----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sat Nov 22 16:12:01 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). include("xtremeOptions.txt"). ------- start included file xtremeOptions.txt------- assign(max_weight,19). assign(max_distinct_vars,3). assign(max_literals,1). assign(max_mem,64000). formula_list(usable). all x (x=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] x=x. end_of_list. ------- end included file xtremeOptions.txt------- 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("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("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("xx.txt"). ------- start included file xx.txt------- formula_list(usable). all x (k(x,U)=U->i(I,k(x,r(x)))). -(all x (k(x,U)=U<->i(I,k(x,r(x))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,U)!=U|i(I,k(x,r(x))). 0 [] k($c1,U)=U|i(I,k($c1,r($c1))). 0 [] k($c1,U)!=U| -i(I,k($c1,r($c1))). end_of_list. ------- end included file xx.txt------- SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2. This ia a non-Horn set with equality. The strategy will be Knuth-Bendix, ordered hyper_res, factoring, and unit deletion, 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: set(unit_deletion). dependent: set(factor). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=11): 3 [] k(x,U)!=U|i(I,k(x,r(x))). ** KEPT (pick-wt=11): 4 [] k($c1,U)!=U| -i(I,k($c1,r($c1))). ------------> process sos: ** KEPT (pick-wt=3): 5 [] x=x. ** KEPT (pick-wt=7): 6 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 8 [copy,7,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 9 [new_demod,8] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 10 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 11 [new_demod,10] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 13 [copy,12,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 14 [new_demod,13] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 15 [] r(r(x))=x. ---> New Demodulator: 16 [new_demod,15] r(r(x))=x. ** KEPT (pick-wt=10): 17 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 18 [new_demod,17] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 19 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 20 [new_demod,19] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=13): 22 [copy,21,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 23 [new_demod,22] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=5): 24 [] k(x,I)=x. ---> New Demodulator: 25 [new_demod,24] k(x,I)=x. ** KEPT (pick-wt=13): 26 [] u(k(r(x),c(k(x,y))),c(y))=c(y). ---> New Demodulator: 27 [new_demod,26] u(k(r(x),c(k(x,y))),c(y))=c(y). ** KEPT (pick-wt=4): 29 [copy,28,flip.1] c(I)=D. ---> New Demodulator: 30 [new_demod,29] c(I)=D. ** KEPT (pick-wt=5): 32 [copy,31,flip.1] u(I,D)=U. ---> New Demodulator: 33 [new_demod,32] u(I,D)=U. ** KEPT (pick-wt=4): 35 [copy,34,flip.1] c(U)=Z. ---> New Demodulator: 36 [new_demod,35] c(U)=Z. ** KEPT (pick-wt=11): 37 [] k($c1,U)=U|i(I,k($c1,r($c1))). Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] x=x. Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 36. ======= end of input processing ======= =========== start of search =========== -----> EMPTY CLAUSE at 0.39 sec ----> 3815 [back_demod,4,demod,3814,unit_del,5,165] $F. Length of proof is 120. Level of proof is 29. ---------------- PROOF ---------------- 1 [] -i(x,y)|u(x,y)=y. 2 [] i(x,y)|u(x,y)!=y. 3 [] k(x,U)!=U|i(I,k(x,r(x))). 4 [] k($c1,U)!=U| -i(I,k($c1,r($c1))). 5 [] x=x. 6 [] u(x,y)=u(y,x). 7 [] u(x,u(y,z))=u(u(x,y),z). 9,8 [copy,7,flip.1] u(u(x,y),z)=u(x,u(y,z)). 11,10 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 12 [] k(x,k(y,z))=k(k(x,y),z). 14,13 [copy,12,flip.1] k(k(x,y),z)=k(x,k(y,z)). 16,15 [] r(r(x))=x. 17 [] r(u(x,y))=u(r(x),r(y)). 19 [] r(k(x,y))=k(r(y),r(x)). 21 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 22 [copy,21,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). 25,24 [] k(x,I)=x. 26 [] u(k(r(x),c(k(x,y))),c(y))=c(y). 28 [] D=c(I). 30,29 [copy,28,flip.1] c(I)=D. 31 [] U=u(I,D). 33,32 [copy,31,flip.1] u(I,D)=U. 34 [] Z=c(U). 36,35 [copy,34,flip.1] c(U)=Z. 37 [] k($c1,U)=U|i(I,k($c1,r($c1))). 39,38 [para_into,32.1.1,6.1.1] u(D,I)=U. 40 [para_into,17.1.1.1,38.1.1] r(U)=u(r(D),r(I)). 43,42 [para_into,8.1.1.1,38.1.1] u(U,x)=u(D,u(I,x)). 46 [para_into,8.1.1.1,6.1.1,demod,9] u(x,u(y,z))=u(y,u(x,z)). 47 [para_into,8.1.1,6.1.1] 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)). 49 [para_into,42.1.1,6.1.1] u(x,U)=u(D,u(I,x)). 50 [copy,49,flip.1] u(D,u(I,x))=u(x,U). 51 [para_into,49.1.1,8.1.1] u(x,u(y,U))=u(D,u(I,u(x,y))). 52 [copy,51,flip.1] u(D,u(I,u(x,y)))=u(x,u(y,U)). 53 [para_from,49.1.1,8.1.1.1,demod,9,9,43] u(D,u(I,u(x,y)))=u(x,u(D,u(I,y))). 54 [copy,53,flip.1] u(x,u(D,u(I,y)))=u(D,u(I,u(x,y))). 57 [para_into,50.1.1.2,6.1.1] u(D,u(x,I))=u(x,U). 58 [para_into,50.1.1,6.1.1,demod,9] u(I,u(x,D))=u(x,U). 59 [copy,57,flip.1] u(x,U)=u(D,u(x,I)). 60 [copy,58,flip.1] u(x,U)=u(I,u(x,D)). 63 [para_into,10.1.1.1.1.1,35.1.1,demod,36] u(c(u(Z,x)),c(u(Z,c(x))))=U. 65 [para_into,10.1.1.1.1.1,29.1.1,demod,30] u(c(u(D,x)),c(u(D,c(x))))=I. 67 [para_into,10.1.1.1.1,49.1.1,demod,36] u(c(u(D,u(I,c(x)))),c(u(c(x),Z)))=x. 69 [para_into,10.1.1.1.1,6.1.1] u(c(u(x,c(y))),c(u(c(y),c(x))))=y. 71 [para_into,10.1.1.2.1.2,35.1.1] u(c(u(c(x),U)),c(u(c(x),Z)))=x. 77 [para_into,10.1.1,6.1.1] u(c(u(c(x),c(y))),c(u(c(x),y)))=x. 81 [para_from,10.1.1,8.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(x),c(y))),z))=u(x,z). 93 [para_from,60.1.1,10.1.1.1.1,demod,36] u(c(u(I,u(c(x),D))),c(u(c(x),Z)))=x. 95 [para_into,19.1.1.1,24.1.1,flip.1] k(r(I),r(x))=r(x). 105 [para_into,95.1.1.2,15.1.1,demod,16] k(r(I),x)=x. 107 [hyper,105,3,demod,16,25] i(I,r(I)). 