TSTP Solution File: GRP429-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP429-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n026.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 11:19:03 EDT 2022

% Result   : Unsatisfiable 1.58s 1.84s
% Output   : Refutation 1.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP429-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n026.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 05:29:51 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.58/1.84  ============================== Prover9 ===============================
% 1.58/1.84  Prover9 (32) version 2009-11A, November 2009.
% 1.58/1.84  Process 27072 was started by sandbox on n026.cluster.edu,
% 1.58/1.84  Tue Jun 14 05:29:52 2022
% 1.58/1.84  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26712_n026.cluster.edu".
% 1.58/1.84  ============================== end of head ===========================
% 1.58/1.84  
% 1.58/1.84  ============================== INPUT =================================
% 1.58/1.84  
% 1.58/1.84  % Reading from file /tmp/Prover9_26712_n026.cluster.edu
% 1.58/1.84  
% 1.58/1.84  set(prolog_style_variables).
% 1.58/1.84  set(auto2).
% 1.58/1.84      % set(auto2) -> set(auto).
% 1.58/1.84      % set(auto) -> set(auto_inference).
% 1.58/1.84      % set(auto) -> set(auto_setup).
% 1.58/1.84      % set(auto_setup) -> set(predicate_elim).
% 1.58/1.84      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.58/1.84      % set(auto) -> set(auto_limits).
% 1.58/1.84      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.58/1.84      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.58/1.84      % set(auto) -> set(auto_denials).
% 1.58/1.84      % set(auto) -> set(auto_process).
% 1.58/1.84      % set(auto2) -> assign(new_constants, 1).
% 1.58/1.84      % set(auto2) -> assign(fold_denial_max, 3).
% 1.58/1.84      % set(auto2) -> assign(max_weight, "200.000").
% 1.58/1.84      % set(auto2) -> assign(max_hours, 1).
% 1.58/1.84      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.58/1.84      % set(auto2) -> assign(max_seconds, 0).
% 1.58/1.84      % set(auto2) -> assign(max_minutes, 5).
% 1.58/1.84      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.58/1.84      % set(auto2) -> set(sort_initial_sos).
% 1.58/1.84      % set(auto2) -> assign(sos_limit, -1).
% 1.58/1.84      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.58/1.84      % set(auto2) -> assign(max_megs, 400).
% 1.58/1.84      % set(auto2) -> assign(stats, some).
% 1.58/1.84      % set(auto2) -> clear(echo_input).
% 1.58/1.84      % set(auto2) -> set(quiet).
% 1.58/1.84      % set(auto2) -> clear(print_initial_clauses).
% 1.58/1.84      % set(auto2) -> clear(print_given).
% 1.58/1.84  assign(lrs_ticks,-1).
% 1.58/1.84  assign(sos_limit,10000).
% 1.58/1.84  assign(order,kbo).
% 1.58/1.84  set(lex_order_vars).
% 1.58/1.84  clear(print_given).
% 1.58/1.84  
% 1.58/1.84  % formulas(sos).  % not echoed (2 formulas)
% 1.58/1.84  
% 1.58/1.84  ============================== end of input ==========================
% 1.58/1.84  
% 1.58/1.84  % From the command line: assign(max_seconds, 300).
% 1.58/1.84  
% 1.58/1.84  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.58/1.84  
% 1.58/1.84  % Formulas that are not ordinary clauses:
% 1.58/1.84  
% 1.58/1.84  ============================== end of process non-clausal formulas ===
% 1.58/1.84  
% 1.58/1.84  ============================== PROCESS INITIAL CLAUSES ===============
% 1.58/1.84  
% 1.58/1.84  ============================== PREDICATE ELIMINATION =================
% 1.58/1.84  
% 1.58/1.84  ============================== end predicate elimination =============
% 1.58/1.84  
% 1.58/1.84  Auto_denials:
% 1.58/1.84    % copying label prove_these_axioms_3 to answer in negative clause
% 1.58/1.84  
% 1.58/1.84  Term ordering decisions:
% 1.58/1.84  
% 1.58/1.84  % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.58/1.84  Function symbol KB weights:  a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.58/1.84  
% 1.58/1.84  ============================== end of process initial clauses ========
% 1.58/1.84  
% 1.58/1.84  ============================== CLAUSES FOR SEARCH ====================
% 1.58/1.84  
% 1.58/1.84  ============================== end of clauses for search =============
% 1.58/1.84  
% 1.58/1.84  ============================== SEARCH ================================
% 1.58/1.84  
% 1.58/1.84  % Starting search at 0.01 seconds.
% 1.58/1.84  
% 1.58/1.84  ============================== PROOF =================================
% 1.58/1.84  % SZS status Unsatisfiable
% 1.58/1.84  % SZS output start Refutation
% 1.58/1.84  
% 1.58/1.84  % Proof 1 at 0.77 (+ 0.01) seconds: prove_these_axioms_3.
% 1.58/1.84  % Length of proof is 145.
% 1.58/1.84  % Level of proof is 36.
% 1.58/1.84  % Maximum clause weight is 72.000.
% 1.58/1.84  % Given clauses 55.
