----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 15:34:28 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("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("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("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("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("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("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("11booleanLaws.txt"). ------- start included file 11booleanLaws.txt------- formula_list(usable). all x y (c(n(x,y))=u(c(x),c(y))). all x y (c(u(x,y))=n(c(x),c(y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(n(x,y))=u(c(x),c(y)). 0 [] c(u(x,y))=n(c(x),c(y)). end_of_list. ------- end included file 11booleanLaws.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("xix_b_ghost.txt"). ------- start included file xix_b_ghost.txt------- formula_list(usable). -(all x y (k(x,r(y))=Z->n(k(U,x),k(U,y))=Z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] k($c2,r($c1))=Z. 0 [] n(k(U,$c2),k(U,$c1))!=Z. end_of_list. ------- end included file xix_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=9): 4 [] n(k(U,$c2),k(U,$c1))!=Z. ------------> process sos: ** KEPT (pick-wt=10): 6 [copy,5,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 7 [new_demod,6] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=10): 9 [copy,8,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 10 [new_demod,9] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=4): 12 [copy,11,flip.1] c(I)=D. ---> New Demodulator: 13 [new_demod,12] c(I)=D. ** KEPT (pick-wt=5): 15 [copy,14,flip.1] u(I,D)=U. ---> New Demodulator: 16 [new_demod,15] u(I,D)=U. ** KEPT (pick-wt=4): 18 [copy,17,flip.1] c(U)=Z. ---> New Demodulator: 19 [new_demod,18] c(U)=Z. ** KEPT (pick-wt=7): 20 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 22 [copy,21,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 23 [new_demod,22] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=11): 25 [copy,24,demod,7] u(c(u(c(x),y)),n(x,y))=x. ---> New Demodulator: 26 [new_demod,25] u(c(u(c(x),y)),n(x,y))=x. ** KEPT (pick-wt=11): 28 [copy,27,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 29 [new_demod,28] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 30 [] r(r(x))=x. ---> New Demodulator: 31 [new_demod,30] r(r(x))=x. ** KEPT (pick-wt=10): 32 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 33 [new_demod,32] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 34 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 35 [new_demod,34] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=5): 36 [] k(x,I)=x. ---> New Demodulator: 37 [new_demod,36] k(x,I)=x. ** KEPT (pick-wt=13): 38 [] u(k(r(x),c(k(x,y))),c(y))=c(y). ---> New Demodulator: 39 [new_demod,38] u(k(r(x),c(k(x,y))),c(y))=c(y). ** KEPT (pick-wt=5): 40 [] c(c(x))=x. ---> New Demodulator: 41 [new_demod,40] c(c(x))=x. ** KEPT (pick-wt=11): 43 [copy,42,demod,33] u(r(x),r(y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 44 [] r(c(x))=c(r(x)). ---> New Demodulator: 45 [new_demod,44] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 46 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 47 [new_demod,46] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=3): 49 [copy,48,demod,31] x=x. ** KEPT (pick-wt=10): 50 