%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP384_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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  : 300s
% DateTime : Tue May  7 07:51:07 EDT 2024

% Result   : Theorem 22.05s 5.99s
% Output   : Refutation 22.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1436
% Syntax   : Number of formulae    : 2090 ( 437 unt; 784 typ;   0 def)
%            Number of atoms       : 3142 (1540 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 17780 (  20   ~;   0   |; 843   &;15924   @)
%                                         (  51 <=>; 942  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Number of types       :  215 ( 214 usr)
%            Number of type conns  : 1053 (1053   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  573 ( 570 usr;  55 con; 0-4 aty)
%            Number of variables   : 4055 (   0   ^4019   !;  36   ?;4055   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'B_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_a_prod_update_a_b_prod_update_fun$\'_type',type,
    '\'C_a_prod_update_a_b_prod_update_fun$\'': $tType ).

thf('\'A_update_set_a_update_fun$\'_type',type,
    '\'A_update_set_a_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_a_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_a_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_b_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_b_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_a_a_prod_update_fun$\'_type',type,
    '\'B_update_a_a_prod_update_fun$\'': $tType ).

thf('\'B_c_prod_update_b_b_prod_update_fun$\'_type',type,
    '\'B_c_prod_update_b_b_prod_update_fun$\'': $tType ).

thf('\'C_c_prod_update_b_b_prod_update_fun$\'_type',type,
    '\'C_c_prod_update_b_b_prod_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_a_prod_update_c_update_fun$\'_type',type,
    '\'A_a_prod_update_c_update_fun$\'': $tType ).

thf('\'A_update_set$\'_type',type,
    '\'A_update_set$\'': $tType ).

thf('\'C_update_c_update_fun_bool_fun$\'_type',type,
    '\'C_update_c_update_fun_bool_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'': $tType ).

thf('\'B_c_prod_update_a_update_fun$\'_type',type,
    '\'B_c_prod_update_a_update_fun$\'': $tType ).

thf('\'A_a_prod_update$\'_type',type,
    '\'A_a_prod_update$\'': $tType ).

thf('\'B_update_a_c_prod_update_fun$\'_type',type,
    '\'B_update_a_c_prod_update_fun$\'': $tType ).

thf('\'C_b_prod_update_b_c_prod_update_fun$\'_type',type,
    '\'C_b_prod_update_b_c_prod_update_fun$\'': $tType ).

thf('\'B_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_a_update_b_update_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_a_update_b_update_fun_fun$\'': $tType ).

thf('\'B_update_c_update_fun_b_update_c_update_fun_fun$\'_type',type,
    '\'B_update_c_update_fun_b_update_c_update_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_c_update_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_c_update_fun_fun$\'': $tType ).

thf('\'C_update_b_update_fun_c_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_b_update_fun_c_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_b_update_a_update_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'': $tType ).

thf('\'B_c_prod_update_a_a_prod_update_fun$\'_type',type,
    '\'B_c_prod_update_a_a_prod_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_c_a_prod_update_fun$\'_type',type,
    '\'B_update_c_a_prod_update_fun$\'': $tType ).

thf('\'C_update_c_update_fun_a_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_a_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_a_prod_update$\'_type',type,
    '\'C_a_prod_update$\'': $tType ).

thf('\'A_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update$\'_type',type,
    '\'A_update$\'': $tType ).

thf('\'C_update_c_update_fun_b_update_c_update_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_b_update_c_update_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_a_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_a_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_b_prod_update$\'_type',type,
    '\'B_b_prod_update$\'': $tType ).

thf('\'B_update_a_update_fun$\'_type',type,
    '\'B_update_a_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_a_update_b_update_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_a_update_b_update_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_b_prod_update_b_a_prod_update_fun$\'_type',type,
    '\'A_b_prod_update_b_a_prod_update_fun$\'': $tType ).

thf('\'A_a_prod_update_a_a_prod_update_fun$\'_type',type,
    '\'A_a_prod_update_a_a_prod_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_a_update_a_update_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_c_update_c_update_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'': $tType ).

thf('\'A_a_prod_update_b_update_fun$\'_type',type,
    '\'A_a_prod_update_b_update_fun$\'': $tType ).

thf('\'B_c_prod_update_b_c_prod_update_fun$\'_type',type,
    '\'B_c_prod_update_b_c_prod_update_fun$\'': $tType ).

thf('\'C_c_prod_update_a_update_fun$\'_type',type,
    '\'C_c_prod_update_a_update_fun$\'': $tType ).

thf('\'A_update_set_a_update_set_fun$\'_type',type,
    '\'A_update_set_a_update_set_fun$\'': $tType ).

thf('\'C_b_prod_update_b_b_prod_update_fun$\'_type',type,
    '\'C_b_prod_update_b_b_prod_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_c_prod_update_a_c_prod_update_fun$\'_type',type,
    '\'A_c_prod_update_a_c_prod_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_set$\'_type',type,
    '\'C_update_a_update_fun_set$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_b_update_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_b_update_fun_fun$\'': $tType ).

thf('\'A_c_prod_update$\'_type',type,
    '\'A_c_prod_update$\'': $tType ).

thf('\'C_update_c_update_fun_b_update_b_update_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'': $tType ).

thf('\'B_update_c_update_bool_fun_fun$\'_type',type,
    '\'B_update_c_update_bool_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_c_update_b_update_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_c_update_b_update_fun_fun$\'': $tType ).

thf('\'C_update_b_update_fun_c_update_c_update_fun_fun$\'_type',type,
    '\'C_update_b_update_fun_c_update_c_update_fun_fun$\'': $tType ).

thf('\'C_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_set$\'_type',type,
    '\'A_update_b_update_fun_set$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'': $tType ).

thf('\'B_b_prod_update_b_c_prod_update_fun$\'_type',type,
    '\'B_b_prod_update_b_c_prod_update_fun$\'': $tType ).

thf('\'A_update_a_update_bool_fun_fun$\'_type',type,
    '\'A_update_a_update_bool_fun_fun$\'': $tType ).

thf('\'C_a_prod_update_b_update_fun$\'_type',type,
    '\'C_a_prod_update_b_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_c_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_c_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_b_prod_update_b_update_fun$\'_type',type,
    '\'C_b_prod_update_b_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_c_prod_update_b_c_prod_update_fun$\'_type',type,
    '\'C_c_prod_update_b_c_prod_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_a_prod_update_b_a_prod_update_fun$\'_type',type,
    '\'B_a_prod_update_b_a_prod_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_b_update_fun_bool_fun$\'_type',type,
    '\'B_update_b_update_fun_bool_fun$\'': $tType ).

thf('\'B_b_prod_update_b_update_fun$\'_type',type,
    '\'B_b_prod_update_b_update_fun$\'': $tType ).

thf('\'A_update_a_c_prod_update_fun$\'_type',type,
    '\'A_update_a_c_prod_update_fun$\'': $tType ).

thf('\'C_update_c_update_fun_c_update_b_update_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_c_update_b_update_fun_fun$\'': $tType ).

thf('\'B_b_prod_update_a_a_prod_update_fun$\'_type',type,
    '\'B_b_prod_update_a_a_prod_update_fun$\'': $tType ).

thf('\'C_c_prod_update_c_c_prod_update_fun$\'_type',type,
    '\'C_c_prod_update_c_c_prod_update_fun$\'': $tType ).

thf('\'A_update_a_update_fun$\'_type',type,
    '\'A_update_a_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun$\'_type',type,
    '\'A_update_b_update_fun$\'': $tType ).

thf('\'C_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_bool_fun$\'_type',type,
    '\'A_update_a_update_fun_bool_fun$\'': $tType ).

thf('\'C_c_prod_update$\'_type',type,
    '\'C_c_prod_update$\'': $tType ).

thf('\'A_a_prod_update_c_c_prod_update_fun$\'_type',type,
    '\'A_a_prod_update_c_c_prod_update_fun$\'': $tType ).

thf('\'B_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_b_update_fun_c_update_b_update_fun_fun$\'_type',type,
    '\'C_update_b_update_fun_c_update_b_update_fun_fun$\'': $tType ).

thf('\'A_b_prod_update_a_b_prod_update_fun$\'_type',type,
    '\'A_b_prod_update_a_b_prod_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_set$\'_type',type,
    '\'B_update_a_update_fun_set$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_c_update_fun$\'_type',type,
    '\'B_update_c_update_fun$\'': $tType ).

thf('\'C_update_b_update_fun$\'_type',type,
    '\'C_update_b_update_fun$\'': $tType ).

thf('\'B_a_prod_update_a_b_prod_update_fun$\'_type',type,
    '\'B_a_prod_update_a_b_prod_update_fun$\'': $tType ).

thf('\'C_c_prod_update_c_update_fun$\'_type',type,
    '\'C_c_prod_update_c_update_fun$\'': $tType ).

thf('\'C_update_bool_fun$\'_type',type,
    '\'C_update_bool_fun$\'': $tType ).

thf('\'C_update$\'_type',type,
    '\'C_update$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_a_update_c_update_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'': $tType ).

thf('\'B_a_prod_update_a_update_fun$\'_type',type,
    '\'B_a_prod_update_a_update_fun$\'': $tType ).

thf('\'C_update_set_c_update_set_fun$\'_type',type,
    '\'C_update_set_c_update_set_fun$\'': $tType ).

thf('\'C_update_c_update_fun_c_update_c_update_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'B_b_prod_update_c_update_fun$\'_type',type,
    '\'B_b_prod_update_c_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_c_update_a_update_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_c_update_a_update_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_a_update_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_a_update_fun_fun$\'': $tType ).

thf('\'C_c_prod_update_b_update_fun$\'_type',type,
    '\'C_c_prod_update_b_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_bool_fun$\'_type',type,
    '\'B_update_a_update_fun_bool_fun$\'': $tType ).

thf('\'C_update_b_update_fun_a_update_a_update_fun_fun$\'_type',type,
    '\'C_update_b_update_fun_a_update_a_update_fun_fun$\'': $tType ).

thf('\'B_b_prod_update_b_b_prod_update_fun$\'_type',type,
    '\'B_b_prod_update_b_b_prod_update_fun$\'': $tType ).

thf('\'C_a_prod_update_b_a_prod_update_fun$\'_type',type,
    '\'C_a_prod_update_b_a_prod_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_c_update_a_update_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_c_update_a_update_fun_fun$\'': $tType ).

thf('\'B_update_b_update_fun_c_update_c_update_fun_fun$\'_type',type,
    '\'B_update_b_update_fun_c_update_c_update_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_b_update_fun_a_update_a_update_fun_fun$\'_type',type,
    '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'': $tType ).

thf('\'C_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun$\'_type',type,
    '\'A_update_c_update_fun$\'': $tType ).

thf('\'A_update_c_update_fun_b_update_a_update_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'': $tType ).

thf('\'A_update_c_c_prod_update_fun$\'_type',type,
    '\'A_update_c_c_prod_update_fun$\'': $tType ).

thf('\'C_a_prod_update_c_update_fun$\'_type',type,
    '\'C_a_prod_update_c_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_set_b_update_set_fun$\'_type',type,
    '\'B_update_set_b_update_set_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'': $tType ).

thf('\'A_a_prod_update_b_b_prod_update_fun$\'_type',type,
    '\'A_a_prod_update_b_b_prod_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_b_prod_update$\'_type',type,
    '\'A_b_prod_update$\'': $tType ).

thf('\'B_update_set_b_update_fun$\'_type',type,
    '\'B_update_set_b_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_b_update_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_b_update_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_a_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_a_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_a_prod_update_a_c_prod_update_fun$\'_type',type,
    '\'B_a_prod_update_a_c_prod_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_c_prod_update_b_update_fun$\'_type',type,
    '\'A_c_prod_update_b_update_fun$\'': $tType ).

thf('\'B_update_b_update_fun$\'_type',type,
    '\'B_update_b_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_a_prod_update_fun$\'_type',type,
    '\'A_update_c_a_prod_update_fun$\'': $tType ).

thf('\'C_update_c_update_fun_a_update_a_update_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'': $tType ).

thf('\'A_a_prod_update_a_update_fun$\'_type',type,
    '\'A_a_prod_update_a_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_b_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_b_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_b_prod_update_a_update_fun$\'_type',type,
    '\'B_b_prod_update_a_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_bool_fun$\'_type',type,
    '\'A_update_c_update_fun_bool_fun$\'': $tType ).

thf('\'C_b_prod_update_c_b_prod_update_fun$\'_type',type,
    '\'C_b_prod_update_c_b_prod_update_fun$\'': $tType ).

thf('\'A_b_prod_update_a_update_fun$\'_type',type,
    '\'A_b_prod_update_a_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'': $tType ).

thf('\'C_c_prod_update_a_a_prod_update_fun$\'_type',type,
    '\'C_c_prod_update_a_a_prod_update_fun$\'': $tType ).

thf('\'B_update_set$\'_type',type,
    '\'B_update_set$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_b_prod_update_c_a_prod_update_fun$\'_type',type,
    '\'A_b_prod_update_c_a_prod_update_fun$\'': $tType ).

thf('\'C_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_b_update_bool_fun_fun$\'_type',type,
    '\'C_update_b_update_bool_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun$\'_type',type,
    '\'C_update_a_update_fun$\'': $tType ).

thf('\'B_update$\'_type',type,
    '\'B_update$\'': $tType ).

thf('\'B_update_a_update_fun_a_update_c_update_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_a_update_c_update_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'C_a_prod_update_c_a_prod_update_fun$\'_type',type,
    '\'C_a_prod_update_c_a_prod_update_fun$\'': $tType ).

thf('\'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_b_update_fun_b_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_b_update_fun_b_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_a_prod_update_b_c_prod_update_fun$\'_type',type,
    '\'A_a_prod_update_b_c_prod_update_fun$\'': $tType ).

thf('\'C_update_c_update_fun_c_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'C_update_c_update_fun_c_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_a_update_bool_fun_fun$\'_type',type,
    '\'C_update_a_update_bool_fun_fun$\'': $tType ).

thf('\'B_c_prod_update_c_update_fun$\'_type',type,
    '\'B_c_prod_update_c_update_fun$\'': $tType ).

thf('\'C_b_prod_update_a_a_prod_update_fun$\'_type',type,
    '\'C_b_prod_update_a_a_prod_update_fun$\'': $tType ).

thf('\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_b_update_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_b_update_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_c_update_fun$\'_type',type,
    '\'C_update_c_update_fun$\'': $tType ).

thf('\'A_update_b_update_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_bool_fun_fun$\'': $tType ).

thf('\'C_update_set_c_update_fun$\'_type',type,
    '\'C_update_set_c_update_fun$\'': $tType ).

thf('\'A_update_a_update_fun_b_update_b_update_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'': $tType ).

thf('\'A_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'': $tType ).

thf('\'B_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'': $tType ).

thf('\'C_a_prod_update_a_c_prod_update_fun$\'_type',type,
    '\'C_a_prod_update_a_c_prod_update_fun$\'': $tType ).

thf('\'A_update_a_update_fun_b_update_c_update_fun_fun$\'_type',type,
    '\'A_update_a_update_fun_b_update_c_update_fun_fun$\'': $tType ).

thf('\'A_c_prod_update_c_update_fun$\'_type',type,
    '\'A_c_prod_update_c_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_a_update_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'': $tType ).

thf('\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'': $tType ).

thf('\'B_c_prod_update_b_update_fun$\'_type',type,
    '\'B_c_prod_update_b_update_fun$\'': $tType ).

thf('\'A_a_prod_update_c_b_prod_update_fun$\'_type',type,
    '\'A_a_prod_update_c_b_prod_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'_type',type,
    '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'': $tType ).

thf('\'B_update_a_update_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_bool_fun_fun$\'': $tType ).

thf('\'B_update_bool_fun$\'_type',type,
    '\'B_update_bool_fun$\'': $tType ).

thf('\'B_update_b_update_bool_fun_fun$\'_type',type,
    '\'B_update_b_update_bool_fun_fun$\'': $tType ).

thf('\'B_update_b_update_fun_b_update_b_update_fun_fun$\'_type',type,
    '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'': $tType ).

thf('\'C_b_prod_update_c_update_fun$\'_type',type,
    '\'C_b_prod_update_c_update_fun$\'': $tType ).

thf('\'A_update_b_update_fun_bool_fun$\'_type',type,
    '\'A_update_b_update_fun_bool_fun$\'': $tType ).

thf('\'C_update_a_update_fun_bool_fun$\'_type',type,
    '\'C_update_a_update_fun_bool_fun$\'': $tType ).

thf('\'A_update_c_update_bool_fun_fun$\'_type',type,
    '\'A_update_c_update_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'': $tType ).

thf('\'B_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'C_update_c_update_bool_fun_fun$\'_type',type,
    '\'C_update_c_update_bool_fun_fun$\'': $tType ).

thf('\'A_update_bool_fun$\'_type',type,
    '\'A_update_bool_fun$\'': $tType ).

thf('\'B_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'_type',type,
    '\'B_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_c_update_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_c_update_fun_fun$\'': $tType ).

thf('\'C_b_prod_update_a_update_fun$\'_type',type,
    '\'C_b_prod_update_a_update_fun$\'': $tType ).

thf('\'C_update_a_update_fun_c_update_c_update_fun_fun$\'_type',type,
    '\'C_update_a_update_fun_c_update_c_update_fun_fun$\'': $tType ).

thf('\'B_a_prod_update$\'_type',type,
    '\'B_a_prod_update$\'': $tType ).

thf('\'B_update_a_update_fun_a_update_b_update_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'': $tType ).

thf('\'C_update_set$\'_type',type,
    '\'C_update_set$\'': $tType ).

thf('\'B_update_a_update_fun_b_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'_type',type,
    '\'B_update_a_update_fun_b_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'': $tType ).

thf('\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'_type',type,
    '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'': $tType ).

thf('\'inj_on$d\'_type',type,
    '\'inj_on$d\'': '\'A_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_set$\'' > $o ).

thf('\'fun_app$at\'_type',type,
    '\'fun_app$at\'': '\'B_b_prod_update_a_update_fun$\'' > '\'B_b_prod_update$\'' > '\'A_update$\'' ).

thf('\'preregister$h\'_type',type,
    '\'preregister$h\'': '\'C_update_b_update_fun$\'' > $o ).

thf('\'iso_tuple_surjective_proof_assist$a\'_type',type,
    '\'iso_tuple_surjective_proof_assist$a\'': '\'B_update$\'' > '\'B_update$\'' > '\'B_update_b_update_fun$\'' > $o ).

thf('\'uus$\'_type',type,
    '\'uus$\'': '\'A_update_a_update_bool_fun_fun$\'' ).

thf('\'uvb$\'_type',type,
    '\'uvb$\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$au\'_type',type,
    '\'rel_fun$au\'': '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'register_tensor$aa\'_type',type,
    '\'register_tensor$aa\'': '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'B_a_prod_update_a_b_prod_update_fun$\'' ).

thf('\'fun_app$ar\'_type',type,
    '\'fun_app$ar\'': '\'B_b_prod_update_a_a_prod_update_fun$\'' > '\'B_b_prod_update$\'' > '\'A_a_prod_update$\'' ).

thf('\'comp$v\'_type',type,
    '\'comp$v\'': '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'fun_app$z\'_type',type,
    '\'fun_app$z\'': '\'C_update_c_update_fun$\'' > '\'C_update$\'' > '\'C_update$\'' ).

thf('\'fun_app$bw\'_type',type,
    '\'fun_app$bw\'': '\'C_update_c_update_fun_bool_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'top$b\'_type',type,
    '\'top$b\'': '\'B_update_set$\'' ).

thf('\'less_eq$a\'_type',type,
    '\'less_eq$a\'': '\'A_update_set$\'' > '\'A_update_set$\'' > $o ).

thf('\'comp$av\'_type',type,
    '\'comp$av\'': '\'A_update_b_update_fun$\'' > '\'C_b_prod_update_a_update_fun$\'' > '\'C_b_prod_update_b_update_fun$\'' ).

thf('\'register_pair$c\'_type',type,
    '\'register_pair$c\'': '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_c_prod_update_c_update_fun$\'' ).

thf('\'register_pair$r\'_type',type,
    '\'register_pair$r\'': '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_b_prod_update_b_update_fun$\'' ).

thf('\'uuq$\'_type',type,
    '\'uuq$\'': '\'C_update_c_update_bool_fun_fun$\'' ).

thf('\'fun_app$bx\'_type',type,
    '\'fun_app$bx\'': '\'C_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun_bool_fun$\'' ).

thf('\'comp$at\'_type',type,
    '\'comp$at\'': '\'C_b_prod_update_a_update_fun$\'' > '\'A_a_prod_update_c_b_prod_update_fun$\'' > '\'A_a_prod_update_a_update_fun$\'' ).

thf('\'map_fun$am\'_type',type,
    '\'map_fun$am\'': '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' ).

thf('\'member$\'_type',type,
    '\'member$\'': '\'A_update$\'' > '\'A_update_set$\'' > $o ).

thf('\'comp$ar\'_type',type,
    '\'comp$ar\'': '\'A_a_prod_update_c_update_fun$\'' > '\'C_b_prod_update_a_a_prod_update_fun$\'' > '\'C_b_prod_update_c_update_fun$\'' ).

thf('\'image$e\'_type',type,
    '\'image$e\'': '\'B_update_b_update_fun$\'' > '\'B_update_set_b_update_set_fun$\'' ).

thf('\'compatible$m\'_type',type,
    '\'compatible$m\'': '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'register_pair$k\'_type',type,
    '\'register_pair$k\'': '\'B_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'B_a_prod_update_a_update_fun$\'' ).

thf('\'rel_fun$h\'_type',type,
    '\'rel_fun$h\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'comp$j\'_type',type,
    '\'comp$j\'': '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'rel_fun$be\'_type',type,
    '\'rel_fun$be\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'uug$\'_type',type,
    '\'uug$\'': '\'B_update_a_update_fun$\'' > '\'B_update_c_a_prod_update_fun$\'' ).

thf('\'fun_app$ca\'_type',type,
    '\'fun_app$ca\'': '\'A_update_a_update_fun_bool_fun$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$z\'_type',type,
    '\'rel_fun$z\'': '\'A_update_c_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > $o ).

thf('\'fun_app$aj\'_type',type,
    '\'fun_app$aj\'': '\'B_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'register_tensor$f\'_type',type,
    '\'register_tensor$f\'': '\'A_update_a_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'A_c_prod_update_a_c_prod_update_fun$\'' ).

thf('\'map_fun$ap\'_type',type,
    '\'map_fun$ap\'': '\'C_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'B_update_a_update_fun_c_update_a_update_fun_fun$\'' ).

thf('\'member$a\'_type',type,
    '\'member$a\'': '\'B_update$\'' > '\'B_update_set$\'' > $o ).

thf('\'pred_fun$b\'_type',type,
    '\'pred_fun$b\'': '\'B_update_bool_fun$\'' > '\'A_update_bool_fun$\'' > '\'B_update_a_update_fun$\'' > $o ).

thf('\'map_fun$b\'_type',type,
    '\'map_fun$b\'': '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'comp$bh\'_type',type,
    '\'comp$bh\'': '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'compatible$s\'_type',type,
    '\'compatible$s\'': '\'A_update_a_c_prod_update_fun$\'' > '\'B_update_a_c_prod_update_fun$\'' > $o ).

thf('\'type_definition$d\'_type',type,
    '\'type_definition$d\'': '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_set$\'' > $o ).

thf('\'fun_app$be\'_type',type,
    '\'fun_app$be\'': '\'A_update_b_update_fun_c_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'f$\'_type',type,
    '\'f$\'': '\'B_update_a_update_fun$\'' ).

thf('\'pred_fun$\'_type',type,
    '\'pred_fun$\'': '\'A_update_bool_fun$\'' > '\'B_update_bool_fun$\'' > '\'A_update_b_update_fun$\'' > $o ).

thf('\'fun_app$aw\'_type',type,
    '\'fun_app$aw\'': '\'B_update_a_update_fun_a_update_c_update_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'comp$az\'_type',type,
    '\'comp$az\'': '\'A_update_c_update_fun$\'' > '\'C_b_prod_update_a_update_fun$\'' > '\'C_b_prod_update_c_update_fun$\'' ).

thf('\'inv_into$g\'_type',type,
    '\'inv_into$g\'': '\'B_update_set$\'' > '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'uu$\'_type',type,
    '\'uu$\'': '\'A_update$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'comp$bk\'_type',type,
    '\'comp$bk\'': '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_b_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'id$b\'_type',type,
    '\'id$b\'': '\'A_update_a_update_fun$\'' ).

thf('\'fun_app$br\'_type',type,
    '\'fun_app$br\'': '\'C_update_set_c_update_set_fun$\'' > '\'C_update_set$\'' > '\'C_update_set$\'' ).

thf('\'fun_app$o\'_type',type,
    '\'fun_app$o\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun_bool_fun$\'' ).

thf('\'rel_fun$bf\'_type',type,
    '\'rel_fun$bf\'': '\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$ba\'_type',type,
    '\'rel_fun$ba\'': '\'A_update_b_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'iso_tuple_update_accessor_eq_assist$b\'_type',type,
    '\'iso_tuple_update_accessor_eq_assist$b\'': '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' ).

thf('\'uua$\'_type',type,
    '\'uua$\'': '\'C_update$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'fun_app$cc\'_type',type,
    '\'fun_app$cc\'': '\'B_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun_bool_fun$\'' ).

thf('\'fun_app$\'_type',type,
    '\'fun_app$\'': '\'A_update_b_update_fun_bool_fun$\'' > '\'A_update_b_update_fun$\'' > $o ).

thf('\'rel_fun$al\'_type',type,
    '\'rel_fun$al\'': '\'C_update_b_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' > '\'C_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'id$u\'_type',type,
    '\'id$u\'': '\'C_update_set_c_update_set_fun$\'' ).

thf('\'inv_into$h\'_type',type,
    '\'inv_into$h\'': '\'C_update_set$\'' > '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' ).

thf('\'register_tensor$a\'_type',type,
    '\'register_tensor$a\'': '\'C_update_c_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'C_b_prod_update_c_b_prod_update_fun$\'' ).

thf('\'inj_on$c\'_type',type,
    '\'inj_on$c\'': '\'A_update_c_update_fun$\'' > '\'A_update_set$\'' > $o ).

thf('\'map_fun$v\'_type',type,
    '\'map_fun$v\'': '\'B_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'B_update_c_update_fun_b_update_c_update_fun_fun$\'' ).

thf('\'rel_fun$b\'_type',type,
    '\'rel_fun$b\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'A_update_c_update_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'id$k\'_type',type,
    '\'id$k\'': '\'A_a_prod_update_a_a_prod_update_fun$\'' ).

thf('\'comp$n\'_type',type,
    '\'comp$n\'': '\'A_a_prod_update_b_b_prod_update_fun$\'' > '\'B_c_prod_update_a_a_prod_update_fun$\'' > '\'B_c_prod_update_b_b_prod_update_fun$\'' ).

thf('\'fun_app$w\'_type',type,
    '\'fun_app$w\'': '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun$\'' ).

thf('\'rel_fun$af\'_type',type,
    '\'rel_fun$af\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' > '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$g\'_type',type,
    '\'fun_app$g\'': '\'A_update_c_update_fun$\'' > '\'A_update$\'' > '\'C_update$\'' ).

thf('\'preregister$\'_type',type,
    '\'preregister$\'': '\'C_update_c_update_fun$\'' > $o ).

thf('\'register_tensor$j\'_type',type,
    '\'register_tensor$j\'': '\'A_update_c_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_b_prod_update_c_a_prod_update_fun$\'' ).

thf('\'register_pair$e\'_type',type,
    '\'register_pair$e\'': '\'C_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_c_prod_update_b_update_fun$\'' ).

thf('\'rel_fun$bs\'_type',type,
    '\'rel_fun$bs\'': '\'C_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'map_fun$ac\'_type',type,
    '\'map_fun$ac\'': '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' ).

thf('\'the_inv_into$\'_type',type,
    '\'the_inv_into$\'': '\'C_update_set$\'' > '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'id$c\'_type',type,
    '\'id$c\'': '\'C_c_prod_update_c_c_prod_update_fun$\'' ).

thf('\'uur$\'_type',type,
    '\'uur$\'': '\'B_update_b_update_bool_fun_fun$\'' ).

thf('\'tensor_update$c\'_type',type,
    '\'tensor_update$c\'': '\'C_update$\'' > '\'A_update$\'' > '\'C_a_prod_update$\'' ).

thf('\'register_pair$a\'_type',type,
    '\'register_pair$a\'': '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_a_prod_update_a_update_fun$\'' ).

thf('\'register_pair$i\'_type',type,
    '\'register_pair$i\'': '\'A_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'A_c_prod_update_b_update_fun$\'' ).

thf('\'map_fun$a\'_type',type,
    '\'map_fun$a\'': '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'comp$af\'_type',type,
    '\'comp$af\'': '\'B_update_c_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' ).

thf('\'comp$o\'_type',type,
    '\'comp$o\'': '\'A_a_prod_update_b_b_prod_update_fun$\'' > '\'B_b_prod_update_a_a_prod_update_fun$\'' > '\'B_b_prod_update_b_b_prod_update_fun$\'' ).

thf('\'fcomp$c\'_type',type,
    '\'fcomp$c\'': '\'C_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'compatible$w\'_type',type,
    '\'compatible$w\'': '\'B_update_a_c_prod_update_fun$\'' > '\'A_update_a_c_prod_update_fun$\'' > $o ).

thf('\'rel_fun$bi\'_type',type,
    '\'rel_fun$bi\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_b_update_fun_b_update_c_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'comp$ab\'_type',type,
    '\'comp$ab\'': '\'A_update_c_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'grp$g\'_type',type,
    '\'grp$g\'': '\'B_update_a_update_fun_set$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'iso_register$d\'_type',type,
    '\'iso_register$d\'': '\'C_update_c_update_fun$\'' > $o ).

thf('\'tensor_update$f\'_type',type,
    '\'tensor_update$f\'': '\'B_update$\'' > '\'B_update$\'' > '\'B_b_prod_update$\'' ).

thf('\'quotient3$f\'_type',type,
    '\'quotient3$f\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > $o ).

thf('\'register_tensor$v\'_type',type,
    '\'register_tensor$v\'': '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'C_b_prod_update_b_c_prod_update_fun$\'' ).

thf('\'register_tensor$b\'_type',type,
    '\'register_tensor$b\'': '\'C_update_c_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'C_a_prod_update_c_a_prod_update_fun$\'' ).

thf('\'fun_app$r\'_type',type,
    '\'fun_app$r\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun_bool_fun$\'' ).

thf('\'grp$b\'_type',type,
    '\'grp$b\'': '\'A_update_set$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' ).

thf('\'fun_app$bs\'_type',type,
    '\'fun_app$bs\'': '\'B_update_set_b_update_set_fun$\'' > '\'B_update_set$\'' > '\'B_update_set$\'' ).

thf('\'map_fun$ar\'_type',type,
    '\'map_fun$ar\'': '\'A_update_b_update_fun_a_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' ).

thf('\'register_pair$l\'_type',type,
    '\'register_pair$l\'': '\'A_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_b_prod_update_a_update_fun$\'' ).

thf('\'uuy$\'_type',type,
    '\'uuy$\'': '\'A_update_set$\'' > '\'B_update_a_update_fun_bool_fun$\'' ).

thf('\'fun_app$ak\'_type',type,
    '\'fun_app$ak\'': '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'inj_on$m\'_type',type,
    '\'inj_on$m\'': '\'B_update_b_update_fun$\'' > '\'B_update_set$\'' > $o ).

thf('\'comp$k\'_type',type,
    '\'comp$k\'': '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'fun_app$n\'_type',type,
    '\'fun_app$n\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update$\'' > '\'A_update_bool_fun$\'' ).

thf('\'uva$\'_type',type,
    '\'uva$\'': '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'compatible$g\'_type',type,
    '\'compatible$g\'': '\'C_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > $o ).

thf('\'fun_app$az\'_type',type,
    '\'fun_app$az\'': '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'quotient3$b\'_type',type,
    '\'quotient3$b\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$bv\'_type',type,
    '\'rel_fun$bv\'': '\'B_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$am\'_type',type,
    '\'rel_fun$am\'': '\'C_update_b_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$m\'_type',type,
    '\'rel_fun$m\'': '\'A_update_c_update_bool_fun_fun$\'' > '\'B_update_a_update_bool_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'map_fun$s\'_type',type,
    '\'map_fun$s\'': '\'C_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_a_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'inj_on$h\'_type',type,
    '\'inj_on$h\'': '\'B_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_a_update_fun_set$\'' > $o ).

thf('\'register_tensor$ab\'_type',type,
    '\'register_tensor$ab\'': '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'C_a_prod_update_a_c_prod_update_fun$\'' ).

thf('\'rel_fun$bh\'_type',type,
    '\'rel_fun$bh\'': '\'A_update_b_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'fun_app$am\'_type',type,
    '\'fun_app$am\'': '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'type_definition$f\'_type',type,
    '\'type_definition$f\'': '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_set$\'' > $o ).

thf('\'tensor_update$d\'_type',type,
    '\'tensor_update$d\'': '\'A_update$\'' > '\'B_update$\'' > '\'A_b_prod_update$\'' ).

thf('\'register_tensor$i\'_type',type,
    '\'register_tensor$i\'': '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_a_prod_update_c_c_prod_update_fun$\'' ).

thf('\'fun_app$k\'_type',type,
    '\'fun_app$k\'': '\'B_update_bool_fun$\'' > '\'B_update$\'' > $o ).

thf('\'id$q\'_type',type,
    '\'id$q\'': '\'B_update_c_update_fun_b_update_c_update_fun_fun$\'' ).

thf('\'rel_fun$bl\'_type',type,
    '\'rel_fun$bl\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'fun_app$bo\'_type',type,
    '\'fun_app$bo\'': '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'map_fun$f\'_type',type,
    '\'map_fun$f\'': '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'' ).

thf('\'map_fun$o\'_type',type,
    '\'map_fun$o\'': '\'A_update_c_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'rel_fun$o\'_type',type,
    '\'rel_fun$o\'': '\'B_update_a_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'map_fun$ad\'_type',type,
    '\'map_fun$ad\'': '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun_b_update_c_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' ).

thf('\'id$f\'_type',type,
    '\'id$f\'': '\'B_c_prod_update_b_c_prod_update_fun$\'' ).

thf('\'comp$b\'_type',type,
    '\'comp$b\'': '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' ).

thf('\'map_fun$g\'_type',type,
    '\'map_fun$g\'': '\'A_update_a_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'A_update_b_update_fun_a_update_c_update_fun_fun$\'' ).

thf('\'map_fun$c\'_type',type,
    '\'map_fun$c\'': '\'A_update_b_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'B_update_a_update_fun_a_update_c_update_fun_fun$\'' ).

thf('\'id$e\'_type',type,
    '\'id$e\'': '\'C_a_prod_update_c_a_prod_update_fun$\'' ).

thf('\'register_tensor$c\'_type',type,
    '\'register_tensor$c\'': '\'B_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'B_c_prod_update_b_c_prod_update_fun$\'' ).

thf('\'uuu$\'_type',type,
    '\'uuu$\'': '\'C_update_set$\'' > '\'C_update_a_update_fun$\'' > '\'C_update$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'fun_app$ag\'_type',type,
    '\'fun_app$ag\'': '\'C_update_a_update_fun$\'' > '\'C_update$\'' > '\'A_update$\'' ).

thf('\'fun_app$ce\'_type',type,
    '\'fun_app$ce\'': '\'A_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'B_update_b_update_fun_bool_fun$\'' ).

thf('\'uun$\'_type',type,
    '\'uun$\'': '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_bool_fun$\'' ).

thf('\'pred_fun$d\'_type',type,
    '\'pred_fun$d\'': '\'C_update_bool_fun$\'' > '\'C_update_bool_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'fun_app$ab\'_type',type,
    '\'fun_app$ab\'': '\'A_update_a_update_fun$\'' > '\'A_update$\'' > '\'A_update$\'' ).

thf('\'comp$q\'_type',type,
    '\'comp$q\'': '\'A_a_prod_update_b_c_prod_update_fun$\'' > '\'C_b_prod_update_a_a_prod_update_fun$\'' > '\'C_b_prod_update_b_c_prod_update_fun$\'' ).

thf('\'rel_fun$bt\'_type',type,
    '\'rel_fun$bt\'': '\'C_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' > '\'C_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'image$f\'_type',type,
    '\'image$f\'': '\'A_update_a_update_fun$\'' > '\'A_update_set_a_update_set_fun$\'' ).

thf('\'register_tensor$m\'_type',type,
    '\'register_tensor$m\'': '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_a_prod_update_b_b_prod_update_fun$\'' ).

thf('\'fun_app$bl\'_type',type,
    '\'fun_app$bl\'': '\'A_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'iso_tuple_update_accessor_eq_assist$a\'_type',type,
    '\'iso_tuple_update_accessor_eq_assist$a\'': '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' ).

thf('\'collect$a\'_type',type,
    '\'collect$a\'': '\'C_update_a_update_fun_bool_fun$\'' > '\'C_update_a_update_fun_set$\'' ).

