============================== Prover9 =============================== Prover9 (32) version June-2006C, June 2006. Process 13131 was started by mccune on cleo.thornwood, Mon Jun 19 16:41:41 2006 The command was "/home/mccune/bin/prover9 -f cs.in NA.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file cs.in op(450,infix,@). op(400,infix_right,*). assign(new_constants,1). assign(max_weight,25). clauses(sos). x * y != x * z | y = z. x * y != z * y | x = z. (x * y) * z = x * y * z. x * y * (y @ x) = y * x. end_of_list. % Reading from file NA.in clauses(sos). (x @ y) * z = z * (x @ y). end_of_list. clauses(sos). (A @ B) @ C != D @ (F @ G) # answer(A). end_of_list. ============================== end of input ========================== ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: clauses(usable). end_of_list. clauses(sos). 1 x * y != x * z | y = z. [input]. 2 x * y != z * y | x = z. [input]. 3 (x * y) * z = x * y * z. [input]. 4 x * y * (y @ x) = y * x. [input]. 5 (x @ y) * z = z * (x @ y). [input]. 6 (A @ B) @ C != D @ (F @ G) # answer(A). [input]. end_of_list. clauses(demodulators). end_of_list. Predicate elimination: (none). Auto_denials: no changes. Term ordering decisions: Relation symbol precedence: lex([ = ]). Function symbol precedence: lex([ A, B, C, D, F, G, *, @ ]). After inverse_order: Function symbol precedence: lex([ A, B, C, D, F, G, *, @ ]). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). % set(hyper_resolution). % (nonunit Horn with equality) % set(neg_ur_resolution). % (nonunit Horn with equality) % assign(para_lit_limit, 2). % (nonunit Horn with equality) Auto_process settings: no changes. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: clauses(usable). end_of_list. clauses(sos). 7 x * y != x * z | y = z. [input]. 8 x * y != z * y | x = z. [input]. 9 (x * y) * z = x * y * z. [input]. 10 x * y * (y @ x) = y * x. [input]. 11 (x @ y) * z = z * (x @ y). [input]. 12 (A @ B) @ C != D @ (F @ G) # answer(A). [input]. end_of_list. clauses(demodulators). 9 (x * y) * z = x * y * z. [input]. 10 x * y * (y @ x) = y * x. [input]. 11 (x @ y) * z = z * (x @ y). [input]. % (lex-dep) end_of_list. clauses(denials). end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=10): 7 x * y != x * z | y = z. [input]. given #2 (I,wt=10): 8 x * y != z * y | x = z. [input]. given #3 (I,wt=11): 9 (x * y) * z = x * y * z. [input]. given #4 (I,wt=11): 10 x * y * (y @ x) = y * x. [input]. given #5 (I,wt=11): 11 (x @ y) * z = z * (x @ y). [input]. given #6 (I,wt=11): 12 (A @ B) @ C != D @ (F @ G) # answer(A). [input]. given #7 (F,wt=15): 29 ((A @ B) @ C) * x != (D @ (F @ G)) * x # answer(A). [ur(8,b,12,a)]. given #8 (F,wt=15): 30 x * ((A @ B) @ C) != x * (D @ (F @ G)) # answer(A). [ur(7,b,12,a)]. given #9 (T,wt=7): 15 x * (x @ x) = x. [hyper(7,a,10,a)]. given #10 (T,wt=10): 37 x * y != x | x @ x = y. [para(15(a,1),7(a,1)),flip(a)]. given #11 (A,wt=14): 13 x * y * z != x * y * u | z = u. [para(9(a,1),7(a,1)),demod(9(4))]. given #12 (F,wt=15): 34 (D @ (F @ G)) * x != x * ((A @ B) @ C) # answer(A). [para(11(a,1),29(a,1)),flip(a)]. given #13 (F,wt=15): 35 ((A @ B) @ C) * x != x * (D @ (F @ G)) # answer(A). [para(11(a,1),29(a,2))]. given #14 (T,wt=10): 38 x * (y @ y) != y | y = x. [para(15(a,1),8(a,1)),flip(a)]. given #15 (T,wt=10): 39 x * (y @ y) != y | x = y. [para(15(a,1),8(a,2))]. given #16 (A,wt=14): 14 x * y * z != u * z | x * y = u. [para(9(a,1),8(a,1))]. given #17 (F,wt=19): 31 x * ((A @ B) @ C) * y != x * (D @ (F @ G)) * y # answer(A). [ur(7,b,29,a)]. given #18 (F,wt=19): 36 x * y * ((A @ B) @ C) != x * y * (D @ (F @ G)) # answer(A). [ur(7,b,30,a)]. given #19 (T,wt=10): 70 (x @ x) * y != x | x = y. [para(11(a,2),38(a,1))]. given #20 (T,wt=10): 71 (x @ x) * y != x | y = x. [para(11(a,2),39(a,1))]. given #21 (A,wt=14): 16 x * y != z * x | z * (z @ x) = y. [para(10(a,1),7(a,1)),flip(a)]. given #22 (F,wt=17): 87 C * (A @ B) * (D @ (F @ G)) != C * (A @ B) # answer(A). [para(10(a,1),36(a,1)),demod(11(5)),flip(a)]. given #23 (F,wt=17): 88 (F @ G) * D * ((A @ B) @ C) != D * (F @ G) # answer(A). [para(10(a,1),36(a,2))]. given #24 (T,wt=9): 93 x * (x @ (y @ z)) = x. [hyper(16,a,11,a)]. given #25 (T,wt=9): 94 x * (x @ x * x) = x. [hyper(16,a,9,a)]. given #26 (A,wt=14): 17 x * y * (y @ z) != y * z | z = x. [para(10(a,1),8(a,1)),flip(a)]. given #27 (F,wt=9): 118 D * ((A @ B) @ C) != D # answer(A). [para(93(a,1),30(a,2))]. given #28 (F,wt=13): 124 x * D * ((A @ B) @ C) != x * D # answer(A). [para(93(a,1),36(a,2,2))]. given #29 (T,wt=9): 110 x @ (y @ z) = x @ x. [hyper(37,a,93,a),flip(a)]. given #30 (T,wt=9): 128 x @ x * x = x @ x. [hyper(37,a,94,a),flip(a)]. given #31 (A,wt=14): 18 x * y * (y @ z) != y * z | x = z. [para(10(a,1),8(a,2))]. given #32 (F,wt=9): 150 (A @ B) @ C != D @ D # answer(A). [para(110(a,1),12(a,2))]. given #33 (F,wt=11): 164 (A @ B) @ C != D @ (x @ y) # answer(A). [para(110(a,2),150(a,2))]. given #34 (T,wt=10): 133 x * y != y * y | y = x. [para(15(a,1),17(a,1,2))]. given #35 (T,wt=10): 134 x * y != y | y @ y = x. [para(15(a,1),17(a,2)),demod(93(3))]. given #36 (A,wt=15): 19 x * y * (y @ x) * z = y * x * z. [para(10(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)]. ============================== PROOF ================================= % Proof 1 at 0.02 (+ 0.00) seconds: A. % Length of proof is 20. % Level of proof is 6. % Maximum clause weight is 15. % Given clauses 36. 7 x * y != x * z | y = z. [input]. 8 x * y != z * y | x = z. [input]. 9 (x * y) * z = x * y * z. [input]. 10 x * y * (y @ x) = y * x. [input]. 11 (x @ y) * z = z * (x @ y). [input]. 12 (A @ B) @ C != D @ (F @ G) # answer(A). [input]. 13 x * y * z != x * y * u | z = u. [para(9(a,1),7(a,1)),demod(9(4))]. 15 x * (x @ x) = x. [hyper(7,a,10,a)]. 16 x * y != z * x | z * (z @ x) = y. [para(10(a,1),7(a,1)),flip(a)]. 19 x * y * (y @ x) * z = y * x * z. [para(10(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)]. 29 ((A @ B) @ C) * x != (D @ (F @ G)) * x # answer(A). [ur(8,b,12,a)]. 34 (D @ (F @ G)) * x != x * ((A @ B) @ C) # answer(A). [para(11(a,1),29(a,1)),flip(a)]. 37 x * y != x | x @ x = y. [para(15(a,1),7(a,1)),flip(a)]. 93 x * (x @ (y @ z)) = x. [hyper(16,a,11,a)]. 95 (x @ y) * ((x @ y) @ z) = x @ y. [hyper(16,a,11,a(flip))]. 110 x @ (y @ z) = x @ x. [hyper(37,a,93,a),flip(a)]. 153 (D @ D) * x != x * ((A @ B) @ C) # answer(A). [para(110(a,1),34(a,1,1))]. 177 (x @ x) * y = y. [hyper(13,a,19,a)]. 202 x * ((A @ B) @ C) != x # answer(A). [back_demod(153),demod(177(4)),flip(a)]. 203 $F # answer(A). [resolve(202,a,95,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=36. Generated=747. Kept=196. proofs=1. Usable=28. Sos=120. Demods=23. Denials=0. Limbo=25, Disabled=28. Hints=0. Weight_deleted=122. Literals_deleted=0. Forward_subsumed=429. Back_subsumed=12. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=25 (1 lex), Back_demodulated=10. Back_unit_deleted=0. Demod_attempts=11058. Demod_rewrites=622. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=1248. Nonunit_bsub_feature_tests=381. Megabytes=0.23. User_CPU=0.02, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 13131 exit (max_proofs) Mon Jun 19 16:41:41 2006