----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 16:56:45 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,30000). assign(max_weight,18). 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("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("28booleanLaws.txt"). ------- start included file 28booleanLaws.txt------- formula_list(usable). all x (n(x,x)=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,x)=x. end_of_list. ------- end included file 28booleanLaws.txt------- include("viii.txt"). ------- start included file viii.txt------- formula_list(usable). all x y w v i(k(n(x,w),n(y,v)),n(k(x,y),k(w,v))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(n(x,w),n(y,v)),n(k(x,y),k(w,v))). end_of_list. ------- end included file viii.txt------- include("x_a.txt"). ------- start included file x_a.txt------- formula_list(usable). all x y z i(n(k(x,z),c(k(y,z))),k(n(x,c(y)),z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(n(k(x,z),c(k(y,z))),k(n(x,c(y)),z)). end_of_list. ------- end included file x_a.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)))))). all y v w i(n(k(y,v),w),k(n(y,k(w,r(v))),n(v,k(r(y),w)))). all y v w i(n(k(y,v),w),k(y,n(v,k(r(y),w)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(n(w,k(n(y,z),v)),n(w,u(k(n(y,z),n(v,x)),k(y,n(v,c(x)))))). 0 [] i(n(k(y,v),w),k(n(y,k(w,r(v))),n(v,k(r(y),w)))). 0 [] i(n(k(y,v),w),k(y,n(v,k(r(y),w)))). end_of_list. ------- end included file xv_a.txt------- include("xxvii_a_ghost.txt"). ------- start included file xxvii_a_ghost.txt------- formula_list(usable). all x z (u(x,I)=I->u(k(x,z),z)=z). all x y z (i(x,y)->i(k(z,x),k(z,y))). all x y (n(x,y)=n(y,x)). all x y i(n(x,y),y). all x y z (i(x,y)->i(n(z,x),n(z,y))). all x (k(I,x)=x). all x y z (i(x,y)->i(k(x,z),k(y,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,I)!=I|u(k(x,z),z)=z. 0 [] -i(x,y)|i(k(z,x),k(z,y)). 0 [] n(x,y)=n(y,x). 0 [] i(n(x,y),y). 0 [] -i(x,y)|i(n(z,x),n(z,y)). 0 [] k(I,x)=x. 0 [] -i(x,y)|i(k(x,z),k(y,z)). end_of_list. ------- end included file xxvii_a_ghost.txt------- include("xxvii_a.txt"). ------- start included file xxvii_a.txt------- formula_list(usable). all x y z (i(k(r(x),x),I)->i(n(k(x,y),k(x,z)),k(x,n(y,z)))). -(all x y z (i(k(r(x),x),I)->k(x,n(y,z))=n(k(x,y),k(x,z)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))). 0 [] i(k(r($c3),$c3),I). 0 [] k($c3,n($c2,$c1))!=n(k($c3,$c2),k($c3,$c1)). end_of_list. ------- end included file xxvii_a.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=9): 1 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=9): 2 [] -i(x,y)| -i(y,x)|x=y. ** KEPT (pick-wt=12): 3 [] u(x,I)!=I|u(k(x,y),y)=y. ** KEPT (pick-wt=10): 4 [] -i(x,y)|i(k(z,x),k(z,y)). ** KEPT (pick-wt=10): 5 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=10): 6 [] -i(x,y)|i(k(x,z),k(y,z)). ** KEPT (pick-wt=19): 7 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))). ** KEPT (pick-wt=13): 9 [copy,8,flip.1] n(k($c3,$c2),k($c3,$c1))!=k($c3,n($c2,$c1)). ------------> process sos: ** KEPT (pick-wt=11): 11 [copy,10,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 12 [new_demod,11] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=11): 14 [copy,13,flip.1] d(d(x,y),z)=d(x,d(y,z)). ---> New Demodulator: 15 [new_demod,14] d(d(x,y),z)=d(x,d(y,z)). ** KEPT (pick-wt=5): 16 [] u(x,Z)=x. ---> New Demodulator: 17 [new_demod,16] u(x,Z)=x. ** KEPT (pick-wt=5): 18 [] n(x,x)=x. ---> New Demodulator: 19 [new_demod,18] n(x,x)=x. ** KEPT (pick-wt=15): 20 [] i(k(n(x,y),n(z,u)),n(k(x,z),k(y,u))). ** KEPT (pick-wt=15): 21 [] i(n(k(x,y),c(k(z,y))),k(n(x,c(z)),y)). ** KEPT (pick-wt=24): 22 [] i(n(x,k(n(y,z),u)),n(x,u(k(n(y,z),n(u,v)),k(y,n(u,c(v)))))). ** KEPT (pick-wt=19): 23 [] i(n(k(x,y),z),k(n(x,k(z,r(y))),n(y,k(r(x),z)))). ** KEPT (pick-wt=14): 24 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). ** KEPT (pick-wt=7): 25 [] n(x,y)=n(y,x). ** KEPT (pick-wt=5): 26 [] i(n(x,y),y). ** KEPT (pick-wt=5): 27 [] k(I,x)=x. ---> New Demodulator: 28 [new_demod,27] k(I,x)=x. ** KEPT (pick-wt=6): 29 [] i(k(r($c3),$c3),I). >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] n(x,y)=n(y,x). >>>> Starting back demodulation with 28. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.05 sec ----> 442 [binary,440.1,9.1] $F. Length of proof is 4. Level of proof is 2. ---------------- PROOF ---------------- 2 [] -i(x,y)| -i(y,x)|x=y. 7 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))). 8 [] k($c3,n($c2,$c1))!=n(k($c3,$c2),k($c3,$c1)). 9 [copy,8,flip.1] n(k($c3,$c2),k($c3,$c1))!=k($c3,n($c2,$c1)). 18 [] n(x,x)=x. 20 [] i(k(n(x,y),n(z,u)),n(k(x,z),k(y,u))). 29 [] i(k(r($c3),$c3),I). 37 [hyper,29,7] i(n(k($c3,x),k($c3,y)),k($c3,n(x,y))). 44 [para_into,20.1.1.1,18.1.1] i(k(x,n(y,z)),n(k(x,y),k(x,z))). 440 [hyper,44,2,37] n(k($c3,x),k($c3,y))=k($c3,n(x,y)). 442 [binary,440.1,9.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 56 clauses generated 1916 clauses kept 431 clauses forward subsumed 393 clauses back subsumed 1 Kbytes malloced 351 ----------- times (seconds) ----------- user CPU time 0.26 (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 16:56:46 2003