TSTP Solution File: GRP414-1 by EQP---0.9e

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP414-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n014.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 08:46:33 EDT 2022

% Result   : Unsatisfiable 1.88s 2.24s
% Output   : Refutation 1.88s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),C),
    file('GRP414-1.p',unknown),
    [] ).

cnf(2,plain,
    ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
    file('GRP414-1.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),D),
    inference(para,[status(thm),theory(equality)],[1,1]),
    [iquote('para(1,1)')] ).

cnf(4,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A)),multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C)))),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,1]),1]),
    [iquote('para(1,1),flip(1)')] ).

cnf(5,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))))),E),
    inference(para,[status(thm),theory(equality)],[3,1]),
    [iquote('para(3,1)')] ).

cnf(6,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),D))),E))),
    inference(para,[status(thm),theory(equality)],[1,3]),
    [iquote('para(1,3)')] ).

cnf(7,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(D,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),B))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),B))),E)),inverse(C)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),B))),E))))),
    inference(flip,[status(thm),theory(equality)],[6]),
    [iquote('flip(6)')] ).

cnf(8,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)),inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),F))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))),F),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,1]),4]),
    [iquote('para(4,1),demod([4])')] ).

cnf(9,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(inverse(A)))),D))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),E))),A))),E),
    inference(para,[status(thm),theory(equality)],[4,1]),
    [iquote('para(4,1)')] ).

cnf(10,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))),C),
    inference(para,[status(thm),theory(equality)],[4,1]),
    [iquote('para(4,1)')] ).

cnf(11,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(D))),C))),D)),
    inference(para,[status(thm),theory(equality)],[1,10]),
    [iquote('para(1,10)')] ).

cnf(12,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),C))),A),multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(C,B))))),
    inference(flip,[status(thm),theory(equality)],[11]),
    [iquote('flip(11)')] ).

cnf(16,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),D))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)))),
    inference(para,[status(thm),theory(equality)],[3,3]),
    [iquote('para(3,3)')] ).

cnf(17,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(E,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(E,inverse(F))),B))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(E,inverse(F))),B))),F)),inverse(D)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(E,inverse(F))),B))),F))))),
    inference(flip,[status(thm),theory(equality)],[16]),
    [iquote('flip(16)')] ).

cnf(20,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),multiply(multiply(inverse(B),B),inverse(C))))),A),C),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[10,11]),1]),
    [iquote('para(10,11),flip(1)')] ).

cnf(22,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),multiply(inverse(multiply(multiply(inverse(D),D),inverse(B))),multiply(multiply(inverse(D),D),inverse(C)))),
    inference(para,[status(thm),theory(equality)],[20,10]),
    [iquote('para(20,10)')] ).

cnf(26,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(C))),F))),C)))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(C))),F))),C)))),B)),inverse(multiply(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))),G))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(C))),F))),C)))),B)))),G),
    inference(para,[status(thm),theory(equality)],[4,3]),
    [iquote('para(4,3)')] ).

cnf(34,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(inverse(E),F))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))))),F),
    inference(para,[status(thm),theory(equality)],[5,1]),
    [iquote('para(5,1)')] ).

cnf(35,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(E)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))))),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),E))),F))),
    inference(para,[status(thm),theory(equality)],[1,5]),
    [iquote('para(1,5)')] ).

cnf(36,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(D,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),inverse(multiply(inverse(F),B))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),inverse(multiply(inverse(F),B))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))),inverse(C)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),inverse(multiply(inverse(F),B))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)))))),
    inference(flip,[status(thm),theory(equality)],[35]),
    [iquote('flip(35)')] ).

cnf(38,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(multiply(C,A)))))),C),
    inference(para,[status(thm),theory(equality)],[12,1]),
    [iquote('para(12,1)')] ).

cnf(43,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(E)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),G))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),G))),F)),inverse(multiply(inverse(G),E))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),G))),F)))),
    inference(para,[status(thm),theory(equality)],[3,5]),
    [iquote('para(3,5)')] ).

cnf(45,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))),multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(C,B))))),
    inference(para,[status(thm),theory(equality)],[38,10]),
    [iquote('para(38,10)')] ).

cnf(67,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C)))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[20,45]),20]),
    [iquote('para(20,45),demod([20])')] ).

cnf(70,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),C),multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),C))),E))))),
    inference(para,[status(thm),theory(equality)],[1,67]),
    [iquote('para(1,67)')] ).

cnf(75,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),C),multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(inverse(multiply(E,inverse(A))),multiply(E,inverse(multiply(C,A)))))))),
    inference(para,[status(thm),theory(equality)],[38,67]),
    [iquote('para(38,67)')] ).

cnf(80,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(B),C)))),A)),C),
    inference(para,[status(thm),theory(equality)],[6,3]),
    [iquote('para(6,3)')] ).

cnf(102,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(C),inverse(B))),D))),B)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)))),inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(F),inverse(G))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)),inverse(H))),C))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)),inverse(H))),C))),H)),inverse(D)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),F))),E)),inverse(H))),C))),H))))),G))),
    inference(para,[status(thm),theory(equality)],[6,6]),
    [iquote('para(6,6)')] ).

cnf(103,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D)),inverse(C))),F))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D)),inverse(C))),F))),C)),inverse(G)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D)),inverse(C))),F))),C))))),A)),multiply(E,inverse(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(F),inverse(H))),G))),H)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),B))),D))))),
    inference(flip,[status(thm),theory(equality)],[102]),
    [iquote('flip(102)')] ).

cnf(104,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(B),inverse(D))),C))),D))),
    inference(para,[status(thm),theory(equality)],[6,6]),
    [iquote('para(6,6)')] ).

cnf(115,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(multiply(D,inverse(B))),multiply(D,C))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[80,67]),80]),
    [iquote('para(80,67),demod([80])')] ).

cnf(118,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,D)))),B))),multiply(A,D)),
    inference(para,[status(thm),theory(equality)],[115,1]),
    [iquote('para(115,1)')] ).

cnf(128,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(D,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),inverse(G)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(C),inverse(H))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(F),inverse(I))),G))),I)))),H))),
    inference(para,[status(thm),theory(equality)],[7,6]),
    [iquote('para(7,6)')] ).

cnf(129,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(D),inverse(C))),E))),C)))),A)),multiply(F,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(F,inverse(G))),B))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(F,inverse(G))),B))),G)),multiply(H,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),D))),I)),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),D))),I)),inverse(E)),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),D))),I))))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(F,inverse(G))),B))),G))))),
    inference(flip,[status(thm),theory(equality)],[128]),
    [iquote('flip(128)')] ).

cnf(134,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)),C),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[118,1]),1]),1]),
    [iquote('para(118,1),demod([1]),flip(1)')] ).

cnf(139,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)),inverse(F)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))),inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),F))),G))),
    inference(para,[status(thm),theory(equality)],[1,8]),
    [iquote('para(1,8)')] ).

cnf(140,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),multiply(B,inverse(multiply(multiply(multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(G))),E))),G)),inverse(F)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(G))),E))),G))))),
    inference(flip,[status(thm),theory(equality)],[139]),
    [iquote('flip(139)')] ).

cnf(141,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(B,inverse(inverse(A)))),multiply(B,C)))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(C,D))),A))),D),
    inference(para,[status(thm),theory(equality)],[134,1]),
    [iquote('para(134,1)')] ).

cnf(143,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),C),B)))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,C)))),D)),
    inference(para,[status(thm),theory(equality)],[134,10]),
    [iquote('para(134,10)')] ).

cnf(158,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(E)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))))),inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)),inverse(multiply(inverse(multiply(inverse(D),multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))))),E))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)))),
    inference(para,[status(thm),theory(equality)],[8,5]),
    [iquote('para(8,5)')] ).

cnf(159,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),inverse(multiply(inverse(multiply(inverse(E),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),F))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D))),multiply(G,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),E))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),E))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(F)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),E))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)))))),
    inference(flip,[status(thm),theory(equality)],[158]),
    [iquote('flip(158)')] ).

cnf(161,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)),inverse(F)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G))),inverse(multiply(inverse(I),F))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),inverse(G))),H))),G))))),
    inference(para,[status(thm),theory(equality)],[5,8]),
    [iquote('para(5,8)')] ).

cnf(162,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A))),inverse(multiply(inverse(G),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)))),multiply(B,inverse(multiply(multiply(multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(I))),E))),I)),inverse(H)),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(I))),E))),I))))),
    inference(flip,[status(thm),theory(equality)],[161]),
    [iquote('flip(161)')] ).

cnf(211,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(multiply(B,inverse(multiply(C,D)))),multiply(B,inverse(multiply(C,D)))),inverse(A))),inverse(multiply(B,inverse(D)))))),A),multiply(inverse(multiply(multiply(inverse(D),D),inverse(multiply(B,inverse(multiply(C,D)))))),C)),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[38,11]),1]),
    [iquote('para(38,11),flip(1)')] ).

cnf(221,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(inverse(A)))),D))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(E)),A))),inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)),inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))))),E))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)))),
    inference(para,[status(thm),theory(equality)],[8,9]),
    [iquote('para(8,9)')] ).

cnf(222,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),inverse(multiply(inverse(multiply(multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(G)),F))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),H))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D))),multiply(multiply(multiply(inverse(inverse(I)),inverse(I)),inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),inverse(inverse(I)))),G))),inverse(multiply(multiply(multiply(inverse(I),I),inverse(H)),I)))),
    inference(flip,[status(thm),theory(equality)],[221]),
    [iquote('flip(221)')] ).

cnf(237,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),E),D))))))),multiply(inverse(multiply(F,inverse(B))),multiply(F,E))),
    inference(para,[status(thm),theory(equality)],[75,115]),
    [iquote('para(75,115)')] ).

cnf(238,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(inverse(multiply(E,inverse(F))),multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),C),F)))))))),
    inference(flip,[status(thm),theory(equality)],[237]),
    [iquote('flip(237)')] ).

cnf(258,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))),multiply(multiply(multiply(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(G))),F))),G)),inverse(multiply(inverse(multiply(multiply(inverse(B),B),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))))),C))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(G))),F))),G))),
    inference(para,[status(thm),theory(equality)],[8,10]),
    [iquote('para(8,10)')] ).

cnf(259,plain,
    equal(multiply(multiply(multiply(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),inverse(multiply(inverse(multiply(multiply(inverse(E),E),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),F))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),multiply(inverse(multiply(G,inverse(E))),multiply(G,inverse(multiply(F,E))))),
    inference(flip,[status(thm),theory(equality)],[258]),
    [iquote('flip(258)')] ).

cnf(260,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),inverse(C)))),E))))),F))),C))),F),
    inference(para,[status(thm),theory(equality)],[70,1]),
    [iquote('para(70,1)')] ).

cnf(286,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(inverse(multiply(E,inverse(A))),multiply(E,inverse(multiply(inverse(C),A)))))))),F))),C))),F),
    inference(para,[status(thm),theory(equality)],[75,1]),
    [iquote('para(75,1)')] ).

cnf(324,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(B,inverse(inverse(A)))),multiply(B,inverse(multiply(C,inverse(D))))))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(E)),A))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D)))),
    inference(para,[status(thm),theory(equality)],[10,141]),
    [iquote('para(10,141)')] ).

cnf(325,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(inverse(D)),inverse(D)),inverse(multiply(inverse(multiply(E,inverse(inverse(D)))),multiply(E,inverse(multiply(A,inverse(B))))))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(C)),D)))),
    inference(flip,[status(thm),theory(equality)],[324]),
    [iquote('flip(324)')] ).

cnf(351,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(B),inverse(D))),C))),D)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[104,10]),10]),
    [iquote('para(104,10),demod([10])')] ).

cnf(373,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),C))),A),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(B,inverse(D))),C))),D)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[134,351]),134]),
    [iquote('para(134,351),demod([134])')] ).

cnf(404,plain,
    equal(multiply(multiply(multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),B)),inverse(multiply(inverse(multiply(D,A)),E))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),B)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(D,inverse(F))),E))),F)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[134,373]),134]),
    [iquote('para(134,373),demod([134])')] ).

cnf(405,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),C))),A),multiply(multiply(multiply(D,multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),multiply(F,D)))),E)),inverse(multiply(inverse(multiply(B,D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),multiply(F,D)))),E))),
    inference(flip,[status(thm),theory(equality)],[404]),
    [iquote('flip(404)')] ).

cnf(423,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E)))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(C),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(C),inverse(G))),H))),G)),inverse(multiply(inverse(H),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(I))),F))),I)))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(C),inverse(G))),H))),G)))),
    inference(para,[status(thm),theory(equality)],[4,16]),
    [iquote('para(4,16)')] ).

cnf(424,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),inverse(D))),G))),D)))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(H,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),B))),I)),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),B))),I)),multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(G)),F)))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),B))),I))))),
    inference(flip,[status(thm),theory(equality)],[423]),
    [iquote('flip(423)')] ).

cnf(451,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),A),C),
    inference(para,[status(thm),theory(equality)],[143,10]),
    [iquote('para(143,10)')] ).

cnf(454,plain,
    equal(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),inverse(D))),C),multiply(inverse(multiply(E,inverse(D))),multiply(E,A))),
    inference(para,[status(thm),theory(equality)],[451,115]),
    [iquote('para(451,115)')] ).

cnf(455,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(E))))),inverse(B))),E)),
    inference(flip,[status(thm),theory(equality)],[454]),
    [iquote('flip(454)')] ).

cnf(479,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,E))))))),inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),multiply(F,inverse(A))))),inverse(D)))),
    inference(para,[status(thm),theory(equality)],[454,38]),
    [iquote('para(454,38)')] ).

cnf(480,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),inverse(D))),multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(E,inverse(C))),multiply(E,inverse(multiply(inverse(multiply(F,inverse(D))),multiply(F,A)))))))),
    inference(flip,[status(thm),theory(equality)],[479]),
    [iquote('flip(479)')] ).

cnf(503,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(D,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),inverse(G)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(C),inverse(H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(F),inverse(I))),J))),I)),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(F),inverse(I))),J))),I)),inverse(multiply(inverse(J),G))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(F),inverse(I))),J))),I))))),H))),
    inference(para,[status(thm),theory(equality)],[17,6]),
    [iquote('para(17,6)')] ).

cnf(504,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(D),inverse(C))),E))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(D),inverse(C))),E))),C)),inverse(multiply(inverse(E),F))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(D),inverse(C))),E))),C))))),A)),multiply(G,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H)),multiply(I,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),D))),J)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),D))),J)),inverse(F)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),D))),J))))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H))))),
    inference(flip,[status(thm),theory(equality)],[503]),
    [iquote('flip(503)')] ).

cnf(521,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),multiply(C,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(C,inverse(D))),E))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(C,inverse(D))),E))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(C,inverse(D))),E))),D))))),B)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),F))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),
    inference(para,[status(thm),theory(equality)],[17,10]),
    [iquote('para(17,10)')] ).

cnf(522,plain,
    equal(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(inverse(multiply(E,inverse(F))),multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),multiply(G,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H)),inverse(D)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H))))),F))))),
    inference(flip,[status(thm),theory(equality)],[521]),
    [iquote('flip(521)')] ).

cnf(529,plain,
    equal(multiply(inverse(multiply(A,inverse(multiply(B,inverse(C))))),multiply(A,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),multiply(B,inverse(C)))))),E),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[455,10]),451]),
    [iquote('para(455,10),demod([451])')] ).

