----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 21:00:24 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). 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("xv_a.txt"). ------- start included file xv_a.txt------- formula_list(usable). all x y z v w i(n(w,k(n(y,z),v)),n(w,u(k(n(y,z),n(v,x)),k(y,n(v,c(x)))))). all y v w i(n(k(y,v),w),k(n(y,k(w,r(v))),n(v,k(r(y),w)))). all y v w i(n(k(y,v),w),k(y,n(v,k(r(y),w)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(n(w,k(n(y,z),v)),n(w,u(k(n(y,z),n(v,x)),k(y,n(v,c(x)))))). 0 [] i(n(k(y,v),w),k(n(y,k(w,r(v))),n(v,k(r(y),w)))). 0 [] i(n(k(y,v),w),k(y,n(v,k(r(y),w)))). end_of_list. ------- end included file xv_a.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("xxviii_a_ghost.txt"). ------- start included file xxviii_a_ghost.txt------- formula_list(usable). all x y z i(k(r(x),n(k(x,z),y)),k(r(x),k(x,n(z,k(r(x),y))))). all x y z (i(k(r(x),x),I)->i(k(r(x),k(x,n(z,k(r(x),y)))),k(I,n(z,k(r(x),y))))). -(all x y z i(n(k(r(x),y),z),k(r(x),n(y,k(x,z))))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r(x),n(k(x,z),y)),k(r(x),k(x,n(z,k(r(x),y))))). 0 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(z,k(r(x),y)))),k(I,n(z,k(r(x),y)))). 0 [] -i(n(k(r($c3),$c2),$c1),k(r($c3),n($c2,k($c3,$c1)))). 0 [] end_of_formula. end_of_list. ------- end included file xxviii_a_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=10): 1 [] -i(x,y)|i(k(x,z),k(y,z)). ** KEPT (pick-wt=10): 2 [] -i(x,y)|i(k(z,x),k(z,y)). ** KEPT (pick-wt=10): 3 [] -i(x,y)|i(d(x,z),d(y,z)). ** KEPT (pick-wt=10): 4 [] -i(x,y)|i(d(z,x),d(z,y)). ** KEPT (pick-wt=8): 5 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=26): 6 [] -i(k(r(x),x),I)|i(k(r(x),k(x,n(y,k(r(x),z)))),k(I,n(y,k(r(x),z)))). ** KEPT (pick-wt=15): 7 [] -i(n(k(r($c3),$c2),$c1),k(r($c3),n($c2,k($c3,$c1)))). ------------> process sos: ** 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=24): 17 [] i(n(x,k(n(y,z),u)),n(x,u(k(n(y,z),n(u,v)),k(y,n(u,c(v)))))). ** KEPT (pick-wt=19): 18 [] i(n(k(x,y),z),k(n(x,k(z,r(y))),n(y,k(r(x),z)))). ** KEPT (pick-wt=14): 19 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). ** KEPT (pick-wt=20): 20 [] i(k(r(x),n(k(x,y),z)),k(r(x),k(x,n(y,k(r(x),z))))). ** KEPT (pick-wt=1): 21 [] end_of_formula. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.02 sec ----> 133 [binary,132.1,7.1] $F. Length of proof is 1. Level of proof is 1. ---------------- PROOF ---------------- 7 [] -i(n(k(r($c3),$c2),$c1),k(r($c3),n($c2,k($c3,$c1)))). 11 [] r(r(x))=x. 19 [] i(n(k(x,y),z),k(x,n(y,k(r(x),z)))). 132 [para_into,19.1.2.2.2.1,11.1.1] i(n(k(r(x),y),z),k(r(x),n(y,k(x,z)))). 133 [binary,132.1,7.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 21 clauses generated 154 clauses kept 127 clauses forward subsumed 47 clauses back subsumed 5 Kbytes malloced 223 ----------- 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 Sun Nov 30 21:00:24 2003