----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 21:03:40 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). include("xxviii_b_ghost.txt"). ------- start included file xxviii_b_ghost.txt------- formula_list(usable). all x y z (i(k(r(x),x),I)->k(r(x),n(r(y),k(x,r(z))))=n(k(r(x),r(y)),r(z))). all x y z (r(k(r(x),n(r(y),k(x,r(z)))))=k(n(k(z,r(x)),y),x)). all x y z (r(n(k(r(x),r(y)),r(z)))=n(z,k(y,x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),x),I)|k(r(x),n(r(y),k(x,r(z))))=n(k(r(x),r(y)),r(z)). 0 [] r(k(r(x),n(r(y),k(x,r(z)))))=k(n(k(z,r(x)),y),x). 0 [] r(n(k(r(x),r(y)),r(z)))=n(z,k(y,x)). end_of_list. ------- end included file xxviii_b_ghost.txt------- include("xxviii_b.txt"). ------- start included file xxviii_b.txt------- formula_list(usable). -(all x y z (i(k(r(x),x),I)->k(n(k(z,r(x)),y),x)=n(z,k(y,x)))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r($c3),$c3),I). 0 [] k(n(k($c1,r($c3)),$c2),$c3)!=n($c1,k($c2,$c3)). 0 [] end_of_formula. end_of_list. ------- end included file xxviii_b.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=25): 2 [copy,1,flip.2] -i(k(r(x),x),I)|n(k(r(x),r(y)),r(z))=k(r(x),n(r(y),k(x,r(z)))). ** KEPT (pick-wt=14): 3 [] k(n(k($c1,r($c3)),$c2),$c3)!=n($c1,k($c2,$c3)). ------------> process sos: ** KEPT (pick-wt=20): 4 [] r(k(r(x),n(r(y),k(x,r(z)))))=k(n(k(z,r(x)),y),x). ---> New Demodulator: 5 [new_demod,4] r(k(r(x),n(r(y),k(x,r(z)))))=k(n(k(z,r(x)),y),x). ** KEPT (pick-wt=15): 6 [] r(n(k(r(x),r(y)),r(z)))=n(z,k(y,x)). ---> New Demodulator: 7 [new_demod,6] r(n(k(r(x),r(y)),r(z)))=n(z,k(y,x)). ** KEPT (pick-wt=6): 8 [] i(k(r($c3),$c3),I). ** KEPT (pick-wt=1): 9 [] end_of_formula. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.02 sec ----> 112 [binary,110.1,3.1] $F. Length of proof is 3. Level of proof is 3. ---------------- PROOF ---------------- 1 [] -i(k(r(x),x),I)|k(r(x),n(r(y),k(x,r(z))))=n(k(r(x),r(y)),r(z)). 2 [copy,1,flip.2] -i(k(r(x),x),I)|n(k(r(x),r(y)),r(z))=k(r(x),n(r(y),k(x,r(z)))). 3 [] k(n(k($c1,r($c3)),$c2),$c3)!=n($c1,k($c2,$c3)). 5,4 [] r(k(r(x),n(r(y),k(x,r(z)))))=k(n(k(z,r(x)),y),x). 6 [] r(n(k(r(x),r(y)),r(z)))=n(z,k(y,x)). 8 [] i(k(r($c3),$c3),I). 21 [hyper,8,2] n(k(r($c3),r(x)),r(y))=k(r($c3),n(r(x),k($c3,r(y)))). 110 [para_from,21.1.1,6.1.1.1,demod,5] k(n(k(x,r($c3)),y),$c3)=n(x,k(y,$c3)). 112 [binary,110.1,3.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 8 clauses generated 80 clauses kept 67 clauses forward subsumed 28 clauses back subsumed 0 Kbytes malloced 606 ----------- 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 1 (0 hr, 0 min, 1 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 21:03:41 2003