TSTP Solution File: GRP432-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP432-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 0.71s 1.04s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP432-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n006.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 20:41:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.04 ============================== Prover9 ===============================
% 0.71/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.04 Process 24481 was started by sandbox on n006.cluster.edu,
% 0.71/1.04 Mon Jun 13 20:41:42 2022
% 0.71/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24328_n006.cluster.edu".
% 0.71/1.04 ============================== end of head ===========================
% 0.71/1.04
% 0.71/1.04 ============================== INPUT =================================
% 0.71/1.04
% 0.71/1.04 % Reading from file /tmp/Prover9_24328_n006.cluster.edu
% 0.71/1.04
% 0.71/1.04 set(prolog_style_variables).
% 0.71/1.04 set(auto2).
% 0.71/1.04 % set(auto2) -> set(auto).
% 0.71/1.04 % set(auto) -> set(auto_inference).
% 0.71/1.04 % set(auto) -> set(auto_setup).
% 0.71/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.04 % set(auto) -> set(auto_limits).
% 0.71/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.04 % set(auto) -> set(auto_denials).
% 0.71/1.04 % set(auto) -> set(auto_process).
% 0.71/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.04 % set(auto2) -> assign(stats, some).
% 0.71/1.04 % set(auto2) -> clear(echo_input).
% 0.71/1.04 % set(auto2) -> set(quiet).
% 0.71/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.04 % set(auto2) -> clear(print_given).
% 0.71/1.04 assign(lrs_ticks,-1).
% 0.71/1.04 assign(sos_limit,10000).
% 0.71/1.04 assign(order,kbo).
% 0.71/1.04 set(lex_order_vars).
% 0.71/1.04 clear(print_given).
% 0.71/1.04
% 0.71/1.04 % formulas(sos). % not echoed (2 formulas)
% 0.71/1.04
% 0.71/1.04 ============================== end of input ==========================
% 0.71/1.04
% 0.71/1.04 % From the command line: assign(max_seconds, 300).
% 0.71/1.04
% 0.71/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.04
% 0.71/1.04 % Formulas that are not ordinary clauses:
% 0.71/1.04
% 0.71/1.04 ============================== end of process non-clausal formulas ===
% 0.71/1.04
% 0.71/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.04
% 0.71/1.04 ============================== PREDICATE ELIMINATION =================
% 0.71/1.04
% 0.71/1.04 ============================== end predicate elimination =============
% 0.71/1.04
% 0.71/1.04 Auto_denials:
% 0.71/1.04 % copying label prove_these_axioms_3 to answer in negative clause
% 0.71/1.04
% 0.71/1.04 Term ordering decisions:
% 0.71/1.04
% 0.71/1.04 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.71/1.04 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 0.71/1.04
% 0.71/1.04 ============================== end of process initial clauses ========
% 0.71/1.04
% 0.71/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.04
% 0.71/1.04 ============================== end of clauses for search =============
% 0.71/1.04
% 0.71/1.04 ============================== SEARCH ================================
% 0.71/1.04
% 0.71/1.04 % Starting search at 0.01 seconds.
% 0.71/1.04
% 0.71/1.04 ============================== PROOF =================================
% 0.71/1.04 % SZS status Unsatisfiable
% 0.71/1.04 % SZS output start Refutation
% 0.71/1.04
% 0.71/1.04 % Proof 1 at 0.06 (+ 0.00) seconds: prove_these_axioms_3.
% 0.71/1.04 % Length of proof is 60.
% 0.71/1.04 % Level of proof is 21.
% 0.71/1.04 % Maximum clause weight is 40.000.
% 0.71/1.04 % Given clauses 18.
% 0.71/1.04
% 0.71/1.04 1 multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D # label(single_axiom) # label(axiom). [assumption].
% 0.71/1.04 2 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.71/1.04 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))].
% 0.71/1.04 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))].
% 0.71/1.04 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))].
% 0.71/1.04 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)].
% 0.71/1.04 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))].
% 0.71/1.04 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))].
% 0.71/1.04 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)].
% 0.71/1.04 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))].
% 0.71/1.04 101 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)])].
% 0.71/1.04 103 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))].
% 0.71/1.04 154 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(101(a,1),1(a,1,2,1))].
% 0.71/1.04 159 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)].
% 0.71/1.04 160 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))].
% 0.71/1.04 164 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)].
% 0.71/1.04 170 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)].
% 0.71/1.04 189 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))].
% 0.71/1.04 192 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))].
% 0.71/1.04 195 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)].
% 0.71/1.04 196 multiply(A,inverse(A)) = c_0. [new_symbol(154)].
% 0.71/1.04 200 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)])].
% 0.71/1.04 203 multiply(inverse(multiply(c_0,inverse(multiply(A,B)))),inverse(multiply(B,c_0))) = A. [back_rewrite(192),rewrite([196(2),196(7)])].
