----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 19:26:04 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_distinct_vars,3). assign(max_literals,1). assign(max_mem,30000). assign(max_weight,20). 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("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("ix_a.txt"). ------- start included file ix_a.txt------- formula_list(usable). all x (k(x,I)=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,I)=x. end_of_list. ------- end included file ix_a.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("cycleLawsB.txt"). ------- start included file cycleLawsB.txt------- formula_list(usable). all x y z (n(y,k(x,n(z,c(k(r(x),y)))))=Z). all x y z v (n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y)). all x y z (n(y,k(n(x,c(k(y,r(z)))),z))=Z). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(y,k(x,n(z,c(k(r(x),y)))))=Z. 0 [] n(k(x,z),y)=n(u(k(n(x,v),z),k(n(x,c(v)),z)),y). 0 [] n(y,k(n(x,c(k(y,r(z)))),z))=Z. end_of_list. ------- end included file cycleLawsB.txt------- include("cycleLawC.txt"). ------- start included file cycleLawC.txt------- formula_list(usable). all x y z (n(y,k(n(x,k(y,r(z))),z))=n(k(x,z),y)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(y,k(n(x,k(y,r(z))),z))=n(k(x,z),y). end_of_list. ------- end included file cycleLawC.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("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("xxi_a_ghost.txt"). ------- start included file xxi_a_ghost.txt------- formula_list(usable). all x (n(x,I)=n(r(x),I)). all x y (n(k(x,n(r(x),y)),I)=n(k(x,y),I)). all x y (n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,I)=n(r(x),I). 0 [] n(k(x,n(r(x),y)),I)=n(k(x,y),I). 0 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). end_of_list. ------- end included file xxi_a_ghost.txt------- include("xxi_b_ghost.txt"). ------- start included file xxi_b_ghost.txt------- formula_list(usable). -(all x i(k(x,U),k(n(k(x,r(x)),I),U))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k($c1,U),k(n(k($c1,r($c1)),I),U)). end_of_list. ------- end included file xxi_b_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=12): 1 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 2 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=8): 3 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=8): 4 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 5 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=12): 6 [] -i(k($c1,U),k(n(k($c1,r($c1)),I),U)). ------------> 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=11): 14 [copy,13,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 15 [new_demod,14] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 16 [] r(r(x))=x. ---> New Demodulator: 17 [new_demod,16] r(r(x))=x. ** KEPT (pick-wt=10): 18 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 19 [new_demod,18] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 20 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 21 [new_demod,20] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=10): 23 [copy,22,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 24 [new_demod,23] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=4): 26 [copy,25,flip.1] c(I)=D. ---> New Demodulator: 27 [new_demod,26] c(I)=D. ** KEPT (pick-wt=5): 29 [copy,28,flip.1] u(I,D)=U. ---> New Demodulator: 30 [new_demod,29] u(I,D)=U. ** KEPT (pick-wt=4): 32 [copy,31,flip.1] c(U)=Z. ---> New Demodulator: 33 [new_demod,32] c(U)=Z. ** KEPT (pick-wt=5): 34 [] k(x,I)=x. ---> New Demodulator: 35 [new_demod,34] k(x,I)=x. ** KEPT (pick-wt=5): 36 [] c(c(x))=x. ---> New Demodulator: 37 [new_demod,36] c(c(x))=x. ** KEPT (pick-wt=11): 39 [copy,38,demod,19] u(r(x),r(y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 40 [] r(c(x))=c(r(x)). ---> New Demodulator: 41 [new_demod,40] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 42 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 43 [new_demod,42] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=3): 45 [copy,44,demod,17] x=x. ** KEPT (pick-wt=10): 46 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 47 [new_demod,46] r(d(x,y))=d(r(y),r(x)). Following clause subsumed by 45 during input processing: 0 [demod,21] k(r(y),r(x))=k(r(y),r(x)). ** KEPT (pick-wt=4): 48 [] r(I)=I. ---> New Demodulator: 49 [new_demod,48] r(I)=I. ** KEPT (pick-wt=4): 50 [] r(Z)=Z. ---> New Demodulator: 51 [new_demod,50] r(Z)=Z. ** KEPT (pick-wt=4): 52 [] r(U)=U. ---> New Demodulator: 53 [new_demod,52] r(U)=U. ** KEPT (pick-wt=13): 54 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ---> New Demodulator: 55 [new_demod,54] n(x,k(y,n(z,c(k(r(y),x)))))=Z. ** KEPT (pick-wt=20): 57 [copy,56,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). ---> New Demodulator: 58 [new_demod,57] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). ** KEPT (pick-wt=13): 59 [] n(x,k(n(y,c(k(x,r(z)))),z))=Z. ---> New Demodulator: 60 [new_demod,59] n(x,k(n(y,c(k(x,r(z)))),z))=Z. ** KEPT (pick-wt=16): 61 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). ** KEPT (pick-wt=24): 62 [] 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): 63 [] i(n(k(x,y),z),k(n(x,k(z,r(y))),n(y,k(r(x),z)))). ** KEPT (pick-wt=14): 64 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). ** KEPT (pick-wt=8): 66 [copy,65,flip.1] n(r(x),I)=n(x,I). ---> New Demodulator: 67 [new_demod,66] n(r(x),I)=n(x,I). ** KEPT (pick-wt=14): 68 [] n(k(x,n(r(x),y)),I)=n(k(x,y),I). ---> New Demodulator: 69 [new_demod,68] n(k(x,n(r(x),y)),I)=n(k(x,y),I). ** KEPT (pick-wt=17): 70 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). ---> New Demodulator: 71 [new_demod,70] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). 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. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 24. >> back demodulating 11 with 24. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 35. >>>> Starting back demodulation with 37. Following clause subsumed by 45 during input processing: 0 [copy,39,flip.1] u(r(x),r(y))=u(r(x),r(y)). >>>> Starting back demodulation with 41. >>>> Starting back demodulation with 43. Following clause subsumed by 45 during input processing: 0 [copy,45,flip.1] x=x. 45 back subsumes 39. >>>> Starting back demodulation with 47. >>>> Starting back demodulation with 49. >>>> Starting back demodulation with 51. >>>> Starting back demodulation with 53. >>>> Starting back demodulation with 55. >>>> Starting back demodulation with 58. >>>> Starting back demodulation with 60. ** KEPT (pick-wt=16): 74 [copy,61,flip.