============================== Prover9 =============================== Prover9 (32) version June-2006C, June 2006. Process 13123 was started by mccune on cleo.thornwood, Mon Jun 19 16:41:34 2006 The command was "/home/mccune/bin/prover9 -f cs.in DN.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 DN.in clauses(sos). (x @ y) * (z @ y) = x * z @ y. end_of_list. clauses(sos). (A @ B) * C != C * (A @ B) # answer(N). 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 @ y) = x * z @ y. [input]. 6 (A @ B) * C != C * (A @ B) # answer(N). [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, *, @ ]). After inverse_order: Function symbol precedence: lex([ A, B, C, *, @ ]). 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 = (x @ z) * (y @ z). [copy(5),flip(a)]. 12 (A @ B) * C != C * (A @ B) # answer(N). [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 = (x @ z) * (y @ z). [copy(5),flip(a)]. 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=13): 11 x * y @ z = (x @ z) * (y @ z). [copy(5),flip(a)]. given #6 (I,wt=11): 12 (A @ B) * C != C * (A @ B) # answer(N). [input]. given #7 (F,wt=15): 23 (A @ B) * C * x != C * (A @ B) * x # answer(N). [ur(8,b,12,a),demod(9(6),9(12))]. given #8 (F,wt=15): 24 x * (A @ B) * C != x * C * (A @ B) # answer(N). [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): 31 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): 37 C * (A @ B) * (C @ C) != (A @ B) * C # answer(N). [para(15(a,1),23(a,1,2)),flip(a)]. given #13 (F,wt=17): 27 C * (A @ B) * (C @ (A @ B)) != C * (A @ B) # answer(N). [para(10(a,1),23(a,1)),flip(a)]. given #14 (T,wt=10): 32 x * (y @ y) != y | y = x. [para(15(a,1),8(a,1)),flip(a)]. given #15 (T,wt=10): 33 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=17): 29 (A @ B) * C * ((A @ B) @ C) != (A @ B) * C # answer(N). [para(10(a,1),23(a,2))]. given #18 (F,wt=19): 25 x * (A @ B) * C * y != x * C * (A @ B) * y # answer(N). [ur(7,b,23,a)]. given #19 (T,wt=11): 34 x * (x @ x) * y = x * y. [para(15(a,1),9(a,1,1)),flip(a)]. given #20 (T,wt=7): 67 (x @ x) * y = y. [hyper(13,a,34,a)]. 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=19): 26 C * (A @ B) * x * (x @ C) != (A @ B) * x * C # answer(N). [para(10(a,1),23(a,1,2)),flip(a)]. given #23 (F,wt=17): 89 C * (A @ B) * ((x @ x) @ C) != (A @ B) * C # answer(N). [para(67(a,1),26(a,1,2,2)),demod(67(15))]. given #24 (T,wt=6): 86 x != y | y = x. [para(15(a,1),16(a,2)),demod(67(2),75(4),15(3))]. given #25 (T,wt=9): 74 x * ((y @ y) @ x) = x. [para(67(a,1),10(a,1,2)),demod(67(5))]. 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=19): 30 x * y * (A @ B) * C != x * y * C * (A @ B) # answer(N). [ur(7,b,24,a)]. given #28 (F,wt=19): 38 (A @ B) * C * ((A @ B) @ (A @ B)) != C * (A @ B) # answer(N). [para(15(a,1),23(a,2,2))]. given #29 (T,wt=9): 81 x * (x @ x * x) = x. [hyper(16,a,9,a)]. given #30 (T,wt=9): 93 (x @ x) @ y = y @ y. [hyper(31,a,74,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=19): 49 x * C * (A @ B) * (C @ C) != x * (A @ B) * C # answer(N). [ur(7,b,37,a)]. given #33 (F,wt=19): 100 (A @ B) * C * ((x @ x) @ (A @ B)) != C * (A @ B) # answer(N). [para(74(a,1),23(a,2,2))]. given #34 (T,wt=9): 115 x @ x * x = x @ x. [hyper(31,a,81,a),flip(a)]. given #35 (T,wt=9): 119 ((x @ x) @ y) * z = z. [para(93(a,2),67(a,1,1))]. 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)]. given #37 (F,wt=15): 163 B * A * C * (A @ B) != A * B * C # answer(N). [para(19(a,1),30(a,1)),flip(a)]. given #38 (F,wt=19): 120 C * (A @ B) * (((x @ x) @ y) @ C) != (A @ B) * C # answer(N). [para(93(a,2),89(a,1,2,2,1))]. given #39 (T,wt=10): 73 x * y != y | z @ z = x. [para(67(a,1),8(a,1)),flip(a)]. NOTE: New constant: 0 x @ x = c_0. [new_symbol(173)]. NOTE: New Function symbol precedence: lex([ A, B, C, c_0, *, @ ]). given #40 (T,wt=5): 176 x @ x = c_0. [new_symbol(173)]. given #41 (A,wt=17): 20 x * y * z * (z @ x * y) = z * x * y. [para(10(a,1),9(a,1)),flip(a)]. given #42 (F,wt=19): 167 B * A * C * (A @ B) * x != A * B * C * x # answer(N). [ur(14,b,163,a),demod(9(9),9(8),9(16),9(15))]. ============================== PROOF ================================= % Proof 1 at 0.02 (+ 0.00) seconds: N. % Length of proof is 15. % Level of proof is 5. % Maximum clause weight is 19. % Given clauses 42. 5 (x @ y) * (z @ y) = x * z @ y. [input]. 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 = (x @ z) * (y @ z). [copy(5),flip(a)]. 12 (A @ B) * C != C * (A @ B) # answer(N). [input]. 14 x * y * z != u * z | x * y = u. [para(9(a,1),8(a,1))]. 19 x * y * (y @ x) * z = y * x * z. [para(10(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)]. 21 x * y * z * (y @ x) * (z @ x) = y * z * x. [para(9(a,1),10(a,1,2)),demod(11(2),9(8))]. 24 x * (A @ B) * C != x * C * (A @ B) # answer(N). [ur(7,b,12,a)]. 30 x * y * (A @ B) * C != x * y * C * (A @ B) # answer(N). [ur(7,b,24,a)]. 163 B * A * C * (A @ B) != A * B * C # answer(N). [para(19(a,1),30(a,1)),flip(a)]. 167 B * A * C * (A @ B) * x != A * B * C * x # answer(N). [ur(14,b,163,a),demod(9(9),9(8),9(16),9(15))]. 219 $F # answer(N). [para(10(a,1),167(a,2,2)),demod(21(13)),xx(a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=42. Generated=982. Kept=212. proofs=1. Usable=24. Sos=86. Demods=28. Denials=0. Limbo=4, Disabled=104. Hints=0. Weight_deleted=158. Literals_deleted=0. Forward_subsumed=611. Back_subsumed=6. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=61 (0 lex), Back_demodulated=92. Back_unit_deleted=0. Demod_attempts=14796. Demod_rewrites=1447. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=1372. Nonunit_bsub_feature_tests=792. Megabytes=0.21. User_CPU=0.02, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 13123 exit (max_proofs) Mon Jun 19 16:41:34 2006