----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sat Nov 22 00:44:53 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))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(U,x)=d(Z,k(U,x)). 0 [] k($c1,U)!=d(k($c1,U),Z). 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] d(k($c1,U),Z)!=k($c1,U). ------------> 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). 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. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 10. sos_size=1453 ----> UNIT CONFLICT at 13.25 sec ----> 7003 [binary,7001.1,2.1] $F. Length of proof is 151. Level of proof is 35. ---------------- PROOF ---------------- 1 [] k($c1,U)!=d(k($c1,U),Z). 2 [copy,1,flip.1] d(k($c1,U),Z)!=k($c1,U). 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)). 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). 43 [para_into,5.1.1.1,3.1.1,demod,6] u(x,u(y,z))=u(y,u(x,z)). 44 [para_into,5.1.1,3.1.1] u(x,u(y,z))=u(y,u(z,x)). 45 [copy,44,flip.1] u(x,u(y,z))=u(z,u(x,y)). 49,48 [para_into,29.1.1,3.1.1] u(D,I)=U. 51,50 [para_from,29.1.1,5.1.1.1] u(U,x)=u(I,u(D,x)). 52 [para_into,7.1.1.1.1.1,32.1.1,demod,33] u(c(u(Z,x)),c(u(Z,c(x))))=U. 54 [para_into,7.1.1.1.1.1,26.1.1,demod,27] u(c(u(D,x)),c(u(D,c(x))))=I. 58 [para_into,7.1.1.1.1,3.1.1] u(c(u(x,c(y))),c(u(c(y),c(x))))=y. 60 [para_into,7.1.1.2.1.2,32.1.1] u(c(u(c(x),U)),c(u(c(x),Z)))=x. 66 [para_into,7.1.1.2.1,3.1.1] u(c(u(c(x),y)),c(u(c(y),c(x))))=x. 68 [para_into,7.1.1,3.1.1] u(c(u(c(x),c(y))),c(u(c(x),y)))=x. 70 [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). 73,72 [para_into,38.1.1.2,21.1.1,demod,22] d(Z,U)=U. 74 [para_into,50.1.1,3.1.1] u(x,U)=u(I,u(D,x)). 75 [copy,74,flip.1] u(I,u(D,x))=u(x,U). 76 [para_into,10.1.1.1,21.1.1,flip.1] k(x,k(I,y))=k(x,y). 78 [para_into,74.1.1,5.1.1] u(x,u(y,U))=u(I,u(D,u(x,y))). 79 [copy,78,flip.1] u(I,u(D,u(x,y)))=u(x,u(y,U)). 80 [para_from,74.1.1,7.1.1.1.1,demod,33] u(c(u(I,u(D,c(x)))),c(u(c(x),Z)))=x. 86 [para_into,75.1.1.2,3.1.1] u(I,u(x,D))=u(x,U). 87 [para_into,75.1.1,3.1.1,demod,6] u(D,u(x,I))=u(x,U). 89 [copy,87,flip.1] u(x,U)=u(D,u(x,I)). 97 [para_into,14.1.1.1,48.1.1] r(U)=u(r(D),r(I)). 99 [para_into,14.1.1.1,7.1.1,flip.1] u(r(c(u(c(x),y))),r(c(u(c(x),c(y)))))=r(x). 103 [para_into,87.1.1.2,5.1.1,demod,6] u(D,u(x,u(y,I)))=u(x,u(y,U)). 104 [para_into,87.1.1.2,3.1.1] u(D,u(I,x))=u(x,U). 105 [copy,103,flip.1] u(x,u(y,U))=u(D,u(x,u(y,I))). 106 [copy,104,flip.1] u(x,U)=u(D,u(I,x)). 115 [para_from,89.1.1,7.1.1.1.1,demod,33] u(c(u(D,u(c(x),I))),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,127.1.1,76.1.1,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,97,demod,132] r(U)=u(r(D),I). 