----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Fri Nov 21 23:12:09 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))). -(all x y (c(d(x,y))=k(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(k(x,y))=d(c(x),c(y)). 0 [] c(d($c2,$c1))!=k(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(d($c2,$c1))!=k(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). ** KEPT (pick-wt=10): 20 [] c(k(x,y))=d(c(x),c(y)). ---> New Demodulator: 21 [new_demod,20] c(k(x,y))=d(c(x),c(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. >>>> Starting back demodulation with 21. >> back demodulating 18 with 21. >>>> Starting back demodulation with 23. ======= end of input processing ======= =========== start of search =========== Resetting weight limit to 19. sos_size=3085 ----> UNIT CONFLICT at 1.98 sec ----> 5102 [binary,5100.1,1.1] $F. Length of proof is 29. Level of proof is 11. ---------------- PROOF ---------------- 1 [] c(d($c2,$c1))!=k(c($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). 21,20 [] c(k(x,y))=d(c(x),c(y)). 23,22 [back_demod,18,demod,21] d(c(c(x)),c(c(y)))=d(x,y). 27 [para_into,4.1.1.1,2.1.1,demod,5] u(x,u(y,z))=u(y,u(x,z)). 28 [para_into,4.1.1,2.1.1] u(x,u(y,z))=u(y,u(z,x)). 29 [copy,28,flip.1] u(x,u(y,z))=u(z,u(x,y)). 39 [para_into,6.1.1.1.1.1,20.1.1,demod,21] u(c(u(d(c(x),c(y)),z)),c(u(d(c(x),c(y)),c(z))))=k(x,y). 45 [para_into,6.1.1.1.1,2.1.1] u(c(u(x,c(y))),c(u(c(y),c(x))))=y. 51 [para_into,6.1.1.2.1,2.1.1] u(c(u(c(x),y)),c(u(c(y),c(x))))=x. 57 [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). 59 [para_from,6.1.1,27.1.1.2,flip.1] u(c(u(c(x),y)),u(z,c(u(c(x),c(y)))))=u(z,x). 71 [para_into,29.1.1.2,6.1.1,flip.1] u(c(u(c(x),c(y))),u(z,c(u(c(x),y))))=u(z,x). 114 [para_into,45.1.1.2.1,2.1.1] u(c(u(x,c(y))),c(u(c(x),c(y))))=y. 116 [para_into,45.1.1,2.1.1] u(c(u(c(x),c(y))),c(u(y,c(x))))=x. 170 [para_from,51.1.1,4.1.1.1,flip.1] u(c(u(c(x),y)),u(c(u(c(y),c(x))),z))=u(x,z). 173 [para_from,51.1.1,29.1.1.2,flip.1] u(c(u(c(x),c(y))),u(z,c(u(c(y),x))))=u(z,y). 232 [para_into,114.1.1,2.1.1] u(c(u(c(x),c(y))),c(u(x,c(y))))=y. 554 [para_into,39.1.1.1.1.1,22.1.1,demod,23] u(c(u(d(x,y),z)),c(u(d(x,y),c(z))))=k(c(x),c(y)). 2200 [para_into,57.1.1.2,232.1.1] u(c(u(c(x),y)),y)=u(x,c(u(x,c(y)))). 2236 [copy,2200,flip.1] u(x,c(u(x,c(y))))=u(c(u(c(x),y)),y). 3419,3418 [para_into,59.1.1.2,232.1.1,flip.1] u(c(u(c(c(x)),c(y))),x)=u(c(u(c(x),y)),y). 4378 [para_into,71.1.1.2,232.1.1,demod,3419] u(c(u(c(x),c(c(y)))),y)=u(c(u(c(x),y)),y). 4592,4591 [para_into,170.1.1.2,4378.1.1] u(c(u(c(c(x)),y)),u(c(u(c(y),x)),x))=u(c(x),x). 4599 [para_into,173.1.1.2,2236.1.1,demod,4592] u(c(x),x)=u(c(y),y). 4679 [para_from,4599.1.1,116.1.1.2.1] u(c(u(c(x),c(c(c(x))))),c(u(c(y),y)))=x. 4692,4691 [para_from,4599.1.1,45.1.1.2.1] u(c(u(x,c(c(x)))),c(u(c(y),y)))=c(x). 4815,4814 [back_demod,4679,demod,4692] c(c(x))=x. 5084,5083 [para_from,4814.1.1,6.1.1.2.1.1,demod,4815] u(c(u(x,y)),c(u(x,c(y))))=c(x). 5100 [back_demod,554,demod,5084] c(d(x,y))=k(c(x),c(y)). 5102 [binary,5100.1,1.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 153 clauses generated 21624 clauses kept 3835 clauses forward subsumed 8639 clauses back subsumed 14 Kbytes malloced 4598 ----------- times (seconds) ----------- user CPU time 2.18 (0 hr, 0 min, 2 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 23:12:12 2003