----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 21:06:30 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("xxx_a.txt"). ------- start included file xxx_a.txt------- formula_list(usable). all x y (i(k(r(x),x),I)&k(x,U)=U->c(k(x,y))=k(x,c(y))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(k(r(x),x),I)|k(x,U)!=U|c(k(x,y))=k(x,c(y)). 0 [] end_of_formula. end_of_list. ------- end included file xxx_a.txt------- include("xxx_b.txt"). ------- start included file xxx_b.txt------- formula_list(usable). -(all x y (i(k(r(x),x),I)&k(x,U)=U->c(k(y,r(x)))=k(c(y),r(x)))). end_of_formula. end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r($c2),$c2),I). 0 [] k($c2,U)=U. 0 [] c(k($c1,r($c2)))!=k(c($c1),r($c2)). 0 [] end_of_formula. end_of_list. ------- end included file xxx_b.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. This is a Horn set with equality. The strategy will be Knuth-Bendix and hyper_res, with positive clauses in sos and nonpositive clauses in usable. dependent: set(knuth_bendix). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). dependent: set(hyper_res). dependent: clear(order_hyper). ------------> process usable: ** KEPT (pick-wt=8): 1 [] -i(x,y)|i(r(x),r(y)). ** KEPT (pick-wt=20): 2 [] -i(k(r(x),x),I)|k(x,U)!=U|c(k(x,y))=k(x,c(y)). ** KEPT (pick-wt=11): 3 [] c(k($c1,r($c2)))!=k(c($c1),r($c2)). ------------> process sos: ** KEPT (pick-wt=10): 4 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 5 [new_demod,4] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=7): 6 [] r(c(x))=c(r(x)). ---> New Demodulator: 7 [new_demod,6] r(c(x))=c(r(x)). ** KEPT (pick-wt=10): 8 [] r(n(x,y))=n(r(x),r(y)). ---> New Demodulator: 9 [new_demod,8] r(n(x,y))=n(r(x),r(y)). ** KEPT (pick-wt=5): 10 [] r(r(x))=x. ---> New Demodulator: 11 [new_demod,10] r(r(x))=x. ** KEPT (pick-wt=10): 12 [] r(d(x,y))=d(r(y),r(x)). ---> New Demodulator: 13 [new_demod,12] r(d(x,y))=d(r(y),r(x)). ** KEPT (pick-wt=10): 14 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 15 [new_demod,14] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=4): 16 [] r(I)=I. ---> New Demodulator: 17 [new_demod,16] r(I)=I. ** KEPT (pick-wt=4): 18 [] r(Z)=Z. ---> New Demodulator: 19 [new_demod,18] r(Z)=Z. ** KEPT (pick-wt=4): 20 [] r(U)=U. ---> New Demodulator: 21 [new_demod,20] r(U)=U. ** KEPT (pick-wt=1): 22 [] end_of_formula. ** KEPT (pick-wt=6): 23 [] i(k(r($c2),$c2),I). ** KEPT (pick-wt=5): 24 [] k($c2,U)=U. ---> New Demodulator: 25 [new_demod,24] k($c2,U)=U. Following clause subsumed by 22 during input processing: 0 [] end_of_formula. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> 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 25. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 13. sos_size=4485 ----> UNIT CONFLICT at 1.06 sec ----> 5393 [binary,5391.1,3.1] $F. Length of proof is 3. Level of proof is 3. ---------------- PROOF ---------------- 2 [] -i(k(r(x),x),I)|k(x,U)!=U|c(k(x,y))=k(x,c(y)). 3 [] c(k($c1,r($c2)))!=k(c($c1),r($c2)). 7,6 [] r(c(x))=c(r(x)). 11,10 [] r(r(x))=x. 15,14 [] r(k(x,y))=k(r(y),r(x)). 23 [] i(k(r($c2),$c2),I). 24 [] k($c2,U)=U. 59 [hyper,23,2,24] c(k($c2,x))=k($c2,c(x)). 211 [para_from,59.1.1,6.1.1.1,demod,15,7,15,flip.1] c(k(r(x),r($c2)))=k(c(r(x)),r($c2)). 5391 [para_into,211.1.1.1.1,10.1.1,demod,11] c(k(x,r($c2)))=k(c(x),r($c2)). 5393 [binary,5391.1,3.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 696 clauses generated 10436 clauses kept 5369 clauses forward subsumed 1898 clauses back subsumed 29 Kbytes malloced 4279 ----------- times (seconds) ----------- user CPU time 1.26 (0 hr, 0 min, 1 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 21:06:31 2003