TSTP Solution File: GRP442-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP442-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 11:19:07 EDT 2022
% Result : Unsatisfiable 0.70s 1.06s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP442-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:00:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.06 ============================== Prover9 ===============================
% 0.70/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.06 Process 11295 was started by sandbox2 on n010.cluster.edu,
% 0.70/1.06 Mon Jun 13 13:00:25 2022
% 0.70/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11142_n010.cluster.edu".
% 0.70/1.06 ============================== end of head ===========================
% 0.70/1.06
% 0.70/1.06 ============================== INPUT =================================
% 0.70/1.06
% 0.70/1.06 % Reading from file /tmp/Prover9_11142_n010.cluster.edu
% 0.70/1.06
% 0.70/1.06 set(prolog_style_variables).
% 0.70/1.06 set(auto2).
% 0.70/1.06 % set(auto2) -> set(auto).
% 0.70/1.06 % set(auto) -> set(auto_inference).
% 0.70/1.06 % set(auto) -> set(auto_setup).
% 0.70/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.06 % set(auto) -> set(auto_limits).
% 0.70/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.06 % set(auto) -> set(auto_denials).
% 0.70/1.06 % set(auto) -> set(auto_process).
% 0.70/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.06 % set(auto2) -> assign(stats, some).
% 0.70/1.06 % set(auto2) -> clear(echo_input).
% 0.70/1.06 % set(auto2) -> set(quiet).
% 0.70/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.06 % set(auto2) -> clear(print_given).
% 0.70/1.06 assign(lrs_ticks,-1).
% 0.70/1.06 assign(sos_limit,10000).
% 0.70/1.06 assign(order,kbo).
% 0.70/1.06 set(lex_order_vars).
% 0.70/1.06 clear(print_given).
% 0.70/1.06
% 0.70/1.06 % formulas(sos). % not echoed (2 formulas)
% 0.70/1.06
% 0.70/1.06 ============================== end of input ==========================
% 0.70/1.06
% 0.70/1.06 % From the command line: assign(max_seconds, 300).
% 0.70/1.06
% 0.70/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.06
% 0.70/1.06 % Formulas that are not ordinary clauses:
% 0.70/1.06
% 0.70/1.06 ============================== end of process non-clausal formulas ===
% 0.70/1.06
% 0.70/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.06
% 0.70/1.06 ============================== PREDICATE ELIMINATION =================
% 0.70/1.06
% 0.70/1.06 ============================== end predicate elimination =============
% 0.70/1.06
% 0.70/1.06 Auto_denials:
% 0.70/1.06 % copying label prove_these_axioms_1 to answer in negative clause
% 0.70/1.06
% 0.70/1.06 Term ordering decisions:
% 0.70/1.06
% 0.70/1.06 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.70/1.06 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 0.70/1.06
% 0.70/1.06 ============================== end of process initial clauses ========
% 0.70/1.06
% 0.70/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.06
% 0.70/1.06 ============================== end of clauses for search =============
% 0.70/1.06
% 0.70/1.06 ============================== SEARCH ================================
% 0.70/1.06
% 0.70/1.06 % Starting search at 0.01 seconds.
% 0.70/1.06
% 0.70/1.06 ============================== PROOF =================================
% 0.70/1.06 % SZS status Unsatisfiable
% 0.70/1.06 % SZS output start Refutation
% 0.70/1.06
% 0.70/1.06 % Proof 1 at 0.10 (+ 0.00) seconds: prove_these_axioms_1.
% 0.70/1.06 % Length of proof is 55.
% 0.70/1.06 % Level of proof is 20.
% 0.70/1.06 % Maximum clause weight is 39.000.
% 0.70/1.06 % Given clauses 29.
% 0.70/1.06
% 0.70/1.06 1 inverse(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B))))))) = D # label(single_axiom) # label(axiom). [assumption].
% 0.70/1.06 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 0.70/1.06 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 0.70/1.06 5 inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,A)))),multiply(multiply(E,inverse(E)),C)))) = D. [para(1(a,1),1(a,1,1,2,2,2))].