thf('\'inj_on$j\'_type',type,
    '\'inj_on$j\'': '\'C_update_c_update_fun$\'' > '\'C_update_set$\'' > $o ).

thf('\'map_fun$q\'_type',type,
    '\'map_fun$q\'': '\'A_update_c_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'C_update_b_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'register$f\'_type',type,
    '\'register$f\'': '\'B_a_prod_update_a_c_prod_update_fun$\'' > $o ).

thf('\'quotient3$d\'_type',type,
    '\'quotient3$d\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'C_update_a_update_fun$\'' > $o ).

thf('\'compatible$v\'_type',type,
    '\'compatible$v\'': '\'A_update_c_a_prod_update_fun$\'' > '\'B_update_c_a_prod_update_fun$\'' > $o ).

thf('\'fun_app$bv\'_type',type,
    '\'fun_app$bv\'': '\'A_update_set_a_update_fun$\'' > '\'A_update_set$\'' > '\'A_update$\'' ).

thf('\'register$i\'_type',type,
    '\'register$i\'': '\'B_update_c_update_fun$\'' > $o ).

thf('\'comp$bl\'_type',type,
    '\'comp$bl\'': '\'A_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'register_pair$p\'_type',type,
    '\'register_pair$p\'': '\'C_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_c_prod_update_a_update_fun$\'' ).

thf('\'the_inv_into$e\'_type',type,
    '\'the_inv_into$e\'': '\'A_update_set$\'' > '\'A_update_c_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'fcomp$\'_type',type,
    '\'fcomp$\'': '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'grp$i\'_type',type,
    '\'grp$i\'': '\'C_update_a_update_fun_set$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'image$\'_type',type,
    '\'image$\'': '\'A_update_b_update_fun$\'' > '\'A_update_set$\'' > '\'B_update_set$\'' ).

thf('\'comp$aq\'_type',type,
    '\'comp$aq\'': '\'B_a_prod_update_a_update_fun$\'' > '\'A_b_prod_update_b_a_prod_update_fun$\'' > '\'A_b_prod_update_a_update_fun$\'' ).

thf('\'rel_fun$y\'_type',type,
    '\'rel_fun$y\'': '\'A_update_b_update_bool_fun_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' > '\'A_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$ay\'_type',type,
    '\'fun_app$ay\'': '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'rel_fun$bb\'_type',type,
    '\'rel_fun$bb\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'B_update_c_update_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'id$l\'_type',type,
    '\'id$l\'': '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'map_fun$h\'_type',type,
    '\'map_fun$h\'': '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'rel_fun$bj\'_type',type,
    '\'rel_fun$bj\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_c_update_bool_fun_fun$\'' > '\'B_update_b_update_fun_b_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'map_fun$au\'_type',type,
    '\'map_fun$au\'': '\'B_update_a_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' ).

thf('\'register_tensor$z\'_type',type,
    '\'register_tensor$z\'': '\'C_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'C_a_prod_update_b_a_prod_update_fun$\'' ).

thf('\'rel_fun$bc\'_type',type,
    '\'rel_fun$bc\'': '\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_b_update_fun_c_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'fun_app$ae\'_type',type,
    '\'fun_app$ae\'': '\'C_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'rel_fun$bm\'_type',type,
    '\'rel_fun$bm\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'image$g\'_type',type,
    '\'image$g\'': '\'B_update_c_update_fun$\'' > '\'B_update_set$\'' > '\'C_update_set$\'' ).

thf('\'inj_on$e\'_type',type,
    '\'inj_on$e\'': '\'C_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_set$\'' > $o ).

thf('\'map_fun$av\'_type',type,
    '\'map_fun$av\'': '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'grp$d\'_type',type,
    '\'grp$d\'': '\'A_update_b_update_fun_set$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$i\'_type',type,
    '\'rel_fun$i\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$bc\'_type',type,
    '\'fun_app$bc\'': '\'A_update_c_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'id$n\'_type',type,
    '\'id$n\'': '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'uuw$\'_type',type,
    '\'uuw$\'': '\'B_update_set$\'' > '\'A_update_b_update_fun_bool_fun$\'' ).

thf('\'iso_register$a\'_type',type,
    '\'iso_register$a\'': '\'A_update_b_update_fun$\'' > $o ).

thf('\'fun_app$bp\'_type',type,
    '\'fun_app$bp\'': '\'B_update_b_update_fun_c_update_c_update_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'register_pair$s\'_type',type,
    '\'register_pair$s\'': '\'B_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'B_c_prod_update_c_update_fun$\'' ).

thf('\'fun_app$h\'_type',type,
    '\'fun_app$h\'': '\'A_update_c_a_prod_update_fun$\'' > '\'A_update$\'' > '\'C_a_prod_update$\'' ).

thf('\'type_definition$c\'_type',type,
    '\'type_definition$c\'': '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_update_set$\'' > $o ).

thf('\'inj_on$i\'_type',type,
    '\'inj_on$i\'': '\'A_update_a_update_fun$\'' > '\'A_update_set$\'' > $o ).

thf('\'fun_app$bk\'_type',type,
    '\'fun_app$bk\'': '\'C_update_b_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'fun_app$u\'_type',type,
    '\'fun_app$u\'': '\'A_update_b_update_fun$\'' > '\'A_update$\'' > '\'B_update$\'' ).

thf('\'rel_fun$j\'_type',type,
    '\'rel_fun$j\'': '\'B_update_a_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'rel_fun$bd\'_type',type,
    '\'rel_fun$bd\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'B_update_c_update_bool_fun_fun$\'' > '\'C_update_b_update_fun_c_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'id$d\'_type',type,
    '\'id$d\'': '\'C_b_prod_update_c_b_prod_update_fun$\'' ).

thf('\'inj_on$a\'_type',type,
    '\'inj_on$a\'': '\'C_update_a_update_fun$\'' > '\'C_update_set$\'' > $o ).

thf('\'grp$a\'_type',type,
    '\'grp$a\'': '\'B_update_set$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' ).

thf('\'rel_fun$a\'_type',type,
    '\'rel_fun$a\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'A_update_c_update_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$a\'_type',type,
    '\'fun_app$a\'': '\'C_update_a_update_fun_bool_fun$\'' > '\'C_update_a_update_fun$\'' > $o ).

thf('\'map_fun$aq\'_type',type,
    '\'map_fun$aq\'': '\'B_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun_b_update_c_update_fun_fun$\'' ).

thf('\'rel_fun$at\'_type',type,
    '\'rel_fun$at\'': '\'C_update_b_update_bool_fun_fun$\'' > '\'C_update_b_update_bool_fun_fun$\'' > '\'C_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'comp_update$\'_type',type,
    '\'comp_update$\'': '\'C_update$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'pred_DEADID$\'_type',type,
    '\'pred_DEADID$\'': '\'C_update_bool_fun$\'' ).

thf('\'rel_fun$q\'_type',type,
    '\'rel_fun$q\'': '\'A_update_b_update_bool_fun_fun$\'' > '\'B_update_a_update_bool_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$ao\'_type',type,
    '\'rel_fun$ao\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'C_update_b_update_bool_fun_fun$\'' > '\'A_update_c_update_fun_a_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'register$c\'_type',type,
    '\'register$c\'': '\'A_update_b_update_fun$\'' > $o ).

thf('\'comp$a\'_type',type,
    '\'comp$a\'': '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' ).

thf('\'preregister$b\'_type',type,
    '\'preregister$b\'': '\'A_update_a_update_fun$\'' > $o ).

thf('\'register$l\'_type',type,
    '\'register$l\'': '\'A_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$ab\'_type',type,
    '\'rel_fun$ab\'': '\'C_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun_a_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'' ).

thf('\'compatible$j\'_type',type,
    '\'compatible$j\'': '\'C_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > $o ).

thf('\'comp$bi\'_type',type,
    '\'comp$bi\'': '\'A_update_b_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'' ).

thf('\'register_tensor$n\'_type',type,
    '\'register_tensor$n\'': '\'C_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_c_prod_update_a_a_prod_update_fun$\'' ).

thf('\'map_fun$aa\'_type',type,
    '\'map_fun$aa\'': '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' ).

thf('\'comp$ap\'_type',type,
    '\'comp$ap\'': '\'A_c_prod_update_b_update_fun$\'' > '\'C_a_prod_update_a_c_prod_update_fun$\'' > '\'C_a_prod_update_b_update_fun$\'' ).

thf('\'uuk$\'_type',type,
    '\'uuk$\'': '\'A_update_bool_fun$\'' ).

thf('\'uue$\'_type',type,
    '\'uue$\'': '\'A_update_c_update_fun$\'' > '\'A_update_a_c_prod_update_fun$\'' ).

thf('\'quotient3$h\'_type',type,
    '\'quotient3$h\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' > $o ).

thf('\'quotient3$c\'_type',type,
    '\'quotient3$c\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > $o ).

thf('\'rel_fun$br\'_type',type,
    '\'rel_fun$br\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'rel_fun$aw\'_type',type,
    '\'rel_fun$aw\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' > '\'B_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'the_inv_into$g\'_type',type,
    '\'the_inv_into$g\'': '\'C_update_set$\'' > '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' ).

thf('\'comp$ah\'_type',type,
    '\'comp$ah\'': '\'C_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'map_fun$af\'_type',type,
    '\'map_fun$af\'': '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' ).

thf('\'rel_fun$ae\'_type',type,
    '\'rel_fun$ae\'': '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'uum$\'_type',type,
    '\'uum$\'': '\'C_update_bool_fun$\'' ).

thf('\'member$b\'_type',type,
    '\'member$b\'': '\'C_update$\'' > '\'C_update_set$\'' > $o ).

thf('\'rel_fun$x\'_type',type,
    '\'rel_fun$x\'': '\'A_update_b_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$d\'_type',type,
    '\'rel_fun$d\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'comp$d\'_type',type,
    '\'comp$d\'': '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' ).

thf('\'rel_fun$bx\'_type',type,
    '\'rel_fun$bx\'': '\'B_update_c_update_bool_fun_fun$\'' > '\'B_update_c_update_bool_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'the_inv_into$b\'_type',type,
    '\'the_inv_into$b\'': '\'A_update_set$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'fun_app$as\'_type',type,
    '\'fun_app$as\'': '\'A_a_prod_update_c_update_fun$\'' > '\'A_a_prod_update$\'' > '\'C_update$\'' ).

thf('\'uuv$\'_type',type,
    '\'uuv$\'': '\'B_update_set$\'' > '\'B_update_a_update_fun$\'' > '\'B_update$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'map_fun$i\'_type',type,
    '\'map_fun$i\'': '\'A_update_a_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'A_update_c_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'fun_app$aq\'_type',type,
    '\'fun_app$aq\'': '\'B_a_prod_update_a_c_prod_update_fun$\'' > '\'B_a_prod_update$\'' > '\'A_c_prod_update$\'' ).

thf('\'fun_app$d\'_type',type,
    '\'fun_app$d\'': '\'B_update_a_update_fun$\'' > '\'B_update$\'' > '\'A_update$\'' ).

thf('\'comp$bn\'_type',type,
    '\'comp$bn\'': '\'A_update_bool_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_bool_fun$\'' ).

thf('\'fun_app$by\'_type',type,
    '\'fun_app$by\'': '\'B_update_b_update_fun_bool_fun$\'' > '\'B_update_b_update_fun$\'' > $o ).

thf('\'id$m\'_type',type,
    '\'id$m\'': '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'inv_into$b\'_type',type,
    '\'inv_into$b\'': '\'A_update_set$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'register_tensor$k\'_type',type,
    '\'register_tensor$k\'': '\'B_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'B_a_prod_update_a_c_prod_update_fun$\'' ).

thf('\'register_tensor$d\'_type',type,
    '\'register_tensor$d\'': '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_b_prod_update_b_b_prod_update_fun$\'' ).

thf('\'id$j\'_type',type,
    '\'id$j\'': '\'A_b_prod_update_a_b_prod_update_fun$\'' ).

thf('\'register_pair$f\'_type',type,
    '\'register_pair$f\'': '\'B_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'B_c_prod_update_a_update_fun$\'' ).

thf('\'map_fun$al\'_type',type,
    '\'map_fun$al\'': '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' ).

thf('\'map_fun$ak\'_type',type,
    '\'map_fun$ak\'': '\'A_update_b_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' ).

thf('\'comp$aj\'_type',type,
    '\'comp$aj\'': '\'B_update_c_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'uux$\'_type',type,
    '\'uux$\'': '\'A_update_set$\'' > '\'C_update_a_update_fun_bool_fun$\'' ).

thf('\'id$g\'_type',type,
    '\'id$g\'': '\'B_b_prod_update_b_b_prod_update_fun$\'' ).

thf('\'rel_fun$an\'_type',type,
    '\'rel_fun$an\'': '\'A_update_c_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'iso_tuple_surjective_proof_assist$\'_type',type,
    '\'iso_tuple_surjective_proof_assist$\'': '\'C_update$\'' > '\'C_update$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'map_fun$aw\'_type',type,
    '\'map_fun$aw\'': '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_update_b_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'inj_on$b\'_type',type,
    '\'inj_on$b\'': '\'B_update_a_update_fun$\'' > '\'B_update_set$\'' > $o ).

thf('\'comp$bb\'_type',type,
    '\'comp$bb\'': '\'A_update_c_update_fun$\'' > '\'B_b_prod_update_a_update_fun$\'' > '\'B_b_prod_update_c_update_fun$\'' ).

thf('\'pred_fun$c\'_type',type,
    '\'pred_fun$c\'': '\'A_update_bool_fun$\'' > '\'A_update_bool_fun$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$az\'_type',type,
    '\'rel_fun$az\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'C_update_b_update_bool_fun_fun$\'' > '\'B_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'map_fun$u\'_type',type,
    '\'map_fun$u\'': '\'C_update_c_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'C_update_b_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'quotient3$a\'_type',type,
    '\'quotient3$a\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > $o ).

thf('\'top$c\'_type',type,
    '\'top$c\'': '\'A_update_b_update_fun_set$\'' ).

thf('\'rel_fun$bw\'_type',type,
    '\'rel_fun$bw\'': '\'B_update_c_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$x\'_type',type,
    '\'fun_app$x\'': '\'C_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'map_fun$ab\'_type',type,
    '\'map_fun$ab\'': '\'C_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' ).

thf('\'fun_app$q\'_type',type,
    '\'fun_app$q\'': '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun_bool_fun$\'' ).

thf('\'rel_fun$ap\'_type',type,
    '\'rel_fun$ap\'': '\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun_c_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'comp$bd\'_type',type,
    '\'comp$bd\'': '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'comp$i\'_type',type,
    '\'comp$i\'': '\'B_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'fun_app$bt\'_type',type,
    '\'fun_app$bt\'': '\'C_update_set_c_update_fun$\'' > '\'C_update_set$\'' > '\'C_update$\'' ).

thf('\'id$\'_type',type,
    '\'id$\'': '\'C_update_c_update_fun$\'' ).

thf('\'comp$s\'_type',type,
    '\'comp$s\'': '\'A_a_prod_update_b_c_prod_update_fun$\'' > '\'B_b_prod_update_a_a_prod_update_fun$\'' > '\'B_b_prod_update_b_c_prod_update_fun$\'' ).

thf('\'uul$\'_type',type,
    '\'uul$\'': '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_bool_fun$\'' ).

thf('\'quotient3$g\'_type',type,
    '\'quotient3$g\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' > $o ).

thf('\'compatible$e\'_type',type,
    '\'compatible$e\'': '\'A_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > $o ).

thf('\'rel_fun$g\'_type',type,
    '\'rel_fun$g\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'' ).

thf('\'relcompp$a\'_type',type,
    '\'relcompp$a\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' ).

thf('\'fun_app$bu\'_type',type,
    '\'fun_app$bu\'': '\'B_update_set_b_update_fun$\'' > '\'B_update_set$\'' > '\'B_update$\'' ).

thf('\'iso_register$e\'_type',type,
    '\'iso_register$e\'': '\'B_update_c_update_fun$\'' > $o ).

thf('\'grp$\'_type',type,
    '\'grp$\'': '\'C_update_set$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' ).

thf('\'rel_fun$ar\'_type',type,
    '\'rel_fun$ar\'': '\'A_update_c_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'id$a\'_type',type,
    '\'id$a\'': '\'B_update_b_update_fun$\'' ).

thf('\'preregister$c\'_type',type,
    '\'preregister$c\'': '\'A_update_c_update_fun$\'' > $o ).

thf('\'rel_fun$c\'_type',type,
    '\'rel_fun$c\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'image$d\'_type',type,
    '\'image$d\'': '\'C_update_c_update_fun$\'' > '\'C_update_set_c_update_set_fun$\'' ).

thf('\'register_tensor$o\'_type',type,
    '\'register_tensor$o\'': '\'C_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_c_prod_update_b_b_prod_update_fun$\'' ).

thf('\'compatible$n\'_type',type,
    '\'compatible$n\'': '\'C_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' > $o ).

thf('\'comp$ay\'_type',type,
    '\'comp$ay\'': '\'A_update_c_update_fun$\'' > '\'C_c_prod_update_a_update_fun$\'' > '\'C_c_prod_update_c_update_fun$\'' ).

thf('\'rel_fun$ag\'_type',type,
    '\'rel_fun$ag\'': '\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'image$a\'_type',type,
    '\'image$a\'': '\'C_update_a_update_fun$\'' > '\'C_update_set$\'' > '\'A_update_set$\'' ).

thf('\'iso_tuple_update_accessor_cong_assist$e\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$e\'': '\'B_update_b_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_b_update_fun$\'' > $o ).

thf('\'map_fun$ae\'_type',type,
    '\'map_fun$ae\'': '\'B_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_a_update_fun_b_update_c_update_fun_fun$\'' ).

thf('\'type_definition$h\'_type',type,
    '\'type_definition$h\'': '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_set$\'' > $o ).

thf('\'less_eq$\'_type',type,
    '\'less_eq$\'': '\'B_update_set$\'' > '\'B_update_set$\'' > $o ).

thf('\'the_inv_into$f\'_type',type,
    '\'the_inv_into$f\'': '\'B_update_set$\'' > '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'fun_app$ap\'_type',type,
    '\'fun_app$ap\'': '\'A_b_prod_update_c_a_prod_update_fun$\'' > '\'A_b_prod_update$\'' > '\'C_a_prod_update$\'' ).

thf('\'rel_fun$p\'_type',type,
    '\'rel_fun$p\'': '\'A_update_b_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$t\'_type',type,
    '\'rel_fun$t\'': '\'B_update_a_update_bool_fun_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'comp$am\'_type',type,
    '\'comp$am\'': '\'A_a_prod_update_b_update_fun$\'' > '\'C_c_prod_update_a_a_prod_update_fun$\'' > '\'C_c_prod_update_b_update_fun$\'' ).

thf('\'iso_register$b\'_type',type,
    '\'iso_register$b\'': '\'A_update_c_update_fun$\'' > $o ).

thf('\'register$\'_type',type,
    '\'register$\'': '\'A_update_c_update_fun$\'' > $o ).

thf('\'tensor_update$e\'_type',type,
    '\'tensor_update$e\'': '\'B_update$\'' > '\'A_update$\'' > '\'B_a_prod_update$\'' ).

thf('\'rel_fun$bq\'_type',type,
    '\'rel_fun$bq\'': '\'B_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' > '\'B_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'compatible$f\'_type',type,
    '\'compatible$f\'': '\'B_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'register_pair$q\'_type',type,
    '\'register_pair$q\'': '\'B_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'B_c_prod_update_b_update_fun$\'' ).

thf('\'fun_app$v\'_type',type,
    '\'fun_app$v\'': '\'B_update_a_update_fun_b_update_c_update_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_c_update_fun$\'' ).

thf('\'uuf$\'_type',type,
    '\'uuf$\'': '\'B_update_a_update_fun$\'' > '\'B_update_a_c_prod_update_fun$\'' ).

thf('\'rel_fun$ac\'_type',type,
    '\'rel_fun$ac\'': '\'C_update_a_update_bool_fun_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' > '\'C_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$an\'_type',type,
    '\'fun_app$an\'': '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'comp_update$a\'_type',type,
    '\'comp_update$a\'': '\'A_update$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'rel_fun$e\'_type',type,
    '\'rel_fun$e\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > $o ).

thf('\'rel_fun$l\'_type',type,
    '\'rel_fun$l\'': '\'A_update_b_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'comp$bo\'_type',type,
    '\'comp$bo\'': '\'C_update_bool_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_bool_fun$\'' ).

thf('\'uuo$\'_type',type,
    '\'uuo$\'': '\'B_update_bool_fun$\'' ).

thf('\'bijection$a\'_type',type,
    '\'bijection$a\'': '\'B_update_b_update_fun$\'' > $o ).

thf('\'register_tensor$r\'_type',type,
    '\'register_tensor$r\'': '\'B_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'B_c_prod_update_a_a_prod_update_fun$\'' ).

thf('\'inv_into$e\'_type',type,
    '\'inv_into$e\'': '\'B_update_set$\'' > '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'register$b\'_type',type,
    '\'register$b\'': '\'C_update_a_update_fun$\'' > $o ).

thf('\'id$r\'_type',type,
    '\'id$r\'': '\'B_update_a_update_fun_b_update_a_update_fun_fun$\'' ).

thf('\'rel_fun$v\'_type',type,
    '\'rel_fun$v\'': '\'A_update_c_update_bool_fun_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' > '\'A_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'register_tensor$l\'_type',type,
    '\'register_tensor$l\'': '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_b_prod_update_a_a_prod_update_fun$\'' ).

thf('\'register_tensor$h\'_type',type,
    '\'register_tensor$h\'': '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_a_prod_update_a_a_prod_update_fun$\'' ).

thf('\'top$a\'_type',type,
    '\'top$a\'': '\'C_update_set$\'' ).

thf('\'fun_app$bh\'_type',type,
    '\'fun_app$bh\'': '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'uub$\'_type',type,
    '\'uub$\'': '\'B_update$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'compatible$h\'_type',type,
    '\'compatible$h\'': '\'C_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > $o ).

thf('\'register_pair$b\'_type',type,
    '\'register_pair$b\'': '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_a_prod_update_c_update_fun$\'' ).

thf('\'register_pair$g\'_type',type,
    '\'register_pair$g\'': '\'A_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'A_c_prod_update_c_update_fun$\'' ).

thf('\'map_fun$p\'_type',type,
    '\'map_fun$p\'': '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'fun_app$ad\'_type',type,
    '\'fun_app$ad\'': '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'register_tensor$e\'_type',type,
    '\'register_tensor$e\'': '\'B_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'B_a_prod_update_b_a_prod_update_fun$\'' ).

thf('\'fun_app$ac\'_type',type,
    '\'fun_app$ac\'': '\'A_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'rel_fun$ah\'_type',type,
    '\'rel_fun$ah\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'register_pair$j\'_type',type,
    '\'register_pair$j\'': '\'C_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'C_a_prod_update_b_update_fun$\'' ).

thf('\'relcompp$b\'_type',type,
    '\'relcompp$b\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' ).

thf('\'fun_app$m\'_type',type,
    '\'fun_app$m\'': '\'A_update_bool_fun$\'' > '\'A_update$\'' > $o ).

thf('\'map_fun$m\'_type',type,
    '\'map_fun$m\'': '\'C_update_c_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'' ).

thf('\'fcomp$a\'_type',type,
    '\'fcomp$a\'': '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'register_tensor$ac\'_type',type,
    '\'register_tensor$ac\'': '\'A_update_c_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_a_prod_update_c_b_prod_update_fun$\'' ).

thf('\'rel_fun$aj\'_type',type,
    '\'rel_fun$aj\'': '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'image$h\'_type',type,
    '\'image$h\'': '\'C_update_b_update_fun$\'' > '\'C_update_set$\'' > '\'B_update_set$\'' ).

thf('\'uup$\'_type',type,
    '\'uup$\'': '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_bool_fun$\'' ).

thf('\'comp$f\'_type',type,
    '\'comp$f\'': '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'comp$ao\'_type',type,
    '\'comp$ao\'': '\'A_c_prod_update_c_update_fun$\'' > '\'C_a_prod_update_a_c_prod_update_fun$\'' > '\'C_a_prod_update_c_update_fun$\'' ).

thf('\'rel_fun$bo\'_type',type,
    '\'rel_fun$bo\'': '\'B_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'map_fun$ag\'_type',type,
    '\'map_fun$ag\'': '\'C_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' ).

thf('\'map_fun$j\'_type',type,
    '\'map_fun$j\'': '\'A_update_a_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'A_update_b_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'comp$au\'_type',type,
    '\'comp$au\'': '\'A_update_b_update_fun$\'' > '\'C_c_prod_update_a_update_fun$\'' > '\'C_c_prod_update_b_update_fun$\'' ).

thf('\'register$m\'_type',type,
    '\'register$m\'': '\'A_a_prod_update_c_update_fun$\'' > $o ).

thf('\'comp$ak\'_type',type,
    '\'comp$ak\'': '\'B_b_prod_update_a_update_fun$\'' > '\'A_a_prod_update_b_b_prod_update_fun$\'' > '\'A_a_prod_update_a_update_fun$\'' ).

thf('\'type_definition$e\'_type',type,
    '\'type_definition$e\'': '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_set$\'' > $o ).

thf('\'rel_fun$ak\'_type',type,
    '\'rel_fun$ak\'': '\'C_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'comp$h\'_type',type,
    '\'comp$h\'': '\'C_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' ).

thf('\'compatible$\'_type',type,
    '\'compatible$\'': '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > $o ).

thf('\'iso_register$h\'_type',type,
    '\'iso_register$h\'': '\'A_update_a_update_fun$\'' > $o ).

thf('\'fun_app$al\'_type',type,
    '\'fun_app$al\'': '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'id$w\'_type',type,
    '\'id$w\'': '\'A_update_set_a_update_set_fun$\'' ).

thf('\'register_pair$\'_type',type,
    '\'register_pair$\'': '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_b_prod_update_a_update_fun$\'' ).

thf('\'iso_register$g\'_type',type,
    '\'iso_register$g\'': '\'B_update_b_update_fun$\'' > $o ).

thf('\'register_tensor$p\'_type',type,
    '\'register_tensor$p\'': '\'C_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'C_b_prod_update_a_a_prod_update_fun$\'' ).

thf('\'vimage$b\'_type',type,
    '\'vimage$b\'': '\'A_update_a_update_fun$\'' > '\'A_update_set_a_update_set_fun$\'' ).

thf('\'register$h\'_type',type,
    '\'register$h\'': '\'C_update_c_update_fun$\'' > $o ).

thf('\'id$s\'_type',type,
    '\'id$s\'': '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'' ).

thf('\'preregister$g\'_type',type,
    '\'preregister$g\'': '\'B_update_c_update_fun$\'' > $o ).

thf('\'rel_fun$bu\'_type',type,
    '\'rel_fun$bu\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'rel_fun$as\'_type',type,
    '\'rel_fun$as\'': '\'C_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'fun_app$bq\'_type',type,
    '\'fun_app$bq\'': '\'A_update_set_a_update_set_fun$\'' > '\'A_update_set$\'' > '\'A_update_set$\'' ).

thf('\'rel_fun$by\'_type',type,
    '\'rel_fun$by\'': '\'B_update_a_update_bool_fun_fun$\'' > '\'B_update_a_update_bool_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'conversep$a\'_type',type,
    '\'conversep$a\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' ).

thf('\'register_pair$n\'_type',type,
    '\'register_pair$n\'': '\'C_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'C_b_prod_update_b_update_fun$\'' ).

thf('\'rel_fun$bg\'_type',type,
    '\'rel_fun$bg\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'B_update_b_update_bool_fun_fun$\'' > '\'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'register_pair$h\'_type',type,
    '\'register_pair$h\'': '\'C_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'C_a_prod_update_c_update_fun$\'' ).

thf('\'fcomp$b\'_type',type,
    '\'fcomp$b\'': '\'B_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' ).

thf('\'register_tensor$q\'_type',type,
    '\'register_tensor$q\'': '\'C_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'C_b_prod_update_b_b_prod_update_fun$\'' ).

thf('\'comp$ag\'_type',type,
    '\'comp$ag\'': '\'C_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'compatible$d\'_type',type,
    '\'compatible$d\'': '\'A_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'map_fun$ao\'_type',type,
    '\'map_fun$ao\'': '\'B_update_a_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_b_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' ).

thf('\'compatible$k\'_type',type,
    '\'compatible$k\'': '\'B_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > $o ).

thf('\'comp$\'_type',type,
    '\'comp$\'': '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' ).

thf('\'preregister$e\'_type',type,
    '\'preregister$e\'': '\'A_update_b_update_fun$\'' > $o ).

thf('\'image$b\'_type',type,
    '\'image$b\'': '\'B_update_a_update_fun$\'' > '\'B_update_set$\'' > '\'A_update_set$\'' ).

thf('\'comp_update$b\'_type',type,
    '\'comp_update$b\'': '\'B_update$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'comp$bf\'_type',type,
    '\'comp$bf\'': '\'B_update_a_update_fun_a_update_c_update_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_c_update_fun_fun$\'' ).

thf('\'compatible$q\'_type',type,
    '\'compatible$q\'': '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'map_fun$an\'_type',type,
    '\'map_fun$an\'': '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' ).

thf('\'register$d\'_type',type,
    '\'register$d\'': '\'A_a_prod_update_c_c_prod_update_fun$\'' > $o ).

thf('\'fun_app$p\'_type',type,
    '\'fun_app$p\'': '\'A_update_c_update_fun_bool_fun$\'' > '\'A_update_c_update_fun$\'' > $o ).

thf('\'compatible$p\'_type',type,
    '\'compatible$p\'': '\'B_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' > $o ).

thf('\'comp$l\'_type',type,
    '\'comp$l\'': '\'A_a_prod_update_b_b_prod_update_fun$\'' > '\'C_c_prod_update_a_a_prod_update_fun$\'' > '\'C_c_prod_update_b_b_prod_update_fun$\'' ).

thf('\'collect$b\'_type',type,
    '\'collect$b\'': '\'B_update_a_update_fun_bool_fun$\'' > '\'B_update_a_update_fun_set$\'' ).

thf('\'register_tensor$u\'_type',type,
    '\'register_tensor$u\'': '\'C_update_b_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_c_prod_update_b_c_prod_update_fun$\'' ).

thf('\'pred_fun$e\'_type',type,
    '\'pred_fun$e\'': '\'B_update_bool_fun$\'' > '\'C_update_bool_fun$\'' > '\'B_update_c_update_fun$\'' > $o ).

thf('\'pred_fun$a\'_type',type,
    '\'pred_fun$a\'': '\'C_update_bool_fun$\'' > '\'A_update_bool_fun$\'' > '\'C_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$bk\'_type',type,
    '\'rel_fun$bk\'': '\'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'rel_fun$f\'_type',type,
    '\'rel_fun$f\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'rel_fun$s\'_type',type,
    '\'rel_fun$s\'': '\'B_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'fun_app$bg\'_type',type,
    '\'fun_app$bg\'': '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'iso_tuple_update_accessor_cong_assist$g\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$g\'': '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun$\'' > $o ).

thf('\'uut$\'_type',type,
    '\'uut$\'': '\'A_update_set$\'' > '\'A_update_b_update_fun$\'' > '\'A_update$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'rel_fun$bn\'_type',type,
    '\'rel_fun$bn\'': '\'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun_c_update_a_update_fun_c_update_c_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > $o ).

thf('\'comp$g\'_type',type,
    '\'comp$g\'': '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'comp$x\'_type',type,
    '\'comp$x\'': '\'B_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'register_pair$o\'_type',type,
    '\'register_pair$o\'': '\'C_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'C_b_prod_update_a_update_fun$\'' ).

thf('\'bijection$\'_type',type,
    '\'bijection$\'': '\'C_update_c_update_fun$\'' > $o ).

thf('\'pred_fun$g\'_type',type,
    '\'pred_fun$g\'': '\'B_update_bool_fun$\'' > '\'B_update_bool_fun$\'' > '\'B_update_b_update_fun$\'' > $o ).

thf('\'iso_tuple_update_accessor_cong_assist$d\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$d\'': '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_c_update_fun$\'' > $o ).

thf('\'top$\'_type',type,
    '\'top$\'': '\'A_update_set$\'' ).

thf('\'comp$r\'_type',type,
    '\'comp$r\'': '\'A_a_prod_update_b_c_prod_update_fun$\'' > '\'B_c_prod_update_a_a_prod_update_fun$\'' > '\'B_c_prod_update_b_c_prod_update_fun$\'' ).

thf('\'compatible$a\'_type',type,
    '\'compatible$a\'': '\'A_update_c_update_fun$\'' > '\'A_update_c_update_fun$\'' > $o ).

thf('\'register_pair$m\'_type',type,
    '\'register_pair$m\'': '\'C_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'C_b_prod_update_c_update_fun$\'' ).

thf('\'map_fun$n\'_type',type,
    '\'map_fun$n\'': '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'rel_fun$u\'_type',type,
    '\'rel_fun$u\'': '\'A_update_b_update_fun_c_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'the_inv_into$a\'_type',type,
    '\'the_inv_into$a\'': '\'B_update_set$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'register_pair$d\'_type',type,
    '\'register_pair$d\'': '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_a_prod_update_b_update_fun$\'' ).

thf('\'register$a\'_type',type,
    '\'register$a\'': '\'B_update_a_update_fun$\'' > $o ).

thf('\'map_fun$ai\'_type',type,
    '\'map_fun$ai\'': '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' ).

thf('\'iso_register$f\'_type',type,
    '\'iso_register$f\'': '\'C_update_b_update_fun$\'' > $o ).

thf('\'map_fun$as\'_type',type,
    '\'map_fun$as\'': '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' ).

thf('\'iso_register$c\'_type',type,
    '\'iso_register$c\'': '\'B_update_a_update_fun$\'' > $o ).

thf('\'comp$m\'_type',type,
    '\'comp$m\'': '\'A_a_prod_update_b_b_prod_update_fun$\'' > '\'C_b_prod_update_a_a_prod_update_fun$\'' > '\'C_b_prod_update_b_b_prod_update_fun$\'' ).

thf('\'comp$as\'_type',type,
    '\'comp$as\'': '\'A_a_prod_update_b_update_fun$\'' > '\'C_b_prod_update_a_a_prod_update_fun$\'' > '\'C_b_prod_update_b_update_fun$\'' ).

thf('\'fun_app$bm\'_type',type,
    '\'fun_app$bm\'': '\'C_update_c_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'inv_into$\'_type',type,
    '\'inv_into$\'': '\'B_update_set$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'vimage$\'_type',type,
    '\'vimage$\'': '\'C_update_c_update_fun$\'' > '\'C_update_set_c_update_set_fun$\'' ).

thf('\'iso_tuple_update_accessor_cong_assist$h\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$h\'': '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_a_update_fun$\'' > $o ).

thf('\'type_definition$\'_type',type,
    '\'type_definition$\'': '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_set$\'' > $o ).

thf('\'conversep$b\'_type',type,
    '\'conversep$b\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' ).

thf('\'grp$e\'_type',type,
    '\'grp$e\'': '\'A_update_set$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_c_update_bool_fun_fun$\'' ).

thf('\'rel_fun$\'_type',type,
    '\'rel_fun$\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'B_update_a_update_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'id$v\'_type',type,
    '\'id$v\'': '\'B_update_set_b_update_set_fun$\'' ).

thf('\'preregister$f\'_type',type,
    '\'preregister$f\'': '\'C_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$bp\'_type',type,
    '\'rel_fun$bp\'': '\'B_update_c_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' > '\'B_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'comp$y\'_type',type,
    '\'comp$y\'': '\'B_update_a_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'fun_app$aa\'_type',type,
    '\'fun_app$aa\'': '\'B_update_b_update_fun$\'' > '\'B_update$\'' > '\'B_update$\'' ).

thf('\'comp$ae\'_type',type,
    '\'comp$ae\'': '\'B_update_a_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'compatible$o\'_type',type,
    '\'compatible$o\'': '\'B_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'f$a\'_type',type,
    '\'f$a\'': '\'A_update_b_update_fun$\'' ).

thf('\'comp$bp\'_type',type,
    '\'comp$bp\'': '\'B_update_bool_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_bool_fun$\'' ).

thf('\'iso_tuple_update_accessor_cong_assist$c\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$c\'': '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_c_update_fun$\'' > $o ).

thf('\'rel_fun$ai\'_type',type,
    '\'rel_fun$ai\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'comp$bm\'_type',type,
    '\'comp$bm\'': '\'A_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_b_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'fun_app$bb\'_type',type,
    '\'fun_app$bb\'': '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'conversep$\'_type',type,
    '\'conversep$\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' ).

thf('\'map_fun$x\'_type',type,
    '\'map_fun$x\'': '\'B_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'B_update_a_update_fun_b_update_a_update_fun_fun$\'' ).

