TSTP Solution File: GRP431-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP431-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 11:19:04 EDT 2022
% Result : Unsatisfiable 0.83s 1.08s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP431-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 19:40:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.83/1.08 ============================== Prover9 ===============================
% 0.83/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.08 Process 30612 was started by sandbox on n004.cluster.edu,
% 0.83/1.08 Mon Jun 13 19:40:09 2022
% 0.83/1.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30459_n004.cluster.edu".
% 0.83/1.08 ============================== end of head ===========================
% 0.83/1.08
% 0.83/1.08 ============================== INPUT =================================
% 0.83/1.08
% 0.83/1.08 % Reading from file /tmp/Prover9_30459_n004.cluster.edu
% 0.83/1.08
% 0.83/1.08 set(prolog_style_variables).
% 0.83/1.08 set(auto2).
% 0.83/1.08 % set(auto2) -> set(auto).
% 0.83/1.08 % set(auto) -> set(auto_inference).
% 0.83/1.08 % set(auto) -> set(auto_setup).
% 0.83/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.08 % set(auto) -> set(auto_limits).
% 0.83/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.08 % set(auto) -> set(auto_denials).
% 0.83/1.08 % set(auto) -> set(auto_process).
% 0.83/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.08 % set(auto2) -> assign(stats, some).
% 0.83/1.08 % set(auto2) -> clear(echo_input).
% 0.83/1.08 % set(auto2) -> set(quiet).
% 0.83/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.08 % set(auto2) -> clear(print_given).
% 0.83/1.08 assign(lrs_ticks,-1).
% 0.83/1.08 assign(sos_limit,10000).
% 0.83/1.08 assign(order,kbo).
% 0.83/1.08 set(lex_order_vars).
% 0.83/1.08 clear(print_given).
% 0.83/1.08
% 0.83/1.08 % formulas(sos). % not echoed (2 formulas)
% 0.83/1.08
% 0.83/1.08 ============================== end of input ==========================
% 0.83/1.08
% 0.83/1.08 % From the command line: assign(max_seconds, 300).
% 0.83/1.08
% 0.83/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.08
% 0.83/1.08 % Formulas that are not ordinary clauses:
% 0.83/1.08
% 0.83/1.08 ============================== end of process non-clausal formulas ===
% 0.83/1.08
% 0.83/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.08
% 0.83/1.08 ============================== PREDICATE ELIMINATION =================
% 0.83/1.08
% 0.83/1.08 ============================== end predicate elimination =============
% 0.83/1.08
% 0.83/1.08 Auto_denials:
% 0.83/1.08 % copying label prove_these_axioms_2 to answer in negative clause
% 0.83/1.08
% 0.83/1.08 Term ordering decisions:
% 0.83/1.08
% 0.83/1.08 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.83/1.08 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 0.83/1.08
% 0.83/1.08 ============================== end of process initial clauses ========
% 0.83/1.08
% 0.83/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.08
% 0.83/1.08 ============================== end of clauses for search =============
% 0.83/1.08
% 0.83/1.08 ============================== SEARCH ================================
% 0.83/1.08
% 0.83/1.08 % Starting search at 0.01 seconds.
% 0.83/1.08
% 0.83/1.08 ============================== PROOF =================================
% 0.83/1.08 % SZS status Unsatisfiable
% 0.83/1.08 % SZS output start Refutation
% 0.83/1.08
% 0.83/1.08 % Proof 1 at 0.10 (+ 0.01) seconds: prove_these_axioms_2.
% 0.83/1.08 % Length of proof is 65.
% 0.83/1.08 % Level of proof is 21.
% 0.83/1.08 % Maximum clause weight is 40.000.
% 0.83/1.08 % Given clauses 18.
% 0.83/1.08
% 0.83/1.08 1 multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D # label(single_axiom) # label(axiom). [assumption].
% 0.83/1.08 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.83/1.08 3 multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),E))),multiply(multiply(multiply(F,inverse(F)),inverse(D)),A)))) = E. [para(1(a,1),1(a,1,2,1,2,1,2,1))].
% 0.83/1.08 4 multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),multiply(E,inverse(E))),multiply(C,A)))) = D. [para(1(a,1),1(a,1,2,1,2,1))].
% 0.83/1.08 5 multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(E,F)))))),inverse(multiply(F,C))) = E. [para(1(a,1),1(a,1,2,1,2))].