cnf(534,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(D,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E)),inverse(G)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(C),inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(C),inverse(H))),I))),H)),inverse(multiply(inverse(I),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(inverse(F),inverse(J))),K))),J)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(inverse(F),inverse(J))),K))),J)),inverse(multiply(inverse(K),G))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(inverse(F),inverse(J))),K))),J))))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(C),inverse(H))),I))),H)))),
    inference(para,[status(thm),theory(equality)],[17,16]),
    [iquote('para(17,16)')] ).

cnf(535,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(E),inverse(D))),F))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(E),inverse(D))),F))),D)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(E),inverse(D))),F))),D))))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(H,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),B))),I)),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),B))),I)),multiply(J,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(K),K),inverse(multiply(inverse(multiply(J,inverse(K))),E))),K)),multiply(multiply(multiply(inverse(K),K),inverse(multiply(inverse(multiply(J,inverse(K))),E))),K)),inverse(G)),multiply(multiply(multiply(inverse(K),K),inverse(multiply(inverse(multiply(J,inverse(K))),E))),K))))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(H,inverse(I))),B))),I))))),
    inference(flip,[status(thm),theory(equality)],[534]),
    [iquote('flip(534)')] ).

cnf(537,plain,
    equal(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B))),inverse(C)),multiply(multiply(inverse(D),D),inverse(C))),
    inference(para,[status(thm),theory(equality)],[529,38]),
    [iquote('para(529,38)')] ).

cnf(539,plain,
    equal(multiply(inverse(multiply(A,inverse(multiply(B,inverse(C))))),multiply(A,inverse(multiply(D,multiply(B,inverse(C)))))),multiply(inverse(multiply(E,inverse(F))),multiply(E,inverse(multiply(D,F))))),
    inference(para,[status(thm),theory(equality)],[38,529]),
    [iquote('para(38,529)')] ).

cnf(550,plain,
    equal(multiply(inverse(A),A),multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(C)))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[537,38]),38]),
    [iquote('para(537,38),demod([38])')] ).

cnf(551,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B))),multiply(inverse(C),C)),
    inference(flip,[status(thm),theory(equality)],[550]),
    [iquote('flip(550)')] ).

cnf(561,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(C)))),D))),A))),D),
    inference(para,[status(thm),theory(equality)],[550,1]),
    [iquote('para(550,1)')] ).

cnf(569,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(B),B),inverse(C))),multiply(multiply(inverse(B),B),inverse(C))),inverse(D)),multiply(multiply(multiply(inverse(inverse(C)),inverse(C)),inverse(multiply(inverse(multiply(A,inverse(inverse(C)))),E))),inverse(C))))),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(E),inverse(F))),D))),F))),
    inference(para,[status(thm),theory(equality)],[22,6]),
    [iquote('para(22,6)')] ).

cnf(570,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(D,inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(E),E),inverse(F))),multiply(multiply(inverse(E),E),inverse(F))),inverse(C)),multiply(multiply(multiply(inverse(inverse(F)),inverse(F)),inverse(multiply(inverse(multiply(D,inverse(inverse(F)))),B))),inverse(F)))))),
    inference(flip,[status(thm),theory(equality)],[569]),
    [iquote('flip(569)')] ).

cnf(571,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(D),inverse(C))),E))),C))),multiply(inverse(multiply(multiply(inverse(F),F),inverse(B))),multiply(multiply(inverse(F),F),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(A,inverse(G))),D))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(A,inverse(G))),D))),G)),inverse(E)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(A,inverse(G))),D))),G)))))),
    inference(para,[status(thm),theory(equality)],[6,22]),
    [iquote('para(6,22)')] ).

cnf(572,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),multiply(multiply(inverse(A),A),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)),inverse(F)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C))))),multiply(inverse(multiply(D,inverse(B))),inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),F))),G)))),
    inference(flip,[status(thm),theory(equality)],[571]),
    [iquote('flip(571)')] ).

cnf(573,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))),B))),multiply(A,inverse(B))),
    inference(para,[status(thm),theory(equality)],[551,1]),
    [iquote('para(551,1)')] ).

cnf(583,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),C),multiply(inverse(multiply(multiply(inverse(D),D),inverse(B))),multiply(multiply(inverse(D),D),inverse(multiply(multiply(multiply(multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(G)),F))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),inverse(H))),G))),H)),inverse(multiply(inverse(multiply(A,multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(G)),F))))),C))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),inverse(H))),G))),H)))))),
    inference(para,[status(thm),theory(equality)],[8,22]),
    [iquote('para(8,22)')] ).

cnf(584,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),multiply(multiply(inverse(A),A),inverse(multiply(multiply(multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(F))),E))),F)),inverse(multiply(inverse(multiply(G,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),H))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(F))),E))),F))))),multiply(inverse(multiply(G,inverse(B))),H)),
    inference(flip,[status(thm),theory(equality)],[583]),
    [iquote('flip(583)')] ).

cnf(592,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(B),B),inverse(C))),multiply(multiply(inverse(B),B),inverse(C))),inverse(D)),multiply(multiply(multiply(inverse(inverse(C)),inverse(C)),inverse(multiply(inverse(multiply(A,inverse(inverse(C)))),E))),inverse(C))))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(E),inverse(F))),G))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(E),inverse(F))),G))),F)),inverse(multiply(inverse(G),D))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(E),inverse(F))),G))),F)))),
    inference(para,[status(thm),theory(equality)],[22,16]),
    [iquote('para(22,16)')] ).

cnf(593,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(E,inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(F),F),inverse(G))),multiply(multiply(inverse(F),F),inverse(G))),inverse(D)),multiply(multiply(multiply(inverse(inverse(G)),inverse(G)),inverse(multiply(inverse(multiply(E,inverse(inverse(G)))),B))),inverse(G)))))),
    inference(flip,[status(thm),theory(equality)],[592]),
    [iquote('flip(592)')] ).

cnf(598,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A)),inverse(A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[573,1]),1]),1]),
    [iquote('para(573,1),demod([1]),flip(1)')] ).

cnf(604,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(B),B))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(A)),C))),A))),C),
    inference(para,[status(thm),theory(equality)],[598,1]),
    [iquote('para(598,1)')] ).

cnf(606,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A),A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[598,10]),10]),1]),
    [iquote('para(598,10),demod([10]),flip(1)')] ).

cnf(607,plain,
    equal(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),inverse(C))),A),multiply(inverse(multiply(D,inverse(C))),multiply(D,A))),
    inference(para,[status(thm),theory(equality)],[606,115]),
    [iquote('para(606,115)')] ).

cnf(608,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(D),D))),inverse(B))),C)),
    inference(flip,[status(thm),theory(equality)],[607]),
    [iquote('flip(607)')] ).

cnf(666,plain,
    equal(multiply(multiply(inverse(A),A),inverse(B)),multiply(multiply(inverse(C),C),inverse(B))),
    inference(para,[status(thm),theory(equality)],[537,537]),
    [iquote('para(537,537)')] ).

cnf(674,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(C))),D))),C))),D),
    inference(para,[status(thm),theory(equality)],[666,1]),
    [iquote('para(666,1)')] ).

cnf(678,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(C))),multiply(multiply(multiply(multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)),inverse(multiply(inverse(multiply(multiply(inverse(E),E),multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))))),J))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I))))),C)))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(C))),multiply(multiply(multiply(multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)),inverse(multiply(inverse(multiply(multiply(inverse(E),E),multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))))),J))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I))))),C)))),B)),inverse(multiply(multiply(D,inverse(multiply(J,E))),K))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(C))),multiply(multiply(multiply(multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I)),inverse(multiply(inverse(multiply(multiply(inverse(E),E),multiply(F,inverse(multiply(multiply(multiply(inverse(G),G),inverse(H)),G))))),J))),multiply(multiply(multiply(inverse(I),I),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(G))),inverse(I))),H))),I))))),C)))),B)))),K),
    inference(para,[status(thm),theory(equality)],[8,26]),
    [iquote('para(8,26)')] ).

cnf(681,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),B)))),D),
    inference(para,[status(thm),theory(equality)],[666,10]),
    [iquote('para(666,10)')] ).

cnf(688,plain,
    equal(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),C))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),C))),inverse(multiply(inverse(D),D))),inverse(C))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),C))),B),
    inference(para,[status(thm),theory(equality)],[606,681]),
    [iquote('para(606,681)')] ).

cnf(689,plain,
    equal(multiply(inverse(A),A),multiply(inverse(B),B)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[666,38]),38]),
    [iquote('para(666,38),demod([38])')] ).

cnf(691,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(multiply(D,C)))))),D),
    inference(para,[status(thm),theory(equality)],[666,38]),
    [iquote('para(666,38)')] ).

cnf(696,plain,
    equal(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(C),C)),multiply(inverse(multiply(D,inverse(B))),multiply(D,A))),
    inference(para,[status(thm),theory(equality)],[689,115]),
    [iquote('para(689,115)')] ).

cnf(697,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(multiply(inverse(C),inverse(B))),multiply(inverse(D),D))),
    inference(flip,[status(thm),theory(equality)],[696]),
    [iquote('flip(696)')] ).

cnf(710,plain,
    equal(multiply(inverse(multiply(inverse(inverse(A)),inverse(A))),multiply(inverse(B),B)),multiply(inverse(C),C)),
    inference(para,[status(thm),theory(equality)],[697,689]),
    [iquote('para(697,689)')] ).

cnf(711,plain,
    equal(multiply(inverse(A),A),multiply(inverse(multiply(inverse(inverse(B)),inverse(B))),multiply(inverse(C),C))),
    inference(flip,[status(thm),theory(equality)],[710]),
    [iquote('flip(710)')] ).

cnf(745,plain,
    equal(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(multiply(inverse(inverse(C)),inverse(C))),multiply(inverse(D),D))),multiply(inverse(multiply(E,inverse(B))),multiply(E,A))),
    inference(para,[status(thm),theory(equality)],[711,115]),
    [iquote('para(711,115)')] ).

cnf(746,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(multiply(inverse(C),inverse(B))),multiply(inverse(multiply(inverse(inverse(D)),inverse(D))),multiply(inverse(E),E)))),
    inference(flip,[status(thm),theory(equality)],[745]),
    [iquote('flip(745)')] ).

cnf(758,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D)))),E))),A))),E),
    inference(para,[status(thm),theory(equality)],[689,561]),
    [iquote('para(689,561)')] ).

cnf(773,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(B),B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(A)),D))),A))),D),
    inference(para,[status(thm),theory(equality)],[689,604]),
    [iquote('para(689,604)')] ).

cnf(776,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))),inverse(multiply(inverse(G),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))),inverse(multiply(inverse(G),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)))),inverse(multiply(inverse(H),D))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))),inverse(multiply(inverse(G),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)))))),
    inference(para,[status(thm),theory(equality)],[34,3]),
    [iquote('para(34,3)')] ).

cnf(777,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)))),inverse(multiply(inverse(E),F))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))))),multiply(G,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H)),inverse(F)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),B))),H))))),
    inference(flip,[status(thm),theory(equality)],[776]),
    [iquote('flip(776)')] ).

cnf(784,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(C))),D),multiply(inverse(multiply(E,inverse(C))),multiply(E,multiply(A,inverse(multiply(multiply(multiply(inverse(F),F),inverse(D)),B)))))),
    inference(para,[status(thm),theory(equality)],[681,115]),
    [iquote('para(681,115)')] ).

cnf(785,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),F))))),multiply(inverse(multiply(inverse(multiply(C,inverse(F))),inverse(B))),E)),
    inference(flip,[status(thm),theory(equality)],[784]),
    [iquote('flip(784)')] ).

cnf(799,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(F)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))))),inverse(multiply(multiply(multiply(multiply(G,inverse(multiply(multiply(multiply(inverse(H),H),inverse(I)),H))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(inverse(multiply(G,inverse(H))),inverse(J))),I))),J)),inverse(multiply(inverse(multiply(inverse(E),multiply(G,inverse(multiply(multiply(multiply(inverse(H),H),inverse(I)),H))))),F))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(inverse(multiply(G,inverse(H))),inverse(J))),I))),J)))),
    inference(para,[status(thm),theory(equality)],[8,34]),
    [iquote('para(8,34)')] ).

cnf(800,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),inverse(multiply(inverse(multiply(inverse(E),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),F))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D))),multiply(G,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(multiply(inverse(J),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(multiply(inverse(J),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)))),inverse(F)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(multiply(inverse(J),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))))))),
    inference(flip,[status(thm),theory(equality)],[799]),
    [iquote('flip(799)')] ).

cnf(809,plain,
    equal(multiply(inverse(multiply(A,inverse(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),inverse(E))),F))),E))))),multiply(A,inverse(F))),D),
    inference(para,[status(thm),theory(equality)],[674,681]),
    [iquote('para(674,681)')] ).

cnf(834,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(inverse(C),C)))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(D))),inverse(B)))),D)),
    inference(para,[status(thm),theory(equality)],[689,11]),
    [iquote('para(689,11)')] ).

cnf(835,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),inverse(B)))),A),multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(multiply(inverse(D),D))))),
    inference(flip,[status(thm),theory(equality)],[834]),
    [iquote('flip(834)')] ).

cnf(838,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))),inverse(F)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)))),inverse(multiply(inverse(J),F))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G))),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)),inverse(multiply(inverse(H),I))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(E),inverse(G))),H))),G)))))),
    inference(para,[status(thm),theory(equality)],[34,34]),
    [iquote('para(34,34)')] ).

cnf(839,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)))),inverse(multiply(inverse(E),F))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))))),multiply(G,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(multiply(inverse(J),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(multiply(inverse(J),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)))),inverse(F)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))),inverse(multiply(inverse(J),B))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H)),inverse(multiply(inverse(I),J))),multiply(multiply(multiply(inverse(H),H),inverse(multiply(inverse(multiply(G,inverse(H))),I))),H))))))),
    inference(flip,[status(thm),theory(equality)],[838]),
    [iquote('flip(838)')] ).

cnf(840,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(B,inverse(E))),D))),E)),
    inference(para,[status(thm),theory(equality)],[689,373]),
    [iquote('para(689,373)')] ).

cnf(846,plain,
    equal(multiply(inverse(multiply(inverse(inverse(multiply(A,multiply(B,inverse(C))))),inverse(multiply(B,inverse(C))))),multiply(inverse(D),D)),multiply(inverse(multiply(E,inverse(F))),multiply(E,inverse(multiply(A,F))))),
    inference(para,[status(thm),theory(equality)],[689,539]),
    [iquote('para(689,539)')] ).

cnf(847,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))),multiply(inverse(multiply(inverse(inverse(multiply(C,multiply(D,inverse(E))))),inverse(multiply(D,inverse(E))))),multiply(inverse(F),F))),
    inference(flip,[status(thm),theory(equality)],[846]),
    [iquote('flip(846)')] ).

cnf(848,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),B)),C))),D),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(inverse(D)),inverse(E))),C))),E)),
    inference(para,[status(thm),theory(equality)],[689,840]),
    [iquote('para(689,840)')] ).

cnf(849,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(A))),C))),A),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(E),E)),C))),B)),
    inference(flip,[status(thm),theory(equality)],[848]),
    [iquote('flip(848)')] ).

cnf(850,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C),C),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[689,840]),451]),
    [iquote('para(689,840),demod([451])')] ).

cnf(851,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(B)),C))),B)),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[773]),850]),
    [iquote('back_demod(773),demod([850])')] ).

cnf(852,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),A))),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[688]),850]),
    [iquote('back_demod(688),demod([850])')] ).

cnf(853,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B)))),C),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[758]),852]),
    [iquote('back_demod(758),demod([852])')] ).

