nop(A,A),nop(A,B)). 13 [binary,7.1,2.1] el(x,nop(y,x)). 14 [binary,7.1,1.1] el(x,nop(x,y)). 15 [para_into,13.1.2,6.2.1] el(x,y)| -el(nop(z,x),nop(y,y)). 18 [para_into,14.1.2,6.2.1] el(x,y)| -el(nop(x,z),nop(y,y)). 24 [binary,15.2,2.2] el(x,y)|nop(z,x)!=y. 32 [binary,24.1,6.1] nop(x,y)!=nop(z,z)|y=z. 46 [binary,18.2,2.2] el(x,y)|nop(x,z)!=y. 55 [binary,46.1,6.1] nop(x,y)!=nop(z,z)|x=z. 63 [binary,32.2,5.2] nop(x,D)!=nop(B,B)|C!=A. 185 [para_into,63.2.1,55.2.1] nop(x,D)!=nop(B,B)|y!=A|nop(C,z)!=nop(y,y). 190 [factor,185.1.3] nop(C,D)!=nop(B,B)|B!=A. 336,335 [190,split_neg.2] nop(C,D)=nop(B,B). 337 [190,split.2] B!=A. 369 [back_demod,11,demod,336] nop(nop(C,C),nop(B,B))=nop(nop(A,A),nop(A,B)). 372 [binary,337.1,32.2] nop(x,B)!=nop(A,A). 376 [copy,372,flip.1] nop(A,A)!=nop(x,B). 408,407 [binary,335.1,55.1] C=B. 411 [back_demod,369,demod,408,408] nop(nop(B,B),nop(B,B))=nop(nop(A,A),nop(A,B)). 633 [binary,376.1,55.2] nop(nop(A,A),x)!=nop(nop(y,B),nop(y,B)). 640 [copy,633,flip.1] nop(nop(x,B),nop(x,B))!=nop(nop(A,A),y). 641 [binary,640.1,411.1] $F. ------------ end of proof ------------- ------- statistics (process 8725) ------- clauses given 27 clauses generated 820 clauses kept 631 clauses forward subsumed 354 clauses back subsumed 45 Kbytes malloced 1953 ----------- times (seconds) ----------- user CPU time 0.09 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8725 finished Mon Aug 2 15:31:09 2004 Refuted case [2].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8716) ------- clauses given 17 clauses generated 454 clauses kept 330 clauses forward subsumed 131 clauses back subsumed 2 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.04 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8716 finished Mon Aug 2 15:31:09 2004 otter-3.3f/examples/split/pair.in0100644000076400007640000000104606472070015016437 0ustar mccunemccune% Naive set theory % If two ordered pairs are equal, their components are equal. set(auto1). set(binary_res). set(split_when_given). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level, 1). list(usable). x = x. % Definition of non-ordered pair. z != x | el(z, nop(x,y)). z != y | el(z, nop(x,y)). -el(z,nop(x,y)) | z=x | z=y. % Definition of ordered pair. op(x,y) = nop(nop(x,x),nop(x,y)). % Denial of theorem. op(A,B) = op(C,D). A != C | B != D. end_of_list. otter-3.3f/examples/split/zebra2.out0100664000076400007640000014371510103522217017076 0ustar mccunemccune----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:11 2004 The command was "../../bin/otter". The process ID is 8831. set(binary_res). dependent: set(factor). dependent: set(unit_deletion). set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(process_input). dependent: set(lrpo). set(split_when_given). dependent: set(back_unit_deletion). clear(print_kept). clear(print_given). clear(print_new_demod). clear(print_back_demod). clear(print_back_sub). assign(stats_level,1). list(usable). 0 [] x=x. 0 [] x=1|x=2|x=3|x=4|x=5. 0 [] 1!=2. 0 [] 1!=3. 0 [] 1!=4. 0 [] 1!=5. 0 [] 2!=3. 0 [] 2!=4. 0 [] 2!=5. 0 [] 3!=4. 0 [] 3!=5. 0 [] 4!=5. 0 [] red!=green. 0 [] red!=ivory. 0 [] red!=ayellow. 0 [] red!=blue. 0 [] green!=ivory. 0 [] green!=ayellow. 0 [] green!=blue. 0 [] ivory!=ayellow. 0 [] ivory!=blue. 0 [] ayellow!=blue. 0 [] eng!=aspan. 0 [] eng!=aukra. 0 [] eng!=norw. 0 [] eng!=japan. 0 [] aspan!=aukra. 0 [] aspan!=norw. 0 [] aspan!=japan. 0 [] aukra!=norw. 0 [] aukra!=japan. 0 [] norw!=japan. 0 [] dog!=asnail. 0 [] dog!=fox. 0 [] dog!=horse. 0 [] dog!=azebra. 0 [] asnail!=fox. 0 [] asnail!=horse. 0 [] asnail!=azebra. 0 [] fox!=horse. 0 [] fox!=azebra. 0 [] horse!=azebra. 0 [] coffee!=atea. 0 [] coffee!=milk. 0 [] coffee!=orange. 0 [] coffee!=apple. 0 [] atea!=milk. 0 [] atea!=orange. 0 [] atea!=apple. 0 [] milk!=orange. 0 [] milk!=apple. 0 [] orange!=apple. 0 [] old!=kool. 0 [] old!=chest. 0 [] old!=lucky. 0 [] old!=parli. 0 [] kool!=chest. 0 [] kool!=lucky. 0 [] kool!=parli. 0 [] chest!=lucky. 0 [] chest!=parli. 0 [] lucky!=parli. end_of_list. list(sos). 0 [] eng=red. 0 [] aspan=dog. 0 [] coffee=green. 0 [] aukra=atea. 0 [] old=asnail. 0 [] kool=ayellow. 0 [] milk=3. 0 [] norw=1. 0 [] lucky=orange. 0 [] japan=parli. 0 [] blue=2. 0 [] ivory!=5. 0 [] green!=1. 0 [] ivory!=1|green=2. 0 [] ivory!=2|green=3. 0 [] ivory!=3|green=4. 0 [] ivory!=4|green=5. 0 [] ivory=1|green!=2. 0 [] ivory=2|green!=3. 0 [] ivory=3|green!=4. 0 [] ivory=4|green!=5. 0 [] kool!=1|horse=2. 0 [] kool!=2|horse=1|horse=3. 0 [] kool!=3|horse=2|horse=4. 0 [] kool!=4|horse=3|horse=5. 0 [] kool!=5|horse=4. 0 [] horse!=1|kool=2. 0 [] horse!=2|kool=1|kool=3. 0 [] horse!=3|kool=2|kool=4. 0 [] horse!=4|kool=3|kool=5. 0 [] horse!=5|kool=4. 0 [] chest!=1|fox=2. 0 [] chest!=2|fox=1|fox=3. 0 [] chest!=3|fox=2|fox=4. 0 [] chest!=4|fox=3|fox=5. 0 [] chest!=5|fox=4. 0 [] fox!=1|chest=2. 0 [] fox!=2|chest=1|chest=3. 0 [] fox!=3|chest=2|chest=4. 0 [] fox!=4|chest=3|chest=5. 0 [] fox!=5|chest=4. end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 1 [] x=x. ** KEPT (pick-wt=15): 2 [] x=1|x=2|x=3|x=4|x=5. ** KEPT (pick-wt=3): 4 [copy,3,flip.1] 2!=1. ** KEPT (pick-wt=3): 6 [copy,5,flip.1] 3!=1. ** KEPT (pick-wt=3): 8 [copy,7,flip.1] 4!=1. ** KEPT (pick-wt=3): 10 [copy,9,flip.1] 5!=1. ** KEPT (pick-wt=3): 12 [copy,11,flip.1] 3!=2. ** KEPT (pick-wt=3): 14 [copy,13,flip.1] 4!=2. ** KEPT (pick-wt=3): 16 [copy,15,flip.1] 5!=2. ** KEPT (pick-wt=3): 18 [copy,17,flip.1] 4!=3. ** KEPT (pick-wt=3): 20 [copy,19,flip.1] 5!=3. ** KEPT (pick-wt=3): 22 [copy,21,flip.1] 5!=4. ** KEPT (pick-wt=3): 23 [] red!=green. ** KEPT (pick-wt=3): 24 [] red!=ivory. ** KEPT (pick-wt=3): 25 [] red!=ayellow. ** KEPT (pick-wt=3): 26 [] red!=blue. ** KEPT (pick-wt=3): 28 [copy,27,flip.1] ivory!=green. ** KEPT (pick-wt=3): 29 [] green!=ayellow. ** KEPT (pick-wt=3): 30 [] green!=blue. ** KEPT (pick-wt=3): 31 [] ivory!=ayellow. ** KEPT (pick-wt=3): 32 [] ivory!=blue. ** KEPT (pick-wt=3): 34 [copy,33,flip.1] blue!=ayellow. ** KEPT (pick-wt=3): 35 [] eng!=aspan. ** KEPT (pick-wt=3): 36 [] eng!=aukra. ** KEPT (pick-wt=3): 38 [copy,37,flip.1] norw!=eng. ** KEPT (pick-wt=3): 40 [copy,39,flip.1] japan!=eng. ** KEPT (pick-wt=3): 42 [copy,41,flip.1] aukra!=aspan. ** KEPT (pick-wt=3): 44 [copy,43,flip.1] norw!=aspan. ** KEPT (pick-wt=3): 46 [copy,45,flip.1] japan!=aspan. ** KEPT (pick-wt=3): 48 [copy,47,flip.1] norw!=aukra. ** KEPT (pick-wt=3): 50 [copy,49,flip.1] japan!=aukra. ** KEPT (pick-wt=3): 51 [] norw!=japan. ** KEPT (pick-wt=3): 52 [] dog!=asnail. ** KEPT (pick-wt=3): 54 [copy,53,flip.1] fox!=dog. ** KEPT (pick-wt=3): 56 [copy,55,flip.1] horse!=dog. ** KEPT (pick-wt=3): 57 [] dog!=azebra. ** KEPT (pick-wt=3): 59 [copy,58,flip.1] fox!=asnail. ** KEPT (pick-wt=3): 61 [copy,60,flip.1] horse!=asnail. ** KEPT (pick-wt=3): 63 [copy,62,flip.1] azebra!=asnail. ** KEPT (pick-wt=3): 65 [copy,64,flip.1] horse!=fox. ** KEPT (pick-wt=3): 66 [] fox!=azebra. ** KEPT (pick-wt=3): 67 [] horse!=azebra. ** KEPT (pick-wt=3): 68 [] coffee!=atea. ** KEPT (pick-wt=3): 70 [copy,69,flip.1] milk!=coffee. ** KEPT (pick-wt=3): 72 [copy,71,flip.1] orange!=coffee. ** KEPT (pick-wt=3): 73 [] coffee!=apple. ** KEPT (pick-wt=3): 75 [copy,74,flip.1] milk!=atea. ** KEPT (pick-wt=3): 77 [copy,76,flip.1] orange!=atea. ** KEPT (pick-wt=3): 78 [] atea!=apple. ** KEPT (pick-wt=3): 80 [copy,79,flip.1] orange!=milk. ** KEPT (pick-wt=3): 81 [] milk!=apple. ** KEPT (pick-wt=3): 82 [] orange!=apple. ** KEPT (pick-wt=3): 83 [] old!=kool. ** KEPT (pick-wt=3): 84 [] old!=chest. ** KEPT (pick-wt=3): 85 [] old!=lucky. ** KEPT (pick-wt=3): 87 [copy,86,flip.1] parli!=old. ** KEPT (pick-wt=3): 88 [] kool!=chest. ** KEPT (pick-wt=3): 90 [copy,89,flip.1] lucky!=kool. ** KEPT (pick-wt=3): 92 [copy,91,flip.1] parli!=kool. ** KEPT (pick-wt=3): 94 [copy,93,flip.1] lucky!=chest. ** KEPT (pick-wt=3): 96 [copy,95,flip.1] parli!=chest. ** KEPT (pick-wt=3): 98 [copy,97,flip.1] parli!=lucky. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. >>>> Starting back unit deletion with 1. >>>> Starting back unit deletion with 4. >>>> Starting back unit deletion with 6. >>>> Starting back unit deletion with 8. >>>> Starting back unit deletion with 10. >>>> Starting back unit deletion with 12. >>>> Starting back unit deletion with 14. >>>> Starting back unit deletion with 16. >>>> Starting back unit deletion with 18. >>>> Starting back unit deletion with 20. >>>> Starting back unit deletion with 22. >>>> Starting back unit deletion with 23. >>>> Starting back unit deletion with 24. >>>> Starting back unit deletion with 25. >>>> Starting back unit deletion with 26. >>>> Starting back unit deletion with 28. >>>> Starting back unit deletion with 29. >>>> Starting back unit deletion with 30. >>>> Starting back unit deletion with 31. >>>> Starting back unit deletion with 32. >>>> Starting back unit deletion with 34. >>>> Starting back unit deletion with 35. >>>> Starting back unit deletion with 36. >>>> Starting back unit deletion with 38. >>>> Starting back unit deletion with 40. >>>> Starting back unit deletion with 42. >>>> Starting back unit deletion with 44. >>>> Starting back unit deletion with 46. >>>> Starting back unit deletion with 48. >>>> Starting back unit deletion with 50. >>>> Starting back unit deletion with 51. >>>> Starting back unit deletion with 52. >>>> Starting back unit deletion with 54. >>>> Starting back unit deletion with 56. >>>> Starting back unit deletion with 57. >>>> Starting back unit deletion with 59. >>>> Starting back unit deletion with 61. >>>> Starting back unit deletion with 63. >>>> Starting back unit deletion with 65. >>>> Starting back unit deletion with 66. >>>> Starting back unit deletion with 67. >>>> Starting back unit deletion with 68. >>>> Starting back unit deletion with 70. >>>> Starting back unit deletion with 72. >>>> Starting back unit deletion with 73. >>>> Starting back unit deletion with 75. >>>> Starting back unit deletion with 77. >>>> Starting back unit deletion with 78. >>>> Starting back unit deletion with 80. >>>> Starting back unit deletion with 81. >>>> Starting back unit deletion with 82. >>>> Starting back unit deletion with 83. >>>> Starting