TSTP Solution File: GRP601-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP601-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 11:19:47 EDT 2022
% Result : Unsatisfiable 0.74s 1.05s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP601-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 21:22:38 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.74/1.05 ============================== Prover9 ===============================
% 0.74/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.05 Process 24316 was started by sandbox on n028.cluster.edu,
% 0.74/1.05 Mon Jun 13 21:22:38 2022
% 0.74/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24163_n028.cluster.edu".
% 0.74/1.05 ============================== end of head ===========================
% 0.74/1.05
% 0.74/1.05 ============================== INPUT =================================
% 0.74/1.05
% 0.74/1.05 % Reading from file /tmp/Prover9_24163_n028.cluster.edu
% 0.74/1.05
% 0.74/1.05 set(prolog_style_variables).
% 0.74/1.05 set(auto2).
% 0.74/1.05 % set(auto2) -> set(auto).
% 0.74/1.05 % set(auto) -> set(auto_inference).
% 0.74/1.05 % set(auto) -> set(auto_setup).
% 0.74/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.05 % set(auto) -> set(auto_limits).
% 0.74/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.05 % set(auto) -> set(auto_denials).
% 0.74/1.05 % set(auto) -> set(auto_process).
% 0.74/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.05 % set(auto2) -> assign(stats, some).
% 0.74/1.05 % set(auto2) -> clear(echo_input).
% 0.74/1.05 % set(auto2) -> set(quiet).
% 0.74/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.05 % set(auto2) -> clear(print_given).
% 0.74/1.05 assign(lrs_ticks,-1).
% 0.74/1.05 assign(sos_limit,10000).
% 0.74/1.05 assign(order,kbo).
% 0.74/1.05 set(lex_order_vars).
% 0.74/1.05 clear(print_given).
% 0.74/1.05
% 0.74/1.05 % formulas(sos). % not echoed (3 formulas)
% 0.74/1.05
% 0.74/1.05 ============================== end of input ==========================
% 0.74/1.05
% 0.74/1.05 % From the command line: assign(max_seconds, 300).
% 0.74/1.05
% 0.74/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.05
% 0.74/1.05 % Formulas that are not ordinary clauses:
% 0.74/1.05
% 0.74/1.05 ============================== end of process non-clausal formulas ===
% 0.74/1.05
% 0.74/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.05
% 0.74/1.05 ============================== PREDICATE ELIMINATION =================
% 0.74/1.05
% 0.74/1.05 ============================== end predicate elimination =============
% 0.74/1.05
% 0.74/1.05 Auto_denials:
% 0.74/1.05 % copying label prove_these_axioms_1 to answer in negative clause
% 0.74/1.05
% 0.74/1.05 Term ordering decisions:
% 0.74/1.05
% 0.74/1.05 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.74/1.05 Function symbol KB weights: a1=1. b1=1. double_divide=1. multiply=1. inverse=0.
% 0.74/1.05
% 0.74/1.05 ============================== end of process initial clauses ========
% 0.74/1.05
% 0.74/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.05
% 0.74/1.05 ============================== end of clauses for search =============
% 0.74/1.05
% 0.74/1.05 ============================== SEARCH ================================
% 0.74/1.05
% 0.74/1.05 % Starting search at 0.01 seconds.
% 0.74/1.05
% 0.74/1.05 ============================== PROOF =================================
% 0.74/1.05 % SZS status Unsatisfiable
% 0.74/1.05 % SZS output start Refutation
% 0.74/1.05
% 0.74/1.05 % Proof 1 at 0.06 (+ 0.00) seconds: prove_these_axioms_1.
% 0.74/1.05 % Length of proof is 59.
% 0.74/1.05 % Level of proof is 24.
% 0.74/1.05 % Maximum clause weight is 28.000.
% 0.74/1.05 % Given clauses 15.
% 0.74/1.05
% 0.74/1.05 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.74/1.05 2 inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.74/1.05 3 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.74/1.05 4 inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) # answer(prove_these_axioms_1). [copy(3),rewrite([1(4),1(9)]),flip(a)].
