----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sat Nov 22 00:45:09 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). 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)))). 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,$c1)!=k(U,d(Z,$c1)). 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(U,d(Z,$c1))!=d(Z,$c1). ------------> 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). 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. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 10. sos_size=1385 ----> UNIT CONFLICT at 2.07 sec ----> 6784 [binary,6782.1,2.1] $F. Length of proof is 115. Level of proof is 30. ---------------- PROOF ---------------- 1 [] d(Z,$c1)!=k(U,d(Z,$c1)). 2 [copy,1,flip.1] k(U,d(Z,$c1))!=d(Z,$c1). 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)). 16 [] r(k(x,y))=k(r(y),r(x)). 18 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 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). 46 [para_into,5.1.1.1,3.1.1,demod,6] u(x,u(y,z))=u(y,u(x,z)). 47 [para_into,5.1.1,3.1.1] u(x,u(y,z))=u(y,u(z,x)). 48 [copy,47,flip.1] u(x,u(y,z))=u(z,u(x,y)). 52,51 [para_into,29.1.1,3.1.1] u(D,I)=U. 54,53 [para_from,29.1.1,5.1.1.1] u(U,x)=u(I,u(D,x)). 55 [para_into,7.1.1.1.1.1,32.1.1,demod,33] u(c(u(Z,x)),c(u(Z,c(x))))=U. 57 [para_into,7.1.1.1.1.1,26.1.1,demod,27] u(c(u(D,x)),c(u(D,c(x))))=I. 63 [para_into,7.1.1.2.1.2,32.1.1] u(c(u(c(x),U)),c(u(c(x),Z)))=x. 69 [para_into,7.1.1.2.1,3.1.1] u(c(u(c(x),y)),c(u(c(y),c(x))))=x. 71 [para_into,7.1.1,3.1.1] u(c(u(c(x),c(y))),c(u(c(x),y)))=x. 73 [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). 76,75 [para_into,38.1.1.2,21.1.1,demod,22] d(Z,U)=U. 77 [para_into,10.1.1.1,21.1.1,flip.1] k(x,k(I,y))=k(x,y). 81 [para_into,53.1.1,3.1.1] u(x,U)=u(I,u(D,x)). 82 [copy,81,flip.1] u(I,u(D,x))=u(x,U). 83 [para_into,81.1.1,5.1.1] u(x,u(y,U))=u(I,u(D,u(x,y))). 84 [copy,83,flip.1] u(I,u(D,u(x,y)))=u(x,u(y,U)). 85 [para_from,81.1.1,7.1.1.1.1,demod,33] u(c(u(I,u(D,c(x)))),c(u(c(x),Z)))=x. 91 [para_into,82.1.1.2,3.1.1] u(I,u(x,D))=u(x,U). 92 [para_into,82.1.1,3.1.1,demod,6] u(D,u(x,I))=u(x,U). 93 [copy,91,flip.1] u(x,U)=u(I,u(x,D)). 94 [copy,92,flip.1] u(x,U)=u(D,u(x,I)). 99 [para_into,14.1.1.1,51.1.1] r(U)=u(r(D),r(I)). 108 [para_into,92.1.1.2,3.1.1] u(D,u(I,x))=u(x,U). 110 [copy,108,flip.1] u(x,U)=u(D,u(I,x)). 115 [para_from,93.1.1,7.1.1.1.1,demod,33] u(c(u(I,u(c(x),D))),c(u(c(x),Z)))=x. 119 [para_into,16.1.1.1,21.1.1,flip.1] k(r(I),r(x))=r(x). 128,127 [para_into,119.1.1.2,12.1.1,demod,13] k(r(I),x)=x. 130,129 [para_into,127.1.1,77.1.1,demod,128,flip.1] k(I,x)=x. 132,131 [para_into,127.1.1,21.1.1] r(I)=I. 136,135 [back_demod,99,demod,132] r(U)=u(r(D),I). 