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 51 [new_demod,50] r(d(x,y))=d(r(y),r(x)). Following clause subsumed by 49 during input processing: 0 [demod,35] k(r(y),r(x))=k(r(y),r(x)). ** KEPT (pick-wt=4): 52 [] r(I)=I. ---> New Demodulator: 53 [new_demod,52] r(I)=I. ** KEPT (pick-wt=4): 54 [] r(Z)=Z. ---> New Demodulator: 55 [new_demod,54] r(Z)=Z. ** KEPT (pick-wt=4): 56 [] r(U)=U. ---> New Demodulator: 57 [new_demod,56] r(U)=U. ** KEPT (pick-wt=10): 58 [] c(n(x,y))=u(c(x),c(y)). ---> New Demodulator: 59 [new_demod,58] c(n(x,y))=u(c(x),c(y)). ** KEPT (pick-wt=10): 60 [] c(u(x,y))=n(c(x),c(y)). ---> New Demodulator: 61 [new_demod,60] c(u(x,y))=n(c(x),c(y)). ** KEPT (pick-wt=16): 62 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). ** KEPT (pick-wt=6): 63 [] k($c2,r($c1))=Z. ---> New Demodulator: 64 [new_demod,63] k($c2,r($c1))=Z. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 19. Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 29. >>>> Starting back demodulation with 31. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 35. >>>> Starting back demodulation with 37. >>>> Starting back demodulation with 39. >>>> Starting back demodulation with 41. Following clause subsumed by 49 during input processing: 0 [copy,43,flip.1] u(r(x),r(y))=u(r(x),r(y)). >>>> Starting back demodulation with 45. >>>> Starting back demodulation with 47. Following clause subsumed by 49 during input processing: 0 [copy,49,flip.1] x=x. 49 back subsumes 43. >>>> Starting back demodulation with 51. >>>> Starting back demodulation with 53. >>>> Starting back demodulation with 55. >>>> Starting back demodulation with 57. >>>> Starting back demodulation with 59. >>>> Starting back demodulation with 61. >> back demodulating 25 with 61. >> back demodulating 6 with 61. >> back demodulating 2 with 61. >> back demodulating 1 with 61. ** KEPT (pick-wt=16): 69 [copy,62,flip.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)). >>>> Starting back demodulation with 64. >>>> Starting back demodulation with 66. Following clause subsumed by 62 during input processing: 0 [copy,69,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 10. sos_size=6051 Resetting weight limit to 9. sos_size=6296 ----> UNIT CONFLICT at 18.61 sec ----> 10248 [binary,10247.1,49.1] $F. Length of proof is 58. Level of proof is 17. ---------------- PROOF ---------------- 1 [] u(x,y)!=y|c(u(y,c(x)))=Z. 4 [] n(k(U,$c2),k(U,$c1))!=Z. 5 [] n(x,y)=c(u(c(x),c(y))). 7,6 [copy,5,flip.1] c(u(c(x),c(y)))=n(x,y). 8 [] d(x,y)=c(k(c(x),c(y))). 9 [copy,8,flip.1] c(k(c(x),c(y)))=d(x,y). 11 [] D=c(I). 13,12 [copy,11,flip.1] c(I)=D. 17 [] Z=c(U). 19,18 [copy,17,flip.1] c(U)=Z. 20 [] u(x,y)=u(y,x). 24 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 25 [copy,24,demod,7] u(c(u(c(x),y)),n(x,y))=x. 27 [] k(x,k(y,z))=k(k(x,y),z). 29,28 [copy,27,flip.1] k(k(x,y),z)=k(x,k(y,z)). 31,30 [] r(r(x))=x. 34 [] r(k(x,y))=k(r(y),r(x)). 36 [] k(x,I)=x. 38 [] u(k(r(x),c(k(x,y))),c(y))=c(y). 41,40 [] c(c(x))=x. 45,44 [] r(c(x))=c(r(x)). 48 [] r(r(x))=x. 49 [copy,48,demod,31] x=x. 51,50 [] r(d(x,y))=d(r(y),r(x)). 53,52 [] r(I)=I. 55,54 [] r(Z)=Z. 57,56 [] r(U)=U. 61,60 [] c(u(x,y))=n(c(x),c(y)). 62 [] n(x,k(n(y,k(x,r(z))),z))=n(k(y,z),x). 63 [] k($c2,r($c1))=Z. 65 [back_demod,25,demod,61,41] u(n(x,c(y)),n(x,y))=x. 68 [back_demod,1,demod,61,41] u(x,y)!