137 [para_into,19.1.1.1,129.1.1] u(x,k(y,x))=k(u(I,y),x). 145 [copy,137,flip.1] k(u(I,x),y)=u(y,k(x,y)). 163,162 [para_into,35.1.1.1.1,32.1.1] c(k(Z,c(x)))=d(U,x). 168 [para_into,35.1.1.1.2,32.1.1] c(k(c(x),Z))=d(x,U). 179,178 [para_into,23.1.1.1.1,131.1.1,demod,130,130] u(c(x),c(x))=c(x). 184 [para_into,23.1.1.1.1,12.1.1] u(k(x,c(k(r(x),y))),c(y))=c(y). 186 [para_into,23.1.1.1.2.1,21.1.1,demod,27,27] u(k(r(x),c(x)),D)=D. 203,202 [para_into,178.1.1.1,32.1.1,demod,33,33] u(Z,Z)=Z. 205,204 [para_into,178.1.1.1,26.1.1,demod,27,27] u(D,D)=D. 216 [para_from,202.1.1,5.1.1.1,flip.1] u(Z,u(Z,x))=u(Z,x). 219,218 [para_from,204.1.1,86.1.1.2,demod,30,flip.1] u(D,U)=U. 233,232 [para_into,43.1.1.2,202.1.1,flip.1] u(Z,u(x,Z))=u(x,Z). 447 [para_from,186.1.1,86.1.1.2,demod,30,flip.1] u(k(r(x),c(x)),U)=U. 472 [para_into,52.1.1.1.1,202.1.1] u(c(Z),c(u(Z,c(Z))))=U. 476 [para_into,52.1.1.1.1,89.1.1,demod,33,203] u(c(u(D,u(Z,I))),c(Z))=U. 504 [para_into,52.1.1.2.1.2,162.1.1] u(c(u(Z,k(Z,c(x)))),c(u(Z,d(U,x))))=U. 547 [para_into,54.1.1.1.1,218.1.1,demod,33,33] u(Z,c(u(D,Z)))=I. 556,555 [para_into,54.1.1.1.1,48.1.1,demod,33,27,205] u(Z,c(D))=I. 600,599 [para_into,555.1.1,3.1.1] u(c(D),Z)=I. 604,603 [para_from,555.1.1,216.1.1.2,demod,556] u(Z,I)=I. 618,617 [back_demod,476,demod,604,49,33] u(Z,c(Z))=U. 619 [back_demod,472,demod,618,33] u(c(Z),Z)=U. 622,621 [para_into,603.1.1,3.1.1] u(I,Z)=I. 624,623 [para_from,603.1.1,87.1.1.2,demod,49,flip.1] u(Z,U)=U. 629 [para_from,603.1.1,45.1.1.2,flip.1] u(I,u(x,Z))=u(x,I). 737 [para_from,599.1.1,7.1.1.1.1,demod,27] u(D,c(u(c(D),c(Z))))=D. 755 [para_from,619.1.1,7.1.1.1.1,demod,33,179] u(Z,c(c(Z)))=Z. 816,815 [para_into,58.1.1.2.1.2,35.1.1] u(c(u(k(c(x),c(y)),c(z))),c(u(c(z),d(x,y))))=z. 833 [para_into,58.1.1,3.1.1] u(c(u(c(x),c(y))),c(u(y,c(x))))=x. 855 [para_into,755.1.1,3.1.1] u(c(c(Z)),Z)=Z. 891 [para_into,60.1.1.2.1,855.1.1] u(c(u(c(c(Z)),U)),c(Z))=c(Z). 925 [para_from,547.1.1,52.1.1.2.1,demod,233,27] u(c(u(D,Z)),D)=U. 1410 [para_into,629.1.1.2,855.1.1,demod,622,flip.1] u(c(c(Z)),I)=I. 1414 [para_into,629.1.1.2,599.1.1,flip.1] u(c(D),I)=u(I,I). 1484 [para_into,68.1.1.2.1,925.1.1,demod,33] u(c(u(c(u(D,Z)),c(D))),Z)=u(D,Z). 1547,1546 [para_from,1410.1.1,87.1.1.2,demod,49,flip.1] u(c(c(Z)),U)=U. 1567,1566 [back_demod,891,demod,1547,33,618,flip.1] c(Z)=U. 1586 [back_demod,737,demod,1567] u(D,c(u(c(D),U)))=D. 1599,1598 [para_from,1566.1.1,58.1.1.2.1.1,demod,1567,51] u(c(u(x,U)),c(u(I,u(D,c(x)))))=Z. 1601,1600 [para_from,1566.1.1,35.1.1.1.2] c(k(c(x),U))=d(x,Z). 