TSTP Solution File: GRP407-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP407-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:18:58 EDT 2022
% Result : Unsatisfiable 1.86s 2.13s
% Output : Refutation 1.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP407-1 : TPTP v8.1.0. Released v2.6.0.
% 0.09/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Mon Jun 13 17:40:24 EDT 2022
% 0.16/0.36 % CPUTime :
% 1.86/2.13 ============================== Prover9 ===============================
% 1.86/2.13 Prover9 (32) version 2009-11A, November 2009.
% 1.86/2.13 Process 12442 was started by sandbox on n019.cluster.edu,
% 1.86/2.13 Mon Jun 13 17:40:25 2022
% 1.86/2.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12289_n019.cluster.edu".
% 1.86/2.13 ============================== end of head ===========================
% 1.86/2.13
% 1.86/2.13 ============================== INPUT =================================
% 1.86/2.13
% 1.86/2.13 % Reading from file /tmp/Prover9_12289_n019.cluster.edu
% 1.86/2.13
% 1.86/2.13 set(prolog_style_variables).
% 1.86/2.13 set(auto2).
% 1.86/2.13 % set(auto2) -> set(auto).
% 1.86/2.13 % set(auto) -> set(auto_inference).
% 1.86/2.13 % set(auto) -> set(auto_setup).
% 1.86/2.13 % set(auto_setup) -> set(predicate_elim).
% 1.86/2.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.86/2.13 % set(auto) -> set(auto_limits).
% 1.86/2.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.86/2.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.86/2.13 % set(auto) -> set(auto_denials).
% 1.86/2.13 % set(auto) -> set(auto_process).
% 1.86/2.13 % set(auto2) -> assign(new_constants, 1).
% 1.86/2.13 % set(auto2) -> assign(fold_denial_max, 3).
% 1.86/2.13 % set(auto2) -> assign(max_weight, "200.000").
% 1.86/2.13 % set(auto2) -> assign(max_hours, 1).
% 1.86/2.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.86/2.13 % set(auto2) -> assign(max_seconds, 0).
% 1.86/2.13 % set(auto2) -> assign(max_minutes, 5).
% 1.86/2.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.86/2.13 % set(auto2) -> set(sort_initial_sos).
% 1.86/2.13 % set(auto2) -> assign(sos_limit, -1).
% 1.86/2.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.86/2.13 % set(auto2) -> assign(max_megs, 400).
% 1.86/2.13 % set(auto2) -> assign(stats, some).
% 1.86/2.13 % set(auto2) -> clear(echo_input).
% 1.86/2.13 % set(auto2) -> set(quiet).
% 1.86/2.13 % set(auto2) -> clear(print_initial_clauses).
% 1.86/2.13 % set(auto2) -> clear(print_given).
% 1.86/2.13 assign(lrs_ticks,-1).
% 1.86/2.13 assign(sos_limit,10000).
% 1.86/2.13 assign(order,kbo).
% 1.86/2.13 set(lex_order_vars).
% 1.86/2.13 clear(print_given).
% 1.86/2.13
% 1.86/2.13 % formulas(sos). % not echoed (2 formulas)
% 1.86/2.13
% 1.86/2.13 ============================== end of input ==========================
% 1.86/2.13
% 1.86/2.13 % From the command line: assign(max_seconds, 300).
% 1.86/2.13
% 1.86/2.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.86/2.13
% 1.86/2.13 % Formulas that are not ordinary clauses:
% 1.86/2.13
% 1.86/2.13 ============================== end of process non-clausal formulas ===
% 1.86/2.13
% 1.86/2.13 ============================== PROCESS INITIAL CLAUSES ===============
% 1.86/2.13
% 1.86/2.13 ============================== PREDICATE ELIMINATION =================
% 1.86/2.13
% 1.86/2.13 ============================== end predicate elimination =============
% 1.86/2.13
% 1.86/2.13 Auto_denials:
% 1.86/2.13 % copying label prove_these_axioms_2 to answer in negative clause
% 1.86/2.13
% 1.86/2.13 Term ordering decisions:
% 1.86/2.13
% 1.86/2.13 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.86/2.13 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 1.86/2.13
% 1.86/2.13 ============================== end of process initial clauses ========
% 1.86/2.13
% 1.86/2.13 ============================== CLAUSES FOR SEARCH ====================
% 1.86/2.13
% 1.86/2.13 ============================== end of clauses for search =============
% 1.86/2.13
% 1.86/2.13 ============================== SEARCH ================================
% 1.86/2.13
% 1.86/2.13 % Starting search at 0.01 seconds.
% 1.86/2.13
% 1.86/2.13 ============================== PROOF =================================
% 1.86/2.13 % SZS status Unsatisfiable
% 1.86/2.13 % SZS output start Refutation
% 1.86/2.13
% 1.86/2.13 % Proof 1 at 1.09 (+ 0.01) seconds: prove_these_axioms_2.
% 1.86/2.13 % Length of proof is 145.
% 1.86/2.13 % Level of proof is 35.
% 1.86/2.13 % Maximum clause weight is 156.000.
% 1.86/2.13 % Given clauses 27.
% 1.86/2.13
% 1.86/2.13 1 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C # label(single_axiom) # label(axiom). [assumption].
% 1.86/2.13 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 1.86/2.13 3 multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))))))) = C. [para(1(a,1),1(a,1,2,1,1,1,1,1))].