139 [para_into,19.1.1.1,129.1.1] u(x,k(y,x))=k(u(I,y),x). 143,142 [para_into,19.1.1.2,129.1.1] u(k(x,y),y)=k(u(x,I),y). 147 [copy,139,flip.1] k(u(I,x),y)=u(y,k(x,y)). 163,162 [para_into,23.1.1.1.1,131.1.1,demod,130,130] u(c(x),c(x))=c(x). 170 [para_into,23.1.1.1.2.1,21.1.1,demod,27,27] u(k(r(x),c(x)),D)=D. 174 [para_into,23.1.1,3.1.1] u(c(x),k(r(y),c(k(y,x))))=c(x). 181,180 [para_into,162.1.1.1,32.1.1,demod,33,33] u(Z,Z)=Z. 183,182 [para_into,162.1.1.1,26.1.1,demod,27,27] u(D,D)=D. 194 [para_from,180.1.1,5.1.1.1,flip.1] u(Z,u(Z,x))=u(Z,x). 197,196 [para_from,182.1.1,91.1.1.2,demod,30,flip.1] u(D,U)=U. 214 [para_into,35.1.1.1.2,32.1.1] c(k(c(x),Z))=d(x,U). 252 [para_from,170.1.1,91.1.1.2,demod,30,flip.1] u(k(r(x),c(x)),U)=U. 267,266 [para_into,46.1.1.2,180.1.1,flip.1] u(Z,u(x,Z))=u(x,Z). 527 [para_into,55.1.1.1.1,180.1.1] u(c(Z),c(u(Z,c(Z))))=U. 531 [para_into,55.1.1.1.1,94.1.1,demod,33,181] u(c(u(D,u(Z,I))),c(Z))=U. 629 [para_into,57.1.1.1.1,196.1.1,demod,33,33] u(Z,c(u(D,Z)))=I. 638,637 [para_into,57.1.1.1.1,51.1.1,demod,33,27,183] u(Z,c(D))=I. 682,681 [para_into,637.1.1,3.1.1] u(c(D),Z)=I. 686,685 [para_from,637.1.1,194.1.1.2,demod,638] u(Z,I)=I. 700,699 [back_demod,531,demod,686,52,33] u(Z,c(Z))=U. 701 [back_demod,527,demod,700,33] u(c(Z),Z)=U. 704,703 [para_into,685.1.1,3.1.1] u(I,Z)=I. 706,705 [para_from,685.1.1,92.1.1.2,demod,52,flip.1] u(Z,U)=U. 711 [para_from,685.1.1,48.1.1.2,flip.1] u(I,u(x,Z))=u(x,I). 726,725 [para_from,705.1.1,46.1.1.2,flip.1] u(Z,u(x,U))=u(x,U). 821 [para_from,681.1.1,7.1.1.1.1,demod,27] u(D,c(u(c(D),c(Z))))=D. 839 [para_from,701.1.1,7.1.1.1.1,demod,33,163] u(Z,c(c(Z)))=Z. 939 [para_into,839.1.1,3.1.1] u(c(c(Z)),Z)=Z. 975 [para_into,63.1.1.2.1,939.1.1] u(c(u(c(c(Z)),U)),c(Z))=c(Z). 1009 [para_from,629.1.1,55.1.1.2.1,demod,267,27] u(c(u(D,Z)),D)=U. 1313 [para_into,69.1.1.1.1,1009.1.1,demod,33] u(Z,c(u(c(D),c(u(D,Z)))))=u(D,Z). 1438 [para_into,711.1.1.2,939.1.1,demod,704,flip.1] u(c(c(Z)),I)=I. 1442 [para_into,711.1.1.2,681.1.1,flip.1] u(c(D),I)=u(I,I). 1457,1456 [para_from,1438.1.1,92.1.1.2,demod,52,flip.1] u(c(c(Z)),U)=U. 1475,1474 [back_demod,975,demod,1457,33,700,flip.1] c(Z)=U. 1494 [back_demod,821,demod,1475] u(D,c(u(c(D),U)))=D. 1562 [para_into,71.1.1.2.1,1009.1.1,demod,33] u(c(u(c(u(D,Z)),c(D))),Z)=u(D,Z). 1624 [para_from,1474.1.1,214.1.1.1.1,demod,76] c(k(U,Z))=U. 1634 [para_from,1474.1.1,162.1.1.2,demod,1475,54,197,1475] u(I,U)=U. 1644 [para_from,1474.1.1,35.1.1.1.1] c(k(U,c(x)))=d(Z,x). 