TSTP Solution File: GRP436-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP436-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 11:19:05 EDT 2022

% Result   : Unsatisfiable 1.44s 1.71s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP436-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 13 22:09:24 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.44/1.71  ============================== Prover9 ===============================
% 1.44/1.71  Prover9 (32) version 2009-11A, November 2009.
% 1.44/1.71  Process 22469 was started by sandbox on n019.cluster.edu,
% 1.44/1.71  Mon Jun 13 22:09:25 2022
% 1.44/1.71  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22315_n019.cluster.edu".
% 1.44/1.71  ============================== end of head ===========================
% 1.44/1.71  
% 1.44/1.71  ============================== INPUT =================================
% 1.44/1.71  
% 1.44/1.71  % Reading from file /tmp/Prover9_22315_n019.cluster.edu
% 1.44/1.71  
% 1.44/1.71  set(prolog_style_variables).
% 1.44/1.71  set(auto2).
% 1.44/1.71      % set(auto2) -> set(auto).
% 1.44/1.71      % set(auto) -> set(auto_inference).
% 1.44/1.71      % set(auto) -> set(auto_setup).
% 1.44/1.71      % set(auto_setup) -> set(predicate_elim).
% 1.44/1.71      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.44/1.71      % set(auto) -> set(auto_limits).
% 1.44/1.71      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.44/1.71      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.44/1.71      % set(auto) -> set(auto_denials).
% 1.44/1.71      % set(auto) -> set(auto_process).
% 1.44/1.71      % set(auto2) -> assign(new_constants, 1).
% 1.44/1.71      % set(auto2) -> assign(fold_denial_max, 3).
% 1.44/1.71      % set(auto2) -> assign(max_weight, "200.000").
% 1.44/1.71      % set(auto2) -> assign(max_hours, 1).
% 1.44/1.71      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.44/1.71      % set(auto2) -> assign(max_seconds, 0).
% 1.44/1.71      % set(auto2) -> assign(max_minutes, 5).
% 1.44/1.71      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.44/1.71      % set(auto2) -> set(sort_initial_sos).
% 1.44/1.71      % set(auto2) -> assign(sos_limit, -1).
% 1.44/1.71      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.44/1.71      % set(auto2) -> assign(max_megs, 400).
% 1.44/1.71      % set(auto2) -> assign(stats, some).
% 1.44/1.71      % set(auto2) -> clear(echo_input).
% 1.44/1.71      % set(auto2) -> set(quiet).
% 1.44/1.71      % set(auto2) -> clear(print_initial_clauses).
% 1.44/1.71      % set(auto2) -> clear(print_given).
% 1.44/1.71  assign(lrs_ticks,-1).
% 1.44/1.71  assign(sos_limit,10000).
% 1.44/1.71  assign(order,kbo).
% 1.44/1.71  set(lex_order_vars).
% 1.44/1.71  clear(print_given).
% 1.44/1.71  
% 1.44/1.71  % formulas(sos).  % not echoed (2 formulas)
% 1.44/1.71  
% 1.44/1.71  ============================== end of input ==========================
% 1.44/1.71  
% 1.44/1.71  % From the command line: assign(max_seconds, 300).
% 1.44/1.71  
% 1.44/1.71  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.44/1.71  
% 1.44/1.71  % Formulas that are not ordinary clauses:
% 1.44/1.71  
% 1.44/1.71  ============================== end of process non-clausal formulas ===
% 1.44/1.71  
% 1.44/1.71  ============================== PROCESS INITIAL CLAUSES ===============
% 1.44/1.71  
% 1.44/1.71  ============================== PREDICATE ELIMINATION =================
% 1.44/1.71  
% 1.44/1.71  ============================== end predicate elimination =============
% 1.44/1.71  
% 1.44/1.71  Auto_denials:
% 1.44/1.71    % copying label prove_these_axioms_1 to answer in negative clause
% 1.44/1.71  
% 1.44/1.71  Term ordering decisions:
% 1.44/1.71  
% 1.44/1.71  % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.44/1.71  Function symbol KB weights:  a1=1. b1=1. multiply=1. inverse=0.
% 1.44/1.71  
% 1.44/1.71  ============================== end of process initial clauses ========
% 1.44/1.71  
% 1.44/1.71  ============================== CLAUSES FOR SEARCH ====================
% 1.44/1.71  
% 1.44/1.71  ============================== end of clauses for search =============
% 1.44/1.71  
% 1.44/1.71  ============================== SEARCH ================================
% 1.44/1.71  
% 1.44/1.71  % Starting search at 0.01 seconds.
% 1.44/1.71  
% 1.44/1.71  ============================== PROOF =================================
% 1.44/1.71  % SZS status Unsatisfiable
% 1.44/1.71  % SZS output start Refutation
% 1.44/1.71  
% 1.44/1.71  % Proof 1 at 0.69 (+ 0.01) seconds: prove_these_axioms_1.
% 1.44/1.71  % Length of proof is 166.
% 1.44/1.71  % Level of proof is 46.
% 1.44/1.71  % Maximum clause weight is 62.000.
% 1.44/1.71  % Given clauses 47.
% 1.44/1.71  
% 1.44/1.71  1 multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D # label(single_axiom) # label(axiom).  [assumption].
% 1.44/1.71  2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1).  [assumption].
% 1.44/1.71  3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1).  [copy(2),flip(a)].
% 1.44/1.71  4 multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E)))),multiply(F,multiply(multiply(inverse(F),inverse(D)),A))))) = E.  [para(1(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.44/1.71  5 multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,D))),inverse(E))),multiply(E,multiply(C,A))))) = D.  [para(1(a,1),1(a,1,2,1,2,2,1))].
