TSTP Solution File: GRP414-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP414-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:18:59 EDT 2022
% Result : Unsatisfiable 3.41s 3.68s
% Output : Refutation 3.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP414-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 13:20:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.41/3.68 ============================== Prover9 ===============================
% 3.41/3.68 Prover9 (32) version 2009-11A, November 2009.
% 3.41/3.68 Process 3585 was started by sandbox on n005.cluster.edu,
% 3.41/3.68 Tue Jun 14 13:20:24 2022
% 3.41/3.68 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3432_n005.cluster.edu".
% 3.41/3.68 ============================== end of head ===========================
% 3.41/3.68
% 3.41/3.68 ============================== INPUT =================================
% 3.41/3.68
% 3.41/3.68 % Reading from file /tmp/Prover9_3432_n005.cluster.edu
% 3.41/3.68
% 3.41/3.68 set(prolog_style_variables).
% 3.41/3.68 set(auto2).
% 3.41/3.68 % set(auto2) -> set(auto).
% 3.41/3.68 % set(auto) -> set(auto_inference).
% 3.41/3.68 % set(auto) -> set(auto_setup).
% 3.41/3.68 % set(auto_setup) -> set(predicate_elim).
% 3.41/3.68 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.41/3.68 % set(auto) -> set(auto_limits).
% 3.41/3.68 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.41/3.68 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.41/3.68 % set(auto) -> set(auto_denials).
% 3.41/3.68 % set(auto) -> set(auto_process).
% 3.41/3.68 % set(auto2) -> assign(new_constants, 1).
% 3.41/3.68 % set(auto2) -> assign(fold_denial_max, 3).
% 3.41/3.68 % set(auto2) -> assign(max_weight, "200.000").
% 3.41/3.68 % set(auto2) -> assign(max_hours, 1).
% 3.41/3.68 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.41/3.68 % set(auto2) -> assign(max_seconds, 0).
% 3.41/3.68 % set(auto2) -> assign(max_minutes, 5).
% 3.41/3.68 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.41/3.68 % set(auto2) -> set(sort_initial_sos).
% 3.41/3.68 % set(auto2) -> assign(sos_limit, -1).
% 3.41/3.68 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.41/3.68 % set(auto2) -> assign(max_megs, 400).
% 3.41/3.68 % set(auto2) -> assign(stats, some).
% 3.41/3.68 % set(auto2) -> clear(echo_input).
% 3.41/3.68 % set(auto2) -> set(quiet).
% 3.41/3.68 % set(auto2) -> clear(print_initial_clauses).
% 3.41/3.68 % set(auto2) -> clear(print_given).
% 3.41/3.68 assign(lrs_ticks,-1).
% 3.41/3.68 assign(sos_limit,10000).
% 3.41/3.68 assign(order,kbo).
% 3.41/3.68 set(lex_order_vars).
% 3.41/3.68 clear(print_given).
% 3.41/3.68
% 3.41/3.68 % formulas(sos). % not echoed (2 formulas)
% 3.41/3.68
% 3.41/3.68 ============================== end of input ==========================
% 3.41/3.68
% 3.41/3.68 % From the command line: assign(max_seconds, 300).
% 3.41/3.68
% 3.41/3.68 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.41/3.68
% 3.41/3.68 % Formulas that are not ordinary clauses:
% 3.41/3.68
% 3.41/3.68 ============================== end of process non-clausal formulas ===
% 3.41/3.68
% 3.41/3.68 ============================== PROCESS INITIAL CLAUSES ===============
% 3.41/3.68
% 3.41/3.68 ============================== PREDICATE ELIMINATION =================
% 3.41/3.68
% 3.41/3.68 ============================== end predicate elimination =============
% 3.41/3.68
% 3.41/3.68 Auto_denials:
% 3.41/3.68 % copying label prove_these_axioms_3 to answer in negative clause
% 3.41/3.68
% 3.41/3.68 Term ordering decisions:
% 3.41/3.68
% 3.41/3.68 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 3.41/3.68 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 3.41/3.68
% 3.41/3.68 ============================== end of process initial clauses ========
% 3.41/3.68
% 3.41/3.68 ============================== CLAUSES FOR SEARCH ====================
% 3.41/3.68
% 3.41/3.68 ============================== end of clauses for search =============
% 3.41/3.68
% 3.41/3.68 ============================== SEARCH ================================
% 3.41/3.68
% 3.41/3.68 % Starting search at 0.01 seconds.
% 3.41/3.68
% 3.41/3.68 ============================== PROOF =================================
% 3.41/3.68 % SZS status Unsatisfiable
% 3.41/3.68 % SZS output start Refutation
% 3.41/3.68
% 3.41/3.68 % Proof 1 at 2.69 (+ 0.03) seconds: prove_these_axioms_3.
% 3.41/3.68 % Length of proof is 153.
% 3.41/3.68 % Level of proof is 35.
% 3.41/3.68 % Maximum clause weight is 145.000.
% 3.41/3.68 % Given clauses 71.
% 3.41/3.68
% 3.41/3.68 1 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C # label(single_axiom) # label(axiom). [assumption].