% 1.86/2.13 4 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(B),multiply(inverse(B),B))))). [para(1(a,1),1(a,1,2,1,1,1)),flip(a)].
% 1.86/2.13 6 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E)))))))) = multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),multiply(inverse(D),D))))). [para(3(a,1),1(a,1,2,1,1,1)),flip(a)].
% 1.86/2.13 7 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))))))). [para(1(a,1),3(a,1,2,1,1,1)),flip(a)].
% 1.86/2.13 17 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(B),multiply(inverse(B),B)))))) = C. [para(4(a,1),1(a,1,2))].
% 1.86/2.13 43 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C))),multiply(inverse(B),multiply(inverse(B),B)))) = C. [para(4(a,2),3(a,1)),rewrite([1(11)])].
% 1.86/2.13 44 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,inverse(multiply(inverse(A),multiply(inverse(D),multiply(inverse(D),D)))))),multiply(inverse(multiply(C,inverse(multiply(inverse(A),multiply(inverse(D),multiply(inverse(D),D)))))),multiply(C,inverse(multiply(inverse(A),multiply(inverse(D),multiply(inverse(D),D))))))))) = multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),multiply(inverse(D),D))))). [para(3(a,1),4(a,1,1,1,1,1,1)),rewrite([6(48),6(57),6(66)])].
% 1.86/2.13 53 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(multiply(D,E)),B)),F))),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,multiply(D,inverse(multiply(inverse(F),multiply(inverse(E),multiply(inverse(E),E)))))). [para(4(a,1),4(a,2,2))].
% 1.86/2.13 63 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(multiply(D,E)),inverse(multiply(inverse(C),multiply(inverse(multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),multiply(inverse(E),E)))))),multiply(inverse(multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),multiply(inverse(E),E)))))),multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),multiply(inverse(E),E)))))))))). [para(17(a,1),4(a,1,1,1,1,1,1,1,1))].
% 1.86/2.13 100 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(43(a,1),17(a,1,2,2)),flip(a)].
% 1.86/2.13 101 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(B),multiply(inverse(B),B)))) = C. [para(43(a,1),43(a,1,1,1,1,1,1,1)),rewrite([43(15)])].
% 1.86/2.13 132 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),D))),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(multiply(E,D)),multiply(E,multiply(inverse(B),B))))). [para(100(a,1),4(a,2,2,1))].
% 1.86/2.13 146 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,multiply(inverse(B),B)))))) = multiply(inverse(B),D). [para(100(a,1),17(a,1,2,2,1))].
% 1.86/2.13 152 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(100(a,1),100(a,1))].
% 1.86/2.13 180 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),multiply(inverse(C),multiply(inverse(C),C)))))),multiply(A,E)) = multiply(inverse(D),multiply(B,E)). [para(1(a,1),152(a,1,1,1)),flip(a)].
% 1.86/2.13 181 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),multiply(inverse(D),multiply(inverse(D),D)))))) = multiply(inverse(multiply(C,B)),E). [para(1(a,1),152(a,1,2)),flip(a)].
% 1.86/2.13 188 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(E),multiply(inverse(E),E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(E),multiply(inverse(E),E)))))))))),multiply(A,F)) = multiply(inverse(C),multiply(D,F)). [para(3(a,1),152(a,1,1,1)),flip(a)].
% 1.86/2.13 192 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(C,D))),E)),multiply(inverse(multiply(C,D)),multiply(inverse(multiply(F,D)),multiply(F,D))))) = multiply(A,inverse(multiply(inverse(E),multiply(inverse(B),multiply(inverse(B),B))))). [para(152(a,1),4(a,1,1,2,2))].
% 1.86/2.13 197 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(B,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D. [para(152(a,1),17(a,1,2,2,1,2,2))].
% 1.86/2.13 207 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)). [para(152(a,1),152(a,1,1,1))].
% 1.86/2.13 208 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))). [para(152(a,1),152(a,1,2))].
% 1.86/2.13 235 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)). [para(101(a,1),152(a,1,1)),flip(a)].
% 1.86/2.13 247 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(D,multiply(inverse(B),B)))))) = multiply(inverse(B),inverse(multiply(inverse(multiply(inverse(E),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),multiply(inverse(F),multiply(inverse(F),F))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),multiply(inverse(F),multiply(inverse(F),F))))),inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),multiply(inverse(F),multiply(inverse(F),F))))))))). [para(3(a,1),146(a,1,2,2,1,1,1))].
% 1.86/2.13 250 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),multiply(inverse(A),A)))) = inverse(multiply(inverse(multiply(C,B)),multiply(C,multiply(inverse(A),A)))). [para(146(a,1),4(a,1,1,1,1)),rewrite([1(27)])].
% 1.86/2.13 264 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,E))),multiply(inverse(multiply(F,D)),multiply(inverse(B),B)))))) = multiply(inverse(B),multiply(F,E)). [para(152(a,1),146(a,1,2,2,1,1,1))].
% 1.86/2.13 280 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),D) = multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),D). [para(1(a,1),207(a,1,2)),rewrite([181(23)])].
% 1.86/2.13 487 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,C)),multiply(inverse(F),F))))) = multiply(A,inverse(multiply(inverse(multiply(inverse(F),multiply(E,D))),multiply(inverse(F),multiply(inverse(F),F))))). [para(207(a,2),6(a,2,2,1)),rewrite([6(48)]),flip(a)].
