TSTP Solution File: GRP777-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP777-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:21:01 EDT 2022
% Result : Unsatisfiable 1.37s 1.66s
% Output : Refutation 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : GRP777-10 : TPTP v8.1.0. Released v8.1.0.
% 0.09/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 03:49:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.37/1.66 ============================== Prover9 ===============================
% 1.37/1.66 Prover9 (32) version 2009-11A, November 2009.
% 1.37/1.66 Process 21315 was started by sandbox on n007.cluster.edu,
% 1.37/1.66 Tue Jun 14 03:49:25 2022
% 1.37/1.66 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21161_n007.cluster.edu".
% 1.37/1.66 ============================== end of head ===========================
% 1.37/1.66
% 1.37/1.66 ============================== INPUT =================================
% 1.37/1.66
% 1.37/1.66 % Reading from file /tmp/Prover9_21161_n007.cluster.edu
% 1.37/1.66
% 1.37/1.66 set(prolog_style_variables).
% 1.37/1.66 set(auto2).
% 1.37/1.66 % set(auto2) -> set(auto).
% 1.37/1.66 % set(auto) -> set(auto_inference).
% 1.37/1.66 % set(auto) -> set(auto_setup).
% 1.37/1.66 % set(auto_setup) -> set(predicate_elim).
% 1.37/1.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.37/1.66 % set(auto) -> set(auto_limits).
% 1.37/1.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.37/1.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.37/1.66 % set(auto) -> set(auto_denials).
% 1.37/1.66 % set(auto) -> set(auto_process).
% 1.37/1.66 % set(auto2) -> assign(new_constants, 1).
% 1.37/1.66 % set(auto2) -> assign(fold_denial_max, 3).
% 1.37/1.66 % set(auto2) -> assign(max_weight, "200.000").
% 1.37/1.66 % set(auto2) -> assign(max_hours, 1).
% 1.37/1.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.37/1.66 % set(auto2) -> assign(max_seconds, 0).
% 1.37/1.66 % set(auto2) -> assign(max_minutes, 5).
% 1.37/1.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.37/1.66 % set(auto2) -> set(sort_initial_sos).
% 1.37/1.66 % set(auto2) -> assign(sos_limit, -1).
% 1.37/1.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.37/1.66 % set(auto2) -> assign(max_megs, 400).
% 1.37/1.66 % set(auto2) -> assign(stats, some).
% 1.37/1.66 % set(auto2) -> clear(echo_input).
% 1.37/1.66 % set(auto2) -> set(quiet).
% 1.37/1.66 % set(auto2) -> clear(print_initial_clauses).
% 1.37/1.66 % set(auto2) -> clear(print_given).
% 1.37/1.66 assign(lrs_ticks,-1).
% 1.37/1.66 assign(sos_limit,10000).
% 1.37/1.66 assign(order,kbo).
% 1.37/1.66 set(lex_order_vars).
% 1.37/1.66 clear(print_given).
% 1.37/1.66
% 1.37/1.66 % formulas(sos). % not echoed (10 formulas)
% 1.37/1.66
% 1.37/1.66 ============================== end of input ==========================
% 1.37/1.66
% 1.37/1.66 % From the command line: assign(max_seconds, 300).
% 1.37/1.66
% 1.37/1.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.37/1.66
% 1.37/1.66 % Formulas that are not ordinary clauses:
% 1.37/1.66
% 1.37/1.66 ============================== end of process non-clausal formulas ===
% 1.37/1.66
% 1.37/1.66 ============================== PROCESS INITIAL CLAUSES ===============
% 1.37/1.66
% 1.37/1.66 ============================== PREDICATE ELIMINATION =================
% 1.37/1.66
% 1.37/1.66 ============================== end predicate elimination =============
% 1.37/1.66
% 1.37/1.66 Auto_denials:
% 1.37/1.66 % copying label goal to answer in negative clause
% 1.37/1.66
% 1.37/1.66 Term ordering decisions:
% 1.37/1.66 Function symbol KB weights: a=1. b=1. c=1. x0=1. product=1. difference=1. quotient=1. bigC=1.
