----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 17:43:37 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_distinct_vars,3). assign(max_literals,1). assign(max_mem,64000). assign(max_weight,19). formula_list(usable). all x (x=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] x=x. end_of_list. 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("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("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("ii.txt"). ------- start included file ii.txt------- formula_list(usable). k(U,U)=U. r(U)=U&r(Z)=Z&r(I)=I&r(D)=D. end_of_list. -------> usable clausifies to: list(usable). 0 [] k(U,U)=U. 0 [] r(U)=U. 0 [] r(Z)=Z. 0 [] r(I)=I. 0 [] r(D)=D. end_of_list. ------- end included file ii.txt------- include("xii.txt"). ------- start included file xii.txt------- formula_list(usable). all x y z (i(k(x,y),c(z))<->i(k(r(x),z),c(y))). all x y z (i(k(x,y),c(z))<->i(k(z,r(y)),c(x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)). 0 [] i(k(x,y),c(z))| -i(k(r(x),z),c(y)). 0 [] -i(k(x,y),c(z))|i(k(z,r(y)),c(x)). 0 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)). end_of_list. ------- end included file xii.txt------- include("xxix_ghost.txt"). ------- start included file xxix_ghost.txt------- formula_list(usable). all x i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). -(all x i(k(r(x),n(x,d(c(x),I))),I)). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). 0 [] -i(k(r($c1),n($c1,d(c($c1),I))),I). end_of_list. ------- end included file xxix_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=13): 3 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)). ** KEPT (pick-wt=13): 4 [] i(k(x,y),c(z))| -i(k(r(x),z),c(y)). ** KEPT (pick-wt=13): 5 [] -i(k(x,y),c(z))|i(k(z,r(y)),c(x)). ** KEPT (pick-wt=13): 6 [] i(k(x,y),c(z))| -i(k(z,r(y)),c(x)). ** KEPT (pick-wt=11): 7 [] -i(k(r($c1),n($c1,d(c($c1),I))),I). ------------> process sos: ** KEPT (pick-wt=3): 8 [] x=x. ** KEPT (pick-wt=7): 9 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 11 [copy,10,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 12 [new_demod,11] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 13 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 14 [new_demod,13] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=10): 16 [copy,15,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 17 [new_demod,16] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=10): 19 [copy,18,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 20 [new_demod,19] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=5): 21 [] k(U,U)=U. ---> New Demodulator: 22 [new_demod,21] k(U,U)=U. ** KEPT (pick-wt=4): 23 [] r(U)=U. ---> New Demodulator: 24 [new_demod,23] r(U)=U. ** KEPT (pick-wt=4): 25 [] r(Z)=Z. ---> New Demodulator: 26 [new_demod,25] r(Z)=Z. ** KEPT (pick-wt=4): 27 [] r(I)=I. ---> New Demodulator: 28 [new_demod,27] r(I)=I. ** KEPT (pick-wt=4): 29 [] r(D)=D. ---> New Demodulator: 30 [new_demod,29] r(D)=D. ** KEPT (pick-wt=13): 31 [] i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] x=x. Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 17. >> back demodulating 13 with 17. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 33. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.08 sec ----> 1022 [binary,1021.1,7.1] $F. Length of proof is 35. Level of proof is 14. ---------------- PROOF ---------------- 3 [] -i(k(x,y),c(z))|i(k(r(x),z),c(y)). 7 [] -i(k(r($c1),n($c1,d(c($c1),I))),I). 9 [] u(x,y)=u(y,x). 10 [] u(x,u(y,z))=u(u(x,y),z). 12,11 [copy,10,flip.1] u(u(x,y),z)=u(x,u(y,z)). 13 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 15 [] n(x,y)=c(u(c(x),c(y))). 17,16 [copy,15,flip.1] c(u(c(x),c(y)))=n(x,y). 18 [] d(x,y)=c(k(c(x),c(y))). 19 [copy,18,flip.1] c(k(c(x),c(y)))=d(x,y). 31 [] i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). 32 [back_demod,13,demod,17] u(c(u(c(x),y)),n(x,y))=x. 34 [para_into,16.1.1.1.1,16.1.1] c(u(n(x,y),c(z)))=n(u(c(x),c(y)),z). 36 [para_into,16.1.1.1.2,16.1.1] c(u(c(x),n(y,z)))=n(x,u(c(y),c(z))). 38 [para_into,16.1.1.1,9.1.1,demod,17] n(x,y)=n(y,x). 52 [para_into,11.1.1.1,9.1.1,demod,12] u(x,u(y,z))=u(y,u(x,z)). 57 [para_into,32.1.1.1.1,9.1.1] u(c(u(x,c(y))),n(y,x))=y. 59 [para_into,32.1.1.1,16.1.1] u(n(x,y),n(x,c(y)))=x. 64,63 [para_into,32.1.1,9.1.1] u(n(x,y),c(u(c(x),y)))=x. 67 [para_into,59.1.1.1,38.1.1] u(n(x,y),n(y,c(x)))=y. 77 [para_from,59.1.1,11.1.1.1,flip.1] u(n(x,y),u(n(x,c(y)),z))=u(x,z). 83 [para_into,67.1.1.2,38.1.1] u(n(x,y),n(c(x),y))=y. 87 [para_from,67.1.1,11.1.1.1,flip.1] u(n(x,y),u(n(y,c(x)),z))=u(y,z). 99 [hyper,31,3] i(k(r(x),n(x,c(k(x,c(I))))),c(c(I))). 112 [para_into,83.1.1,9.1.1] u(n(c(x),y),n(x,y))=y. 150,149 [para_into,52.1.1.2,59.1.1,flip.1] u(n(x,y),u(z,n(x,c(y))))=u(z,x). 166 [para_into,57.1.1.2,38.1.1] u(c(u(x,c(y))),n(x,y))=y. 168 [para_into,57.1.1,9.1.1] u(n(x,y),c(u(y,c(x))))=x. 170 [para_from,57.1.1,36.1.1.1,flip.1] n(u(x,c(y)),u(c(y),c(x)))=c(y). 240 [para_into,166.1.1,9.1.1] u(n(x,y),c(u(x,c(y))))=y. 259 [para_from,168.1.1,34.1.1.1,flip.1] n(u(c(x),c(y)),u(y,c(x)))=c(x). 471,470 [para_into,77.1.1.2,240.1.1,flip.1] u(x,c(u(x,c(c(y)))))=u(n(x,y),c(y)). 477,476 [para_into,77.1.1.2,112.1.1] u(n(c(x),y),c(y))=u(c(x),n(x,c(y))). 639 [para_into,87.1.1.2,240.1.1,demod,471] u(n(x,y),c(x))=u(n(y,x),c(x)). 659 [para_from,639.1.1,87.1.1.2,demod,477,150] u(c(x),x)=u(y,c(y)). 703 [para_from,659.1.1,259.1.1.2] n(u(c(x),c(c(c(x)))),u(y,c(y)))=c(x). 708,707 [para_from,659.1.1,170.1.1.2] n(u(x,c(c(x))),u(y,c(y)))=c(c(x)). 742 [back_demod,703,demod,708] c(c(c(x)))=c(x). 825,824 [para_from,742.1.1,16.1.1.1.1,demod,17,flip.1] n(c(c(x)),y)=n(x,y). 829,828 [para_from,742.1.1,63.1.1.2.1.1,demod,825,64,flip.1] c(c(x))=x. 876 [back_demod,99,demod,829] i(k(r(x),n(x,c(k(x,c(I))))),I). 976,975 [para_from,828.1.1,19.1.1.1.1] c(k(x,c(y)))=d(c(x),y). 1021 [back_demod,876,demod,976] i(k(r(x),n(x,d(c(x),I))),I). 1022 [binary,1021.1,7.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 68 clauses generated 2384 clauses kept 610 clauses forward subsumed 1127 clauses back subsumed 4 Kbytes malloced 766 ----------- times (seconds) ----------- user CPU time 0.29 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 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 17:43:37 2003