1655,1654 [para_into,1634.1.1,110.1.1] u(D,u(I,I))=U. 1664 [para_from,1624.1.1,23.1.1.1.2,demod,136,1475,143,6,1475] k(u(r(D),u(I,I)),U)=U. 1789,1788 [para_into,73.1.1.2,162.1.1,demod,8,flip.1] u(x,c(u(c(x),c(y))))=x. 1809 [para_into,73.1.1.2,7.1.1,demod,1789] u(c(u(c(x),y)),x)=x. 1847,1846 [para_from,1654.1.1,14.1.1.1,demod,136,15,132,132,flip.1] u(r(D),u(I,I))=u(r(D),I). 1853 [back_demod,1664,demod,1847] k(u(r(D),I),U)=U. 1863,1862 [para_from,1442.1.1,92.1.1.2,demod,1655,flip.1] u(c(D),U)=U. 1886,1885 [back_demod,1494,demod,1863,33] u(D,Z)=D. 1890 [back_demod,1562,demod,1886,163,1886] u(c(c(D)),Z)=D. 1894 [back_demod,1313,demod,1886,163,1886] u(Z,c(c(D)))=D. 1963 [para_from,83.1.1,7.1.1.1.1] u(c(u(I,u(D,u(c(x),y)))),c(u(c(x),c(u(y,U)))))=x. 1984 [para_from,1890.1.1,7.1.1.1.1,demod,1475] u(c(D),c(u(c(c(D)),U)))=c(D). 1997,1996 [para_into,84.1.1.2.2,1894.1.1,demod,183,30,726,flip.1] u(c(c(D)),U)=U. 2006 [back_demod,1984,demod,1997,33,682,flip.1] c(D)=I. 2041,2040 [para_from,2006.1.1,35.1.1.1.2,demod,22] c(c(x))=d(x,D). 2056 [para_from,2006.1.1,252.1.1.1.2,demod,22] u(r(D),U)=U. 2336 [para_from,85.1.1,69.1.1.2.1] u(c(u(c(u(c(x),Z)),u(I,u(D,c(x))))),c(x))=u(c(x),Z). 2369,2368 [para_into,2056.1.1,94.1.1] u(D,u(r(D),I))=U. 2373,2372 [para_from,2056.1.1,14.1.1.1,demod,136,13,136,2369] u(r(D),I)=U. 2378 [back_demod,1853,demod,2373] k(U,U)=U. 2391,2390 [back_demod,135,demod,2373] r(U)=U. 2510 [para_from,2378.1.1,10.1.1.1,flip.1] k(U,k(U,x))=k(U,x). 3205,3204 [para_into,1809.1.1.1.1.1,2006.1.1] u(c(u(I,x)),D)=D. 3254 [para_into,1809.1.1.1.1,83.1.1] u(c(u(I,u(D,u(c(x),y)))),x)=x. 3432 [para_from,1809.1.1,83.1.1.2,demod,33,flip.1] u(I,u(D,u(x,c(u(Z,y)))))=u(x,U). 3441,3440 [para_from,1809.1.1,115.1.1.2.1,demod,1475,54,3205,30,33,1475,706,1475,54,flip.1] u(I,u(D,x))=U. 3473,3472 [back_demod,3432,demod,3441,flip.1] u(x,U)=U. 3483,3482 [back_demod,3254,demod,3441,33] u(Z,x)=x. 3516,3515 [back_demod,2336,demod,3441,3473,33,3483,flip.1] u(c(x),Z)=c(x). 3524,3523 [back_demod,1963,demod,3441,33,3473,33,3516,2041,3483] d(x,D)=x. 3752,3751 [back_demod,2040,demod,3524] c(c(x))=x. 3896,3895 [para_from,3751.1.1,1644.1.1.1.2] c(k(U,x))=d(Z,c(x)). 3958,3957 [para_into,147.1.1.1,3472.1.1,flip.1] u(x,k(U,x))=k(U,x). 4629 [para_from,2510.1.1,174.1.1.2.2.1,demod,3896,2391,3896,3958,3896] k(U,d(Z,c(x)))=d(Z,c(x)). 6782 [para_into,4629.1.1.2.2,3751.1.1,demod,3752] k(U,d(Z,x))=d(Z,x). 6784 [binary,6782.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 715 clauses generated 85479 clauses kept 3607 clauses forward subsumed 54622 clauses back subsumed 32 Kbytes malloced 4311 ----------- times (seconds) ----------- user CPU time 2.27 (0 hr, 0 min, 2 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 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 00:45:11 2003