----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Fri Nov 21 22:51:37 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,7). assign(max_distinct_vars,2). 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("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("peirceanAx2.txt"). ------- start included file peirceanAx2.txt------- formula_list(usable). all x (k(x,I)=x). all x y (u(k(r(x),c(k(x,y))),c(y))=c(y)). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,I)=x. 0 [] u(k(r(x),c(k(x,y))),c(y))=c(y). end_of_list. ------- end included file peirceanAx2.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("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("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. 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. end_of_list. ------- end included file i.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=8): 3 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=4): 4 [] r(Z)!=Z. ------------> 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=5): 20 [] k(x,I)=x. ---> New Demodulator: 21 [new_demod,20] k(x,I)=x. ** KEPT (pick-wt=13): 22 [] u(k(r(x),c(k(x,y))),c(y))=c(y). ---> New Demodulator: 23 [new_demod,22] u(k(r(x),c(k(x,y))),c(y))=c(y). ** KEPT (pick-wt=10): 25 [copy,24,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 26 [new_demod,25] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=4): 28 [copy,27,flip.1] c(I)=D. ---> New Demodulator: 29 [new_demod,28] c(I)=D. ** KEPT (pick-wt=5): 31 [copy,30,flip.1] u(I,D)=U. ---> New Demodulator: 32 [new_demod,31] u(I,D)=U. ** KEPT (pick-wt=4): 34 [copy,33,flip.1] c(U)=Z. ---> New Demodulator: 35 [new_demod,34] c(U)=Z. ** KEPT (pick-wt=10): 37 [copy,36,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 38 [new_demod,37] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=11): 40 [copy,39,demod,17] u(r(x),r(y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 41 [] r(c(x))=c(r(x)). ---> New Demodulator: 42 [new_demod,41] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 43 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 44 [new_demod,43] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=3): 46 [copy,45,demod,15] x=x. ** KEPT (pick-wt=10): 47 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 48 [new_demod,47] r(d(x,y))=d(r(y),r(x)). Following clause subsumed by 46 during input processing: 0 [demod,19] k(r(y),r(x))=k(r(y),r(x)). ** KEPT (pick-wt=4): 49 [] r(I)=I. ---> New Demodulator: 50 [new_demod,49] r(I)=I. 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 21. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 26. >> back demodulating 9 with 26. >>>> Starting back demodulation with 29. >>>> Starting back demodulation with 32. >>>> Starting back demodulation with 35. >>>> Starting back demodulation with 38. Following clause subsumed by 46 during input processing: 0 [copy,40,flip.1] u(r(x),r(y))=u(r(x),r(y)). >>>> Starting back demodulation with 42. >>>> Starting back demodulation with 44. Following clause subsumed by 46 during input processing: 0 [copy,46,flip.1] x=x. 46 back subsumes 40. >>>> Starting back demodulation with 48. >>>> Starting back demodulation with 50. >>>> Starting back demodulation with 52. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.03 sec ----> 71 [binary,70.1,46.1] $F. Length of proof is 10. Level of proof is 4. ---------------- PROOF ---------------- 4 [] r(Z)!=Z. 5 [] u(x,y)=u(y,x). 15,14 [] r(r(x))=x. 16 [] r(u(x,y))=u(r(x),r(y)). 27 [] D=c(I). 29,28 [copy,27,flip.1] c(I)=D. 30 [] U=u(I,D). 31 [copy,30,flip.1] u(I,D)=U. 33 [] Z=c(U). 35,34 [copy,33,flip.1] c(U)=Z. 41 [] r(c(x))=c(r(x)). 45 [] r(r(x))=x. 46 [copy,45,demod,15] x=x. 50,49 [] r(I)=I. 54,53 [para_into,31.1.1,5.1.1] u(D,I)=U. 64,63 [para_into,41.1.1.1,34.1.1] r(Z)=c(r(U)). 66,65 [para_into,41.1.1.1,28.1.1,demod,50,29] r(D)=D. 67 [back_demod,4,demod,64] c(r(U))!=Z. 69,68 [para_into,16.1.1.1,53.1.1,demod,66,50,54] r(U)=U. 70 [back_demod,67,demod,69,35] Z!=Z. 71 [binary,70.1,46.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 16 clauses generated 79 clauses kept 35 clauses forward subsumed 40 clauses back subsumed 1 Kbytes malloced 127 ----------- times (seconds) ----------- user CPU time 0.23 (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 Fri Nov 21 22:51:37 2003