----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 19:27:31 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)). -(all x i(k(n(k(x,r(x)),I),U),k(x,U))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(x,U),k(n(k(x,r(x)),I),U)). 0 [] -i(k(n(k($c1,r($c1)),I),U),k($c1,U)). end_of_list. ------- end included file xxi_b_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=12): 1 [] u(x,y)!=y|c(u(y,c(x)))=Z. ** KEPT (pick-wt=12): 2 [] c(u(x,c(y)))!=Z|u(y,x)=x. ** KEPT (pick-wt=8): 3 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=8): 4 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 5 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=12): 6 [] -i(k(n(k($c1,r($c1)),I),U),k($c1,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). ** KEPT (pick-wt=12): 72 [] i(k(x,U),k(n(k(x,r(x)),I),U)). 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): 75 [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 74. Following clause subsumed by 61 during input processing: 0 [copy,75,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=9816 ----> UNIT CONFLICT at 50.95 sec ----> 25250 [binary,25249.1,1324.1] $F. Length of proof is 145. Level of proof is 25. ---------------- PROOF ---------------- 3 [] -i(x,y)|i(r(x),r(y)). 4 [] -i(x,y)|u(x,y)=y. 5 [] i(x,y)|u(x,y)!=y. 6 [] -i(k(n(k($c1,r($c1)),I),U),k($c1,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). 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)). 43,42 [] r(n(x,y))=n(r(x),r(y)). 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)))). 65 [] n(x,I)=n(r(x),I). 66 [copy,65,flip.1] n(r(x),I)=n(x,I). 70 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). 72 [] i(k(x,U),k(n(k(x,r(x)),I),U)). 73 [back_demod,11,demod,24] u(c(u(c(x),y)),n(x,y))=x. 76 [para_into,9.1.1.1,7.1.1,demod,10] u(x,u(y,z))=u(y,u(x,z)). 77 [para_into,9.1.1,7.1.1] u(x,u(y,z))=u(y,u(z,x)). 78 [copy,77,flip.1] u(x,u(y,z))=u(z,u(x,y)). 80,79 [para_into,29.1.1,7.1.1] u(D,I)=U. 82,81 [para_from,29.1.1,9.1.1.1] u(U,x)=u(I,u(D,x)). 86,85 [para_into,36.1.1.1,32.1.1] c(Z)=U. 87 [para_into,36.1.1.1,26.1.1] c(D)=I. 101 [para_into,20.1.1.1,34.1.1,demod,49,flip.1] k(I,r(x))=r(x). 116,115 [para_into,101.1.1.2,16.1.1,demod,17] k(I,x)=x. 128,127 [para_into,23.1.1.1.1,36.1.1] c(u(x,c(y)))=n(c(x),y). 130,129 [para_into,23.1.1.1.1,23.1.1,demod,128] n(c(n(x,y)),z)=n(u(c(x),c(y)),z). 136,135 [para_into,23.1.1.1.2,36.1.1] c(u(c(x),y))=n(x,c(y)). 137 [para_into,23.1.1.1.2,23.1.1,demod,136] n(x,c(n(y,z)))=n(x,u(c(y),c(z))). 139 [para_into,23.1.1.1,7.1.1,demod,128,37] n(x,y)=n(y,x). 