% 3.41/3.68 2 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 3.41/3.68 3 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = D. [para(1(a,1),1(a,1,2,1,1,2,1,1,1))].
% 3.41/3.68 4 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)). [para(1(a,1),1(a,1,2,1,1,2,1))].
% 3.41/3.68 6 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A)),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A))) = multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(E)),C))). [para(3(a,1),1(a,1,2,1,1,2,1)),flip(a)].
% 3.41/3.68 8 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),D))),E)). [para(1(a,1),3(a,1,2,1,1,2,1))].
% 3.41/3.68 11 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),D))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))). [para(3(a,1),3(a,1,2,1,1,2,1))].
% 3.41/3.68 14 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),inverse(C))),E))),C)))),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D)). [para(4(a,1),1(a,1,2,1,1,2,1))].
% 3.41/3.68 19 multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(inverse(A)))),D))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),E))),A))) = E. [para(4(a,2),1(a,1,2,1,1,2,1,1))].
% 3.41/3.68 20 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))) = C. [para(4(a,2),1(a,1,2))].
% 3.41/3.68 21 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(C),C),inverse(D))),E))),D)))),A)) = multiply(B,inverse(multiply(E,C))). [para(1(a,1),4(a,1,2,1,1)),flip(a)].
% 3.41/3.68 35 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(B),C)))),A)) = C. [para(4(a,1),3(a,1)),rewrite([1(13)])].
% 3.41/3.68 101 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)) = C. [para(35(a,1),35(a,1,1,1,2,1,1,1,1)),rewrite([35(18)])].
% 3.41/3.68 119 inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),inverse(multiply(inverse(multiply(D,inverse(inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),multiply(D,E)))),inverse(B))),inverse(A))),C))),A))) = E. [para(4(a,1),101(a,1,1))].
% 3.41/3.68 126 multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)). [para(101(a,1),20(a,1,2,2))].
% 3.41/3.68 138 multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),D))),B)))),multiply(A,E)) = multiply(inverse(D),multiply(C,E)). [para(1(a,1),126(a,1,1,1)),flip(a)].
% 3.41/3.68 150 multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))),multiply(A,D)) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(B))),inverse(E))),C))),E))),multiply(F,D)). [para(4(a,1),126(a,1,1,1)),flip(a)].
% 3.41/3.68 152 multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),multiply(A,E)) = multiply(inverse(D),multiply(inverse(multiply(B,inverse(C))),E)). [para(4(a,2),126(a,1,1,1,2)),rewrite([138(28)])].
% 3.41/3.68 156 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(101(a,1),126(a,1,1,1,2)),rewrite([101(15)])].
% 3.41/3.68 173 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))) = multiply(inverse(multiply(D,B)),E). [para(1(a,1),156(a,1,2)),flip(a)].
% 3.41/3.68 184 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(D,C)),multiply(D,C)),inverse(E)),multiply(B,C))))) = E. [para(156(a,1),20(a,1,2,2,1,1,1))].
% 3.41/3.68 185 multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))) = multiply(inverse(multiply(inverse(multiply(C,inverse(D))),B)),E). [para(20(a,1),156(a,1,2)),flip(a)].
% 3.41/3.68 187 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,C)),inverse(A))),multiply(inverse(multiply(D,C)),multiply(D,E))))),A)) = multiply(B,E). [para(156(a,1),101(a,1,1,1,2,1,2))].
% 3.41/3.68 188 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(E,inverse(B))),multiply(E,D)))),C)). [para(101(a,1),156(a,1,1)),flip(a)].
% 3.41/3.68 195 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(156(a,1),156(a,1,1,1))].
% 3.41/3.68 196 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(156(a,1),156(a,1,2))].
% 3.41/3.68 200 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),195(a,1,2)),rewrite([173(23)])].
% 3.41/3.68 305 multiply(A,inverse(multiply(multiply(multiply(B,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,B)))),C)),inverse(E)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,B)))),C)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(F))),V6))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(F))),V6))),F)),inverse(multiply(inverse(V6),E))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(F))),V6))),F))). [para(101(a,1),6(a,1,1,1,1,1,1,1,2,1,1,1,1,1,2)),rewrite([101(25),101(41),101(52)]),flip(a)].
% 3.41/3.68 335 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),196(a,1,1,1)),rewrite([138(23)])].
% 3.41/3.68 341 multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))),multiply(A,multiply(D,E))) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,V6)),inverse(B))),inverse(F))),C))),F))),multiply(inverse(multiply(V7,V6)),multiply(V7,E))). [para(4(a,1),196(a,1,1,1)),flip(a)].
% 3.41/3.68 365 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(196(a,1),195(a,1))].
% 3.41/3.68 376 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),E)),multiply(inverse(multiply(F,multiply(inverse(multiply(B,V6)),D))),multiply(F,V7))) = multiply(inverse(multiply(V8,E)),multiply(V8,multiply(inverse(multiply(inverse(multiply(V9,V6)),multiply(V9,C))),V7))). [para(195(a,1),196(a,1,1,1,1,1))].
% 3.41/3.68 430 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))). [para(101(a,1),335(a,1,1)),rewrite([101(16)])].