% 0.74/1.05 5 inverse(double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,D)))))) = inverse(double_divide(inverse(double_divide(C,B)),D)). [para(2(a,1),2(a,1,1,1,1,2)),flip(a)].
% 0.74/1.05 6 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B. [para(5(a,1),2(a,1,1,1))].
% 0.74/1.05 7 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(C,D))))),B))) = D. [para(2(a,1),6(a,1,1,1,1,1))].
% 0.74/1.05 8 inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),D)),double_divide(E,D))) = inverse(double_divide(B,double_divide(E,double_divide(A,C)))). [para(5(a,1),6(a,1,1,1,1,1))].
% 0.74/1.05 11 inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C. [para(6(a,1),6(a,1,1,1))].
% 0.74/1.05 14 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)). [para(11(a,1),6(a,1,1,1,1,1))].
% 0.74/1.05 17 inverse(double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,C)),double_divide(C,double_divide(B,D)))) = D. [para(11(a,1),11(a,1,1,2,1))].
% 0.74/1.05 20 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(inverse(double_divide(C,D)),double_divide(C,E)),B))) = double_divide(E,double_divide(D,A)). [para(17(a,1),6(a,1,1,1,1,1))].
% 0.74/1.05 43 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,inverse(double_divide(D,double_divide(C,E))))))) = inverse(double_divide(D,double_divide(B,E))). [para(2(a,1),14(a,1,1,1)),flip(a)].
% 0.74/1.05 51 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C. [para(14(a,1),6(a,1))].
% 0.74/1.05 55 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(inverse(double_divide(C,D)),E)))) = inverse(double_divide(D,double_divide(B,double_divide(C,E)))). [para(6(a,1),14(a,1,1,1)),flip(a)].
% 0.74/1.05 61 inverse(double_divide(A,double_divide(B,double_divide(inverse(double_divide(C,D)),double_divide(C,A))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)). [para(11(a,1),14(a,1,1,1))].
% 0.74/1.05 68 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,double_divide(D,E)),B))) = double_divide(E,double_divide(double_divide(inverse(double_divide(F,D)),double_divide(F,C)),A)). [para(17(a,1),14(a,2,1))].
% 0.74/1.05 76 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(inverse(double_divide(A,inverse(inverse(double_divide(inverse(double_divide(D,E)),double_divide(B,E)))))),C))) = D. [para(14(a,2),7(a,1,1,2,1,1,2,1))].
% 0.74/1.05 82 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,D),B))) = double_divide(double_divide(inverse(double_divide(E,C)),double_divide(E,F)),double_divide(inverse(double_divide(F,D)),A)). [para(14(a,1),14(a,2,1))].
% 0.74/1.05 85 inverse(inverse(double_divide(inverse(double_divide(A,B)),double_divide(A,B)))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)). [para(14(a,2),14(a,1,1))].
% 0.74/1.05 95 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))). [para(51(a,1),6(a,1,1,1,1,1,1))].
% 0.74/1.05 114 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,D)),inverse(double_divide(A,E)))),B))) = double_divide(C,inverse(double_divide(D,E))). [para(51(a,1),7(a,1,1,2,1,1,2,1,2))].
% 0.74/1.05 115 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)). [para(51(a,1),7(a,1,1,2,1,1,2,1)),rewrite([95(10)])].
% 0.74/1.05 128 inverse(inverse(double_divide(A,double_divide(B,A)))) = B. [back_rewrite(76),rewrite([95(15),115(10),115(6)])].
% 0.74/1.05 137 inverse(inverse(double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,C)))))) = inverse(double_divide(A,D)). [para(14(a,2),128(a,1,1,1,2))].
% 0.74/1.05 139 inverse(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),C))) = inverse(double_divide(A,B)). [para(51(a,1),128(a,1,1,1,2))].
% 0.74/1.05 140 inverse(inverse(A)) = A. [para(51(a,1),128(a,1,1,1))].