% 1.37/1.66
% 1.37/1.66 ============================== end of process initial clauses ========
% 1.37/1.66
% 1.37/1.66 ============================== CLAUSES FOR SEARCH ====================
% 1.37/1.66
% 1.37/1.66 ============================== end of clauses for search =============
% 1.37/1.66
% 1.37/1.66 ============================== SEARCH ================================
% 1.37/1.66
% 1.37/1.66 % Starting search at 0.01 seconds.
% 1.37/1.66
% 1.37/1.66 ============================== PROOF =================================
% 1.37/1.66 % SZS status Unsatisfiable
% 1.37/1.66 % SZS output start Refutation
% 1.37/1.66
% 1.37/1.66 % Proof 1 at 0.64 (+ 0.02) seconds: goal.
% 1.37/1.66 % Length of proof is 83.
% 1.37/1.66 % Level of proof is 22.
% 1.37/1.66 % Maximum clause weight is 23.000.
% 1.37/1.66 % Given clauses 130.
% 1.37/1.66
% 1.37/1.66 1 product(A,A) = A # label(sos06) # label(axiom). [assumption].
% 1.37/1.66 2 difference(A,product(A,B)) = B # label(sos01) # label(axiom). [assumption].
% 1.37/1.66 3 product(A,difference(A,B)) = B # label(sos02) # label(axiom). [assumption].
% 1.37/1.66 4 quotient(product(A,B),B) = A # label(sos03) # label(axiom). [assumption].
% 1.37/1.66 5 product(quotient(A,B),B) = A # label(sos04) # label(axiom). [assumption].
% 1.37/1.66 6 product(product(a,c),product(c,b)) = product(a,b) # label(sos09) # label(axiom). [assumption].
% 1.37/1.66 7 bigC(A,B,C) = product(product(A,B),product(C,A)) # label(sos08) # label(axiom). [assumption].
% 1.37/1.66 8 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom). [assumption].
% 1.37/1.66 9 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom). [assumption].
% 1.37/1.66 10 bigC(a,b,x0) != bigC(c,c,x0) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 1.37/1.66 11 product(product(a,b),product(x0,a)) != product(c,product(x0,c)) # answer(goal). [copy(10),rewrite([7(4),7(11),1(10)])].
% 1.37/1.66 14 quotient(A,difference(B,A)) = B. [para(3(a,1),4(a,1,1))].
% 1.37/1.66 15 difference(quotient(A,B),A) = B. [para(5(a,1),2(a,1,2))].
% 1.37/1.66 16 difference(product(a,c),product(a,b)) = product(c,b). [para(6(a,1),2(a,1,2))].
% 1.37/1.66 18 difference(product(product(A,B),B),B) = product(B,product(B,A)). [para(8(a,1),2(a,1,2))].
% 1.37/1.66 21 quotient(A,product(A,product(A,B))) = product(product(B,A),A). [para(8(a,1),4(a,1,1))].
% 1.37/1.66 28 product(product(A,B),product(A,C)) = product(A,product(B,C)). [para(1(a,1),9(a,1,1)),flip(a)].
% 1.37/1.66 29 product(product(A,B),product(C,B)) = product(product(A,C),B). [para(1(a,1),9(a,1,2)),flip(a)].
% 1.37/1.66 31 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)). [para(3(a,1),9(a,1,1)),flip(a)].
% 1.37/1.66 35 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B). [para(5(a,1),9(a,1,2)),flip(a)].
% 1.37/1.66 52 product(A,product(A,quotient(B,A))) = difference(product(B,A),A). [para(5(a,1),18(a,1,1,1)),flip(a)].
% 1.37/1.66 68 product(product(A,B),A) = product(A,product(B,A)). [para(1(a,1),28(a,1,2))].
% 1.37/1.66 71 product(A,product(difference(A,B),C)) = product(B,product(A,C)). [para(3(a,1),28(a,1,1)),flip(a)].