% 0.71/1.04 206 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)].
% 0.71/1.04 225 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)])].
% 0.71/1.04 230 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)].
% 0.71/1.04 234 multiply(A,inverse(multiply(inverse(B),multiply(c_0,A)))) = B. [back_rewrite(160),rewrite([196(3),196(4),196(5)])].
% 0.71/1.04 235 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)])].
% 0.71/1.04 287 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)])].
% 0.71/1.04 315 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)])].
% 0.71/1.04 341 multiply(c_0,multiply(inverse(c_0),A)) = A. [back_rewrite(33),rewrite([196(2),196(3),206(9)])].
% 0.71/1.04 349 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)].
% 0.71/1.04 361 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)])].
% 0.71/1.04 362 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)].
% 0.71/1.04 389 multiply(c_0,c_0) = inverse(inverse(c_0)). [para(196(a,1),341(a,1,2))].
% 0.71/1.04 390 multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),A) = multiply(inverse(c_0),A). [back_rewrite(287),rewrite([389(4)])].
% 0.71/1.04 391 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))].
% 0.71/1.04 407 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)].
% 0.71/1.04 416 inverse(multiply(inverse(A),c_0)) = multiply(c_0,A). [para(234(a,1),341(a,1,2)),rewrite([196(7)]),flip(a)].
% 0.71/1.04 429 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)])].
% 0.71/1.04 432 multiply(inverse(A),c_0) = inverse(A). [para(234(a,1),203(a,1,1,1)),rewrite([389(4),416(7),196(5)])].
% 0.71/1.04 436 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)])].
% 0.71/1.04 445 multiply(c_0,A) = inverse(inverse(A)). [back_rewrite(416),rewrite([432(3)]),flip(a)].
% 0.71/1.04 452 multiply(inverse(inverse(inverse(inverse(inverse(A))))),inverse(inverse(inverse(c_0)))) = inverse(A). [back_rewrite(436),rewrite([445(3),445(4)])].
% 0.71/1.04 456 inverse(inverse(c_0)) = c_0. [back_rewrite(429),rewrite([445(6),452(12)])].
% 0.71/1.04 464 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)])].
% 0.71/1.04 472 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)].
% 0.71/1.04 473 multiply(inverse(c_0),A) = inverse(inverse(A)). [back_rewrite(390),rewrite([456(4),196(4),445(2)]),flip(a)].
% 0.71/1.04 483 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)])].
% 0.71/1.04 484 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)])].
% 0.71/1.04 488 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(341),rewrite([473(4),445(4)])].
% 0.71/1.04 493 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)].
% 0.71/1.04 513 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)])].
% 0.71/1.04 524 multiply(inverse(inverse(A)),B) = multiply(A,B). [back_rewrite(472),rewrite([473(3),488(7),488(7)])].
% 0.71/1.04 527 inverse(inverse(inverse(multiply(inverse(A),B)))) = multiply(inverse(B),A). [back_rewrite(484),rewrite([524(4),488(9)])].
% 0.71/1.04 528 inverse(inverse(inverse(multiply(A,B)))) = inverse(multiply(A,B)). [back_rewrite(483),rewrite([488(5),488(5)]),flip(a)].
% 0.71/1.04 553 inverse(multiply(inverse(multiply(A,B)),inverse(inverse(inverse(C))))) = multiply(multiply(C,A),B). [back_rewrite(513),rewrite([528(9),524(11)])].
% 0.71/1.04 564 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(527),rewrite([528(5)])].
% 0.71/1.04 581 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [back_rewrite(553),rewrite([564(7),488(4)]),flip(a)].
% 0.71/1.04 582 $F # answer(prove_these_axioms_3). [resolve(581,a,2,a)].
% 0.71/1.04
% 0.71/1.04 % SZS output end Refutation
% 0.71/1.04 ============================== end of proof ==========================
% 0.71/1.04
% 0.71/1.04 ============================== STATISTICS ============================
% 0.71/1.04
% 0.71/1.04 Given=18. Generated=834. Kept=581. proofs=1.
% 0.71/1.04 Usable=2. Sos=27. Demods=45. Limbo=17, Disabled=536. Hints=0.
% 0.71/1.04 Megabytes=0.83.
% 0.71/1.04 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.71/1.04
% 0.71/1.04 ============================== end of statistics =====================
% 0.71/1.04
% 0.71/1.04 ============================== end of search =========================
% 0.71/1.04
% 0.71/1.04 THEOREM PROVED
% 0.71/1.04 % SZS status Unsatisfiable
% 0.71/1.04
% 0.71/1.04 Exiting with 1 proof.
% 0.71/1.04
% 0.71/1.04 Process 24481 exit (max_proofs) Mon Jun 13 20:41:42 2022
% 0.71/1.04 Prover9 interrupted
%------------------------------------------------------------------------------