----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sat Nov 22 00:45:21 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). 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("peirceanAx1.txt"). ------- start included file peirceanAx1.txt------- formula_list(usable). all x y z (k(u(x,y),z)=u(k(x,z),k(y,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(u(x,y),z)=u(k(x,z),k(y,z)). end_of_list. ------- end included file peirceanAx1.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("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("xiv.txt"). ------- start included file xiv.txt------- formula_list(usable). all x (k(U,x)=d(Z,k(U,x))). all x (k(x,U)=d(k(x,U),Z)). all x (d(Z,x)=k(U,d(Z,x))). -(all x (d(x,Z)=k(d(x,Z),U))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(U,x)=d(Z,k(U,x)). 0 [] k(x,U)=d(k(x,U),Z). 0 [] d(Z,x)=k(U,d(Z,x)). 0 [] d($c1,Z)!=k(d($c1,Z),U). end_of_list. ------- end included file xiv.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. 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). ------------> process usable: ** KEPT (pick-wt=9): 2 [copy,1,flip.1] k(d($c1,Z),U)!=d($c1,Z). ------------> process sos: ** KEPT (pick-wt=7): 3 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 5 [copy,4,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 6 [new_demod,5] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 7 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 8 [new_demod,7] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 10 [copy,9,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 11 [new_demod,10] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 12 [] r(r(x))=x. ---> New Demodulator: 13 [new_demod,12] r(r(x))=x. ** KEPT (pick-wt=10): 14 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 15 [new_demod,14] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 16 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 17 [new_demod,16] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=13): 19 [copy,18,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 20 [new_demod,19] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=5): 21 [] k(x,I)=x. ---> New Demodulator: 22 [new_demod,21] k(x,I)=x. ** KEPT (pick-wt=13): 23 [] u(k(r(x),c(k(x,y))),c(y))=c(y). ---> New Demodulator: 24 [new_demod,23] u(k(r(x),c(k(x,y))),c(y))=c(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=10): 35 [copy,34,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 36 [new_demod,35] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=9): 38 [copy,37,flip.1] d(Z,k(U,x))=k(U,x). ---> New Demodulator: 39 [new_demod,38] d(Z,k(U,x))=k(U,x). ** KEPT (pick-wt=9): 41 [copy,40,flip.1] d(k(x,U),Z)=k(x,U). ---> New Demodulator: 42 [new_demod,41] d(k(x,U),Z)=k(x,U). ** KEPT (pick-wt=9): 44 [copy,43,flip.1] k(U,d(Z,x))=d(Z,x). ---> New Demodulator: 45 [new_demod,44] k(U,d(Z,x))=d(Z,x). Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 39. >>>> Starting back demodulation with 42. >>>> Starting back demodulation with 45. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 10. sos_size=1407 ----> UNIT CONFLICT at 13.06 sec ----> 6978 [binary,6976.1,2.1] $F. Length of proof is 156. Level of proof is 33. ---------------- PROOF ---------------- 1 [] d($c1,Z)!=k(d($c1,Z),U). 2 [copy,1,flip.1] k(d($c1,Z),U)!=d($c1,Z). 3 [] u(x,y)=u(y,x). 4 [] u(x,u(y,z))=u(u(x,y),z). 6,5 [copy,4,flip.1] u(u(x,y),z)=u(x,u(y,z)). 8,7 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 9 [] k(x,k(y,z))=k(k(x,y),z). 10 [copy,9,flip.1] k(k(x,y),z)=k(x,k(y,z)). 13,12 [] r(r(x))=x. 15,14 [] r(u(x,y))=u(r(x),r(y)). 17,16 [] r(k(x,y))=k(r(y),r(x)). 18 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 20,19 [copy,18,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). 22,21 [] k(x,I)=x. 23 [] u(k(r(x),c(k(x,y))),c(y))=c(y). 25 [] D=c(I). 27,26 [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). 33,32 [copy,31,flip.1] c(U)=Z. 34 [] d(x,y)=c(k(c(x),c(y))). 35 [copy,34,flip.1] c(k(c(x),c(y)))=d(x,y). 37 [] k(U,x)=d(Z,k(U,x)). 38 [copy,37,flip.1] d(Z,k(U,x))=k(U,x). 40 [] k(x,U)=d(k(x,U),Z). 41 [copy,40,flip.1] d(k(x,U),Z)=k(x,U). 43 [] d(Z,x)=k(U,d(Z,x)). 44 [copy,43,flip.1] k(U,d(Z,x))=d(Z,x). 49 [para_into,5.1.1.1,3.1.1,demod,6] u(x,u(y,z))=u(y,u(x,z)). 50 [para_into,5.1.1,3.1.1] u(x,u(y,z))=u(y,u(z,x)). 51 [copy,50,flip.1] u(x,u(y,z))=u(z,u(x,y)). 55,54 [para_into,29.1.1,3.1.1] u(D,I)=U. 57,56 [para_from,29.1.1,5.1.1.1] u(U,x)=u(I,u(D,x)). 58 [para_into,7.1.1.1.1.1,32.1.1,demod,33] u(c(u(Z,x)),c(u(Z,c(x))))=U. 60 [para_into,7.1.1.1.1.1,26.1.1,demod,27] u(c(u(D,x)),c(u(D,c(x))))=I. 64 [para_into,7.1.1.1.1,3.1.1] u(c(u(x,c(y))),c(u(c(y),c(x))))=y. 66 [para_into,7.1.1.2.1.2,32.1.1] u(c(u(c(x),U)),c(u(c(x),Z)))=x. 72 [para_into,7.1.1.2.1,3.1.1] u(c(u(c(x),y)),c(u(c(y),c(x))))=x. 74 [para_into,7.1.1,3.1.1] u(c(u(c(x),c(y))),c(u(c(x),y)))=x. 76 [para_from,7.1.1,5.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(x),c(y))),z))=u(x,z). 79,78 [para_into,38.1.1.2,21.1.1,demod,22] d(Z,U)=U. 80 [para_into,10.1.1.1,21.1.1,flip.1] k(x,k(I,y))=k(x,y). 85,84 [para_into,44.1.1.2,78.1.1,demod,79] k(U,U)=U. 93,92 [para_from,84.1.1,41.1.1.1,demod,85] d(U,Z)=U. 94 [para_into,56.1.1,3.1.1] u(x,U)=u(I,u(D,x)). 95 [copy,94,flip.1] u(I,u(D,x))=u(x,U). 98 [para_into,14.1.1.1,54.1.1] r(U)=u(r(D),r(I)). 110 [para_into,16.1.1.1,21.1.1,flip.1] k(r(I),r(x))=r(x). 119,118 [para_into,110.1.1.2,12.1.1,demod,13] k(r(I),x)=x. 121,120 [para_into,118.1.1,80.1.1,demod,119,flip.1] k(I,x)=x. 123,122 [para_into,118.1.1,21.1.1] r(I)=I. 129,128 [back_demod,98,demod,123] r(U)=u(r(D),I). 