thf('\'map_fun$l\'_type',type,
    '\'map_fun$l\'': '\'A_update_c_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'C_update_a_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'comp$t\'_type',type,
    '\'comp$t\'': '\'A_b_prod_update_b_a_prod_update_fun$\'' > '\'C_a_prod_update_a_b_prod_update_fun$\'' > '\'C_a_prod_update_b_a_prod_update_fun$\'' ).

thf('\'grp$c\'_type',type,
    '\'grp$c\'': '\'B_update_set$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_a_update_bool_fun_fun$\'' ).

thf('\'register$n\'_type',type,
    '\'register$n\'': '\'B_b_prod_update_a_update_fun$\'' > $o ).

thf('\'fun_app$bj\'_type',type,
    '\'fun_app$bj\'': '\'C_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'quotient3$e\'_type',type,
    '\'quotient3$e\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' > $o ).

thf('\'bijection$b\'_type',type,
    '\'bijection$b\'': '\'A_update_a_update_fun$\'' > $o ).

thf('\'rel_fun$ay\'_type',type,
    '\'rel_fun$ay\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' ).

thf('\'comp$aa\'_type',type,
    '\'comp$aa\'': '\'A_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'fun_app$bi\'_type',type,
    '\'fun_app$bi\'': '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'rel_fun$av\'_type',type,
    '\'rel_fun$av\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' > '\'B_update_c_update_fun_b_update_c_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_c_update_fun_fun_bool_fun_fun$\'' ).

thf('\'pred_fun$f\'_type',type,
    '\'pred_fun$f\'': '\'C_update_bool_fun$\'' > '\'B_update_bool_fun$\'' > '\'C_update_b_update_fun$\'' > $o ).

thf('\'register$e\'_type',type,
    '\'register$e\'': '\'A_b_prod_update_c_a_prod_update_fun$\'' > $o ).

thf('\'compatible$l\'_type',type,
    '\'compatible$l\'': '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > $o ).

thf('\'rel_fun$aa\'_type',type,
    '\'rel_fun$aa\'': '\'A_update_b_update_bool_fun_fun$\'' > '\'C_update_a_update_bool_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'pred_DEADID$b\'_type',type,
    '\'pred_DEADID$b\'': '\'A_update_bool_fun$\'' ).

thf('\'register_pair$t\'_type',type,
    '\'register_pair$t\'': '\'B_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_b_prod_update_c_update_fun$\'' ).

thf('\'fun_app$bd\'_type',type,
    '\'fun_app$bd\'': '\'A_update_b_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'tensor_update$a\'_type',type,
    '\'tensor_update$a\'': '\'A_update$\'' > '\'A_update$\'' > '\'A_a_prod_update$\'' ).

thf('\'fun_app$y\'_type',type,
    '\'fun_app$y\'': '\'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'C_update_a_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'rel_fun$n\'_type',type,
    '\'rel_fun$n\'': '\'A_update_c_update_bool_fun_fun$\'' > '\'A_update_c_update_bool_fun_fun$\'' > '\'A_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'comp$z\'_type',type,
    '\'comp$z\'': '\'C_update_a_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'inv_into$c\'_type',type,
    '\'inv_into$c\'': '\'A_update_set$\'' > '\'A_update_c_update_fun$\'' > '\'C_update_a_update_fun$\'' ).

thf('\'inj_on$\'_type',type,
    '\'inj_on$\'': '\'A_update_b_update_fun$\'' > '\'A_update_set$\'' > $o ).

thf('\'fun_app$bn\'_type',type,
    '\'fun_app$bn\'': '\'C_update_b_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' ).

thf('\'fun_app$av\'_type',type,
    '\'fun_app$av\'': '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'fun_app$cb\'_type',type,
    '\'fun_app$cb\'': '\'C_update_c_update_fun_a_update_a_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'A_update_a_update_fun_bool_fun$\'' ).

thf('\'compatible$i\'_type',type,
    '\'compatible$i\'': '\'C_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > $o ).

thf('\'comp$al\'_type',type,
    '\'comp$al\'': '\'A_a_prod_update_c_update_fun$\'' > '\'C_c_prod_update_a_a_prod_update_fun$\'' > '\'C_c_prod_update_c_update_fun$\'' ).

thf('\'top$e\'_type',type,
    '\'top$e\'': '\'B_update_a_update_fun_set$\'' ).

thf('\'compatible$b\'_type',type,
    '\'compatible$b\'': '\'A_update_b_update_fun$\'' > '\'A_update_b_update_fun$\'' > $o ).

thf('\'grp$h\'_type',type,
    '\'grp$h\'': '\'A_update_set$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_b_update_bool_fun_fun$\'' ).

thf('\'rel_fun$k\'_type',type,
    '\'rel_fun$k\'': '\'B_update_a_update_bool_fun_fun$\'' > '\'A_update_c_update_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'id_update$b\'_type',type,
    '\'id_update$b\'': '\'B_update$\'' ).

thf('\'register_tensor$w\'_type',type,
    '\'register_tensor$w\'': '\'B_update_b_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_b_prod_update_b_c_prod_update_fun$\'' ).

thf('\'fun_app$bz\'_type',type,
    '\'fun_app$bz\'': '\'C_update_c_update_fun_b_update_b_update_fun_bool_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'B_update_b_update_fun_bool_fun$\'' ).

thf('\'type_definition$g\'_type',type,
    '\'type_definition$g\'': '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_set$\'' > $o ).

thf('\'map_fun$ah\'_type',type,
    '\'map_fun$ah\'': '\'A_update_b_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' ).

thf('\'map_fun$aj\'_type',type,
    '\'map_fun$aj\'': '\'B_update_a_update_fun_a_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' ).

thf('\'fun_app$cd\'_type',type,
    '\'fun_app$cd\'': '\'A_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'C_update_c_update_fun_bool_fun$\'' ).

thf('\'compatible$t\'_type',type,
    '\'compatible$t\'': '\'B_update_c_a_prod_update_fun$\'' > '\'A_update_c_a_prod_update_fun$\'' > $o ).

thf('\'rel_fun$w\'_type',type,
    '\'rel_fun$w\'': '\'B_update_a_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'A_update_b_update_fun_a_update_a_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'rel_fun$ax\'_type',type,
    '\'rel_fun$ax\'': '\'A_update_c_update_fun_a_update_b_update_fun_bool_fun_fun$\'' > '\'B_update_a_update_fun_b_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_bool_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > $o ).

thf('\'compatible$c\'_type',type,
    '\'compatible$c\'': '\'B_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > $o ).

thf('\'iso_tuple_update_accessor_cong_assist$f\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$f\'': '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'A_update_b_update_fun$\'' > $o ).

thf('\'comp$aw\'_type',type,
    '\'comp$aw\'': '\'A_update_b_update_fun$\'' > '\'B_c_prod_update_a_update_fun$\'' > '\'B_c_prod_update_b_update_fun$\'' ).

thf('\'inj_on$l\'_type',type,
    '\'inj_on$l\'': '\'C_update_b_update_fun$\'' > '\'C_update_set$\'' > $o ).

thf('\'id$h\'_type',type,
    '\'id$h\'': '\'B_a_prod_update_b_a_prod_update_fun$\'' ).

thf('\'grp$j\'_type',type,
    '\'grp$j\'': '\'B_update_a_update_fun_set$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_fun$\'' > '\'B_update_a_update_fun_b_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'type_definition$b\'_type',type,
    '\'type_definition$b\'': '\'A_update_c_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'C_update_set$\'' > $o ).

thf('\'iso_tuple_update_accessor_cong_assist$\'_type',type,
    '\'iso_tuple_update_accessor_cong_assist$\'': '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'relcompp$\'_type',type,
    '\'relcompp$\'': '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' > '\'A_update_a_update_bool_fun_fun$\'' ).

thf('\'fun_app$i\'_type',type,
    '\'fun_app$i\'': '\'C_update_bool_fun$\'' > '\'C_update$\'' > $o ).

thf('\'fun_app$t\'_type',type,
    '\'fun_app$t\'': '\'A_update_a_c_prod_update_fun$\'' > '\'A_update$\'' > '\'A_c_prod_update$\'' ).

thf('\'map_fun$at\'_type',type,
    '\'map_fun$at\'': '\'A_update_b_update_fun_a_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' > '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' ).

thf('\'register$k\'_type',type,
    '\'register$k\'': '\'B_update_b_update_fun$\'' > $o ).

thf('\'map_fun$d\'_type',type,
    '\'map_fun$d\'': '\'B_update_a_update_fun$\'' > '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'' ).

thf('\'register$j\'_type',type,
    '\'register$j\'': '\'C_update_b_update_fun$\'' > $o ).

thf('\'comp$u\'_type',type,
    '\'comp$u\'': '\'A_b_prod_update_b_a_prod_update_fun$\'' > '\'B_a_prod_update_a_b_prod_update_fun$\'' > '\'B_a_prod_update_b_a_prod_update_fun$\'' ).

thf('\'iso_tuple_surjective_proof_assist$b\'_type',type,
    '\'iso_tuple_surjective_proof_assist$b\'': '\'A_update$\'' > '\'A_update$\'' > '\'A_update_a_update_fun$\'' > $o ).

thf('\'map_fun$r\'_type',type,
    '\'map_fun$r\'': '\'C_update_c_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'fun_app$ax\'_type',type,
    '\'fun_app$ax\'': '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'type_definition$a\'_type',type,
    '\'type_definition$a\'': '\'B_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_set$\'' > $o ).

thf('\'comp$c\'_type',type,
    '\'comp$c\'': '\'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$\'' ).

thf('\'comp$w\'_type',type,
    '\'comp$w\'': '\'A_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'iso_register$\'_type',type,
    '\'iso_register$\'': '\'C_update_a_update_fun$\'' > $o ).

thf('\'preregister$a\'_type',type,
    '\'preregister$a\'': '\'B_update_b_update_fun$\'' > $o ).

thf('\'comp$ax\'_type',type,
    '\'comp$ax\'': '\'A_update_b_update_fun$\'' > '\'B_b_prod_update_a_update_fun$\'' > '\'B_b_prod_update_b_update_fun$\'' ).

thf('\'id$t\'_type',type,
    '\'id$t\'': '\'A_update_b_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'fun_app$bf\'_type',type,
    '\'fun_app$bf\'': '\'C_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'uuh$\'_type',type,
    '\'uuh$\'': '\'A_update_c_update_fun$\'' > '\'A_update_c_a_prod_update_fun$\'' ).

thf('\'register_tensor$y\'_type',type,
    '\'register_tensor$y\'': '\'C_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'C_a_prod_update_a_b_prod_update_fun$\'' ).

thf('\'fun_app$j\'_type',type,
    '\'fun_app$j\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update$\'' > '\'C_update_bool_fun$\'' ).

thf('\'register_tensor$g\'_type',type,
    '\'register_tensor$g\'': '\'A_update_a_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'A_b_prod_update_a_b_prod_update_fun$\'' ).

thf('\'comp$ac\'_type',type,
    '\'comp$ac\'': '\'C_update_a_update_fun$\'' > '\'B_update_c_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'top$d\'_type',type,
    '\'top$d\'': '\'C_update_a_update_fun_set$\'' ).

thf('\'g$a\'_type',type,
    '\'g$a\'': '\'C_update_a_update_fun$\'' ).

thf('\'the_inv_into$d\'_type',type,
    '\'the_inv_into$d\'': '\'C_update_set$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'uuz$\'_type',type,
    '\'uuz$\'': '\'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'fun_app$ba\'_type',type,
    '\'fun_app$ba\'': '\'A_update_b_update_fun_a_update_c_update_fun_fun$\'' > '\'A_update_b_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'preregister$d\'_type',type,
    '\'preregister$d\'': '\'B_update_a_update_fun$\'' > $o ).

thf('\'register_tensor$s\'_type',type,
    '\'register_tensor$s\'': '\'B_update_b_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'B_c_prod_update_b_b_prod_update_fun$\'' ).

thf('\'pred_DEADID$a\'_type',type,
    '\'pred_DEADID$a\'': '\'B_update_bool_fun$\'' ).

thf('\'register$g\'_type',type,
    '\'register$g\'': '\'B_b_prod_update_a_a_prod_update_fun$\'' > $o ).

thf('\'inv_into$a\'_type',type,
    '\'inv_into$a\'': '\'C_update_set$\'' > '\'C_update_a_update_fun$\'' > '\'A_update_c_update_fun$\'' ).

thf('\'the_inv_into$h\'_type',type,
    '\'the_inv_into$h\'': '\'B_update_set$\'' > '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'comp$an\'_type',type,
    '\'comp$an\'': '\'B_c_prod_update_a_update_fun$\'' > '\'A_a_prod_update_b_c_prod_update_fun$\'' > '\'A_a_prod_update_a_update_fun$\'' ).

thf('\'register_tensor$\'_type',type,
    '\'register_tensor$\'': '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_c_prod_update_c_c_prod_update_fun$\'' ).

thf('\'iso_tuple_update_accessor_eq_assist$\'_type',type,
    '\'iso_tuple_update_accessor_eq_assist$\'': '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_bool_fun_fun$\'' ).

thf('\'fun_app$b\'_type',type,
    '\'fun_app$b\'': '\'B_update_a_update_fun_bool_fun$\'' > '\'B_update_a_update_fun$\'' > $o ).

thf('\'inj_on$g\'_type',type,
    '\'inj_on$g\'': '\'C_update_a_update_fun_c_update_b_update_fun_fun$\'' > '\'C_update_a_update_fun_set$\'' > $o ).

thf('\'vimage$a\'_type',type,
    '\'vimage$a\'': '\'B_update_b_update_fun$\'' > '\'B_update_set_b_update_set_fun$\'' ).

thf('\'map_fun$w\'_type',type,
    '\'map_fun$w\'': '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' > '\'B_update_b_update_fun_b_update_b_update_fun_fun$\'' ).

thf('\'fun_app$cf\'_type',type,
    '\'fun_app$cf\'': '\'A_update_a_update_fun_a_update_a_update_fun_bool_fun_fun$\'' > '\'A_update_a_update_fun$\'' > '\'A_update_a_update_fun_bool_fun$\'' ).

thf('\'rel_fun$ad\'_type',type,
    '\'rel_fun$ad\'': '\'C_update_a_update_bool_fun_fun$\'' > '\'C_update_a_update_bool_fun_fun$\'' > '\'C_update_c_update_fun_a_update_a_update_fun_bool_fun_fun$\'' ).

thf('\'image$c\'_type',type,
    '\'image$c\'': '\'A_update_c_update_fun$\'' > '\'A_update_set$\'' > '\'C_update_set$\'' ).

thf('\'comp$bg\'_type',type,
    '\'comp$bg\'': '\'B_update_a_update_fun_a_update_b_update_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_c_update_fun_a_update_b_update_fun_fun$\'' ).

thf('\'register_tensor$x\'_type',type,
    '\'register_tensor$x\'': '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_b_prod_update_b_a_prod_update_fun$\'' ).

thf('\'id_update$a\'_type',type,
    '\'id_update$a\'': '\'A_update$\'' ).

thf('\'map_fun$\'_type',type,
    '\'map_fun$\'': '\'A_update_b_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'comp$ba\'_type',type,
    '\'comp$ba\'': '\'A_update_c_update_fun$\'' > '\'B_c_prod_update_a_update_fun$\'' > '\'B_c_prod_update_c_update_fun$\'' ).

thf('\'rel_fun$r\'_type',type,
    '\'rel_fun$r\'': '\'A_update_b_update_bool_fun_fun$\'' > '\'A_update_c_update_bool_fun_fun$\'' > '\'A_update_a_update_fun_b_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'collect$\'_type',type,
    '\'collect$\'': '\'A_update_b_update_fun_bool_fun$\'' > '\'A_update_b_update_fun_set$\'' ).

thf('\'comp$e\'_type',type,
    '\'comp$e\'': '\'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$\'' ).

thf('\'tensor_update$\'_type',type,
    '\'tensor_update$\'': '\'A_update$\'' > '\'C_update$\'' > '\'A_c_prod_update$\'' ).

thf('\'g$\'_type',type,
    '\'g$\'': '\'A_update_c_update_fun$\'' ).

thf('\'fun_app$af\'_type',type,
    '\'fun_app$af\'': '\'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$\'' > '\'A_update_c_update_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'id$i\'_type',type,
    '\'id$i\'': '\'A_c_prod_update_a_c_prod_update_fun$\'' ).

thf('\'fun_app$ah\'_type',type,
    '\'fun_app$ah\'': '\'B_update_c_update_fun$\'' > '\'B_update$\'' > '\'C_update$\'' ).

thf('\'comp$ai\'_type',type,
    '\'comp$ai\'': '\'C_update_b_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_update_b_update_fun$\'' ).

thf('\'quotient3$\'_type',type,
    '\'quotient3$\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_c_update_fun$\'' > '\'C_update_c_update_fun$\'' > $o ).

thf('\'grp$f\'_type',type,
    '\'grp$f\'': '\'C_update_a_update_fun_set$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_a_update_fun_c_update_c_update_fun_bool_fun_fun$\'' ).

thf('\'comp$bj\'_type',type,
    '\'comp$bj\'': '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'' > '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'fun_app$l\'_type',type,
    '\'fun_app$l\'': '\'B_update_b_update_bool_fun_fun$\'' > '\'B_update$\'' > '\'B_update_bool_fun$\'' ).

thf('\'comp$bc\'_type',type,
    '\'comp$bc\'': '\'B_update_a_update_fun$\'' > '\'A_a_prod_update_b_update_fun$\'' > '\'A_a_prod_update_a_update_fun$\'' ).

thf('\'id$o\'_type',type,
    '\'id$o\'': '\'C_update_b_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'fun_app$ai\'_type',type,
    '\'fun_app$ai\'': '\'C_update_b_update_fun$\'' > '\'C_update$\'' > '\'B_update$\'' ).

thf('\'rel_fun$aq\'_type',type,
    '\'rel_fun$aq\'': '\'C_update_c_update_bool_fun_fun$\'' > '\'C_update_b_update_bool_fun_fun$\'' > '\'C_update_c_update_fun_c_update_b_update_fun_bool_fun_fun$\'' ).

thf('\'the_inv_into$c\'_type',type,
    '\'the_inv_into$c\'': '\'A_update_set$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' ).

thf('\'map_fun$t\'_type',type,
    '\'map_fun$t\'': '\'C_update_c_update_fun$\'' > '\'C_update_b_update_fun$\'' > '\'C_update_c_update_fun_c_update_b_update_fun_fun$\'' ).

thf('\'id$p\'_type',type,
    '\'id$p\'': '\'C_update_a_update_fun_c_update_a_update_fun_fun$\'' ).

thf('\'comp$p\'_type',type,
    '\'comp$p\'': '\'A_a_prod_update_b_c_prod_update_fun$\'' > '\'C_c_prod_update_a_a_prod_update_fun$\'' > '\'C_c_prod_update_b_c_prod_update_fun$\'' ).

thf('\'inv_into$d\'_type',type,
    '\'inv_into$d\'': '\'C_update_set$\'' > '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'' ).

thf('\'map_fun$e\'_type',type,
    '\'map_fun$e\'': '\'A_update_a_update_fun$\'' > '\'C_update_c_update_fun$\'' > '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'' ).

thf('\'inj_on$f\'_type',type,
    '\'inj_on$f\'': '\'B_update_a_update_fun_b_update_c_update_fun_fun$\'' > '\'B_update_a_update_fun_set$\'' > $o ).

thf('\'comp$be\'_type',type,
    '\'comp$be\'': '\'B_update_a_update_fun_a_update_c_update_fun_fun$\'' > '\'A_update_c_update_fun_b_update_a_update_fun_fun$\'' > '\'A_update_c_update_fun_a_update_c_update_fun_fun$\'' ).

thf('\'fun_app$au\'_type',type,
    '\'fun_app$au\'': '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'' > '\'B_update_b_update_fun$\'' > '\'A_update_a_update_fun$\'' ).

thf('\'inj_on$k\'_type',type,
    '\'inj_on$k\'': '\'B_update_c_update_fun$\'' > '\'B_update_set$\'' > $o ).

thf('\'map_fun$k\'_type',type,
    '\'map_fun$k\'': '\'C_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun_c_update_a_update_fun_fun$\'' ).

thf('\'fcomp$d\'_type',type,
    '\'fcomp$d\'': '\'B_update_a_update_fun$\'' > '\'A_update_b_update_fun$\'' > '\'B_update_b_update_fun$\'' ).

thf('\'register_tensor$t\'_type',type,
    '\'register_tensor$t\'': '\'A_update_b_update_fun$\'' > '\'A_update_c_update_fun$\'' > '\'A_a_prod_update_b_c_prod_update_fun$\'' ).

thf('\'comp$ad\'_type',type,
    '\'comp$ad\'': '\'A_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' > '\'B_update_a_update_fun$\'' ).

thf('\'inv_into$f\'_type',type,
    '\'inv_into$f\'': '\'A_update_set$\'' > '\'A_update_a_update_fun_a_update_a_update_fun_fun$\'' ).

thf(419,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$ae\'' @ A @ B )
        = C )
     => ( ( '\'comp$i\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom136) ).

thf(2163,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$ae\'' @ A @ B )
        = C )
     => ( ( '\'comp$i\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(431,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$g\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ '\'uuq$\'' @ A ) ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).

thf(2199,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$g\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ '\'uuq$\'' @ A ) ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(114,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
         => ( ( '\'fun_app$u\'' @ B @ D )
            = ( '\'fun_app$u\'' @ C @ D ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom558) ).

thf(1036,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
         => ( ( '\'fun_app$u\'' @ B @ D )
            = ( '\'fun_app$u\'' @ C @ D ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(35,axiom,
    ! [A: '\'A_update_set$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'rel_fun$a\'' @ '\'uuq$\'' @ ( '\'grp$e\'' @ A @ B ) )
      = ( '\'grp$f\'' @ ( '\'collect$a\'' @ ( '\'uux$\'' @ A ) ) @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom606) ).

thf(760,plain,
    ! [A: '\'A_update_set$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'rel_fun$a\'' @ '\'uuq$\'' @ ( '\'grp$e\'' @ A @ B ) )
      = ( '\'grp$f\'' @ ( '\'collect$a\'' @ ( '\'uux$\'' @ A ) ) @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(401,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$p\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).

thf(2109,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$p\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(272,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$j\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$l\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$n\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).

thf(1633,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$j\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$l\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$n\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(491,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ B )
        & ( '\'inj_on$c\'' @ C @ ( '\'image$b\'' @ A @ B ) ) )
     => ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).

thf(2412,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ B )
        & ( '\'inj_on$c\'' @ C @ ( '\'image$b\'' @ A @ B ) ) )
     => ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(647,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'B_update_c_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'C_update_c_update_fun$\'',G: '\'C_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$c\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'comp$\'' @ D @ G ) ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$aj\'' @ D @ H ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).

thf(2921,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'B_update_c_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'C_update_c_update_fun$\'',G: '\'C_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$c\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'comp$\'' @ D @ G ) ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$aj\'' @ D @ H ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(344,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$aa\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ab\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ F @ A ) ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).

thf(1899,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$aa\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ab\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ F @ A ) ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(83,axiom,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ! [B: '\'A_update$\''] :
          ( ( '\'fun_app$ab\'' @ A @ B )
          = B )
    <=> ( A = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).

thf(941,plain,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( ! [B: '\'A_update$\''] :
            ( ( '\'fun_app$ab\'' @ A @ B )
            = B )
       => ( A = '\'id$b\'' ) )
      & ( ( A = '\'id$b\'' )
       => ! [B: '\'A_update$\''] :
            ( ( '\'fun_app$ab\'' @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(40,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( '\'iso_register$a\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).

thf(777,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( '\'iso_register$a\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(7,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'register$l\'' @ A )
        & ( '\'register$l\'' @ B )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( '\'iso_register$h\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom101) ).

thf(666,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'register$l\'' @ A )
        & ( '\'register$l\'' @ B )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( '\'iso_register$h\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(251,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$z\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ A ) ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).

thf(1549,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$z\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ A ) ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(236,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$h\'' @ B ) )
     => ( '\'register$\'' @ ( '\'comp$ah\'' @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).

thf(1501,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$h\'' @ B ) )
     => ( '\'register$\'' @ ( '\'comp$ah\'' @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(504,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom177) ).

thf(2452,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(593,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( '\'iso_tuple_surjective_proof_assist$\'' @ A @ B @ '\'id$\'' )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).

thf(2744,plain,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( '\'iso_tuple_surjective_proof_assist$\'' @ A @ B @ '\'id$\'' )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(637,axiom,
    ! [A: '\'A_update_set$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'rel_fun$c\'' @ '\'uuq$\'' @ ( '\'grp$h\'' @ A @ B ) )
      = ( '\'grp$i\'' @ ( '\'collect$a\'' @ ( '\'uux$\'' @ A ) ) @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom608) ).

thf(2889,plain,
    ! [A: '\'A_update_set$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'rel_fun$c\'' @ '\'uuq$\'' @ ( '\'grp$h\'' @ A @ B ) )
      = ( '\'grp$i\'' @ ( '\'collect$a\'' @ ( '\'uux$\'' @ A ) ) @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(154,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).

thf(1190,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(607,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) )
        & ( ! [E: '\'B_update$\''] :
              ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
              = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom156) ).

thf(2787,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ~ ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) )
        & ~ ! [E: '\'B_update$\''] :
              ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
              = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(516,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).

thf(2499,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(128,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$aa\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ A ) ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom213) ).

thf(1083,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$aa\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ A ) ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(370,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$a\'' @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).

thf(1982,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$a\'' @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(159,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$ai\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom616) ).

thf(1211,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$ai\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(462,axiom,
    ! [A: '\'B_update_c_update_fun$\''] :
      ( ( '\'iso_register$e\'' @ A )
    <=> ( ( '\'register$i\'' @ A )
        & ? [B: '\'C_update_b_update_fun$\''] :
            ( ( '\'register$j\'' @ B )
            & ( ( '\'comp$\'' @ A @ B )
              = '\'id$\'' )
            & ( ( '\'comp$v\'' @ B @ A )
              = '\'id$a\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).

thf(2309,plain,
    ! [A: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'iso_register$e\'' @ A )
       => ( ( '\'register$i\'' @ A )
          & ? [B: '\'C_update_b_update_fun$\''] :
              ( ( '\'register$j\'' @ B )
              & ( ( '\'comp$\'' @ A @ B )
                = '\'id$\'' )
              & ( ( '\'comp$v\'' @ B @ A )
                = '\'id$a\'' ) ) ) )
      & ( ( ( '\'register$i\'' @ A )
          & ? [B: '\'C_update_b_update_fun$\''] :
              ( ( '\'register$j\'' @ B )
              & ( ( '\'comp$\'' @ A @ B )
                = '\'id$\'' )
              & ( ( '\'comp$v\'' @ B @ A )
                = '\'id$a\'' ) ) )
       => ( '\'iso_register$e\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(102,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$w\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$x\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$y\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).

thf(1005,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$w\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$x\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$y\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(13,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uuh$\'' @ A ) @ B )
      = ( '\'tensor_update$c\'' @ ( '\'fun_app$g\'' @ A @ B ) @ '\'id_update$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).

thf(683,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uuh$\'' @ A ) @ B )
      = ( '\'tensor_update$c\'' @ ( '\'fun_app$g\'' @ A @ B ) @ '\'id_update$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(175,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$g\'' @ ( '\'register_tensor$l\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom77) ).

thf(1290,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$g\'' @ ( '\'register_tensor$l\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(554,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).

thf(2622,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(220,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ C @ B ) ) @ ( '\'inv_into$b\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).

thf(1443,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ C @ B ) ) @ ( '\'inv_into$b\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(208,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$a\'' @ B @ '\'top$a\'' ) )
     => ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ '\'top$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).

thf(1401,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$a\'' @ B @ '\'top$a\'' ) )
     => ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ '\'top$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(446,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$b\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$as\'' @ ( '\'register_pair$d\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_pair$n\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).

thf(2248,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$b\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$as\'' @ ( '\'register_pair$d\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_pair$n\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(125,axiom,
    ! [A: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).

thf(1073,plain,
    ! [A: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(572,axiom,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ! [B: '\'C_update$\''] :
          ( ( '\'fun_app$z\'' @ A @ B )
          = B )
    <=> ( A = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).

thf(2671,plain,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( ! [B: '\'C_update$\''] :
            ( ( '\'fun_app$z\'' @ A @ B )
            = B )
       => ( A = '\'id$\'' ) )
      & ( ( A = '\'id$\'' )
       => ! [B: '\'C_update$\''] :
            ( ( '\'fun_app$z\'' @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(295,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$ai\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom635) ).

thf(1728,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$ai\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(63,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update$\'',C: '\'B_update$\''] :
      ( ( '\'register$a\'' @ A )
     => ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ B ) ) @ ( '\'fun_app$d\'' @ A @ C ) )
        = ( '\'fun_app$d\'' @ A @ ( '\'fun_app$aa\'' @ ( '\'comp_update$b\'' @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom279) ).

thf(873,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update$\'',C: '\'B_update$\''] :
      ( ( '\'register$a\'' @ A )
     => ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ B ) ) @ ( '\'fun_app$d\'' @ A @ C ) )
        = ( '\'fun_app$d\'' @ A @ ( '\'fun_app$aa\'' @ ( '\'comp_update$b\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(11,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$bd\'' @ ( '\'map_fun$\'' @ A @ B ) @ ( '\'map_fun$a\'' @ C @ D ) )
      = ( '\'map_fun$b\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).

thf(677,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$bd\'' @ ( '\'map_fun$\'' @ A @ B ) @ ( '\'map_fun$a\'' @ C @ D ) )
      = ( '\'map_fun$b\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(477,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$e\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$\'' @ D ) )
     => ( ( '\'comp$ap\'' @ ( '\'register_pair$i\'' @ A @ B ) @ ( '\'register_tensor$ab\'' @ C @ D ) )
        = ( '\'register_pair$j\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'comp$ai\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).

thf(2363,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$e\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$\'' @ D ) )
     => ( ( '\'comp$ap\'' @ ( '\'register_pair$i\'' @ A @ B ) @ ( '\'register_tensor$ab\'' @ C @ D ) )
        = ( '\'register_pair$j\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'comp$ai\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(333,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$x\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ C )
          = F ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ E @ A ) ) @ B )
        = ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom118) ).

thf(1855,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$x\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ C )
          = F ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ E @ A ) ) @ B )
        = ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(261,axiom,
    ( ( '\'map_fun$x\'' @ '\'id$a\'' @ '\'id$b\'' )
    = '\'id$r\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).

thf(1596,plain,
    ( ( '\'map_fun$x\'' @ '\'id$a\'' @ '\'id$b\'' )
    = '\'id$r\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(399,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$bl\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'map_fun$o\'' @ C @ D ) )
      = ( '\'map_fun$t\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).

thf(2104,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$bl\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'map_fun$o\'' @ C @ D ) )
      = ( '\'map_fun$t\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(485,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$v\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) )
      = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$ai\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).

thf(2395,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$v\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) )
      = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$ai\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(389,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bh\'' @ ( '\'rel_fun$bb\'' @ A @ B ) @ ( '\'rel_fun$bi\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$bj\'' @ '\'uur$\'' @ B ) ) @ '\'comp$e\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).

thf(2062,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bh\'' @ ( '\'rel_fun$bb\'' @ A @ B ) @ ( '\'rel_fun$bi\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$bj\'' @ '\'uur$\'' @ B ) ) @ '\'comp$e\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(403,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$c\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$o\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).

thf(2114,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$c\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$o\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(170,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'register_tensor$j\'' @ A @ B ) @ ( '\'tensor_update$d\'' @ C @ D ) )
        = ( '\'tensor_update$c\'' @ ( '\'fun_app$g\'' @ A @ C ) @ ( '\'fun_app$d\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom202) ).

thf(1269,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'register_tensor$j\'' @ A @ B ) @ ( '\'tensor_update$d\'' @ C @ D ) )
        = ( '\'tensor_update$c\'' @ ( '\'fun_app$g\'' @ A @ C ) @ ( '\'fun_app$d\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(628,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$y\'' @ A @ B )
        = C )
     => ( ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).

thf(2854,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$y\'' @ A @ B )
        = C )
     => ( ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(247,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'B_update_c_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'B_update_c_update_fun$\'',G: '\'B_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$c\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$c\'' @ E @ F @ '\'top$b\'' )
        & ( ( '\'comp$\'' @ ( '\'comp$af\'' @ D @ G ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$aj\'' @ D @ H ) @ A ) ) @ ( '\'comp$ae\'' @ ( '\'comp$ad\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).

thf(1533,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'B_update_c_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'B_update_c_update_fun$\'',G: '\'B_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$c\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$c\'' @ E @ F @ '\'top$b\'' )
        & ( ( '\'comp$\'' @ ( '\'comp$af\'' @ D @ G ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$aj\'' @ D @ H ) @ A ) ) @ ( '\'comp$ae\'' @ ( '\'comp$ad\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(115,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$cc\'' @ ( '\'rel_fun$bm\'' @ A @ A ) @ '\'id$a\'' ) @ '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom661) ).

thf(1041,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$cc\'' @ ( '\'rel_fun$bm\'' @ A @ A ) @ '\'id$a\'' ) @ '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(61,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ '\'top$b\'' )
      = ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ '\'top$b\'' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).

thf(861,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ '\'top$b\'' )
      = ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ '\'top$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(577,axiom,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ '\'id$\'' ) @ B ) )
      = ( '\'fun_app$bt\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).

thf(2686,plain,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ '\'id$\'' ) @ B ) )
      = ( '\'fun_app$bt\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(297,axiom,
    '\'quotient3$a\'' @ '\'uur$\'' @ '\'id$a\'' @ '\'id$a\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).

thf(1735,plain,
    '\'quotient3$a\'' @ '\'uur$\'' @ '\'id$a\'' @ '\'id$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(172,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'B_update$\''] :
            ( ( '\'member$a\'' @ E @ ( '\'image$\'' @ B @ '\'top$\'' ) )
           => ( ( '\'fun_app$d\'' @ C @ E )
              = ( '\'fun_app$d\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).

thf(1275,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'B_update$\''] :
            ( ( '\'member$a\'' @ E @ ( '\'image$\'' @ B @ '\'top$\'' ) )
           => ( ( '\'fun_app$d\'' @ C @ E )
              = ( '\'fun_app$d\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(75,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update$\''] :
      ( ( A
        = ( '\'fun_app$ab\'' @ B @ C ) )
     => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ ( '\'iso_tuple_update_accessor_eq_assist$b\'' @ '\'id$n\'' @ '\'id$b\'' @ C @ B ) @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).

thf(913,plain,
    ! [A: '\'A_update$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update$\''] :
      ( ( A
        = ( '\'fun_app$ab\'' @ B @ C ) )
     => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ ( '\'iso_tuple_update_accessor_eq_assist$b\'' @ '\'id$n\'' @ '\'id$b\'' @ C @ B ) @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(275,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'quotient3$e\'' @ A @ B @ C )
     => ( ( '\'fun_app$av\'' @ ( '\'map_fun$a\'' @ C @ B ) @ '\'id$b\'' )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).

thf(1640,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'quotient3$e\'' @ A @ B @ C )
     => ( ( '\'fun_app$av\'' @ ( '\'map_fun$a\'' @ C @ B ) @ '\'id$b\'' )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(238,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( ( '\'fun_app$aq\'' @ ( '\'register_tensor$k\'' @ A @ B ) @ ( '\'tensor_update$e\'' @ C @ D ) )
        = ( '\'tensor_update$\'' @ ( '\'fun_app$d\'' @ A @ C ) @ ( '\'fun_app$g\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom203) ).

thf(1507,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( ( '\'fun_app$aq\'' @ ( '\'register_tensor$k\'' @ A @ B ) @ ( '\'tensor_update$e\'' @ C @ D ) )
        = ( '\'tensor_update$\'' @ ( '\'fun_app$d\'' @ A @ C ) @ ( '\'fun_app$g\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(8,axiom,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( '\'bijection$b\'' @ A )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ A ) )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom467) ).

thf(670,plain,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( '\'bijection$b\'' @ A )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ A ) )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(429,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$b\'' @ B @ '\'top$b\'' ) )
     => ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ '\'top$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).

thf(2195,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$b\'' @ B @ '\'top$b\'' ) )
     => ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ '\'top$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(290,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\''] :
      ( ( '\'fun_app$bl\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'fun_app$bj\'' @ ( '\'map_fun$q\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bn\'' @ ( '\'map_fun$u\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).

thf(1705,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\''] :
      ( ( '\'fun_app$bl\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'fun_app$bj\'' @ ( '\'map_fun$q\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bn\'' @ ( '\'map_fun$u\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(51,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).

thf(814,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(186,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'A_update_a_update_fun$\'',H: '\'B_update_a_update_fun$\'',I: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$d\'' @ A @ B @ '\'top$b\'' )
        & ( '\'type_definition$e\'' @ C @ D @ '\'top$\'' )
        & ( '\'type_definition$e\'' @ E @ F @ '\'top$\'' )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ D ) @ G ) ) @ E )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ ( '\'comp$ad\'' @ D @ H ) @ A ) ) @ ( '\'comp$w\'' @ ( '\'comp$x\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).

