----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 17:37:21 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("i.txt"). ------- start included file i.txt------- formula_list(usable). all x y (i(x,y)->i(r(x),r(y))). all x y (r(u(x,y))=u(r(x),r(y))). all x (r(c(x))=c(r(x))). all x y (r(n(x,y))=n(r(x),r(y))). all x (r(r(x))=x). all x y (r(d(x,y))=d(r(y),r(x))). all x y (r(k(x,y))=k(r(y),r(x))). r(I)=I. r(Z)=Z. r(U)=U. end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|i(r(x),r(y)). 0 [] r(u(x,y))=u(r(x),r(y)). 0 [] r(c(x))=c(r(x)). 0 [] r(n(x,y))=n(r(x),r(y)). 0 [] r(r(x))=x. 0 [] r(d(x,y))=d(r(y),r(x)). 0 [] r(k(x,y))=k(r(y),r(x)). 0 [] r(I)=I. 0 [] r(Z)=Z. 0 [] r(U)=U. end_of_list. ------- end included file i.txt------- include("xxvii_a.txt"). ------- start included file xxvii_a.txt------- formula_list(usable). all x y z (i(k(r(x),x),I)->i(n(k(x,y),k(x,z)),k(x,n(y,z)))). all x y z (i(k(r(x),x),I)->k(x,n(y,z))=n(k(x,y),k(x,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))). 0 [] -i(k(r(x),x),I)|k(x,n(y,z))=n(k(x,y),k(x,z)). end_of_list. ------- end included file xxvii_a.txt------- include("xxvii_b_ghost.txt"). ------- start included file xxvii_b_ghost.txt------- formula_list(usable). -(all x y z (i(k(r(x),x),I)->k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r($c3),$c3),I). 0 [] k($c3,r(n($c2,$c1)))!=n(k($c3,r($c2)),k($c3,r($c1))). end_of_list. ------- end included file xxvii_b_ghost.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=19): 2 [] -i(k(r(x),x),I)|i(n(k(x,y),k(x,z)),k(x,n(y,z))). ** KEPT (pick-wt=19): 4 [copy,3,flip.2] -i(k(r(x),x),I)|n(k(x,y),k(x,z))=k(x,n(y,z)). ** KEPT (pick-wt=16): 5 [] k($c3,r(n($c2,$c1)))!=n(k($c3,r($c2)),k($c3,r($c1))). ------------> process sos: ** KEPT (pick-wt=10): 6 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 7 [new_demod,6] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 8 [] r(c(x))=c(r(x)). ---> New Demodulator: 9 [new_demod,8] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 10 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 11 [new_demod,10] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 12 [] r(r(x))=x. ---> New Demodulator: 13 [new_demod,12] r(r(x))=x. ** KEPT (pick-wt=10): 14 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 15 [new_demod,14] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 16 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 17 [new_demod,16] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 18 [] r(I)=I. ---> New Demodulator: 19 [new_demod,18] r(I)=I. ** KEPT (pick-wt=4): 20 [] r(Z)=Z. ---> New Demodulator: 21 [new_demod,20] r(Z)=Z. ** KEPT (pick-wt=4): 22 [] r(U)=U. ---> New Demodulator: 23 [new_demod,22] r(U)=U. ** KEPT (pick-wt=6): 24 [] i(k(r($c3),$c3),I). >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >> back demodulating 5 with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 21. >>>> Starting back demodulation with 23. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.01 sec ----> 66 [binary,64.1,25.1] $F. Length of proof is 3. Level of proof is 2. ---------------- PROOF ---------------- 3 [] -i(k(r(x),x),I)|k(x,n(y,z))=n(k(x,y),k(x,z)). 4 [copy,3,flip.2] -i(k(r(x),x),I)|n(k(x,y),k(x,z))=k(x,n(y,z)). 5 [] k($c3,r(n($c2,$c1)))!=n(k($c3,r($c2)),k($c3,r($c1))). 11,10 [] r(n(x,y))=n(r(x),r(y)). 24 [] i(k(r($c3),$c3),I). 25 [back_demod,5,demod,11,flip.1] n(k($c3,r($c2)),k($c3,r($c1)))!=k($c3,n(r($c2),r($c1))). 64 [hyper,24,4] n(k($c3,x),k($c3,y))=k($c3,n(x,y)). 66 [binary,64.1,25.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 12 clauses generated 52 clauses kept 54 clauses forward subsumed 22 clauses back subsumed 8 Kbytes malloced 159 ----------- times (seconds) ----------- user CPU time 0.21 (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 17:37:21 2003