----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 18:33:08 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("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("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("xxix_ghost.txt"). ------- start included file xxix_ghost.txt------- formula_list(usable). all x i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). all x i(k(r(x),n(x,d(c(x),I))),I). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). 0 [] i(k(r(x),n(x,d(c(x),I))),I). end_of_list. ------- end included file xxix_ghost.txt------- include("xxix_b_ghost.txt"). ------- start included file xxix_b_ghost.txt------- formula_list(usable). all x y i(k(r(n(x,d(c(x),I))),y),k(r(x),y)). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r(n(x,d(c(x),I))),y),k(r(x),y)). end_of_list. ------- end included file xxix_b_ghost.txt------- include("xxix.txt"). ------- start included file xxix.txt------- formula_list(usable). -(all x i(k(r(n(x,d(c(x),I))),n(x,d(c(x),I))),I)). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(n($c1,d(c($c1),I))),n($c1,d(c($c1),I))),I). end_of_list. ------- end included file xxix.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=16): 5 [] -i(k(r(n($c1,d(c($c1),I))),n($c1,d(c($c1),I))),I). ------------> process sos: ** KEPT (pick-wt=5): 6 [] u(x,x)=x. ---> New Demodulator: 7 [new_demod,6] u(x,x)=x. ** KEPT (pick-wt=13): 8 [] i(k(x,c(I)),c(n(x,c(k(x,c(I)))))). ** KEPT (pick-wt=11): 9 [] i(k(r(x),n(x,d(c(x),I))),I). ** KEPT (pick-wt=14): 10 [] i(k(r(n(x,d(c(x),I))),y),k(r(x),y)). >>>> Starting back demodulation with 7. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.02 sec ----> 37 [binary,36.1,5.1] $F. Length of proof is 4. Level of proof is 3. ---------------- PROOF ---------------- 1 [] -i(x,y)|u(x,y)=y. 2 [] i(x,y)|u(x,y)!=y. 3 [] u(x,y)!=y|u(y,z)!=z|u(x,z)=z. 5 [] -i(k(r(n($c1,d(c($c1),I))),n($c1,d(c($c1),I))),I). 9 [] i(k(r(x),n(x,d(c(x),I))),I). 10 [] i(k(r(n(x,d(c(x),I))),y),k(r(x),y)). 14 [hyper,9,1] u(k(r(x),n(x,d(c(x),I))),I)=I. 18 [hyper,10,1] u(k(r(n(x,d(c(x),I))),y),k(r(x),y))=k(r(x),y). 28 [hyper,18,3,14] u(k(r(n(x,d(c(x),I))),n(x,d(c(x),I))),I)=I. 36 [hyper,28,2] i(k(r(n(x,d(c(x),I))),n(x,d(c(x),I))),I). 37 [binary,36.1,5.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 9 clauses generated 56 clauses kept 26 clauses forward subsumed 39 clauses back subsumed 1 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 Sun Nov 30 18:33:08 2003