% 1.44/1.71  6 multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(E,F))))))),inverse(multiply(F,multiply(D,C)))) = E.  [para(1(a,1),1(a,1,2,1,2,2))].
% 1.44/1.71  11 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(E,F))))))) = multiply(V6,inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(V7,multiply(multiply(inverse(V7),inverse(E)),V6))))).  [para(1(a,1),4(a,1,2,1,1,1,2,2)),flip(a)].
% 1.44/1.71  19 multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(D))),multiply(D,multiply(E,A))))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(C,E))),inverse(B))).  [para(5(a,1),1(a,1,2,1,2,2,1))].
% 1.44/1.71  59 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(F,inverse(multiply(multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(B,D))),inverse(A))))),inverse(V8))),multiply(V8,multiply(E,F))))).  [para(19(a,1),5(a,1,2,1,1,2,1,2,1)),flip(a)].
% 1.44/1.71  63 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B))) = D.  [para(19(a,1),5(a,1))].
% 1.44/1.71  85 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(C)),D))),inverse(F))).  [para(1(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.44/1.71  90 inverse(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(C)),F)))) = multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(multiply(inverse(V7),inverse(D)),F))),inverse(V7))).  [para(4(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.44/1.71  91 multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(B)),inverse(C))).  [para(4(a,1),63(a,1,2,1,2,1,1)),rewrite([1(10)])].
% 1.44/1.71  94 multiply(inverse(A),inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(multiply(inverse(A),inverse(multiply(D,E))),D))),F))),inverse(C))),E))) = F.  [para(63(a,1),5(a,1,2,1,2))].
% 1.44/1.71  97 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(C),inverse(multiply(V6,B))),V6))),D))),inverse(F))).  [para(63(a,1),19(a,1,2,1,1))].
% 1.44/1.71  104 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B)) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(D)),A))),inverse(F))).  [para(63(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.44/1.71  113 multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(E))))),inverse(F))),multiply(F,multiply(V6,A))))) = multiply(multiply(inverse(V6),inverse(D)),inverse(E)).  [para(91(a,1),5(a,1,2,1,1,2,1,2,1))].
% 1.44/1.71  125 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(multiply(inverse(E),inverse(multiply(B,D))),inverse(A)).  [back_rewrite(59),rewrite([113(25)])].
% 1.44/1.71  137 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(E,multiply(multiply(inverse(E),inverse(F)),V6)))),multiply(V7,multiply(multiply(inverse(V7),inverse(inverse(multiply(V8,multiply(V9,multiply(multiply(inverse(V9),inverse(multiply(D,V8))),multiply(inverse(C),inverse(multiply(F,B))))))))),A))))) = V6.  [para(6(a,1),4(a,1,2,1,1,1,2,2,1,2,1))].
% 1.44/1.71  175 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(D,E))),D))),F))),inverse(B)) = inverse(multiply(E,multiply(C,multiply(F,A)))).  [para(63(a,1),125(a,1,1,1)),flip(a)].
% 1.44/1.71  177 multiply(multiply(inverse(inverse(A)),inverse(multiply(B,multiply(inverse(C),inverse(multiply(multiply(inverse(A),inverse(multiply(D,E))),D)))))),inverse(F)) = inverse(multiply(multiply(F,multiply(B,inverse(C))),E)).  [para(63(a,1),125(a,1,1,2)),flip(a)].
% 1.44/1.71  194 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))).  [back_rewrite(97),rewrite([175(19)])].
% 1.44/1.71  195 multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(C,multiply(A,multiply(D,B))))),C))) = D.  [back_rewrite(94),rewrite([175(15)])].
% 1.44/1.71  203 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))),inverse(E))) = D.  [para(195(a,1),63(a,1,2,1,2,1,1))].
% 1.44/1.71  205 multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))) = multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(E,D))),E))).  [para(63(a,1),195(a,1,2,1,1,2,1,2))].
% 1.44/1.71  229 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(D,inverse(E)))))),inverse(F))) = multiply(E,multiply(multiply(V6,inverse(multiply(B,multiply(C,multiply(D,V6))))),inverse(F))).  [para(194(a,1),91(a,1,2,1)),flip(a)].
% 1.44/1.71  345 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(multiply(inverse(A),inverse(multiply(D,C))),D)).  [para(205(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([63(19)])].
% 1.44/1.71  385 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(A)))))),B)) = inverse(D).  [para(4(a,1),345(a,1,1,1)),rewrite([1(9)]),flip(a)].
% 1.44/1.71  409 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(multiply(inverse(D),inverse(multiply(E,F))),E)))))),inverse(V6))) = multiply(inverse(D),inverse(multiply(multiply(V6,multiply(B,C)),F))).  [para(345(a,1),203(a,1,2,1,2,1,2,2))].
% 1.44/1.71  445 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C))))) = inverse(D).  [para(195(a,1),385(a,1,1,1)),rewrite([125(10)])].
% 1.44/1.71  449 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B)) = inverse(D).  [para(194(a,1),385(a,1,1,1))].
% 1.44/1.71  469 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))),B)) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),inverse(multiply(D,E))),inverse(C))))).  [para(1(a,1),449(a,1,1,1,2,1,2,2,1))].
% 1.44/1.71  489 multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))),inverse(B)) = inverse(D).  [para(125(a,1),449(a,1,1,1,2)),rewrite([125(15)])].
% 1.44/1.71  776 multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))) = multiply(E,inverse(multiply(inverse(B),multiply(F,multiply(multiply(inverse(F),inverse(inverse(D))),E))))).  [para(489(a,1),1(a,1,2,1,2,2,1,2,1)),flip(a)].
% 1.44/1.71  780 multiply(inverse(A),inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C))))) = inverse(A).  [para(489(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([409(23)])].
