----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 15:40:14 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("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("dDef.txt"). ------- start included file dDef.txt------- formula_list(usable). all x y (d(x,y)=c(k(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] d(x,y)=c(k(c(x),c(y))). end_of_list. ------- end included file dDef.txt------- include("15_16booleanLaws.txt"). ------- start included file 15_16booleanLaws.txt------- formula_list(usable). all x (c(c(x))=x). all x y (u(x,y)=y->c(u(y,c(x)))=Z). all x y (c(u(y,c(x)))=Z->u(x,y)=y). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(c(x))=x. 0 [] u(x,y)!=y|c(u(y,c(x)))=Z. 0 [] c(u(y,c(x)))!=Z|u(x,y)=y. end_of_list. ------- end included file 15_16booleanLaws.txt------- include("xix_a_ghost.txt"). ------- start included file xix_a_ghost.txt------- formula_list(usable). all x y (k(c(x),c(r(y)))=Z<->i(k(U,c(x)),y)). all x y (c(k(c(x),c(r(y))))=U<->i(k(U,c(x)),y)). all x y (i(x,y)<->u(c(x),y)=U). all x y (c(k(c(x),c(r(y))))=U<->u(c(k(U,c(x))),y)=U). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(c(x),c(r(y)))!=Z|i(k(U,c(x)),y). 0 [] k(c(x),c(r(y)))=Z| -i(k(U,c(x)),y). 0 [] c(k(c(x),c(r(y))))!=U|i(k(U,c(x)),y). 0 [] c(k(c(x),c(r(y))))=U| -i(k(U,c(x)),y). 0 [] -i(x,y)|u(c(x),y)=U. 0 [] i(x,y)|u(c(x),y)!=U. 0 [] c(k(c(x),c(r(y))))!=U|u(c(k(U,c(x))),y)=U. 0 [] c(k(c(x),c(r(y))))=U|u(c(k(U,c(x))),y)!=U. end_of_list. ------- end included file xix_a_ghost.txt------- include("xix_b_ghost.txt"). ------- start included file xix_b_ghost.txt------- formula_list(usable). all x y (k(x,r(y))=Z->n(k(U,x),k(U,y))=Z). all x y (n(k(U,x),k(U,y))=Z->k(x,r(y))=Z). all x y (u(d(Z,x),d(Z,y))=U->d(x,r(y))=U). all x y (d(x,r(y))=U->u(d(Z,x),d(Z,y))=U). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,r(y))!=Z|n(k(U,x),k(U,y))=Z. 0 [] n(k(U,x),k(U,y))!=Z|k(x,r(y))=Z. 0 [] u(d(Z,x),d(Z,y))!=U|d(x,r(y))=U. 0 [] d(x,r(y))!=U|u(d(Z,x),d(Z,y))=U. end_of_list. ------- end included file xix_b_ghost.txt------- include("xix.txt"). ------- start included file xix.txt------- formula_list(usable). all x y (d(x,r(y))=U<->u(d(Z,x),y)=U). -(all x y (d(x,r(y))=U<->u(d(Z,x),d(Z,y))=U)). end_of_list. -------> usable clausifies to: list(usable). 0 [] d(x,r(y))!=U|u(d(Z,x),y)=U. 0 [] d(x,r(y))=U|u(d(Z,x),y)!=U. 0 [] d($c2,r($c1))=U|u(d(Z,$c2),d(Z,$c1))=U. 0 [] d($c2,r($c1))!=U|u(d(Z,$c2),d(Z,$c1))!=U. end_of_list. ------- end included file xix.txt------- SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2. This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, 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: set(unit_deletion). dependent: set(factor). ------------> process usable: ** KEPT (pick-wt=12): 1 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 2 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=14): 3 [] k(c(x),c(r(y)))!