----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 00:40:34 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). all x y z v (n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y)). -(all x y z (n(y,k(n(x,c(k(y,r(z)))),z))=Z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(y,k(x,n(z,c(k(r(x),y)))))=Z. 0 [] n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y). 0 [] n($c2,k(n($c3,c(k($c2,r($c1)))),$c1))!=Z. end_of_list. ------- end included file cycleLawsB.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=10): 1 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=10): 2 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=12): 4 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 5 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=8): 6 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=16): 7 [] u(x,y)!=y|u(k(z,x),k(z,y))=k(z,y). ** KEPT (pick-wt=15): 8 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x). ** KEPT (pick-wt=16): 9 [] u(x,y)!=y|u(k(x,z),k(y,z))=k(y,z). ** KEPT (pick-wt=13): 10 [] n($c2,k(n($c3,c(k($c2,r($c1)))),$c1))!=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. ** KEPT (pick-wt=13): 52 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ---> New Demodulator: 53 [new_demod,52] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ** KEPT (pick-wt=11): 55 [copy,54,demod,13,21] n(k(x,y),z)=n(k(x,y),z). >>>> 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. >>>> Starting back demodulation with 53. Following clause subsumed by 55 during input processing: 0 [copy,55,flip.1] n(k(x,y),z)=n(k(x,y),z). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.14 sec ----> 1442 [binary,1441.1,99.1] $F. Length of proof is 14. Level of proof is 7. ---------------- PROOF ---------------- 5 [] c(u(x,c(y)))!=Z|u(y,x)=x. 8 [] u(x,y)!=y|u(c(u(z,y)),c(x))=c(x). 10 [] n($c2,k(n($c3,c(k($c2,r($c1)))),$c1))!=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). 23,22 [] u(x,Z)=x. 25,24 [] c(c(x))=x. 29,28 [] r(c(x))=c(r(x)). 31,30 [] r(n(x,y))=n(r(x),r(y)). 33,32 [] r(r(x))=x. 37,36 [] r(k(x,y))=k(r(y),r(x)). 40 [] r(Z)=Z. 52 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z. 78 [para_into,15.1.1.1,8.2.1,demod,25,flip.1] n(u(x,y),z)=z|u(z,y)!=y. 93 [hyper,22,8,demod,23] u(c(x),c(Z))=c(Z). 99 [para_into,22.1.1,22.1.1] x=x. 100 [para_into,22.1.1,5.2.1] Z=x|c(u(Z,c(x)))!=Z. 123,122 [para_from,24.1.1,15.1.1.1.1] c(u(x,c(y)))=n(c(x),y). 132 [back_demod,100,demod,123] Z=x|n(c(Z),x)!=Z. 254,253 [para_into,93.1.1.1,24.1.1] u(x,c(Z))=c(Z). 353,352 [para_into,52.1.1.2.2.2.1.1,32.1.1] n(x,k(r(y),n(z,c(k(y,x)))))=Z. 918,917 [hyper,78,253,demod,254] n(c(Z),x)=x. 920 [back_demod,132,demod,918] Z=x|x!=Z. 1004 [para_from,920.1.1,40.1.1.1] r(x)=Z|x!=Z. 1177 [para_into,1004.1.1,32.1.1] x=Z|r(x)!=Z. 1441 [para_from,1177.1.1,10.1.1,demod,31,37,31,29,37,33,353] Z!=Z. 1442 [binary,1441.1,99.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 123 clauses generated 3402 clauses kept 1330 clauses forward subsumed 2187 clauses back subsumed 65 Kbytes malloced 1053 ----------- times (seconds) ----------- user CPU time 0.34 (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 00:40:34 2003