cnf(857,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)),multiply(inverse(inverse(B)),C)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[608]),850]),
    [iquote('back_demod(608),demod([850])')] ).

cnf(860,plain,
    equal(multiply(inverse(multiply(inverse(inverse(A)),inverse(A))),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[853]),857]),
    [iquote('back_demod(853),demod([857])')] ).

cnf(861,plain,
    equal(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(C),C)),multiply(inverse(inverse(B)),A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[746]),857,860]),1]),
    [iquote('back_demod(746),demod([857,860]),flip(1)')] ).

cnf(862,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),multiply(inverse(inverse(multiply(C,inverse(D)))),inverse(multiply(B,multiply(C,inverse(D)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[847]),857,861]),
    [iquote('back_demod(847),demod([857,861])')] ).

cnf(863,plain,
    equal(multiply(inverse(inverse(multiply(A,inverse(B)))),inverse(multiply(C,multiply(A,inverse(B))))),multiply(inverse(inverse(D)),inverse(multiply(C,D)))),
    inference(flip,[status(thm),theory(equality)],[862]),
    [iquote('flip(862)')] ).

cnf(870,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),inverse(B)))),A),multiply(inverse(inverse(B)),inverse(multiply(inverse(C),C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[835]),857]),
    [iquote('back_demod(835),demod([857])')] ).

cnf(871,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(multiply(inverse(A),A),inverse(C))),inverse(A)))),C)),
    inference(flip,[status(thm),theory(equality)],[870]),
    [iquote('flip(870)')] ).

cnf(875,plain,
    equal(multiply(inverse(inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),inverse(D))),E))),D)))),inverse(E)),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[809]),857]),
    [iquote('back_demod(809),demod([857])')] ).

cnf(880,plain,
    equal(multiply(inverse(inverse(A)),multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),E)))),multiply(inverse(multiply(inverse(multiply(B,inverse(E))),inverse(A))),D)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[785]),857]),
    [iquote('back_demod(785),demod([857])')] ).

cnf(881,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(C))),D),multiply(inverse(inverse(C)),multiply(A,inverse(multiply(multiply(multiply(inverse(E),E),inverse(D)),B))))),
    inference(flip,[status(thm),theory(equality)],[880]),
    [iquote('flip(880)')] ).

cnf(925,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[691]),857]),
    [iquote('back_demod(691),demod([857])')] ).

cnf(931,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(E,inverse(multiply(multiply(multiply(inverse(inverse(F)),inverse(F)),inverse(D)),multiply(multiply(multiply(inverse(inverse(F)),inverse(F)),inverse(multiply(inverse(multiply(E,inverse(inverse(F)))),B))),inverse(F)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[593]),857]),
    [iquote('back_demod(593),demod([857])')] ).

cnf(932,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(C)),multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(multiply(A,inverse(inverse(B)))),D))),inverse(B))))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(D),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(D),inverse(E))),F))),E)),inverse(multiply(inverse(F),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(D),inverse(E))),F))),E)))),
    inference(flip,[status(thm),theory(equality)],[931]),
    [iquote('flip(931)')] ).

cnf(938,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)),inverse(multiply(inverse(multiply(F,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),G))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))),multiply(inverse(multiply(F,inverse(A))),G)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[584]),857]),
    [iquote('back_demod(584),demod([857])')] ).

cnf(939,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),C),multiply(inverse(inverse(B)),inverse(multiply(multiply(multiply(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(G))),F))),G)),inverse(multiply(inverse(multiply(A,multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))))),C))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(G))),F))),G))))),
    inference(flip,[status(thm),theory(equality)],[938]),
    [iquote('flip(938)')] ).

cnf(942,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),D))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),D))),B)),inverse(E)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),D))),B)))),multiply(inverse(multiply(C,inverse(A))),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),E))),F)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[572]),857]),
    [iquote('back_demod(572),demod([857])')] ).

cnf(943,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(D),inverse(C))),E))),C))),multiply(inverse(inverse(B)),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(A,inverse(F))),D))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(A,inverse(F))),D))),F)),inverse(E)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(A,inverse(F))),D))),F))))),
    inference(flip,[status(thm),theory(equality)],[942]),
    [iquote('flip(942)')] ).

cnf(944,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(D,inverse(multiply(multiply(multiply(inverse(inverse(E)),inverse(E)),inverse(C)),multiply(multiply(multiply(inverse(inverse(E)),inverse(E)),inverse(multiply(inverse(multiply(D,inverse(inverse(E)))),B))),inverse(E)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[570]),857]),
    [iquote('back_demod(570),demod([857])')] ).

cnf(945,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(C)),multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(multiply(A,inverse(inverse(B)))),D))),inverse(B))))),inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(D),inverse(E))),C))),E))),
    inference(flip,[status(thm),theory(equality)],[944]),
    [iquote('flip(944)')] ).

cnf(961,plain,
    equal(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(inverse(inverse(E)),inverse(multiply(multiply(multiply(inverse(E),E),multiply(F,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(F,inverse(G))),B))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(F,inverse(G))),B))),G)),inverse(D)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(F,inverse(G))),B))),G))))),E)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[522]),857]),
    [iquote('back_demod(522),demod([857])')] ).

cnf(962,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(inverse(A),A),multiply(B,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),inverse(E)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C))))),A))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),G))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),G))),F)),inverse(multiply(inverse(G),E))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(D),inverse(F))),G))),F))),
    inference(flip,[status(thm),theory(equality)],[961]),
    [iquote('flip(961)')] ).

cnf(972,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(A)),inverse(B)))),inverse(C))),multiply(multiply(inverse(B),B),inverse(multiply(inverse(inverse(B)),inverse(multiply(inverse(inverse(C)),A)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[480]),857,857,857]),
    [iquote('back_demod(480),demod([857,857,857])')] ).

cnf(973,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(B)),C))))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(C)),inverse(A)))),inverse(B)))),
    inference(flip,[status(thm),theory(equality)],[972]),
    [iquote('flip(972)')] ).

cnf(984,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(A)),inverse(B)))),A),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[451]),857]),
    [iquote('back_demod(451),demod([857])')] ).

cnf(991,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),C))),A),multiply(multiply(multiply(D,multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(inverse(E)),D))),E)),inverse(multiply(inverse(multiply(B,D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(inverse(E)),D))),E))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[405]),857,857]),
    [iquote('back_demod(405),demod([857,857])')] ).

cnf(992,plain,
    equal(multiply(multiply(multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(inverse(B)),A))),B)),inverse(multiply(inverse(multiply(C,A)),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(inverse(B)),A))),B)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(C,inverse(E))),D))),E)),
    inference(flip,[status(thm),theory(equality)],[991]),
    [iquote('flip(991)')] ).

cnf(1013,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(inverse(D)),inverse(D)),inverse(multiply(inverse(inverse(inverse(D))),inverse(multiply(A,inverse(B)))))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(C)),D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[325]),857]),
    [iquote('back_demod(325),demod([857])')] ).

cnf(1014,plain,
    equal(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,inverse(C)))))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(D)),A))),multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C)))),
    inference(flip,[status(thm),theory(equality)],[1013]),
    [iquote('flip(1013)')] ).

cnf(1041,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(multiply(inverse(inverse(A)),inverse(multiply(inverse(C),A)))))),D))),C))),D),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[286]),857,857]),
    [iquote('back_demod(286),demod([857,857])')] ).

cnf(1048,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(A,inverse(D))),inverse(C)))),D)))),E))),C))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[260]),857]),
    [iquote('back_demod(260),demod([857])')] ).

cnf(1049,plain,
    equal(multiply(multiply(multiply(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),inverse(multiply(inverse(multiply(multiply(inverse(E),E),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),F))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),multiply(inverse(inverse(E)),inverse(multiply(F,E)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[259]),857]),
    [iquote('back_demod(259),demod([857])')] ).

cnf(1050,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),multiply(multiply(multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(F))),E))),F)),inverse(multiply(inverse(multiply(multiply(inverse(A),A),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),B))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(F))),E))),F))),
    inference(flip,[status(thm),theory(equality)],[1049]),
    [iquote('flip(1049)')] ).

cnf(1066,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(B)),inverse(multiply(multiply(multiply(inverse(B),B),C),B))))),multiply(inverse(inverse(A)),C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[238]),857,857,857]),1]),
    [iquote('back_demod(238),demod([857,857,857]),flip(1)')] ).

cnf(1076,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(inverse(multiply(B,C))),inverse(multiply(B,C))),inverse(A))),inverse(multiply(D,inverse(C)))))),A),multiply(inverse(multiply(multiply(inverse(C),C),inverse(multiply(D,inverse(multiply(B,C)))))),B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[211]),857]),
    [iquote('back_demod(211),demod([857])')] ).

cnf(1077,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(multiply(B,inverse(multiply(C,A)))))),C),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(inverse(multiply(C,A))),inverse(multiply(C,A))),inverse(D))),inverse(multiply(B,inverse(A)))))),D)),
    inference(flip,[status(thm),theory(equality)],[1076]),
    [iquote('flip(1076)')] ).

cnf(1098,plain,
    equal(multiply(inverse(multiply(inverse(A),A)),B),B),
    inference(para,[status(thm),theory(equality)],[689,860]),
    [iquote('para(689,860)')] ).

cnf(1099,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(A))),C))),A),multiply(multiply(multiply(inverse(D),D),inverse(C)),B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[849]),1098]),
    [iquote('back_demod(849),demod([1098])')] ).

cnf(1100,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(B)),C),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(inverse(C)),inverse(D))),B))),D)),
    inference(flip,[status(thm),theory(equality)],[1099]),
    [iquote('flip(1099)')] ).

cnf(1116,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(B)),inverse(multiply(inverse(C),C))))),inverse(B)),
    inference(para,[status(thm),theory(equality)],[689,925]),
    [iquote('para(689,925)')] ).

cnf(1221,plain,
    equal(multiply(inverse(inverse(multiply(inverse(inverse(A)),inverse(A)))),inverse(multiply(B,multiply(inverse(C),C)))),multiply(inverse(inverse(D)),inverse(multiply(B,D)))),
    inference(para,[status(thm),theory(equality)],[689,863]),
    [iquote('para(689,863)')] ).

cnf(1222,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),multiply(inverse(inverse(multiply(inverse(inverse(C)),inverse(C)))),inverse(multiply(B,multiply(inverse(D),D))))),
    inference(flip,[status(thm),theory(equality)],[1221]),
    [iquote('flip(1221)')] ).

cnf(1223,plain,
    equal(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,inverse(A)))),multiply(inverse(inverse(C)),inverse(multiply(B,C)))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1098,863]),1098]),
    [iquote('para(1098,863),demod([1098])')] ).

cnf(1224,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),multiply(inverse(inverse(inverse(C))),inverse(multiply(B,inverse(C))))),
    inference(flip,[status(thm),theory(equality)],[1223]),
    [iquote('flip(1223)')] ).

cnf(1230,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))),multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(A),inverse(C))))),
    inference(para,[status(thm),theory(equality)],[689,1224]),
    [iquote('para(689,1224)')] ).

cnf(1231,plain,
    equal(multiply(inverse(inverse(inverse(A))),inverse(multiply(inverse(B),inverse(A)))),multiply(inverse(inverse(B)),inverse(multiply(inverse(C),C)))),
    inference(flip,[status(thm),theory(equality)],[1230]),
    [iquote('flip(1230)')] ).

cnf(1251,plain,
    equal(multiply(inverse(inverse(inverse(A))),inverse(inverse(A))),multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C)))),
    inference(para,[status(thm),theory(equality)],[1098,1231]),
    [iquote('para(1098,1231)')] ).

cnf(1253,plain,
    equal(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B))),multiply(inverse(C),C)),
    inference(para,[status(thm),theory(equality)],[1251,689]),
    [iquote('para(1251,689)')] ).

cnf(1254,plain,
    equal(multiply(inverse(A),A),multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C)))),
    inference(flip,[status(thm),theory(equality)],[1253]),
    [iquote('flip(1253)')] ).

cnf(1301,plain,
    equal(inverse(multiply(multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(C)),D))),C)),D),
    inference(para,[status(thm),theory(equality)],[1254,851]),
    [iquote('para(1254,851)')] ).

cnf(1326,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(B)),inverse(multiply(multiply(multiply(inverse(C),C),D),B))))),multiply(inverse(inverse(A)),D)),
    inference(para,[status(thm),theory(equality)],[689,1066]),
    [iquote('para(689,1066)')] ).

cnf(1344,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(G,inverse(F))),H))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(G,inverse(F))),H))),F)),inverse(multiply(inverse(H),B))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(G,inverse(F))),H))),F))))),I)))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(G,multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(I)),E))))),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,43]),1]),
    [iquote('para(4,43),flip(1)')] ).

cnf(1345,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),inverse(multiply(inverse(C),C))))),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[851,1116]),851]),
    [iquote('para(851,1116),demod([851])')] ).

cnf(1346,plain,
    equal(multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(B),B)))),multiply(inverse(C),C)),
    inference(para,[status(thm),theory(equality)],[1098,1345]),
    [iquote('para(1098,1345)')] ).

cnf(1366,plain,
    equal(multiply(multiply(inverse(A),A),inverse(multiply(B,inverse(multiply(inverse(C),C))))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(inverse(E)),B))),E)),
    inference(para,[status(thm),theory(equality)],[851,1345]),
    [iquote('para(851,1345)')] ).

cnf(1367,plain,
    equal(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(B)),C))),B),multiply(multiply(inverse(D),D),inverse(multiply(C,inverse(multiply(inverse(E),E)))))),
    inference(flip,[status(thm),theory(equality)],[1366]),
    [iquote('flip(1366)')] ).

cnf(1389,plain,
    equal(inverse(inverse(inverse(multiply(inverse(A),A)))),multiply(inverse(B),B)),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1346,925]),1345]),
    [iquote('para(1346,925),demod([1345])')] ).

cnf(1390,plain,
    equal(multiply(inverse(A),A),inverse(inverse(inverse(multiply(inverse(B),B))))),
    inference(flip,[status(thm),theory(equality)],[1389]),
    [iquote('flip(1389)')] ).

cnf(1404,plain,
    equal(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C))),inverse(F)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),D))),C)))))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(H),inverse(G))),I))),G)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(H),inverse(G))),I))),G)),inverse(multiply(inverse(I),multiply(inverse(multiply(inverse(E),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(A,inverse(J))),K))),J)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(A,inverse(J))),K))),J)),inverse(multiply(inverse(K),H))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(A,inverse(J))),K))),J))))),F)))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(H),inverse(G))),I))),G)))),
    inference(para,[status(thm),theory(equality)],[36,43]),
    [iquote('para(36,43)')] ).

cnf(1405,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A)),inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(D),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),G))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),G))),E)),inverse(multiply(inverse(G),B))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),G))),E))))),H)))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),C))),A))),multiply(F,multiply(I,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J)),inverse(multiply(inverse(K),D))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J)),inverse(multiply(inverse(K),D))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J))),inverse(H)),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J)),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J)),inverse(multiply(inverse(K),D))),multiply(multiply(multiply(inverse(J),J),inverse(multiply(inverse(multiply(I,inverse(J))),K))),J))))))),
    inference(flip,[status(thm),theory(equality)],[1404]),
    [iquote('flip(1404)')] ).

cnf(1429,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),inverse(inverse(multiply(inverse(C),C))))),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1389,851]),1098]),
    [iquote('para(1389,851),demod([1098])')] ).