back unit deletion with 84. >>>> Starting back unit deletion with 85. >>>> Starting back unit deletion with 87. >>>> Starting back unit deletion with 88. >>>> Starting back unit deletion with 90. >>>> Starting back unit deletion with 92. >>>> Starting back unit deletion with 94. >>>> Starting back unit deletion with 96. >>>> Starting back unit deletion with 98. ------------> process sos: ** KEPT (pick-wt=3): 100 [copy,99,flip.1] red=eng. ---> New Demodulator: 101 [new_demod,100] red=eng. ** KEPT (pick-wt=3): 103 [copy,102,flip.1] dog=aspan. ---> New Demodulator: 104 [new_demod,103] dog=aspan. ** KEPT (pick-wt=3): 106 [copy,105,flip.1] green=coffee. ---> New Demodulator: 107 [new_demod,106] green=coffee. ** KEPT (pick-wt=3): 108 [] aukra=atea. ---> New Demodulator: 109 [new_demod,108] aukra=atea. ** KEPT (pick-wt=3): 110 [] old=asnail. ---> New Demodulator: 111 [new_demod,110] old=asnail. ** KEPT (pick-wt=3): 112 [] kool=ayellow. ---> New Demodulator: 113 [new_demod,112] kool=ayellow. ** KEPT (pick-wt=3): 114 [] milk=3. ---> New Demodulator: 115 [new_demod,114] milk=3. ** KEPT (pick-wt=3): 116 [] norw=1. ---> New Demodulator: 117 [new_demod,116] norw=1. ** KEPT (pick-wt=3): 119 [copy,118,flip.1] orange=lucky. ---> New Demodulator: 120 [new_demod,119] orange=lucky. ** KEPT (pick-wt=3): 122 [copy,121,flip.1] parli=japan. ---> New Demodulator: 123 [new_demod,122] parli=japan. ** KEPT (pick-wt=3): 124 [] blue=2. ---> New Demodulator: 125 [new_demod,124] blue=2. ** KEPT (pick-wt=3): 126 [] ivory!=5. ** KEPT (pick-wt=3): 128 [copy,127,demod,107] coffee!=1. ** KEPT (pick-wt=6): 130 [copy,129,demod,107] ivory!=1|coffee=2. ** KEPT (pick-wt=6): 132 [copy,131,demod,107] ivory!=2|coffee=3. ** KEPT (pick-wt=6): 134 [copy,133,demod,107] ivory!=3|coffee=4. ** KEPT (pick-wt=6): 136 [copy,135,demod,107] ivory!=4|coffee=5. ** KEPT (pick-wt=6): 138 [copy,137,demod,107] ivory=1|coffee!=2. ** KEPT (pick-wt=6): 140 [copy,139,demod,107] ivory=2|coffee!=3. ** KEPT (pick-wt=6): 142 [copy,141,demod,107] ivory=3|coffee!=4. ** KEPT (pick-wt=6): 144 [copy,143,demod,107] ivory=4|coffee!=5. ** KEPT (pick-wt=6): 146 [copy,145,demod,113] ayellow!=1|horse=2. ** KEPT (pick-wt=9): 148 [copy,147,demod,113] ayellow!=2|horse=1|horse=3. ** KEPT (pick-wt=9): 150 [copy,149,demod,113] ayellow!=3|horse=2|horse=4. ** KEPT (pick-wt=9): 152 [copy,151,demod,113] ayellow!=4|horse=3|horse=5. ** KEPT (pick-wt=6): 154 [copy,153,demod,113] ayellow!=5|horse=4. ** KEPT (pick-wt=6): 156 [copy,155,demod,113] horse!=1|ayellow=2. ** KEPT (pick-wt=9): 158 [copy,157,demod,113,113] horse!=2|ayellow=1|ayellow=3. ** KEPT (pick-wt=9): 160 [copy,159,demod,113,113] horse!=3|ayellow=2|ayellow=4. ** KEPT (pick-wt=9): 162 [copy,161,demod,113,113] horse!=4|ayellow=3|ayellow=5. ** KEPT (pick-wt=6): 164 [copy,163,demod,113] horse!=5|ayellow=4. ** KEPT (pick-wt=6): 165 [] chest!=1|fox=2. ** KEPT (pick-wt=9): 166 [] chest!=2|fox=1|fox=3. ** KEPT (pick-wt=9): 167 [] chest!=3|fox=2|fox=4. ** KEPT (pick-wt=9): 168 [] chest!=4|fox=3|fox=5. ** KEPT (pick-wt=6): 169 [] chest!=5|fox=4. ** KEPT (pick-wt=6): 170 [] fox!=1|chest=2. ** KEPT (pick-wt=9): 171 [] fox!=2|chest=1|chest=3. ** KEPT (pick-wt=9): 172 [] fox!=3|chest=2|chest=4. ** KEPT (pick-wt=9): 173 [] fox!=4|chest=3|chest=5. ** KEPT (pick-wt=6): 174 [] fox!=5|chest=4. >>>> Starting back demodulation with 101. >> back demodulating 26 with 101. >> back demodulating 25 with 101. >> back demodulating 24 with 101. >> back demodulating 23 with 101. >>>> Starting back unit deletion with 100. >>>> Starting back demodulation with 104. >> back demodulating 57 with 104. >> back demodulating 56 with 104. >> back demodulating 54 with 104. >> back demodulating 52 with 104. >>>> Starting back unit deletion with 103. >>>> Starting back demodulation with 107. >> back demodulating 30 with 107. >> back demodulating 29 with 107. >> back demodulating 28 with 107. >>>> Starting back unit deletion with 106. >>>> Starting back demodulation with 109. >> back demodulating 50 with 109. >> back demodulating 48 with 109. >> back demodulating 42 with 109. >> back demodulating 36 with 109. >>>> Starting back unit deletion with 108. >>>> Starting back demodulation with 111. >> back demodulating 87 with 111. >> back demodulating 85 with 111. >> back demodulating 84 with 111. >> back demodulating 83 with 111. >>>> Starting back unit deletion with 110. >>>> Starting back demodulation with 113. >> back demodulating 92 with 113. >> back demodulating 90 with 113. >> back demodulating 88 with 113. >>>> Starting back unit deletion with 112. >>>> Starting back demodulation with 115. >> back demodulating 81 with 115. >> back demodulating 80 with 115. >> back demodulating 75 with 115. >> back demodulating 70 with 115. >>>> Starting back unit deletion with 114. >>>> Starting back demodulation with 117. >> back demodulating 51 with 117. >> back demodulating 44 with 117. >> back demodulating 38 with 117. >>>> Starting back unit deletion with 116. >>>> Starting back demodulation with 120. >> back demodulating 82 with 120. >> back demodulating 77 with 120. >> back demodulating 72 with 120. >>>> Starting back unit deletion with 119. >>>> Starting back demodulation with 123. >> back demodulating 98 with 123. >> back demodulating 96 with 123. >>>> Starting back unit deletion with 122. >>>> Starting back demodulation with 125. >> back demodulating 34 with 125. >> back demodulating 32 with 125. >>>> Starting back unit deletion with 124. >>>> Starting back unit deletion with 126. >>>> Starting back unit deletion with 128. >>>> Starting back unit deletion with 175. >>>> Starting back unit deletion with 176. >>>> Starting back unit deletion with 177. >>>> Starting back unit deletion with 178. >>>> Starting back unit deletion with 179. >>>> Starting back unit deletion with 180. >>>> Starting back unit deletion with 181. >>>> Starting back unit deletion with 182. 183 back subsumes 138. >>>> Starting back unit deletion with 183. ** KEPT (pick-wt=3): 211 [back_unit_del,183.1,130.2] ivory!=1. >>>> Starting back unit deletion with 184. >>>> Starting back unit deletion with 185. >>>> Starting back unit deletion with 186. >>>> Starting back unit deletion with 187. >>>> Starting back unit deletion with 188. >>>> Starting back unit deletion with 189. >>>> Starting back unit deletion with 190. >>>> Starting back unit deletion with 191. >>>> Starting back unit deletion with 192. >>>> Starting back unit deletion with 193. >>>> Starting back unit deletion with 194. >>>> Starting back unit deletion with 195. >>>> Starting back unit deletion with 196. >>>> Starting back unit deletion with 197. >>>> Starting back unit deletion with 198. >>>> Starting back unit deletion with 199. 200 back subsumes 140. >>>> Starting back unit deletion with 200. Following clause subsumed by 210 during input processing: 0 [back_unit_del,200.1,132.2] ivory!=2. >>>> Starting back unit deletion with 201. >>>> Starting back unit deletion with 202. >>>> Starting back unit deletion with 203. >>>> Starting back unit deletion with 204. >>>> Starting back unit deletion with 205. >>>> Starting back unit deletion with 206. >>>> Starting back unit deletion with 207. >>>> Starting back unit deletion with 208. 209 back subsumes 148. >>>> Starting back unit deletion with 209. ** KEPT (pick-wt=6): 212 [back_unit_del,209.1,160.2] horse!=3|ayellow=4. ** KEPT (pick-wt=3): 213 [back_unit_del,209.1,156.2] horse!=1. 210 back subsumes 132. >>>> Starting back unit deletion with 210. 211 back subsumes 130. >>>> Starting back unit deletion with 211. 212 back subsumes 160. 213 back subsumes 156. >>>> Starting back unit deletion with 213. ======= end of input processing ======= =========== start of search =========== Splitting on clause 134 [copy,133,demod,107] ivory!=3|coffee=4. Case [1] (process 8832): Assumption: 300 [134,split.1] ivory!=3. Splitting on clause 169 [] chest!=5|fox=4. Case [1.1] (process 8833): Assumption: 402 [169,split.1.1] chest!=5. Splitting on clause 170 [] fox!=1|chest=2. Case [1.1.1] (process 8834): Assumption: 407 [170,split.1.1.1] fox!=1. Splitting on clause 174 [] fox!=5|chest=4. Case [1.1.1.1] (process 8835): Assumption: 412 [174,split.1.1.1.1] fox!=5. Splitting on clause 347 [back_unit_del,321.1,251.3] aspan!=4|atea=2. Case [1.1.1.1.1] (process 8836): Assumption: 416 [347,split.1.1.1.1.1] aspan!=4. Splitting on clause 348 [back_unit_del,321.1,217.1] atea=2|atea=4. --- refuted case [1.1.1.1.1.1] Case [1.1.1.1.1.1] (process 8837): Assumption: 432 [348,split.1.1.1.1.1.1] atea=2. -----> EMPTY CLAUSE at 0.00 sec ----> 443 [back_demod,392,demod,435,437,unit_del,1,14] $F. Length of proof is 110. Level of proof is 15. Case [1.1.1.1.1.1] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 13 [] 2!=4. 14 [copy,13,flip.1] 4!=2. 19 [] 3!=5. 20 [copy,19,flip.1] 5!=3. 23 [] red!=green. 24 [] red!=ivory. 25 [] red!=ayellow. 26 [] red!=blue. 29 [] green!=ayellow. 30 [] green!=blue. 31 [] ivory!=ayellow. 32 [] ivory!=blue. 33 [] ayellow!=blue. 34 [copy,33,flip.1] blue!=ayellow. 35 [] eng!=aspan. 37 [] eng!=norw. 38 [copy,37,flip.1] norw!=eng. 39 [] eng!=japan. 40 [copy,39,flip.1] japan!=eng. 41 [] aspan!=aukra. 42 [copy,41,flip.1] aukra!=aspan. 43 [] aspan!=norw. 44 [copy,43,flip.1] norw!=aspan. 45 [] aspan!=japan. 46 [copy,45,flip.1] japan!=aspan. 47 [] aukra!=norw. 48 [copy,47,flip.1] norw!=aukra. 49 [] aukra!=japan. 50 [copy,49,flip.1] japan!=aukra. 51 [] norw!=japan. 55 [] dog!=horse. 56 [copy,55,flip.1] horse!=dog. 68 [] coffee!=atea. 69 [] coffee!=milk. 70 [copy,69,flip.1] milk!=coffee. 71 [] coffee!=orange. 72 [copy,71,flip.1] orange!=coffee. 74 [] atea!=milk. 75 [copy,74,flip.1] milk!=atea. 76 [] atea!=orange. 77 [copy,76,flip.1] orange!=atea. 79 [] milk!=orange. 80 [copy,79,flip.1] orange!=milk. 89 [] kool!=lucky. 90 [copy,89,flip.1] lucky!=kool. 97 [] lucky!=parli. 98 [copy,97,flip.1] parli!=lucky. 99 [] eng=red. 101,100 [copy,99,flip.1] red=eng. 102 [] aspan=dog. 104,103 [copy,102,flip.1] dog=aspan. 105 [] coffee=green. 107,106 [copy,105,flip.1] green=coffee. 109,108 [] aukra=atea. 113,112 [] kool=ayellow. 115,114 [] milk=3. 117,116 [] norw=1. 