TSTP Solution File: GRP430-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP430-1 : 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 11:19:03 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
% 0.03/0.12 % Problem : GRP430-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 10:34:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.70/1.06 ============================== Prover9 ===============================
% 0.70/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.06 Process 5044 was started by sandbox2 on n012.cluster.edu,
% 0.70/1.06 Tue Jun 14 10:34:11 2022
% 0.70/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4890_n012.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_4890_n012.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 0.11 (+ 0.00) seconds: prove_these_axioms_1.
% 0.70/1.06 % Length of proof is 101.
% 0.70/1.06 % Level of proof is 23.
% 0.70/1.06 % Maximum clause weight is 50.000.
% 0.70/1.06 % Given clauses 21.
% 0.70/1.06
% 0.70/1.06 1 multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D # label(single_axiom) # label(axiom). [assumption].
% 0.70/1.06 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 4 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))].
% 0.70/1.06 5 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))].
% 0.70/1.06 6 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))].
% 0.70/1.06 8 multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),multiply(E,A)))) = inverse(multiply(F,multiply(multiply(multiply(V6,inverse(V6)),inverse(multiply(C,F))),E))). [para(4(a,1),1(a,1,2,1,2,1))].
% 0.70/1.06 19 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(5(a,1),1(a,1,2,1,2,1)),flip(a)].
% 0.70/1.06 34 multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(D,multiply(E,inverse(E))),multiply(B,C))))))) = D. [para(19(a,1),1(a,1,2,1,2))].
% 0.70/1.06 52 multiply(A,inverse(multiply(multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(E,B)))),multiply(C,A)))) = E. [para(19(a,1),5(a,1,2,1,1))].
% 0.70/1.06 54 multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,E))),multiply(F,inverse(F))))),multiply(V6,inverse(V6))),multiply(V7,A)))) = inverse(multiply(multiply(D,multiply(V8,inverse(V8))),multiply(E,V7))). [para(19(a,2),5(a,1,2,1,1,1,2,1))].
% 0.70/1.06 71 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),52(a,1,2,1,1)),flip(a)].
% 0.70/1.06 91 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(19(a,1),52(a,1,2,1))].
% 0.70/1.06 96 multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(E),C))) = E. [para(34(a,1),1(a,1,2,1,2))].
% 0.70/1.06 98 multiply(multiply(A,inverse(A)),inverse(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,multiply(E,inverse(E)))))),C))) = D. [para(1(a,1),34(a,1,2,1,2))].
% 0.70/1.06 102 multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),A))),D)) = D. [para(34(a,1),4(a,1,2,1,2)),rewrite([96(22)])].
% 0.70/1.06 104 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(34(a,1),5(a,1,2,1,1,1,2,1))].
% 0.70/1.06 109 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(C))))),multiply(D,inverse(D))) = multiply(inverse(multiply(E,multiply(F,inverse(multiply(multiply(V6,multiply(V7,inverse(V7))),multiply(E,F)))))),inverse(multiply(multiply(B,multiply(V8,inverse(V8))),V6))). [para(34(a,1),19(a,2,2,1,2))].
% 0.70/1.06 131 multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,C))),multiply(multiply(F,inverse(F)),inverse(multiply(V6,V7))))))))),multiply(V8,inverse(V8))) = multiply(inverse(multiply(V7,E)),inverse(multiply(multiply(B,multiply(V9,inverse(V9))),V6))). [para(6(a,1),19(a,2,2,1,2))].
% 0.70/1.06 146 multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),multiply(multiply(E,inverse(E)),inverse(multiply(F,V6)))))),multiply(inverse(multiply(V6,D)),inverse(multiply(multiply(V7,multiply(V8,inverse(V8))),F)))))) = V7. [para(6(a,1),34(a,1,2,1,2,2,1,2))].
% 0.70/1.06 155 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(102(a,1),1(a,1,2,1))].
% 0.70/1.06 160 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(102(a,1),4(a,1,2,1,1,1,2)),flip(a)].
% 0.70/1.06 161 multiply(A,inverse(multiply(inverse(B),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),A)))) = B. [para(102(a,1),4(a,1,2,1,1,1))].