thf(1327,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'A_update_a_update_fun$\'',H: '\'B_update_a_update_fun$\'',I: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$d\'' @ A @ B @ '\'top$b\'' )
        & ( '\'type_definition$e\'' @ C @ D @ '\'top$\'' )
        & ( '\'type_definition$e\'' @ E @ F @ '\'top$\'' )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ D ) @ G ) ) @ E )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ ( '\'comp$ad\'' @ D @ H ) @ A ) ) @ ( '\'comp$w\'' @ ( '\'comp$x\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(509,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ B )
     => ( ( '\'inj_on$\'' @ C @ ( '\'image$a\'' @ A @ B ) )
      <=> ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).

thf(2476,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ B )
     => ( ( ( '\'inj_on$\'' @ C @ ( '\'image$a\'' @ A @ B ) )
         => ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ B ) )
        & ( ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ B )
         => ( '\'inj_on$\'' @ C @ ( '\'image$a\'' @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(420,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$c\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).

thf(2168,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$c\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(132,axiom,
    ! [A: '\'A_update_set$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$a\'' @ ( '\'uux$\'' @ A ) @ B )
    <=> ( '\'less_eq$a\'' @ ( '\'image$a\'' @ B @ '\'top$a\'' ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).

thf(1095,plain,
    ! [A: '\'A_update_set$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$a\'' @ ( '\'uux$\'' @ A ) @ B )
       => ( '\'less_eq$a\'' @ ( '\'image$a\'' @ B @ '\'top$a\'' ) @ A ) )
      & ( ( '\'less_eq$a\'' @ ( '\'image$a\'' @ B @ '\'top$a\'' ) @ A )
       => ( '\'fun_app$a\'' @ ( '\'uux$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(328,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'compatible$a\'' @ A @ B )
    <=> ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).

thf(1835,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$a\'' @ A @ B )
       => ( ( '\'register$\'' @ A )
          & ( '\'register$\'' @ B )
          & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
              ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
              = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) ) )
      & ( ( ( '\'register$\'' @ A )
          & ( '\'register$\'' @ B )
          & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
              ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
              = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) )
       => ( '\'compatible$a\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(385,axiom,
    ! [A: '\'C_update_bool_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'pred_fun$e\'' @ '\'uuo$\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) )
    <=> ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'comp$bo\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom351) ).

thf(2046,plain,
    ! [A: '\'C_update_bool_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'pred_fun$e\'' @ '\'uuo$\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) )
       => ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'comp$bo\'' @ A @ B ) @ C ) )
      & ( ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'comp$bo\'' @ A @ B ) @ C )
       => ( '\'pred_fun$e\'' @ '\'uuo$\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(204,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).

thf(1391,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(42,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ C ) )
      = ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).

thf(782,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ C ) )
      = ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(22,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'register$k\'' @ A )
        & ( '\'register$k\'' @ B )
        & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( '\'iso_register$g\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).

thf(709,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'register$k\'' @ A )
        & ( '\'register$k\'' @ B )
        & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( '\'iso_register$g\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(277,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$d\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$d\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$aa\'' @ ( '\'map_fun$d\'' @ E @ I ) @ ( '\'map_fun$ab\'' @ ( '\'map_fun$l\'' @ B @ F ) @ ( '\'map_fun$n\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$d\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).

thf(1650,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$d\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$d\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$aa\'' @ ( '\'map_fun$d\'' @ E @ I ) @ ( '\'map_fun$ab\'' @ ( '\'map_fun$l\'' @ B @ F ) @ ( '\'map_fun$n\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$d\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(196,axiom,
    ! [A: '\'A_update$\'',B: '\'B_update$\''] :
      ( ( '\'fun_app$d\'' @ ( '\'uu$\'' @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).

thf(1359,plain,
    ! [A: '\'A_update$\'',B: '\'B_update$\''] :
      ( ( '\'fun_app$d\'' @ ( '\'uu$\'' @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(294,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ E ) ) @ ( '\'fun_app$g\'' @ B @ F ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ F ) ) @ ( '\'fun_app$g\'' @ A @ E ) ) ) )
     => ( ( '\'fun_app$as\'' @ ( '\'register_pair$b\'' @ A @ B ) @ ( '\'tensor_update$a\'' @ C @ D ) )
        = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).

thf(1724,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ E ) ) @ ( '\'fun_app$g\'' @ B @ F ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ F ) ) @ ( '\'fun_app$g\'' @ A @ E ) ) ) )
     => ( ( '\'fun_app$as\'' @ ( '\'register_pair$b\'' @ A @ B ) @ ( '\'tensor_update$a\'' @ C @ D ) )
        = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(521,axiom,
    '\'iso_register$d\'' @ '\'id$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).

thf(2516,plain,
    '\'iso_register$d\'' @ '\'id$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(391,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$aj\'' @ B @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).

thf(2067,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$aj\'' @ B @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(317,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$h\'' @ B @ C ) )
     => ( ( '\'register_pair$c\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) )
        = ( '\'comp$ay\'' @ A @ ( '\'register_pair$p\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).

thf(1803,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$h\'' @ B @ C ) )
     => ( ( '\'register_pair$c\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) )
        = ( '\'comp$ay\'' @ A @ ( '\'register_pair$p\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(342,axiom,
    '\'preregister$a\'' @ '\'id$a\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).

thf(1887,plain,
    '\'preregister$a\'' @ '\'id$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(164,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$x\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).

thf(1243,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$x\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(310,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).

thf(1782,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(410,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$n\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$r\'' @ C @ D ) )
        = ( '\'register_tensor$s\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).

thf(2136,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$n\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$r\'' @ C @ D ) )
        = ( '\'register_tensor$s\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(241,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( ( '\'inv_into$b\'' @ '\'top$\'' @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).

thf(1518,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( ( '\'inv_into$b\'' @ '\'top$\'' @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(527,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$q\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_tensor$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).

thf(2531,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$q\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_tensor$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(488,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$ai\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'comp$i\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).

thf(2405,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$ai\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'comp$i\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(230,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'uu$\'' @ A ) ) @ B ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).

thf(1482,plain,
    ! [A: '\'A_update$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'uu$\'' @ A ) ) @ B ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(166,axiom,
    ! [A: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).

thf(1254,plain,
    ! [A: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(566,axiom,
    ! [A: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ '\'id$\'' @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).

thf(2654,plain,
    ! [A: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ '\'id$\'' @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(590,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'the_inv_into$g\'' @ C @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'the_inv_into$\'' @ C @ B ) ) @ ( '\'the_inv_into$b\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom603) ).

thf(2735,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'the_inv_into$g\'' @ C @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'the_inv_into$\'' @ C @ B ) ) @ ( '\'the_inv_into$b\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(383,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$ah\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom211) ).

thf(2039,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$ah\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(43,axiom,
    ! [A: '\'B_update_bool_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'pred_fun$g\'' @ '\'uuo$\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) )
    <=> ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'comp$bp\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom353) ).

thf(785,plain,
    ! [A: '\'B_update_bool_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'pred_fun$g\'' @ '\'uuo$\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) )
       => ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'comp$bp\'' @ A @ B ) @ C ) )
      & ( ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'comp$bp\'' @ A @ B ) @ C )
       => ( '\'pred_fun$g\'' @ '\'uuo$\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(187,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cf\'' @ ( '\'rel_fun$i\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom656) ).

thf(1330,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cf\'' @ ( '\'rel_fun$i\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(185,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ E ) )
        = ( '\'fun_app$d\'' @ C @ ( '\'fun_app$u\'' @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).

thf(1323,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ E ) )
        = ( '\'fun_app$d\'' @ C @ ( '\'fun_app$u\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(47,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$ar\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$as\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$at\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom638) ).

thf(802,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$ar\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$as\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$at\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(513,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C
          = ( '\'comp$z\'' @ D @ E ) ) )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) @ G )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$z\'' @ B @ E ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).

thf(2488,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C
          = ( '\'comp$z\'' @ D @ E ) ) )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) @ G )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$z\'' @ B @ E ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(373,axiom,
    ( ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
        ( ( ( '\'register$a\'' @ A )
          & ( '\'register$\'' @ B )
          & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ '\'f$a\'' ) @ A )
            = '\'id$a\'' )
          & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ '\'f$a\'' )
            = '\'id$b\'' )
          & ( ( '\'comp$k\'' @ '\'g$a\'' @ B )
            = '\'id$b\'' )
          & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ '\'g$a\'' )
            = '\'id$\'' ) )
       => $false )
   => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).

thf(1992,plain,
    ~ ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
        ~ ( ( '\'register$a\'' @ A )
          & ( '\'register$\'' @ B )
          & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ '\'f$a\'' ) @ A )
            = '\'id$a\'' )
          & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ '\'f$a\'' )
            = '\'id$b\'' )
          & ( ( '\'comp$k\'' @ '\'g$a\'' @ B )
            = '\'id$b\'' )
          & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ '\'g$a\'' )
            = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(120,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$c\'' @ A @ '\'top$\'' )
        = '\'top$a\'' )
    <=> ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).

thf(1055,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$c\'' @ A @ '\'top$\'' )
          = '\'top$a\'' )
       => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) )
          = '\'id$\'' ) )
      & ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) )
          = '\'id$\'' )
       => ( ( '\'image$c\'' @ A @ '\'top$\'' )
          = '\'top$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(24,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\''] :
      ( ( '\'fun_app$au\'' @ ( '\'map_fun$\'' @ A @ B ) @ ( '\'fun_app$av\'' @ ( '\'map_fun$a\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$al\'' @ ( '\'map_fun$b\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).

thf(724,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\''] :
      ( ( '\'fun_app$au\'' @ ( '\'map_fun$\'' @ A @ B ) @ ( '\'fun_app$av\'' @ ( '\'map_fun$a\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$al\'' @ ( '\'map_fun$b\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(548,axiom,
    ! [A: '\'C_update$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'uua$\'' @ A ) ) @ B ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).

thf(2603,plain,
    ! [A: '\'C_update$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'uua$\'' @ A ) ) @ B ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(466,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$au\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$av\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$aw\'' @ '\'uur$\'' @ B ) ) @ '\'comp$a\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom623) ).

thf(2328,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$au\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$av\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$aw\'' @ '\'uur$\'' @ B ) ) @ '\'comp$a\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(239,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$b\'' @ A @ B )
        & ( '\'register$a\'' @ C ) )
     => ( '\'compatible$q\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).

thf(1511,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$b\'' @ A @ B )
        & ( '\'register$a\'' @ C ) )
     => ( '\'compatible$q\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(76,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$d\'' @ A @ B @ '\'top$b\'' )
        & ( C = '\'id$a\'' ) )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ C ) ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).

thf(917,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$d\'' @ A @ B @ '\'top$b\'' )
        & ( C = '\'id$a\'' ) )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ C ) ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(19,axiom,
    ! [A: '\'A_update_set$\''] : ( '\'inj_on$i\'' @ '\'id$b\'' @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).

thf(702,plain,
    ! [A: '\'A_update_set$\''] : ( '\'inj_on$i\'' @ '\'id$b\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(32,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$t\'' @ ( '\'uue$\'' @ A ) @ B )
      = ( '\'tensor_update$\'' @ '\'id_update$a\'' @ ( '\'fun_app$g\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).

thf(751,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$t\'' @ ( '\'uue$\'' @ A ) @ B )
      = ( '\'tensor_update$\'' @ '\'id_update$a\'' @ ( '\'fun_app$g\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(575,axiom,
    ! [A: '\'C_update_set$\''] : ( '\'inj_on$j\'' @ '\'id$\'' @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).

thf(2682,plain,
    ! [A: '\'C_update_set$\''] : ( '\'inj_on$j\'' @ '\'id$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(325,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom401) ).

thf(1826,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(426,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'B_update$\''] :
            ( ( '\'member$a\'' @ E @ B )
           => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).

thf(2185,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'B_update$\''] :
            ( ( '\'member$a\'' @ E @ B )
           => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(257,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( '\'iso_register$a\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).

thf(1577,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( '\'iso_register$a\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(224,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
              & ( ( '\'fun_app$u\'' @ C @ E )
                = ( '\'fun_app$u\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A )
          = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).

thf(1455,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
              & ( ( '\'fun_app$u\'' @ C @ E )
                = ( '\'fun_app$u\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A )
          = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(640,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'C_update$\''] :
            ( ( '\'member$b\'' @ E @ B )
           => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).

thf(2897,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'C_update$\''] :
            ( ( '\'member$b\'' @ E @ B )
           => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(81,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update$\'',D: '\'B_update_b_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ab\'' @ B @ C ) )
        = ( '\'fun_app$aa\'' @ D @ ( '\'fun_app$u\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ A ) ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).

thf(934,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update$\'',D: '\'B_update_b_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ab\'' @ B @ C ) )
        = ( '\'fun_app$aa\'' @ D @ ( '\'fun_app$u\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ A ) ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(540,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom217) ).

thf(2571,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(475,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'inv_into$g\'' @ C @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'inv_into$\'' @ C @ B ) ) @ ( '\'inv_into$c\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).

thf(2356,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'inv_into$g\'' @ C @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'inv_into$\'' @ C @ B ) ) @ ( '\'inv_into$c\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(494,axiom,
    ( ( '\'map_fun$u\'' @ '\'id$\'' @ '\'id$a\'' )
    = '\'id$o\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).

thf(2420,plain,
    ( ( '\'map_fun$u\'' @ '\'id$\'' @ '\'id$a\'' )
    = '\'id$o\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(52,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( A = B )
    <=> ? [C: '\'A_update$\''] :
          ( ( '\'member$\'' @ C @ '\'top$\'' )
          & ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ C )
            = A )
          & ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ C )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom392) ).

thf(817,plain,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( ( A = B )
       => ? [C: '\'A_update$\''] :
            ( ( '\'member$\'' @ C @ '\'top$\'' )
            & ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ C )
              = A )
            & ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ C )
              = B ) ) )
      & ( ? [C: '\'A_update$\''] :
            ( ( '\'member$\'' @ C @ '\'top$\'' )
            & ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ C )
              = A )
            & ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ C )
              = B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(316,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$c\'' @ A @ B )
        & ( '\'register$c\'' @ C )
        & ( '\'register$\'' @ D ) )
     => ( ( '\'comp$an\'' @ ( '\'register_pair$f\'' @ A @ B ) @ ( '\'register_tensor$t\'' @ C @ D ) )
        = ( '\'register_pair$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) @ ( '\'comp$k\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).

thf(1800,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$c\'' @ A @ B )
        & ( '\'register$c\'' @ C )
        & ( '\'register$\'' @ D ) )
     => ( ( '\'comp$an\'' @ ( '\'register_pair$f\'' @ A @ B ) @ ( '\'register_tensor$t\'' @ C @ D ) )
        = ( '\'register_pair$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) @ ( '\'comp$k\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(129,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).

thf(1087,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(105,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'compatible$v\'' @ ( '\'uuh$\'' @ A ) @ ( '\'uug$\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).

thf(1013,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'compatible$v\'' @ ( '\'uuh$\'' @ A ) @ ( '\'uug$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(138,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
        = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).

thf(1115,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
        = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(353,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).

thf(1931,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(417,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$v\'' @ A @ B )
          = '\'id$a\'' )
        & ( ( '\'comp$\'' @ B @ A )
          = '\'id$\'' ) )
     => ( ( '\'inv_into$h\'' @ '\'top$a\'' @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).

thf(2158,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$v\'' @ A @ B )
          = '\'id$a\'' )
        & ( ( '\'comp$\'' @ B @ A )
          = '\'id$\'' ) )
     => ( ( '\'inv_into$h\'' @ '\'top$a\'' @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(380,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom226) ).

thf(2024,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(321,axiom,
    ( ( '\'register_tensor$h\'' @ '\'id$b\'' @ '\'id$b\'' )
    = '\'id$k\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).

thf(1815,plain,
    ( ( '\'register_tensor$h\'' @ '\'id$b\'' @ '\'id$b\'' )
    = '\'id$k\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(197,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ C ) )
      = ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).

thf(1362,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ C ) )
      = ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(133,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).

thf(1100,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(165,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'uup$\'' @ A @ B ) @ C )
    <=> ( ( '\'fun_app$u\'' @ A @ C )
        = ( '\'fun_app$u\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).

thf(1247,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( ( '\'fun_app$m\'' @ ( '\'uup$\'' @ A @ B ) @ C )
       => ( ( '\'fun_app$u\'' @ A @ C )
          = ( '\'fun_app$u\'' @ B @ C ) ) )
      & ( ( ( '\'fun_app$u\'' @ A @ C )
          = ( '\'fun_app$u\'' @ B @ C ) )
       => ( '\'fun_app$m\'' @ ( '\'uup$\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(535,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$bx\'' @ ( '\'rel_fun$ai\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom657) ).

thf(2552,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$bx\'' @ ( '\'rel_fun$ai\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(229,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'fun_app$ax\'' @ ( '\'map_fun$d\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$ay\'' @ ( '\'map_fun$e\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).

thf(1479,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'fun_app$ax\'' @ ( '\'map_fun$d\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$ay\'' @ ( '\'map_fun$e\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(265,axiom,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ '\'id$a\'' ) @ B ) )
      = ( '\'fun_app$bu\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom579) ).

thf(1609,plain,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ '\'id$a\'' ) @ B ) )
      = ( '\'fun_app$bu\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(424,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$ac\'' @ A @ B )
        = C )
     => ( ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom135) ).

thf(2178,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$ac\'' @ A @ B )
        = C )
     => ( ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(213,axiom,
    ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ '\'id$a\'' ) @ '\'top$b\'' )
    = '\'top$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).

thf(1415,plain,
    ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ '\'id$a\'' ) @ '\'top$b\'' )
    = '\'top$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(609,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$aa\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).

thf(2794,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$aa\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(136,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).

thf(1109,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(54,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ C @ B ) ) @ ( '\'inv_into$c\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).

thf(834,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ C @ B ) ) @ ( '\'inv_into$c\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(406,axiom,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ '\'id$\'' ) @ B ) )
      = ( '\'fun_app$bt\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom578) ).

thf(2122,plain,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ '\'id$\'' ) @ B ) )
      = ( '\'fun_app$bt\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(530,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).

thf(2540,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(363,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'compatible$t\'' @ ( '\'uug$\'' @ A ) @ ( '\'uuh$\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).

thf(1960,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'compatible$t\'' @ ( '\'uug$\'' @ A ) @ ( '\'uuh$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(604,axiom,
    ( ( '\'map_fun$p\'' @ '\'id$\'' @ '\'id$\'' )
    = '\'id$l\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).

thf(2777,plain,
    ( ( '\'map_fun$p\'' @ '\'id$\'' @ '\'id$\'' )
    = '\'id$l\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(152,axiom,
    ! [A: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$ce\'' @ ( '\'rel_fun$y\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom655) ).

thf(1183,plain,
    ! [A: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$ce\'' @ ( '\'rel_fun$y\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(72,axiom,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).

thf(905,plain,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(552,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$\'' @ A @ B )
          = '\'id$\'' )
        & ( ( '\'comp$v\'' @ B @ A )
          = '\'id$a\'' ) )
     => ( ( '\'inv_into$g\'' @ '\'top$b\'' @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).

thf(2616,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$\'' @ A @ B )
          = '\'id$\'' )
        & ( ( '\'comp$v\'' @ B @ A )
          = '\'id$a\'' ) )
     => ( ( '\'inv_into$g\'' @ '\'top$b\'' @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(358,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).

thf(1946,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(225,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$y\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ A ) ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom137) ).

thf(1465,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$y\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ A ) ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(465,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$y\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom113) ).

thf(2324,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$y\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(381,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$an\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ap\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$aq\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom637) ).

thf(2027,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$an\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ap\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$aq\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(459,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'B_update_b_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ D @ E @ F )
        & ! [H: '\'B_update$\'',I: '\'B_update$\''] :
            ( ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ H ) @ I )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ H ) @ H )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$d\'' @ B @ H ) ) @ ( '\'fun_app$d\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ ( '\'fun_app$u\'' @ C @ H ) ) @ ( '\'fun_app$u\'' @ C @ I ) ) ) )
     => ( '\'quotient3$h\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ G @ A ) ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).

thf(2291,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'B_update_b_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ D @ E @ F )
        & ! [H: '\'B_update$\'',I: '\'B_update$\''] :
            ( ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ H ) @ I )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ H ) @ H )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$d\'' @ B @ H ) ) @ ( '\'fun_app$d\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ ( '\'fun_app$u\'' @ C @ H ) ) @ ( '\'fun_app$u\'' @ C @ I ) ) ) )
     => ( '\'quotient3$h\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ G @ A ) ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(108,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_b_update_fun$\'',I: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$g\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$g\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$at\'' @ ( '\'map_fun$g\'' @ E @ I ) @ ( '\'map_fun$au\'' @ ( '\'map_fun$ap\'' @ B @ F ) @ ( '\'map_fun$av\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$e\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).

thf(1020,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_b_update_fun$\'',I: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$g\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$g\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$at\'' @ ( '\'map_fun$g\'' @ E @ I ) @ ( '\'map_fun$au\'' @ ( '\'map_fun$ap\'' @ B @ F ) @ ( '\'map_fun$av\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$e\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(258,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'B_update_b_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ D @ E @ F )
        & ! [H: '\'B_update$\'',I: '\'B_update$\''] :
            ( ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ H ) @ I )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ H ) @ H )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$d\'' @ B @ H ) ) @ ( '\'fun_app$d\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ ( '\'fun_app$u\'' @ C @ H ) ) @ ( '\'fun_app$u\'' @ C @ I ) ) ) )
     => ( '\'quotient3$a\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ G @ A ) ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).

thf(1581,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'B_update_b_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ D @ E @ F )
        & ! [H: '\'B_update$\'',I: '\'B_update$\''] :
            ( ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ H ) @ I )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ H ) @ H )
              & ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$d\'' @ B @ H ) ) @ ( '\'fun_app$d\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ G @ ( '\'fun_app$u\'' @ C @ H ) ) @ ( '\'fun_app$u\'' @ C @ I ) ) ) )
     => ( '\'quotient3$a\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ G @ A ) ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(469,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$ac\'' @ ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ B @ E ) ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).

thf(2335,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$ac\'' @ ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ B @ E ) ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(388,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$ae\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$i\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom116) ).

thf(2058,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$ae\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$i\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(524,axiom,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$bz\'' @ ( '\'rel_fun$at\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom658) ).

thf(2523,plain,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$bz\'' @ ( '\'rel_fun$at\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(244,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$k\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$a\'' @ ( '\'comp$y\'' @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom196) ).

thf(1526,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$k\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$a\'' @ ( '\'comp$y\'' @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(99,axiom,
    ( ( '\'vimage$a\'' @ '\'id$a\'' )
    = '\'id$v\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom667) ).

thf(998,plain,
    ( ( '\'vimage$a\'' @ '\'id$a\'' )
    = '\'id$v\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(458,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$aj\'' @ A @ B )
        = C )
     => ( ( '\'comp$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom144) ).

thf(2286,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$aj\'' @ A @ B )
        = C )
     => ( ( '\'comp$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(612,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$a\'' @ B @ '\'top$a\'' ) )
     => ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ '\'top$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom537) ).

thf(2804,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$a\'' @ B @ '\'top$a\'' ) )
     => ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ '\'top$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(242,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$ai\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom621) ).

thf(1521,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$ai\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(433,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
        = ( '\'comp$i\'' @ '\'id$a\'' @ C ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$ai\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).

thf(2205,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
        = ( '\'comp$i\'' @ '\'id$a\'' @ C ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$ai\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(636,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
        & ( C
          = ( '\'comp$ae\'' @ D @ E ) ) )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) @ G )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$ae\'' @ B @ E ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).

thf(2884,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
        & ( C
          = ( '\'comp$ae\'' @ D @ E ) ) )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) @ G )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$ae\'' @ B @ E ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(621,axiom,
    ! [A: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$cd\'' @ ( '\'rel_fun$n\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom654) ).

thf(2833,plain,
    ! [A: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$cd\'' @ ( '\'rel_fun$n\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(457,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$ac\'' @ A @ B )
        = C )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).

thf(2281,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$ac\'' @ A @ B )
        = C )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(64,axiom,
    ! [A: '\'A_update_b_update_bool_fun_fun$\'',B: '\'C_update_a_update_bool_fun_fun$\'',C: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$z\'' @ ( '\'rel_fun$aa\'' @ A @ B ) @ ( '\'rel_fun$ab\'' @ ( '\'rel_fun$ac\'' @ C @ A ) @ ( '\'rel_fun$ad\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom615) ).

thf(877,plain,
    ! [A: '\'A_update_b_update_bool_fun_fun$\'',B: '\'C_update_a_update_bool_fun_fun$\'',C: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$z\'' @ ( '\'rel_fun$aa\'' @ A @ B ) @ ( '\'rel_fun$ab\'' @ ( '\'rel_fun$ac\'' @ C @ A ) @ ( '\'rel_fun$ad\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(427,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'C_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$b\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$b\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$k\'' @ ( '\'comp$z\'' @ D @ G ) @ E )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ ( '\'comp$k\'' @ D @ H ) @ A ) ) @ ( '\'comp$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).

thf(2190,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'C_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$b\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$b\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$k\'' @ ( '\'comp$z\'' @ D @ G ) @ E )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ ( '\'comp$k\'' @ D @ H ) @ A ) ) @ ( '\'comp$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(139,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( '\'inj_on$d\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ '\'top$c\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).

thf(1119,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( '\'inj_on$d\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ '\'top$c\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(269,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$\'' @ '\'uuk$\'' @ ( '\'uul$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).

thf(1622,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$\'' @ '\'uuk$\'' @ ( '\'uul$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(496,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).

thf(2424,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(205,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'inj_on$a\'' @ A @ B )
        & ( '\'inj_on$c\'' @ C @ ( '\'image$a\'' @ A @ B ) ) )
     => ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).

thf(1394,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'inj_on$a\'' @ A @ B )
        & ( '\'inj_on$c\'' @ C @ ( '\'image$a\'' @ A @ B ) ) )
     => ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(603,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$ae\'' @ A @ B )
        = C )
     => ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).

thf(2772,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$ae\'' @ A @ B )
        = C )
     => ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(595,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).

thf(2750,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(210,axiom,
    ! [A: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).

thf(1405,plain,
    ! [A: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(264,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'image$\'' @ A @ B )
          = '\'top$b\'' )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ B )
           => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).

thf(1604,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'image$\'' @ A @ B )
          = '\'top$b\'' )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ B )
           => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(376,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$ax\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ay\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$az\'' @ '\'uur$\'' @ B ) ) @ '\'comp$a\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom624) ).

thf(2011,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$ax\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ay\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$az\'' @ '\'uur$\'' @ B ) ) @ '\'comp$a\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(45,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( '\'register$b\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).

thf(793,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( '\'register$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(78,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$f\'' @ ( '\'register_tensor$k\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).

thf(925,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$f\'' @ ( '\'register_tensor$k\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(190,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$y\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'comp$x\'' @ B @ D ) )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).

thf(1338,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$y\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'comp$x\'' @ B @ D ) )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(296,axiom,
    ! [A: '\'B_update_set$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$\'' @ ( '\'uuw$\'' @ A ) @ B )
    <=> ( '\'less_eq$\'' @ ( '\'image$\'' @ B @ '\'top$\'' ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).

thf(1730,plain,
    ! [A: '\'B_update_set$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$\'' @ ( '\'uuw$\'' @ A ) @ B )
       => ( '\'less_eq$\'' @ ( '\'image$\'' @ B @ '\'top$\'' ) @ A ) )
      & ( ( '\'less_eq$\'' @ ( '\'image$\'' @ B @ '\'top$\'' ) @ A )
       => ( '\'fun_app$\'' @ ( '\'uuw$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(541,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$aj\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ E ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).

thf(2574,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$aj\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ E ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(5,axiom,
    ( ( '\'map_fun$w\'' @ '\'id$a\'' @ '\'id$a\'' )
    = '\'id$m\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom339) ).

thf(661,plain,
    ( ( '\'map_fun$w\'' @ '\'id$a\'' @ '\'id$a\'' )
    = '\'id$m\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(226,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update$\''] :
      ( ( ( '\'member$\'' @ A @ B )
        & ( '\'inj_on$\'' @ C @ B ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'uut$\'' @ B @ C @ D ) ) @ C ) @ A )
        = ( '\'fun_app$ab\'' @ '\'id$b\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom594) ).

thf(1470,plain,
    ! [A: '\'A_update$\'',B: '\'A_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update$\''] :
      ( ( ( '\'member$\'' @ A @ B )
        & ( '\'inj_on$\'' @ C @ B ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'uut$\'' @ B @ C @ D ) ) @ C ) @ A )
        = ( '\'fun_app$ab\'' @ '\'id$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(291,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
    <=> ( ( '\'register$c\'' @ A )
        & ? [B: '\'B_update_a_update_fun$\''] :
            ( ( '\'register$a\'' @ B )
            & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
              = '\'id$a\'' )
            & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
              = '\'id$b\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).

thf(1708,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'iso_register$a\'' @ A )
       => ( ( '\'register$c\'' @ A )
          & ? [B: '\'B_update_a_update_fun$\''] :
              ( ( '\'register$a\'' @ B )
              & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
                = '\'id$a\'' )
              & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
                = '\'id$b\'' ) ) ) )
      & ( ( ( '\'register$c\'' @ A )
          & ? [B: '\'B_update_a_update_fun$\''] :
              ( ( '\'register$a\'' @ B )
              & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
                = '\'id$a\'' )
              & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
                = '\'id$b\'' ) ) )
       => ( '\'iso_register$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(396,axiom,
    ! [A: '\'A_update_set$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'rel_fun$b\'' @ '\'uur$\'' @ ( '\'grp$e\'' @ A @ B ) )
      = ( '\'grp$g\'' @ ( '\'collect$b\'' @ ( '\'uuy$\'' @ A ) ) @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom607) ).

thf(2083,plain,
    ! [A: '\'A_update_set$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'rel_fun$b\'' @ '\'uur$\'' @ ( '\'grp$e\'' @ A @ B ) )
      = ( '\'grp$g\'' @ ( '\'collect$b\'' @ ( '\'uuy$\'' @ A ) ) @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(298,axiom,
    ! [A: '\'B_update$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$u\'' @ ( '\'uub$\'' @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).

thf(1736,plain,
    ! [A: '\'B_update$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$u\'' @ ( '\'uub$\'' @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(568,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\''] :
      ( ( '\'fun_app$bl\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'fun_app$bi\'' @ ( '\'map_fun$o\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bm\'' @ ( '\'map_fun$t\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).

thf(2660,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\''] :
      ( ( '\'fun_app$bl\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'fun_app$bi\'' @ ( '\'map_fun$o\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bm\'' @ ( '\'map_fun$t\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(642,axiom,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bu\'' @ '\'uvb$\'' @ ( '\'rel_fun$bv\'' @ ( '\'rel_fun$bp\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bw\'' @ A @ '\'uur$\'' ) ) @ '\'comp$e\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom646) ).

thf(2905,plain,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bu\'' @ '\'uvb$\'' @ ( '\'rel_fun$bv\'' @ ( '\'rel_fun$bp\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bw\'' @ A @ '\'uur$\'' ) ) @ '\'comp$e\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(483,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$z\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom114) ).

thf(2382,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$z\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(74,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).

thf(910,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(30,axiom,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( '\'bijection$b\'' @ A )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ A ) ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).

thf(746,plain,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( '\'bijection$b\'' @ A )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ A ) ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(191,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'B_update$\''] :
            ( ( '\'member$a\'' @ E @ B )
           => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).

thf(1343,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'B_update$\''] :
            ( ( '\'member$a\'' @ E @ B )
           => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(409,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).

thf(2133,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(549,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$an\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ap\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$aq\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$d\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom622) ).

thf(2606,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$an\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ap\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$aq\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$d\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(324,axiom,
    ! [A: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$ce\'' @ ( '\'rel_fun$y\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom664) ).

thf(1824,plain,
    ! [A: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$ce\'' @ ( '\'rel_fun$y\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(526,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).

thf(2528,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(340,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'compatible$w\'' @ ( '\'uuf$\'' @ A ) @ ( '\'uue$\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom333) ).

thf(1883,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'compatible$w\'' @ ( '\'uuf$\'' @ A ) @ ( '\'uue$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(451,axiom,
    ( ( '\'register_tensor$\'' @ '\'id$\'' @ '\'id$\'' )
    = '\'id$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).

thf(2264,plain,
    ( ( '\'register_tensor$\'' @ '\'id$\'' @ '\'id$\'' )
    = '\'id$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(489,axiom,
    '\'preregister$\'' @ '\'id$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).

thf(2409,plain,
    '\'preregister$\'' @ '\'id$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(547,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$be\'' @ '\'uvb$\'' @ ( '\'rel_fun$bf\'' @ ( '\'rel_fun$ah\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bg\'' @ A @ '\'uur$\'' ) ) @ '\'comp$b\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom644) ).

thf(2601,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$be\'' @ '\'uvb$\'' @ ( '\'rel_fun$bf\'' @ ( '\'rel_fun$ah\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bg\'' @ A @ '\'uur$\'' ) ) @ '\'comp$b\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(497,axiom,
    ! [A: '\'B_update_bool_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'pred_fun$f\'' @ '\'uum$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
    <=> ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'comp$bp\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).

thf(2428,plain,
    ! [A: '\'B_update_bool_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'pred_fun$f\'' @ '\'uum$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
       => ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'comp$bp\'' @ A @ B ) @ C ) )
      & ( ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'comp$bp\'' @ A @ B ) @ C )
       => ( '\'pred_fun$f\'' @ '\'uum$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(492,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\''] :
      ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'comp$ae\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).

thf(2414,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\''] :
      ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'comp$ae\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(26,axiom,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ '\'id$b\'' ) @ B ) )
      = ( '\'fun_app$bv\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).

thf(729,plain,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ '\'id$b\'' ) @ B ) )
      = ( '\'fun_app$bv\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(498,axiom,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( '\'bijection$\'' @ A )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ A ) ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).

thf(2433,plain,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( '\'bijection$\'' @ A )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ A ) ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(65,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( '\'iso_tuple_surjective_proof_assist$a\'' @ A @ B @ '\'id$a\'' )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).

thf(879,plain,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( '\'iso_tuple_surjective_proof_assist$a\'' @ A @ B @ '\'id$a\'' )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(360,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$x\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ E ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom127) ).

thf(1951,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$x\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ E ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(343,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
    <=> ( ( '\'register$b\'' @ A )
        & ? [B: '\'A_update_c_update_fun$\''] :
            ( ( '\'register$\'' @ B )
            & ( ( '\'comp$k\'' @ A @ B )
              = '\'id$b\'' )
            & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
              = '\'id$\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).

thf(1888,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'iso_register$\'' @ A )
       => ( ( '\'register$b\'' @ A )
          & ? [B: '\'A_update_c_update_fun$\''] :
              ( ( '\'register$\'' @ B )
              & ( ( '\'comp$k\'' @ A @ B )
                = '\'id$b\'' )
              & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
                = '\'id$\'' ) ) ) )
      & ( ( ( '\'register$b\'' @ A )
          & ? [B: '\'A_update_c_update_fun$\''] :
              ( ( '\'register$\'' @ B )
              & ( ( '\'comp$k\'' @ A @ B )
                = '\'id$b\'' )
              & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
                = '\'id$\'' ) ) )
       => ( '\'iso_register$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(286,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$j\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$l\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$n\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom611) ).

thf(1687,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$j\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$l\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$n\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(312,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update$\''] :
      ( ( A
        = ( '\'fun_app$aa\'' @ B @ C ) )
     => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ ( '\'iso_tuple_update_accessor_eq_assist$a\'' @ '\'id$m\'' @ '\'id$a\'' @ C @ B ) @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).

thf(1787,plain,
    ! [A: '\'B_update$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update$\''] :
      ( ( A
        = ( '\'fun_app$aa\'' @ B @ C ) )
     => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ ( '\'iso_tuple_update_accessor_eq_assist$a\'' @ '\'id$m\'' @ '\'id$a\'' @ C @ B ) @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(279,axiom,
    ! [A: '\'B_update_set$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'member$\'' @ D @ ( '\'image$b\'' @ B @ A ) )
       => ( ( '\'fun_app$u\'' @ ( '\'uuv$\'' @ A @ B @ C ) @ D )
          = ( '\'fun_app$u\'' @ ( '\'the_inv_into$a\'' @ A @ B ) @ D ) ) )
      & ( ~ ( '\'member$\'' @ D @ ( '\'image$b\'' @ B @ A ) )
       => ( ( '\'fun_app$u\'' @ ( '\'uuv$\'' @ A @ B @ C ) @ D )
          = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).

thf(1656,plain,
    ! [A: '\'B_update_set$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'member$\'' @ D @ ( '\'image$b\'' @ B @ A ) )
       => ( ( '\'fun_app$u\'' @ ( '\'uuv$\'' @ A @ B @ C ) @ D )
          = ( '\'fun_app$u\'' @ ( '\'the_inv_into$a\'' @ A @ B ) @ D ) ) )
      & ( ~ ( '\'member$\'' @ D @ ( '\'image$b\'' @ B @ A ) )
       => ( ( '\'fun_app$u\'' @ ( '\'uuv$\'' @ A @ B @ C ) @ D )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(111,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$ah\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).