130 [para_into,19.1.1.1,120.1.1] u(x,k(y,x))=k(u(I,y),x). 140,139 [para_into,19.1.1.2,120.1.1] u(k(x,y),y)=k(u(x,I),y). 149 [para_into,19.1.1,3.1.1,demod,20] k(u(x,y),z)=k(u(y,x),z). 150 [copy,130,flip.1] k(u(I,x),y)=u(y,k(x,y)). 165 [para_into,95.1.1.2,3.1.1] u(I,u(x,D))=u(x,U). 166 [para_into,95.1.1,3.1.1,demod,6] u(D,u(x,I))=u(x,U). 168 [copy,166,flip.1] u(x,U)=u(D,u(x,I)). 174,173 [para_into,23.1.1.1.1,122.1.1,demod,121,121] u(c(x),c(x))=c(x). 183 [para_into,23.1.1.1.2.1,84.1.1,demod,129,33,33,140,6,33] k(u(r(D),u(I,I)),Z)=Z. 187 [para_into,23.1.1.1.2.1,21.1.1,demod,27,27] u(k(r(x),c(x)),D)=D. 198,197 [para_into,173.1.1.1,32.1.1,demod,33,33] u(Z,Z)=Z. 200,199 [para_into,173.1.1.1,26.1.1,demod,27,27] u(D,D)=D. 211 [para_from,197.1.1,5.1.1.1,flip.1] u(Z,u(Z,x))=u(Z,x). 214,213 [para_from,199.1.1,165.1.1.2,demod,30,flip.1] u(D,U)=U. 226,225 [para_into,35.1.1.1.1,32.1.1] c(k(Z,c(x)))=d(U,x). 231 [para_into,35.1.1.1.2,32.1.1] c(k(c(x),Z))=d(x,U). 252 [para_into,166.1.1.2,3.1.1] u(D,u(I,x))=u(x,U). 254 [copy,252,flip.1] u(x,U)=u(D,u(I,x)). 270,269 [para_into,49.1.1.2,197.1.1,flip.1] u(Z,u(x,Z))=u(x,Z). 306 [para_into,187.1.1,3.1.1] u(D,k(r(x),c(x)))=D. 308 [para_from,187.1.1,165.1.1.2,demod,30,flip.1] u(k(r(x),c(x)),U)=U. 494 [para_into,58.1.1.1.1,197.1.1] u(c(Z),c(u(Z,c(Z))))=U. 496 [para_into,58.1.1.1.1,168.1.1,demod,33,198] u(c(u(D,u(Z,I))),c(Z))=U. 524 [para_into,58.1.1.2.1.2,225.1.1] u(c(u(Z,k(Z,c(x)))),c(u(Z,d(U,x))))=U. 530 [para_into,58.1.1.2.1.2,26.1.1] u(c(u(Z,I)),c(u(Z,D)))=U. 578 [para_into,60.1.1.1.1,254.1.1,demod,30,214,33,33] u(Z,c(u(D,Z)))=I. 589,588 [para_into,60.1.1.1.1,54.1.1,demod,33,27,200] u(Z,c(D))=I. 637,636 [para_from,588.1.1,211.1.1.2,demod,589] u(Z,I)=I. 648 [back_demod,530,demod,637,27] u(D,c(u(Z,D)))=U. 651,650 [back_demod,496,demod,637,55,33] u(Z,c(Z))=U. 652 [back_demod,494,demod,651,33] u(c(Z),Z)=U. 655,654 [para_into,636.1.1,3.1.1] u(I,Z)=I. 657,656 [para_from,636.1.1,166.1.1.2,demod,55,flip.1] u(Z,U)=U. 662 [para_from,636.1.1,51.1.1.2,flip.1] u(I,u(x,Z))=u(x,I). 788 [para_from,652.1.1,7.1.1.1.1,demod,33,174] u(Z,c(c(Z)))=Z. 888 [para_into,788.1.1,3.1.1] u(c(c(Z)),Z)=Z. 924 [para_into,66.1.1.2.1,888.1.1] u(c(u(c(c(Z)),U)),c(Z))=c(Z). 958 [para_from,578.1.1,58.1.1.2.1,demod,270,27] u(c(u(D,Z)),D)=U. 990 [para_into,648.1.1.2.1,3.1.1] u(D,c(u(D,Z)))=U. 1200 [para_from,990.1.1,60.1.1.1.1,demod,33] u(Z,c(u(D,c(c(u(D,Z))))))=I. 1354 [para_into,306.1.1.2.1,128.1.1,demod,33] u(D,k(u(r(D),I),Z))=D. 1499 [para_into,74.1.1.2.1,958.1.1,demod,33] u(c(u(c(u(D,Z)),c(D))),Z)=u(D,Z). 1563 [para_into,662.1.1.2,888.1.1,demod,655,flip.1] u(c(c(Z)),I)=I. 1582,1581 [para_from,1563.1.1,166.1.1.2,demod,55,flip.1] u(c(c(Z)),U)=U. 1602,1601 [back_demod,924,demod,1582,33,651,flip.1] c(Z)=U. 1634,1633 [para_from,1601.1.1,64.1.1.2.1.1,demod,1602,57] u(c(u(x,U)),c(u(I,u(D,c(x)))))=Z. 1636,1635 [para_from,1601.1.1,35.1.1.1.2] c(k(c(x),U))=d(x,Z). 