=Z|i(k(U,c(x)),y). ** KEPT (pick-wt=14): 4 [] k(c(x),c(r(y)))=Z| -i(k(U,c(x)),y). ** KEPT (pick-wt=15): 5 [] c(k(c(x),c(r(y))))!=U|i(k(U,c(x)),y). ** KEPT (pick-wt=15): 6 [] c(k(c(x),c(r(y))))=U| -i(k(U,c(x)),y). ** KEPT (pick-wt=9): 7 [] -i(x,y)|u(c(x),y)=U. ** KEPT (pick-wt=9): 8 [] i(x,y)|u(c(x),y)!=U. ** KEPT (pick-wt=18): 9 [] c(k(c(x),c(r(y))))!=U|u(c(k(U,c(x))),y)=U. ** KEPT (pick-wt=18): 10 [] c(k(c(x),c(r(y))))=U|u(c(k(U,c(x))),y)!=U. ** KEPT (pick-wt=15): 11 [] k(x,r(y))!=Z|n(k(U,x),k(U,y))=Z. ** KEPT (pick-wt=15): 12 [] n(k(U,x),k(U,y))!=Z|k(x,r(y))=Z. ** KEPT (pick-wt=15): 13 [] u(d(Z,x),d(Z,y))!=U|d(x,r(y))=U. ** KEPT (pick-wt=15): 14 [] d(x,r(y))!=U|u(d(Z,x),d(Z,y))=U. ** KEPT (pick-wt=13): 15 [] d(x,r(y))!=U|u(d(Z,x),y)=U. ** KEPT (pick-wt=13): 16 [] d(x,r(y))=U|u(d(Z,x),y)!=U. ** KEPT (pick-wt=15): 17 [] d($c2,r($c1))!=U|u(d(Z,$c2),d(Z,$c1))!=U. ------------> process sos: ** KEPT (pick-wt=4): 19 [copy,18,flip.1] c(I)=D. ---> New Demodulator: 20 [new_demod,19] c(I)=D. ** KEPT (pick-wt=5): 22 [copy,21,flip.1] u(I,D)=U. ---> New Demodulator: 23 [new_demod,22] u(I,D)=U. ** KEPT (pick-wt=4): 25 [copy,24,flip.1] c(U)=Z. ---> New Demodulator: 26 [new_demod,25] c(U)=Z. ** KEPT (pick-wt=10): 28 [copy,27,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 29 [new_demod,28] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=5): 30 [] c(c(x))=x. ---> New Demodulator: 31 [new_demod,30] c(c(x))=x. ** KEPT (pick-wt=15): 32 [] d($c2,r($c1))=U|u(d(Z,$c2),d(Z,$c1))=U. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 29. >> back demodulating 10 with 29. >> back demodulating 9 with 29. >> back demodulating 6 with 29. >> back demodulating 5 with 29. >>>> Starting back demodulation with 31. ======= end of input processing ======= =========== start of search =========== -----> EMPTY CLAUSE at 0.02 sec ----> 105 [back_demod,17,demod,104,101,unit_del,84,84] $F. Length of proof is 3. Level of proof is 1. ---------------- PROOF ---------------- 13 [] u(d(Z,x),d(Z,y))!=U|d(x,r(y))=U. 14 [] d(x,r(y))!=U|u(d(Z,x),d(Z,y))=U. 17 [] d($c2,r($c1))!=U|u(d(Z,$c2),d(Z,$c1))!=U. 30 [] c(c(x))=x. 32 [] d($c2,r($c1))=U|u(d(Z,$c2),d(Z,$c1))=U. 84 [para_into,30.1.1,30.1.1] x=x. 101,100 [hyper,32,14,factor_simp] u(d(Z,$c2),d(Z,$c1))=U. 104,103 [hyper,32,13,factor_simp] d($c2,r($c1))=U. 105 [back_demod,17,demod,104,101,unit_del,84,84] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 11 clauses generated 77 clauses kept 82 clauses forward subsumed 40 clauses back subsumed 13 Kbytes malloced 159 ----------- 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 15:40:14 2003