----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Fri Nov 21 23:11:54 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). 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("iii.txt"). ------- start included file iii.txt------- formula_list(usable). -(all x y (c(k(x,y))=d(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(k($c2,$c1))!=d(c($c2),c($c1)). end_of_list. ------- end included file iii.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=10): 1 [] c(k($c2,$c1))!=d(c($c2),c($c1)). ------------> process sos: ** KEPT (pick-wt=7): 2 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 4 [copy,3,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 5 [new_demod,4] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 6 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 7 [new_demod,6] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 9 [copy,8,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 10 [new_demod,9] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 11 [] r(r(x))=x. ---> New Demodulator: 12 [new_demod,11] r(r(x))=x. ** KEPT (pick-wt=10): 13 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 14 [new_demod,13] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 15 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 16 [new_demod,15] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=10): 18 [copy,17,flip.1] c(k(c(x),c(y)))=d(x,y). ---> New Demodulator: 19 [new_demod,18] c(k(c(x),c(y)))=d(x,y). Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 19. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 19. sos_size=2812 ----> UNIT CONFLICT at 1.78 sec ----> 5346 [binary,5344.1,1.1] $F. Length of proof is 26. Level of proof is 11. ---------------- PROOF ---------------- 1 [] c(k($c2,$c1))!=d(c($c2),c($c1)). 2 [] u(x,y)=u(y,x). 3 [] u(x,u(y,z))=u(u(x,y),z). 5,4 [copy,3,flip.1] u(u(x,y),z)=u(x,u(y,z)). 6 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 17 [] d(x,y)=c(k(c(x),c(y))). 18 [copy,17,flip.1] c(k(c(x),c(y)))=d(x,y). 23 [para_into,4.1.1.1,2.1.1,demod,5] u(x,u(y,z))=u(y,u(x,z)). 24 [para_into,4.1.1,2.1.1] u(x,u(y,z))=u(y,u(z,x)). 25 [copy,24,flip.1] u(x,u(y,z))=u(z,u(x,y)). 48 [para_into,6.1.1.1.1,2.1.1] u(c(u(x,c(y))),c(u(c(y),c(x))))=y. 54 [para_into,6.1.1.2.1,2.1.1] u(c(u(c(x),y)),c(u(c(y),c(x))))=x. 60 [para_from,6.1.1,4.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(x),c(y))),z))=u(x,z). 62 [para_from,6.1.1,23.1.1.2,flip.1] u(c(u(c(x),y)),u(z,c(u(c(x),c(y)))))=u(z,x). 65 [para_into,25.1.1.2,6.1.1,flip.1] u(c(u(c(x),c(y))),u(z,c(u(c(x),y))))=u(z,x). 100 [para_into,48.1.1.2.1,2.1.1] u(c(u(x,c(y))),c(u(c(x),c(y))))=y. 102 [para_into,48.1.1,2.1.1] u(c(u(c(x),c(y))),c(u(y,c(x))))=x. 168 [para_from,54.1.1,4.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(y),c(x))),z))=u(x,z). 171 [para_from,54.1.1,25.1.1.2,flip.1] u(c(u(c(x),c(y))),u(z,c(u(c(y),x))))=u(z,y). 238 [para_into,100.1.1,2.1.1] u(c(u(c(x),c(y))),c(u(x,c(y))))=y. 2859 [para_into,60.1.1.2,238.1.1] u(c(u(c(x),y)),y)=u(x,c(u(x,c(y)))). 2895 [copy,2859,flip.1] u(x,c(u(x,c(y))))=u(c(u(c(x),y)),y). 4371,4370 [para_into,62.1.1.2,238.1.1,flip.1] u(c(u(c(c(x)),c(y))),x)=u(c(u(c(x),y)),y). 4438 [para_into,65.1.1.2,238.1.1,demod,4371] u(c(u(c(x),c(c(y)))),y)=u(c(u(c(x),y)),y). 4662,4661 [para_into,168.1.1.2,4438.1.1] u(c(u(c(c(x)),y)),u(c(u(c(y),x)),x))=u(c(x),x). 4669 [para_into,171.1.1.2,2895.1.1,demod,4662] u(c(x),x)=u(c(y),y). 4753 [para_from,4669.1.1,102.1.1.2.1] u(c(u(c(x),c(c(c(x))))),c(u(c(y),y)))=x. 4766,4765 [para_from,4669.1.1,48.1.1.2.1] u(c(u(x,c(c(x)))),c(u(c(y),y)))=c(x). 4888 [back_demod,4753,demod,4766] c(c(x))=x. 5099 [para_from,4888.1.1,18.1.1.1.2] c(k(c(x),y))=d(x,c(y)). 5344 [para_into,5099.1.1.1.1,4888.1.1] c(k(x,y))=d(c(x),c(y)). 5346 [binary,5344.1,1.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 144 clauses generated 24477 clauses kept 3877 clauses forward subsumed 9250 clauses back subsumed 20 Kbytes malloced 4662 ----------- times (seconds) ----------- user CPU time 1.98 (0 hr, 0 min, 1 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 2 (0 hr, 0 min, 2 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 23:11:56 2003