% 0.70/1.06 13 inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))),multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(F,inverse(F)),C)))) = D. [para(5(a,1),1(a,1,1,2,2,2))].
% 0.70/1.06 21 multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))) = inverse(multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(multiply(F,inverse(F)),C),multiply(multiply(V6,inverse(V6)),D)))). [para(5(a,1),5(a,1,1,2,1,2)),flip(a)].
% 0.70/1.06 75 multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,C)))) = D. [para(21(a,2),13(a,1))].
% 0.70/1.06 100 multiply(multiply(A,inverse(A)),B) = multiply(multiply(C,inverse(C)),B). [para(5(a,1),75(a,1,2,1,1)),rewrite([1(11)])].
% 0.70/1.06 152 inverse(multiply(A,multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),inverse(multiply(E,multiply(A,B))))))) = E. [para(100(a,1),1(a,1,1,2,2,1))].
% 0.70/1.06 154 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(100(a,1),1(a,1,1,2,2,2,1)),rewrite([1(11)])].
% 0.70/1.06 181 multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))) = inverse(multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(multiply(F,inverse(F)),C),multiply(multiply(multiply(V6,inverse(V6)),inverse(multiply(V7,inverse(V7)))),D)))). [para(100(a,1),21(a,2,1,2,2,1))].
% 0.70/1.06 182 multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(inverse(multiply(C,inverse(C))),D)))) = inverse(multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(F,inverse(F)),multiply(multiply(V6,inverse(V6)),D)))). [para(100(a,1),21(a,2,1,2))].
% 0.70/1.06 185 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,D)))) = E. [para(100(a,1),75(a,1,1))].
% 0.70/1.06 199 multiply(A,inverse(A)) = c_0. [new_symbol(154)].
% 0.70/1.06 212 multiply(c_0,inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,B)))) = C. [back_rewrite(185),rewrite([199(2),199(3),199(4)])].
% 0.70/1.06 215 inverse(multiply(multiply(c_0,A),multiply(c_0,multiply(c_0,B)))) = multiply(c_0,inverse(multiply(A,multiply(inverse(c_0),B)))). [back_rewrite(182),rewrite([199(2),199(3),199(9),199(11),199(12)]),flip(a)].
% 0.70/1.06 216 inverse(multiply(multiply(c_0,A),multiply(multiply(c_0,B),multiply(c_0,C)))) = multiply(c_0,inverse(multiply(A,multiply(B,C)))). [back_rewrite(181),rewrite([199(2),199(7),199(9),199(11),199(12),199(13)]),flip(a)].
% 0.70/1.06 231 inverse(multiply(A,multiply(B,multiply(c_0,inverse(multiply(C,multiply(A,B))))))) = C. [back_rewrite(152),rewrite([199(2),199(3),199(4)])].
% 0.70/1.06 249 multiply(c_0,inverse(multiply(inverse(multiply(A,c_0)),multiply(A,B)))) = inverse(B). [para(199(a,1),212(a,1,2,1,1,1,2))].
% 0.70/1.06 251 multiply(c_0,inverse(multiply(inverse(multiply(A,c_0)),c_0))) = inverse(inverse(A)). [para(199(a,1),249(a,1,2,1,2))].
% 0.70/1.06 284 inverse(multiply(A,multiply(inverse(A),multiply(c_0,inverse(multiply(B,c_0)))))) = B. [para(199(a,1),231(a,1,1,2,2,2,1,2))].
% 0.70/1.06 292 multiply(multiply(A,multiply(inverse(A),multiply(c_0,inverse(multiply(B,c_0))))),B) = c_0. [para(284(a,1),199(a,1,2))].
% 0.70/1.06 293 inverse(multiply(A,multiply(inverse(A),inverse(inverse(B))))) = inverse(multiply(B,c_0)). [para(251(a,1),284(a,1,1,2,2))].
% 0.70/1.06 326 multiply(c_0,inverse(multiply(inverse(c_0),c_0))) = inverse(c_0). [para(292(a,1),251(a,1,2,1,1,1)),rewrite([284(17)])].