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)). >>>> Starting back demodulation with 67. >>>> Starting back demodulation with 69. >>>> Starting back demodulation with 71. >>>> Starting back demodulation with 73. Following clause subsumed by 61 during input processing: 0 [copy,74,flip.1] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 11. sos_size=9758 ----> UNIT CONFLICT at 51.61 sec ----> 25057 [binary,25056.1,1294.1] $F. Length of proof is 130. Level of proof is 25. ---------------- PROOF ---------------- 4 [] -i(x,y)|u(x,y)=y. 5 [] i(x,y)|u(x,y)!=y. 6 [] -i(k($c1,U),k(n(k($c1,r($c1)),I),U)). 7 [] u(x,y)=u(y,x). 8 [] u(x,u(y,z))=u(u(x,y),z). 10,9 [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 [] k(x,k(y,z))=k(k(x,y),z). 15,14 [copy,13,flip.1] k(k(x,y),z)=k(x,k(y,z)). 17,16 [] r(r(x))=x. 21,20 [] r(k(x,y))=k(r(y),r(x)). 22 [] n(x,y)=c(u(c(x),c(y))). 24,23 [copy,22,flip.1] c(u(c(x),c(y)))=n(x,y). 25 [] D=c(I). 26 [copy,25,flip.1] c(I)=D. 28 [] U=u(I,D). 30,29 [copy,28,flip.1] u(I,D)=U. 31 [] Z=c(U). 32 [copy,31,flip.1] c(U)=Z. 35,34 [] k(x,I)=x. 37,36 [] c(c(x))=x. 41,40 [] r(c(x))=c(r(x)). 49,48 [] r(I)=I. 50 [] r(Z)=Z. 53,52 [] r(U)=U. 54 [] n(x,k(y,n(z,c(k(r(y),x)))))=Z. 56 [] n(k(x,y),z)=n(u(k(n(x,u),y),k(n(x,c(u)),y)),z). 58,57 [copy,56,flip.1] n(u(k(n(x,y),z),k(n(x,c(y)),z)),u)=n(k(x,z),u). 61 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). 62 [] i(n(x,k(n(y,z),u)),n(x,u(k(n(y,z),n(u,v)),k(y,n(u,c(v)))))). 63 [] i(n(k(x,y),z),k(n(x,k(z,r(y))),n(y,k(r(x),z)))). 64 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). 70 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). 72 [back_demod,11,demod,24] u(c(u(c(x),y)),n(x,y))=x. 75 [para_into,9.1.1.1,7.1.1,demod,10] u(x,u(y,z))=u(y,u(x,z)). 76 [para_into,9.1.1,7.1.1] u(x,u(y,z))=u(y,u(z,x)). 77 [copy,76,flip.1] u(x,u(y,z))=u(z,u(x,y)). 81,80 [para_from,29.1.1,9.1.1.1] u(U,x)=u(I,u(D,x)). 85,84 [para_into,36.1.1.1,32.1.1] c(Z)=U. 86 [para_into,36.1.1.1,26.1.1] c(D)=I. 100 [para_into,20.1.1.1,34.1.1,demod,49,flip.1] k(I,r(x))=r(x). 115,114 [para_into,100.1.1.2,16.1.1,demod,17] k(I,x)=x. 127,126 [para_into,23.1.1.1.1,36.1.1] c(u(x,c(y)))=n(c(x),y). 129,128 [para_into,23.1.1.1.1,23.1.1,demod,127] n(c(n(x,y)),z)=n(u(c(x),c(y)),z). 135,134 [para_into,23.1.1.1.2,36.1.1] c(u(c(x),y))=n(x,c(y)). 136 [para_into,23.1.1.1.2,23.1.1,demod,135] n(x,c(n(y,z)))=n(x,u(c(y),c(z))). 138 [para_into,23.1.1.1,7.1.1,demod,127,37] n(x,y)=n(y,x). 140,139 [back_demod,72,demod,135] u(n(x,c(y)),n(x,y))=x. 150 [para_into,80.1.1,7.1.1] u(x,U)=u(I,u(D,x)). 151 [copy,150,flip.1] u(I,u(D,x))=u(x,U). 162 [para_into,151.1.1.2,7.1.1] u(I,u(x,D))=u(x,U). 164 [copy,162,flip.1] u(x,U)=u(I,u(x,D)). 200 [para_into,54.1.1.2.2.2.1.1,52.1.1] n(x,k(U,n(y,c(k(U,x)))))=Z. 204 [para_into,54.1.1.2.2.2.1.1,48.1.1,demod,115,115] n(x,n(y,c(x)))=Z. 209,208 [para_into,54.1.1.2.2.2.1.1,16.1.1] n(x,k(r(y),n(z,c(k(y,x)))))=Z. 214 [para_into,54.1.1,138.1.1] n(k(x,n(y,c(k(r(x),z)))),z)=Z. 218 [para_into,204.1.1.2.2,86.1.1] n(D,n(x,I))=Z. 222 [para_into,204.1.1.2.2,36.1.1] n(c(x),n(y,x))=Z. 226 [para_into,204.1.1.2.2,26.1.1] n(I,n(x,D))=Z. 228 [para_into,204.1.1.2,138.1.1] n(x,n(c(x),y))=Z. 232 [para_into,218.1.1.2,138.1.1] n(D,n(I,x))=Z. 268 [para_into,232.1.1.2,226.1.1] n(D,Z)=Z. 274 [para_into,268.1.1,138.1.1] n(Z,D)=Z. 280 [para_from,274.1.1,226.1.1.2] n(I,Z)=Z. 313 [para_into,61.1.1.2.1.2.2,52.1.1] n(x,k(n(y,k(x,U)),U))=n(k(y,U),x). 