----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 16:06:18 2003 The command was "otter". set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). clear(print_given). include("nDef.txt"). ------- start included file nDef.txt------- formula_list(usable). all x y (n(x,y)=c(u(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,y)=c(u(c(x),c(y))). end_of_list. ------- end included file nDef.txt------- include("uzDef.txt"). ------- start included file uzDef.txt------- formula_list(usable). D=c(I). U=u(I,D). Z=c(U). end_of_list. -------> usable clausifies to: list(usable). 0 [] D=c(I). 0 [] U=u(I,D). 0 [] Z=c(U). end_of_list. ------- end included file uzDef.txt------- include("20To24booleanLaws.txt"). ------- start included file 20To24booleanLaws.txt------- formula_list(usable). all x y (n(x,y)=n(y,x)). all x y (n(x,c(y))=Z->u(x,y)=y). all x y (u(x,y)=y->n(x,c(y))=Z). all x y (n(x,y)=Z&u(x,y)=U->c(x)=y). all x y (c(x)=y->n(x,y)=Z). all x y (c(x)=y->u(x,y)=U). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,y)=n(y,x). 0 [] n(x,c(y))!=Z|u(x,y)=y. 0 [] u(x,y)!=y|n(x,c(y))=Z. 0 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. 0 [] c(x)!=y|n(x,y)=Z. 0 [] c(x)!=y|u(x,y)=U. end_of_list. ------- end included file 20To24booleanLaws.txt------- include("xxiv_a.txt"). ------- start included file xxiv_a.txt------- formula_list(usable). all x (n(k(n(I,x),U),k(n(I,c(x)),U))=Z). all x (u(k(n(I,x),U),k(n(I,c(x)),U))=U). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(k(n(I,x),U),k(n(I,c(x)),U))=Z. 0 [] u(k(n(I,x),U),k(n(I,c(x)),U))=U. end_of_list. ------- end included file xxiv_a.txt------- include("xxiv.txt"). ------- start included file xxiv.txt------- formula_list(usable). -(all x (c(k(n(I,x),U))=k(n(I,c(x)),U))). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(k(n(I,$c1),U))!=k(n(I,c($c1)),U). end_of_list. ------- end included file xxiv.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=11): 1 [] n(x,c(y))!=Z|u(x,y)=y. ** KEPT (pick-wt=11): 2 [] u(x,y)!=y|n(x,c(y))=Z. ** KEPT (pick-wt=14): 3 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. ** KEPT (pick-wt=9): 4 [] c(x)!=y|n(x,y)=Z. ** KEPT (pick-wt=9): 5 [] c(x)!=y|u(x,y)=U. ** KEPT (pick-wt=13): 6 [] c(k(n(I,$c1),U))!=k(n(I,c($c1)),U). ------------> process sos: ** KEPT (pick-wt=10): 8 [copy,7,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 9 [new_demod,8] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=4): 11 [copy,10,flip.1] c(I)=D. ---> New Demodulator: 12 [new_demod,11] c(I)=D. ** KEPT (pick-wt=5): 14 [copy,13,flip.1] u(I,D)=U. ---> New Demodulator: 15 [new_demod,14] u(I,D)=U. ** KEPT (pick-wt=4): 17 [copy,16,flip.1] c(U)=Z. ---> New Demodulator: 18 [new_demod,17] c(U)=Z. ** KEPT (pick-wt=7): 19 [] n(x,y)=n(y,x). ** KEPT (pick-wt=14): 20 [] n(k(n(I,x),U),k(n(I,c(x)),U))=Z. ---> New Demodulator: 21 [new_demod,20] n(k(n(I,x),U),k(n(I,c(x)),U))=Z. ** KEPT (pick-wt=14): 22 [] u(k(n(I,x),U),k(n(I,c(x)),U))=U. ---> New Demodulator: 23 [new_demod,22] u(k(n(I,x),U),k(n(I,c(x)),U))=U. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 18. Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] n(x,y)=n(y,x). >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.03 sec ----> 122 [binary,120.1,6.1] $F. Length of proof is 1. Level of proof is 1. ---------------- PROOF ---------------- 3 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. 6 [] c(k(n(I,$c1),U))!=k(n(I,c($c1)),U). 20 [] n(k(n(I,x),U),k(n(I,c(x)),U))=Z. 22 [] u(k(n(I,x),U),k(n(I,c(x)),U))=U. 120 [hyper,22,3,20] c(k(n(I,x),U))=k(n(I,c(x)),U). 122 [binary,120.1,6.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 21 clauses generated 182 clauses kept 90 clauses forward subsumed 100 clauses back subsumed 0 Kbytes malloced 191 ----------- times (seconds) ----------- user CPU time 0.23 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) hyper_res time 0.00 para_into time 0.00 para_from time 0.00 for_sub time 0.00 back_sub time 0.00 conflict time 0.00 demod time 0.00 That finishes the proof of the theorem. Process 0 finished Sun Nov 30 16:06:18 2003