% 1.44/1.71  806 inverse(multiply(inverse(A),multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))))) = inverse(multiply(multiply(inverse(A),inverse(multiply(E,multiply(inverse(D),inverse(C))))),E)).  [para(489(a,1),445(a,1,1,2,2,1,2,1))].
% 1.44/1.71  817 multiply(A,inverse(multiply(inverse(multiply(multiply(inverse(B),inverse(C)),multiply(D,multiply(inverse(D),E)))),multiply(F,multiply(multiply(inverse(F),inverse(multiply(V6,multiply(multiply(inverse(V6),inverse(inverse(C))),inverse(inverse(B)))))),A))))) = E.  [para(780(a,1),4(a,1,2,1,1,1,2,2,1))].
% 1.44/1.71  820 inverse(multiply(multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),inverse(inverse(C)))),multiply(inverse(C),inverse(B)))) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(inverse(F))),inverse(F)))),inverse(E))).  [para(780(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.44/1.71  822 multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(inverse(C),inverse(B))).  [para(780(a,1),91(a,1,2,1)),rewrite([780(19)])].
% 1.44/1.71  853 multiply(inverse(A),inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(E)),B))))),C),multiply(multiply(inverse(E),inverse(inverse(F))),inverse(inverse(V6)))),multiply(inverse(V6),inverse(F))))) = inverse(A).  [para(449(a,1),780(a,1,2,1,1,2,1,1))].
% 1.44/1.71  874 multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(inverse(D))),inverse(inverse(A))))))),inverse(B)) = inverse(D).  [para(780(a,1),489(a,1,1,2,1,1))].
% 1.44/1.71  929 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(E)))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(V6,multiply(V7,V8))),multiply(D,C))),multiply(V9,multiply(multiply(inverse(V9),inverse(inverse(multiply(V10,multiply(V11,multiply(multiply(inverse(V11),inverse(multiply(V8,V10))),multiply(inverse(V7),inverse(multiply(E,V6))))))))),F))))).  [para(6(a,1),11(a,1,1,2,2,2,2,1))].
% 1.44/1.71  1088 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(multiply(V6,multiply(multiply(inverse(V6),inverse(inverse(V7))),inverse(inverse(V8)))),multiply(inverse(V8),inverse(V7)))),multiply(D,C))),multiply(V9,multiply(multiply(inverse(V9),inverse(inverse(E))),F))))).  [para(780(a,1),11(a,1,1,2,2,2,2,1))].
% 1.44/1.71  1089 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(D))))) = multiply(E,inverse(multiply(inverse(multiply(multiply(inverse(F),inverse(V6)),multiply(D,C))),multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(V8,multiply(multiply(inverse(V8),inverse(inverse(V6))),inverse(inverse(F)))))),E))))).  [para(780(a,1),11(a,1,1,2,2,2))].
% 1.44/1.71  1161 multiply(A,inverse(A)) = multiply(B,inverse(B)).  [para(780(a,1),822(a,1,2)),rewrite([780(17)])].
% 1.44/1.71  1171 multiply(A,inverse(A)) = c_0.  [new_symbol(1161)].
% 1.44/1.71  1174 multiply(A,inverse(multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(c_0)),A))))) = B.  [para(1171(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.44/1.71  1175 multiply(inverse(multiply(inverse(A),inverse(multiply(B,C)))),inverse(multiply(C,multiply(A,c_0)))) = B.  [para(1171(a,1),1(a,1,2,1,2,2))].
% 1.44/1.71  1180 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(c_0)),C))),inverse(B))) = inverse(C).  [para(1171(a,1),63(a,1,2,1,2,1,1,2,1))].
% 1.44/1.71  1181 multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),inverse(C))) = multiply(B,multiply(c_0,inverse(C))).  [para(1171(a,1),91(a,1,2,1)),flip(a)].
% 1.44/1.71  1186 inverse(multiply(multiply(A,c_0),multiply(B,multiply(C,D)))) = multiply(multiply(inverse(D),inverse(multiply(B,C))),inverse(A)).  [para(1171(a,1),125(a,1,1,1,2))].
% 1.44/1.71  1190 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(inverse(D),inverse(multiply(B,multiply(C,c_0)))).  [para(1171(a,1),194(a,1,2,1,2,2)),flip(a)].
% 1.44/1.71  1198 inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B)) = inverse(multiply(multiply(inverse(A),inverse(c_0)),C)).  [para(1171(a,1),345(a,1,1,1,2,1)),flip(a)].
% 1.44/1.71  1200 inverse(multiply(multiply(inverse(c_0),inverse(multiply(A,multiply(B,c_0)))),A)) = inverse(inverse(B)).  [para(1171(a,1),449(a,1,1,1,2,1,2,2,1)),rewrite([1190(6)])].
% 1.44/1.71  1220 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(inverse(E),F))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(E,c_0)))).  [para(1171(a,1),11(a,2,2,1,2,2,1)),rewrite([1190(22)])].
% 1.44/1.71  1223 multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,c_0).  [para(1171(a,1),822(a,1,2)),flip(a)].
% 1.44/1.71  1226 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(D))))) = multiply(inverse(multiply(inverse(E),inverse(multiply(F,multiply(c_0,inverse(inverse(V6))))))),inverse(multiply(inverse(multiply(multiply(inverse(V6),inverse(F)),multiply(D,C))),multiply(E,c_0)))).  [back_rewrite(1089),rewrite([1181(24),1190(28)])].
% 1.44/1.71  1227 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(multiply(inverse(F),inverse(inverse(E)))),inverse(multiply(inverse(multiply(inverse(multiply(multiply(V6,multiply(c_0,inverse(inverse(V7)))),multiply(inverse(V7),inverse(V6)))),multiply(D,C))),multiply(F,c_0)))).  [back_rewrite(1088),rewrite([1181(20),1190(34)])].