% 1.86/2.13 534 multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(A),multiply(inverse(multiply(E,C)),multiply(E,D))). [para(1(a,1),208(a,1,1,1)),rewrite([180(23)])].
% 1.86/2.13 615 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))). [para(208(a,1),207(a,1))].
% 1.86/2.13 704 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))). [para(101(a,1),534(a,1,1)),rewrite([101(16)])].
% 1.86/2.13 973 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D)))),multiply(inverse(multiply(E,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))) = multiply(E,D). [para(615(a,1),4(a,1,1,1,1)),rewrite([1(28)])].
% 1.86/2.13 1003 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),E)),multiply(inverse(multiply(F,multiply(V6,D))),multiply(F,multiply(V6,C))))))) = multiply(inverse(multiply(B,C)),E). [para(615(a,1),146(a,1,2,2,1,2))].
% 1.86/2.13 1039 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),E)),multiply(inverse(multiply(F,D)),multiply(F,multiply(A,multiply(B,V6))))) = multiply(inverse(multiply(V7,E)),multiply(V7,multiply(inverse(multiply(V8,multiply(V9,C))),multiply(V8,multiply(V9,V6))))). [para(615(a,1),208(a,2,2,2))].
% 1.86/2.13 1073 inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(C),C)))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(C),C)))). [para(152(a,1),250(a,1,1))].
% 1.86/2.13 1086 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),multiply(inverse(E),E)))) = inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(F,multiply(inverse(E),E)))). [para(207(a,2),250(a,1,1))].
% 1.86/2.13 1119 inverse(multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(B),B)))) = inverse(multiply(inverse(multiply(D,multiply(E,C))),multiply(D,multiply(E,B)))). [para(615(a,1),250(a,1,1)),flip(a)].
% 1.86/2.13 1138 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(multiply(E,C)),multiply(E,multiply(A,B))))) = inverse(multiply(inverse(multiply(F,D)),multiply(F,multiply(inverse(multiply(V6,B)),multiply(V6,B))))). [para(208(a,1),1073(a,1,1,2))].
% 1.86/2.13 1519 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(B),B))) = C. [para(235(a,2),17(a,1,2,2,1)),rewrite([146(30)])].
% 1.86/2.13 1610 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),B)),multiply(F,multiply(inverse(multiply(inverse(multiply(V6,E)),multiply(V6,F))),V7)))) = multiply(inverse(multiply(V8,C)),multiply(V8,multiply(A,multiply(D,V7)))). [para(235(a,1),208(a,1,2,2))].
% 1.86/2.13 1633 multiply(A,multiply(inverse(multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),D)),multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),V6)))) = multiply(A,multiply(inverse(multiply(V7,D)),multiply(V7,multiply(B,V6)))). [para(235(a,1),704(a,1,2,2))].
% 1.86/2.13 1712 multiply(inverse(multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,D)))),multiply(A,inverse(multiply(inverse(E),multiply(inverse(multiply(F,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D))),multiply(inverse(multiply(V7,multiply(B,D))),multiply(V7,multiply(B,D)))))))) = E. [para(235(a,1),197(a,1,2,2,1,2,1,1))].
% 1.86/2.13 1717 multiply(inverse(multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,D)))),multiply(A,inverse(multiply(inverse(E),multiply(inverse(multiply(F,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D))),multiply(inverse(multiply(V7,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D))),multiply(V7,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D)))))))) = E. [para(235(a,2),197(a,1,1,1,2))].
% 1.86/2.13 1751 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),D)),C)),multiply(inverse(D),multiply(inverse(D),D)))) = multiply(inverse(B),multiply(inverse(B),B)). [para(1519(a,1),101(a,1,1,1,1,2))].
% 1.86/2.13 1784 multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(D)))),E))),multiply(A,D)) = multiply(inverse(multiply(F,multiply(V6,E))),multiply(F,multiply(V6,multiply(inverse(C),multiply(inverse(C),C))))). [para(1519(a,1),615(a,1,2,2))].
% 1.86/2.13 1785 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),D))),C) = multiply(inverse(multiply(E,multiply(F,D))),multiply(E,multiply(F,multiply(inverse(B),B)))). [para(1519(a,1),615(a,1,2))].
% 1.86/2.13 1799 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(C),C). [para(1519(a,1),235(a,2,2))].
% 1.86/2.13 1805 multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C))))),D)),multiply(inverse(A),multiply(inverse(A),A))))) = D. [para(1799(a,2),1(a,1,2,1,1,1,1,1))].
% 1.86/2.13 1807 multiply(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),a2) != a2 # answer(prove_these_axioms_2). [para(1799(a,2),2(a,1,1))].
% 1.86/2.13 1830 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(inverse(E),inverse(multiply(inverse(D),multiply(inverse(E),multiply(inverse(E),E))))). [para(1799(a,2),4(a,1,1,1,1,1,1,1,1))].
% 1.86/2.13 1832 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),multiply(inverse(C),C)))) = C. [para(1799(a,2),4(a,1,1,1,1)),rewrite([1(30)])].