109,108 [para_into,105.1.1,24.1.1] r(I)=I. 110 [back_demod,107,demod,109] i(I,I). 112,111 [back_demod,105,demod,109] k(I,x)=x. 113 [back_demod,40,demod,109] r(U)=u(r(D),I). 116,115 [hyper,110,1] u(I,I)=I. 120 [para_from,111.1.1,22.1.1.1] u(x,k(y,x))=k(u(I,y),x). 121 [copy,120,flip.1] k(u(I,x),y)=u(y,k(x,y)). 122 [para_from,115.1.1,57.1.1.2,demod,39,flip.1] u(I,U)=U. 131,130 [para_into,26.1.1.1.1,108.1.1,demod,112,112] u(c(x),c(x))=c(x). 138 [para_into,26.1.1.1.2.1,24.1.1,demod,30,30] u(k(r(x),c(x)),D)=D. 140 [para_into,26.1.1.2,35.1.1,demod,36] u(k(r(x),c(k(x,U))),Z)=Z. 152,151 [para_into,130.1.1.1,35.1.1,demod,36,36] u(Z,Z)=Z. 154,153 [para_into,130.1.1.1,29.1.1,demod,30,30] u(D,D)=D. 165 [para_from,37.1.1,3.1.1,unit_del,5,factor_simp] i(I,k($c1,r($c1))). 168 [para_from,151.1.1,8.1.1.1,flip.1] u(Z,u(Z,x))=u(Z,x). 171,170 [para_from,153.1.1,58.1.1.2,demod,33,flip.1] u(D,U)=U. 206 [hyper,165,1] u(I,k($c1,r($c1)))=k($c1,r($c1)). 283 [para_into,138.1.1,6.1.1] u(D,k(r(x),c(x)))=D. 318 [hyper,168,2] i(Z,u(Z,x)). 336 [para_into,318.1.2,48.1.1] i(Z,u(x,u(Z,y))). 451 [para_into,63.1.1.1.1,151.1.1] u(c(Z),c(u(Z,c(Z))))=U. 457 [para_into,63.1.1.1.1,59.1.1,demod,36,152] u(c(u(D,u(Z,I))),c(Z))=U. 473 [para_into,63.1.1.2.1.2,29.1.1] u(c(u(Z,I)),c(u(Z,D)))=U. 562,561 [para_into,65.1.1.1.1,38.1.1,demod,36,30,154] u(Z,c(D))=I. 587,586 [para_into,561.1.1,6.1.1] u(c(D),Z)=I. 588 [para_from,561.1.1,336.1.2.2] i(Z,u(x,I)). 593,592 [para_from,561.1.1,168.1.1.2,demod,562] u(Z,I)=I. 601 [para_from,561.1.1,53.1.1.2.2,demod,116,39,flip.1] u(Z,u(D,u(I,c(D))))=U. 609 [back_demod,473,demod,593,30] u(D,c(u(Z,D)))=U. 612,611 [back_demod,457,demod,593,39,36] u(Z,c(Z))=U. 613 [back_demod,451,demod,612,36] u(c(Z),Z)=U. 619 [para_into,588.1.2,42.1.1,demod,116,39] i(Z,U). 623,622 [hyper,619,1] u(Z,U)=U. 624 [para_into,67.1.1.2.1,6.1.1] u(c(u(D,u(I,c(x)))),c(u(Z,c(x))))=x. 626 [para_into,67.1.1,6.1.1] u(c(u(c(x),Z)),c(u(D,u(I,c(x)))))=x. 635 [para_from,67.1.1,8.1.1.1,flip.1] u(c(u(D,u(I,c(x)))),u(c(u(c(x),Z)),y))=u(x,y). 638,637 [para_into,592.1.1,6.1.1] u(I,Z)=I. 655,654 [para_from,622.1.1,46.1.1.2,flip.1] u(Z,u(x,U))=u(x,U). 659,658 [para_from,622.1.1,8.1.1.1,demod,43,43,flip.1] u(Z,u(D,u(I,x)))=u(D,u(I,x)). 661,660 [back_demod,601,demod,659] u(D,u(I,c(D)))=U. 703,702 [para_from,586.1.1,67.1.1.2.1,demod,661,36,30] u(Z,D)=D. 711 [back_demod,609,demod,703] u(D,c(D))=U. 717,716 [para_into,702.1.1,6.1.1] u(D,Z)=D. 719 [para_from,702.1.1,48.1.1.2,flip.1] u(D,u(x,Z))=u(x,D). 734 [para_from,71.1.1,10.1.1.2.1] u(c(u(c(u(c(x),U)),u(c(x),Z))),c(x))=u(c(x),U). 