----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 01:38:05 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_literals,1). include("i.txt"). ------- start included file i.txt------- formula_list(usable). all x y (i(x,y)->i(r(x),r(y))). all x y (r(u(x,y))=u(r(x),r(y))). all x (r(c(x))=c(r(x))). all x y (r(n(x,y))=n(r(x),r(y))). all x (r(r(x))=x). all x y (r(d(x,y))=d(r(y),r(x))). all x y (r(k(x,y))=k(r(y),r(x))). r(I)=I. r(Z)=Z. r(U)=U. end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|i(r(x),r(y)). 0 [] r(u(x,y))=u(r(x),r(y)). 0 [] r(c(x))=c(r(x)). 0 [] r(n(x,y))=n(r(x),r(y)). 0 [] r(r(x))=x. 0 [] r(d(x,y))=d(r(y),r(x)). 0 [] r(k(x,y))=k(r(y),r(x)). 0 [] r(I)=I. 0 [] r(Z)=Z. 0 [] r(U)=U. end_of_list. ------- end included file i.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("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("xv_b.txt"). ------- start included file xv_b.txt------- formula_list(usable). -(all x y z i(n(k(x,y),z),k(n(k(z,r(y)),x),y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(n(k($c3,$c2),$c1),k(n(k($c1,r($c2)),$c3),$c2)). end_of_list. ------- end included file xv_b.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=11): 2 [] n(x,c(y))!=Z|u(x,y)=y. ** KEPT (pick-wt=11): 3 [] u(x,y)!=y|n(x,c(y))=Z. ** KEPT (pick-wt=14): 4 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. ** KEPT (pick-wt=9): 5 [] c(x)!=y|n(x,y)=Z. ** KEPT (pick-wt=9): 6 [] c(x)!=y|u(x,y)=U. ** KEPT (pick-wt=14): 7 [] -i(n(k($c3,$c2),$c1),k(n(k($c1,r($c2)),$c3),$c2)). ------------> process sos: ** KEPT (pick-wt=10): 8 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 9 [new_demod,8] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 10 [] r(c(x))=c(r(x)). ---> New Demodulator: 11 [new_demod,10] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 12 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 13 [new_demod,12] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 14 [] r(r(x))=x. ---> New Demodulator: 15 [new_demod,14] r(r(x))=x. ** KEPT (pick-wt=10): 16 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 17 [new_demod,16] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 18 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 19 [new_demod,18] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 20 [] r(I)=I. ---> New Demodulator: 21 [new_demod,20] r(I)=I. ** KEPT (pick-wt=4): 22 [] r(Z)=Z. ---> New Demodulator: 23 [new_demod,22] r(Z)=Z. ** KEPT (pick-wt=4): 24 [] r(U)=U. ---> New Demodulator: 25 [new_demod,24] r(U)=U. ** KEPT (pick-wt=7): 26 [] n(x,y)=n(y,x). ** KEPT (pick-wt=24): 27 [] 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): 28 [] i(n(k(x,y),z),k(n(x,k(z,r(y))),n(y,k(r(x),z)))). ** KEPT (pick-wt=14): 29 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 25. Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] n(x,y)=n(y,x). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.10 sec ----> 891 [binary,890.1,47.1] $F. Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] -i(x,y)|i(r(x),r(y)). 7 [] -i(n(k($c3,$c2),$c1),k(n(k($c1,r($c2)),$c3),$c2)). 13,12 [] r(n(x,y))=n(r(x),r(y)). 15,14 [] r(r(x))=x. 19,18 [] r(k(x,y))=k(r(y),r(x)). 26 [] n(x,y)=n(y,x). 29 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). 47 [para_from,26.1.1,7.1.2.1] -i(n(k($c3,$c2),$c1),k(n($c3,k($c1,r($c2))),$c2)). 51 [hyper,29,1,demod,13,19,19,13,19,15] i(n(k(r(x),r(y)),r(z)),k(n(r(x),k(r(z),y)),r(y))). 152 [para_into,51.1.1.1.1,14.1.1,demod,15] i(n(k(x,r(y)),r(z)),k(n(x,k(r(z),y)),r(y))). 885 [para_into,152.1.1.2,14.1.1,demod,15] i(n(k(x,r(y)),z),k(n(x,k(z,y)),r(y))). 890 [para_into,885.1.1.1.2,14.1.1,demod,15] i(n(k(x,y),z),k(n(x,k(z,r(y))),y)). 891 [binary,890.1,47.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 183 clauses generated 2759 clauses kept 876 clauses forward subsumed 1118 clauses back subsumed 218 Kbytes malloced 1181 ----------- times (seconds) ----------- user CPU time 0.30 (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 Sun Nov 30 01:38:05 2003