118 [] lucky=orange. 120,119 [copy,118,flip.1] orange=lucky. 121 [] japan=parli. 123,122 [copy,121,flip.1] parli=japan. 125,124 [] blue=2. 126 [] ivory!=5. 127 [] green!=1. 128 [copy,127,demod,107] coffee!=1. 129 [] ivory!=1|green=2. 130 [copy,129,demod,107] ivory!=1|coffee=2. 133 [] ivory!=3|green=4. 134 [copy,133,demod,107] ivory!=3|coffee=4. 135 [] ivory!=4|green=5. 136 [copy,135,demod,107] ivory!=4|coffee=5. 141 [] ivory=3|green!=4. 142 [copy,141,demod,107] ivory=3|coffee!=4. 155 [] horse!=1|kool=2. 156 [copy,155,demod,113] horse!=1|ayellow=2. 159 [] horse!=3|kool=2|kool=4. 160 [copy,159,demod,113,113] horse!=3|ayellow=2|ayellow=4. 161 [] horse!=4|kool=3|kool=5. 162 [copy,161,demod,113,113] horse!=4|ayellow=3|ayellow=5. 163 [] horse!=5|kool=4. 164 [copy,163,demod,113] horse!=5|ayellow=4. 175 [back_demod,26,demod,101,125] eng!=2. 176 [back_demod,25,demod,101] eng!=ayellow. 177 [back_demod,24,demod,101,flip.1] ivory!=eng. 178 [back_demod,23,demod,101,107] eng!=coffee. 180 [back_demod,56,demod,104] horse!=aspan. 183 [back_demod,30,demod,107,125] coffee!=2. 184 [back_demod,29,demod,107] coffee!=ayellow. 186 [back_demod,50,demod,109] japan!=atea. 187 [back_demod,48,demod,117,109,flip.1] atea!=1. 188 [back_demod,42,demod,109] atea!=aspan. 195 [back_demod,90,demod,113] lucky!=ayellow. 198 [back_demod,80,demod,120,115] lucky!=3. 199 [back_demod,75,demod,115,flip.1] atea!=3. 200 [back_demod,70,demod,115,flip.1] coffee!=3. 201 [back_demod,51,demod,117,flip.1] japan!=1. 202 [back_demod,44,demod,117,flip.1] aspan!=1. 203 [back_demod,38,demod,117,flip.1] eng!=1. 205 [back_demod,77,demod,120] lucky!=atea. 206 [back_demod,72,demod,120] lucky!=coffee. 207 [back_demod,98,demod,123,flip.1] lucky!=japan. 209 [back_demod,34,demod,125,flip.1] ayellow!=2. 210 [back_demod,32,demod,125] ivory!=2. 211 [back_unit_del,183.1,130.2] ivory!=1. 212 [back_unit_del,209.1,160.2] horse!=3|ayellow=4. 213 [back_unit_del,209.1,156.2] horse!=1. 215 [para_into,103.1.1,2.5.1,demod,104,104,104,104,unit_del,202,flip.1] aspan=5|aspan=2|aspan=3|aspan=4. 217 [para_into,108.1.1,2.5.1,demod,109,109,109,109,unit_del,187,199,flip.1] atea=5|atea=2|atea=4. 218 [para_into,112.1.1,2.5.1,demod,113,113,113,113,unit_del,209,flip.1] ayellow=5|ayellow=1|ayellow=3|ayellow=4. 221 [binary,126.1,2.5,unit_del,211,210] ivory=3|ivory=4. 224 [para_into,176.1.1,2.3.1,unit_del,203,175,flip.1] ayellow!=3|eng=4|eng=5. 225 [para_into,177.1.1,2.4.1,unit_del,211,210,126,flip.1] eng!=4|ivory=3. 227 [para_into,178.1.1,2.5.1,unit_del,203,175,flip.1] coffee!=5|eng=3|eng=4. 236 [para_into,180.1.1,2.2.1,unit_del,213,flip.1] aspan!=2|horse=3|horse=4|horse=5. 245 [para_into,184.1.1,2.5.1,unit_del,128,183,200,flip.1] ayellow!=5|coffee=4. 249 [para_into,186.1.1,2.2.1,unit_del,201,flip.1] atea!=2|japan=3|japan=4|japan=5. 251 [para_into,188.1.1,2.4.1,unit_del,187,199,flip.1] aspan!=4|atea=2|atea=5. 289 [para_into,205.1.1,2.2.1,unit_del,198,flip.1] atea!=2|lucky=1|lucky=4|lucky=5. 293 [para_into,207.1.1,2.4.1,unit_del,198,flip.1] japan!=4|lucky=1|lucky=2|lucky=5. 300 [134,split.1] ivory!=3. 301 [back_unit_del,300.1,225.2] eng!=4. 303,302 [back_unit_del,300.1,221.1] ivory=4. 304 [back_unit_del,300.1,142.1] coffee!=4. 306 [back_unit_del,301.1,227.3] coffee!=5|eng=3. 307 [back_unit_del,301.1,224.2] ayellow!=3|eng=5. 311,310 [back_demod,136,demod,303,unit_del,1] coffee=5. 312 [back_demod,31,demod,303,flip.1] ayellow!=4. 313 [back_unit_del,304.1,245.2] ayellow!=5. 315,314 [back_demod,306,demod,311,unit_del,1] eng=3. 317 [back_demod,206,demod,311] lucky!=5. 321 [back_demod,68,demod,311,flip.1] atea!=5. 325 [back_unit_del,312.1,218.4,unit_del,313] ayellow=1|ayellow=3. 326 [back_unit_del,312.1,212.2] horse!=3. 327 [back_unit_del,312.1,164.2] horse!=5. 328 [back_unit_del,313.1,162.3] horse!=4|ayellow=3. 329 [back_demod,307,demod,315,unit_del,20] ayellow!=3. 332 [back_demod,40,demod,315] japan!=3. 333 [back_demod,35,demod,315,flip.1] aspan!=3. 335 [back_unit_del,317.1,293.4] japan!=4|lucky=1|lucky=2. 336 [back_unit_del,317.1,289.4] atea!=2|lucky=1|lucky=4. 347 [back_unit_del,321.1,251.3] aspan!=4|atea=2. 348 [back_unit_del,321.1,217.1] atea=2|atea=4. 350 [back_unit_del,326.1,236.2,unit_del,327] aspan!=2|horse=4. 352 [back_unit_del,329.1,328.2] horse!=4. 354,353 [back_unit_del,329.1,325.2] ayellow=1. 362 [back_unit_del,332.1,249.2] atea!=2|japan=4|japan=5. 368 [back_unit_del,333.1,215.3] aspan=5|aspan=2|aspan=4. 369 [back_unit_del,352.1,350.2] aspan!=2. 375 [back_demod,195,demod,354] lucky!=1. 378 [back_unit_del,369.1,368.2] aspan=5|aspan=4. 391 [back_unit_del,375.1,336.2] atea!=2|lucky=4. 392 [back_unit_del,375.1,335.2] japan!=4|lucky=2. 416 [347,split.1.1.1.1.1] aspan!=4. 419,418 [back_unit_del,416.1,378.2] aspan=5. 425 [back_demod,46,demod,419] japan!=5. 428 [back_unit_del,425.1,362.3] atea!=2|japan=4. 433,432 [348,split.1.1.1.1.1.1] atea=2. 435,434 [back_demod,428,demod,433,unit_del,1] japan=4. 437,436 [back_demod,391,demod,433,unit_del,1] lucky=4. 443 [back_demod,392,demod,435,437,unit_del,1,14] $F. ------------ end of proof ------------- ------- statistics (process 8837) ------- clauses given 85 clauses generated 578 clauses kept 357 clauses forward subsumed 460 clauses back subsumed 143 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8837 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1.1.1.1]. --- refuted case [1.1.1.1.1.2] Case [1.1.1.1.1.2] (process 8838): Assumption: 433 [348,split.1.1.1.1.1.2] atea=4. -----> EMPTY CLAUSE at 0.00 sec ----> 443 [back_demod,393,demod,436,438,unit_del,1,14] $F. Length of proof is 110. Level of proof is 15. Case [1.1.1.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 13 [] 2!=4. 14 [copy,13,flip.1] 4!=2. 19 [] 3!=5. 20 [copy,19,flip.1] 5!=3. 23 [] red!=green. 24 [] red!=ivory. 25 [] red!=ayellow. 26 [] red!=blue. 29 [] green!=ayellow. 30 [] green!=blue. 31 [] ivory!=ayellow. 32 [] ivory!=blue. 33 [] ayellow!=blue. 34 [copy,33,flip.1] blue!=ayellow. 35 [] eng!=aspan. 37 [] eng!=norw. 38 [copy,37,flip.1] norw!=eng. 39 [] eng!=japan. 40 [copy,39,flip.1] japan!=eng. 41 [] aspan!=aukra. 42 [copy,41,flip.1] aukra!=aspan. 43 [] aspan!=norw. 44 [copy,43,flip.1] norw!=aspan. 45 [] aspan!=japan. 46 [copy,45,flip.1] japan!=aspan. 47 [] aukra!=norw. 48 [copy,47,flip.1] norw!=aukra. 49 [] aukra!=japan. 50 [copy,49,flip.1] japan!=aukra. 51 [] norw!=japan. 55 [] dog!=horse. 56 [copy,55,flip.1] horse!=dog. 68 [] coffee!=atea. 69 [] coffee!=milk. 70 [copy,69,flip.1] milk!=coffee. 71 [] coffee!=orange. 72 [copy,71,flip.1] orange!=coffee. 74 [] atea!=milk. 75 [copy,74,flip.1] milk!=atea. 76 [] atea!=orange. 77 [copy,76,flip.1] orange!=atea. 79 [] milk!=orange. 80 [copy,79,flip.1] orange!=milk. 89 [] kool!=lucky. 90 [copy,89,flip.1] lucky!=kool. 97 [] lucky!=parli. 98 [copy,97,flip.1] parli!=lucky. 99 [] eng=red. 101,100 [copy,99,flip.1] red=eng. 102 [] aspan=dog. 104,103 [copy,102,flip.1] dog=aspan. 105 [] coffee=green. 107,106 [copy,105,flip.1] green=coffee. 109,108 [] aukra=atea. 113,112 [] kool=ayellow. 115,114 [] milk=3. 117,116 [] norw=1. 118 [] lucky=orange. 120,119 [copy,118,flip.1] orange=lucky. 121 [] japan=parli. 123,122 [copy,121,flip.1] parli=japan. 125,124 [] blue=2. 126 [] ivory!=5. 127 [] green!=1. 128 [copy,127,demod,107] coffee!=1. 129 [] ivory!=1|green=2. 130 [copy,129,demod,107] ivory!=1|coffee=2. 133 [] ivory!=3|green=4. 134 [copy,133,demod,107] ivory!=3|coffee=4. 135 [] ivory!=4|green=5. 136 [copy,135,demod,107] ivory!=4|coffee=5. 141 [] ivory=3|green!=4. 142 [copy,141,demod,107] ivory=3|coffee!=4. 155 [] horse!=1|kool=2. 156 [copy,155,demod,113] horse!=1|ayellow=2. 159 [] horse!=3|kool=2|kool=4. 160 [copy,159,demod,113,113] horse!=3|ayellow=2|ayellow=4. 161 [] horse!=4|kool=3|kool=5. 162 [copy,161,demod,113,113] horse!=4|ayellow=3|ayellow=5. 163 [] horse!=5|kool=4. 164 [copy,163,demod,113] horse!=5|ayellow=4. 175 [back_demod,26,demod,101,125] eng!=2. 176 [back_demod,25,demod,101] eng!=ayellow. 177 [back_demod,24,demod,101,flip.1] ivory!=eng. 178 [back_demod,23,demod,101,107] eng!=coffee. 180 [back_demod,56,demod,104] horse!=aspan. 183 [back_demod,30,demod,107,125] coffee!=2. 184 [back_demod,29,demod,107] coffee!=ayellow. 186 [back_demod,50,demod,109] japan!=atea. 187 [back_demod,48,demod,117,109,flip.1] atea!=1. 188 [back_demod,42,demod,109] atea!=aspan. 195 [back_demod,90,demod,113] lucky!=ayellow. 198 [back_demod,80,demod,120,115] lucky!=3. 199 [back_demod,75,demod,115,flip.1] atea!=3. 200 [back_demod,70,demod,115,flip.1] coffee!=3. 201 [back_demod,51,demod,117,flip.1] japan!=1. 202 [back_demod,44,demod,117,flip.1] aspan!=1. 203 [back_demod,38,demod,117,flip.1] eng!=1. 205 [back_demod,77,demod,120] lucky!=atea. 206 [back_demod,72,demod,120] lucky!=coffee. 207 [back_demod,98,demod,123,flip.1] lucky!=japan. 209 [back_demod,34,demod,125,flip.1] ayellow!=2. 210 [back_demod,32,demod,125] ivory!=2. 211 [back_unit_del,183.1,130.2] ivory!=1. 212 [back_unit_del,209.1,160.2] horse!=3|ayellow=4. 213 [back_unit_del,209.1,156.2] horse!=1. 215 [para_into,103.1.1,2.5.1,demod,104,104,104,104,unit_del,202,flip.1] aspan=5|aspan=2|aspan=3|aspan=4. 217 [para_into,108.1.1,2.5.1,demod,109,109,109,109,unit_del,187,199,flip.1] atea=5|atea=2|atea=4. 218 [para_into,112.1.1,2.5.1,demod,113,113,113,113,unit_del,209,flip.1] ayellow=5|ayellow=1|ayellow=3|ayellow=4. 221 [binary,126.1,2.5,unit_del,211,210] ivory=3|ivory=4. 224 [para_into,176.1.1,2.3.1,unit_del,203,175,flip.1] ayellow!=3|eng=4|eng=5. 225 [para_into,177.1.1,2.4.1,unit_del,211,210,126,flip.1] eng!=4|ivory=3. 227 [para_into,178.1.1,2.5.1,unit_del,203,175,flip.1] coffee!=5|eng=3|eng=4. 236 [para_into,180.1.1,2.2.1,unit_del,213,flip.1] aspan!=2|horse=3|horse=4|horse=5. 245 [para_into,184.1.1,2.5.1,unit_del,128,183,200,flip.1] ayellow!=5|coffee=4. 248 [para_into,186.1.1,2.4.1,unit_del,201,flip.1] atea!=4|japan=2|japan=3|japan=5. 251 [para_into,188.1.1,2.4.1,unit_del,187,199,flip.1] aspan!=4|atea=2|atea=5. 288 [para_into,205.1.1,2.4.1,unit_del,198,flip.1] atea!=4|lucky=1|lucky=2|lucky=5. 294 [para_into,207.1.1,2.2.1,unit_del,198,flip.1] japan!=2|lucky=1|lucky=4|lucky=5. 300 [134,split.1] ivory!=3. 301 [back_unit_del,300.1,225.2] eng!