----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 22:13:20 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). 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("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("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("booleanLaws.txt"). ------- start included file booleanLaws.txt------- include("1To4booleanLaws.txt"). ------- start included file 1To4booleanLaws.txt------- formula_list(usable). all x y z (i(x,u(y,z))->i(n(x,c(z)),y)). all x y z (i(x,y)->i(u(z,x),u(z,y))). all x y (x=u(n(x,c(y)),n(x,y))). all x y i(n(x,y),y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,u(y,z))|i(n(x,c(z)),y). 0 [] -i(x,y)|i(u(z,x),u(z,y)). 0 [] x=u(n(x,c(y)),n(x,y)). 0 [] i(n(x,y),y). end_of_list. ------- end included file 1To4booleanLaws.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)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u($c1,Z)!=$c1. end_of_list. ------- end included file 9_10booleanLaws.txt------- ------- end included file booleanLaws.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=11): 3 [] -i(x,u(y,z))|i(n(x,c(z)),y). ** KEPT (pick-wt=10): 4 [] -i(x,y)|i(u(z,x),u(z,y)). Following clause subsumed by 4 during input processing: 0 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=10): 5 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=5): 6 [] u($c1,Z)!=$c1. ------------> process sos: ** KEPT (pick-wt=7): 7 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 9 [copy,8,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 10 [new_demod,9] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 11 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 12 [new_demod,11] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=10): 14 [copy,13,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 15 [new_demod,14] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=4): 17 [copy,16,flip.1] c(I)=D. ---> New Demodulator: 18 [new_demod,17] c(I)=D. ** KEPT (pick-wt=5): 20 [copy,19,flip.1] u(I,D)=U. ---> New Demodulator: 21 [new_demod,20] u(I,D)=U. ** KEPT (pick-wt=4): 23 [copy,22,flip.1] c(U)=Z. ---> New Demodulator: 24 [new_demod,23] c(U)=Z. ** KEPT (pick-wt=10): 26 [copy,25,flip.1] u(n(x,c(y)),n(x,y))=x. ---> New Demodulator: 27 [new_demod,26] u(n(x,c(y)),n(x,y))=x. ** KEPT (pick-wt=5): 28 [] i(n(x,y),y). Following clause subsumed by 28 during input processing: 0 [] i(n(x,y),y). ** KEPT (pick-wt=11): 29 [] i(n(x,u(y,z)),u(y,n(x,z))). ** KEPT (pick-wt=10): 31 [copy,30,flip.1] u(n(x,y),n(x,c(y)))=x. ---> New Demodulator: 32 [new_demod,31] u(n(x,y),n(x,c(y)))=x. Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 15. >> back demodulating 11 with 15. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 32. >>>> Starting back demodulation with 34. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.05 sec ----> 764 [binary,762.1,36.1] $F. Length of proof is 36. Level of proof is 16. ---------------- PROOF ---------------- 1 [] -i(x,y)|u(x,y)=y. 4 [] -i(x,y)|i(u(z,x),u(z,y)). 6 [] u($c1,Z)!=$c1. 7 [] u(x,y)=u(y,x). 8 [] u(x,u(y,z))=u(u(x,y),z). 9 [copy,8,flip.1] u(u(x,y),z)=u(x,u(y,z)). 11 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 13 [] n(x,y)=c(u(c(x),c(y))). 15,14 [copy,13,flip.1] c(u(c(x),c(y)))=n(x,y). 16 [] D=c(I). 17 [copy,16,flip.1] c(I)=D. 19 [] U=u(I,D). 20 [copy,19,flip.1] u(I,D)=U. 22 [] Z=c(U). 24,23 [copy,22,flip.1] c(U)=Z. 25 [] x=u(n(x,c(y)),n(x,y)). 26 [copy,25,flip.1] u(n(x,c(y)),n(x,y))=x. 28 [] i(n(x,y),y). 33 [back_demod,11,demod,15] u(c(u(c(x),y)),n(x,y))=x. 36 [para_from,7.1.1,6.1.1] u(Z,$c1)!=$c1. 40 [para_into,9.1.1,7.1.1] u(x,u(y,z))=u(y,u(z,x)). 41 [copy,40,flip.1] u(x,u(y,z))=u(z,u(x,y)). 44,43 [para_into,20.1.1,7.1.1] u(D,I)=U. 45 [para_from,20.1.1,9.1.1.1] u(U,x)=u(I,u(D,x)). 48 [hyper,28,4] i(u(x,n(y,z)),u(x,z)). 50 [hyper,28,1] u(n(x,y),y)=y. 64 [para_into,14.1.1.1,7.1.1,demod,15] n(x,y)=n(y,x). 67 [para_into,50.1.1,7.1.1] u(x,n(y,x))=x. 69 [para_from,50.1.1,9.1.1.1,flip.1] u(n(x,y),u(y,z))=u(y,z). 71 [para_into,26.1.1.1.2,23.1.1] u(n(x,Z),n(x,U))=x. 89 [para_into,67.1.1.2,64.1.1] u(x,n(x,y))=x. 160 [para_into,48.1.1,89.1.1] i(x,u(x,y)). 182 [para_into,160.1.2,43.1.1] i(D,U). 209 [para_from,33.1.1,160.1.2] i(c(u(c(x),y)),x). 214 [hyper,182,1] u(D,U)=U. 355 [para_into,209.1.1.1.1,23.1.1] i(c(u(Z,x)),U). 356 [para_into,209.1.1.1.1,17.1.1] i(c(u(D,x)),I). 386 [para_into,355.1.1.1,7.1.1] i(c(u(x,Z)),U). 395 [para_into,356.1.1.1,214.1.1,demod,24] i(Z,I). 402 [hyper,395,1] u(Z,I)=I. 430,429 [para_from,402.1.1,41.1.1.2,flip.1] u(I,u(x,Z))=u(x,I). 447 [para_into,386.1.1.1,45.1.1,demod,430,44,24] i(Z,U). 472,471 [hyper,447,1] u(Z,U)=U. 643,642 [para_into,69.1.1.2,471.1.1,demod,472] u(n(x,Z),U)=U. 723 [para_from,71.1.1,48.1.1,demod,643] i(x,U). 736 [hyper,723,1] u(x,U)=U. 756 [para_from,736.1.1,209.1.1.1,demod,24] i(Z,x). 762 [hyper,756,1] u(Z,x)=x. 764 [binary,762.1,36.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 94 clauses generated 1330 clauses kept 559 clauses forward subsumed 649 clauses back subsumed 77 Kbytes malloced 479 ----------- 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 Nov 30 22:13:20 2003