% 1.58/1.84  
% 1.58/1.84  1 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),D),inverse(multiply(B,D))))) = C # label(single_axiom) # label(axiom).  [assumption].
% 1.58/1.84  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].
% 1.58/1.84  3 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(inverse(A)),C))),F),inverse(multiply(E,F)))).  [para(1(a,1),1(a,1,2,1,1,1,1,2))].
% 1.58/1.84  4 multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(A),E)))),B))),F),inverse(multiply(D,F))))))))) = E.  [para(1(a,1),1(a,1,2,1,1))].
% 1.58/1.84  6 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(inverse(A))),D))),E),inverse(multiply(C,E)))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))).  [para(3(a,1),1(a,1,2,1,1,1,1,2))].
% 1.58/1.84  8 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(B)),E))),V7),inverse(multiply(V6,V7)))))))) = C.  [para(3(a,1),1(a,1,2,1,2,1))].
% 1.58/1.84  10 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),multiply(inverse(B),C)))),D),inverse(multiply(A,D)))) = C.  [para(3(a,1),1(a,1))].
% 1.58/1.84  14 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D)))))) = C.  [para(3(a,2),1(a,1,2))].
% 1.58/1.84  81 multiply(inverse(inverse(A)),multiply(inverse(A),B)) = multiply(inverse(C),multiply(C,B)).  [para(10(a,1),14(a,1,2,2)),flip(a)].
% 1.58/1.84  85 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),D),inverse(multiply(A,D)))) = C.  [para(10(a,1),10(a,1,1,1,1,1,2,1,1)),rewrite([10(15)])].
% 1.58/1.84  87 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(inverse(A),D))))) = C.  [para(81(a,1),1(a,1,2,1,1,1,1))].
% 1.58/1.84  109 multiply(inverse(A),multiply(A,B)) = multiply(inverse(C),multiply(C,B)).  [para(81(a,1),81(a,1))].
% 1.58/1.84  119 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(E,D)))))) = multiply(E,C).  [para(109(a,1),14(a,1,2,2,1,1,1,1))].
% 1.58/1.84  120 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(B),multiply(B,C)),inverse(multiply(D,multiply(multiply(inverse(D),E),C))))))) = E.  [para(109(a,1),14(a,1,2,2,1,1))].
% 1.58/1.84  122 multiply(inverse(inverse(A)),multiply(inverse(B),multiply(B,C))) = multiply(inverse(D),multiply(D,multiply(A,C))).  [para(109(a,1),109(a,1,2))].
% 1.58/1.84  186 multiply(inverse(inverse(A)),multiply(inverse(B),multiply(B,C))) = multiply(inverse(inverse(A)),multiply(inverse(D),multiply(D,C))).  [para(109(a,1),122(a,2,2))].
% 1.58/1.84  223 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,multiply(multiply(inverse(C),multiply(inverse(D),multiply(D,E))),B))))) = E.  [para(109(a,1),85(a,1,1,1))].
% 1.58/1.84  260 multiply(A,inverse(multiply(multiply(inverse(B),multiply(B,C)),inverse(multiply(inverse(A),multiply(multiply(inverse(D),multiply(D,E)),C)))))) = E.  [para(109(a,1),87(a,1,2,1,1))].
% 1.58/1.84  417 multiply(inverse(A),multiply(inverse(B),multiply(B,C))) = multiply(inverse(A),multiply(inverse(D),multiply(D,C))).  [para(85(a,1),186(a,1,1,1)),rewrite([85(16)])].
% 1.58/1.84  437 multiply(A,multiply(inverse(B),multiply(B,C))) = multiply(A,multiply(inverse(D),multiply(D,C))).  [para(85(a,1),417(a,1,1)),rewrite([85(15)])].
% 1.58/1.84  444 multiply(inverse(A),multiply(A,multiply(inverse(B),multiply(B,C)))) = multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,C)))).  [para(437(a,1),109(a,1,2))].
% 1.58/1.84  510 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(inverse(A))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F))))))),V6),inverse(multiply(C,V6)))))),V7),inverse(multiply(B,V7))))) = inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(V8),multiply(inverse(inverse(inverse(V9))),E))),V10),inverse(multiply(V8,V10))))),V11),inverse(multiply(V9,V11)))).  [para(3(a,1),6(a,2,1,1,1,1))].
% 1.58/1.84  773 multiply(inverse(A),multiply(A,inverse(inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(multiply(inverse(C),multiply(C,D))),inverse(multiply(E,F))))),V6))),V7),inverse(multiply(B,V7))))))) = multiply(multiply(inverse(multiply(inverse(E),V6)),F),D).  [para(3(a,1),119(a,1,2,2,1))].
% 1.58/1.84  792 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(E,D)))))) = multiply(E,inverse(multiply(F,inverse(multiply(V6,inverse(multiply(multiply(inverse(multiply(inverse(V7),multiply(inverse(inverse(multiply(inverse(V6),multiply(inverse(B),C)))),F))),V8),inverse(multiply(V7,V8))))))))).  [para(4(a,1),119(a,1,2,2,1,1,1,1,2))].