=4. 303,302 [back_unit_del,300.1,221.1] ivory=4. 304 [back_unit_del,300.1,142.1] coffee!=4. 306 [back_unit_del,301.1,227.3] coffee!=5|eng=3. 307 [back_unit_del,301.1,224.2] ayellow!=3|eng=5. 311,310 [back_demod,136,demod,303,unit_del,1] coffee=5. 312 [back_demod,31,demod,303,flip.1] ayellow!=4. 313 [back_unit_del,304.1,245.2] ayellow!=5. 315,314 [back_demod,306,demod,311,unit_del,1] eng=3. 317 [back_demod,206,demod,311] lucky!=5. 321 [back_demod,68,demod,311,flip.1] atea!=5. 325 [back_unit_del,312.1,218.4,unit_del,313] ayellow=1|ayellow=3. 326 [back_unit_del,312.1,212.2] horse!=3. 327 [back_unit_del,312.1,164.2] horse!=5. 328 [back_unit_del,313.1,162.3] horse!=4|ayellow=3. 329 [back_demod,307,demod,315,unit_del,20] ayellow!=3. 332 [back_demod,40,demod,315] japan!=3. 333 [back_demod,35,demod,315,flip.1] aspan!=3. 334 [back_unit_del,317.1,294.4] japan!=2|lucky=1|lucky=4. 337 [back_unit_del,317.1,288.4] atea!=4|lucky=1|lucky=2. 347 [back_unit_del,321.1,251.3] aspan!=4|atea=2. 348 [back_unit_del,321.1,217.1] atea=2|atea=4. 350 [back_unit_del,326.1,236.2,unit_del,327] aspan!=2|horse=4. 352 [back_unit_del,329.1,328.2] horse!=4. 354,353 [back_unit_del,329.1,325.2] ayellow=1. 363 [back_unit_del,332.1,248.3] atea!=4|japan=2|japan=5. 368 [back_unit_del,333.1,215.3] aspan=5|aspan=2|aspan=4. 369 [back_unit_del,352.1,350.2] aspan!=2. 375 [back_demod,195,demod,354] lucky!=1. 378 [back_unit_del,369.1,368.2] aspan=5|aspan=4. 390 [back_unit_del,375.1,337.2] atea!=4|lucky=2. 393 [back_unit_del,375.1,334.2] japan!=2|lucky=4. 416 [347,split.1.1.1.1.1] aspan!=4. 419,418 [back_unit_del,416.1,378.2] aspan=5. 425 [back_demod,46,demod,419] japan!=5. 427 [back_unit_del,425.1,363.3] atea!=4|japan=2. 434,433 [348,split.1.1.1.1.1.2] atea=4. 436,435 [back_demod,427,demod,434,unit_del,1] japan=2. 438,437 [back_demod,390,demod,434,unit_del,1] lucky=2. 443 [back_demod,393,demod,436,438,unit_del,1,14] $F. ------------ end of proof ------------- ------- statistics (process 8838) ------- clauses given 85 clauses generated 578 clauses kept 357 clauses forward subsumed 459 clauses back subsumed 145 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8838 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1.1.1.2]. ------- statistics (process 8836) ------- clauses given 85 clauses generated 578 clauses kept 350 clauses forward subsumed 449 clauses back subsumed 143 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8836 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1.1.1]. --- refuted case [1.1.1.1.2] Case [1.1.1.1.2] (process 8839): Assumption: 418 [347,split.1.1.1.1.2] atea=2. -----> EMPTY CLAUSE at 0.00 sec ----> 441 [back_unit_del,427.1,361.3,demod,440,431,unit_del,1,16] $F. Length of proof is 114. Level of proof is 17. Case [1.1.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 15 [] 2!=5. 16 [copy,15,flip.1] 5!=2. 19 [] 3!=5. 20 [copy,19,flip.1] 5!=3. 21 [] 4!=5. 22 [copy,21,flip.1] 5!=4. 23 [] red!=green. 24 [] red!=ivory. 25 [] red!=ayellow. 26 [] red!=blue. 29 [] green!=ayellow. 30 [] green!=blue. 31 [] ivory!=ayellow. 32 [] ivory!=blue. 33 [] ayellow!=blue. 34 [copy,33,flip.1] blue!=ayellow. 35 [] eng!=aspan. 37 [] eng!=norw. 38 [copy,37,flip.1] norw!=eng. 39 [] eng!=japan. 40 [copy,39,flip.1] japan!=eng. 41 [] aspan!=aukra. 42 [copy,41,flip.1] aukra!=aspan. 43 [] aspan!=norw. 44 [copy,43,flip.1] norw!=aspan. 45 [] aspan!=japan. 46 [copy,45,flip.1] japan!=aspan. 47 [] aukra!=norw. 48 [copy,47,flip.1] norw!=aukra. 49 [] aukra!=japan. 50 [copy,49,flip.1] japan!=aukra. 51 [] norw!=japan. 52 [] dog!=asnail. 53 [] dog!=fox. 54 [copy,53,flip.1] fox!=dog. 55 [] dog!=horse. 56 [copy,55,flip.1] horse!=dog. 58 [] asnail!=fox. 59 [copy,58,flip.1] fox!=asnail. 60 [] asnail!=horse. 61 [copy,60,flip.1] horse!=asnail. 64 [] fox!=horse. 65 [copy,64,flip.1] horse!=fox. 68 [] coffee!=atea. 69 [] coffee!=milk. 70 [copy,69,flip.1] milk!=coffee. 74 [] atea!=milk. 75 [copy,74,flip.1] milk!=atea. 83 [] old!=kool. 86 [] old!=parli. 87 [copy,86,flip.1] parli!=old. 99 [] eng=red. 101,100 [copy,99,flip.1] red=eng. 102 [] aspan=dog. 104,103 [copy,102,flip.1] dog=aspan. 105 [] coffee=green. 107,106 [copy,105,flip.1] green=coffee. 109,108 [] aukra=atea. 111,110 [] old=asnail. 113,112 [] kool=ayellow. 115,114 [] milk=3. 117,116 [] norw=1. 121 [] japan=parli. 123,122 [copy,121,flip.1] parli=japan. 125,124 [] blue=2. 126 [] ivory!=5. 127 [] green!=1. 128 [copy,127,demod,107] coffee!=1. 129 [] ivory!=1|green=2. 130 [copy,129,demod,107] ivory!=1|coffee=2. 133 [] ivory!=3|green=4. 134 [copy,133,demod,107] ivory!=3|coffee=4. 135 [] ivory!=4|green=5. 136 [copy,135,demod,107] ivory!=4|coffee=5. 141 [] ivory=3|green!=4. 142 [copy,141,demod,107] ivory=3|coffee!=4. 155 [] horse!=1|kool=2. 156 [copy,155,demod,113] horse!=1|ayellow=2. 159 [] horse!=3|kool=2|kool=4. 160 [copy,159,demod,113,113] horse!=3|ayellow=2|ayellow=4. 161 [] horse!=4|kool=3|kool=5. 162 [copy,161,demod,113,113] horse!=4|ayellow=3|ayellow=5. 163 [] horse!=5|kool=4. 164 [copy,163,demod,113] horse!=5|ayellow=4. 170 [] fox!=1|chest=2. 174 [] fox!=5|chest=4. 175 [back_demod,26,demod,101,125] eng!=2. 176 [back_demod,25,demod,101] eng!=ayellow. 177 [back_demod,24,demod,101,flip.1] ivory!=eng. 178 [back_demod,23,demod,101,107] eng!=coffee. 180 [back_demod,56,demod,104] horse!=aspan. 181 [back_demod,54,demod,104] fox!=aspan. 182 [back_demod,52,demod,104] aspan!=asnail. 183 [back_demod,30,demod,107,125] coffee!=2. 184 [back_demod,29,demod,107] coffee!=ayellow. 186 [back_demod,50,demod,109] japan!=atea. 187 [back_demod,48,demod,117,109,flip.1] atea!=1. 188 [back_demod,42,demod,109] atea!=aspan. 190 [back_demod,87,demod,123,111] japan!=asnail. 193 [back_demod,83,demod,111,113,flip.1] ayellow!=asnail. 199 [back_demod,75,demod,115,flip.1] atea!=3. 200 [back_demod,70,demod,115,flip.1] coffee!=3. 201 [back_demod,51,demod,117,flip.1] japan!=1. 202 [back_demod,44,demod,117,flip.1] aspan!=1. 203 [back_demod,38,demod,117,flip.1] eng!=1. 209 [back_demod,34,demod,125,flip.1] ayellow!=2. 210 [back_demod,32,demod,125] ivory!=2. 211 [back_unit_del,183.1,130.2] ivory!=1. 212 [back_unit_del,209.1,160.2] horse!=3|ayellow=4. 213 [back_unit_del,209.1,156.2] horse!=1. 221 [binary,126.1,2.5,unit_del,211,210] ivory=3|ivory=4. 224 [para_into,176.1.1,2.3.1,unit_del,203,175,flip.1] ayellow!=3|eng=4|eng=5. 225 [para_into,177.1.1,2.4.1,unit_del,211,210,126,flip.1] eng!=4|ivory=3. 227 [para_into,178.1.1,2.5.1,unit_del,203,175,flip.1] coffee!=5|eng=3|eng=4. 236 [para_into,180.1.1,2.2.1,unit_del,213,flip.1] aspan!=2|horse=3|horse=4|horse=5. 238 [para_into,181.1.1,2.4.1,flip.1] aspan!=4|fox=1|fox=2|fox=3|fox=5. 242 [para_into,182.1.1,2.4.1,unit_del,202,flip.1] asnail!=4|aspan=2|aspan=3|aspan=5. 245 [para_into,184.1.1,2.5.1,unit_del,128,183,200,flip.1] ayellow!=5|coffee=4. 249 [para_into,186.1.1,2.2.1,unit_del,201,flip.1] atea!=2|japan=3|japan=4|japan=5. 251 [para_into,188.1.1,2.4.1,unit_del,187,199,flip.1] aspan!=4|atea=2|atea=5. 255 [para_into,190.1.1,2.5.1,unit_del,201,flip.1] asnail!=5|japan=2|japan=3|japan=4. 271 [para_into,193.1.1,2.1.1,unit_del,209,flip.1] asnail!=1|ayellow=3|ayellow=4|ayellow=5. 299 [binary,213.1,2.1] horse=2|horse=3|horse=4|horse=5. 300 [134,split.1] ivory!=3. 301 [back_unit_del,300.1,225.2] eng!=4. 303,302 [back_unit_del,300.1,221.1] ivory=4. 304 [back_unit_del,300.1,142.1] coffee!=4. 306 [back_unit_del,301.1,227.3] coffee!=5|eng=3. 307 [back_unit_del,301.1,224.2] ayellow!=3|eng=5. 311,310 [back_demod,136,demod,303,unit_del,1] coffee=5. 312 [back_demod,31,demod,303,flip.1] ayellow!=4. 313 [back_unit_del,304.1,245.2] ayellow!=5. 315,314 [back_demod,306,demod,311,unit_del,1] eng=3. 321 [back_demod,68,demod,311,flip.1] atea!=5. 322 [back_unit_del,312.1,271.3,unit_del,313] asnail!=1|ayellow=3. 326 [back_unit_del,312.1,212.2] horse!=3. 327 [back_unit_del,312.1,164.2] horse!=5. 328 [back_unit_del,313.1,162.3] horse!=4|ayellow=3. 329 [back_demod,307,demod,315,unit_del,20] ayellow!=3. 332 [back_demod,40,demod,315] japan!=3. 333 [back_demod,35,demod,315,flip.1] aspan!=3. 347 [back_unit_del,321.1,251.3] aspan!=4|atea=2. 349 [back_unit_del,326.1,299.2,unit_del,327] horse=2|horse=4. 350 [back_unit_del,326.1,236.2,unit_del,327] aspan!=2|horse=4. 352 [back_unit_del,329.1,328.2] horse!=4. 355 [back_unit_del,329.1,322.2] asnail!=1. 361 [back_unit_del,332.1,255.3] asnail!=5|japan=2|japan=4. 362 [back_unit_del,332.1,249.2] atea!=2|japan=4|japan=5. 366 [back_unit_del,333.1,242.3] asnail!=4|aspan=2|aspan=5. 369 [back_unit_del,352.1,350.2] aspan!=2. 371,370 [back_unit_del,352.1,349.2] horse=2. 380 [back_unit_del,369.1,366.2] asnail!=4|aspan=5. 382 [back_demod,65,demod,371,flip.1] fox!=2. 383 [back_demod,61,demod,371,flip.1] asnail!=2. 396 [back_unit_del,382.1,238.3] aspan!=4|fox=1|fox=3|fox=5. 399 [binary,355.1,2.1,unit_del,383] asnail=3|asnail=4|asnail=5. 407 [170,split.1.1.1] fox!=1. 410 [back_unit_del,407.1,396.2] aspan!=4|fox=3|fox=5. 412 [174,split.1.1.1.1] fox!=5. 413 [back_unit_del,412.1,410.3] aspan!=4|fox=3. 417,416 [347,split_neg.1.1.1.1.2] aspan=4. 419,418 [347,split.1.1.1.1.2] atea=2. 421,420 [back_demod,413,demod,417,unit_del,1] fox=3. 423 [back_demod,380,demod,417,unit_del,22] asnail!=4. 427 [back_demod,46,demod,417] japan!=4. 431,430 [back_demod,362,demod,419,unit_del,1,427] japan=5. 438 [back_demod,59,demod,421,flip.1] asnail!=3. 440,439 [back_unit_del,423.1,399.2,unit_del,438] asnail=5. 441 [back_unit_del,427.1,361.3,demod,440,431,unit_del,1,16] $F. ------------ end of proof ------------- ------- statistics (process 8839) ------- clauses given 79 clauses generated 540 clauses kept 353 clauses forward subsumed 433 clauses back subsumed 136 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8839 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1.1.2]. ------- statistics (process 8835) ------- clauses given 79 clauses generated 537 clauses kept 336 clauses forward subsumed 408 clauses back subsumed 131 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8835 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1.1]. --- refuted case [1.1.1.2] Case [1.1.1.2] (process 8840): Assumption: 414 [174,split.1.1.1.2] chest=4. -----> EMPTY CLAUSE at 0.00 sec ----> 435 [back_demod,347,demod,424,unit_del,1,431] $F. Length of proof is 105. Level of proof is 15. Case [1.1.1.2] ---------------- PROOF ---------------- 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 19 [] 3!