% 1.37/1.66 85 quotient(product(A,B),product(A,product(B,product(B,C)))) = product(A,product(product(C,B),B)). [para(28(a,1),21(a,1,2,2)),rewrite([28(5),28(8),28(9)])].
% 1.37/1.66 102 quotient(product(A,product(B,A)),A) = product(A,B). [para(68(a,1),4(a,1,1))].
% 1.37/1.66 112 quotient(product(A,B),A) = product(A,quotient(B,A)). [para(5(a,1),102(a,1,1,2))].
% 1.37/1.66 118 product(A,quotient(difference(A,B),A)) = quotient(B,A). [para(3(a,1),112(a,1,1)),flip(a)].
% 1.37/1.66 123 difference(product(A,quotient(B,A)),product(A,B)) = A. [para(112(a,1),15(a,1,1))].
% 1.37/1.66 127 quotient(difference(A,B),A) = difference(A,quotient(B,A)). [para(118(a,1),2(a,1,2)),flip(a)].
% 1.37/1.66 146 product(difference(A,quotient(B,A)),A) = difference(A,B). [para(127(a,1),5(a,1,1))].
% 1.37/1.66 147 difference(difference(A,quotient(B,A)),difference(A,B)) = A. [para(127(a,1),15(a,1,1))].
% 1.37/1.66 153 difference(A,product(B,A)) = product(difference(A,B),A). [para(4(a,1),146(a,1,1,2)),flip(a)].
% 1.37/1.66 159 difference(product(difference(A,B),A),A) = product(A,quotient(B,A)). [para(146(a,1),18(a,1,1,1)),rewrite([3(6)])].
% 1.37/1.66 214 quotient(product(A,B),product(difference(B,A),B)) = B. [para(153(a,1),14(a,1,2))].
% 1.37/1.66 229 difference(product(difference(A,B),A),product(B,A)) = B. [para(214(a,1),146(a,1,1,2)),rewrite([159(3),31(5),5(2),1(1)]),flip(a)].
% 1.37/1.66 230 difference(product(A,quotient(B,A)),B) = product(difference(A,B),A). [para(214(a,1),147(a,1,1,2)),rewrite([159(3),229(6)])].
% 1.37/1.66 234 product(product(difference(A,B),A),B) = product(B,A). [para(229(a,1),3(a,1,2))].
% 1.37/1.66 236 difference(difference(A,B),B) = quotient(B,A). [para(5(a,1),229(a,1,2)),rewrite([146(3)])].
% 1.37/1.66 238 product(difference(A,B),A) = product(B,quotient(A,B)). [para(229(a,1),14(a,1,2)),rewrite([112(2)]),flip(a)].
% 1.37/1.66 243 quotient(A,product(difference(B,A),B)) = product(B,quotient(A,B)). [para(229(a,1),127(a,1,1)),rewrite([214(9),159(6)])].
% 1.37/1.66 264 product(difference(A,B),quotient(B,A)) = B. [para(236(a,1),3(a,1,2))].
% 1.37/1.66 266 quotient(product(A,B),product(A,quotient(B,A))) = B. [para(123(a,1),236(a,1,1)),rewrite([2(2)]),flip(a)].
% 1.37/1.66 299 product(product(A,quotient(B,A)),B) = product(B,quotient(B,A)). [para(15(a,1),234(a,1,1,1))].
% 1.37/1.66 326 difference(difference(A,B),product(B,quotient(A,B))) = A. [para(238(a,1),2(a,1,2))].
% 1.37/1.66 327 difference(A,product(difference(B,A),B)) = quotient(B,A). [para(238(a,2),2(a,1,2))].
% 1.37/1.66 346 product(A,product(difference(B,A),B)) = difference(product(B,A),A). [para(238(a,2),18(a,2,2)),rewrite([5(2)]),flip(a)].