% 1.58/1.84  804 multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),D),E) = multiply(inverse(F),multiply(F,inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(V6,E))),inverse(multiply(A,D))),C)))).  [para(85(a,1),119(a,1,2,2,1,2)),flip(a)].
% 1.58/1.84  1172 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(inverse(inverse(C)),multiply(multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,F)))),B))))) = multiply(C,F).  [para(444(a,1),223(a,1,1,2,1,2,1))].
% 1.58/1.84  1235 multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,inverse(C)))) = B.  [para(14(a,1),260(a,1,2,1,2,1)),rewrite([14(14)])].
% 1.58/1.84  1302 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(inverse(C),multiply(multiply(inverse(D),multiply(D,E)),B))))) = inverse(multiply(multiply(inverse(F),multiply(F,V6)),inverse(multiply(V7,multiply(multiply(inverse(V7),multiply(inverse(C),E)),V6))))).  [para(260(a,1),223(a,1,1,2,1,2,1,2,2)),flip(a)].
% 1.58/1.84  1312 multiply(A,inverse(multiply(B,inverse(B)))) = inverse(multiply(multiply(inverse(multiply(inverse(C),A)),D),inverse(multiply(C,D)))).  [para(3(a,1),1235(a,1,1,2)),rewrite([1(13)])].
% 1.58/1.84  1322 multiply(inverse(inverse(A)),multiply(inverse(multiply(inverse(B),multiply(B,C))),C)) = multiply(inverse(D),multiply(D,multiply(A,inverse(multiply(E,inverse(E)))))).  [para(1235(a,1),122(a,1,2,2))].
% 1.58/1.84  1335 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,inverse(multiply(F,inverse(F))))))).  [para(1235(a,1),444(a,1,2,2,2))].
% 1.58/1.84  1349 multiply(inverse(multiply(inverse(A),multiply(A,B))),B) = multiply(inverse(multiply(inverse(C),multiply(C,D))),D).  [para(1235(a,1),119(a,1,2))].
% 1.58/1.84  1356 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),C),inverse(multiply(D,multiply(multiply(inverse(D),E),inverse(multiply(F,inverse(F)))))))))) = E.  [para(1235(a,1),120(a,1,2,2,1,1,2))].
% 1.58/1.84  1506 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(E),F))),inverse(multiply(multiply(inverse(multiply(inverse(V6),V7)),V8),inverse(multiply(V6,V8))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V9),multiply(inverse(inverse(D)),V7))),V10),inverse(multiply(V9,V10)))))))),inverse(F))))) = multiply(E,C).  [para(8(a,1),119(a,1,2,2,1,2,1))].
% 1.58/1.84  1585 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),C),inverse(multiply(D,E)))))) = multiply(D,E).  [para(1349(a,1),14(a,1,2,2,1,1))].
% 1.58/1.84  1587 multiply(inverse(inverse(A)),multiply(inverse(multiply(inverse(B),multiply(B,C))),C)) = A.  [para(1349(a,1),14(a,1,2)),rewrite([14(11)])].
% 1.58/1.84  1649 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(C,inverse(C))))) = B.  [back_rewrite(1356),rewrite([1585(18)])].
% 1.58/1.84  1651 multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,inverse(C)))))) = B.  [back_rewrite(1322),rewrite([1587(8)]),flip(a)].
% 1.58/1.84  1742 multiply(inverse(A),multiply(A,multiply(B,multiply(C,inverse(multiply(D,inverse(D))))))) = multiply(inverse(inverse(B)),C).  [para(1651(a,1),109(a,1,2)),flip(a)].
% 1.58/1.84  1763 multiply(inverse(inverse(inverse(A))),A) = multiply(inverse(inverse(inverse(B))),B).  [para(1651(a,1),444(a,1,2)),rewrite([1742(13)])].
% 1.58/1.84  1797 multiply(A,inverse(multiply(B,inverse(B)))) = multiply(A,inverse(multiply(C,inverse(C)))).  [para(1651(a,1),1235(a,1,1))].
% 1.58/1.84  1799 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = inverse(multiply(inverse(D),multiply(D,inverse(multiply(E,inverse(E)))))).  [para(1349(a,1),1651(a,1,2,2))].
% 1.58/1.84  1801 multiply(inverse(inverse(inverse(A))),A) = multiply(inverse(B),multiply(B,multiply(inverse(multiply(inverse(C),multiply(C,D))),D))).  [back_rewrite(1335),rewrite([1742(17)]),flip(a)].
% 1.58/1.84  1802 multiply(inverse(inverse(inverse(A))),A) = c_0.  [new_symbol(1763)].
% 1.58/1.84  1803 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = c_0.  [back_rewrite(1801),rewrite([1802(4)]),flip(a)].
% 1.58/1.84  1805 inverse(multiply(inverse(A),multiply(A,inverse(multiply(B,inverse(B)))))) = c_0.  [back_rewrite(1799),rewrite([1803(8)]),flip(a)].
% 1.58/1.84  1822 multiply(inverse(A),multiply(A,B)) = multiply(inverse(inverse(inverse(inverse(B)))),c_0).  [para(1802(a,1),109(a,1,2)),flip(a)].