=5. 20 [copy,19,flip.1] 5!=3. 21 [] 4!=5. 22 [copy,21,flip.1] 5!=4. 23 [] red!=green. 24 [] red!=ivory. 25 [] red!=ayellow. 26 [] red!=blue. 29 [] green!=ayellow. 30 [] green!=blue. 31 [] ivory!=ayellow. 32 [] ivory!=blue. 33 [] ayellow!=blue. 34 [copy,33,flip.1] blue!=ayellow. 35 [] eng!=aspan. 37 [] eng!=norw. 38 [copy,37,flip.1] norw!=eng. 41 [] aspan!=aukra. 42 [copy,41,flip.1] aukra!=aspan. 43 [] aspan!=norw. 44 [copy,43,flip.1] norw!=aspan. 47 [] aukra!=norw. 48 [copy,47,flip.1] norw!=aukra. 53 [] dog!=fox. 54 [copy,53,flip.1] fox!=dog. 55 [] dog!=horse. 56 [copy,55,flip.1] horse!=dog. 64 [] fox!=horse. 65 [copy,64,flip.1] horse!=fox. 68 [] coffee!=atea. 69 [] coffee!=milk. 70 [copy,69,flip.1] milk!=coffee. 71 [] coffee!=orange. 72 [copy,71,flip.1] orange!=coffee. 74 [] atea!=milk. 75 [copy,74,flip.1] milk!=atea. 76 [] atea!=orange. 77 [copy,76,flip.1] orange!=atea. 79 [] milk!=orange. 80 [copy,79,flip.1] orange!=milk. 89 [] kool!=lucky. 90 [copy,89,flip.1] lucky!=kool. 93 [] chest!=lucky. 94 [copy,93,flip.1] lucky!=chest. 99 [] eng=red. 101,100 [copy,99,flip.1] red=eng. 102 [] aspan=dog. 104,103 [copy,102,flip.1] dog=aspan. 105 [] coffee=green. 107,106 [copy,105,flip.1] green=coffee. 109,108 [] aukra=atea. 113,112 [] kool=ayellow. 115,114 [] milk=3. 117,116 [] norw=1. 118 [] lucky=orange. 120,119 [copy,118,flip.1] orange=lucky. 125,124 [] blue=2. 126 [] ivory!=5. 127 [] green!=1. 128 [copy,127,demod,107] coffee!=1. 129 [] ivory!=1|green=2. 130 [copy,129,demod,107] ivory!=1|coffee=2. 133 [] ivory!=3|green=4. 134 [copy,133,demod,107] ivory!=3|coffee=4. 135 [] ivory!=4|green=5. 136 [copy,135,demod,107] ivory!=4|coffee=5. 141 [] ivory=3|green!=4. 142 [copy,141,demod,107] ivory=3|coffee!=4. 155 [] horse!=1|kool=2. 156 [copy,155,demod,113] horse!=1|ayellow=2. 159 [] horse!=3|kool=2|kool=4. 160 [copy,159,demod,113,113] horse!=3|ayellow=2|ayellow=4. 161 [] horse!=4|kool=3|kool=5. 162 [copy,161,demod,113,113] horse!=4|ayellow=3|ayellow=5. 163 [] horse!=5|kool=4. 164 [copy,163,demod,113] horse!=5|ayellow=4. 170 [] fox!=1|chest=2. 174 [] fox!=5|chest=4. 175 [back_demod,26,demod,101,125] eng!=2. 176 [back_demod,25,demod,101] eng!=ayellow. 177 [back_demod,24,demod,101,flip.1] ivory!=eng. 178 [back_demod,23,demod,101,107] eng!=coffee. 180 [back_demod,56,demod,104] horse!=aspan. 181 [back_demod,54,demod,104] fox!=aspan. 183 [back_demod,30,demod,107,125] coffee!=2. 184 [back_demod,29,demod,107] coffee!=ayellow. 187 [back_demod,48,demod,117,109,flip.1] atea!=1. 188 [back_demod,42,demod,109] atea!=aspan. 195 [back_demod,90,demod,113] lucky!=ayellow. 198 [back_demod,80,demod,120,115] lucky!=3. 199 [back_demod,75,demod,115,flip.1] atea!=3. 200 [back_demod,70,demod,115,flip.1] coffee!=3. 202 [back_demod,44,demod,117,flip.1] aspan!=1. 203 [back_demod,38,demod,117,flip.1] eng!=1. 205 [back_demod,77,demod,120] lucky!=atea. 206 [back_demod,72,demod,120] lucky!=coffee. 209 [back_demod,34,demod,125,flip.1] ayellow!=2. 210 [back_demod,32,demod,125] ivory!=2. 211 [back_unit_del,183.1,130.2] ivory!=1. 212 [back_unit_del,209.1,160.2] horse!=3|ayellow=4. 213 [back_unit_del,209.1,156.2] horse!=1. 215 [para_into,103.1.1,2.5.1,demod,104,104,104,104,unit_del,202,flip.1] aspan=5|aspan=2|aspan=3|aspan=4. 218 [para_into,112.1.1,2.5.1,demod,113,113,113,113,unit_del,209,flip.1] ayellow=5|ayellow=1|ayellow=3|ayellow=4. 221 [binary,126.1,2.5,unit_del,211,210] ivory=3|ivory=4. 224 [para_into,176.1.1,2.3.1,unit_del,203,175,flip.1] ayellow!=3|eng=4|eng=5. 225 [para_into,177.1.1,2.4.1,unit_del,211,210,126,flip.1] eng!=4|ivory=3. 227 [para_into,178.1.1,2.5.1,unit_del,203,175,flip.1] coffee!=5|eng=3|eng=4. 236 [para_into,180.1.1,2.2.1,unit_del,213,flip.1] aspan!=2|horse=3|horse=4|horse=5. 237 [para_into,181.1.1,2.5.1,flip.1] aspan!=5|fox=1|fox=2|fox=3|fox=4. 245 [para_into,184.1.1,2.5.1,unit_del,128,183,200,flip.1] ayellow!=5|coffee=4. 251 [para_into,188.1.1,2.4.1,unit_del,187,199,flip.1] aspan!=4|atea=2|atea=5. 289 [para_into,205.1.1,2.2.1,unit_del,198,flip.1] atea!=2|lucky=1|lucky=4|lucky=5. 299 [binary,213.1,2.1] horse=2|horse=3|horse=4|horse=5. 300 [134,split.1] ivory!=3. 301 [back_unit_del,300.1,225.2] eng!=4. 303,302 [back_unit_del,300.1,221.1] ivory=4. 304 [back_unit_del,300.1,142.1] coffee!=4. 306 [back_unit_del,301.1,227.3] coffee!=5|eng=3. 307 [back_unit_del,301.1,224.2] ayellow!=3|eng=5. 311,310 [back_demod,136,demod,303,unit_del,1] coffee=5. 312 [back_demod,31,demod,303,flip.1] ayellow!=4. 313 [back_unit_del,304.1,245.2] ayellow!=5. 315,314 [back_demod,306,demod,311,unit_del,1] eng=3. 317 [back_demod,206,demod,311] lucky!=5. 321 [back_demod,68,demod,311,flip.1] atea!=5. 325 [back_unit_del,312.1,218.4,unit_del,313] ayellow=1|ayellow=3. 326 [back_unit_del,312.1,212.2] horse!=3. 327 [back_unit_del,312.1,164.2] horse!=5. 328 [back_unit_del,313.1,162.3] horse!=4|ayellow=3. 329 [back_demod,307,demod,315,unit_del,20] ayellow!=3. 333 [back_demod,35,demod,315,flip.1] aspan!=3. 336 [back_unit_del,317.1,289.4] atea!=2|lucky=1|lucky=4. 347 [back_unit_del,321.1,251.3] aspan!=4|atea=2. 349 [back_unit_del,326.1,299.2,unit_del,327] horse=2|horse=4. 350 [back_unit_del,326.1,236.2,unit_del,327] aspan!=2|horse=4. 352 [back_unit_del,329.1,328.2] horse!=4. 354,353 [back_unit_del,329.1,325.2] ayellow=1. 368 [back_unit_del,333.1,215.3] aspan=5|aspan=2|aspan=4. 369 [back_unit_del,352.1,350.2] aspan!=2. 371,370 [back_unit_del,352.1,349.2] horse=2. 375 [back_demod,195,demod,354] lucky!=1. 378 [back_unit_del,369.1,368.2] aspan=5|aspan=4. 382 [back_demod,65,demod,371,flip.1] fox!=2. 391 [back_unit_del,375.1,336.2] atea!=2|lucky=4. 397 [back_unit_del,382.1,237.3] aspan!=5|fox=1|fox=3|fox=4. 407 [170,split.1.1.1] fox!=1. 409 [back_unit_del,407.1,397.2] aspan!=5|fox=3|fox=4. 413,412 [174,split_neg.1.1.1.2] fox=5. 415,414 [174,split.1.1.1.2] chest=4. 416 [back_demod,409,demod,413,413,unit_del,20,22] aspan!=5. 422 [back_demod,94,demod,415] lucky!=4. 424,423 [back_unit_del,416.1,378.1] aspan=4. 431 [back_unit_del,422.1,391.2] atea!=2. 435 [back_demod,347,demod,424,unit_del,1,431] $F. ------------ end of proof ------------- ------- statistics (process 8840) ------- clauses given 77 clauses generated 539 clauses kept 350 clauses forward subsumed 424 clauses back subsumed 136 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8840 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1.2]. ------- statistics (process 8834) ------- clauses given 77 clauses generated 528 clauses kept 332 clauses forward subsumed 402 clauses back subsumed 127 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8834 finished Mon Aug 2 15:31:11 2004 Refuted case [1.1.1]. Possible model detected on branch [1.1.2]. Case [1.1.2] (process 8841): Assumption: 409 [170,split.1.1.2] chest=2. Possible model detected on branch [1.1.2]. Here are the clauses in Usable and SoS. It seems that no more inferences or splitting can be done. If the search strategy is complete, these clauses should lead to a model of the input. list(usable). 1 [] x=x. 2 [] x=1|x=2|x=3|x=4|x=5. 4 [copy,3,flip.1] 2!=1. 6 [copy,5,flip.1] 3!=1. 8 [copy,7,flip.1] 4!=1. 10 [copy,9,flip.1] 5!=1. 12 [copy,11,flip.1] 3!=2. 14 [copy,13,flip.1] 4!=2. 16 [copy,15,flip.1] 5!=2. 18 [copy,17,flip.1] 4!=3. 20 [copy,19,flip.1] 5!=3. 22 [copy,21,flip.1] 5!=4. 114 [] milk=3. 116 [] norw=1. 124 [] blue=2. 302 [back_unit_del,300.1,221.1] ivory=4. 310 [back_demod,136,demod,303,unit_del,1] coffee=5. 314 [back_demod,306,demod,311,unit_del,1] eng=3. 318 [back_demod,106,demod,311] green=5. 330 [back_demod,100,demod,315] red=3. 353 [back_unit_del,329.1,325.2] ayellow=1. 370 [back_unit_del,352.1,349.2] horse=2. 376 [back_demod,112,demod,354] kool=1. 407 [170,split_neg.1.1.2] fox=1. 409 [170,split.1.1.2] chest=2. 425 [back_unit_del,414.1,372.1] lucky=4. 428 [back_unit_del,421.1,412.1] japan=5. 430 [back_unit_del,422.1,348.2] atea=2. 433 [back_unit_del,424.1,399.2,unit_del,427] asnail=3. 435 [back_demod,119,demod,426] orange=4. 437 [back_demod,122,demod,429] parli=5. 440 [back_demod,108,demod,431] aukra=2. 443 [back_demod,110,demod,434] old=3. 446 [back_unit_del,439.1,378.1] aspan=4. 448 [back_unit_del,442.1,432.2] apple=1. 450 [back_unit_del,445.1,417.2,demod,447,unit_del,1] azebra=5. 452 [back_demod,103,demod,447] dog=4. end_of_list. list(sos). end_of_list. ------- statistics (process 8841) ------- clauses given 89 clauses generated 637 clauses kept 360 clauses forward subsumed 562 clauses back subsumed 143 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8841 finished Mon Aug 2 15:31:11 2004 ------- statistics (process 8833) ------- clauses given 75 clauses generated 518 clauses kept 327 clauses forward subsumed 396 clauses back subsumed 123 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.00 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8833 finished Mon Aug 2 15:31:11 2004 ------- statistics (process 8832) ------- clauses given 73 clauses generated 508 clauses kept 322 clauses forward subsumed 390 clauses back subsumed 117 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8832 finished Mon Aug 2 15:31:11 2004 ------- statistics (process 8831) ------- clauses given 52 clauses generated 297 clauses kept 228 clauses forward subsumed 209 clauses back subsumed 7 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8831 finished Mon Aug 2 15:31:11 2004 otter-3.3f/examples/split/GRP025-1.in0100644000076400007640000001044406767772062016545 0ustar mccunemccune%-------------------------------------------------------------------------- % File : GRP025-1 : TPTP v2.0.0. Bugfixed v1.2.1. % Domain : Group Theory (Named groups) % Problem : All groups of order 2 are isomorphic % Version : [McCharen, et al., 1976] axioms. % Theorem formulation : Does not prove full generality. % English : If G1 has exactly two elements and G2 has exactly two % elements, then there exists an isomorphism [a one-to-one and % onto homomorphism] between