% 3.41/3.68 853 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(multiply(C,inverse(D))))))),E) = multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(F,A)),multiply(F,E)))),D))). [para(188(a,2),1(a,1,2,1,1,2,1)),flip(a)].
% 3.41/3.68 866 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C)))) = multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(V6,inverse(B))),multiply(V6,E)))),inverse(C))),inverse(F))),D))),F))). [para(4(a,1),188(a,2,2))].
% 3.41/3.68 873 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),D) = inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(C,inverse(E))),multiply(inverse(multiply(F,A)),multiply(F,D))))),E)). [para(188(a,2),101(a,1,1,1,2,1,2)),flip(a)].
% 3.41/3.68 875 multiply(inverse(multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,D)))),B))),multiply(A,E)) = multiply(F,multiply(multiply(multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,D)))),B)),inverse(multiply(inverse(multiply(V6,D)),multiply(V6,F)))),E)). [para(101(a,1),188(a,2,2,1,1,1)),rewrite([101(36)])].
% 3.41/3.68 913 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(B,C)),multiply(B,C)),inverse(D)),multiply(B,C)))) = multiply(A,inverse(multiply(multiply(multiply(E,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(F,inverse(C))),multiply(F,E)))),C)),inverse(D)),multiply(B,C)))). [para(188(a,1),6(a,2,2,1,1,1)),rewrite([6(47)])].
% 3.41/3.68 951 multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D)))),multiply(A,multiply(E,F))) = multiply(inverse(multiply(V6,multiply(V7,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(V8,inverse(C))),multiply(V8,E)))),D)))),multiply(V6,multiply(V7,F))). [para(188(a,2),365(a,1,1,1,2))].
% 3.41/3.68 1086 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,C))),inverse(D))),E))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),F))),V7)). [para(200(a,1),8(a,1,2,1,2,1,2,1,1,1))].
% 3.41/3.68 1108 multiply(inverse(multiply(A,B)),inverse(multiply(multiply(multiply(multiply(A,C),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(D))),multiply(inverse(multiply(E,B)),multiply(E,C))))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(V6,inverse(D))),multiply(V6,multiply(A,C))))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),inverse(V7))),F))),V7)). [para(196(a,1),8(a,1,2,1,2,1,2,1)),rewrite([187(18)])].
% 3.41/3.68 1184 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(multiply(A,inverse(B))))))),E)))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(multiply(A,inverse(B))))))),E)))),B)),inverse(F)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(V6,C)),multiply(V6,E)))),B)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(multiply(A,inverse(B))))))),E)),inverse(V7))),F))),V7)). [para(188(a,2),8(a,1,2,1,2,1,2,1))].
% 3.41/3.68 1573 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,C))),inverse(D))),E))),D)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),V8))),V7)),multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),V8))),V7)),inverse(multiply(inverse(V8),F))),multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),V8))),V7))). [para(200(a,1),11(a,1,2,1,2,1,2,1,1,1))].
% 3.41/3.68 1924 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))),multiply(F,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(V6,inverse(B))),multiply(V6,F)))),V7))) = multiply(inverse(E),multiply(D,multiply(A,V7))). [para(188(a,1),138(a,1,2))].
% 3.41/3.68 1945 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),C))),A)),multiply(inverse(multiply(D,inverse(B))),E)) = multiply(inverse(multiply(F,multiply(D,inverse(multiply(C,B))))),multiply(F,E)). [para(1(a,1),152(a,1,1,1,2,2,1,1)),flip(a)].
% 3.41/3.68 1962 multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),D),C))))),multiply(A,E)) = multiply(D,multiply(inverse(multiply(B,inverse(C))),E)). [para(101(a,1),152(a,1,1,1,2,2,1,1,2)),rewrite([101(21)])].
% 3.41/3.68 2162 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),C),B))))),D) = multiply(C,D). [para(1(a,1),1962(a,2,2)),rewrite([173(23)])].
% 3.41/3.68 2282 multiply(multiply(inverse(multiply(A,B)),multiply(A,C)),D) = multiply(multiply(inverse(multiply(E,B)),multiply(E,C)),D). [para(430(a,1),2162(a,1,1,1,2,2,1,1)),rewrite([2162(16)])].
% 3.41/3.68 2515 multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(B,inverse(inverse(A)))),multiply(B,C)))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(E))),inverse(D))),F))),D)))),A))) = inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E)). [para(101(a,1),14(a,1,2,1,1,2,1,1,1,2,1,1,1,1,1,1))].
% 3.41/3.68 2518 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(C))),inverse(F))),inverse(D))),V6))),D)))),C)))) = multiply(inverse(multiply(E,B)),inverse(multiply(multiply(multiply(inverse(F),F),inverse(V6)),F))). [para(14(a,1),156(a,1,2)),flip(a)].
% 3.41/3.68 2549 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),inverse(D))),V6))),D)))),inverse(C))),multiply(inverse(V6),V7)))),C)))),B))) = multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(V7)),F))). [para(14(a,2),6(a,1))].