% 1.58/1.84  1827 multiply(inverse(inverse(inverse(inverse(multiply(A,B))))),c_0) = multiply(inverse(inverse(A)),multiply(inverse(inverse(inverse(inverse(B)))),c_0)).  [para(1802(a,1),122(a,1,2,2)),rewrite([1822(13)]),flip(a)].
% 1.58/1.84  1847 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),B),inverse(c_0))))))),c_0) = multiply(inverse(inverse(inverse(B))),A).  [para(1802(a,1),119(a,1,2,2,1,2,1)),rewrite([1822(4),1822(15)])].
% 1.58/1.84  1856 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(B,multiply(multiply(inverse(B),C),A))))))))),c_0) = C.  [para(1802(a,1),120(a,1,2,2,1,1,2)),rewrite([1822(16)])].
% 1.58/1.84  1862 multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),B))),inverse(multiply(multiply(inverse(inverse(inverse(inverse(B)))),c_0),inverse(c_0)))) = A.  [para(1802(a,1),260(a,1,2,1,2,1)),rewrite([1822(3),1822(12)])].
% 1.58/1.84  1865 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(B,inverse(B))))) = A.  [para(1802(a,1),1649(a,1,2,1))].
% 1.58/1.84  1870 inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0)) = c_0.  [back_rewrite(1805),rewrite([1822(6)])].
% 1.58/1.84  2031 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(C),D))),inverse(multiply(multiply(inverse(multiply(inverse(E),F)),V6),inverse(multiply(E,V6))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V7),multiply(inverse(inverse(B)),F))),V8),inverse(multiply(V7,V8)))))))),inverse(D))))))),c_0) = multiply(C,A).  [back_rewrite(1506),rewrite([1822(4),1822(42)])].
% 1.58/1.84  2133 inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(inverse(B),multiply(multiply(inverse(inverse(inverse(inverse(C)))),c_0),A))))) = inverse(multiply(multiply(inverse(inverse(inverse(inverse(D)))),c_0),inverse(multiply(E,multiply(multiply(inverse(E),multiply(inverse(B),C)),D))))).  [back_rewrite(1302),rewrite([1822(3),1822(10),1822(21)])].
% 1.58/1.84  2251 inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(inverse(inverse(B)),multiply(multiply(inverse(inverse(inverse(inverse(inverse(inverse(C)))))),multiply(inverse(inverse(inverse(inverse(c_0)))),c_0)),A))))) = multiply(B,C).  [back_rewrite(1172),rewrite([1822(3),1822(12),1822(17),1827(20)])].
% 1.58/1.84  2483 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),inverse(multiply(B,C))),D)))))),c_0) = multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(inverse(inverse(D)))),c_0))),C),A).  [back_rewrite(804),rewrite([1822(4),1822(15),1822(26)]),flip(a)].
% 1.58/1.84  2492 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(D,C)))))))),c_0) = multiply(D,inverse(multiply(E,inverse(multiply(F,inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(multiply(inverse(F),multiply(inverse(A),B)))),E))),V7),inverse(multiply(V6,V7))))))))).  [back_rewrite(792),rewrite([1822(11)])].
% 1.58/1.84  2509 multiply(inverse(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(B)))),c_0)),inverse(multiply(C,D))))),E))),F),inverse(multiply(A,F))))))))),c_0) = multiply(multiply(inverse(multiply(inverse(C),E)),D),B).  [back_rewrite(773),rewrite([1822(5),1822(25)])].
% 1.58/1.84  2848 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(B),C))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F)))))),multiply(inverse(inverse(inverse(inverse(inverse(C))))),c_0))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(A)),E))),V7),inverse(multiply(V6,V7)))))),V8) = multiply(B,V8).  [back_rewrite(2031),rewrite([2483(45)])].
% 1.58/1.84  2935 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(c_0,inverse(multiply(C,inverse(C)))))),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),A)),F),inverse(multiply(E,F)))).  [para(1865(a,1),3(a,2,1,1,1,1,2))].
% 1.58/1.84  2936 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(E))),multiply(inverse(inverse(A)),C))),multiply(c_0,inverse(multiply(F,inverse(F))))),inverse(E))).  [para(1865(a,1),3(a,2,1,2,1))].
% 1.58/1.84  2938 multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),C))),D),inverse(multiply(A,D))) = multiply(inverse(multiply(B,inverse(multiply(multiply(inverse(multiply(inverse(E),C)),F),inverse(multiply(E,F)))))),multiply(c_0,inverse(multiply(V6,inverse(V6))))).  [para(3(a,2),1865(a,1,1,1)),flip(a)].
% 1.58/1.84  2944 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(inverse(A))),D))),multiply(c_0,inverse(multiply(E,inverse(E))))),inverse(C))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))).  [para(1865(a,1),6(a,1,2,1,1,1,1,2,1,2,1))].
% 1.58/1.84  2948 multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),inverse(multiply(multiply(inverse(multiply(inverse(F),multiply(inverse(inverse(inverse(D))),B))),V6),inverse(multiply(F,V6)))))),V7),inverse(multiply(E,V7)))))),multiply(c_0,inverse(multiply(V8,inverse(V8))))).  [para(6(a,2),1865(a,1,1,1)),flip(a)].