141,140 [back_demod,73,demod,136] u(n(x,c(y)),n(x,y))=x. 142 [para_into,139.1.1,66.1.1,flip.1] n(I,r(x))=n(x,I). 147 [para_into,142.1.1.2,20.1.1] n(I,k(r(x),r(y)))=n(k(y,x),I). 151 [para_into,81.1.1,7.1.1] u(x,U)=u(I,u(D,x)). 152 [copy,151,flip.1] u(I,u(D,x))=u(x,U). 164 [para_into,152.1.1,7.1.1,demod,10] u(D,u(x,I))=u(x,U). 166 [copy,164,flip.1] u(x,U)=u(D,u(x,I)). 170 [para_into,164.1.1.2,7.1.1] u(D,u(I,x))=u(x,U). 184,183 [para_into,170.1.1.2,166.1.1,demod,82,flip.1] u(I,u(D,U))=u(D,u(D,u(I,I))). 201 [para_into,54.1.1.2.2.2.1.1,52.1.1] n(x,k(U,n(y,c(k(U,x)))))=Z. 205 [para_into,54.1.1.2.2.2.1.1,48.1.1,demod,116,116] n(x,n(y,c(x)))=Z. 210,209 [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. 215 [para_into,54.1.1,139.1.1] n(k(x,n(y,c(k(r(x),z)))),z)=Z. 219 [para_into,205.1.1.2.2,87.1.1] n(D,n(x,I))=Z. 223 [para_into,205.1.1.2.2,36.1.1] n(c(x),n(y,x))=Z. 227 [para_into,205.1.1.2.2,26.1.1] n(I,n(x,D))=Z. 229 [para_into,205.1.1.2,139.1.1] n(x,n(c(x),y))=Z. 233 [para_into,219.1.1.2,139.1.1] n(D,n(I,x))=Z. 269 [para_into,233.1.1.2,227.1.1] n(D,Z)=Z. 275 [para_into,269.1.1,139.1.1] n(Z,D)=Z. 281 [para_from,275.1.1,227.1.1.2] n(I,Z)=Z. 315 [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). 317,316 [para_into,61.1.1.2.1.2.2,48.1.1,demod,35,35,35] n(x,n(y,x))=n(y,x). 330 [copy,315,flip.1] n(k(x,Z),y)=n(y,k(n(x,k(y,Z)),Z)). 344 [para_into,62.1.2.2.1.2,281.1.1,demod,35,86] i(n(x,n(y,z)),n(x,u(k(n(y,z),Z),k(y,n(I,U))))). 358 [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)))). 369 [para_into,64.1.1.1,115.1.1,demod,49,116,116] i(n(x,y),n(x,y)). 370 [para_into,64.1.1.1,34.1.1] i(n(x,y),k(x,n(I,k(r(x),y)))). 371 [para_into,64.1.1,205.1.1,demod,210] i(Z,k(x,Z)). 383 [para_into,371.1.2,115.1.1] i(Z,Z). 386,385 [hyper,383,4] u(Z,Z)=Z. 431 [para_into,369.1.1,139.1.1] i(n(x,y),n(y,x)). 439 [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). 498 [para_into,223.1.1.2,139.1.1] n(c(x),n(x,y))=Z. 509,508 [para_into,229.1.1.2,229.1.1] n(x,Z)=Z. 521 [para_into,508.1.1,139.1.1] n(Z,x)=Z. 531 [para_into,72.1.1,115.1.1,demod,49,35] i(U,k(n(I,I),U)). 546,545 [para_from,521.1.1,54.1.1.2.2] n(x,k(y,Z))=Z. 555,554 [back_demod,330,demod,546,546] n(k(x,Z),y)=Z. 569 [hyper,531,3,demod,53,21,53,43,49,49] i(U,k(U,n(I,I))). 577 [para_into,545.1.1.2,14.1.1] n(x,k(y,k(z,Z)))=Z. 594 [hyper,569,4,demod,82] u(I,u(D,k(U,n(I,I))))=k(U,n(I,I)). 596 [para_into,76.1.1.2,385.1.1,flip.1] u(Z,u(x,Z))=u(x,Z). 619 [para_into,498.1.1,139.1.1] n(n(x,y),c(x))=Z. 656 [para_into,316.1.1.2,139.1.1] n(x,n(x,y))=n(y,x). 