cnf(1430,plain,
    equal(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(multiply(inverse(B),B),C))),inverse(multiply(inverse(D),D)))),C),
    inference(para,[status(thm),theory(equality)],[1389,851]),
    [iquote('para(1389,851)')] ).

cnf(1433,plain,
    equal(multiply(multiply(inverse(A),A),inverse(inverse(multiply(B,inverse(inverse(multiply(inverse(C),C))))))),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1389,925]),1098]),
    [iquote('para(1389,925),demod([1098])')] ).

cnf(1440,plain,
    equal(multiply(multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))),inverse(multiply(multiply(inverse(B),B),inverse(C)))),inverse(multiply(inverse(A),A))),C),
    inference(para,[status(thm),theory(equality)],[1389,984]),
    [iquote('para(1389,984)')] ).

cnf(1500,plain,
    equal(inverse(multiply(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),inverse(B)),inverse(inverse(multiply(inverse(C),C))))),B),
    inference(para,[status(thm),theory(equality)],[1390,1429]),
    [iquote('para(1390,1429)')] ).

cnf(1648,plain,
    equal(inverse(multiply(A,inverse(inverse(multiply(inverse(B),B))))),multiply(inverse(inverse(C)),inverse(multiply(A,C)))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1389,1223]),1098]),
    [iquote('para(1389,1223),demod([1098])')] ).

cnf(1649,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),inverse(multiply(B,inverse(inverse(multiply(inverse(C),C)))))),
    inference(flip,[status(thm),theory(equality)],[1648]),
    [iquote('flip(1648)')] ).

cnf(1662,plain,
    equal(multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),B)))),A))),C),C),
    inference(para,[status(thm),theory(equality)],[1648,1098]),
    [iquote('para(1648,1098)')] ).

cnf(1663,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(A),inverse(inverse(multiply(inverse(C),C)))))),
    inference(para,[status(thm),theory(equality)],[689,1649]),
    [iquote('para(689,1649)')] ).

cnf(1664,plain,
    equal(inverse(multiply(inverse(A),inverse(inverse(multiply(inverse(B),B))))),multiply(inverse(inverse(A)),inverse(multiply(inverse(C),C)))),
    inference(flip,[status(thm),theory(equality)],[1663]),
    [iquote('flip(1663)')] ).

cnf(1723,plain,
    equal(multiply(inverse(inverse(multiply(inverse(A),A))),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1389,1662]),1345]),
    [iquote('para(1389,1662),demod([1345])')] ).

cnf(1730,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),inverse(multiply(inverse(C),C))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1440]),1723,1098]),
    [iquote('back_demod(1440),demod([1723,1098])')] ).

cnf(1736,plain,
    equal(inverse(multiply(inverse(multiply(inverse(inverse(A)),B)),A)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1301]),1723,1098]),
    [iquote('back_demod(1301),demod([1723,1098])')] ).

cnf(1740,plain,
    equal(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1254]),1723]),
    [iquote('back_demod(1254),demod([1723])')] ).

cnf(1741,plain,
    equal(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)),
    inference(flip,[status(thm),theory(equality)],[1740]),
    [iquote('flip(1740)')] ).

cnf(1742,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),inverse(multiply(B,multiply(inverse(C),C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1222]),1723]),
    [iquote('back_demod(1222),demod([1723])')] ).

cnf(1743,plain,
    equal(inverse(multiply(A,multiply(inverse(B),B))),multiply(inverse(inverse(C)),inverse(multiply(A,C)))),
    inference(flip,[status(thm),theory(equality)],[1742]),
    [iquote('flip(1742)')] ).

cnf(1750,plain,
    equal(multiply(multiply(inverse(A),A),B),B),
    inference(para,[status(thm),theory(equality)],[1741,1098]),
    [iquote('para(1741,1098)')] ).

cnf(1768,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1730]),1750]),
    [iquote('back_demod(1730),demod([1750])')] ).

cnf(1771,plain,
    equal(inverse(multiply(inverse(A),inverse(inverse(multiply(inverse(B),B))))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1664]),1768]),
    [iquote('back_demod(1664),demod([1768])')] ).

cnf(1779,plain,
    equal(multiply(inverse(multiply(inverse(inverse(A)),inverse(B))),A),B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[871]),1768,1750,1750]),1]),
    [iquote('back_demod(871),demod([1768,1750,1750]),flip(1)')] ).

cnf(1988,plain,
    equal(inverse(inverse(multiply(A,inverse(inverse(multiply(inverse(B),B)))))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1433]),1750]),
    [iquote('back_demod(1433),demod([1750])')] ).

cnf(1989,plain,
    equal(inverse(multiply(inverse(A),inverse(multiply(inverse(B),B)))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1430]),1750,1750]),
    [iquote('back_demod(1430),demod([1750,1750])')] ).

cnf(2002,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(multiply(E,inverse(F))),C)),F))))),G))),multiply(inverse(multiply(inverse(multiply(inverse(D),inverse(H))),A)),H))),multiply(E,multiply(I,inverse(multiply(inverse(G),multiply(inverse(multiply(inverse(J),B)),multiply(inverse(multiply(inverse(multiply(I,inverse(K))),J)),K))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1405]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(1405),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2003,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(D),E)),multiply(inverse(multiply(inverse(multiply(B,inverse(F))),D)),F)))))),inverse(multiply(inverse(multiply(inverse(G),multiply(inverse(multiply(inverse(E),inverse(multiply(inverse(multiply(inverse(H),I)),multiply(inverse(multiply(inverse(multiply(A,inverse(J))),H)),J))))),C))),multiply(inverse(multiply(inverse(multiply(inverse(I),inverse(K))),G)),K)))),
    inference(flip,[status(thm),theory(equality)],[2002]),
    [iquote('flip(2002)')] ).

cnf(2032,plain,
    equal(multiply(inverse(multiply(inverse(inverse(A)),B)),A),inverse(multiply(B,inverse(multiply(inverse(C),C))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1367]),1750,1750]),
    [iquote('back_demod(1367),demod([1750,1750])')] ).

cnf(2033,plain,
    equal(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(inverse(multiply(inverse(inverse(C)),A)),C)),
    inference(flip,[status(thm),theory(equality)],[2032]),
    [iquote('flip(2032)')] ).

cnf(2054,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(multiply(inverse(multiply(inverse(D),E)),multiply(inverse(multiply(inverse(multiply(F,inverse(G))),D)),G))))),H))),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(I))),A)),I))),multiply(F,multiply(B,inverse(multiply(inverse(H),C))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1344]),1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(1344),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2065,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))),multiply(inverse(inverse(A)),C)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1326]),1750]),
    [iquote('back_demod(1326),demod([1750])')] ).

cnf(2066,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(A)),inverse(B))),C)),B))),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1041]),1750,2065,1750]),
    [iquote('back_demod(1041),demod([1750,2065,1750])')] ).

cnf(2259,plain,
    equal(multiply(inverse(multiply(inverse(multiply(inverse(inverse(A)),inverse(B))),C)),B),multiply(inverse(C),A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1100]),1750,1750]),1]),
    [iquote('back_demod(1100),demod([1750,1750]),flip(1)')] ).

cnf(2260,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),A))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2066]),2259]),
    [iquote('back_demod(2066),demod([2259])')] ).

cnf(2289,plain,
    equal(multiply(inverse(inverse(multiply(A,inverse(multiply(B,C))))),B),multiply(A,inverse(C))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1077]),1750,1750,1750,1779]),
    [iquote('back_demod(1077),demod([1750,1750,1750,1779])')] ).

cnf(2305,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(B,A))),multiply(multiply(multiply(multiply(C,inverse(multiply(inverse(D),E))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(E))),inverse(F))),D)),F)),inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(D),E)))),B))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(E))),inverse(F))),D)),F))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1050]),1750,1750,1750,1750,1750]),
    [iquote('back_demod(1050),demod([1750,1750,1750,1750,1750])')] ).

cnf(2306,plain,
    equal(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D)),inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),E))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D)),multiply(inverse(inverse(F)),inverse(multiply(E,F)))),
    inference(flip,[status(thm),theory(equality)],[2305]),
    [iquote('flip(2305)')] ).

cnf(2307,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),C)))),E)),D))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1048]),1750,1750]),
    [iquote('back_demod(1048),demod([1750,1750])')] ).

cnf(2331,plain,
    equal(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,inverse(C))))),inverse(multiply(inverse(D),A))),multiply(B,inverse(multiply(inverse(D),C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1014]),1750,1750,1750]),
    [iquote('back_demod(1014),demod([1750,1750,1750])')] ).

cnf(2332,plain,
    equal(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(inverse(inverse(inverse(D))),inverse(multiply(A,inverse(C))))),inverse(multiply(inverse(B),D)))),
    inference(flip,[status(thm),theory(equality)],[2331]),
    [iquote('flip(2331)')] ).

cnf(2340,plain,
    equal(multiply(multiply(multiply(A,multiply(inverse(multiply(inverse(inverse(B)),A)),B)),inverse(multiply(inverse(multiply(C,A)),D))),multiply(inverse(multiply(inverse(inverse(B)),A)),B)),multiply(inverse(multiply(inverse(multiply(C,inverse(E))),D)),E)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[992]),1750,1750,1750]),
    [iquote('back_demod(992),demod([1750,1750,1750])')] ).

cnf(2341,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),C)),B),multiply(multiply(multiply(D,multiply(inverse(multiply(inverse(inverse(E)),D)),E)),inverse(multiply(inverse(multiply(A,D)),C))),multiply(inverse(multiply(inverse(inverse(E)),D)),E))),
    inference(flip,[status(thm),theory(equality)],[2340]),
    [iquote('flip(2340)')] ).

cnf(2350,plain,
    equal(inverse(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(B)),C)))),inverse(multiply(inverse(multiply(inverse(inverse(C)),inverse(A))),inverse(B)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[973]),1750,1750]),
    [iquote('back_demod(973),demod([1750,1750])')] ).

cnf(2351,plain,
    equal(inverse(multiply(inverse(multiply(inverse(inverse(A)),inverse(B))),inverse(C))),inverse(multiply(inverse(inverse(B)),inverse(multiply(inverse(inverse(C)),A))))),
    inference(flip,[status(thm),theory(equality)],[2350]),
    [iquote('flip(2350)')] ).

cnf(2355,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),A))),multiply(inverse(multiply(inverse(F),C)),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(G))),F)),G))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[962]),1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(962),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2356,plain,
    equal(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(multiply(inverse(C),inverse(D))),A)),D)),multiply(inverse(inverse(E)),inverse(multiply(multiply(F,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(F,inverse(G))),C)),G)))),E)))),
    inference(flip,[status(thm),theory(equality)],[2355]),
    [iquote('flip(2355)')] ).

cnf(2362,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,inverse(inverse(C)))),D)),inverse(C))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(D),inverse(E))),B)),E))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[945]),1750,1750,1750]),
    [iquote('back_demod(945),demod([1750,1750,1750])')] ).

cnf(2363,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),C)),B)),multiply(D,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(D,inverse(inverse(E)))),A)),inverse(E)))))),
    inference(flip,[status(thm),theory(equality)],[2362]),
    [iquote('flip(2362)')] ).

cnf(2364,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(C),inverse(D))),E)),D))),multiply(inverse(inverse(B)),inverse(multiply(inverse(E),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),C)),F))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[943]),1750,1750,1750,1750,1750]),
    [iquote('back_demod(943),demod([1750,1750,1750,1750,1750])')] ).

cnf(2365,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(C,inverse(D))),E)),D)))),multiply(inverse(multiply(C,inverse(A))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(F))),B)),F)))),
    inference(flip,[status(thm),theory(equality)],[2364]),
    [iquote('flip(2364)')] ).

cnf(2368,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),C),multiply(inverse(inverse(B)),inverse(multiply(multiply(multiply(multiply(D,inverse(multiply(inverse(E),F))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(F))),inverse(G))),E)),G)),inverse(multiply(inverse(multiply(A,multiply(D,inverse(multiply(inverse(E),F))))),C))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(F))),inverse(G))),E)),G))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[939]),1750,1750,1750,1750]),
    [iquote('back_demod(939),demod([1750,1750,1750,1750])')] ).

cnf(2369,plain,
    equal(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(E))),C)),E)),inverse(multiply(inverse(multiply(F,multiply(B,inverse(multiply(inverse(C),D))))),G))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(E))),C)),E)))),multiply(inverse(multiply(F,inverse(A))),G)),
    inference(flip,[status(thm),theory(equality)],[2368]),
    [iquote('flip(2368)')] ).

cnf(2375,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,inverse(inverse(C)))),D)),inverse(C))))),inverse(multiply(inverse(multiply(inverse(E),B)),multiply(inverse(multiply(inverse(multiply(inverse(D),inverse(F))),E)),F)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[932]),1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(932),demod([1750,1750,1750,1750,1750,1750])')] ).

cnf(2376,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(multiply(inverse(C),inverse(D))),A)),D))),multiply(E,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(E,inverse(inverse(F)))),C)),inverse(F)))))),
    inference(flip,[status(thm),theory(equality)],[2375]),
    [iquote('flip(2375)')] ).

cnf(2399,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(C))),D),multiply(inverse(inverse(C)),multiply(A,inverse(multiply(inverse(D),B))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[881]),1750]),
    [iquote('back_demod(881),demod([1750])')] ).

cnf(2400,plain,
    equal(multiply(inverse(inverse(A)),multiply(B,inverse(multiply(inverse(C),D)))),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(A))),C)),
    inference(flip,[status(thm),theory(equality)],[2399]),
    [iquote('flip(2399)')] ).

cnf(2403,plain,
    equal(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),C)),B)))),inverse(C)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[875]),1750,1750]),
    [iquote('back_demod(875),demod([1750,1750])')] ).

cnf(2407,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(C),A)),multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(F))),D)),F))))),multiply(G,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(H),E)),multiply(inverse(multiply(inverse(I),H)),multiply(inverse(multiply(inverse(multiply(G,inverse(J))),I)),J))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[839]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(839),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2408,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(E),C)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),E)),F)))))),inverse(multiply(inverse(multiply(inverse(G),B)),multiply(inverse(multiply(inverse(H),G)),multiply(inverse(multiply(inverse(I),H)),multiply(inverse(multiply(inverse(multiply(inverse(D),inverse(J))),I)),J)))))),
    inference(flip,[status(thm),theory(equality)],[2407]),
    [iquote('flip(2407)')] ).

cnf(2423,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D)),inverse(multiply(inverse(multiply(inverse(E),multiply(A,inverse(multiply(inverse(B),C))))),F))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D))),multiply(G,inverse(multiply(inverse(F),multiply(inverse(multiply(inverse(H),E)),multiply(inverse(multiply(inverse(I),H)),multiply(inverse(multiply(inverse(multiply(G,inverse(J))),I)),J))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[800]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(800),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2424,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(E),C)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),E)),F)))))),inverse(multiply(multiply(multiply(multiply(G,inverse(multiply(inverse(H),I))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(G,inverse(I))),inverse(J))),H)),J)),inverse(multiply(inverse(multiply(inverse(D),multiply(G,inverse(multiply(inverse(H),I))))),B))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(G,inverse(I))),inverse(J))),H)),J)))),
    inference(flip,[status(thm),theory(equality)],[2423]),
    [iquote('flip(2423)')] ).

cnf(2440,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(C),A)),multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(F))),D)),F))))),multiply(G,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(G,inverse(H))),E)),H))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[777]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(777),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2441,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,inverse(C))),D)),C)))),inverse(multiply(inverse(multiply(inverse(E),B)),multiply(inverse(multiply(inverse(F),E)),multiply(inverse(multiply(inverse(G),F)),multiply(inverse(multiply(inverse(multiply(inverse(D),inverse(H))),G)),H)))))),
    inference(flip,[status(thm),theory(equality)],[2440]),
    [iquote('flip(2440)')] ).

