TSTP Solution File: GRP404-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP404-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:18:57 EDT 2022
% Result : Unsatisfiable 2.88s 3.17s
% Output : Refutation 2.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP404-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 01:47:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.88/3.17 ============================== Prover9 ===============================
% 2.88/3.17 Prover9 (32) version 2009-11A, November 2009.
% 2.88/3.17 Process 32612 was started by sandbox on n008.cluster.edu,
% 2.88/3.17 Tue Jun 14 01:47:38 2022
% 2.88/3.17 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32458_n008.cluster.edu".
% 2.88/3.17 ============================== end of head ===========================
% 2.88/3.17
% 2.88/3.17 ============================== INPUT =================================
% 2.88/3.17
% 2.88/3.17 % Reading from file /tmp/Prover9_32458_n008.cluster.edu
% 2.88/3.17
% 2.88/3.17 set(prolog_style_variables).
% 2.88/3.17 set(auto2).
% 2.88/3.17 % set(auto2) -> set(auto).
% 2.88/3.17 % set(auto) -> set(auto_inference).
% 2.88/3.17 % set(auto) -> set(auto_setup).
% 2.88/3.17 % set(auto_setup) -> set(predicate_elim).
% 2.88/3.17 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.88/3.17 % set(auto) -> set(auto_limits).
% 2.88/3.17 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.88/3.17 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.88/3.17 % set(auto) -> set(auto_denials).
% 2.88/3.17 % set(auto) -> set(auto_process).
% 2.88/3.17 % set(auto2) -> assign(new_constants, 1).
% 2.88/3.17 % set(auto2) -> assign(fold_denial_max, 3).
% 2.88/3.17 % set(auto2) -> assign(max_weight, "200.000").
% 2.88/3.17 % set(auto2) -> assign(max_hours, 1).
% 2.88/3.17 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.88/3.17 % set(auto2) -> assign(max_seconds, 0).
% 2.88/3.17 % set(auto2) -> assign(max_minutes, 5).
% 2.88/3.17 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.88/3.17 % set(auto2) -> set(sort_initial_sos).
% 2.88/3.17 % set(auto2) -> assign(sos_limit, -1).
% 2.88/3.17 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.88/3.17 % set(auto2) -> assign(max_megs, 400).
% 2.88/3.17 % set(auto2) -> assign(stats, some).
% 2.88/3.17 % set(auto2) -> clear(echo_input).
% 2.88/3.17 % set(auto2) -> set(quiet).
% 2.88/3.17 % set(auto2) -> clear(print_initial_clauses).
% 2.88/3.17 % set(auto2) -> clear(print_given).
% 2.88/3.17 assign(lrs_ticks,-1).
% 2.88/3.17 assign(sos_limit,10000).
% 2.88/3.17 assign(order,kbo).
% 2.88/3.17 set(lex_order_vars).
% 2.88/3.17 clear(print_given).
% 2.88/3.17
% 2.88/3.17 % formulas(sos). % not echoed (2 formulas)
% 2.88/3.17
% 2.88/3.17 ============================== end of input ==========================
% 2.88/3.17
% 2.88/3.17 % From the command line: assign(max_seconds, 300).
% 2.88/3.17
% 2.88/3.17 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.88/3.17
% 2.88/3.17 % Formulas that are not ordinary clauses:
% 2.88/3.17
% 2.88/3.17 ============================== end of process non-clausal formulas ===
% 2.88/3.17
% 2.88/3.17 ============================== PROCESS INITIAL CLAUSES ===============
% 2.88/3.17
% 2.88/3.17 ============================== PREDICATE ELIMINATION =================
% 2.88/3.17
% 2.88/3.17 ============================== end predicate elimination =============
% 2.88/3.17
% 2.88/3.17 Auto_denials:
% 2.88/3.17 % copying label prove_these_axioms_2 to answer in negative clause
% 2.88/3.17
% 2.88/3.17 Term ordering decisions:
% 2.88/3.17
% 2.88/3.17 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 2.88/3.17 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 2.88/3.17
% 2.88/3.17 ============================== end of process initial clauses ========
% 2.88/3.17
% 2.88/3.17 ============================== CLAUSES FOR SEARCH ====================
% 2.88/3.17
% 2.88/3.17 ============================== end of clauses for search =============
% 2.88/3.17
% 2.88/3.17 ============================== SEARCH ================================
% 2.88/3.17
% 2.88/3.17 % Starting search at 0.01 seconds.
% 2.88/3.17
% 2.88/3.17 ============================== PROOF =================================
% 2.88/3.17 % SZS status Unsatisfiable
% 2.88/3.17 % SZS output start Refutation
% 2.88/3.17
% 2.88/3.17 % Proof 1 at 2.21 (+ 0.02) seconds: prove_these_axioms_2.
% 2.88/3.17 % Length of proof is 143.
% 2.88/3.17 % Level of proof is 34.
% 2.88/3.17 % Maximum clause weight is 150.000.
% 2.88/3.17 % Given clauses 39.
% 2.88/3.17
% 2.88/3.17 1 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))))) = C # label(single_axiom) # label(axiom). [assumption].
% 2.88/3.17 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 2.88/3.17 3 multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D)))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))))))))) = C. [para(1(a,1),1(a,1,2,1,1,1,1,1))].
% 2.88/3.17 4 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,multiply(inverse(B),B)))))). [para(1(a,1),1(a,1,2,1,1,1)),flip(a)].
