----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Mon Dec 29 22:38:57 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). assign(max_distinct_vars,3). assign(max_literals,1). assign(max_mem,40000). assign(max_weight,24). include("1To4booleanLaws.txt"). ------- start included file 1To4booleanLaws.txt------- formula_list(usable). all x y z (i(x,u(y,z))->i(n(x,c(z)),y)). all x y z (i(x,y)->i(u(z,x),u(z,y))). all x y (x=u(n(x,c(y)),n(x,y))). all x y i(n(x,y),y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,u(y,z))|i(n(x,c(z)),y). 0 [] -i(x,y)|i(u(z,x),u(z,y)). 0 [] x=u(n(x,c(y)),n(x,y)). 0 [] i(n(x,y),y). end_of_list. ------- end included file 1To4booleanLaws.txt------- include("13booleanLaws.txt"). ------- start included file 13booleanLaws.txt------- formula_list(usable). all x y (i(x,y)&i(y,x)->x=y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)| -i(y,x)|x=y. end_of_list. ------- end included file 13booleanLaws.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("26_27booleanLaws.txt"). ------- start included file 26_27booleanLaws.txt------- formula_list(usable). all x y z (i(x,y)&i(x,z)->i(x,n(y,z))). all x y (i(n(x,y),x)&i(n(x,y),y)). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). 0 [] i(n(x,y),x). 0 [] i(n(x,y),y). end_of_list. ------- end included file 26_27booleanLaws.txt------- include("29booleanLaws.txt"). ------- start included file 29booleanLaws.txt------- formula_list(usable). all x y z (i(x,y)&i(x,z)->i(x,n(y,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). end_of_list. ------- end included file 29booleanLaws.txt------- include("30booleanLaws.txt"). ------- start included file 30booleanLaws.txt------- formula_list(usable). all x y z w (n(n(x,y),n(z,w))=n(n(x,w),n(z,y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(n(x,y),n(z,w))=n(n(x,w),n(z,y)). end_of_list. ------- end included file 30booleanLaws.txt------- include("subIdLaws_a.txt"). ------- start included file subIdLaws_a.txt------- formula_list(usable). all x y z w (i(x,I)&i(y,I)->k(n(x,y),n(z,w))=n(n(k(x,z),k(y,z)),n(k(x,w),k(y,w)))). all x y z w i(n(k(x,z),k(y,w)),k(k(x,r(x)),k(y,w))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,I)| -i(y,I)|k(n(x,y),n(z,w))=n(n(k(x,z),k(y,z)),n(k(x,w),k(y,w))). 0 [] i(n(k(x,z),k(y,w)),k(k(x,r(x)),k(y,w))). end_of_list. ------- end included file subIdLaws_a.txt------- include("subIdLaws_b.txt"). ------- start included file subIdLaws_b.txt------- formula_list(usable). all x y z w (i(x,I)&i(y,I)->i(n(k(x,z),k(y,w)),k(y,z))). all x y z w (i(x,I)&i(y,I)->i(n(k(x,z),k(y,w)),k(x,w))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,w)),k(y,z)). 0 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,w)),k(x,w)). end_of_list. ------- end included file subIdLaws_b.txt------- include("xxiii_a.txt"). ------- start included file xxiii_a.txt------- formula_list(usable). -(all x y z v (i(x,I)&i(z,I)->k(n(x,z),n(y,v))=n(k(x,y),k(z,v)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i($c4,I). 0 [] i($c2,I). 0 [] k(n($c4,$c2),n($c3,$c1))!