----- Otter 3.2, August 2001 ----- The process was started by ??? on ???, Sun Nov 30 22:17:05 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,20). assign(max_distinct_vars,3). assign(max_literals,1). 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("iDef.txt"). ------- start included file iDef.txt------- formula_list(usable). all x y (i(x,y)<->u(x,y)=y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,y)|u(x,y)=y. 0 [] i(x,y)|u(x,y)!=y. end_of_list. ------- end included file iDef.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("booleanLaws.txt"). ------- start included file booleanLaws.txt------- include("1To4booleanLaws.txt"). ------- start included file 1To4booleanLaws.txt------- formula_list(usable). all x y z (i(x,u(y,z))->i(n(x,c(z)),y)). all x y z (i(x,y)->i(u(z,x),u(z,y))). all x y (x=u(n(x,c(y)),n(x,y))). all x y i(n(x,y),y). end_of_list. -------> usable clausifies to: list(usable). 0 [] -i(x,u(y,z))|i(n(x,c(z)),y). 0 [] -i(x,y)|i(u(z,x),u(z,y)). 0 [] x=u(n(x,c(y)),n(x,y)). 0 [] i(n(x,y),y). end_of_list. ------- end included file 1To4booleanLaws.txt------- include("4To8booleanLaws.txt"). ------- start included file 4To8booleanLaws.txt------- formula_list(usable). all x y i(n(x,y),y). all x y z i(n(x,u(y,z)),u(y,n(x,z))). all x y (x=u(n(x,y),n(x,c(y)))). all x y z (i(x,y)->i(u(z,x),u(z,y))). all x y z (i(x,y)->i(n(z,x),n(z,y))). end_of_list. -------> usable clausifies to: list(usable). 0 [] i(n(x,y),y). 0 [] i(n(x,u(y,z)),u(y,n(x,z))). 0 [] x=u(n(x,y),n(x,c(y))). 0 [] -i(x,y)|i(u(z,x),u(z,y)). 0 [] -i(x,y)|i(n(z,x),n(z,y)). end_of_list. ------- end included file 4To8booleanLaws.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("11booleanLaws.txt"). ------- start included file 11booleanLaws.txt------- formula_list(usable). -(all x y (c(n(x,y))=u(c(x),c(y)))). end_of_list. -------> usable clausifies to: list(usable). 0 [] c(n($c2,$c1))!=u(c($c2),c($c1)). end_of_list. ------- end included file 11booleanLaws.txt------- ------- end included file booleanLaws.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=8): 1 [] -i(x,y)|u(x,y)=y. ** KEPT (pick-wt=8): 2 [] i(x,y)|u(x,y)!=y. ** KEPT (pick-wt=11): 3 [] -i(x,u(y,z))|i(n(x,c(z)),y). ** KEPT (pick-wt=10): 4 [] -i(x,y)|i(u(z,x),u(z,y)). Following clause subsumed by 4 during input processing: 0 [] -i(x,y)|i(u(z,x),u(z,y)). ** KEPT (pick-wt=10): 5 [] -i(x,y)|i(n(z,x),n(z,y)). ** KEPT (pick-wt=9): 6 [] -i(x,y)| -i(y,z)|i(x,z). ** KEPT (pick-wt=10): 7 [] c(n($c2,$c1))!=u(c($c2),c($c1)). ------------> process sos: ** KEPT (pick-wt=7): 8 [] u(x,y)=u(y,x). ** KEPT (pick-wt=11): 10 [copy,9,flip.1] u(u(x,y),z)=u(x,u(y,z)). ---> New Demodulator: 11 [new_demod,10] u(u(x,y),z)=u(x,u(y,z)). ** KEPT (pick-wt=14): 12 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ---> New Demodulator: 13 [new_demod,12] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. ** KEPT (pick-wt=10): 15 [copy,14,flip.1] c(u(c(x),c(y)))=n(x,y). ---> New Demodulator: 16 [new_demod,15] c(u(c(x),c(y)))=n(x,y). ** KEPT (pick-wt=4): 18 [copy,17,flip.1] c(I)=D. ---> New Demodulator: 19 [new_demod,18] c(I)=D. ** KEPT (pick-wt=5): 21 [copy,20,flip.1] u(I,D)=U. ---> New Demodulator: 22 [new_demod,21] u(I,D)=U. ** KEPT (pick-wt=4): 24 [copy,23,flip.1] c(U)=Z. ---> New Demodulator: 25 [new_demod,24] c(U)=Z. ** KEPT (pick-wt=10): 27 [copy,26,flip.1] u(n(x,c(y)),n(x,y))=x. ---> New Demodulator: 28 [new_demod,27] u(n(x,c(y)),n(x,y))=x. ** KEPT (pick-wt=5): 29 [] i(n(x,y),y). Following clause subsumed by 29 during input processing: 0 [] i(n(x,y),y). ** KEPT (pick-wt=11): 30 [] i(n(x,u(y,z)),u(y,n(x,z))). ** KEPT (pick-wt=10): 32 [copy,31,flip.1] u(n(x,y),n(x,c(y)))=x. ---> New Demodulator: 33 [new_demod,32] u(n(x,y),n(x,c(y)))=x. ** KEPT (pick-wt=5): 34 [] u(x,Z)=x. ---> New Demodulator: 35 [new_demod,34] u(x,Z)=x. Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] u(x,y)=u(y,x). >>>> Starting back demodulation with 11. >>>> Starting back demodulation with 13. >>>> Starting back demodulation with 16. >> back demodulating 12 with 16. >>>> Starting back demodulation with 19. >>>> Starting back demodulation with 22. >>>> Starting back demodulation with 25. >>>> Starting back demodulation with 28. >>>> Starting back demodulation with 33. >>>> Starting back demodulation with 35. >>>> Starting back demodulation with 37. ======= end of input processing ======= =========== start of search =========== ----> UNIT CONFLICT at 0.04 sec ----> 264 [binary,262.1,7.1] $F. Length of proof is 11. Level of proof is 6. ---------------- PROOF ---------------- 1 [] -i(x,y)|u(x,y)=y. 7 [] c(n($c2,$c1))!=u(c($c2),c($c1)). 8 [] u(x,y)=u(y,x). 12 [] u(c(u(c(x),y)),c(u(c(x),c(y))))=x. 14 [] n(x,y)=c(u(c(x),c(y))). 16,15 [copy,14,flip.1] c(u(c(x),c(y)))=n(x,y). 23 [] Z=c(U). 24 [copy,23,flip.1] c(U)=Z. 29 [] i(n(x,y),y). 35,34 [] u(x,Z)=x. 36 [back_demod,12,demod,16] u(c(u(c(x),y)),n(x,y))=x. 53 [hyper,29,1] u(n(x,y),y)=y. 58,57 [para_into,34.1.1,8.1.1] u(Z,x)=x. 60,59 [para_into,15.1.1.1.1,24.1.1,demod,58] c(c(x))=n(U,x). 181 [para_into,36.1.1.1.1,34.1.1,demod,60] u(n(U,x),n(x,Z))=x. 227,226 [para_into,53.1.1,34.1.1] n(x,Z)=Z. 231,230 [back_demod,181,demod,227,35] n(U,x)=x. 238 [back_demod,59,demod,231] c(c(x))=x. 262 [para_into,238.1.1.1,15.1.1] c(n(x,y))=u(c(x),c(y)). 264 [binary,262.1,7.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 43 clauses generated 649 clauses kept 178 clauses forward subsumed 372 clauses back subsumed 23 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 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 22:17:05 2003