% 1.44/1.71  1235 multiply(multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))),inverse(A)) = inverse(B).  [back_rewrite(874),rewrite([1181(11),1190(11)])].
% 1.44/1.71  1278 inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))) = multiply(C,multiply(multiply(inverse(C),inverse(multiply(multiply(inverse(D),inverse(inverse(E))),inverse(E)))),inverse(D))).  [back_rewrite(820),rewrite([1181(8)])].
% 1.44/1.71  1281 multiply(inverse(multiply(inverse(A),inverse(multiply(B,multiply(c_0,inverse(inverse(C))))))),inverse(multiply(inverse(multiply(multiply(inverse(C),inverse(B)),multiply(D,multiply(inverse(D),E)))),multiply(A,c_0)))) = E.  [back_rewrite(817),rewrite([1181(17),1190(21)])].
% 1.44/1.71  1286 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(C),inverse(D))))),B)) = inverse(multiply(inverse(A),multiply(D,multiply(c_0,inverse(inverse(C)))))).  [back_rewrite(806),rewrite([1181(9)]),flip(a)].
% 1.44/1.71  1290 multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(multiply(inverse(B),multiply(A,c_0)))) = B.  [back_rewrite(1174),rewrite([1190(10)])].
% 1.44/1.71  1453 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(E)))))) = multiply(inverse(multiply(inverse(F),inverse(inverse(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(V8,V6))),multiply(inverse(V9),inverse(multiply(E,V10)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(V10,multiply(V9,V8))),multiply(D,C))),multiply(F,c_0)))).  [back_rewrite(929),rewrite([1190(37)])].
% 1.44/1.71  1493 multiply(inverse(A),inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(B),inverse(C))),inverse(multiply(D,multiply(B,c_0)))),D),multiply(multiply(inverse(C),inverse(inverse(E))),inverse(inverse(F)))),multiply(inverse(F),inverse(E))))) = inverse(A).  [back_rewrite(853),rewrite([1190(9)])].
% 1.44/1.71  1506 multiply(inverse(multiply(inverse(A),inverse(inverse(B)))),inverse(multiply(inverse(C),multiply(A,c_0)))) = multiply(inverse(c_0),inverse(multiply(inverse(C),multiply(B,c_0)))).  [back_rewrite(776),rewrite([1286(11),1190(11),1190(18)]),flip(a)].
% 1.44/1.71  1696 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)) = inverse(multiply(D,multiply(E,multiply(multiply(inverse(E),inverse(multiply(A,D))),inverse(C))))).  [back_rewrite(469),rewrite([1190(5)])].
% 1.44/1.71  1794 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(D,inverse(E)))))),inverse(F))) = multiply(E,multiply(multiply(inverse(D),inverse(multiply(B,multiply(C,c_0)))),inverse(F))).  [back_rewrite(229),rewrite([1190(15)])].
% 1.44/1.71  1821 multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(D,multiply(multiply(inverse(D),inverse(E)),F)))),multiply(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(C,V6))),multiply(inverse(B),inverse(multiply(E,A)))))),c_0)))) = F.  [back_rewrite(137),rewrite([1190(30),1506(31)])].
% 1.44/1.71  1874 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(E)))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(F,multiply(V6,V7))),multiply(D,C))),multiply(multiply(V8,multiply(V9,multiply(multiply(inverse(V9),inverse(multiply(V7,V8))),multiply(inverse(V6),inverse(multiply(E,F)))))),c_0)))).  [back_rewrite(1453),rewrite([1506(38)])].
% 1.44/1.71  1883 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(multiply(F,multiply(c_0,inverse(inverse(V6)))),multiply(inverse(V6),inverse(F)))),multiply(D,C))),multiply(E,c_0)))).  [back_rewrite(1227),rewrite([1506(35)])].
% 1.44/1.71  1912 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(D,c_0))) = multiply(multiply(inverse(inverse(inverse(D))),inverse(multiply(B,inverse(C)))),inverse(A)).  [para(1223(a,1),125(a,1,1,2))].
% 1.44/1.71  1916 inverse(multiply(multiply(inverse(A),inverse(multiply(B,c_0))),C)) = inverse(multiply(inverse(A),multiply(inverse(B),multiply(c_0,inverse(inverse(C)))))).  [para(1223(a,1),345(a,1,1,1,2,1)),rewrite([1286(17)])].
% 1.44/1.71  1980 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(multiply(inverse(C),inverse(multiply(D,E))),D),A))),F)))) = multiply(inverse(F),inverse(multiply(E,multiply(C,c_0)))).  [para(205(a,1),85(a,2,2,1,2,1,1)),rewrite([175(27),1190(18)])].
% 1.44/1.71  2016 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(inverse(C))),D))),inverse(B))) = multiply(inverse(D),inverse(multiply(multiply(C,c_0),multiply(c_0,c_0)))).  [para(1200(a,1),85(a,2,2,1,2,1,1,2)),rewrite([1980(16)]),flip(a)].
% 1.44/1.71  2047 inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))) = multiply(inverse(inverse(C)),inverse(multiply(multiply(C,c_0),multiply(c_0,c_0)))).  [back_rewrite(1278),rewrite([2016(22)])].
% 1.44/1.71  2051 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))),inverse(B))) = multiply(c_0,inverse(C)).  [para(1235(a,1),91(a,1,2)),flip(a)].
% 1.44/1.71  2054 inverse(multiply(multiply(A,c_0),multiply(c_0,inverse(A)))) = multiply(inverse(inverse(B)),inverse(multiply(multiply(B,c_0),multiply(c_0,c_0)))).  [para(1235(a,1),85(a,1,1,2,2)),rewrite([2016(19)])].