=n(k($c4,$c3),k($c2,$c1)). end_of_list. ------- end included file xxiii_a.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 [] -i(x,u(y,z))|i(n(x,c(z)),y). ** KEPT (pick-wt=10): 2 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,x)|x=y. ** KEPT (pick-wt=11): 4 [] n(x,c(y))!=Z|u(x,y)=y. ** KEPT (pick-wt=11): 5 [] u(x,y)!=y|n(x,c(y))=Z. ** KEPT (pick-wt=14): 6 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. ** KEPT (pick-wt=9): 7 [] c(x)!=y|n(x,y)=Z. ** KEPT (pick-wt=9): 8 [] c(x)!=y|u(x,y)=U. ** KEPT (pick-wt=11): 9 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). Following clause subsumed by 9 during input processing: 0 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). ** KEPT (pick-wt=29): 11 [copy,10,flip.3] -i(x,I)| -i(y,I)|n(n(k(x,z),k(y,z)),n(k(x,u),k(y,u)))=k(n(x,y),n(z,u)). ** KEPT (pick-wt=17): 12 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,u)),k(y,z)). ** KEPT (pick-wt=17): 13 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,u)),k(x,u)). ** KEPT (pick-wt=15): 15 [copy,14,flip.1] n(k($c4,$c3),k($c2,$c1))!=k(n($c4,$c2),n($c3,$c1)). ------------> process sos: ** KEPT (pick-wt=10): 17 [copy,16,flip.1] u(n(x,c(y)),n(x,y))=x. ---> New Demodulator: 18 [new_demod,17] u(n(x,c(y)),n(x,y))=x. ** KEPT (pick-wt=5): 19 [] i(n(x,y),y). ** KEPT (pick-wt=7): 20 [] n(x,y)=n(y,x). ** KEPT (pick-wt=5): 21 [] i(n(x,y),x). Following clause subsumed by 19 during input processing: 0 [] i(n(x,y),y). ** KEPT (pick-wt=15): 22 [] n(n(x,y),n(z,u))=n(n(x,u),n(z,y)). ** KEPT (pick-wt=16): 23 [] i(n(k(x,y),k(z,u)),k(k(x,r(x)),k(z,u))). ** KEPT (pick-wt=3): 24 [] i($c4,I). ** KEPT (pick-wt=3): 25 [] i($c2,I). >>>> Starting back demodulation with 18. Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] n(x,y)=n(y,x). Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] n(n(x,y),n(z,u))=n(n(x,u),n(z,y)). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 16.66 sec ----> 21485 [binary,21484.1,596.1] $F. Length of proof is 49. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -i(x,u(y,z))|i(n(x,c(z)),y). 2 [] -i(x,y)|i(u(z,x),u(z,y)). 3 [] -i(x,y)| -i(y,x)|x=y. 4 [] n(x,c(y))!=Z|u(x,y)=y. 6 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. 7 [] c(x)!=y|n(x,y)=Z. 9 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). 10 [] -i(x,I)| -i(y,I)|k(n(x,y),n(z,u))=n(n(k(x,z),k(y,z)),n(k(x,u),k(y,u))). 11 [copy,10,flip.3] -i(x,I)| -i(y,I)|n(n(k(x,z),k(y,z)),n(k(x,u),k(y,u)))=k(n(x,y),n(z,u)). 12 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,u)),k(y,z)). 13 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,u)),k(x,u)). 14 [] k(n($c4,$c2),n($c3,$c1))!=n(k($c4,$c3),k($c2,$c1)). 15 [copy,14,flip.1] n(k($c4,$c3),k($c2,$c1))!=k(n($c4,$c2),n($c3,$c1)). 16 [] x=u(n(x,c(y)),n(x,y)). 17 [copy,16,flip.1] u(n(x,c(y)),n(x,y))=x. 19 [] i(n(x,y),y). 20 [] n(x,y)=n(y,x). 21 [] i(n(x,y),x). 22 [] n(n(x,y),n(z,u))=n(n(x,u),n(z,y)). 24 [] i($c4,I). 25 [] i($c2,I). 26 [para_into,17.1.1,17.1.1] x=x. 32 [hyper,25,13,24] i(n(k($c2,x),k($c4,y)),k($c2,y)). 