% 1.58/1.84  2955 multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0) = multiply(c_0,inverse(multiply(B,inverse(B)))).  [para(1865(a,1),1649(a,1,2,1)),rewrite([1822(6)])].
% 1.58/1.84  2956 inverse(multiply(c_0,inverse(multiply(A,inverse(A))))) = c_0.  [para(1865(a,1),1802(a,1))].
% 1.58/1.84  2968 multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(c_0),C))),F),inverse(multiply(E,F)))).  [para(2956(a,1),3(a,2,1,1,1,1,2,1,1))].
% 1.58/1.84  2969 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(c_0),multiply(inverse(inverse(A)),C))),inverse(multiply(E,inverse(E)))),c_0)).  [para(2956(a,1),3(a,2,1,2))].
% 1.58/1.84  2978 multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(c_0)),D))),E),inverse(multiply(C,E)))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))).  [para(2956(a,1),6(a,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1))].
% 1.58/1.84  2980 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(c_0),inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(inverse(A))),C))),D),inverse(multiply(B,D)))))),inverse(multiply(E,inverse(E)))),c_0))) = inverse(multiply(multiply(inverse(multiply(inverse(F),C)),V6),inverse(multiply(F,V6)))).  [para(2956(a,1),6(a,1,2,1,2))].
% 1.58/1.84  2981 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(inverse(A))),D))),E),inverse(multiply(C,E)))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(c_0,D)),V6),inverse(multiply(multiply(c_0,inverse(multiply(V7,inverse(V7)))),V6)))).  [para(2956(a,1),6(a,2,1,1,1,1,1))].
% 1.58/1.84  2991 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(multiply(c_0,inverse(multiply(C,inverse(C)))),c_0)))) = B.  [para(2956(a,1),1649(a,1,2,2,1,2))].
% 1.58/1.84  2997 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(multiply(c_0,inverse(multiply(B,inverse(B)))),c_0)))) = A.  [para(2956(a,1),1865(a,1,2,2,1,2))].
% 1.58/1.84  3007 multiply(c_0,multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),B)) = multiply(inverse(inverse(inverse(inverse(B)))),c_0).  [para(2956(a,1),1822(a,1,1))].
% 1.58/1.84  3010 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(multiply(B,inverse(B)))))))),multiply(inverse(A),C))),c_0),c_0))) = C.  [para(1870(a,1),1(a,1,2,1,2))].
% 1.58/1.84  3011 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),C),inverse(multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(D,inverse(D))))))),c_0),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(inverse(A)),B))),F),inverse(multiply(E,F)))).  [para(1870(a,1),3(a,1,2,1,1,1,1,1))].
% 1.58/1.84  3013 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(multiply(B,inverse(B)))))))),C)),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(A)),C))),E),inverse(multiply(D,E)))).  [para(1870(a,1),3(a,1,2,1,2))].
% 1.58/1.84  3015 multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0),inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(c_0),C))),F),inverse(multiply(E,F)))).  [para(1870(a,1),3(a,2,1,1,1,1,2,1,1))].
% 1.58/1.84  3197 inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))).  [para(1797(a,1),1(a,1,2,1,1,1,1,2)),rewrite([1(14)])].
% 1.58/1.84  3225 multiply(inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))),inverse(multiply(B,inverse(B)))) = c_0.  [para(1797(a,1),1802(a,1))].
% 1.58/1.84  3231 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))))) = A.  [para(1797(a,1),1865(a,1,2,2,1))].
% 1.58/1.84  3267 multiply(inverse(inverse(inverse(multiply(A,inverse(A))))),multiply(B,inverse(B))) = c_0.  [para(3197(a,1),1802(a,1,1,1,1))].
% 1.58/1.84  3273 multiply(A,inverse(A)) = multiply(B,inverse(B)).  [para(3197(a,1),1865(a,1,1,1)),rewrite([1865(10)])].
% 1.58/1.84  3304 multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)).  [para(3273(a,1),1649(a,1,2))].
% 1.58/1.84  3308 multiply(inverse(inverse(inverse(inverse(inverse(A))))),c_0) = inverse(inverse(inverse(A))).  [para(3273(a,1),1822(a,1,2)),rewrite([3304(4)]),flip(a)].
% 1.58/1.84  3309 inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))) = c_0.  [para(3273(a,1),1870(a,1,1,1,1,1,1,1,1)),rewrite([3308(9)])].
% 1.58/1.84  3310 multiply(multiply(inverse(c_0),c_0),c_0) = multiply(A,inverse(A)).  [para(1870(a,1),3273(a,1,2)),rewrite([3309(6)])].
% 1.58/1.84  3323 inverse(c_0) = c_0.  [back_rewrite(3267),rewrite([3304(8),3309(6)])].
% 1.58/1.84  3355 multiply(multiply(c_0,c_0),inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(c_0,B))),E),inverse(multiply(D,E)))).  [back_rewrite(3015),rewrite([3309(6),3323(2),3323(15)])].