% 1.44/1.71  2058 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))),inverse(D))) = multiply(multiply(inverse(C),inverse(c_0)),multiply(B,inverse(D))).  [para(1290(a,1),91(a,1,2,1)),flip(a)].
% 1.44/1.71  2064 inverse(multiply(multiply(inverse(A),inverse(c_0)),multiply(inverse(B),multiply(C,c_0)))) = inverse(multiply(multiply(inverse(A),inverse(B)),inverse(multiply(inverse(C),inverse(c_0))))).  [para(1290(a,1),345(a,1,1,1,2,1)),rewrite([1198(21)]),flip(a)].
% 1.44/1.71  2067 multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0))))) = multiply(multiply(inverse(C),inverse(c_0)),B).  [para(1290(a,1),822(a,1,2)),flip(a)].
% 1.44/1.71  2068 multiply(multiply(inverse(c_0),inverse(multiply(A,multiply(B,c_0)))),A) = inverse(B).  [para(1200(a,1),1290(a,1,2,1,1)),rewrite([1290(12)]),flip(a)].
% 1.44/1.71  2074 multiply(multiply(inverse(A),inverse(c_0)),c_0) = multiply(c_0,inverse(A)).  [back_rewrite(2051),rewrite([2058(10),1171(6)])].
% 1.44/1.71  2086 multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(c_0))),inverse(multiply(inverse(B),multiply(c_0,inverse(A))))) = B.  [para(2074(a,1),1290(a,1,2,1,2))].
% 1.44/1.71  2161 inverse(multiply(inverse(multiply(multiply(inverse(A),inverse(inverse(B))),multiply(C,multiply(multiply(inverse(C),inverse(multiply(B,c_0))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(A)),F)))) = multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(multiply(inverse(V7),inverse(D)),F))),inverse(V7))).  [para(1223(a,1),90(a,1,1,1,1,2,2,1,2,1))].
% 1.44/1.71  2246 multiply(inverse(A),inverse(multiply(multiply(B,c_0),multiply(c_0,inverse(B))))) = inverse(A).  [para(1290(a,1),1175(a,1,1,1)),rewrite([2074(9)])].
% 1.44/1.71  2249 multiply(inverse(multiply(inverse(A),inverse(inverse(B)))),inverse(multiply(C,multiply(A,c_0)))) = multiply(inverse(c_0),inverse(multiply(C,multiply(B,c_0)))).  [para(2068(a,1),1175(a,1,1,1,2,1))].
% 1.44/1.71  2271 multiply(inverse(A),inverse(multiply(multiply(c_0,c_0),c_0))) = inverse(A).  [para(1171(a,1),2246(a,1,2,1,2))].
% 1.44/1.71  2285 multiply(inverse(inverse(A)),inverse(multiply(multiply(A,c_0),multiply(c_0,c_0)))) = inverse(multiply(multiply(c_0,c_0),c_0)).  [para(2271(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([2016(12)])].
% 1.44/1.71  2292 inverse(multiply(inverse(A),multiply(inverse(B),multiply(c_0,inverse(inverse(B)))))) = inverse(multiply(inverse(A),multiply(c_0,c_0))).  [para(2271(a,1),345(a,1,1,1)),rewrite([1916(13)]),flip(a)].
% 1.44/1.71  2296 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(C)),D))),inverse(F))),inverse(multiply(multiply(c_0,c_0),c_0))).  [para(85(a,1),2271(a,1,1)),flip(a)].
% 1.44/1.71  2301 multiply(inverse(inverse(A)),inverse(multiply(c_0,multiply(A,c_0)))) = multiply(c_0,c_0).  [para(2271(a,1),1175(a,1,1,1))].
% 1.44/1.71  2302 inverse(multiply(multiply(A,c_0),multiply(c_0,inverse(A)))) = inverse(multiply(multiply(c_0,c_0),c_0)).  [back_rewrite(2054),rewrite([2285(17)])].
% 1.44/1.71  2303 inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))) = inverse(multiply(multiply(c_0,c_0),c_0)).  [back_rewrite(2047),rewrite([2285(20)])].
% 1.44/1.71  2310 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,c_0),c_0)),multiply(D,C))),multiply(E,c_0)))).  [back_rewrite(1883),rewrite([2303(24)])].
% 1.44/1.71  2318 inverse(multiply(c_0,multiply(A,c_0))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0))).  [para(2301(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([1916(11),1794(17),2068(15)]),flip(a)].
% 1.44/1.71  2323 multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(c_0,c_0)))),inverse(B)) = inverse(A).  [para(2301(a,1),85(a,1,1,2,2,1)),rewrite([1186(10),1180(21)])].
% 1.44/1.71  2345 multiply(multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(C)),D))),inverse(B))),inverse(multiply(E,A))),inverse(F)) = inverse(multiply(multiply(F,multiply(E,inverse(D))),C)).  [para(104(a,1),125(a,1,1,2,2)),rewrite([125(16),177(30)])].
% 1.44/1.71  2390 multiply(A,multiply(multiply(inverse(A),inverse(multiply(c_0,inverse(B)))),inverse(B))) = inverse(c_0).  [para(2074(a,1),104(a,2,2,1,2,1)),rewrite([1916(9),2292(11),2323(11)]),flip(a)].
% 1.44/1.71  2418 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(c_0,c_0),c_0)))),C))),inverse(B)) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(inverse(E),A))),inverse(E))).  [para(2271(a,1),104(a,2,2,1,2,1,1))].
% 1.44/1.71  2441 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)) = inverse(multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(C))),inverse(inverse(c_0)))),c_0)).  [para(2318(a,1),345(a,1,1,1,2)),flip(a)].