% 0.83/1.08 18 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(multiply(B,multiply(F,inverse(F))),multiply(C,E)))). [para(4(a,1),1(a,1,2,1,2,1)),flip(a)].
% 0.83/1.08 33 multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(D,multiply(E,inverse(E))),multiply(B,C))))))) = D. [para(18(a,1),1(a,1,2,1,2))].
% 0.83/1.08 51 multiply(A,inverse(multiply(multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(E,B)))),multiply(C,A)))) = E. [para(18(a,1),4(a,1,2,1,1))].
% 0.83/1.08 70 multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,multiply(D,inverse(D)))))) = multiply(E,inverse(multiply(B,multiply(C,E)))). [para(1(a,1),51(a,1,2,1,1)),flip(a)].
% 0.83/1.08 90 multiply(inverse(A),inverse(multiply(B,inverse(multiply(multiply(multiply(A,multiply(C,inverse(C))),multiply(D,inverse(D))),multiply(multiply(E,multiply(F,inverse(F))),B)))))) = E. [para(18(a,1),51(a,1,2,1))].
% 0.83/1.08 95 multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(E),C))) = E. [para(33(a,1),1(a,1,2,1,2))].
% 0.83/1.08 101 multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),A))),D)) = D. [para(33(a,1),3(a,1,2,1,2)),rewrite([95(22)])].
% 0.83/1.08 103 multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),multiply(multiply(E,inverse(E)),A)))) = inverse(multiply(F,multiply(V6,inverse(multiply(multiply(C,multiply(V7,inverse(V7))),multiply(F,V6)))))). [para(33(a,1),4(a,1,2,1,1,1,2,1))].
% 0.83/1.08 154 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(101(a,1),1(a,1,2,1))].
% 0.83/1.08 159 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(multiply(D,E)))))),F) = multiply(V6,inverse(multiply(inverse(multiply(E,F)),multiply(multiply(multiply(V7,inverse(V7)),inverse(D)),V6)))). [para(101(a,1),3(a,1,2,1,1,1,2)),flip(a)].
% 0.83/1.08 160 multiply(A,inverse(multiply(inverse(B),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),A)))) = B. [para(101(a,1),3(a,1,2,1,1,1))].
% 0.83/1.08 164 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),C))),D) = multiply(E,inverse(multiply(multiply(multiply(multiply(F,inverse(F)),inverse(D)),multiply(V6,inverse(V6))),multiply(C,E)))). [para(101(a,1),4(a,1,2,1,1,1,2,1)),flip(a)].
% 0.83/1.08 170 multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(multiply(F,inverse(F)),multiply(multiply(V6,inverse(V6)),inverse(multiply(B,D))))))). [para(101(a,1),18(a,1)),flip(a)].
% 0.83/1.08 189 multiply(inverse(multiply(A,inverse(A))),B) = inverse(multiply(C,multiply(D,inverse(multiply(multiply(B,multiply(E,inverse(E))),multiply(C,D)))))). [para(33(a,1),101(a,1,2))].
% 0.83/1.08 192 multiply(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,C)))),inverse(multiply(C,multiply(D,inverse(D))))) = B. [para(101(a,1),5(a,1,1,1))].
% 0.83/1.08 195 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,inverse(D)),E)))))),F) = multiply(E,F). [para(101(a,1),101(a,1,2)),flip(a)].
% 0.83/1.08 196 multiply(A,inverse(A)) = c_0. [new_symbol(154)].
% 0.83/1.08 200 multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(c_0,A)))))),B) = multiply(A,B). [back_rewrite(195),rewrite([196(2),196(3),196(4),196(5)])].
% 0.83/1.08 203 multiply(inverse(multiply(c_0,inverse(multiply(A,B)))),inverse(multiply(B,c_0))) = A. [back_rewrite(192),rewrite([196(2),196(7)])].
% 0.83/1.08 206 inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,c_0),multiply(A,B)))))) = multiply(inverse(c_0),C). [back_rewrite(189),rewrite([196(2),196(5)]),flip(a)].
% 0.83/1.08 225 multiply(A,inverse(multiply(multiply(B,c_0),multiply(C,A)))) = inverse(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(B,C))))))). [back_rewrite(170),rewrite([196(2),196(8),196(9),196(10)])].
% 0.83/1.08 230 multiply(A,inverse(multiply(multiply(multiply(c_0,inverse(B)),c_0),multiply(C,A)))) = multiply(multiply(c_0,inverse(multiply(c_0,C))),B). [back_rewrite(164),rewrite([196(2),196(3),196(8),196(11)]),flip(a)].