% 3.41/3.68 2570 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(multiply(multiply(inverse(D),D),inverse(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(D))),inverse(V6))),inverse(E))),V7))),E)))),D))))) = multiply(A,multiply(inverse(multiply(F,C)),inverse(multiply(multiply(multiply(inverse(V6),V6),inverse(V7)),V6)))). [para(14(a,1),430(a,1,2,2)),flip(a)].
% 3.41/3.68 3451 multiply(inverse(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(B,inverse(inverse(A)))),multiply(B,C)))),D)),E) = multiply(inverse(multiply(F,D)),multiply(F,inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(C,E))),A)))). [para(101(a,1),173(a,1,2,2,1,1,2,1,1)),flip(a)].
% 3.41/3.68 3455 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(173(a,1),195(a,2,1,1)),rewrite([173(14)])].
% 3.41/3.68 3491 multiply(inverse(multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),D))),multiply(inverse(multiply(E,B)),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(V6,inverse(F))),V7))),F)))) = multiply(inverse(multiply(V6,multiply(E,D))),V7). [para(188(a,1),173(a,1,1,1))].
% 3.41/3.68 3976 multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(inverse(B)))),E))),inverse(B))),inverse(inverse(A)))),multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),F)))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(F,V6))),A))) = V6. [para(19(a,1),19(a,1,2,1,1,2,1,1))].
% 3.41/3.68 3981 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(D,F)),inverse(E))),V6))),E)))) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),V6). [para(1(a,1),3455(a,1,2)),flip(a)].
% 3.41/3.68 4312 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),C)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(D))),E))),D)) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,inverse(multiply(E,B))))). [para(1(a,1),185(a,1,2,2,2,1,1)),flip(a)].
% 3.41/3.68 4672 multiply(A,inverse(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))) = multiply(A,inverse(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))). [para(4(a,1),21(a,2,2,1)),rewrite([21(42)])].
% 3.41/3.68 4752 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))),A)) = inverse(A). [para(188(a,2),21(a,1,1,1,2,1)),rewrite([1(22)])].
% 3.41/3.68 4779 multiply(multiply(A,inverse(multiply(B,C))),multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),F))),D))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),F))),D))),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),F))),D))))),multiply(multiply(multiply(inverse(V6),V6),inverse(multiply(inverse(multiply(multiply(inverse(C),C),inverse(V6))),B))),V6)))),V7)) = multiply(inverse(F),multiply(E,V7)). [para(21(a,1),138(a,1,1))].
% 3.41/3.68 4878 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A)) = inverse(A). [para(1(a,1),4752(a,1,1,1,2,1,1,1)),rewrite([1(14)])].
% 3.41/3.68 4892 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))),A) = A. [para(4752(a,1),20(a,1,2,2,1,1,2)),rewrite([20(11)]),flip(a)].
% 3.41/3.68 4928 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),multiply(B,C))))) = D. [para(4752(a,1),184(a,1,2,2,1,1,1,1)),rewrite([4892(14)])].
% 3.41/3.68 5021 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A) = A. [para(4878(a,1),20(a,1,2,2,1,1,2)),rewrite([20(11)]),flip(a)].
% 3.41/3.68 5022 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B))) = multiply(inverse(C),C). [para(4878(a,1),20(a,1,2,2))].
% 3.41/3.68 5027 multiply(inverse(multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C))),multiply(inverse(multiply(D,A)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)). [para(4878(a,1),195(a,1,1,1,1))].
% 3.41/3.68 5036 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(C),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(F),F))),multiply(A,E))). [para(4878(a,1),196(a,2,1))].
% 3.41/3.68 5046 multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)) = multiply(D,multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(E,inverse(A))),multiply(E,D)))),C)). [para(4878(a,1),188(a,1,1))].
% 3.41/3.68 5076 multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))) = multiply(inverse(multiply(D,A)),E). [para(4878(a,1),173(a,1,1))].
% 3.41/3.68 5088 multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))) = multiply(inverse(multiply(inverse(multiply(C,inverse(D))),A)),E). [para(4878(a,1),185(a,1,1))].
% 3.41/3.68 5102 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))),inverse(A))),B))),A)) = B. [para(5021(a,1),101(a,1,1,1,2,1,2))].
% 3.41/3.68 5105 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),A) = multiply(inverse(multiply(D,C)),multiply(D,A)). [para(5021(a,1),156(a,1,2))].
% 3.41/3.68 5111 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,C)),multiply(E,D))))),A) = A. [para(195(a,2),5021(a,1,1,2,1))].
% 3.41/3.68 5116 multiply(inverse(multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,B)),inverse(multiply(inverse(C),C))),D)),multiply(A,B)) = multiply(inverse(multiply(inverse(multiply(A,E)),D)),multiply(inverse(multiply(F,E)),multiply(F,B))). [para(5021(a,1),196(a,2,2)),flip(a)].
% 3.41/3.68 5130 multiply(inverse(multiply(A,B)),multiply(A,B)) = multiply(inverse(B),B). [para(5021(a,1),188(a,2,2))].
% 3.41/3.68 5152 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),E),D))))),A) = multiply(E,multiply(inverse(multiply(C,inverse(D))),A)). [para(5021(a,1),1962(a,1,2))].
