----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 16:00:41 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,64000). assign(max_weight,15). 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("peirceanAx1.txt"). ------- start included file peirceanAx1.txt------- formula_list(usable). 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(u(x,y),z)=u(k(x,z),k(y,z)). end_of_list. ------- end included file peirceanAx1.txt------- include("nDef.txt"). ------- start included file nDef.txt------- formula_list(usable). all x y (n(x,y)=c(u(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,y)=c(u(c(x),c(y))). end_of_list. ------- end included file nDef.txt------- include("uzDef.txt"). ------- start included file uzDef.txt------- formula_list(usable). D=c(I). U=u(I,D). Z=c(U). end_of_list. -------> usable clausifies to: list(usable). 0 [] D=c(I). 0 [] U=u(I,D). 0 [] Z=c(U). end_of_list. ------- end included file uzDef.txt------- include("ix_a.txt"). ------- start included file ix_a.txt------- formula_list(usable). all x (k(x,I)=x). end_of_list. -------> usable clausifies to: list(usable). 0 [] k(x,I)=x. end_of_list. ------- end included file ix_a.txt------- include("cycleLawA.txt"). ------- start included file cycleLawA.txt------- formula_list(usable). all x y z (n(x,k(z,r(y)))=Z->n(z,k(x,y))=Z). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(x,k(z,r(y)))!=Z|n(z,k(x,y))=Z. end_of_list. ------- end included file cycleLawA.txt------- include("xxiv_a.txt"). ------- start included file xxiv_a.txt------- formula_list(usable). all x (n(k(n(I,x),U),k(n(I,c(x)),U))=Z). -(all x (u(k(n(I,x),U),k(n(I,c(x)),U))=U)). end_of_list. -------> usable clausifies to: list(usable). 0 [] n(k(n(I,x),U),k(n(I,c(x)),U))=Z. 0 [] u(k(n(I,$c1),U),k(n(I,c($c1)),U))!=U. end_of_list. ------- end included file xxiv_a.txt------- SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. 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=15): 1 [] n(x,k(y,r(z)))!=Z|n(y,k(x,z))=Z. ** KEPT (pick-wt=14): 2 [] u(k(n(I,$c1),U),k(n(I,c($c1)),U))!=U. ------------> 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=13): 19 [copy,18,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). ---> New Demodulator: 20 [new_demod,19] u(k(x,y),k(z,y))=k(u(x,z),y). ** KEPT (pick-wt=10): 22 [copy,21,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 23 [new_demod,22] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=4): 25 [copy,24,flip.1] c(I)=D. ---> New Demodulator: 26 [new_demod,25] c(I)=D. ** KEPT (pick-wt=5): 28 [copy,27,flip.1] u(I,D)=U. ---> New Demodulator: 29 [new_demod,28] u(I,D)=U. ** KEPT (pick-wt=4): 31 [copy,30,flip.1] c(U)=Z. ---> New Demodulator: 32 [new_demod,31] c(U)=Z. ** KEPT (pick-wt=5): 33 [] k(x,I)=x. ---> New Demodulator: 34 [new_demod,33] k(x,I)=x. ** KEPT (pick-wt=14): 35 [] n(k(n(I,x),U),k(n(I,c(x)),U))=Z. ---> New Demodulator: 36 [new_demod,35] n(k(n(I,x),U),k(n(I,c(x)),U))=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. >> back demodulating 2 with 20. >>>> Starting back demodulation with 23. >> back demodulating 7 with 23. >>>> Starting back demodulation with 26. >>>> Starting back demodulation with 29. >>>> Starting back demodulation with 32. >>>> Starting back demodulation with 34. >>>> Starting back demodulation with 36. >>>> Starting back demodulation with 39. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.04 sec ----> 221 [binary,220.1,47.1] $F. Length of proof is 12. Level of proof is 4. ---------------- PROOF ---------------- 2 [] u(k(n(I,$c1),U),k(n(I,c($c1)),U))!=U. 7 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 9 [] k(x,k(y,z))=k(k(x,y),z). 10 [copy,9,flip.1] k(k(x,y),z)=k(x,k(y,z)). 13,12 [] r(r(x))=x. 16 [] r(k(x,y))=k(r(y),r(x)). 18 [] k(u(x,y),z)=u(k(x,z),k(y,z)). 20,19 [copy,18,flip.1] u(k(x,y),k(z,y))=k(u(x,z),y). 21 [] n(x,y)=c(u(c(x),c(y))). 23,22 [copy,21,flip.1] c(u(c(x),c(y)))=n(x,y). 33 [] k(x,I)=x. 37 [back_demod,2,demod,20] k(u(n(I,$c1),n(I,c($c1))),U)!=U. 38 [back_demod,7,demod,23] u(c(u(c(x),y)),n(x,y))=x. 47 [para_into,12.1.1,12.1.1] x=x. 52 [para_into,10.1.1.1,33.1.1,flip.1] k(x,k(I,y))=k(x,y). 81 [para_into,16.1.1.1,33.1.1,flip.1] k(r(I),r(x))=r(x). 90,89 [para_into,81.1.1.2,12.1.1,demod,13] k(r(I),x)=x. 92,91 [para_into,89.1.1,52.1.1,demod,90,flip.1] k(I,x)=x. 215,214 [para_into,38.1.1.1,22.1.1] u(n(x,y),n(x,c(y)))=x. 220 [back_demod,37,demod,215,92] U!=U. 221 [binary,220.1,47.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 44 clauses generated 366 clauses kept 131 clauses forward subsumed 269 clauses back subsumed 5 Kbytes malloced 223 ----------- times (seconds) ----------- user CPU time 0.24 (0 hr, 0 min, 0 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 16:00:42 2003