cnf(2465,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(C,D))),E)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(G))),multiply(multiply(multiply(multiply(H,inverse(multiply(inverse(I),J))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(H,inverse(J))),inverse(K))),I)),K)),inverse(multiply(inverse(multiply(H,inverse(multiply(inverse(I),J)))),C))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(H,inverse(J))),inverse(K))),I)),K)))),G))),F)))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[678]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(678),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2501,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(inverse(multiply(inverse(D),inverse(E))),B)),E)))),multiply(inverse(multiply(inverse(multiply(inverse(F),inverse(G))),A)),G))),multiply(H,inverse(multiply(multiply(I,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(I,inverse(J))),D)),J)))),multiply(inverse(multiply(inverse(multiply(H,inverse(K))),F)),K))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[535]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(535),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2502,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),G)),F)))),inverse(multiply(inverse(multiply(inverse(H),multiply(inverse(multiply(inverse(I),C)),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(J))),I)),J)))),multiply(inverse(multiply(inverse(multiply(inverse(G),inverse(K))),H)),K)))),
    inference(flip,[status(thm),theory(equality)],[2501]),
    [iquote('flip(2501)')] ).

cnf(2513,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(F))),C)),F)))),B)),multiply(G,inverse(multiply(multiply(H,inverse(multiply(inverse(D),multiply(inverse(multiply(inverse(multiply(H,inverse(I))),E)),I)))),multiply(inverse(multiply(inverse(multiply(G,inverse(J))),A)),J))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[504]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(504),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2514,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),G)),F)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(G),inverse(H))),multiply(inverse(multiply(inverse(I),C)),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(J))),I)),J)))),H))),
    inference(flip,[status(thm),theory(equality)],[2513]),
    [iquote('flip(2513)')] ).

cnf(2554,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(D))),E)),D))),multiply(inverse(multiply(inverse(multiply(inverse(F),inverse(G))),A)),G))),multiply(H,inverse(multiply(multiply(B,inverse(multiply(inverse(E),C))),multiply(inverse(multiply(inverse(multiply(H,inverse(I))),F)),I))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[424]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(424),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2555,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),F)),E)))),inverse(multiply(inverse(multiply(inverse(G),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(H))),C)),H))),multiply(inverse(multiply(inverse(multiply(inverse(F),inverse(I))),G)),I)))),
    inference(flip,[status(thm),theory(equality)],[2554]),
    [iquote('flip(2554)')] ).

cnf(2574,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D)),inverse(multiply(inverse(multiply(multiply(E,inverse(multiply(inverse(F),G))),multiply(A,inverse(multiply(inverse(B),C))))),H))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(G))),inverse(inverse(I)))),F)),inverse(multiply(inverse(H),I)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[222]),1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(222),demod([1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2575,plain,
    equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(inverse(C)))),D)),inverse(multiply(inverse(E),C))),inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(inverse(G),H))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(H))),inverse(I))),G)),I)),inverse(multiply(inverse(multiply(multiply(A,inverse(multiply(inverse(D),B))),multiply(F,inverse(multiply(inverse(G),H))))),E))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(H))),inverse(I))),G)),I)))),
    inference(flip,[status(thm),theory(equality)],[2574]),
    [iquote('flip(2574)')] ).

cnf(2615,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(C),A)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,inverse(multiply(inverse(F),G))))),inverse(H))),C)),H)))),multiply(D,inverse(multiply(multiply(multiply(multiply(E,inverse(multiply(inverse(F),G))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(G))),inverse(I))),F)),I)),inverse(B)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(G))),inverse(I))),F)),I))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[162]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(162),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2616,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(E))),C)),E)),inverse(F)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(E))),C)),E)))),inverse(multiply(inverse(multiply(inverse(G),F)),multiply(inverse(multiply(inverse(H),G)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(C),D))))),inverse(I))),H)),I))))),
    inference(flip,[status(thm),theory(equality)],[2615]),
    [iquote('flip(2615)')] ).

cnf(2618,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D)),inverse(multiply(inverse(multiply(inverse(E),multiply(A,inverse(multiply(inverse(B),C))))),F))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(D))),B)),D))),multiply(G,inverse(multiply(inverse(F),multiply(inverse(multiply(inverse(H),E)),multiply(inverse(multiply(inverse(multiply(G,inverse(I))),H)),I)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[159]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(159),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2619,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),C)),E))))),inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(inverse(G),H))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(H))),inverse(I))),G)),I)),inverse(multiply(inverse(multiply(inverse(D),multiply(F,inverse(multiply(inverse(G),H))))),B))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(H))),inverse(I))),G)),I)))),
    inference(flip,[status(thm),theory(equality)],[2618]),
    [iquote('flip(2618)')] ).

cnf(2628,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(C),D))))),inverse(E))),F)),E)),multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(G))),C)),G)),inverse(F)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(G))),C)),G))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[140]),1750,1750,1750,1750,1750]),
    [iquote('back_demod(140),demod([1750,1750,1750,1750,1750])')] ).

cnf(2629,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(E))),C)),E)),inverse(F)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(D))),inverse(E))),C)),E)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(C),D))))),inverse(G))),F)),G))),
    inference(flip,[status(thm),theory(equality)],[2628]),
    [iquote('flip(2628)')] ).

cnf(2635,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(multiply(inverse(multiply(inverse(C),inverse(D))),E)),D))),B)),multiply(F,inverse(multiply(multiply(G,inverse(multiply(inverse(E),multiply(inverse(multiply(inverse(multiply(G,inverse(H))),C)),H)))),multiply(inverse(multiply(inverse(multiply(F,inverse(I))),A)),I))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[129]),1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(129),demod([1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2636,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),G)),F)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(G),inverse(H))),multiply(inverse(multiply(inverse(multiply(inverse(E),inverse(I))),C)),I))),H))),
    inference(flip,[status(thm),theory(equality)],[2635]),
    [iquote('flip(2635)')] ).

cnf(2644,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(multiply(multiply(C,multiply(inverse(multiply(inverse(inverse(D)),C)),D)),inverse(E)),multiply(inverse(multiply(inverse(inverse(D)),C)),D)))),B)),multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(C),inverse(G))),E)),G)),multiply(inverse(multiply(inverse(multiply(F,inverse(H))),A)),H))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[103]),1750,1750,1750,1750,1736,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750]),
    [iquote('back_demod(103),demod([1750,1750,1750,1750,1736,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750,1750])')] ).

cnf(2645,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),inverse(C))),D)),C)),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),F)),E)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(F),inverse(G))),multiply(multiply(multiply(B,multiply(inverse(multiply(inverse(inverse(H)),B)),H)),inverse(D)),multiply(inverse(multiply(inverse(inverse(H)),B)),H)))),G))),
    inference(flip,[status(thm),theory(equality)],[2644]),
    [iquote('flip(2644)')] ).

cnf(2682,plain,
    equal(inverse(multiply(inverse(inverse(A)),B)),multiply(inverse(B),inverse(A))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[861,862]),1723,2260]),
    [iquote('para(861,862),demod([1723,2260])')] ).

cnf(2694,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),inverse(C))),D)),C)),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),F)),E)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(F),inverse(G))),multiply(multiply(multiply(B,multiply(multiply(inverse(B),inverse(H)),H)),inverse(D)),multiply(multiply(inverse(B),inverse(H)),H)))),G))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2645]),2682,2682]),
    [iquote('back_demod(2645),demod([2682,2682])')] ).

cnf(2695,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),multiply(multiply(multiply(C,multiply(multiply(inverse(C),inverse(D)),D)),inverse(E)),multiply(multiply(inverse(C),inverse(D)),D)))),B)),multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(C),inverse(G))),E)),G)),multiply(inverse(multiply(inverse(multiply(F,inverse(H))),A)),H))))),
    inference(flip,[status(thm),theory(equality)],[2694]),
    [iquote('flip(2694)')] ).

cnf(2773,plain,
    equal(inverse(multiply(multiply(inverse(inverse(A)),inverse(B)),inverse(C))),multiply(inverse(multiply(inverse(B),inverse(C))),inverse(A))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2351]),2682,2682,2682]),
    [iquote('back_demod(2351),demod([2682,2682,2682])')] ).

cnf(2774,plain,
    equal(multiply(A,inverse(inverse(multiply(inverse(B),B)))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1500]),2773,1771]),
    [iquote('back_demod(1500),demod([2773,1771])')] ).

cnf(2775,plain,
    equal(inverse(inverse(A)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1988]),2774]),
    [iquote('back_demod(1988),demod([2774])')] ).

cnf(2776,plain,
    equal(multiply(A,multiply(inverse(B),B)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2774]),2775]),
    [iquote('back_demod(2774),demod([2775])')] ).

cnf(2777,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1743]),2776,2775]),1]),
    [iquote('back_demod(1743),demod([2776,2775]),flip(1)')] ).

cnf(2778,plain,
    equal(inverse(multiply(inverse(A),inverse(B))),multiply(B,A)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[861]),2776,2775]),
    [iquote('back_demod(861),demod([2776,2775])')] ).

cnf(2912,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,B),multiply(multiply(multiply(C,multiply(multiply(inverse(C),inverse(D)),D)),inverse(E)),multiply(multiply(inverse(C),inverse(D)),D)))),A)),multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(multiply(G,C),E)),G)),multiply(inverse(multiply(inverse(multiply(F,inverse(H))),B)),H))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2695]),2778,2778]),
    [iquote('back_demod(2695),demod([2778,2778])')] ).

cnf(2913,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(multiply(B,C),D)),B)),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),F)),E)))),inverse(multiply(inverse(multiply(multiply(G,F),multiply(multiply(multiply(C,multiply(multiply(inverse(C),inverse(H)),H)),inverse(D)),multiply(multiply(inverse(C),inverse(H)),H)))),G))),
    inference(flip,[status(thm),theory(equality)],[2912]),
    [iquote('flip(2912)')] ).

cnf(2953,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),G)),F)))),inverse(multiply(inverse(multiply(multiply(H,G),multiply(inverse(multiply(multiply(I,E),C)),I))),H))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2636]),2778,2778]),
    [iquote('back_demod(2636),demod([2778,2778])')] ).

cnf(2954,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,B),multiply(inverse(multiply(multiply(C,D),E)),C))),A)),multiply(F,inverse(multiply(multiply(G,inverse(multiply(inverse(E),multiply(inverse(multiply(inverse(multiply(G,inverse(H))),D)),H)))),multiply(inverse(multiply(inverse(multiply(F,inverse(I))),B)),I))))),
    inference(flip,[status(thm),theory(equality)],[2953]),
    [iquote('flip(2953)')] ).

cnf(2959,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)),inverse(F)),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)))),inverse(multiply(inverse(multiply(multiply(G,multiply(A,multiply(B,inverse(multiply(inverse(C),D))))),F)),G))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2629]),2778,2778,2778]),
    [iquote('back_demod(2629),demod([2778,2778,2778])')] ).

cnf(2960,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,multiply(B,multiply(C,inverse(multiply(inverse(D),E))))),F)),A)),multiply(B,inverse(multiply(multiply(multiply(multiply(C,inverse(multiply(inverse(D),E))),multiply(inverse(multiply(multiply(G,multiply(C,inverse(E))),D)),G)),inverse(F)),multiply(inverse(multiply(multiply(G,multiply(C,inverse(E))),D)),G))))),
    inference(flip,[status(thm),theory(equality)],[2959]),
    [iquote('flip(2959)')] ).

cnf(2968,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),C)),E))))),inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(inverse(G),H))),multiply(inverse(multiply(multiply(I,multiply(F,inverse(H))),G)),I)),inverse(multiply(inverse(multiply(inverse(D),multiply(F,inverse(multiply(inverse(G),H))))),B))),multiply(inverse(multiply(multiply(I,multiply(F,inverse(H))),G)),I)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2619]),2778,2778]),
    [iquote('back_demod(2619),demod([2778,2778])')] ).

cnf(2969,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D)),inverse(multiply(inverse(multiply(inverse(E),multiply(A,inverse(multiply(inverse(B),C))))),F))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D))),multiply(G,inverse(multiply(inverse(F),multiply(inverse(multiply(inverse(H),E)),multiply(inverse(multiply(inverse(multiply(G,inverse(I))),H)),I)))))),
    inference(flip,[status(thm),theory(equality)],[2968]),
    [iquote('flip(2968)')] ).

cnf(2970,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)),inverse(F)),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)))),inverse(multiply(inverse(multiply(inverse(G),F)),multiply(inverse(multiply(inverse(H),G)),multiply(inverse(multiply(multiply(I,multiply(A,multiply(B,inverse(multiply(inverse(C),D))))),H)),I))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2616]),2778,2778,2778]),
    [iquote('back_demod(2616),demod([2778,2778,2778])')] ).

cnf(2971,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(C),A)),multiply(inverse(multiply(multiply(D,multiply(E,multiply(F,inverse(multiply(inverse(G),H))))),C)),D)))),multiply(E,inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(inverse(G),H))),multiply(inverse(multiply(multiply(I,multiply(F,inverse(H))),G)),I)),inverse(B)),multiply(inverse(multiply(multiply(I,multiply(F,inverse(H))),G)),I))))),
    inference(flip,[status(thm),theory(equality)],[2970]),
    [iquote('flip(2970)')] ).

cnf(2996,plain,
    equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),C)),D)),inverse(multiply(inverse(E),C))),inverse(multiply(multiply(multiply(multiply(F,inverse(multiply(inverse(G),H))),multiply(inverse(multiply(multiply(I,multiply(F,inverse(H))),G)),I)),inverse(multiply(inverse(multiply(multiply(A,inverse(multiply(inverse(D),B))),multiply(F,inverse(multiply(inverse(G),H))))),E))),multiply(inverse(multiply(multiply(I,multiply(F,inverse(H))),G)),I)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2575]),2775,2778,2778]),
    [iquote('back_demod(2575),demod([2775,2778,2778])')] ).

cnf(2997,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D)),inverse(multiply(inverse(multiply(multiply(E,inverse(multiply(inverse(F),G))),multiply(A,inverse(multiply(inverse(B),C))))),H))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(G))),I)),F)),inverse(multiply(inverse(H),I)))),
    inference(flip,[status(thm),theory(equality)],[2996]),
    [iquote('flip(2996)')] ).

cnf(3004,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(inverse(multiply(A,inverse(E))),F)),E)))),inverse(multiply(inverse(multiply(inverse(G),multiply(inverse(multiply(multiply(H,multiply(B,inverse(D))),C)),H))),multiply(inverse(multiply(multiply(I,F),G)),I)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2555]),2778,2778]),
    [iquote('back_demod(2555),demod([2778,2778])')] ).

cnf(3005,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(multiply(B,multiply(C,inverse(D))),E)),B))),multiply(inverse(multiply(multiply(F,G),A)),F))),multiply(H,inverse(multiply(multiply(C,inverse(multiply(inverse(E),D))),multiply(inverse(multiply(inverse(multiply(H,inverse(I))),G)),I))))),
    inference(flip,[status(thm),theory(equality)],[3004]),
    [iquote('flip(3004)')] ).

cnf(3026,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),G)),F)))),inverse(multiply(inverse(multiply(multiply(H,G),multiply(inverse(multiply(inverse(I),C)),multiply(inverse(multiply(multiply(J,E),I)),J)))),H))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2514]),2778,2778]),
    [iquote('back_demod(2514),demod([2778,2778])')] ).

