TSTP Solution File: GRP062-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP062-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 11:17:00 EDT 2022
% Result : Unsatisfiable 0.82s 1.10s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP062-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:10:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.82/1.10 ============================== Prover9 ===============================
% 0.82/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.10 Process 25539 was started by sandbox2 on n005.cluster.edu,
% 0.82/1.10 Mon Jun 13 10:10:39 2022
% 0.82/1.10 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25235_n005.cluster.edu".
% 0.82/1.10 ============================== end of head ===========================
% 0.82/1.10
% 0.82/1.10 ============================== INPUT =================================
% 0.82/1.10
% 0.82/1.10 % Reading from file /tmp/Prover9_25235_n005.cluster.edu
% 0.82/1.10
% 0.82/1.10 set(prolog_style_variables).
% 0.82/1.10 set(auto2).
% 0.82/1.10 % set(auto2) -> set(auto).
% 0.82/1.10 % set(auto) -> set(auto_inference).
% 0.82/1.10 % set(auto) -> set(auto_setup).
% 0.82/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.10 % set(auto) -> set(auto_limits).
% 0.82/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.10 % set(auto) -> set(auto_denials).
% 0.82/1.10 % set(auto) -> set(auto_process).
% 0.82/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.10 % set(auto2) -> assign(stats, some).
% 0.82/1.10 % set(auto2) -> clear(echo_input).
% 0.82/1.10 % set(auto2) -> set(quiet).
% 0.82/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.10 % set(auto2) -> clear(print_given).
% 0.82/1.10 assign(lrs_ticks,-1).
% 0.82/1.10 assign(sos_limit,10000).
% 0.82/1.10 assign(order,kbo).
% 0.82/1.10 set(lex_order_vars).
% 0.82/1.10 clear(print_given).
% 0.82/1.10
% 0.82/1.10 % formulas(sos). % not echoed (2 formulas)
% 0.82/1.10
% 0.82/1.10 ============================== end of input ==========================
% 0.82/1.10
% 0.82/1.10 % From the command line: assign(max_seconds, 300).
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.10
% 0.82/1.10 % Formulas that are not ordinary clauses:
% 0.82/1.10
% 0.82/1.10 ============================== end of process non-clausal formulas ===
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.10
% 0.82/1.10 ============================== PREDICATE ELIMINATION =================
% 0.82/1.10
% 0.82/1.10 ============================== end predicate elimination =============
% 0.82/1.10
% 0.82/1.10 Auto_denials:
% 0.82/1.10 % copying label prove_these_axioms to answer in negative clause
% 0.82/1.10
% 0.82/1.10 Term ordering decisions:
% 0.82/1.10
% 0.82/1.10 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.82/1.10 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 0.82/1.10
% 0.82/1.10 ============================== end of process initial clauses ========
% 0.82/1.10
% 0.82/1.10 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.10
% 0.82/1.10 ============================== end of clauses for search =============
% 0.82/1.10
% 0.82/1.10 ============================== SEARCH ================================
% 0.82/1.10
% 0.82/1.10 % Starting search at 0.01 seconds.
% 0.82/1.10
% 0.82/1.10 ============================== PROOF =================================
% 0.82/1.10 % SZS status Unsatisfiable
% 0.82/1.10 % SZS output start Refutation
% 0.82/1.10
% 0.82/1.10 % Proof 1 at 0.12 (+ 0.00) seconds: prove_these_axioms.
% 0.82/1.10 % Length of proof is 83.
% 0.82/1.10 % Level of proof is 27.
% 0.82/1.10 % Maximum clause weight is 39.000.
% 0.82/1.10 % Given clauses 44.
% 0.82/1.10
% 0.82/1.10 1 inverse(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B))))))) = D # label(single_axiom) # label(axiom). [assumption].
% 0.82/1.10 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.82/1.10 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [copy(2),flip(a)].
% 0.82/1.10 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))].
% 0.82/1.10 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))].
% 0.82/1.10 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)].
% 0.82/1.10 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))].
% 0.82/1.10 100 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)])].
% 0.82/1.10 152 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))].
% 0.82/1.10 154 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(100(a,1),1(a,1,1,2,2,2,1)),rewrite([1(11)])].
% 0.82/1.10 181 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))].
% 0.82/1.10 182 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))].
% 0.82/1.10 185 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))].