657 [para_into,316.1.1,498.1.1,flip.1] n(x,c(x))=Z. 664,663 [para_into,316.1.1,229.1.1,flip.1] n(c(x),x)=Z. 862,861 [para_into,127.1.1.1.2,36.1.1] c(u(x,y))=n(c(x),c(y)). 863 [para_into,127.1.1.1,9.1.1,demod,862,862,37,862,flip.1] n(n(c(x),c(y)),z)=n(c(x),n(c(y),z)). 1027 [para_into,137.1.1,663.1.1,demod,37,flip.1] n(n(x,y),u(c(x),c(y)))=Z. 1040,1039 [para_into,656.1.1.2,656.1.1,demod,317,flip.1] n(n(x,y),x)=n(y,x). 1097 [para_into,140.1.1.1.2,85.1.1,demod,509] u(n(x,U),Z)=x. 1107 [para_into,140.1.1.1,663.1.1,demod,37,37] u(Z,n(x,x))=x. 1112,1111 [para_into,140.1.1.1,619.1.1,demod,1040] u(Z,n(x,y))=n(y,x). 1120,1119 [para_into,140.1.1.1,554.1.1,demod,555,386,flip.1] k(x,Z)=Z. 1121 [para_into,140.1.1.1,139.1.1] u(n(c(x),y),n(y,x))=y. 1126,1125 [para_into,140.1.1.1,129.1.1,demod,130,141,flip.1] c(n(x,y))=u(c(x),c(y)). 1127 [para_into,140.1.1.1,57.1.1,demod,58,141,flip.1] u(k(n(x,y),z),k(n(x,c(y)),z))=k(x,z). 1137 [para_into,140.1.1.2,657.1.1,demod,37] u(n(x,x),Z)=x. 1144,1143 [para_into,140.1.1.2,619.1.1,demod,37,1040] u(n(x,y),Z)=n(y,x). 1146,1145 [para_into,140.1.1.2,577.1.1,demod,1120,1120,86,1144] n(U,x)=x. 1159 [para_into,140.1.1.2,229.1.1,demod,1126,37,1144] n(u(x,c(y)),x)=x. 1186,1185 [back_demod,1107,demod,1112] n(x,x)=x. 1210 [back_demod,344,demod,1120] i(n(x,n(y,z)),n(x,u(Z,k(y,n(I,U))))). 1262,1261 [back_demod,1137,demod,1186] u(x,Z)=x. 1266,1265 [back_demod,1097,demod,1262] n(x,U)=x. 1281 [back_demod,594,demod,1186,35,184,1186,35] u(D,u(D,u(I,I)))=U. 1283 [back_demod,569,demod,1186,35] i(U,U). 1286,1285 [back_demod,439,demod,1266,1266] n(k(x,r(x)),I)=n(k(x,U),I). 1292,1291 [back_demod,596,demod,1262,1262] u(Z,x)=x. 1309 [back_demod,1210,demod,1266,35,1292] i(n(x,n(y,z)),n(x,y)). 1324 [back_demod,6,demod,1286] -i(k(n(k($c1,U),I),U),k($c1,U)). 1332 [hyper,1283,4,demod,82] u(I,u(D,U))=U. 1338 [para_from,1145.1.1,431.1.2,demod,1266] i(x,x). 1342 [para_from,1145.1.1,140.1.1.1,demod,1146] u(c(x),x)=U. 1347,1346 [hyper,1338,4] u(x,x)=x. 1349,1348 [back_demod,1281,demod,1347,80] u(D,U)=U. 1350 [back_demod,1332,demod,1349] u(I,U)=U. 1380 [para_into,147.1.1.2.1,52.1.1] n(I,k(U,r(x)))=n(k(x,U),I). 1418 [para_from,1350.1.1,78.1.1.2,demod,82] u(x,U)=u(I,u(D,u(x,I))). 1421 [copy,1418,flip.1] u(I,u(D,u(x,I)))=u(x,U). 1422 [para_into,1342.1.1.1,36.1.1] u(x,c(x))=U. 1430 [para_from,1342.1.1,78.1.1.2,flip.1] u(x,u(y,c(x)))=u(y,U). 1480 [para_into,1159.1.1.1.2,36.1.1] n(u(x,y),x)=x. 1505,1504 [para_into,1480.1.1.1,81.1.1,demod,1266] u(I,u(D,x))=U. 1512 [para_into,1480.1.1.1,7.1.1] n(u(x,y),y)=y. 1523,1522 [back_demod,1421,demod,1505,flip.1] u(x,U)=U. 1540 [back_demod,1430,demod,1523] u(x,u(y,c(x)))=U. 1731 [para_into,1540.1.1,9.1.1,demod,862] u(x,u(y,u(z,n(c(x),c(y)))))=U. 2010 [para_into,1309.1.1.2,1145.1.1,demod,1266] i(n(x,y),x). 