=y|n(c(y),x)=Z. 69 [copy,62,flip.1] n(k(x,y),z)=n(z,k(n(x,k(z,r(y))),y)). 93,92 [para_into,40.1.1.1,18.1.1] c(Z)=U. 95,94 [para_into,40.1.1.1,12.1.1] c(D)=I. 97,96 [para_into,40.1.1.1,9.1.1] c(d(x,y))=k(c(x),c(y)). 98 [para_from,40.1.1,9.1.1.1.2] c(k(c(x),y))=d(x,c(y)). 148,147 [para_into,34.1.1.1,63.1.1,demod,55,31,flip.1] k($c1,r($c2))=Z. 149 [para_into,34.1.1.1,36.1.1,demod,53,flip.1] k(I,r(x))=r(x). 179 [para_into,38.1.1.1.1,52.1.1] u(k(I,c(k(I,x))),c(x))=c(x). 193 [para_into,38.1.1.1.2.1,36.1.1,demod,13,13] u(k(r(x),c(x)),D)=D. 201 [para_into,38.1.1.2,18.1.1,demod,19] u(k(r(x),c(k(x,U))),Z)=Z. 256,255 [para_into,149.1.1.2,30.1.1,demod,31] k(I,x)=x. 257 [back_demod,179,demod,256,256] u(c(x),c(x))=c(x). 304 [para_into,257.1.1.1,40.1.1,demod,41,41] u(x,x)=x. 338 [para_into,60.1.1.1,304.1.1,flip.1] n(c(x),c(x))=c(x). 355 [para_into,62.1.1.2.1.2.2,54.1.1] n(x,k(n(y,k(x,Z)),Z))=n(k(y,Z),x). 363 [para_into,62.1.1.2.1.2.2,30.1.1] n(x,k(n(y,k(x,z)),r(z)))=n(k(y,r(z)),x). 395 [para_into,338.1.1.1,40.1.1,demod,41,41] n(x,x)=x. 417 [para_into,65.1.1.1.2,18.1.1] u(n(x,Z),n(x,U))=x. 423 [para_into,65.1.1.2,395.1.1] u(n(x,c(x)),x)=x. 482 [hyper,68,304] n(c(x),x)=Z. 548 [para_from,69.1.1,4.1.1,demod,29,148] n(k(U,$c1),k(n(U,k(U,Z)),$c2))!=Z. 557,556 [para_into,482.1.1.1,40.1.1] n(x,c(x))=Z. 562,561 [back_demod,423,demod,557] u(Z,x)=x. 564 [para_from,482.1.1,62.1.1.2.1,flip.1] n(k(c(k(x,r(y))),y),x)=n(x,k(Z,y)). 568 [hyper,561,68] n(c(x),Z)=Z. 571,570 [para_into,561.1.1,20.1.1] u(x,Z)=x. 575 [back_demod,201,demod,571] k(r(x),c(k(x,U)))=Z. 577 [para_from,561.1.1,60.1.1.1,demod,93,flip.1] n(U,c(x))=c(x). 646,645 [para_into,98.1.1.1.1,40.1.1] c(k(x,y))=d(c(x),c(y)). 653 [back_demod,575,demod,646,19] k(r(x),d(c(x),Z))=Z. 655 [back_demod,564,demod,646] n(k(d(c(x),c(r(y))),y),x)=n(x,k(Z,y)). 705,704 [para_into,568.1.1.1,40.1.1] n(x,Z)=Z. 709,708 [back_demod,417,demod,705,562] n(x,U)=x. 827,826 [para_into,577.1.1.2,40.1.1,demod,41] n(U,x)=x. 831 [back_demod,548,demod,827,29] n(k(U,$c1),k(U,k(Z,$c2)))!=Z. 7567 [para_into,193.1.1.1.1,56.1.1,demod,19] u(k(U,Z),D)=D. 7621 [hyper,7567,68,demod,95] n(I,k(U,Z))=Z. 8195 [para_into,653.1.1.1,54.1.1,demod,93] k(Z,d(U,Z))=Z. 8200,8199 [para_from,653.1.1,34.1.1.1,demod,55,51,55,45,31,flip.1] k(d(Z,c(r(x))),x)=Z. 8205 [para_from,8195.1.1,34.1.1.1,demod,55,51,55,57,55,flip.1] k(d(Z,U),Z)=Z. 8379,8378 [para_into,355.1.1.2.1,7621.1.1,demod,827,256,709] k(Z,Z)=Z. 8619 [para_into,363.1.1.2.1.2,8205.1.1,demod,705,55,8379,705,55,flip.1] n(k(x,Z),d(Z,U))=Z. 10075 [para_into,645.1.1.1,8195.1.1,demod,93,93,97,19,93,flip.1] d(U,k(Z,U))=U. 10111,10110 [para_into,655.1.1.1.1.1,18.1.1,demod,8200,709,827,flip.1] k(Z,x)=Z. 10114 [back_demod,10075,demod,10111] d(U,Z)=U. 10177 [back_demod,831,demod,10111] n(k(U,$c1),k(U,Z))!=Z. 10244,10243 [para_from,10114.1.1,50.1.1.1,demod,57,55,57,flip.1] d(Z,U)=U. 10246,10245 [back_demod,8619,demod,10244,709] k(x,Z)=Z. 10247 [back_demod,10177,demod,10246,705] Z!=Z. 10248 [binary,10247.1,49.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 1378 clauses generated 397978 clauses kept 9476 clauses forward subsumed 103191 clauses back subsumed 1447 Kbytes malloced 5300 ----------- times (seconds) ----------- user CPU time 18.81 (0 hr, 0 min, 18 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 18 (0 hr, 0 min, 18 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 15:34:46 2003