TSTP Solution File: GRP435-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP435-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:19:05 EDT 2022
% Result : Unsatisfiable 0.69s 1.02s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP435-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n012.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 21:52:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.69/1.02 ============================== Prover9 ===============================
% 0.69/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.69/1.02 Process 29396 was started by sandbox2 on n012.cluster.edu,
% 0.69/1.02 Mon Jun 13 21:52:41 2022
% 0.69/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29243_n012.cluster.edu".
% 0.69/1.02 ============================== end of head ===========================
% 0.69/1.02
% 0.69/1.02 ============================== INPUT =================================
% 0.69/1.02
% 0.69/1.02 % Reading from file /tmp/Prover9_29243_n012.cluster.edu
% 0.69/1.02
% 0.69/1.02 set(prolog_style_variables).
% 0.69/1.02 set(auto2).
% 0.69/1.02 % set(auto2) -> set(auto).
% 0.69/1.02 % set(auto) -> set(auto_inference).
% 0.69/1.02 % set(auto) -> set(auto_setup).
% 0.69/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.69/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/1.02 % set(auto) -> set(auto_limits).
% 0.69/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/1.02 % set(auto) -> set(auto_denials).
% 0.69/1.02 % set(auto) -> set(auto_process).
% 0.69/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.69/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.69/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.69/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.69/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.69/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.69/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.69/1.02 % set(auto2) -> assign(stats, some).
% 0.69/1.02 % set(auto2) -> clear(echo_input).
% 0.69/1.02 % set(auto2) -> set(quiet).
% 0.69/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.69/1.02 % set(auto2) -> clear(print_given).
% 0.69/1.02 assign(lrs_ticks,-1).
% 0.69/1.02 assign(sos_limit,10000).
% 0.69/1.02 assign(order,kbo).
% 0.69/1.02 set(lex_order_vars).
% 0.69/1.02 clear(print_given).
% 0.69/1.02
% 0.69/1.02 % formulas(sos). % not echoed (2 formulas)
% 0.69/1.02
% 0.69/1.02 ============================== end of input ==========================
% 0.69/1.02
% 0.69/1.02 % From the command line: assign(max_seconds, 300).
% 0.69/1.02
% 0.69/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/1.02
% 0.69/1.02 % Formulas that are not ordinary clauses:
% 0.69/1.02
% 0.69/1.02 ============================== end of process non-clausal formulas ===
% 0.69/1.02
% 0.69/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.69/1.02
% 0.69/1.02 ============================== PREDICATE ELIMINATION =================
% 0.69/1.02
% 0.69/1.02 ============================== end predicate elimination =============
% 0.69/1.02
% 0.69/1.02 Auto_denials:
% 0.69/1.02 % copying label prove_these_axioms_3 to answer in negative clause
% 0.69/1.02
% 0.69/1.02 Term ordering decisions:
% 0.69/1.02
% 0.69/1.02 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.69/1.02 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 0.69/1.02
% 0.69/1.02 ============================== end of process initial clauses ========
% 0.69/1.02
% 0.69/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.69/1.02
% 0.69/1.02 ============================== end of clauses for search =============
% 0.69/1.02
% 0.69/1.02 ============================== SEARCH ================================
% 0.69/1.02
% 0.69/1.02 % Starting search at 0.01 seconds.
% 0.69/1.02
% 0.69/1.02 ============================== PROOF =================================
% 0.69/1.02 % SZS status Unsatisfiable
% 0.69/1.02 % SZS output start Refutation
% 0.69/1.02
% 0.69/1.02 % Proof 1 at 0.07 (+ 0.00) seconds: prove_these_axioms_3.
% 0.69/1.02 % Length of proof is 64.
% 0.69/1.02 % Level of proof is 24.
% 0.69/1.02 % Maximum clause weight is 34.000.
% 0.69/1.02 % Given clauses 65.
% 0.69/1.02
% 0.69/1.02 1 inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.69/1.02 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].
