----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sat Nov 29 22:43:32 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). formula_list(usable). all x (x=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] x=x. end_of_list. 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("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("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("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("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("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("vi.txt"). ------- start included file vi.txt------- formula_list(usable). all x y z (d(x,n(y,z))=n(d(x,y),d(x,z))). -(all x y z (d(n(x,y),z)=n(d(x,z),d(y,z)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] d(x,n(y,z))=n(d(x,y),d(x,z)). 0 [] d(n($c3,$c2),$c1)!=n(d($c3,$c1),d($c2,$c1)). end_of_list. ------- end included file vi.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=15): 3 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z. ** KEPT (pick-wt=13): 4 [] u(x,y)!=y|u(c(y),c(x))=c(x). ** KEPT (pick-wt=13): 6 [copy,5,flip.1] n(d($c3,$c1),d($c2,$c1))!=d(n($c3,$c2),$c1). ------------> process sos: ** KEPT (pick-wt=3): 7 [] x=x. ** KEPT (pick-wt=11): 9 [copy,8,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 10 [new_demod,9] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 11 [] r(r(x))=x. ---> New Demodulator: 12 [new_demod,11] r(r(x))=x. ** KEPT (pick-wt=10): 13 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 14 [new_demod,13] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 15 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 16 [new_demod,15] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=13): 18 [copy,17,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 19 [new_demod,18] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=10): 21 [copy,20,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 22 [new_demod,21] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=10): 24 [copy,23,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 25 [new_demod,24] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=10): 26 [] c(n(x,y))=u(c(x),c(y)). ---> New Demodulator: 27 [new_demod,26] c(n(x,y))=u(c(x),c(y)). ** KEPT (pick-wt=10): 28 [] c(u(x,y))=n(c(x),c(y)). ---> New Demodulator: 29 [new_demod,28] c(u(x,y))=n(c(x),c(y)). ** KEPT (pick-wt=5): 30 [] u(x,x)=x. ---> New Demodulator: 31 [new_demod,30] u(x,x)=x. ** KEPT (pick-wt=13): 33 [copy,32,flip.1] n(d(x,y),d(x,z))=d(x,n(y,z)). ---> New Demodulator: 34 [new_demod,33] n(d(x,y),d(x,z))=d(x,n(y,z)). Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] x=x. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 27. >>>> Starting back demodulation with 29. >> back demodulating 21 with 29. >>>> Starting back demodulation with 31. >>>> Starting back demodulation with 34. >>>> Starting back demodulation with 36. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.02 sec ----> 80 [binary,78.1,6.1] $F. Length of proof is 6. Level of proof is 3. ---------------- PROOF ---------------- 5 [] d(n($c3,$c2),$c1)!=n(d($c3,$c1),d($c2,$c1)). 6 [copy,5,flip.1] n(d($c3,$c1),d($c2,$c1))!=d(n($c3,$c2),$c1). 17 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 18 [copy,17,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). 23 [] d(x,y)=c(k(c(x),c(y))). 25,24 [copy,23,flip.1] c(k(c(x),c(y)))=d(x,y). 26 [] c(n(x,y))=u(c(x),c(y)). 28 [] c(u(x,y))=n(c(x),c(y)). 47 [para_from,26.1.1,24.1.1.1.1] c(k(u(c(x),c(y)),c(z)))=d(n(x,y),z). 72,71 [para_from,18.1.1,28.1.1.1] c(k(u(x,y),z))=n(c(k(x,z)),c(k(y,z))). 78 [back_demod,47,demod,72,25,25] n(d(x,y),d(z,y))=d(n(x,z),y). 80 [binary,78.1,6.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 11 clauses generated 76 clauses kept 49 clauses forward subsumed 45 clauses back subsumed 0 Kbytes malloced 159 ----------- times (seconds) ----------- user CPU time 0.22 (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 Sat Nov 29 22:43:32 2003