% 1.44/1.71  2453 multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(multiply(multiply(inverse(inverse(inverse(B))),inverse(inverse(c_0))),multiply(A,c_0)))) = multiply(c_0,multiply(B,c_0)).  [para(2318(a,1),1290(a,1,2,1,1))].
% 1.44/1.71  2471 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),multiply(inverse(inverse(inverse(C))),inverse(inverse(c_0)))),c_0))),inverse(B)) = multiply(inverse(A),inverse(inverse(C))).  [para(2318(a,1),104(a,1,1,2,1,1,2)),rewrite([1916(24),1794(30),2068(28)])].
% 1.44/1.71  2475 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = multiply(inverse(C),inverse(inverse(multiply(c_0,c_0)))).  [back_rewrite(2418),rewrite([2441(12),2471(19)]),flip(a)].
% 1.44/1.71  2494 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(D))))) = inverse(multiply(multiply(inverse(C),multiply(inverse(inverse(inverse(D))),inverse(inverse(c_0)))),c_0)).  [back_rewrite(1696),rewrite([2441(8)]),flip(a)].
% 1.44/1.71  2529 multiply(inverse(multiply(inverse(A),inverse(multiply(B,multiply(c_0,inverse(inverse(C))))))),inverse(multiply(inverse(multiply(multiply(inverse(C),inverse(B)),multiply(D,E))),multiply(A,c_0)))) = inverse(multiply(multiply(inverse(E),multiply(inverse(inverse(inverse(D))),inverse(inverse(c_0)))),c_0)).  [back_rewrite(1226),rewrite([2494(9)]),flip(a)].
% 1.44/1.71  2540 inverse(multiply(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0)))),c_0)) = B.  [back_rewrite(1281),rewrite([2529(22)])].
% 1.44/1.71  2602 multiply(inverse(multiply(A,c_0)),inverse(inverse(multiply(c_0,c_0)))) = multiply(c_0,inverse(A)).  [para(2302(a,1),63(a,1,2,1,2,1,1,2)),rewrite([2271(9),2475(10)])].
% 1.44/1.71  2614 multiply(multiply(A,c_0),multiply(c_0,inverse(A))) = multiply(multiply(c_0,c_0),c_0).  [para(2302(a,1),1290(a,1,2,1,1)),rewrite([1290(16)]),flip(a)].
% 1.44/1.71  2617 inverse(multiply(multiply(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(C)),F))),multiply(c_0,inverse(F))),D)) = inverse(multiply(multiply(c_0,c_0),c_0)).  [para(90(a,1),2302(a,1,1,2,2)),rewrite([1186(30),2345(30)])].
% 1.44/1.71  2623 multiply(multiply(inverse(inverse(inverse(multiply(c_0,c_0)))),inverse(multiply(A,inverse(multiply(B,c_0))))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(multiply(A,c_0))),inverse(C)).  [para(2614(a,1),125(a,1,1,2)),rewrite([1912(12)])].
% 1.44/1.71  2709 multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)),inverse(inverse(multiply(c_0,c_0)))) = multiply(c_0,inverse(multiply(inverse(A),inverse(multiply(c_0,C))))).  [para(345(a,1),2602(a,1,1))].
% 1.44/1.71  2716 multiply(inverse(multiply(inverse(A),inverse(multiply(c_0,inverse(B))))),inverse(multiply(inverse(inverse(multiply(c_0,c_0))),multiply(A,c_0)))) = inverse(multiply(B,c_0)).  [para(2602(a,1),1175(a,1,1,1,2,1))].
% 1.44/1.71  2734 inverse(multiply(inverse(c_0),inverse(c_0))) = c_0.  [para(1290(a,1),2323(a,1,1)),rewrite([1171(2)]),flip(a)].
% 1.44/1.71  2740 multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))) = multiply(inverse(B),inverse(multiply(inverse(A),multiply(c_0,c_0)))).  [para(2323(a,1),1175(a,1,1,1,2,1)),rewrite([2249(11)])].
% 1.44/1.71  2742 multiply(multiply(inverse(A),inverse(inverse(B))),inverse(B)) = multiply(inverse(A),inverse(inverse(c_0))).  [para(2323(a,1),104(a,1,1,2,1)),rewrite([1916(15),1794(21),2068(19)])].
% 1.44/1.71  2752 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(multiply(c_0,inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B))),inverse(A))) = C.  [para(2734(a,1),63(a,1,2,1,1))].
% 1.44/1.71  2762 inverse(multiply(multiply(inverse(A),c_0),inverse(c_0))) = inverse(multiply(c_0,inverse(A))).  [para(2734(a,1),345(a,1,1,1,2)),rewrite([1198(15),2074(13)])].
% 1.44/1.71  2763 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(c_0,inverse(A))) = multiply(B,multiply(inverse(B),inverse(A))).  [para(2734(a,1),822(a,1,2,1))].
% 1.44/1.71  2765 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(c_0,inverse(inverse(A)))) = multiply(A,c_0).  [para(2734(a,1),1223(a,1,2,1))].
% 1.44/1.71  2786 multiply(multiply(c_0,inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B))),inverse(A)) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(C)),multiply(inverse(c_0),inverse(c_0))))),inverse(E))).  [para(2734(a,1),104(a,1,1,1))].
% 1.44/1.71  2792 inverse(multiply(c_0,c_0)) = multiply(inverse(inverse(c_0)),inverse(inverse(c_0))).  [para(2734(a,1),2318(a,2,1,1,1)),rewrite([2074(8),1171(5)])].
% 1.44/1.71  2794 multiply(multiply(c_0,c_0),c_0) = multiply(c_0,multiply(c_0,c_0)).  [para(2734(a,1),2614(a,1,2,2)),rewrite([2074(7),1171(4)]),flip(a)].