% 1.86/2.13 1841 multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D))))))),multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D)))),multiply(multiply(B,inverse(multiply(inverse(E),multiply(inverse(C),multiply(inverse(C),C))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D))))))) = multiply(inverse(F),F). [para(4(a,1),1799(a,1,2,2,2,1))].
% 1.86/2.13 1846 multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(B),B))))),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))) = A. [para(1799(a,2),17(a,1,2))].
% 1.86/2.13 1859 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),D)) = multiply(inverse(multiply(E,C)),multiply(E,D)). [para(1799(a,2),152(a,1,1,1))].
% 1.86/2.13 1860 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))) = multiply(inverse(multiply(E,B)),multiply(E,A)). [para(1799(a,2),152(a,1,2))].
% 1.86/2.13 1884 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C))),multiply(inverse(D),D)) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,multiply(inverse(B),multiply(inverse(B),B))))). [para(1799(a,1),207(a,1,2))].
% 1.86/2.13 1889 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D)))))),multiply(inverse(multiply(E,B)),F)) = multiply(inverse(multiply(V6,multiply(E,A))),multiply(V6,F)). [para(1799(a,2),207(a,1,1,1,2))].
% 1.86/2.13 1893 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(multiply(C,D)),E)) = multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,D))),multiply(inverse(multiply(C,V6)),E)). [para(1799(a,2),207(a,2,1,1)),flip(a)].
% 1.86/2.13 1894 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(inverse(E),multiply(D,C))),multiply(inverse(multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))),multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6))))). [para(1799(a,2),207(a,2,2))].
% 1.86/2.13 1925 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),D))),E) = multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,D))),E). [para(1799(a,2),280(a,1,1,1,1,1))].
% 1.86/2.13 1926 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D)))))),E) = multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,A))),E). [para(1799(a,2),280(a,1,1,1,2))].
% 1.86/2.13 1940 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(D),B)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(E,multiply(inverse(F),multiply(inverse(F),F)))))) = multiply(inverse(multiply(V6,C)),multiply(V6,multiply(A,D))). [para(1799(a,2),208(a,1,2,2))].
% 1.86/2.13 1941 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),multiply(D,E))) = multiply(inverse(multiply(inverse(multiply(D,F)),C)),multiply(inverse(multiply(V6,F)),multiply(V6,E))). [para(1799(a,2),208(a,2,1,1)),flip(a)].
% 1.86/2.13 1943 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E))))) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),multiply(inverse(multiply(V6,F)),multiply(V6,B))). [para(1799(a,2),208(a,2,2)),flip(a)].
% 1.86/2.13 1953 multiply(A,multiply(inverse(multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C))))),multiply(inverse(D),E))) = multiply(A,multiply(inverse(multiply(F,D)),multiply(F,E))). [para(1799(a,2),704(a,1,2,1,1))].
% 1.86/2.13 1954 multiply(A,multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E)))))) = multiply(A,multiply(inverse(multiply(F,C)),multiply(F,B))). [para(1799(a,2),704(a,1,2,2))].
% 1.86/2.13 1958 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(F),multiply(inverse(F),F))))),A)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(E,multiply(inverse(F),multiply(inverse(F),F)))))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(F),multiply(inverse(F),F))))),A)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(E,multiply(inverse(F),multiply(inverse(F),F)))))))),inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(F),multiply(inverse(F),F))))),A)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(inverse(V6),V6))))))))). [para(1799(a,1),7(a,2,2,1,2,2,2,1,2,2))].
% 1.86/2.13 1959 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),C)),multiply(inverse(D),multiply(inverse(D),D)))) = multiply(E,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(E,F)),D)),multiply(inverse(F),multiply(inverse(F),F))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(E,F)),D)),multiply(inverse(F),multiply(inverse(F),F))))),inverse(multiply(inverse(multiply(inverse(multiply(E,F)),D)),multiply(inverse(F),multiply(inverse(F),F))))))))). [para(1799(a,2),7(a,1,1,1,1,1,1))].
% 1.86/2.13 1967 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))),multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))))))). [para(1799(a,2),7(a,2,2,1,2,2))].
% 1.86/2.13 1971 multiply(inverse(A),A) = multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(B,D)),E)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(B,D)),E)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(B,D)),E)),multiply(inverse(D),multiply(inverse(D),D))))))))),multiply(inverse(multiply(inverse(multiply(inverse(E),F)),C)),multiply(inverse(F),multiply(inverse(F),F)))). [para(7(a,1),1799(a,1,1)),flip(a)].
% 1.86/2.13 1978 multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E)))))) = multiply(inverse(multiply(F,multiply(V6,C))),multiply(F,multiply(V6,B))). [para(1799(a,2),615(a,1,2,2))].
% 1.86/2.13 2022 multiply(inverse(multiply(A,multiply(inverse(B),B))),multiply(A,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(multiply(F,B)),multiply(F,B))))))) = C. [para(1799(a,2),197(a,1,2,2,1,2,1,1))].
% 1.86/2.13 2033 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))))),multiply(A,E)) = multiply(F,multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,F))),E)). [para(1799(a,2),235(a,1,1,1,2,2))].
% 1.86/2.13 2034 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(multiply(inverse(C),multiply(inverse(C),C))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)). [para(1799(a,2),235(a,1,1,1))].
% 1.86/2.13 2035 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(B),B)))),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,E))),A)). [para(1799(a,2),235(a,1,2))].