% 1.37/1.66 348 quotient(A,product(A,B)) = product(A,quotient(A,B)). [para(238(a,1),21(a,2,1)),rewrite([3(2),299(5)])].
% 1.37/1.66 355 product(product(A,quotient(B,A)),difference(B,A)) = product(difference(B,A),A). [para(238(a,1),68(a,1,1)),rewrite([3(7)])].
% 1.37/1.66 368 difference(A,product(B,quotient(A,B))) = product(difference(A,difference(A,B)),A). [para(238(a,1),153(a,1,2))].
% 1.37/1.66 426 product(A,product(B,quotient(A,C))) = product(product(C,B),A). [para(264(a,1),31(a,1,2)),flip(a)].
% 1.37/1.66 444 difference(difference(product(A,B),B),product(B,A)) = product(A,B). [para(4(a,1),326(a,1,2,2))].
% 1.37/1.66 458 difference(product(A,B),B) = product(difference(A,B),B). [para(326(a,1),234(a,1,1,1)),rewrite([3(2),52(3),355(6)])].
% 1.37/1.66 462 difference(product(difference(A,B),B),product(B,A)) = product(A,B). [back_rewrite(444),rewrite([458(2)])].
% 1.37/1.66 471 product(A,product(difference(B,A),B)) = product(difference(B,A),A). [back_rewrite(346),rewrite([458(5)])].
% 1.37/1.66 481 product(A,product(A,quotient(B,A))) = product(difference(B,A),A). [back_rewrite(52),rewrite([458(5)])].
% 1.37/1.66 483 difference(product(A,B),product(B,A)) = product(A,quotient(A,B)). [para(2(a,1),327(a,1,2,1)),rewrite([348(5)])].
% 1.37/1.66 484 difference(A,product(B,quotient(A,B))) = quotient(quotient(A,B),A). [para(15(a,1),327(a,1,2,1))].
% 1.37/1.66 497 product(difference(A,difference(A,B)),A) = quotient(quotient(A,B),A). [back_rewrite(368),rewrite([484(3)]),flip(a)].
% 1.37/1.66 600 product(A,quotient(A,difference(A,B))) = quotient(A,B). [para(3(a,1),348(a,1,2)),flip(a)].
% 1.37/1.66 624 product(difference(quotient(A,B),B),B) = difference(A,B). [para(5(a,1),458(a,1,1)),flip(a)].
% 1.37/1.66 638 quotient(A,product(B,A)) = product(quotient(A,B),A). [para(458(a,1),236(a,1,1)),rewrite([458(3),236(2)]),flip(a)].
% 1.37/1.66 680 quotient(A,difference(A,B)) = difference(A,quotient(A,B)). [para(600(a,1),2(a,1,2)),flip(a)].
% 1.37/1.66 690 quotient(difference(A,B),B) = difference(quotient(A,B),B). [para(624(a,1),4(a,1,1))].
% 1.37/1.66 703 product(quotient(A,quotient(B,A)),A) = quotient(A,B). [para(236(a,1),624(a,2)),rewrite([690(2),236(3)])].
% 1.37/1.66 764 product(product(difference(A,B),C),B) = product(B,product(C,A)). [para(264(a,1),35(a,1,1)),flip(a)].
% 1.37/1.66 824 quotient(quotient(A,B),A) = quotient(A,quotient(B,A)). [para(327(a,1),680(a,1,2)),rewrite([243(5),484(5)]),flip(a)].
% 1.37/1.66 856 product(difference(A,difference(A,B)),A) = quotient(A,quotient(B,A)). [back_rewrite(497),rewrite([824(5)])].
% 1.37/1.66 1070 product(quotient(A,B),difference(A,B)) = product(B,A). [para(624(a,1),71(a,1,2)),rewrite([5(5)])].
% 1.37/1.66 1115 product(quotient(product(a,c),product(a,b)),product(c,b)) = product(a,product(b,c)). [para(16(a,1),1070(a,1,2)),rewrite([28(18)])].
