----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 00:53:03 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_seconds,7). include("4To8booleanLaws.txt"). ------- start included file 4To8booleanLaws.txt------- formula_list(usable). all x y i(n(x,y),y). all x y z i(n(x,u(y,z)),u(y,n(x,z))). all x y (x=u(n(x,y),n(x,c(y)))). all x y z (i(x,y)->i(u(z,x),u(z,y))). all x y z (i(x,y)->i(n(z,x),n(z,y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(n(x,y),y). 0 [] i(n(x,u(y,z)),u(y,n(x,z))). 0 [] x=u(n(x,y),n(x,c(y))). 0 [] -i(x,y)|i(u(z,x),u(z,y)). 0 [] -i(x,y)|i(n(z,x),n(z,y)). end_of_list. ------- end included file 4To8booleanLaws.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("monotLaws.txt"). ------- start included file monotLaws.txt------- include("1To3monotLaws.txt"). ------- start included file 1To3monotLaws.txt------- formula_list(usable). all x y z (u(x,y)=y->u(k(z,x),k(z,y))=k(z,y)). all x y z (u(x,y)=y->u(c(u(z,y)),c(x))=c(x)). all x y z (u(x,y)=y->u(k(x,z),k(y,z))=k(y,z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y). 0 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x). 0 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z). end_of_list. ------- end included file 1To3monotLaws.txt------- include("4_5monotLaws.txt"). ------- start included file 4_5monotLaws.txt------- formula_list(usable). all x y w v i(k(n(x,w),n(y,v)),k(x,y)). all x y w v i(k(n(x,w),n(y,v)),k(w,v)). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(n(x,w),n(y,v)),k(x,y)). 0 [] i(k(n(x,w),n(y,v)),k(w,v)). end_of_list. ------- end included file 4_5monotLaws.txt------- ------- end included file monotLaws.txt------- include("cycleLawsB.txt"). ------- start included file cycleLawsB.txt------- formula_list(usable). all x y z (n(y,k(x,n(z,c(k(r(x),y)))))=Z). all x y z v (n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y)). all x y z (n(y,k(n(x,c(k(y,r(z)))),z))=Z). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(y,k(x,n(z,c(k(r(x),y)))))=Z. 0 [] n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y). 0 [] n(y,k(n(x,c(k(y,r(z)))),z))=Z. end_of_list. ------- end included file cycleLawsB.txt------- include("cycleLawC.txt"). ------- start included file cycleLawC.txt------- formula_list(usable). all x y z (n(y,k(n(x,k(y,r(z))),z))=n(k(x,z),y)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(y,k(n(x,k(y,r(z))),z))=n(k(x,z),y). end_of_list. ------- end included file cycleLawC.txt------- include("xv_a_ghost.txt"). ------- start included file xv_a_ghost.txt------- formula_list(usable). all y z v i(k(n(y,z),v),k(y,v)). -(all x y z v i(u(k(n(y,z),n(v,x)),k(n(y,z),n(v,c(x)))),u(k(n(y,z),n(v,x)),k(y,n(v,c(x)))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(n(y,z),v),k(y,v)). 0 [] -i(u(k(n($c3,$c2),n($c1,$c4)),k(n($c3,$c2),n($c1,c($c4)))),u(k(n($c3,$c2),n($c1,$c4)),k($c3,n($c1,c($c4))))). end_of_list. ------- end included file xv_a_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=10): 1 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=10): 2 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=16): 4 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y). ** KEPT (pick-wt=15): 5 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x). ** KEPT (pick-wt=16): 6 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z). ** KEPT (pick-wt=31): 7 [] -i(u(k(n($c3,$c2),n($c1,$c4)),k(n($c3,$c2),n($c1,c($c4)))),u(k(n($c3,$c2),n($c1,$c4)),k($c3,n($c1,c($c4))))). ------------> process sos: ** KEPT (pick-wt=5): 8 [] i(n(x,y),y). ** KEPT (pick-wt=11): 9 [] i(n(x,u(y,z)),u(y,n(x,z))). ** KEPT (pick-wt=10): 11 [copy,10,flip.1] u(n(x,y),n(x,c(y)))=x. ---> New Demodulator: 12 [new_demod,11] u(n(x,y),n(x,c(y)))=x. ** KEPT (pick-wt=5): 13 [] u(x,Z)=x. ---> New Demodulator: 14 [new_demod,13] u(x,Z)=x. ** KEPT (pick-wt=11): 15 [] i(k(n(x,y),n(z,u)),k(x,z)). ** KEPT (pick-wt=11): 16 [] i(k(n(x,y),n(z,u)),k(y,u)). ** KEPT (pick-wt=13): 17 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ---> New Demodulator: 18 [new_demod,17] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ** KEPT (pick-wt=20): 20 [copy,19,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). ---> New Demodulator: 21 [new_demod,20] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). ** KEPT (pick-wt=13): 22 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z. ---> New Demodulator: 23 [new_demod,22] n(x,k(n(y,c(k(x,r(z)))),z))=Z. ** KEPT (pick-wt=16): 24 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). ** KEPT (pick-wt=9): 25 [] i(k(n(x,y),z),k(x,z)). >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. ** KEPT (pick-wt=16): 26 [copy,24,flip.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)). Following clause subsumed by 24 during input processing: 0 [copy,26,flip.1] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.03 sec ----> 100 [binary,99.1,7.1] $F. Length of proof is 1. Level of proof is 1. ---------------- PROOF ---------------- 1 [] -i(x,y)|i(u(z,x),u(z,y)). 7 [] -i(u(k(n($c3,$c2),n($c1,$c4)),k(n($c3,$c2),n($c1,c($c4)))),u(k(n($c3,$c2),n($c1,$c4)),k($c3,n($c1,c($c4))))). 25 [] i(k(n(x,y),z),k(x,z)). 99 [hyper,25,1] i(u(x,k(n(y,z),u)),u(x,k(y,u))). 100 [binary,99.1,7.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 12 clauses generated 85 clauses kept 86 clauses forward subsumed 20 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 1 (0 hr, 0 min, 1 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 00:53:04 2003