757 [para_from,611.1.1,69.1.1.1.1,demod,36,131] u(Z,c(c(Z)))=Z. 874 [para_into,77.1.1.2.1,613.1.1,demod,131,36] u(c(c(Z)),Z)=Z. 899 [para_from,711.1.1,69.1.1.1.1,demod,36,131] u(Z,c(c(D)))=D. 978,977 [para_into,81.1.1.2,130.1.1,demod,11,flip.1] u(x,c(u(c(x),c(y))))=x. 981 [para_into,81.1.1.2,10.1.1,demod,978] u(c(u(c(x),y)),x)=x. 999,998 [para_from,757.1.1,52.1.1.2.2,demod,638,39,655,flip.1] u(c(c(Z)),U)=U. 1002,1001 [para_from,874.1.1,71.1.1.2.1,demod,999,36,612,flip.1] c(Z)=U. 1041 [para_from,899.1.1,69.1.1.1.1,demod,1002] u(c(D),c(u(c(c(D)),U)))=c(D). 1052,1051 [para_from,899.1.1,52.1.1.2.2,demod,33,171,655,flip.1] u(c(c(D)),U)=U. 1053 [back_demod,1041,demod,1052,36,587,flip.1] c(D)=I. 1067 [para_from,1053.1.1,283.1.1.2.2,demod,25] u(D,r(D))=D. 1071,1070 [para_from,1053.1.1,138.1.1.1.2,demod,25] u(r(D),D)=D. 1100,1099 [para_from,1067.1.1,17.1.1.1,demod,16,1071] r(D)=D. 1120 [back_demod,113,demod,1100,39] r(U)=U. 1346 [para_into,120.1.1,42.1.1] u(D,u(I,k(x,U)))=k(u(I,x),U). 1400 [para_into,121.1.1.1,122.1.1,flip.1] u(x,k(U,x))=k(U,x). 1628 [para_into,140.1.1.1.1,1120.1.1] u(k(U,c(k(U,U))),Z)=Z. 1952 [hyper,981,2] i(c(u(c(x),y)),x). 1979 [para_into,981.1.1.1.1,54.1.1] u(c(u(D,u(I,u(c(x),y)))),x)=x. 2034,2033 [para_from,981.1.1,719.1.1.2,demod,717,1002,43,flip.1] u(c(u(D,u(I,x))),D)=D. 2052,2051 [para_from,981.1.1,93.1.1.2.1,demod,1002,43,2034,33,36,1002,623,1002,43,flip.1] u(D,u(I,x))=U. 2063,2062 [para_from,981.1.1,51.1.1.2,demod,36,2052] u(x,U)=U. 2086,2085 [back_demod,1979,demod,2052,36] u(Z,x)=x. 2089 [back_demod,1346,demod,2052,flip.1] k(u(I,x),U)=U. 2108,2107 [back_demod,635,demod,2052,36,2086] u(c(u(c(x),Z)),y)=u(x,y). 2115,2114 [back_demod,626,demod,2052,36,2108] u(x,Z)=x. 2117,2116 [back_demod,624,demod,2052,36,2086,2086] c(c(x))=x. 2156 [back_demod,734,demod,2063,36,2115,2086,2117,2063] u(x,c(x))=U. 2183 [back_demod,140,demod,2115] k(r(x),c(k(x,U)))=Z. 2189 [back_demod,1628,demod,2115] k(U,c(k(U,U)))=Z. 2290 [para_from,2156.1.1,47.1.1.2,demod,2063,flip.1] u(x,u(c(x),y))=U. 2351 [para_into,1952.1.1.1,981.1.1] i(c(x),u(c(x),y)). 2389,2388 [para_into,2089.1.1.1,2156.1.1] k(U,U)=U. 2397,2396 [back_demod,2189,demod,2389,36] k(U,Z)=Z. 2433,2432 [para_from,2396.1.1,22.1.1.2,demod,2115,2063,2397] k(x,Z)=Z. 2502 [para_into,2351.1.1,2116.1.1,demod,2117] i(x,u(x,y)). 2508 [para_into,2502.1.2,120.1.1] i(x,k(u(I,y),x)). 2582 [para_into,2508.1.2.1,206.1.1,demod,14] i(x,k($c1,k(r($c1),x))). 3366 [para_from,1400.1.1,2290.1.1.2] u(x,k(U,c(x)))=U. 3763 [para_from,2183.1.1,2582.1.2.2,demod,2433] i(c(k($c1,U)),Z). 3776 [hyper,3763,1,demod,2115] c(k($c1,U))=Z. 3814,3813 [para_from,3776.1.1,3366.1.1.2.2,demod,2433,2115] k($c1,U)=U. 3815 [back_demod,4,demod,3814,unit_del,5,165] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 402 clauses generated 14811 clauses kept 2388 clauses forward subsumed 12585 clauses back subsumed 133 Kbytes malloced 2075 ----------- times (seconds) ----------- user CPU time 0.60 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 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 Sat Nov 22 16:12:02 2003