2075 [para_into,2010.1.1,1512.1.1] i(x,u(y,x)). 2078 [para_into,2010.1.1,316.1.1] i(n(x,y),y). 2085 [para_into,2010.1.1,66.1.1] i(n(x,I),r(x)). 2092 [para_into,2075.1.2,77.1.1] i(u(x,y),u(x,u(y,z))). 2096 [hyper,2078,4] u(n(x,y),y)=y. 2144 [para_into,2085.1.1,139.1.1] i(n(I,x),r(x)). 2164 [hyper,2144,4] u(n(I,x),r(x))=r(x). 2266 [para_into,2096.1.1,7.1.1] u(x,n(y,x))=x. 2326,2325 [para_from,2266.1.1,9.1.1.1,flip.1] u(x,u(n(y,x),z))=u(x,z). 2381 [para_into,201.1.1.2.2,1512.1.1] n(x,k(U,c(k(U,x))))=Z. 3471 [para_into,2092.1.2.2,2096.1.1] i(u(x,n(y,z)),u(x,z)). 3504 [para_from,2164.1.1,1480.1.1.1] n(r(x),n(I,x))=n(I,x). 4909 [para_into,370.1.1,1145.1.1,demod,53] i(x,k(U,n(I,k(U,x)))). 9075 [para_from,1121.1.1,3471.1.1] i(x,u(n(c(y),x),y)). 9134 [hyper,9075,4,demod,2326,flip.1] u(n(c(x),y),x)=u(y,x). 10445 [para_into,2381.1.1,1145.1.1] k(U,c(k(U,U)))=Z. 10465 [para_from,2381.1.1,358.1.2.1,demod,41,21,53,1266,41,21,53,664,1120] i(k(x,c(k(r(x),U))),Z). 10498,10497 [para_into,863.1.1.1.2,36.1.1,demod,37] n(n(c(x),y),z)=n(c(x),n(y,z)). 10680 [para_from,10445.1.1,4909.1.2.2.2,demod,509,1120] i(c(k(U,U)),Z). 10696 [hyper,10680,4,demod,1262] c(k(U,U))=Z. 10714,10713 [para_from,10696.1.1,1422.1.1.2,demod,1262] k(U,U)=U. 11954 [hyper,10465,4,demod,1262] k(x,c(k(r(x),U)))=Z. 12586 [para_into,1027.1.1.2.1,36.1.1,demod,10498] n(c(x),n(y,u(x,c(y))))=Z. 14366 [para_from,11954.1.1,215.1.1.1.2.2.1,demod,86,1266,17] n(k(x,y),c(k(x,U)))=Z. 24655 [para_from,12586.1.1,9134.1.1.1,demod,1292,flip.1] u(n(x,u(y,c(x))),y)=y. 24659 [hyper,24655,5] i(n(x,u(y,c(x))),y). 24681 [para_into,24659.1.1.2,7.1.1] i(n(x,u(c(x),y)),y). 24688 [para_into,24681.1.1.2,1731.1.1,demod,1266,37] i(x,u(y,u(z,n(x,c(y))))). 24765 [para_into,24688.1.2.2.2,14366.1.1,demod,1262] i(k(x,y),u(k(x,U),z)). 24818 [para_into,24765.1.2,1127.1.1] i(k(n(x,y),z),k(x,U)). 24895 [para_into,24818.1.1.1,3504.1.1] i(k(n(I,x),y),k(r(x),U)). 25249 [para_into,24895.1.1.1,1380.1.1,demod,21,17,53,15,10714] i(k(n(k(x,U),I),y),k(x,U)). 25250 [binary,25249.1,1324.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 4745 clauses generated 1506727 clauses kept 19550 clauses forward subsumed 964598 clauses back subsumed 1305 Kbytes malloced 13635 ----------- times (seconds) ----------- user CPU time 51.16 (0 hr, 0 min, 51 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 51 (0 hr, 0 min, 51 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 19:28:22 2003