% 0.82/1.10 199 multiply(A,inverse(A)) = c_0. [new_symbol(154)].
% 0.82/1.10 212 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)])].
% 0.82/1.10 215 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)].
% 0.82/1.10 216 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)].
% 0.82/1.10 231 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)])].
% 0.82/1.10 249 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))].
% 0.82/1.10 250 multiply(c_0,inverse(multiply(inverse(multiply(A,multiply(inverse(A),B))),c_0))) = B. [para(199(a,1),212(a,1,2,1,2))].
% 0.82/1.10 251 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))].
% 0.82/1.10 284 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))].
% 0.82/1.10 292 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))].
% 0.82/1.10 293 inverse(multiply(A,multiply(inverse(A),inverse(inverse(B))))) = inverse(multiply(B,c_0)). [para(251(a,1),284(a,1,1,2,2))].
% 0.82/1.10 326 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)])].
% 0.82/1.10 328 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)].
% 0.82/1.10 334 inverse(multiply(A,multiply(inverse(A),inverse(c_0)))) = inverse(c_0). [para(292(a,1),293(a,2,1)),rewrite([284(11)])].
% 0.82/1.10 337 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))].
% 0.82/1.10 345 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)])].
% 0.82/1.10 367 inverse(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. [para(215(a,1),284(a,1,1,2,1))].
% 0.82/1.10 370 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))].
% 0.82/1.10 375 multiply(c_0,multiply(inverse(c_0),multiply(c_0,A))) = A. [para(345(a,1),212(a,1,2))].
% 0.82/1.10 376 multiply(c_0,multiply(inverse(c_0),c_0)) = inverse(c_0). [para(345(a,1),249(a,1,2))].
% 0.82/1.10 377 multiply(c_0,inverse(multiply(inverse(multiply(multiply(inverse(A),multiply(inverse(c_0),c_0)),multiply(A,B))),c_0))) = B. [para(345(a,1),250(a,1,2,1,1,1,2,1))].
% 0.82/1.10 378 multiply(A,multiply(B,multiply(c_0,inverse(multiply(C,multiply(A,B)))))) = inverse(multiply(C,multiply(inverse(c_0),c_0))). [para(231(a,1),345(a,1,1,1)),flip(a)].
% 0.82/1.10 380 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)].
% 0.82/1.10 384 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)].
% 0.82/1.10 387 multiply(A,multiply(inverse(A),inverse(c_0))) = c_0. [para(334(a,1),345(a,1,1,1)),rewrite([345(8)]),flip(a)].
% 0.82/1.10 388 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))].
% 0.82/1.10 389 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))].
% 0.82/1.10 391 multiply(inverse(inverse(A)),multiply(inverse(c_0),c_0)) = A. [back_rewrite(231),rewrite([378(7),389(6),389(7)])].
% 0.82/1.10 394 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)])].
% 0.82/1.10 396 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)])].
% 0.82/1.10 398 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)])].
% 0.82/1.10 400 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)])].
% 0.82/1.10 410 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)].
% 0.82/1.10 433 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))].
% 0.82/1.10 437 multiply(c_0,inverse(multiply(inverse(A),c_0))) = multiply(c_0,A). [para(375(a,1),212(a,1,2,1,1,1)),rewrite([199(6)])].
% 0.82/1.10 438 multiply(c_0,inverse(multiply(inverse(multiply(c_0,multiply(multiply(inverse(c_0),multiply(c_0,A)),B))),A))) = B. [para(375(a,1),212(a,1,2,1,2))].
% 0.82/1.10 439 inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,B))) = multiply(c_0,multiply(inverse(c_0),C)). [para(212(a,1),375(a,1,2,2)),flip(a)].
% 0.82/1.10 442 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)].
% 0.82/1.10 448 multiply(inverse(c_0),c_0) = c_0. [para(376(a,1),375(a,1,2,2)),rewrite([410(6),199(4)]),flip(a)].
% 0.82/1.10 452 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)].
% 0.82/1.10 454 multiply(c_0,multiply(multiply(inverse(A),c_0),multiply(A,B))) = B. [back_rewrite(377),rewrite([448(6),437(11)])].
% 0.82/1.10 457 multiply(c_0,multiply(A,c_0)) = inverse(inverse(A)). [back_rewrite(251),rewrite([442(7)])].
% 0.82/1.10 475 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)])].