them. % Refs : McCharen J.D., Overbeek R.A., Wos L.A. (1976), Problems and % Experiments for and with Automated Theorem Proving Programs, % IEEE Transactions on Computers C-25(8), 773-782. % Source : [ANL] % Names : G8 [McCharen, et al., 1976] % Status : unsatisfiable % Rating : 0.50 v2.0.0 % Syntax : Number of clauses : 33 ( 2 non-Horn; 25 unit; 27 RR) % Number of literals : 50 ( 8 equality) % Maximal clause size : 4 ( 1 average) % Number of predicates : 3 ( 0 propositional; 2-4 arity) % Number of functors : 13 ( 9 constant; 0-3 arity) % Number of variables : 39 ( 0 singleton) % Maximal term depth : 2 ( 1 average) % Comments : In order to prove the theorem, the group tables and % a particular homomorphism are specified, and the % contradiction comes from the fact that this is the actual % isomorphism. Not only is this formulation cheating, but also % it does not prove the theorem in full generality. % : A substitution axiom, missing in the ANL presentation, % is included. % : tptp2X: -fotter:hypothesis:[set(auto),set(tptp_eq)] -trm_equality:stfp GRP025-1.p % Bugfixes : v1.2.1 - Bugfix in GRP006-0.ax. %-------------------------------------------------------------------------- set(prolog_style_variables). set(auto2). set(tptp_eq). set(split_when_given). set(split_pos). list(usable). % reflexivity, axiom. equal(A,A). % identity_in_group, axiom. group_member(identity_for(A),A). % left_identity, axiom. product(A,identity_for(A),B,B). % right_identity, axiom. product(A,B,identity_for(A),B). % inverse_in_group, axiom. -group_member(A,B) | group_member(inverse(B,A),B). % left_inverse, axiom. product(A,inverse(A,B),B,identity_for(A)). % right_inverse, axiom. product(A,B,inverse(A,B),identity_for(A)). % total_function1_1, axiom. -group_member(A,B) | -group_member(C,B) | product(B,A,C,multiply(B,A,C)). % total_function1_2, axiom. -group_member(A,B) | -group_member(C,B) | group_member(multiply(B,A,C),B). % total_function2, axiom. -product(A,B,C,D) | -product(A,B,C,E) | equal(E,D). % associativity1, axiom. -product(A,B,C,D) | -product(A,C,E,F) | -product(A,D,E,G) | product(A,B,F,G). % associativity2, axiom. -product(A,B,C,D) | -product(A,C,E,F) | -product(A,B,F,G) | product(A,D,E,G). end_of_list. list(sos). % a_member_of_group1, hypothesis. group_member(a,g1). % b_member_of_group1, hypothesis. group_member(b,g1). % c_member_of_group2, hypothesis. group_member(c,g2). % d_member_of_group2, hypothesis. group_member(d,g2). % a_and_b_only_members_of_group1, hypothesis. -group_member(A,g1) | equal(A,a) | equal(A,b). % c_and_d_only_members_of_group2, hypothesis. -group_member(A,g2) | equal(A,c) | equal(A,d). % a_times_a_is_a, hypothesis. product(g1,a,a,a). % a_times_b_is_b, hypothesis. product(g1,a,b,b). % b_times_a_is_b, hypothesis. product(g1,b,a,b). % b_times_b_is_a, hypothesis. product(g1,b,b,a). % c_times_c_is_c, hypothesis. product(g2,c,c,c). % c_times_d_is_d, hypothesis. product(g2,c,d,d). % d_times_c_is_d, hypothesis. product(g2,d,c,d). % d_times_d_is_c, hypothesis. product(g2,d,d,c). % a_maps_to_c, hypothesis. equal(an_isomorphism(a),c). % b_maps_to_d, hypothesis. equal(an_isomorphism(b),d). % d1_member_of_group1, hypothesis. group_member(d1,g1). % d2_member_of_group1, hypothesis. group_member(d2,g1). % d3_member_of_group1, hypothesis. group_member(d3,g1). % d1_times_d2_is_d3, hypothesis. product(g1,d1,d2,d3). % prove_product_holds_in_group2, conjecture. -product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)). end_of_list. %-------------------------------------------------------------------------- otter-3.3f/examples/split/GEO010-2.out0100664000076400007640000007026010103522213016671 0ustar mccunemccune WARNING, with splitting, max_seconds is checked against the wall clock. ----- Otter 3.3f, August 2004 ----- The process was started by mccune on gyro.thornwood, Mon Aug 2 15:31:06 2004 The command was "../../bin/otter". The process ID is 8628. set(prolog_style_variables). set(auto2). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 20000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). set(tptp_eq). set(split_when_given). dependent: set(back_unit_deletion). dependent: set(unit_deletion). set(split_pos). assign(split_depth,10). list(usable). 0 [] equal(A,A). 0 [] equidistant(A,B,B,A). 0 [] -equidistant(A,B,C,D)| -equidistant(A,B,E,F)|equidistant(C,D,E,F). 0 [] -equidistant(A,B,C,C)|equal(A,B). 0 [] between(A,B,extension(A,B,C,D)). 0 [] equidistant(A,extension(B,A,C,D),C,D). 0 [] -equidistant(A,B,C,D)| -equidistant(B,E,D,F)| -equidistant(A,G,C,H)| -equidistant(B,G,D,H)| -between(A,B,E)| -between(C,D,F)|equal(A,B)|equidistant(E,G,F,H). 0 [] -between(A,B,A)|equal(A,B). 0 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). 0 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). 0 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). 0 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). 0 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). 0 [] -equidistant(A,B,A,C)| -equidistant(D,B,D,C)| -equidistant(E,B,E,C)|between(A,D,E)|between(D,E,A)|between(E,A,D)|equal(B,C). 0 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,D,euclid1(A,D,B,E,C)). 0 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,E,euclid2(A,D,B,E,C)). 0 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)). 0 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|between(C,continuous(A,B,C,F,D,E),E). 0 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|equidistant(A,F,A,continuous(A,B,C,F,D,E)). 0 [] -between(A,B,C)|colinear(A,B,C). 0 [] -between(A,B,C)|colinear(C,A,B). 0 [] -between(A,B,C)|colinear(B,C,A). 0 [] -colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B). end_of_list. list(sos). 0 [] colinear(a,b,c). 0 [] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,a,b)| -colinear(c,b,a). end_of_list. Every positive clause in sos is ground (or sos is empty); therefore we move all positive usable clauses to sos. Properties of input clauses: prop=0, horn=0, equality=1, symmetry=0, max_lits=8. Setting hyper_res, because there are nonunits. dependent: set(hyper_res). Setting ur_res, because this is a nonunit set containing either equality literals or non-Horn clauses. dependent: set(ur_res). Setting factor and unit_deletion, because there are non-Horn clauses. dependent: set(factor). Equality is present, so we set the knuth_bendix flag. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). As an incomplete heuristic, we paramodulate with units only. dependent: set(para_from_units_only). dependent: set(para_into_units_only). ------------> process usable: ** KEPT (pick-wt=15): 1 [] -equidistant(A,B,C,D)| -equidistant(A,B,E,F)|equidistant(C,D,E,F). ** KEPT (pick-wt=8): 2 [] -equidistant(A,B,C,C)|equal(A,B). ** KEPT (pick-wt=36): 3 [] -equidistant(A,B,C,D)| -equidistant(B,E,D,F)| -equidistant(A,G,C,H)| -equidistant(B,G,D,H)| -between(A,B,E)| -between(C,D,F)|equal(A,B)|equidistant(E,G,F,H). ** KEPT (pick-wt=7): 4 [] -between(A,B,A)|equal(A,B). ** KEPT (pick-wt=17): 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). ** KEPT (pick-wt=17): 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). ** KEPT (pick-wt=4): 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3). ** KEPT (pick-wt=4): 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1). ** KEPT (pick-wt=4): 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2). ** KEPT (pick-wt=30): 10 [] -equidistant(A,B,A,C)| -equidistant(D,B,D,C)| -equidistant(E,B,E,C)|between(A,D,E)|between(D,E,A)|between(E,A,D)|equal(B,C). ** KEPT (pick-wt=20): 11 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,D,euclid1(A,D,B,E,C)). ** KEPT (pick-wt=20): 12 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(A,E,euclid2(A,D,B,E,C)). ** KEPT (pick-wt=25): 13 [] -between(A,B,C)| -between(D,B,E)|equal(A,B)|between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)). ** KEPT (pick-wt=28): 14 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|between(C,continuous(A,B,C,F,D,E),E). ** KEPT (pick-wt=29): 15 [] -equidistant(A,B,A,C)| -equidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|equidistant(A,F,A,continuous(A,B,C,F,D,E)). ** KEPT (pick-wt=8): 16 [] -between(A,B,C)|colinear(A,B,C). ** KEPT (pick-wt=8): 17 [] -between(A,B,C)|colinear(C,A,B). ** KEPT (pick-wt=8): 18 [] -between(A,B,C)|colinear(B,C,A). ** KEPT (pick-wt=16): 19 [] -colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B). >>>> Starting back unit deletion with 7. >>>> Starting back unit deletion with 8. >>>> Starting back unit deletion with 9. ------------> process sos: ** KEPT (pick-wt=4): 39 [] colinear(a,b,c). ** KEPT (pick-wt=20): 40 [] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,a,b)| -colinear(c,b,a). ** KEPT (pick-wt=3): 41 [] equal(A,A). ** KEPT (pick-wt=5): 42 [] equidistant(A,B,B,A). ** KEPT (pick-wt=8): 43 [] between(A,B,extension(A,B,C,D)). ** KEPT (pick-wt=9): 44 [] equidistant(A,extension(B,A,C,D),C,D). >>>> Starting back unit deletion with 39. Following clause subsumed by 41 during input processing: 0 [copy,41,flip.1] equal(A,A). >>>> Starting back unit deletion with 41. 42 back subsumes 36. >>>> Starting back unit deletion with 42. 0 [back_unit_del,42.1,35.3] -equidistant(E2518,F2518,E2518,F2518)| -equidistant(F2518,G2518,F2518,G2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,F2518,G2518,F2518). ** KEPT (pick-wt=22): 45 [back_unit_del,42.1,35.3] -equidistant(A,B,A,B)| -equidistant(B,C,B,C)| -between(A,B,C)|equal(A,B)|equidistant(C,B,C,B). >>>> Starting back unit deletion with 43. >>>> Starting back unit deletion with 44. 45 back subsumes 35. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=4) 39 [] colinear(a,b,c). given clause #2: (wt=3) 41 [] equal(A,A). given clause #3: (wt=5) 42 [] equidistant(A,B,B,A). 0 [back_unit_del,47.1,23.2] -equidistant(E2518,F2518,E2518,F2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). 