thf(1027,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$ah\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(34,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'quotient3$c\'' @ A @ B @ C )
     => ( ( '\'fun_app$au\'' @ ( '\'map_fun$\'' @ C @ B ) @ '\'id$a\'' )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).

thf(757,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'quotient3$c\'' @ A @ B @ C )
     => ( ( '\'fun_app$au\'' @ ( '\'map_fun$\'' @ C @ B ) @ '\'id$a\'' )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(435,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) ) @ B )
        = ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).

thf(2211,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) ) @ B )
        = ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(533,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ba\'' @ ( '\'rel_fun$bb\'' @ A @ B ) @ ( '\'rel_fun$bc\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$bd\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$b\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).

thf(2547,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ba\'' @ ( '\'rel_fun$bb\'' @ A @ B ) @ ( '\'rel_fun$bc\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$bd\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$b\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(347,axiom,
    ! [A: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).

thf(1910,plain,
    ! [A: '\'A_update$\''] :
      ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(256,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$x\'' @ B @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).

thf(1573,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$x\'' @ B @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(355,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'quotient3$e\'' @ A @ B @ C )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).

thf(1938,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'quotient3$e\'' @ A @ B @ C )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(598,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$o\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$p\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$r\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom612) ).

thf(2758,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$o\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$p\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$r\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(112,axiom,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'image$b\'' @ B @ ( '\'image$\'' @ C @ D ) ) )
      = ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom589) ).

thf(1032,plain,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'image$b\'' @ B @ ( '\'image$\'' @ C @ D ) ) )
      = ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(263,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( '\'iso_register$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).

thf(1602,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( '\'iso_register$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(198,axiom,
    ! [A: '\'A_update_set$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'member$a\'' @ D @ ( '\'image$\'' @ B @ A ) )
       => ( ( '\'fun_app$d\'' @ ( '\'uut$\'' @ A @ B @ C ) @ D )
          = ( '\'fun_app$d\'' @ ( '\'the_inv_into$b\'' @ A @ B ) @ D ) ) )
      & ( ~ ( '\'member$a\'' @ D @ ( '\'image$\'' @ B @ A ) )
       => ( ( '\'fun_app$d\'' @ ( '\'uut$\'' @ A @ B @ C ) @ D )
          = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).

thf(1365,plain,
    ! [A: '\'A_update_set$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'member$a\'' @ D @ ( '\'image$\'' @ B @ A ) )
       => ( ( '\'fun_app$d\'' @ ( '\'uut$\'' @ A @ B @ C ) @ D )
          = ( '\'fun_app$d\'' @ ( '\'the_inv_into$b\'' @ A @ B ) @ D ) ) )
      & ( ~ ( '\'member$a\'' @ D @ ( '\'image$\'' @ B @ A ) )
       => ( ( '\'fun_app$d\'' @ ( '\'uut$\'' @ A @ B @ C ) @ D )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(556,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_b_update_fun$\'',I: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$g\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$ar\'' @ ( '\'map_fun$g\'' @ E @ I ) @ ( '\'map_fun$as\'' @ ( '\'map_fun$m\'' @ B @ F ) @ ( '\'map_fun$t\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom371) ).

thf(2628,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_b_update_fun$\'',I: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$g\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$ar\'' @ ( '\'map_fun$g\'' @ E @ I ) @ ( '\'map_fun$as\'' @ ( '\'map_fun$m\'' @ B @ F ) @ ( '\'map_fun$t\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(569,axiom,
    ! [A: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cb\'' @ ( '\'rel_fun$ad\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom659) ).

thf(2663,plain,
    ! [A: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cb\'' @ ( '\'rel_fun$ad\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(619,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$ai\'' @ A @ B )
        = C )
     => ( ( '\'comp$v\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).

thf(2826,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$ai\'' @ A @ B )
        = C )
     => ( ( '\'comp$v\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(617,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bf\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'map_fun$f\'' @ C @ D ) )
      = ( '\'map_fun$g\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).

thf(2820,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bf\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'map_fun$f\'' @ C @ D ) )
      = ( '\'map_fun$g\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(460,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$ah\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom151) ).

thf(2300,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$ah\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(144,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$w\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
      = ( '\'comp$x\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).

thf(1143,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$w\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
      = ( '\'comp$x\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(639,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$an\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ap\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$aq\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom618) ).

thf(2895,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$an\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$ap\'' @ ( '\'rel_fun$ah\'' @ C @ A ) @ ( '\'rel_fun$aq\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(281,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
     => ( '\'iso_register$\'' @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).

thf(1672,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
     => ( '\'iso_register$\'' @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(249,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$k\'' @ ( '\'uul$\'' @ A @ B ) @ C )
    <=> ( ( '\'fun_app$d\'' @ A @ C )
        = ( '\'fun_app$d\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).

thf(1540,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( ( '\'fun_app$k\'' @ ( '\'uul$\'' @ A @ B ) @ C )
       => ( ( '\'fun_app$d\'' @ A @ C )
          = ( '\'fun_app$d\'' @ B @ C ) ) )
      & ( ( ( '\'fun_app$d\'' @ A @ C )
          = ( '\'fun_app$d\'' @ B @ C ) )
       => ( '\'fun_app$k\'' @ ( '\'uul$\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(557,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\''] :
      ( ( '\'fun_app$bh\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'fun_app$bj\'' @ ( '\'map_fun$q\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bk\'' @ ( '\'map_fun$r\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).

thf(2631,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\''] :
      ( ( '\'fun_app$bh\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'fun_app$bj\'' @ ( '\'map_fun$q\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bk\'' @ ( '\'map_fun$r\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(302,axiom,
    ! [A: '\'B_update_set$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'rel_fun$\'' @ '\'uus$\'' @ ( '\'grp$c\'' @ A @ B ) )
      = ( '\'grp$d\'' @ ( '\'collect$\'' @ ( '\'uuw$\'' @ A ) ) @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom605) ).

thf(1755,plain,
    ! [A: '\'B_update_set$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'rel_fun$\'' @ '\'uus$\'' @ ( '\'grp$c\'' @ A @ B ) )
      = ( '\'grp$d\'' @ ( '\'collect$\'' @ ( '\'uuw$\'' @ A ) ) @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(559,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$b\'' @ A )
        & ( '\'register$c\'' @ B ) )
     => ( '\'register$j\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).

thf(2638,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$b\'' @ A )
        & ( '\'register$c\'' @ B ) )
     => ( '\'register$j\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(453,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).

thf(2268,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(445,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$i\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$x\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).

thf(2245,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$i\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$x\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(193,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$an\'' @ ( '\'the_inv_into$h\'' @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'the_inv_into$a\'' @ C @ B ) ) @ ( '\'the_inv_into$b\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).

thf(1350,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$an\'' @ ( '\'the_inv_into$h\'' @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'the_inv_into$a\'' @ C @ B ) ) @ ( '\'the_inv_into$b\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(331,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ah\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom182) ).

thf(1851,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ah\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(307,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$l\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).

thf(1772,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$l\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(84,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ C )
      = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'comp$w\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).

thf(948,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ C )
      = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'comp$w\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(611,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$l\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_tensor$o\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).

thf(2801,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$l\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_tensor$o\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(314,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$be\'' @ ( '\'map_fun$k\'' @ A @ B ) @ ( '\'fun_app$bf\'' @ ( '\'map_fun$l\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bg\'' @ ( '\'map_fun$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom313) ).

thf(1794,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$be\'' @ ( '\'map_fun$k\'' @ A @ B ) @ ( '\'fun_app$bf\'' @ ( '\'map_fun$l\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bg\'' @ ( '\'map_fun$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(107,axiom,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom588) ).

thf(1017,plain,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(476,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$x\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$i\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ E ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom125) ).

thf(2359,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$x\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$i\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ E ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(140,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ! [E: '\'B_update$\'',F: '\'B_update$\''] :
            ( ( ( '\'member$a\'' @ E @ ( '\'image$\'' @ A @ '\'top$\'' ) )
              & ( '\'member$a\'' @ F @ ( '\'image$\'' @ B @ '\'top$\'' ) )
              & ( ( '\'fun_app$d\'' @ C @ E )
                = ( '\'fun_app$d\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).

thf(1121,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ! [E: '\'B_update$\'',F: '\'B_update$\''] :
            ( ( ( '\'member$a\'' @ E @ ( '\'image$\'' @ A @ '\'top$\'' ) )
              & ( '\'member$a\'' @ F @ ( '\'image$\'' @ B @ '\'top$\'' ) )
              & ( ( '\'fun_app$d\'' @ C @ E )
                = ( '\'fun_app$d\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(586,axiom,
    '\'register$h\'' @ '\'id$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).

thf(2724,plain,
    '\'register$h\'' @ '\'id$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(292,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ B )
        & ( '\'inj_on$\'' @ C @ ( '\'image$b\'' @ A @ B ) ) )
     => ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).

thf(1719,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ B )
        & ( '\'inj_on$\'' @ C @ ( '\'image$b\'' @ A @ B ) ) )
     => ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(529,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ ( '\'comp$y\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).

thf(2537,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( '\'comp$af\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ ( '\'comp$y\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(464,axiom,
    '\'iso_tuple_update_accessor_cong_assist$\'' @ '\'id$l\'' @ '\'id$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).

thf(2323,plain,
    '\'iso_tuple_update_accessor_cong_assist$\'' @ '\'id$l\'' @ '\'id$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(176,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'C_update$\''] :
            ( ( '\'member$b\'' @ E @ B )
           => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).

thf(1292,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ B )
          = '\'top$\'' )
        & ! [E: '\'C_update$\''] :
            ( ( '\'member$b\'' @ E @ B )
           => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ E )
              = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ A ) @ E ) ) ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(538,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$ah\'' @ A @ B )
        = C )
     => ( ( '\'comp$h\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom142) ).

thf(2561,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$ah\'' @ A @ B )
        = C )
     => ( ( '\'comp$h\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(299,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ G @ H ) @ I )
              & ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ A @ H ) @ H )
              & ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ D @ ( '\'fun_app$u\'' @ B @ H ) ) @ ( '\'fun_app$u\'' @ B @ I ) ) )
        & ! [H: '\'B_update$\'',I: '\'B_update$\''] :
            ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ D @ H ) @ I )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ G @ ( '\'fun_app$d\'' @ C @ H ) ) @ ( '\'fun_app$d\'' @ C @ I ) ) ) )
     => ( '\'quotient3$b\'' @ ( '\'relcompp$\'' @ A @ ( '\'relcompp$\'' @ G @ A ) ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ B ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).

thf(1739,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ G @ H ) @ I )
              & ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ A @ H ) @ H )
              & ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ D @ ( '\'fun_app$u\'' @ B @ H ) ) @ ( '\'fun_app$u\'' @ B @ I ) ) )
        & ! [H: '\'B_update$\'',I: '\'B_update$\''] :
            ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ D @ H ) @ I )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ G @ ( '\'fun_app$d\'' @ C @ H ) ) @ ( '\'fun_app$d\'' @ C @ I ) ) ) )
     => ( '\'quotient3$b\'' @ ( '\'relcompp$\'' @ A @ ( '\'relcompp$\'' @ G @ A ) ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ B ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(631,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$ae\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
      = ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).

thf(2868,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$ae\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
      = ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(443,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ '\'top$b\'' )
          = '\'top$\'' )
        & ( ( '\'image$c\'' @ B @ '\'top$\'' )
          = '\'top$a\'' ) )
     => ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) @ '\'top$b\'' )
        = '\'top$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).

thf(2240,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ '\'top$b\'' )
          = '\'top$\'' )
        & ( ( '\'image$c\'' @ B @ '\'top$\'' )
          = '\'top$a\'' ) )
     => ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) @ '\'top$b\'' )
        = '\'top$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(551,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$d\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$e\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$af\'' @ ( '\'map_fun$f\'' @ E @ I ) @ ( '\'map_fun$ag\'' @ ( '\'map_fun$l\'' @ B @ F ) @ ( '\'map_fun$s\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).

thf(2613,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$d\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$e\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$af\'' @ ( '\'map_fun$f\'' @ E @ I ) @ ( '\'map_fun$ag\'' @ ( '\'map_fun$l\'' @ B @ F ) @ ( '\'map_fun$s\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(221,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ '\'uuq$\'' @ A ) ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).

thf(1446,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ '\'uuq$\'' @ A ) ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(507,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$s\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$u\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$v\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom613) ).

thf(2460,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$s\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$u\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$v\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(233,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_a_update_fun$\'',I: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ D @ E @ F )
        & ( '\'quotient3$f\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$aj\'' @ ( '\'map_fun$c\'' @ E @ I ) @ ( '\'map_fun$ak\'' @ ( '\'map_fun$k\'' @ B @ F ) @ ( '\'map_fun$o\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$c\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).

thf(1493,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_a_update_fun$\'',I: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ D @ E @ F )
        & ( '\'quotient3$f\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$aj\'' @ ( '\'map_fun$c\'' @ E @ I ) @ ( '\'map_fun$ak\'' @ ( '\'map_fun$k\'' @ B @ F ) @ ( '\'map_fun$o\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$c\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(610,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ '\'top$a\'' )
          = '\'top$\'' )
        & ( ( '\'image$\'' @ B @ '\'top$\'' )
          = '\'top$b\'' ) )
     => ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) @ '\'top$a\'' )
        = '\'top$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).

thf(2798,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ '\'top$a\'' )
          = '\'top$\'' )
        & ( ( '\'image$\'' @ B @ '\'top$\'' )
          = '\'top$b\'' ) )
     => ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) @ '\'top$a\'' )
        = '\'top$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(71,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$w\'' @ A @ B )
          = ( '\'comp$x\'' @ C @ D ) )
        & ( ( '\'comp$y\'' @ E @ C )
          = F ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).

thf(901,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$w\'' @ A @ B )
          = ( '\'comp$x\'' @ C @ D ) )
        & ( ( '\'comp$y\'' @ E @ C )
          = F ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(14,axiom,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( '\'bijection$a\'' @ A )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ A ) )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom466) ).

thf(686,plain,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( '\'bijection$a\'' @ A )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ A ) )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(216,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
    <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom577) ).

thf(1424,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
       => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
          = '\'id$a\'' ) )
      & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
          = '\'id$a\'' )
       => ( '\'inj_on$b\'' @ A @ '\'top$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(505,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'inv_into$h\'' @ C @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'inv_into$a\'' @ C @ B ) ) @ ( '\'inv_into$b\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).

thf(2455,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'B_update$\''] :
      ( ( ( '\'inj_on$\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'inv_into$h\'' @ C @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'inv_into$a\'' @ C @ B ) ) @ ( '\'inv_into$b\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(313,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) )
     => ( '\'register$m\'' @ ( '\'register_pair$b\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).

thf(1791,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) )
     => ( '\'register$m\'' @ ( '\'register_pair$b\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(422,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$s\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$l\'' @ C @ D ) )
        = ( '\'register_tensor$w\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).

thf(2172,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$s\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$l\'' @ C @ D ) )
        = ( '\'register_tensor$w\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(266,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'compatible$b\'' @ B @ C ) )
     => ( ( '\'register_pair$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) )
        = ( '\'comp$bc\'' @ A @ ( '\'register_pair$d\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).

thf(1612,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'compatible$b\'' @ B @ C ) )
     => ( ( '\'register_pair$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) )
        = ( '\'comp$bc\'' @ A @ ( '\'register_pair$d\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(564,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\''] :
      ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ ( '\'comp$ac\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom168) ).

thf(2649,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\''] :
      ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ ( '\'comp$ac\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(91,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$d\'' @ ( '\'register_tensor$i\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).

thf(970,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$d\'' @ ( '\'register_tensor$i\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(55,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$\'' @ ( '\'fun_app$r\'' @ '\'uvb$\'' @ A ) @ B )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).

thf(837,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$\'' @ ( '\'fun_app$r\'' @ '\'uvb$\'' @ A ) @ B )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$\'' @ ( '\'fun_app$r\'' @ '\'uvb$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(177,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
           => ( ( '\'fun_app$u\'' @ C @ E )
              = ( '\'fun_app$u\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).

thf(1297,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
           => ( ( '\'fun_app$u\'' @ C @ E )
              = ( '\'fun_app$u\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(246,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\''] :
      ( ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ C ) )
      = ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).

thf(1530,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\''] :
      ( ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ C ) )
      = ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(169,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( '\'iso_tuple_surjective_proof_assist$b\'' @ A @ B @ '\'id$b\'' )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).

thf(1266,plain,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( '\'iso_tuple_surjective_proof_assist$b\'' @ A @ B @ '\'id$b\'' )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(518,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'B_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C
          = ( '\'comp$ac\'' @ D @ E ) ) )
     => ( ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ C ) @ G )
        = ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ac\'' @ B @ E ) ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).

thf(2505,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'B_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C
          = ( '\'comp$ac\'' @ D @ E ) ) )
     => ( ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ C ) @ G )
        = ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ac\'' @ B @ E ) ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(515,axiom,
    ( ( '\'register_tensor$a\'' @ '\'id$\'' @ '\'id$a\'' )
    = '\'id$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).

thf(2497,plain,
    ( ( '\'register_tensor$a\'' @ '\'id$\'' @ '\'id$a\'' )
    = '\'id$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(539,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$ae\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$w\'' @ B @ E ) ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).

thf(2566,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$ae\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$w\'' @ B @ E ) ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(371,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'uua$\'' @ A ) ) @ B ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).

thf(1984,plain,
    ! [A: '\'C_update$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'uua$\'' @ A ) ) @ B ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(101,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).

thf(1002,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(454,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'C_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$f\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$b\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$k\'' @ ( '\'comp$ae\'' @ D @ G ) @ E )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ H ) @ A ) ) @ ( '\'comp$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).

thf(2272,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'C_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$f\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$b\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$k\'' @ ( '\'comp$ae\'' @ D @ G ) @ E )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ H ) @ A ) ) @ ( '\'comp$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(479,axiom,
    ! [A: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$cd\'' @ ( '\'rel_fun$n\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom663) ).

thf(2370,plain,
    ! [A: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$cd\'' @ ( '\'rel_fun$n\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(503,axiom,
    ( ( '\'register_tensor$f\'' @ '\'id$b\'' @ '\'id$\'' )
    = '\'id$i\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).

thf(2450,plain,
    ( ( '\'register_tensor$f\'' @ '\'id$b\'' @ '\'id$\'' )
    = '\'id$i\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(407,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$x\'' @ A @ B )
        = C )
     => ( ( '\'comp$i\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).

thf(2125,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$x\'' @ A @ B )
        = C )
     => ( ( '\'comp$i\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(95,axiom,
    ( '\'uur$\''
    = ( '\'grp$a\'' @ '\'top$b\'' @ '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).

thf(985,plain,
    ( '\'uur$\''
    = ( '\'grp$a\'' @ '\'top$b\'' @ '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(146,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'A_update_a_update_bool_fun_fun$\'',C: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ ( '\'rel_fun$f\'' @ A @ B ) @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ C @ A ) @ ( '\'rel_fun$i\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom610) ).

thf(1150,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'A_update_a_update_bool_fun_fun$\'',C: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ ( '\'rel_fun$f\'' @ A @ B ) @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ C @ A ) @ ( '\'rel_fun$i\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(523,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ai\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$ag\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ E ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).

thf(2519,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ai\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$ag\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ E ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(625,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
        & ( C = '\'id$b\'' ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ B @ C ) ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).

thf(2845,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
        & ( C = '\'id$b\'' ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ B @ C ) ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(546,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).

thf(2598,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(141,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
     => ( '\'register$\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).

thf(1131,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
     => ( '\'register$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(1,conjecture,
    ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ '\'g$\'' ) @ '\'f$\'' ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ '\'f$a\'' ) @ '\'g$a\'' ) )
    = '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture29) ).

thf(2,negated_conjecture,
    ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ '\'g$\'' ) @ '\'f$\'' ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ '\'f$a\'' ) @ '\'g$a\'' ) )
   != '\'id$\'' ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(654,plain,
    ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ '\'g$\'' ) @ '\'f$\'' ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ '\'f$a\'' ) @ '\'g$a\'' ) )
   != '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(627,axiom,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).

thf(2851,plain,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(444,axiom,
    ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ '\'g$\'' ) @ '\'g$a\'' )
    = '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).

thf(2243,plain,
    ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ '\'g$\'' ) @ '\'g$a\'' )
    = '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(369,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'C_update_c_update_fun$\'',G: '\'C_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ D ) @ G ) ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom433) ).

thf(1979,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'C_update_c_update_fun$\'',G: '\'C_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ D ) @ G ) ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(41,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'quotient3$c\'' @ A @ B @ C )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).

thf(779,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'quotient3$c\'' @ A @ B @ C )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(558,axiom,
    ! [A: '\'B_update_b_update_fun_c_update_c_update_fun_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$e\'' @ A @ B )
     => ( ( '\'fun_app$bp\'' @ A @ '\'id$a\'' )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).

thf(2634,plain,
    ! [A: '\'B_update_b_update_fun_c_update_c_update_fun_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$e\'' @ A @ B )
     => ( ( '\'fun_app$bp\'' @ A @ '\'id$a\'' )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(183,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$bk\'' @ '\'uvb$\'' @ ( '\'rel_fun$bl\'' @ ( '\'rel_fun$f\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bm\'' @ A @ '\'uur$\'' ) ) @ '\'comp$e\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom647) ).

thf(1318,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$bk\'' @ '\'uvb$\'' @ ( '\'rel_fun$bl\'' @ ( '\'rel_fun$f\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bm\'' @ A @ '\'uur$\'' ) ) @ '\'comp$e\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(649,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$ac\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).

thf(2926,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$ac\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(157,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$b\'' @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).

thf(1202,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$b\'' @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(82,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'image$\'' @ A @ '\'top$\'' )
          = '\'top$b\'' )
        & ( ( '\'image$b\'' @ B @ '\'top$b\'' )
          = '\'top$\'' ) )
     => ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ) @ '\'top$\'' )
        = '\'top$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).

thf(938,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'image$\'' @ A @ '\'top$\'' )
          = '\'top$b\'' )
        & ( ( '\'image$b\'' @ B @ '\'top$b\'' )
          = '\'top$\'' ) )
     => ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ) @ '\'top$\'' )
        = '\'top$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(580,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$aj\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$af\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ E ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom126) ).

thf(2702,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$aj\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$af\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ E ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(309,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$r\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$r\'' @ C @ D ) )
        = ( '\'register_tensor$c\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).

thf(1779,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$r\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$r\'' @ C @ D ) )
        = ( '\'register_tensor$c\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(384,axiom,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).

thf(2043,plain,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(77,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
        = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).

thf(921,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
        = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(330,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$w\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ A ) ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).

thf(1846,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$w\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ A ) ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(113,axiom,
    '\'preregister$b\'' @ '\'id$b\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).

thf(1035,plain,
    '\'preregister$b\'' @ '\'id$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(124,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$c\'' @ B ) )
     => ( '\'register$k\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).

thf(1071,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$c\'' @ B ) )
     => ( '\'register$k\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(500,axiom,
    ( ( '\'register_tensor$b\'' @ '\'id$\'' @ '\'id$b\'' )
    = '\'id$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).

thf(2440,plain,
    ( ( '\'register_tensor$b\'' @ '\'id$\'' @ '\'id$b\'' )
    = '\'id$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(280,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'compatible$\'' @ A @ B )
    <=> ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).

thf(1663,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
       => ( ( '\'register$a\'' @ A )
          & ( '\'register$a\'' @ B )
          & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
              ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
              = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) ) )
      & ( ( ( '\'register$a\'' @ A )
          & ( '\'register$a\'' @ B )
          & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
              ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
              = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) )
       => ( '\'compatible$\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(562,axiom,
    ! [A: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cb\'' @ ( '\'rel_fun$ad\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom650) ).

thf(2645,plain,
    ! [A: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cb\'' @ ( '\'rel_fun$ad\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(86,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
        & ( '\'inj_on$\'' @ B @ '\'top$\'' ) )
     => ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ '\'top$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).

thf(953,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
        & ( '\'inj_on$\'' @ B @ '\'top$\'' ) )
     => ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ '\'top$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(153,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$z\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ A ) ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).

thf(1185,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'comp$z\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ A ) ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(346,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = '\'id$a\'' )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).

thf(1906,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = '\'id$a\'' )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(652,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
    <=> ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).

thf(2936,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
       => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
          = '\'id$\'' ) )
      & ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
          = '\'id$\'' )
       => ( '\'inj_on$a\'' @ A @ '\'top$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(145,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$y\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).

thf(1146,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$y\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$w\'' @ E @ C )
          = F ) )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(284,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C = '\'id$b\'' ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ B @ C ) ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).

thf(1680,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C = '\'id$b\'' ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ B @ C ) ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(134,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ B )
     => ( ( '\'inj_on$b\'' @ C @ ( '\'image$\'' @ A @ B ) )
      <=> ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).

thf(1103,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ B )
     => ( ( ( '\'inj_on$b\'' @ C @ ( '\'image$\'' @ A @ B ) )
         => ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ B ) )
        & ( ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ B )
         => ( '\'inj_on$b\'' @ C @ ( '\'image$\'' @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(455,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( '\'quotient3$\'' @ A @ B @ C )
     => ( ( '\'fun_app$am\'' @ ( '\'map_fun$p\'' @ C @ B ) @ '\'id$\'' )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom373) ).

thf(2275,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( '\'quotient3$\'' @ A @ B @ C )
     => ( ( '\'fun_app$am\'' @ ( '\'map_fun$p\'' @ C @ B ) @ '\'id$\'' )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(544,axiom,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( '\'bijection$\'' @ A )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ A ) )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom465) ).

thf(2585,plain,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( '\'bijection$\'' @ A )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ A ) )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(171,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$h\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ '\'top$e\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).

thf(1273,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$h\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ '\'top$e\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(15,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'fun_app$b\'' @ ( '\'fun_app$o\'' @ '\'uuz$\'' @ A ) @ B )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).

thf(689,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$b\'' @ ( '\'fun_app$o\'' @ '\'uuz$\'' @ A ) @ B )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$b\'' @ ( '\'fun_app$o\'' @ '\'uuz$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(481,axiom,
    ( ( '\'comp$k\'' @ '\'g$a\'' @ '\'g$\'' )
    = '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).

thf(2376,plain,
    ( ( '\'comp$k\'' @ '\'g$a\'' @ '\'g$\'' )
    = '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(28,axiom,
    ! [A: '\'B_update_set$\''] : ( '\'inj_on$m\'' @ '\'id$a\'' @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).

thf(733,plain,
    ! [A: '\'B_update_set$\''] : ( '\'inj_on$m\'' @ '\'id$a\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(450,axiom,
    ! [A: '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$d\'' @ A @ B )
     => ( ( '\'fun_app$bi\'' @ A @ '\'id$\'' )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).

thf(2260,plain,
    ! [A: '\'C_update_c_update_fun_a_update_a_update_fun_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$d\'' @ A @ B )
     => ( ( '\'fun_app$bi\'' @ A @ '\'id$\'' )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(148,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ '\'uuq$\'' @ A ) @ B )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).

thf(1154,plain,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ '\'uuq$\'' @ A ) @ B )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ '\'uuq$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(327,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'A_update_a_update_bool_fun_fun$\'',C: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ ( '\'rel_fun$f\'' @ A @ B ) @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ C @ A ) @ ( '\'rel_fun$i\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).

thf(1833,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'A_update_a_update_bool_fun_fun$\'',C: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ ( '\'rel_fun$f\'' @ A @ B ) @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ C @ A ) @ ( '\'rel_fun$i\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(588,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$ai\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom152) ).

thf(2727,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$ai\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(103,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ '\'top$a\'' )
      = ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ '\'top$a\'' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom565) ).

thf(1007,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ '\'top$a\'' )
      = ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ '\'top$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(349,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'fun_app$p\'' @ ( '\'fun_app$q\'' @ '\'uva$\'' @ A ) @ B )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).

thf(1916,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$p\'' @ ( '\'fun_app$q\'' @ '\'uva$\'' @ A ) @ B )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$p\'' @ ( '\'fun_app$q\'' @ '\'uva$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(629,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'the_inv_into$\'' @ '\'top$a\'' @ A ) ) @ A ) @ B )
        = ( '\'fun_app$z\'' @ '\'id$\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom598) ).

thf(2859,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'the_inv_into$\'' @ '\'top$a\'' @ A ) ) @ A ) @ B )
        = ( '\'fun_app$z\'' @ '\'id$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(27,axiom,
    '\'register$k\'' @ '\'id$a\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom190) ).

thf(732,plain,
    '\'register$k\'' @ '\'id$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(608,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).

thf(2791,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(268,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$cc\'' @ ( '\'rel_fun$bm\'' @ A @ A ) @ '\'id$a\'' ) @ '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom652) ).

thf(1620,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$cc\'' @ ( '\'rel_fun$bm\'' @ A @ A ) @ '\'id$a\'' ) @ '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(301,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\'',D: '\'A_update$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ ( '\'image$\'' @ B @ C ) )
        & ( '\'inj_on$\'' @ B @ C )
        & ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ C @ B ) ) @ ( '\'inv_into$\'' @ ( '\'image$\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).

thf(1752,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\'',D: '\'A_update$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ ( '\'image$\'' @ B @ C ) )
        & ( '\'inj_on$\'' @ B @ C )
        & ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ C @ B ) ) @ ( '\'inv_into$\'' @ ( '\'image$\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(352,axiom,
    ( ( '\'register_tensor$d\'' @ '\'id$a\'' @ '\'id$a\'' )
    = '\'id$g\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom61) ).

thf(1929,plain,
    ( ( '\'register_tensor$d\'' @ '\'id$a\'' @ '\'id$a\'' )
    = '\'id$g\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(378,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\''] :
      ( ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'comp$ac\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).

thf(2016,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\''] :
      ( ( '\'comp$v\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'comp$ac\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(202,axiom,
    '\'quotient3$b\'' @ '\'uus$\'' @ '\'id$b\'' @ '\'id$b\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).

thf(1388,plain,
    '\'quotient3$b\'' @ '\'uus$\'' @ '\'id$b\'' @ '\'id$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(613,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C = '\'id$\'' ) )
     => ( ( '\'comp$k\'' @ ( '\'comp$z\'' @ B @ C ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).

thf(2806,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C = '\'id$\'' ) )
     => ( ( '\'comp$k\'' @ ( '\'comp$z\'' @ B @ C ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(232,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C
          = ( '\'comp$z\'' @ D @ E ) ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) ) @ G )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$z\'' @ B @ E ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).

thf(1488,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
        & ( C
          = ( '\'comp$z\'' @ D @ E ) ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) ) @ G )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$z\'' @ B @ E ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(267,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ B )
     => ( ( '\'inj_on$\'' @ C @ ( '\'image$b\'' @ A @ B ) )
      <=> ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom511) ).

thf(1615,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ B )
     => ( ( ( '\'inj_on$\'' @ C @ ( '\'image$b\'' @ A @ B ) )
         => ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ B ) )
        & ( ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ B )
         => ( '\'inj_on$\'' @ C @ ( '\'image$b\'' @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(203,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'preregister$d\'' @ A )
        & ( '\'preregister$e\'' @ B ) )
     => ( '\'preregister$a\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).

thf(1389,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'preregister$d\'' @ A )
        & ( '\'preregister$e\'' @ B ) )
     => ( '\'preregister$a\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(525,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'B_update_c_update_fun$\'',E: '\'B_update_c_update_fun$\'',F: '\'C_update_b_update_fun$\'',G: '\'C_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$c\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$a\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$h\'' @ ( '\'comp$\'' @ D @ G ) @ E )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ ( '\'comp$aj\'' @ D @ H ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).

thf(2525,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_b_update_fun$\'',D: '\'B_update_c_update_fun$\'',E: '\'B_update_c_update_fun$\'',F: '\'C_update_b_update_fun$\'',G: '\'C_update_b_update_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$c\'' @ C @ D @ '\'top$b\'' )
        & ( '\'type_definition$a\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$h\'' @ ( '\'comp$\'' @ D @ G ) @ E )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ ( '\'comp$aj\'' @ D @ H ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(567,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'B_update_c_update_fun$\'',G: '\'B_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$c\'' @ E @ F @ '\'top$b\'' )
        & ( ( '\'comp$\'' @ ( '\'comp$h\'' @ D @ G ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$ae\'' @ ( '\'comp$ad\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).

thf(2657,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'B_update_c_update_fun$\'',G: '\'B_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$c\'' @ E @ F @ '\'top$b\'' )
        & ( ( '\'comp$\'' @ ( '\'comp$h\'' @ D @ G ) @ E )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$ae\'' @ ( '\'comp$ad\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(626,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$b\'' @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).

thf(2849,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$b\'' @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(88,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$d\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$\'' @ D ) )
     => ( ( '\'comp$ao\'' @ ( '\'register_pair$g\'' @ A @ B ) @ ( '\'register_tensor$ab\'' @ C @ D ) )
        = ( '\'register_pair$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) @ ( '\'comp$ah\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom238) ).

thf(958,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$d\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$\'' @ D ) )
     => ( ( '\'comp$ao\'' @ ( '\'register_pair$g\'' @ A @ B ) @ ( '\'register_tensor$ab\'' @ C @ D ) )
        = ( '\'register_pair$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) @ ( '\'comp$ah\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(209,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'register$\'' @ A )
     => ( '\'preregister$c\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).

thf(1403,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'register$\'' @ A )
     => ( '\'preregister$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(289,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( C = '\'id$b\'' ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ C ) ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).

thf(1701,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( C = '\'id$b\'' ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ C ) ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(486,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$d\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$ac\'' @ ( '\'map_fun$d\'' @ E @ I ) @ ( '\'map_fun$ad\'' @ ( '\'map_fun$h\'' @ B @ F ) @ ( '\'map_fun$ae\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).

thf(2398,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$d\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$ac\'' @ ( '\'map_fun$d\'' @ E @ I ) @ ( '\'map_fun$ad\'' @ ( '\'map_fun$h\'' @ B @ F ) @ ( '\'map_fun$ae\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(418,axiom,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bx\'' @ A @ A @ '\'id$a\'' @ '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom660) ).

thf(2161,plain,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bx\'' @ A @ A @ '\'id$a\'' @ '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(237,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'uun$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).

thf(1503,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'uun$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(428,axiom,
    ( ( '\'register_tensor$c\'' @ '\'id$a\'' @ '\'id$\'' )
    = '\'id$f\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).

thf(2193,plain,
    ( ( '\'register_tensor$c\'' @ '\'id$a\'' @ '\'id$\'' )
    = '\'id$f\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(438,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).

thf(2220,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'type_definition$b\'' @ A @ B @ '\'top$a\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(382,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
              & ( ( '\'fun_app$g\'' @ C @ E )
                = ( '\'fun_app$g\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).

thf(2029,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
              & ( ( '\'fun_app$g\'' @ C @ E )
                = ( '\'fun_app$g\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(181,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$y\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ E )
          = F ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'comp$x\'' @ B @ E ) )
        = ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).

thf(1312,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$y\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ E )
          = F ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'comp$x\'' @ B @ E ) )
        = ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(591,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( ( '\'register$i\'' @ A )
        & ( '\'register$j\'' @ B )
        & ( ( '\'comp$\'' @ A @ B )
          = '\'id$\'' )
        & ( ( '\'comp$v\'' @ B @ A )
          = '\'id$a\'' ) )
     => ( '\'iso_register$e\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom98) ).

thf(2738,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( ( '\'register$i\'' @ A )
        & ( '\'register$j\'' @ B )
        & ( ( '\'comp$\'' @ A @ B )
          = '\'id$\'' )
        & ( ( '\'comp$v\'' @ B @ A )
          = '\'id$a\'' ) )
     => ( '\'iso_register$e\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(23,axiom,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( '\'iso_register$h\'' @ A )
    <=> ( ( '\'register$l\'' @ A )
        & ? [B: '\'A_update_a_update_fun$\''] :
            ( ( '\'register$l\'' @ B )
            & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
              = '\'id$b\'' )
            & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
              = '\'id$b\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom92) ).

thf(713,plain,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'iso_register$h\'' @ A )
       => ( ( '\'register$l\'' @ A )
          & ? [B: '\'A_update_a_update_fun$\''] :
              ( ( '\'register$l\'' @ B )
              & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
                = '\'id$b\'' )
              & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
                = '\'id$b\'' ) ) ) )
      & ( ( ( '\'register$l\'' @ A )
          & ? [B: '\'A_update_a_update_fun$\''] :
              ( ( '\'register$l\'' @ B )
              & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
                = '\'id$b\'' )
              & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
                = '\'id$b\'' ) ) )
       => ( '\'iso_register$h\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(273,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$be\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'map_fun$d\'' @ C @ D ) )
      = ( '\'map_fun$e\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).

thf(1635,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$be\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'map_fun$d\'' @ C @ D ) )
      = ( '\'map_fun$e\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(163,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ah\'' @ B @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).

