----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 19:46:38 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("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("xxi_a_ghost.txt"). ------- start included file xxi_a_ghost.txt------- formula_list(usable). all x (n(x,I)=n(r(x),I)). all x y (n(k(x,n(r(x),y)),I)=n(k(x,y),I)). all x y (n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,I)=n(r(x),I). 0 [] n(k(x,n(r(x),y)),I)=n(k(x,y),I). 0 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). end_of_list. ------- end included file xxi_a_ghost.txt------- include("xxi_b_ghost.txt"). ------- start included file xxi_b_ghost.txt------- formula_list(usable). all x i(k(x,U),k(n(k(x,r(x)),I),U)). all x i(k(n(k(x,r(x)),I),U),k(x,U)). all x (k(x,U)=k(n(k(x,r(x)),I),U)). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(x,U),k(n(k(x,r(x)),I),U)). 0 [] i(k(n(k(x,r(x)),I),U),k(x,U)). 0 [] k(x,U)=k(n(k(x,r(x)),I),U). end_of_list. ------- end included file xxi_b_ghost.txt------- include("xxi.txt"). ------- start included file xxi.txt------- formula_list(usable). -(all x y (k(n(k(x,y),I),U)=k(n(x,r(y)),U))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(n(k($c2,$c1),I),U)!=k(n($c2,r($c1)),U). end_of_list. ------- end included file xxi.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)|i(r(x),r(y)). ** KEPT (pick-wt=14): 3 [copy,2,flip.1] k(n($c2,r($c1)),U)!=k(n(k($c2,$c1),I),U). ------------> process sos: ** KEPT (pick-wt=10): 4 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 5 [new_demod,4] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 6 [] r(c(x))=c(r(x)). ---> New Demodulator: 7 [new_demod,6] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 8 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 9 [new_demod,8] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 10 [] r(r(x))=x. ---> New Demodulator: 11 [new_demod,10] r(r(x))=x. ** KEPT (pick-wt=10): 12 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 13 [new_demod,12] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 14 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 15 [new_demod,14] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 16 [] r(I)=I. ---> New Demodulator: 17 [new_demod,16] r(I)=I. ** KEPT (pick-wt=4): 18 [] r(Z)=Z. ---> New Demodulator: 19 [new_demod,18] r(Z)=Z. ** KEPT (pick-wt=4): 20 [] r(U)=U. ---> New Demodulator: 21 [new_demod,20] r(U)=U. ** KEPT (pick-wt=8): 23 [copy,22,flip.1] n(r(x),I)=n(x,I). ---> New Demodulator: 24 [new_demod,23] n(r(x),I)=n(x,I). ** KEPT (pick-wt=14): 25 [] n(k(x,n(r(x),y)),I)=n(k(x,y),I). ---> New Demodulator: 26 [new_demod,25] n(k(x,n(r(x),y)),I)=n(k(x,y),I). ** KEPT (pick-wt=17): 27 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). ---> New Demodulator: 28 [new_demod,27] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). ** KEPT (pick-wt=12): 29 [] i(k(x,U),k(n(k(x,r(x)),I),U)). ** KEPT (pick-wt=12): 30 [] i(k(n(k(x,r(x)),I),U),k(x,U)). ** KEPT (pick-wt=12): 32 [copy,31,flip.1] k(n(k(x,r(x)),I),U)=k(x,U). ---> New Demodulator: 33 [new_demod,32] k(n(k(x,r(x)),I),U)=k(x,U). >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 33. >> back demodulating 30 with 33. >> back demodulating 29 with 33. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.07 sec ----> 1132 [binary,1131.1,3.1] $F. Length of proof is 7. Level of proof is 5. ---------------- PROOF ---------------- 2 [] k(n(k($c2,$c1),I),U)!=k(n($c2,r($c1)),U). 3 [copy,2,flip.1] k(n($c2,r($c1)),U)!=k(n(k($c2,$c1),I),U). 8 [] r(n(x,y))=n(r(x),r(y)). 10 [] r(r(x))=x. 27 [] n(k(n(x,r(y)),n(r(x),y)),I)=n(k(x,y),I). 31 [] k(x,U)=k(n(k(x,r(x)),I),U). 32 [copy,31,flip.1] k(n(k(x,r(x)),I),U)=k(x,U). 80 [para_into,32.1.1.1.1.2,8.1.1] k(n(k(n(x,y),n(r(x),r(y))),I),U)=k(n(x,y),U). 127,126 [para_into,27.1.1.1.1.2,10.1.1] n(k(n(x,y),n(r(x),r(y))),I)=n(k(x,r(y)),I). 152 [back_demod,80,demod,127] k(n(k(x,r(y)),I),U)=k(n(x,y),U). 1120 [para_into,152.1.1.1.1.2,10.1.1] k(n(k(x,y),I),U)=k(n(x,r(y)),U). 1131 [copy,1120,flip.1] k(n(x,r(y)),U)=k(n(k(x,y),I),U). 1132 [binary,1131.1,3.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 92 clauses generated 1217 clauses kept 717 clauses forward subsumed 810 clauses back subsumed 11 Kbytes malloced 1117 ----------- times (seconds) ----------- user CPU time 0.27 (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 19:46:38 2003