% 3.41/3.68 5159 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,A)) = multiply(C,A). [para(2282(a,1),5021(a,1,1)),rewrite([5130(4)])].
% 3.41/3.68 5182 multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),A))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),A))),inverse(multiply(inverse(C),C))),inverse(A))),D)),B) = multiply(inverse(multiply(E,D)),multiply(E,inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),A)))). [para(5021(a,1),185(a,1,2,2)),flip(a)].
% 3.41/3.68 5198 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),multiply(D,A)) = multiply(inverse(multiply(inverse(multiply(D,E)),C)),multiply(inverse(multiply(F,E)),multiply(F,A))). [back_rewrite(5116),rewrite([5130(4)])].
% 3.41/3.68 5209 multiply(inverse(inverse(A)),inverse(A)) = multiply(inverse(B),B). [back_rewrite(5022),rewrite([5130(6)])].
% 3.41/3.68 5923 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,C))),inverse(D))),V6))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(V8),E))),multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(V6),inverse(V7))),V8))),V7))). [back_rewrite(1573),rewrite([5130(35),5130(48)])].
% 3.41/3.68 6027 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(D,E)),multiply(D,F)))),B)))) = inverse(multiply(multiply(multiply(inverse(V6),V6),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(V7,inverse(E))),multiply(V7,inverse(multiply(A,inverse(B))))))),F)),inverse(V6))),C))),V6)). [back_rewrite(1184),rewrite([5130(46)])].
% 3.41/3.68 6106 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,C))),inverse(D))),V6))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(V6),inverse(V7))),E))),V7)). [back_rewrite(1086),rewrite([5130(35)])].
% 3.41/3.68 6195 multiply(A,inverse(multiply(multiply(multiply(B,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,B)))),C)),inverse(E)),multiply(F,C)))) = multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(E)),multiply(F,C)))). [back_rewrite(913),rewrite([5130(4)]),flip(a)].
% 3.41/3.68 6426 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,E)))),B)))) = inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(V6),C))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,E)),inverse(F))),V6))),F))). [back_rewrite(305),rewrite([6195(26),5130(41)])].
% 3.41/3.68 6489 multiply(inverse(inverse(A)),inverse(A)) = c_0. [new_symbol(5209)].
% 3.41/3.68 6694 multiply(inverse(A),A) = c_0. [back_rewrite(5209),rewrite([6489(4)]),flip(a)].
% 3.41/3.68 6701 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(c_0,inverse(C)),D)))) = multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(c_0)),inverse(D))),B)),C). [back_rewrite(5182),rewrite([6694(2),6694(8),6694(12),6694(3),6694(14)]),flip(a)].
% 3.41/3.68 6739 multiply(multiply(A,inverse(multiply(B,C))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(c_0,inverse(V6))),B))),V6)))),V7)) = multiply(inverse(F),multiply(D,V7)). [back_rewrite(4779),rewrite([6694(5),6694(15),6694(23),6694(9),6694(21),6694(22)])].
% 3.41/3.68 6794 multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(inverse(C)))),D))),inverse(C))),inverse(inverse(E)))),multiply(multiply(A,inverse(multiply(multiply(c_0,inverse(D)),B))),F)))),inverse(multiply(multiply(c_0,inverse(multiply(F,V6))),E))) = V6. [back_rewrite(3976),rewrite([6694(4),6694(5),6694(21),6694(31)])].
% 3.41/3.68 6867 multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(inverse(B)))),multiply(A,C)))),D)),E) = multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(c_0)),inverse(B))),D)),multiply(C,E)). [back_rewrite(3451),rewrite([6694(4),6694(16),6701(22)])].
% 3.41/3.68 6954 multiply(multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(inverse(B)))),multiply(A,C)))),inverse(multiply(multiply(c_0,inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(E))),F))),E)))),B))) = inverse(multiply(multiply(c_0,inverse(F)),D)). [back_rewrite(2515),rewrite([6694(4),6694(11),6694(12),6694(29)])].
% 3.41/3.68 7004 inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(c_0)),inverse(multiply(multiply(c_0,inverse(A)),B)))),inverse(B))),multiply(C,inverse(D)))),A))),D))) = C. [back_rewrite(119),rewrite([6694(2),6694(3),6694(9),6694(13),6694(4),6867(19)])].
% 3.41/3.68 7224 multiply(A,inverse(multiply(multiply(c_0,inverse(B)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,E)))),D)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(F),B))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,E)),inverse(V6))),F))),V6))). [back_rewrite(6426),rewrite([6694(2),6694(5),6694(17),6694(22)])].
% 3.41/3.68 7473 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(c_0,inverse(D)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),inverse(F))),V6))),F)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(V6),inverse(V7))),D))),V7)). [back_rewrite(6106),rewrite([6694(7),6694(10),6694(26)])].
% 3.41/3.68 7523 multiply(A,inverse(multiply(multiply(c_0,inverse(B)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(C,D)),multiply(C,E)))),F)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(V6,inverse(D))),multiply(V6,inverse(multiply(A,inverse(F))))))),E)),inverse(V7))),B))),V7)). [back_rewrite(6027),rewrite([6694(2),6694(5),6694(16),6694(17)])].