% 0.69/1.02 3 inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))) = multiply(E,inverse(E)). [para(1(a,1),1(a,1,1,1,1,1))].
% 0.69/1.02 7 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))),E)),F),inverse(F)),multiply(V6,inverse(V6)))) = E. [para(3(a,2),1(a,1,1,1,1,1,1,1))].
% 0.69/1.02 8 inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D))))),E),F),multiply(V6,inverse(V6)))) = inverse(multiply(E,F)). [para(3(a,2),1(a,1,1,1,1,1,1))].
% 0.69/1.02 14 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(3(a,1),3(a,1))].
% 0.69/1.02 20 multiply(A,inverse(A)) = c_0. [new_symbol(14)].
% 0.69/1.02 31 inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0))),D),E),c_0)) = inverse(multiply(D,E)). [back_rewrite(8),rewrite([20(8),20(14)])].
% 0.69/1.02 32 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0)),D)),E),inverse(E)),c_0)) = D. [back_rewrite(7),rewrite([20(8),20(16)])].
% 0.69/1.02 36 inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0)) = c_0. [back_rewrite(3),rewrite([20(8),20(11)])].
% 0.69/1.02 37 inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),c_0)) = C. [back_rewrite(1),rewrite([20(7)])].
% 0.69/1.02 38 inverse(multiply(multiply(multiply(inverse(multiply(c_0,A)),B),inverse(B)),c_0)) = A. [back_rewrite(32),rewrite([36(9)])].
% 0.69/1.02 39 inverse(multiply(multiply(multiply(inverse(c_0),A),B),c_0)) = inverse(multiply(A,B)). [back_rewrite(31),rewrite([36(9)])].
% 0.69/1.02 45 inverse(multiply(multiply(c_0,inverse(inverse(inverse(multiply(c_0,A))))),c_0)) = A. [para(20(a,1),38(a,1,1,1,1))].
% 0.69/1.02 48 inverse(multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),c_0)) = inverse(c_0). [para(20(a,1),45(a,1,1,1,2,1,1,1))].
% 0.69/1.02 50 multiply(multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),c_0),inverse(c_0)) = c_0. [para(48(a,1),20(a,1,2))].
% 0.69/1.02 63 inverse(multiply(multiply(c_0,A),c_0)) = inverse(multiply(inverse(inverse(c_0)),A)). [para(20(a,1),39(a,1,1,1,1))].
% 0.69/1.02 64 inverse(multiply(A,inverse(multiply(inverse(c_0),A)))) = inverse(multiply(c_0,c_0)). [para(20(a,1),39(a,1,1,1)),flip(a)].
% 0.69/1.02 66 inverse(multiply(inverse(inverse(c_0)),inverse(inverse(inverse(multiply(c_0,A)))))) = A. [para(45(a,1),39(a,2)),rewrite([39(15),63(10)])].
% 0.69/1.02 69 inverse(multiply(inverse(inverse(c_0)),inverse(c_0))) = inverse(multiply(c_0,c_0)). [para(20(a,1),63(a,1,1,1)),flip(a)].
% 0.69/1.02 72 multiply(multiply(inverse(inverse(c_0)),inverse(c_0)),inverse(multiply(c_0,c_0))) = c_0. [para(69(a,1),20(a,1,2))].
% 0.69/1.02 84 inverse(multiply(inverse(c_0),c_0)) = c_0. [para(64(a,1),38(a,1,1,1,1,1)),rewrite([38(10)]),flip(a)].
% 0.69/1.02 89 multiply(multiply(inverse(c_0),c_0),c_0) = c_0. [para(84(a,1),20(a,1,2))].
% 0.69/1.02 99 inverse(multiply(multiply(inverse(c_0),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0)) = c_0. [para(50(a,1),36(a,1,1,1,1,2,1,1)),rewrite([39(17)])].
% 0.69/1.02 100 inverse(multiply(multiply(inverse(multiply(multiply(A,B),inverse(c_0))),A),B)) = c_0. [para(36(a,1),39(a,1)),flip(a)].