% 0.74/1.05 141 double_divide(double_divide(A,inverse(double_divide(B,C))),C) = inverse(double_divide(A,B)). [back_rewrite(139),rewrite([140(6)])].
% 0.74/1.05 143 double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,C)))) = inverse(double_divide(A,D)). [back_rewrite(137),rewrite([140(9)])].
% 0.74/1.05 150 double_divide(A,double_divide(B,A)) = B. [back_rewrite(128),rewrite([140(4)])].
% 0.74/1.05 153 double_divide(inverse(double_divide(A,B)),double_divide(A,B)) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)). [back_rewrite(85),rewrite([140(6)])].
% 0.74/1.05 181 inverse(double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,D)))))) = inverse(double_divide(A,double_divide(B,double_divide(inverse(double_divide(F,E)),double_divide(F,C))))). [para(14(a,2),8(a,2,1,2,2)),rewrite([8(12)]),flip(a)].
% 0.74/1.05 186 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(C,B))) = inverse(double_divide(D,double_divide(C,double_divide(E,double_divide(E,inverse(double_divide(D,A))))))). [para(51(a,1),8(a,1,1,1,1,1,1))].
% 0.74/1.05 189 double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,C)),inverse(double_divide(B,D)))))) = inverse(double_divide(C,D)). [para(51(a,1),8(a,2,1,2)),rewrite([95(13)])].
% 0.74/1.05 196 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,D),B))) = double_divide(inverse(C),double_divide(D,A)). [para(150(a,1),14(a,2,1,1))].
% 0.74/1.05 199 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(C))) = double_divide(C,B). [para(150(a,1),51(a,1,2,2,1))].
% 0.74/1.05 200 double_divide(double_divide(A,B),A) = B. [para(150(a,1),150(a,1,2))].
% 0.74/1.05 204 double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,C)),double_divide(inverse(double_divide(C,D)),E)) = double_divide(inverse(B),double_divide(D,E)). [back_rewrite(82),rewrite([196(6)]),flip(a)].
% 0.74/1.05 207 double_divide(A,double_divide(double_divide(inverse(double_divide(B,C)),double_divide(B,D)),E)) = double_divide(inverse(D),double_divide(double_divide(C,A),E)). [back_rewrite(68),rewrite([196(7)]),flip(a)].
% 0.74/1.05 209 inverse(double_divide(inverse(A),inverse(double_divide(B,C)))) = double_divide(A,double_divide(B,C)). [back_rewrite(20),rewrite([207(8),141(5)])].
% 0.74/1.05 221 inverse(double_divide(A,double_divide(B,double_divide(C,D)))) = double_divide(double_divide(inverse(double_divide(C,A)),D),B). [back_rewrite(55),rewrite([199(8)]),flip(a)].
% 0.74/1.05 222 double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,C)))),D) = inverse(double_divide(B,double_divide(D,C))). [back_rewrite(43),rewrite([199(9)])].
% 0.74/1.05 225 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))). [back_rewrite(114),rewrite([209(8),196(8),200(4)])].
% 0.74/1.05 246 inverse(double_divide(A,double_divide(B,inverse(double_divide(A,C))))) = inverse(double_divide(inverse(C),inverse(B))). [back_rewrite(186),rewrite([225(5),150(3),221(11),225(10),222(11)]),flip(a)].
% 0.74/1.05 249 double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,D)))))),E) = inverse(double_divide(B,double_divide(E,inverse(double_divide(D,inverse(C)))))). [back_rewrite(181),rewrite([225(4),150(2),225(10),221(13),225(12)]),flip(a)].
% 0.74/1.05 263 double_divide(A,inverse(double_divide(B,double_divide(A,C)))) = inverse(double_divide(C,inverse(B))). [back_rewrite(61),rewrite([225(4),221(7),225(6),249(7),246(6),140(2),225(7)]),flip(a)].