% 3.41/3.68 7615 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(c_0,inverse(D)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),inverse(F))),V6))),F)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(V7),D))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(V6),inverse(V8))),V7))),V8))). [back_rewrite(5923),rewrite([6694(7),6694(10),6694(26),6694(31)])].
% 3.41/3.68 8021 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(multiply(c_0,inverse(c_0)),C)),multiply(A,E)). [back_rewrite(5198),rewrite([6694(2),6694(3)]),flip(a)].
% 3.41/3.68 8051 multiply(multiply(c_0,inverse(c_0)),multiply(A,B)) = multiply(A,B). [back_rewrite(5159),rewrite([6694(2),6694(3)])].
% 3.41/3.68 8055 multiply(inverse(multiply(A,inverse(multiply(multiply(c_0,B),C)))),D) = multiply(B,multiply(inverse(multiply(A,inverse(C))),D)). [back_rewrite(5152),rewrite([6694(2),6694(3),6694(6),8051(10)])].
% 3.41/3.68 8076 multiply(multiply(c_0,inverse(c_0)),A) = A. [back_rewrite(5111),rewrite([6694(2),8021(11),8051(7),6694(5)])].
% 3.41/3.68 8078 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C). [back_rewrite(5105),rewrite([6694(2),6694(3),8076(5)]),flip(a)].
% 3.41/3.68 8080 inverse(multiply(multiply(c_0,inverse(multiply(inverse(inverse(A)),B))),A)) = B. [back_rewrite(5102),rewrite([6694(2),6694(3),6694(4),8076(7)])].
% 3.41/3.68 8087 multiply(inverse(A),multiply(B,inverse(multiply(multiply(c_0,inverse(C)),D)))) = multiply(inverse(multiply(inverse(multiply(B,inverse(D))),A)),C). [back_rewrite(5088),rewrite([6694(3),6694(4),6694(7),8076(12)])].
% 3.41/3.68 8090 multiply(inverse(A),inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(B,inverse(C))),D))),C))) = multiply(inverse(multiply(B,A)),D). [back_rewrite(5076),rewrite([6694(3),6694(4),6694(7),8076(15)])].
% 3.41/3.68 8092 multiply(A,multiply(multiply(c_0,inverse(multiply(inverse(inverse(B)),A))),C)) = multiply(inverse(B),C). [back_rewrite(5046),rewrite([6694(3),6694(4),8076(6),6694(4),8078(8)]),flip(a)].
% 3.41/3.68 8093 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),D)) = multiply(inverse(C),multiply(A,D)). [back_rewrite(5036),rewrite([8078(8),6694(10),6694(11),8076(14)])].
% 3.41/3.68 8094 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,A)),D)) = multiply(inverse(multiply(C,B)),D). [back_rewrite(5027),rewrite([6694(3),6694(4),8076(6),8078(12)])].
% 3.41/3.68 8097 multiply(inverse(c_0),A) = A. [back_rewrite(4928),rewrite([6694(6),8087(12),6694(8)])].
% 3.41/3.68 8154 multiply(A,inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(D))),E))),D)))) = multiply(A,inverse(multiply(B,inverse(multiply(multiply(c_0,inverse(E)),C))))). [back_rewrite(4672),rewrite([6694(2),6694(10)]),flip(a)].
% 3.41/3.68 8273 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),C)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(c_0,inverse(D))),E))),D)) = multiply(inverse(C),multiply(A,inverse(multiply(E,B)))). [back_rewrite(4312),rewrite([6694(7),6694(8),8078(22)])].
% 3.41/3.68 8321 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(D),B)),E)) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),E). [back_rewrite(3981),rewrite([6694(8),8090(18),8078(8)])].
% 3.41/3.68 8355 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(D,A))),E)) = multiply(inverse(multiply(C,multiply(D,B))),E). [back_rewrite(3491),rewrite([6694(2),8078(6),8092(8),6694(7),8090(15)])].
% 3.41/3.68 8415 multiply(A,multiply(inverse(multiply(B,C)),inverse(multiply(multiply(c_0,inverse(D)),E)))) = multiply(A,multiply(inverse(multiply(inverse(inverse(E)),multiply(B,C))),D)). [back_rewrite(2570),rewrite([6694(4),6694(5),8154(20),8087(18),8078(5),8087(14),8093(10),6694(11)]),flip(a)].
% 3.41/3.68 8419 multiply(A,inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),multiply(A,inverse(D)))),E))),D))) = multiply(B,inverse(multiply(multiply(c_0,inverse(E)),C))). [back_rewrite(2549),rewrite([6694(2),6694(3),6694(7),8090(18),8093(17),8080(17),6694(16)])].
% 3.41/3.68 8426 multiply(inverse(multiply(A,B)),inverse(multiply(multiply(c_0,inverse(C)),D))) = multiply(inverse(multiply(inverse(inverse(D)),multiply(A,B))),C). [back_rewrite(2518),rewrite([6694(4),6694(5),8154(20),8087(18),8078(5),8415(14),8355(12),6694(10)]),flip(a)].
