----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Mon Dec 29 22:40:31 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). assign(max_distinct_vars,4). assign(max_literals,1). assign(max_mem,30000). assign(max_weight,26). 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("xxii.txt"). ------- start included file xxii.txt------- formula_list(usable). all x (i(x,I)->k(x,x)=x). all x (i(x,I)->r(x)=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,I)|k(x,x)=x. 0 [] -i(x,I)|r(x)=x. end_of_list. ------- end included file xxii.txt------- include("xxiii_a.txt"). ------- start included file xxiii_a.txt------- formula_list(usable). all x y z v (i(x,I)&i(z,I)->k(n(x,z),n(y,v))=n(k(x,y),k(z,v))). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,I)| -i(z,I)|k(n(x,z),n(y,v))=n(k(x,y),k(z,v)). end_of_list. ------- end included file xxiii_a.txt------- include("xxiii_b.txt"). ------- start included file xxiii_b.txt------- formula_list(usable). -(all x y z v (i(x,I)&i(z,I)->k(n(y,v),n(x,z))=n(k(y,x),k(v,z)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i($c4,I). 0 [] i($c2,I). 0 [] k(n($c3,$c1),n($c4,$c2))!=n(k($c3,$c4),k($c1,$c2)). end_of_list. ------- end included file xxiii_b.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)|i(r(x),r(y)). ** KEPT (pick-wt=8): 2 [] -i(x,I)|k(x,x)=x. ** KEPT (pick-wt=7): 3 [] -i(x,I)|r(x)=x. ** KEPT (pick-wt=21): 5 [copy,4,flip.3] -i(x,I)| -i(y,I)|n(k(x,z),k(y,u))=k(n(x,y),n(z,u)). ** KEPT (pick-wt=15): 7 [copy,6,flip.1] n(k($c3,$c4),k($c1,$c2))!=k(n($c3,$c1),n($c4,$c2)). ------------> process sos: ** KEPT (pick-wt=10): 8 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 9 [new_demod,8] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 10 [] r(c(x))=c(r(x)). ---> New Demodulator: 11 [new_demod,10] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 12 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 13 [new_demod,12] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 14 [] r(r(x))=x. ---> New Demodulator: 15 [new_demod,14] r(r(x))=x. ** KEPT (pick-wt=10): 16 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 17 [new_demod,16] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 18 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 19 [new_demod,18] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 20 [] r(I)=I. ---> New Demodulator: 21 [new_demod,20] r(I)=I. ** KEPT (pick-wt=4): 22 [] r(Z)=Z. ---> New Demodulator: 23 [new_demod,22] r(Z)=Z. ** KEPT (pick-wt=4): 24 [] r(U)=U. ---> New Demodulator: 25 [new_demod,24] r(U)=U. ** KEPT (pick-wt=3): 26 [] i($c4,I). ** KEPT (pick-wt=3): 27 [] i($c2,I). >>>> Starting back demodulation with 9. >>>> Starting back demodulation 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. >>>> Starting back demodulation with 25. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.03 sec ----> 357 [binary,355.1,7.1] $F. Length of proof is 8. Level of proof is 5. ---------------- PROOF ---------------- 3 [] -i(x,I)|r(x)=x. 4 [] -i(x,I)| -i(y,I)|k(n(x,y),n(z,u))=n(k(x,z),k(y,u)). 5 [copy,4,flip.3] -i(x,I)| -i(y,I)|n(k(x,z),k(y,u))=k(n(x,y),n(z,u)). 6 [] k(n($c3,$c1),n($c4,$c2))!=n(k($c3,$c4),k($c1,$c2)). 7 [copy,6,flip.1] n(k($c3,$c4),k($c1,$c2))!=k(n($c3,$c1),n($c4,$c2)). 13,12 [] r(n(x,y))=n(r(x),r(y)). 15,14 [] r(r(x))=x. 19,18 [] r(k(x,y))=k(r(y),r(x)). 26 [] i($c4,I). 27 [] i($c2,I). 33,32 [hyper,26,3] r($c4)=$c4. 38 [hyper,27,5,26] n(k($c4,x),k($c2,y))=k(n($c4,$c2),n(x,y)). 44,43 [hyper,27,3] r($c2)=$c2. 87 [para_from,38.1.1,12.1.1.1,demod,19,13,13,33,44,19,33,19,44,flip.1] n(k(r(x),$c4),k(r(y),$c2))=k(n(r(x),r(y)),n($c4,$c2)). 247 [para_into,87.1.1.1.1,14.1.1,demod,15] n(k(x,$c4),k(r(y),$c2))=k(n(x,r(y)),n($c4,$c2)). 355 [para_into,247.1.1.2.1,14.1.1,demod,15] n(k(x,$c4),k(y,$c2))=k(n(x,y),n($c4,$c2)). 357 [binary,355.1,7.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 61 clauses generated 550 clauses kept 188 clauses forward subsumed 375 clauses back subsumed 14 Kbytes malloced 287 ----------- times (seconds) ----------- user CPU time 0.23 (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 Mon Dec 29 22:40:31 2003