----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Dec 14 00:17:36 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("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("dDef.txt"). ------- start included file dDef.txt------- formula_list(usable). all x y (d(x,y)=c(k(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] d(x,y)=c(k(c(x),c(y))). end_of_list. ------- end included file dDef.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("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("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("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(x,y),z))=k(U,n(k(r(x),z),y)). end_of_list. ------- end included file xvi_a.txt------- include("xvi_b_ghost.txt"). ------- start included file xvi_b_ghost.txt------- formula_list(usable). -(all x y z (k(U,n(c(d(x,y)),c(z)))=k(U,n(c(d(r(x),z)),c(y))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(U,n(c(d($c3,$c2)),c($c1)))!=k(U,n(c(d(r($c3),$c1)),c($c2))). end_of_list. ------- end included file xvi_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=9): 1 [] -i(x,y)| -i(y,x)|x=y. ** KEPT (pick-wt=12): 2 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 3 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=8): 4 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=20): 6 [copy,5,flip.1] k(U,n(c(d(r($c3),$c1)),c($c2)))!=k(U,n(c(d($c3,$c2)),c($c1))). ------------> process sos: ** KEPT (pick-wt=10): 8 [copy,7,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 9 [new_demod,8] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=10): 11 [copy,10,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 12 [new_demod,11] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=4): 14 [copy,13,flip.1] c(I)=D. ---> New Demodulator: 15 [new_demod,14] c(I)=D. ** KEPT (pick-wt=5): 17 [copy,16,flip.1] u(I,D)=U. ---> New Demodulator: 18 [new_demod,17] u(I,D)=U. ** KEPT (pick-wt=4): 20 [copy,19,flip.1] c(U)=Z. ---> New Demodulator: 21 [new_demod,20] c(U)=Z. ** KEPT (pick-wt=5): 22 [] c(c(x))=x. ---> New Demodulator: 23 [new_demod,22] c(c(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=7): 26 [] r(c(x))=c(r(x)). ---> New Demodulator: 27 [new_demod,26] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 28 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 29 [new_demod,28] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 30 [] r(r(x))=x. ---> New Demodulator: 31 [new_demod,30] r(r(x))=x. ** KEPT (pick-wt=10): 32 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 33 [new_demod,32] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 34 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 35 [new_demod,34] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 36 [] r(I)=I. ---> New Demodulator: 37 [new_demod,36] r(I)=I. ** KEPT (pick-wt=4): 38 [] r(Z)=Z. ---> New Demodulator: 39 [new_demod,38] r(Z)=Z. ** KEPT (pick-wt=4): 40 [] r(U)=U. ---> New Demodulator: 41 [new_demod,40] r(U)=U. ** KEPT (pick-wt=16): 42 [] i(k(U,n(k(x,y),z)),k(U,n(k(r(x),z),y))). ** KEPT (pick-wt=16): 43 [] i(k(U,n(k(r(x),y),z)),k(U,n(k(x,z),y))). ** KEPT (pick-wt=16): 44 [] k(U,n(k(x,y),z))=k(U,n(k(r(x),z),y)). >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 15. >>>> 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 33. >>>> Starting back demodulation with 35. >>>> Starting back demodulation with 37. >>>> Starting back demodulation with 39. >>>> Starting back demodulation with 41. ** KEPT (pick-wt=16): 45 [copy,44,flip.1] k(U,n(k(r(x),y),z))=k(U,n(k(x,z),y)). Following clause subsumed by 44 during input processing: 0 [copy,45,flip.1] k(U,n(k(x,y),z))=k(U,n(k(r(x),z),y)). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.04 sec ----> 453 [binary,452.1,134.1] $F. Length of proof is 6. Level of proof is 3. ---------------- PROOF ---------------- 5 [] k(U,n(c(d($c3,$c2)),c($c1)))!=k(U,n(c(d(r($c3),$c1)),c($c2))). 6 [copy,5,flip.1] k(U,n(c(d(r($c3),$c1)),c($c2)))!=k(U,n(c(d($c3,$c2)),c($c1))). 10 [] d(x,y)=c(k(c(x),c(y))). 11 [copy,10,flip.1] c(k(c(x),c(y)))=d(x,y). 22 [] c(c(x))=x. 26 [] r(c(x))=c(r(x)). 44 [] k(U,n(k(x,y),z))=k(U,n(k(r(x),z),y)). 45 [copy,44,flip.1] k(U,n(k(r(x),y),z))=k(U,n(k(x,z),y)). 128,127 [para_into,22.1.1.1,11.1.1] c(d(x,y))=k(c(x),c(y)). 134 [back_demod,6,demod,128,128] k(U,n(k(c(r($c3)),c($c1)),c($c2)))!=k(U,n(k(c($c3),c($c2)),c($c1))). 452 [para_into,45.1.1.2.1.1,26.1.1] k(U,n(k(c(r(x)),y),z))=k(U,n(k(c(x),z),y)). 453 [binary,452.1,134.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 51 clauses generated 581 clauses kept 404 clauses forward subsumed 171 clauses back subsumed 8 Kbytes malloced 383 ----------- times (seconds) ----------- user CPU time 0.24 (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 Dec 14 00:17:37 2003