----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Dec 14 00:19:09 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,3). assign(max_weight,19). 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("peirceanAx0.txt"). ------- start included file peirceanAx0.txt------- formula_list(usable). all x y z (k(x,k(y,z))=k(k(x,y),z)). all x (r(r(x))=x). all x y (r(u(x,y))=u(r(x),r(y))). all x y (r(k(x,y))=k(r(y),r(x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,k(y,z))=k(k(x,y),z). 0 [] r(r(x))=x. 0 [] r(u(x,y))=u(r(x),r(y)). 0 [] r(k(x,y))=k(r(y),r(x)). end_of_list. ------- end included file peirceanAx0.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("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("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("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(x,y)),c(z)))=k(U,n(c(d(r(x),z)),c(y))). end_of_list. ------- end included file xvi_b_ghost.txt------- include("xvi_b.txt"). ------- start included file xvi_b.txt------- formula_list(usable). -(all x y z (d(Z,u(d(x,y),z))=d(Z,u(d(r(x),z),y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] d(Z,u(d($c3,$c2),$c1))!=d(Z,u(d(r($c3),$c1),$c2)). end_of_list. ------- end included file xvi_b.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=12): 1 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 2 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=16): 4 [copy,3,flip.1] d(Z,u(d(r($c3),$c1),$c2))!=d(Z,u(d($c3,$c2),$c1)). ------------> process sos: ** KEPT (pick-wt=7): 5 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 7 [copy,6,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 8 [new_demod,7] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 9 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 10 [new_demod,9] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 12 [copy,11,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 13 [new_demod,12] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 14 [] r(r(x))=x. ---> New Demodulator: 15 [new_demod,14] r(r(x))=x. ** KEPT (pick-wt=10): 16 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 17 [new_demod,16] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 18 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 19 [new_demod,18] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=10): 21 [copy,20,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 22 [new_demod,21] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=10): 24 [copy,23,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 25 [new_demod,24] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=4): 27 [copy,26,flip.1] c(I)=D. ---> New Demodulator: 28 [new_demod,27] c(I)=D. ** KEPT (pick-wt=5): 30 [copy,29,flip.1] u(I,D)=U. ---> New Demodulator: 31 [new_demod,30] u(I,D)=U. ** KEPT (pick-wt=4): 33 [copy,32,flip.1] c(U)=Z. ---> New Demodulator: 34 [new_demod,33] c(U)=Z. ** KEPT (pick-wt=5): 35 [] c(c(x))=x. ---> New Demodulator: 36 [new_demod,35] c(c(x))=x. ** KEPT (pick-wt=20): 37 [] k(U,n(c(d(x,y)),c(z)))=k(U,n(c(d(r(x),z)),c(y))). Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 22. >> back demodulating 9 with 22. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 31. >>>> Starting back demodulation with 34. >>>> Starting back demodulation with 36. ** KEPT (pick-wt=20): 40 [copy,37,flip.1] k(U,n(c(d(r(x),y)),c(z)))=k(U,n(c(d(x,z)),c(y))). >>>> Starting back demodulation with 39. Following clause subsumed by 37 during input processing: 0 [copy,40,flip.1] k(U,n(c(d(x,y)),c(z)))=k(U,n(c(d(r(x),z)),c(y))). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.08 sec ----> 835 [binary,834.1,4.1] $F. Length of proof is 10. Level of proof is 5. ---------------- PROOF ---------------- 3 [] d(Z,u(d($c3,$c2),$c1))!=d(Z,u(d(r($c3),$c1),$c2)). 4 [copy,3,flip.1] d(Z,u(d(r($c3),$c1),$c2))!=d(Z,u(d($c3,$c2),$c1)). 20 [] n(x,y)=c(u(c(x),c(y))). 21 [copy,20,flip.1] c(u(c(x),c(y)))=n(x,y). 23 [] d(x,y)=c(k(c(x),c(y))). 24 [copy,23,flip.1] c(k(c(x),c(y)))=d(x,y). 32 [] Z=c(U). 34,33 [copy,32,flip.1] c(U)=Z. 35 [] c(c(x))=x. 37 [] k(U,n(c(d(x,y)),c(z)))=k(U,n(c(d(r(x),z)),c(y))). 96 [para_into,21.1.1.1.1,35.1.1] c(u(x,c(y)))=n(c(x),y). 119 [para_into,24.1.1.1.1,35.1.1] c(k(x,c(y)))=d(c(x),y). 137 [para_into,96.1.1.1.2,35.1.1] c(u(x,y))=n(c(x),c(y)). 403,402 [para_into,119.1.1.1.2,35.1.1] c(k(x,y))=d(c(x),c(y)). 452,451 [para_from,137.1.1,35.1.1.1] c(n(c(x),c(y)))=u(x,y). 834 [para_into,402.1.1.1,37.1.1,demod,403,34,452,34,452] d(Z,u(d(r(x),y),z))=d(Z,u(d(x,z),y)). 835 [binary,834.1,4.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 85 clauses generated 1331 clauses kept 530 clauses forward subsumed 988 clauses back subsumed 14 Kbytes malloced 606 ----------- times (seconds) ----------- user CPU time 0.28 (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 00:19:09 2003