% 2.88/3.17 7 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(D,inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),inverse(multiply(E,multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),inverse(multiply(E,multiply(inverse(E),E)))))),inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),inverse(multiply(E,multiply(inverse(E),E))))))))))). [para(1(a,1),3(a,1,2,1,1,1)),flip(a)].
% 2.88/3.17 14 inverse(multiply(A,multiply(inverse(A),A))) = multiply(inverse(multiply(inverse(multiply(B,C)),A)),inverse(multiply(multiply(B,inverse(multiply(inverse(D),inverse(multiply(C,multiply(inverse(C),C)))))),inverse(multiply(D,multiply(inverse(D),D)))))). [para(4(a,1),1(a,1,2,1,1)),flip(a)].
% 2.88/3.17 16 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),inverse(multiply(B,multiply(inverse(B),B))))))) = C. [para(4(a,1),1(a,1,2))].
% 2.88/3.17 42 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C))),inverse(multiply(B,multiply(inverse(B),B))))) = C. [para(4(a,2),3(a,1)),rewrite([1(11)])].
% 2.88/3.17 94 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(42(a,1),16(a,1,2,2)),flip(a)].
% 2.88/3.17 95 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B))))) = C. [para(42(a,1),42(a,1,1,1,1,1,1,1)),rewrite([42(15)])].
% 2.88/3.17 141 multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),D)))))))),multiply(A,E)) = multiply(inverse(C),multiply(inverse(multiply(B,D)),E)). [para(16(a,1),94(a,1,1,1)),flip(a)].
% 2.88/3.17 144 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(94(a,1),94(a,1))].
% 2.88/3.17 171 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D. [para(144(a,1),1(a,1,2,1,2,1,2))].
% 2.88/3.17 172 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),inverse(multiply(C,multiply(inverse(C),C))))))),multiply(A,E)) = multiply(inverse(D),multiply(B,E)). [para(1(a,1),144(a,1,1,1)),flip(a)].
% 2.88/3.17 173 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),inverse(multiply(D,multiply(inverse(D),D))))))) = multiply(inverse(multiply(C,B)),E). [para(1(a,1),144(a,1,2)),flip(a)].
% 2.88/3.17 199 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(144(a,1),144(a,1,1,1))].
% 2.88/3.17 200 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(144(a,1),144(a,1,2))].
% 2.88/3.17 225 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)). [para(95(a,1),144(a,1,1)),flip(a)].
% 2.88/3.17 227 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C)))))) = D. [para(144(a,1),95(a,1,1,2,1,2))].
% 2.88/3.17 235 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),multiply(inverse(multiply(D,F)),E)). [para(1(a,1),199(a,1,1,1,2)),rewrite([141(23)])].
% 2.88/3.17 236 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),199(a,1,2)),rewrite([173(23)])].
% 2.88/3.17 451 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),200(a,1,1,1)),rewrite([172(23)])].
% 2.88/3.17 514 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(200(a,1),199(a,1))].
% 2.88/3.17 598 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))). [para(95(a,1),451(a,1,1)),rewrite([95(16)])].
% 2.88/3.17 747 multiply(A,multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,E)))) = multiply(A,multiply(inverse(multiply(F,multiply(V6,D))),multiply(F,multiply(V6,E)))). [para(514(a,1),598(a,1,2))].
% 2.88/3.17 938 inverse(multiply(A,multiply(inverse(A),A))) = multiply(inverse(multiply(B,A)),inverse(multiply(C,inverse(multiply(multiply(B,C),multiply(inverse(multiply(D,C)),multiply(D,C))))))). [para(95(a,1),171(a,1,2,1,1)),flip(a)].
% 2.88/3.17 1131 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),C)),multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),F)))),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,F). [para(225(a,1),95(a,1,1,1,1,2))].
% 2.88/3.17 1136 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)). [para(95(a,1),225(a,1,1))].
% 2.88/3.17 1203 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,multiply(inverse(multiply(C,B)),multiply(C,D)))) = multiply(E,multiply(inverse(multiply(F,multiply(V6,E))),multiply(F,multiply(V6,D)))). [para(200(a,1),225(a,2,2))].
% 2.88/3.17 1284 multiply(A,multiply(inverse(multiply(inverse(B),multiply(C,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(B),multiply(C,E))),D)). [para(1(a,1),1136(a,1,2,1,1,1,1)),rewrite([172(20)])].
% 2.88/3.17 1543 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(C,multiply(inverse(multiply(inverse(D),multiply(E,C))),F)))),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(inverse(multiply(inverse(D),multiply(E,A))),F). [para(1284(a,1),95(a,1,1,1,1,2))].
% 2.88/3.17 1544 multiply(A,multiply(inverse(multiply(B,multiply(C,A))),D)) = multiply(E,multiply(inverse(multiply(B,multiply(C,E))),D)). [para(95(a,1),1284(a,1,2,1,1,1)),rewrite([95(16)])].
% 2.88/3.17 1647 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(B,multiply(inverse(B),B)))))))),D) = multiply(C,D). [back_rewrite(1131),rewrite([1543(23)])].
% 2.88/3.17 1780 multiply(inverse(multiply(A,multiply(B,inverse(multiply(C,inverse(multiply(D,multiply(inverse(D),D)))))))),multiply(A,E)) = multiply(C,multiply(inverse(multiply(B,D)),E)). [para(1647(a,1),144(a,1)),flip(a)].
% 2.88/3.17 2328 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),E)) = multiply(A,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,D))),E)). [para(144(a,1),1780(a,2,2,1,1)),rewrite([1780(16)])].
