----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 00:17:13 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_seconds,4). 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("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("17To19booleanLaws.txt"). ------- start included file 17To19booleanLaws.txt------- formula_list(usable). all x (u(x,x)=x). all x y z (u(x,y)=y&u(y,z)=z->u(x,z)=z). all x y (u(x,y)=y->u(c(y),c(x))=c(x)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,x)=x. 0 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z. 0 [] u(x,y)!=y|u(c(y),c(x))=c(x). end_of_list. ------- end included file 17To19booleanLaws.txt------- include("vii.txt"). ------- start included file vii.txt------- formula_list(usable). all x y z (i(x,y)->i(k(x,z),k(y,z))). all x y z (i(x,y)->i(k(z,x),k(z,y))). all x y z (i(x,y)->i(d(x,z),d(y,z))). all x y z (i(x,y)->i(d(z,x),d(z,y))). all x y (i(x,y)->i(r(x),r(y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|i(k(x,z),k(y,z)). 0 [] -i(x,y)|i(k(z,x),k(z,y)). 0 [] -i(x,y)|i(d(x,z),d(y,z)). 0 [] -i(x,y)|i(d(z,x),d(z,y)). 0 [] -i(x,y)|i(r(x),r(y)). end_of_list. ------- end included file vii.txt------- include("xxvi.txt"). ------- start included file xxvi.txt------- formula_list(usable). -(all x y (i(k(r(x),x),I)&i(k(r(y),y),I)->i(k(r(k(x,y)),k(x,y)),I))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r($c2),$c2),I). 0 [] i(k(r($c1),$c1),I). 0 [] -i(k(r(k($c2,$c1)),k($c2,$c1)),I). 0 [] end_of_formula. end_of_list. ------- end included file xxvi.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. 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=15): 3 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z. ** KEPT (pick-wt=13): 4 [] u(x,y)!=y|u(c(y),c(x))=c(x). ** KEPT (pick-wt=10): 5 [] -i(x,y)|i(k(x,z),k(y,z)). ** KEPT (pick-wt=10): 6 [] -i(x,y)|i(k(z,x),k(z,y)). ** KEPT (pick-wt=10): 7 [] -i(x,y)|i(d(x,z),d(y,z)). ** KEPT (pick-wt=10): 8 [] -i(x,y)|i(d(z,x),d(z,y)). ** KEPT (pick-wt=8): 9 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=10): 10 [] -i(k(r(k($c2,$c1)),k($c2,$c1)),I). ------------> process sos: ** KEPT (pick-wt=11): 12 [copy,11,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 13 [new_demod,12] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 14 [] r(r(x))=x. ---> New Demodulator: 15 [new_demod,14] r(r(x))=x. ** KEPT (pick-wt=10): 16 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 17 [new_demod,16] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 18 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 19 [new_demod,18] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=5): 20 [] k(x,I)=x. ---> New Demodulator: 21 [new_demod,20] k(x,I)=x. ** KEPT (pick-wt=13): 22 [] u(k(r(x),c(k(x,y))),c(y))=c(y). ---> New Demodulator: 23 [new_demod,22] u(k(r(x),c(k(x,y))),c(y))=c(y). ** KEPT (pick-wt=5): 24 [] u(x,x)=x. ---> New Demodulator: 25 [new_demod,24] u(x,x)=x. ** KEPT (pick-wt=6): 26 [] i(k(r($c2),$c2),I). ** KEPT (pick-wt=6): 27 [] i(k(r($c1),$c1),I). ** KEPT (pick-wt=1): 28 [] end_of_formula. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >> back demodulating 10 with 19. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. >>>> Starting back demodulation with 25. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 15. sos_size=3134 ----> UNIT CONFLICT at 3.71 sec ----> 4900 [binary,4899.1,29.1] $F. Length of proof is 13. Level of proof is 5. ---------------- PROOF ---------------- 1 [] -i(x,y)|u(x,y)=y. 2 [] i(x,y)|u(x,y)!=y. 3 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z. 5 [] -i(x,y)|i(k(x,z),k(y,z)). 6 [] -i(x,y)|i(k(z,x),k(z,y)). 10 [] -i(k(r(k($c2,$c1)),k($c2,$c1)),I). 11 [] k(x,k(y,z))=k(k(x,y),z). 13,12 [copy,11,flip.1] k(k(x,y),z)=k(x,k(y,z)). 15,14 [] r(r(x))=x. 16 [] r(u(x,y))=u(r(x),r(y)). 19,18 [] r(k(x,y))=k(r(y),r(x)). 21,20 [] k(x,I)=x. 26 [] i(k(r($c2),$c2),I). 27 [] i(k(r($c1),$c1),I). 29 [back_demod,10,demod,19,13] -i(k(r($c1),k(r($c2),k($c2,$c1))),I). 36 [para_into,14.1.1,14.1.1] x=x. 44 [para_into,16.1.1.1,3.3.1,flip.1] u(r(x),r(y))=r(y)|u(x,z)!=z|u(z,y)!=y. 52 [hyper,26,6,demod,21] i(k(x,k(r($c2),$c2)),x). 61 [hyper,27,1] u(k(r($c1),$c1),I)=I. 63 [para_into,18.1.1.1,20.1.1,flip.1] k(r(I),r(x))=r(x). 109 [hyper,52,5,demod,13,13] i(k(x,k(r($c2),k($c2,y))),k(x,y)). 131 [para_into,63.1.1.2,14.1.1,demod,15] k(r(I),x)=x. 134,133 [para_into,131.1.1,20.1.1] r(I)=I. 245 [para_into,44.2.1,1.2.1] u(r(x),r(y))=r(y)|z!=z|u(z,y)!=y| -i(x,z). 4794 [hyper,245,36,61,109,demod,19,19,19,15,13,15,13,13,134,134] u(k(r($c1),k(r($c2),k($c2,$c1))),I)=I. 4899 [hyper,4794,2] i(k(r($c1),k(r($c2),k($c2,$c1))),I). 4900 [binary,4899.1,29.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 487 clauses generated 64615 clauses kept 4151 clauses forward subsumed 33885 clauses back subsumed 88 Kbytes malloced 4151 ----------- times (seconds) ----------- user CPU time 3.92 (0 hr, 0 min, 3 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 4 (0 hr, 0 min, 4 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 00:17:17 2003