----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Fri Nov 21 23:15:54 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_seconds,5). include("booleanAx.txt"). ------- start included file booleanAx.txt------- include("1_2booleanAx.txt"). ------- start included file 1_2booleanAx.txt------- formula_list(usable). all x y (u(x,y)=u(y,x)). all x y z (u(x,u(y,z))=u(u(x,y),z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,y)=u(y,x). 0 [] u(x,u(y,z))=u(u(x,y),z). end_of_list. ------- end included file 1_2booleanAx.txt------- include("3booleanAx.txt"). ------- start included file 3booleanAx.txt------- formula_list(usable). all x y (u(c(u(c(x),y)),c(u(c(x),c(y))))=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. end_of_list. ------- end included file 3booleanAx.txt------- ------- end included file booleanAx.txt------- include("peirceanAx0.txt"). ------- start included file peirceanAx0.txt------- formula_list(usable). all x y z (k(x,k(y,z))=k(k(x,y),z)). all x (r(r(x))=x). all x y (r(u(x,y))=u(r(x),r(y))). all x y (r(k(x,y))=k(r(y),r(x))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,k(y,z))=k(k(x,y),z). 0 [] r(r(x))=x. 0 [] r(u(x,y))=u(r(x),r(y)). 0 [] r(k(x,y))=k(r(y),r(x)). end_of_list. ------- end included file peirceanAx0.txt------- include("dDef.txt"). ------- start included file dDef.txt------- formula_list(usable). all x y (d(x,y)=c(k(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] d(x,y)=c(k(c(x),c(y))). end_of_list. ------- end included file dDef.txt------- include("iv.txt"). ------- start included file iv.txt------- formula_list(usable). all x y z (k(x,k(y,z))=k(k(x,y),z)). -(all x y z (d(x,d(y,z))=d(d(x,y),z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,k(y,z))=k(k(x,y),z). 0 [] d($c3,d($c2,$c1))!=d(d($c3,$c2),$c1). end_of_list. ------- end included file iv.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. 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). ------------> process usable: ** KEPT (pick-wt=11): 2 [copy,1,flip.1] d(d($c3,$c2),$c1)!=d($c3,d($c2,$c1)). ------------> process sos: ** KEPT (pick-wt=7): 3 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 5 [copy,4,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 6 [new_demod,5] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 7 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 8 [new_demod,7] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 10 [copy,9,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 11 [new_demod,10] k(k(x,y),z)=k(x,k(y,z)). ** 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(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 15 [new_demod,14] r(u(x,y))=u(r(x),r(y)). ** 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=10): 19 [copy,18,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 20 [new_demod,19] c(k(c(x),c(y)))=d(x,y). ** KEPT (pick-wt=11): 22 [copy,21,demod,11] k(x,k(y,z))=k(x,k(y,z)). Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 15. >>>> Starting back demodulation with 17. >>>> Starting back demodulation with 20. Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] k(x,k(y,z))=k(x,k(y,z)). ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 19. sos_size=2812 Resetting weight limit to 17. sos_size=2961 Resetting weight limit to 15. sos_size=3395 Resetting weight limit to 13. sos_size=2068 ----> UNIT CONFLICT at 3.63 sec ----> 6773 [binary,6771.1,2.1] $F. Length of proof is 30. Level of proof is 12. ---------------- PROOF ---------------- 1 [] d($c3,d($c2,$c1))!=d(d($c3,$c2),$c1). 2 [copy,1,flip.1] d(d($c3,$c2),$c1)!=d($c3,d($c2,$c1)). 3 [] u(x,y)=u(y,x). 4 [] u(x,u(y,z))=u(u(x,y),z). 6,5 [copy,4,flip.1] u(u(x,y),z)=u(x,u(y,z)). 7 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 9 [] k(x,k(y,z))=k(k(x,y),z). 11,10 [copy,9,flip.1] k(k(x,y),z)=k(x,k(y,z)). 18 [] d(x,y)=c(k(c(x),c(y))). 19 [copy,18,flip.1] c(k(c(x),c(y)))=d(x,y). 26 [para_into,5.1.1.1,3.1.1,demod,6] u(x,u(y,z))=u(y,u(x,z)). 27 [para_into,5.1.1,3.1.1] u(x,u(y,z))=u(y,u(z,x)). 28 [copy,27,flip.1] u(x,u(y,z))=u(z,u(x,y)). 51 [para_into,7.1.1.1.1,3.1.1] u(c(u(x,c(y))),c(u(c(y),c(x))))=y. 57 [para_into,7.1.1.2.1,3.1.1] u(c(u(c(x),y)),c(u(c(y),c(x))))=x. 63 [para_from,7.1.1,5.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(x),c(y))),z))=u(x,z). 65 [para_from,7.1.1,26.1.1.2,flip.1] u(c(u(c(x),y)),u(z,c(u(c(x),c(y)))))=u(z,x). 68 [para_into,28.1.1.2,7.1.1,flip.1] u(c(u(c(x),c(y))),u(z,c(u(c(x),y))))=u(z,x). 103 [para_into,51.1.1.2.1,3.1.1] u(c(u(x,c(y))),c(u(c(x),c(y))))=y. 105 [para_into,51.1.1,3.1.1] u(c(u(c(x),c(y))),c(u(y,c(x))))=x. 171 [para_from,57.1.1,5.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(y),c(x))),z))=u(x,z). 174 [para_from,57.1.1,28.1.1.2,flip.1] u(c(u(c(x),c(y))),u(z,c(u(c(y),x))))=u(z,y). 241 [para_into,103.1.1,3.1.1] u(c(u(c(x),c(y))),c(u(x,c(y))))=y. 2862 [para_into,63.1.1.2,241.1.1] u(c(u(c(x),y)),y)=u(x,c(u(x,c(y)))). 2898 [copy,2862,flip.1] u(x,c(u(x,c(y))))=u(c(u(c(x),y)),y). 4374,4373 [para_into,65.1.1.2,241.1.1,flip.1] u(c(u(c(c(x)),c(y))),x)=u(c(u(c(x),y)),y). 4441 [para_into,68.1.1.2,241.1.1,demod,4374] u(c(u(c(x),c(c(y)))),y)=u(c(u(c(x),y)),y). 4665,4664 [para_into,171.1.1.2,4441.1.1] u(c(u(c(c(x)),y)),u(c(u(c(y),x)),x))=u(c(x),x). 4672 [para_into,174.1.1.2,2898.1.1,demod,4665] u(c(x),x)=u(c(y),y). 4756 [para_from,4672.1.1,105.1.1.2.1] u(c(u(c(x),c(c(c(x))))),c(u(c(y),y)))=x. 4769,4768 [para_from,4672.1.1,51.1.1.2.1] u(c(u(x,c(c(x)))),c(u(c(y),y)))=c(x). 4892,4891 [back_demod,4756,demod,4769] c(c(x))=x. 5032 [para_into,4891.1.1.1,19.1.1] c(d(x,y))=k(c(x),c(y)). 5103,5102 [para_from,4891.1.1,19.1.1.1.2] c(k(c(x),y))=d(x,c(y)). 5345 [para_into,5102.1.1.1.1,5032.1.1,demod,11,5103,5103,flip.1] d(d(x,y),c(z))=d(x,d(y,c(z))). 6771 [para_into,5345.1.1.2,4891.1.1,demod,4892] d(d(x,y),z)=d(x,d(y,z)). 6773 [binary,6771.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 293 clauses generated 57006 clauses kept 5091 clauses forward subsumed 28983 clauses back subsumed 311 Kbytes malloced 5237 ----------- times (seconds) ----------- user CPU time 3.83 (0 hr, 0 min, 3 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 3 (0 hr, 0 min, 3 sec) 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 Fri Nov 21 23:15:57 2003