1608 [para_from,1566.1.1,178.1.1.2,demod,1567,51,219,1567] u(I,U)=U. 1613,1612 [para_from,1566.1.1,168.1.1.1.1,demod,73] c(k(U,Z))=U. 1637,1636 [para_into,1608.1.1,106.1.1] u(D,u(I,I))=U. 1651,1650 [para_from,1612.1.1,58.1.1.2.1.1,demod,1613,51,1599,flip.1] k(U,Z)=Z. 1755,1754 [para_into,70.1.1.2,178.1.1,demod,8,flip.1] u(x,c(u(c(x),c(y))))=x. 1775 [para_into,70.1.1.2,7.1.1,demod,1755] u(c(u(c(x),y)),x)=x. 1798 [para_from,1650.1.1,19.1.1.1,demod,51] u(Z,k(x,Z))=k(u(I,u(D,x)),Z). 1825,1824 [para_from,1414.1.1,87.1.1.2,demod,1637,flip.1] u(c(D),U)=U. 1848,1847 [back_demod,1586,demod,1825,33] u(D,Z)=D. 1852 [back_demod,1484,demod,1848,179,1848] u(c(c(D)),Z)=D. 1905 [para_from,78.1.1,68.1.1.2.1] u(c(u(c(x),c(u(y,U)))),c(u(I,u(D,u(c(x),y)))))=x. 1913 [para_from,78.1.1,7.1.1.1.1] u(c(u(I,u(D,u(c(x),y)))),c(u(c(x),c(u(y,U)))))=x. 1964 [para_from,1852.1.1,7.1.1.1.1,demod,1567] u(c(D),c(u(c(c(D)),U)))=c(D). 1967,1966 [para_from,1852.1.1,79.1.1.2.2,demod,205,30,624,flip.1] u(c(c(D)),U)=U. 1976 [back_demod,1964,demod,1967,33,600,flip.1] c(D)=I. 1999,1998 [para_from,1976.1.1,35.1.1.1.2,demod,22] c(c(x))=d(x,D). 2006 [para_from,1976.1.1,447.1.1.1.2,demod,22] u(r(D),U)=U. 2298 [para_from,80.1.1,66.1.1.2.1] u(c(u(c(u(c(x),Z)),u(I,u(D,c(x))))),c(x))=u(c(x),Z). 2337,2336 [para_into,2006.1.1,89.1.1] u(D,u(r(D),I))=U. 2341,2340 [para_from,2006.1.1,14.1.1.1,demod,136,13,136,2337] u(r(D),I)=U. 2357,2356 [back_demod,135,demod,2341] r(U)=U. 2493,2492 [para_into,1998.1.1.1,35.1.1] c(d(x,y))=d(k(c(x),c(y)),D). 2568 [para_into,99.1.1.1.1.1,60.1.1,demod,1999,15,2357] u(r(c(x)),r(c(u(c(u(c(x),U)),d(u(c(x),Z),D)))))=u(r(c(x)),U). 2680 [para_from,105.1.1,99.1.1.1.1.1] u(r(c(u(D,u(c(x),u(y,I))))),r(c(u(c(x),c(u(y,U))))))=r(x). 2968 [para_from,1600.1.1,23.1.1.2,demod,1601] u(k(r(x),c(k(x,k(c(y),U)))),d(y,Z))=d(y,Z). 3170 [para_into,1775.1.1.1.1,78.1.1] u(c(u(I,u(D,u(c(x),y)))),x)=x. 3184 [para_into,1775.1.1,105.1.1] u(D,u(c(u(c(u(x,U)),y)),u(x,I)))=u(x,U). 3343,3342 [para_from,1775.1.1,629.1.1.2,demod,622,1567,51,flip.1] u(c(u(I,u(D,x))),I)=I. 3358 [para_from,1775.1.1,78.1.1.2,demod,33,flip.1] u(I,u(D,u(x,c(u(Z,y)))))=u(x,U). 3369,3368 [para_from,1775.1.1,115.1.1.2.1,demod,1567,51,3343,49,33,1567,624,1567,51,flip.1] u(I,u(D,x))=U. 3401,3400 [back_demod,3358,demod,3369,flip.1] u(x,U)=U. 3411,3410 [back_demod,3170,demod,3369,33] u(Z,x)=x. 3438,3437 [back_demod,2298,demod,3369,3401,33,3411,flip.1] u(c(x),Z)=c(x). 