% 0.83/1.08 234 multiply(A,inverse(multiply(inverse(B),multiply(c_0,A)))) = B. [back_rewrite(160),rewrite([196(3),196(4),196(5)])].
% 0.83/1.08 235 multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(A,B)))))),C) = multiply(D,inverse(multiply(inverse(multiply(B,C)),multiply(multiply(c_0,inverse(A)),D)))). [back_rewrite(159),rewrite([196(2),196(3),196(4),196(14)])].
% 0.83/1.08 287 multiply(multiply(c_0,inverse(multiply(c_0,c_0))),A) = multiply(inverse(c_0),A). [back_rewrite(103),rewrite([196(2),196(5),196(7),230(10),196(9),206(15)])].
% 0.83/1.08 299 multiply(inverse(A),inverse(multiply(B,inverse(multiply(multiply(multiply(A,c_0),c_0),multiply(multiply(C,c_0),B)))))) = C. [back_rewrite(90),rewrite([196(3),196(5),196(7)])].
% 0.83/1.08 315 multiply(c_0,inverse(multiply(A,multiply(B,c_0)))) = multiply(C,inverse(multiply(A,multiply(B,C)))). [back_rewrite(70),rewrite([196(2),196(3)])].
% 0.83/1.08 341 multiply(c_0,multiply(inverse(c_0),A)) = A. [back_rewrite(33),rewrite([196(2),196(3),206(9)])].
% 0.83/1.08 349 multiply(A,inverse(multiply(multiply(B,c_0),multiply(C,A)))) = multiply(multiply(c_0,inverse(multiply(B,C))),c_0). [back_rewrite(18),rewrite([196(2),196(6),196(8)]),flip(a)].
% 0.83/1.08 358 multiply(inverse(A),inverse(multiply(multiply(multiply(c_0,inverse(multiply(A,B))),c_0),c_0))) = B. [back_rewrite(299),rewrite([349(11),349(9)])].
% 0.83/1.08 361 multiply(multiply(c_0,inverse(multiply(multiply(c_0,inverse(A)),B))),c_0) = multiply(multiply(c_0,inverse(multiply(c_0,B))),A). [back_rewrite(230),rewrite([349(9)])].
% 0.83/1.08 362 inverse(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(A,B))))))) = multiply(multiply(c_0,inverse(multiply(A,B))),c_0). [back_rewrite(225),rewrite([349(6)]),flip(a)].
% 0.83/1.08 389 multiply(c_0,c_0) = inverse(inverse(c_0)). [para(196(a,1),341(a,1,2))].
% 0.83/1.08 390 multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),A) = multiply(inverse(c_0),A). [back_rewrite(287),rewrite([389(4)])].
% 0.83/1.08 391 multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(A))))),B) = multiply(multiply(inverse(c_0),A),B). [para(341(a,1),200(a,1,1,2,1,2,2,1))].
% 0.83/1.08 407 multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(multiply(c_0,inverse(D)),A)))) = multiply(multiply(inverse(c_0),multiply(D,B)),C). [back_rewrite(235),rewrite([391(10)]),flip(a)].
% 0.83/1.08 416 inverse(multiply(inverse(A),c_0)) = multiply(c_0,A). [para(234(a,1),341(a,1,2)),rewrite([196(7)]),flip(a)].
% 0.83/1.08 429 multiply(inverse(multiply(c_0,inverse(inverse(inverse(c_0))))),inverse(inverse(inverse(c_0)))) = c_0. [para(389(a,1),203(a,1,1,1,2,1)),rewrite([389(10)])].
% 0.83/1.08 432 multiply(inverse(A),c_0) = inverse(A). [para(234(a,1),203(a,1,1,1)),rewrite([389(4),416(7),196(5)])].
% 0.83/1.08 436 multiply(inverse(multiply(c_0,multiply(c_0,A))),inverse(inverse(inverse(c_0)))) = inverse(A). [para(416(a,1),203(a,1,1,1,2)),rewrite([389(8)])].
% 0.83/1.08 445 multiply(c_0,A) = inverse(inverse(A)). [back_rewrite(416),rewrite([432(3)]),flip(a)].
% 0.83/1.08 452 multiply(inverse(inverse(inverse(inverse(inverse(A))))),inverse(inverse(inverse(c_0)))) = inverse(A). [back_rewrite(436),rewrite([445(3),445(4)])].