% 2.88/3.17 3062 multiply(A,multiply(B,multiply(inverse(multiply(C,D)),multiply(C,E)))) = multiply(A,multiply(B,multiply(inverse(multiply(F,D)),multiply(F,E)))). [para(1647(a,1),747(a,1,2)),rewrite([1780(18)])].
% 2.88/3.17 3310 inverse(multiply(inverse(inverse(multiply(A,multiply(inverse(A),A)))),inverse(multiply(A,multiply(inverse(A),A))))) = multiply(B,inverse(multiply(inverse(inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(B,D)),C),multiply(inverse(multiply(E,C)),multiply(E,C))))))),inverse(multiply(D,multiply(inverse(D),D)))))). [para(938(a,2),4(a,1,1,1,1))].
% 2.88/3.17 3325 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(B,multiply(inverse(B),B)))) = C. [para(938(a,2),16(a,1,2))].
% 2.88/3.17 3334 multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))) = multiply(inverse(multiply(D,C)),multiply(D,inverse(multiply(E,inverse(multiply(multiply(A,E),multiply(inverse(multiply(F,E)),multiply(F,E)))))))). [para(938(a,2),144(a,1,2))].
% 2.88/3.17 3443 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(D,inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(E),E)))),A)),inverse(multiply(multiply(E,multiply(inverse(E),E)),multiply(inverse(multiply(E,multiply(inverse(E),E))),multiply(E,multiply(inverse(E),E))))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(E),E)))),A)),inverse(multiply(multiply(E,multiply(inverse(E),E)),multiply(inverse(multiply(E,multiply(inverse(E),E))),multiply(E,multiply(inverse(E),E)))))))),inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(E),E)))),A)),inverse(multiply(multiply(E,multiply(inverse(E),E)),multiply(multiply(inverse(multiply(F,E)),inverse(multiply(V6,inverse(multiply(multiply(F,V6),multiply(inverse(multiply(V7,V6)),multiply(V7,V6))))))),multiply(E,multiply(inverse(E),E))))))))))))). [para(938(a,1),7(a,2,2,1,2,1,2,2,1,2,1,2,1))].
% 2.88/3.17 3461 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C)))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C))))))),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C))))))))) = multiply(inverse(D),inverse(multiply(F,inverse(multiply(multiply(A,F),multiply(inverse(multiply(V6,F)),multiply(V6,F))))))). [para(171(a,1),938(a,2,1,1))].
% 2.88/3.17 3526 inverse(multiply(multiply(A,inverse(multiply(B,inverse(multiply(C,multiply(inverse(C),C)))))),multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,multiply(inverse(C),C))))))),multiply(A,inverse(multiply(B,inverse(multiply(C,multiply(inverse(C),C))))))))) = multiply(B,inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(A,C)),D),multiply(inverse(multiply(E,D)),multiply(E,D))))))). [para(938(a,2),1647(a,1))].
% 2.88/3.17 3666 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),E)),inverse(multiply(D,multiply(inverse(D),D))))))),inverse(multiply(B,multiply(inverse(B),B)))) = multiply(inverse(E),inverse(multiply(C,multiply(inverse(C),C)))). [para(4(a,2),3325(a,1,1,1,2))].
% 2.88/3.17 3715 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),inverse(multiply(D,multiply(inverse(D),D))))). [para(3325(a,1),1136(a,1,2))].
% 2.88/3.17 3720 multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),inverse(D)))),inverse(multiply(multiply(B,inverse(multiply(A,inverse(multiply(C,multiply(inverse(C),C)))))),multiply(inverse(multiply(B,inverse(multiply(A,inverse(multiply(C,multiply(inverse(C),C))))))),multiply(B,inverse(multiply(A,inverse(multiply(C,multiply(inverse(C),C)))))))))) = D. [para(1647(a,1),3325(a,1,1,1))].
% 2.88/3.17 3789 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(inverse(multiply(E,F)),B)),inverse(multiply(multiply(E,inverse(multiply(inverse(V6),inverse(multiply(F,multiply(inverse(F),F)))))),inverse(multiply(V6,multiply(inverse(V6),V6))))))))). [para(14(a,1),4(a,2,2,1,2))].
% 2.88/3.17 3826 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C)))) = multiply(inverse(multiply(E,D)),multiply(E,inverse(multiply(multiply(A,inverse(multiply(inverse(F),inverse(multiply(B,multiply(inverse(B),B)))))),inverse(multiply(F,multiply(inverse(F),F))))))). [para(14(a,2),144(a,1,2))].
% 2.88/3.17 3836 inverse(multiply(inverse(multiply(A,multiply(inverse(A),A))),multiply(inverse(inverse(multiply(A,multiply(inverse(A),A)))),inverse(multiply(A,multiply(inverse(A),A)))))) = multiply(B,inverse(multiply(multiply(inverse(multiply(C,A)),inverse(multiply(inverse(D),inverse(multiply(multiply(C,B),multiply(inverse(multiply(C,B)),multiply(C,B))))))),inverse(multiply(D,multiply(inverse(D),D)))))). [para(95(a,1),14(a,2,1))].
% 2.88/3.17 3845 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B)))) = multiply(inverse(multiply(D,multiply(inverse(multiply(E,F)),C))),multiply(D,inverse(multiply(multiply(E,inverse(multiply(inverse(V6),inverse(multiply(F,multiply(inverse(F),F)))))),inverse(multiply(V6,multiply(inverse(V6),V6))))))). [para(14(a,2),199(a,1,2))].