cnf(3027,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(multiply(E,F),C)),E)))),A)),multiply(G,inverse(multiply(multiply(H,inverse(multiply(inverse(D),multiply(inverse(multiply(inverse(multiply(H,inverse(I))),F)),I)))),multiply(inverse(multiply(inverse(multiply(G,inverse(J))),B)),J))))),
    inference(flip,[status(thm),theory(equality)],[3026]),
    [iquote('flip(3026)')] ).

cnf(3038,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(B,inverse(D))),E)),D)))),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),G)),F)))),inverse(multiply(inverse(multiply(inverse(H),multiply(inverse(multiply(inverse(I),C)),multiply(inverse(multiply(multiply(J,E),I)),J)))),multiply(inverse(multiply(multiply(K,G),H)),K)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2502]),2778,2778]),
    [iquote('back_demod(2502),demod([2778,2778])')] ).

cnf(3039,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(multiply(D,E),B)),D)))),multiply(inverse(multiply(multiply(F,G),A)),F))),multiply(H,inverse(multiply(multiply(I,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(I,inverse(J))),E)),J)))),multiply(inverse(multiply(inverse(multiply(H,inverse(K))),G)),K))))),
    inference(flip,[status(thm),theory(equality)],[3038]),
    [iquote('flip(3038)')] ).

cnf(3058,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(C,D))),E)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),multiply(inverse(multiply(multiply(G,multiply(B,inverse(D))),multiply(multiply(multiply(multiply(H,inverse(multiply(inverse(I),J))),multiply(inverse(multiply(multiply(K,multiply(H,inverse(J))),I)),K)),inverse(multiply(inverse(multiply(H,inverse(multiply(inverse(I),J)))),C))),multiply(inverse(multiply(multiply(K,multiply(H,inverse(J))),I)),K)))),G))),F)))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2465]),2778,2778,2778]),
    [iquote('back_demod(2465),demod([2778,2778,2778])')] ).

cnf(3065,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,inverse(C))),D)),C)))),inverse(multiply(inverse(multiply(inverse(E),B)),multiply(inverse(multiply(inverse(F),E)),multiply(inverse(multiply(inverse(G),F)),multiply(inverse(multiply(multiply(H,D),G)),H)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2441]),2778]),
    [iquote('back_demod(2441),demod([2778])')] ).

cnf(3066,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(C),A)),multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(multiply(E,F),D)),E))))),multiply(G,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(G,inverse(H))),F)),H))))),
    inference(flip,[status(thm),theory(equality)],[3065]),
    [iquote('flip(3065)')] ).

cnf(3077,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(E),C)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),E)),F)))))),inverse(multiply(multiply(multiply(multiply(G,inverse(multiply(inverse(H),I))),multiply(inverse(multiply(multiply(J,multiply(G,inverse(I))),H)),J)),inverse(multiply(inverse(multiply(inverse(D),multiply(G,inverse(multiply(inverse(H),I))))),B))),multiply(inverse(multiply(multiply(J,multiply(G,inverse(I))),H)),J)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2424]),2778,2778]),
    [iquote('back_demod(2424),demod([2778,2778])')] ).

cnf(3078,plain,
    equal(inverse(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D)),inverse(multiply(inverse(multiply(inverse(E),multiply(A,inverse(multiply(inverse(B),C))))),F))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D))),multiply(G,inverse(multiply(inverse(F),multiply(inverse(multiply(inverse(H),E)),multiply(inverse(multiply(inverse(I),H)),multiply(inverse(multiply(inverse(multiply(G,inverse(J))),I)),J))))))),
    inference(flip,[status(thm),theory(equality)],[3077]),
    [iquote('flip(3077)')] ).

cnf(3082,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(E),C)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),E)),F)))))),inverse(multiply(inverse(multiply(inverse(G),B)),multiply(inverse(multiply(inverse(H),G)),multiply(inverse(multiply(inverse(I),H)),multiply(inverse(multiply(multiply(J,D),I)),J)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2408]),2778]),
    [iquote('back_demod(2408),demod([2778])')] ).

cnf(3083,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(inverse(C),A)),multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(multiply(E,F),D)),E))))),multiply(G,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(H),F)),multiply(inverse(multiply(inverse(I),H)),multiply(inverse(multiply(inverse(multiply(G,inverse(J))),I)),J))))))),
    inference(flip,[status(thm),theory(equality)],[3082]),
    [iquote('flip(3082)')] ).

cnf(3084,plain,
    equal(multiply(inverse(multiply(inverse(multiply(multiply(A,B),C)),A)),inverse(C)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2403]),2778,2775]),
    [iquote('back_demod(2403),demod([2778,2775])')] ).

cnf(3085,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),multiply(multiply(A,multiply(B,inverse(D))),C)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2400]),2775,2778]),
    [iquote('back_demod(2400),demod([2775,2778])')] ).

cnf(3086,plain,
    equal(multiply(multiply(A,multiply(B,inverse(C))),D),multiply(A,multiply(B,inverse(multiply(inverse(D),C))))),
    inference(flip,[status(thm),theory(equality)],[3085]),
    [iquote('flip(3085)')] ).

cnf(3095,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(multiply(C,D),A)),C))),multiply(E,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(E,F)),D)),inverse(F)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2376]),2778,2775]),
    [iquote('back_demod(2376),demod([2778,2775])')] ).

cnf(3096,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,C)),D)),inverse(C))))),inverse(multiply(inverse(multiply(inverse(E),B)),multiply(inverse(multiply(multiply(F,D),E)),F)))),
    inference(flip,[status(thm),theory(equality)],[3095]),
    [iquote('flip(3095)')] ).

cnf(3099,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)),inverse(multiply(inverse(multiply(F,multiply(B,inverse(multiply(inverse(C),D))))),G))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)))),multiply(inverse(multiply(F,inverse(A))),G)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2369]),2775,2778,2778]),
    [iquote('back_demod(2369),demod([2775,2778,2778])')] ).

cnf(3100,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),C),multiply(B,inverse(multiply(multiply(multiply(multiply(D,inverse(multiply(inverse(E),F))),multiply(inverse(multiply(multiply(G,multiply(D,inverse(F))),E)),G)),inverse(multiply(inverse(multiply(A,multiply(D,inverse(multiply(inverse(E),F))))),C))),multiply(inverse(multiply(multiply(G,multiply(D,inverse(F))),E)),G))))),
    inference(flip,[status(thm),theory(equality)],[3099]),
    [iquote('flip(3099)')] ).

cnf(3101,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(C,inverse(D))),E)),D)))),multiply(inverse(multiply(C,inverse(A))),inverse(multiply(inverse(multiply(multiply(F,E),B)),F)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2365]),2775,2778]),
    [iquote('back_demod(2365),demod([2775,2778])')] ).

cnf(3102,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(inverse(multiply(multiply(C,D),E)),C))),multiply(B,inverse(multiply(inverse(E),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),D)),F))))),
    inference(flip,[status(thm),theory(equality)],[3101]),
    [iquote('flip(3101)')] ).

cnf(3103,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,B),C)),A)),multiply(D,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(D,E)),B)),inverse(E)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2363]),2778,2775]),
    [iquote('back_demod(2363),demod([2778,2775])')] ).

cnf(3104,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,C)),D)),inverse(C))))),inverse(multiply(inverse(multiply(multiply(E,D),B)),E))),
    inference(flip,[status(thm),theory(equality)],[3103]),
    [iquote('flip(3103)')] ).

cnf(3106,plain,
    equal(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(multiply(C,D),A)),C)),inverse(multiply(E,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(E,inverse(F))),D)),F)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2356]),2778,2775,2777]),
    [iquote('back_demod(2356),demod([2778,2775,2777])')] ).

cnf(3107,plain,
    equal(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,inverse(C))),D)),C))))),multiply(inverse(multiply(inverse(E),B)),multiply(inverse(multiply(multiply(F,D),E)),F))),
    inference(flip,[status(thm),theory(equality)],[3106]),
    [iquote('flip(3106)')] ).

cnf(3110,plain,
    equal(inverse(multiply(A,inverse(multiply(B,C)))),multiply(B,multiply(C,inverse(A)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2350]),2775,2775,2775,2778]),
    [iquote('back_demod(2350),demod([2775,2775,2775,2778])')] ).

cnf(3111,plain,
    equal(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),D)),C),inverse(B))),multiply(inverse(multiply(inverse(E),A)),multiply(inverse(multiply(multiply(F,D),E)),F))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3107]),3110]),
    [iquote('back_demod(3107),demod([3110])')] ).

cnf(3112,plain,
    equal(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(multiply(C,D),A)),C)),multiply(inverse(B),multiply(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),D)),F),inverse(E)))),
    inference(flip,[status(thm),theory(equality)],[3111]),
    [iquote('flip(3111)')] ).

cnf(3113,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(C,D))),E)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),multiply(inverse(multiply(multiply(G,multiply(B,inverse(D))),multiply(multiply(multiply(multiply(H,inverse(multiply(inverse(I),J))),multiply(inverse(multiply(multiply(K,multiply(H,inverse(J))),I)),K)),inverse(multiply(multiply(inverse(I),multiply(J,inverse(H))),C))),multiply(inverse(multiply(multiply(K,multiply(H,inverse(J))),I)),K)))),G))),F)))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3058]),3110]),
    [iquote('back_demod(3058),demod([3110])')] ).

cnf(3128,plain,
    equal(multiply(A,inverse(multiply(inverse(B),C))),multiply(multiply(A,multiply(inverse(C),D)),inverse(multiply(inverse(B),D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2332]),2775,3110,2775]),
    [iquote('back_demod(2332),demod([2775,3110,2775])')] ).

cnf(3129,plain,
    equal(multiply(multiply(A,multiply(inverse(B),C)),inverse(multiply(inverse(D),C))),multiply(A,inverse(multiply(inverse(D),B)))),
    inference(flip,[status(thm),theory(equality)],[3128]),
    [iquote('flip(3128)')] ).

cnf(3137,plain,
    equal(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(inverse(multiply(multiply(multiply(C,multiply(A,inverse(D))),multiply(D,inverse(B))),E)),C))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2307]),2775,2778,3110]),
    [iquote('back_demod(2307),demod([2775,2778,3110])')] ).

cnf(3138,plain,
    equal(multiply(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D)),inverse(multiply(multiply(inverse(B),multiply(C,inverse(A))),E))),multiply(inverse(multiply(multiply(D,multiply(A,inverse(C))),B)),D)),inverse(E)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2306]),2778,3110,2778,2775,2777]),
    [iquote('back_demod(2306),demod([2778,3110,2778,2775,2777])')] ).

cnf(3145,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(C,D))),E)),multiply(inverse(multiply(inverse(multiply(A,inverse(F))),multiply(inverse(multiply(multiply(G,multiply(B,inverse(D))),inverse(C))),G))),F)))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3113]),3138]),
    [iquote('back_demod(3113),demod([3138])')] ).

cnf(3146,plain,
    equal(multiply(inverse(multiply(A,multiply(B,inverse(C)))),A),multiply(C,inverse(B))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2289]),3110]),
    [iquote('back_demod(2289),demod([3110])')] ).

cnf(3183,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(B),C)),multiply(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),B)),E),multiply(F,inverse(G)))),H))),multiply(inverse(multiply(multiply(I,C),A)),I))),multiply(D,multiply(F,inverse(multiply(inverse(H),G))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2054]),3110,2775,2778]),
    [iquote('back_demod(2054),demod([3110,2775,2778])')] ).

cnf(3189,plain,
    equal(multiply(inverse(A),multiply(A,inverse(B))),multiply(inverse(multiply(C,B)),C)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2033]),3110,2775]),
    [iquote('back_demod(2033),demod([3110,2775])')] ).

cnf(3190,plain,
    equal(multiply(inverse(multiply(A,B)),A),multiply(inverse(C),multiply(C,inverse(B)))),
    inference(flip,[status(thm),theory(equality)],[3189]),
    [iquote('flip(3189)')] ).

cnf(3191,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(D),E)),multiply(inverse(multiply(inverse(multiply(B,inverse(F))),D)),F)))))),inverse(multiply(inverse(multiply(inverse(G),multiply(multiply(inverse(multiply(inverse(H),I)),multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(J))),H)),J),E)),C))),multiply(inverse(multiply(multiply(K,I),G)),K)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2003]),3110,2775,2778]),
    [iquote('back_demod(2003),demod([3110,2775,2778])')] ).

cnf(3192,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(B),C)),multiply(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),B)),E),F)),G))),multiply(inverse(multiply(multiply(H,C),A)),H))),multiply(D,multiply(I,inverse(multiply(inverse(G),multiply(inverse(multiply(inverse(J),F)),multiply(inverse(multiply(inverse(multiply(I,inverse(K))),J)),K))))))),
    inference(flip,[status(thm),theory(equality)],[3191]),
    [iquote('flip(3191)')] ).

cnf(3193,plain,
    equal(multiply(inverse(A),multiply(A,B)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1989]),3110,2775]),
    [iquote('back_demod(1989),demod([3110,2775])')] ).

cnf(3194,plain,
    equal(multiply(inverse(multiply(A,B)),A),inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3190]),3193]),
    [iquote('back_demod(3190),demod([3193])')] ).

cnf(3195,plain,
    equal(inverse(multiply(A,inverse(B))),multiply(B,inverse(A))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3146]),3194]),
    [iquote('back_demod(3146),demod([3194])')] ).

cnf(3196,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(B),C)),multiply(multiply(inverse(multiply(multiply(D,inverse(E)),B)),D),F)),G))),multiply(inverse(multiply(multiply(H,C),A)),H))),multiply(E,multiply(I,inverse(multiply(inverse(G),multiply(inverse(multiply(inverse(J),F)),multiply(inverse(multiply(multiply(K,inverse(I)),J)),K))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3192]),3195,3195]),
    [iquote('back_demod(3192),demod([3195,3195])')] ).

cnf(3197,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(D),E)),multiply(inverse(multiply(multiply(F,inverse(B)),D)),F)))))),inverse(multiply(inverse(multiply(inverse(G),multiply(multiply(inverse(multiply(inverse(H),I)),multiply(multiply(inverse(multiply(multiply(J,inverse(A)),H)),J),E)),C))),multiply(inverse(multiply(multiply(K,I),G)),K)))),
    inference(flip,[status(thm),theory(equality)],[3196]),
    [iquote('flip(3196)')] ).

cnf(3203,plain,
    equal(inverse(multiply(inverse(multiply(inverse(A),multiply(multiply(inverse(multiply(inverse(B),C)),multiply(multiply(inverse(multiply(multiply(D,inverse(E)),B)),D),multiply(F,inverse(G)))),H))),multiply(inverse(multiply(multiply(I,C),A)),I))),multiply(E,multiply(F,inverse(multiply(inverse(H),G))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3183]),3195]),
    [iquote('back_demod(3183),demod([3195])')] ).

cnf(3238,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(C,D))),E)),multiply(inverse(multiply(multiply(F,inverse(A)),multiply(multiply(C,inverse(multiply(G,multiply(B,inverse(D))))),G))),F)))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3145]),3195,3195]),
    [iquote('back_demod(3145),demod([3195,3195])')] ).

cnf(3245,plain,
    equal(multiply(multiply(A,inverse(B)),inverse(multiply(inverse(multiply(multiply(multiply(C,multiply(B,inverse(D))),multiply(D,inverse(A))),E)),C))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3137]),3195]),
    [iquote('back_demod(3137),demod([3195])')] ).