% 3.41/3.68 8498 multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(c_0,inverse(A))),B))),A)),multiply(inverse(multiply(C,inverse(D))),E)) = multiply(inverse(multiply(C,inverse(multiply(B,D)))),E). [back_rewrite(1945),rewrite([6694(2),6694(3),8078(22)])].
% 3.41/3.68 8502 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(inverse(C),E)) = multiply(inverse(D),multiply(A,multiply(B,E))). [back_rewrite(1924),rewrite([6694(4),8090(12),6694(7),8078(11),8092(13)])].
% 3.41/3.68 8523 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),inverse(C))),D))),C)) = multiply(inverse(multiply(inverse(B),A)),D). [back_rewrite(1108),rewrite([6694(5),8078(13),8093(12),8092(12),6694(4),6694(7),8078(12),8426(16),8080(9),8078(4),6694(6),8078(9)]),flip(a)].
% 3.41/3.68 8528 multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(inverse(A)),B))),C)),D) = multiply(inverse(multiply(inverse(A),C)),multiply(B,D)). [back_rewrite(951),rewrite([8078(4),8078(7),6694(7),8078(11),8078(18),8078(16)]),flip(a)].
% 3.41/3.68 8534 multiply(A,multiply(multiply(c_0,inverse(multiply(inverse(B),A))),C)) = multiply(B,C). [back_rewrite(875),rewrite([6694(2),8078(6),8078(11),8080(8),6694(3),8078(7),8092(9),6694(3),8078(6)]),flip(a)].
% 3.41/3.68 8535 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(B))),multiply(inverse(C),D)))),B)) = multiply(multiply(c_0,inverse(multiply(inverse(inverse(C)),A))),D). [back_rewrite(873),rewrite([6694(2),8078(6),6694(9),8078(15)]),flip(a)].
% 3.41/3.68 8538 multiply(inverse(A),inverse(multiply(multiply(c_0,inverse(B)),C))) = multiply(inverse(multiply(inverse(inverse(C)),A)),B). [back_rewrite(866),rewrite([6694(4),8087(9),8078(5),6694(7),6694(8),8078(12),8528(17),8419(20)]),flip(a)].
% 3.41/3.68 8542 multiply(multiply(c_0,inverse(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(C)))))),D) = multiply(B,inverse(multiply(multiply(c_0,inverse(multiply(inverse(A),D))),C))). [back_rewrite(853),rewrite([6694(2),8078(9),6694(12),8078(15)])].
% 3.41/3.68 8549 multiply(inverse(inverse(multiply(multiply(c_0,inverse(A)),B))),multiply(C,D)) = multiply(inverse(A),multiply(inverse(inverse(B)),multiply(C,D))). [back_rewrite(341),rewrite([6694(2),8078(10),6694(10),8523(22),8078(19),8502(18)])].
% 3.41/3.68 8557 multiply(inverse(inverse(multiply(multiply(c_0,inverse(A)),B))),C) = multiply(inverse(A),multiply(inverse(inverse(B)),C)). [back_rewrite(150),rewrite([6694(2),8078(9),6694(9),8549(22),8093(20),8078(13)])].
% 3.41/3.68 8569 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(C))),D))),C)) = multiply(A,inverse(multiply(multiply(c_0,inverse(D)),B))). [back_rewrite(4),rewrite([6694(2),6694(8)]),flip(a)].
% 3.41/3.68 8571 multiply(multiply(c_0,inverse(multiply(inverse(inverse(inverse(A))),B))),inverse(multiply(multiply(c_0,inverse(multiply(B,C))),A))) = C. [back_rewrite(6794),rewrite([8569(15),8078(19)])].
% 3.41/3.68 8643 inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),c_0)),multiply(B,inverse(C)))),A))),C))) = B. [back_rewrite(7004),rewrite([8076(11),8557(9),6694(6)])].
% 3.41/3.68 8674 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),D) = multiply(inverse(C),multiply(inverse(multiply(inverse(B),A)),D)). [back_rewrite(376),rewrite([8078(5),8078(13),8321(12),8078(4),8078(12),8078(14)])].
% 3.41/3.68 8738 inverse(multiply(multiply(c_0,inverse(multiply(inverse(A),B))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(C),inverse(D))),A))),D))) = multiply(inverse(multiply(inverse(C),c_0)),B). [back_rewrite(7615),rewrite([8078(4),8078(11),8674(14),8538(20),8080(12),8093(8),6694(3)]),flip(a)].
% 3.41/3.68 8744 multiply(A,inverse(multiply(multiply(c_0,inverse(B)),multiply(multiply(c_0,inverse(multiply(inverse(C),D))),E)))) = multiply(A,inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(D),C)),B))),E))). [back_rewrite(7523),rewrite([8078(8),8078(22),8542(23),8055(24),8674(24),8535(28),8542(24)])].
% 3.41/3.68 8751 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(A),inverse(B))),C))),B)) = multiply(inverse(multiply(inverse(A),c_0)),C). [back_rewrite(7473),rewrite([8078(4),8078(11),8674(14),8744(20),8674(11),8538(18),8355(16),6694(7)]),flip(a)].