% 0.70/1.06 328 multiply(A,multiply(inverse(A),multiply(c_0,inverse(multiply(multiply(B,C),c_0))))) = inverse(multiply(B,multiply(C,c_0))). [para(292(a,1),231(a,1,1,2,2,2,1)),rewrite([199(4)]),flip(a)].
% 0.70/1.06 334 inverse(multiply(A,multiply(inverse(A),inverse(c_0)))) = inverse(c_0). [para(292(a,1),293(a,2,1)),rewrite([284(11)])].
% 0.70/1.06 337 multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(c_0))),multiply(A,c_0)))) = inverse(multiply(inverse(c_0),c_0)). [para(326(a,1),212(a,1,2,1,1,1,2))].
% 0.70/1.06 345 inverse(multiply(inverse(A),multiply(inverse(c_0),c_0))) = A. [para(334(a,1),231(a,1,1,2,2,2)),rewrite([199(7)])].
% 0.70/1.06 370 multiply(multiply(multiply(multiply(c_0,A),multiply(c_0,multiply(c_0,B))),multiply(multiply(c_0,inverse(multiply(A,multiply(inverse(c_0),B)))),multiply(c_0,inverse(multiply(C,c_0))))),C) = c_0. [para(215(a,1),292(a,1,1,2,1))].
% 0.70/1.06 375 multiply(c_0,multiply(inverse(c_0),multiply(c_0,A))) = A. [para(345(a,1),212(a,1,2))].
% 0.70/1.06 376 multiply(c_0,multiply(inverse(c_0),c_0)) = inverse(c_0). [para(345(a,1),249(a,1,2))].
% 0.70/1.06 380 multiply(A,multiply(inverse(A),multiply(c_0,inverse(multiply(B,c_0))))) = inverse(multiply(B,multiply(inverse(c_0),c_0))). [para(284(a,1),345(a,1,1,1)),flip(a)].
% 0.70/1.06 384 multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,c_0). [para(293(a,1),345(a,1,1,1)),rewrite([345(9)]),flip(a)].
% 0.70/1.06 387 multiply(A,multiply(inverse(A),inverse(c_0))) = c_0. [para(334(a,1),345(a,1,1,1)),rewrite([345(8)]),flip(a)].
% 0.70/1.06 388 inverse(multiply(multiply(c_0,inverse(multiply(A,multiply(inverse(c_0),B)))),multiply(inverse(c_0),c_0))) = multiply(multiply(c_0,A),multiply(c_0,multiply(c_0,B))). [para(215(a,1),345(a,1,1,1))].
% 0.70/1.06 389 inverse(multiply(A,multiply(inverse(c_0),c_0))) = multiply(inverse(A),multiply(inverse(c_0),c_0)). [para(345(a,1),345(a,1,1,1))].
% 0.70/1.06 394 multiply(inverse(multiply(A,B)),multiply(inverse(c_0),c_0)) = inverse(multiply(A,multiply(B,c_0))). [back_rewrite(328),rewrite([380(9),389(7)])].
% 0.70/1.06 396 inverse(multiply(c_0,multiply(inverse(multiply(A,multiply(inverse(c_0),B))),c_0))) = multiply(multiply(c_0,A),multiply(c_0,multiply(c_0,B))). [back_rewrite(388),rewrite([389(13),394(13)])].
% 0.70/1.06 398 multiply(A,multiply(inverse(A),multiply(c_0,inverse(multiply(B,c_0))))) = multiply(inverse(B),multiply(inverse(c_0),c_0)). [back_rewrite(380),rewrite([389(14)])].
% 0.70/1.06 400 inverse(multiply(inverse(c_0),c_0)) = multiply(inverse(c_0),c_0). [para(376(a,1),212(a,1,2,1,1,1,2)),rewrite([337(10)])].
% 0.70/1.06 410 multiply(inverse(A),inverse(c_0)) = inverse(A). [para(387(a,1),212(a,1,2,1,1,1,2)),rewrite([249(8)]),flip(a)].