% 1.58/1.84  3357 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),C),inverse(multiply(multiply(c_0,c_0),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(A)),B))),E),inverse(multiply(D,E)))).  [back_rewrite(3011),rewrite([3309(10),3323(6)])].
% 1.58/1.84  3362 multiply(c_0,inverse(multiply(A,inverse(A)))) = multiply(c_0,c_0).  [back_rewrite(2955),rewrite([3309(6),3323(2)]),flip(a)].
% 1.58/1.84  3363 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(B),C))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F)))))),inverse(inverse(inverse(C))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(A)),E))),V7),inverse(multiply(V6,V7)))))),V8) = multiply(B,V8).  [back_rewrite(2848),rewrite([3308(22)])].
% 1.58/1.84  3410 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(B)))),c_0)),inverse(multiply(C,D))))),E))),F),inverse(multiply(A,F))))))) = multiply(multiply(inverse(multiply(inverse(C),E)),D),B).  [back_rewrite(2509),rewrite([3308(28)])].
% 1.58/1.84  3419 multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(E),F)))),B))),V6),inverse(multiply(D,V6))))))))) = inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(E),F)),V7),inverse(multiply(A,V7)))))).  [back_rewrite(2492),rewrite([3308(14)]),flip(a)].
% 1.58/1.84  3517 inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(B,multiply(multiply(inverse(B),C),A))))))) = C.  [back_rewrite(1856),rewrite([3308(19)])].
% 1.58/1.84  3518 inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),B),c_0)))) = multiply(inverse(inverse(inverse(B))),A).  [back_rewrite(1847),rewrite([3323(10),3308(17)])].
% 1.58/1.84  3521 multiply(c_0,c_0) = c_0.  [back_rewrite(3225),rewrite([3309(6),3362(5)])].
% 1.58/1.84  3537 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),C))),D),inverse(multiply(A,D)))) = multiply(B,inverse(multiply(multiply(inverse(multiply(c_0,C)),c_0),c_0))).  [back_rewrite(3013),rewrite([3309(6),3323(2),3323(2)]),flip(a)].
% 1.58/1.84  3538 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,multiply(inverse(A),B))),c_0),c_0))) = B.  [back_rewrite(3010),rewrite([3309(6),3323(2),3323(2)])].
% 1.58/1.84  3540 multiply(A,inverse(A)) = c_0.  [back_rewrite(3310),rewrite([3323(2),3521(3),3521(3)]),flip(a)].
% 1.58/1.84  3549 inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C)))) = inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0)).  [back_rewrite(2980),rewrite([3323(2),3537(13),3540(15),3323(15),3538(19)]),flip(a)].
% 1.58/1.84  3551 multiply(c_0,inverse(multiply(multiply(inverse(multiply(c_0,inverse(multiply(multiply(inverse(multiply(c_0,multiply(c_0,A))),c_0),c_0)))),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)).  [back_rewrite(2978),rewrite([3540(3),3323(3),3521(3),3323(5),3323(5),3549(12),3549(19),3549(28)])].
% 1.58/1.84  3552 inverse(multiply(multiply(inverse(multiply(c_0,multiply(inverse(inverse(A)),B))),c_0),c_0)) = multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0))).  [back_rewrite(2969),rewrite([3549(8),3323(11),3540(17),3323(17)]),flip(a)].
% 1.58/1.84  3553 inverse(multiply(multiply(inverse(multiply(c_0,multiply(c_0,A))),c_0),c_0)) = multiply(c_0,inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0))).  [back_rewrite(2968),rewrite([3540(3),3323(3),3521(3),3549(9),3323(13),3549(20)]),flip(a)].
% 1.58/1.84  3560 inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(inverse(inverse(B)),multiply(inverse(inverse(inverse(inverse(C)))),A))))) = multiply(B,C).  [back_rewrite(2251),rewrite([3323(16),3323(16),3323(16),3323(16),3521(17),3308(16)])].
% 1.58/1.84  3564 multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),B))),inverse(multiply(multiply(inverse(inverse(inverse(inverse(B)))),c_0),c_0))) = A.  [back_rewrite(1862),rewrite([3323(17)])].
% 1.58/1.84  3596 multiply(c_0,multiply(c_0,A)) = multiply(inverse(inverse(inverse(inverse(A)))),c_0).  [back_rewrite(3007),rewrite([3540(4),3323(4),3521(4)])].
% 1.58/1.84  3597 multiply(inverse(inverse(A)),c_0) = A.  [back_rewrite(2997),rewrite([3540(6),3323(6),3521(6),3521(6),3323(5),3521(5)])].
% 1.58/1.84  3601 multiply(A,multiply(multiply(inverse(A),B),c_0)) = B.  [back_rewrite(2991),rewrite([3540(5),3323(5),3521(5),3521(5),3323(4)])].
% 1.58/1.84  3607 inverse(multiply(multiply(inverse(multiply(c_0,A)),B),inverse(multiply(c_0,B)))) = inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)).  [back_rewrite(2981),rewrite([3549(13),3552(13),3549(18),3538(19),3540(15),3323(15),3521(15)]),flip(a)].