34 [hyper,25,12,24] i(n(k($c2,x),k($c4,y)),k($c4,x)). 37 [hyper,25,11,24] n(n(k($c4,x),k($c2,x)),n(k($c4,y),k($c2,y)))=k(n($c4,$c2),n(x,y)). 39 [hyper,25,11,24] n(n(k($c2,x),k($c4,x)),n(k($c2,y),k($c4,y)))=k(n($c2,$c4),n(x,y)). 45 [hyper,26,7] n(x,c(x))=Z. 57 [hyper,19,1] i(n(n(x,u(y,z)),c(z)),y). 58 [para_from,20.1.1,15.1.1] n(k($c2,$c1),k($c4,$c3))!=k(n($c4,$c2),n($c3,$c1)). 84 [hyper,45,4] u(x,x)=x. 90 [para_from,45.1.1,21.1.1] i(Z,x). 93 [para_from,45.1.1,17.1.1.1] u(Z,n(x,x))=x. 123 [hyper,90,3,21] n(Z,x)=Z. 126,125 [hyper,90,3,19] n(x,Z)=Z. 127 [hyper,90,2] i(u(x,Z),u(x,y)). 143,142 [hyper,123,4] u(Z,x)=x. 145,144 [back_demod,93,demod,143] n(x,x)=x. 152 [para_from,125.1.1,17.1.1.2] u(n(x,c(Z)),Z)=x. 155,154 [hyper,142,6,123] c(Z)=U. 156 [back_demod,152,demod,155] u(n(x,U),Z)=x. 160 [para_from,144.1.1,22.1.1.1] n(x,n(y,z))=n(n(x,z),n(y,x)). 161 [para_from,144.1.1,21.1.1] i(x,x). 304 [hyper,32,9,161] i(n(k($c2,x),k($c4,y)),n(k($c2,y),n(k($c2,x),k($c4,y)))). 409 [hyper,34,9,161] i(n(k($c2,x),k($c4,y)),n(k($c4,x),n(k($c2,x),k($c4,y)))). 420 [para_into,127.1.2,84.1.1] i(u(x,Z),x). 460 [hyper,420,9,127] i(u(x,Z),n(x,u(x,y))). 470 [hyper,156,6,125,demod,145] c(U)=Z. 481 [para_into,37.1.1.2,20.1.1] n(n(k($c4,x),k($c2,x)),n(k($c2,y),k($c4,y)))=k(n($c4,$c2),n(x,y)). 484,483 [para_into,37.1.1,144.1.1,demod,145] n(k($c4,x),k($c2,x))=k(n($c4,$c2),x). 489,488 [back_demod,481,demod,484] n(k(n($c4,$c2),x),n(k($c2,y),k($c4,y)))=k(n($c4,$c2),n(x,y)). 532,531 [para_from,470.1.1,17.1.1.1.2,demod,126,143] n(x,U)=x. 535,534 [back_demod,156,demod,532] u(x,Z)=x. 538 [back_demod,460,demod,535] i(x,n(x,u(x,y))). 546 [para_from,531.1.1,22.1.1.2,demod,532] n(n(x,y),z)=n(x,n(z,y)). 581,580 [para_into,39.1.1.1,20.1.1,demod,484,489] k(n($c4,$c2),n(x,y))=k(n($c2,$c4),n(x,y)). 584 [para_into,39.1.1,22.1.1] n(n(k($c2,x),k($c4,y)),n(k($c2,y),k($c4,x)))=k(n($c2,$c4),n(x,y)). 596 [back_demod,58,demod,581] n(k($c2,$c1),k($c4,$c3))!=k(n($c2,$c4),n($c3,$c1)). 706 [hyper,538,3,21] n(x,u(x,y))=x. 1070 [hyper,57,3,90,demod,143,flip.1] n(n(x,y),c(y))=Z. 1843 [hyper,1070,4] u(n(x,y),y)=y. 1865 [para_into,1843.1.1.1,20.1.1] u(n(x,y),x)=x. 1881 [para_from,1865.1.1,706.1.1.2] n(n(x,y),x)=n(x,y). 5353,5352 [para_into,160.1.1.2,20.1.1,flip.1] n(n(x,y),n(z,x))=n(x,n(y,z)). 12924,12923 [hyper,304,3,19] n(k($c2,x),n(k($c2,y),k($c4,x)))=n(k($c2,y),k($c4,x)). 18516,18515 [hyper,409,3,19] n(k($c4,x),n(k($c2,x),k($c4,y)))=n(k($c2,x),k($c4,y)). 19385,19384 [para_into,546.1.1.1,1881.1.1,demod,5353] n(n(x,y),z)=n(x,n(y,z)). 21484 [back_demod,584,demod,19385,18516,12924] n(k($c2,x),k($c4,y))=k(n($c2,$c4),n(y,x)). 21485 [binary,21484.1,596.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 696 clauses generated 94275 clauses kept 20443 clauses forward subsumed 37565 clauses back subsumed 713 Kbytes malloced 10442 ----------- times (seconds) ----------- user CPU time 16.86 (0 hr, 0 min, 16 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 17 (0 hr, 0 min, 17 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 Mon Dec 29 22:39:14 2003