3446,3445 [back_demod,1913,demod,3369,33,3401,33,3438,1999,3411] d(x,D)=x. 3450,3449 [back_demod,1905,demod,3401,33,3438,1999,3446,3369,33] u(x,Z)=x. 3451 [back_demod,1798,demod,3411,3369,1651] k(x,Z)=Z. 3460,3459 [back_demod,50,demod,3369] u(U,x)=U. 3472,3471 [back_demod,3184,demod,3401,33,3411,3401] u(D,u(c(x),u(y,I)))=U. 3479 [back_demod,2680,demod,3472,33,3401,33,3450,1999,3446] u(r(Z),r(x))=r(x). 3489 [back_demod,2568,demod,3401,33,3450,3446,3411,1999,3446,3401] u(r(c(x)),r(x))=U. 3533 [back_demod,504,demod,3411,163,3411,2493,33,3446] u(d(U,x),k(Z,c(x)))=U. 3586,3585 [back_demod,2492,demod,3446] c(d(x,y))=k(c(x),c(y)). 3660,3659 [back_demod,1998,demod,3446] c(c(x))=x. 3763 [para_from,3451.1.1,16.1.1.1,flip.1] k(r(Z),r(x))=r(Z). 3775 [para_from,3659.1.1,35.1.1.1.2] c(k(c(x),y))=d(x,c(y)). 3780,3779 [para_from,3659.1.1,1600.1.1.1.1] c(k(x,U))=d(c(x),Z). 3792,3791 [para_from,3659.1.1,35.1.1.1.1] c(k(x,c(y)))=d(c(x),y). 3906 [para_into,145.1.1.1,3400.1.1,flip.1] u(x,k(U,x))=k(U,x). 4188 [para_into,3479.1.1.2,12.1.1,demod,13] u(r(Z),x)=x. 4203,4202 [para_into,4188.1.1,3449.1.1] r(Z)=Z. 4212 [back_demod,3763,demod,4203,4203] k(Z,r(x))=Z. 4299,4298 [para_into,4212.1.1.2,12.1.1] k(Z,x)=Z. 4307,4306 [back_demod,3533,demod,4299,3450] d(U,x)=U. 4316 [para_from,3489.1.1,5.1.1.1,demod,3460,flip.1] u(r(c(x)),u(r(x),y))=U. 4476 [para_into,184.1.1.2,32.1.1,demod,3780,3450,33] k(x,d(c(r(x)),Z))=Z. 5568,5567 [para_into,3779.1.1.1,10.1.1] c(k(x,k(y,U)))=d(c(k(x,y)),Z). 5571 [back_demod,2968,demod,5568,3792] u(k(r(x),d(d(c(x),y),Z)),d(y,Z))=d(y,Z). 6425,6424 [para_into,3775.1.1.1.1,3659.1.1] c(k(x,y))=d(c(x),c(y)). 6426 [para_into,3775.1.1.1,4476.1.1,demod,1567,3586,3660,1567,flip.1] d(x,k(r(c(x)),U))=U. 6432 [para_into,6426.1.1.2.1.1,3659.1.1] d(c(x),k(r(x),U))=U. 6434 [para_into,6432.1.1.2.1,12.1.1] d(c(r(x)),k(x,U))=U. 6439 [para_into,4316.1.1.2,3906.1.1] u(r(c(x)),k(U,r(x)))=U. 6559 [para_from,6439.1.1,14.1.1.1,demod,2357,13,17,13,2357,flip.1] u(c(x),k(x,U))=U. 6563 [para_into,6559.1.1,3.1.1] u(k(x,U),c(x))=U. 6593 [para_from,6563.1.1,833.1.1.2.1,demod,6425,33,33,3450] c(u(c(x),d(c(x),Z)))=x. 6698,6697 [para_into,6593.1.1.1.1,3659.1.1,demod,3660] c(u(x,d(x,Z)))=c(x). 6704,6703 [para_from,6697.1.1,815.1.1.2.1.1,demod,6698,816,flip.1] u(x,d(x,Z))=x. 7001 [para_into,5571.1.1.1.2.1,6434.1.1,demod,13,4307,6704,flip.1] d(k(x,U),Z)=k(x,U). 7003 [binary,7001.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 1394 clauses generated 586236 clauses kept 3797 clauses forward subsumed 263757 clauses back subsumed 38 Kbytes malloced 4726 ----------- times (seconds) ----------- user CPU time 13.45 (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 00:45:06 2003