% 0.82/1.10 483 inverse(c_0) = c_0. [back_rewrite(400),rewrite([448(4),448(6)])].
% 0.82/1.10 485 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)])].
% 0.82/1.10 487 multiply(inverse(inverse(A)),multiply(c_0,c_0)) = A. [back_rewrite(391),rewrite([483(4)])].
% 0.82/1.10 503 multiply(c_0,inverse(multiply(inverse(multiply(c_0,multiply(multiply(c_0,multiply(c_0,A)),B))),A))) = B. [back_rewrite(438),rewrite([483(4)])].
% 0.82/1.10 507 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)].
% 0.82/1.10 516 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)].
% 0.82/1.10 523 multiply(c_0,c_0) = c_0. [back_rewrite(448),rewrite([483(2)])].
% 0.82/1.10 526 inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,B))) = multiply(c_0,multiply(c_0,C)). [back_rewrite(439),rewrite([483(9)])].
% 0.82/1.10 532 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(410),rewrite([483(3)])].
% 0.82/1.10 534 multiply(inverse(A),A) = c_0. [back_rewrite(370),rewrite([507(7),483(10),516(13),485(22),523(4),532(3)])].
% 0.82/1.10 535 inverse(inverse(A)) = A. [back_rewrite(367),rewrite([507(7),483(10),516(13),485(22),523(4),532(3)])].
% 0.82/1.10 560 multiply(A,c_0) = A. [back_rewrite(487),rewrite([535(2),523(3)])].
% 0.82/1.10 565 multiply(c_0,multiply(inverse(A),multiply(A,B))) = B. [back_rewrite(454),rewrite([560(4)])].
% 0.82/1.10 566 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3),rewrite([534(4),534(5),534(7)]),xx(a)].
% 0.82/1.10 581 multiply(c_0,A) = A. [back_rewrite(457),rewrite([560(3),535(4)])].
% 0.82/1.10 582 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(384),rewrite([535(3),560(5)])].
% 0.82/1.10 583 inverse(multiply(inverse(multiply(A,B)),A)) = B. [back_rewrite(503),rewrite([581(5),581(4),581(4),581(6)])].
% 0.82/1.10 591 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(566),rewrite([581(3)]),xx(a)].
% 0.82/1.10 592 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(565),rewrite([581(5)])].
% 0.82/1.10 594 inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,B))) = C. [back_rewrite(526),rewrite([581(9),581(8)])].
% 0.82/1.10 599 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(583(a,1),535(a,1,1)),flip(a)].
% 0.82/1.10 600 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [para(582(a,1),583(a,1,1,1,1))].
% 0.82/1.10 602 multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C. [back_rewrite(594),rewrite([600(6)])].
% 0.82/1.10 608 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(592(a,1),599(a,1,1,1)),flip(a)].
% 0.82/1.10 609 multiply(multiply(inverse(A),inverse(B)),multiply(B,multiply(A,C))) = C. [back_rewrite(602),rewrite([608(2)])].
% 0.82/1.10 623 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(609(a,1),592(a,1,2)),rewrite([608(4),535(2),535(2)])].
% 0.82/1.10 624 $F # answer(prove_these_axioms). [resolve(623,a,591,a)].
% 0.82/1.10
% 0.82/1.10 % SZS output end Refutation
% 0.82/1.10 ============================== end of proof ==========================
% 0.82/1.10
% 0.82/1.10 ============================== STATISTICS ============================
% 0.82/1.10
% 0.82/1.10 Given=44. Generated=1377. Kept=622. proofs=1.
% 0.82/1.10 Usable=13. Sos=8. Demods=23. Limbo=3, Disabled=599. Hints=0.
% 0.82/1.10 Megabytes=0.88.
% 0.82/1.10 User_CPU=0.12, System_CPU=0.00, Wall_clock=1.
% 0.82/1.10
% 0.82/1.10 ============================== end of statistics =====================
% 0.82/1.10
% 0.82/1.10 ============================== end of search =========================
% 0.82/1.10
% 0.82/1.10 THEOREM PROVED
% 0.82/1.10 % SZS status Unsatisfiable
% 0.82/1.10
% 0.82/1.10 Exiting with 1 proof.
% 0.82/1.10
% 0.82/1.10 Process 25539 exit (max_proofs) Mon Jun 13 10:10:40 2022
% 0.82/1.10 Prover9 interrupted
%------------------------------------------------------------------------------