% 0.69/1.02 127 inverse(multiply(multiply(multiply(inverse(multiply(c_0,c_0)),A),B),c_0)) = inverse(multiply(inverse(c_0),multiply(A,B))). [para(64(a,1),37(a,1,1,1,1,1))].
% 0.69/1.02 135 inverse(multiply(multiply(multiply(inverse(multiply(c_0,A)),multiply(multiply(inverse(c_0),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0)),c_0),c_0)) = A. [para(99(a,1),38(a,1,1,1,2))].
% 0.69/1.02 139 inverse(multiply(inverse(inverse(c_0)),multiply(c_0,inverse(inverse(inverse(c_0)))))) = c_0. [para(99(a,1),37(a,1,1,1,1,1)),rewrite([20(4),63(11)])].
% 0.69/1.02 140 multiply(multiply(inverse(inverse(c_0)),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0) = c_0. [para(139(a,1),20(a,1,2))].
% 0.69/1.02 144 inverse(multiply(multiply(inverse(c_0),A),inverse(A))) = c_0. [para(20(a,1),100(a,1,1,1,1,1,1)),rewrite([20(4)])].
% 0.69/1.02 151 inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(c_0)),inverse(c_0))),inverse(multiply(c_0,c_0)))) = c_0. [para(72(a,1),100(a,1,1,1,1,1,1)),rewrite([20(4)])].
% 0.69/1.02 155 inverse(multiply(multiply(multiply(c_0,inverse(multiply(multiply(A,B),inverse(c_0)))),A),c_0)) = B. [para(100(a,1),37(a,1,1,1,1,1))].
% 0.69/1.02 201 inverse(multiply(inverse(inverse(c_0)),A)) = inverse(A). [para(144(a,1),37(a,1,1,1,1,1)),rewrite([20(4),63(5)])].
% 0.69/1.02 204 inverse(multiply(c_0,c_0)) = c_0. [para(144(a,1),100(a,1,1,1,1)),rewrite([20(4)])].
% 0.69/1.02 219 inverse(inverse(c_0)) = c_0. [back_rewrite(69),rewrite([201(7),204(7)])].
% 0.69/1.02 221 inverse(multiply(c_0,inverse(inverse(inverse(multiply(c_0,A)))))) = A. [back_rewrite(66),rewrite([219(3)])].
% 0.69/1.02 222 inverse(multiply(multiply(c_0,A),c_0)) = inverse(multiply(c_0,A)). [back_rewrite(63),rewrite([219(8)])].
% 0.69/1.02 227 inverse(c_0) = c_0. [back_rewrite(151),rewrite([219(5),20(6),204(8),89(6)])].
% 0.69/1.02 228 inverse(multiply(multiply(multiply(c_0,A),B),c_0)) = inverse(multiply(c_0,multiply(A,B))). [back_rewrite(127),rewrite([204(4),227(8)])].
% 0.69/1.02 245 inverse(multiply(c_0,A)) = inverse(A). [back_rewrite(201),rewrite([227(2),227(2)])].
% 0.69/1.02 251 multiply(multiply(c_0,multiply(c_0,c_0)),c_0) = c_0. [back_rewrite(140),rewrite([227(2),227(2),227(4),227(4),227(4)])].
% 0.69/1.02 254 inverse(multiply(multiply(multiply(inverse(A),c_0),c_0),c_0)) = A. [back_rewrite(135),rewrite([245(3),227(3),227(5),227(5),227(5),251(8)])].
% 0.69/1.02 285 inverse(multiply(inverse(multiply(multiply(A,B),c_0)),A)) = B. [back_rewrite(155),rewrite([227(4),228(10),245(8)])].
% 0.69/1.02 323 inverse(multiply(multiply(c_0,A),c_0)) = inverse(A). [back_rewrite(222),rewrite([245(8)])].
% 0.69/1.02 324 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(221),rewrite([245(4),245(6)])].