314 [para_into,61.1.1.2.1.2.2,50.1.1] n(x,k(n(y,k(x,Z)),Z))=n(k(y,Z),x). 316,315 [para_into,61.1.1.2.1.2.2,48.1.1,demod,35,35,35] n(x,n(y,x))=n(y,x). 319 [para_into,61.1.1.2.1.2,114.1.1] n(I,k(n(x,r(y)),y))=n(k(x,y),I). 329 [copy,314,flip.1] n(k(x,Z),y)=n(y,k(n(x,k(y,Z)),Z)). 343 [para_into,62.1.2.2.1.2,280.1.1,demod,35,85] i(n(x,n(y,z)),n(x,u(k(n(y,z),Z),k(y,n(I,U))))). 357 [para_into,63.1.2.1.2.2,16.1.1] i(n(k(x,r(y)),z),k(n(x,k(z,y)),n(r(y),k(r(x),z)))). 368 [para_into,64.1.1.1,114.1.1,demod,49,115,115] i(n(x,y),n(x,y)). 369 [para_into,64.1.1.1,34.1.1] i(n(x,y),k(x,n(I,k(r(x),y)))). 370 [para_into,64.1.1,204.1.1,demod,209] i(Z,k(x,Z)). 382 [para_into,370.1.2,114.1.1] i(Z,Z). 385,384 [hyper,382,4] u(Z,Z)=Z. 430 [para_into,368.1.1,138.1.1] i(n(x,y),n(y,x)). 438 [para_into,70.1.1.1.1.2,52.1.1] n(k(n(x,U),n(r(x),U)),I)=n(k(x,U),I). 497 [para_into,222.1.1.2,138.1.1] n(c(x),n(x,y))=Z. 508,507 [para_into,228.1.1.2,228.1.1] n(x,Z)=Z. 520 [para_into,507.1.1,138.1.1] n(Z,x)=Z. 538,537 [para_from,520.1.1,54.1.1.2.2] n(x,k(y,Z))=Z. 547,546 [back_demod,329,demod,538,538] n(k(x,Z),y)=Z. 565 [para_into,537.1.1.2,14.1.1] n(x,k(y,k(z,Z)))=Z. 574 [para_into,75.1.1.2,384.1.1,flip.1] u(Z,u(x,Z))=u(x,Z). 595 [para_into,497.1.1,138.1.1] n(n(x,y),c(x))=Z. 632 [para_into,315.1.1.2,138.1.1] n(x,n(x,y))=n(y,x). 633 [para_into,315.1.1,497.1.1,flip.1] n(x,c(x))=Z. 640,639 [para_into,315.1.1,228.1.1,flip.1] n(c(x),x)=Z. 838,837 [para_into,126.1.1.1.2,36.1.1] c(u(x,y))=n(c(x),c(y)). 839 [para_into,126.1.1.1,9.1.1,demod,838,838,37,838,flip.1] n(n(c(x),c(y)),z)=n(c(x),n(c(y),z)). 1003 [para_into,136.1.1,639.1.1,demod,37,flip.1] n(n(x,y),u(c(x),c(y)))=Z. 1016,1015 [para_into,632.1.1.2,632.1.1,demod,316,flip.1] n(n(x,y),x)=n(y,x). 1073 [para_into,139.1.1.1.2,84.1.1,demod,508] u(n(x,U),Z)=x. 1083 [para_into,139.1.1.1,639.1.1,demod,37,37] u(Z,n(x,x))=x. 1088,1087 [para_into,139.1.1.1,595.1.1,demod,1016] u(Z,n(x,y))=n(y,x). 1096,1095 [para_into,139.1.1.1,546.1.1,demod,547,385,flip.1] k(x,Z)=Z. 1097 [para_into,139.1.1.1,138.1.1] u(n(c(x),y),n(y,x))=y. 1102,1101 [para_into,139.1.1.1,128.1.1,demod,129,140,flip.1] c(n(x,y))=u(c(x),c(y)). 1103 [para_into,139.1.1.1,57.1.1,demod,58,140,flip.1] u(k(n(x,y),z),k(n(x,c(y)),z))=k(x,z). 1113 [para_into,139.1.1.2,633.1.1,demod,37] u(n(x,x),Z)=x. 1120,1119 [para_into,139.1.1.2,595.1.1,demod,37,1016] u(n(x,y),Z)=n(y,x). 1122,1121 [para_into,139.1.1.2,565.1.1,demod,1096,1096,85,1120] n(U,x)=x. 1135 [para_into,139.1.1.2,228.1.1,demod,1102,37,1120] n(u(x,c(y)),x)=x. 1162,1161 [back_demod,1083,demod,1088] n(x,x)=x. 1186 [back_demod,343,demod,1096] i(n(x,n(y,z)),n(x,u(Z,k(y,n(I,U))))). 1238,1237 [back_demod,1113,demod,1162] u(x,Z)=x. 1242,1241 [back_demod,1073,demod,1238] n(x,U)=x. 1259,1258 [back_demod,438,demod,1242,1242] n(k(x,r(x)),I)=n(k(x,U),I). 1265,1264 [back_demod,574,demod,1238,1238] u(Z,x)=x. 1282 [back_demod,1186,demod,1242,35,1265] i(n(x,n(y,z)),n(x,y)). 