----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Mon Dec 29 22:34:31 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,4). 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("9_10booleanLaws.txt"). ------- start included file 9_10booleanLaws.txt------- formula_list(usable). all x (u(x,Z)=x). all x y z (i(x,y)&i(y,z)->i(x,z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,Z)=x. 0 [] -i(x,y)| -i(y,z)|i(x,z). end_of_list. ------- end included file 9_10booleanLaws.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("iv.txt"). ------- start included file iv.txt------- formula_list(usable). all x y z (k(x,k(y,z))=k(k(x,y),z)). all x y z (d(x,d(y,z))=d(d(x,y),z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,k(y,z))=k(k(x,y),z). 0 [] d(x,d(y,z))=d(d(x,y),z). end_of_list. ------- end included file iv.txt------- include("xxii.txt"). ------- start included file xxii.txt------- formula_list(usable). all x (i(x,I)->k(x,x)=x). all x (i(x,I)->r(x)=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,I)|k(x,x)=x. 0 [] -i(x,I)|r(x)=x. end_of_list. ------- end included file xxii.txt------- include("vii.txt"). ------- start included file vii.txt------- formula_list(usable). all x y z (i(x,y)->i(k(x,z),k(y,z))). all x y z (i(x,y)->i(k(z,x),k(z,y))). all x y z (i(x,y)->i(d(x,z),d(y,z))). all x y z (i(x,y)->i(d(z,x),d(z,y))). all x y (i(x,y)->i(r(x),r(y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|i(k(x,z),k(y,z)). 0 [] -i(x,y)|i(k(z,x),k(z,y)). 0 [] -i(x,y)|i(d(x,z),d(y,z)). 0 [] -i(x,y)|i(d(z,x),d(z,y)). 0 [] -i(x,y)|i(r(x),r(y)). end_of_list. ------- end included file vii.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("subId_ghost.txt"). ------- start included file subId_ghost.txt------- formula_list(usable). all x z (i(x,I)&i(z,I)->k(x,z)=n(x,z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,I)| -i(z,I)|k(x,z)=n(x,z). end_of_list. ------- end included file subId_ghost.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($c4,I). 0 [] i($c3,I). 0 [] -i(n(k($c4,$c2),k($c3,$c1)),k($c4,$c1)). end_of_list. ------- end included file subIdLaws_b.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,z)|i(x,z). ** KEPT (pick-wt=9): 4 [] -i(x,y)| -i(y,x)|x=y. ** KEPT (pick-wt=11): 5 [] n(x,c(y))!=Z|u(x,y)=y. ** KEPT (pick-wt=11): 6 [] u(x,y)!=y|n(x,c(y))=Z. ** KEPT (pick-wt=14): 7 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. ** KEPT (pick-wt=9): 8 [] c(x)!=y|n(x,y)=Z. ** KEPT (pick-wt=9): 9 [] c(x)!=y|u(x,y)=U. ** KEPT (pick-wt=11): 10 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). Following clause subsumed by 10 during input processing: 0 [] -i(x,y)| -i(x,z)|i(x,n(y,z)). ** KEPT (pick-wt=8): 11 [] -i(x,I)|k(x,x)=x. ** KEPT (pick-wt=7): 12 [] -i(x,I)|r(x)=x. ** KEPT (pick-wt=10): 13 [] -i(x,y)|i(k(x,z),k(y,z)). ** KEPT (pick-wt=10): 14 [] -i(x,y)|i(k(z,x),k(z,y)). ** KEPT (pick-wt=10): 15 [] -i(x,y)|i(d(x,z),d(y,z)). ** KEPT (pick-wt=10): 16 [] -i(x,y)|i(d(z,x),d(z,y)). ** KEPT (pick-wt=8): 17 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=13): 19 [copy,18,flip.3] -i(x,I)| -i(y,I)|n(x,y)=k(x,y). ** KEPT (pick-wt=29): 21 [copy,20,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): 22 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,u)),k(y,z)). ** KEPT (pick-wt=11): 23 [] -i(n(k($c4,$c2),k($c3,$c1)),k($c4,$c1)). ------------> process sos: ** KEPT (pick-wt=10): 25 [copy,24,flip.1] u(n(x,c(y)),n(x,y))=x. ---> New Demodulator: 26 [new_demod,25] u(n(x,c(y)),n(x,y))=x. ** KEPT (pick-wt=5): 27 [] i(n(x,y),y). ** KEPT (pick-wt=5): 28 [] u(x,Z)=x. ---> New Demodulator: 29 [new_demod,28] u(x,Z)=x. ** KEPT (pick-wt=7): 30 [] n(x,y)=n(y,x). ** KEPT (pick-wt=5): 31 [] i(n(x,y),x). Following clause subsumed by 27 during input processing: 0 [] i(n(x,y),y). ** KEPT (pick-wt=11): 33 [copy,32,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 34 [new_demod,33] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=11): 36 [copy,35,flip.1] d(d(x,y),z)=d(x,d(y,z)). ---> New Demodulator: 37 [new_demod,36] d(d(x,y),z)=d(x,d(y,z)). ** KEPT (pick-wt=15): 38 [] n(n(x,y),n(z,u))=n(n(x,u),n(z,y)). ** KEPT (pick-wt=16): 40 [copy,39,demod,34] i(n(k(x,y),k(z,u)),k(x,k(r(x),k(z,u)))). ** KEPT (pick-wt=3): 41 [] i($c4,I). ** KEPT (pick-wt=3): 42 [] i($c3,I). >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 29. Following clause subsumed by 30 during input processing: 0 [copy,30,flip.1] n(x,y)=n(y,x). >>>> Starting back demodulation with 34. >>>> Starting back demodulation with 37. Following clause subsumed by 38 during input processing: 0 [copy,38,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 0.04 sec ----> 153 [binary,152.1,65.1] $F. Length of proof is 2. Level of proof is 1. ---------------- PROOF ---------------- 22 [] -i(x,I)| -i(y,I)|i(n(k(x,z),k(y,u)),k(y,z)). 23 [] -i(n(k($c4,$c2),k($c3,$c1)),k($c4,$c1)). 30 [] n(x,y)=n(y,x). 41 [] i($c4,I). 42 [] i($c3,I). 65 [hyper,42,22,41] i(n(k($c3,x),k($c4,y)),k($c4,x)). 152 [para_from,30.1.1,23.1.1] -i(n(k($c3,$c1),k($c4,$c2)),k($c4,$c1)). 153 [binary,152.1,65.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 11 clauses generated 173 clauses kept 115 clauses forward subsumed 31 clauses back subsumed 0 Kbytes malloced 191 ----------- times (seconds) ----------- user CPU time 0.24 (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 Mon Dec 29 22:34:31 2003