% 0.83/1.08 456 inverse(inverse(c_0)) = c_0. [back_rewrite(429),rewrite([445(6),452(12)])].
% 0.83/1.08 464 multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(inverse(inverse(inverse(D))),A)))) = multiply(multiply(inverse(c_0),multiply(D,B)),C). [back_rewrite(407),rewrite([445(5)])].
% 0.83/1.08 472 multiply(multiply(inverse(c_0),A),B) = multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A)))))))),B). [back_rewrite(391),rewrite([445(5),445(6),445(8)]),flip(a)].
% 0.83/1.08 473 multiply(inverse(c_0),A) = inverse(inverse(A)). [back_rewrite(390),rewrite([456(4),196(4),445(2)]),flip(a)].
% 0.83/1.08 483 inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(A,B)))))))))) = inverse(inverse(inverse(multiply(A,B)))). [back_rewrite(362),rewrite([445(6),445(7),445(9),445(14),432(16)])].
% 0.83/1.08 484 inverse(inverse(inverse(multiply(inverse(inverse(inverse(A))),B)))) = multiply(inverse(inverse(inverse(inverse(inverse(B))))),A). [back_rewrite(361),rewrite([445(4),445(7),432(9),445(10),445(12)])].
% 0.83/1.08 485 multiply(inverse(A),inverse(inverse(inverse(inverse(multiply(A,B)))))) = B. [back_rewrite(358),rewrite([445(5),432(7),432(7)])].
% 0.83/1.08 488 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(341),rewrite([473(4),445(4)])].
% 0.83/1.08 493 multiply(A,inverse(multiply(B,multiply(C,A)))) = inverse(inverse(inverse(multiply(B,multiply(C,c_0))))). [back_rewrite(315),rewrite([445(6)]),flip(a)].
% 0.83/1.08 513 inverse(inverse(inverse(multiply(inverse(multiply(A,B)),inverse(inverse(inverse(C))))))) = multiply(inverse(inverse(multiply(C,A))),B). [back_rewrite(464),rewrite([493(9),432(7),473(13)])].
% 0.83/1.08 524 multiply(inverse(inverse(A)),B) = multiply(A,B). [back_rewrite(472),rewrite([473(3),488(7),488(7)])].
% 0.83/1.08 526 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(485),rewrite([488(6)])].
% 0.83/1.08 527 inverse(inverse(inverse(multiply(inverse(A),B)))) = multiply(inverse(B),A). [back_rewrite(484),rewrite([524(4),488(9)])].
% 0.83/1.08 528 inverse(inverse(inverse(multiply(A,B)))) = inverse(multiply(A,B)). [back_rewrite(483),rewrite([488(5),488(5)]),flip(a)].
% 0.83/1.08 553 inverse(multiply(inverse(multiply(A,B)),inverse(inverse(inverse(C))))) = multiply(multiply(C,A),B). [back_rewrite(513),rewrite([528(9),524(11)])].
% 0.83/1.08 564 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(527),rewrite([528(5)])].
% 0.83/1.08 581 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [back_rewrite(553),rewrite([564(7),488(4)]),flip(a)].
% 0.83/1.08 588 $F # answer(prove_these_axioms_2). [back_rewrite(2),rewrite([581(6),526(6)]),xx(a)].
% 0.83/1.08
% 0.83/1.08 % SZS output end Refutation
% 0.83/1.08 ============================== end of proof ==========================
% 0.83/1.08
% 0.83/1.08 ============================== STATISTICS ============================
% 0.83/1.08
% 0.83/1.08 Given=18. Generated=865. Kept=587. proofs=1.
% 0.83/1.08 Usable=1. Sos=13. Demods=21. Limbo=7, Disabled=568. Hints=0.
% 0.83/1.08 Megabytes=0.84.
% 0.83/1.08 User_CPU=0.10, System_CPU=0.01, Wall_clock=0.
% 0.83/1.08
% 0.83/1.08 ============================== end of statistics =====================
% 0.83/1.08
% 0.83/1.08 ============================== end of search =========================
% 0.83/1.08
% 0.83/1.08 THEOREM PROVED
% 0.83/1.08 % SZS status Unsatisfiable
% 0.83/1.08
% 0.83/1.08 Exiting with 1 proof.
% 0.83/1.08
% 0.83/1.08 Process 30612 exit (max_proofs) Mon Jun 13 19:40:09 2022
% 0.83/1.08 Prover9 interrupted
%------------------------------------------------------------------------------