----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 17:38:27 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)))). all x y z (r(k(x,r(n(y,z))))=k(n(y,z),r(x))). -(all x y z (r(n(k(x,r(y)),k(x,r(z))))=n(k(y,r(x)),k(z,r(x))))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),x),I)|k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z))). 0 [] r(k(x,r(n(y,z))))=k(n(y,z),r(x)). 0 [] r(n(k($c3,r($c2)),k($c3,r($c1))))!=n(k($c2,r($c3)),k($c1,r($c3))). 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=22): 5 [] -i(k(r(x),x),I)|k(x,r(n(y,z)))=n(k(x,r(y)),k(x,r(z))). ** KEPT (pick-wt=20): 6 [] r(n(k($c3,r($c2)),k($c3,r($c1))))!=n(k($c2,r($c3)),k($c1,r($c3))). ------------> process sos: ** KEPT (pick-wt=10): 7 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 8 [new_demod,7] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 9 [] r(c(x))=c(r(x)). ---> New Demodulator: 10 [new_demod,9] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 11 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 12 [new_demod,11] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 13 [] r(r(x))=x. ---> New Demodulator: 14 [new_demod,13] r(r(x))=x. ** KEPT (pick-wt=10): 15 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 16 [new_demod,15] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 17 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 18 [new_demod,17] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 19 [] r(I)=I. ---> New Demodulator: 20 [new_demod,19] r(I)=I. ** KEPT (pick-wt=4): 21 [] r(Z)=Z. ---> New Demodulator: 22 [new_demod,21] r(Z)=Z. ** KEPT (pick-wt=4): 23 [] r(U)=U. ---> New Demodulator: 24 [new_demod,23] r(U)=U. ** KEPT (pick-wt=13): 26 [copy,25,demod,12,18,12,14,14] k(n(x,y),r(z))=k(n(x,y),r(z)). >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. >> back demodulating 6 with 12. >> back demodulating 5 with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 18. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 24. Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] k(n(x,y),r(z))=k(n(x,y),r(z)). Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] n(k($c2,r($c3)),k($c1,r($c3)))!=n(k($c2,r($c3)),k($c1,r($c3))). ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.02 sec ----> 57 [binary,56.1,27.1] $F. Length of proof is 2. Level of proof is 1. ---------------- PROOF ---------------- 6 [] r(n(k($c3,r($c2)),k($c3,r($c1))))!=n(k($c2,r($c3)),k($c1,r($c3))). 12,11 [] r(n(x,y))=n(r(x),r(y)). 14,13 [] r(r(x))=x. 18,17 [] r(k(x,y))=k(r(y),r(x)). 27 [back_demod,6,demod,12,18,14,18,14] n(k($c2,r($c3)),k($c1,r($c3)))!=n(k($c2,r($c3)),k($c1,r($c3))). 56 [para_into,13.1.1,13.1.1] x=x. 57 [binary,56.1,27.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 9 clauses generated 37 clauses kept 45 clauses forward subsumed 16 clauses back subsumed 0 Kbytes malloced 127 ----------- 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 17:38:27 2003