% 1.86/2.13 2038 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C)) = multiply(B,multiply(inverse(multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E))))),C)). [para(1799(a,2),235(a,2,2,1,1))].
% 1.86/2.13 2051 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E)))))) = C. [para(1799(a,2),1519(a,1,2,2))].
% 1.86/2.13 2052 multiply(inverse(A),A) = multiply(inverse(B),B). [para(1519(a,1),1799(a,1,1,1)),rewrite([1519(12)])].
% 1.86/2.13 2059 multiply(inverse(A),A) = c_0. [new_symbol(2052)].
% 1.86/2.13 2060 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),c_0)) = C. [back_rewrite(2051),rewrite([2059(10),2059(15),2059(17)])].
% 1.86/2.13 2069 multiply(inverse(multiply(A,multiply(inverse(B),c_0))),multiply(A,C)) = multiply(B,multiply(inverse(c_0),C)). [back_rewrite(2038),rewrite([2059(3),2059(10),2059(15),2059(17)])].
% 1.86/2.14 2072 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(inverse(D),multiply(inverse(C),c_0))),c_0). [back_rewrite(2035),rewrite([2059(4),2059(9),2059(14),2059(16)]),flip(a)].
% 1.86/2.14 2073 multiply(inverse(multiply(inverse(A),multiply(inverse(B),c_0))),c_0) = multiply(inverse(c_0),multiply(inverse(multiply(inverse(B),c_0)),A)). [back_rewrite(2034),rewrite([2059(3),2059(8),2059(10),2059(5),2072(15)]),flip(a)].
% 1.86/2.14 2074 multiply(inverse(c_0),multiply(inverse(multiply(inverse(A),c_0)),B)) = multiply(A,multiply(inverse(c_0),B)). [back_rewrite(2033),rewrite([2059(4),2059(9),2059(11),2069(7),2072(11),2073(12)]),flip(a)].
% 1.86/2.14 2079 multiply(inverse(multiply(A,c_0)),multiply(A,inverse(multiply(inverse(B),c_0)))) = B. [back_rewrite(2022),rewrite([2059(2),2059(7),2059(12),2059(14),2059(10),2059(8)])].
% 1.86/2.14 2094 multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,c_0)) = multiply(inverse(multiply(D,multiply(E,C))),multiply(D,multiply(E,B))). [back_rewrite(1978),rewrite([2059(7),2059(12),2059(14)])].
% 1.86/2.14 2098 multiply(multiply(A,inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),multiply(inverse(C),c_0)))),c_0)))),multiply(inverse(multiply(inverse(multiply(inverse(D),E)),B)),multiply(inverse(E),c_0))) = c_0. [back_rewrite(1971),rewrite([2059(2),2059(9),2059(19),2059(29),2059(32),2059(25)]),flip(a)].
% 1.86/2.14 2101 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),c_0))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),c_0)))),c_0)))). [back_rewrite(1967),rewrite([2059(8),2059(18),2059(24),2059(29),2059(31)])].
% 1.86/2.14 2103 multiply(A,inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),multiply(inverse(C),c_0)))),c_0)))) = inverse(multiply(inverse(multiply(inverse(c_0),B)),multiply(inverse(D),c_0))). [back_rewrite(1959),rewrite([2059(3),2059(8),2059(10),2059(7),2059(17),2059(27),2059(37),2059(40)]),flip(a)].
% 1.86/2.14 2104 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),c_0))) = inverse(multiply(inverse(multiply(inverse(c_0),C)),multiply(inverse(A),c_0))). [back_rewrite(1958),rewrite([2059(8),2059(14),2059(22),2059(27),2059(32),2059(34),2059(32),2059(40),2059(45),2059(50),2059(52),2059(50),2059(58),2059(62),2059(65),2103(34)])].
% 1.86/2.14 2105 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(inverse(D),C)),c_0)). [back_rewrite(1954),rewrite([2059(6),2059(11),2059(13)]),flip(a)].
% 1.86/2.14 2106 multiply(A,multiply(inverse(multiply(inverse(B),C)),c_0)) = multiply(A,multiply(inverse(c_0),multiply(inverse(C),B))). [back_rewrite(1953),rewrite([2059(3),2059(8),2059(10),2105(11)]),flip(a)].
% 1.86/2.14 2111 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(c_0),multiply(inverse(B),D))) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),c_0). [back_rewrite(1943),rewrite([2059(7),2059(12),2059(14),2105(15),2106(16)]),flip(a)].
% 1.86/2.14 2113 multiply(inverse(multiply(inverse(multiply(A,B)),C)),c_0) = multiply(inverse(c_0),multiply(inverse(C),multiply(A,B))). [back_rewrite(1941),rewrite([2059(3),2059(8),2059(10),2105(15),2106(16),2111(16)]),flip(a)].
% 1.86/2.14 2114 multiply(inverse(multiply(A,B)),multiply(A,multiply(C,D))) = multiply(inverse(c_0),multiply(inverse(B),multiply(C,D))). [back_rewrite(1940),rewrite([2059(10),2059(15),2059(17),2106(10),2111(10),2113(6)]),flip(a)].
% 1.86/2.14 2116 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),D) = multiply(inverse(multiply(inverse(multiply(inverse(C),B)),c_0)),D). [back_rewrite(1926),rewrite([2059(6),2059(11),2059(13)]),flip(a)].