thf(1239,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ah\'' @ B @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(188,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ '\'top$b\'' )
          = '\'top$\'' )
        & ( ( '\'image$\'' @ B @ '\'top$\'' )
          = '\'top$b\'' ) )
     => ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ) @ '\'top$b\'' )
        = '\'top$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).

thf(1332,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ '\'top$b\'' )
          = '\'top$\'' )
        & ( ( '\'image$\'' @ B @ '\'top$\'' )
          = '\'top$b\'' ) )
     => ( ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ) @ '\'top$b\'' )
        = '\'top$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(501,axiom,
    ! [A: '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$\'' @ A @ B )
     => ( ( '\'fun_app$am\'' @ A @ '\'id$\'' )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).

thf(2442,plain,
    ! [A: '\'C_update_c_update_fun_c_update_c_update_fun_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$\'' @ A @ B )
     => ( ( '\'fun_app$am\'' @ A @ '\'id$\'' )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(387,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'comp$ae\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom164) ).

thf(2055,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'comp$ae\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(581,axiom,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( A = '\'id$\'' )
     => ( ( '\'relcompp$a\'' @ ( '\'conversep$\'' @ ( '\'grp$\'' @ '\'top$a\'' @ A ) ) @ ( '\'grp$\'' @ '\'top$a\'' @ A ) )
        = ( '\'grp$\'' @ '\'top$a\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).

thf(2706,plain,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( A = '\'id$\'' )
     => ( ( '\'relcompp$a\'' @ ( '\'conversep$\'' @ ( '\'grp$\'' @ '\'top$a\'' @ A ) ) @ ( '\'grp$\'' @ '\'top$a\'' @ A ) )
        = ( '\'grp$\'' @ '\'top$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(48,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$o\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$l\'' @ C @ D ) )
        = ( '\'register_tensor$d\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom81) ).

thf(804,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$o\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$l\'' @ C @ D ) )
        = ( '\'register_tensor$d\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(20,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).

thf(704,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ B ) @ A )
          = '\'id$b\'' ) )
     => ( ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(414,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'B_update_c_update_fun$\'',F: '\'C_update_b_update_fun$\'',G: '\'C_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$a\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$h\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ D ) @ G ) @ E )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).

thf(2148,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'B_update_c_update_fun$\'',F: '\'C_update_b_update_fun$\'',G: '\'C_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$a\'' @ E @ F @ '\'top$a\'' )
        & ( ( '\'comp$h\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ D ) @ G ) @ E )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$ac\'' @ ( '\'comp$aa\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(305,axiom,
    ! [A: '\'B_update$\''] :
      ( ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ ( '\'fun_app$aa\'' @ '\'id$a\'' @ A ) )
    <=> ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).

thf(1765,plain,
    ! [A: '\'B_update$\''] :
      ( ( ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ ( '\'fun_app$aa\'' @ '\'id$a\'' @ A ) )
       => ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ A ) )
      & ( ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ A )
       => ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ ( '\'fun_app$aa\'' @ '\'id$a\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(130,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = ( '\'fun_app$d\'' @ D @ ( '\'fun_app$u\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom220) ).

thf(1090,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = ( '\'fun_app$d\'' @ D @ ( '\'fun_app$u\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(274,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$l\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).

thf(1638,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$l\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(161,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
    <=> ( ( '\'register$a\'' @ A )
        & ? [B: '\'A_update_b_update_fun$\''] :
            ( ( '\'register$c\'' @ B )
            & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
              = '\'id$b\'' )
            & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
              = '\'id$a\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).

thf(1224,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'iso_register$c\'' @ A )
       => ( ( '\'register$a\'' @ A )
          & ? [B: '\'A_update_b_update_fun$\''] :
              ( ( '\'register$c\'' @ B )
              & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
                = '\'id$b\'' )
              & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
                = '\'id$a\'' ) ) ) )
      & ( ( ( '\'register$a\'' @ A )
          & ? [B: '\'A_update_b_update_fun$\''] :
              ( ( '\'register$c\'' @ B )
              & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
                = '\'id$b\'' )
              & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
                = '\'id$a\'' ) ) )
       => ( '\'iso_register$c\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(519,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$c\'' @ B @ C ) )
     => ( ( '\'register_pair$q\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) )
        = ( '\'comp$aw\'' @ A @ ( '\'register_pair$f\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).

thf(2510,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$c\'' @ B @ C ) )
     => ( ( '\'register_pair$q\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) )
        = ( '\'comp$aw\'' @ A @ ( '\'register_pair$f\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(472,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$ah\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).

thf(2346,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$ah\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$d\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(394,axiom,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$br\'' @ '\'uvb$\'' @ ( '\'rel_fun$bs\'' @ ( '\'rel_fun$al\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bt\'' @ A @ '\'uur$\'' ) ) @ '\'comp$b\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom645) ).

thf(2079,plain,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$br\'' @ '\'uvb$\'' @ ( '\'rel_fun$bs\'' @ ( '\'rel_fun$al\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bt\'' @ A @ '\'uur$\'' ) ) @ '\'comp$b\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(585,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'comp$ab\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).

thf(2721,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
      = ( '\'comp$ab\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(574,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'quotient3$d\'' @ A @ B @ C )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).

thf(2679,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'quotient3$d\'' @ A @ B @ C )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(53,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$g\'' @ A @ B )
        & ( '\'register$\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$at\'' @ ( '\'register_pair$o\'' @ A @ B ) @ ( '\'register_tensor$ac\'' @ C @ D ) )
        = ( '\'register_pair$a\'' @ ( '\'comp$k\'' @ A @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom243) ).

thf(831,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$g\'' @ A @ B )
        & ( '\'register$\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$at\'' @ ( '\'register_pair$o\'' @ A @ B ) @ ( '\'register_tensor$ac\'' @ C @ D ) )
        = ( '\'register_pair$a\'' @ ( '\'comp$k\'' @ A @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(211,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ B @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).

thf(1408,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ B @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(173,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) )
     => ( '\'compatible$a\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).

thf(1282,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$\'' @ B )
        & ! [C: '\'A_update$\'',D: '\'A_update$\''] :
            ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ C ) ) @ ( '\'fun_app$g\'' @ B @ D ) )
            = ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ A @ C ) ) ) )
     => ( '\'compatible$a\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(514,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$\'' @ A @ B @ '\'top$a\'' )
        & ( C = '\'id$\'' ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ C ) ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).

thf(2493,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$\'' @ A @ B @ '\'top$a\'' )
        & ( C = '\'id$\'' ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ C ) ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(495,axiom,
    ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ '\'f$\'' ) @ '\'f$a\'' )
    = '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).

thf(2422,plain,
    ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ '\'f$\'' ) @ '\'f$a\'' )
    = '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(318,axiom,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom590) ).

thf(1806,plain,
    ! [A: '\'C_update_set_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bt\'' @ A @ ( '\'image$c\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bt\'' @ A @ ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(398,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
           => ( ( '\'fun_app$g\'' @ C @ E )
              = ( '\'fun_app$g\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).

thf(2097,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$b\'' @ B @ '\'top$b\'' ) )
           => ( ( '\'fun_app$g\'' @ C @ E )
              = ( '\'fun_app$g\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(98,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$b\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).

thf(996,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$b\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(404,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( A = B )
     => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ ( '\'grp$\'' @ '\'top$a\'' @ '\'id$\'' ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).

thf(2116,plain,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( A = B )
     => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ ( '\'grp$\'' @ '\'top$a\'' @ '\'id$\'' ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(653,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'preregister$d\'' @ A )
        & ( '\'preregister$c\'' @ B ) )
     => ( '\'preregister$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).

thf(2943,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'preregister$d\'' @ A )
        & ( '\'preregister$c\'' @ B ) )
     => ( '\'preregister$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(116,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$ar\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$as\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$at\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom619) ).

thf(1043,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_b_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$ar\'' @ ( '\'rel_fun$ao\'' @ A @ B ) @ ( '\'rel_fun$as\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$at\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(482,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$ae\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112) ).

thf(2378,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$ae\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(150,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ! [D: '\'B_update$\''] :
          ( ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ '\'top$\'' ) )
         => ( ( '\'fun_app$d\'' @ B @ D )
            = ( '\'fun_app$d\'' @ C @ D ) ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).

thf(1175,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ! [D: '\'B_update$\''] :
          ( ( '\'member$a\'' @ D @ ( '\'image$\'' @ A @ '\'top$\'' ) )
         => ( ( '\'fun_app$d\'' @ B @ D )
            = ( '\'fun_app$d\'' @ C @ D ) ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(415,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'uun$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).

thf(2151,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'uun$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(561,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bk\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'map_fun$q\'' @ C @ D ) )
      = ( '\'map_fun$r\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).

thf(2642,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bk\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'map_fun$q\'' @ C @ D ) )
      = ( '\'map_fun$r\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(441,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ah\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$h\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ E ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom122) ).

thf(2229,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ah\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$h\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ E ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(255,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$h\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom248) ).

thf(1571,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$h\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(632,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom227) ).

thf(2871,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(200,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$ad\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).

thf(1376,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$ad\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(430,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).

thf(2197,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(366,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( ( '\'fun_app$d\'' @ A @ '\'id_update$b\'' )
        = '\'id_update$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).

thf(1969,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( ( '\'fun_app$d\'' @ A @ '\'id_update$b\'' )
        = '\'id_update$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(179,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ ( '\'rel_fun$f\'' @ A @ B ) @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ '\'uus$\'' @ A ) @ ( '\'rel_fun$i\'' @ '\'uus$\'' @ B ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom620) ).

thf(1307,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ ( '\'rel_fun$f\'' @ A @ B ) @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ '\'uus$\'' @ A ) @ ( '\'rel_fun$i\'' @ '\'uus$\'' @ B ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(68,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ D ) )
        = ( '\'fun_app$ab\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).

thf(890,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ D ) )
        = ( '\'fun_app$ab\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(50,axiom,
    ! [A: '\'C_update$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uua$\'' @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).

thf(811,plain,
    ! [A: '\'C_update$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uua$\'' @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(592,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$f\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ '\'top$e\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).

thf(2742,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$f\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ '\'top$e\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(60,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bh\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'map_fun$f\'' @ C @ D ) )
      = ( '\'map_fun$j\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).

thf(858,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bh\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'map_fun$f\'' @ C @ D ) )
      = ( '\'map_fun$j\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(555,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$a\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$ar\'' @ ( '\'register_pair$b\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_pair$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom241) ).

thf(2625,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$a\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$ar\'' @ ( '\'register_pair$b\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_pair$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(402,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).

thf(2111,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(335,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$ad\'' @ A @ B )
          = ( '\'comp$y\'' @ C @ D ) )
        & ( ( '\'comp$x\'' @ D @ E )
          = F ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ E ) )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).

thf(1862,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'comp$ad\'' @ A @ B )
          = ( '\'comp$y\'' @ C @ D ) )
        & ( ( '\'comp$x\'' @ D @ E )
          = F ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ E ) )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(490,axiom,
    ( ( '\'map_fun$e\'' @ '\'id$b\'' @ '\'id$\'' )
    = '\'id$s\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).

thf(2410,plain,
    ( ( '\'map_fun$e\'' @ '\'id$b\'' @ '\'id$\'' )
    = '\'id$s\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(69,axiom,
    ! [A: '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$h\'' @ A @ B )
     => ( ( '\'fun_app$av\'' @ A @ '\'id$b\'' )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).

thf(895,plain,
    ! [A: '\'A_update_a_update_fun_b_update_b_update_fun_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$h\'' @ A @ B )
     => ( ( '\'fun_app$av\'' @ A @ '\'id$b\'' )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(633,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$ai\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom208) ).

thf(2874,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$ai\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'comp$\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(456,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$c\'' @ B @ C ) )
     => ( ( '\'register_pair$s\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) )
        = ( '\'comp$ba\'' @ A @ ( '\'register_pair$f\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).

thf(2278,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$c\'' @ B @ C ) )
     => ( ( '\'register_pair$s\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) )
        = ( '\'comp$ba\'' @ A @ ( '\'register_pair$f\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(201,axiom,
    ! [A: '\'C_update_set$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'member$\'' @ D @ ( '\'image$a\'' @ B @ A ) )
       => ( ( '\'fun_app$g\'' @ ( '\'uuu$\'' @ A @ B @ C ) @ D )
          = ( '\'fun_app$g\'' @ ( '\'the_inv_into$\'' @ A @ B ) @ D ) ) )
      & ( ~ ( '\'member$\'' @ D @ ( '\'image$a\'' @ B @ A ) )
       => ( ( '\'fun_app$g\'' @ ( '\'uuu$\'' @ A @ B @ C ) @ D )
          = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).

thf(1381,plain,
    ! [A: '\'C_update_set$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update$\''] :
      ( ( ( '\'member$\'' @ D @ ( '\'image$a\'' @ B @ A ) )
       => ( ( '\'fun_app$g\'' @ ( '\'uuu$\'' @ A @ B @ C ) @ D )
          = ( '\'fun_app$g\'' @ ( '\'the_inv_into$\'' @ A @ B ) @ D ) ) )
      & ( ~ ( '\'member$\'' @ D @ ( '\'image$a\'' @ B @ A ) )
       => ( ( '\'fun_app$g\'' @ ( '\'uuu$\'' @ A @ B @ C ) @ D )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(624,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$p\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_tensor$u\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).

thf(2842,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$p\'' @ ( '\'register_tensor$t\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_tensor$u\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(542,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).

thf(2578,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(615,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$a\'' @ A @ B @ '\'top$a\'' )
        & ( C = '\'id$\'' ) )
     => ( ( '\'comp$v\'' @ ( '\'comp$ag\'' @ B @ C ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).

thf(2812,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$a\'' @ A @ B @ '\'top$a\'' )
        & ( C = '\'id$\'' ) )
     => ( ( '\'comp$v\'' @ ( '\'comp$ag\'' @ B @ C ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(127,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'comp$k\'' @ B @ A )
          = '\'id$b\'' ) )
     => ( ( '\'inv_into$c\'' @ '\'top$\'' @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).

thf(1080,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'comp$k\'' @ B @ A )
          = '\'id$b\'' ) )
     => ( ( '\'inv_into$c\'' @ '\'top$\'' @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(502,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
          = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) )
        & ( ! [E: '\'C_update$\''] :
              ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
              = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom157) ).

thf(2446,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ~ ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
          = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) )
        & ~ ! [E: '\'C_update$\''] :
              ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
              = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(597,axiom,
    '\'register$\'' @ '\'g$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).

thf(2757,plain,
    '\'register$\'' @ '\'g$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(57,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).

thf(848,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(18,axiom,
    ( ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ '\'id$a\'' )
    = '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).

thf(700,plain,
    ( ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ '\'id$a\'' )
    = '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(253,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ B )
     => ( ( '\'inj_on$c\'' @ C @ ( '\'image$a\'' @ A @ B ) )
      <=> ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom508) ).

thf(1556,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ B )
     => ( ( ( '\'inj_on$c\'' @ C @ ( '\'image$a\'' @ A @ B ) )
         => ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ B ) )
        & ( ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ B )
         => ( '\'inj_on$c\'' @ C @ ( '\'image$a\'' @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(563,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$au\'' @ '\'uva$\'' @ ( '\'rel_fun$av\'' @ ( '\'rel_fun$f\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$aw\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$a\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom643) ).

thf(2647,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$au\'' @ '\'uva$\'' @ ( '\'rel_fun$av\'' @ ( '\'rel_fun$f\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$aw\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$a\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(582,axiom,
    ! [A: '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$c\'' @ A @ B )
     => ( ( '\'fun_app$bo\'' @ A @ '\'id$\'' )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom319) ).

thf(2710,plain,
    ! [A: '\'C_update_c_update_fun_b_update_b_update_fun_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$c\'' @ A @ B )
     => ( ( '\'fun_app$bo\'' @ A @ '\'id$\'' )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(644,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).

thf(2911,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(323,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = '\'id$\'' )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).

thf(1820,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = '\'id$\'' )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(206,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ C )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'comp$z\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).

thf(1396,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ C )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'comp$z\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(351,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_c_update_fun$\'',I: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$al\'' @ ( '\'map_fun$e\'' @ E @ I ) @ ( '\'map_fun$am\'' @ ( '\'map_fun$m\'' @ B @ F ) @ ( '\'map_fun$p\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$d\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).

thf(1926,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_c_update_fun$\'',I: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$al\'' @ ( '\'map_fun$e\'' @ E @ I ) @ ( '\'map_fun$am\'' @ ( '\'map_fun$m\'' @ B @ F ) @ ( '\'map_fun$p\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$d\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(245,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$by\'' @ A @ A @ '\'id$a\'' @ '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom662) ).

thf(1528,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$by\'' @ A @ A @ '\'id$a\'' @ '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(397,axiom,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( '\'iso_register$d\'' @ A )
    <=> ( ( '\'register$h\'' @ A )
        & ? [B: '\'C_update_c_update_fun$\''] :
            ( ( '\'register$h\'' @ B )
            & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
              = '\'id$\'' )
            & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
              = '\'id$\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).

thf(2086,plain,
    ! [A: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'iso_register$d\'' @ A )
       => ( ( '\'register$h\'' @ A )
          & ? [B: '\'C_update_c_update_fun$\''] :
              ( ( '\'register$h\'' @ B )
              & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
                = '\'id$\'' )
              & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
                = '\'id$\'' ) ) ) )
      & ( ( ( '\'register$h\'' @ A )
          & ? [B: '\'C_update_c_update_fun$\''] :
              ( ( '\'register$h\'' @ B )
              & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
                = '\'id$\'' )
              & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
                = '\'id$\'' ) ) )
       => ( '\'iso_register$d\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(276,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'image$b\'' @ A @ '\'top$b\'' )
        = '\'top$\'' )
    <=> ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).

thf(1643,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'image$b\'' @ A @ '\'top$b\'' )
          = '\'top$\'' )
       => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) )
          = '\'id$b\'' ) )
      & ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) )
          = '\'id$b\'' )
       => ( ( '\'image$b\'' @ A @ '\'top$b\'' )
          = '\'top$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(411,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).

thf(2139,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(137,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\''] :
      ( ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$b\'' @ A @ ( '\'image$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).

thf(1113,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\''] :
      ( ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$b\'' @ A @ ( '\'image$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(100,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$bk\'' @ ( '\'rel_fun$h\'' @ A @ B ) @ ( '\'rel_fun$bl\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$bm\'' @ '\'uur$\'' @ B ) ) @ '\'comp$e\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom628) ).

thf(1000,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$bk\'' @ ( '\'rel_fun$h\'' @ A @ B ) @ ( '\'rel_fun$bl\'' @ ( '\'rel_fun$f\'' @ '\'uur$\'' @ A ) @ ( '\'rel_fun$bm\'' @ '\'uur$\'' @ B ) ) @ '\'comp$e\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(234,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ '\'top$\'' )
      = ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ '\'top$\'' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).

thf(1496,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ '\'top$\'' )
      = ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ '\'top$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(58,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ '\'id$a\'' ) @ C ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$aa\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).

thf(851,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ '\'id$a\'' ) @ C ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$aa\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(288,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
    <=> ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).

thf(1694,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
       => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
          = '\'id$b\'' ) )
      & ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
          = '\'id$b\'' )
       => ( '\'inj_on$\'' @ A @ '\'top$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(601,axiom,
    '\'iso_register$\'' @ '\'g$a\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).

thf(2770,plain,
    '\'iso_register$\'' @ '\'g$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(94,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ B )
        & ( '\'inj_on$b\'' @ C @ ( '\'image$\'' @ A @ B ) ) )
     => ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).

thf(983,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ B )
        & ( '\'inj_on$b\'' @ C @ ( '\'image$\'' @ A @ B ) ) )
     => ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(393,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'member$b\'' @ A @ B )
        & ( '\'inj_on$a\'' @ C @ B ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'uuu$\'' @ B @ C @ D ) ) @ C ) @ A )
        = ( '\'fun_app$z\'' @ '\'id$\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom595) ).

thf(2075,plain,
    ! [A: '\'C_update$\'',B: '\'C_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'member$b\'' @ A @ B )
        & ( '\'inj_on$a\'' @ C @ B ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'uuu$\'' @ B @ C @ D ) ) @ C ) @ A )
        = ( '\'fun_app$z\'' @ '\'id$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(227,axiom,
    ( ( '\'register_tensor$e\'' @ '\'id$a\'' @ '\'id$b\'' )
    = '\'id$h\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom62) ).

thf(1474,plain,
    ( ( '\'register_tensor$e\'' @ '\'id$a\'' @ '\'id$b\'' )
    = '\'id$h\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(473,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'quotient3$d\'' @ A @ B @ C )
     => ( ( '\'fun_app$bh\'' @ ( '\'map_fun$n\'' @ C @ B ) @ '\'id$b\'' )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).

thf(2350,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'quotient3$d\'' @ A @ B @ C )
     => ( ( '\'fun_app$bh\'' @ ( '\'map_fun$n\'' @ C @ B ) @ '\'id$b\'' )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(587,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$g\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$n\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom249) ).

thf(2725,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'compatible$g\'' @ A @ B )
        & ( '\'register$\'' @ C ) )
     => ( '\'compatible$n\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(487,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'register$j\'' @ A )
        & ( '\'register$i\'' @ B )
        & ( ( '\'comp$v\'' @ A @ B )
          = '\'id$a\'' )
        & ( ( '\'comp$\'' @ B @ A )
          = '\'id$\'' ) )
     => ( '\'iso_register$f\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom99) ).

thf(2401,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'B_update_c_update_fun$\''] :
      ( ( ( '\'register$j\'' @ A )
        & ( '\'register$i\'' @ B )
        & ( ( '\'comp$v\'' @ A @ B )
          = '\'id$a\'' )
        & ( ( '\'comp$\'' @ B @ A )
          = '\'id$\'' ) )
     => ( '\'iso_register$f\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(260,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( '\'preregister$d\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).

thf(1594,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( '\'preregister$d\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(160,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'iso_register$b\'' @ A )
    <=> ( ( '\'register$\'' @ A )
        & ? [B: '\'C_update_a_update_fun$\''] :
            ( ( '\'register$b\'' @ B )
            & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
              = '\'id$\'' )
            & ( ( '\'comp$k\'' @ B @ A )
              = '\'id$b\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).

thf(1213,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'iso_register$b\'' @ A )
       => ( ( '\'register$\'' @ A )
          & ? [B: '\'C_update_a_update_fun$\''] :
              ( ( '\'register$b\'' @ B )
              & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
                = '\'id$\'' )
              & ( ( '\'comp$k\'' @ B @ A )
                = '\'id$b\'' ) ) ) )
      & ( ( ( '\'register$\'' @ A )
          & ? [B: '\'C_update_a_update_fun$\''] :
              ( ( '\'register$b\'' @ B )
              & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
                = '\'id$\'' )
              & ( ( '\'comp$k\'' @ B @ A )
                = '\'id$b\'' ) ) )
       => ( '\'iso_register$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(622,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$bg\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'map_fun$d\'' @ C @ D ) )
      = ( '\'map_fun$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).

thf(2835,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$bg\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'map_fun$d\'' @ C @ D ) )
      = ( '\'map_fun$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(386,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$c\'' @ A @ B @ '\'top$b\'' )
        & ( C = '\'id$a\'' ) )
     => ( ( '\'comp$\'' @ ( '\'comp$af\'' @ B @ C ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).

thf(2051,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$c\'' @ A @ B @ '\'top$b\'' )
        & ( C = '\'id$a\'' ) )
     => ( ( '\'comp$\'' @ ( '\'comp$af\'' @ B @ C ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(600,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$z\'' @ A @ B )
        = C )
     => ( ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).

thf(2765,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'comp$z\'' @ A @ B )
        = C )
     => ( ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(510,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'fun_app$az\'' @ ( '\'map_fun$f\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$ba\'' @ ( '\'map_fun$g\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).

thf(2481,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'map_fun$c\'' @ A @ B ) @ ( '\'fun_app$az\'' @ ( '\'map_fun$f\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$ba\'' @ ( '\'map_fun$g\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(390,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$aj\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).

thf(2064,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$\'' @ A @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$aj\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(106,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$w\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$x\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$y\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$e\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom633) ).

thf(1015,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$w\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$x\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$y\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$e\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(270,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).

thf(1626,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(319,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).

thf(1809,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(570,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'compatible$b\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$am\'' @ ( '\'register_pair$d\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_pair$e\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom236) ).

thf(2665,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'compatible$b\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$am\'' @ ( '\'register_pair$d\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_pair$e\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(79,axiom,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$e\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ '\'top$d\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).

thf(927,plain,
    ! [A: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$e\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ '\'top$d\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(31,axiom,
    ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ '\'id$b\'' ) @ '\'top$\'' )
    = '\'top$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).

thf(749,plain,
    ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ '\'id$b\'' ) @ '\'top$\'' )
    = '\'top$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(576,axiom,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bx\'' @ A @ A @ '\'id$a\'' @ '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom651) ).

thf(2684,plain,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bx\'' @ A @ A @ '\'id$a\'' @ '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(468,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$be\'' @ ( '\'rel_fun$h\'' @ A @ B ) @ ( '\'rel_fun$bf\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$bg\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$b\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom626) ).

thf(2333,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'B_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$be\'' @ ( '\'rel_fun$h\'' @ A @ B ) @ ( '\'rel_fun$bf\'' @ ( '\'rel_fun$ah\'' @ '\'uuq$\'' @ A ) @ ( '\'rel_fun$bg\'' @ '\'uuq$\'' @ B ) ) @ '\'comp$b\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(362,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ '\'uva$\'' @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$ai\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom640) ).

thf(1958,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$ae\'' @ '\'uva$\'' @ ( '\'rel_fun$ag\'' @ ( '\'rel_fun$ah\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$ai\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$d\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(33,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\''] :
      ( ( ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).

thf(754,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'B_update_b_update_fun$\''] :
      ( ( ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
          = '\'id$a\'' )
        & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(90,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cf\'' @ ( '\'rel_fun$i\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom665) ).

thf(968,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'fun_app$ca\'' @ ( '\'fun_app$cf\'' @ ( '\'rel_fun$i\'' @ A @ A ) @ '\'id$b\'' ) @ '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(543,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ '\'top$b\'' )
      = ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ '\'top$b\'' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom566) ).

thf(2582,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ '\'top$b\'' )
      = ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ '\'top$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(118,axiom,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom593) ).

thf(1049,plain,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$b\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(374,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$z\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).

thf(2005,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$ag\'' @ A @ ( '\'fun_app$z\'' @ B @ C ) )
        = ( '\'fun_app$ab\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ F ) @ A ) @ B ) @ C )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$w\'' @ F @ D ) ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(126,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( A = B )
     => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ ( '\'grp$b\'' @ '\'top$\'' @ '\'id$b\'' ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).

thf(1076,plain,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( A = B )
     => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ ( '\'grp$b\'' @ '\'top$\'' @ '\'id$b\'' ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(10,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( '\'register$a\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).

thf(675,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( '\'register$a\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(645,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
         => ( ( '\'fun_app$u\'' @ B @ D )
            = ( '\'fun_app$u\'' @ C @ D ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).

thf(2914,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
         => ( ( '\'fun_app$u\'' @ B @ D )
            = ( '\'fun_app$u\'' @ C @ D ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(616,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$ac\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).

thf(2816,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$ac\'' @ A @ B )
          = ( '\'comp$ad\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'comp$h\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(178,axiom,
    ! [A: '\'A_update_set$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'rel_fun$d\'' @ '\'uur$\'' @ ( '\'grp$h\'' @ A @ B ) )
      = ( '\'grp$j\'' @ ( '\'collect$b\'' @ ( '\'uuy$\'' @ A ) ) @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom609) ).

thf(1304,plain,
    ! [A: '\'A_update_set$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'rel_fun$d\'' @ '\'uur$\'' @ ( '\'grp$h\'' @ A @ B ) )
      = ( '\'grp$j\'' @ ( '\'collect$b\'' @ ( '\'uuy$\'' @ A ) ) @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(338,axiom,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ! [B: '\'B_update$\''] :
          ( ( '\'fun_app$aa\'' @ A @ B )
          = B )
    <=> ( A = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).

thf(1873,plain,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( ! [B: '\'B_update$\''] :
            ( ( '\'fun_app$aa\'' @ A @ B )
            = B )
       => ( A = '\'id$a\'' ) )
      & ( ( A = '\'id$a\'' )
       => ! [B: '\'B_update$\''] :
            ( ( '\'fun_app$aa\'' @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(303,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) ) @ G )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$w\'' @ ( '\'comp$w\'' @ B @ E ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).

thf(1758,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) ) @ G )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$w\'' @ ( '\'comp$w\'' @ B @ E ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(400,axiom,
    ( ( '\'map_fun$v\'' @ '\'id$a\'' @ '\'id$\'' )
    = '\'id$q\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).

thf(2107,plain,
    ( ( '\'map_fun$v\'' @ '\'id$a\'' @ '\'id$\'' )
    = '\'id$q\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(46,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$\'' @ A @ '\'top$\'' )
        = '\'top$b\'' )
    <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).

thf(795,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'image$\'' @ A @ '\'top$\'' )
          = '\'top$b\'' )
       => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) )
          = '\'id$a\'' ) )
      & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) )
          = '\'id$a\'' )
       => ( ( '\'image$\'' @ A @ '\'top$\'' )
          = '\'top$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(606,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ ( '\'comp$z\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).

thf(2784,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\''] :
      ( ( '\'comp$ag\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ ( '\'comp$z\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(12,axiom,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ '\'id$b\'' ) @ B ) )
      = ( '\'fun_app$bv\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom583) ).

thf(680,plain,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ '\'id$b\'' ) @ B ) )
      = ( '\'fun_app$bv\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,axiom,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( '\'bijection$a\'' @ A )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ A ) ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).

thf(663,plain,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( '\'bijection$a\'' @ A )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ ( '\'fun_app$an\'' @ ( '\'inv_into$e\'' @ '\'top$b\'' ) @ A ) ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(565,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$aj\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ak\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$am\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom617) ).

thf(2652,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$aj\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ak\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$am\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(634,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).

thf(2878,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(285,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
        & ( '\'register$c\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$ak\'' @ ( '\'register_pair$\'' @ A @ B ) @ ( '\'register_tensor$m\'' @ C @ D ) )
        = ( '\'register_pair$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).

thf(1684,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$\'' @ A @ B )
        & ( '\'register$c\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$ak\'' @ ( '\'register_pair$\'' @ A @ B ) @ ( '\'register_tensor$m\'' @ C @ D ) )
        = ( '\'register_pair$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(520,axiom,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom592) ).

thf(2513,plain,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(306,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$by\'' @ A @ A @ '\'id$a\'' @ '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom653) ).

thf(1770,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$by\'' @ A @ A @ '\'id$a\'' @ '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(59,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fcomp$d\'' @ A @ B )
      = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom233) ).

thf(855,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fcomp$d\'' @ A @ B )
      = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(110,axiom,
    ( '\'uus$\''
    = ( '\'grp$b\'' @ '\'top$\'' @ '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).

thf(1025,plain,
    ( '\'uus$\''
    = ( '\'grp$b\'' @ '\'top$\'' @ '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(21,axiom,
    ( ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ '\'id$b\'' )
    = '\'id$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).

thf(707,plain,
    ( ( '\'fun_app$al\'' @ ( '\'inv_into$f\'' @ '\'top$\'' ) @ '\'id$b\'' )
    = '\'id$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(545,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
              & ( ( '\'fun_app$u\'' @ C @ E )
                = ( '\'fun_app$u\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A )
          = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).

thf(2588,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
              & ( ( '\'fun_app$u\'' @ C @ E )
                = ( '\'fun_app$u\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A )
          = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(573,axiom,
    '\'iso_register$a\'' @ '\'f$a\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).

thf(2678,plain,
    '\'iso_register$a\'' @ '\'f$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(423,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$h\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ah\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).

thf(2175,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$h\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ C ) )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ah\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(484,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ D @ E @ F )
        & ! [H: '\'C_update$\'',I: '\'C_update$\''] :
            ( ( ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ H ) @ I )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ H ) @ H )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$ag\'' @ B @ H ) ) @ ( '\'fun_app$ag\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ ( '\'fun_app$g\'' @ C @ H ) ) @ ( '\'fun_app$g\'' @ C @ I ) ) ) )
     => ( '\'quotient3$g\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ G @ A ) ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).

thf(2386,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_b_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ D @ E @ F )
        & ! [H: '\'C_update$\'',I: '\'C_update$\''] :
            ( ( ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ H ) @ I )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ H ) @ H )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$ag\'' @ B @ H ) ) @ ( '\'fun_app$ag\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ ( '\'fun_app$g\'' @ C @ H ) ) @ ( '\'fun_app$g\'' @ C @ I ) ) ) )
     => ( '\'quotient3$g\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ G @ A ) ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(250,axiom,
    ( ( '\'vimage$b\'' @ '\'id$b\'' )
    = '\'id$w\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom668) ).

thf(1547,plain,
    ( ( '\'vimage$b\'' @ '\'id$b\'' )
    = '\'id$w\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(300,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$b\'' @ B )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'comp$k\'' @ B @ A )
          = '\'id$b\'' ) )
     => ( '\'iso_register$b\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom102) ).

thf(1748,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$b\'' @ B )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'comp$k\'' @ B @ A )
          = '\'id$b\'' ) )
     => ( '\'iso_register$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(630,axiom,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$aj\'' @ A @ B )
        = C )
     => ( ( '\'comp$af\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom146) ).

thf(2863,plain,
    ! [A: '\'B_update_c_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$aj\'' @ A @ B )
        = C )
     => ( ( '\'comp$af\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(262,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'register_tensor$l\'' @ A @ B ) @ ( '\'tensor_update$f\'' @ C @ D ) )
        = ( '\'tensor_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) @ ( '\'fun_app$d\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).

thf(1598,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'register_tensor$l\'' @ A @ B ) @ ( '\'tensor_update$f\'' @ C @ D ) )
        = ( '\'tensor_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) @ ( '\'fun_app$d\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(589,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$g\'' @ B @ C ) )
     => ( ( '\'register_pair$n\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) )
        = ( '\'comp$av\'' @ A @ ( '\'register_pair$o\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).

thf(2732,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$g\'' @ B @ C ) )
     => ( ( '\'register_pair$n\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) )
        = ( '\'comp$av\'' @ A @ ( '\'register_pair$o\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(356,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$bi\'' @ ( '\'map_fun$k\'' @ A @ B ) @ ( '\'map_fun$l\'' @ C @ D ) )
      = ( '\'map_fun$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).

thf(1941,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$bi\'' @ ( '\'map_fun$k\'' @ A @ B ) @ ( '\'map_fun$l\'' @ C @ D ) )
      = ( '\'map_fun$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(620,axiom,
    ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ '\'id$\'' ) @ '\'top$a\'' )
    = '\'top$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).

thf(2831,plain,
    ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ '\'id$\'' ) @ '\'top$a\'' )
    = '\'top$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(578,axiom,
    ! [A: '\'C_update_b_update_fun$\''] :
      ( ( '\'iso_register$f\'' @ A )
    <=> ( ( '\'register$j\'' @ A )
        & ? [B: '\'B_update_c_update_fun$\''] :
            ( ( '\'register$i\'' @ B )
            & ( ( '\'comp$v\'' @ A @ B )
              = '\'id$a\'' )
            & ( ( '\'comp$\'' @ B @ A )
              = '\'id$\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom90) ).

thf(2689,plain,
    ! [A: '\'C_update_b_update_fun$\''] :
      ( ( ( '\'iso_register$f\'' @ A )
       => ( ( '\'register$j\'' @ A )
          & ? [B: '\'B_update_c_update_fun$\''] :
              ( ( '\'register$i\'' @ B )
              & ( ( '\'comp$v\'' @ A @ B )
                = '\'id$a\'' )
              & ( ( '\'comp$\'' @ B @ A )
                = '\'id$\'' ) ) ) )
      & ( ( ( '\'register$j\'' @ A )
          & ? [B: '\'B_update_c_update_fun$\''] :
              ( ( '\'register$i\'' @ B )
              & ( ( '\'comp$v\'' @ A @ B )
                = '\'id$a\'' )
              & ( ( '\'comp$\'' @ B @ A )
                = '\'id$\'' ) ) )
       => ( '\'iso_register$f\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(9,axiom,
    ( ( '\'image$f\'' @ '\'id$b\'' )
    = '\'id$w\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).

thf(673,plain,
    ( ( '\'image$f\'' @ '\'id$b\'' )
    = '\'id$w\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(372,axiom,
    ! [A: '\'A_update$\''] :
      ( ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ ( '\'fun_app$ab\'' @ '\'id$b\'' @ A ) )
    <=> ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).

thf(1987,plain,
    ! [A: '\'A_update$\''] :
      ( ( ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ ( '\'fun_app$ab\'' @ '\'id$b\'' @ A ) )
       => ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ A ) )
      & ( ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ A )
       => ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ ( '\'fun_app$ab\'' @ '\'id$b\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(223,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) )
     => ( '\'register$n\'' @ ( '\'register_pair$\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).