% 0.70/1.06 165 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(102(a,1),5(a,1,2,1,1,1,2,1)),flip(a)].
% 0.70/1.06 171 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(102(a,1),19(a,1)),flip(a)].
% 0.70/1.06 190 multiply(inverse(multiply(A,inverse(A))),B) = inverse(multiply(C,multiply(D,inverse(multiply(multiply(B,multiply(E,inverse(E))),multiply(C,D)))))). [para(34(a,1),102(a,1,2))].
% 0.70/1.06 193 multiply(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,C)))),inverse(multiply(C,multiply(D,inverse(D))))) = B. [para(102(a,1),6(a,1,1,1))].
% 0.70/1.06 196 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(102(a,1),102(a,1,2)),flip(a)].
% 0.70/1.06 197 multiply(A,inverse(A)) = c_0. [new_symbol(155)].
% 0.70/1.06 201 multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(c_0,A)))))),B) = multiply(A,B). [back_rewrite(196),rewrite([197(2),197(3),197(4),197(5)])].
% 0.70/1.06 204 multiply(inverse(multiply(c_0,inverse(multiply(A,B)))),inverse(multiply(B,c_0))) = A. [back_rewrite(193),rewrite([197(2),197(7)])].
% 0.70/1.06 207 inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,c_0),multiply(A,B)))))) = multiply(inverse(c_0),C). [back_rewrite(190),rewrite([197(2),197(5)]),flip(a)].
% 0.70/1.06 226 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(171),rewrite([197(2),197(8),197(9),197(10)])].
% 0.70/1.06 231 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(165),rewrite([197(2),197(3),197(8),197(11)]),flip(a)].
% 0.70/1.06 235 multiply(A,inverse(multiply(inverse(B),multiply(c_0,A)))) = B. [back_rewrite(161),rewrite([197(3),197(4),197(5)])].
% 0.70/1.06 236 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(160),rewrite([197(2),197(3),197(4),197(14)])].
% 0.70/1.06 248 multiply(c_0,inverse(multiply(inverse(multiply(A,multiply(multiply(c_0,inverse(multiply(B,A))),multiply(c_0,inverse(multiply(C,D)))))),multiply(inverse(multiply(D,B)),inverse(multiply(multiply(E,c_0),C)))))) = E. [back_rewrite(146),rewrite([197(2),197(3),197(7),197(16)])].
% 0.70/1.06 263 multiply(multiply(c_0,inverse(multiply(A,inverse(multiply(B,multiply(multiply(c_0,inverse(multiply(C,B))),multiply(c_0,inverse(multiply(D,E))))))))),c_0) = multiply(inverse(multiply(E,C)),inverse(multiply(multiply(A,c_0),D))). [back_rewrite(131),rewrite([197(2),197(3),197(7),197(17),197(21)])].
% 0.70/1.06 285 multiply(multiply(inverse(c_0),A),inverse(multiply(multiply(B,c_0),A))) = multiply(multiply(c_0,inverse(multiply(B,c_0))),c_0). [back_rewrite(109),rewrite([197(2),197(3),197(7),197(9),207(15),197(12)]),flip(a)].
% 0.70/1.06 288 multiply(multiply(c_0,inverse(multiply(c_0,c_0))),A) = multiply(inverse(c_0),A). [back_rewrite(104),rewrite([197(2),197(5),197(7),231(10),197(9),207(15)])].
% 0.70/1.06 290 multiply(A,multiply(multiply(c_0,inverse(multiply(c_0,A))),B)) = B. [back_rewrite(102),rewrite([197(2),197(3)])].
% 0.70/1.06 293 multiply(c_0,inverse(multiply(multiply(c_0,inverse(multiply(A,multiply(B,c_0)))),A))) = B. [back_rewrite(98),rewrite([197(2),197(3),197(4)])].
% 0.70/1.06 300 multiply(inverse(A),inverse(multiply(B,inverse(multiply(multiply(multiply(A,c_0),c_0),multiply(multiply(C,c_0),B)))))) = C. [back_rewrite(91),rewrite([197(3),197(5),197(7)])].