% 1.37/1.66 1661 difference(product(A,quotient(A,B)),product(B,A)) = product(difference(A,B),B). [para(123(a,1),230(a,2,1)),rewrite([266(6),299(3),481(7)])].
% 1.37/1.66 2155 product(difference(A,product(B,C)),A) = product(C,quotient(A,B)). [para(426(a,1),2(a,1,2)),rewrite([153(3)])].
% 1.37/1.66 2714 difference(product(difference(product(A,quotient(B,C)),B),B),product(product(C,A),B)) = product(product(A,quotient(B,C)),B). [para(426(a,1),462(a,1,2))].
% 1.37/1.66 2780 product(difference(A,product(B,C)),product(B,C)) = product(product(B,C),product(C,quotient(A,B))). [para(471(a,1),29(a,2)),rewrite([2155(3),2155(6),29(7)]),flip(a)].
% 1.37/1.66 3890 product(A,quotient(product(B,C),A)) = product(difference(C,A),B). [para(764(a,1),4(a,1,1)),rewrite([112(3)])].
% 1.37/1.66 3898 product(product(difference(A,product(B,C)),B),C) = product(product(B,C),product(C,A)). [para(764(a,1),29(a,1)),flip(a)].
% 1.37/1.66 3929 product(product(difference(A,B),C),product(C,A)) = product(product(C,A),quotient(product(C,A),B)). [para(299(a,1),764(a,2)),rewrite([3890(3),3890(7),29(7),3898(6)])].
% 1.37/1.66 3945 product(difference(product(A,B),C),C) = product(C,product(difference(B,C),A)). [para(764(a,1),462(a,1,2)),rewrite([2780(6),14(4),3929(4),1661(7)])].
% 1.37/1.66 4087 product(product(A,quotient(B,C)),B) = product(B,quotient(B,product(C,A))). [back_rewrite(2714),rewrite([3945(4),15(2),483(5)]),flip(a)].
% 1.37/1.66 5358 quotient(product(A,B),product(A,C)) = product(A,quotient(B,C)). [para(856(a,1),85(a,2,2,1)),rewrite([3(4),3(3),703(6)])].
% 1.37/1.66 5472 product(product(a,c),c) = product(a,product(b,c)). [back_rewrite(1115),rewrite([5358(7),35(9)])].
% 1.37/1.66 5580 product(c,quotient(c,a)) = product(a,b). [para(5472(a,1),112(a,1,1)),rewrite([5358(9),4(6),638(11),29(12),4087(10),1(8)]),flip(a)].
% 1.37/1.66 5689 product(product(a,b),product(A,a)) = product(c,product(A,c)). [para(5580(a,1),35(a,1,1)),rewrite([68(10)])].
% 1.37/1.66 5690 $F # answer(goal). [resolve(5689,a,11,a)].
% 1.37/1.66
% 1.37/1.66 % SZS output end Refutation
% 1.37/1.66 ============================== end of proof ==========================
% 1.37/1.66
% 1.37/1.66 ============================== STATISTICS ============================
% 1.37/1.66
% 1.37/1.66 Given=130. Generated=15504. Kept=5688. proofs=1.
% 1.37/1.66 Usable=102. Sos=3336. Demods=2914. Limbo=18, Disabled=2241. Hints=0.
% 1.37/1.66 Megabytes=7.07.
% 1.37/1.66 User_CPU=0.64, System_CPU=0.02, Wall_clock=0.
% 1.37/1.66
% 1.37/1.66 ============================== end of statistics =====================
% 1.37/1.66
% 1.37/1.66 ============================== end of search =========================
% 1.37/1.66
% 1.37/1.66 THEOREM PROVED
% 1.37/1.66 % SZS status Unsatisfiable
% 1.37/1.66
% 1.37/1.66 Exiting with 1 proof.
% 1.37/1.66
% 1.37/1.66 Process 21315 exit (max_proofs) Tue Jun 14 03:49:25 2022
% 1.37/1.66 Prover9 interrupted
%------------------------------------------------------------------------------