----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sat Nov 29 22:48:40 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(x,y),z)=n(d(x,z),d(y,z)). end_of_list. ------- end included file vi.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)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i($c3,$c2). 0 [] -i(k($c3,$c1),k($c2,$c1)). end_of_list. ------- end included file vii.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=7): 5 [] -i(k($c3,$c1),k($c2,$c1)). ------------> process sos: ** KEPT (pick-wt=3): 6 [] x=x. ** KEPT (pick-wt=11): 8 [copy,7,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 9 [new_demod,8] k(k(x,y),z)=k(x,k(y,z)). ** 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(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 13 [new_demod,12] r(u(x,y))=u(r(x),r(y)). ** 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=13): 17 [copy,16,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 18 [new_demod,17] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=10): 20 [copy,19,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 21 [new_demod,20] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=10): 23 [copy,22,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 24 [new_demod,23] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=10): 25 [] c(n(x,y))=u(c(x),c(y)). ---> New Demodulator: 26 [new_demod,25] c(n(x,y))=u(c(x),c(y)). ** KEPT (pick-wt=10): 27 [] c(u(x,y))=n(c(x),c(y)). ---> New Demodulator: 28 [new_demod,27] c(u(x,y))=n(c(x),c(y)). ** KEPT (pick-wt=5): 29 [] u(x,x)=x. ---> New Demodulator: 30 [new_demod,29] u(x,x)=x. ** KEPT (pick-wt=13): 32 [copy,31,flip.1] n(d(x,y),d(x,z))=d(x,n(y,z)). ---> New Demodulator: 33 [new_demod,32] n(d(x,y),d(x,z))=d(x,n(y,z)). ** KEPT (pick-wt=13): 35 [copy,34,flip.1] n(d(x,y),d(z,y))=d(n(x,z),y). ---> New Demodulator: 36 [new_demod,35] n(d(x,y),d(z,y))=d(n(x,z),y). ** KEPT (pick-wt=3): 37 [] i($c3,$c2). Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] x=x. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 28. >> back demodulating 20 with 28. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 39. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 17. sos_size=3492 ----> UNIT CONFLICT at 2.07 sec ----> 4529 [binary,4528.1,5.1] $F. Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] -i(x,y)|u(x,y)=y. 2 [] i(x,y)|u(x,y)!=y. 5 [] -i(k($c3,$c1),k($c2,$c1)). 6 [] x=x. 16 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 17 [copy,16,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). 37 [] i($c3,$c2). 40 [hyper,37,1] u($c3,$c2)=$c2. 87 [para_from,17.1.1,2.2.1] i(k(x,y),k(z,y))|k(u(x,z),y)!=k(z,y). 2021 [para_into,87.2.1.1,40.1.1] i(k($c3,x),k($c2,x))|k($c2,x)!=k($c2,x). 4528 [hyper,2021,6] i(k($c3,x),k($c2,x)). 4529 [binary,4528.1,5.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 199 clauses generated 10949 clauses kept 4256 clauses forward subsumed 6847 clauses back subsumed 165 Kbytes malloced 4119 ----------- times (seconds) ----------- user CPU time 2.46 (0 hr, 0 min, 2 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 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 22:48:42 2003