----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 19:18:43 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,3). assign(max_literals,1). assign(max_mem,30000). assign(max_weight,20). 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("ii.txt"). ------- start included file ii.txt------- formula_list(usable). k(U,U)=U. r(U)=U&r(Z)=Z&r(I)=I&r(D)=D. end_of_list. -------> usable clausifies to: list(usable). 0 [] k(U,U)=U. 0 [] r(U)=U. 0 [] r(Z)=Z. 0 [] r(I)=I. 0 [] r(D)=D. end_of_list. ------- end included file ii.txt------- include("v.txt"). ------- start included file v.txt------- formula_list(usable). all x y z (k(x,u(y,z))=u(k(x,y),k(x,z))). all x y z (k(u(x,y),z)=u(k(x,z),k(y,z))). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,u(y,z))=u(k(x,y),k(x,z)). 0 [] k(u(x,y),z)=u(k(x,z),k(y,z)). end_of_list. ------- end included file v.txt------- include("9_10booleanLaws.txt"). ------- start included file 9_10booleanLaws.txt------- formula_list(usable). all x (u(x,Z)=x). all x y z (i(x,y)&i(y,z)->i(x,z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] u(x,Z)=x. 0 [] -i(x,y)| -i(y,z)|i(x,z). end_of_list. ------- end included file 9_10booleanLaws.txt------- include("12booleanLaws.txt"). ------- start included file 12booleanLaws.txt------- formula_list(usable). all x y z (i(x,z)&i(y,z)->i(u(x,y),z)). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,z)| -i(y,z)|i(u(x,y),z). end_of_list. ------- end included file 12booleanLaws.txt------- include("13booleanLaws.txt"). ------- start included file 13booleanLaws.txt------- formula_list(usable). all x y (i(x,y)&i(y,x)->x=y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)| -i(y,x)|x=y. end_of_list. ------- end included file 13booleanLaws.txt------- include("xxxi_ghost.txt"). ------- start included file xxxi_ghost.txt------- formula_list(usable). all x y (n(k(x,U),k(y,U))=Z->k(r(x),y)=Z). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(k(x,U),k(y,U))!=Z|k(r(x),y)=Z. end_of_list. ------- end included file xxxi_ghost.txt------- include("xxxi.txt"). ------- start included file xxxi.txt------- formula_list(usable). -(all x y (i(k(r(x),x),I)&i(k(r(y),y),I)&n(k(x,U),k(y,U))=Z->i(k(r(u(x,y)),u(x,y)),I))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(k(r($c2),$c2),I). 0 [] i(k(r($c1),$c1),I). 0 [] n(k($c2,U),k($c1,U))=Z. 0 [] -i(k(r(u($c2,$c1)),u($c2,$c1)),I). end_of_list. ------- end included file xxxi.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=9): 1 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=11): 2 [] -i(x,y)| -i(z,y)|i(u(x,z),y). ** KEPT (pick-wt=9): 3 [] -i(x,y)| -i(y,x)|x=y. ** KEPT (pick-wt=15): 4 [] n(k(x,U),k(y,U))!=Z|k(r(x),y)=Z. ** KEPT (pick-wt=10): 5 [] -i(k(r(u($c2,$c1)),u($c2,$c1)),I). ------------> process sos: ** KEPT (pick-wt=7): 6 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 8 [copy,7,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 9 [new_demod,8] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 10 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 11 [new_demod,10] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=11): 13 [copy,12,flip.1] k(k(x,y),z)=k(x,k(y,z)). ---> New Demodulator: 14 [new_demod,13] k(k(x,y),z)=k(x,k(y,z)). ** KEPT (pick-wt=5): 15 [] r(r(x))=x. ---> New Demodulator: 16 [new_demod,15] r(r(x))=x. ** KEPT (pick-wt=10): 17 [] r(u(x,y))=u(r(x),r(y)). ---> New Demodulator: 18 [new_demod,17] r(u(x,y))=u(r(x),r(y)). ** KEPT (pick-wt=10): 19 [] r(k(x,y))=k(r(y),r(x)). ---> New Demodulator: 20 [new_demod,19] r(k(x,y))=k(r(y),r(x)). ** KEPT (pick-wt=5): 21 [] k(U,U)=U. ---> New Demodulator: 22 [new_demod,21] k(U,U)=U. ** KEPT (pick-wt=4): 23 [] r(U)=U. ---> New Demodulator: 24 [new_demod,23] r(U)=U. ** KEPT (pick-wt=4): 25 [] r(Z)=Z. ---> New Demodulator: 26 [new_demod,25] r(Z)=Z. ** KEPT (pick-wt=4): 27 [] r(I)=I. ---> New Demodulator: 28 [new_demod,27] r(I)=I. ** KEPT (pick-wt=4): 29 [] r(D)=D. ---> New Demodulator: 30 [new_demod,29] r(D)=D. ** KEPT (pick-wt=13): 32 [copy,31,flip.1] u(k(x,y),k(x,z))=k(x,u(y,z)). ---> New Demodulator: 33 [new_demod,32] u(k(x,y),k(x,z))=k(x,u(y,z)). ** KEPT (pick-wt=13): 35 [copy,34,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 36 [new_demod,35] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=5): 37 [] u(x,Z)=x. ---> New Demodulator: 38 [new_demod,37] u(x,Z)=x. ** KEPT (pick-wt=6): 39 [] i(k(r($c2),$c2),I). ** KEPT (pick-wt=6): 40 [] i(k(r($c1),$c1),I). ** KEPT (pick-wt=9): 41 [] n(k($c2,U),k($c1,U))=Z. ---> New Demodulator: 42 [new_demod,41] n(k($c2,U),k($c1,U))=Z. Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 9. >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 14. >>>> Starting back demodulation with 16. >>>> Starting back demodulation with 18. >> back demodulating 5 with 18. >>>> Starting back demodulation with 20. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 24. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 30. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 38. >>>> Starting back demodulation with 42. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.27 sec ----> 2516 [binary,2515.1,528.1] $F. Length of proof is 14. Level of proof is 6. ---------------- PROOF ---------------- 2 [] -i(x,y)| -i(z,y)|i(u(x,z),y). 4 [] n(k(x,U),k(y,U))!=Z|k(r(x),y)=Z. 5 [] -i(k(r(u($c2,$c1)),u($c2,$c1)),I). 6 [] u(x,y)=u(y,x). 16,15 [] r(r(x))=x. 18,17 [] r(u(x,y))=u(r(x),r(y)). 19 [] r(k(x,y))=k(r(y),r(x)). 26,25 [] r(Z)=Z. 31 [] k(x,u(y,z))=u(k(x,y),k(x,z)). 32 [copy,31,flip.1] u(k(x,y),k(x,z))=k(x,u(y,z)). 34 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 35 [copy,34,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). 38,37 [] u(x,Z)=x. 39 [] i(k(r($c2),$c2),I). 40 [] i(k(r($c1),$c1),I). 41 [] n(k($c2,U),k($c1,U))=Z. 43 [back_demod,5,demod,18] -i(k(u(r($c2),r($c1)),u($c2,$c1)),I). 64,63 [para_into,37.1.1,6.1.1] u(Z,x)=x. 72 [hyper,40,2,39] i(u(k(r($c1),$c1),k(r($c2),$c2)),I). 85 [hyper,41,4] k(r($c2),$c1)=Z. 89 [para_into,19.1.1.1,85.1.1,demod,26,16,flip.1] k(r($c1),$c2)=Z. 132 [para_into,43.1.1.1,6.1.1] -i(k(u(r($c1),r($c2)),u($c2,$c1)),I). 143 [para_into,35.1.1.1,89.1.1,demod,64,flip.1] k(u(r($c1),x),$c2)=k(x,$c2). 156 [para_into,35.1.1.2,85.1.1,demod,38,flip.1] k(u(x,r($c2)),$c1)=k(x,$c1). 175 [para_from,143.1.1,32.1.1.2] u(k(u(r($c1),x),y),k(x,$c2))=k(u(r($c1),x),u(y,$c2)). 528 [para_into,132.1.1.2,6.1.1] -i(k(u(r($c1),r($c2)),u($c1,$c2)),I). 2500,2499 [para_into,175.1.1.1,156.1.1] u(k(r($c1),$c1),k(r($c2),$c2))=k(u(r($c1),r($c2)),u($c1,$c2)). 2515 [back_demod,72,demod,2500] i(k(u(r($c1),r($c2)),u($c1,$c2)),I). 2516 [binary,2515.1,528.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 241 clauses generated 8935 clauses kept 1487 clauses forward subsumed 4115 clauses back subsumed 15 Kbytes malloced 1852 ----------- times (seconds) ----------- user CPU time 0.47 (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 Sun Nov 30 19:18:43 2003