% 1.86/2.14 2117 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),c_0)),C) = multiply(inverse(multiply(inverse(c_0),multiply(inverse(B),A))),C). [back_rewrite(1925),rewrite([2059(3),2059(8),2059(10),2116(13)]),flip(a)].
% 1.86/2.14 2123 multiply(inverse(multiply(inverse(c_0),multiply(inverse(A),B))),multiply(inverse(multiply(C,A)),D)) = multiply(inverse(multiply(inverse(D),multiply(C,B))),c_0). [back_rewrite(1894),rewrite([2116(9),2117(10),2059(17),2059(22),2059(24)])].
% 1.86/2.14 2124 multiply(inverse(multiply(inverse(A),multiply(B,C))),c_0) = multiply(inverse(c_0),multiply(inverse(multiply(B,C)),A)). [back_rewrite(1893),rewrite([2059(3),2059(8),2059(10),2116(15),2117(16),2123(16)]),flip(a)].
% 1.86/2.14 2126 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(inverse(c_0),multiply(inverse(multiply(B,C)),D)). [back_rewrite(1889),rewrite([2059(6),2059(11),2059(13),2117(10),2123(10),2124(6)]),flip(a)].
% 1.86/2.14 2127 multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(A),multiply(inverse(B),c_0)))) = multiply(inverse(multiply(B,multiply(inverse(c_0),A))),c_0). [back_rewrite(1884),rewrite([2059(3),2126(7),2074(8),2059(7),2059(13),2114(16),2114(16)]),flip(a)].
% 1.86/2.14 2135 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(1860),rewrite([2059(6),2059(11),2059(13)]),flip(a)].
% 1.86/2.14 2136 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(1859),rewrite([2059(3),2059(8),2059(10),2135(9)]),flip(a)].
% 1.86/2.14 2138 multiply(inverse(c_0),multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(A),c_0))))) = B. [back_rewrite(1846),rewrite([2059(4),2059(12),2059(17),2059(19),2136(11)])].
% 1.86/2.14 2140 multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(c_0),A)),multiply(inverse(multiply(B,C)),c_0))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),A)),multiply(inverse(D),c_0)))),multiply(multiply(B,inverse(multiply(inverse(A),multiply(inverse(C),c_0)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),A)),multiply(inverse(D),c_0)))))) = c_0. [back_rewrite(1841),rewrite([2059(9),2104(11),2059(19),2104(21),2059(29),2059(43),2104(45),2059(48),2059(60),2135(65),2135(63),2136(44),2136(47),2136(46),2059(49)])].
% 1.86/2.14 2148 inverse(multiply(inverse(c_0),multiply(inverse(A),c_0))) = A. [back_rewrite(1832),rewrite([2059(3),2059(8),2059(10),2059(5)])].
% 1.86/2.14 2149 multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(A),c_0)))) = B. [back_rewrite(1830),rewrite([2059(3),2059(8),2059(10),2059(9),2104(11),2059(8),2136(6),2148(7),2059(5)]),flip(a)].
% 1.86/2.14 2152 multiply(c_0,a2) != a2 # answer(prove_these_axioms_2). [back_rewrite(1807),rewrite([2059(3),2059(8),2059(10)])].
% 1.86/2.14 2153 multiply(inverse(c_0),A) = A. [back_rewrite(1805),rewrite([2059(4),2059(9),2059(11),2059(8),2149(11)])].
% 1.86/2.14 2166 multiply(inverse(multiply(inverse(inverse(A)),B)),A) = multiply(inverse(B),c_0). [back_rewrite(1785),rewrite([2135(5),2136(6),2153(6),2135(7),2136(6),2153(6),2059(10),2135(12),2135(10),2136(11),2153(10),2153(8)])].
% 1.86/2.14 2167 multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),C)),B) = multiply(inverse(C),multiply(inverse(A),c_0)). [back_rewrite(1784),rewrite([2135(5),2136(6),2153(6),2135(9),2136(10),2153(10),2059(13),2135(16),2135(14),2136(15),2153(15),2136(15),2153(15)])].
% 1.86/2.14 2190 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(1751),rewrite([2135(5),2136(6),2153(6),2167(7),2059(9),2135(10),2153(6),2136(6),2153(5),2153(3),2059(4)]),flip(a)].
% 1.86/2.14 2223 inverse(multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(B),C))),D)))))),inverse(multiply(inverse(D),inverse(C))))) = A. [back_rewrite(1717),rewrite([2059(3),2190(3),2135(5),2190(6),2135(11),2190(12),2135(18),2190(19),2135(25),2190(26),2059(28),2190(16),2135(18),2190(19)])].
% 1.86/2.14 2228 multiply(A,c_0) = A. [back_rewrite(1712),rewrite([2059(3),2190(3),2135(5),2190(6),2135(11),2190(12),2059(20),2190(16),2135(18),2223(17)])].
% 1.86/2.14 2303 multiply(A,multiply(inverse(multiply(inverse(multiply(B,inverse(C))),D)),multiply(E,multiply(inverse(inverse(multiply(inverse(E),C))),F)))) = multiply(A,inverse(multiply(inverse(multiply(B,F)),D))). [back_rewrite(1633),rewrite([2059(3),2228(3),2135(9),2228(10),2135(18),2228(19)])].