% 0.69/1.02 343 inverse(multiply(multiply(multiply(inverse(A),B),inverse(B)),c_0)) = A. [back_rewrite(38),rewrite([245(3)])].
% 0.69/1.02 354 multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0) = c_0. [para(36(a,1),324(a,1,1,1,1)),rewrite([227(2),227(2),227(2)]),flip(a)].
% 0.69/1.02 356 multiply(c_0,A) = A. [para(245(a,1),324(a,1,1,1,1)),rewrite([324(4)]),flip(a)].
% 0.69/1.02 370 inverse(multiply(A,c_0)) = inverse(A). [back_rewrite(323),rewrite([356(2)])].
% 0.69/1.02 390 inverse(multiply(multiply(inverse(A),B),inverse(B))) = A. [back_rewrite(343),rewrite([370(7)])].
% 0.69/1.02 393 inverse(multiply(inverse(multiply(A,B)),A)) = B. [back_rewrite(285),rewrite([370(4)])].
% 0.69/1.02 394 inverse(inverse(A)) = A. [back_rewrite(254),rewrite([370(8),370(6),370(4)])].
% 0.69/1.02 407 multiply(A,c_0) = A. [para(370(a,1),394(a,1,1)),rewrite([394(2)]),flip(a)].
% 0.69/1.02 414 multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C) = c_0. [back_rewrite(354),rewrite([407(8)])].
% 0.69/1.02 416 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(393(a,1),394(a,1,1)),flip(a)].
% 0.69/1.02 423 multiply(A,multiply(inverse(A),B)) = B. [para(390(a,1),416(a,1,1)),rewrite([394(5)])].
% 0.69/1.02 426 multiply(inverse(A),multiply(A,B)) = B. [para(394(a,1),423(a,1,2,1))].
% 0.69/1.02 427 multiply(multiply(A,B),inverse(B)) = A. [para(416(a,1),423(a,1,2))].
% 0.69/1.02 432 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(426(a,1),416(a,1,1,1)),flip(a)].
% 0.69/1.02 433 multiply(multiply(A,multiply(multiply(inverse(A),multiply(inverse(B),inverse(C))),C)),B) = c_0. [back_rewrite(414),rewrite([432(3),432(3)])].
% 0.69/1.02 444 multiply(multiply(inverse(A),multiply(multiply(A,B),C)),inverse(C)) = B. [para(433(a,1),426(a,1,2)),rewrite([432(8),432(7),432(7),432(5),394(3),394(3),394(4),407(8)])].
% 0.69/1.02 487 multiply(multiply(A,multiply(B,C)),inverse(C)) = multiply(A,B). [para(426(a,1),444(a,1,1,2,1)),rewrite([394(2)])].
% 0.69/1.02 493 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(487(a,1),427(a,1,1)),rewrite([394(3)])].
% 0.69/1.02 494 $F # answer(prove_these_axioms_3). [resolve(493,a,2,a)].
% 0.69/1.02
% 0.69/1.02 % SZS output end Refutation
% 0.69/1.02 ============================== end of proof ==========================
% 0.69/1.02
% 0.69/1.02 ============================== STATISTICS ============================
% 0.69/1.02
% 0.69/1.02 Given=65. Generated=1446. Kept=493. proofs=1.
% 0.69/1.02 Usable=21. Sos=30. Demods=53. Limbo=3, Disabled=440. Hints=0.
% 0.69/1.02 Megabytes=0.48.
% 0.69/1.02 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.69/1.02
% 0.69/1.02 ============================== end of statistics =====================
% 0.69/1.02
% 0.69/1.02 ============================== end of search =========================
% 0.69/1.02
% 0.69/1.02 THEOREM PROVED
% 0.69/1.02 % SZS status Unsatisfiable
% 0.69/1.02
% 0.69/1.02 Exiting with 1 proof.
% 0.69/1.02
% 0.69/1.02 Process 29396 exit (max_proofs) Mon Jun 13 21:52:41 2022
% 0.69/1.02 Prover9 interrupted
%------------------------------------------------------------------------------