----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 01:40:47 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,20). assign(max_distinct_vars,3). assign(max_literals,1). assign(max_mem,64000). assign(max_weight,23). formula_list(usable). all x (x=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] x=x. end_of_list. include("booleanAx.txt"). ------- start included file booleanAx.txt------- include("1_2booleanAx.txt"). ------- start included file 1_2booleanAx.txt------- formula_list(usable). all x y (u(x,y)=u(y,x)). all x y z (u(x,u(y,z))=u(u(x,y),z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,y)=u(y,x). 0 [] u(x,u(y,z))=u(u(x,y),z). end_of_list. ------- end included file 1_2booleanAx.txt------- include("3booleanAx.txt"). ------- start included file 3booleanAx.txt------- formula_list(usable). all x y (u(c(u(c(x),y)),c(u(c(x),c(y))))=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. end_of_list. ------- end included file 3booleanAx.txt------- ------- end included file booleanAx.txt------- include("peirceanAx0.txt"). ------- start included file peirceanAx0.txt------- formula_list(usable). all x y z (k(x,k(y,z))=k(k(x,y),z)). all x (r(r(x))=x). all x y (r(u(x,y))=u(r(x),r(y))). all x y (r(k(x,y))=k(r(y),r(x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,k(y,z))=k(k(x,y),z). 0 [] r(r(x))=x. 0 [] r(u(x,y))=u(r(x),r(y)). 0 [] r(k(x,y))=k(r(y),r(x)). end_of_list. ------- end included file peirceanAx0.txt------- include("peirceanAx2.txt"). ------- start included file peirceanAx2.txt------- formula_list(usable). all x (k(x,I)=x). all x y (u(k(r(x),c(k(x,y))),c(y))=c(y)). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,I)=x. 0 [] u(k(r(x),c(k(x,y))),c(y))=c(y). end_of_list. ------- end included file peirceanAx2.txt------- include("iDef.txt"). ------- start included file iDef.txt------- formula_list(usable). all x y (i(x,y)<->u(x,y)=y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|u(x,y)=y. 0 [] i(x,y)|u(x,y)!=y. end_of_list. ------- end included file iDef.txt------- include("uzDef.txt"). ------- start included file uzDef.txt------- formula_list(usable). D=c(I). U=u(I,D). Z=c(U). end_of_list. -------> usable clausifies to: list(usable). 0 [] D=c(I). 0 [] U=u(I,D). 0 [] Z=c(U). end_of_list. ------- end included file uzDef.txt------- include("monotLaws.txt"). ------- start included file monotLaws.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("4_5monotLaws.txt"). ------- start included file 4_5monotLaws.txt------- formula_list(usable). all x y w v i(k(n(x,w),n(y,v)),k(x,y)). all x y w v i(k(n(x,w),n(y,v)),k(w,v)). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(n(x,w),n(y,v)),k(x,y)). 0 [] i(k(n(x,w),n(y,v)),k(w,v)). end_of_list. ------- end included file 4_5monotLaws.txt------- ------- end included file monotLaws.txt------- include("xii.txt"). ------- start included file xii.txt------- formula_list(usable). all x y z (i(k(x,y),c(z))<->i(k(r(x),z),c(y))). all x y z (i(k(x,y),c(z))<->i(k(z,r(y)),c(x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)). 0 [] i(k(x,y),c(z))| -i(k(r(x),z),c(y)). 0 [] -i(k(x,y),c(z))|i(k(z,r(y)),c(x)). 0 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)). end_of_list. ------- end included file xii.txt------- include("xviii_ghost.txt"). ------- start included file xviii_ghost.txt------- formula_list(usable). all x y z (i(k(r(x),y),z)->i(k(x,c(z)),c(y))). -(all x y z i(k(x,c(k(c(y),c(z)))),c(k(c(k(x,y)),c(z))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),y),z)|i(k(x,c(z)),c(y)). 0 [] -i(k($c3,c(k(c($c2),c($c1)))),c(k(c(k($c3,$c2)),c($c1)))). end_of_list. ------- end included file xviii_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. 