% 1.86/2.14 2321 multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(multiply(D,E)),B))) = inverse(multiply(inverse(multiply(A,multiply(D,E))),C)). [back_rewrite(1610),rewrite([2059(7),2228(7),2135(13),2228(14),2303(17),2135(15),2228(16)])].
% 1.86/2.14 2639 inverse(multiply(inverse(multiply(A,B)),A)) = inverse(inverse(B)). [back_rewrite(1138),rewrite([2135(11),2228(12),2321(11),2059(4),2153(3),2059(8),2228(6)]),flip(a)].
% 1.86/2.14 2649 inverse(inverse(inverse(multiply(inverse(A),B)))) = inverse(inverse(multiply(inverse(B),A))). [back_rewrite(1119),rewrite([2059(6),2228(6),2639(6),2135(10),2135(8),2228(9),2228(10)]),flip(a)].
% 1.86/2.14 2654 inverse(multiply(inverse(inverse(multiply(inverse(A),B))),inverse(multiply(C,B)))) = inverse(inverse(multiply(C,A))). [back_rewrite(1086),rewrite([2135(4),2228(5),2059(8),2228(8),2059(13),2228(13),2639(13)])].
% 1.86/2.14 2674 inverse(inverse(multiply(A,B))) = multiply(A,B). [back_rewrite(973),rewrite([2135(6),2135(4),2228(5),2228(6),2649(5),2059(10),2228(8),2654(8)])].
% 1.86/2.14 2907 multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(D,C))))) = multiply(A,multiply(D,B)). [back_rewrite(487),rewrite([2135(4),2228(5),2674(4),2059(6),2228(6),2059(14),2228(14),2639(14),2674(10)])].
% 1.86/2.14 3032 inverse(multiply(inverse(multiply(A,B)),C)) = multiply(inverse(C),multiply(A,B)). [back_rewrite(264),rewrite([2135(6),2228(7),2674(6),2059(8),2228(8),2907(9),2135(5),2228(6)])].
% 1.86/2.14 3045 multiply(inverse(A),multiply(inverse(multiply(multiply(multiply(inverse(B),multiply(C,D)),inverse(D)),multiply(multiply(multiply(inverse(B),multiply(C,D)),inverse(D)),inverse(multiply(multiply(inverse(B),multiply(C,D)),inverse(D)))))),multiply(inverse(B),E))) = inverse(multiply(multiply(inverse(E),C),A)). [back_rewrite(247),rewrite([2059(5),2228(5),2135(7),2674(4),2228(6),3032(12),2059(14),2228(14),2674(15),3032(17),2059(19),2228(19),2674(20),3032(22),2059(24),2228(24),3032(28)]),flip(a)].
% 1.86/2.14 3052 multiply(A,multiply(multiply(inverse(A),B),C)) = inverse(multiply(inverse(C),inverse(B))). [back_rewrite(235),rewrite([2059(3),2228(3),2135(5),2228(6),2135(8),2228(9),2674(8)]),flip(a)].
% 1.86/2.14 3077 inverse(multiply(inverse(A),inverse(multiply(B,C)))) = multiply(B,inverse(multiply(inverse(A),inverse(C)))). [back_rewrite(192),rewrite([3032(5),2059(12),2228(10),3032(10),2674(3),3052(7),2059(9),2228(9)])].
% 1.86/2.14 3081 multiply(multiply(inverse(A),B),C) = multiply(inverse(A),multiply(B,C)). [back_rewrite(188),rewrite([3032(7),2059(9),2228(9),2674(10),3032(12),2059(14),2228(14),2674(15),3032(17),2059(19),2228(19),3032(23),2135(26),3045(24),2674(5),2228(5)])].
% 1.86/2.14 3096 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,inverse(inverse(C))). [back_rewrite(132),rewrite([3032(4),3081(6),2059(10),2228(10),2639(10),2674(6),2059(8),2228(8),2639(8)])].
% 1.86/2.14 3097 inverse(multiply(inverse(A),multiply(B,inverse(B)))) = A. [back_rewrite(101),rewrite([2135(4),2228(5),2674(4),2059(5),2228(5),3081(4)])].
% 1.86/2.14 3102 inverse(multiply(inverse(A),multiply(inverse(B),multiply(C,inverse(C))))) = inverse(multiply(inverse(A),inverse(B))). [back_rewrite(63),rewrite([3032(5),2059(7),2228(7),3081(6),3081(5),2059(14),2228(14),2059(20),2228(20),2059(26),2228(26),2059(28),2228(18),3077(18),2674(15),2135(17),2674(14),3081(13),3081(12),2059(11),2228(11),2228(13)])].
% 1.86/2.14 3111 multiply(A,multiply(multiply(B,C),D)) = multiply(A,multiply(B,inverse(multiply(inverse(D),inverse(C))))). [back_rewrite(53),rewrite([3032(4),3032(7),3081(7),3081(8),3096(7),2674(5),2059(9),2228(9),2639(9),2674(5),2059(7),2228(7)])].
% 1.86/2.14 3117 multiply(A,inverse(multiply(inverse(B),inverse(C)))) = multiply(A,multiply(inverse(inverse(C)),B)). [back_rewrite(44),rewrite([2059(7),2228(7),2059(13),2228(13),2059(19),2228(19),2059(21),2228(11),3077(11),2674(8),2135(7),2228(6),2674(5),2059(8),2228(8)]),flip(a)].