% 1.44/1.71  2801 multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))),c_0) = inverse(A).  [para(2734(a,1),2323(a,1,1,2,1,1)),rewrite([2318(7),2734(16)])].
% 1.44/1.71  2803 multiply(inverse(multiply(inverse(A),inverse(multiply(c_0,inverse(B))))),inverse(multiply(inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0)))),multiply(A,c_0)))) = inverse(multiply(B,c_0)).  [back_rewrite(2716),rewrite([2792(11)])].
% 1.44/1.71  2807 multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))) = multiply(c_0,inverse(multiply(inverse(A),inverse(multiply(c_0,C))))).  [back_rewrite(2709),rewrite([2792(10)])].
% 1.44/1.71  2811 multiply(multiply(inverse(inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))),inverse(multiply(A,inverse(multiply(B,c_0))))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(multiply(A,c_0))),inverse(C)).  [back_rewrite(2623),rewrite([2792(4)])].
% 1.44/1.71  2813 multiply(inverse(multiply(A,c_0)),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))) = multiply(c_0,inverse(A)).  [back_rewrite(2602),rewrite([2792(7)])].
% 1.44/1.71  2819 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = multiply(inverse(C),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))).  [back_rewrite(2475),rewrite([2792(13)])].
% 1.44/1.71  2835 inverse(multiply(multiply(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(C)),F))),multiply(c_0,inverse(F))),D)) = multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0))).  [back_rewrite(2617),rewrite([2794(25),2318(26)])].
% 1.44/1.71  2845 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0))),multiply(D,C))),multiply(E,c_0)))).  [back_rewrite(2310),rewrite([2794(19),2318(20)])].
% 1.44/1.71  2852 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(C)),D))),inverse(F))),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))).  [back_rewrite(2296),rewrite([2794(23),2318(24)])].
% 1.44/1.71  2857 multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))) = inverse(A).  [back_rewrite(2271),rewrite([2794(6),2318(7)])].
% 1.44/1.71  2859 multiply(inverse(A),c_0) = inverse(A).  [back_rewrite(2801),rewrite([2857(10)])].
% 1.44/1.71  2871 inverse(multiply(inverse(A),inverse(c_0))) = inverse(multiply(c_0,inverse(A))).  [back_rewrite(2762),rewrite([2859(3)])].
% 1.44/1.71  2876 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,inverse(D)))) = multiply(multiply(inverse(c_0),inverse(multiply(B,inverse(D)))),inverse(A)).  [para(2859(a,1),125(a,1,1,2,2))].
% 1.44/1.71  2888 multiply(multiply(inverse(A),inverse(multiply(inverse(B),inverse(inverse(c_0))))),inverse(B)) = inverse(A).  [para(2859(a,1),104(a,1,1,2,1,1,2,1)),rewrite([2742(7),1180(21)])].
% 1.44/1.71  2889 inverse(multiply(c_0,inverse(A))) = multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(c_0))).  [para(2859(a,1),2318(a,1,1,2))].
% 1.44/1.71  2893 multiply(c_0,c_0) = c_0.  [para(2734(a,1),2859(a,1,1)),rewrite([2734(9)])].
% 1.44/1.71  2901 multiply(inverse(A),inverse(c_0)) = inverse(A).  [back_rewrite(1493),rewrite([2876(24),2742(9),2441(21),2540(25),2888(12)])].
% 1.44/1.71  2913 multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))) = multiply(inverse(B),inverse(inverse(A))).  [back_rewrite(2740),rewrite([2893(13),2859(12)])].
% 1.44/1.71  2920 multiply(inverse(A),inverse(inverse(c_0))) = inverse(A).  [back_rewrite(2323),rewrite([2893(5),2859(4),2742(6)])].
% 1.44/1.71  2968 inverse(inverse(inverse(inverse(A)))) = inverse(inverse(A)).  [back_rewrite(2871),rewrite([2901(4),2889(6),2920(10)]),flip(a)].
% 1.44/1.71  2971 inverse(multiply(A,c_0)) = inverse(A).  [back_rewrite(2803),rewrite([2889(5),2968(5),2920(7),2920(12),2249(14),2913(11),2968(6),2920(5)]),flip(a)].
% 1.44/1.71  2975 inverse(c_0) = c_0.  [back_rewrite(2390),rewrite([2889(5),2968(5),2920(7),2742(6),2920(5),1171(2)]),flip(a)].
% 1.44/1.71  2982 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = inverse(C).  [back_rewrite(2819),rewrite([2975(11),2975(11),2975(12),2975(12),2893(12),2975(11),2859(11)])].
% 1.44/1.71  2985 multiply(c_0,inverse(A)) = inverse(A).  [back_rewrite(2813),rewrite([2971(3),2975(3),2975(3),2975(4),2975(4),2893(4),2975(3),2859(3)]),flip(a)].
% 1.44/1.71  2987 multiply(inverse(multiply(A,inverse(B))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(A)),inverse(C)).  [back_rewrite(2811),rewrite([2975(2),2975(2),2975(3),2975(3),2893(3),2975(2),2975(2),2971(4),2985(5),2971(10)])].
% 1.44/1.71  2988 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(inverse(A),inverse(multiply(c_0,C)))).  [back_rewrite(2807),rewrite([2975(8),2975(8),2975(9),2975(9),2893(9),2975(8),2859(8),2985(14)])].
% 1.44/1.71  3010 inverse(inverse(multiply(c_0,A))) = inverse(inverse(A)).  [back_rewrite(2786),rewrite([2988(7),2985(8),2987(8),2742(9),2975(6),2975(6),2859(6),2975(10),2975(11),2893(11),2971(11),2982(13)])].