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)|u(x,y)=y. ** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=16): 3 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y). ** KEPT (pick-wt=15): 4 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x). ** KEPT (pick-wt=16): 5 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z). ** KEPT (pick-wt=13): 6 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)). ** KEPT (pick-wt=13): 7 [] i(k(x,y),c(z))| -i(k(r(x),z),c(y)). ** KEPT (pick-wt=13): 8 [] -i(k(x,y),c(z))|i(k(z,r(y)),c(x)). ** KEPT (pick-wt=13): 9 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)). ** KEPT (pick-wt=13): 10 [] -i(k(r(x),y),z)|i(k(x,c(z)),c(y)). ** KEPT (pick-wt=17): 11 [] -i(k($c3,c(k(c($c2),c($c1)))),c(k(c(k($c3,$c2)),c($c1)))). ------------> process sos: ** KEPT (pick-wt=3): 12 [] x=x. ** KEPT (pick-wt=7): 13 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 15 [copy,14,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 16 [new_demod,15] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 17 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 18 [new_demod,17] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 20 [copy,19,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 21 [new_demod,20] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 22 [] r(r(x))=x. ---> New Demodulator: 23 [new_demod,22] r(r(x))=x. ** KEPT (pick-wt=10): 24 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 25 [new_demod,24] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 26 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 27 [new_demod,26] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=5): 28 [] k(x,I)=x. ---> New Demodulator: 29 [new_demod,28] k(x,I)=x. ** KEPT (pick-wt=13): 30 [] u(k(r(x),c(k(x,y))),c(y))=c(y). ---> New Demodulator: 31 [new_demod,30] u(k(r(x),c(k(x,y))),c(y))=c(y). ** KEPT (pick-wt=4): 33 [copy,32,flip.1] c(I)=D. ---> New Demodulator: 34 [new_demod,33] c(I)=D. ** KEPT (pick-wt=5): 36 [copy,35,flip.1] u(I,D)=U. ---> New Demodulator: 37 [new_demod,36] u(I,D)=U. ** KEPT (pick-wt=4): 39 [copy,38,flip.1] c(U)=Z. ---> New Demodulator: 40 [new_demod,39] c(U)=Z. ** KEPT (pick-wt=11): 41 [] i(k(n(x,y),n(z,u)),k(x,z)). ** KEPT (pick-wt=11): 42 [] i(k(n(x,y),n(z,u)),k(y,u)). Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] x=x. Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 29. >>>> Starting back demodulation with 31. >>>> Starting back demodulation with 34. >>>> Starting back demodulation with 37. >>>> Starting back demodulation with 40. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.94 sec ----> 6542 [binary,6541.1,11.1] $F. Length of proof is 4. Level of proof is 4. ---------------- PROOF ---------------- 2 [] i(x,y)|u(x,y)!=y. 5 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z). 10 [] -i(k(r(x),y),z)|i(k(x,c(z)),c(y)). 11 [] -i(k($c3,c(k(c($c2),c($c1)))),c(k(c(k($c3,$c2)),c($c1)))). 19 [] k(x,k(y,z))=k(k(x,y),z). 21,20 [copy,19,flip.1] k(k(x,y),z)=k(x,k(y,z)). 30 [] u(k(r(x),c(k(x,y))),c(y))=c(y). 122 [hyper,30,5,demod,21] u(k(r(x),k(c(k(x,y)),z)),k(c(y),z))=k(c(y),z). 1439 [hyper,122,2] i(k(r(x),k(c(k(x,y)),z)),k(c(y),z)). 6541 [hyper,1439,10] i(k(x,c(k(c(y),z))),c(k(c(k(x,y)),z))). 6542 [binary,6541.1,11.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 596 clauses generated 36136 clauses kept 4375 clauses forward subsumed 29614 clauses back subsumed 104 Kbytes malloced 3736 ----------- times (seconds) ----------- user CPU time 1.14 (0 hr, 0 min, 1 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 01:40:48 2003