cnf(3254,plain,
    equal(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(multiply(C,D),A)),C)),multiply(inverse(B),multiply(multiply(inverse(multiply(multiply(E,inverse(F)),D)),E),inverse(F)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3112]),3195]),
    [iquote('back_demod(3112),demod([3195])')] ).

cnf(3255,plain,
    equal(multiply(inverse(A),multiply(multiply(inverse(multiply(multiply(B,inverse(C)),D)),B),inverse(C))),multiply(inverse(multiply(inverse(E),A)),multiply(inverse(multiply(multiply(F,D),E)),F))),
    inference(flip,[status(thm),theory(equality)],[3254]),
    [iquote('flip(3254)')] ).

cnf(3256,plain,
    equal(multiply(multiply(A,B),inverse(C)),multiply(A,multiply(B,inverse(C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3110]),3195]),
    [iquote('back_demod(3110),demod([3195])')] ).

cnf(3257,plain,
    equal(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(multiply(C,D),A)),C)),multiply(inverse(B),inverse(D))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3255]),3256,3194]),1]),
    [iquote('back_demod(3255),demod([3256,3194]),flip(1)')] ).

cnf(3287,plain,
    equal(multiply(A,multiply(multiply(inverse(multiply(inverse(B),A)),multiply(multiply(inverse(multiply(multiply(C,inverse(D)),B)),C),multiply(E,inverse(F)))),G)),multiply(D,multiply(E,inverse(multiply(inverse(G),F))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3203]),3257,3195,2775]),
    [iquote('back_demod(3203),demod([3257,3195,2775])')] ).

cnf(3288,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),multiply(E,multiply(multiply(inverse(multiply(inverse(F),E)),multiply(multiply(inverse(multiply(multiply(G,inverse(A)),F)),G),multiply(B,inverse(D)))),C))),
    inference(flip,[status(thm),theory(equality)],[3287]),
    [iquote('flip(3287)')] ).

cnf(3294,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),multiply(inverse(D),B))))),multiply(E,multiply(multiply(inverse(multiply(inverse(F),E)),multiply(multiply(inverse(multiply(multiply(G,inverse(A)),F)),G),D)),C))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3197]),3257,2775,3257,3195,2775]),
    [iquote('back_demod(3197),demod([3257,2775,3257,3195,2775])')] ).

cnf(3295,plain,
    equal(multiply(A,multiply(multiply(inverse(multiply(inverse(B),A)),multiply(multiply(inverse(multiply(multiply(C,inverse(D)),B)),C),E)),F)),multiply(D,multiply(G,inverse(multiply(inverse(F),multiply(inverse(E),G)))))),
    inference(flip,[status(thm),theory(equality)],[3294]),
    [iquote('flip(3294)')] ).

cnf(3297,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(A,C)),D)),inverse(C))))),multiply(D,B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3096]),3257,3195,2775]),
    [iquote('back_demod(3096),demod([3257,3195,2775])')] ).

cnf(3298,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,B),C)),A)),multiply(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3104]),3297]),1]),
    [iquote('back_demod(3104),demod([3297]),flip(1)')] ).

cnf(3300,plain,
    equal(multiply(multiply(A,inverse(B)),multiply(C,D)),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(multiply(E,inverse(B)),C)),E))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3102]),3195,3298,3195]),
    [iquote('back_demod(3102),demod([3195,3298,3195])')] ).

cnf(3301,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(multiply(C,inverse(D)),E)),C)))),multiply(multiply(A,inverse(D)),multiply(E,B))),
    inference(flip,[status(thm),theory(equality)],[3300]),
    [iquote('flip(3300)')] ).

cnf(3302,plain,
    equal(multiply(A,multiply(B,inverse(B))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3084]),3298,3256]),
    [iquote('back_demod(3084),demod([3298,3256])')] ).

cnf(3308,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(multiply(multiply(D,inverse(B)),E)),D)))),multiply(inverse(multiply(multiply(F,inverse(A)),G)),F)))),multiply(G,multiply(inverse(C),inverse(E)))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3027]),3257,3298,3195,3195]),1]),
    [iquote('back_demod(3027),demod([3257,3298,3195,3195]),flip(1)')] ).

cnf(3316,plain,
    equal(multiply(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),E),multiply(A,inverse(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(F,multiply(B,inverse(D))),C)),multiply(F,inverse(E)))),multiply(inverse(multiply(multiply(F,multiply(B,inverse(D))),C)),F))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2960]),3298,3256,3256]),
    [iquote('back_demod(2960),demod([3298,3256,3256])')] ).

cnf(3317,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),multiply(E,inverse(F)))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),E)))),multiply(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),F)),
    inference(flip,[status(thm),theory(equality)],[3316]),
    [iquote('flip(3316)')] ).

cnf(3320,plain,
    equal(multiply(A,multiply(inverse(multiply(multiply(B,C),D)),B)),multiply(A,multiply(inverse(D),inverse(C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2954]),3298,3195,3195,3308]),
    [iquote('back_demod(2954),demod([3298,3195,3195,3308])')] ).

cnf(3323,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),multiply(E,inverse(F)))),multiply(inverse(C),multiply(D,inverse(B)))))),multiply(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),F)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3317]),3320,3195]),
    [iquote('back_demod(3317),demod([3320,3195])')] ).

cnf(3324,plain,
    equal(multiply(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),E),multiply(A,inverse(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(multiply(multiply(F,multiply(B,inverse(D))),C)),multiply(F,inverse(E)))),multiply(inverse(C),multiply(D,inverse(B))))))),
    inference(flip,[status(thm),theory(equality)],[3323]),
    [iquote('flip(3323)')] ).

cnf(3332,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(D),B)))),multiply(inverse(E),A)))),multiply(E,multiply(inverse(C),inverse(D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3308]),3320,2775,3320,2775]),
    [iquote('back_demod(3308),demod([3320,2775,3320,2775])')] ).

cnf(3338,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),D)))),multiply(multiply(A,inverse(D)),multiply(C,B))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3301]),3320,2775]),
    [iquote('back_demod(3301),demod([3320,2775])')] ).

cnf(3339,plain,
    equal(multiply(multiply(A,inverse(B)),multiply(C,D)),multiply(A,inverse(multiply(inverse(D),multiply(inverse(C),B))))),
    inference(flip,[status(thm),theory(equality)],[3338]),
    [iquote('flip(3338)')] ).

cnf(3359,plain,
    equal(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),inverse(C))),multiply(inverse(B),inverse(C))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3257]),3320]),
    [iquote('back_demod(3257),demod([3320])')] ).

cnf(3371,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(multiply(B,inverse(multiply(C,D))),E)),multiply(inverse(multiply(multiply(C,inverse(multiply(F,multiply(B,inverse(D))))),F)),A)))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3238]),3320,2775]),
    [iquote('back_demod(3238),demod([3320,2775])')] ).

cnf(3379,plain,
    equal(multiply(multiply(A,inverse(B)),C),multiply(A,inverse(multiply(multiply(multiply(D,inverse(multiply(inverse(E),F))),multiply(inverse(E),multiply(F,multiply(inverse(D),inverse(multiply(inverse(multiply(B,multiply(D,inverse(multiply(inverse(E),F))))),C)))))),multiply(inverse(E),multiply(F,inverse(D))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3100]),3195,3320,3195,3256,3256,3256,3320,3195]),
    [iquote('back_demod(3100),demod([3195,3320,3195,3256,3256,3256,3320,3195])')] ).

cnf(3380,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(B,inverse(multiply(inverse(C),D))),multiply(inverse(C),multiply(D,multiply(inverse(B),inverse(multiply(inverse(multiply(E,multiply(B,inverse(multiply(inverse(C),D))))),F)))))),multiply(inverse(C),multiply(D,inverse(B)))))),multiply(multiply(A,inverse(E)),F)),
    inference(flip,[status(thm),theory(equality)],[3379]),
    [iquote('flip(3379)')] ).

cnf(3383,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(inverse(E),C)),multiply(inverse(E),A)))))),multiply(D,B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3083]),3320,3359,3359,3359,3195,2775,3195,3320,2775]),1]),
    [iquote('back_demod(3083),demod([3320,3359,3359,3359,3195,2775,3195,3320,2775]),flip(1)')] ).

cnf(3386,plain,
    equal(inverse(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(B),multiply(C,multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(D),multiply(A,inverse(multiply(inverse(B),C))))),E)))))),multiply(inverse(B),multiply(C,inverse(A))))),multiply(D,E)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3078]),3320,3195,3256,3256,3256,3320,3195,3195,3320,2775,3383]),
    [iquote('back_demod(3078),demod([3320,3195,3256,3256,3256,3320,3195,3195,3320,2775,3383])')] ).

cnf(3391,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),A)))),multiply(C,B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3066]),3320,3359,3359,3359,3195,2775,3195,3320,2775]),1]),
    [iquote('back_demod(3066),demod([3320,3359,3359,3359,3195,2775,3195,3320,2775]),flip(1)')] ).

cnf(3396,plain,
    equal(multiply(multiply(multiply(A,inverse(multiply(B,multiply(C,inverse(D))))),B),multiply(multiply(C,inverse(multiply(A,D))),E)),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3371]),3391]),
    [iquote('back_demod(3371),demod([3391])')] ).

cnf(3418,plain,
    equal(multiply(A,inverse(multiply(multiply(B,C),multiply(inverse(D),A)))),multiply(D,multiply(inverse(C),inverse(B)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3332]),3391]),
    [iquote('back_demod(3332),demod([3391])')] ).

cnf(3425,plain,
    equal(multiply(A,multiply(multiply(inverse(multiply(inverse(B),A)),multiply(multiply(inverse(multiply(multiply(C,inverse(D)),B)),C),E)),F)),multiply(D,multiply(E,F))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3295]),3391]),
    [iquote('back_demod(3295),demod([3391])')] ).

cnf(3426,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),multiply(A,multiply(multiply(B,inverse(D)),C))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3288]),3425]),
    [iquote('back_demod(3288),demod([3425])')] ).

cnf(3427,plain,
    equal(multiply(A,multiply(multiply(B,inverse(C)),D)),multiply(A,multiply(B,inverse(multiply(inverse(D),C))))),
    inference(flip,[status(thm),theory(equality)],[3426]),
    [iquote('flip(3426)')] ).

cnf(3441,plain,
    equal(inverse(multiply(A,multiply(B,inverse(C)))),multiply(C,multiply(inverse(B),inverse(A)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3039]),3320,3359,3320,3359,3195,2775,3256,3195,3320,2775,3391,3195,3320,2775,3418]),
    [iquote('back_demod(3039),demod([3320,3359,3320,3359,3195,2775,3256,3195,3320,2775,3391,3195,3320,2775,3418])')] ).

cnf(3469,plain,
    equal(multiply(multiply(multiply(A,multiply(B,multiply(inverse(C),inverse(D)))),D),multiply(multiply(C,inverse(multiply(A,B))),E)),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3396]),3441]),
    [iquote('back_demod(3396),demod([3441])')] ).

cnf(3470,plain,
    equal(inverse(multiply(multiply(multiply(A,inverse(multiply(inverse(B),C))),multiply(inverse(B),multiply(C,multiply(inverse(A),inverse(multiply(multiply(multiply(inverse(B),C),multiply(inverse(A),D)),E)))))),multiply(inverse(B),multiply(C,inverse(A))))),multiply(D,E)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3386]),3441,2775]),
    [iquote('back_demod(3386),demod([3441,2775])')] ).

cnf(3474,plain,
    equal(multiply(multiply(A,inverse(B)),C),multiply(A,multiply(inverse(B),C))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3380]),3441,3470]),1]),
    [iquote('back_demod(3380),demod([3441,3470]),flip(1)')] ).

cnf(3478,plain,
    equal(multiply(multiply(multiply(A,multiply(B,multiply(inverse(C),inverse(D)))),D),multiply(C,multiply(inverse(multiply(A,B)),E))),E),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3469]),3474]),
    [iquote('back_demod(3469),demod([3474])')] ).

cnf(3491,plain,
    equal(multiply(A,multiply(B,inverse(multiply(inverse(C),D)))),multiply(A,multiply(B,multiply(inverse(D),C)))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3427]),3474]),1]),
    [iquote('back_demod(3427),demod([3474]),flip(1)')] ).

cnf(3509,plain,
    equal(multiply(multiply(A,multiply(B,multiply(inverse(C),D))),E),multiply(A,inverse(multiply(multiply(B,multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(multiply(F,multiply(B,inverse(C))),D)),multiply(F,inverse(E))))),multiply(inverse(D),multiply(C,inverse(B))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3324]),3491,3474]),
    [iquote('back_demod(3324),demod([3491,3474])')] ).

cnf(3510,plain,
    equal(multiply(A,inverse(multiply(multiply(B,multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(multiply(E,multiply(B,inverse(D))),C)),multiply(E,inverse(F))))),multiply(inverse(C),multiply(D,inverse(B)))))),multiply(multiply(A,multiply(B,multiply(inverse(D),C))),F)),
    inference(flip,[status(thm),theory(equality)],[3509]),
    [iquote('flip(3509)')] ).

cnf(3514,plain,
    equal(multiply(multiply(A,multiply(B,inverse(C))),D),multiply(A,multiply(B,multiply(inverse(C),D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3086]),3491]),
    [iquote('back_demod(3086),demod([3491])')] ).

cnf(3517,plain,
    equal(multiply(A,inverse(multiply(multiply(B,multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(E,multiply(B,multiply(inverse(D),C)))),multiply(E,inverse(F))))),multiply(inverse(C),multiply(D,inverse(B)))))),multiply(multiply(A,multiply(B,multiply(inverse(D),C))),F)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3510]),3514]),
    [iquote('back_demod(3510),demod([3514])')] ).

cnf(3518,plain,
    equal(multiply(multiply(A,multiply(B,multiply(inverse(C),D))),E),multiply(A,inverse(multiply(multiply(B,multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(F,multiply(B,multiply(inverse(C),D)))),multiply(F,inverse(E))))),multiply(inverse(D),multiply(C,inverse(B))))))),
    inference(flip,[status(thm),theory(equality)],[3517]),
    [iquote('flip(3517)')] ).

cnf(3534,plain,
    equal(multiply(A,multiply(inverse(A),B)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3245]),3514,3193,3514,3194,2775,3474,3193]),
    [iquote('back_demod(3245),demod([3514,3193,3514,3194,2775,3474,3193])')] ).

cnf(3547,plain,
    equal(multiply(A,inverse(multiply(B,multiply(inverse(multiply(inverse(C),D)),multiply(inverse(E),A))))),multiply(E,inverse(multiply(B,multiply(inverse(D),C))))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3005]),3514,3194,3195,2775,3320,3441,2775,2777,3195,3474,3194,3256,3491]),1]),
    [iquote('back_demod(3005),demod([3514,3194,3195,2775,3320,3441,2775,2777,3195,3474,3194,3256,3491]),flip(1)')] ).

cnf(3550,plain,
    equal(inverse(multiply(A,multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(A,multiply(inverse(C),B))),multiply(inverse(D),multiply(E,multiply(inverse(F),G))))))),multiply(inverse(multiply(inverse(multiply(F,multiply(inverse(E),H))),G)),inverse(multiply(inverse(D),H)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2997]),3514,3194,3256,3491,3474,3256,3256,3491,3514,3194,3256,3256,3256,3256,3256,3256,3256,2777,3302,3491,3195,3474]),
    [iquote('back_demod(2997),demod([3514,3194,3256,3491,3474,3256,3256,3491,3514,3194,3256,3256,3256,3256,3256,3256,3256,2777,3302,3491,3195,3474])')] ).

