----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 20:55:03 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). 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("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))). all x y z (i(k(r(x),x),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(x),x),I)|i(k(r(x),n(y,k(x,z))),n(k(r(x),y),z)). 0 [] -i(k(r(x),x),I)|k(r(x),n(y,k(x,z)))=n(k(r(x),y),z). 0 [] end_of_formula. end_of_list. ------- end included file xxviii_a.txt------- include("xxviii_b_ghost.txt"). ------- start included file xxviii_b_ghost.txt------- formula_list(usable). -(all x y z (i(k(r(x),x),I)->k(r(x),n(r(y),k(x,r(z))))=n(k(r(x),r(y)),r(z)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r($c3),$c3),I). 0 [] k(r($c3),n(r($c2),k($c3,r($c1))))!=n(k(r($c3),r($c2)),r($c1)). end_of_list. ------- end included file xxviii_b_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=11): 2 [] n(x,c(y))!=Z|u(x,y)=y. ** KEPT (pick-wt=11): 3 [] u(x,y)!=y|n(x,c(y))=Z. ** KEPT (pick-wt=14): 4 [] n(x,y)!=Z|u(x,y)!=U|c(x)=y. ** KEPT (pick-wt=9): 5 [] c(x)!=y|n(x,y)=Z. ** KEPT (pick-wt=9): 6 [] c(x)!=y|u(x,y)=U. ** KEPT (pick-wt=24): 7 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(y,k(r(x),z)))),n(k(r(x),z),y)). ** KEPT (pick-wt=21): 8 [] -i(k(r(x),x),I)|i(k(r(x),n(y,k(x,z))),n(k(r(x),y),z)). ** KEPT (pick-wt=21): 10 [copy,9,flip.2] -i(k(r(x),x),I)|n(k(r(x),y),z)=k(r(x),n(y,k(x,z))). ** KEPT (pick-wt=19): 12 [copy,11,flip.1] n(k(r($c3),r($c2)),r($c1))!=k(r($c3),n(r($c2),k($c3,r($c1)))). ------------> process sos: ** KEPT (pick-wt=10): 13 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 14 [new_demod,13] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 15 [] r(c(x))=c(r(x)). ---> New Demodulator: 16 [new_demod,15] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 17 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 18 [new_demod,17] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 19 [] r(r(x))=x. ---> New Demodulator: 20 [new_demod,19] r(r(x))=x. ** KEPT (pick-wt=10): 21 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 22 [new_demod,21] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 23 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 24 [new_demod,23] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 25 [] r(I)=I. ---> New Demodulator: 26 [new_demod,25] r(I)=I. ** KEPT (pick-wt=4): 27 [] r(Z)=Z. ---> New Demodulator: 28 [new_demod,27] r(Z)=Z. ** KEPT (pick-wt=4): 29 [] r(U)=U. ---> New Demodulator: 30 [new_demod,29] r(U)=U. ** KEPT (pick-wt=7): 31 [] n(x,y)=n(y,x). ** KEPT (pick-wt=1): 32 [] end_of_formula. ** KEPT (pick-wt=6): 33 [] i(k(r($c3),$c3),I). >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 30. Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] n(x,y)=n(y,x). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.02 sec ----> 90 [binary,88.1,12.1] $F. Length of proof is 3. Level of proof is 2. ---------------- PROOF ---------------- 9 [] -i(k(r(x),x),I)|k(r(x),n(y,k(x,z)))=n(k(r(x),y),z). 10 [copy,9,flip.2] -i(k(r(x),x),I)|n(k(r(x),y),z)=k(r(x),n(y,k(x,z))). 11 [] k(r($c3),n(r($c2),k($c3,r($c1))))!=n(k(r($c3),r($c2)),r($c1)). 12 [copy,11,flip.1] n(k(r($c3),r($c2)),r($c1))!=k(r($c3),n(r($c2),k($c3,r($c1)))). 33 [] i(k(r($c3),$c3),I). 88 [hyper,33,10] n(k(r($c3),x),y)=k(r($c3),n(x,k($c3,y))). 90 [binary,88.1,12.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 13 clauses generated 108 clauses kept 75 clauses forward subsumed 65 clauses back subsumed 8 Kbytes malloced 191 ----------- times (seconds) ----------- user CPU time 0.22 (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 20:55:04 2003