% 1.58/1.84  3619 multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))) = multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0).  [back_rewrite(2948),rewrite([3549(20),3552(20),3549(25),3538(26),3540(19),3323(19),3521(19),3597(18)])].
% 1.58/1.84  3622 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(B))),multiply(inverse(inverse(inverse(A))),C))),c_0),inverse(B))))),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(c_0,C)),c_0),c_0)).  [back_rewrite(2944),rewrite([3540(13),3323(13),3521(13),3619(21),3619(30)])].
% 1.58/1.84  3627 multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0)))),c_0) = multiply(multiply(inverse(multiply(c_0,multiply(inverse(inverse(A)),B))),c_0),c_0).  [back_rewrite(2938),rewrite([3619(10),3619(17),3540(23),3323(23),3521(23)]),flip(a)].
% 1.58/1.84  3628 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(A)),B))),c_0),inverse(C))).  [back_rewrite(2936),rewrite([3619(7),3540(20),3323(20),3521(20)])].
% 1.58/1.84  3629 inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)) = multiply(A,c_0).  [back_rewrite(2935),rewrite([3540(4),3323(4),3521(4),3619(8),3521(3),3323(2),3521(3),3521(3),3323(2),3619(9)]),flip(a)].
% 1.58/1.84  3670 inverse(inverse(inverse(multiply(multiply(inverse(inverse(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,C))))),D),c_0)))) = multiply(multiply(inverse(multiply(inverse(B),D)),C),A).  [back_rewrite(3410),rewrite([3597(7),3619(16),3629(17)])].
% 1.58/1.84  3683 multiply(multiply(inverse(inverse(A)),B),c_0) = multiply(A,multiply(B,c_0)).  [back_rewrite(3357),rewrite([3521(7),3607(9),3629(8),3619(13),3629(14)]),flip(a)].
% 1.58/1.84  3684 multiply(c_0,multiply(A,c_0)) = inverse(multiply(inverse(A),c_0)).  [back_rewrite(3355),rewrite([3521(3),3619(8),3629(9),3619(13),3596(8),3597(10),3597(9)])].
% 1.58/1.84  3765 inverse(multiply(multiply(inverse(A),c_0),c_0)) = multiply(multiply(A,c_0),c_0).  [back_rewrite(510),rewrite([3619(12),3629(13),3619(14),3629(15),3683(9),3619(13),3629(14),3601(9),3619(15),3629(16),3683(10),3619(13),3684(8),3597(11)]),flip(a)].
% 1.58/1.84  3809 multiply(A,inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(D),E)))),B)),c_0),c_0)))))) = inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(A,F)))))).  [back_rewrite(3419),rewrite([3619(14),3765(15)])].
% 1.58/1.84  3834 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(B),C))),multiply(multiply(multiply(c_0,D),c_0),c_0))),inverse(inverse(inverse(C))))),inverse(multiply(multiply(multiply(c_0,multiply(inverse(inverse(A)),D)),c_0),c_0))),E) = multiply(B,E).  [back_rewrite(3363),rewrite([3619(12),3765(13),3619(28),3765(29)])].
% 1.58/1.84  3937 multiply(A,c_0) = inverse(inverse(A)).  [back_rewrite(3304),rewrite([3540(2)])].
% 1.58/1.84  3948 inverse(inverse(inverse(inverse(A)))) = A.  [back_rewrite(3231),rewrite([3540(5),3540(6),3323(6),3937(6),3323(5),3323(5),3323(5),3937(5),3323(4),3323(4),3937(4)])].
% 1.58/1.84  3988 inverse(inverse(multiply(c_0,A))) = inverse(inverse(A)).  [back_rewrite(1312),rewrite([3540(2),3323(2),3937(2),3619(9),3937(7),3937(9),3948(8)]),flip(a)].
% 1.58/1.84  3993 multiply(c_0,inverse(inverse(A))) = inverse(inverse(A)).  [back_rewrite(3551),rewrite([3596(6),3948(6),3937(4),3937(7),3948(6),3937(5),3948(6),3937(6),3988(5),3937(6),3948(5),3937(9),3988(8),3937(9),3948(8)])].
% 1.58/1.84  3995 inverse(inverse(A)) = A.  [back_rewrite(3553),rewrite([3596(4),3948(4),3937(2),3937(5),3948(4),3937(3),3948(4),3937(6),3988(5),3937(6),3948(5),3993(4)]),flip(a)].
% 1.58/1.84  3999 multiply(multiply(A,B),inverse(B)) = A.  [back_rewrite(3564),rewrite([3995(2),3995(2),3937(2),3995(2),3995(3),3995(3),3995(3),3937(3),3995(3),3937(3),3995(3)])].
% 1.58/1.84  4002 inverse(multiply(A,inverse(multiply(B,multiply(C,A))))) = multiply(B,C).  [back_rewrite(3560),rewrite([3995(2),3995(2),3937(2),3995(2),3995(2),3995(2),3995(2)])].
% 1.58/1.84  4004 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A).  [back_rewrite(3518),rewrite([3995(2),3995(2),3937(2),3995(2),3937(4),3995(4),3995(4),3995(5)])].