% 0.70/1.06 316 multiply(c_0,inverse(multiply(A,multiply(B,c_0)))) = multiply(C,inverse(multiply(A,multiply(B,C)))). [back_rewrite(71),rewrite([197(2),197(3)])].
% 0.70/1.06 326 multiply(multiply(c_0,inverse(multiply(c_0,A))),multiply(multiply(c_0,inverse(multiply(B,C))),c_0)) = inverse(multiply(multiply(B,c_0),multiply(C,A))). [back_rewrite(54),rewrite([197(2),197(3),197(7),197(11),231(15),197(14)])].
% 0.70/1.06 342 multiply(c_0,multiply(inverse(c_0),A)) = A. [back_rewrite(34),rewrite([197(2),197(3),207(9)])].
% 0.70/1.06 350 multiply(A,inverse(multiply(multiply(B,c_0),multiply(C,A)))) = multiply(multiply(c_0,inverse(multiply(B,C))),c_0). [back_rewrite(19),rewrite([197(2),197(6),197(8)]),flip(a)].
% 0.70/1.06 356 multiply(multiply(c_0,inverse(multiply(multiply(c_0,inverse(A)),B))),c_0) = inverse(multiply(C,multiply(multiply(c_0,inverse(multiply(A,C))),B))). [back_rewrite(8),rewrite([197(2),197(5),350(9),197(11)])].
% 0.70/1.06 359 multiply(inverse(A),inverse(multiply(multiply(multiply(c_0,inverse(multiply(A,B))),c_0),c_0))) = B. [back_rewrite(300),rewrite([350(11),350(9)])].
% 0.70/1.06 362 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(231),rewrite([350(9)])].
% 0.70/1.06 363 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(226),rewrite([350(6)]),flip(a)].
% 0.70/1.06 366 inverse(multiply(A,multiply(multiply(c_0,inverse(multiply(B,A))),C))) = multiply(multiply(c_0,inverse(multiply(c_0,C))),B). [back_rewrite(356),rewrite([362(9)]),flip(a)].
% 0.70/1.06 380 multiply(multiply(c_0,inverse(multiply(A,multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(B,C)))))),D)))),c_0) = multiply(inverse(multiply(C,D)),inverse(multiply(multiply(A,c_0),B))). [back_rewrite(263),rewrite([366(12)])].
% 0.70/1.06 384 multiply(c_0,inverse(multiply(multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(multiply(A,B)))))),C),multiply(inverse(multiply(B,C)),inverse(multiply(multiply(D,c_0),A)))))) = D. [back_rewrite(248),rewrite([366(12)])].
% 0.70/1.06 390 multiply(c_0,c_0) = inverse(inverse(c_0)). [para(197(a,1),342(a,1,2))].
% 0.70/1.06 391 multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),A) = multiply(inverse(c_0),A). [back_rewrite(288),rewrite([390(4)])].
% 0.70/1.06 392 multiply(multiply(c_0,inverse(multiply(c_0,multiply(c_0,inverse(A))))),B) = multiply(multiply(inverse(c_0),A),B). [para(342(a,1),201(a,1,1,2,1,2,2,1))].
% 0.70/1.06 398 multiply(c_0,inverse(multiply(multiply(multiply(inverse(c_0),multiply(A,B)),C),multiply(inverse(multiply(B,C)),inverse(multiply(multiply(D,c_0),A)))))) = D. [back_rewrite(384),rewrite([392(11)])].
% 0.70/1.06 401 multiply(multiply(c_0,inverse(multiply(A,multiply(multiply(inverse(c_0),multiply(B,C)),D)))),c_0) = multiply(inverse(multiply(C,D)),inverse(multiply(multiply(A,c_0),B))). [back_rewrite(380),rewrite([392(11)])].
% 0.70/1.06 408 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(236),rewrite([392(10)]),flip(a)].
% 0.70/1.06 417 inverse(multiply(inverse(A),c_0)) = multiply(c_0,A). [para(235(a,1),342(a,1,2)),rewrite([197(7)]),flip(a)].