% 2.88/3.17 3946 inverse(multiply(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,multiply(inverse(C),C)))))),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(inverse(multiply(A,C)),inverse(multiply(inverse(inverse(multiply(multiply(D,E),multiply(inverse(multiply(D,E)),multiply(D,E))))),inverse(multiply(multiply(D,E),multiply(inverse(multiply(F,E)),multiply(F,E))))))). [para(14(a,2),171(a,1,2,1,1,1)),flip(a)].
% 2.88/3.17 3965 multiply(inverse(multiply(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,multiply(inverse(C),C)))))),inverse(multiply(B,multiply(inverse(B),B))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),E)),inverse(multiply(D,multiply(inverse(D),D))))),F)) = multiply(inverse(multiply(V6,inverse(multiply(E,multiply(inverse(E),E))))),multiply(V6,F)). [para(14(a,2),225(a,2,2,1,1,2)),flip(a)].
% 2.88/3.17 3976 multiply(inverse(multiply(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,multiply(inverse(C),C)))))),inverse(multiply(B,multiply(inverse(B),B))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),E)),inverse(multiply(D,multiply(inverse(D),D))))),F)) = multiply(V6,multiply(inverse(multiply(inverse(multiply(V7,E)),multiply(V7,V6))),F)). [para(14(a,2),1136(a,1,2,1,1,2))].
% 2.88/3.17 4134 inverse(multiply(A,multiply(inverse(A),A))) = multiply(inverse(multiply(inverse(multiply(B,C)),A)),inverse(multiply(multiply(B,inverse(multiply(inverse(D),inverse(multiply(C,multiply(inverse(C),C)))))),multiply(inverse(multiply(E,D)),inverse(multiply(F,inverse(multiply(multiply(E,F),multiply(inverse(multiply(V6,F)),multiply(V6,F)))))))))). [para(938(a,1),14(a,2,2,1,2))].
% 2.88/3.17 4161 multiply(multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C))))),a2) != a2 # answer(prove_these_axioms_2). [para(3715(a,1),2(a,1,1))].
% 2.88/3.17 4178 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C)))))),D)),E)),inverse(multiply(D,multiply(inverse(D),D))))) = multiply(inverse(F),inverse(multiply(inverse(E),inverse(multiply(F,multiply(inverse(F),F)))))). [para(3715(a,1),4(a,1,1,1,1,1,1,1,1))].
% 2.88/3.17 4183 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B))))),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(D,multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,D))),inverse(multiply(F,multiply(inverse(F),F))))))). [para(3715(a,1),4(a,2,2,1))].
% 2.88/3.17 4186 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),B)),inverse(multiply(multiply(C,D),multiply(inverse(multiply(C,D)),multiply(C,D)))))) = multiply(C,inverse(multiply(inverse(B),inverse(multiply(D,multiply(inverse(D),D)))))). [para(3715(a,2),4(a,1,1,1,1,1,1)),rewrite([3325(17),3325(18),3325(20)])].
% 2.88/3.17 4187 inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,multiply(inverse(B),B))))) = B. [para(3715(a,2),4(a,1,1,1,1)),rewrite([3325(23),1(20)])].
% 2.88/3.17 4196 inverse(multiply(A,multiply(inverse(A),A))) = multiply(inverse(multiply(B,A)),multiply(B,inverse(multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,multiply(inverse(E),E)))))))). [para(3715(a,1),16(a,1,2,2,1)),flip(a)].
% 2.88/3.17 4197 multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),B)))))),B)),multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,multiply(inverse(E),E)))))) = A. [para(3715(a,1),16(a,1,2))].
% 2.88/3.17 4205 multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C)))))),multiply(inverse(D),E)) = multiply(inverse(multiply(F,D)),multiply(F,E)). [para(3715(a,1),144(a,1,1,1))].
% 2.88/3.17 4206 multiply(inverse(multiply(inverse(A),B)),multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,multiply(inverse(E),E)))))) = multiply(inverse(multiply(F,B)),multiply(F,A)). [para(3715(a,1),144(a,1,2))].
% 2.88/3.17 4225 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(F,multiply(inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,F))),inverse(multiply(V7,multiply(inverse(V7),V7)))))). [para(3715(a,1),199(a,2,2))].
% 2.88/3.17 4226 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),multiply(D,C))) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,E))),inverse(multiply(V6,multiply(inverse(V6),V6))))). [para(3715(a,1),199(a,2))].
% 2.88/3.17 4239 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C)))))),multiply(inverse(D),E))),F) = multiply(inverse(multiply(inverse(multiply(V6,D)),multiply(V6,E))),F). [para(3715(a,1),236(a,1,1,1,1,1))].
% 2.88/3.17 4240 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,multiply(inverse(E),E))))))),F) = multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,A))),F). [para(3715(a,1),236(a,1,1,1,2))].
% 2.88/3.17 4241 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,B))),C) = multiply(inverse(multiply(D,multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,D))),inverse(multiply(F,multiply(inverse(F),F)))))),C). [para(3715(a,1),236(a,1,1,1)),flip(a)].
% 2.88/3.17 4246 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,E)),multiply(D,F))))),multiply(C,B))),inverse(multiply(inverse(multiply(inverse(multiply(V6,E)),multiply(V6,F))),multiply(inverse(inverse(multiply(inverse(multiply(D,E)),multiply(D,F)))),inverse(multiply(inverse(multiply(D,E)),multiply(D,F)))))))). [para(236(a,1),3715(a,2,2,2,1))].
