----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 01:10:48 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,5). 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("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("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("v.txt"). ------- start included file v.txt------- formula_list(usable). all x y z (k(x,u(y,z))=u(k(x,y),k(x,z))). all x y z (k(u(x,y),z)=u(k(x,z),k(y,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,u(y,z))=u(k(x,y),k(x,z)). 0 [] k(u(x,y),z)=u(k(x,z),k(y,z)). end_of_list. ------- end included file v.txt------- include("ix_b.txt"). ------- start included file ix_b.txt------- formula_list(usable). all x (k(I,x)=x). all x i(x,k(x,U)). all x i(x,k(U,x)). all x i(d(Z,x),x). all x i(d(x,Z),x). all x (k(U,U)=U). all x (d(Z,Z)=Z). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(I,x)=x. 0 [] i(x,k(x,U)). 0 [] i(x,k(U,x)). 0 [] i(d(Z,x),x). 0 [] i(d(x,Z),x). 0 [] k(U,U)=U. 0 [] d(Z,Z)=Z. end_of_list. ------- end included file ix_b.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(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. ------- end included file xv_a_ghost.txt------- include("xv_a.txt"). ------- start included file xv_a.txt------- formula_list(usable). -(all x y z v w i(n(w,k(n(y,z),v)),n(w,u(k(n(y,z),n(v,x)),k(y,n(v,c(x))))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(n($c1,k(n($c4,$c3),$c2)),n($c1,u(k(n($c4,$c3),n($c2,$c5)),k($c4,n($c2,c($c5)))))). end_of_list. ------- end included file xv_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=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=24): 7 [] -i(n($c1,k(n($c4,$c3),$c2)),n($c1,u(k(n($c4,$c3),n($c2,$c5)),k($c4,n($c2,c($c5)))))). ------------> 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=13): 15 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ---> New Demodulator: 16 [new_demod,15] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ** KEPT (pick-wt=20): 18 [copy,17,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). ---> New Demodulator: 19 [new_demod,18] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). ** KEPT (pick-wt=13): 20 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z. ---> New Demodulator: 21 [new_demod,20] n(x,k(n(y,c(k(x,r(z)))),z))=Z. ** KEPT (pick-wt=16): 22 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). ** KEPT (pick-wt=13): 24 [copy,23,flip.1] u(k(x,y),k(x,z))=k(x,u(y,z)). ---> New Demodulator: 25 [new_demod,24] u(k(x,y),k(x,z))=k(x,u(y,z)). ** KEPT (pick-wt=13): 27 [copy,26,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 28 [new_demod,27] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=5): 29 [] k(I,x)=x. ---> New Demodulator: 30 [new_demod,29] k(I,x)=x. ** KEPT (pick-wt=5): 31 [] i(x,k(x,U)). ** KEPT (pick-wt=5): 32 [] i(x,k(U,x)). ** KEPT (pick-wt=5): 33 [] i(d(Z,x),x). ** KEPT (pick-wt=5): 34 [] i(d(x,Z),x). ** KEPT (pick-wt=5): 35 [] k(U,U)=U. ---> New Demodulator: 36 [new_demod,35] k(U,U)=U. ** KEPT (pick-wt=5): 37 [] d(Z,Z)=Z. ---> New Demodulator: 38 [new_demod,37] d(Z,Z)=Z. ** KEPT (pick-wt=9): 39 [] i(k(n(x,y),z),k(x,z)). ** KEPT (pick-wt=20): 41 [copy,40,demod,25,12] i(k(n(x,y),z),u(k(n(x,y),n(z,u)),k(x,n(z,c(u))))). >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 21. ** KEPT (pick-wt=16): 42 [copy,22,flip.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)). >>>> Starting back demodulation with 25. >> back demodulating 4 with 25. >>>> Starting back demodulation with 28. >> back demodulating 18 with 28. >> back demodulating 6 with 28. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 38. Following clause subsumed by 22 during input processing: 0 [copy,42,flip.1] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). Following clause subsumed by 44 during input processing: 0 [copy,44,flip.1] n(k(x,y),z)=n(k(x,y),z). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.05 sec ----> 597 [binary,596.1,7.1] $F. Length of proof is 4. Level of proof is 3. ---------------- PROOF ---------------- 2 [] -i(x,y)|i(n(z,x),n(z,y)). 7 [] -i(n($c1,k(n($c4,$c3),$c2)),n($c1,u(k(n($c4,$c3),n($c2,$c5)),k($c4,n($c2,c($c5)))))). 10 [] x=u(n(x,y),n(x,c(y))). 12,11 [copy,10,flip.1] u(n(x,y),n(x,c(y)))=x. 23 [] k(x,u(y,z))=u(k(x,y),k(x,z)). 25,24 [copy,23,flip.1] u(k(x,y),k(x,z))=k(x,u(y,z)). 40 [] i(u(k(n(x,y),n(z,u)),k(n(x,y),n(z,c(u)))),u(k(n(x,y),n(z,u)),k(x,n(z,c(u))))). 41 [copy,40,demod,25,12] i(k(n(x,y),z),u(k(n(x,y),n(z,u)),k(x,n(z,c(u))))). 596 [hyper,41,2] i(n(x,k(n(y,z),u)),n(x,u(k(n(y,z),n(u,v)),k(y,n(u,c(v)))))). 597 [binary,596.1,7.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 46 clauses generated 780 clauses kept 567 clauses forward subsumed 256 clauses back subsumed 6 Kbytes malloced 447 ----------- times (seconds) ----------- user CPU time 0.25 (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 01:10:49 2003