% 0.70/1.06 430 multiply(inverse(multiply(c_0,inverse(inverse(inverse(c_0))))),inverse(inverse(inverse(c_0)))) = c_0. [para(390(a,1),204(a,1,1,1,2,1)),rewrite([390(10)])].
% 0.70/1.06 433 multiply(inverse(A),c_0) = inverse(A). [para(235(a,1),204(a,1,1,1)),rewrite([390(4),417(7),197(5)])].
% 0.70/1.06 437 multiply(inverse(multiply(c_0,multiply(c_0,A))),inverse(inverse(inverse(c_0)))) = inverse(A). [para(417(a,1),204(a,1,1,1,2)),rewrite([390(8)])].
% 0.70/1.06 446 multiply(c_0,A) = inverse(inverse(A)). [back_rewrite(417),rewrite([433(3)]),flip(a)].
% 0.70/1.06 453 multiply(inverse(inverse(inverse(inverse(inverse(A))))),inverse(inverse(inverse(c_0)))) = inverse(A). [back_rewrite(437),rewrite([446(3),446(4)])].
% 0.70/1.06 457 inverse(inverse(c_0)) = c_0. [back_rewrite(430),rewrite([446(6),453(12)])].
% 0.70/1.06 465 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(408),rewrite([446(5)])].
% 0.70/1.06 470 inverse(inverse(inverse(multiply(A,multiply(multiply(inverse(c_0),multiply(B,C)),D))))) = multiply(inverse(multiply(C,D)),inverse(multiply(multiply(A,c_0),B))). [back_rewrite(401),rewrite([446(9),433(11)])].
% 0.70/1.06 471 inverse(inverse(inverse(multiply(multiply(multiply(inverse(c_0),multiply(A,B)),C),multiply(inverse(multiply(B,C)),inverse(multiply(multiply(D,c_0),A))))))) = D. [back_rewrite(398),rewrite([446(16)])].
% 0.70/1.06 473 multiply(multiply(inverse(c_0),A),B) = multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A)))))))),B). [back_rewrite(392),rewrite([446(5),446(6),446(8)]),flip(a)].
% 0.70/1.06 474 multiply(inverse(c_0),A) = inverse(inverse(A)). [back_rewrite(391),rewrite([457(4),197(4),446(2)]),flip(a)].
% 0.70/1.06 484 inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(A,B)))))))))) = inverse(inverse(inverse(multiply(A,B)))). [back_rewrite(363),rewrite([446(6),446(7),446(9),446(14),433(16)])].
% 0.70/1.06 485 inverse(inverse(inverse(multiply(inverse(inverse(inverse(A))),B)))) = multiply(inverse(inverse(inverse(inverse(inverse(B))))),A). [back_rewrite(362),rewrite([446(4),446(7),433(9),446(10),446(12)])].
% 0.70/1.06 486 multiply(inverse(A),inverse(inverse(inverse(inverse(multiply(A,B)))))) = B. [back_rewrite(359),rewrite([446(5),433(7),433(7)])].
% 0.70/1.06 489 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(342),rewrite([474(4),446(4)])].
% 0.70/1.06 492 inverse(multiply(multiply(A,c_0),multiply(B,C))) = multiply(inverse(C),inverse(inverse(inverse(multiply(A,B))))). [back_rewrite(326),rewrite([446(3),446(5),489(4),446(5),433(7)]),flip(a)].
% 0.70/1.06 494 multiply(A,inverse(multiply(B,multiply(C,A)))) = inverse(inverse(inverse(multiply(B,multiply(C,c_0))))). [back_rewrite(316),rewrite([446(6)]),flip(a)].
% 0.70/1.06 495 multiply(inverse(A),multiply(A,multiply(B,c_0))) = B. [back_rewrite(293),rewrite([494(7),446(10),485(10),489(4)])].
% 0.70/1.06 496 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(290),rewrite([446(3),446(5),489(4)])].
% 0.70/1.06 497 multiply(inverse(inverse(A)),inverse(multiply(multiply(B,c_0),A))) = inverse(inverse(inverse(multiply(B,c_0)))). [back_rewrite(285),rewrite([474(3),446(12),433(14)])].