% 2.88/3.17 4266 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(inverse(multiply(A,E)),C)),multiply(F,multiply(inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,F))),inverse(multiply(V7,multiply(inverse(V7),V7)))))). [para(3715(a,1),200(a,2,2))].
% 2.88/3.17 4280 multiply(A,multiply(inverse(multiply(inverse(B),C)),multiply(D,multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,D))),inverse(multiply(F,multiply(inverse(F),F))))))) = multiply(A,multiply(inverse(multiply(V6,C)),multiply(V6,B))). [para(3715(a,1),598(a,1,2,2))].
% 2.88/3.17 4304 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(D,inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),inverse(multiply(E,multiply(inverse(E),E))))),multiply(F,multiply(inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,F))),inverse(multiply(V7,multiply(inverse(V7),V7)))))))))). [para(3715(a,1),7(a,2,2,1,2,1,2))].
% 2.88/3.17 4306 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),B)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(D,inverse(multiply(inverse(B),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(E,multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(E,multiply(inverse(E),E)))))),inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(E,multiply(inverse(E),E))))))))))). [para(3715(a,2),7(a,1,1,1,1,1,1)),rewrite([3325(16),3325(16),3325(17)])].
% 2.88/3.17 4341 multiply(inverse(multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),B))))),multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,multiply(inverse(E),E)))))) = multiply(F,multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,F))),A)). [para(3715(a,1),225(a,1,2))].
% 2.88/3.17 4345 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,multiply(inverse(multiply(C,B)),multiply(C,D)))) = multiply(D,multiply(E,multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,E))),inverse(multiply(V6,multiply(inverse(V6),V6)))))). [para(3715(a,1),225(a,2,2))].
% 2.88/3.17 4349 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,multiply(inverse(multiply(C,B)),multiply(C,D)))) = multiply(D,multiply(inverse(E),E)). [para(3715(a,2),225(a,2,2)),rewrite([3325(21)])].
% 2.88/3.17 4357 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(C,multiply(inverse(multiply(E,multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,E))),inverse(multiply(V6,multiply(inverse(V6),V6)))))),D)). [para(3715(a,1),1136(a,1,2,1,1)),flip(a)].
% 2.88/3.17 4375 multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),A))),D)) = multiply(C,multiply(inverse(multiply(B,multiply(E,multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,E))),inverse(multiply(V6,multiply(inverse(V6),V6))))))),D)). [para(3715(a,1),1544(a,1,2,1,1,2)),flip(a)].
% 2.88/3.17 4386 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(D,multiply(inverse(multiply(E,F)),multiply(E,inverse(multiply(D,inverse(multiply(F,multiply(inverse(F),F)))))))). [para(3715(a,1),1647(a,1))].
% 2.88/3.17 4388 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(C,D)),multiply(C,inverse(multiply(B,inverse(multiply(D,multiply(inverse(D),D)))))))). [para(3715(a,2),1647(a,1)),rewrite([3325(23)])].
% 2.88/3.17 4433 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(C,multiply(inverse(multiply(inverse(multiply(D,multiply(E,F))),multiply(D,C))),B))),inverse(multiply(inverse(multiply(multiply(E,F),multiply(inverse(multiply(V6,F)),multiply(V6,F)))),multiply(inverse(inverse(multiply(multiply(E,F),multiply(inverse(multiply(V6,F)),multiply(V6,F))))),inverse(multiply(multiply(E,F),multiply(inverse(multiply(V6,F)),multiply(V6,F))))))))). [para(227(a,1),3715(a,2,2,1,1,1))].
% 2.88/3.17 4446 multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(B),C)),multiply(D,multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,D))),inverse(multiply(F,multiply(inverse(F),F))))))),V6)) = multiply(A,multiply(inverse(multiply(inverse(multiply(V7,C)),multiply(V7,B))),V6)). [para(3715(a,1),2328(a,1,2,1,1,2))].
% 2.88/3.17 4447 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,C)),multiply(E,D)))) = multiply(A,multiply(F,multiply(inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,F))),inverse(multiply(V7,multiply(inverse(V7),V7)))))). [para(3715(a,1),2328(a,1,2)),flip(a)].
% 2.88/3.17 4460 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(inverse(multiply(A,E)),C)),multiply(inverse(F),F)). [para(3715(a,2),235(a,1,2)),rewrite([3325(25)]),flip(a)].
% 2.88/3.17 4491 multiply(A,multiply(B,multiply(inverse(multiply(inverse(C),D)),multiply(E,multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,E))),inverse(multiply(V6,multiply(inverse(V6),V6)))))))) = multiply(A,multiply(B,multiply(inverse(multiply(V7,D)),multiply(V7,C)))). [para(3715(a,1),3062(a,1,2,2,2))].
% 2.88/3.17 4492 multiply(A,multiply(B,multiply(inverse(multiply(C,D)),multiply(C,D)))) = multiply(A,multiply(B,multiply(E,multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,E))),inverse(multiply(V6,multiply(inverse(V6),V6))))))). [para(3715(a,1),3062(a,1,2,2)),flip(a)].
% 2.88/3.17 4521 multiply(inverse(A),A) = multiply(inverse(B),B). [para(3325(a,1),3715(a,2,2))].
% 2.88/3.17 4551 multiply(inverse(A),A) = c_0. [new_symbol(4521)].
% 2.88/3.17 4621 multiply(A,multiply(B,multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),inverse(multiply(E,c_0)))))) = multiply(A,multiply(B,c_0)). [back_rewrite(4492),rewrite([4551(4),4551(10)]),flip(a)].
