----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Dec 14 00:16:08 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_literals,1). assign(max_distinct_vars,4). assign(max_weight,18). 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("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("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("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("iv.txt"). ------- start included file iv.txt------- formula_list(usable). all x y z (k(x,k(y,z))=k(k(x,y),z)). all x y z (d(x,d(y,z))=d(d(x,y),z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,k(y,z))=k(k(x,y),z). 0 [] d(x,d(y,z))=d(d(x,y),z). end_of_list. ------- end included file iv.txt------- include("vii.txt"). ------- start included file vii.txt------- formula_list(usable). all x y z (i(x,y)->i(k(x,z),k(y,z))). all x y z (i(x,y)->i(k(z,x),k(z,y))). all x y z (i(x,y)->i(d(x,z),d(y,z))). all x y z (i(x,y)->i(d(z,x),d(z,y))). all x y (i(x,y)->i(r(x),r(y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|i(k(x,z),k(y,z)). 0 [] -i(x,y)|i(k(z,x),k(z,y)). 0 [] -i(x,y)|i(d(x,z),d(y,z)). 0 [] -i(x,y)|i(d(z,x),d(z,y)). 0 [] -i(x,y)|i(r(x),r(y)). end_of_list. ------- end included file vii.txt------- include("xv_a.txt"). ------- start included file xv_a.txt------- formula_list(usable). all x y z v w i(n(w,k(n(y,z),v)),n(w,u(k(n(y,z),n(v,x)),k(y,n(v,c(x)))))). all y v w i(n(k(y,v),w),k(n(y,k(w,r(v))),n(v,k(r(y),w)))). all y v w i(n(k(y,v),w),k(y,n(v,k(r(y),w)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(n(w,k(n(y,z),v)),n(w,u(k(n(y,z),n(v,x)),k(y,n(v,c(x)))))). 0 [] i(n(k(y,v),w),k(n(y,k(w,r(v))),n(v,k(r(y),w)))). 0 [] i(n(k(y,v),w),k(y,n(v,k(r(y),w)))). end_of_list. ------- end included file xv_a.txt------- include("xvi_a.txt"). ------- start included file xvi_a.txt------- formula_list(usable). all y v w i(k(U,n(k(y,v),w)),k(U,n(k(r(y),w),v))). all y v w i(k(U,n(k(r(y),w),v)),k(U,n(k(y,v),w))). -(all x y z (k(U,n(k(x,y),z))=k(U,n(k(r(x),z),y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(U,n(k(y,v),w)),k(U,n(k(r(y),w),v))). 0 [] i(k(U,n(k(r(y),w),v)),k(U,n(k(y,v),w))). 0 [] k(U,n(k($c3,$c2),$c1))!=k(U,n(k(r($c3),$c1),$c2)). end_of_list. ------- end included file xvi_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=8): 1 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=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=8): 10 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=10): 11 [] -i(x,y)|i(k(x,z),k(y,z)). ** KEPT (pick-wt=10): 12 [] -i(x,y)|i(k(z,x),k(z,y)). ** KEPT (pick-wt=10): 13 [] -i(x,y)|i(d(x,z),d(y,z)). ** KEPT (pick-wt=10): 14 [] -i(x,y)|i(d(z,x),d(z,y)). Following clause subsumed by 10 during input processing: 0 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=16): 16 [copy,15,flip.1] k(U,n(k(r($c3),$c1),$c2))!=k(U,n(k($c3,$c2),$c1)). ------------> process sos: ** KEPT (pick-wt=7): 17 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 19 [copy,18,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 20 [new_demod,19] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 21 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 22 [new_demod,21] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=4): 24 [copy,23,flip.1] c(I)=D. ---> New Demodulator: 25 [new_demod,24] c(I)=D. ** KEPT (pick-wt=5): 27 [copy,26,flip.1] u(I,D)=U. ---> New Demodulator: 28 [new_demod,27] u(I,D)=U. ** KEPT (pick-wt=4): 30 [copy,29,flip.1] c(U)=Z. ---> New Demodulator: 31 [new_demod,30] c(U)=Z. ** KEPT (pick-wt=5): 32 [] u(x,Z)=x. ---> New Demodulator: 33 [new_demod,32] u(x,Z)=x. ** KEPT (pick-wt=7): 34 [] n(x,y)=n(y,x). ** KEPT (pick-wt=10): 35 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 36 [new_demod,35] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 37 [] r(c(x))=c(r(x)). ---> New Demodulator: 38 [new_demod,37] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 39 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 40 [new_demod,39] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 41 [] r(r(x))=x. ---> New Demodulator: 42 [new_demod,41] r(r(x))=x. ** KEPT (pick-wt=10): 43 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 44 [new_demod,43] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 45 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 46 [new_demod,45] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 47 [] r(I)=I. ---> New Demodulator: 48 [new_demod,47] r(I)=I. ** KEPT (pick-wt=4): 49 [] r(Z)=Z. ---> New Demodulator: 50 [new_demod,49] r(Z)=Z. ** KEPT (pick-wt=4): 51 [] r(U)=U. ---> New Demodulator: 52 [new_demod,51] r(U)=U. ** KEPT (pick-wt=11): 54 [copy,53,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 55 [new_demod,54] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=11): 57 [copy,56,flip.1] d(d(x,y),z)=d(x,d(y,z)). ---> New Demodulator: 58 [new_demod,57] d(d(x,y),z)=d(x,d(y,z)). ** KEPT (pick-wt=24): 59 [] i(n(x,k(n(y,z),u)),n(x,u(k(n(y,z),n(u,v)),k(y,n(u,c(v)))))). ** KEPT (pick-wt=19): 60 [] i(n(k(x,y),z),k(n(x,k(z,r(y))),n(y,k(r(x),z)))). ** KEPT (pick-wt=14): 61 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). ** KEPT (pick-wt=16): 62 [] i(k(U,n(k(x,y),z)),k(U,n(k(r(x),z),y))). ** KEPT (pick-wt=16): 63 [] i(k(U,n(k(r(x),y),z)),k(U,n(k(x,z),y))). Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 31. >>>> Starting back demodulation with 33. Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] n(x,y)=n(y,x). >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 38. >>>> Starting back demodulation with 40. >>>> Starting back demodulation with 42. >>>> Starting back demodulation with 44. >>>> Starting back demodulation with 46. >>>> Starting back demodulation with 48. >>>> Starting back demodulation with 50. >>>> Starting back demodulation with 52. >>>> Starting back demodulation with 55. >>>> Starting back demodulation with 58. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.06 sec ----> 364 [binary,363.1,16.1] $F. Length of proof is 2. Level of proof is 1. ---------------- PROOF ---------------- 4 [] -i(x,y)| -i(y,x)|x=y. 15 [] k(U,n(k($c3,$c2),$c1))!=k(U,n(k(r($c3),$c1),$c2)). 16 [copy,15,flip.1] k(U,n(k(r($c3),$c1),$c2))!=k(U,n(k($c3,$c2),$c1)). 62 [] i(k(U,n(k(x,y),z)),k(U,n(k(r(x),z),y))). 63 [] i(k(U,n(k(r(x),y),z)),k(U,n(k(x,z),y))). 363 [hyper,63,4,62] k(U,n(k(r(x),y),z))=k(U,n(k(x,z),y)). 364 [binary,363.1,16.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 76 clauses generated 1352 clauses kept 270 clauses forward subsumed 552 clauses back subsumed 11 Kbytes malloced 319 ----------- times (seconds) ----------- user CPU time 0.26 (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 Dec 14 00:16:08 2003