1642,1641 [para_from,1601.1.1,231.1.1.1.1,demod,79] c(k(U,Z))=U. 1646,1645 [para_from,1601.1.1,225.1.1.1.2,demod,93] c(k(Z,U))=U. 1651 [para_from,1601.1.1,173.1.1.2,demod,1602,57,214,1602] u(I,U)=U. 1671 [para_into,1651.1.1,254.1.1] u(D,u(I,I))=U. 1678 [para_from,1651.1.1,49.1.1.2,flip.1] u(I,u(x,U))=u(x,U). 1786,1785 [para_into,76.1.1.2,173.1.1,demod,8,flip.1] u(x,c(u(c(x),c(y))))=x. 1804 [para_into,76.1.1.2,7.1.1,demod,1786] u(c(u(c(x),y)),x)=x. 1828,1827 [para_from,1641.1.1,64.1.1.2.1.1,demod,1642,57,1634,flip.1] k(U,Z)=Z. 1833 [para_from,1827.1.1,19.1.1.1,demod,57] u(Z,k(x,Z))=k(u(I,u(D,x)),Z). 1835 [para_from,1827.1.1,16.1.1.1,demod,129,flip.1] k(r(Z),u(r(D),I))=r(Z). 1850,1849 [para_from,1645.1.1,64.1.1.2.1.1,demod,1646,57,1634,flip.1] k(Z,U)=Z. 1856,1855 [para_from,1849.1.1,19.1.1.2] u(k(x,U),Z)=k(u(x,Z),U). 1857 [para_from,1849.1.1,23.1.1.1.2.1,demod,1602,33,1856,33] k(u(r(Z),Z),U)=Z. 1868,1867 [para_from,1671.1.1,14.1.1.1,demod,129,15,123,123,flip.1] u(r(D),u(I,I))=u(r(D),I). 1879,1878 [back_demod,183,demod,1868] k(u(r(D),I),Z)=Z. 1884,1883 [back_demod,1354,demod,1879] u(D,Z)=D. 1891 [back_demod,1499,demod,1884,174,1884] u(c(c(D)),Z)=D. 1900,1899 [back_demod,1200,demod,1884] u(Z,c(u(D,c(c(D)))))=I. 1947 [para_from,1891.1.1,662.1.1.2,demod,30,flip.1] u(c(c(D)),I)=U. 2086,2085 [para_from,1947.1.1,72.1.1.1.1,demod,33,27,1900,flip.1] c(D)=I. 2104,2103 [para_from,2085.1.1,35.1.1.1.2,demod,22] c(c(x))=d(x,D). 2121 [para_from,2085.1.1,308.1.1.1.2,demod,22] u(r(D),U)=U. 2123 [para_from,2085.1.1,306.1.1.2.2,demod,22] u(D,r(D))=D. 2126,2125 [para_from,2085.1.1,187.1.1.1.2,demod,22] u(r(D),D)=D. 2128,2127 [para_from,2085.1.1,173.1.1.2,demod,2086,2086] u(I,I)=I. 2438,2437 [para_into,2121.1.1,168.1.1] u(D,u(r(D),I))=U. 2440,2439 [para_from,2121.1.1,14.1.1.1,demod,129,13,129,2438] u(r(D),I)=U. 2473 [back_demod,1835,demod,2440] k(r(Z),U)=r(Z). 2482,2481 [back_demod,128,demod,2440] r(U)=U. 2496,2495 [para_from,2123.1.1,14.1.1.1,demod,13,2126] r(D)=D. 2566,2565 [para_into,130.1.1.2,120.1.1,demod,2128,121] u(x,x)=x. 2609 [para_into,2565.1.1,49.1.1,demod,6,2566] u(x,u(x,y))=u(x,y). 2648,2647 [para_into,2103.1.1.1,35.1.1] c(d(x,y))=d(k(c(x),c(y)),D). 2744,2743 [para_from,2473.1.1,10.1.1.1,flip.1] k(r(Z),k(U,x))=k(r(Z),x). 2909 [para_into,1857.1.1.1,3.1.1] k(u(Z,r(Z)),U)=Z. 2971 [para_from,2909.1.1,10.1.1.1,flip.1] k(u(Z,r(Z)),k(U,x))=k(Z,x). 3060,3059 [para_into,149.1.1.1,254.1.1,demod,57,flip.1] k(u(I,u(D,x)),y)=k(u(D,u(I,x)),y). 3086 [back_demod,1833,demod,3060] u(Z,k(x,Z))=k(u(D,u(I,x)),Z). 3139 [para_from,1635.1.1,23.1.1.1.2,demod,33,33] u(k(r(c(x)),d(x,Z)),Z)=Z. 3143 [para_from,1635.1.1,23.1.1.2,demod,1636] u(k(r(x),c(k(x,k(c(y),U)))),d(y,Z))=d(y,Z). 