% 0.74/1.05 278 inverse(double_divide(A,double_divide(B,double_divide(C,D)))) = double_divide(double_divide(C,inverse(double_divide(A,D))),B). [back_rewrite(221),rewrite([225(7)])].
% 0.74/1.05 285 inverse(double_divide(A,inverse(double_divide(B,C)))) = double_divide(inverse(C),double_divide(A,B)). [back_rewrite(204),rewrite([225(4),263(4),225(6),225(7),263(7),140(4),225(3)])].
% 0.74/1.05 288 inverse(double_divide(inverse(A),inverse(B))) = double_divide(A,B). [back_rewrite(199),rewrite([225(5),263(5)])].
% 0.74/1.05 292 inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)). [back_rewrite(189),rewrite([225(5),285(4),278(6),150(3),150(5)]),flip(a)].
% 0.74/1.05 304 double_divide(double_divide(inverse(A),inverse(B)),double_divide(B,A)) = double_divide(double_divide(inverse(C),inverse(D)),double_divide(D,C)). [back_rewrite(153),rewrite([292(2),292(7)])].
% 0.74/1.05 305 double_divide(double_divide(A,B),double_divide(double_divide(inverse(C),inverse(D)),double_divide(B,C))) = double_divide(inverse(D),inverse(A)). [back_rewrite(143),rewrite([292(3),292(7),292(3),292(8),140(6),140(6),292(9)])].
% 0.74/1.05 376 double_divide(A,B) = double_divide(B,A). [back_rewrite(288),rewrite([292(4),140(2),140(2)])].
% 0.74/1.05 379 double_divide(double_divide(A,B),inverse(C)) = double_divide(inverse(B),double_divide(C,A)). [back_rewrite(285),rewrite([292(2),376(3),292(5),292(4),140(2),140(2),376(1)])].
% 0.74/1.05 381 double_divide(double_divide(A,inverse(B)),double_divide(C,D)) = double_divide(B,double_divide(A,double_divide(inverse(C),inverse(D)))). [back_rewrite(278),rewrite([292(4),292(3),292(2),376(3),379(5),140(2),379(5),292(3),140(2),292(6),376(7),376(9)])].
% 0.74/1.05 390 double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) # answer(prove_these_axioms_1). [back_rewrite(4),rewrite([292(5),140(3),292(9),140(7)])].
% 0.74/1.05 409 double_divide(double_divide(A,B),double_divide(C,inverse(B))) = double_divide(inverse(A),inverse(C)). [back_rewrite(305),rewrite([381(6),150(6),376(7)])].
% 0.74/1.05 429 double_divide(A,inverse(A)) = double_divide(B,inverse(B)). [back_rewrite(304),rewrite([376(4),376(5),409(5),140(3),376(2),376(6),376(7),409(7),140(5),376(4)])].
% 0.74/1.05 430 $F # answer(prove_these_axioms_1). [resolve(429,a,390,a)].
% 0.74/1.05
% 0.74/1.05 % SZS output end Refutation
% 0.74/1.05 ============================== end of proof ==========================
% 0.74/1.05
% 0.74/1.05 ============================== STATISTICS ============================
% 0.74/1.05
% 0.74/1.05 Given=15. Generated=633. Kept=428. proofs=1.
% 0.74/1.05 Usable=2. Sos=29. Demods=67. Limbo=57, Disabled=342. Hints=0.
% 0.74/1.05 Megabytes=0.46.
% 0.74/1.05 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.74/1.05
% 0.74/1.05 ============================== end of statistics =====================
% 0.74/1.05
% 0.74/1.05 ============================== end of search =========================
% 0.74/1.05
% 0.74/1.05 THEOREM PROVED
% 0.74/1.05 % SZS status Unsatisfiable
% 0.74/1.05
% 0.74/1.05 Exiting with 1 proof.
% 0.74/1.05
% 0.74/1.05 Process 24316 exit (max_proofs) Mon Jun 13 21:22:38 2022
% 0.74/1.05 Prover9 interrupted
%------------------------------------------------------------------------------