0 [back_unit_del,47.1,23.1] -equidistant(F2518,G2518,F2518,G2518)| -equidistant(E2518,H2518,E2518,I2518)| -equidistant(F2518,H2518,F2518,I2518)| -between(E2518,F2518,G2518)|equal(E2518,F2518)|equidistant(G2518,H2518,G2518,I2518). given clause #4: (wt=5) 47 [hyper,42,20] equidistant(A,B,A,B). given clause #5: (wt=8) 43 [] between(A,B,extension(A,B,C,D)). given clause #6: (wt=20) 40 [] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,a,b)| -colinear(c,b,a). given clause #7: (wt=8) 55 [hyper,43,18] colinear(A,extension(B,A,C,D),B). given clause #8: (wt=8) 56 [hyper,43,17] colinear(extension(A,B,C,D),A,B). given clause #9: (wt=8) 57 [hyper,43,16] colinear(A,B,extension(A,B,C,D)). given clause #10: (wt=9) 44 [] equidistant(A,extension(B,A,C,D),C,D). given clause #11: (wt=12) 46 [hyper,39,19] between(a,b,c)|between(b,c,a)|between(c,a,b). Splitting on clause 46 [hyper,39,19] between(a,b,c)|between(b,c,a)|between(c,a,b). Case [1] (process 8629): Assumption: 71 [46,split.1] between(a,b,c). given clause #12: (wt=4) 71 [46,split.1] between(a,b,c). 0 [back_unit_del,77.1,40.3] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(c,a,b)| -colinear(c,b,a). 0 [back_unit_del,78.1,40.4] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,b,a). given clause #13: (wt=4) 77 [hyper,71,18] colinear(b,c,a). given clause #14: (wt=4) 78 [hyper,71,17] colinear(c,a,b). given clause #15: (wt=7) 66 [hyper,44,2,flip.1] equal(extension(A,B,C,C),B). 0 [back_unit_del,87.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,88.1,21.3] -equidistant(E2518,F2518,G2518,H2518)| -equidistant(F2518,I2518,H2518,J2518)| -between(E2518,F2518,I2518)| -between(G2518,H2518,J2518)|equal(E2518,F2518)|equidistant(I2518,F2518,J2518,H2518). 0 [back_unit_del,89.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,90.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,91.1,38.2] -equidistant(E2518,E2518,E2518,F2518)|equidistant(E2518,E2518,E2518,continuous(E2518,E2518,F2518,E2518,E2518,F2518)). 0 [back_unit_del,91.1,37.2] -equidistant(E2518,E2518,E2518,F2518)|between(F2518,continuous(E2518,E2518,F2518,E2518,E2518,F2518),F2518). 0 [back_unit_del,91.1,32.2] -equidistant(E2518,F2518,E2518,G2518)| -between(F2518,H2518,F2518)|equidistant(E2518,H2518,E2518,continuous(E2518,F2518,G2518,H2518,F2518,G2518)). 0 [back_unit_del,91.1,30.2] -equidistant(E2518,F2518,E2518,G2518)| -between(F2518,H2518,F2518)|between(G2518,continuous(E2518,F2518,G2518,H2518,F2518,G2518),G2518). given clause #16: (wt=19) 49 [hyper,43,33,47,47] equidistant(A,A,A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C))). given clause #17: (wt=4) 87 [para_from,66.1.1,55.1.2] colinear(A,A,B). given clause #18: (wt=4) 89 [para_from,66.1.1,57.1.3] colinear(A,B,B). given clause #19: (wt=4) 90 [para_from,66.1.1,56.1.1] colinear(A,B,A). given clause #20: (wt=4) 91 [para_from,66.1.1,43.1.3] between(A,B,B). given clause #21: (wt=22) 50 [hyper,43,31,47,47] between(A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C)),extension(A,A,B,C)). given clause #22: (wt=5) 88 [para_from,66.1.1,44.1.2] equidistant(A,A,B,B). given clause #23: (wt=9) 68 [hyper,44,1,42] equidistant(extension(A,B,C,D),B,C,D). given clause #24: (wt=9) 69 [hyper,44,1,47] equidistant(A,B,C,extension(D,C,A,B)). given clause #25: (wt=9) 70 [hyper,44,1,42] equidistant(A,B,extension(C,D,A,B),D). given clause #26: (wt=13) 54 [hyper,43,24] between(A,inner_pasch(B,A,extension(B,A,C,D),A,B),B). given clause #27: (wt=9) 75 [hyper,71,24] between(b,inner_pasch(a,b,c,b,a),a).  Resetting weight limit to 12. Resetting weight limit to 12. sos_size=288 given clause #28: (wt=9) 151 [hyper,91,6,91] between(A,inner_pasch(B,A,A,A,C),B). given clause #29: (wt=8) 454 [hyper,151,4,flip.1] equal(inner_pasch(A,A,A,A,B),A). given clause #30: (wt=9) 152 [hyper,91,6,71] between(c,inner_pasch(a,b,c,c,A),a). given clause #31: (wt=37) 58 [hyper,43,13,43] equal(A,B)|between(euclid1(A,C,B,extension(C,B,D,E),extension(A,B,F,G)),extension(A,B,F,G),euclid2(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #32: (wt=9) 154 [hyper,91,6,71] between(b,inner_pasch(A,c,c,b,a),A). given clause #33: (wt=8) 462 [hyper,154,4,flip.1] equal(inner_pasch(b,c,c,b,a),b). given clause #34: (wt=9) 156 [hyper,91,5,91] between(A,inner_pasch(B,A,A,A,C),C). 0 [back_unit_del,469.1,33.3] -equidistant(E2518,E2518,E2518,F2518)| -equidistant(E2518,G2518,E2518,H2518)|equidistant(E2518,E2518,E2518,continuous(E2518,E2518,F2518,E2518,G2518,H2518)). 0 [back_unit_del,469.1,31.3] -equidistant(E2518,E2518,E2518,F2518)| -equidistant(E2518,G2518,E2518,H2518)|between(F2518,continuous(E2518,E2518,F2518,E2518,G2518,H2518),H2518). given clause #35: (wt=4) 469 [para_into,156.1.2,454.1.1] between(A,A,B). given clause #36: (wt=24) 59 [hyper,43,12,43] equal(A,B)|between(A,extension(C,B,D,E),euclid2(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #37: (wt=8) 467 [hyper,156,4,flip.1] equal(inner_pasch(A,B,B,B,B),B). given clause #38: (wt=9) 157 [hyper,91,5,71] between(b,inner_pasch(a,b,c,c,A),A). given clause #39: (wt=8) 496 [hyper,157,4,flip.1] equal(inner_pasch(a,b,c,c,b),b). given clause #40: (wt=4) 498 [para_from,496.1.1,152.1.2] between(c,b,a). --- refuted case [1] 0 [back_unit_del,501.1,86.2] -colinear(a,c,b)| -colinear(c,b,a). -----> EMPTY CLAUSE at 0.46 sec ----> 532 [back_unit_del,501.1,86.2,unit_del,502,503] $F. Length of proof is 14. Level of proof is 6. Case [1] ---------------- PROOF ---------------- 2 [] -equidistant(A,B,C,C)|equal(A,B). 4 [] -between(A,B,A)|equal(A,B). 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). 16 [] -between(A,B,C)|colinear(A,B,C). 17 [] -between(A,B,C)|colinear(C,A,B). 18 [] -between(A,B,C)|colinear(B,C,A). 19 [] -colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B). 39 [] colinear(a,b,c). 40 [] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,a,b)| -colinear(c,b,a). 43 [] between(A,B,extension(A,B,C,D)). 44 [] equidistant(A,extension(B,A,C,D),C,D). 46 [hyper,39,19] between(a,b,c)|between(b,c,a)|between(c,a,b). 66 [hyper,44,2,flip.1] equal(extension(A,B,C,C),B). 71 [46,split.1] between(a,b,c). 77 [hyper,71,18] colinear(b,c,a). 78 [hyper,71,17] colinear(c,a,b). 86 [back_unit_del,77.1,40.3,unit_del,78] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(c,b,a). 91 [para_from,66.1.1,43.1.3] between(A,B,B). 152 [hyper,91,6,71] between(c,inner_pasch(a,b,c,c,A),a). 157 [hyper,91,5,71] between(b,inner_pasch(a,b,c,c,A),A). 496 [hyper,157,4,flip.1] equal(inner_pasch(a,b,c,c,b),b). 498 [para_from,496.1.1,152.1.2] between(c,b,a). 501 [hyper,498,18] colinear(b,a,c). 502 [hyper,498,17] colinear(a,c,b). 503 [hyper,498,16] colinear(c,b,a). 532 [back_unit_del,501.1,86.2,unit_del,502,503] $F. ------------ end of proof ------------- ------- statistics (process 8629) ------- clauses given 40 clauses generated 7651 clauses kept 525 clauses forward subsumed 3674 clauses back subsumed 88 Kbytes malloced 7812 ----------- times (seconds) ----------- user CPU time 0.46 (0 hr, 0 min, 0 sec) system CPU time 0.02 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) Process 8629 finished Mon Aug 2 15:31:06 2004 Refuted case [1]. Case [2] (process 8630): Assumption: 72 [46,split.2] between(b,c,a). given clause #12: (wt=4) 71 [46,split_neg.2] -between(a,b,c). given clause #13: (wt=4) 72 [46,split.2] between(b,c,a). 0 [back_unit_del,78.1,40.4] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,b,a). 0 [back_unit_del,79.1,40.3] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(c,a,b)| -colinear(c,b,a). given clause #14: (wt=4) 78 [hyper,72,18] colinear(c,a,b). given clause #15: (wt=4) 79 [hyper,72,16] colinear(b,c,a). given clause #16: (wt=19) 49 [hyper,43,33,47,47] equidistant(A,A,A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C))). given clause #17: (wt=7) 66 [hyper,44,2,flip.1] equal(extension(A,B,C,C),B). 0 [back_unit_del,96.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,97.1,21.3] -equidistant(E2518,F2518,G2518,H2518)| -equidistant(F2518,I2518,H2518,J2518)| -between(E2518,F2518,I2518)| -between(G2518,H2518,J2518)|equal(E2518,F2518)|equidistant(I2518,F2518,J2518,H2518). 0 [back_unit_del,98.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,99.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,100.1,38.2] -equidistant(E2518,E2518,E2518,F2518)|equidistant(E2518,E2518,E2518,continuous(E2518,E2518,F2518,E2518,E2518,F2518)). 0 [back_unit_del,100.1,37.2] -equidistant(E2518,E2518,E2518,F2518)|between(F2518,continuous(E2518,E2518,F2518,E2518,E2518,F2518),F2518). 0 [back_unit_del,100.1,32.2] -equidistant(E2518,F2518,E2518,G2518)| -between(F2518,H2518,F2518)|equidistant(E2518,H2518,E2518,continuous(E2518,F2518,G2518,H2518,F2518,G2518)). 0 [back_unit_del,100.1,30.2] -equidistant(E2518,F2518,E2518,G2518)| -between(F2518,H2518,F2518)|between(G2518,continuous(E2518,F2518,G2518,H2518,F2518,G2518),G2518). given clause #18: (wt=4) 96 [para_from,66.1.1,55.1.2] colinear(A,A,B). given clause #19: (wt=4) 98 [para_from,66.1.1,57.1.3] colinear(A,B,B). given clause #20: (wt=4) 99 [para_from,66.1.1,56.1.1] colinear(A,B,A). given clause #21: (wt=22) 50 [hyper,43,31,47,47] between(A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C)),extension(A,A,B,C)). given clause #22: (wt=4) 100 [para_from,66.1.1,43.1.3] between(A,B,B). given clause #23: (wt=5) 97 [para_from,66.1.1,44.1.2] equidistant(A,A,B,B). given clause #24: (wt=9) 68 [hyper,44,1,42] equidistant(extension(A,B,C,D),B,C,D). given clause #25: (wt=9) 69 [hyper,44,1,47] equidistant(A,B,C,extension(D,C,A,B)). given clause #26: (wt=13) 54 [hyper,43,24] between(A,inner_pasch(B,A,extension(B,A,C,D),A,B),B). given clause #27: (wt=9) 70 [hyper,44,1,42] equidistant(A,B,extension(C,D,A,B),D).  Resetting weight limit to 12. Resetting weight limit to 12. sos_size=299 given clause #28: (wt=9) 76 [hyper,72,24] between(c,inner_pasch(b,c,a,c,b),b). given clause #29: (wt=9) 193 [hyper,100,6,100] between(A,inner_pasch(B,A,A,A,C),B). given clause #30: (wt=8) 449 [hyper,193,4,flip.1] equal(inner_pasch(A,A,A,A,B),A). given clause #31: (wt=37) 58 [hyper,43,13,43] equal(A,B)|between(euclid1(A,C,B,extension(C,B,D,E),extension(A,B,F,G)),extension(A,B,F,G),euclid2(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #32: (wt=9) 194 [hyper,100,6,72] between(a,inner_pasch(b,c,a,a,A),b). given clause #33: (wt=9) 197 [hyper,100,6,72] between(c,inner_pasch(A,a,a,c,b),A). given clause #34: (wt=8) 457 [hyper,197,4,flip.1] equal(inner_pasch(c,a,a,c,b),c). given clause #35: (wt=9) 200 [hyper,100,5,100] between(A,inner_pasch(B,A,A,A,C),C). 