3225 [para_into,1678.1.1.2,254.1.1] u(I,u(D,u(I,x)))=u(x,U). 3228 [copy,3225,flip.1] u(x,U)=u(I,u(D,u(I,x))). 3418,3417 [para_from,1804.1.1,165.1.1.2,demod,30,2086,flip.1] u(c(u(I,x)),U)=U. 3432,3431 [para_from,1804.1.1,66.1.1.2.1,demod,1602,57,3418,33,1602,657,1602,57,flip.1] u(I,u(D,x))=U. 3464,3463 [back_demod,3228,demod,3432] u(x,U)=U. 3593,3592 [back_demod,254,demod,3464,flip.1] u(D,u(I,x))=U. 3664 [back_demod,3086,demod,3593,1828] u(Z,k(x,Z))=Z. 3696 [para_into,150.1.1.1,29.1.1,flip.1] u(x,k(D,x))=k(U,x). 3726,3725 [para_from,3463.1.1,1804.1.1.1.1,demod,33] u(Z,x)=x. 3728,3727 [para_from,3463.1.1,76.1.1.1.1,demod,33,33,3726] u(c(u(c(x),Z)),y)=u(x,y). 3730,3729 [para_from,3463.1.1,74.1.1.2.1,demod,33,33,3728] u(x,Z)=x. 3732,3731 [para_from,3463.1.1,72.1.1.1.1,demod,33,33,3726,2104,3726] d(x,D)=x. 3737 [back_demod,3664,demod,3726] k(x,Z)=Z. 3764,3763 [back_demod,2971,demod,3726,2744] k(r(Z),x)=k(Z,x). 3775 [back_demod,524,demod,3726,226,3726,2648,33,3732] u(d(U,x),k(Z,c(x)))=U. 3791 [back_demod,3139,demod,3730] k(r(c(x)),d(x,Z))=Z. 3900,3899 [back_demod,2103,demod,3732] c(c(x))=x. 3936,3935 [back_demod,2473,demod,3764,1850,flip.1] r(Z)=Z. 3989 [para_from,3737.1.1,16.1.1.1,demod,3936,3936,flip.1] k(Z,r(x))=Z. 4067 [para_from,3899.1.1,35.1.1.1.2] c(k(c(x),y))=d(x,c(y)). 4071 [para_from,3899.1.1,1635.1.1.1.1] c(k(x,U))=d(c(x),Z). 4084,4083 [para_from,3899.1.1,35.1.1.1.1] c(k(x,c(y)))=d(c(x),y). 4202,4201 [para_into,3989.1.1.2,12.1.1] k(Z,x)=Z. 4208,4207 [back_demod,3775,demod,4202,3730] d(U,x)=U. 5566 [para_from,3696.1.1,14.1.1.1,demod,17,2482,17,2496,flip.1] u(r(x),k(r(x),D))=k(r(x),U). 5763 [para_from,3791.1.1,16.1.1.1,demod,3936,13,flip.1] k(r(d(x,Z)),c(x))=Z. 6047,6046 [para_into,4071.1.1.1,10.1.1] c(k(x,k(y,U)))=d(c(k(x,y)),Z). 6058 [back_demod,3143,demod,6047,4084] u(k(r(x),d(d(c(x),y),Z)),d(y,Z))=d(y,Z). 6423 [para_into,4067.1.1.1.1,3899.1.1] c(k(x,y))=d(c(x),c(y)). 6588 [para_into,6423.1.1.1,5763.1.1,demod,1602,3900,flip.1] d(c(r(d(x,Z))),x)=U. 6829,6828 [para_into,5566.1.1.1,12.1.1,demod,13,13] u(x,k(x,D))=k(x,U). 6838 [para_from,6828.1.1,2609.1.1.2,demod,6829] u(x,k(x,U))=k(x,U). 6843,6842 [para_into,6838.1.1,3.1.1] u(k(x,U),x)=k(x,U). 6976 [para_into,6058.1.1.1.2.1,6588.1.1,demod,13,4208,6843] k(d(x,Z),U)=d(x,Z). 6978 [binary,6976.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 1398 clauses generated 562932 clauses kept 3694 clauses forward subsumed 237783 clauses back subsumed 35 Kbytes malloced 4694 ----------- times (seconds) ----------- user CPU time 13.26 (0 hr, 0 min, 13 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 13 (0 hr, 0 min, 13 sec) 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 Sat Nov 22 00:45:34 2003