----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 20:00:15 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,2). assign(max_mem,20000). assign(max_weight,25). 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("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("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("xxviii_a_ghost.txt"). ------- start included file xxviii_a_ghost.txt------- formula_list(usable). all x y z i(k(r(x),n(k(x,z),y)),k(r(x),k(x,n(z,k(r(x),y))))). all x y z (i(k(r(x),x),I)->i(k(r(x),k(x,n(z,k(r(x),y)))),k(I,n(z,k(r(x),y))))). all x y z i(n(k(r(x),y),z),k(r(x),n(y,k(x,z)))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r(x),n(k(x,z),y)),k(r(x),k(x,n(z,k(r(x),y))))). 0 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(z,k(r(x),y)))),k(I,n(z,k(r(x),y)))). 0 [] i(n(k(r(x),y),z),k(r(x),n(y,k(x,z)))). 0 [] end_of_formula. end_of_list. ------- end included file xxviii_a_ghost.txt------- include("xxviii_a.txt"). ------- start included file xxviii_a.txt------- formula_list(usable). all x y z (i(k(r(x),x),I)->i(k(r(x),k(x,n(z,k(r(x),y)))),n(k(r(x),y),z))). -(all x y z (i(k(r(x),x),I)->i(k(r(x),n(y,k(x,z))),n(k(r(x),y),z)))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(z,k(r(x),y)))),n(k(r(x),y),z)). 0 [] i(k(r($c3),$c3),I). 0 [] -i(k(r($c3),n($c2,k($c3,$c1))),n(k(r($c3),$c2),$c1)). 0 [] end_of_formula. end_of_list. ------- end included file xxviii_a.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=10): 1 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=10): 2 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=9): 4 [] -i(x,y)| -i(y,x)|x=y. ** KEPT (pick-wt=11): 5 [] n(x,c(y))!=Z|u(x,y)=y. ** KEPT (pick-wt=11): 6 [] u(x,y)!=y|n(x,c(y))=Z. ** KEPT (pick-wt=14): 7 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. ** KEPT (pick-wt=9): 8 [] c(x)!=y|n(x,y)=Z. ** KEPT (pick-wt=9): 9 [] c(x)!=y|u(x,y)=U. ** KEPT (pick-wt=26): 10 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(y,k(r(x),z)))),k(I,n(y,k(r(x),z)))). ** KEPT (pick-wt=24): 11 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(y,k(r(x),z)))),n(k(r(x),z),y)). ** KEPT (pick-wt=15): 12 [] -i(k(r($c3),n($c2,k($c3,$c1))),n(k(r($c3),$c2),$c1)). ------------> process sos: ** KEPT (pick-wt=5): 13 [] i(n(x,y),y). ** KEPT (pick-wt=11): 14 [] i(n(x,u(y,z)),u(y,n(x,z))). ** KEPT (pick-wt=10): 16 [copy,15,flip.1] u(n(x,y),n(x,c(y)))=x. ---> New Demodulator: 17 [new_demod,16] u(n(x,y),n(x,c(y)))=x. ** KEPT (pick-wt=5): 18 [] u(x,Z)=x. ---> New Demodulator: 19 [new_demod,18] u(x,Z)=x. ** KEPT (pick-wt=7): 20 [] n(x,y)=n(y,x). ** KEPT (pick-wt=5): 21 [] k(I,x)=x. ---> New Demodulator: 22 [new_demod,21] k(I,x)=x. ** KEPT (pick-wt=5): 23 [] i(x,k(x,U)). ** KEPT (pick-wt=5): 24 [] i(x,k(U,x)). ** KEPT (pick-wt=5): 25 [] i(d(Z,x),x). ** KEPT (pick-wt=5): 26 [] i(d(x,Z),x). ** KEPT (pick-wt=5): 27 [] k(U,U)=U. ---> New Demodulator: 28 [new_demod,27] k(U,U)=U. ** KEPT (pick-wt=5): 29 [] d(Z,Z)=Z. ---> New Demodulator: 30 [new_demod,29] d(Z,Z)=Z. ** KEPT (pick-wt=20): 31 [] i(k(r(x),n(k(x,y),z)),k(r(x),k(x,n(y,k(r(x),z))))). ** KEPT (pick-wt=15): 32 [] i(n(k(r(x),y),z),k(r(x),n(y,k(x,z)))). ** KEPT (pick-wt=1): 33 [] end_of_formula. ** KEPT (pick-wt=6): 34 [] i(k(r($c3),$c3),I). Following clause subsumed by 33 during input processing: 0 [] end_of_formula. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] n(x,y)=n(y,x). >>>> Starting back demodulation with 22. >> back demodulating 10 with 22. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 30. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 1.64 sec ----> 7802 [binary,7801.1,12.1] $F. Length of proof is 3. Level of proof is 2. ---------------- PROOF ---------------- 3 [] -i(x,y)| -i(y,z)|i(x,z). 11 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(y,k(r(x),z)))),n(k(r(x),z),y)). 12 [] -i(k(r($c3),n($c2,k($c3,$c1))),n(k(r($c3),$c2),$c1)). 20 [] n(x,y)=n(y,x). 31 [] i(k(r(x),n(k(x,y),z)),k(r(x),k(x,n(y,k(r(x),z))))). 34 [] i(k(r($c3),$c3),I). 151 [para_into,31.1.1.2,20.1.1] i(k(r(x),n(y,k(x,z))),k(r(x),k(x,n(z,k(r(x),y))))). 185 [hyper,34,11] i(k(r($c3),k($c3,n(x,k(r($c3),y)))),n(k(r($c3),y),x)). 7801 [hyper,185,3,151] i(k(r($c3),n(x,k($c3,y))),n(k(r($c3),x),y)). 7802 [binary,7801.1,12.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 316 clauses generated 29717 clauses kept 7693 clauses forward subsumed 13276 clauses back subsumed 624 Kbytes malloced 3768 ----------- times (seconds) ----------- user CPU time 1.85 (0 hr, 0 min, 1 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 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 20:00:17 2003