cnf(3551,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),C))),D)),inverse(multiply(inverse(E),C))),inverse(multiply(F,multiply(inverse(multiply(inverse(G),H)),multiply(inverse(multiply(F,multiply(inverse(H),G))),multiply(inverse(E),multiply(B,multiply(inverse(A),D)))))))),
    inference(flip,[status(thm),theory(equality)],[3550]),
    [iquote('flip(3550)')] ).

cnf(3557,plain,
    equal(multiply(multiply(A,multiply(B,multiply(inverse(C),D))),E),multiply(A,inverse(multiply(B,multiply(inverse(multiply(inverse(D),C)),multiply(inverse(multiply(B,multiply(inverse(C),D))),multiply(inverse(E),inverse(multiply(B,multiply(inverse(C),D)))))))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2971]),3491,3320,3359,3359,3195,2775,3514,3194,3256,3256,3256,3514,3194,3256,3256,3256]),
    [iquote('back_demod(2971),demod([3491,3320,3359,3359,3195,2775,3514,3194,3256,3256,3256,3514,3194,3256,3256,3256])')] ).

cnf(3558,plain,
    equal(multiply(A,inverse(multiply(B,multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(B,multiply(inverse(D),C))),multiply(inverse(E),inverse(multiply(B,multiply(inverse(D),C))))))))),multiply(multiply(A,multiply(B,multiply(inverse(D),C))),E)),
    inference(flip,[status(thm),theory(equality)],[3557]),
    [iquote('flip(3557)')] ).

cnf(3559,plain,
    equal(inverse(multiply(A,multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(A,multiply(inverse(C),B))),multiply(inverse(D),inverse(E)))))),multiply(E,D)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2969]),3514,3194,3256,3491,3256,3256,3491,3514,3194,3256,3256,3256,3256,3256,3256,2777,3302,3195,3474,3194,3491,3547,3391]),
    [iquote('back_demod(2969),demod([3514,3194,3256,3491,3256,3256,3491,3514,3194,3256,3256,3256,3256,3256,3256,2777,3302,3195,3474,3194,3491,3547,3391])')] ).

cnf(3560,plain,
    equal(multiply(multiply(A,multiply(B,multiply(inverse(C),D))),E),multiply(A,multiply(multiply(B,multiply(inverse(C),D)),E))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3558]),3559]),1]),
    [iquote('back_demod(3558),demod([3559]),flip(1)')] ).

cnf(3566,plain,
    equal(multiply(A,inverse(multiply(B,multiply(multiply(inverse(multiply(inverse(C),D)),multiply(inverse(multiply(E,multiply(B,multiply(inverse(D),C)))),multiply(E,inverse(F)))),multiply(inverse(C),multiply(D,inverse(B))))))),multiply(A,multiply(multiply(B,multiply(inverse(D),C)),F))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3518]),3560,3560]),1]),
    [iquote('back_demod(3518),demod([3560,3560]),flip(1)')] ).

cnf(3575,plain,
    equal(multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3478]),3560,3514,2776,3514,3193]),
    [iquote('back_demod(3478),demod([3560,3514,2776,3514,3193])')] ).

cnf(3615,plain,
    equal(multiply(A,inverse(multiply(B,multiply(C,multiply(inverse(D),A))))),multiply(D,multiply(inverse(C),inverse(B)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2913]),3298,3195,3474,3194,3256,3491,3474,2776,3256,3534,3474,2776,3441,2775,3514,3194,3441]),
    [iquote('back_demod(2913),demod([3298,3195,3474,3194,3256,3491,3474,2776,3256,3534,3474,2776,3441,2775,3514,3194,3441])')] ).

cnf(3618,plain,
    equal(multiply(A,inverse(multiply(B,multiply(inverse(C),D)))),multiply(A,multiply(inverse(D),multiply(C,inverse(B))))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3547]),3615,2775,3256]),1]),
    [iquote('back_demod(3547),demod([3615,2775,3256]),flip(1)')] ).

cnf(3649,plain,
    equal(multiply(A,inverse(multiply(B,C))),multiply(A,multiply(inverse(C),inverse(B)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3418]),3618,3534]),
    [iquote('back_demod(3418),demod([3618,3534])')] ).

cnf(3669,plain,
    equal(inverse(multiply(inverse(A),B)),multiply(inverse(B),A)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2341]),3195,3474,3194,2775,3194,3649,2775,3474,3534,2775,3194,3256,3256,3302]),
    [iquote('back_demod(2341),demod([3195,3474,3194,2775,3194,3649,2775,3474,3534,2775,3194,3256,3256,3302])')] ).

cnf(3706,plain,
    equal(multiply(A,multiply(inverse(multiply(multiply(multiply(inverse(B),C),multiply(inverse(multiply(D,multiply(E,multiply(inverse(B),C)))),multiply(D,inverse(F)))),multiply(inverse(C),multiply(B,inverse(E))))),inverse(E))),multiply(A,multiply(multiply(E,multiply(inverse(B),C)),F))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3566]),3669,3649]),
    [iquote('back_demod(3566),demod([3669,3649])')] ).

cnf(3709,plain,
    equal(multiply(inverse(A),multiply(multiply(B,multiply(inverse(C),D)),multiply(inverse(D),E))),multiply(inverse(multiply(C,multiply(inverse(B),A))),E)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3551]),3669,3669,3560,3669,3575,3669]),
    [iquote('back_demod(3551),demod([3669,3669,3560,3669,3575,3669])')] ).

cnf(3710,plain,
    equal(multiply(inverse(multiply(A,multiply(inverse(B),C))),D),multiply(inverse(C),multiply(multiply(B,multiply(inverse(A),E)),multiply(inverse(E),D)))),
    inference(flip,[status(thm),theory(equality)],[3709]),
    [iquote('flip(3709)')] ).

cnf(3722,plain,
    equal(multiply(A,multiply(multiply(multiply(inverse(A),B),multiply(multiply(inverse(B),C),D)),E)),multiply(C,multiply(D,E))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3425]),3669,3474,3194,3669]),
    [iquote('back_demod(3425),demod([3669,3474,3194,3669])')] ).

cnf(3730,plain,
    equal(multiply(A,multiply(multiply(inverse(B),C),D)),multiply(A,multiply(inverse(B),multiply(C,D)))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3339]),3474,3669,3669]),1]),
    [iquote('back_demod(3339),demod([3474,3669,3669]),flip(1)')] ).

cnf(3734,plain,
    equal(multiply(A,multiply(multiply(multiply(inverse(A),B),multiply(inverse(B),multiply(C,D))),E)),multiply(C,multiply(D,E))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3722]),3730]),
    [iquote('back_demod(3722),demod([3730])')] ).

cnf(3782,plain,
    equal(multiply(multiply(A,multiply(inverse(B),C)),multiply(inverse(C),D)),multiply(A,multiply(inverse(B),D))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3129]),3669,3669]),
    [iquote('back_demod(3129),demod([3669,3669])')] ).

cnf(3783,plain,
    equal(multiply(inverse(multiply(A,multiply(inverse(B),C))),D),multiply(inverse(C),multiply(B,multiply(inverse(A),D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3710]),3782]),
    [iquote('back_demod(3710),demod([3782])')] ).

cnf(3797,plain,
    equal(multiply(A,multiply(multiply(B,multiply(inverse(C),D)),E)),multiply(A,multiply(B,multiply(inverse(C),multiply(D,E))))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3706]),3783,3195,3783,3195,3669,3256,3560,3782,3193,3302,3474,2776,3474]),1]),
    [iquote('back_demod(3706),demod([3783,3195,3783,3195,3669,3256,3560,3782,3193,3302,3474,2776,3474]),flip(1)')] ).

cnf(3803,plain,
    equal(multiply(multiply(A,B),C),multiply(A,multiply(B,C))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[3734]),3797,3730,3534,3534]),
    [iquote('back_demod(3734),demod([3797,3730,3534,3534])')] ).

cnf(3804,plain,
    $false,
    inference(conflict,[status(thm)],[3803,2]),
    [iquote('conflict(3803,2)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP414-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % Command  : tptp2X_and_run_eqp %s
% 0.12/0.33  % Computer : n014.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 13:21:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.88/2.24  ----- EQP 0.9e, May 2009 -----
% 1.88/2.24  The job began on n014.cluster.edu, Tue Jun 14 13:21:37 2022
% 1.88/2.24  The command was "./eqp09e".
% 1.88/2.24  
% 1.88/2.24  set(prolog_style_variables).
% 1.88/2.24  set(lrpo).
% 1.88/2.24  set(basic_paramod).
% 1.88/2.24  set(functional_subsume).
% 1.88/2.24  set(ordered_paramod).
% 1.88/2.24  set(prime_paramod).
% 1.88/2.24  set(para_pairs).
% 1.88/2.24  assign(pick_given_ratio,4).
% 1.88/2.24  clear(print_kept).
% 1.88/2.24  clear(print_new_demod).
% 1.88/2.24  clear(print_back_demod).
% 1.88/2.24  clear(print_given).
% 1.88/2.24  assign(max_mem,64000).
% 1.88/2.24  end_of_commands.
% 1.88/2.24  
% 1.88/2.24  Usable:
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Sos:
% 1.88/2.24  0 (wt=-1) [] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C.
% 1.88/2.24  0 (wt=-1) [] -(multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3))).
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Demodulators:
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Passive:
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Starting to process input.
% 1.88/2.24  
% 1.88/2.24  ** KEPT: 1 (wt=20) [] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C.
% 1.88/2.24  1 is a new demodulator.
% 1.88/2.24  
% 1.88/2.24  ** KEPT: 2 (wt=11) [] -(multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3))).
% 1.88/2.24  ---------------- PROOF FOUND ----------------
% 1.88/2.24  % SZS status Unsatisfiable
% 1.88/2.24  
% 1.88/2.24  
% 1.88/2.24  After processing input:
% 1.88/2.24  
% 1.88/2.24  Usable:
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Sos:
% 1.88/2.24  2 (wt=11) [] -(multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3))).
% 1.88/2.24  1 (wt=20) [] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C.
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Demodulators:
% 1.88/2.24  1 (wt=20) [] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C.
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  Passive:
% 1.88/2.24  end_of_list.
% 1.88/2.24  
% 1.88/2.24  UNIT CONFLICT from 3803 and 2 at   1.08 seconds.
% 1.88/2.24  
% 1.88/2.24  ---------------- PROOF ----------------
% 1.88/2.24  % SZS output start Refutation
% See solution above
% 1.88/2.25  ------------ end of proof -------------
% 1.88/2.25  
% 1.88/2.25  
% 1.88/2.25  ------------- memory usage ------------
% 1.88/2.25  Memory dynamically allocated (tp_alloc): 41992.
% 1.88/2.25    type (bytes each)        gets      frees     in use      avail      bytes
% 1.88/2.25  sym_ent (  96)               56          0         56          0      5.2 K
% 1.88/2.25  term (  16)             1428206     970671     457535       1073   8942.3 K
% 1.88/2.25  gen_ptr (   8)          4255651     657680    3597971        404  28112.3 K
% 1.88/2.25  context ( 808)           767899     767897          2         11     10.3 K
% 1.88/2.25  trail (  12)             199988     199988          0         14      0.2 K
% 1.88/2.25  bt_node (  68)            47699      47696          3        522     34.9 K
% 1.88/2.25  ac_position (285432)          0          0          0          0      0.0 K
% 1.88/2.25  ac_match_pos (14044)          0          0          0          0      0.0 K
% 1.88/2.25  ac_match_free_vars_pos (4020)
% 1.88/2.25                                0          0          0          0      0.0 K
% 1.88/2.25  discrim (  12)           444538     422887      21651     275095   3477.5 K
% 1.88/2.25  flat (  40)             5669715    5669715          0       1595     62.3 K
% 1.88/2.25  discrim_pos (  12)        39037      39037          0          1      0.0 K
% 1.88/2.25  fpa_head (  12)           13319          0      13319          0    156.1 K
% 1.88/2.25  fpa_tree (  28)           20374      20374          0         73      2.0 K
% 1.88/2.25  fpa_pos (  36)             5576       5576          0          1      0.0 K
% 1.88/2.25  literal (  12)            13615       9812       3803          1     44.6 K
% 1.88/2.25  clause (  24)             13615       9812       3803          1     89.2 K
% 1.88/2.25  list (  12)                1832       1747         85          1      1.0 K
% 1.88/2.25  list_pos (  20)           25740      14508      11232        242    224.1 K
% 1.88/2.25  pair_index (   40)              2          0          2          0      0.1 K
% 1.88/2.25  
% 1.88/2.25  -------------- statistics -------------
% 1.88/2.25  Clauses input                  2
% 1.88/2.25    Usable input                   0
% 1.88/2.25    Sos input                      2
% 1.88/2.25    Demodulators input             0
% 1.88/2.25    Passive input                  0
% 1.88/2.25  
% 1.88/2.25  Processed BS (before search)   2
% 1.88/2.25  Forward subsumed BS            0
% 1.88/2.25  Kept BS                        2
% 1.88/2.25  New demodulators BS            1
% 1.88/2.25  Back demodulated BS            0
% 1.88/2.25  
% 1.88/2.25  Clauses or pairs given      1760
% 1.88/2.25  Clauses generated           7184
% 1.88/2.25  Forward subsumed            3383
% 1.88/2.25  Deleted by weight              0
% 1.88/2.25  Deleted by variable count      0
% 1.88/2.25  Kept                        3801
% 1.88/2.25  New demodulators            1772
% 1.88/2.25  Back demodulated            3199
% 1.88/2.25  Ordered paramod prunes         0
% 1.88/2.25  Basic paramod prunes       44106
% 1.88/2.25  Prime paramod prunes          33
% 1.88/2.25  Semantic prunes                0
% 1.88/2.25  
% 1.88/2.25  Rewrite attmepts          655554
% 1.88/2.25  Rewrites                   36656
% 1.88/2.25  
% 1.88/2.25  FPA overloads                  0
% 1.88/2.25  FPA underloads                 0
% 1.88/2.25  
% 1.88/2.25  Usable size                    0
% 1.88/2.25  Sos size                     603
% 1.88/2.25  Demodulators size            258
% 1.88/2.25  Passive size                   0
% 1.88/2.25  Disabled size               3199
% 1.88/2.25  
% 1.88/2.25  Proofs found                   1
% 1.88/2.25  
% 1.88/2.25  ----------- times (seconds) ----------- Tue Jun 14 13:21:38 2022
% 1.88/2.25  
% 1.88/2.25  user CPU time             1.09   (0 hr, 0 min, 1 sec)
% 1.88/2.25  system CPU time           0.10   (0 hr, 0 min, 0 sec)
% 1.88/2.25  wall-clock time           1      (0 hr, 0 min, 1 sec)
% 1.88/2.25  input time                0.00
% 1.88/2.25  paramodulation time       0.04
% 1.88/2.25  demodulation time         0.18
% 1.88/2.25  orient time               0.03
% 1.88/2.25  weigh time                0.01
% 1.88/2.25  forward subsume time      0.02
% 1.88/2.25  back demod find time      0.16
% 1.88/2.25  conflict time             0.00
% 1.88/2.25  LRPO time                 0.02
% 1.88/2.25  store clause time         0.51
% 1.88/2.25  disable clause time       0.06
% 1.88/2.25  prime paramod time        0.02
% 1.88/2.25  semantics time            0.00
% 1.88/2.25  
% 1.88/2.25  EQP interrupted
%------------------------------------------------------------------------------