TSTP Solution File: GRP404-1 by Prover9---1109a

View Problem - 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
%------------------------------------------------------------------------------