% 0.70/1.06 433 inverse(multiply(multiply(c_0,A),multiply(inverse(c_0),multiply(c_0,B)))) = multiply(c_0,inverse(multiply(A,multiply(multiply(inverse(c_0),c_0),B)))). [para(376(a,1),216(a,1,1,2,1))].
% 0.70/1.06 442 inverse(multiply(inverse(multiply(A,c_0)),c_0)) = multiply(A,c_0). [para(251(a,1),375(a,1,2,2)),rewrite([384(7)]),flip(a)].
% 0.70/1.06 448 multiply(inverse(c_0),c_0) = c_0. [para(376(a,1),375(a,1,2,2)),rewrite([410(6),199(4)]),flip(a)].
% 0.70/1.06 452 multiply(inverse(c_0),multiply(c_0,A)) = multiply(c_0,multiply(inverse(c_0),A)). [para(375(a,1),375(a,1,2,2)),flip(a)].
% 0.70/1.06 457 multiply(c_0,multiply(A,c_0)) = inverse(inverse(A)). [back_rewrite(251),rewrite([442(7)])].
% 0.70/1.06 475 inverse(multiply(multiply(c_0,A),multiply(c_0,multiply(inverse(c_0),B)))) = multiply(c_0,inverse(multiply(A,multiply(c_0,B)))). [back_rewrite(433),rewrite([452(7),448(14)])].
% 0.70/1.06 483 inverse(c_0) = c_0. [back_rewrite(400),rewrite([448(4),448(6)])].
% 0.70/1.06 485 multiply(A,multiply(inverse(A),multiply(c_0,inverse(multiply(B,c_0))))) = multiply(inverse(B),multiply(c_0,c_0)). [back_rewrite(398),rewrite([483(11)])].
% 0.70/1.06 507 multiply(multiply(c_0,A),multiply(c_0,multiply(c_0,B))) = inverse(inverse(inverse(inverse(multiply(A,multiply(c_0,B)))))). [back_rewrite(396),rewrite([483(3),457(8)]),flip(a)].
% 0.70/1.06 516 multiply(c_0,inverse(multiply(A,multiply(c_0,B)))) = inverse(inverse(inverse(inverse(inverse(multiply(A,multiply(c_0,B))))))). [back_rewrite(475),rewrite([483(5),507(7)]),flip(a)].
% 0.70/1.06 523 multiply(c_0,c_0) = c_0. [back_rewrite(448),rewrite([483(2)])].
% 0.70/1.06 532 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(410),rewrite([483(3)])].
% 0.70/1.06 534 multiply(inverse(A),A) = c_0. [back_rewrite(370),rewrite([507(7),483(10),516(13),485(22),523(4),532(3)])].
% 0.70/1.06 566 $F # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([534(4),534(5)]),xx(a)].
% 0.70/1.06
% 0.70/1.06 % SZS output end Refutation
% 0.70/1.06 ============================== end of proof ==========================
% 0.70/1.06
% 0.70/1.06 ============================== STATISTICS ============================
% 0.70/1.06
% 0.70/1.06 Given=29. Generated=1124. Kept=564. proofs=1.
% 0.70/1.06 Usable=2. Sos=51. Demods=83. Limbo=32, Disabled=481. Hints=0.
% 0.70/1.06 Megabytes=0.85.
% 0.70/1.06 User_CPU=0.10, System_CPU=0.00, Wall_clock=0.
% 0.70/1.06
% 0.70/1.06 ============================== end of statistics =====================
% 0.70/1.06
% 0.70/1.06 ============================== end of search =========================
% 0.70/1.06
% 0.70/1.06 THEOREM PROVED
% 0.70/1.06 % SZS status Unsatisfiable
% 0.70/1.06
% 0.70/1.06 Exiting with 1 proof.
% 0.70/1.06
% 0.70/1.06 Process 11295 exit (max_proofs) Mon Jun 13 13:00:25 2022
% 0.70/1.06 Prover9 interrupted
%------------------------------------------------------------------------------