thf(1452,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) )
     => ( '\'register$n\'' @ ( '\'register_pair$\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(579,axiom,
    ( ( '\'map_fun$m\'' @ '\'id$\'' @ '\'id$b\'' )
    = '\'id$p\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).

thf(2700,plain,
    ( ( '\'map_fun$m\'' @ '\'id$\'' @ '\'id$b\'' )
    = '\'id$p\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(337,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ah\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ E ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).

thf(1869,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ah\'' @ A @ B )
          = ( '\'comp$ab\'' @ C @ D ) )
        & ( ( '\'comp$aa\'' @ D @ E )
          = F ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ E ) )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(311,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$a\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ '\'uur$\'' @ A ) ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).

thf(1785,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$e\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$a\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ '\'uur$\'' @ A ) ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(162,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = '\'id$b\'' )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).

thf(1235,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = '\'id$b\'' )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(437,axiom,
    '\'register$a\'' @ '\'f$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).

thf(2219,plain,
    '\'register$a\'' @ '\'f$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(304,axiom,
    ( ( '\'map_fun$j\'' @ '\'id$b\'' @ '\'id$a\'' )
    = '\'id$t\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).

thf(1763,plain,
    ( ( '\'map_fun$j\'' @ '\'id$b\'' @ '\'id$a\'' )
    = '\'id$t\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(174,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$z\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom150) ).

thf(1285,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$z\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(594,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$m\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_tensor$q\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).

thf(2747,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$m\'' @ ( '\'register_tensor$m\'' @ A @ B ) @ ( '\'register_tensor$p\'' @ C @ D ) )
        = ( '\'register_tensor$q\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(235,axiom,
    ( ( '\'image$e\'' @ '\'id$a\'' )
    = '\'id$v\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).

thf(1499,plain,
    ( ( '\'image$e\'' @ '\'id$a\'' )
    = '\'id$v\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(512,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$c\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$k\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).

thf(2486,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$c\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$k\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(85,axiom,
    ! [A: '\'A_update_b_update_bool_fun_fun$\'',B: '\'C_update_a_update_bool_fun_fun$\'',C: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$z\'' @ ( '\'rel_fun$aa\'' @ A @ B ) @ ( '\'rel_fun$ab\'' @ ( '\'rel_fun$ac\'' @ C @ A ) @ ( '\'rel_fun$ad\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).

thf(951,plain,
    ! [A: '\'A_update_b_update_bool_fun_fun$\'',B: '\'C_update_a_update_bool_fun_fun$\'',C: '\'C_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$z\'' @ ( '\'rel_fun$aa\'' @ A @ B ) @ ( '\'rel_fun$ab\'' @ ( '\'rel_fun$ac\'' @ C @ A ) @ ( '\'rel_fun$ad\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(532,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$i\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).

thf(2545,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$i\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(354,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [E: '\'B_update$\'',F: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ E ) ) @ ( '\'fun_app$d\'' @ B @ F ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ F ) ) @ ( '\'fun_app$d\'' @ A @ E ) ) ) )
     => ( ( '\'fun_app$at\'' @ ( '\'register_pair$\'' @ A @ B ) @ ( '\'tensor_update$f\'' @ C @ D ) )
        = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom267) ).

thf(1934,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'B_update$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [E: '\'B_update$\'',F: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ E ) ) @ ( '\'fun_app$d\'' @ B @ F ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ F ) ) @ ( '\'fun_app$d\'' @ A @ E ) ) ) )
     => ( ( '\'fun_app$at\'' @ ( '\'register_pair$\'' @ A @ B ) @ ( '\'tensor_update$f\'' @ C @ D ) )
        = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(167,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
          = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) )
        & ( ! [E: '\'B_update$\''] :
              ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
              = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).

thf(1257,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ~ ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
          = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) )
        & ~ ! [E: '\'B_update$\''] :
              ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
              = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(248,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ '\'id$\'' ) @ C ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$z\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).

thf(1536,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update$\''] :
      ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
        = ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ '\'id$\'' ) @ C ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ D ) )
        = ( '\'fun_app$z\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(531,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$s\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$u\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$v\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$b\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom632) ).

thf(2543,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_bool_fun_fun$\'',C: '\'A_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$s\'' @ ( '\'rel_fun$t\'' @ A @ B ) @ ( '\'rel_fun$u\'' @ ( '\'rel_fun$m\'' @ C @ A ) @ ( '\'rel_fun$v\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(62,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ D @ E @ F )
        & ! [H: '\'C_update$\'',I: '\'C_update$\''] :
            ( ( ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ H ) @ I )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ H ) @ H )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$ag\'' @ B @ H ) ) @ ( '\'fun_app$ag\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ ( '\'fun_app$g\'' @ C @ H ) ) @ ( '\'fun_app$g\'' @ C @ I ) ) ) )
     => ( '\'quotient3$\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ G @ A ) ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).

thf(864,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'C_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\''] :
      ( ( ( '\'quotient3$f\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ D @ E @ F )
        & ! [H: '\'C_update$\'',I: '\'C_update$\''] :
            ( ( ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ H ) @ I )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ H ) @ H )
              & ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ A @ I ) @ I ) )
           => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ ( '\'fun_app$ag\'' @ B @ H ) ) @ ( '\'fun_app$ag\'' @ B @ I ) ) )
        & ! [H: '\'A_update$\'',I: '\'A_update$\''] :
            ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ D @ H ) @ I )
           => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ G @ ( '\'fun_app$g\'' @ C @ H ) ) @ ( '\'fun_app$g\'' @ C @ I ) ) ) )
     => ( '\'quotient3$\'' @ ( '\'relcompp$a\'' @ A @ ( '\'relcompp$a\'' @ G @ A ) ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ B ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(25,axiom,
    ! [A: '\'A_update$\''] :
      ( ( '\'fun_app$m\'' @ '\'uuk$\'' @ A )
    <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).

thf(727,plain,
    ! [A: '\'A_update$\''] : ( '\'fun_app$m\'' @ '\'uuk$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(143,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom468) ).

thf(1140,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(315,axiom,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ '\'id$a\'' ) @ B ) )
      = ( '\'fun_app$bu\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).

thf(1797,plain,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'B_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'fun_app$bs\'' @ ( '\'image$e\'' @ '\'id$a\'' ) @ B ) )
      = ( '\'fun_app$bu\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(452,axiom,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bn\'' @ '\'uva$\'' @ ( '\'rel_fun$bo\'' @ ( '\'rel_fun$bp\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bq\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$a\'' @ '\'comp$d\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom642) ).

thf(2266,plain,
    ! [A: '\'B_update_c_update_bool_fun_fun$\''] : ( '\'rel_fun$bn\'' @ '\'uva$\'' @ ( '\'rel_fun$bo\'' @ ( '\'rel_fun$bp\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$bq\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$a\'' @ '\'comp$d\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(97,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$z\'' @ ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ B @ E ) ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).

thf(991,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$g\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$z\'' @ ( '\'comp$aa\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$ab\'' @ B @ E ) ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(623,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
        = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).

thf(2838,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
        = ( '\'fun_app$u\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(537,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ C ) )
      = ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).

thf(2558,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ C ) )
      = ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(3,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( '\'quotient3$b\'' @ A @ B @ C )
     => ( ( '\'fun_app$al\'' @ ( '\'map_fun$b\'' @ C @ B ) @ '\'id$b\'' )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom381) ).

thf(656,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_a_update_fun$\''] :
      ( ( '\'quotient3$b\'' @ A @ B @ C )
     => ( ( '\'fun_app$al\'' @ ( '\'map_fun$b\'' @ C @ B ) @ '\'id$b\'' )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(109,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( '\'register$c\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).

thf(1023,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_register$a\'' @ A )
     => ( '\'register$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(194,axiom,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( A = '\'id$b\'' )
     => ( ( '\'relcompp$\'' @ ( '\'conversep$b\'' @ ( '\'grp$b\'' @ '\'top$\'' @ A ) ) @ ( '\'grp$b\'' @ '\'top$\'' @ A ) )
        = ( '\'grp$b\'' @ '\'top$\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).

thf(1353,plain,
    ! [A: '\'A_update_a_update_fun$\''] :
      ( ( A = '\'id$b\'' )
     => ( ( '\'relcompp$\'' @ ( '\'conversep$b\'' @ ( '\'grp$b\'' @ '\'top$\'' @ A ) ) @ ( '\'grp$b\'' @ '\'top$\'' @ A ) )
        = ( '\'grp$b\'' @ '\'top$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(361,axiom,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'image$b\'' @ B @ ( '\'image$\'' @ C @ D ) ) )
      = ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).

thf(1955,plain,
    ! [A: '\'A_update_set_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_set$\''] :
      ( ( '\'fun_app$bv\'' @ A @ ( '\'image$b\'' @ B @ ( '\'image$\'' @ C @ D ) ) )
      = ( '\'fun_app$bv\'' @ A @ ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(413,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( '\'quotient3$f\'' @ A @ B @ C )
     => ( ( '\'fun_app$bi\'' @ ( '\'map_fun$o\'' @ C @ B ) @ '\'id$\'' )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).

thf(2145,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( '\'quotient3$f\'' @ A @ B @ C )
     => ( ( '\'fun_app$bi\'' @ ( '\'map_fun$o\'' @ C @ B ) @ '\'id$\'' )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(231,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\''] :
      ( ( '\'fun_app$bh\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'fun_app$bi\'' @ ( '\'map_fun$o\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$am\'' @ ( '\'map_fun$p\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).

thf(1485,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'C_update_c_update_fun$\''] :
      ( ( '\'fun_app$bh\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'fun_app$bi\'' @ ( '\'map_fun$o\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$am\'' @ ( '\'map_fun$p\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(367,axiom,
    ! [A: '\'C_update_bool_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'pred_fun$d\'' @ '\'uum$\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) )
    <=> ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'comp$bo\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).

thf(1972,plain,
    ! [A: '\'C_update_bool_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'pred_fun$d\'' @ '\'uum$\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) )
       => ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'comp$bo\'' @ A @ B ) @ C ) )
      & ( ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'comp$bo\'' @ A @ B ) @ C )
       => ( '\'pred_fun$d\'' @ '\'uum$\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(463,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$g\'' @ B @ C ) )
     => ( ( '\'register_pair$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ C ) )
        = ( '\'comp$az\'' @ A @ ( '\'register_pair$o\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).

thf(2320,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$g\'' @ B @ C ) )
     => ( ( '\'register_pair$m\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ C ) )
        = ( '\'comp$az\'' @ A @ ( '\'register_pair$o\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(119,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'comp$y\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).

thf(1052,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
      = ( '\'comp$y\'' @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(199,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$b\'' @ A )
        & ( '\'register$\'' @ B )
        & ( ( '\'comp$k\'' @ A @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( '\'iso_register$\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).

thf(1372,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$b\'' @ A )
        & ( '\'register$\'' @ B )
        & ( ( '\'comp$k\'' @ A @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( '\'iso_register$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(638,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).

thf(2892,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(599,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
         => ( ( '\'fun_app$g\'' @ B @ D )
            = ( '\'fun_app$g\'' @ C @ D ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).

thf(2760,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ '\'top$b\'' ) )
         => ( ( '\'fun_app$g\'' @ B @ D )
            = ( '\'fun_app$g\'' @ C @ D ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(506,axiom,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$bz\'' @ ( '\'rel_fun$at\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom649) ).

thf(2458,plain,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'fun_app$by\'' @ ( '\'fun_app$bz\'' @ ( '\'rel_fun$at\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(182,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).

thf(1316,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\''] :
      ( ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(151,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'fcomp$a\'' @ A @ B )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).

thf(1180,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'fcomp$a\'' @ A @ B )
      = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(365,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bm\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'map_fun$q\'' @ C @ D ) )
      = ( '\'map_fun$u\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).

thf(1966,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( '\'comp$bm\'' @ ( '\'map_fun$s\'' @ A @ B ) @ ( '\'map_fun$q\'' @ C @ D ) )
      = ( '\'map_fun$u\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(252,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'uub$\'' @ A ) ) @ B ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).

thf(1553,plain,
    ! [A: '\'B_update$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'uub$\'' @ A ) ) @ B ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(359,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$e\'' @ ( '\'register_tensor$j\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom75) ).

thf(1949,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'register$e\'' @ ( '\'register_tensor$j\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(322,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$e\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$ah\'' @ ( '\'map_fun$f\'' @ E @ I ) @ ( '\'map_fun$ai\'' @ ( '\'map_fun$h\'' @ B @ F ) @ ( '\'map_fun$a\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$e\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).

thf(1817,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_b_update_bool_fun_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'A_update_b_update_fun$\'',G: '\'A_update_a_update_bool_fun_fun$\'',H: '\'A_update_b_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ D @ E @ F )
        & ( '\'quotient3$e\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$ah\'' @ ( '\'map_fun$f\'' @ E @ I ) @ ( '\'map_fun$ai\'' @ ( '\'map_fun$h\'' @ B @ F ) @ ( '\'map_fun$a\'' @ C @ H ) ) @ '\'comp$c\'' )
        = '\'comp$e\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(348,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\'',D: '\'A_update$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ ( '\'image$\'' @ B @ C ) )
        & ( '\'inj_on$\'' @ B @ C )
        & ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'the_inv_into$c\'' @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'the_inv_into$b\'' @ C @ B ) ) @ ( '\'the_inv_into$a\'' @ ( '\'image$\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom600) ).

thf(1913,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\'',D: '\'A_update$\''] :
      ( ( ( '\'inj_on$b\'' @ A @ ( '\'image$\'' @ B @ C ) )
        & ( '\'inj_on$\'' @ B @ C )
        & ( '\'member$\'' @ D @ ( '\'image$b\'' @ A @ ( '\'image$\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$al\'' @ ( '\'the_inv_into$c\'' @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'the_inv_into$b\'' @ C @ B ) ) @ ( '\'the_inv_into$a\'' @ ( '\'image$\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(212,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$u\'' @ ( '\'register_tensor$x\'' @ A @ B ) @ ( '\'register_tensor$aa\'' @ C @ D ) )
        = ( '\'register_tensor$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom87) ).

thf(1412,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B )
        & ( '\'register$a\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$u\'' @ ( '\'register_tensor$x\'' @ A @ B ) @ ( '\'register_tensor$aa\'' @ C @ D ) )
        = ( '\'register_tensor$e\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(436,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ai\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$v\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ E ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom123) ).

thf(2215,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_a_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\''] :
      ( ( ( ( '\'comp$ai\'' @ A @ B )
          = ( '\'comp$w\'' @ C @ D ) )
        & ( ( '\'comp$ad\'' @ D @ E )
          = F ) )
     => ( ( '\'comp$v\'' @ A @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ E ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(434,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'preregister$f\'' @ A )
        & ( '\'preregister$e\'' @ B ) )
     => ( '\'preregister$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).

thf(2209,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'preregister$f\'' @ A )
        & ( '\'preregister$e\'' @ B ) )
     => ( '\'preregister$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(222,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'the_inv_into$a\'' @ '\'top$b\'' @ A ) ) @ A ) @ B )
        = ( '\'fun_app$aa\'' @ '\'id$a\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom599) ).

thf(1448,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'the_inv_into$a\'' @ '\'top$b\'' @ A ) ) @ A ) @ B )
        = ( '\'fun_app$aa\'' @ '\'id$a\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(135,axiom,
    '\'iso_register$g\'' @ '\'id$a\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).

thf(1108,plain,
    '\'iso_register$g\'' @ '\'id$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(215,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$k\'' @ A @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( ( '\'inv_into$a\'' @ '\'top$a\'' @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).

thf(1421,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$k\'' @ A @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( ( '\'inv_into$a\'' @ '\'top$a\'' @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(377,axiom,
    ! [A: '\'B_update$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'uub$\'' @ A ) ) @ B ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).

thf(2013,plain,
    ! [A: '\'B_update$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\''] :
      ( ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'uub$\'' @ A ) ) @ B ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(648,axiom,
    ( ( '\'vimage$\'' @ '\'id$\'' )
    = '\'id$u\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom666) ).

thf(2924,plain,
    ( ( '\'vimage$\'' @ '\'id$\'' )
    = '\'id$u\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(93,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'uun$\'' @ A @ B ) @ C )
    <=> ( ( '\'fun_app$g\'' @ A @ C )
        = ( '\'fun_app$g\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).

thf(976,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update$\''] :
      ( ( ( '\'fun_app$m\'' @ ( '\'uun$\'' @ A @ B ) @ C )
       => ( ( '\'fun_app$g\'' @ A @ C )
          = ( '\'fun_app$g\'' @ B @ C ) ) )
      & ( ( ( '\'fun_app$g\'' @ A @ C )
          = ( '\'fun_app$g\'' @ B @ C ) )
       => ( '\'fun_app$m\'' @ ( '\'uun$\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(329,axiom,
    ( ( '\'register_tensor$g\'' @ '\'id$b\'' @ '\'id$a\'' )
    = '\'id$j\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).

thf(1844,plain,
    ( ( '\'register_tensor$g\'' @ '\'id$b\'' @ '\'id$a\'' )
    = '\'id$j\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(104,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = ( '\'fun_app$d\'' @ D @ ( '\'fun_app$u\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).

thf(1010,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ C ) )
        = ( '\'fun_app$d\'' @ D @ ( '\'fun_app$u\'' @ E @ C ) ) )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(461,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
        = ( '\'comp$h\'' @ '\'id$\'' @ C ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$ah\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).

thf(2305,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
        = ( '\'comp$h\'' @ '\'id$\'' @ C ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$ah\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(646,axiom,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$o\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$p\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$r\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).

thf(2919,plain,
    ! [A: '\'B_update_a_update_bool_fun_fun$\'',B: '\'A_update_c_update_bool_fun_fun$\'',C: '\'A_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$o\'' @ ( '\'rel_fun$k\'' @ A @ B ) @ ( '\'rel_fun$p\'' @ ( '\'rel_fun$q\'' @ C @ A ) @ ( '\'rel_fun$r\'' @ C @ B ) ) @ '\'comp$c\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(471,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ B ) )
     => ( ( '\'fun_app$z\'' @ '\'id$\'' @ A )
        = ( '\'fun_app$z\'' @ '\'id$\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).

thf(2342,plain,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ B ) )
     => ( ( '\'fun_app$z\'' @ '\'id$\'' @ A )
        = ( '\'fun_app$z\'' @ '\'id$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(56,axiom,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( A = '\'id$a\'' )
     => ( ( '\'relcompp$b\'' @ ( '\'conversep$a\'' @ ( '\'grp$a\'' @ '\'top$b\'' @ A ) ) @ ( '\'grp$a\'' @ '\'top$b\'' @ A ) )
        = ( '\'grp$a\'' @ '\'top$b\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).

thf(844,plain,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( A = '\'id$a\'' )
     => ( ( '\'relcompp$b\'' @ ( '\'conversep$a\'' @ ( '\'grp$a\'' @ '\'top$b\'' @ A ) ) @ ( '\'grp$a\'' @ '\'top$b\'' @ A ) )
        = ( '\'grp$a\'' @ '\'top$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(440,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$\'' @ B @ C ) )
     => ( ( '\'register_pair$t\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ C ) )
        = ( '\'comp$bb\'' @ A @ ( '\'register_pair$\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).

thf(2226,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'compatible$\'' @ B @ C ) )
     => ( ( '\'register_pair$t\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ C ) )
        = ( '\'comp$bb\'' @ A @ ( '\'register_pair$\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(336,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).

thf(1866,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(392,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$ai\'' @ B @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).

thf(2071,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_b_update_fun$\''] :
      ( ( '\'inj_on$a\'' @ A @ '\'top$a\'' )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$ai\'' @ B @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(38,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'uup$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).

thf(771,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$b\'' @ '\'uuo$\'' @ ( '\'uup$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(643,axiom,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'register$h\'' @ A )
        & ( '\'register$h\'' @ B )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( '\'iso_register$d\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).

thf(2907,plain,
    ! [A: '\'C_update_c_update_fun$\'',B: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'register$h\'' @ A )
        & ( '\'register$h\'' @ B )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ A ) @ B )
          = '\'id$\'' )
        & ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ B ) @ A )
          = '\'id$\'' ) )
     => ( '\'iso_register$d\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(259,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$z\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).

thf(1590,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_c_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\'',F: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'comp$z\'' @ A @ B )
          = ( '\'comp$aa\'' @ C @ D ) )
        & ( ( '\'comp$ab\'' @ E @ C )
          = F ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(17,axiom,
    '\'register$l\'' @ '\'id$b\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).

thf(699,plain,
    '\'register$l\'' @ '\'id$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(228,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'compatible$a\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$al\'' @ ( '\'register_pair$b\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_pair$c\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).

thf(1476,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'compatible$a\'' @ A @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$b\'' @ D ) )
     => ( ( '\'comp$al\'' @ ( '\'register_pair$b\'' @ A @ B ) @ ( '\'register_tensor$n\'' @ C @ D ) )
        = ( '\'register_pair$c\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(282,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
        & ( C = '\'id$a\'' ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ B @ C ) ) @ A )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).

thf(1674,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
        & ( C = '\'id$a\'' ) )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ B @ C ) ) @ A )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(447,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).

thf(2251,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ ( '\'inv_into$b\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(345,axiom,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).

thf(1903,plain,
    ! [A: '\'B_update_a_update_fun$\''] :
      ( ( '\'iso_register$c\'' @ A )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(536,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'B_update$\''] :
      ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
        = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).

thf(2554,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'B_update$\''] :
      ( ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B )
        = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ D ) )
     => ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ E ) )
        = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$d\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(121,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$bb\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'fun_app$az\'' @ ( '\'map_fun$f\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bd\'' @ ( '\'map_fun$j\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom312) ).

thf(1062,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$bb\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'fun_app$az\'' @ ( '\'map_fun$f\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bd\'' @ ( '\'map_fun$j\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(618,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$ab\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
      = ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).

thf(2823,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'comp$ab\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
      = ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(271,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).

thf(1629,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$c\'' @ A @ '\'top$\'' )
     => ( ( '\'comp$ah\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ ( '\'inv_into$c\'' @ '\'top$\'' @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(332,axiom,
    '\'iso_register$h\'' @ '\'id$b\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).

thf(1854,plain,
    '\'iso_register$h\'' @ '\'id$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(550,axiom,
    ! [A: '\'C_update$\''] :
      ( ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ ( '\'fun_app$z\'' @ '\'id$\'' @ A ) )
    <=> ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).

thf(2608,plain,
    ! [A: '\'C_update$\''] :
      ( ( ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ ( '\'fun_app$z\'' @ '\'id$\'' @ A ) )
       => ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ A ) )
      & ( ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ A )
       => ( '\'fun_app$i\'' @ '\'pred_DEADID$\'' @ ( '\'fun_app$z\'' @ '\'id$\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(651,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$bx\'' @ ( '\'rel_fun$ai\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom648) ).

thf(2934,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\''] : ( '\'fun_app$bw\'' @ ( '\'fun_app$bx\'' @ ( '\'rel_fun$ai\'' @ A @ A ) @ '\'id$\'' ) @ '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(89,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
           => ( ( '\'fun_app$g\'' @ C @ E )
              = ( '\'fun_app$g\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).

thf(961,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
           => ( ( '\'fun_app$g\'' @ C @ E )
              = ( '\'fun_app$g\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(293,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$bj\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'map_fun$o\'' @ C @ D ) )
      = ( '\'map_fun$p\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).

thf(1721,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$bj\'' @ ( '\'map_fun$n\'' @ A @ B ) @ ( '\'map_fun$o\'' @ C @ D ) )
      = ( '\'map_fun$p\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(243,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ '\'top$a\'' )
          = '\'top$\'' )
        & ( ( '\'image$c\'' @ B @ '\'top$\'' )
          = '\'top$a\'' ) )
     => ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ) @ '\'top$a\'' )
        = '\'top$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).

thf(1523,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( ( '\'image$a\'' @ A @ '\'top$a\'' )
          = '\'top$\'' )
        & ( ( '\'image$c\'' @ B @ '\'top$\'' )
          = '\'top$a\'' ) )
     => ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ) @ '\'top$a\'' )
        = '\'top$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(408,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'fcomp$b\'' @ A @ B )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom231) ).

thf(2130,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( '\'fcomp$b\'' @ A @ B )
      = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(375,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$h\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ '\'uur$\'' @ A ) ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).

thf(2009,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'quotient3$c\'' @ A @ B @ C )
        & ( '\'quotient3$d\'' @ '\'uus$\'' @ D @ E ) )
     => ( '\'quotient3$h\'' @ ( '\'relcompp$b\'' @ A @ ( '\'relcompp$b\'' @ '\'uur$\'' @ A ) ) @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ D ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(508,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( A = B )
    <=> ? [C: '\'C_update$\''] :
          ( ( '\'member$b\'' @ C @ '\'top$a\'' )
          & ( ( '\'fun_app$z\'' @ '\'id$\'' @ C )
            = A )
          & ( ( '\'fun_app$z\'' @ '\'id$\'' @ C )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom390) ).

thf(2462,plain,
    ! [A: '\'C_update$\'',B: '\'C_update$\''] :
      ( ( ( A = B )
       => ? [C: '\'C_update$\''] :
            ( ( '\'member$b\'' @ C @ '\'top$a\'' )
            & ( ( '\'fun_app$z\'' @ '\'id$\'' @ C )
              = A )
            & ( ( '\'fun_app$z\'' @ '\'id$\'' @ C )
              = B ) ) )
      & ( ? [C: '\'C_update$\''] :
            ( ( '\'member$b\'' @ C @ '\'top$a\'' )
            & ( ( '\'fun_app$z\'' @ '\'id$\'' @ C )
              = A )
            & ( ( '\'fun_app$z\'' @ '\'id$\'' @ C )
              = B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(155,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'the_inv_into$b\'' @ '\'top$\'' @ A ) ) @ A ) @ B )
        = ( '\'fun_app$ab\'' @ '\'id$b\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).

thf(1193,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( ( '\'fun_app$ab\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'the_inv_into$b\'' @ '\'top$\'' @ A ) ) @ A ) @ B )
        = ( '\'fun_app$ab\'' @ '\'id$b\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(425,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$g\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$j\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).

thf(2183,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$g\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$j\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(36,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update$\'',C: '\'A_update$\''] :
      ( ( '\'register$\'' @ A )
     => ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ B ) ) @ ( '\'fun_app$g\'' @ A @ C ) )
        = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).

thf(763,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'A_update$\'',C: '\'A_update$\''] :
      ( ( '\'register$\'' @ A )
     => ( ( '\'fun_app$z\'' @ ( '\'comp_update$\'' @ ( '\'fun_app$g\'' @ A @ B ) ) @ ( '\'fun_app$g\'' @ A @ C ) )
        = ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(240,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$x\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom147) ).

thf(1513,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$x\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ D ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(70,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'preregister$e\'' @ A )
        & ( '\'preregister$d\'' @ B ) )
     => ( '\'preregister$b\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).

thf(899,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'preregister$e\'' @ A )
        & ( '\'preregister$d\'' @ B ) )
     => ( '\'preregister$b\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(180,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).

thf(1309,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$ag\'' @ E @ C ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(117,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).

thf(1045,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ '\'top$b\'' )
     => ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ ( '\'inv_into$\'' @ '\'top$b\'' @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(149,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( A = B )
    <=> ? [C: '\'B_update$\''] :
          ( ( '\'member$a\'' @ C @ '\'top$b\'' )
          & ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ C )
            = A )
          & ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ C )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).

thf(1161,plain,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( ( A = B )
       => ? [C: '\'B_update$\''] :
            ( ( '\'member$a\'' @ C @ '\'top$b\'' )
            & ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ C )
              = A )
            & ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ C )
              = B ) ) )
      & ( ? [C: '\'B_update$\''] :
            ( ( '\'member$a\'' @ C @ '\'top$b\'' )
            & ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ C )
              = A )
            & ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ C )
              = B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(287,axiom,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$x\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ D @ A ) ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).

thf(1689,plain,
    ! [A: '\'B_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'comp$x\'' @ A @ B )
        = C )
     => ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$y\'' @ D @ A ) ) @ B )
        = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(395,axiom,
    ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ '\'f$a\'' ) @ '\'f$\'' )
    = '\'id$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).

thf(2081,plain,
    ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ '\'f$a\'' ) @ '\'f$\'' )
    = '\'id$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(219,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( ( '\'comp$k\'' @ A @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).

thf(1440,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( ( '\'comp$k\'' @ A @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(80,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
         => ( ( '\'fun_app$g\'' @ B @ D )
            = ( '\'fun_app$g\'' @ C @ D ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).

thf(929,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_c_update_fun$\''] :
      ( ! [D: '\'A_update$\''] :
          ( ( '\'member$\'' @ D @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
         => ( ( '\'fun_app$g\'' @ B @ D )
            = ( '\'fun_app$g\'' @ C @ D ) ) )
     => ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(467,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'B_update_c_update_fun$\''] :
      ( ( '\'quotient3$g\'' @ A @ B @ C )
     => ( ( '\'fun_app$bo\'' @ ( '\'map_fun$av\'' @ C @ B ) @ '\'id$\'' )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).

thf(2330,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'B_update_c_update_fun$\''] :
      ( ( '\'quotient3$g\'' @ A @ B @ C )
     => ( ( '\'fun_app$bo\'' @ ( '\'map_fun$av\'' @ C @ B ) @ '\'id$\'' )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(641,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'B_update_b_update_fun$\'',F: '\'B_update_b_update_fun$\'',G: '\'B_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$d\'' @ E @ F @ '\'top$b\'' )
        & ( ( '\'comp$af\'' @ ( '\'comp$h\'' @ D @ G ) @ E )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$y\'' @ ( '\'comp$ad\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ H ) @ I )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).

thf(2902,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'C_update_c_update_fun$\'',D: '\'C_update_c_update_fun$\'',E: '\'B_update_b_update_fun$\'',F: '\'B_update_b_update_fun$\'',G: '\'B_update_c_update_fun$\'',H: '\'A_update_c_update_fun$\'',I: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$e\'' @ A @ B @ '\'top$\'' )
        & ( '\'type_definition$\'' @ C @ D @ '\'top$a\'' )
        & ( '\'type_definition$d\'' @ E @ F @ '\'top$b\'' )
        & ( ( '\'comp$af\'' @ ( '\'comp$h\'' @ D @ G ) @ E )
          = ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ ( '\'comp$ab\'' @ ( '\'comp$ah\'' @ D @ H ) @ A ) ) @ ( '\'comp$y\'' @ ( '\'comp$ad\'' @ B @ I ) @ E ) ) ) )
     => ( ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ H ) @ I )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(405,axiom,
    ( ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ '\'id$\'' )
    = '\'id$\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).

thf(2120,plain,
    ( ( '\'fun_app$am\'' @ ( '\'inv_into$d\'' @ '\'top$a\'' ) @ '\'id$\'' )
    = '\'id$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(605,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$ai\'' @ A @ B )
        = C )
     => ( ( '\'comp$ag\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom141) ).

thf(2779,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'comp$ai\'' @ A @ B )
        = C )
     => ( ( '\'comp$ag\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ D ) )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(379,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ B )
     => ( ( '\'inj_on$c\'' @ C @ ( '\'image$b\'' @ A @ B ) )
      <=> ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).

thf(2019,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_set$\'',C: '\'A_update_c_update_fun$\''] :
      ( ( '\'inj_on$b\'' @ A @ B )
     => ( ( ( '\'inj_on$c\'' @ C @ ( '\'image$b\'' @ A @ B ) )
         => ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ B ) )
        & ( ( '\'inj_on$k\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ C ) @ A ) @ B )
         => ( '\'inj_on$c\'' @ C @ ( '\'image$b\'' @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(412,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( '\'fun_app$bb\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'fun_app$ax\'' @ ( '\'map_fun$d\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bc\'' @ ( '\'map_fun$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom311) ).

thf(2142,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'C_update_a_update_fun$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( '\'fun_app$bb\'' @ ( '\'map_fun$h\'' @ A @ B ) @ ( '\'fun_app$ax\'' @ ( '\'map_fun$d\'' @ C @ D ) @ E ) )
      = ( '\'fun_app$bc\'' @ ( '\'map_fun$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(192,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$c\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).

thf(1348,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$j\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$c\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(308,axiom,
    ! [A: '\'A_update_set$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'fun_app$b\'' @ ( '\'uuy$\'' @ A ) @ B )
    <=> ( '\'less_eq$a\'' @ ( '\'image$b\'' @ B @ '\'top$b\'' ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).

thf(1774,plain,
    ! [A: '\'A_update_set$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'fun_app$b\'' @ ( '\'uuy$\'' @ A ) @ B )
       => ( '\'less_eq$a\'' @ ( '\'image$b\'' @ B @ '\'top$b\'' ) @ A ) )
      & ( ( '\'less_eq$a\'' @ ( '\'image$b\'' @ B @ '\'top$b\'' ) @ A )
       => ( '\'fun_app$b\'' @ ( '\'uuy$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(522,axiom,
    ( '\'uuq$\''
    = ( '\'grp$\'' @ '\'top$a\'' @ '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).

thf(2517,plain,
    ( '\'uuq$\''
    = ( '\'grp$\'' @ '\'top$a\'' @ '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(283,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'compatible$s\'' @ ( '\'uue$\'' @ A ) @ ( '\'uuf$\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).

thf(1678,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$\'' @ A )
        & ( '\'register$a\'' @ B ) )
     => ( '\'compatible$s\'' @ ( '\'uue$\'' @ A ) @ ( '\'uuf$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(584,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$h\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$i\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).

thf(2719,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'compatible$h\'' @ A @ B )
        & ( '\'register$c\'' @ C ) )
     => ( '\'compatible$i\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(442,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
           => ( ( '\'fun_app$u\'' @ C @ E )
              = ( '\'fun_app$u\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom562) ).

thf(2233,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'A_update$\''] :
            ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
           => ( ( '\'fun_app$u\'' @ C @ E )
              = ( '\'fun_app$u\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(44,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$\'' @ B @ C ) )
     => ( ( '\'register_pair$r\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) )
        = ( '\'comp$ax\'' @ A @ ( '\'register_pair$\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).

thf(790,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$\'' @ B @ C ) )
     => ( ( '\'register_pair$r\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ C ) )
        = ( '\'comp$ax\'' @ A @ ( '\'register_pair$\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(29,axiom,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( '\'iso_register$g\'' @ A )
    <=> ( ( '\'register$k\'' @ A )
        & ? [B: '\'B_update_b_update_fun$\''] :
            ( ( '\'register$k\'' @ B )
            & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
              = '\'id$a\'' )
            & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
              = '\'id$a\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).

thf(735,plain,
    ! [A: '\'B_update_b_update_fun$\''] :
      ( ( ( '\'iso_register$g\'' @ A )
       => ( ( '\'register$k\'' @ A )
          & ? [B: '\'B_update_b_update_fun$\''] :
              ( ( '\'register$k\'' @ B )
              & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
                = '\'id$a\'' )
              & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
                = '\'id$a\'' ) ) ) )
      & ( ( ( '\'register$k\'' @ A )
          & ? [B: '\'B_update_b_update_fun$\''] :
              ( ( '\'register$k\'' @ B )
              & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ A ) @ B )
                = '\'id$a\'' )
              & ( ( '\'fun_app$an\'' @ ( '\'comp$j\'' @ B ) @ A )
                = '\'id$a\'' ) ) )
       => ( '\'iso_register$g\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(650,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).

thf(2930,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ A ) @ B )
        = ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ E ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(449,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$a\'' @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).

thf(2258,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$a\'' @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(142,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ '\'uur$\'' @ A ) @ B )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).

thf(1133,plain,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ '\'uur$\'' @ A ) @ B )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ '\'uur$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(416,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'C_update_b_update_fun$\''] :
      ( ( '\'quotient3$h\'' @ A @ B @ C )
     => ( ( '\'fun_app$bp\'' @ ( '\'map_fun$aw\'' @ C @ B ) @ '\'id$a\'' )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).

thf(2155,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_c_update_fun$\'',C: '\'C_update_b_update_fun$\''] :
      ( ( '\'quotient3$h\'' @ A @ B @ C )
     => ( ( '\'fun_app$bp\'' @ ( '\'map_fun$aw\'' @ C @ B ) @ '\'id$a\'' )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(528,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).

thf(2534,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_c_update_fun$\'',E: '\'C_update_a_update_fun$\'',F: '\'C_update$\''] :
      ( ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$g\'' @ D @ ( '\'fun_app$ag\'' @ E @ F ) ) )
     => ( ( '\'fun_app$ah\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(448,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'the_inv_into$f\'' @ C @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'the_inv_into$a\'' @ C @ B ) ) @ ( '\'the_inv_into$e\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).

thf(2255,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$b\'' @ B @ C ) )
        & ( '\'inj_on$b\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$b\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$ai\'' @ ( '\'the_inv_into$f\'' @ C @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$ai\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'the_inv_into$a\'' @ C @ B ) ) @ ( '\'the_inv_into$e\'' @ ( '\'image$b\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(432,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) ) @ B )
        = ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).

thf(2201,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$b\'' @ C @ D ) )
     => ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) ) @ B )
        = ( '\'image$g\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ E ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(49,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( A = B )
     => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ ( '\'grp$a\'' @ '\'top$b\'' @ '\'id$a\'' ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).