1294 [back_demod,6,demod,1259] -i(k($c1,U),k(n(k($c1,U),I),U)). 1306 [para_from,1121.1.1,430.1.2,demod,1242] i(x,x). 1310 [para_from,1121.1.1,139.1.1.1,demod,1122] u(c(x),x)=U. 1315,1314 [hyper,1306,4] u(x,x)=x. 1332 [para_into,1314.1.1,164.1.1,demod,81,1315,30] u(I,U)=U. 1345 [para_from,1332.1.1,77.1.1.2,demod,81] u(x,U)=u(I,u(D,u(x,I))). 1348 [copy,1345,flip.1] u(I,u(D,u(x,I)))=u(x,U). 1394 [para_into,1310.1.1.1,36.1.1] u(x,c(x))=U. 1402 [para_from,1310.1.1,77.1.1.2,flip.1] u(x,u(y,c(x)))=u(y,U). 1452 [para_into,1135.1.1.1.2,36.1.1] n(u(x,y),x)=x. 1477,1476 [para_into,1452.1.1.1,80.1.1,demod,1242] u(I,u(D,x))=U. 1484 [para_into,1452.1.1.1,7.1.1] n(u(x,y),y)=y. 1495,1494 [back_demod,1348,demod,1477,flip.1] u(x,U)=U. 1512 [back_demod,1402,demod,1495] u(x,u(y,c(x)))=U. 1654 [para_into,1512.1.1,9.1.1,demod,838] u(x,u(y,u(z,n(c(x),c(y)))))=U. 1982 [para_into,1282.1.1.2,1121.1.1,demod,1242] i(n(x,y),x). 2047 [para_into,1982.1.1,1484.1.1] i(x,u(y,x)). 2050 [para_into,1982.1.1,315.1.1] i(n(x,y),y). 2059 [para_into,2047.1.2,76.1.1] i(u(x,y),u(x,u(y,z))). 2068 [hyper,2050,4] u(n(x,y),y)=y. 2217 [para_into,2068.1.1,7.1.1] u(x,n(y,x))=x. 2298,2297 [para_from,2217.1.1,9.1.1.1,flip.1] u(x,u(n(y,x),z))=u(x,z). 2360 [para_into,200.1.1.2.2,1484.1.1] n(x,k(U,c(k(U,x))))=Z. 3372 [para_into,2059.1.2.2,2068.1.1] i(u(x,n(y,z)),u(x,z)). 3870 [para_from,319.1.1,313.1.1.2.1,demod,53,1242,115,53,1242,1122] n(x,k(n(k(x,U),I),U))=x. 4881 [para_into,369.1.1,1121.1.1,demod,53] i(x,k(U,n(I,k(U,x)))). 9188 [para_from,1097.1.1,3372.1.1] i(x,u(n(c(y),x),y)). 9212 [hyper,9188,4,demod,2298,flip.1] u(n(c(x),y),x)=u(y,x). 10271,10270 [para_into,839.1.1.1.2,36.1.1,demod,37] n(n(c(x),y),z)=n(c(x),n(y,z)). 10826 [para_into,2360.1.1,1121.1.1] k(U,c(k(U,U)))=Z. 10848 [para_from,2360.1.1,357.1.2.1,demod,41,21,53,1242,41,21,53,640,1096] i(k(x,c(k(r(x),U))),Z). 10876 [para_from,10826.1.1,4881.1.2.2.2,demod,508,1096] i(c(k(U,U)),Z). 10892 [hyper,10876,4,demod,1238] c(k(U,U))=Z. 10946,10945 [para_from,10892.1.1,1394.1.1.2,demod,1238] k(U,U)=U. 12202 [hyper,10848,4,demod,1238] k(x,c(k(r(x),U)))=Z. 12340 [para_into,1003.1.1.2.1,36.1.1,demod,10271] n(c(x),n(y,u(x,c(y))))=Z. 14590 [para_from,12202.1.1,214.1.1.1.2.2.1,demod,85,1242,17] n(k(x,y),c(k(x,U)))=Z. 24717 [para_from,12340.1.1,9212.1.1.1,demod,1265,flip.1] u(n(x,u(y,c(x))),y)=y. 24721 [hyper,24717,5] i(n(x,u(y,c(x))),y). 24743 [para_into,24721.1.1.2,7.1.1] i(n(x,u(c(x),y)),y). 24750 [para_into,24743.1.1.2,1654.1.1,demod,1242,37] i(x,u(y,u(z,n(x,c(y))))). 24855 [para_into,24750.1.2.2.2,14590.1.1,demod,1238] i(k(x,y),u(k(x,U),z)). 24907 [para_into,24855.1.2,1103.1.1] i(k(n(x,y),z),k(x,U)). 24993 [para_into,24907.1.1.1,315.1.1] i(k(n(x,y),z),k(y,U)). 25056 [para_into,24993.1.1.1,3870.1.1,demod,15,10946] i(k(x,y),k(n(k(x,U),I),U)). 25057 [binary,25056.1,1294.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 4642 clauses generated 1456104 clauses kept 19348 clauses forward subsumed 936844 clauses back subsumed 1190 Kbytes malloced 13571 ----------- times (seconds) ----------- user CPU time 51.82 (0 hr, 0 min, 51 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 52 (0 hr, 0 min, 52 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 19:26:56 2003