% 1.44/1.71  3016 multiply(A,c_0) = inverse(inverse(A)).  [back_rewrite(2765),rewrite([2975(2),2975(3),2893(3),2985(5),2985(4)]),flip(a)].
% 1.44/1.71  3017 multiply(A,multiply(inverse(A),inverse(B))) = inverse(B).  [back_rewrite(2763),rewrite([2975(2),2975(3),3016(3),2975(2),2975(2),2985(4),2985(3)]),flip(a)].
% 1.44/1.71  3020 inverse(inverse(A)) = A.  [back_rewrite(2752),rewrite([2975(2),2975(3),3016(3),2975(2),2975(2),2988(8),2985(9),2987(9),3010(5),2742(8),2975(5),2975(5),3016(5),2968(5),2985(4)])].
% 1.44/1.72  3028 multiply(A,inverse(multiply(inverse(B),A))) = multiply(c_0,B).  [back_rewrite(2453),rewrite([2975(3),3016(3),3020(2),3020(2),3020(2),2975(3),2975(3),3016(3),3020(2),3016(3),3020(3),3016(7),3020(7)])].
% 1.44/1.72  3041 multiply(c_0,A) = A.  [back_rewrite(2086),rewrite([2975(3),3016(3),3020(2),3020(2),2975(2),3016(2),3020(2),2985(5),3028(6)])].
% 1.44/1.72  3044 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A).  [back_rewrite(2067),rewrite([3016(4),3020(4),3017(6),2975(6),3016(6),3020(5)])].
% 1.44/1.72  3046 inverse(multiply(multiply(inverse(A),inverse(B)),C)) = multiply(multiply(inverse(C),B),A).  [back_rewrite(2064),rewrite([2975(3),3016(3),3020(2),3016(4),3020(4),3044(5),3044(3),2975(9),3016(9),3020(8),3020(8)]),flip(a)].
% 1.44/1.72  3073 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),E))))) = multiply(inverse(E),multiply(D,C)).  [back_rewrite(2845),rewrite([3020(7),2975(12),2975(13),2975(13),2975(13),2975(14),2975(14),3016(14),2975(13),2975(13),3041(14),3016(15),3020(15),3044(15),3041(15)])].
% 1.44/1.72  3084 inverse(multiply(multiply(inverse(multiply(A,B)),multiply(C,multiply(D,E))),inverse(multiply(multiply(F,C),multiply(D,E))))) = multiply(F,multiply(A,B)).  [back_rewrite(1874),rewrite([3073(11),3020(2),2975(4),3044(9),3016(21),3073(20),3020(11),3041(15)]),flip(a)].
% 1.44/1.72  3102 multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C))) = C.  [back_rewrite(1821),rewrite([2975(2),3044(11),3016(23),3073(22),3020(13),3084(16),3041(8)])].
% 1.44/1.72  3136 multiply(multiply(inverse(A),B),multiply(C,D)) = multiply(inverse(A),multiply(B,multiply(C,D))).  [back_rewrite(1220),rewrite([3044(8),3073(12),3044(3),2975(6),3016(10),3020(10),3044(10),3041(10)])].
% 1.44/1.72  3150 multiply(A,multiply(multiply(inverse(A),multiply(multiply(inverse(B),C),D)),inverse(D))) = multiply(inverse(B),C).  [back_rewrite(2161),rewrite([3020(3),3016(5),3020(5),3136(8),3102(7),3044(3),3136(8),3102(7),3044(3),3046(8)]),flip(a)].
% 1.44/1.72  3174 multiply(multiply(inverse(A),B),inverse(B)) = inverse(A).  [back_rewrite(2888),rewrite([2975(4),2975(4),3016(4),3020(3),3020(3)])].
% 1.44/1.72  3176 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(inverse(D),C).  [back_rewrite(2852),rewrite([3046(14),3150(16),2975(12),2975(12),2975(12),2975(13),2975(13),3016(13),2975(12),2975(12),3016(12),3044(11),3044(11)])].
% 1.44/1.72  3182 multiply(inverse(A),A) = c_0.  [back_rewrite(2835),rewrite([3176(8),3136(8),3102(7),3041(5),3174(4),3044(3),2975(4),2975(4),2975(4),2975(5),2975(5),3016(5),2975(4),2975(4)])].
% 1.44/1.72  3290 $F # answer(prove_these_axioms_1).  [back_rewrite(3),rewrite([3182(4),3182(5)]),xx(a)].
% 1.44/1.72  
% 1.44/1.72  % SZS output end Refutation
% 1.44/1.72  ============================== end of proof ==========================
% 1.44/1.72  
% 1.44/1.72  ============================== STATISTICS ============================
% 1.44/1.72  
% 1.44/1.72  Given=47. Generated=6393. Kept=3288. proofs=1.
% 1.44/1.72  Usable=1. Sos=67. Demods=166. Limbo=108, Disabled=3114. Hints=0.
% 1.44/1.72  Megabytes=5.69.
% 1.44/1.72  User_CPU=0.69, System_CPU=0.01, Wall_clock=1.
% 1.44/1.72  
% 1.44/1.72  ============================== end of statistics =====================
% 1.44/1.72  
% 1.44/1.72  ============================== end of search =========================
% 1.44/1.72  
% 1.44/1.72  THEOREM PROVED
% 1.44/1.72  % SZS status Unsatisfiable
% 1.44/1.72  
% 1.44/1.72  Exiting with 1 proof.
% 1.44/1.72  
% 1.44/1.72  Process 22469 exit (max_proofs) Mon Jun 13 22:09:26 2022
% 1.44/1.72  Prover9 interrupted
%------------------------------------------------------------------------------