% 2.88/3.17 4622 multiply(A,multiply(B,multiply(inverse(multiply(C,D)),multiply(C,E)))) = multiply(A,multiply(B,multiply(inverse(multiply(inverse(E),D)),c_0))). [back_rewrite(4491),rewrite([4551(10),4621(15)]),flip(a)].
% 2.88/3.17 4653 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(inverse(multiply(A,E)),C)),c_0). [back_rewrite(4460),rewrite([4551(15)])].
% 2.88/3.17 4665 multiply(A,multiply(B,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),inverse(multiply(D,c_0))))) = multiply(A,c_0). [back_rewrite(4447),rewrite([4653(10),4551(4),4551(4),4551(9)]),flip(a)].
% 2.88/3.17 4666 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),E)) = multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(D),C)),c_0)),E)). [back_rewrite(4446),rewrite([4551(10),4665(14)]),flip(a)].
% 2.88/3.17 4678 multiply(A,multiply(inverse(multiply(B,multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(C,D))),c_0)),A))),inverse(multiply(inverse(multiply(multiply(C,D),c_0)),c_0)))) = c_0. [back_rewrite(4433),rewrite([4551(2),4666(9),4551(16),4551(20),4551(25),4551(25)]),flip(a)].
% 2.88/3.17 4718 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(A,inverse(multiply(C,c_0))))))) = c_0. [back_rewrite(4388),rewrite([4551(2),4551(5)]),flip(a)].
% 2.88/3.17 4720 multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(A),B)),c_0)),inverse(multiply(B,c_0)))) = c_0. [back_rewrite(4386),rewrite([4551(7),4666(10),4551(15),4718(21)])].
% 2.88/3.17 4730 multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),A))),D)) = multiply(C,multiply(inverse(multiply(B,c_0)),D)). [back_rewrite(4375),rewrite([4551(13),4666(16),4720(17)])].
% 2.88/3.17 4741 multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(A),B)),c_0)),C)) = multiply(B,multiply(inverse(c_0),C)). [back_rewrite(4357),rewrite([4666(7),4551(15),4666(18),4720(19)])].
% 2.88/3.17 4748 multiply(inverse(multiply(A,inverse(multiply(B,c_0)))),multiply(A,multiply(inverse(multiply(inverse(C),B)),c_0))) = multiply(C,c_0). [back_rewrite(4349),rewrite([4551(2),4622(11),4551(14)])].
% 2.88/3.17 4752 multiply(A,multiply(B,multiply(inverse(c_0),inverse(multiply(B,c_0))))) = multiply(A,c_0). [back_rewrite(4345),rewrite([4551(2),4622(11),4748(12),4551(9),4666(12),4741(13)]),flip(a)].
% 2.88/3.17 4755 multiply(inverse(multiply(inverse(A),inverse(multiply(B,c_0)))),c_0) = multiply(B,multiply(inverse(c_0),A)). [back_rewrite(4341),rewrite([4551(3),4551(13),4666(16),4741(17),4752(14),4666(15),4741(16)])].
% 2.88/3.17 4784 multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,multiply(inverse(c_0),multiply(inverse(multiply(A,C)),D))))))) = inverse(multiply(inverse(multiply(inverse(c_0),B)),inverse(multiply(D,c_0)))). [back_rewrite(4306),rewrite([4551(2),4551(6),4551(16),4551(25),4551(35),4551(39),4755(21)]),flip(a)].
% 2.88/3.17 4786 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),inverse(multiply(B,c_0)))) = inverse(multiply(inverse(multiply(inverse(c_0),C)),inverse(multiply(A,c_0)))). [back_rewrite(4304),rewrite([4551(7),4551(17),4551(27),4666(30),4741(31),4752(28),4755(22),4784(22)])].
% 2.88/3.17 4805 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(inverse(D),C)),c_0)). [back_rewrite(4280),rewrite([4551(10),4666(13),4741(14),4752(11)]),flip(a)].
% 2.88/3.17 4818 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(D),B)),c_0)) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),c_0). [back_rewrite(4266),rewrite([4805(9),4551(21),4666(24),4741(25),4752(22)])].
% 2.88/3.17 4833 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),c_0)))) = c_0. [back_rewrite(4246),rewrite([4551(2),4551(28),4666(21),4741(22)]),flip(a)].
% 2.88/3.17 4837 multiply(inverse(multiply(A,multiply(inverse(c_0),inverse(multiply(A,c_0))))),B) = multiply(inverse(c_0),B). [back_rewrite(4241),rewrite([4551(4),4551(10),4666(13),4741(14)]),flip(a)].
% 2.88/3.17 4838 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),D) = multiply(inverse(multiply(inverse(multiply(inverse(C),B)),c_0)),D). [back_rewrite(4240),rewrite([4551(10),4666(13),4741(14),4752(11)]),flip(a)].
% 2.88/3.17 4839 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),c_0)),C) = multiply(inverse(multiply(inverse(c_0),multiply(inverse(B),A))),C). [back_rewrite(4239),rewrite([4551(7),4838(9),4741(11),4837(11),4838(13)]),flip(a)].
% 2.88/3.17 4850 multiply(A,multiply(inverse(c_0),inverse(multiply(A,c_0)))) = c_0. [back_rewrite(4226),rewrite([4805(10),4818(11),4551(4),4551(4),4551(8),4838(10),4839(11),4730(12),4551(5)]),flip(a)].