% 3.41/3.68 8765 multiply(inverse(multiply(inverse(multiply(A,B)),c_0)),C) = multiply(A,multiply(inverse(multiply(inverse(B),c_0)),C)). [back_rewrite(7224),rewrite([8078(9),8744(13),8751(10),8738(23)]),flip(a)].
% 3.41/3.68 8780 inverse(multiply(multiply(c_0,inverse(A)),B)) = multiply(inverse(multiply(inverse(inverse(B)),c_0)),A). [back_rewrite(6954),rewrite([8078(7),8751(20),8765(15),8571(20)]),flip(a)].
% 3.41/3.68 8829 multiply(inverse(multiply(inverse(multiply(A,c_0)),B)),C) = multiply(inverse(B),multiply(A,C)). [back_rewrite(6739),rewrite([8780(16),8094(17),8273(24),8534(18)])].
% 3.41/3.68 8980 inverse(multiply(inverse(multiply(A,c_0)),c_0)) = A. [back_rewrite(8643),rewrite([8829(10),6694(6),8780(10),8094(11)])].
% 3.41/3.68 8999 multiply(multiply(inverse(multiply(c_0,c_0)),A),multiply(inverse(multiply(B,inverse(C))),D)) = multiply(inverse(multiply(B,inverse(multiply(A,C)))),D). [back_rewrite(8498),rewrite([8780(10),8094(11)])].
% 3.41/3.68 9108 multiply(c_0,inverse(c_0)) = inverse(c_0). [para(8076(a,1),8980(a,1,1,1,1)),rewrite([6694(4)]),flip(a)].
% 3.41/3.68 9109 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(B),A). [para(6694(a,1),8078(a,1,2))].
% 3.41/3.68 9110 multiply(inverse(inverse(c_0)),multiply(c_0,A)) = multiply(inverse(inverse(c_0)),A). [para(9108(a,1),8078(a,1,1,1))].
% 3.41/3.68 9113 multiply(inverse(multiply(c_0,A)),B) = multiply(inverse(A),B). [para(9110(a,1),8078(a,1,1,1)),rewrite([8078(10)]),flip(a)].
% 3.41/3.68 9126 multiply(inverse(multiply(A,inverse(multiply(B,C)))),D) = multiply(B,multiply(inverse(multiply(A,inverse(C))),D)). [back_rewrite(8999),rewrite([9113(5),8097(3)]),flip(a)].
% 3.41/3.68 9210 inverse(c_0) = c_0. [para(9113(a,1),8980(a,1,1)),rewrite([6694(4)])].
% 3.41/3.68 9214 multiply(c_0,A) = A. [back_rewrite(8097),rewrite([9210(2)])].
% 3.41/3.68 9272 multiply(A,multiply(inverse(multiply(inverse(B),A)),C)) = multiply(B,C). [back_rewrite(8534),rewrite([9214(5)])].
% 3.41/3.68 9335 multiply(A,multiply(inverse(A),B)) = multiply(B,c_0). [para(6694(a,1),9272(a,1,2)),flip(a)].
% 3.41/3.68 9342 multiply(inverse(multiply(inverse(A),B)),C) = multiply(multiply(inverse(B),A),C). [para(9109(a,1),9272(a,1,2,1,1)),rewrite([9214(6)])].
% 3.41/3.68 9353 multiply(A,c_0) = A. [para(9210(a,1),9272(a,1,2,1,1,1)),rewrite([9214(2),9335(3),9214(4)])].
% 3.41/3.68 9354 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(9272(a,1),9214(a,1)),rewrite([9353(4)]),flip(a)].
% 3.41/3.68 9356 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(9272(a,1),9272(a,1,2)),rewrite([9126(9),9342(8),9354(6),9335(7),9353(6)]),flip(a)].
% 3.41/3.68 9357 $F # answer(prove_these_axioms_3). [resolve(9356,a,2,a)].
% 3.41/3.68
% 3.41/3.68 % SZS output end Refutation
% 3.41/3.68 ============================== end of proof ==========================
% 3.41/3.68
% 3.41/3.68 ============================== STATISTICS ============================
% 3.41/3.68
% 3.41/3.68 Given=71. Generated=22972. Kept=9356. proofs=1.
% 3.41/3.68 Usable=10. Sos=99. Demods=121. Limbo=21, Disabled=9227. Hints=0.
% 3.41/3.68 Megabytes=22.77.
% 3.41/3.68 User_CPU=2.69, System_CPU=0.03, Wall_clock=3.
% 3.41/3.68
% 3.41/3.68 ============================== end of statistics =====================
% 3.41/3.68
% 3.41/3.68 ============================== end of search =========================
% 3.41/3.68
% 3.41/3.68 THEOREM PROVED
% 3.41/3.68 % SZS status Unsatisfiable
% 3.41/3.68
% 3.41/3.68 Exiting with 1 proof.
% 3.41/3.68
% 3.41/3.68 Process 3585 exit (max_proofs) Tue Jun 14 13:20:27 2022
% 3.41/3.68 Prover9 interrupted
%------------------------------------------------------------------------------