thf(807,plain,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( A = B )
     => ( '\'fun_app$k\'' @ ( '\'fun_app$l\'' @ ( '\'grp$a\'' @ '\'top$b\'' @ '\'id$a\'' ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(189,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( ( '\'inv_into$\'' @ '\'top$b\'' @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).

thf(1335,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( ( '\'inv_into$\'' @ '\'top$b\'' @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(254,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
              & ( ( '\'fun_app$g\'' @ C @ E )
                = ( '\'fun_app$g\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).

thf(1561,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'A_update_c_update_fun$\''] :
      ( ( ! [E: '\'A_update$\'',F: '\'A_update$\''] :
            ( ( ( '\'member$\'' @ E @ ( '\'image$a\'' @ A @ '\'top$a\'' ) )
              & ( '\'member$\'' @ F @ ( '\'image$a\'' @ B @ '\'top$a\'' ) )
              & ( ( '\'fun_app$g\'' @ C @ E )
                = ( '\'fun_app$g\'' @ D @ F ) ) )
           => ( E = F ) )
        & ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ A )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ D ) @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(478,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'uup$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).

thf(2366,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( A = B )
        & ( '\'pred_fun$a\'' @ '\'uum$\'' @ ( '\'uup$\'' @ C @ D ) @ B ) )
     => ( ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A )
        = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(156,axiom,
    ! [A: '\'A_update_bool_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'pred_fun$c\'' @ '\'uuk$\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
    <=> ( '\'pred_fun$\'' @ '\'uuk$\'' @ ( '\'comp$bn\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).

thf(1197,plain,
    ! [A: '\'A_update_bool_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'pred_fun$c\'' @ '\'uuk$\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
       => ( '\'pred_fun$\'' @ '\'uuk$\'' @ ( '\'comp$bn\'' @ A @ B ) @ C ) )
      & ( ( '\'pred_fun$\'' @ '\'uuk$\'' @ ( '\'comp$bn\'' @ A @ B ) @ C )
       => ( '\'pred_fun$c\'' @ '\'uuk$\'' @ A @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(583,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
        & ( C
          = ( '\'comp$ae\'' @ D @ E ) ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) ) @ G )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$ae\'' @ B @ E ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).

thf(2714,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'C_update_b_update_fun$\'',F: '\'A_update_c_update_fun$\'',G: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'type_definition$f\'' @ A @ B @ '\'top$b\'' )
        & ( C
          = ( '\'comp$ae\'' @ D @ E ) ) )
     => ( ( '\'fun_app$am\'' @ ( '\'comp$g\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ F ) @ C ) ) @ G )
        = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'comp$aj\'' @ ( '\'fun_app$v\'' @ ( '\'fun_app$w\'' @ '\'comp$a\'' @ F ) @ D ) @ A ) ) @ ( '\'comp$z\'' @ ( '\'comp$ae\'' @ B @ E ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(439,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ C ) )
      = ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).

thf(2223,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\''] :
      ( ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ C ) )
      = ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(16,axiom,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( '\'quotient3$a\'' @ A @ B @ C )
     => ( ( '\'fun_app$an\'' @ ( '\'map_fun$w\'' @ C @ B ) @ '\'id$a\'' )
        = '\'id$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).

thf(696,plain,
    ! [A: '\'B_update_b_update_bool_fun_fun$\'',B: '\'B_update_b_update_fun$\'',C: '\'B_update_b_update_fun$\''] :
      ( ( '\'quotient3$a\'' @ A @ B @ C )
     => ( ( '\'fun_app$an\'' @ ( '\'map_fun$w\'' @ C @ B ) @ '\'id$a\'' )
        = '\'id$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(87,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$am\'' @ ( '\'the_inv_into$d\'' @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'the_inv_into$\'' @ C @ B ) ) @ ( '\'the_inv_into$e\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom601) ).

thf(955,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_set$\'',D: '\'C_update$\''] :
      ( ( ( '\'inj_on$c\'' @ A @ ( '\'image$a\'' @ B @ C ) )
        & ( '\'inj_on$a\'' @ B @ C )
        & ( '\'member$b\'' @ D @ ( '\'image$c\'' @ A @ ( '\'image$a\'' @ B @ C ) ) ) )
     => ( ( '\'fun_app$z\'' @ ( '\'fun_app$am\'' @ ( '\'the_inv_into$d\'' @ C ) @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B ) ) @ D )
        = ( '\'fun_app$z\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ ( '\'the_inv_into$\'' @ C @ B ) ) @ ( '\'the_inv_into$e\'' @ ( '\'image$a\'' @ B @ C ) @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(218,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) )
        & ( ! [E: '\'A_update$\''] :
              ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ E ) )
              = ( '\'fun_app$d\'' @ C @ ( '\'fun_app$u\'' @ D @ E ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).

thf(1436,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ~ ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
          = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ D ) )
        & ~ ! [E: '\'A_update$\''] :
              ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ E ) )
              = ( '\'fun_app$d\'' @ C @ ( '\'fun_app$u\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(334,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).

thf(1859,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\''] :
      ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
      = ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(37,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ B ) )
     => ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ A )
        = ( '\'fun_app$ab\'' @ '\'id$b\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).

thf(767,plain,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$m\'' @ '\'pred_DEADID$b\'' @ B ) )
     => ( ( '\'fun_app$ab\'' @ '\'id$b\'' @ A )
        = ( '\'fun_app$ab\'' @ '\'id$b\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(493,axiom,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_c_update_fun$\'',I: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$g\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$an\'' @ ( '\'map_fun$e\'' @ E @ I ) @ ( '\'map_fun$ao\'' @ ( '\'map_fun$ap\'' @ B @ F ) @ ( '\'map_fun$aq\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$a\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).

thf(2417,plain,
    ! [A: '\'C_update_c_update_bool_fun_fun$\'',B: '\'C_update_b_update_fun$\'',C: '\'B_update_c_update_fun$\'',D: '\'A_update_a_update_bool_fun_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'A_update_a_update_fun$\'',G: '\'C_update_c_update_bool_fun_fun$\'',H: '\'C_update_c_update_fun$\'',I: '\'C_update_c_update_fun$\''] :
      ( ( ( '\'quotient3$g\'' @ A @ B @ C )
        & ( '\'quotient3$b\'' @ D @ E @ F )
        & ( '\'quotient3$\'' @ G @ H @ I ) )
     => ( ( '\'map_fun$an\'' @ ( '\'map_fun$e\'' @ E @ I ) @ ( '\'map_fun$ao\'' @ ( '\'map_fun$ap\'' @ B @ F ) @ ( '\'map_fun$aq\'' @ C @ H ) ) @ '\'comp$d\'' )
        = '\'comp$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(553,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ '\'top$a\'' )
      = ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ '\'top$a\'' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).

thf(2619,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ '\'top$a\'' )
      = ( '\'image$\'' @ A @ ( '\'image$a\'' @ B @ '\'top$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(122,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_set$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'image$\'' @ A @ B )
        = ( '\'image$\'' @ C @ D ) )
     => ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).

thf(1065,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'A_update_set$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_set$\'',E: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'image$\'' @ A @ B )
        = ( '\'image$\'' @ C @ D ) )
     => ( ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$bq\'' @ ( '\'image$f\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ E ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(470,axiom,
    ( ( '\'image$d\'' @ '\'id$\'' )
    = '\'id$u\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).

thf(2340,plain,
    ( ( '\'image$d\'' @ '\'id$\'' )
    = '\'id$u\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(571,axiom,
    ! [A: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ '\'id$\'' @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).

thf(2668,plain,
    ! [A: '\'C_update$\''] :
      ( ( '\'fun_app$z\'' @ '\'id$\'' @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(67,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ '\'id$b\'' ) @ C ) )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ D ) )
        = ( '\'fun_app$ab\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).

thf(886,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_a_update_fun$\'',D: '\'A_update$\''] :
      ( ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
        = ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ '\'id$b\'' ) @ C ) )
     => ( ( '\'fun_app$d\'' @ A @ ( '\'fun_app$u\'' @ B @ D ) )
        = ( '\'fun_app$ab\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(534,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fcomp$c\'' @ A @ B )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).

thf(2549,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'fcomp$c\'' @ A @ B )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(614,axiom,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$g\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ '\'top$d\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).

thf(2810,plain,
    ! [A: '\'A_update_b_update_fun$\''] :
      ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
     => ( '\'inj_on$g\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ '\'top$d\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(168,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$y\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ B @ E ) ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).

thf(1261,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'A_update_b_update_fun$\'',E: '\'A_update_a_update_fun$\'',F: '\'B_update_a_update_fun$\'',G: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'type_definition$h\'' @ A @ B @ '\'top$\'' )
        & ( C
          = ( '\'comp$w\'' @ D @ E ) ) )
     => ( ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ C ) @ G )
        = ( '\'comp$y\'' @ ( '\'comp$ad\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ F ) @ D ) @ A ) @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'comp$w\'' @ B @ E ) ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(147,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ '\'uuz$\'' @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ A @ '\'uur$\'' ) @ ( '\'rel_fun$i\'' @ A @ '\'uus$\'' ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom639) ).

thf(1152,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\''] : ( '\'rel_fun$e\'' @ '\'uuz$\'' @ ( '\'rel_fun$g\'' @ ( '\'rel_fun$h\'' @ A @ '\'uur$\'' ) @ ( '\'rel_fun$i\'' @ A @ '\'uus$\'' ) ) @ '\'comp$c\'' @ '\'comp$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(195,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$l\'' @ B ) )
     => ( '\'register$a\'' @ ( '\'comp$ad\'' @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom199) ).

thf(1357,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$l\'' @ B ) )
     => ( '\'register$a\'' @ ( '\'comp$ad\'' @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(73,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\''] :
      ( ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$\'' @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).

thf(908,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'A_update_set$\''] :
      ( ( '\'inj_on$i\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B ) @ C )
     => ( '\'inj_on$\'' @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(350,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) )
     => ( '\'compatible$\'' @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).

thf(1923,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$a\'' @ B )
        & ! [C: '\'B_update$\'',D: '\'B_update$\''] :
            ( ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ A @ C ) ) @ ( '\'fun_app$d\'' @ B @ D ) )
            = ( '\'fun_app$ab\'' @ ( '\'comp_update$a\'' @ ( '\'fun_app$d\'' @ B @ D ) ) @ ( '\'fun_app$d\'' @ A @ C ) ) ) )
     => ( '\'compatible$\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(207,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$l\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$\'' @ ( '\'comp$ab\'' @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).

thf(1399,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'register$l\'' @ A )
        & ( '\'register$\'' @ B ) )
     => ( '\'register$\'' @ ( '\'comp$ab\'' @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(480,axiom,
    ! [A: '\'C_update$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update$\''] :
      ( ( A
        = ( '\'fun_app$z\'' @ B @ C ) )
     => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ ( '\'iso_tuple_update_accessor_eq_assist$\'' @ '\'id$l\'' @ '\'id$\'' @ C @ B ) @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).

thf(2372,plain,
    ! [A: '\'C_update$\'',B: '\'C_update_c_update_fun$\'',C: '\'C_update$\''] :
      ( ( A
        = ( '\'fun_app$z\'' @ B @ C ) )
     => ( '\'fun_app$i\'' @ ( '\'fun_app$j\'' @ ( '\'iso_tuple_update_accessor_eq_assist$\'' @ '\'id$l\'' @ '\'id$\'' @ C @ B ) @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(131,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$b\'' @ B @ '\'top$b\'' ) )
     => ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ '\'top$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom538) ).

thf(1093,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'inj_on$\'' @ A @ '\'top$\'' )
        & ( '\'inj_on$b\'' @ B @ '\'top$b\'' ) )
     => ( '\'inj_on$m\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ '\'top$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(474,axiom,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).

thf(2353,plain,
    ! [A: '\'B_update_set_b_update_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\''] :
      ( ( '\'fun_app$bu\'' @ A @ ( '\'image$\'' @ B @ ( '\'image$a\'' @ C @ D ) ) )
      = ( '\'fun_app$bu\'' @ A @ ( '\'image$h\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ B ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(517,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$t\'' @ ( '\'register_tensor$x\'' @ A @ B ) @ ( '\'register_tensor$y\'' @ C @ D ) )
        = ( '\'register_tensor$z\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).

thf(2502,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\'',D: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'register$a\'' @ B )
        & ( '\'register$b\'' @ C )
        & ( '\'register$c\'' @ D ) )
     => ( ( '\'comp$t\'' @ ( '\'register_tensor$x\'' @ A @ B ) @ ( '\'register_tensor$y\'' @ C @ D ) )
        = ( '\'register_tensor$z\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(96,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'member$a\'' @ A @ B )
        & ( '\'inj_on$b\'' @ C @ B ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'uuv$\'' @ B @ C @ D ) ) @ C ) @ A )
        = ( '\'fun_app$aa\'' @ '\'id$a\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom596) ).

thf(987,plain,
    ! [A: '\'B_update$\'',B: '\'B_update_set$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'member$a\'' @ A @ B )
        & ( '\'inj_on$b\'' @ C @ B ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ ( '\'uuv$\'' @ B @ C @ D ) ) @ C ) @ A )
        = ( '\'fun_app$aa\'' @ '\'id$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(326,axiom,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ B ) )
     => ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ A )
        = ( '\'fun_app$aa\'' @ '\'id$a\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).

thf(1829,plain,
    ! [A: '\'B_update$\'',B: '\'B_update$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$k\'' @ '\'pred_DEADID$a\'' @ B ) )
     => ( ( '\'fun_app$aa\'' @ '\'id$a\'' @ A )
        = ( '\'fun_app$aa\'' @ '\'id$a\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(368,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'preregister$f\'' @ A )
        & ( '\'preregister$c\'' @ B ) )
     => ( '\'preregister$\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).

thf(1977,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'preregister$f\'' @ A )
        & ( '\'preregister$c\'' @ B ) )
     => ( '\'preregister$\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(339,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'fcomp$\'' @ A @ B )
      = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom229) ).

thf(1880,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\''] :
      ( ( '\'fcomp$\'' @ A @ B )
      = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(217,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$aa\'' @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom153) ).

thf(1431,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update_b_update_fun$\'',D: '\'B_update$\''] :
      ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B )
        = C )
     => ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ D ) )
        = ( '\'fun_app$aa\'' @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(511,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$aj\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ak\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$am\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom636) ).

thf(2484,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'C_update_c_update_bool_fun_fun$\'',C: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$aj\'' @ ( '\'rel_fun$af\'' @ A @ B ) @ ( '\'rel_fun$ak\'' @ ( '\'rel_fun$al\'' @ C @ A ) @ ( '\'rel_fun$am\'' @ C @ B ) ) @ '\'comp$d\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(341,axiom,
    ! [A: '\'B_update$\''] :
      ( ( '\'fun_app$k\'' @ '\'uuo$\'' @ A )
    <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).

thf(1885,plain,
    ! [A: '\'B_update$\''] : ( '\'fun_app$k\'' @ '\'uuo$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(596,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$h\'' @ B @ C ) )
     => ( ( '\'register_pair$e\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) )
        = ( '\'comp$au\'' @ A @ ( '\'register_pair$p\'' @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom255) ).

thf(2754,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( ( '\'register$c\'' @ A )
        & ( '\'compatible$h\'' @ B @ C ) )
     => ( ( '\'register_pair$e\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ B ) @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ A ) @ C ) )
        = ( '\'comp$au\'' @ A @ ( '\'register_pair$p\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(560,axiom,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$aj\'' @ '\'uva$\'' @ ( '\'rel_fun$ak\'' @ ( '\'rel_fun$al\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$am\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$d\'' @ '\'comp$a\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom641) ).

thf(2640,plain,
    ! [A: '\'C_update_b_update_bool_fun_fun$\''] : ( '\'rel_fun$aj\'' @ '\'uva$\'' @ ( '\'rel_fun$ak\'' @ ( '\'rel_fun$al\'' @ A @ '\'uus$\'' ) @ ( '\'rel_fun$am\'' @ A @ '\'uuq$\'' ) ) @ '\'comp$d\'' @ '\'comp$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(184,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$f\'' @ A @ B )
        & ( '\'register$c\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$aq\'' @ ( '\'register_pair$k\'' @ A @ B ) @ ( '\'register_tensor$x\'' @ C @ D ) )
        = ( '\'register_pair$l\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) @ ( '\'comp$ad\'' @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom240) ).

thf(1320,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\'',D: '\'B_update_a_update_fun$\''] :
      ( ( ( '\'compatible$f\'' @ A @ B )
        & ( '\'register$c\'' @ C )
        & ( '\'register$a\'' @ D ) )
     => ( ( '\'comp$aq\'' @ ( '\'register_pair$k\'' @ A @ B ) @ ( '\'register_tensor$x\'' @ C @ D ) )
        = ( '\'register_pair$l\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ C ) @ ( '\'comp$ad\'' @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(364,axiom,
    ! [A: '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$f\'' @ A @ B )
     => ( ( '\'fun_app$au\'' @ A @ '\'id$a\'' )
        = '\'id$b\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).

thf(1962,plain,
    ! [A: '\'B_update_b_update_fun_a_update_a_update_fun_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$f\'' @ A @ B )
     => ( ( '\'fun_app$au\'' @ A @ '\'id$a\'' )
        = '\'id$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(635,axiom,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$ag\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$ai\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).

thf(2881,plain,
    ! [A: '\'C_update_b_update_fun$\'',B: '\'A_update_c_update_fun$\'',C: '\'C_update_a_update_fun$\''] :
      ( ( '\'comp$ag\'' @ A @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ B ) @ C ) )
      = ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ ( '\'comp$ai\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(4,axiom,
    ( ( '\'map_fun$b\'' @ '\'id$b\'' @ '\'id$b\'' )
    = '\'id$n\'' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).

thf(659,plain,
    ( ( '\'map_fun$b\'' @ '\'id$b\'' @ '\'id$b\'' )
    = '\'id$n\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(499,axiom,
    ! [A: '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$g\'' @ A @ B )
     => ( ( '\'fun_app$bh\'' @ A @ '\'id$b\'' )
        = '\'id$\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).

thf(2436,plain,
    ! [A: '\'A_update_a_update_fun_c_update_c_update_fun_fun$\'',B: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_tuple_update_accessor_cong_assist$g\'' @ A @ B )
     => ( ( '\'fun_app$bh\'' @ A @ '\'id$b\'' )
        = '\'id$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(39,axiom,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( '\'iso_register$b\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).

thf(775,plain,
    ! [A: '\'C_update_a_update_fun$\''] :
      ( ( '\'iso_register$\'' @ A )
     => ( '\'iso_register$b\'' @ ( '\'inv_into$a\'' @ '\'top$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(421,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$a\'' @ A @ B )
        & ( '\'inj_on$\'' @ C @ ( '\'image$a\'' @ A @ B ) ) )
     => ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).

thf(2170,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'inj_on$a\'' @ A @ B )
        & ( '\'inj_on$\'' @ C @ ( '\'image$a\'' @ A @ B ) ) )
     => ( '\'inj_on$l\'' @ ( '\'fun_app$x\'' @ ( '\'fun_app$y\'' @ '\'comp$b\'' @ C ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(123,axiom,
    ! [A: '\'C_update$\''] :
      ( ( '\'fun_app$i\'' @ '\'uum$\'' @ A )
    <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).

thf(1069,plain,
    ! [A: '\'C_update$\''] : ( '\'fun_app$i\'' @ '\'uum$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(66,axiom,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ( ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) )
        & ( ! [E: '\'C_update$\''] :
              ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
              = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom155) ).

thf(882,plain,
    ! [A: '\'A_update_c_update_fun$\'',B: '\'C_update_a_update_fun$\'',C: '\'A_update_c_update_fun$\'',D: '\'C_update_a_update_fun$\''] :
      ~ ( ( ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ A ) @ B )
          = ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ C ) @ D ) )
        & ~ ! [E: '\'C_update$\''] :
              ( ( '\'fun_app$g\'' @ A @ ( '\'fun_app$ag\'' @ B @ E ) )
              = ( '\'fun_app$g\'' @ C @ ( '\'fun_app$ag\'' @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(278,axiom,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
      = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom181) ).

thf(1653,plain,
    ! [A: '\'A_update_a_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'A_update_b_update_fun$\''] :
      ( ( '\'fun_app$al\'' @ ( '\'comp$f\'' @ A ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ B ) @ C ) )
      = ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ ( '\'comp$ad\'' @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(357,axiom,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ '\'uur$\'' @ D @ E ) )
     => ( '\'quotient3$b\'' @ ( '\'relcompp$\'' @ A @ ( '\'relcompp$\'' @ '\'uus$\'' @ A ) ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).

thf(1944,plain,
    ! [A: '\'A_update_a_update_bool_fun_fun$\'',B: '\'A_update_b_update_fun$\'',C: '\'B_update_a_update_fun$\'',D: '\'B_update_a_update_fun$\'',E: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'quotient3$e\'' @ A @ B @ C )
        & ( '\'quotient3$c\'' @ '\'uur$\'' @ D @ E ) )
     => ( '\'quotient3$b\'' @ ( '\'relcompp$\'' @ A @ ( '\'relcompp$\'' @ '\'uus$\'' @ A ) ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ D ) @ B ) @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(158,axiom,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ '\'uus$\'' @ A ) @ B )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).

thf(1204,plain,
    ! [A: '\'A_update$\'',B: '\'A_update$\''] :
      ( ( ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ '\'uus$\'' @ A ) @ B )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$m\'' @ ( '\'fun_app$n\'' @ '\'uus$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(320,axiom,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).

thf(1812,plain,
    ! [A: '\'A_update_b_update_fun$\'',B: '\'B_update_a_update_fun$\'',C: '\'B_update$\'',D: '\'A_update_b_update_fun$\'',E: '\'B_update_a_update_fun$\'',F: '\'B_update$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( '\'fun_app$d\'' @ B @ C ) )
        = ( '\'fun_app$u\'' @ D @ ( '\'fun_app$d\'' @ E @ F ) ) )
     => ( ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ A ) @ B ) @ C )
        = ( '\'fun_app$aa\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ D ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(214,axiom,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).

thf(1417,plain,
    ! [A: '\'C_update_a_update_fun$\'',B: '\'C_update_set$\'',C: '\'C_update_a_update_fun$\'',D: '\'C_update_set$\'',E: '\'A_update_c_update_fun$\''] :
      ( ( ( '\'image$a\'' @ A @ B )
        = ( '\'image$a\'' @ C @ D ) )
     => ( ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ A ) ) @ B )
        = ( '\'fun_app$br\'' @ ( '\'image$d\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ '\'comp$d\'' @ E ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(92,axiom,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( '\'iso_register$c\'' @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).

thf(972,plain,
    ! [A: '\'B_update_a_update_fun$\'',B: '\'A_update_b_update_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
        & ( '\'register$c\'' @ B )
        & ( ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ '\'comp$c\'' @ A ) @ B )
          = '\'id$b\'' )
        & ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'comp$e\'' @ B ) @ A )
          = '\'id$a\'' ) )
     => ( '\'iso_register$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(602,axiom,
    '\'quotient3$\'' @ '\'uuq$\'' @ '\'id$\'' @ '\'id$\'',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).

thf(2771,plain,
    '\'quotient3$\'' @ '\'uuq$\'' @ '\'id$\'' @ '\'id$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(2978,plain,
    $false,
    inference(cvc4,[status(thm)],[2163,2199,1036,760,2109,1633,2412,2921,1899,941,777,666,1549,1501,2452,2744,2889,1190,2787,2499,1083,1982,1211,2309,1005,683,1290,2622,1443,1401,2248,1073,2671,1728,873,677,2363,1855,1596,2104,2395,2062,2114,1269,2854,1533,1041,861,2686,1735,1275,913,1640,1507,670,2195,1705,814,1327,2476,2168,1095,1835,2046,1391,782,709,1650,1359,1724,2516,2067,1803,1887,1243,1782,2136,1518,2531,2405,1482,1254,2654,2735,2039,785,1330,1323,802,2488,1992,1055,724,2603,2328,1511,917,702,751,2682,1826,2185,1577,1455,2897,934,2571,2356,2420,817,1800,1087,1013,1115,1931,2158,2024,1815,1362,1100,1247,2552,1479,1609,2178,1415,2794,1109,834,2122,2540,1960,2777,1183,905,2616,1946,1465,2324,2027,2291,1020,1581,2335,2058,2523,1526,998,2286,2804,1521,2205,2884,2833,2281,877,2190,1119,1622,2424,1394,2772,2750,1405,1604,2011,793,925,1338,1730,2574,661,1470,1708,2083,1736,2660,2905,2382,910,746,1343,2133,2606,1824,2528,1883,2264,2409,2601,2428,2414,729,2433,879,1951,1888,1687,1787,1656,1027,757,2211,2547,1910,1573,1938,2758,1032,1602,1365,2628,2663,2826,2820,2300,1143,2895,1672,1540,2631,1755,2638,2268,2245,1350,1851,1772,948,2801,1794,1017,2359,1121,2724,1719,2537,2323,1292,2561,1739,2868,2240,2613,1446,2460,1493,2798,901,686,1424,2455,1791,2172,1612,2649,970,837,1297,1530,1266,2505,2497,2566,1984,1002,2272,2370,2450,2125,985,1150,2519,2845,2598,1131,654,2851,2243,1979,779,2634,1318,2926,1202,938,2702,1779,2043,921,1846,1035,1071,2440,1663,2645,953,1185,1906,2936,1146,1680,1103,2275,2585,1273,689,2376,733,2260,1154,1833,2727,1007,1916,2859,732,2791,1620,1752,1929,2016,1388,2806,1488,1615,1389,2525,2657,2849,958,1403,1701,2398,2161,1503,2193,2220,2029,1312,2738,713,1635,1239,1332,2442,2055,2706,804,704,2148,1765,1090,1638,1224,2510,2346,2079,2721,2679,831,1408,1282,2493,2422,1806,2097,996,2116,2943,1043,2378,1175,2151,2642,2229,1571,2871,1376,2197,1969,1307,890,811,2742,858,2625,2111,1862,2410,895,2874,2278,1381,2842,2578,2812,1080,2446,2757,848,700,1556,2647,2710,2911,1820,1396,1926,1528,2086,1643,2139,1113,1000,1496,851,1694,2770,983,2075,1474,2350,2725,2401,1594,1213,2835,2051,2765,2481,2064,1015,1626,1809,2665,927,749,2684,2333,1958,754,968,2582,1049,2005,1076,675,2914,2816,1304,1873,1758,2107,795,2784,680,663,2652,2878,1684,2513,1770,855,1025,707,2588,2678,2175,2386,1547,1748,2863,1598,2732,1941,2831,2689,673,1987,1452,2700,1869,1785,1235,2219,1763,1285,2747,1499,2486,951,2545,1934,1257,1536,2543,864,727,1140,1797,2266,991,2838,2558,656,1023,1353,1955,2145,1485,1972,2320,1052,1372,2892,2760,2458,1316,1180,1966,1553,1949,1817,1913,1412,2215,2209,1448,1108,1421,2013,2924,976,1844,1010,2305,2919,2342,844,2226,1866,2071,771,2907,1590,699,1476,1674,2251,1903,2554,1062,2823,1629,1854,2608,2934,961,1721,1523,2130,2009,2462,1193,2183,763,1513,899,1309,1045,1161,1689,2081,1440,929,2330,2902,2120,2779,2019,2142,1348,1774,2517,1678,2719,2233,790,735,2930,2258,1133,2155,2534,2255,2201,807,1335,1561,2366,1197,2714,2223,696,955,1436,1859,767,2417,2619,1065,2340,2668,886,2549,2810,1261,1152,1357,908,1923,1399,2372,1093,2353,2502,987,1829,1977,1880,1431,2484,1885,2754,2640,1320,1962,2881,659,2436,775,2170,1069,882,1653,1944,1204,1812,1417,972,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP384_1 : TPTP v8.1.2. Released v8.0.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n007.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 14:30:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.57/1.24  % [INFO] 	 Parsing done (372ms). 
% 2.57/1.25  % [INFO] 	 Running in sequential loop mode. 
% 3.16/1.45  % [INFO] 	 eprover registered as external prover. 
% 3.16/1.45  % [INFO] 	 cvc4 registered as external prover. 
% 3.16/1.45  % [INFO] 	 Scanning for conjecture ... 
% 3.42/1.63  % [INFO] 	 Found a conjecture and 668 axioms. Running axiom selection ... 
% 4.58/1.86  % [INFO] 	 Axiom selection finished. Selected 651 axioms (removed 17 axioms). 
% 5.58/2.17  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 5.58/2.19  % [INFO] 	 Type checking passed. 
% 5.58/2.19  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 21.89/5.98  % External prover 'cvc4' found a proof!
% 21.89/5.98  % [INFO] 	 Killing All external provers ... 
% 22.05/5.99  % Time passed: 5460ms (effective reasoning time: 4732ms)
% 22.05/5.99  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 22.05/5.99  % Axioms used in derivation (651): axiom32, axiom635, axiom260, axiom280, axiom127, axiom626, axiom315, axiom546, axiom116, axiom527, axiom611, axiom452, axiom491, axiom241, axiom28, axiom76, axiom273, axiom61, axiom230, axiom100, axiom6, axiom564, axiom503, axiom553, axiom54, axiom549, axiom480, axiom396, axiom25, axiom369, axiom404, axiom474, axiom333, axiom221, axiom295, axiom485, axiom214, axiom516, axiom307, axiom496, axiom284, axiom662, axiom423, axiom65, axiom575, axiom36, axiom203, axiom142, axiom311, axiom169, axiom622, axiom531, axiom291, axiom441, axiom507, axiom430, axiom600, axiom50, axiom158, axiom131, axiom10, axiom386, axiom580, axiom344, axiom138, axiom508, axiom392, axiom597, axiom337, axiom119, axiom210, axiom407, axiom191, axiom17, axiom401, axiom397, axiom460, axiom354, axiom587, axiom477, axiom467, axiom257, axiom579, axiom22, axiom619, axiom412, axiom654, axiom147, axiom524, axiom434, axiom341, axiom504, axiom173, axiom638, axiom109, axiom348, axiom184, axiom376, axiom172, axiom535, axiom266, axiom445, axiom42, axiom513, axiom239, axiom300, axiom350, axiom561, axiom329, axiom372, axiom195, axiom162, axiom583, axiom358, axiom161, axiom632, axiom616, axiom542, axiom123, axiom246, axiom592, axiom383, axiom605, axiom2, axiom134, axiom33, axiom150, axiom104, axiom456, axiom87, axiom572, axiom11, axiom568, axiom130, axiom557, axiom235, axiom98, axiom473, axiom39, axiom608, axiom499, axiom650, axiom418, axiom484, axiom112, axiom304, axiom488, axiom643, axiom225, axiom520, axiom365, axiom251, axiom64, axiom578, axiom530, axiom636, axiom179, axiom283, axiom126, axiom314, axiom539, axiom427, axiom625, axiom591, axiom642, axiom59, axiom247, axiom48, axiom217, axiom343, axiom27, axiom352, axiom411, axiom294, axiom437, axiom601, axiom236, axiom151, axiom115, axiom623, axiom94, axiom83, axiom101, axiom336, axiom308, axiom321, axiom35, axiom647, axiom78, axiom24, axiom661, axiom668, axiom278, axiom272, axiom228, axiom405, axiom455, axiom475, axiom121, axiom132, axiom56, axiom466, axiom137, axiom563, axiom206, axiom53, axiom318, axiom60, axiom631, axiom0, axiom574, axiom490, axiom240, axiom290, axiom433, axiom143, axiom359, axiom416, axiom489, axiom545, axiom108, axiom395, axiom387, axiom16, axiom459, axiom400, axiom517, axiom258, axiom75, axiom325, axiom653, axiom448, axiom552, axiom385, axiom478, axiom157, axiom658, axiom90, axiom168, axiom528, axiom332, axiom9, axiom303, axiom612, axiom366, axiom207, axiom494, axiom538, axiom133, axiom80, axiom371, axiom567, axiom586, axiom422, axiom185, axiom472, axiom202, axiom252, axiom146, axiom97, axiom192, axiom355, axiom391, axiom604, axiom263, axiom415, axiom589, axiom254, axiom444, axiom657, axiom82, axiom45, axiom541, axiom360, axiom398, axiom382, axiom483, axiom229, axiom174, axiom556, axiom639, axiom319, axiom347, axiom646, axiom180, axiom67, axiom213, axiom534, axiom450, axiom196, axiom523, axiom232, axiom615, axiom629, axiom243, axiom426, axiom72, axiom461, axiom463, axiom310, axiom664, axiom449, axiom438, axiom267, axiom89, axiom224, axiom122, axiom38, axiom419, axiom377, axiom500, axiom91, axiom1, axiom105, axiom218, axiom86, axiom163, axiom408, axiom111, axiom120, axiom665, axiom512, axiom660, axiom297, axiom447, axiom52, axiom156, axiom511, axiom279, axiom390, axiom37, axiom212, axiom602, axiom432, axiom223, axiom571, axiom641, axiom12, axiom501, axiom342, axiom381, axiom193, axiom34, axiom630, axiom544, axiom152, axiom425, axiom167, axiom607, axiom454, axiom205, axiom364, axiom628, axiom79, axiom190, axiom573, axiom443, axiom96, axiom149, axiom189, axiom375, axiom23, axiom560, axiom93, axiom595, axiom562, axiom41, axiom394, axiom667, axiom227, axiom182, axiom476, axiom216, axiom409, axiom286, axiom313, axiom618, axiom118, axiom275, axiom63, axiom19, axiom458, axiom613, axiom102, axiom8, axiom410, axiom320, axiom30, axiom178, axiom370, axiom479, axiom659, axiom428, axiom259, axiom74, axiom276, axiom451, axiom570, axiom509, axiom233, axiom220, axiom598, axiom302, axiom367, axiom378, axiom57, axiom599, axiom85, axiom652, axiom566, axiom145, axiom471, axiom506, axiom186, axiom497, axiom164, axiom374, axiom614, axiom440, axiom129, axiom581, axiom282, axiom271, axiom287, axiom255, axiom153, axiom324, axiom71, axiom462, axiom114, axiom244, axiom620, axiom594, axiom136, axiom414, axiom106, axiom533, axiom181, axiom403, axiom522, axiom436, axiom482, axiom555, axiom486, axiom346, axiom645, axiom262, axiom68, axiom335, axiom170, axiom656, axiom268, axiom293, axiom175, axiom237, axiom26, axiom493, axiom356, axiom298, axiom439, axiom634, axiom469, axiom110, axiom125, axiom603, axiom49, axiom577, axiom219, axiom197, axiom46, axiom585, axiom248, axiom421, axiom590, axiom18, axiom338, axiom242, axiom666, axiom379, axiom558, axiom663, axiom510, axiom199, axiom547, axiom389, axiom226, axiom166, axiom526, axiom559, axiom457, axiom521, axiom651, axiom88, axiom442, axiom92, axiom399, axiom66, axiom345, axiom464, axiom204, axiom296, axiom569, axiom215, axiom576, axiom596, axiom141, axiom357, axiom274, axiom117, axiom393, axiom621, axiom44, axiom222, axiom323, axiom446, axiom84, axiom554, axiom269, axiom453, axiom81, axiom502, axiom103, axiom7, axiom515, axiom231, axiom306, axiom155, axiom495, axiom640, axiom368, axiom211, axiom550, axiom565, axiom99, axiom148, axiom128, axiom316, axiom285, axiom540, axiom537, axiom349, axiom249, axiom183, axiom301, axiom649, axiom361, axiom429, axiom532, axiom177, axiom31, axiom380, axiom188, axiom264, axiom431, axiom208, axiom20, axiom588, axiom627, axiom159, axiom487, axiom609, axiom519, axiom402, axiom384, axiom551, axiom73, axiom107, axiom171, axiom417, axiom339, axiom154, axiom40, axiom265, axiom165, axiom47, axiom518, axiom270, axiom113, axiom176, axiom305, axiom187, axiom317, axiom135, axiom277, axiom198, axiom529, axiom144, axiom55, axiom584, axiom281, axiom424, axiom633, axiom593, axiom245, axiom644, axiom69, axiom536, axiom373, axiom435, axiom312, axiom95, axiom70, axiom238, axiom617, axiom465, axiom543, axiom299, axiom351, axiom261, axiom413, axiom256, axiom655, axiom160, axiom582, axiom514, axiom43, axiom481, axiom124, axiom505, axiom606, axiom77, axiom406, axiom388, axiom637, axiom420, axiom62, axiom498, axiom21, axiom139, axiom200, axiom250, axiom292, axiom525, axiom234, axiom362, axiom51, axiom548, axiom309, axiom610, axiom470, axiom648, axiom209, axiom468, axiom492, axiom328, axiom140, axiom58, axiom624, axiom340, axiom194, axiom353
% 22.05/5.99  % No. of inferences in proof: 1306
% 22.05/5.99  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5460 ms resp. 4732 ms w/o parsing
% 22.88/6.25  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.88/6.25  % [INFO] 	 Killing All external provers ... 
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