% 2.88/3.17 4851 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(4225),rewrite([4838(9),4839(10),4551(21),4838(23),4839(24),4730(25),4551(18),4850(21)])].
% 2.88/3.17 4859 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(4206),rewrite([4551(10),4838(12),4839(13),4730(14),4551(7),4850(10)]),flip(a)].
% 2.88/3.17 4860 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(4205),rewrite([4859(4),4551(8),4839(10),4730(11),4551(4),4850(7),4859(9)]),flip(a)].
% 2.88/3.17 4864 multiply(inverse(c_0),multiply(inverse(A),inverse(multiply(inverse(B),inverse(multiply(A,c_0)))))) = B. [back_rewrite(4197),rewrite([4551(3),4859(13),4860(14),4551(17),4730(20),4551(13),4850(16),4860(11)])].
% 2.88/3.17 4865 multiply(inverse(c_0),multiply(inverse(A),inverse(c_0))) = inverse(multiply(A,c_0)). [back_rewrite(4196),rewrite([4551(2),4859(9),4860(10),4551(13),4730(16),4551(9),4850(12),4859(9),4860(10)]),flip(a)].
% 2.88/3.17 4871 inverse(multiply(inverse(c_0),inverse(multiply(A,c_0)))) = A. [back_rewrite(4187),rewrite([4551(2),4551(4)])].
% 2.88/3.17 4872 inverse(multiply(inverse(multiply(inverse(c_0),A)),inverse(multiply(multiply(B,C),c_0)))) = multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,c_0))))). [back_rewrite(4186),rewrite([4551(2),4551(9),4551(13)])].
% 2.88/3.17 4874 inverse(multiply(A,inverse(multiply(multiply(B,A),c_0)))) = multiply(B,inverse(c_0)). [back_rewrite(4183),rewrite([4551(6),4551(11),4786(14),4871(7),4859(10),4860(11),4551(14),4730(17),4551(10),4850(13)])].
% 2.88/3.17 4875 inverse(multiply(inverse(multiply(inverse(c_0),A)),inverse(multiply(c_0,c_0)))) = multiply(inverse(B),inverse(multiply(inverse(A),inverse(multiply(B,c_0))))). [back_rewrite(4178),rewrite([4859(4),4860(5),4551(8),4730(11),4551(4),4850(7),4551(8),4786(11),4551(14)])].
% 2.88/3.17 4881 multiply(c_0,a2) != a2 # answer(prove_these_axioms_2). [back_rewrite(4161),rewrite([4859(4),4860(5),4551(8),4730(11),4551(4),4850(7)])].
% 2.88/3.17 4907 multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,c_0))))),inverse(multiply(D,c_0))))) = inverse(multiply(C,c_0)). [back_rewrite(4134),rewrite([4551(2),4551(10),4551(21),4874(22),4859(20),4860(21),4865(21)]),flip(a)].
% 2.88/3.17 4965 multiply(inverse(multiply(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,c_0))))),inverse(multiply(B,c_0)))),multiply(multiply(A,inverse(multiply(inverse(D),inverse(multiply(C,c_0))))),E)) = multiply(D,multiply(inverse(c_0),E)). [back_rewrite(3976),rewrite([4551(3),4551(9),4551(20),4786(23),4872(22),4859(25),4860(26),4730(29),4551(25)])].
% 2.88/3.17 4970 multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,c_0))),B)) = multiply(A,multiply(inverse(c_0),B)). [back_rewrite(3965),rewrite([4551(3),4551(9),4551(20),4786(23),4872(22),4965(21),4551(6),4859(11),4860(12)]),flip(a)].
% 2.88/3.17 4977 inverse(multiply(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,c_0))))),inverse(multiply(B,c_0)))) = multiply(inverse(multiply(A,C)),inverse(c_0)). [back_rewrite(3946),rewrite([4551(3),4551(9),4551(19),4551(24),4551(24)])].
% 2.88/3.17 5008 multiply(inverse(multiply(inverse(c_0),multiply(inverse(A),B))),inverse(multiply(A,c_0))) = multiply(inverse(c_0),inverse(multiply(B,c_0))). [back_rewrite(3845),rewrite([4859(4),4860(5),4551(8),4551(18),4551(24),4977(27),4859(22),4859(20),4860(17),4860(20),4860(19),4865(19)])].
% 2.88/3.17 5012 inverse(multiply(inverse(multiply(A,c_0)),c_0)) = multiply(A,multiply(inverse(c_0),inverse(c_0))). [back_rewrite(3836),rewrite([4551(2),4551(5),4551(9),4551(11),4551(14),4551(18),4977(21),4859(10),4860(11),4730(16),4551(10)])].
% 2.88/3.17 5014 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,c_0))) = multiply(inverse(c_0),multiply(inverse(D),multiply(inverse(multiply(A,B)),inverse(c_0)))). [back_rewrite(3826),rewrite([4551(8),4551(15),4551(21),4977(24),4859(19),4860(20)])].
% 2.88/3.17 5028 inverse(multiply(inverse(c_0),multiply(inverse(A),multiply(inverse(multiply(B,C)),inverse(c_0))))) = multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,c_0))))). [back_rewrite(3789),rewrite([4551(8),5014(10),4551(19),4551(25),4977(28),4859(22),4860(19),4865(19)])].
% 2.88/3.17 5046 multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),inverse(D)))),inverse(multiply(multiply(B,inverse(multiply(A,inverse(multiply(C,c_0))))),c_0))) = D. [back_rewrite(3720),rewrite([4551(8),4551(14),4551(21),4551(26)])].