0 [back_unit_del,464.1,33.3] -equidistant(E2518,E2518,E2518,F2518)| -equidistant(E2518,G2518,E2518,H2518)|equidistant(E2518,E2518,E2518,continuous(E2518,E2518,F2518,E2518,G2518,H2518)). 0 [back_unit_del,464.1,31.3] -equidistant(E2518,E2518,E2518,F2518)| -equidistant(E2518,G2518,E2518,H2518)|between(F2518,continuous(E2518,E2518,F2518,E2518,G2518,H2518),H2518). given clause #36: (wt=24) 59 [hyper,43,12,43] equal(A,B)|between(A,extension(C,B,D,E),euclid2(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #37: (wt=4) 464 [para_into,200.1.2,449.1.1] between(A,A,B). given clause #38: (wt=8) 462 [hyper,200,4,flip.1] equal(inner_pasch(A,B,B,B,B),B). given clause #39: (wt=9) 201 [hyper,100,5,72] between(c,inner_pasch(b,c,a,a,A),A). given clause #40: (wt=8) 491 [hyper,201,4,flip.1] equal(inner_pasch(b,c,a,a,c),c). given clause #41: (wt=20) 60 [hyper,43,11,43] equal(A,B)|between(A,C,euclid1(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #42: (wt=4) 493 [para_from,491.1.1,194.1.2] between(a,c,b). --- refuted case [2] 0 [back_unit_del,496.1,87.3] -colinear(a,c,b)| -colinear(b,a,c). -----> EMPTY CLAUSE at 0.46 sec ----> 527 [back_unit_del,496.1,87.3,unit_del,498,497] $F. Length of proof is 14. Level of proof is 6. Case [2] ---------------- PROOF ---------------- 2 [] -equidistant(A,B,C,C)|equal(A,B). 4 [] -between(A,B,A)|equal(A,B). 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). 16 [] -between(A,B,C)|colinear(A,B,C). 17 [] -between(A,B,C)|colinear(C,A,B). 18 [] -between(A,B,C)|colinear(B,C,A). 19 [] -colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B). 39 [] colinear(a,b,c). 40 [] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,a,b)| -colinear(c,b,a). 43 [] between(A,B,extension(A,B,C,D)). 44 [] equidistant(A,extension(B,A,C,D),C,D). 46 [hyper,39,19] between(a,b,c)|between(b,c,a)|between(c,a,b). 66 [hyper,44,2,flip.1] equal(extension(A,B,C,C),B). 72 [46,split.2] between(b,c,a). 78 [hyper,72,18] colinear(c,a,b). 79 [hyper,72,16] colinear(b,c,a). 87 [back_unit_del,78.1,40.4,unit_del,79] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(c,b,a). 100 [para_from,66.1.1,43.1.3] between(A,B,B). 194 [hyper,100,6,72] between(a,inner_pasch(b,c,a,a,A),b). 201 [hyper,100,5,72] between(c,inner_pasch(b,c,a,a,A),A). 491 [hyper,201,4,flip.1] equal(inner_pasch(b,c,a,a,c),c). 493 [para_from,491.1.1,194.1.2] between(a,c,b). 496 [hyper,493,18] colinear(c,b,a). 497 [hyper,493,17] colinear(b,a,c). 498 [hyper,493,16] colinear(a,c,b). 527 [back_unit_del,496.1,87.3,unit_del,498,497] $F. ------------ end of proof ------------- ------- statistics (process 8630) ------- clauses given 42 clauses generated 7652 clauses kept 520 clauses forward subsumed 3606 clauses back subsumed 93 Kbytes malloced 7812 ----------- times (seconds) ----------- user CPU time 0.46 (0 hr, 0 min, 0 sec) system CPU time 0.02 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8630 finished Mon Aug 2 15:31:07 2004 Refuted case [2]. Case [3] (process 8631): Assumption: 73 [46,split.3] between(c,a,b). given clause #12: (wt=4) 71 [46,split_neg.3] -between(a,b,c). given clause #13: (wt=4) 72 [46,split_neg.3] -between(b,c,a). given clause #14: (wt=4) 73 [46,split.3] between(c,a,b). 0 [back_unit_del,79.1,40.3] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(c,a,b)| -colinear(c,b,a). 0 [back_unit_del,80.1,40.4] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,b,a). given clause #15: (wt=4) 79 [hyper,73,17] colinear(b,c,a). given clause #16: (wt=19) 49 [hyper,43,33,47,47] equidistant(A,A,A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C))). given clause #17: (wt=4) 80 [hyper,73,16] colinear(c,a,b). given clause #18: (wt=7) 66 [hyper,44,2,flip.1] equal(extension(A,B,C,C),B). 0 [back_unit_del,97.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,98.1,21.3] -equidistant(E2518,F2518,G2518,H2518)| -equidistant(F2518,I2518,H2518,J2518)| -between(E2518,F2518,I2518)| -between(G2518,H2518,J2518)|equal(E2518,F2518)|equidistant(I2518,F2518,J2518,H2518). 0 [back_unit_del,99.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,100.1,34.1] between(E2518,E2518,E2518). 0 [back_unit_del,101.1,38.2] -equidistant(E2518,E2518,E2518,F2518)|equidistant(E2518,E2518,E2518,continuous(E2518,E2518,F2518,E2518,E2518,F2518)). 0 [back_unit_del,101.1,37.2] -equidistant(E2518,E2518,E2518,F2518)|between(F2518,continuous(E2518,E2518,F2518,E2518,E2518,F2518),F2518). 0 [back_unit_del,101.1,32.2] -equidistant(E2518,F2518,E2518,G2518)| -between(F2518,H2518,F2518)|equidistant(E2518,H2518,E2518,continuous(E2518,F2518,G2518,H2518,F2518,G2518)). 0 [back_unit_del,101.1,30.2] -equidistant(E2518,F2518,E2518,G2518)| -between(F2518,H2518,F2518)|between(G2518,continuous(E2518,F2518,G2518,H2518,F2518,G2518),G2518). given clause #19: (wt=4) 97 [para_from,66.1.1,55.1.2] colinear(A,A,B). given clause #20: (wt=4) 99 [para_from,66.1.1,57.1.3] colinear(A,B,B). given clause #21: (wt=22) 50 [hyper,43,31,47,47] between(A,continuous(A,A,A,A,extension(A,A,B,C),extension(A,A,B,C)),extension(A,A,B,C)). given clause #22: (wt=4) 100 [para_from,66.1.1,56.1.1] colinear(A,B,A). given clause #23: (wt=4) 101 [para_from,66.1.1,43.1.3] between(A,B,B). given clause #24: (wt=5) 98 [para_from,66.1.1,44.1.2] equidistant(A,A,B,B). given clause #25: (wt=9) 68 [hyper,44,1,42] equidistant(extension(A,B,C,D),B,C,D). given clause #26: (wt=13) 54 [hyper,43,24] between(A,inner_pasch(B,A,extension(B,A,C,D),A,B),B). given clause #27: (wt=9) 69 [hyper,44,1,47] equidistant(A,B,C,extension(D,C,A,B)). given clause #28: (wt=9) 70 [hyper,44,1,42] equidistant(A,B,extension(C,D,A,B),D).  Resetting weight limit to 12. Resetting weight limit to 12. sos_size=299 given clause #29: (wt=9) 77 [hyper,73,24] between(a,inner_pasch(c,a,b,a,c),c). given clause #30: (wt=9) 194 [hyper,101,6,101] between(A,inner_pasch(B,A,A,A,C),B). given clause #31: (wt=37) 58 [hyper,43,13,43] equal(A,B)|between(euclid1(A,C,B,extension(C,B,D,E),extension(A,B,F,G)),extension(A,B,F,G),euclid2(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #32: (wt=8) 434 [hyper,194,4,flip.1] equal(inner_pasch(A,A,A,A,B),A). given clause #33: (wt=9) 195 [hyper,101,6,73] between(b,inner_pasch(c,a,b,b,A),c). given clause #34: (wt=9) 198 [hyper,101,6,73] between(a,inner_pasch(A,b,b,a,c),A). given clause #35: (wt=8) 442 [hyper,198,4,flip.1] equal(inner_pasch(a,b,b,a,c),a). given clause #36: (wt=24) 59 [hyper,43,12,43] equal(A,B)|between(A,extension(C,B,D,E),euclid2(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #37: (wt=9) 201 [hyper,101,5,101] between(A,inner_pasch(B,A,A,A,C),C). 0 [back_unit_del,449.1,33.3] -equidistant(E2518,E2518,E2518,F2518)| -equidistant(E2518,G2518,E2518,H2518)|equidistant(E2518,E2518,E2518,continuous(E2518,E2518,F2518,E2518,G2518,H2518)). 0 [back_unit_del,449.1,31.3] -equidistant(E2518,E2518,E2518,F2518)| -equidistant(E2518,G2518,E2518,H2518)|between(F2518,continuous(E2518,E2518,F2518,E2518,G2518,H2518),H2518). given clause #38: (wt=4) 449 [para_into,201.1.2,434.1.1] between(A,A,B). given clause #39: (wt=8) 447 [hyper,201,4,flip.1] equal(inner_pasch(A,B,B,B,B),B). given clause #40: (wt=9) 202 [hyper,101,5,73] between(a,inner_pasch(c,a,b,b,A),A). given clause #41: (wt=20) 60 [hyper,43,11,43] equal(A,B)|between(A,C,euclid1(A,C,B,extension(C,B,D,E),extension(A,B,F,G))). given clause #42: (wt=8) 476 [hyper,202,4,flip.1] equal(inner_pasch(c,a,b,b,a),a). given clause #43: (wt=4) 478 [para_from,476.1.1,195.1.2] between(b,a,c). --- refuted case [3] 0 [back_unit_del,481.1,88.1] -colinear(b,a,c)| -colinear(c,b,a). -----> EMPTY CLAUSE at 0.46 sec ----> 512 [back_unit_del,481.1,88.1,unit_del,483,482] $F. Length of proof is 14. Level of proof is 6. Case [3] ---------------- PROOF ---------------- 2 [] -equidistant(A,B,C,C)|equal(A,B). 4 [] -between(A,B,A)|equal(A,B). 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D). 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A). 16 [] -between(A,B,C)|colinear(A,B,C). 17 [] -between(A,B,C)|colinear(C,A,B). 18 [] -between(A,B,C)|colinear(B,C,A). 19 [] -colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B). 39 [] colinear(a,b,c). 40 [] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(b,c,a)| -colinear(c,a,b)| -colinear(c,b,a). 43 [] between(A,B,extension(A,B,C,D)). 44 [] equidistant(A,extension(B,A,C,D),C,D). 46 [hyper,39,19] between(a,b,c)|between(b,c,a)|between(c,a,b). 66 [hyper,44,2,flip.1] equal(extension(A,B,C,C),B). 73 [46,split.3] between(c,a,b). 79 [hyper,73,17] colinear(b,c,a). 80 [hyper,73,16] colinear(c,a,b). 88 [back_unit_del,79.1,40.3,unit_del,80] -colinear(a,c,b)| -colinear(b,a,c)| -colinear(c,b,a). 101 [para_from,66.1.1,43.1.3] between(A,B,B). 195 [hyper,101,6,73] between(b,inner_pasch(c,a,b,b,A),c). 202 [hyper,101,5,73] between(a,inner_pasch(c,a,b,b,A),A). 476 [hyper,202,4,flip.1] equal(inner_pasch(c,a,b,b,a),a). 478 [para_from,476.1.1,195.1.2] between(b,a,c). 481 [hyper,478,18] colinear(a,c,b). 482 [hyper,478,17] colinear(c,b,a). 483 [hyper,478,16] colinear(b,a,c). 512 [back_unit_del,481.1,88.1,unit_del,483,482] $F. ------------ end of proof ------------- ------- statistics (process 8631) ------- clauses given 43 clauses generated 7659 clauses kept 505 clauses forward subsumed 3619 clauses back subsumed 87 Kbytes malloced 7812 ----------- times (seconds) ----------- user CPU time 0.46 (0 hr, 0 min, 0 sec) system CPU time 0.02 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8631 finished Mon Aug 2 15:31:07 2004 Refuted case [3].  That finishes the proof of the theorem. That finishes the proof of the theorem. ------- statistics (process 8628) ------- clauses given 11 clauses generated 275 clauses kept 69 clauses forward subsumed 222 clauses back subsumed 9 Kbytes malloced 976 ----------- times (seconds) ----------- user CPU time 0.03 (0 hr, 0 min, 0 sec) system CPU time 0.01 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) Process 8628 finished Mon Aug 2 15:31:07 2004 otter-3.3f/make-install0100755000076400007640000000004310000602607014474 0ustar mccunemccune#!/bin/csh ./QuickInstall no_make