----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 00:39:51 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("peirceanAx1.txt"). ------- start included file peirceanAx1.txt------- formula_list(usable). all x y z (k(u(x,y),z)=u(k(x,z),k(y,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(u(x,y),z)=u(k(x,z),k(y,z)). end_of_list. ------- end included file peirceanAx1.txt------- include("nDef.txt"). ------- start included file nDef.txt------- formula_list(usable). all x y (n(x,y)=c(u(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,y)=c(u(c(x),c(y))). end_of_list. ------- end included file nDef.txt------- 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("15_16booleanLaws.txt"). ------- start included file 15_16booleanLaws.txt------- formula_list(usable). all x (c(c(x))=x). all x y (u(x,y)=y->c(u(y,c(x)))=Z). all x y (c(u(y,c(x)))=Z->u(x,y)=y). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(c(x))=x. 0 [] u(x,y)!=y|c(u(y,c(x)))=Z. 0 [] c(u(y,c(x)))!=Z|u(x,y)=y. end_of_list. ------- end included file 15_16booleanLaws.txt------- 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("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("cycleLaw.txt"). ------- start included file cycleLaw.txt------- formula_list(usable). all x y z (u(k(r(x),c(u(c(z),k(x,y)))),c(y))=c(y)). all x (k(x,I)=x). all x (k(I,x)=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(k(r(x),c(u(c(z),k(x,y)))),c(y))=c(y). 0 [] k(x,I)=x. 0 [] k(I,x)=x. end_of_list. ------- end included file cycleLaw.txt------- include("cycleLawsB.txt"). ------- start included file cycleLawsB.txt------- formula_list(usable). -(all x y z (n(y,k(x,n(z,c(k(r(x),y)))))=Z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n($c2,k($c3,n($c1,c(k(r($c3),$c2)))))!=Z. end_of_list. ------- end included file cycleLawsB.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=10): 1 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=10): 2 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=12): 4 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 5 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=8): 6 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=16): 7 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y). ** KEPT (pick-wt=15): 8 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x). ** KEPT (pick-wt=16): 9 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z). ** KEPT (pick-wt=13): 10 [] n($c2,k($c3,n($c1,c(k(r($c3),$c2)))))!=Z. ------------> process sos: ** KEPT (pick-wt=13): 12 [copy,11,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 13 [new_demod,12] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=10): 15 [copy,14,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 16 [new_demod,15] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=5): 17 [] i(n(x,y),y). ** KEPT (pick-wt=11): 18 [] i(n(x,u(y,z)),u(y,n(x,z))). ** KEPT (pick-wt=10): 20 [copy,19,flip.1] u(n(x,y),n(x,c(y)))=x. ---> New Demodulator: 21 [new_demod,20] u(n(x,y),n(x,c(y)))=x. ** KEPT (pick-wt=5): 22 [] u(x,Z)=x. ---> New Demodulator: 23 [new_demod,22] u(x,Z)=x. ** KEPT (pick-wt=5): 24 [] c(c(x))=x. ---> New Demodulator: 25 [new_demod,24] c(c(x))=x. ** KEPT (pick-wt=10): 26 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 27 [new_demod,26] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 28 [] r(c(x))=c(r(x)). ---> New Demodulator: 29 [new_demod,28] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 30 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 31 [new_demod,30] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 32 [] r(r(x))=x. ---> New Demodulator: 33 [new_demod,32] r(r(x))=x. ** KEPT (pick-wt=10): 34 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 35 [new_demod,34] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 36 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 37 [new_demod,36] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 38 [] r(I)=I. ---> New Demodulator: 39 [new_demod,38] r(I)=I. ** KEPT (pick-wt=4): 40 [] r(Z)=Z. ---> New Demodulator: 41 [new_demod,40] r(Z)=Z. ** KEPT (pick-wt=4): 42 [] r(U)=U. ---> New Demodulator: 43 [new_demod,42] r(U)=U. ** KEPT (pick-wt=11): 44 [] i(k(n(x,y),n(z,u)),k(x,z)). ** KEPT (pick-wt=11): 45 [] i(k(n(x,y),n(z,u)),k(y,u)). ** KEPT (pick-wt=16): 46 [] u(k(r(x),c(u(c(y),k(x,z)))),c(z))=c(z). ---> New Demodulator: 47 [new_demod,46] u(k(r(x),c(u(c(y),k(x,z)))),c(z))=c(z). ** KEPT (pick-wt=5): 48 [] k(x,I)=x. ---> New Demodulator: 49 [new_demod,48] k(x,I)=x. ** KEPT (pick-wt=5): 50 [] k(I,x)=x. ---> New Demodulator: 51 [new_demod,50] k(I,x)=x. >>>> Starting back demodulation with 13. >> back demodulating 9 with 13. >>>> Starting back demodulation with 16. >>>> 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 33. >>>> Starting back demodulation with 35. >>>> Starting back demodulation with 37. >>>> Starting back demodulation with 39. >>>> Starting back demodulation with 41. >>>> Starting back demodulation with 43. >>>> Starting back demodulation with 47. >>>> Starting back demodulation with 49. >>>> Starting back demodulation with 51. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 9. sos_size=5609 -----> EMPTY CLAUSE at 2.05 sec ----> 6985 [hyper,3283,95,95] $F. Length of proof is 8. Level of proof is 5. ---------------- PROOF ---------------- 4 [] u(x,y)!=y|c(u(y,c(x)))=Z. 10 [] n($c2,k($c3,n($c1,c(k(r($c3),$c2)))))!=Z. 14 [] n(x,y)=c(u(c(x),c(y))). 15 [copy,14,flip.1] c(u(c(x),c(y)))=n(x,y). 22 [] u(x,Z)=x. 24 [] c(c(x))=x. 32 [] r(r(x))=x. 46 [] u(k(r(x),c(u(c(y),k(x,z)))),c(z))=c(z). 77 [para_into,15.1.1,4.2.1,flip.1] n(x,y)=Z|u(y,c(x))!=c(x). 95 [para_into,22.1.1,22.1.1] x=x. 116,115 [para_from,24.1.1,15.1.1.1.2] c(u(c(x),y))=n(x,c(y)). 123 [back_demod,46,demod,116] u(k(r(x),n(y,c(k(x,z)))),c(z))=c(z). 988 [para_from,77.1.1,10.1.1] Z!=Z|u(k($c3,n($c1,c(k(r($c3),$c2)))),c($c2))!=c($c2). 3253,3252 [para_into,123.1.1.1.1,32.1.1] u(k(x,n(y,c(k(r(x),z)))),c(z))=c(z). 3283 [back_demod,988,demod,3253] Z!=Z|c($c2)!=c($c2). 6985 [hyper,3283,95,95] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 255 clauses generated 16737 clauses kept 6831 clauses forward subsumed 10017 clauses back subsumed 283 Kbytes malloced 4023 ----------- times (seconds) ----------- user CPU time 2.35 (0 hr, 0 min, 2 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 00:39:53 2003