% 2.88/3.17 5069 multiply(inverse(c_0),inverse(multiply(A,multiply(inverse(c_0),B)))) = multiply(inverse(B),inverse(multiply(A,c_0))). [back_rewrite(3666),rewrite([4551(10),5014(12),5028(13),4859(10),4860(11),4551(14),5008(16),4860(10),4970(10),4551(11)])].
% 2.88/3.17 5105 inverse(multiply(multiply(A,inverse(multiply(B,inverse(multiply(C,c_0))))),c_0)) = multiply(B,multiply(inverse(multiply(A,C)),inverse(c_0))). [back_rewrite(3526),rewrite([4551(2),4551(8),4551(15),4551(20),4551(16),4874(17)])].
% 2.88/3.17 5121 inverse(multiply(multiply(A,B),multiply(inverse(c_0),multiply(inverse(multiply(C,multiply(A,B))),D)))) = multiply(inverse(D),multiply(C,inverse(c_0))). [back_rewrite(3461),rewrite([4551(10),4551(21),4551(33),4551(35),4860(13),4970(13),4551(16),4874(17)])].
% 2.88/3.17 5125 multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),multiply(A,inverse(c_0)))))) = inverse(multiply(inverse(multiply(inverse(c_0),B)),inverse(multiply(C,c_0)))). [back_rewrite(3443),rewrite([4551(7),4786(10),4551(12),4551(18),4551(20),4551(23),4551(24),4551(25),4551(31),4551(33),4551(36),4551(37),4551(39),4551(45),4551(52),4874(53),4859(51),4860(52),4865(52),4551(50),4551(51),4551(51),4860(25),4970(25),5121(22)]),flip(a)].
% 2.88/3.17 5148 multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,c_0))) = multiply(inverse(c_0),multiply(inverse(C),multiply(A,inverse(c_0)))). [back_rewrite(3334),rewrite([4551(6),4551(15),4874(16),4859(15),4860(16)])].
% 2.88/3.17 5152 inverse(multiply(inverse(c_0),inverse(c_0))) = inverse(c_0). [back_rewrite(3310),rewrite([4551(2),4551(6),4551(8),4551(9),4874(10),4551(10),5148(12),5125(14),4551(6),4551(8)]),flip(a)].
% 2.88/3.17 5619 multiply(A,multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(A),B)))) = multiply(B,c_0). [back_rewrite(1203),rewrite([4551(2),4859(9),4860(10),4859(12),5008(10),4871(7),4859(8),4859(6),4860(7),4860(10),4860(9)]),flip(a)].
% 2.88/3.17 5840 multiply(c_0,c_0) = c_0. [back_rewrite(4678),rewrite([4860(6),4730(9),4551(5),5012(13),4859(14),5152(6),4860(9),4860(8),5619(10)])].
% 2.88/3.17 5885 inverse(c_0) = c_0. [back_rewrite(4833),rewrite([4859(4),4860(5),4859(12),4860(13),4860(16),4860(15),5069(18),4551(13),4851(13),4551(5),4860(8),4865(8),5840(3)])].
% 2.88/3.17 5928 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(c_0,multiply(inverse(B),C)). [back_rewrite(4859),rewrite([4860(9),5885(6)])].
% 2.88/3.17 5975 multiply(c_0,multiply(inverse(A),c_0)) = inverse(multiply(A,c_0)). [back_rewrite(4907),rewrite([4977(16),5885(8),5928(9)])].
% 2.88/3.17 6033 multiply(c_0,inverse(multiply(inverse(A),c_0))) = A. [back_rewrite(5046),rewrite([5105(15),5885(10),5928(12),5928(11),5975(7)])].
% 2.88/3.17 6060 multiply(inverse(A),inverse(multiply(inverse(B),inverse(multiply(A,c_0))))) = inverse(multiply(inverse(multiply(c_0,B)),c_0)). [back_rewrite(4875),rewrite([5885(2),5840(6),5885(5)]),flip(a)].
% 2.88/3.17 6119 multiply(c_0,A) = A. [back_rewrite(4864),rewrite([5885(2),6060(9),6033(8)])].
% 2.88/3.17 6120 $F # answer(prove_these_axioms_2). [resolve(6119,a,4881,a)].
% 2.88/3.17
% 2.88/3.17 % SZS output end Refutation
% 2.88/3.17 ============================== end of proof ==========================
% 2.88/3.17
% 2.88/3.17 ============================== STATISTICS ============================
% 2.88/3.17
% 2.88/3.17 Given=39. Generated=16108. Kept=6119. proofs=1.
% 2.88/3.17 Usable=2. Sos=315. Demods=876. Limbo=703, Disabled=5100. Hints=0.
% 2.88/3.17 Megabytes=18.93.
% 2.88/3.17 User_CPU=2.21, System_CPU=0.02, Wall_clock=2.
% 2.88/3.17
% 2.88/3.17 ============================== end of statistics =====================
% 2.88/3.17
% 2.88/3.17 ============================== end of search =========================
% 2.88/3.17
% 2.88/3.17 THEOREM PROVED
% 2.88/3.17 % SZS status Unsatisfiable
% 2.88/3.17
% 2.88/3.17 Exiting with 1 proof.
% 2.88/3.17
% 2.88/3.17 Process 32612 exit (max_proofs) Tue Jun 14 01:47:40 2022
% 2.88/3.18 Prover9 interrupted
%------------------------------------------------------------------------------