% 1.86/2.14 3130 inverse(inverse(A)) = A. [back_rewrite(17),rewrite([2059(6),2228(6),3117(7),2135(7),2166(5),2228(3),2228(4)])].
% 1.86/2.14 3149 inverse(multiply(inverse(A),inverse(B))) = multiply(B,A). [back_rewrite(2073),rewrite([2228(4),2228(6),2228(9),3130(8),2153(8)])].
% 1.86/2.14 3151 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(2079),rewrite([2228(2),2228(4),3130(3)])].
% 1.86/2.14 3153 multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),multiply(A,inverse(multiply(D,inverse(D)))))))) = multiply(C,B). [back_rewrite(2101),rewrite([3032(5),2228(7),3081(6),3081(5),3102(7),3149(4),3032(6),2228(8),3081(7),3111(7),3130(5),3130(10),2228(10)]),flip(a)].
% 1.86/2.14 3155 multiply(A,inverse(A)) = c_0. [back_rewrite(2098),rewrite([3032(5),2228(7),3081(6),3111(6),3130(4),3130(9),2228(9),3153(10),3032(6),2228(8),3081(7),3081(6),3096(8),3097(5)])].
% 1.86/2.14 3168 inverse(multiply(inverse(A),multiply(B,C))) = multiply(inverse(C),multiply(inverse(B),A)). [back_rewrite(1039),rewrite([3032(5),3081(5),3111(5),3149(6),3111(4),3149(5),2135(12),3032(11),2228(12),2135(11),2135(7),2135(5),2228(6),3130(5),2228(5),2228(6),2135(12),2135(10),2228(11),3130(10),2228(10),2135(10),3032(9),2228(10)])].
% 1.86/2.14 3174 multiply(inverse(multiply(A,B)),C) = multiply(inverse(B),multiply(inverse(A),C)). [back_rewrite(1003),rewrite([2135(7),2228(8),3130(7),3081(6),3168(7),2135(13),2135(11),2228(12),3130(11),2228(11),3081(10),3096(9),3130(7),2059(6),2228(6),3130(5),2135(5),3168(4),2228(6)]),flip(a)].
% 1.86/2.14 3178 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(2094),rewrite([2228(6),3174(5),2059(5),2228(5),3174(9),3151(9),3174(7),3151(7)])].
% 1.86/2.14 3180 multiply(multiply(A,B),inverse(B)) = A. [back_rewrite(2060),rewrite([3174(5),3151(5),3178(4),3130(2),2228(4)])].
% 1.86/2.14 3183 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(2127),rewrite([2228(8),2153(8),2153(6),2153(6),2228(7)]),flip(a)].
% 1.86/2.14 3184 inverse(c_0) = c_0. [back_rewrite(2140),rewrite([2153(7),3183(7),2228(10),3183(10),3183(8),3130(6),3130(6),3130(7),3183(8),3081(10),3183(11),3183(9),3130(9),3130(10),3081(9),3081(10),3111(10),3183(11),3130(9),3130(9),3183(11),3183(9),3183(8),3081(11),3130(13),3081(12),3081(11),2228(15),3081(14),3081(13),3180(12),3096(12),3183(9),3130(7),3130(7),3183(7),3096(9),3130(6),3155(6),2228(10),3183(10),3130(8),3130(8),3183(10),3081(12),3183(13),3183(11),3130(11),3130(12),3081(11),3081(12),3111(12),3183(13),3130(11),3130(11),3183(13),3183(11),3183(10),3081(13),3130(15),3081(14),3081(13),2228(17),3081(16),3081(15),3180(14),3111(15),3183(12),3183(10),3130(8),3130(8),3130(9),3183(10),3096(12),3130(9),3180(9),3155(8),2228(8),2153(7),2153(5)])].
% 1.86/2.14 3187 multiply(c_0,A) = A. [back_rewrite(2138),rewrite([3184(2),2228(6),3183(6),3130(4),3130(4),3151(4)])].
% 1.86/2.14 3188 $F # answer(prove_these_axioms_2). [resolve(3187,a,2152,a)].
% 1.86/2.14
% 1.86/2.14 % SZS output end Refutation
% 1.86/2.14 ============================== end of proof ==========================
% 1.86/2.14
% 1.86/2.14 ============================== STATISTICS ============================
% 1.86/2.14
% 1.86/2.14 Given=27. Generated=7647. Kept=3187. proofs=1.
% 1.86/2.14 Usable=0. Sos=21. Demods=805. Limbo=1038, Disabled=2129. Hints=0.
% 1.86/2.14 Megabytes=9.06.
% 1.86/2.14 User_CPU=1.09, System_CPU=0.01, Wall_clock=1.
% 1.86/2.14
% 1.86/2.14 ============================== end of statistics =====================
% 1.86/2.14
% 1.86/2.14 ============================== end of search =========================
% 1.86/2.14
% 1.86/2.14 THEOREM PROVED
% 1.86/2.14 % SZS status Unsatisfiable
% 1.86/2.14
% 1.86/2.14 Exiting with 1 proof.
% 1.86/2.14
% 1.86/2.14 Process 12442 exit (max_proofs) Mon Jun 13 17:40:26 2022
% 1.86/2.14 Prover9 interrupted
%------------------------------------------------------------------------------