% 1.58/1.84  4005 multiply(A,multiply(inverse(A),B)) = B.  [back_rewrite(3517),rewrite([3995(2),3995(2),3937(2),3995(2),4002(7),3995(5)])].
% 1.58/1.84  4048 inverse(multiply(A,multiply(inverse(multiply(B,A)),C))) = multiply(inverse(C),B).  [back_rewrite(2133),rewrite([3995(2),3995(2),3937(2),3995(2),3995(3),3995(3),3937(3),3995(3),4004(4),3995(7),3995(7),3937(7),3995(7),4002(14),4005(10)])].
% 1.58/1.84  4051 multiply(inverse(A),multiply(A,B)) = B.  [back_rewrite(1822),rewrite([3995(5),3995(5),3937(5),3995(5)])].
% 1.58/1.84  4058 multiply(A,multiply(c_0,B)) = multiply(A,B).  [back_rewrite(3628),rewrite([3937(5),3995(4),3937(5),3995(4),3995(4),3995(5),3995(6),4004(7),3937(8),4004(7),4004(7),3999(8),3995(6)])].
% 1.58/1.84  4059 inverse(multiply(c_0,multiply(A,B))) = inverse(multiply(A,B)).  [back_rewrite(3627),rewrite([3937(5),3995(4),3937(5),3995(4),3995(4),4058(3),3937(4),3995(3),3995(5),3937(8),3995(7),3937(8),3995(7)]),flip(a)].
% 1.58/1.84  4061 multiply(c_0,A) = A.  [back_rewrite(3622),rewrite([3995(3),3995(4),4004(6),4004(4),3937(6),3995(6),3999(6),4004(4),4059(5),4004(3),3937(4),4004(3),4004(3),3937(4),4004(3),4004(3),4004(3),4005(3),3937(5),3995(4),3937(5),3995(4),3995(4)]),flip(a)].
% 1.58/1.84  4073 multiply(multiply(multiply(inverse(A),B),C),D) = multiply(inverse(A),multiply(multiply(B,C),D)).  [back_rewrite(3670),rewrite([3995(2),4004(5),3995(3),3937(6),4004(5),4004(5),4004(5),4004(5),4004(5),4004(7)]),flip(a)].
% 1.58/1.84  4087 multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(B,C))),D) = multiply(A,D).  [back_rewrite(3834),rewrite([4004(5),4004(3),4061(5),3937(5),3995(5),3937(5),3995(5),4073(4),4004(5),3995(6),3999(6),3995(4),3995(5),4061(5),3937(5),3995(5),3937(5),3995(5)])].
% 1.58/1.84  4088 multiply(inverse(multiply(multiply(A,B),inverse(multiply(C,B)))),D) = multiply(C,multiply(inverse(A),D)).  [back_rewrite(3809),rewrite([4004(6),4004(4),4061(7),3937(7),4004(6),4004(6),3937(7),4004(6),4004(6),4048(7),4005(5),4004(3),4004(6),4073(9),4004(10),4004(10),4004(10)]),flip(a)].
% 1.58/1.84  4122 multiply(A,inverse(multiply(B,A))) = inverse(B).  [para(4051(a,1),3999(a,1,1))].
% 1.58/1.84  4125 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)).  [para(3999(a,1),4122(a,1,2,1)),flip(a)].
% 1.58/1.84  4143 multiply(multiply(multiply(A,B),multiply(inverse(B),inverse(C))),D) = multiply(A,multiply(inverse(C),D)).  [back_rewrite(4088),rewrite([4125(3),4125(6),4125(4),3995(2),3995(2),4125(3)])].
% 1.58/1.84  4144 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,C).  [back_rewrite(4087),rewrite([4125(4),4143(7)])].
% 1.58/1.84  4160 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).  [para(3999(a,1),4144(a,1,1)),rewrite([3995(2)]),flip(a)].
% 1.58/1.84  4161 $F # answer(prove_these_axioms_3).  [resolve(4160,a,2,a)].
% 1.58/1.84  
% 1.58/1.84  % SZS output end Refutation
% 1.58/1.84  ============================== end of proof ==========================
% 1.58/1.84  
% 1.58/1.84  ============================== STATISTICS ============================
% 1.58/1.84  
% 1.58/1.84  Given=55. Generated=8289. Kept=4160. proofs=1.
% 1.58/1.84  Usable=12. Sos=5. Demods=16. Limbo=0, Disabled=4144. Hints=0.
% 1.58/1.84  Megabytes=7.98.
% 1.58/1.84  User_CPU=0.77, System_CPU=0.01, Wall_clock=1.
% 1.58/1.84  
% 1.58/1.84  ============================== end of statistics =====================
% 1.58/1.84  
% 1.58/1.84  ============================== end of search =========================
% 1.58/1.84  
% 1.58/1.84  THEOREM PROVED
% 1.58/1.84  % SZS status Unsatisfiable
% 1.58/1.84  
% 1.58/1.84  Exiting with 1 proof.
% 1.58/1.84  
% 1.58/1.84  Process 27072 exit (max_proofs) Tue Jun 14 05:29:53 2022
% 1.58/1.84  Prover9 interrupted
%------------------------------------------------------------------------------