% 0.70/1.06 508 inverse(inverse(inverse(multiply(multiply(inverse(inverse(multiply(A,B))),C),multiply(inverse(multiply(B,C)),inverse(multiply(multiply(D,c_0),A))))))) = D. [back_rewrite(471),rewrite([474(4)])].
% 0.70/1.06 509 multiply(inverse(multiply(A,B)),inverse(multiply(multiply(C,c_0),D))) = inverse(inverse(inverse(multiply(C,multiply(inverse(inverse(multiply(D,A))),B))))). [back_rewrite(470),rewrite([474(4)]),flip(a)].
% 0.70/1.06 514 inverse(inverse(inverse(multiply(inverse(multiply(A,B)),inverse(inverse(inverse(C))))))) = multiply(inverse(inverse(multiply(C,A))),B). [back_rewrite(465),rewrite([494(9),433(7),474(13)])].
% 0.70/1.06 525 multiply(inverse(inverse(A)),B) = multiply(A,B). [back_rewrite(473),rewrite([474(3),489(7),489(7)])].
% 0.70/1.06 527 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(486),rewrite([489(6)])].
% 0.70/1.06 528 inverse(inverse(inverse(multiply(inverse(A),B)))) = multiply(inverse(B),A). [back_rewrite(485),rewrite([525(4),489(9)])].
% 0.70/1.06 529 inverse(inverse(inverse(multiply(A,B)))) = inverse(multiply(A,B)). [back_rewrite(484),rewrite([489(5),489(5)]),flip(a)].
% 0.70/1.06 544 inverse(multiply(multiply(multiply(A,B),C),inverse(multiply(D,multiply(multiply(A,B),C))))) = D. [back_rewrite(508),rewrite([525(4),509(9),525(6),529(8),529(10)])].
% 0.70/1.06 554 inverse(multiply(inverse(multiply(A,B)),inverse(inverse(inverse(C))))) = multiply(multiply(C,A),B). [back_rewrite(514),rewrite([529(9),525(11)])].
% 0.70/1.06 559 multiply(inverse(multiply(A,B)),inverse(multiply(multiply(C,c_0),D))) = inverse(multiply(C,multiply(multiply(D,A),B))). [back_rewrite(509),rewrite([525(11),529(13)])].
% 0.70/1.06 563 multiply(A,inverse(multiply(multiply(B,c_0),A))) = inverse(multiply(B,c_0)). [back_rewrite(497),rewrite([525(7),529(10)])].
% 0.70/1.06 564 multiply(A,c_0) = A. [back_rewrite(495),rewrite([527(5)])].
% 0.70/1.06 565 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(528),rewrite([529(5)])].
% 0.70/1.06 569 inverse(multiply(A,multiply(B,C))) = multiply(inverse(C),inverse(multiply(A,B))). [back_rewrite(492),rewrite([564(2),529(8)])].
% 0.70/1.06 574 multiply(A,inverse(multiply(B,A))) = inverse(B). [back_rewrite(563),rewrite([564(2),564(5)])].
% 0.70/1.06 575 multiply(inverse(multiply(A,B)),inverse(multiply(C,D))) = multiply(inverse(B),multiply(inverse(A),inverse(multiply(C,D)))). [back_rewrite(559),rewrite([564(4),569(9),569(9)])].
% 0.70/1.06 582 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [back_rewrite(554),rewrite([565(7),489(4)]),flip(a)].
% 0.70/1.06 583 inverse(inverse(A)) = A. [back_rewrite(544),rewrite([582(2),582(4),569(6),575(7),582(9),582(8),496(7),496(5),574(3)])].
% 0.70/1.06 590 multiply(inverse(A),A) = c_0. [para(583(a,1),197(a,1,2))].
% 0.70/1.06 591 $F # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([590(4),590(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=21. Generated=886. Kept=589. proofs=1.
% 0.70/1.06 Usable=4. Sos=5. Demods=10. Limbo=1, Disabled=581. Hints=0.
% 0.70/1.06 Megabytes=0.84.
% 0.70/1.06 User_CPU=0.11, 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 5044 exit (max_proofs) Tue Jun 14 10:34:11 2022
% 0.70/1.06 Prover9 interrupted
%------------------------------------------------------------------------------